DT2H2X---1.9.5.THM-Ref.s

%------------------------------------------------------------------------------
% File     : DT2H2X---1.9.5
% Problem  : ITP270^1 : TPTP v9.2.1. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300

% Computer : n023.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 : Wed Feb 25 09:08:22 AM UTC 2026

% Result   : Theorem 75.95s 17.89s
% Output   : Refutation 72.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   64 (  18 unt;   0 typ;   0 def)
%            Number of atoms       :  304 ( 114 equ;   0 cnn)
%            Maximal formula atoms :    5 (   4 avg)
%            Number of connectives :  457 (  42   ~;  60   |;   3   &; 333   @)
%                                         (   0 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Number of types       :   99 (  98 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 1481 (1478 usr;  77 con; 0-8 aty)
%            Number of variables   :   66 (   0   ^;  66   !;   0   ?;  66   :)

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

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

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

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

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

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

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

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

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

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

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

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

thf(type_def_18,type,
    produc6271795597528267376eger_o: $tType ).

thf(type_def_19,type,
    produc8923325533196201883nteger: $tType ).

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

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

thf(type_def_22,type,
    set_fi4554929511873752355omplex: $tType ).

thf(type_def_23,type,
    filter6041513312241820739omplex: $tType ).

thf(type_def_24,type,
    set_fi7789364187291644575l_real: $tType ).

thf(type_def_25,type,
    filter2146258269922977983l_real: $tType ).

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

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

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

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

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

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

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

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

thf(type_def_34,type,
    set_Pr5085853215250843933omplex: $tType ).

thf(type_def_35,type,
    set_Pr6218003697084177305l_real: $tType ).

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

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

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

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

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

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

thf(type_def_42,type,
    set_li5464603477888414924d_enat: $tType ).

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

thf(type_def_44,type,
    set_li5450038453877631591at_nat: $tType ).

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

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

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

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

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

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

thf(type_def_51,type,
    set_Pr4329608150637261639at_nat: $tType ).

thf(type_def_52,type,
    set_Pr8693737435421807431at_nat: $tType ).

thf(type_def_53,type,
    produc1319942482725812455at_nat: $tType ).

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

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

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

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

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

thf(type_def_59,type,
    set_Pr958786334691620121nt_int: $tType ).

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

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

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

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

thf(type_def_64,type,
    list_P6011104703257516679at_nat: $tType ).

thf(type_def_65,type,
    list_P5464809261938338413at_nat: $tType ).

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

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

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

thf(type_def_69,type,
    list_P4002435161011370285od_o_o: $tType ).

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

thf(type_def_71,type,
    list_P3795440434834930179_o_int: $tType ).

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

thf(type_def_73,type,
    list_P6285523579766656935_o_nat: $tType ).

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

thf(type_def_75,type,
    list_P7495141550334521929T_VEBT: $tType ).

thf(type_def_76,type,
    produc2504756804600209347T_VEBT: $tType ).

thf(type_def_77,type,
    list_P1726324292696863441at_num: $tType ).

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

thf(type_def_79,type,
    list_P3744719386663036955um_num: $tType ).

thf(type_def_80,type,
    list_P3126845725202233233VEBT_o: $tType ).

thf(type_def_81,type,
    produc334124729049499915VEBT_o: $tType ).

thf(type_def_82,type,
    list_P4547456442757143711BT_int: $tType ).

thf(type_def_83,type,
    produc4894624898956917775BT_int: $tType ).

thf(type_def_84,type,
    list_P7037539587688870467BT_nat: $tType ).

thf(type_def_85,type,
    produc9072475918466114483BT_nat: $tType ).

thf(type_def_86,type,
    list_P7413028617227757229T_VEBT: $tType ).

thf(type_def_87,type,
    produc8243902056947475879T_VEBT: $tType ).

thf(type_def_88,type,
    produc3843707927480180839at_nat: $tType ).

thf(type_def_89,type,
    option4927543243414619207at_nat: $tType ).

thf(type_def_90,type,
    produc4953844613479565601on_nat: $tType ).

thf(type_def_91,type,
    produc2233624965454879586on_nat: $tType ).

thf(type_def_92,type,
    produc8306885398267862888on_nat: $tType ).

thf(type_def_93,type,
    produc3447558737645232053on_num: $tType ).

thf(type_def_94,type,
    produc7036089656553540234on_num: $tType ).

thf(type_def_95,type,
    produc1193250871479095198on_num: $tType ).

thf(type_def_96,type,
    produc6121120109295599847at_nat: $tType ).

thf(type_def_97,type,
    produc5491161045314408544at_nat: $tType ).

thf(type_def_98,type,
    produc5542196010084753463at_nat: $tType ).

thf(type_def_99,type,
    produc859450856879609959at_nat: $tType ).

thf(type_def_100,type,
    produc7272778201969148633d_enat: $tType ).

thf(type_def_101,type,
    produc4411394909380815293omplex: $tType ).

thf(type_def_102,type,
    produc2422161461964618553l_real: $tType ).

thf(type_def_103,type,
    product_unit: $tType ).

thf(func_def_0,type,
    produc1319942482725812455at_nat: $tType ).

thf(func_def_1,type,
    produc5542196010084753463at_nat: $tType ).

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

thf(func_def_3,type,
    list_P5464809261938338413at_nat: $tType ).

thf(func_def_4,type,
    set_Pr4329608150637261639at_nat: $tType ).

thf(func_def_5,type,
    produc1193250871479095198on_num: $tType ).

thf(func_def_6,type,
    produc8306885398267862888on_nat: $tType ).

thf(func_def_7,type,
    produc6121120109295599847at_nat: $tType ).

thf(func_def_8,type,
    produc7036089656553540234on_num: $tType ).

thf(func_def_9,type,
    produc2233624965454879586on_nat: $tType ).

thf(func_def_10,type,
    produc3843707927480180839at_nat: $tType ).

thf(func_def_11,type,
    set_Pr8693737435421807431at_nat: $tType ).

thf(func_def_12,type,
    produc859450856879609959at_nat: $tType ).

thf(func_def_13,type,
    set_fi4554929511873752355omplex: $tType ).

thf(func_def_14,type,
    list_P7413028617227757229T_VEBT: $tType ).

thf(func_def_15,type,
    produc3447558737645232053on_num: $tType ).

thf(func_def_16,type,
    produc4953844613479565601on_nat: $tType ).

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

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

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

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

thf(func_def_21,type,
    set_li5450038453877631591at_nat: $tType ).

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

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

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

thf(func_def_25,type,
    produc7272778201969148633d_enat: $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,
    set_Pr6218003697084177305l_real: $tType ).

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

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

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

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

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

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

thf(func_def_37,type,
    set_Pr958786334691620121nt_int: $tType ).

thf(func_def_38,type,
    produc4411394909380815293omplex: $tType ).

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

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

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

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

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

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

thf(func_def_45,type,
    set_li5464603477888414924d_enat: $tType ).

thf(func_def_46,type,
    produc2422161461964618553l_real: $tType ).

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

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

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

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

thf(func_def_51,type,
    list_P4002435161011370285od_o_o: $tType ).

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

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

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

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

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

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

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

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

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

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

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

thf(func_def_63,type,
    list_Extended_enat: $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,
    filter_int: $tType ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(func_def_94,type,
    rat: $tType ).

thf(func_def_95,type,
    num: $tType ).

thf(func_def_96,type,
    nat: $tType ).

thf(func_def_97,type,
    int: $tType ).

thf(func_def_98,type,
    archim2889992004027027881ng_rat: rat > int ).

thf(func_def_99,type,
    archim7802044766580827645g_real: real > int ).

thf(func_def_100,type,
    archim3151403230148437115or_rat: rat > int ).

thf(func_def_101,type,
    archim6058952711729229775r_real: real > int ).

thf(func_def_102,type,
    archimedean_frac_rat: rat > rat ).

thf(func_def_103,type,
    archim2898591450579166408c_real: real > real ).

thf(func_def_104,type,
    archim7778729529865785530nd_rat: rat > int ).

thf(func_def_105,type,
    archim8280529875227126926d_real: real > int ).

thf(func_def_106,type,
    bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat ).

thf(func_def_107,type,
    bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat ).

thf(func_def_108,type,
    bNF_re1962705104956426057at_rat: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( ( nat > rat ) > nat > rat ) > ( ( nat > rat ) > nat > rat ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > $o ).

thf(func_def_109,type,
    bNF_re895249473297799549at_rat: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > nat > rat ) > ( ( nat > rat ) > nat > rat ) > $o ).

thf(func_def_110,type,
    bNF_re728719798268516973at_o_o: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( $o > $o > $o ) > ( ( nat > rat ) > $o ) > ( ( nat > rat ) > $o ) > $o ).

thf(func_def_111,type,
    bNF_re4695409256820837752l_real: ( ( nat > rat ) > real > $o ) > ( ( ( nat > rat ) > nat > rat ) > ( real > real ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > ( real > real > real ) > $o ).

thf(func_def_112,type,
    bNF_re4521903465945308077real_o: ( ( nat > rat ) > real > $o ) > ( ( ( nat > rat ) > $o ) > ( real > $o ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > $o ) > ( real > real > $o ) > $o ).

thf(func_def_113,type,
    bNF_re3023117138289059399t_real: ( ( nat > rat ) > real > $o ) > ( ( nat > rat ) > real > $o ) > ( ( nat > rat ) > nat > rat ) > ( real > real ) > $o ).

thf(func_def_114,type,
    bNF_re4297313714947099218al_o_o: ( ( nat > rat ) > real > $o ) > ( $o > $o > $o ) > ( ( nat > rat ) > $o ) > ( real > $o ) > $o ).

thf(func_def_115,type,
    bNF_re6321650412969554871eger_o: ( int > code_integer > $o ) > ( ( int > $o ) > ( code_integer > $o ) > $o ) > ( int > int > $o ) > ( code_integer > code_integer > $o ) > $o ).

thf(func_def_116,type,
    bNF_re6574881592172037608er_o_o: ( int > code_integer > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( code_integer > $o ) > $o ).

thf(func_def_117,type,
    bNF_re2807294637932363402at_nat: ( int > code_integer > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( code_integer > nat ) > $o ).

thf(func_def_118,type,
    bNF_re6718328864250387230um_num: ( int > code_integer > $o ) > ( num > num > $o ) > ( int > num ) > ( code_integer > num ) > $o ).

thf(func_def_119,type,
    bNF_re3403563459893282935_int_o: ( int > int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).

thf(func_def_120,type,
    bNF_re157797125943740599nt_int: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > product_prod_int_int ) > $o ).

thf(func_def_121,type,
    bNF_re3461391660133120880nt_rat: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > rat ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ).

thf(func_def_122,type,
    bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).

thf(func_def_123,type,
    bNF_re3715656647883201625at_nat: ( int > int > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( int > nat ) > $o ).

thf(func_def_124,type,
    bNF_re7626690874201225453um_num: ( int > int > $o ) > ( num > num > $o ) > ( int > num ) > ( int > num ) > $o ).

thf(func_def_125,type,
    bNF_re6250860962936578807nt_int: ( int > int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ).

thf(func_def_126,type,
    bNF_re2214769303045360666nt_rat: ( int > int > $o ) > ( product_prod_int_int > rat > $o ) > ( int > product_prod_int_int ) > ( int > rat ) > $o ).

thf(func_def_127,type,
    bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).

thf(func_def_128,type,
    bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).

thf(func_def_129,type,
    bNF_re4153400068438556298nteger: ( nat > nat > $o ) > ( int > code_integer > $o ) > ( nat > int ) > ( nat > code_integer ) > $o ).

thf(func_def_130,type,
    bNF_re6650684261131312217nt_int: ( nat > nat > $o ) > ( int > int > $o ) > ( nat > int ) > ( nat > int ) > $o ).

thf(func_def_131,type,
    bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).

thf(func_def_132,type,
    bNF_re7876454716742015248nteger: ( num > num > $o ) > ( ( num > int ) > ( num > code_integer ) > $o ) > ( num > num > int ) > ( num > num > code_integer ) > $o ).

thf(func_def_133,type,
    bNF_re8402795839162346335um_int: ( num > num > $o ) > ( ( num > int ) > ( num > int ) > $o ) > ( num > num > int ) > ( num > num > int ) > $o ).

thf(func_def_134,type,
    bNF_re6501075790457514782nteger: ( num > num > $o ) > ( int > code_integer > $o ) > ( num > int ) > ( num > code_integer ) > $o ).

thf(func_def_135,type,
    bNF_re1822329894187522285nt_int: ( num > num > $o ) > ( int > int > $o ) > ( num > int ) > ( num > int ) > $o ).

thf(func_def_136,type,
    bNF_re8699439704749558557nt_o_o: ( product_prod_int_int > product_prod_int_int > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).

thf(func_def_137,type,
    bNF_re7145576690424134365nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ).

thf(func_def_138,type,
    bNF_re1494630372529172596at_o_o: ( product_prod_int_int > rat > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( rat > $o ) > $o ).

thf(func_def_139,type,
    bNF_re8279943556446156061nt_rat: ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ).

thf(func_def_140,type,
    bNF_re717283939379294677_int_o: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > $o ).

thf(func_def_141,type,
    bNF_re7408651293131936558nt_int: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > $o ).

thf(func_def_142,type,
    bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).

thf(func_def_143,type,
    bNF_re4555766996558763186at_nat: ( product_prod_nat_nat > int > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ).

thf(func_def_144,type,
    bNF_re7400052026677387805at_int: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ).

thf(func_def_145,type,
    bNF_re4202695980764964119_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).

thf(func_def_146,type,
    bNF_re3099431351363272937at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > $o ).

thf(func_def_147,type,
    bNF_re3666534408544137501at_o_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).

thf(func_def_148,type,
    bNF_re8246922863344978751at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > nat ) > $o ).

thf(func_def_149,type,
    bNF_re2241393799969408733at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ).

thf(func_def_150,type,
    binomial: nat > nat > nat ).

thf(func_def_151,type,
    gbinomial_complex: complex > nat > complex ).

thf(func_def_152,type,
    gbinomial_int: int > nat > int ).

thf(func_def_153,type,
    gbinomial_nat: nat > nat > nat ).

thf(func_def_154,type,
    gbinomial_rat: rat > nat > rat ).

thf(func_def_155,type,
    gbinomial_real: real > nat > real ).

thf(func_def_156,type,
    bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).

thf(func_def_157,type,
    bit_and_not_num: num > num > option_num ).

thf(func_def_158,type,
    bit_and_not_num_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_159,type,
    bit_concat_bit: nat > int > int > int ).

thf(func_def_160,type,
    bit_or_not_num_neg: num > num > num ).

thf(func_def_161,type,
    bit_or3848514188828904588eg_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_162,type,
    bit_ri7632146776885996613nteger: code_integer > code_integer ).

thf(func_def_163,type,
    bit_ri7919022796975470100ot_int: int > int ).

thf(func_def_164,type,
    bit_ri6519982836138164636nteger: nat > code_integer > code_integer ).

thf(func_def_165,type,
    bit_ri631733984087533419it_int: nat > int > int ).

thf(func_def_166,type,
    bit_se725231765392027082nd_int: int > int > int ).

thf(func_def_167,type,
    bit_se727722235901077358nd_nat: nat > nat > nat ).

thf(func_def_168,type,
    bit_se8568078237143864401it_int: nat > int > int ).

thf(func_def_169,type,
    bit_se8570568707652914677it_nat: nat > nat > nat ).

thf(func_def_170,type,
    bit_se1345352211410354436nteger: nat > code_integer > code_integer ).

thf(func_def_171,type,
    bit_se2159334234014336723it_int: nat > int > int ).

thf(func_def_172,type,
    bit_se2161824704523386999it_nat: nat > nat > nat ).

thf(func_def_173,type,
    bit_se2000444600071755411sk_int: nat > int ).

thf(func_def_174,type,
    bit_se2002935070580805687sk_nat: nat > nat ).

thf(func_def_175,type,
    bit_se1080825931792720795nteger: code_integer > code_integer > code_integer ).

thf(func_def_176,type,
    bit_se1409905431419307370or_int: int > int > int ).

thf(func_def_177,type,
    bit_se1412395901928357646or_nat: nat > nat > nat ).

thf(func_def_178,type,
    bit_se545348938243370406it_int: nat > int > int ).

thf(func_def_179,type,
    bit_se547839408752420682it_nat: nat > nat > nat ).

thf(func_def_180,type,
    bit_se2793503036327961859nteger: nat > code_integer > code_integer ).

thf(func_def_181,type,
    bit_se7879613467334960850it_int: nat > int > int ).

thf(func_def_182,type,
    bit_se7882103937844011126it_nat: nat > nat > nat ).

thf(func_def_183,type,
    bit_se1745604003318907178nteger: nat > code_integer > code_integer ).

thf(func_def_184,type,
    bit_se2923211474154528505it_int: nat > int > int ).

thf(func_def_185,type,
    bit_se2925701944663578781it_nat: nat > nat > nat ).

thf(func_def_186,type,
    bit_se8260200283734997820nteger: nat > code_integer > code_integer ).

thf(func_def_187,type,
    bit_se4203085406695923979it_int: nat > int > int ).

thf(func_def_188,type,
    bit_se4205575877204974255it_nat: nat > nat > nat ).

thf(func_def_189,type,
    bit_se3222712562003087583nteger: code_integer > code_integer > code_integer ).

thf(func_def_190,type,
    bit_se6526347334894502574or_int: int > int > int ).

thf(func_def_191,type,
    bit_se6528837805403552850or_nat: nat > nat > nat ).

thf(func_def_192,type,
    bit_se1146084159140164899it_int: int > nat > $o ).

thf(func_def_193,type,
    bit_se1148574629649215175it_nat: nat > nat > $o ).

thf(func_def_194,type,
    bit_take_bit_num: nat > num > option_num ).

thf(func_def_195,type,
    bit_un1837492267222099188nd_num: num > num > option_num ).

thf(func_def_196,type,
    bit_un5425074673868309765um_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_197,type,
    bit_un2785000775030745342or_num: num > num > num ).

thf(func_def_198,type,
    bit_un6909899581280750971um_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_199,type,
    bit_un6178654185764691216or_num: num > num > option_num ).

thf(func_def_200,type,
    bit_un3595099601533988841um_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_201,type,
    bit_un7362597486090784418nd_num: num > num > option_num ).

thf(func_def_202,type,
    bit_un4731106466462545111um_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_203,type,
    bit_un6697907153464112080or_num: num > num > num ).

thf(func_def_204,type,
    bit_un4773296044027857193um_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_205,type,
    bit_un2480387367778600638or_num: num > num > option_num ).

thf(func_def_206,type,
    bit_un2901131394128224187um_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_207,type,
    code_Neg: num > code_integer ).

thf(func_def_208,type,
    code_Pos: num > code_integer ).

thf(func_def_209,type,
    code_bit_cut_integer: code_integer > produc6271795597528267376eger_o ).

thf(func_def_210,type,
    code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger ).

thf(func_def_211,type,
    code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger ).

thf(func_def_212,type,
    code_dup: code_integer > code_integer ).

thf(func_def_213,type,
    code_int_of_integer: code_integer > int ).

thf(func_def_214,type,
    code_integer_of_int: int > code_integer ).

thf(func_def_215,type,
    code_integer_of_nat: nat > code_integer ).

thf(func_def_216,type,
    code_integer_of_num: num > code_integer ).

thf(func_def_217,type,
    code_nat_of_integer: code_integer > nat ).

thf(func_def_218,type,
    code_num_of_integer: code_integer > num ).

thf(func_def_219,type,
    code_pcr_integer: int > code_integer > $o ).

thf(func_def_220,type,
    code_sub: num > num > code_integer ).

thf(func_def_221,type,
    code_Target_negative: num > int ).

thf(func_def_222,type,
    code_Target_positive: num > int ).

thf(func_def_223,type,
    code_Target_Nat: code_integer > nat ).

thf(func_def_224,type,
    code_T6385005292777649522of_nat: nat > int ).

thf(func_def_225,type,
    comple2295165028678016749d_enat: set_Extended_enat > extended_enat ).

thf(func_def_226,type,
    comple8358262395181532106omplex: set_fi4554929511873752355omplex > filter6041513312241820739omplex ).

thf(func_def_227,type,
    comple2936214249959783750l_real: set_fi7789364187291644575l_real > filter2146258269922977983l_real ).

thf(func_def_228,type,
    complete_Inf_Inf_int: set_int > int ).

thf(func_def_229,type,
    complete_Inf_Inf_nat: set_nat > nat ).

thf(func_def_230,type,
    comple4887499456419720421f_real: set_real > real ).

thf(func_def_231,type,
    comple7806235888213564991et_nat: set_set_nat > set_nat ).

thf(func_def_232,type,
    comple4398354569131411667d_enat: set_Extended_enat > extended_enat ).

thf(func_def_233,type,
    complete_Sup_Sup_int: set_int > int ).

thf(func_def_234,type,
    complete_Sup_Sup_nat: set_nat > nat ).

thf(func_def_235,type,
    comple1385675409528146559p_real: set_real > real ).

thf(func_def_236,type,
    arg: complex > real ).

thf(func_def_237,type,
    cis: real > complex ).

thf(func_def_238,type,
    cnj: complex > complex ).

thf(func_def_239,type,
    complex2: real > real > complex ).

thf(func_def_240,type,
    im: complex > real ).

thf(func_def_241,type,
    re: complex > real ).

thf(func_def_242,type,
    csqrt: complex > complex ).

thf(func_def_243,type,
    imaginary_unit: complex ).

thf(func_def_244,type,
    rcis: real > real > complex ).

thf(func_def_245,type,
    condit2214826472909112428ve_nat: set_nat > $o ).

thf(func_def_246,type,
    differ6690327859849518006l_real: ( real > real ) > filter_real > $o ).

thf(func_def_247,type,
    has_de1759254742604945161l_real: ( real > real ) > ( real > real ) > filter_real > $o ).

thf(func_def_248,type,
    has_fi5821293074295781190e_real: ( real > real ) > real > filter_real > $o ).

thf(func_def_249,type,
    adjust_div: product_prod_int_int > int ).

thf(func_def_250,type,
    adjust_mod: int > int > int ).

thf(func_def_251,type,
    divmod_nat: nat > nat > product_prod_nat_nat ).

thf(func_def_252,type,
    eucl_rel_int: int > int > product_prod_int_int > $o ).

thf(func_def_253,type,
    unique5706413561485394159nteger: produc8923325533196201883nteger > $o ).

thf(func_def_254,type,
    unique6319869463603278526ux_int: product_prod_int_int > $o ).

thf(func_def_255,type,
    unique6322359934112328802ux_nat: product_prod_nat_nat > $o ).

thf(func_def_256,type,
    unique3479559517661332726nteger: num > num > produc8923325533196201883nteger ).

thf(func_def_257,type,
    unique5052692396658037445od_int: num > num > product_prod_int_int ).

thf(func_def_258,type,
    unique5055182867167087721od_nat: num > num > product_prod_nat_nat ).

thf(func_def_259,type,
    unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_260,type,
    unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).

thf(func_def_261,type,
    unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_262,type,
    euclid4774559944035922753ze_int: int > nat ).

thf(func_def_263,type,
    euclid3395696857347342551nt_int: int > int ).

thf(func_def_264,type,
    extended_eSuc: extended_enat > extended_enat ).

thf(func_def_265,type,
    extended_enat2: nat > extended_enat ).

thf(func_def_266,type,
    extended_Abs_enat: option_nat > extended_enat ).

thf(func_def_267,type,
    extended_Rep_enat: extended_enat > option_nat ).

thf(func_def_268,type,
    extended_case_enat_o: ( nat > $o ) > $o > extended_enat > $o ).

thf(func_def_269,type,
    extend3600170679010898289d_enat: ( nat > extended_enat ) > extended_enat > extended_enat > extended_enat ).

thf(func_def_270,type,
    extend5688581933313929465d_enat: extended_enat ).

thf(func_def_271,type,
    extended_the_enat: extended_enat > nat ).

thf(func_def_272,type,
    comm_s8582702949713902594nteger: code_integer > nat > code_integer ).

thf(func_def_273,type,
    comm_s2602460028002588243omplex: complex > nat > complex ).

thf(func_def_274,type,
    comm_s4660882817536571857er_int: int > nat > int ).

thf(func_def_275,type,
    comm_s4663373288045622133er_nat: nat > nat > nat ).

thf(func_def_276,type,
    comm_s4028243227959126397er_rat: rat > nat > rat ).

thf(func_def_277,type,
    comm_s7457072308508201937r_real: real > nat > real ).

thf(func_def_278,type,
    semiri5044797733671781792omplex: nat > complex ).

thf(func_def_279,type,
    semiri1408675320244567234ct_nat: nat > nat ).

thf(func_def_280,type,
    semiri2265585572941072030t_real: nat > real ).

thf(func_def_281,type,
    invers8013647133539491842omplex: complex > complex ).

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

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

thf(func_def_284,type,
    at_bot_real: filter_real ).

thf(func_def_285,type,
    at_top_int: filter_int ).

thf(func_def_286,type,
    at_top_nat: filter_nat ).

thf(func_def_287,type,
    at_top_real: filter_real ).

thf(func_def_288,type,
    eventually_nat: ( nat > $o ) > filter_nat > $o ).

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

thf(func_def_290,type,
    filterlim_int_nat: ( int > nat ) > filter_nat > filter_int > $o ).

thf(func_def_291,type,
    filterlim_nat_int: ( nat > int ) > filter_int > filter_nat > $o ).

thf(func_def_292,type,
    filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).

thf(func_def_293,type,
    filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).

thf(func_def_294,type,
    filterlim_real_real: ( real > real ) > filter_real > filter_real > $o ).

thf(func_def_295,type,
    filtermap_real_real: ( real > real ) > filter_real > filter_real ).

thf(func_def_296,type,
    princi3496590319149328850omplex: set_Pr5085853215250843933omplex > filter6041513312241820739omplex ).

thf(func_def_297,type,
    princi6114159922880469582l_real: set_Pr6218003697084177305l_real > filter2146258269922977983l_real ).

thf(func_def_298,type,
    finite_card_o: set_o > nat ).

thf(func_def_299,type,
    finite_card_complex: set_complex > nat ).

thf(func_def_300,type,
    finite_card_int: set_int > nat ).

thf(func_def_301,type,
    finite_card_list_nat: set_list_nat > nat ).

thf(func_def_302,type,
    finite_card_nat: set_nat > nat ).

thf(func_def_303,type,
    finite_card_set_nat: set_set_nat > nat ).

thf(func_def_304,type,
    finite_card_char: set_char > nat ).

thf(func_def_305,type,
    finite_finite_o: set_o > $o ).

thf(func_def_306,type,
    finite3207457112153483333omplex: set_complex > $o ).

thf(func_def_307,type,
    finite4001608067531595151d_enat: set_Extended_enat > $o ).

thf(func_def_308,type,
    finite_finite_int: set_int > $o ).

thf(func_def_309,type,
    finite_finite_list_o: set_list_o > $o ).

thf(func_def_310,type,
    finite8712137658972009173omplex: set_list_complex > $o ).

thf(func_def_311,type,
    finite1862508098717546133d_enat: set_li5464603477888414924d_enat > $o ).

thf(func_def_312,type,
    finite3922522038869484883st_int: set_list_int > $o ).

thf(func_def_313,type,
    finite8100373058378681591st_nat: set_list_nat > $o ).

thf(func_def_314,type,
    finite500796754983035824at_nat: set_li5450038453877631591at_nat > $o ).

thf(func_def_315,type,
    finite3004134309566078307T_VEBT: set_list_VEBT_VEBT > $o ).

thf(func_def_316,type,
    finite_finite_nat: set_nat > $o ).

thf(func_def_317,type,
    finite_finite_num: set_num > $o ).

thf(func_def_318,type,
    finite5523153139673422903on_nat: set_option_nat > $o ).

thf(func_def_319,type,
    finite6177210948735845034at_nat: set_Pr1261947904930325089at_nat > $o ).

thf(func_def_320,type,
    finite_finite_rat: set_rat > $o ).

thf(func_def_321,type,
    finite_finite_real: set_real > $o ).

thf(func_def_322,type,
    finite1152437895449049373et_nat: set_set_nat > $o ).

thf(func_def_323,type,
    finite5795047828879050333T_VEBT: set_VEBT_VEBT > $o ).

thf(func_def_324,type,
    bij_be1856998921033663316omplex: ( complex > complex ) > set_complex > set_complex > $o ).

thf(func_def_325,type,
    bij_betw_nat_complex: ( nat > complex ) > set_nat > set_complex > $o ).

thf(func_def_326,type,
    bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).

thf(func_def_327,type,
    comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_328,type,
    comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_329,type,
    comp_int_int_num: ( int > int ) > ( num > int ) > num > int ).

thf(func_def_330,type,
    comp_int_nat_int: ( int > nat ) > ( int > int ) > int > nat ).

thf(func_def_331,type,
    comp_nat_num_int: ( nat > num ) > ( int > nat ) > int > num ).

thf(func_def_332,type,
    comp_nat_real_nat: ( nat > real ) > ( nat > nat ) > nat > real ).

thf(func_def_333,type,
    id_o: $o > $o ).

thf(func_def_334,type,
    id_nat: nat > nat ).

thf(func_def_335,type,
    id_num: num > num ).

thf(func_def_336,type,
    inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).

thf(func_def_337,type,
    inj_on_nat_char: ( nat > char ) > set_nat > $o ).

thf(func_def_338,type,
    inj_on_real_real: ( real > real ) > set_real > $o ).

thf(func_def_339,type,
    map_fu6539832666145259331at_nat: ( code_integer > int ) > ( nat > nat ) > ( int > nat ) > code_integer > nat ).

thf(func_def_340,type,
    map_fu1227494855608507351um_num: ( code_integer > int ) > ( num > num ) > ( int > num ) > code_integer > num ).

thf(func_def_341,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_342,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_343,type,
    map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).

thf(func_def_344,type,
    map_fu2345160673673942751at_nat: ( int > product_prod_nat_nat ) > ( nat > nat ) > ( product_prod_nat_nat > nat ) > int > nat ).

thf(func_def_345,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_346,type,
    map_fu6290471996055670595nteger: ( nat > nat ) > ( int > code_integer ) > ( nat > int ) > nat > code_integer ).

thf(func_def_347,type,
    map_fu898904425404107465nt_o_o: ( rat > product_prod_int_int ) > ( $o > $o ) > ( product_prod_int_int > $o ) > rat > $o ).

thf(func_def_348,type,
    map_fu5673905371560938248nt_rat: ( rat > product_prod_int_int ) > ( product_prod_int_int > rat ) > ( product_prod_int_int > product_prod_int_int ) > rat > rat ).

thf(func_def_349,type,
    map_fu1532550112467129777l_real: ( real > nat > rat ) > ( ( ( nat > rat ) > nat > rat ) > real > real ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > real > real > real ).

thf(func_def_350,type,
    map_fu7146612038024189824t_real: ( real > nat > rat ) > ( ( nat > rat ) > real ) > ( ( nat > rat ) > nat > rat ) > real > real ).

thf(func_def_351,type,
    map_fu1856342031159181835at_o_o: ( real > nat > rat ) > ( $o > $o ) > ( ( nat > rat ) > $o ) > real > $o ).

thf(func_def_352,type,
    strict1292158309912662752at_nat: ( nat > nat ) > set_nat > $o ).

thf(func_def_353,type,
    the_in5290026491893676941l_real: set_real > ( real > real ) > real > real ).

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

thf(func_def_355,type,
    fun_max_strict: set_Pr4329608150637261639at_nat ).

thf(func_def_356,type,
    fun_max_weak: set_Pr4329608150637261639at_nat ).

thf(func_def_357,type,
    fun_min_strict: set_Pr4329608150637261639at_nat ).

thf(func_def_358,type,
    fun_min_weak: set_Pr4329608150637261639at_nat ).

thf(func_def_359,type,
    fun_pair_leq: set_Pr8693737435421807431at_nat ).

thf(func_def_360,type,
    fun_pair_less: set_Pr8693737435421807431at_nat ).

thf(func_def_361,type,
    fun_re2478310338295953701at_nat: produc1319942482725812455at_nat > $o ).

thf(func_def_362,type,
    gcd_Gcd_int: set_int > int ).

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

thf(func_def_364,type,
    bezw: nat > nat > product_prod_int_int ).

thf(func_def_365,type,
    bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_366,type,
    gcd_gcd_Code_integer: code_integer > code_integer > code_integer ).

thf(func_def_367,type,
    gcd_gcd_int: int > int > int ).

thf(func_def_368,type,
    gcd_gcd_nat: nat > nat > nat ).

thf(func_def_369,type,
    gcd_lcm_int: int > int > int ).

thf(func_def_370,type,
    gcd_lcm_nat: nat > nat > nat ).

thf(func_def_371,type,
    gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_372,type,
    abs_abs_Code_integer: code_integer > code_integer ).

thf(func_def_373,type,
    abs_abs_int: int > int ).

thf(func_def_374,type,
    abs_abs_rat: rat > rat ).

thf(func_def_375,type,
    abs_abs_real: real > real ).

thf(func_def_376,type,
    comm_monoid_nat: ( nat > nat > nat ) > nat > $o ).

thf(func_def_377,type,
    minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).

thf(func_def_378,type,
    minus_minus_complex: complex > complex > complex ).

thf(func_def_379,type,
    minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat ).

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

thf(func_def_381,type,
    minus_minus_nat: nat > nat > nat ).

thf(func_def_382,type,
    minus_minus_rat: rat > rat > rat ).

thf(func_def_383,type,
    minus_minus_real: real > real > real ).

thf(func_def_384,type,
    minus_811609699411566653omplex: set_complex > set_complex > set_complex ).

thf(func_def_385,type,
    minus_925952699566721837d_enat: set_Extended_enat > set_Extended_enat > set_Extended_enat ).

thf(func_def_386,type,
    minus_minus_set_int: set_int > set_int > set_int ).

thf(func_def_387,type,
    minus_minus_set_nat: set_nat > set_nat > set_nat ).

thf(func_def_388,type,
    minus_minus_set_real: set_real > set_real > set_real ).

thf(func_def_389,type,
    monoid_nat: ( nat > nat > nat ) > nat > $o ).

thf(func_def_390,type,
    one_one_Code_integer: code_integer ).

thf(func_def_391,type,
    one_one_complex: complex ).

thf(func_def_392,type,
    one_on7984719198319812577d_enat: extended_enat ).

thf(func_def_393,type,
    one_one_int: int ).

thf(func_def_394,type,
    one_one_nat: nat ).

thf(func_def_395,type,
    one_one_rat: rat ).

thf(func_def_396,type,
    one_one_real: real ).

thf(func_def_397,type,
    plus_p5714425477246183910nteger: code_integer > code_integer > code_integer ).

thf(func_def_398,type,
    plus_plus_complex: complex > complex > complex ).

thf(func_def_399,type,
    plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_400,type,
    plus_plus_int: int > int > int ).

thf(func_def_401,type,
    plus_plus_nat: nat > nat > nat ).

thf(func_def_402,type,
    plus_plus_num: num > num > num ).

thf(func_def_403,type,
    plus_plus_rat: rat > rat > rat ).

thf(func_def_404,type,
    plus_plus_real: real > real > real ).

thf(func_def_405,type,
    plus_plus_literal: literal > literal > literal ).

thf(func_def_406,type,
    sgn_sgn_Code_integer: code_integer > code_integer ).

thf(func_def_407,type,
    sgn_sgn_complex: complex > complex ).

thf(func_def_408,type,
    sgn_sgn_int: int > int ).

thf(func_def_409,type,
    sgn_sgn_rat: rat > rat ).

thf(func_def_410,type,
    sgn_sgn_real: real > real ).

thf(func_def_411,type,
    times_3573771949741848930nteger: code_integer > code_integer > code_integer ).

thf(func_def_412,type,
    times_times_complex: complex > complex > complex ).

thf(func_def_413,type,
    times_7803423173614009249d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_414,type,
    times_times_int: int > int > int ).

thf(func_def_415,type,
    times_times_nat: nat > nat > nat ).

thf(func_def_416,type,
    times_times_num: num > num > num ).

thf(func_def_417,type,
    times_times_rat: rat > rat > rat ).

thf(func_def_418,type,
    times_times_real: real > real > real ).

thf(func_def_419,type,
    uminus1351360451143612070nteger: code_integer > code_integer ).

thf(func_def_420,type,
    uminus1482373934393186551omplex: complex > complex ).

thf(func_def_421,type,
    uminus_uminus_int: int > int ).

thf(func_def_422,type,
    uminus_uminus_rat: rat > rat ).

thf(func_def_423,type,
    uminus_uminus_real: real > real ).

thf(func_def_424,type,
    uminus5710092332889474511et_nat: set_nat > set_nat ).

thf(func_def_425,type,
    zero_z3403309356797280102nteger: code_integer ).

thf(func_def_426,type,
    zero_zero_complex: complex ).

thf(func_def_427,type,
    zero_z5237406670263579293d_enat: extended_enat ).

thf(func_def_428,type,
    zero_zero_int: int ).

thf(func_def_429,type,
    zero_zero_nat: nat ).

thf(func_def_430,type,
    zero_zero_rat: rat ).

thf(func_def_431,type,
    zero_zero_real: real ).

thf(func_def_432,type,
    zero_zero_literal: literal ).

thf(func_def_433,type,
    groups7754918857620584856omplex: ( complex > complex ) > set_complex > complex ).

thf(func_def_434,type,
    groups5690904116761175830ex_int: ( complex > int ) > set_complex > int ).

thf(func_def_435,type,
    groups5693394587270226106ex_nat: ( complex > nat ) > set_complex > nat ).

thf(func_def_436,type,
    groups5058264527183730370ex_rat: ( complex > rat ) > set_complex > rat ).

thf(func_def_437,type,
    groups5808333547571424918x_real: ( complex > real ) > set_complex > real ).

thf(func_def_438,type,
    groups2025484359314973016at_int: ( extended_enat > int ) > set_Extended_enat > int ).

thf(func_def_439,type,
    groups2027974829824023292at_nat: ( extended_enat > nat ) > set_Extended_enat > nat ).

thf(func_def_440,type,
    groups1392844769737527556at_rat: ( extended_enat > rat ) > set_Extended_enat > rat ).

thf(func_def_441,type,
    groups4148127829035722712t_real: ( extended_enat > real ) > set_Extended_enat > real ).

thf(func_def_442,type,
    groups7873554091576472773nteger: ( int > code_integer ) > set_int > code_integer ).

thf(func_def_443,type,
    groups3049146728041665814omplex: ( int > complex ) > set_int > complex ).

thf(func_def_444,type,
    groups4538972089207619220nt_int: ( int > int ) > set_int > int ).

thf(func_def_445,type,
    groups4541462559716669496nt_nat: ( int > nat ) > set_int > nat ).

thf(func_def_446,type,
    groups3906332499630173760nt_rat: ( int > rat ) > set_int > rat ).

thf(func_def_447,type,
    groups8778361861064173332t_real: ( int > real ) > set_int > real ).

thf(func_def_448,type,
    groups7501900531339628137nteger: ( nat > code_integer ) > set_nat > code_integer ).

thf(func_def_449,type,
    groups2073611262835488442omplex: ( nat > complex ) > set_nat > complex ).

thf(func_def_450,type,
    groups3539618377306564664at_int: ( nat > int ) > set_nat > int ).

thf(func_def_451,type,
    groups3542108847815614940at_nat: ( nat > nat ) > set_nat > nat ).

thf(func_def_452,type,
    groups2906978787729119204at_rat: ( nat > rat ) > set_nat > rat ).

thf(func_def_453,type,
    groups6591440286371151544t_real: ( nat > real ) > set_nat > real ).

thf(func_def_454,type,
    groups3209896439523537802omplex: ( option_nat > complex ) > set_option_nat > complex ).

thf(func_def_455,type,
    groups1921984841883549356at_nat: ( option_nat > nat ) > set_option_nat > nat ).

thf(func_def_456,type,
    groups4518532050878116744t_real: ( option_nat > real ) > set_option_nat > real ).

thf(func_def_457,type,
    groups977919841031483927at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > nat ).

thf(func_def_458,type,
    groups4567486121110086003t_real: ( product_prod_nat_nat > real ) > set_Pr1261947904930325089at_nat > real ).

thf(func_def_459,type,
    groups7713935264441627589nteger: ( real > code_integer ) > set_real > code_integer ).

thf(func_def_460,type,
    groups5754745047067104278omplex: ( real > complex ) > set_real > complex ).

thf(func_def_461,type,
    groups1932886352136224148al_int: ( real > int ) > set_real > int ).

thf(func_def_462,type,
    groups1935376822645274424al_nat: ( real > nat ) > set_real > nat ).

thf(func_def_463,type,
    groups1300246762558778688al_rat: ( real > rat ) > set_real > rat ).

thf(func_def_464,type,
    groups8097168146408367636l_real: ( real > real ) > set_real > real ).

thf(func_def_465,type,
    groups8255218700646806128omplex: ( set_nat > complex ) > set_set_nat > complex ).

thf(func_def_466,type,
    groups8294997508430121362at_nat: ( set_nat > nat ) > set_set_nat > nat ).

thf(func_def_467,type,
    groups5107569545109728110t_real: ( set_nat > real ) > set_set_nat > real ).

thf(func_def_468,type,
    groups8682486955453173170nteger: ( complex > code_integer ) > set_complex > code_integer ).

thf(func_def_469,type,
    groups3708469109370488835omplex: ( complex > complex ) > set_complex > complex ).

thf(func_def_470,type,
    groups858564598930262913ex_int: ( complex > int ) > set_complex > int ).

thf(func_def_471,type,
    groups861055069439313189ex_nat: ( complex > nat ) > set_complex > nat ).

thf(func_def_472,type,
    groups225925009352817453ex_rat: ( complex > rat ) > set_complex > rat ).

thf(func_def_473,type,
    groups766887009212190081x_real: ( complex > real ) > set_complex > real ).

thf(func_def_474,type,
    groups845124408420398302nteger: ( extended_enat > code_integer ) > set_Extended_enat > code_integer ).

thf(func_def_475,type,
    groups4622424608036095791omplex: ( extended_enat > complex ) > set_Extended_enat > complex ).

thf(func_def_476,type,
    groups2878480467620962989at_int: ( extended_enat > int ) > set_Extended_enat > int ).

thf(func_def_477,type,
    groups2880970938130013265at_nat: ( extended_enat > nat ) > set_Extended_enat > nat ).

thf(func_def_478,type,
    groups2245840878043517529at_rat: ( extended_enat > rat ) > set_Extended_enat > rat ).

thf(func_def_479,type,
    groups97031904164794029t_real: ( extended_enat > real ) > set_Extended_enat > real ).

thf(func_def_480,type,
    groups3827104343326376752nteger: ( int > code_integer ) > set_int > code_integer ).

thf(func_def_481,type,
    groups7440179247065528705omplex: ( int > complex ) > set_int > complex ).

thf(func_def_482,type,
    groups1705073143266064639nt_int: ( int > int ) > set_int > int ).

thf(func_def_483,type,
    groups1707563613775114915nt_nat: ( int > nat ) > set_int > nat ).

thf(func_def_484,type,
    groups1072433553688619179nt_rat: ( int > rat ) > set_int > rat ).

thf(func_def_485,type,
    groups2316167850115554303t_real: ( int > real ) > set_int > real ).

thf(func_def_486,type,
    groups3455450783089532116nteger: ( nat > code_integer ) > set_nat > code_integer ).

thf(func_def_487,type,
    groups6464643781859351333omplex: ( nat > complex ) > set_nat > complex ).

thf(func_def_488,type,
    groups705719431365010083at_int: ( nat > int ) > set_nat > int ).

thf(func_def_489,type,
    groups708209901874060359at_nat: ( nat > nat ) > set_nat > nat ).

thf(func_def_490,type,
    groups73079841787564623at_rat: ( nat > rat ) > set_nat > rat ).

thf(func_def_491,type,
    groups129246275422532515t_real: ( nat > real ) > set_nat > real ).

thf(func_def_492,type,
    groups1917955009447795573omplex: ( option_nat > complex ) > set_option_nat > complex ).

thf(func_def_493,type,
    groups6579596140936342515t_real: ( option_nat > real ) > set_option_nat > real ).

thf(func_def_494,type,
    groups4077766827762148844at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > nat ).

thf(func_def_495,type,
    groups6036352826371341000t_real: ( product_prod_nat_nat > real ) > set_Pr1261947904930325089at_nat > real ).

thf(func_def_496,type,
    groups713298508707869441omplex: ( real > complex ) > set_real > complex ).

thf(func_def_497,type,
    groups4694064378042380927al_int: ( real > int ) > set_real > int ).

thf(func_def_498,type,
    groups4696554848551431203al_nat: ( real > nat ) > set_real > nat ).

thf(func_def_499,type,
    groups4061424788464935467al_rat: ( real > rat ) > set_real > rat ).

thf(func_def_500,type,
    groups1681761925125756287l_real: ( real > real ) > set_real > real ).

thf(func_def_501,type,
    groups1092910753850256091omplex: ( set_nat > complex ) > set_set_nat > complex ).

thf(func_def_502,type,
    groups3619160379726066777t_real: ( set_nat > real ) > set_set_nat > real ).

thf(func_def_503,type,
    groups9116527308978886569_o_int: ( $o > int ) > int > list_o > int ).

thf(func_def_504,type,
    groups4561878855575611511st_nat: list_nat > nat ).

thf(func_def_505,type,
    the_int: ( int > $o ) > int ).

thf(func_def_506,type,
    the_Pr4378521158711661632nt_int: ( product_prod_int_int > $o ) > product_prod_int_int ).

thf(func_def_507,type,
    the_real: ( real > $o ) > real ).

thf(func_def_508,type,
    if_int_int: $o > ( int > int ) > ( int > int ) > int > int ).

thf(func_def_509,type,
    if_nat_rat: $o > ( nat > rat ) > ( nat > rat ) > nat > rat ).

thf(func_def_510,type,
    if_Code_integer: $o > code_integer > code_integer > code_integer ).

thf(func_def_511,type,
    if_complex: $o > complex > complex > complex ).

thf(func_def_512,type,
    if_Extended_enat: $o > extended_enat > extended_enat > extended_enat ).

thf(func_def_513,type,
    if_int: $o > int > int > int ).

thf(func_def_514,type,
    if_list_int: $o > list_int > list_int > list_int ).

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

thf(func_def_516,type,
    if_nat: $o > nat > nat > nat ).

thf(func_def_517,type,
    if_num: $o > num > num > num ).

thf(func_def_518,type,
    if_option_nat: $o > option_nat > option_nat > option_nat ).

thf(func_def_519,type,
    if_option_num: $o > option_num > option_num > option_num ).

thf(func_def_520,type,
    if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o ).

thf(func_def_521,type,
    if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_522,type,
    if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).

thf(func_def_523,type,
    if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_524,type,
    if_rat: $o > rat > rat > rat ).

thf(func_def_525,type,
    if_real: $o > real > real > real ).

thf(func_def_526,type,
    if_set_int: $o > set_int > set_int > set_int ).

thf(func_def_527,type,
    if_set_nat: $o > set_nat > set_nat > set_nat ).

thf(func_def_528,type,
    if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_529,type,
    infini8530281810654367211te_nat: set_nat > nat > nat ).

thf(func_def_530,type,
    abs_Integ: product_prod_nat_nat > int ).

thf(func_def_531,type,
    rep_Integ: int > product_prod_nat_nat ).

thf(func_def_532,type,
    cr_int: product_prod_nat_nat > int > $o ).

thf(func_def_533,type,
    int_ge_less_than: int > set_Pr958786334691620121nt_int ).

thf(func_def_534,type,
    int_ge_less_than2: int > set_Pr958786334691620121nt_int ).

thf(func_def_535,type,
    intrel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_536,type,
    nat2: int > nat ).

thf(func_def_537,type,
    pcr_int: product_prod_nat_nat > int > $o ).

thf(func_def_538,type,
    power_int_real: real > int > real ).

thf(func_def_539,type,
    ring_1_Ints_complex: set_complex ).

thf(func_def_540,type,
    ring_1_Ints_real: set_real ).

thf(func_def_541,type,
    ring_18347121197199848620nteger: int > code_integer ).

thf(func_def_542,type,
    ring_17405671764205052669omplex: int > complex ).

thf(func_def_543,type,
    ring_1_of_int_int: int > int ).

thf(func_def_544,type,
    ring_1_of_int_rat: int > rat ).

thf(func_def_545,type,
    ring_1_of_int_real: int > real ).

thf(func_def_546,type,
    inf_in1870772243966228564d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_547,type,
    inf_inf_int: int > int > int ).

thf(func_def_548,type,
    inf_inf_nat: nat > nat > nat ).

thf(func_def_549,type,
    inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_550,type,
    semila9081495762789891438tr_nat: ( nat > nat > nat ) > nat > $o ).

thf(func_def_551,type,
    semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).

thf(func_def_552,type,
    sup_su3973961784419623482d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_553,type,
    sup_sup_int: int > int > int ).

thf(func_def_554,type,
    sup_sup_nat: nat > nat > nat ).

thf(func_def_555,type,
    sup_sup_set_nat: set_nat > set_nat > set_nat ).

thf(func_def_556,type,
    sup_su5525570899277871387at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).

thf(func_def_557,type,
    lattic921264341876707157d_enat: set_Extended_enat > extended_enat ).

thf(func_def_558,type,
    lattic8263393255366662781ax_int: set_int > int ).

thf(func_def_559,type,
    lattic8265883725875713057ax_nat: set_nat > nat ).

thf(func_def_560,type,
    quotie3684837364556693515t_real: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > real ) > ( real > nat > rat ) > ( ( nat > rat ) > real > $o ) > $o ).

thf(func_def_561,type,
    quotie1194848508323700631at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int > $o ) > $o ).

thf(func_def_562,type,
    bfun_nat_real: ( nat > real ) > filter_nat > $o ).

thf(func_def_563,type,
    at_infinity_real: filter_real ).

thf(func_def_564,type,
    append_int: list_int > list_int > list_int ).

thf(func_def_565,type,
    append_nat: list_nat > list_nat > list_nat ).

thf(func_def_566,type,
    fold_int_int: ( int > int > int ) > list_int > int > int ).

thf(func_def_567,type,
    fold_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).

thf(func_def_568,type,
    last_nat: list_nat > nat ).

thf(func_def_569,type,
    linord2614967742042102400et_nat: set_nat > list_nat ).

thf(func_def_570,type,
    cons_int: int > list_int > list_int ).

thf(func_def_571,type,
    cons_nat: nat > list_nat > list_nat ).

thf(func_def_572,type,
    nil_int: list_int ).

thf(func_def_573,type,
    nil_nat: list_nat ).

thf(func_def_574,type,
    hd_nat: list_nat > nat ).

thf(func_def_575,type,
    map_nat_nat: ( nat > nat ) > list_nat > list_nat ).

thf(func_def_576,type,
    map_VE8901447254227204932T_VEBT: ( vEBT_VEBT > vEBT_VEBT ) > list_VEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_577,type,
    set_o2: list_o > set_o ).

thf(func_def_578,type,
    set_complex2: list_complex > set_complex ).

thf(func_def_579,type,
    set_Extended_enat2: list_Extended_enat > set_Extended_enat ).

thf(func_def_580,type,
    set_int2: list_int > set_int ).

thf(func_def_581,type,
    set_nat2: list_nat > set_nat ).

thf(func_def_582,type,
    set_option_nat2: list_option_nat > set_option_nat ).

thf(func_def_583,type,
    set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_584,type,
    set_Pr3765526544606949372at_nat: list_P5464809261938338413at_nat > set_Pr4329608150637261639at_nat ).

thf(func_def_585,type,
    set_real2: list_real > set_real ).

thf(func_def_586,type,
    set_set_nat2: list_set_nat > set_set_nat ).

thf(func_def_587,type,
    set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).

thf(func_def_588,type,
    size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).

thf(func_def_589,type,
    list_update_o: list_o > nat > $o > list_o ).

thf(func_def_590,type,
    list_update_int: list_int > nat > int > list_int ).

thf(func_def_591,type,
    list_update_nat: list_nat > nat > nat > list_nat ).

thf(func_def_592,type,
    list_u3411377215356412978on_nat: list_option_nat > nat > option_nat > list_option_nat ).

thf(func_def_593,type,
    list_update_real: list_real > nat > real > list_real ).

thf(func_def_594,type,
    list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat ).

thf(func_def_595,type,
    list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_596,type,
    nth_o: list_o > nat > $o ).

thf(func_def_597,type,
    nth_int: list_int > nat > int ).

thf(func_def_598,type,
    nth_nat: list_nat > nat > nat ).

thf(func_def_599,type,
    nth_num: list_num > nat > num ).

thf(func_def_600,type,
    nth_option_nat: list_option_nat > nat > option_nat ).

thf(func_def_601,type,
    nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).

thf(func_def_602,type,
    nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).

thf(func_def_603,type,
    nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).

thf(func_def_604,type,
    nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).

thf(func_def_605,type,
    nth_Pr8326237132889035090at_num: list_P1726324292696863441at_num > nat > product_prod_nat_num ).

thf(func_def_606,type,
    nth_Pr6456567536196504476um_num: list_P3744719386663036955um_num > nat > product_prod_num_num ).

thf(func_def_607,type,
    nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).

thf(func_def_608,type,
    nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).

thf(func_def_609,type,
    nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).

thf(func_def_610,type,
    nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).

thf(func_def_611,type,
    nth_real: list_real > nat > real ).

thf(func_def_612,type,
    nth_set_nat: list_set_nat > nat > set_nat ).

thf(func_def_613,type,
    nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_614,type,
    product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).

thf(func_def_615,type,
    product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).

thf(func_def_616,type,
    product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).

thf(func_def_617,type,
    product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).

thf(func_def_618,type,
    product_nat_num: list_nat > list_num > list_P1726324292696863441at_num ).

thf(func_def_619,type,
    product_num_num: list_num > list_num > list_P3744719386663036955um_num ).

thf(func_def_620,type,
    product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).

thf(func_def_621,type,
    produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).

thf(func_def_622,type,
    produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).

thf(func_def_623,type,
    produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).

thf(func_def_624,type,
    replic7216382294607269926d_enat: nat > extended_enat > list_Extended_enat ).

thf(func_def_625,type,
    replicate_int: nat > int > list_int ).

thf(func_def_626,type,
    replicate_nat: nat > nat > list_nat ).

thf(func_def_627,type,
    replicate_option_nat: nat > option_nat > list_option_nat ).

thf(func_def_628,type,
    replic4235873036481779905at_nat: nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).

thf(func_def_629,type,
    replic2264142908078655527at_nat: nat > produc3843707927480180839at_nat > list_P5464809261938338413at_nat ).

thf(func_def_630,type,
    replicate_real: nat > real > list_real ).

thf(func_def_631,type,
    replicate_set_nat: nat > set_nat > list_set_nat ).

thf(func_def_632,type,
    replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_633,type,
    sorted_wrt_int: ( int > int > $o ) > list_int > $o ).

thf(func_def_634,type,
    sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).

thf(func_def_635,type,
    take_nat: nat > list_nat > list_nat ).

thf(func_def_636,type,
    take_VEBT_VEBT: nat > list_VEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_637,type,
    upt: nat > nat > list_nat ).

thf(func_def_638,type,
    upto: int > int > list_int ).

thf(func_def_639,type,
    upto_aux: int > int > list_int > list_int ).

thf(func_def_640,type,
    upto_rel: product_prod_int_int > product_prod_int_int > $o ).

thf(func_def_641,type,
    suc: nat > nat ).

thf(func_def_642,type,
    compow_nat_nat: nat > ( nat > nat ) > nat > nat ).

thf(func_def_643,type,
    case_nat_o: $o > ( nat > $o ) > nat > $o ).

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

thf(func_def_645,type,
    case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).

thf(func_def_646,type,
    pred: nat > nat ).

thf(func_def_647,type,
    semiri3842193898606819883omplex: set_complex ).

thf(func_def_648,type,
    semiring_1_Nats_int: set_int ).

thf(func_def_649,type,
    semiri4939895301339042750nteger: nat > code_integer ).

thf(func_def_650,type,
    semiri8010041392384452111omplex: nat > complex ).

thf(func_def_651,type,
    semiri4216267220026989637d_enat: nat > extended_enat ).

thf(func_def_652,type,
    semiri1314217659103216013at_int: nat > int ).

thf(func_def_653,type,
    semiri1316708129612266289at_nat: nat > nat ).

thf(func_def_654,type,
    semiri681578069525770553at_rat: nat > rat ).

thf(func_def_655,type,
    semiri5074537144036343181t_real: nat > real ).

thf(func_def_656,type,
    size_size_list_o: list_o > nat ).

thf(func_def_657,type,
    size_s3451745648224563538omplex: list_complex > nat ).

thf(func_def_658,type,
    size_s3941691890525107288d_enat: list_Extended_enat > nat ).

thf(func_def_659,type,
    size_size_list_int: list_int > nat ).

thf(func_def_660,type,
    size_size_list_nat: list_nat > nat ).

thf(func_def_661,type,
    size_size_list_num: list_num > nat ).

thf(func_def_662,type,
    size_s6086282163384603972on_nat: list_option_nat > nat ).

thf(func_def_663,type,
    size_s5460976970255530739at_nat: list_P6011104703257516679at_nat > nat ).

thf(func_def_664,type,
    size_size_list_real: list_real > nat ).

thf(func_def_665,type,
    size_s3254054031482475050et_nat: list_set_nat > nat ).

thf(func_def_666,type,
    size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).

thf(func_def_667,type,
    size_size_num: num > nat ).

thf(func_def_668,type,
    size_size_option_nat: option_nat > nat ).

thf(func_def_669,type,
    size_size_option_num: option_num > nat ).

thf(func_def_670,type,
    size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).

thf(func_def_671,type,
    size_size_char: char > nat ).

thf(func_def_672,type,
    size_size_VEBT_VEBT: vEBT_VEBT > nat ).

thf(func_def_673,type,
    nat_list_decode: nat > list_nat ).

thf(func_def_674,type,
    nat_list_decode_rel: nat > nat > $o ).

thf(func_def_675,type,
    nat_list_encode: list_nat > nat ).

thf(func_def_676,type,
    nat_list_encode_rel: list_nat > list_nat > $o ).

thf(func_def_677,type,
    nat_prod_decode: nat > product_prod_nat_nat ).

thf(func_def_678,type,
    nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).

thf(func_def_679,type,
    nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).

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

thf(func_def_681,type,
    nat_set_decode: nat > set_nat ).

thf(func_def_682,type,
    nat_set_encode: set_nat > nat ).

thf(func_def_683,type,
    nat_triangle: nat > nat ).

thf(func_def_684,type,
    root: nat > real > real ).

thf(func_def_685,type,
    sqrt: real > real ).

thf(func_def_686,type,
    bitM: num > num ).

thf(func_def_687,type,
    inc: num > num ).

thf(func_def_688,type,
    nat_of_num: num > nat ).

thf(func_def_689,type,
    neg_nu8804712462038260780nteger: code_integer > code_integer ).

thf(func_def_690,type,
    neg_nu7009210354673126013omplex: complex > complex ).

thf(func_def_691,type,
    neg_numeral_dbl_int: int > int ).

thf(func_def_692,type,
    neg_numeral_dbl_rat: rat > rat ).

thf(func_def_693,type,
    neg_numeral_dbl_real: real > real ).

thf(func_def_694,type,
    neg_nu7757733837767384882nteger: code_integer > code_integer ).

thf(func_def_695,type,
    neg_nu6511756317524482435omplex: complex > complex ).

thf(func_def_696,type,
    neg_nu3811975205180677377ec_int: int > int ).

thf(func_def_697,type,
    neg_nu3179335615603231917ec_rat: rat > rat ).

thf(func_def_698,type,
    neg_nu6075765906172075777c_real: real > real ).

thf(func_def_699,type,
    neg_nu5831290666863070958nteger: code_integer > code_integer ).

thf(func_def_700,type,
    neg_nu8557863876264182079omplex: complex > complex ).

thf(func_def_701,type,
    neg_nu5851722552734809277nc_int: int > int ).

thf(func_def_702,type,
    neg_nu5219082963157363817nc_rat: rat > rat ).

thf(func_def_703,type,
    neg_nu8295874005876285629c_real: real > real ).

thf(func_def_704,type,
    neg_numeral_sub_int: num > num > int ).

thf(func_def_705,type,
    bit0: num > num ).

thf(func_def_706,type,
    bit1: num > num ).

thf(func_def_707,type,
    one: num ).

thf(func_def_708,type,
    case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).

thf(func_def_709,type,
    size_num: num > nat ).

thf(func_def_710,type,
    num_of_nat: nat > num ).

thf(func_def_711,type,
    numera6620942414471956472nteger: num > code_integer ).

thf(func_def_712,type,
    numera6690914467698888265omplex: num > complex ).

thf(func_def_713,type,
    numera1916890842035813515d_enat: num > extended_enat ).

thf(func_def_714,type,
    numeral_numeral_int: num > int ).

thf(func_def_715,type,
    numeral_numeral_nat: num > nat ).

thf(func_def_716,type,
    numeral_numeral_rat: num > rat ).

thf(func_def_717,type,
    numeral_numeral_real: num > real ).

thf(func_def_718,type,
    pow: num > num > num ).

thf(func_def_719,type,
    pred_numeral: num > nat ).

thf(func_def_720,type,
    sqr: num > num ).

thf(func_def_721,type,
    none_nat: option_nat ).

thf(func_def_722,type,
    none_num: option_num ).

thf(func_def_723,type,
    none_P5556105721700978146at_nat: option4927543243414619207at_nat ).

thf(func_def_724,type,
    some_nat: nat > option_nat ).

thf(func_def_725,type,
    some_num: num > option_num ).

thf(func_def_726,type,
    some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).

thf(func_def_727,type,
    case_o184042715313410164at_nat: $o > ( product_prod_nat_nat > $o ) > option4927543243414619207at_nat > $o ).

thf(func_def_728,type,
    case_option_int_num: int > ( num > int ) > option_num > int ).

thf(func_def_729,type,
    case_option_num_num: num > ( num > num ) > option_num > num ).

thf(func_def_730,type,
    case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).

thf(func_def_731,type,
    map_option_num_num: ( num > num ) > option_num > option_num ).

thf(func_def_732,type,
    the_nat: option_nat > nat ).

thf(func_def_733,type,
    the_num: option_num > num ).

thf(func_def_734,type,
    the_Pr8591224930841456533at_nat: option4927543243414619207at_nat > product_prod_nat_nat ).

thf(func_def_735,type,
    order_underS_nat: set_Pr1261947904930325089at_nat > nat > set_nat ).

thf(func_def_736,type,
    bot_bo4199563552545308370d_enat: extended_enat ).

thf(func_def_737,type,
    bot_bot_nat: nat ).

thf(func_def_738,type,
    bot_bot_set_complex: set_complex ).

thf(func_def_739,type,
    bot_bo7653980558646680370d_enat: set_Extended_enat ).

thf(func_def_740,type,
    bot_bot_set_int: set_int ).

thf(func_def_741,type,
    bot_bot_set_nat: set_nat ).

thf(func_def_742,type,
    bot_bot_set_num: set_num ).

thf(func_def_743,type,
    bot_bo2099793752762293965at_nat: set_Pr1261947904930325089at_nat ).

thf(func_def_744,type,
    bot_bo228742789529271731at_nat: set_Pr4329608150637261639at_nat ).

thf(func_def_745,type,
    bot_bot_set_rat: set_rat ).

thf(func_def_746,type,
    bot_bot_set_real: set_real ).

thf(func_def_747,type,
    bot_bot_set_set_nat: set_set_nat ).

thf(func_def_748,type,
    bot_bo8194388402131092736T_VEBT: set_VEBT_VEBT ).

thf(func_def_749,type,
    ord_Le1955565732374568822d_enat: ( extended_enat > $o ) > extended_enat ).

thf(func_def_750,type,
    ord_Least_nat: ( nat > $o ) > nat ).

thf(func_def_751,type,
    ord_Least_real: ( real > $o ) > real ).

thf(func_def_752,type,
    ord_le6747313008572928689nteger: code_integer > code_integer > $o ).

thf(func_def_753,type,
    ord_le72135733267957522d_enat: extended_enat > extended_enat > $o ).

thf(func_def_754,type,
    ord_less_int: int > int > $o ).

thf(func_def_755,type,
    ord_less_nat: nat > nat > $o ).

thf(func_def_756,type,
    ord_less_num: num > num > $o ).

thf(func_def_757,type,
    ord_less_rat: rat > rat > $o ).

thf(func_def_758,type,
    ord_less_real: real > real > $o ).

thf(func_def_759,type,
    ord_le2529575680413868914d_enat: set_Extended_enat > set_Extended_enat > $o ).

thf(func_def_760,type,
    ord_less_set_int: set_int > set_int > $o ).

thf(func_def_761,type,
    ord_less_set_nat: set_nat > set_nat > $o ).

thf(func_def_762,type,
    ord_less_set_num: set_num > set_num > $o ).

thf(func_def_763,type,
    ord_less_set_rat: set_rat > set_rat > $o ).

thf(func_def_764,type,
    ord_less_set_real: set_real > set_real > $o ).

thf(func_def_765,type,
    ord_less_set_set_nat: set_set_nat > set_set_nat > $o ).

thf(func_def_766,type,
    ord_le3102999989581377725nteger: code_integer > code_integer > $o ).

thf(func_def_767,type,
    ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o ).

thf(func_def_768,type,
    ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o ).

thf(func_def_769,type,
    ord_less_eq_int: int > int > $o ).

thf(func_def_770,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(func_def_771,type,
    ord_less_eq_num: num > num > $o ).

thf(func_def_772,type,
    ord_less_eq_rat: rat > rat > $o ).

thf(func_def_773,type,
    ord_less_eq_real: real > real > $o ).

thf(func_def_774,type,
    ord_less_eq_set_o: set_o > set_o > $o ).

thf(func_def_775,type,
    ord_le211207098394363844omplex: set_complex > set_complex > $o ).

thf(func_def_776,type,
    ord_le7203529160286727270d_enat: set_Extended_enat > set_Extended_enat > $o ).

thf(func_def_777,type,
    ord_less_eq_set_int: set_int > set_int > $o ).

thf(func_def_778,type,
    ord_less_eq_set_nat: set_nat > set_nat > $o ).

thf(func_def_779,type,
    ord_less_eq_set_num: set_num > set_num > $o ).

thf(func_def_780,type,
    ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_781,type,
    ord_less_eq_set_rat: set_rat > set_rat > $o ).

thf(func_def_782,type,
    ord_less_eq_set_real: set_real > set_real > $o ).

thf(func_def_783,type,
    ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o ).

thf(func_def_784,type,
    ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).

thf(func_def_785,type,
    ord_max_Code_integer: code_integer > code_integer > code_integer ).

thf(func_def_786,type,
    ord_ma741700101516333627d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_787,type,
    ord_max_int: int > int > int ).

thf(func_def_788,type,
    ord_max_nat: nat > nat > nat ).

thf(func_def_789,type,
    ord_max_num: num > num > num ).

thf(func_def_790,type,
    ord_max_rat: rat > rat > rat ).

thf(func_def_791,type,
    ord_max_real: real > real > real ).

thf(func_def_792,type,
    ord_ma4205026669011143323d_enat: set_Extended_enat > set_Extended_enat > set_Extended_enat ).

thf(func_def_793,type,
    ord_max_set_int: set_int > set_int > set_int ).

thf(func_def_794,type,
    ord_max_set_nat: set_nat > set_nat > set_nat ).

thf(func_def_795,type,
    ord_max_set_real: set_real > set_real > set_real ).

thf(func_def_796,type,
    ord_mi8085742599997312461d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_797,type,
    ord_min_int: int > int > int ).

thf(func_def_798,type,
    ord_min_nat: nat > nat > nat ).

thf(func_def_799,type,
    order_Greatest_nat: ( nat > $o ) > nat ).

thf(func_def_800,type,
    order_9091379641038594480t_real: ( nat > real ) > $o ).

thf(func_def_801,type,
    order_4130057895858720880d_enat: ( extended_enat > extended_enat ) > $o ).

thf(func_def_802,type,
    order_mono_nat_nat: ( nat > nat ) > $o ).

thf(func_def_803,type,
    order_mono_nat_real: ( nat > real ) > $o ).

thf(func_def_804,type,
    order_mono_real_real: ( real > real ) > $o ).

thf(func_def_805,type,
    order_5726023648592871131at_nat: ( nat > nat ) > $o ).

thf(func_def_806,type,
    order_7092887310737990675l_real: ( real > real ) > $o ).

thf(func_def_807,type,
    ordering_top_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > $o ).

thf(func_def_808,type,
    top_to3028658606643905974d_enat: extended_enat ).

thf(func_def_809,type,
    top_top_set_o: set_o ).

thf(func_def_810,type,
    top_top_set_int: set_int ).

thf(func_def_811,type,
    top_top_set_nat: set_nat ).

thf(func_def_812,type,
    top_to8920198386146353926on_nat: set_option_nat ).

thf(func_def_813,type,
    top_top_set_real: set_real ).

thf(func_def_814,type,
    top_top_set_char: set_char ).

thf(func_def_815,type,
    power_8256067586552552935nteger: code_integer > nat > code_integer ).

thf(func_def_816,type,
    power_power_complex: complex > nat > complex ).

thf(func_def_817,type,
    power_power_int: int > nat > int ).

thf(func_def_818,type,
    power_power_nat: nat > nat > nat ).

thf(func_def_819,type,
    power_power_rat: rat > nat > rat ).

thf(func_def_820,type,
    power_power_real: real > nat > real ).

thf(func_def_821,type,
    produc4035269172776083154on_nat: ( nat > nat > $o ) > produc4953844613479565601on_nat > produc2233624965454879586on_nat ).

thf(func_def_822,type,
    produc8929957630744042906on_nat: ( nat > nat > nat ) > produc4953844613479565601on_nat > produc8306885398267862888on_nat ).

thf(func_def_823,type,
    produc3576312749637752826on_num: ( num > num > $o ) > produc3447558737645232053on_num > produc7036089656553540234on_num ).

thf(func_def_824,type,
    produc5778274026573060048on_num: ( num > num > num ) > produc3447558737645232053on_num > produc1193250871479095198on_num ).

thf(func_def_825,type,
    produc3994169339658061776at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > produc6121120109295599847at_nat > produc5491161045314408544at_nat ).

thf(func_def_826,type,
    produc2899441246263362727at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > produc6121120109295599847at_nat > produc5542196010084753463at_nat ).

thf(func_def_827,type,
    product_Pair_o_o: $o > $o > product_prod_o_o ).

thf(func_def_828,type,
    product_Pair_o_int: $o > int > product_prod_o_int ).

thf(func_def_829,type,
    product_Pair_o_nat: $o > nat > product_prod_o_nat ).

thf(func_def_830,type,
    produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT ).

thf(func_def_831,type,
    produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).

thf(func_def_832,type,
    produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).

thf(func_def_833,type,
    product_Pair_int_int: int > int > product_prod_int_int ).

thf(func_def_834,type,
    product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).

thf(func_def_835,type,
    product_Pair_nat_num: nat > num > product_prod_nat_num ).

thf(func_def_836,type,
    product_Pair_num_num: num > num > product_prod_num_num ).

thf(func_def_837,type,
    produc5098337634421038937on_nat: option_nat > option_nat > produc4953844613479565601on_nat ).

thf(func_def_838,type,
    produc8585076106096196333on_num: option_num > option_num > produc3447558737645232053on_num ).

thf(func_def_839,type,
    produc488173922507101015at_nat: option4927543243414619207at_nat > option4927543243414619207at_nat > produc6121120109295599847at_nat ).

thf(func_def_840,type,
    produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat ).

thf(func_def_841,type,
    produc2922128104949294807at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat ).

thf(func_def_842,type,
    produc9060074326276436823at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > produc1319942482725812455at_nat ).

thf(func_def_843,type,
    produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).

thf(func_def_844,type,
    produc581526299967858633d_enat: vEBT_VEBT > extended_enat > produc7272778201969148633d_enat ).

thf(func_def_845,type,
    produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).

thf(func_def_846,type,
    produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).

thf(func_def_847,type,
    produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).

thf(func_def_848,type,
    produc457027306803732586at_nat: set_nat > ( nat > set_nat ) > set_Pr1261947904930325089at_nat ).

thf(func_def_849,type,
    produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_850,type,
    produc8678311845419106900er_nat: ( code_integer > nat ) > ( code_integer > nat ) > produc8923325533196201883nteger > product_prod_nat_nat ).

thf(func_def_851,type,
    produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).

thf(func_def_852,type,
    produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).

thf(func_def_853,type,
    produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).

thf(func_def_854,type,
    produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).

thf(func_def_855,type,
    produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_856,type,
    produc6771430404735790350plex_o: ( complex > complex > $o ) > produc4411394909380815293omplex > $o ).

thf(func_def_857,type,
    produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).

thf(func_def_858,type,
    produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).

thf(func_def_859,type,
    produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).

thf(func_def_860,type,
    produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_861,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_862,type,
    produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).

thf(func_def_863,type,
    produc2761476792215241774st_nat: ( nat > nat > list_nat ) > product_prod_nat_nat > list_nat ).

thf(func_def_864,type,
    produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).

thf(func_def_865,type,
    produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_866,type,
    produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).

thf(func_def_867,type,
    produc5414030515140494994real_o: ( real > real > $o ) > produc2422161461964618553l_real > $o ).

thf(func_def_868,type,
    product_fst_int_int: product_prod_int_int > int ).

thf(func_def_869,type,
    product_fst_nat_nat: product_prod_nat_nat > nat ).

thf(func_def_870,type,
    product_snd_int_int: product_prod_int_int > int ).

thf(func_def_871,type,
    product_snd_nat_nat: product_prod_nat_nat > nat ).

thf(func_def_872,type,
    abs_Rat: product_prod_int_int > rat ).

thf(func_def_873,type,
    fract: int > int > rat ).

thf(func_def_874,type,
    frct: product_prod_int_int > rat ).

thf(func_def_875,type,
    rep_Rat: rat > product_prod_int_int ).

thf(func_def_876,type,
    field_5140801741446780682s_real: set_real ).

thf(func_def_877,type,
    field_7254667332652039916t_real: rat > real ).

thf(func_def_878,type,
    normalize: product_prod_int_int > product_prod_int_int ).

thf(func_def_879,type,
    pcr_rat: product_prod_int_int > rat > $o ).

thf(func_def_880,type,
    positive: rat > $o ).

thf(func_def_881,type,
    quotient_of: rat > product_prod_int_int ).

thf(func_def_882,type,
    ratrel: product_prod_int_int > product_prod_int_int > $o ).

thf(func_def_883,type,
    real2: ( nat > rat ) > real ).

thf(func_def_884,type,
    cauchy: ( nat > rat ) > $o ).

thf(func_def_885,type,
    cr_real: ( nat > rat ) > real > $o ).

thf(func_def_886,type,
    pcr_real: ( nat > rat ) > real > $o ).

thf(func_def_887,type,
    positive2: real > $o ).

thf(func_def_888,type,
    realrel: ( nat > rat ) > ( nat > rat ) > $o ).

thf(func_def_889,type,
    rep_real: real > nat > rat ).

thf(func_def_890,type,
    vanishes: ( nat > rat ) > $o ).

thf(func_def_891,type,
    real_V2521375963428798218omplex: set_complex ).

thf(func_def_892,type,
    real_V3694042436643373181omplex: complex > complex > real ).

thf(func_def_893,type,
    real_V975177566351809787t_real: real > real > real ).

thf(func_def_894,type,
    real_V1022390504157884413omplex: complex > real ).

thf(func_def_895,type,
    real_V7735802525324610683m_real: real > real ).

thf(func_def_896,type,
    real_V4546457046886955230omplex: real > complex ).

thf(func_def_897,type,
    real_V1803761363581548252l_real: real > real ).

thf(func_def_898,type,
    transp_nat_rat: ( ( nat > rat ) > ( nat > rat ) > $o ) > $o ).

thf(func_def_899,type,
    algebr932160517623751201me_int: int > int > $o ).

thf(func_def_900,type,
    algebr934650988132801477me_nat: nat > nat > $o ).

thf(func_def_901,type,
    divide6298287555418463151nteger: code_integer > code_integer > code_integer ).

thf(func_def_902,type,
    divide1717551699836669952omplex: complex > complex > complex ).

thf(func_def_903,type,
    divide_divide_int: int > int > int ).

thf(func_def_904,type,
    divide_divide_nat: nat > nat > nat ).

thf(func_def_905,type,
    divide_divide_rat: rat > rat > rat ).

thf(func_def_906,type,
    divide_divide_real: real > real > real ).

thf(func_def_907,type,
    dvd_dvd_Code_integer: code_integer > code_integer > $o ).

thf(func_def_908,type,
    dvd_dvd_complex: complex > complex > $o ).

thf(func_def_909,type,
    dvd_dvd_int: int > int > $o ).

thf(func_def_910,type,
    dvd_dvd_nat: nat > nat > $o ).

thf(func_def_911,type,
    dvd_dvd_rat: rat > rat > $o ).

thf(func_def_912,type,
    dvd_dvd_real: real > real > $o ).

thf(func_def_913,type,
    modulo364778990260209775nteger: code_integer > code_integer > code_integer ).

thf(func_def_914,type,
    modulo_modulo_int: int > int > int ).

thf(func_def_915,type,
    modulo_modulo_nat: nat > nat > nat ).

thf(func_def_916,type,
    unit_f2748546683901255202or_nat: nat > nat ).

thf(func_def_917,type,
    zero_n356916108424825756nteger: $o > code_integer ).

thf(func_def_918,type,
    zero_n2684676970156552555ol_int: $o > int ).

thf(func_def_919,type,
    zero_n2687167440665602831ol_nat: $o > nat ).

thf(func_def_920,type,
    suminf_complex: ( nat > complex ) > complex ).

thf(func_def_921,type,
    suminf_int: ( nat > int ) > int ).

thf(func_def_922,type,
    suminf_nat: ( nat > nat ) > nat ).

thf(func_def_923,type,
    suminf_real: ( nat > real ) > real ).

thf(func_def_924,type,
    summable_complex: ( nat > complex ) > $o ).

thf(func_def_925,type,
    summable_int: ( nat > int ) > $o ).

thf(func_def_926,type,
    summable_nat: ( nat > nat ) > $o ).

thf(func_def_927,type,
    summable_real: ( nat > real ) > $o ).

thf(func_def_928,type,
    sums_real: ( nat > real ) > real > $o ).

thf(func_def_929,type,
    collect_complex: ( complex > $o ) > set_complex ).

thf(func_def_930,type,
    collec4429806609662206161d_enat: ( extended_enat > $o ) > set_Extended_enat ).

thf(func_def_931,type,
    collect_int: ( int > $o ) > set_int ).

thf(func_def_932,type,
    collect_list_o: ( list_o > $o ) > set_list_o ).

thf(func_def_933,type,
    collect_list_complex: ( list_complex > $o ) > set_list_complex ).

thf(func_def_934,type,
    collec8433460942617342167d_enat: ( list_Extended_enat > $o ) > set_li5464603477888414924d_enat ).

thf(func_def_935,type,
    collect_list_int: ( list_int > $o ) > set_list_int ).

thf(func_def_936,type,
    collect_list_nat: ( list_nat > $o ) > set_list_nat ).

thf(func_def_937,type,
    collec3343600615725829874at_nat: ( list_P6011104703257516679at_nat > $o ) > set_li5450038453877631591at_nat ).

thf(func_def_938,type,
    collec5608196760682091941T_VEBT: ( list_VEBT_VEBT > $o ) > set_list_VEBT_VEBT ).

thf(func_def_939,type,
    collect_nat: ( nat > $o ) > set_nat ).

thf(func_def_940,type,
    collect_num: ( num > $o ) > set_num ).

thf(func_def_941,type,
    collect_option_nat: ( option_nat > $o ) > set_option_nat ).

thf(func_def_942,type,
    collec8663557070575231912omplex: ( produc4411394909380815293omplex > $o ) > set_Pr5085853215250843933omplex ).

thf(func_def_943,type,
    collec213857154873943460nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).

thf(func_def_944,type,
    collec3392354462482085612at_nat: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).

thf(func_def_945,type,
    collec3799799289383736868l_real: ( produc2422161461964618553l_real > $o ) > set_Pr6218003697084177305l_real ).

thf(func_def_946,type,
    collect_rat: ( rat > $o ) > set_rat ).

thf(func_def_947,type,
    collect_real: ( real > $o ) > set_real ).

thf(func_def_948,type,
    collect_set_nat: ( set_nat > $o ) > set_set_nat ).

thf(func_def_949,type,
    pow_nat: set_nat > set_set_nat ).

thf(func_def_950,type,
    image_80655429650038917d_enat: ( extended_enat > extended_enat ) > set_Extended_enat > set_Extended_enat ).

thf(func_def_951,type,
    image_int_int: ( int > int ) > set_int > set_int ).

thf(func_def_952,type,
    image_int_nat: ( int > nat ) > set_int > set_nat ).

thf(func_def_953,type,
    image_nat_int: ( nat > int ) > set_nat > set_int ).

thf(func_def_954,type,
    image_nat_nat: ( nat > nat ) > set_nat > set_nat ).

thf(func_def_955,type,
    image_nat_real: ( nat > real ) > set_nat > set_real ).

thf(func_def_956,type,
    image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).

thf(func_def_957,type,
    image_nat_char: ( nat > char ) > set_nat > set_char ).

thf(func_def_958,type,
    image_5971271580939081552omplex: ( real > filter6041513312241820739omplex ) > set_real > set_fi4554929511873752355omplex ).

thf(func_def_959,type,
    image_2178119161166701260l_real: ( real > filter2146258269922977983l_real ) > set_real > set_fi7789364187291644575l_real ).

thf(func_def_960,type,
    image_real_real: ( real > real ) > set_real > set_real ).

thf(func_def_961,type,
    image_char_nat: ( char > nat ) > set_char > set_nat ).

thf(func_def_962,type,
    image_VEBT_VEBT_nat: ( vEBT_VEBT > nat ) > set_VEBT_VEBT > set_nat ).

thf(func_def_963,type,
    insert_complex: complex > set_complex > set_complex ).

thf(func_def_964,type,
    insert_Extended_enat: extended_enat > set_Extended_enat > set_Extended_enat ).

thf(func_def_965,type,
    insert_int: int > set_int > set_int ).

thf(func_def_966,type,
    insert_nat: nat > set_nat > set_nat ).

thf(func_def_967,type,
    insert_num: num > set_num > set_num ).

thf(func_def_968,type,
    insert8211810215607154385at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_969,type,
    insert9069300056098147895at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).

thf(func_def_970,type,
    insert_rat: rat > set_rat > set_rat ).

thf(func_def_971,type,
    insert_real: real > set_real > set_real ).

thf(func_def_972,type,
    insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).

thf(func_def_973,type,
    vimage_nat_nat: ( nat > nat ) > set_nat > set_nat ).

thf(func_def_974,type,
    set_fo1517530859248394432omplex: ( nat > complex > complex ) > nat > nat > complex > complex ).

thf(func_def_975,type,
    set_fo2581907887559384638at_int: ( nat > int > int ) > nat > nat > int > int ).

thf(func_def_976,type,
    set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).

thf(func_def_977,type,
    set_fo1949268297981939178at_rat: ( nat > rat > rat ) > nat > nat > rat > rat ).

thf(func_def_978,type,
    set_fo3111899725591712190t_real: ( nat > real > real ) > nat > nat > real > real ).

thf(func_def_979,type,
    set_or5403411693681687835d_enat: extended_enat > extended_enat > set_Extended_enat ).

thf(func_def_980,type,
    set_or1266510415728281911st_int: int > int > set_int ).

thf(func_def_981,type,
    set_or1269000886237332187st_nat: nat > nat > set_nat ).

thf(func_def_982,type,
    set_or7049704709247886629st_num: num > num > set_num ).

thf(func_def_983,type,
    set_or633870826150836451st_rat: rat > rat > set_rat ).

thf(func_def_984,type,
    set_or1222579329274155063t_real: real > real > set_real ).

thf(func_def_985,type,
    set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat ).

thf(func_def_986,type,
    set_or4662586982721622107an_int: int > int > set_int ).

thf(func_def_987,type,
    set_or4665077453230672383an_nat: nat > nat > set_nat ).

thf(func_def_988,type,
    set_ord_atLeast_nat: nat > set_nat ).

thf(func_def_989,type,
    set_ord_atMost_int: int > set_int ).

thf(func_def_990,type,
    set_ord_atMost_nat: nat > set_nat ).

thf(func_def_991,type,
    set_ord_atMost_num: num > set_num ).

thf(func_def_992,type,
    set_ord_atMost_rat: rat > set_rat ).

thf(func_def_993,type,
    set_ord_atMost_real: real > set_real ).

thf(func_def_994,type,
    set_or4236626031148496127et_nat: set_nat > set_set_nat ).

thf(func_def_995,type,
    set_or6656581121297822940st_int: int > int > set_int ).

thf(func_def_996,type,
    set_or6659071591806873216st_nat: nat > nat > set_nat ).

thf(func_def_997,type,
    set_or5832277885323065728an_int: int > int > set_int ).

thf(func_def_998,type,
    set_or5834768355832116004an_nat: nat > nat > set_nat ).

thf(func_def_999,type,
    set_or1633881224788618240n_real: real > real > set_real ).

thf(func_def_1000,type,
    set_or1210151606488870762an_nat: nat > set_nat ).

thf(func_def_1001,type,
    set_or5849166863359141190n_real: real > set_real ).

thf(func_def_1002,type,
    set_ord_lessThan_int: int > set_int ).

thf(func_def_1003,type,
    set_ord_lessThan_nat: nat > set_nat ).

thf(func_def_1004,type,
    set_ord_lessThan_num: num > set_num ).

thf(func_def_1005,type,
    set_ord_lessThan_rat: rat > set_rat ).

thf(func_def_1006,type,
    set_or5984915006950818249n_real: real > set_real ).

thf(func_def_1007,type,
    set_or890127255671739683et_nat: set_nat > set_set_nat ).

thf(func_def_1008,type,
    abort_real: literal > ( product_unit > real ) > real ).

thf(func_def_1009,type,
    literal2: $o > $o > $o > $o > $o > $o > $o > literal > literal ).

thf(func_def_1010,type,
    ascii_of: char > char ).

thf(func_def_1011,type,
    char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).

thf(func_def_1012,type,
    size_char: char > nat ).

thf(func_def_1013,type,
    comm_s629917340098488124ar_nat: char > nat ).

thf(func_def_1014,type,
    integer_of_char: char > code_integer ).

thf(func_def_1015,type,
    unique3096191561947761185of_nat: nat > char ).

thf(func_def_1016,type,
    topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).

thf(func_def_1017,type,
    topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).

thf(func_def_1018,type,
    topolo6980174941875973593q_real: ( nat > real ) > $o ).

thf(func_def_1019,type,
    topolo2177554685111907308n_real: real > set_real > filter_real ).

thf(func_def_1020,type,
    topolo7531315842566124627t_real: ( nat > real ) > $o ).

thf(func_def_1021,type,
    topolo2815343760600316023s_real: real > filter_real ).

thf(func_def_1022,type,
    topolo4055970368930404560y_real: ( nat > real ) > $o ).

thf(func_def_1023,type,
    topolo896644834953643431omplex: filter6041513312241820739omplex ).

thf(func_def_1024,type,
    topolo1511823702728130853y_real: filter2146258269922977983l_real ).

thf(func_def_1025,type,
    arccos: real > real ).

thf(func_def_1026,type,
    arcosh_real: real > real ).

thf(func_def_1027,type,
    arcsin: real > real ).

thf(func_def_1028,type,
    arctan: real > real ).

thf(func_def_1029,type,
    arsinh_real: real > real ).

thf(func_def_1030,type,
    artanh_real: real > real ).

thf(func_def_1031,type,
    cos_complex: complex > complex ).

thf(func_def_1032,type,
    cos_real: real > real ).

thf(func_def_1033,type,
    cos_coeff: nat > real ).

thf(func_def_1034,type,
    cosh_real: real > real ).

thf(func_def_1035,type,
    cot_real: real > real ).

thf(func_def_1036,type,
    exp_complex: complex > complex ).

thf(func_def_1037,type,
    exp_real: real > real ).

thf(func_def_1038,type,
    ln_ln_real: real > real ).

thf(func_def_1039,type,
    log: real > real > real ).

thf(func_def_1040,type,
    pi: real ).

thf(func_def_1041,type,
    powr_real: real > real > real ).

thf(func_def_1042,type,
    powr_real2: real > real > real ).

thf(func_def_1043,type,
    sin_complex: complex > complex ).

thf(func_def_1044,type,
    sin_real: real > real ).

thf(func_def_1045,type,
    sin_coeff: nat > real ).

thf(func_def_1046,type,
    sinh_real: real > real ).

thf(func_def_1047,type,
    tan_complex: complex > complex ).

thf(func_def_1048,type,
    tan_real: real > real ).

thf(func_def_1049,type,
    tanh_real: real > real ).

thf(func_def_1050,type,
    bi_tot896582865486249351at_int: ( product_prod_nat_nat > int > $o ) > $o ).

thf(func_def_1051,type,
    transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_1052,type,
    transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_1053,type,
    type_d7649664348572268762on_nat: ( extended_enat > option_nat ) > ( option_nat > extended_enat ) > set_option_nat > $o ).

thf(func_def_1054,type,
    vEBT_T_i_n_s_e_r_t: vEBT_VEBT > nat > nat ).

thf(func_def_1055,type,
    vEBT_T_i_n_s_e_r_t2: vEBT_VEBT > nat > nat ).

thf(func_def_1056,type,
    vEBT_T5076183648494686801_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_1057,type,
    vEBT_T9217963907923527482_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_1058,type,
    vEBT_T_m_a_x_t: vEBT_VEBT > nat ).

thf(func_def_1059,type,
    vEBT_T_m_e_m_b_e_r: vEBT_VEBT > nat > nat ).

thf(func_def_1060,type,
    vEBT_T_m_e_m_b_e_r2: vEBT_VEBT > nat > nat ).

thf(func_def_1061,type,
    vEBT_T8099345112685741742_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_1062,type,
    vEBT_T5837161174952499735_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_1063,type,
    vEBT_T_m_i_n_N_u_l_l: vEBT_VEBT > nat ).

thf(func_def_1064,type,
    vEBT_T_m_i_n_t: vEBT_VEBT > nat ).

thf(func_def_1065,type,
    vEBT_T_m_i_n_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).

thf(func_def_1066,type,
    vEBT_T_p_r_e_d: vEBT_VEBT > nat > nat ).

thf(func_def_1067,type,
    vEBT_T_p_r_e_d2: vEBT_VEBT > nat > nat ).

thf(func_def_1068,type,
    vEBT_T_p_r_e_d_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_1069,type,
    vEBT_T_p_r_e_d_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_1070,type,
    vEBT_T_s_u_c_c: vEBT_VEBT > nat > nat ).

thf(func_def_1071,type,
    vEBT_T_s_u_c_c2: vEBT_VEBT > nat > nat ).

thf(func_def_1072,type,
    vEBT_T_s_u_c_c_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_1073,type,
    vEBT_T_s_u_c_c_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_1074,type,
    vEBT_Leaf: $o > $o > vEBT_VEBT ).

thf(func_def_1075,type,
    vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1076,type,
    vEBT_size_VEBT: vEBT_VEBT > nat ).

thf(func_def_1077,type,
    vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).

thf(func_def_1078,type,
    vEBT_VEBT_elim_dead: vEBT_VEBT > extended_enat > vEBT_VEBT ).

thf(func_def_1079,type,
    vEBT_V312737461966249ad_rel: produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o ).

thf(func_def_1080,type,
    vEBT_VEBT_high: nat > nat > nat ).

thf(func_def_1081,type,
    vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).

thf(func_def_1082,type,
    vEBT_VEBT_low: nat > nat > nat ).

thf(func_def_1083,type,
    vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).

thf(func_def_1084,type,
    vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_1085,type,
    vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).

thf(func_def_1086,type,
    vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_1087,type,
    vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).

thf(func_def_1088,type,
    vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_1089,type,
    vEBT_invar_vebt: vEBT_VEBT > nat > $o ).

thf(func_def_1090,type,
    vEBT_set_vebt: vEBT_VEBT > set_nat ).

thf(func_def_1091,type,
    vEBT_vebt_buildup: nat > vEBT_VEBT ).

thf(func_def_1092,type,
    vEBT_v4011308405150292612up_rel: nat > nat > $o ).

thf(func_def_1093,type,
    vEBT_T_d_e_l_e_t_e: vEBT_VEBT > nat > nat ).

thf(func_def_1094,type,
    vEBT_T8441311223069195367_e_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_1095,type,
    vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1096,type,
    vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_1097,type,
    vEBT_VEBT_height: vEBT_VEBT > nat ).

thf(func_def_1098,type,
    vEBT_VEBT_height_rel: vEBT_VEBT > vEBT_VEBT > $o ).

thf(func_def_1099,type,
    vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1100,type,
    vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_1101,type,
    vEBT_VEBT_bit_concat: nat > nat > nat > nat ).

thf(func_def_1102,type,
    vEBT_VEBT_minNull: vEBT_VEBT > $o ).

thf(func_def_1103,type,
    vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).

thf(func_def_1104,type,
    vEBT_vebt_member: vEBT_VEBT > nat > $o ).

thf(func_def_1105,type,
    vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_1106,type,
    vEBT_VEBT_add: option_nat > option_nat > option_nat ).

thf(func_def_1107,type,
    vEBT_VEBT_greater: option_nat > option_nat > $o ).

thf(func_def_1108,type,
    vEBT_VEBT_less: option_nat > option_nat > $o ).

thf(func_def_1109,type,
    vEBT_VEBT_lesseq: option_nat > option_nat > $o ).

thf(func_def_1110,type,
    vEBT_VEBT_max_in_set: set_nat > nat > $o ).

thf(func_def_1111,type,
    vEBT_VEBT_min_in_set: set_nat > nat > $o ).

thf(func_def_1112,type,
    vEBT_VEBT_mul: option_nat > option_nat > option_nat ).

thf(func_def_1113,type,
    vEBT_V2881884560877996034ft_nat: ( nat > nat > $o ) > option_nat > option_nat > $o ).

thf(func_def_1114,type,
    vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).

thf(func_def_1115,type,
    vEBT_V819420779217536731ft_num: ( num > num > num ) > option_num > option_num > option_num ).

thf(func_def_1116,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_1117,type,
    vEBT_VEBT_power: option_nat > option_nat > option_nat ).

thf(func_def_1118,type,
    vEBT_vebt_maxt: vEBT_VEBT > option_nat ).

thf(func_def_1119,type,
    vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).

thf(func_def_1120,type,
    vEBT_vebt_mint: vEBT_VEBT > option_nat ).

thf(func_def_1121,type,
    vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).

thf(func_def_1122,type,
    vEBT_is_pred_in_set: set_nat > nat > nat > $o ).

thf(func_def_1123,type,
    vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).

thf(func_def_1124,type,
    vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_1125,type,
    vEBT_is_succ_in_set: set_nat > nat > nat > $o ).

thf(func_def_1126,type,
    vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).

thf(func_def_1127,type,
    vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_1128,type,
    accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).

thf(func_def_1129,type,
    accp_nat: ( nat > nat > $o ) > nat > $o ).

thf(func_def_1130,type,
    accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).

thf(func_def_1131,type,
    accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).

thf(func_def_1132,type,
    accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).

thf(func_def_1133,type,
    accp_P6183159247885693666d_enat: ( produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o ) > produc7272778201969148633d_enat > $o ).

thf(func_def_1134,type,
    accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).

thf(func_def_1135,type,
    accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).

thf(func_def_1136,type,
    less_than: set_Pr1261947904930325089at_nat ).

thf(func_def_1137,type,
    lex_prod_nat_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat ).

thf(func_def_1138,type,
    max_ex8135407076693332796at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat ).

thf(func_def_1139,type,
    min_ex6901939911449802026at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat ).

thf(func_def_1140,type,
    pred_nat: set_Pr1261947904930325089at_nat ).

thf(func_def_1141,type,
    wf_int: set_Pr958786334691620121nt_int > $o ).

thf(func_def_1142,type,
    wf_nat: set_Pr1261947904930325089at_nat > $o ).

thf(func_def_1143,type,
    wf_Pro7803398752247294826at_nat: set_Pr8693737435421807431at_nat > $o ).

thf(func_def_1144,type,
    fChoice_real: ( real > $o ) > real ).

thf(func_def_1145,type,
    member_o: $o > set_o > $o ).

thf(func_def_1146,type,
    member_complex: complex > set_complex > $o ).

thf(func_def_1147,type,
    member_Extended_enat: extended_enat > set_Extended_enat > $o ).

thf(func_def_1148,type,
    member_int: int > set_int > $o ).

thf(func_def_1149,type,
    member_list_o: list_o > set_list_o > $o ).

thf(func_def_1150,type,
    member_list_int: list_int > set_list_int > $o ).

thf(func_def_1151,type,
    member_list_nat: list_nat > set_list_nat > $o ).

thf(func_def_1152,type,
    member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).

thf(func_def_1153,type,
    member_nat: nat > set_nat > $o ).

thf(func_def_1154,type,
    member_num: num > set_num > $o ).

thf(func_def_1155,type,
    member_option_nat: option_nat > set_option_nat > $o ).

thf(func_def_1156,type,
    member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_1157,type,
    member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).

thf(func_def_1158,type,
    member8757157785044589968at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > $o ).

thf(func_def_1159,type,
    member_rat: rat > set_rat > $o ).

thf(func_def_1160,type,
    member_real: real > set_real > $o ).

thf(func_def_1161,type,
    member_set_nat: set_nat > set_set_nat > $o ).

thf(func_def_1162,type,
    member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).

thf(func_def_1163,type,
    deg: nat ).

thf(func_def_1164,type,
    m: nat ).

thf(func_def_1165,type,
    ma: nat ).

thf(func_def_1166,type,
    mi: nat ).

thf(func_def_1167,type,
    na: nat ).

thf(func_def_1168,type,
    summary: vEBT_VEBT ).

thf(func_def_1169,type,
    treeList: list_VEBT_VEBT ).

thf(func_def_1170,type,
    x: nat ).

thf(func_def_1189,type,
    sP0: rat > rat > rat > $o ).

thf(func_def_1190,type,
    sP1: rat > rat > rat > $o ).

thf(func_def_1191,type,
    sP2: rat > rat > rat > $o ).

thf(func_def_1192,type,
    sP3: int > int > int > $o ).

thf(func_def_1193,type,
    sP4: int > int > int > $o ).

thf(func_def_1194,type,
    sP5: int > int > int > $o ).

thf(func_def_1195,type,
    sP6: nat > nat > nat > $o ).

thf(func_def_1196,type,
    sP7: nat > nat > nat > $o ).

thf(func_def_1197,type,
    sP8: nat > nat > nat > $o ).

thf(func_def_1198,type,
    sP9: ( int > $o ) > $o ).

thf(func_def_1199,type,
    sK10: ( nat > int ) > nat ).

thf(func_def_1200,type,
    sK11: ( nat > nat > $o ) > nat ).

thf(func_def_1201,type,
    sK12: ( nat > nat > $o ) > nat ).

thf(func_def_1202,type,
    sK13: ( nat > nat > $o ) > nat ).

thf(func_def_1203,type,
    sK14: ( nat > nat > $o ) > nat ).

thf(func_def_1204,type,
    sK15: nat > nat > nat ).

thf(func_def_1205,type,
    sK16: real > real ).

thf(func_def_1206,type,
    sK17: int > int ).

thf(func_def_1207,type,
    sK18: ( rat > nat ) > rat ).

thf(func_def_1208,type,
    sK19: ( rat > nat ) > rat ).

thf(func_def_1209,type,
    sK20: int > int ).

thf(func_def_1210,type,
    sK21: ( rat > real ) > rat ).

thf(func_def_1211,type,
    sK22: ( rat > real ) > rat ).

thf(func_def_1212,type,
    sK23: ( nat > rat ) > nat ).

thf(func_def_1213,type,
    sK24: real > real > real ).

thf(func_def_1214,type,
    sK25: ( nat > $o ) > nat ).

thf(func_def_1215,type,
    sK26: ( nat > $o ) > nat > nat ).

thf(func_def_1216,type,
    sK27: ( nat > nat > $o ) > nat ).

thf(func_def_1217,type,
    sK28: ( nat > nat > $o ) > nat ).

thf(func_def_1218,type,
    sK29: ( nat > nat > $o ) > nat ).

thf(func_def_1219,type,
    sK30: ( nat > nat > $o ) > nat ).

thf(func_def_1220,type,
    sK31: ( nat > nat > $o ) > nat ).

thf(func_def_1221,type,
    sK32: real > real ).

thf(func_def_1222,type,
    sK33: nat > nat ).

thf(func_def_1223,type,
    sK34: ( nat > rat ) > nat ).

thf(func_def_1224,type,
    sK35: ( nat > rat ) > nat ).

thf(func_def_1225,type,
    sK36: real > nat > real ).

thf(func_def_1226,type,
    sK37: ( nat > nat ) > nat ).

thf(func_def_1227,type,
    sK38: ( nat > $o ) > nat ).

thf(func_def_1228,type,
    sK39: nat > ( nat > $o ) > nat ).

thf(func_def_1229,type,
    sK40: real > real ).

thf(func_def_1230,type,
    sK41: ( int > real ) > int ).

thf(func_def_1231,type,
    sK42: ( int > real ) > int ).

thf(func_def_1232,type,
    sK43: real > real ).

thf(func_def_1233,type,
    sK44: ( real > real ) > real ).

thf(func_def_1234,type,
    sK45: ( real > real ) > real ).

thf(func_def_1235,type,
    sK46: nat > nat ).

thf(func_def_1236,type,
    sK47: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_1237,type,
    sK48: int > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_1238,type,
    sK49: int > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_1239,type,
    sK50: ( real > int ) > real ).

thf(func_def_1240,type,
    sK51: ( real > int ) > real ).

thf(func_def_1241,type,
    sK52: ( nat > $o ) > nat ).

thf(func_def_1242,type,
    sK53: ( nat > $o ) > nat > nat ).

thf(func_def_1243,type,
    sK54: ( real > $o ) > ( real > $o ) > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_1244,type,
    sK55: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_1245,type,
    sK56: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_1246,type,
    sK57: real > real > real ).

thf(func_def_1247,type,
    sK58: ( nat > $o ) > nat > nat ).

thf(func_def_1248,type,
    sK59: int > int ).

thf(func_def_1249,type,
    sK60: ( nat > $o ) > nat ).

thf(func_def_1250,type,
    sK61: nat > ( nat > $o ) > nat ).

thf(func_def_1251,type,
    sK62: nat > ( nat > $o ) > nat ).

thf(func_def_1252,type,
    sK63: real > real ).

thf(func_def_1253,type,
    sK64: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_1254,type,
    sK65: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_1255,type,
    sK66: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_1256,type,
    sK67: ( real > nat ) > real ).

thf(func_def_1257,type,
    sK68: ( real > nat ) > real ).

thf(func_def_1258,type,
    sK69: nat > nat > nat ).

thf(func_def_1259,type,
    sK70: ( rat > int ) > rat ).

thf(func_def_1260,type,
    sK71: ( rat > int ) > rat ).

thf(func_def_1261,type,
    sK72: nat > nat ).

thf(func_def_1262,type,
    sK73: real > real ).

thf(func_def_1263,type,
    sK74: int > int ).

thf(func_def_1264,type,
    sK75: int > ( int > $o ) > int ).

thf(func_def_1265,type,
    sK76: ( nat > nat > $o ) > nat ).

thf(func_def_1266,type,
    sK77: ( nat > nat > $o ) > nat ).

thf(func_def_1267,type,
    sK78: ( nat > nat > $o ) > nat ).

thf(func_def_1268,type,
    sK79: ( nat > nat > $o ) > nat ).

thf(func_def_1269,type,
    sK80: ( nat > $o ) > nat ).

thf(func_def_1270,type,
    sK81: nat > nat ).

thf(func_def_1271,type,
    sK82: nat > nat > nat ).

thf(func_def_1272,type,
    sK83: rat > rat ).

thf(func_def_1273,type,
    sK84: real > real ).

thf(func_def_1274,type,
    sK85: ( nat > nat ) > nat ).

thf(func_def_1275,type,
    sK86: rat > rat ).

thf(func_def_1276,type,
    sK87: ( rat > rat ) > rat ).

thf(func_def_1277,type,
    sK88: ( rat > rat ) > rat ).

thf(func_def_1278,type,
    sK89: ( nat > $o ) > nat ).

thf(func_def_1279,type,
    sK90: ( rat > int ) > rat ).

thf(func_def_1280,type,
    sK91: ( rat > int ) > rat ).

thf(func_def_1281,type,
    sK92: ( nat > nat ) > nat ).

thf(func_def_1282,type,
    sK93: ( nat > nat > $o ) > nat ).

thf(func_def_1283,type,
    sK94: ( nat > nat > $o ) > nat ).

thf(func_def_1284,type,
    sK95: ( nat > nat > $o ) > nat ).

thf(func_def_1285,type,
    sK96: ( nat > nat > $o ) > nat ).

thf(func_def_1286,type,
    sK97: ( nat > nat > $o ) > nat ).

thf(func_def_1287,type,
    sK98: real > real > real ).

thf(func_def_1288,type,
    sK99: ( rat > rat ) > rat ).

thf(func_def_1289,type,
    sK100: ( rat > rat ) > rat ).

thf(func_def_1290,type,
    sK101: ( int > rat ) > int ).

thf(func_def_1291,type,
    sK102: ( int > rat ) > int ).

thf(func_def_1292,type,
    sK103: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_1293,type,
    sK104: int > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_1294,type,
    sK105: int > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_1295,type,
    sK106: ( rat > int ) > rat ).

thf(func_def_1296,type,
    sK107: ( rat > int ) > rat ).

thf(func_def_1297,type,
    sK108: ( rat > rat ) > rat ).

thf(func_def_1298,type,
    sK109: ( rat > rat ) > rat ).

thf(func_def_1299,type,
    sK110: ( nat > rat ) > nat ).

thf(func_def_1300,type,
    sK111: ( nat > rat ) > nat ).

thf(func_def_1301,type,
    sK112: real > real ).

thf(func_def_1302,type,
    sK113: real > real ).

thf(func_def_1303,type,
    sK114: int > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_1304,type,
    sK115: int > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_1305,type,
    sK116: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_1306,type,
    sK117: nat > nat ).

thf(func_def_1307,type,
    sK118: ( rat > rat ) > rat ).

thf(func_def_1308,type,
    sK119: ( rat > rat ) > rat ).

thf(func_def_1309,type,
    sK120: ( nat > $o ) > nat ).

thf(func_def_1310,type,
    sK121: ( nat > rat ) > nat ).

thf(func_def_1311,type,
    sK122: ( nat > rat ) > nat ).

thf(func_def_1312,type,
    sK123: ( nat > $o ) > nat ).

thf(func_def_1313,type,
    sK124: ( nat > real ) > nat ).

thf(func_def_1314,type,
    sK125: ( nat > real ) > nat ).

thf(func_def_1315,type,
    sK126: ( nat > real ) > nat ).

thf(func_def_1316,type,
    sK127: ( nat > real ) > nat ).

thf(func_def_1317,type,
    sK128: nat > nat > nat ).

thf(func_def_1318,type,
    sK129: nat > nat > nat ).

thf(func_def_1319,type,
    sK130: ( nat > int ) > nat ).

thf(func_def_1320,type,
    sK131: ( int > real ) > int ).

thf(func_def_1321,type,
    sK132: ( int > real ) > int ).

thf(func_def_1322,type,
    sK133: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_1323,type,
    sK134: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_1324,type,
    sK135: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_1325,type,
    sK136: ( nat > $o ) > nat ).

thf(func_def_1326,type,
    sK137: real > real > real ).

thf(func_def_1327,type,
    sK138: rat > rat > rat ).

thf(func_def_1328,type,
    sK139: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_1329,type,
    sK140: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_1330,type,
    sK141: ( real > $o ) > ( real > $o ) > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_1331,type,
    sK142: real > real > real > real ).

thf(func_def_1332,type,
    sK143: rat > rat ).

thf(func_def_1333,type,
    sK144: nat > nat ).

thf(func_def_1334,type,
    sK145: ( rat > nat ) > rat ).

thf(func_def_1335,type,
    sK146: ( rat > nat ) > rat ).

thf(func_def_1336,type,
    sK147: ( real > real ) > real ).

thf(func_def_1337,type,
    sK148: ( real > real ) > real ).

thf(func_def_1338,type,
    sK149: ( nat > int ) > nat ).

thf(func_def_1339,type,
    sK150: ( real > real > $o ) > real ).

thf(func_def_1340,type,
    sK151: ( real > real > $o ) > real ).

thf(func_def_1341,type,
    sK152: ( real > real > $o ) > real ).

thf(func_def_1342,type,
    sK153: ( real > real > $o ) > real ).

thf(func_def_1343,type,
    sK154: ( real > real > $o ) > real ).

thf(func_def_1344,type,
    sK155: real > ( real > $o ) > real > real ).

thf(func_def_1345,type,
    sK156: real > real > ( real > $o ) > real ).

thf(func_def_1346,type,
    sK157: real > real > nat ).

thf(func_def_1347,type,
    sK158: ( int > int > $o ) > int ).

thf(func_def_1348,type,
    sK159: ( int > int > $o ) > int ).

thf(func_def_1349,type,
    sK160: ( int > int > $o ) > int ).

thf(func_def_1350,type,
    sK161: ( int > int > $o ) > int ).

thf(func_def_1351,type,
    sK162: ( int > int > $o ) > int ).

thf(func_def_1352,type,
    sK163: nat > nat > nat ).

thf(func_def_1353,type,
    sK164: nat > nat > ( nat > $o ) > nat ).

thf(func_def_1354,type,
    sK165: rat > rat ).

thf(func_def_1355,type,
    sK166: ( rat > rat ) > rat ).

thf(func_def_1356,type,
    sK167: ( rat > rat ) > rat ).

thf(func_def_1357,type,
    sK168: ( nat > real ) > nat ).

thf(func_def_1358,type,
    sK169: ( rat > int ) > rat ).

thf(func_def_1359,type,
    sK170: ( rat > int ) > rat ).

thf(func_def_1360,type,
    sK171: ( real > rat ) > real ).

thf(func_def_1361,type,
    sK172: ( real > rat ) > real ).

thf(func_def_1362,type,
    sK173: real > real > nat ).

thf(func_def_1363,type,
    sK174: ( rat > nat ) > rat ).

thf(func_def_1364,type,
    sK175: ( rat > nat ) > rat ).

thf(func_def_1365,type,
    sK176: ( rat > rat ) > rat ).

thf(func_def_1366,type,
    sK177: ( rat > rat ) > rat ).

thf(func_def_1367,type,
    sK178: rat > rat ).

thf(func_def_1368,type,
    sK179: int > int ).

thf(func_def_1369,type,
    sK180: ( rat > nat ) > rat ).

thf(func_def_1370,type,
    sK181: ( rat > nat ) > rat ).

thf(func_def_1371,type,
    sK182: ( rat > rat > $o ) > rat ).

thf(func_def_1372,type,
    sK183: ( rat > rat > $o ) > rat ).

thf(func_def_1373,type,
    sK184: ( rat > rat > $o ) > rat ).

thf(func_def_1374,type,
    sK185: ( rat > rat > $o ) > rat ).

thf(func_def_1375,type,
    sK186: ( rat > rat > $o ) > rat ).

thf(func_def_1376,type,
    sK187: ( int > rat ) > int ).

thf(func_def_1377,type,
    sK188: ( int > rat ) > int ).

thf(func_def_1378,type,
    sK189: ( rat > nat ) > rat ).

thf(func_def_1379,type,
    sK190: ( rat > nat ) > rat ).

thf(func_def_1380,type,
    sK191: ( nat > rat ) > nat ).

thf(func_def_1381,type,
    sK192: ( nat > rat ) > nat ).

thf(func_def_1382,type,
    sK193: rat > rat ).

thf(func_def_1383,type,
    sK194: nat > nat > nat ).

thf(func_def_1384,type,
    sK195: ( rat > rat ) > rat ).

thf(func_def_1385,type,
    sK196: ( rat > rat ) > rat ).

thf(func_def_1386,type,
    sK197: ( nat > real ) > nat ).

thf(func_def_1387,type,
    sK198: int > int ).

thf(func_def_1388,type,
    sK199: int > int ).

thf(func_def_1389,type,
    sK200: ( nat > nat ) > nat ).

thf(func_def_1390,type,
    sK201: ( nat > nat ) > nat ).

thf(func_def_1391,type,
    sK202: real > real > real > real ).

thf(func_def_1392,type,
    sK203: ( int > rat ) > int ).

thf(func_def_1393,type,
    sK204: ( int > rat ) > int ).

thf(func_def_1394,type,
    sK205: rat > rat > rat ).

thf(func_def_1395,type,
    sK206: ( nat > rat ) > nat ).

thf(func_def_1396,type,
    sK207: nat > nat ).

thf(func_def_1397,type,
    sK208: ( rat > nat ) > rat ).

thf(func_def_1398,type,
    sK209: ( rat > nat ) > rat ).

thf(func_def_1399,type,
    sK210: rat > rat ).

thf(func_def_1400,type,
    sK211: rat > rat > rat ).

thf(func_def_1401,type,
    sK212: real > real ).

thf(func_def_1402,type,
    sK213: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_1403,type,
    sK214: ( real > $o ) > ( real > $o ) > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_1404,type,
    sK215: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_1405,type,
    sK216: ( real > real ) > real ).

thf(func_def_1406,type,
    sK217: ( real > real ) > real ).

thf(func_def_1407,type,
    sK218: int > int ).

thf(func_def_1408,type,
    sK219: ( nat > $o ) > nat ).

thf(func_def_1409,type,
    sK220: ( real > rat ) > real ).

thf(func_def_1410,type,
    sK221: ( real > rat ) > real ).

thf(func_def_1411,type,
    sK222: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_1412,type,
    sK223: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_1413,type,
    sK224: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_1414,type,
    sK225: ( rat > real ) > rat ).

thf(func_def_1415,type,
    sK226: ( rat > real ) > rat ).

thf(func_def_1416,type,
    sK227: nat > nat > nat ).

thf(func_def_1417,type,
    sK228: real > real ).

thf(func_def_1418,type,
    sK229: real > real ).

thf(func_def_1419,type,
    sK230: ( rat > rat ) > rat ).

thf(func_def_1420,type,
    sK231: ( rat > rat ) > rat ).

thf(func_def_1421,type,
    sK232: ( nat > $o ) > nat ).

thf(func_def_1422,type,
    sK233: real > real ).

thf(func_def_1423,type,
    sK234: ( real > int ) > real ).

thf(func_def_1424,type,
    sK235: ( real > int ) > real ).

thf(func_def_1425,type,
    sK236: real > real ).

thf(func_def_1426,type,
    sK237: int > ( int > $o ) > int > int ).

thf(func_def_1427,type,
    sK238: int > ( int > $o ) > int > int ).

thf(func_def_1428,type,
    sK239: nat > nat ).

thf(func_def_1429,type,
    sK240: real > nat > real ).

thf(func_def_1430,type,
    sK241: nat > nat > ( nat > $o ) > nat ).

thf(func_def_1431,type,
    sK242: nat > nat > ( nat > $o ) > nat ).

thf(func_def_1432,type,
    sK243: rat > rat > rat > rat ).

thf(func_def_1433,type,
    sK244: ( rat > int ) > rat ).

thf(func_def_1434,type,
    sK245: ( rat > int ) > rat ).

thf(func_def_1435,type,
    sK246: int > int ).

thf(func_def_1436,type,
    sK247: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_1437,type,
    sK248: ( real > $o ) > ( real > $o ) > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_1438,type,
    sK249: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_1439,type,
    sK250: nat > nat ).

thf(func_def_1440,type,
    sK251: rat > rat ).

thf(func_def_1441,type,
    sK252: real > real ).

thf(func_def_1442,type,
    sK253: int > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_1443,type,
    sK254: int > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_1444,type,
    sK255: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_1445,type,
    sK256: nat > nat ).

thf(func_def_1446,type,
    sK257: real > real ).

thf(func_def_1447,type,
    sK258: ( rat > nat ) > rat ).

thf(func_def_1448,type,
    sK259: ( rat > nat ) > rat ).

thf(func_def_1449,type,
    sK260: ( real > real ) > real ).

thf(func_def_1450,type,
    sK261: ( real > real ) > real ).

thf(func_def_1451,type,
    sK262: ( real > real ) > real ).

thf(func_def_1452,type,
    sK263: ( real > real ) > real ).

thf(func_def_1453,type,
    sK264: nat > ( nat > $o ) > nat ).

thf(func_def_1454,type,
    sK265: nat > ( nat > $o ) > nat ).

thf(func_def_1455,type,
    sK266: ( rat > rat ) > rat ).

thf(func_def_1456,type,
    sK267: ( rat > rat ) > rat ).

thf(func_def_1457,type,
    sK268: nat > nat ).

thf(func_def_1458,type,
    sK269: ( rat > rat > $o ) > rat ).

thf(func_def_1459,type,
    sK270: ( rat > rat > $o ) > rat ).

thf(func_def_1460,type,
    sK271: ( rat > rat > $o ) > rat ).

thf(func_def_1461,type,
    sK272: ( rat > rat > $o ) > rat ).

thf(func_def_1462,type,
    sK273: ( rat > int ) > rat ).

thf(func_def_1463,type,
    sK274: ( rat > int ) > rat ).

thf(func_def_1464,type,
    sK275: ( rat > real ) > rat ).

thf(func_def_1465,type,
    sK276: ( rat > real ) > rat ).

thf(func_def_1466,type,
    sK277: nat > nat ).

thf(func_def_1467,type,
    sK278: nat > nat > nat ).

thf(func_def_1468,type,
    sK279: ( rat > int ) > rat ).

thf(func_def_1469,type,
    sK280: ( rat > int ) > rat ).

thf(func_def_1470,type,
    sK281: ( rat > real ) > rat ).

thf(func_def_1471,type,
    sK282: ( rat > real ) > rat ).

thf(func_def_1472,type,
    sK283: ( rat > int ) > rat ).

thf(func_def_1473,type,
    sK284: ( rat > int ) > rat ).

thf(func_def_1474,type,
    sK285: nat > nat ).

thf(func_def_1475,type,
    sK286: ( rat > real ) > rat ).

thf(func_def_1476,type,
    sK287: ( rat > real ) > rat ).

thf(func_def_1477,type,
    sK288: real > real > real ).

thf(func_def_1478,type,
    sK289: ( nat > $o ) > nat ).

thf(func_def_1479,type,
    sK290: ( rat > rat ) > rat ).

thf(func_def_1480,type,
    sK291: ( rat > rat ) > rat ).

thf(func_def_1481,type,
    sK292: int > ( int > $o ) > int ).

thf(func_def_1482,type,
    sK293: nat > nat ).

thf(func_def_1483,type,
    sK294: ( nat > nat ) > nat ).

thf(func_def_1484,type,
    sK295: ( nat > nat ) > nat ).

thf(func_def_1485,type,
    sK296: ( nat > $o ) > nat ).

thf(func_def_1486,type,
    sK297: ( nat > nat ) > nat ).

thf(func_def_1487,type,
    sK298: ( rat > real ) > rat ).

thf(func_def_1488,type,
    sK299: ( rat > real ) > rat ).

thf(func_def_1489,type,
    sK300: ( real > rat ) > real ).

thf(func_def_1490,type,
    sK301: ( real > rat ) > real ).

thf(func_def_1491,type,
    sK302: ( nat > rat ) > nat ).

thf(func_def_1492,type,
    sK303: ( nat > rat ) > nat ).

thf(func_def_1493,type,
    sK304: rat > rat > rat ).

thf(func_def_1494,type,
    sK305: ( nat > $o ) > nat ).

thf(func_def_1495,type,
    sK306: ( nat > $o ) > nat ).

thf(func_def_1496,type,
    sK307: ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_1497,type,
    sK308: rat > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_1498,type,
    sK309: rat > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_1499,type,
    sK310: ( int > real ) > int ).

thf(func_def_1500,type,
    sK311: ( int > real ) > int ).

thf(func_def_1501,type,
    sK312: ( real > rat ) > real ).

thf(func_def_1502,type,
    sK313: ( real > rat ) > real ).

thf(func_def_1503,type,
    sK314: nat > nat ).

thf(func_def_1504,type,
    sK315: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_1505,type,
    sK316: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_1506,type,
    sK317: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_1507,type,
    sK318: ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_1508,type,
    sK319: rat > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_1509,type,
    sK320: rat > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_1510,type,
    sK321: int > int ).

thf(func_def_1511,type,
    sK322: nat > nat ).

thf(func_def_1512,type,
    sK323: ( nat > rat ) > nat ).

thf(func_def_1513,type,
    sK324: rat > rat > rat > rat ).

thf(func_def_1514,type,
    sK325: ( int > rat ) > int ).

thf(func_def_1515,type,
    sK326: ( int > rat ) > int ).

thf(func_def_1516,type,
    sK327: ( rat > real ) > rat ).

thf(func_def_1517,type,
    sK328: ( rat > real ) > rat ).

thf(func_def_1518,type,
    sK329: ( int > int > $o ) > int ).

thf(func_def_1519,type,
    sK330: ( int > int > $o ) > int ).

thf(func_def_1520,type,
    sK331: ( int > int > $o ) > int ).

thf(func_def_1521,type,
    sK332: ( int > int > $o ) > int ).

thf(func_def_1522,type,
    sK333: rat > rat ).

thf(func_def_1523,type,
    sK334: ( int > $o ) > int > int ).

thf(func_def_1524,type,
    sK335: rat > rat ).

thf(func_def_1525,type,
    sK336: ( real > nat ) > real ).

thf(func_def_1526,type,
    sK337: ( real > nat ) > real ).

thf(func_def_1527,type,
    sK338: ( real > real ) > real ).

thf(func_def_1528,type,
    sK339: ( real > real ) > real ).

thf(func_def_1529,type,
    sK340: rat > rat ).

thf(func_def_1530,type,
    sK341: int > int ).

thf(func_def_1531,type,
    sK342: nat > nat > nat ).

thf(func_def_1532,type,
    sK343: ( nat > int ) > nat ).

thf(func_def_1533,type,
    sK344: nat > ( nat > $o ) > nat ).

thf(func_def_1534,type,
    sK345: nat > nat ).

thf(func_def_1535,type,
    sK346: int > int ).

thf(func_def_1536,type,
    sK347: ( rat > rat ) > rat ).

thf(func_def_1537,type,
    sK348: ( rat > rat ) > rat ).

thf(func_def_1538,type,
    sK349: rat > rat ).

thf(func_def_1539,type,
    sK350: rat > rat ).

thf(func_def_1540,type,
    sK351: ( nat > real ) > nat ).

thf(func_def_1541,type,
    sK352: ( nat > real ) > nat ).

thf(func_def_1542,type,
    sK353: ( real > int ) > real ).

thf(func_def_1543,type,
    sK354: ( real > int ) > real ).

thf(func_def_1544,type,
    sK355: ( nat > rat ) > nat ).

thf(func_def_1545,type,
    sK356: ( nat > rat ) > nat ).

thf(func_def_1546,type,
    sK357: ( rat > nat ) > rat ).

thf(func_def_1547,type,
    sK358: ( rat > nat ) > rat ).

thf(func_def_1548,type,
    sK359: int > int ).

thf(func_def_1549,type,
    sK360: int > int ).

thf(func_def_1550,type,
    sK361: ( nat > rat ) > nat ).

thf(func_def_1551,type,
    sK362: ( nat > rat ) > nat ).

thf(func_def_1552,type,
    sK363: ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_1553,type,
    sK364: rat > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_1554,type,
    sK365: rat > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_1555,type,
    sK366: ( rat > rat ) > rat ).

thf(func_def_1556,type,
    sK367: ( rat > rat ) > rat ).

thf(func_def_1557,type,
    sK368: ( real > rat ) > real ).

thf(func_def_1558,type,
    sK369: ( real > rat ) > real ).

thf(func_def_1559,type,
    sK370: nat > nat ).

thf(func_def_1560,type,
    sK371: nat > nat ).

thf(func_def_1561,type,
    sK372: real > real ).

thf(func_def_1562,type,
    sK373: ( rat > real ) > rat ).

thf(func_def_1563,type,
    sK374: ( rat > real ) > rat ).

thf(func_def_1564,type,
    sK375: ( nat > nat > $o ) > nat ).

thf(func_def_1565,type,
    sK376: ( nat > nat > $o ) > nat ).

thf(func_def_1566,type,
    sK377: ( nat > nat > $o ) > nat ).

thf(func_def_1567,type,
    sK378: ( nat > nat > $o ) > nat ).

thf(func_def_1568,type,
    sK379: ( nat > rat ) > nat ).

thf(func_def_1569,type,
    sK380: nat > nat ).

thf(func_def_1570,type,
    sK381: rat > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_1571,type,
    sK382: rat > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_1572,type,
    sK383: ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_1573,type,
    sK384: ( real > rat ) > real ).

thf(func_def_1574,type,
    sK385: ( real > rat ) > real ).

thf(func_def_1575,type,
    sK386: rat > rat ).

thf(func_def_1576,type,
    sK387: ( nat > $o ) > nat > nat > nat ).

thf(func_def_1577,type,
    sK388: ( nat > nat > $o ) > nat ).

thf(func_def_1578,type,
    sK389: ( nat > nat > $o ) > nat ).

thf(func_def_1579,type,
    sK390: ( nat > nat > $o ) > nat ).

thf(func_def_1580,type,
    sK391: ( nat > nat > $o ) > nat ).

thf(func_def_1581,type,
    sK392: ( nat > nat > $o ) > nat ).

thf(func_def_1582,type,
    sK393: rat > rat ).

thf(func_def_1583,type,
    sK394: real > nat > real ).

thf(func_def_1584,type,
    sK395: nat > nat ).

thf(func_def_1585,type,
    sK396: ( rat > nat ) > rat ).

thf(func_def_1586,type,
    sK397: ( rat > nat ) > rat ).

thf(func_def_1587,type,
    sK398: real > real > real ).

thf(func_def_1588,type,
    sK399: ( real > nat ) > real ).

thf(func_def_1589,type,
    sK400: ( real > nat ) > real ).

thf(func_def_1590,type,
    sK401: ( int > $o ) > int ).

thf(func_def_1591,type,
    sK402: ( int > $o ) > int ).

thf(func_def_1592,type,
    sK403: rat > rat ).

thf(func_def_1593,type,
    ph404: 
      !>[X0: $tType] : X0 ).

thf(f40926,plain,
    $false,
    inference(subsumption_resolution,[status(thm)],[f40884,f36013]) ).

thf(f36013,plain,
    ( $true
    = ( ord_less_nat @ ma @ ( power_power_nat @ ( suc @ one_one_nat ) @ deg ) ) ),
    inference(backward_demodulation,[status(thm)],[f27547,f28220]) ).

thf(f28220,plain,
    ( ( numeral_numeral_nat @ ( bit0 @ one ) )
    = ( suc @ one_one_nat ) ),
    inference(cnf_transformation,[status(thm)],[f2974]) ).

thf(f2974,axiom,
    ( ( numeral_numeral_nat @ ( bit0 @ one ) )
    = ( suc @ one_one_nat ) ),
    file('/export/starexec/sandbox/tmp/tmp.i3enffnfiD/DTF2THF_27763.p',fact_2973_Suc__1) ).

thf(f27547,plain,
    ( ( ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) )
    = $true ),
    inference(cnf_transformation,[status(thm)],[f15241]) ).

thf(f15241,plain,
    ( ( ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) )
    = $true ),
    inference(fool_elimination,[status(thm)],[f15240]) ).

thf(f15240,plain,
    ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ),
    inference(rectify,[status(thm)],[f2]) ).

thf(f2,axiom,
    ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ),
    file('/export/starexec/sandbox/tmp/tmp.i3enffnfiD/DTF2THF_27763.p',fact_1__C5_Ohyps_C_I8_J) ).

thf(f40884,plain,
    ( $true
   != ( ord_less_nat @ ma @ ( power_power_nat @ ( suc @ one_one_nat ) @ deg ) ) ),
    inference(backward_demodulation,[status(thm)],[f36011,f40857]) ).

thf(f40857,plain,
    x = ma,
    inference(subsumption_resolution,[status(thm)],[f40847,f38650]) ).

thf(f38650,plain,
    ( ( $true
      = ( ord_less_eq_nat @ ma @ x ) )
    | ( x = ma ) ),
    inference(trivial_inequality_removal,[status(thm)],[f38614]) ).

thf(f38614,plain,
    ( ( x = ma )
    | ( $true
      = ( ord_less_eq_nat @ ma @ x ) )
    | ( $true != $true ) ),
    inference(superposition,[status(thm)],[f27103,f34992]) ).

thf(f34992,plain,
    ( ( $true
      = ( ord_less_nat @ ma @ x ) )
    | ( x = ma ) ),
    inference(duplicate_literal_removal,[status(thm)],[f34964]) ).

thf(f34964,plain,
    ( ( $true
      = ( ord_less_nat @ ma @ x ) )
    | ( $true
      = ( ord_less_nat @ ma @ x ) )
    | ( x = ma ) ),
    inference(superposition,[status(thm)],[f27547,f33719]) ).

thf(f33719,plain,
    ( ( x
      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) )
    | ( $true
      = ( ord_less_nat @ ma @ x ) )
    | ( x = ma ) ),
    inference(trivial_inequality_removal,[status(thm)],[f33714]) ).

thf(f33714,plain,
    ( ( x = ma )
    | ( x
      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) )
    | ( $true
      = ( ord_less_nat @ ma @ x ) )
    | ( $true != $true ) ),
    inference(superposition,[status(thm)],[f33686,f27547]) ).

thf(f33686,plain,
    ! [X0: nat] :
      ( ( $true
       != ( ord_less_nat @ X0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) )
      | ( $true
        = ( ord_less_nat @ X0 @ x ) )
      | ( x = X0 )
      | ( x
        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ),
    inference(trivial_inequality_removal,[status(thm)],[f33661]) ).

thf(f33661,plain,
    ! [X0: nat] :
      ( ( x = X0 )
      | ( x
        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) )
      | ( $true
       != ( ord_less_nat @ X0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) )
      | ( $true != $true )
      | ( $true
        = ( ord_less_nat @ X0 @ x ) ) ),
    inference(superposition,[status(thm)],[f26969,f33589]) ).

thf(f33589,plain,
    ! [X0: nat] :
      ( ( $true
        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) @ X0 ) )
      | ( x = X0 )
      | ( x
        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) )
      | ( $true
        = ( ord_less_nat @ X0 @ x ) ) ),
    inference(trivial_inequality_removal,[status(thm)],[f33587]) ).

thf(f33587,plain,
    ! [X0: nat] :
      ( ( $true != $true )
      | ( $true
        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) @ X0 ) )
      | ( $true
        = ( ord_less_nat @ X0 @ x ) )
      | ( x
        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) )
      | ( x = X0 ) ),
    inference(superposition,[status(thm)],[f33582,f27201]) ).

thf(f27201,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( ord_less_nat @ X1 @ X0 )
        = $true )
      | ( ( ord_less_nat @ X0 @ X1 )
        = $true )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[status(thm)],[f11894]) ).

thf(f11894,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( ord_less_nat @ X1 @ X0 )
        = $true )
      | ( ( ord_less_nat @ X0 @ X1 )
        = $true )
      | ( X0 = X1 ) ),
    inference(fool_elimination,[status(thm)],[f11893]) ).

thf(f11893,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( ord_less_nat @ X1 @ X0 )
      | ( ord_less_nat @ X0 @ X1 ) ),
    inference(rectify,[status(thm)],[f478]) ).

thf(f478,axiom,
    ! [X14: nat,X13: nat] :
      ( ( X13 = X14 )
      | ( ord_less_nat @ X13 @ X14 )
      | ( ord_less_nat @ X14 @ X13 ) ),
    file('/export/starexec/sandbox/tmp/tmp.i3enffnfiD/DTF2THF_27763.p',fact_477_linorder__less__linear) ).

thf(f33582,plain,
    ! [X0: nat] :
      ( ( $true
       != ( ord_less_nat @ x @ X0 ) )
      | ( x
        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) )
      | ( $true
        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) @ X0 ) ) ),
    inference(trivial_inequality_removal,[status(thm)],[f33576]) ).

thf(f33576,plain,
    ! [X0: nat] :
      ( ( x
        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) )
      | ( $true
        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) @ X0 ) )
      | ( $true
       != ( ord_less_nat @ x @ X0 ) )
      | ( $true != $true ) ),
    inference(superposition,[status(thm)],[f26647,f33381]) ).

thf(f33381,plain,
    ( ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) @ x )
      = $true )
    | ( x
      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ),
    inference(trivial_inequality_removal,[status(thm)],[f33373]) ).

thf(f33373,plain,
    ( ( $true != $true )
    | ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) @ x )
      = $true )
    | ( x
      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ),
    inference(superposition,[status(thm)],[f27519,f27201]) ).

thf(f27519,plain,
    ( ( ord_less_nat @ x @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) )
   != $true ),
    inference(cnf_transformation,[status(thm)],[f23690]) ).

thf(f23690,plain,
    ( ( ord_less_nat @ x @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) )
   != $true ),
    inference(flattening,[status(thm)],[f21077]) ).

thf(f21077,plain,
    ( ( ord_less_nat @ x @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) )
   != $true ),
    inference(fool_elimination,[status(thm)],[f21076]) ).

thf(f21076,plain,
    ~ ( ord_less_nat @ x @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ),
    inference(rectify,[status(thm)],[f10254]) ).

thf(f10254,negated_conjecture,
    ~ ( ord_less_nat @ x @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ),
    inference(negated_conjecture,[status(cth)],[f10253]) ).

thf(f10253,conjecture,
    ord_less_nat @ x @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ),
    file('/export/starexec/sandbox/tmp/tmp.i3enffnfiD/DTF2THF_27763.p',conj_0) ).

thf(f26647,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true
       != ( ord_less_nat @ X2 @ X1 ) )
      | ( ( ord_less_nat @ X1 @ X0 )
       != $true )
      | ( ( ord_less_nat @ X2 @ X0 )
        = $true ) ),
    inference(cnf_transformation,[status(thm)],[f24393]) ).

thf(f24393,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true
       != ( ord_less_nat @ X2 @ X1 ) )
      | ( ( ord_less_nat @ X2 @ X0 )
        = $true )
      | ( ( ord_less_nat @ X1 @ X0 )
       != $true ) ),
    inference(flattening,[status(thm)],[f24392]) ).

thf(f24392,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( ord_less_nat @ X2 @ X0 )
        = $true )
      | ( ( ord_less_nat @ X1 @ X0 )
       != $true )
      | ( $true
       != ( ord_less_nat @ X2 @ X1 ) ) ),
    inference(ennf_transformation,[status(thm)],[f13685]) ).

thf(f13685,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true
        = ( ord_less_nat @ X2 @ X1 ) )
     => ( ( ( ord_less_nat @ X1 @ X0 )
          = $true )
       => ( ( ord_less_nat @ X2 @ X0 )
          = $true ) ) ),
    inference(fool_elimination,[status(thm)],[f13684]) ).

thf(f13684,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ord_less_nat @ X2 @ X1 )
     => ( ( ord_less_nat @ X1 @ X0 )
       => ( ord_less_nat @ X2 @ X0 ) ) ),
    inference(rectify,[status(thm)],[f418]) ).

thf(f418,axiom,
    ! [X15: nat,X14: nat,X13: nat] :
      ( ( ord_less_nat @ X13 @ X14 )
     => ( ( ord_less_nat @ X14 @ X15 )
       => ( ord_less_nat @ X13 @ X15 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.i3enffnfiD/DTF2THF_27763.p',fact_417_order__less__trans) ).

thf(f26969,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( ord_less_nat @ X1 @ X0 )
       != $true )
      | ( ( ord_less_nat @ X0 @ X1 )
       != $true ) ),
    inference(cnf_transformation,[status(thm)],[f25100]) ).

thf(f25100,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( ord_less_nat @ X0 @ X1 )
       != $true )
      | ( ( ord_less_nat @ X1 @ X0 )
       != $true ) ),
    inference(ennf_transformation,[status(thm)],[f23708]) ).

thf(f23708,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( ord_less_nat @ X0 @ X1 )
        = $true )
     => ( ( ord_less_nat @ X1 @ X0 )
       != $true ) ),
    inference(flattening,[status(thm)],[f16452]) ).

thf(f16452,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( ord_less_nat @ X0 @ X1 )
        = $true )
     => ( ( ord_less_nat @ X1 @ X0 )
       != $true ) ),
    inference(fool_elimination,[status(thm)],[f16451]) ).

thf(f16451,plain,
    ! [X0: nat,X1: nat] :
      ( ( ord_less_nat @ X0 @ X1 )
     => ~ ( ord_less_nat @ X1 @ X0 ) ),
    inference(rectify,[status(thm)],[f413]) ).

thf(f413,axiom,
    ! [X7: nat,X8: nat] :
      ( ( ord_less_nat @ X7 @ X8 )
     => ~ ( ord_less_nat @ X8 @ X7 ) ),
    file('/export/starexec/sandbox/tmp/tmp.i3enffnfiD/DTF2THF_27763.p',fact_412_order__less__asym_H) ).

thf(f27103,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( ord_less_nat @ X1 @ X0 )
       != $true )
      | ( ( ord_less_eq_nat @ X1 @ X0 )
        = $true ) ),
    inference(cnf_transformation,[status(thm)],[f24853]) ).

thf(f24853,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( ord_less_eq_nat @ X1 @ X0 )
        = $true )
      | ( ( ord_less_nat @ X1 @ X0 )
       != $true ) ),
    inference(ennf_transformation,[status(thm)],[f18778]) ).

thf(f18778,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( ord_less_nat @ X1 @ X0 )
        = $true )
     => ( ( ord_less_eq_nat @ X1 @ X0 )
        = $true ) ),
    inference(fool_elimination,[status(thm)],[f18777]) ).

thf(f18777,plain,
    ! [X0: nat,X1: nat] :
      ( ( ord_less_nat @ X1 @ X0 )
     => ( ord_less_eq_nat @ X1 @ X0 ) ),
    inference(rectify,[status(thm)],[f621]) ).

thf(f621,axiom,
    ! [X8: nat,X7: nat] :
      ( ( ord_less_nat @ X7 @ X8 )
     => ( ord_less_eq_nat @ X7 @ X8 ) ),
    file('/export/starexec/sandbox/tmp/tmp.i3enffnfiD/DTF2THF_27763.p',fact_620_order_Ostrict__implies__order) ).

thf(f40847,plain,
    ( ( x = ma )
    | ( $true
     != ( ord_less_eq_nat @ ma @ x ) ) ),
    inference(trivial_inequality_removal,[status(thm)],[f40833]) ).

thf(f40833,plain,
    ( ( x = ma )
    | ( $true
     != ( ord_less_eq_nat @ ma @ x ) )
    | ( $true != $true ) ),
    inference(superposition,[status(thm)],[f26773,f28611]) ).

thf(f28611,plain,
    ( ( ord_less_eq_nat @ x @ ma )
    = $true ),
    inference(cnf_transformation,[status(thm)],[f20799]) ).

thf(f20799,plain,
    ( ( ( ord_less_eq_nat @ mi @ x )
      = $true )
    & ( ( ord_less_eq_nat @ x @ ma )
      = $true ) ),
    inference(fool_elimination,[status(thm)],[f20798]) ).

thf(f20798,plain,
    ( ( ord_less_eq_nat @ x @ ma )
    & ( ord_less_eq_nat @ mi @ x ) ),
    inference(rectify,[status(thm)],[f25]) ).

thf(f25,axiom,
    ( ( ord_less_eq_nat @ x @ ma )
    & ( ord_less_eq_nat @ mi @ x ) ),
    file('/export/starexec/sandbox/tmp/tmp.i3enffnfiD/DTF2THF_27763.p',fact_24__092_060open_062x_A_092_060le_062_Ama_A_092_060and_062_Ami_A_092_060le_062_Ax_092_060close_062) ).

thf(f26773,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( ord_less_eq_nat @ X1 @ X0 )
       != $true )
      | ( ( ord_less_eq_nat @ X0 @ X1 )
       != $true )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[status(thm)],[f25046]) ).

thf(f25046,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( ord_less_eq_nat @ X0 @ X1 )
       != $true )
      | ( X0 = X1 )
      | ( ( ord_less_eq_nat @ X1 @ X0 )
       != $true ) ),
    inference(flattening,[status(thm)],[f25045]) ).

thf(f25045,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( ( ord_less_eq_nat @ X1 @ X0 )
       != $true )
      | ( ( ord_less_eq_nat @ X0 @ X1 )
       != $true ) ),
    inference(ennf_transformation,[status(thm)],[f11842]) ).

thf(f11842,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( ord_less_eq_nat @ X0 @ X1 )
        = $true )
     => ( ( ( ord_less_eq_nat @ X1 @ X0 )
          = $true )
       => ( X0 = X1 ) ) ),
    inference(fool_elimination,[status(thm)],[f11841]) ).

thf(f11841,plain,
    ! [X0: nat,X1: nat] :
      ( ( ord_less_eq_nat @ X0 @ X1 )
     => ( ( ord_less_eq_nat @ X1 @ X0 )
       => ( X0 = X1 ) ) ),
    inference(rectify,[status(thm)],[f265]) ).

thf(f265,axiom,
    ! [X8: nat,X7: nat] :
      ( ( ord_less_eq_nat @ X8 @ X7 )
     => ( ( ord_less_eq_nat @ X7 @ X8 )
       => ( X7 = X8 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.i3enffnfiD/DTF2THF_27763.p',fact_264_dual__order_Oantisym) ).

thf(f36011,plain,
    ( $true
   != ( ord_less_nat @ x @ ( power_power_nat @ ( suc @ one_one_nat ) @ deg ) ) ),
    inference(backward_demodulation,[status(thm)],[f27519,f28220]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP270^1 : TPTP v9.2.1. Released v8.1.0.
% 0.10/0.13  % Command  : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.34  % Computer : n023.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Tue Feb 24 08:40:35 EST 2026
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.45  ---- Original DTF file ---
% 0.17/0.45  thf(spec,logic,$$dhol).
% 0.17/0.45  %------------------------------------------------------------------------------
% 0.17/0.45  % File     : ITP270^1 : TPTP v9.2.1. Released v8.1.0.
% 0.17/0.45  % Domain   : Interactive Theorem Proving
% 0.17/0.45  % Problem  : Sledgehammer problem VEBT_DeleteBounds 00283_015243
% 0.17/0.45  % Version  : [Des22] axioms.
% 0.17/0.45  % English  :
% 0.17/0.45  
% 0.17/0.45  % Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.17/0.45  %          : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 0.17/0.45  % Source   : [Des22]
% 0.17/0.45  % Names    : 0074_VEBT_DeleteBounds_00283_015243 [Des22]
% 0.17/0.45  
% 0.17/0.45  % Status   : Theorem
% 0.17/0.45  % Rating   : 0.56 v9.1.0, 0.50 v9.0.0, 0.80 v8.2.0, 0.85 v8.1.0
% 0.17/0.45  % Syntax   : Number of formulae    : 11424 (5763 unt;1171 typ;   0 def)
% 0.17/0.45  %            Number of atoms       : 30127 (13070 equ;   0 cnn)
% 0.17/0.45  %            Maximal formula atoms :   71 (   2 avg)
% 0.17/0.45  %            Number of connectives : 126577 (2956   ~; 504   |;1884   &;109891   @)
% 0.17/0.45  %                                         (   0 <=>;11342  =>;   0  <=;   0 <~>)
% 0.17/0.45  %            Maximal formula depth :   39 (   6 avg)
% 0.17/0.45  %            Number of types       :   99 (  98 usr)
% 0.17/0.45  %            Number of type conns  : 4573 (4573   >;   0   *;   0   +;   0  <<)
% 0.17/0.45  %            Number of symbols     : 1076 (1073 usr;  77 con; 0-8 aty)
% 0.17/0.45  %            Number of variables   : 25764 (2189   ^;22661   !; 914   ?;25764   :)
% 0.17/0.45  % SPC      : TH0_THM_EQU_NAR
% 0.17/0.45  
% 0.17/0.45  % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.17/0.45  %            from the van Emde Boas Trees session in the Archive of Formal
% 0.17/0.45  %            proofs - 
% 0.17/0.45  %            www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 0.17/0.45  %            2022-02-18 12:10:18.943
% 0.17/0.45  %------------------------------------------------------------------------------
% 0.17/0.45  % Could-be-implicit typings (98)
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% 0.17/0.45      produc1319942482725812455at_nat: $tType ).
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% 0.17/0.45      produc5542196010084753463at_nat: $tType ).
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% 0.17/0.45      produc5491161045314408544at_nat: $tType ).
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% 0.17/0.45      bNF_re728719798268516973at_o_o: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( $o > $o > $o ) > ( ( nat > rat ) > $o ) > ( ( nat > rat ) > $o ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal_001_062_I_062_It__Nat__Onat_Mt__Rat__Orat_J_M_062_It__Nat__Onat_Mt__Rat__Orat_J_J_001_062_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 0.17/0.45      bNF_re4695409256820837752l_real: ( ( nat > rat ) > real > $o ) > ( ( ( nat > rat ) > nat > rat ) > ( real > real ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > ( real > real > real ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal_001_062_I_062_It__Nat__Onat_Mt__Rat__Orat_J_M_Eo_J_001_062_It__Real__Oreal_M_Eo_J,type,
% 0.17/0.45      bNF_re4521903465945308077real_o: ( ( nat > rat ) > real > $o ) > ( ( ( nat > rat ) > $o ) > ( real > $o ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > $o ) > ( real > real > $o ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal,type,
% 0.17/0.45      bNF_re3023117138289059399t_real: ( ( nat > rat ) > real > $o ) > ( ( nat > rat ) > real > $o ) > ( ( nat > rat ) > nat > rat ) > ( real > real ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal_001_Eo_001_Eo,type,
% 0.17/0.45      bNF_re4297313714947099218al_o_o: ( ( nat > rat ) > real > $o ) > ( $o > $o > $o ) > ( ( nat > rat ) > $o ) > ( real > $o ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_062_It__Int__Oint_M_Eo_J_001_062_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 0.17/0.45      bNF_re6321650412969554871eger_o: ( int > code_integer > $o ) > ( ( int > $o ) > ( code_integer > $o ) > $o ) > ( int > int > $o ) > ( code_integer > code_integer > $o ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_Eo_001_Eo,type,
% 0.17/0.45      bNF_re6574881592172037608er_o_o: ( int > code_integer > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( code_integer > $o ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.17/0.45      bNF_re2807294637932363402at_nat: ( int > code_integer > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( code_integer > nat ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Num__Onum,type,
% 0.17/0.45      bNF_re6718328864250387230um_num: ( int > code_integer > $o ) > ( num > num > $o ) > ( int > num ) > ( code_integer > num ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 0.17/0.45      bNF_re3403563459893282935_int_o: ( int > int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 0.17/0.45      bNF_re157797125943740599nt_int: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > product_prod_int_int ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Rat__Orat_J,type,
% 0.17/0.45      bNF_re3461391660133120880nt_rat: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > rat ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
% 0.17/0.45      bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.17/0.45      bNF_re3715656647883201625at_nat: ( int > int > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( int > nat ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum,type,
% 0.17/0.45      bNF_re7626690874201225453um_num: ( int > int > $o ) > ( num > num > $o ) > ( int > num ) > ( int > num ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.17/0.45      bNF_re6250860962936578807nt_int: ( int > int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 0.17/0.45      bNF_re2214769303045360666nt_rat: ( int > int > $o ) > ( product_prod_int_int > rat > $o ) > ( int > product_prod_int_int ) > ( int > rat ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.17/0.45      bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
% 0.17/0.45      bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 0.17/0.45      bNF_re4153400068438556298nteger: ( nat > nat > $o ) > ( int > code_integer > $o ) > ( nat > int ) > ( nat > code_integer ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
% 0.17/0.45      bNF_re6650684261131312217nt_int: ( nat > nat > $o ) > ( int > int > $o ) > ( nat > int ) > ( nat > int ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 0.17/0.45      bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001_062_It__Num__Onum_Mt__Int__Oint_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
% 0.17/0.45      bNF_re7876454716742015248nteger: ( num > num > $o ) > ( ( num > int ) > ( num > code_integer ) > $o ) > ( num > num > int ) > ( num > num > code_integer ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001_062_It__Num__Onum_Mt__Int__Oint_J_001_062_It__Num__Onum_Mt__Int__Oint_J,type,
% 0.17/0.45      bNF_re8402795839162346335um_int: ( num > num > $o ) > ( ( num > int ) > ( num > int ) > $o ) > ( num > num > int ) > ( num > num > int ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 0.17/0.45      bNF_re6501075790457514782nteger: ( num > num > $o ) > ( int > code_integer > $o ) > ( num > int ) > ( num > code_integer ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Int__Oint,type,
% 0.17/0.45      bNF_re1822329894187522285nt_int: ( num > num > $o ) > ( int > int > $o ) > ( num > int ) > ( num > int ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001_Eo,type,
% 0.17/0.45      bNF_re8699439704749558557nt_o_o: ( product_prod_int_int > product_prod_int_int > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.17/0.45      bNF_re7145576690424134365nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001_Eo_001_Eo,type,
% 0.17/0.45      bNF_re1494630372529172596at_o_o: ( product_prod_int_int > rat > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( rat > $o ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 0.17/0.45      bNF_re8279943556446156061nt_rat: ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_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,
% 0.17/0.45      bNF_re717283939379294677_int_o: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_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,
% 0.17/0.45      bNF_re7408651293131936558nt_int: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_Eo_001_Eo,type,
% 0.17/0.45      bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.17/0.45      bNF_re4555766996558763186at_nat: ( product_prod_nat_nat > int > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 0.17/0.45      bNF_re7400052026677387805at_int: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_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__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 0.17/0.45      bNF_re4202695980764964119_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_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__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.17/0.45      bNF_re3099431351363272937at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 0.17/0.45      bNF_re3666534408544137501at_o_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.17/0.45      bNF_re8246922863344978751at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > nat ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.17/0.45      bNF_re2241393799969408733at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Binomial_Obinomial,type,
% 0.17/0.45      binomial: nat > nat > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Binomial_Ogbinomial_001t__Complex__Ocomplex,type,
% 0.17/0.45      gbinomial_complex: complex > nat > complex ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Binomial_Ogbinomial_001t__Int__Oint,type,
% 0.17/0.45      gbinomial_int: int > nat > int ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Binomial_Ogbinomial_001t__Nat__Onat,type,
% 0.17/0.45      gbinomial_nat: nat > nat > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Binomial_Ogbinomial_001t__Rat__Orat,type,
% 0.17/0.45      gbinomial_rat: rat > nat > rat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Binomial_Ogbinomial_001t__Real__Oreal,type,
% 0.17/0.45      gbinomial_real: real > nat > real ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Bit__Operations_Oand__int__rel,type,
% 0.17/0.45      bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Bit__Operations_Oand__not__num,type,
% 0.17/0.45      bit_and_not_num: num > num > option_num ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Bit__Operations_Oand__not__num__rel,type,
% 0.17/0.45      bit_and_not_num_rel: product_prod_num_num > product_prod_num_num > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Bit__Operations_Oconcat__bit,type,
% 0.17/0.45      bit_concat_bit: nat > int > int > int ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Bit__Operations_Oor__not__num__neg,type,
% 0.17/0.45      bit_or_not_num_neg: num > num > num ).
% 0.17/0.45  
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% 0.17/0.45      nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 0.17/0.45      nth_real: list_real > nat > real ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.17/0.45      nth_set_nat: list_set_nat > nat > set_nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 0.17/0.45      nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 0.17/0.45      product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 0.17/0.45      product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 0.17/0.45      product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 0.17/0.45      product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Num__Onum,type,
% 0.17/0.45      product_nat_num: list_nat > list_num > list_P1726324292696863441at_num ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oproduct_001t__Num__Onum_001t__Num__Onum,type,
% 0.17/0.45      product_num_num: list_num > list_num > list_P3744719386663036955um_num ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 0.17/0.45      product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 0.17/0.45      produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 0.17/0.45      produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 0.17/0.45      produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oreplicate_001t__Extended____Nat__Oenat,type,
% 0.17/0.45      replic7216382294607269926d_enat: nat > extended_enat > list_Extended_enat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 0.17/0.45      replicate_int: nat > int > list_int ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 0.17/0.45      replicate_nat: nat > nat > list_nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oreplicate_001t__Option__Ooption_It__Nat__Onat_J,type,
% 0.17/0.45      replicate_option_nat: nat > option_nat > list_option_nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oreplicate_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.17/0.45      replic4235873036481779905at_nat: nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oreplicate_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.17/0.45      replic2264142908078655527at_nat: nat > produc3843707927480180839at_nat > list_P5464809261938338413at_nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 0.17/0.45      replicate_real: nat > real > list_real ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oreplicate_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.17/0.45      replicate_set_nat: nat > set_nat > list_set_nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 0.17/0.45      replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 0.17/0.45      sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 0.17/0.45      sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 0.17/0.45      take_nat: nat > list_nat > list_nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Otake_001t__VEBT____Definitions__OVEBT,type,
% 0.17/0.45      take_VEBT_VEBT: nat > list_VEBT_VEBT > list_VEBT_VEBT ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oupt,type,
% 0.17/0.45      upt: nat > nat > list_nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oupto,type,
% 0.17/0.45      upto: int > int > list_int ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oupto__aux,type,
% 0.17/0.45      upto_aux: int > int > list_int > list_int ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_List_Oupto__rel,type,
% 0.17/0.45      upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_OSuc,type,
% 0.17/0.45      suc: nat > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.17/0.45      compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 0.17/0.45      case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 0.17/0.45      case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 0.17/0.45      case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Onat_Opred,type,
% 0.17/0.45      pred: nat > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osemiring__1__class_ONats_001t__Complex__Ocomplex,type,
% 0.17/0.45      semiri3842193898606819883omplex: set_complex ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osemiring__1__class_ONats_001t__Int__Oint,type,
% 0.17/0.45      semiring_1_Nats_int: set_int ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 0.17/0.45      semiri4939895301339042750nteger: nat > code_integer ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 0.17/0.45      semiri8010041392384452111omplex: nat > complex ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
% 0.17/0.45      semiri4216267220026989637d_enat: nat > extended_enat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 0.17/0.45      semiri1314217659103216013at_int: nat > int ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 0.17/0.45      semiri1316708129612266289at_nat: nat > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 0.17/0.45      semiri681578069525770553at_rat: nat > rat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 0.17/0.45      semiri5074537144036343181t_real: nat > real ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 0.17/0.45      size_size_list_o: list_o > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 0.17/0.45      size_s3451745648224563538omplex: list_complex > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Extended____Nat__Oenat_J,type,
% 0.17/0.45      size_s3941691890525107288d_enat: list_Extended_enat > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 0.17/0.45      size_size_list_int: list_int > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 0.17/0.45      size_size_list_nat: list_nat > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
% 0.17/0.45      size_size_list_num: list_num > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Option__Ooption_It__Nat__Onat_J_J,type,
% 0.17/0.45      size_s6086282163384603972on_nat: list_option_nat > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.17/0.45      size_s5460976970255530739at_nat: list_P6011104703257516679at_nat > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 0.17/0.45      size_size_list_real: list_real > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.17/0.45      size_s3254054031482475050et_nat: list_set_nat > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 0.17/0.45      size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 0.17/0.45      size_size_num: num > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Nat__Onat_J,type,
% 0.17/0.45      size_size_option_nat: option_nat > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
% 0.17/0.45      size_size_option_num: option_num > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.17/0.45      size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osize__class_Osize_001t__String__Ochar,type,
% 0.17/0.45      size_size_char: char > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 0.17/0.45      size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat__Bijection_Olist__decode,type,
% 0.17/0.45      nat_list_decode: nat > list_nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat__Bijection_Olist__decode__rel,type,
% 0.17/0.45      nat_list_decode_rel: nat > nat > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat__Bijection_Olist__encode,type,
% 0.17/0.45      nat_list_encode: list_nat > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 0.17/0.45      nat_list_encode_rel: list_nat > list_nat > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat__Bijection_Oprod__decode,type,
% 0.17/0.45      nat_prod_decode: nat > product_prod_nat_nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 0.17/0.45      nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 0.17/0.45      nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 0.17/0.45      nat_prod_encode: product_prod_nat_nat > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat__Bijection_Oset__decode,type,
% 0.17/0.45      nat_set_decode: nat > set_nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat__Bijection_Oset__encode,type,
% 0.17/0.45      nat_set_encode: set_nat > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Nat__Bijection_Otriangle,type,
% 0.17/0.45      nat_triangle: nat > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_NthRoot_Oroot,type,
% 0.17/0.45      root: nat > real > real ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_NthRoot_Osqrt,type,
% 0.17/0.45      sqrt: real > real ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_OBitM,type,
% 0.17/0.45      bitM: num > num ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_Oinc,type,
% 0.17/0.45      inc: num > num ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_Onat__of__num,type,
% 0.17/0.45      nat_of_num: num > nat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 0.17/0.45      neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 0.17/0.45      neg_nu7009210354673126013omplex: complex > complex ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 0.17/0.45      neg_numeral_dbl_int: int > int ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 0.17/0.45      neg_numeral_dbl_rat: rat > rat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 0.17/0.45      neg_numeral_dbl_real: real > real ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 0.17/0.45      neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 0.17/0.45      neg_nu6511756317524482435omplex: complex > complex ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 0.17/0.45      neg_nu3811975205180677377ec_int: int > int ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 0.17/0.45      neg_nu3179335615603231917ec_rat: rat > rat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 0.17/0.45      neg_nu6075765906172075777c_real: real > real ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
% 0.17/0.45      neg_nu5831290666863070958nteger: code_integer > code_integer ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 0.17/0.45      neg_nu8557863876264182079omplex: complex > complex ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 0.17/0.45      neg_nu5851722552734809277nc_int: int > int ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 0.17/0.45      neg_nu5219082963157363817nc_rat: rat > rat ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
% 0.17/0.45      neg_nu8295874005876285629c_real: real > real ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 0.17/0.45      neg_numeral_sub_int: num > num > int ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_Onum_OBit0,type,
% 0.17/0.45      bit0: num > num ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_Onum_OBit1,type,
% 0.17/0.45      bit1: num > num ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_Onum_OOne,type,
% 0.17/0.45      one: num ).
% 0.17/0.45  
% 0.17/0.45  thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
% 0.17/0.45      case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).
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% 0.17/0.46      insert9069300056098147895at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 0.17/0.46  
% 0.17/0.46  thf(sy_c_Set_Oinsert_001t__Rat__Orat,type,
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% 0.17/0.46  
% 0.17/0.46  thf(sy_c_Set_Oinsert_001t__VEBT____Definitions__OVEBT,type,
% 0.17/0.46      insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).
% 0.17/0.46  
% 0.17/0.46  thf(sy_c_Set_Ovimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.17/0.46      vimage_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 0.17/0.46  
% 0.17/0.46  thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Complex__Ocomplex,type,
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% 0.17/0.46  
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% 0.17/0.46  
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% 0.17/0.46  
% 0.17/0.46  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Nat__Onat_J,type,
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% 0.17/0.46  
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% 0.17/0.46  thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
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% 0.17/0.46  
% 0.17/0.46  thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
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% 0.17/0.46  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Int__Oint,type,
% 0.17/0.46      set_ord_atMost_int: int > set_int ).
% 0.17/0.46  
% 0.17/0.46  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
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% 0.17/0.46  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Num__Onum,type,
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% 0.17/0.46  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Rat__Orat,type,
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% 0.17/0.46  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Real__Oreal,type,
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% 0.17/0.46  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Nat__Onat_J,type,
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% 0.17/0.46  
% 0.17/0.46  thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
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% 0.17/0.46  
% 0.17/0.46  thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
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% 0.17/0.46  
% 0.17/0.46  thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
% 0.17/0.46      set_or1210151606488870762an_nat: nat > set_nat ).
% 0.17/0.46  
% 0.17/0.46  thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
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% 0.17/0.46  
% 0.17/0.46  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
% 0.17/0.46      set_ord_lessThan_int: int > set_int ).
% 0.17/0.46  
% 0.17/0.46  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 0.17/0.46      set_ord_lessThan_nat: nat > set_nat ).
% 0.17/0.46  
% 0.17/0.46  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Num__Onum,type,
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% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Rat__Orat,type,
% 0.26/0.46      set_ord_lessThan_rat: rat > set_rat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
% 0.26/0.46      set_or5984915006950818249n_real: real > set_real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.26/0.46      set_or890127255671739683et_nat: set_nat > set_set_nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_String_OCode_Oabort_001t__Real__Oreal,type,
% 0.26/0.46      abort_real: literal > ( product_unit > real ) > real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_String_OLiteral,type,
% 0.26/0.46      literal2: $o > $o > $o > $o > $o > $o > $o > literal > literal ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_String_Oascii__of,type,
% 0.26/0.46      ascii_of: char > char ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_String_Ochar_OChar,type,
% 0.26/0.46      char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_String_Ochar_Osize__char,type,
% 0.26/0.46      size_char: char > nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_String_Ocomm__semiring__1__class_Oof__char_001t__Nat__Onat,type,
% 0.26/0.46      comm_s629917340098488124ar_nat: char > nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_String_Ointeger__of__char,type,
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% 0.26/0.46  
% 0.26/0.46  thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
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% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.26/0.46      topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
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% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 0.26/0.46      topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 0.26/0.46      topolo2177554685111907308n_real: real > set_real > filter_real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Topological__Spaces_Otopological__space__class_Oconvergent_001t__Real__Oreal,type,
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% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
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% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
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% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Complex__Ocomplex,type,
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% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Oarccos,type,
% 0.26/0.46      arccos: real > real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 0.26/0.46      arcosh_real: real > real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Oarcsin,type,
% 0.26/0.46      arcsin: real > real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Oarctan,type,
% 0.26/0.46      arctan: real > real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 0.26/0.46      arsinh_real: real > real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 0.26/0.46      artanh_real: real > real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Ocos_001t__Complex__Ocomplex,type,
% 0.26/0.46      cos_complex: complex > complex ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 0.26/0.46      cos_real: real > real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Ocos__coeff,type,
% 0.26/0.46      cos_coeff: nat > real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 0.26/0.46      cosh_real: real > real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 0.26/0.46      cot_real: real > real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 0.26/0.46      exp_complex: complex > complex ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 0.26/0.46      exp_real: real > real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 0.26/0.46      ln_ln_real: real > real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Olog,type,
% 0.26/0.46      log: real > real > real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Opi,type,
% 0.26/0.46      pi: real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 0.26/0.46      powr_real: real > real > real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Opowr__real,type,
% 0.26/0.46      powr_real2: real > real > real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Osin_001t__Complex__Ocomplex,type,
% 0.26/0.46      sin_complex: complex > complex ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 0.26/0.46      sin_real: real > real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Osin__coeff,type,
% 0.26/0.46      sin_coeff: nat > real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 0.26/0.46      sinh_real: real > real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Otan_001t__Complex__Ocomplex,type,
% 0.26/0.46      tan_complex: complex > complex ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 0.26/0.46      tan_real: real > real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 0.26/0.46      tanh_real: real > real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transfer_Obi__total_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 0.26/0.46      bi_tot896582865486249351at_int: ( product_prod_nat_nat > int > $o ) > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
% 0.26/0.46      transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 0.26/0.46      transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Typedef_Otype__definition_001t__Extended____Nat__Oenat_001t__Option__Ooption_It__Nat__Onat_J,type,
% 0.26/0.46      type_d7649664348572268762on_nat: ( extended_enat > option_nat ) > ( option_nat > extended_enat ) > set_option_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t,type,
% 0.26/0.46      vEBT_T_i_n_s_e_r_t: vEBT_VEBT > nat > nat ).
% 0.26/0.46  
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% 0.26/0.46      vEBT_T_i_n_s_e_r_t2: vEBT_VEBT > nat > nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H__rel,type,
% 0.26/0.46      vEBT_T5076183648494686801_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t__rel,type,
% 0.26/0.46      vEBT_T9217963907923527482_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t,type,
% 0.26/0.46      vEBT_T_m_a_x_t: vEBT_VEBT > nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r,type,
% 0.26/0.46      vEBT_T_m_e_m_b_e_r: vEBT_VEBT > nat > nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H,type,
% 0.26/0.46      vEBT_T_m_e_m_b_e_r2: vEBT_VEBT > nat > nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H__rel,type,
% 0.26/0.46      vEBT_T8099345112685741742_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r__rel,type,
% 0.26/0.46      vEBT_T5837161174952499735_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l,type,
% 0.26/0.46      vEBT_T_m_i_n_N_u_l_l: vEBT_VEBT > nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t,type,
% 0.26/0.46      vEBT_T_m_i_n_t: vEBT_VEBT > nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t__rel,type,
% 0.26/0.46      vEBT_T_m_i_n_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d,type,
% 0.26/0.46      vEBT_T_p_r_e_d: vEBT_VEBT > nat > nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H,type,
% 0.26/0.46      vEBT_T_p_r_e_d2: vEBT_VEBT > nat > nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H__rel,type,
% 0.26/0.46      vEBT_T_p_r_e_d_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d__rel,type,
% 0.26/0.46      vEBT_T_p_r_e_d_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c,type,
% 0.26/0.46      vEBT_T_s_u_c_c: vEBT_VEBT > nat > nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H,type,
% 0.26/0.46      vEBT_T_s_u_c_c2: vEBT_VEBT > nat > nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H__rel,type,
% 0.26/0.46      vEBT_T_s_u_c_c_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c__rel,type,
% 0.26/0.46      vEBT_T_s_u_c_c_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 0.26/0.46      vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 0.26/0.46      vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 0.26/0.46      vEBT_size_VEBT: vEBT_VEBT > nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 0.26/0.46      vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oelim__dead,type,
% 0.26/0.46      vEBT_VEBT_elim_dead: vEBT_VEBT > extended_enat > vEBT_VEBT ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oelim__dead__rel,type,
% 0.26/0.46      vEBT_V312737461966249ad_rel: produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 0.26/0.46      vEBT_VEBT_high: nat > nat > nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 0.26/0.46      vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 0.26/0.46      vEBT_VEBT_low: nat > nat > nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 0.26/0.46      vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 0.26/0.46      vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 0.26/0.46      vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 0.26/0.46      vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 0.26/0.46      vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 0.26/0.46      vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 0.26/0.46      vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 0.26/0.46      vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 0.26/0.46      vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 0.26/0.46      vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__DeleteBounds_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e,type,
% 0.26/0.46      vEBT_T_d_e_l_e_t_e: vEBT_VEBT > nat > nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__DeleteBounds_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e__rel,type,
% 0.26/0.46      vEBT_T8441311223069195367_e_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Delete_Ovebt__delete,type,
% 0.26/0.46      vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Delete_Ovebt__delete__rel,type,
% 0.26/0.46      vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Height_OVEBT__internal_Oheight,type,
% 0.26/0.46      vEBT_VEBT_height: vEBT_VEBT > nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Height_OVEBT__internal_Oheight__rel,type,
% 0.26/0.46      vEBT_VEBT_height_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 0.26/0.46      vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 0.26/0.46      vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 0.26/0.46      vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 0.26/0.46      vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 0.26/0.46      vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Member_Ovebt__member,type,
% 0.26/0.46      vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 0.26/0.46      vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 0.26/0.46      vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 0.26/0.46      vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 0.26/0.46      vEBT_VEBT_less: option_nat > option_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 0.26/0.46      vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 0.26/0.46      vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
% 0.26/0.46      vEBT_VEBT_min_in_set: set_nat > nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Omul,type,
% 0.26/0.46      vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__comp__shift_001t__Nat__Onat,type,
% 0.26/0.46      vEBT_V2881884560877996034ft_nat: ( nat > nat > $o ) > option_nat > option_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Nat__Onat,type,
% 0.26/0.46      vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Num__Onum,type,
% 0.26/0.46      vEBT_V819420779217536731ft_num: ( num > num > num ) > option_num > option_num > option_num ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.26/0.46      vEBT_V1502963449132264192at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Opower,type,
% 0.26/0.46      vEBT_VEBT_power: option_nat > option_nat > option_nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__MinMax_Ovebt__maxt,type,
% 0.26/0.46      vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__MinMax_Ovebt__maxt__rel,type,
% 0.26/0.46      vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__MinMax_Ovebt__mint,type,
% 0.26/0.46      vEBT_vebt_mint: vEBT_VEBT > option_nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__MinMax_Ovebt__mint__rel,type,
% 0.26/0.46      vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Pred_Ois__pred__in__set,type,
% 0.26/0.46      vEBT_is_pred_in_set: set_nat > nat > nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Pred_Ovebt__pred,type,
% 0.26/0.46      vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Pred_Ovebt__pred__rel,type,
% 0.26/0.46      vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Succ_Ois__succ__in__set,type,
% 0.26/0.46      vEBT_is_succ_in_set: set_nat > nat > nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Succ_Ovebt__succ,type,
% 0.26/0.46      vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_VEBT__Succ_Ovebt__succ__rel,type,
% 0.26/0.46      vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 0.26/0.46      accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 0.26/0.46      accp_nat: ( nat > nat > $o ) > nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.26/0.46      accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.26/0.46      accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 0.26/0.46      accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Extended____Nat__Oenat_J,type,
% 0.26/0.46      accp_P6183159247885693666d_enat: ( produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o ) > produc7272778201969148633d_enat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 0.26/0.46      accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 0.26/0.46      accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Wellfounded_Oless__than,type,
% 0.26/0.46      less_than: set_Pr1261947904930325089at_nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Wellfounded_Olex__prod_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.26/0.46      lex_prod_nat_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Wellfounded_Omax__ext_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.26/0.46      max_ex8135407076693332796at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Wellfounded_Omin__ext_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.26/0.46      min_ex6901939911449802026at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Wellfounded_Opred__nat,type,
% 0.26/0.46      pred_nat: set_Pr1261947904930325089at_nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Wellfounded_Owf_001t__Int__Oint,type,
% 0.26/0.46      wf_int: set_Pr958786334691620121nt_int > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
% 0.26/0.46      wf_nat: set_Pr1261947904930325089at_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_Wellfounded_Owf_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.26/0.46      wf_Pro7803398752247294826at_nat: set_Pr8693737435421807431at_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_fChoice_001t__Real__Oreal,type,
% 0.26/0.46      fChoice_real: ( real > $o ) > real ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_member_001_Eo,type,
% 0.26/0.46      member_o: $o > set_o > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_member_001t__Complex__Ocomplex,type,
% 0.26/0.46      member_complex: complex > set_complex > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_member_001t__Extended____Nat__Oenat,type,
% 0.26/0.46      member_Extended_enat: extended_enat > set_Extended_enat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_member_001t__Int__Oint,type,
% 0.26/0.46      member_int: int > set_int > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 0.26/0.46      member_list_o: list_o > set_list_o > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 0.26/0.46      member_list_int: list_int > set_list_int > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 0.26/0.46      member_list_nat: list_nat > set_list_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 0.26/0.46      member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_member_001t__Nat__Onat,type,
% 0.26/0.46      member_nat: nat > set_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_member_001t__Num__Onum,type,
% 0.26/0.46      member_num: num > set_num > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_member_001t__Option__Ooption_It__Nat__Onat_J,type,
% 0.26/0.46      member_option_nat: option_nat > set_option_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.26/0.46      member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.26/0.46      member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.26/0.46      member8757157785044589968at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_member_001t__Rat__Orat,type,
% 0.26/0.46      member_rat: rat > set_rat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_member_001t__Real__Oreal,type,
% 0.26/0.46      member_real: real > set_real > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.26/0.46      member_set_nat: set_nat > set_set_nat > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 0.26/0.46      member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_v_deg____,type,
% 0.26/0.46      deg: nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_v_m____,type,
% 0.26/0.46      m: nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_v_ma____,type,
% 0.26/0.46      ma: nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_v_mi____,type,
% 0.26/0.46      mi: nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_v_na____,type,
% 0.26/0.46      na: nat ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_v_summary____,type,
% 0.26/0.46      summary: vEBT_VEBT ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_v_treeList____,type,
% 0.26/0.46      treeList: list_VEBT_VEBT ).
% 0.26/0.46  
% 0.26/0.46  thf(sy_v_x,type,
% 0.26/0.46      x: nat ).
% 0.26/0.46  
% 0.26/0.46  % Relevant facts (10208)
% 0.26/0.46  thf(fact_0_False,axiom,
% 0.26/0.46      x != mi ).
% 0.26/0.46  
% 0.26/0.46  % False
% 0.26/0.46  thf(fact_1__C5_Ohyps_C_I8_J,axiom,
% 0.26/0.46      ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 0.26/0.46  
% 0.26/0.46  % "5.hyps"(8)
% 0.26/0.46  thf(fact_2__092_060open_062mi_A_060_Ax_092_060close_062,axiom,
% 0.26/0.46      ord_less_nat @ mi @ x ).
% 0.26/0.46  
% 0.26/0.46  % \<open>mi < x\<close>
% 0.26/0.46  thf(fact_3_less__exp,axiom,
% 0.26/0.46      ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % less_exp
% 0.26/0.46  thf(fact_4_semiring__norm_I85_J,axiom,
% 0.26/0.46      ! [M: num] :
% 0.26/0.46        ( ( bit0 @ M )
% 0.26/0.46       != one ) ).
% 0.26/0.46  
% 0.26/0.46  % semiring_norm(85)
% 0.26/0.46  thf(fact_5_semiring__norm_I83_J,axiom,
% 0.26/0.46      ! [N: num] :
% 0.26/0.46        ( one
% 0.26/0.46       != ( bit0 @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % semiring_norm(83)
% 0.26/0.46  thf(fact_6_numeral__less__iff,axiom,
% 0.26/0.46      ! [M: num,N: num] :
% 0.26/0.46        ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 0.26/0.46        = ( ord_less_num @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_less_iff
% 0.26/0.46  thf(fact_7_numeral__less__iff,axiom,
% 0.26/0.46      ! [M: num,N: num] :
% 0.26/0.46        ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 0.26/0.46        = ( ord_less_num @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_less_iff
% 0.26/0.46  thf(fact_8_numeral__less__iff,axiom,
% 0.26/0.46      ! [M: num,N: num] :
% 0.26/0.46        ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.26/0.46        = ( ord_less_num @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_less_iff
% 0.26/0.46  thf(fact_9_numeral__less__iff,axiom,
% 0.26/0.46      ! [M: num,N: num] :
% 0.26/0.46        ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.46        = ( ord_less_num @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_less_iff
% 0.26/0.46  thf(fact_10__092_060open_0622_A_092_060le_062_Adeg_092_060close_062,axiom,
% 0.26/0.46      ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ).
% 0.26/0.46  
% 0.26/0.46  % \<open>2 \<le> deg\<close>
% 0.26/0.46  thf(fact_11_verit__eq__simplify_I8_J,axiom,
% 0.26/0.46      ! [X2: num,Y2: num] :
% 0.26/0.46        ( ( ( bit0 @ X2 )
% 0.26/0.46          = ( bit0 @ Y2 ) )
% 0.26/0.46        = ( X2 = Y2 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % verit_eq_simplify(8)
% 0.26/0.46  thf(fact_12_semiring__norm_I87_J,axiom,
% 0.26/0.46      ! [M: num,N: num] :
% 0.26/0.46        ( ( ( bit0 @ M )
% 0.26/0.46          = ( bit0 @ N ) )
% 0.26/0.46        = ( M = N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % semiring_norm(87)
% 0.26/0.46  thf(fact_13_numeral__eq__iff,axiom,
% 0.26/0.46      ! [M: num,N: num] :
% 0.26/0.46        ( ( ( numera6690914467698888265omplex @ M )
% 0.26/0.46          = ( numera6690914467698888265omplex @ N ) )
% 0.26/0.46        = ( M = N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_eq_iff
% 0.26/0.46  thf(fact_14_numeral__eq__iff,axiom,
% 0.26/0.46      ! [M: num,N: num] :
% 0.26/0.46        ( ( ( numeral_numeral_real @ M )
% 0.26/0.46          = ( numeral_numeral_real @ N ) )
% 0.26/0.46        = ( M = N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_eq_iff
% 0.26/0.46  thf(fact_15_numeral__eq__iff,axiom,
% 0.26/0.46      ! [M: num,N: num] :
% 0.26/0.46        ( ( ( numeral_numeral_rat @ M )
% 0.26/0.46          = ( numeral_numeral_rat @ N ) )
% 0.26/0.46        = ( M = N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_eq_iff
% 0.26/0.46  thf(fact_16_numeral__eq__iff,axiom,
% 0.26/0.46      ! [M: num,N: num] :
% 0.26/0.46        ( ( ( numeral_numeral_nat @ M )
% 0.26/0.46          = ( numeral_numeral_nat @ N ) )
% 0.26/0.46        = ( M = N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_eq_iff
% 0.26/0.46  thf(fact_17_numeral__eq__iff,axiom,
% 0.26/0.46      ! [M: num,N: num] :
% 0.26/0.46        ( ( ( numeral_numeral_int @ M )
% 0.26/0.46          = ( numeral_numeral_int @ N ) )
% 0.26/0.46        = ( M = N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_eq_iff
% 0.26/0.46  thf(fact_18_verit__eq__simplify_I10_J,axiom,
% 0.26/0.46      ! [X2: num] :
% 0.26/0.46        ( one
% 0.26/0.46       != ( bit0 @ X2 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % verit_eq_simplify(10)
% 0.26/0.46  thf(fact_19_local_Opower__def,axiom,
% 0.26/0.46      ( vEBT_VEBT_power
% 0.26/0.46      = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 0.26/0.46  
% 0.26/0.46  % local.power_def
% 0.26/0.46  thf(fact_20__C5_Ohyps_C_I7_J,axiom,
% 0.26/0.46      ord_less_eq_nat @ mi @ ma ).
% 0.26/0.46  
% 0.26/0.46  % "5.hyps"(7)
% 0.26/0.46  thf(fact_21__092_060open_062_092_060not_062_A_Ix_A_061_Ami_A_092_060and_062_Ax_A_061_Ama_J_092_060close_062,axiom,
% 0.26/0.46      ~ ( ( x = mi )
% 0.26/0.46        & ( x = ma ) ) ).
% 0.26/0.46  
% 0.26/0.46  % \<open>\<not> (x = mi \<and> x = ma)\<close>
% 0.26/0.46  thf(fact_22_max__in__set__def,axiom,
% 0.26/0.46      ( vEBT_VEBT_max_in_set
% 0.26/0.46      = ( ^ [Xs: set_nat,X: nat] :
% 0.26/0.46            ( ( member_nat @ X @ Xs )
% 0.26/0.46            & ! [Y: nat] :
% 0.26/0.46                ( ( member_nat @ Y @ Xs )
% 0.26/0.46               => ( ord_less_eq_nat @ Y @ X ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % max_in_set_def
% 0.26/0.46  thf(fact_23_min__in__set__def,axiom,
% 0.26/0.46      ( vEBT_VEBT_min_in_set
% 0.26/0.46      = ( ^ [Xs: set_nat,X: nat] :
% 0.26/0.46            ( ( member_nat @ X @ Xs )
% 0.26/0.46            & ! [Y: nat] :
% 0.26/0.46                ( ( member_nat @ Y @ Xs )
% 0.26/0.46               => ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % min_in_set_def
% 0.26/0.46  thf(fact_24__092_060open_062x_A_092_060le_062_Ama_A_092_060and_062_Ami_A_092_060le_062_Ax_092_060close_062,axiom,
% 0.26/0.46      ( ( ord_less_eq_nat @ x @ ma )
% 0.26/0.46      & ( ord_less_eq_nat @ mi @ x ) ) ).
% 0.26/0.46  
% 0.26/0.46  % \<open>x \<le> ma \<and> mi \<le> x\<close>
% 0.26/0.46  thf(fact_25_numeral__le__iff,axiom,
% 0.26/0.46      ! [M: num,N: num] :
% 0.26/0.46        ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 0.26/0.46        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_le_iff
% 0.26/0.46  thf(fact_26_numeral__le__iff,axiom,
% 0.26/0.46      ! [M: num,N: num] :
% 0.26/0.46        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 0.26/0.46        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_le_iff
% 0.26/0.46  thf(fact_27_numeral__le__iff,axiom,
% 0.26/0.46      ! [M: num,N: num] :
% 0.26/0.46        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.26/0.46        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_le_iff
% 0.26/0.46  thf(fact_28_numeral__le__iff,axiom,
% 0.26/0.46      ! [M: num,N: num] :
% 0.26/0.46        ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.46        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_le_iff
% 0.26/0.46  thf(fact_29_semiring__norm_I78_J,axiom,
% 0.26/0.46      ! [M: num,N: num] :
% 0.26/0.46        ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.26/0.46        = ( ord_less_num @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % semiring_norm(78)
% 0.26/0.46  thf(fact_30_semiring__norm_I75_J,axiom,
% 0.26/0.46      ! [M: num] :
% 0.26/0.46        ~ ( ord_less_num @ M @ one ) ).
% 0.26/0.46  
% 0.26/0.46  % semiring_norm(75)
% 0.26/0.46  thf(fact_31_semiring__norm_I76_J,axiom,
% 0.26/0.46      ! [N: num] : ( ord_less_num @ one @ ( bit0 @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % semiring_norm(76)
% 0.26/0.46  thf(fact_32_verit__comp__simplify1_I2_J,axiom,
% 0.26/0.46      ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 0.26/0.46  
% 0.26/0.46  % verit_comp_simplify1(2)
% 0.26/0.46  thf(fact_33_verit__comp__simplify1_I2_J,axiom,
% 0.26/0.46      ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 0.26/0.46  
% 0.26/0.46  % verit_comp_simplify1(2)
% 0.26/0.46  thf(fact_34_verit__comp__simplify1_I2_J,axiom,
% 0.26/0.46      ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 0.26/0.46  
% 0.26/0.46  % verit_comp_simplify1(2)
% 0.26/0.46  thf(fact_35_verit__comp__simplify1_I2_J,axiom,
% 0.26/0.46      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.26/0.46  
% 0.26/0.46  % verit_comp_simplify1(2)
% 0.26/0.46  thf(fact_36_verit__comp__simplify1_I2_J,axiom,
% 0.26/0.46      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 0.26/0.46  
% 0.26/0.46  % verit_comp_simplify1(2)
% 0.26/0.46  thf(fact_37_verit__la__disequality,axiom,
% 0.26/0.46      ! [A: rat,B: rat] :
% 0.26/0.46        ( ( A = B )
% 0.26/0.46        | ~ ( ord_less_eq_rat @ A @ B )
% 0.26/0.46        | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 0.26/0.46  
% 0.26/0.46  % verit_la_disequality
% 0.26/0.46  thf(fact_38_verit__la__disequality,axiom,
% 0.26/0.46      ! [A: num,B: num] :
% 0.26/0.46        ( ( A = B )
% 0.26/0.46        | ~ ( ord_less_eq_num @ A @ B )
% 0.26/0.46        | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 0.26/0.46  
% 0.26/0.46  % verit_la_disequality
% 0.26/0.46  thf(fact_39_verit__la__disequality,axiom,
% 0.26/0.46      ! [A: nat,B: nat] :
% 0.26/0.46        ( ( A = B )
% 0.26/0.46        | ~ ( ord_less_eq_nat @ A @ B )
% 0.26/0.46        | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 0.26/0.46  
% 0.26/0.46  % verit_la_disequality
% 0.26/0.46  thf(fact_40_verit__la__disequality,axiom,
% 0.26/0.46      ! [A: int,B: int] :
% 0.26/0.46        ( ( A = B )
% 0.26/0.46        | ~ ( ord_less_eq_int @ A @ B )
% 0.26/0.46        | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 0.26/0.46  
% 0.26/0.46  % verit_la_disequality
% 0.26/0.46  thf(fact_41_verit__comp__simplify1_I3_J,axiom,
% 0.26/0.46      ! [B2: real,A2: real] :
% 0.26/0.46        ( ( ~ ( ord_less_eq_real @ B2 @ A2 ) )
% 0.26/0.46        = ( ord_less_real @ A2 @ B2 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % verit_comp_simplify1(3)
% 0.26/0.46  thf(fact_42_verit__comp__simplify1_I3_J,axiom,
% 0.26/0.46      ! [B2: rat,A2: rat] :
% 0.26/0.46        ( ( ~ ( ord_less_eq_rat @ B2 @ A2 ) )
% 0.26/0.46        = ( ord_less_rat @ A2 @ B2 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % verit_comp_simplify1(3)
% 0.26/0.46  thf(fact_43_verit__comp__simplify1_I3_J,axiom,
% 0.26/0.46      ! [B2: num,A2: num] :
% 0.26/0.46        ( ( ~ ( ord_less_eq_num @ B2 @ A2 ) )
% 0.26/0.46        = ( ord_less_num @ A2 @ B2 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % verit_comp_simplify1(3)
% 0.26/0.46  thf(fact_44_verit__comp__simplify1_I3_J,axiom,
% 0.26/0.46      ! [B2: nat,A2: nat] :
% 0.26/0.46        ( ( ~ ( ord_less_eq_nat @ B2 @ A2 ) )
% 0.26/0.46        = ( ord_less_nat @ A2 @ B2 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % verit_comp_simplify1(3)
% 0.26/0.46  thf(fact_45_verit__comp__simplify1_I3_J,axiom,
% 0.26/0.46      ! [B2: int,A2: int] :
% 0.26/0.46        ( ( ~ ( ord_less_eq_int @ B2 @ A2 ) )
% 0.26/0.46        = ( ord_less_int @ A2 @ B2 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % verit_comp_simplify1(3)
% 0.26/0.46  thf(fact_46_power2__nat__le__imp__le,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 0.26/0.46       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % power2_nat_le_imp_le
% 0.26/0.46  thf(fact_47_power2__nat__le__eq__le,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.46        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % power2_nat_le_eq_le
% 0.26/0.46  thf(fact_48_self__le__ge2__pow,axiom,
% 0.26/0.46      ! [K: nat,M: nat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.26/0.46       => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % self_le_ge2_pow
% 0.26/0.46  thf(fact_49_verit__comp__simplify1_I1_J,axiom,
% 0.26/0.46      ! [A: real] :
% 0.26/0.46        ~ ( ord_less_real @ A @ A ) ).
% 0.26/0.46  
% 0.26/0.46  % verit_comp_simplify1(1)
% 0.26/0.46  thf(fact_50_verit__comp__simplify1_I1_J,axiom,
% 0.26/0.46      ! [A: rat] :
% 0.26/0.46        ~ ( ord_less_rat @ A @ A ) ).
% 0.26/0.46  
% 0.26/0.46  % verit_comp_simplify1(1)
% 0.26/0.46  thf(fact_51_verit__comp__simplify1_I1_J,axiom,
% 0.26/0.46      ! [A: num] :
% 0.26/0.46        ~ ( ord_less_num @ A @ A ) ).
% 0.26/0.46  
% 0.26/0.46  % verit_comp_simplify1(1)
% 0.26/0.46  thf(fact_52_verit__comp__simplify1_I1_J,axiom,
% 0.26/0.46      ! [A: nat] :
% 0.26/0.46        ~ ( ord_less_nat @ A @ A ) ).
% 0.26/0.46  
% 0.26/0.46  % verit_comp_simplify1(1)
% 0.26/0.46  thf(fact_53_verit__comp__simplify1_I1_J,axiom,
% 0.26/0.46      ! [A: int] :
% 0.26/0.46        ~ ( ord_less_int @ A @ A ) ).
% 0.26/0.46  
% 0.26/0.46  % verit_comp_simplify1(1)
% 0.26/0.46  thf(fact_54_enat__ord__number_I2_J,axiom,
% 0.26/0.46      ! [M: num,N: num] :
% 0.26/0.46        ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 0.26/0.46        = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % enat_ord_number(2)
% 0.26/0.46  thf(fact_55_power__numeral,axiom,
% 0.26/0.46      ! [K: num,L: num] :
% 0.26/0.46        ( ( power_power_complex @ ( numera6690914467698888265omplex @ K ) @ ( numeral_numeral_nat @ L ) )
% 0.26/0.46        = ( numera6690914467698888265omplex @ ( pow @ K @ L ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % power_numeral
% 0.26/0.46  thf(fact_56_power__numeral,axiom,
% 0.26/0.46      ! [K: num,L: num] :
% 0.26/0.46        ( ( power_power_real @ ( numeral_numeral_real @ K ) @ ( numeral_numeral_nat @ L ) )
% 0.26/0.46        = ( numeral_numeral_real @ ( pow @ K @ L ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % power_numeral
% 0.26/0.46  thf(fact_57_power__numeral,axiom,
% 0.26/0.46      ! [K: num,L: num] :
% 0.26/0.46        ( ( power_power_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_nat @ L ) )
% 0.26/0.46        = ( numeral_numeral_rat @ ( pow @ K @ L ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % power_numeral
% 0.26/0.46  thf(fact_58_power__numeral,axiom,
% 0.26/0.46      ! [K: num,L: num] :
% 0.26/0.46        ( ( power_power_nat @ ( numeral_numeral_nat @ K ) @ ( numeral_numeral_nat @ L ) )
% 0.26/0.46        = ( numeral_numeral_nat @ ( pow @ K @ L ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % power_numeral
% 0.26/0.46  thf(fact_59_power__numeral,axiom,
% 0.26/0.46      ! [K: num,L: num] :
% 0.26/0.46        ( ( power_power_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_nat @ L ) )
% 0.26/0.46        = ( numeral_numeral_int @ ( pow @ K @ L ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % power_numeral
% 0.26/0.46  thf(fact_60_order__refl,axiom,
% 0.26/0.46      ! [X3: set_nat] : ( ord_less_eq_set_nat @ X3 @ X3 ) ).
% 0.26/0.46  
% 0.26/0.46  % order_refl
% 0.26/0.46  thf(fact_61_order__refl,axiom,
% 0.26/0.46      ! [X3: rat] : ( ord_less_eq_rat @ X3 @ X3 ) ).
% 0.26/0.46  
% 0.26/0.46  % order_refl
% 0.26/0.46  thf(fact_62_order__refl,axiom,
% 0.26/0.46      ! [X3: num] : ( ord_less_eq_num @ X3 @ X3 ) ).
% 0.26/0.46  
% 0.26/0.46  % order_refl
% 0.26/0.46  thf(fact_63_order__refl,axiom,
% 0.26/0.46      ! [X3: nat] : ( ord_less_eq_nat @ X3 @ X3 ) ).
% 0.26/0.46  
% 0.26/0.46  % order_refl
% 0.26/0.46  thf(fact_64_order__refl,axiom,
% 0.26/0.46      ! [X3: int] : ( ord_less_eq_int @ X3 @ X3 ) ).
% 0.26/0.46  
% 0.26/0.46  % order_refl
% 0.26/0.46  thf(fact_65_dual__order_Orefl,axiom,
% 0.26/0.46      ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.refl
% 0.26/0.46  thf(fact_66_dual__order_Orefl,axiom,
% 0.26/0.46      ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.refl
% 0.26/0.46  thf(fact_67_dual__order_Orefl,axiom,
% 0.26/0.46      ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.refl
% 0.26/0.46  thf(fact_68_dual__order_Orefl,axiom,
% 0.26/0.46      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.refl
% 0.26/0.46  thf(fact_69_dual__order_Orefl,axiom,
% 0.26/0.46      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.refl
% 0.26/0.46  thf(fact_70_power__shift,axiom,
% 0.26/0.46      ! [X3: nat,Y3: nat,Z: nat] :
% 0.26/0.46        ( ( ( power_power_nat @ X3 @ Y3 )
% 0.26/0.46          = Z )
% 0.26/0.46        = ( ( vEBT_VEBT_power @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) )
% 0.26/0.46          = ( some_nat @ Z ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % power_shift
% 0.26/0.46  thf(fact_71_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.26/0.46      ! [X3: nat,I: num,N: nat] :
% 0.26/0.46        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 0.26/0.46        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_le_numeral_power_cancel_iff
% 0.26/0.46  thf(fact_72_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.26/0.46      ! [X3: nat,I: num,N: nat] :
% 0.26/0.46        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 0.26/0.46        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_le_numeral_power_cancel_iff
% 0.26/0.46  thf(fact_73_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.26/0.46      ! [X3: nat,I: num,N: nat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 0.26/0.46        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_le_numeral_power_cancel_iff
% 0.26/0.46  thf(fact_74_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.26/0.46      ! [X3: nat,I: num,N: nat] :
% 0.26/0.46        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 0.26/0.46        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_le_numeral_power_cancel_iff
% 0.26/0.46  thf(fact_75_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [I: num,N: nat,X3: nat] :
% 0.26/0.46        ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X3 ) )
% 0.26/0.46        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_power_le_of_nat_cancel_iff
% 0.26/0.46  thf(fact_76_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [I: num,N: nat,X3: nat] :
% 0.26/0.46        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X3 ) )
% 0.26/0.46        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_power_le_of_nat_cancel_iff
% 0.26/0.46  thf(fact_77_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [I: num,N: nat,X3: nat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X3 ) )
% 0.26/0.46        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_power_le_of_nat_cancel_iff
% 0.26/0.46  thf(fact_78_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [I: num,N: nat,X3: nat] :
% 0.26/0.46        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X3 ) )
% 0.26/0.46        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_power_le_of_nat_cancel_iff
% 0.26/0.46  thf(fact_79_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.26/0.46      ! [X3: nat,I: num,N: nat] :
% 0.26/0.46        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 0.26/0.46        = ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_less_numeral_power_cancel_iff
% 0.26/0.46  thf(fact_80_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.26/0.46      ! [X3: nat,I: num,N: nat] :
% 0.26/0.46        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 0.26/0.46        = ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_less_numeral_power_cancel_iff
% 0.26/0.46  thf(fact_81_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.26/0.46      ! [X3: nat,I: num,N: nat] :
% 0.26/0.46        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 0.26/0.46        = ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_less_numeral_power_cancel_iff
% 0.26/0.46  thf(fact_82_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.26/0.46      ! [X3: nat,I: num,N: nat] :
% 0.26/0.46        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 0.26/0.46        = ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_less_numeral_power_cancel_iff
% 0.26/0.46  thf(fact_83_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [I: num,N: nat,X3: nat] :
% 0.26/0.46        ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X3 ) )
% 0.26/0.46        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_power_less_of_nat_cancel_iff
% 0.26/0.46  thf(fact_84_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [I: num,N: nat,X3: nat] :
% 0.26/0.46        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X3 ) )
% 0.26/0.46        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_power_less_of_nat_cancel_iff
% 0.26/0.46  thf(fact_85_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [I: num,N: nat,X3: nat] :
% 0.26/0.46        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X3 ) )
% 0.26/0.46        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_power_less_of_nat_cancel_iff
% 0.26/0.46  thf(fact_86_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [I: num,N: nat,X3: nat] :
% 0.26/0.46        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X3 ) )
% 0.26/0.46        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_power_less_of_nat_cancel_iff
% 0.26/0.46  thf(fact_87_nat__descend__induct,axiom,
% 0.26/0.46      ! [N: nat,P: nat > $o,M: nat] :
% 0.26/0.46        ( ! [K2: nat] :
% 0.26/0.46            ( ( ord_less_nat @ N @ K2 )
% 0.26/0.46           => ( P @ K2 ) )
% 0.26/0.46       => ( ! [K2: nat] :
% 0.26/0.46              ( ( ord_less_eq_nat @ K2 @ N )
% 0.26/0.46             => ( ! [I2: nat] :
% 0.26/0.46                    ( ( ord_less_nat @ K2 @ I2 )
% 0.26/0.46                   => ( P @ I2 ) )
% 0.26/0.46               => ( P @ K2 ) ) )
% 0.26/0.46         => ( P @ M ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % nat_descend_induct
% 0.26/0.46  thf(fact_88_less__mono__imp__le__mono,axiom,
% 0.26/0.46      ! [F: nat > nat,I: nat,J: nat] :
% 0.26/0.46        ( ! [I3: nat,J2: nat] :
% 0.26/0.46            ( ( ord_less_nat @ I3 @ J2 )
% 0.26/0.46           => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 0.26/0.46       => ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.46         => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % less_mono_imp_le_mono
% 0.26/0.46  thf(fact_89_of__nat__eq__iff,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ( semiri8010041392384452111omplex @ M )
% 0.26/0.46          = ( semiri8010041392384452111omplex @ N ) )
% 0.26/0.46        = ( M = N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_eq_iff
% 0.26/0.46  thf(fact_90_of__nat__eq__iff,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ( semiri5074537144036343181t_real @ M )
% 0.26/0.46          = ( semiri5074537144036343181t_real @ N ) )
% 0.26/0.46        = ( M = N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_eq_iff
% 0.26/0.46  thf(fact_91_of__nat__eq__iff,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ( semiri681578069525770553at_rat @ M )
% 0.26/0.46          = ( semiri681578069525770553at_rat @ N ) )
% 0.26/0.46        = ( M = N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_eq_iff
% 0.26/0.46  thf(fact_92_of__nat__eq__iff,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ( semiri1316708129612266289at_nat @ M )
% 0.26/0.46          = ( semiri1316708129612266289at_nat @ N ) )
% 0.26/0.46        = ( M = N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_eq_iff
% 0.26/0.46  thf(fact_93_of__nat__eq__iff,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ( semiri1314217659103216013at_int @ M )
% 0.26/0.46          = ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.46        = ( M = N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_eq_iff
% 0.26/0.46  thf(fact_94_semiring__norm_I71_J,axiom,
% 0.26/0.46      ! [M: num,N: num] :
% 0.26/0.46        ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.26/0.46        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % semiring_norm(71)
% 0.26/0.46  thf(fact_95_mem__Collect__eq,axiom,
% 0.26/0.46      ! [A: option_nat,P: option_nat > $o] :
% 0.26/0.46        ( ( member_option_nat @ A @ ( collect_option_nat @ P ) )
% 0.26/0.46        = ( P @ A ) ) ).
% 0.26/0.46  
% 0.26/0.46  % mem_Collect_eq
% 0.26/0.46  thf(fact_96_mem__Collect__eq,axiom,
% 0.26/0.46      ! [A: real,P: real > $o] :
% 0.26/0.46        ( ( member_real @ A @ ( collect_real @ P ) )
% 0.26/0.46        = ( P @ A ) ) ).
% 0.26/0.46  
% 0.26/0.46  % mem_Collect_eq
% 0.26/0.46  thf(fact_97_mem__Collect__eq,axiom,
% 0.26/0.46      ! [A: list_nat,P: list_nat > $o] :
% 0.26/0.46        ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 0.26/0.46        = ( P @ A ) ) ).
% 0.26/0.46  
% 0.26/0.46  % mem_Collect_eq
% 0.26/0.46  thf(fact_98_mem__Collect__eq,axiom,
% 0.26/0.46      ! [A: set_nat,P: set_nat > $o] :
% 0.26/0.46        ( ( member_set_nat @ A @ ( collect_set_nat @ P ) )
% 0.26/0.46        = ( P @ A ) ) ).
% 0.26/0.46  
% 0.26/0.46  % mem_Collect_eq
% 0.26/0.46  thf(fact_99_mem__Collect__eq,axiom,
% 0.26/0.46      ! [A: nat,P: nat > $o] :
% 0.26/0.46        ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.26/0.46        = ( P @ A ) ) ).
% 0.26/0.46  
% 0.26/0.46  % mem_Collect_eq
% 0.26/0.46  thf(fact_100_mem__Collect__eq,axiom,
% 0.26/0.46      ! [A: int,P: int > $o] :
% 0.26/0.46        ( ( member_int @ A @ ( collect_int @ P ) )
% 0.26/0.46        = ( P @ A ) ) ).
% 0.26/0.46  
% 0.26/0.46  % mem_Collect_eq
% 0.26/0.46  thf(fact_101_Collect__mem__eq,axiom,
% 0.26/0.46      ! [A3: set_option_nat] :
% 0.26/0.46        ( ( collect_option_nat
% 0.26/0.46          @ ^ [X: option_nat] : ( member_option_nat @ X @ A3 ) )
% 0.26/0.46        = A3 ) ).
% 0.26/0.46  
% 0.26/0.46  % Collect_mem_eq
% 0.26/0.46  thf(fact_102_Collect__mem__eq,axiom,
% 0.26/0.46      ! [A3: set_real] :
% 0.26/0.46        ( ( collect_real
% 0.26/0.46          @ ^ [X: real] : ( member_real @ X @ A3 ) )
% 0.26/0.46        = A3 ) ).
% 0.26/0.46  
% 0.26/0.46  % Collect_mem_eq
% 0.26/0.46  thf(fact_103_Collect__mem__eq,axiom,
% 0.26/0.46      ! [A3: set_list_nat] :
% 0.26/0.46        ( ( collect_list_nat
% 0.26/0.46          @ ^ [X: list_nat] : ( member_list_nat @ X @ A3 ) )
% 0.26/0.46        = A3 ) ).
% 0.26/0.46  
% 0.26/0.46  % Collect_mem_eq
% 0.26/0.46  thf(fact_104_Collect__mem__eq,axiom,
% 0.26/0.46      ! [A3: set_set_nat] :
% 0.26/0.46        ( ( collect_set_nat
% 0.26/0.46          @ ^ [X: set_nat] : ( member_set_nat @ X @ A3 ) )
% 0.26/0.46        = A3 ) ).
% 0.26/0.46  
% 0.26/0.46  % Collect_mem_eq
% 0.26/0.46  thf(fact_105_Collect__mem__eq,axiom,
% 0.26/0.46      ! [A3: set_nat] :
% 0.26/0.46        ( ( collect_nat
% 0.26/0.46          @ ^ [X: nat] : ( member_nat @ X @ A3 ) )
% 0.26/0.46        = A3 ) ).
% 0.26/0.46  
% 0.26/0.46  % Collect_mem_eq
% 0.26/0.46  thf(fact_106_Collect__mem__eq,axiom,
% 0.26/0.46      ! [A3: set_int] :
% 0.26/0.46        ( ( collect_int
% 0.26/0.46          @ ^ [X: int] : ( member_int @ X @ A3 ) )
% 0.26/0.46        = A3 ) ).
% 0.26/0.46  
% 0.26/0.46  % Collect_mem_eq
% 0.26/0.46  thf(fact_107_Collect__cong,axiom,
% 0.26/0.46      ! [P: real > $o,Q: real > $o] :
% 0.26/0.46        ( ! [X4: real] :
% 0.26/0.46            ( ( P @ X4 )
% 0.26/0.46            = ( Q @ X4 ) )
% 0.26/0.46       => ( ( collect_real @ P )
% 0.26/0.46          = ( collect_real @ Q ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % Collect_cong
% 0.26/0.46  thf(fact_108_Collect__cong,axiom,
% 0.26/0.46      ! [P: list_nat > $o,Q: list_nat > $o] :
% 0.26/0.46        ( ! [X4: list_nat] :
% 0.26/0.46            ( ( P @ X4 )
% 0.26/0.46            = ( Q @ X4 ) )
% 0.26/0.46       => ( ( collect_list_nat @ P )
% 0.26/0.46          = ( collect_list_nat @ Q ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % Collect_cong
% 0.26/0.46  thf(fact_109_Collect__cong,axiom,
% 0.26/0.46      ! [P: set_nat > $o,Q: set_nat > $o] :
% 0.26/0.46        ( ! [X4: set_nat] :
% 0.26/0.46            ( ( P @ X4 )
% 0.26/0.46            = ( Q @ X4 ) )
% 0.26/0.46       => ( ( collect_set_nat @ P )
% 0.26/0.46          = ( collect_set_nat @ Q ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % Collect_cong
% 0.26/0.46  thf(fact_110_Collect__cong,axiom,
% 0.26/0.46      ! [P: nat > $o,Q: nat > $o] :
% 0.26/0.46        ( ! [X4: nat] :
% 0.26/0.46            ( ( P @ X4 )
% 0.26/0.46            = ( Q @ X4 ) )
% 0.26/0.46       => ( ( collect_nat @ P )
% 0.26/0.46          = ( collect_nat @ Q ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % Collect_cong
% 0.26/0.46  thf(fact_111_Collect__cong,axiom,
% 0.26/0.46      ! [P: int > $o,Q: int > $o] :
% 0.26/0.46        ( ! [X4: int] :
% 0.26/0.46            ( ( P @ X4 )
% 0.26/0.46            = ( Q @ X4 ) )
% 0.26/0.46       => ( ( collect_int @ P )
% 0.26/0.46          = ( collect_int @ Q ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % Collect_cong
% 0.26/0.46  thf(fact_112_semiring__norm_I68_J,axiom,
% 0.26/0.46      ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 0.26/0.46  
% 0.26/0.46  % semiring_norm(68)
% 0.26/0.46  thf(fact_113_of__nat__numeral,axiom,
% 0.26/0.46      ! [N: num] :
% 0.26/0.46        ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N ) )
% 0.26/0.46        = ( numera6690914467698888265omplex @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_numeral
% 0.26/0.46  thf(fact_114_of__nat__numeral,axiom,
% 0.26/0.46      ! [N: num] :
% 0.26/0.46        ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 0.26/0.46        = ( numeral_numeral_real @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_numeral
% 0.26/0.46  thf(fact_115_of__nat__numeral,axiom,
% 0.26/0.46      ! [N: num] :
% 0.26/0.46        ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N ) )
% 0.26/0.46        = ( numeral_numeral_rat @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_numeral
% 0.26/0.46  thf(fact_116_of__nat__numeral,axiom,
% 0.26/0.46      ! [N: num] :
% 0.26/0.46        ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 0.26/0.46        = ( numeral_numeral_nat @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_numeral
% 0.26/0.46  thf(fact_117_of__nat__numeral,axiom,
% 0.26/0.46      ! [N: num] :
% 0.26/0.46        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 0.26/0.46        = ( numeral_numeral_int @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_numeral
% 0.26/0.46  thf(fact_118_of__nat__less__iff,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 0.26/0.46        = ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_less_iff
% 0.26/0.46  thf(fact_119_of__nat__less__iff,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 0.26/0.46        = ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_less_iff
% 0.26/0.46  thf(fact_120_of__nat__less__iff,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.26/0.46        = ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_less_iff
% 0.26/0.46  thf(fact_121_of__nat__less__iff,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.46        = ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_less_iff
% 0.26/0.46  thf(fact_122_of__nat__le__iff,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 0.26/0.46        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_le_iff
% 0.26/0.46  thf(fact_123_of__nat__le__iff,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 0.26/0.46        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_le_iff
% 0.26/0.46  thf(fact_124_of__nat__le__iff,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.26/0.46        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_le_iff
% 0.26/0.46  thf(fact_125_of__nat__le__iff,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.46        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_le_iff
% 0.26/0.46  thf(fact_126_of__nat__power,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N ) )
% 0.26/0.46        = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_power
% 0.26/0.46  thf(fact_127_of__nat__power,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N ) )
% 0.26/0.46        = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_power
% 0.26/0.46  thf(fact_128_of__nat__power,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( semiri681578069525770553at_rat @ ( power_power_nat @ M @ N ) )
% 0.26/0.46        = ( power_power_rat @ ( semiri681578069525770553at_rat @ M ) @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_power
% 0.26/0.46  thf(fact_129_of__nat__power,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N ) )
% 0.26/0.46        = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_power
% 0.26/0.46  thf(fact_130_of__nat__power,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N ) )
% 0.26/0.46        = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_power
% 0.26/0.46  thf(fact_131_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.26/0.46      ! [B: nat,W: nat,X3: nat] :
% 0.26/0.46        ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 0.26/0.46          = ( semiri8010041392384452111omplex @ X3 ) )
% 0.26/0.46        = ( ( power_power_nat @ B @ W )
% 0.26/0.46          = X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_eq_of_nat_power_cancel_iff
% 0.26/0.46  thf(fact_132_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.26/0.46      ! [B: nat,W: nat,X3: nat] :
% 0.26/0.46        ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 0.26/0.46          = ( semiri5074537144036343181t_real @ X3 ) )
% 0.26/0.46        = ( ( power_power_nat @ B @ W )
% 0.26/0.46          = X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_eq_of_nat_power_cancel_iff
% 0.26/0.46  thf(fact_133_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.26/0.46      ! [B: nat,W: nat,X3: nat] :
% 0.26/0.46        ( ( ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W )
% 0.26/0.46          = ( semiri681578069525770553at_rat @ X3 ) )
% 0.26/0.46        = ( ( power_power_nat @ B @ W )
% 0.26/0.46          = X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_eq_of_nat_power_cancel_iff
% 0.26/0.46  thf(fact_134_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.26/0.46      ! [B: nat,W: nat,X3: nat] :
% 0.26/0.46        ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 0.26/0.46          = ( semiri1316708129612266289at_nat @ X3 ) )
% 0.26/0.46        = ( ( power_power_nat @ B @ W )
% 0.26/0.46          = X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_eq_of_nat_power_cancel_iff
% 0.26/0.46  thf(fact_135_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.26/0.46      ! [B: nat,W: nat,X3: nat] :
% 0.26/0.46        ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 0.26/0.46          = ( semiri1314217659103216013at_int @ X3 ) )
% 0.26/0.46        = ( ( power_power_nat @ B @ W )
% 0.26/0.46          = X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_eq_of_nat_power_cancel_iff
% 0.26/0.46  thf(fact_136_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [X3: nat,B: nat,W: nat] :
% 0.26/0.46        ( ( ( semiri8010041392384452111omplex @ X3 )
% 0.26/0.46          = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 0.26/0.46        = ( X3
% 0.26/0.46          = ( power_power_nat @ B @ W ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_power_eq_of_nat_cancel_iff
% 0.26/0.46  thf(fact_137_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [X3: nat,B: nat,W: nat] :
% 0.26/0.46        ( ( ( semiri5074537144036343181t_real @ X3 )
% 0.26/0.46          = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 0.26/0.46        = ( X3
% 0.26/0.46          = ( power_power_nat @ B @ W ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_power_eq_of_nat_cancel_iff
% 0.26/0.46  thf(fact_138_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [X3: nat,B: nat,W: nat] :
% 0.26/0.46        ( ( ( semiri681578069525770553at_rat @ X3 )
% 0.26/0.46          = ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 0.26/0.46        = ( X3
% 0.26/0.46          = ( power_power_nat @ B @ W ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_power_eq_of_nat_cancel_iff
% 0.26/0.46  thf(fact_139_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [X3: nat,B: nat,W: nat] :
% 0.26/0.46        ( ( ( semiri1316708129612266289at_nat @ X3 )
% 0.26/0.46          = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 0.26/0.46        = ( X3
% 0.26/0.46          = ( power_power_nat @ B @ W ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_power_eq_of_nat_cancel_iff
% 0.26/0.46  thf(fact_140_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [X3: nat,B: nat,W: nat] :
% 0.26/0.46        ( ( ( semiri1314217659103216013at_int @ X3 )
% 0.26/0.46          = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 0.26/0.46        = ( X3
% 0.26/0.46          = ( power_power_nat @ B @ W ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_power_eq_of_nat_cancel_iff
% 0.26/0.46  thf(fact_141_semiring__norm_I69_J,axiom,
% 0.26/0.46      ! [M: num] :
% 0.26/0.46        ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 0.26/0.46  
% 0.26/0.46  % semiring_norm(69)
% 0.26/0.46  thf(fact_142_enat__ord__number_I1_J,axiom,
% 0.26/0.46      ! [M: num,N: num] :
% 0.26/0.46        ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 0.26/0.46        = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % enat_ord_number(1)
% 0.26/0.46  thf(fact_143_lesseq__shift,axiom,
% 0.26/0.46      ( ord_less_eq_nat
% 0.26/0.46      = ( ^ [X: nat,Y: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X ) @ ( some_nat @ Y ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % lesseq_shift
% 0.26/0.46  thf(fact_144_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [X3: num,N: nat,Y3: nat] :
% 0.26/0.46        ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X3 ) @ N )
% 0.26/0.46          = ( semiri8010041392384452111omplex @ Y3 ) )
% 0.26/0.46        = ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N )
% 0.26/0.46          = Y3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_power_eq_of_nat_cancel_iff
% 0.26/0.46  thf(fact_145_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [X3: num,N: nat,Y3: nat] :
% 0.26/0.46        ( ( ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N )
% 0.26/0.46          = ( semiri5074537144036343181t_real @ Y3 ) )
% 0.26/0.46        = ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N )
% 0.26/0.46          = Y3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_power_eq_of_nat_cancel_iff
% 0.26/0.46  thf(fact_146_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [X3: num,N: nat,Y3: nat] :
% 0.26/0.46        ( ( ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N )
% 0.26/0.46          = ( semiri681578069525770553at_rat @ Y3 ) )
% 0.26/0.46        = ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N )
% 0.26/0.46          = Y3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_power_eq_of_nat_cancel_iff
% 0.26/0.46  thf(fact_147_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [X3: num,N: nat,Y3: nat] :
% 0.26/0.46        ( ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N )
% 0.26/0.46          = ( semiri1316708129612266289at_nat @ Y3 ) )
% 0.26/0.46        = ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N )
% 0.26/0.46          = Y3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_power_eq_of_nat_cancel_iff
% 0.26/0.46  thf(fact_148_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [X3: num,N: nat,Y3: nat] :
% 0.26/0.46        ( ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N )
% 0.26/0.46          = ( semiri1314217659103216013at_int @ Y3 ) )
% 0.26/0.46        = ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N )
% 0.26/0.46          = Y3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % numeral_power_eq_of_nat_cancel_iff
% 0.26/0.46  thf(fact_149_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.26/0.46      ! [Y3: nat,X3: num,N: nat] :
% 0.26/0.46        ( ( ( semiri8010041392384452111omplex @ Y3 )
% 0.26/0.46          = ( power_power_complex @ ( numera6690914467698888265omplex @ X3 ) @ N ) )
% 0.26/0.46        = ( Y3
% 0.26/0.46          = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % real_of_nat_eq_numeral_power_cancel_iff
% 0.26/0.46  thf(fact_150_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.26/0.46      ! [Y3: nat,X3: num,N: nat] :
% 0.26/0.46        ( ( ( semiri5074537144036343181t_real @ Y3 )
% 0.26/0.46          = ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N ) )
% 0.26/0.46        = ( Y3
% 0.26/0.46          = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % real_of_nat_eq_numeral_power_cancel_iff
% 0.26/0.46  thf(fact_151_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.26/0.46      ! [Y3: nat,X3: num,N: nat] :
% 0.26/0.46        ( ( ( semiri681578069525770553at_rat @ Y3 )
% 0.26/0.46          = ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N ) )
% 0.26/0.46        = ( Y3
% 0.26/0.46          = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % real_of_nat_eq_numeral_power_cancel_iff
% 0.26/0.46  thf(fact_152_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.26/0.46      ! [Y3: nat,X3: num,N: nat] :
% 0.26/0.46        ( ( ( semiri1316708129612266289at_nat @ Y3 )
% 0.26/0.46          = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) )
% 0.26/0.46        = ( Y3
% 0.26/0.46          = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % real_of_nat_eq_numeral_power_cancel_iff
% 0.26/0.46  thf(fact_153_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.26/0.46      ! [Y3: nat,X3: num,N: nat] :
% 0.26/0.46        ( ( ( semiri1314217659103216013at_int @ Y3 )
% 0.26/0.46          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) )
% 0.26/0.46        = ( Y3
% 0.26/0.46          = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % real_of_nat_eq_numeral_power_cancel_iff
% 0.26/0.46  thf(fact_154_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.26/0.46      ! [B: nat,W: nat,X3: nat] :
% 0.26/0.46        ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X3 ) )
% 0.26/0.46        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_less_of_nat_power_cancel_iff
% 0.26/0.46  thf(fact_155_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.26/0.46      ! [B: nat,W: nat,X3: nat] :
% 0.26/0.46        ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X3 ) )
% 0.26/0.46        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_less_of_nat_power_cancel_iff
% 0.26/0.46  thf(fact_156_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.26/0.46      ! [B: nat,W: nat,X3: nat] :
% 0.26/0.46        ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X3 ) )
% 0.26/0.46        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_less_of_nat_power_cancel_iff
% 0.26/0.46  thf(fact_157_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.26/0.46      ! [B: nat,W: nat,X3: nat] :
% 0.26/0.46        ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X3 ) )
% 0.26/0.46        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_less_of_nat_power_cancel_iff
% 0.26/0.46  thf(fact_158_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [X3: nat,B: nat,W: nat] :
% 0.26/0.46        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 0.26/0.46        = ( ord_less_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_power_less_of_nat_cancel_iff
% 0.26/0.46  thf(fact_159_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [X3: nat,B: nat,W: nat] :
% 0.26/0.46        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 0.26/0.46        = ( ord_less_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_power_less_of_nat_cancel_iff
% 0.26/0.46  thf(fact_160_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [X3: nat,B: nat,W: nat] :
% 0.26/0.46        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 0.26/0.46        = ( ord_less_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_power_less_of_nat_cancel_iff
% 0.26/0.46  thf(fact_161_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [X3: nat,B: nat,W: nat] :
% 0.26/0.46        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 0.26/0.46        = ( ord_less_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_power_less_of_nat_cancel_iff
% 0.26/0.46  thf(fact_162_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.26/0.46      ! [B: nat,W: nat,X3: nat] :
% 0.26/0.46        ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X3 ) )
% 0.26/0.46        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_le_of_nat_power_cancel_iff
% 0.26/0.46  thf(fact_163_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.26/0.46      ! [B: nat,W: nat,X3: nat] :
% 0.26/0.46        ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X3 ) )
% 0.26/0.46        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_le_of_nat_power_cancel_iff
% 0.26/0.46  thf(fact_164_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.26/0.46      ! [B: nat,W: nat,X3: nat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X3 ) )
% 0.26/0.46        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_le_of_nat_power_cancel_iff
% 0.26/0.46  thf(fact_165_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.26/0.46      ! [B: nat,W: nat,X3: nat] :
% 0.26/0.46        ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X3 ) )
% 0.26/0.46        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_le_of_nat_power_cancel_iff
% 0.26/0.46  thf(fact_166_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [X3: nat,B: nat,W: nat] :
% 0.26/0.46        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 0.26/0.46        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_power_le_of_nat_cancel_iff
% 0.26/0.46  thf(fact_167_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [X3: nat,B: nat,W: nat] :
% 0.26/0.46        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 0.26/0.46        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_power_le_of_nat_cancel_iff
% 0.26/0.46  thf(fact_168_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [X3: nat,B: nat,W: nat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 0.26/0.46        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_power_le_of_nat_cancel_iff
% 0.26/0.46  thf(fact_169_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.26/0.46      ! [X3: nat,B: nat,W: nat] :
% 0.26/0.46        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 0.26/0.46        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_power_le_of_nat_cancel_iff
% 0.26/0.46  thf(fact_170_enat__less__induct,axiom,
% 0.26/0.46      ! [P: extended_enat > $o,N: extended_enat] :
% 0.26/0.46        ( ! [N2: extended_enat] :
% 0.26/0.46            ( ! [M2: extended_enat] :
% 0.26/0.46                ( ( ord_le72135733267957522d_enat @ M2 @ N2 )
% 0.26/0.46               => ( P @ M2 ) )
% 0.26/0.46           => ( P @ N2 ) )
% 0.26/0.46       => ( P @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % enat_less_induct
% 0.26/0.46  thf(fact_171_nat__int__comparison_I3_J,axiom,
% 0.26/0.46      ( ord_less_eq_nat
% 0.26/0.46      = ( ^ [A4: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % nat_int_comparison(3)
% 0.26/0.46  thf(fact_172_int__ops_I3_J,axiom,
% 0.26/0.46      ! [N: num] :
% 0.26/0.46        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 0.26/0.46        = ( numeral_numeral_int @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % int_ops(3)
% 0.26/0.46  thf(fact_173_nat__int__comparison_I2_J,axiom,
% 0.26/0.46      ( ord_less_nat
% 0.26/0.46      = ( ^ [A4: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % nat_int_comparison(2)
% 0.26/0.46  thf(fact_174_le__num__One__iff,axiom,
% 0.26/0.46      ! [X3: num] :
% 0.26/0.46        ( ( ord_less_eq_num @ X3 @ one )
% 0.26/0.46        = ( X3 = one ) ) ).
% 0.26/0.46  
% 0.26/0.46  % le_num_One_iff
% 0.26/0.46  thf(fact_175_less__imp__of__nat__less,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ord_less_nat @ M @ N )
% 0.26/0.46       => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % less_imp_of_nat_less
% 0.26/0.46  thf(fact_176_less__imp__of__nat__less,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ord_less_nat @ M @ N )
% 0.26/0.46       => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % less_imp_of_nat_less
% 0.26/0.46  thf(fact_177_less__imp__of__nat__less,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ord_less_nat @ M @ N )
% 0.26/0.46       => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % less_imp_of_nat_less
% 0.26/0.46  thf(fact_178_less__imp__of__nat__less,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ord_less_nat @ M @ N )
% 0.26/0.46       => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % less_imp_of_nat_less
% 0.26/0.46  thf(fact_179_of__nat__less__imp__less,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 0.26/0.46       => ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_less_imp_less
% 0.26/0.46  thf(fact_180_of__nat__less__imp__less,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 0.26/0.46       => ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_less_imp_less
% 0.26/0.46  thf(fact_181_of__nat__less__imp__less,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.26/0.46       => ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_less_imp_less
% 0.26/0.46  thf(fact_182_of__nat__less__imp__less,axiom,
% 0.26/0.46      ! [M: nat,N: nat] :
% 0.26/0.46        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.46       => ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_less_imp_less
% 0.26/0.46  thf(fact_183_of__nat__mono,axiom,
% 0.26/0.46      ! [I: nat,J: nat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.46       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_mono
% 0.26/0.46  thf(fact_184_of__nat__mono,axiom,
% 0.26/0.46      ! [I: nat,J: nat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.46       => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_mono
% 0.26/0.46  thf(fact_185_of__nat__mono,axiom,
% 0.26/0.46      ! [I: nat,J: nat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.46       => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_mono
% 0.26/0.46  thf(fact_186_of__nat__mono,axiom,
% 0.26/0.46      ! [I: nat,J: nat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.46       => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % of_nat_mono
% 0.26/0.46  thf(fact_187_pow_Osimps_I1_J,axiom,
% 0.26/0.46      ! [X3: num] :
% 0.26/0.46        ( ( pow @ X3 @ one )
% 0.26/0.46        = X3 ) ).
% 0.26/0.46  
% 0.26/0.46  % pow.simps(1)
% 0.26/0.46  thf(fact_188_order__antisym__conv,axiom,
% 0.26/0.46      ! [Y3: set_nat,X3: set_nat] :
% 0.26/0.46        ( ( ord_less_eq_set_nat @ Y3 @ X3 )
% 0.26/0.46       => ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 0.26/0.46          = ( X3 = Y3 ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_antisym_conv
% 0.26/0.46  thf(fact_189_order__antisym__conv,axiom,
% 0.26/0.46      ! [Y3: rat,X3: rat] :
% 0.26/0.46        ( ( ord_less_eq_rat @ Y3 @ X3 )
% 0.26/0.46       => ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.26/0.46          = ( X3 = Y3 ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_antisym_conv
% 0.26/0.46  thf(fact_190_order__antisym__conv,axiom,
% 0.26/0.46      ! [Y3: num,X3: num] :
% 0.26/0.46        ( ( ord_less_eq_num @ Y3 @ X3 )
% 0.26/0.46       => ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.26/0.46          = ( X3 = Y3 ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_antisym_conv
% 0.26/0.46  thf(fact_191_order__antisym__conv,axiom,
% 0.26/0.46      ! [Y3: nat,X3: nat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ Y3 @ X3 )
% 0.26/0.46       => ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.26/0.46          = ( X3 = Y3 ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_antisym_conv
% 0.26/0.46  thf(fact_192_order__antisym__conv,axiom,
% 0.26/0.46      ! [Y3: int,X3: int] :
% 0.26/0.46        ( ( ord_less_eq_int @ Y3 @ X3 )
% 0.26/0.46       => ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.26/0.46          = ( X3 = Y3 ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_antisym_conv
% 0.26/0.46  thf(fact_193_linorder__le__cases,axiom,
% 0.26/0.46      ! [X3: rat,Y3: rat] :
% 0.26/0.46        ( ~ ( ord_less_eq_rat @ X3 @ Y3 )
% 0.26/0.46       => ( ord_less_eq_rat @ Y3 @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % linorder_le_cases
% 0.26/0.46  thf(fact_194_linorder__le__cases,axiom,
% 0.26/0.46      ! [X3: num,Y3: num] :
% 0.26/0.46        ( ~ ( ord_less_eq_num @ X3 @ Y3 )
% 0.26/0.46       => ( ord_less_eq_num @ Y3 @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % linorder_le_cases
% 0.26/0.46  thf(fact_195_linorder__le__cases,axiom,
% 0.26/0.46      ! [X3: nat,Y3: nat] :
% 0.26/0.46        ( ~ ( ord_less_eq_nat @ X3 @ Y3 )
% 0.26/0.46       => ( ord_less_eq_nat @ Y3 @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % linorder_le_cases
% 0.26/0.46  thf(fact_196_linorder__le__cases,axiom,
% 0.26/0.46      ! [X3: int,Y3: int] :
% 0.26/0.46        ( ~ ( ord_less_eq_int @ X3 @ Y3 )
% 0.26/0.46       => ( ord_less_eq_int @ Y3 @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % linorder_le_cases
% 0.26/0.46  thf(fact_197_ord__le__eq__subst,axiom,
% 0.26/0.46      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.26/0.46        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.46       => ( ( ( F @ B )
% 0.26/0.46            = C )
% 0.26/0.46         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_le_eq_subst
% 0.26/0.46  thf(fact_198_ord__le__eq__subst,axiom,
% 0.26/0.46      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.26/0.46        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.46       => ( ( ( F @ B )
% 0.26/0.46            = C )
% 0.26/0.46         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_le_eq_subst
% 0.26/0.46  thf(fact_199_ord__le__eq__subst,axiom,
% 0.26/0.46      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.26/0.46        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.46       => ( ( ( F @ B )
% 0.26/0.46            = C )
% 0.26/0.46         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_le_eq_subst
% 0.26/0.46  thf(fact_200_ord__le__eq__subst,axiom,
% 0.26/0.46      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.26/0.46        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.46       => ( ( ( F @ B )
% 0.26/0.46            = C )
% 0.26/0.46         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_le_eq_subst
% 0.26/0.46  thf(fact_201_ord__le__eq__subst,axiom,
% 0.26/0.46      ! [A: num,B: num,F: num > rat,C: rat] :
% 0.26/0.46        ( ( ord_less_eq_num @ A @ B )
% 0.26/0.46       => ( ( ( F @ B )
% 0.26/0.46            = C )
% 0.26/0.46         => ( ! [X4: num,Y4: num] :
% 0.26/0.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_le_eq_subst
% 0.26/0.46  thf(fact_202_ord__le__eq__subst,axiom,
% 0.26/0.46      ! [A: num,B: num,F: num > num,C: num] :
% 0.26/0.46        ( ( ord_less_eq_num @ A @ B )
% 0.26/0.46       => ( ( ( F @ B )
% 0.26/0.46            = C )
% 0.26/0.46         => ( ! [X4: num,Y4: num] :
% 0.26/0.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_le_eq_subst
% 0.26/0.46  thf(fact_203_ord__le__eq__subst,axiom,
% 0.26/0.46      ! [A: num,B: num,F: num > nat,C: nat] :
% 0.26/0.46        ( ( ord_less_eq_num @ A @ B )
% 0.26/0.46       => ( ( ( F @ B )
% 0.26/0.46            = C )
% 0.26/0.46         => ( ! [X4: num,Y4: num] :
% 0.26/0.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_le_eq_subst
% 0.26/0.46  thf(fact_204_ord__le__eq__subst,axiom,
% 0.26/0.46      ! [A: num,B: num,F: num > int,C: int] :
% 0.26/0.46        ( ( ord_less_eq_num @ A @ B )
% 0.26/0.46       => ( ( ( F @ B )
% 0.26/0.46            = C )
% 0.26/0.46         => ( ! [X4: num,Y4: num] :
% 0.26/0.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_le_eq_subst
% 0.26/0.46  thf(fact_205_ord__le__eq__subst,axiom,
% 0.26/0.46      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.46       => ( ( ( F @ B )
% 0.26/0.46            = C )
% 0.26/0.46         => ( ! [X4: nat,Y4: nat] :
% 0.26/0.46                ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_le_eq_subst
% 0.26/0.46  thf(fact_206_ord__le__eq__subst,axiom,
% 0.26/0.46      ! [A: nat,B: nat,F: nat > num,C: num] :
% 0.26/0.46        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.46       => ( ( ( F @ B )
% 0.26/0.46            = C )
% 0.26/0.46         => ( ! [X4: nat,Y4: nat] :
% 0.26/0.46                ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_le_eq_subst
% 0.26/0.46  thf(fact_207_ord__eq__le__subst,axiom,
% 0.26/0.46      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.26/0.46        ( ( A
% 0.26/0.46          = ( F @ B ) )
% 0.26/0.46       => ( ( ord_less_eq_rat @ B @ C )
% 0.26/0.46         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_eq_le_subst
% 0.26/0.46  thf(fact_208_ord__eq__le__subst,axiom,
% 0.26/0.46      ! [A: num,F: rat > num,B: rat,C: rat] :
% 0.26/0.46        ( ( A
% 0.26/0.46          = ( F @ B ) )
% 0.26/0.46       => ( ( ord_less_eq_rat @ B @ C )
% 0.26/0.46         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_eq_le_subst
% 0.26/0.46  thf(fact_209_ord__eq__le__subst,axiom,
% 0.26/0.46      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 0.26/0.46        ( ( A
% 0.26/0.46          = ( F @ B ) )
% 0.26/0.46       => ( ( ord_less_eq_rat @ B @ C )
% 0.26/0.46         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_eq_le_subst
% 0.26/0.46  thf(fact_210_ord__eq__le__subst,axiom,
% 0.26/0.46      ! [A: int,F: rat > int,B: rat,C: rat] :
% 0.26/0.46        ( ( A
% 0.26/0.46          = ( F @ B ) )
% 0.26/0.46       => ( ( ord_less_eq_rat @ B @ C )
% 0.26/0.46         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_eq_le_subst
% 0.26/0.46  thf(fact_211_ord__eq__le__subst,axiom,
% 0.26/0.46      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.26/0.46        ( ( A
% 0.26/0.46          = ( F @ B ) )
% 0.26/0.46       => ( ( ord_less_eq_num @ B @ C )
% 0.26/0.46         => ( ! [X4: num,Y4: num] :
% 0.26/0.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_eq_le_subst
% 0.26/0.46  thf(fact_212_ord__eq__le__subst,axiom,
% 0.26/0.46      ! [A: num,F: num > num,B: num,C: num] :
% 0.26/0.46        ( ( A
% 0.26/0.46          = ( F @ B ) )
% 0.26/0.46       => ( ( ord_less_eq_num @ B @ C )
% 0.26/0.46         => ( ! [X4: num,Y4: num] :
% 0.26/0.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_eq_le_subst
% 0.26/0.46  thf(fact_213_ord__eq__le__subst,axiom,
% 0.26/0.46      ! [A: nat,F: num > nat,B: num,C: num] :
% 0.26/0.46        ( ( A
% 0.26/0.46          = ( F @ B ) )
% 0.26/0.46       => ( ( ord_less_eq_num @ B @ C )
% 0.26/0.46         => ( ! [X4: num,Y4: num] :
% 0.26/0.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_eq_le_subst
% 0.26/0.46  thf(fact_214_ord__eq__le__subst,axiom,
% 0.26/0.46      ! [A: int,F: num > int,B: num,C: num] :
% 0.26/0.46        ( ( A
% 0.26/0.46          = ( F @ B ) )
% 0.26/0.46       => ( ( ord_less_eq_num @ B @ C )
% 0.26/0.46         => ( ! [X4: num,Y4: num] :
% 0.26/0.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_eq_le_subst
% 0.26/0.46  thf(fact_215_ord__eq__le__subst,axiom,
% 0.26/0.46      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 0.26/0.46        ( ( A
% 0.26/0.46          = ( F @ B ) )
% 0.26/0.46       => ( ( ord_less_eq_nat @ B @ C )
% 0.26/0.46         => ( ! [X4: nat,Y4: nat] :
% 0.26/0.46                ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_eq_le_subst
% 0.26/0.46  thf(fact_216_ord__eq__le__subst,axiom,
% 0.26/0.46      ! [A: num,F: nat > num,B: nat,C: nat] :
% 0.26/0.46        ( ( A
% 0.26/0.46          = ( F @ B ) )
% 0.26/0.46       => ( ( ord_less_eq_nat @ B @ C )
% 0.26/0.46         => ( ! [X4: nat,Y4: nat] :
% 0.26/0.46                ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_eq_le_subst
% 0.26/0.46  thf(fact_217_linorder__linear,axiom,
% 0.26/0.46      ! [X3: rat,Y3: rat] :
% 0.26/0.46        ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.26/0.46        | ( ord_less_eq_rat @ Y3 @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % linorder_linear
% 0.26/0.46  thf(fact_218_linorder__linear,axiom,
% 0.26/0.46      ! [X3: num,Y3: num] :
% 0.26/0.46        ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.26/0.46        | ( ord_less_eq_num @ Y3 @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % linorder_linear
% 0.26/0.46  thf(fact_219_linorder__linear,axiom,
% 0.26/0.46      ! [X3: nat,Y3: nat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.26/0.46        | ( ord_less_eq_nat @ Y3 @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % linorder_linear
% 0.26/0.46  thf(fact_220_linorder__linear,axiom,
% 0.26/0.46      ! [X3: int,Y3: int] :
% 0.26/0.46        ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.26/0.46        | ( ord_less_eq_int @ Y3 @ X3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % linorder_linear
% 0.26/0.46  thf(fact_221_order__eq__refl,axiom,
% 0.26/0.46      ! [X3: set_nat,Y3: set_nat] :
% 0.26/0.46        ( ( X3 = Y3 )
% 0.26/0.46       => ( ord_less_eq_set_nat @ X3 @ Y3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_eq_refl
% 0.26/0.46  thf(fact_222_order__eq__refl,axiom,
% 0.26/0.46      ! [X3: rat,Y3: rat] :
% 0.26/0.46        ( ( X3 = Y3 )
% 0.26/0.46       => ( ord_less_eq_rat @ X3 @ Y3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_eq_refl
% 0.26/0.46  thf(fact_223_order__eq__refl,axiom,
% 0.26/0.46      ! [X3: num,Y3: num] :
% 0.26/0.46        ( ( X3 = Y3 )
% 0.26/0.46       => ( ord_less_eq_num @ X3 @ Y3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_eq_refl
% 0.26/0.46  thf(fact_224_order__eq__refl,axiom,
% 0.26/0.46      ! [X3: nat,Y3: nat] :
% 0.26/0.46        ( ( X3 = Y3 )
% 0.26/0.46       => ( ord_less_eq_nat @ X3 @ Y3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_eq_refl
% 0.26/0.46  thf(fact_225_order__eq__refl,axiom,
% 0.26/0.46      ! [X3: int,Y3: int] :
% 0.26/0.46        ( ( X3 = Y3 )
% 0.26/0.46       => ( ord_less_eq_int @ X3 @ Y3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_eq_refl
% 0.26/0.46  thf(fact_226_order__subst2,axiom,
% 0.26/0.46      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.26/0.46        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.46       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.26/0.46         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_subst2
% 0.26/0.46  thf(fact_227_order__subst2,axiom,
% 0.26/0.46      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.26/0.46        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.46       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 0.26/0.46         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_subst2
% 0.26/0.46  thf(fact_228_order__subst2,axiom,
% 0.26/0.46      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.26/0.46        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.46       => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 0.26/0.46         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_subst2
% 0.26/0.46  thf(fact_229_order__subst2,axiom,
% 0.26/0.46      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.26/0.46        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.46       => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 0.26/0.46         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_subst2
% 0.26/0.46  thf(fact_230_order__subst2,axiom,
% 0.26/0.46      ! [A: num,B: num,F: num > rat,C: rat] :
% 0.26/0.46        ( ( ord_less_eq_num @ A @ B )
% 0.26/0.46       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.26/0.46         => ( ! [X4: num,Y4: num] :
% 0.26/0.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_subst2
% 0.26/0.46  thf(fact_231_order__subst2,axiom,
% 0.26/0.46      ! [A: num,B: num,F: num > num,C: num] :
% 0.26/0.46        ( ( ord_less_eq_num @ A @ B )
% 0.26/0.46       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 0.26/0.46         => ( ! [X4: num,Y4: num] :
% 0.26/0.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_subst2
% 0.26/0.46  thf(fact_232_order__subst2,axiom,
% 0.26/0.46      ! [A: num,B: num,F: num > nat,C: nat] :
% 0.26/0.46        ( ( ord_less_eq_num @ A @ B )
% 0.26/0.46       => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 0.26/0.46         => ( ! [X4: num,Y4: num] :
% 0.26/0.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_subst2
% 0.26/0.46  thf(fact_233_order__subst2,axiom,
% 0.26/0.46      ! [A: num,B: num,F: num > int,C: int] :
% 0.26/0.46        ( ( ord_less_eq_num @ A @ B )
% 0.26/0.46       => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 0.26/0.46         => ( ! [X4: num,Y4: num] :
% 0.26/0.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_subst2
% 0.26/0.46  thf(fact_234_order__subst2,axiom,
% 0.26/0.46      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.46       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.26/0.46         => ( ! [X4: nat,Y4: nat] :
% 0.26/0.46                ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_subst2
% 0.26/0.46  thf(fact_235_order__subst2,axiom,
% 0.26/0.46      ! [A: nat,B: nat,F: nat > num,C: num] :
% 0.26/0.46        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.46       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 0.26/0.46         => ( ! [X4: nat,Y4: nat] :
% 0.26/0.46                ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_subst2
% 0.26/0.46  thf(fact_236_order__subst1,axiom,
% 0.26/0.46      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.26/0.46        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.26/0.46       => ( ( ord_less_eq_rat @ B @ C )
% 0.26/0.46         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_subst1
% 0.26/0.46  thf(fact_237_order__subst1,axiom,
% 0.26/0.46      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.26/0.46        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.26/0.46       => ( ( ord_less_eq_num @ B @ C )
% 0.26/0.46         => ( ! [X4: num,Y4: num] :
% 0.26/0.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_subst1
% 0.26/0.46  thf(fact_238_order__subst1,axiom,
% 0.26/0.46      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 0.26/0.46        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.26/0.46       => ( ( ord_less_eq_nat @ B @ C )
% 0.26/0.46         => ( ! [X4: nat,Y4: nat] :
% 0.26/0.46                ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_subst1
% 0.26/0.46  thf(fact_239_order__subst1,axiom,
% 0.26/0.46      ! [A: rat,F: int > rat,B: int,C: int] :
% 0.26/0.46        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.26/0.46       => ( ( ord_less_eq_int @ B @ C )
% 0.26/0.46         => ( ! [X4: int,Y4: int] :
% 0.26/0.46                ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_subst1
% 0.26/0.46  thf(fact_240_order__subst1,axiom,
% 0.26/0.46      ! [A: num,F: rat > num,B: rat,C: rat] :
% 0.26/0.46        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.26/0.46       => ( ( ord_less_eq_rat @ B @ C )
% 0.26/0.46         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_subst1
% 0.26/0.46  thf(fact_241_order__subst1,axiom,
% 0.26/0.46      ! [A: num,F: num > num,B: num,C: num] :
% 0.26/0.46        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.26/0.46       => ( ( ord_less_eq_num @ B @ C )
% 0.26/0.46         => ( ! [X4: num,Y4: num] :
% 0.26/0.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_subst1
% 0.26/0.46  thf(fact_242_order__subst1,axiom,
% 0.26/0.46      ! [A: num,F: nat > num,B: nat,C: nat] :
% 0.26/0.46        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.26/0.46       => ( ( ord_less_eq_nat @ B @ C )
% 0.26/0.46         => ( ! [X4: nat,Y4: nat] :
% 0.26/0.46                ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_subst1
% 0.26/0.46  thf(fact_243_order__subst1,axiom,
% 0.26/0.46      ! [A: num,F: int > num,B: int,C: int] :
% 0.26/0.46        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.26/0.46       => ( ( ord_less_eq_int @ B @ C )
% 0.26/0.46         => ( ! [X4: int,Y4: int] :
% 0.26/0.46                ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_subst1
% 0.26/0.46  thf(fact_244_order__subst1,axiom,
% 0.26/0.46      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.26/0.46       => ( ( ord_less_eq_rat @ B @ C )
% 0.26/0.46         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_subst1
% 0.26/0.46  thf(fact_245_order__subst1,axiom,
% 0.26/0.46      ! [A: nat,F: num > nat,B: num,C: num] :
% 0.26/0.46        ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.26/0.46       => ( ( ord_less_eq_num @ B @ C )
% 0.26/0.46         => ( ! [X4: num,Y4: num] :
% 0.26/0.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.46               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.46           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_subst1
% 0.26/0.46  thf(fact_246_Orderings_Oorder__eq__iff,axiom,
% 0.26/0.46      ( ( ^ [Y5: set_nat,Z2: set_nat] : ( Y5 = Z2 ) )
% 0.26/0.46      = ( ^ [A4: set_nat,B3: set_nat] :
% 0.26/0.46            ( ( ord_less_eq_set_nat @ A4 @ B3 )
% 0.26/0.46            & ( ord_less_eq_set_nat @ B3 @ A4 ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % Orderings.order_eq_iff
% 0.26/0.46  thf(fact_247_Orderings_Oorder__eq__iff,axiom,
% 0.26/0.46      ( ( ^ [Y5: rat,Z2: rat] : ( Y5 = Z2 ) )
% 0.26/0.46      = ( ^ [A4: rat,B3: rat] :
% 0.26/0.46            ( ( ord_less_eq_rat @ A4 @ B3 )
% 0.26/0.46            & ( ord_less_eq_rat @ B3 @ A4 ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % Orderings.order_eq_iff
% 0.26/0.46  thf(fact_248_Orderings_Oorder__eq__iff,axiom,
% 0.26/0.46      ( ( ^ [Y5: num,Z2: num] : ( Y5 = Z2 ) )
% 0.26/0.46      = ( ^ [A4: num,B3: num] :
% 0.26/0.46            ( ( ord_less_eq_num @ A4 @ B3 )
% 0.26/0.46            & ( ord_less_eq_num @ B3 @ A4 ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % Orderings.order_eq_iff
% 0.26/0.46  thf(fact_249_Orderings_Oorder__eq__iff,axiom,
% 0.26/0.46      ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 0.26/0.46      = ( ^ [A4: nat,B3: nat] :
% 0.26/0.46            ( ( ord_less_eq_nat @ A4 @ B3 )
% 0.26/0.46            & ( ord_less_eq_nat @ B3 @ A4 ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % Orderings.order_eq_iff
% 0.26/0.46  thf(fact_250_Orderings_Oorder__eq__iff,axiom,
% 0.26/0.46      ( ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 0.26/0.46      = ( ^ [A4: int,B3: int] :
% 0.26/0.46            ( ( ord_less_eq_int @ A4 @ B3 )
% 0.26/0.46            & ( ord_less_eq_int @ B3 @ A4 ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % Orderings.order_eq_iff
% 0.26/0.46  thf(fact_251_antisym,axiom,
% 0.26/0.46      ! [A: set_nat,B: set_nat] :
% 0.26/0.46        ( ( ord_less_eq_set_nat @ A @ B )
% 0.26/0.46       => ( ( ord_less_eq_set_nat @ B @ A )
% 0.26/0.46         => ( A = B ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % antisym
% 0.26/0.46  thf(fact_252_antisym,axiom,
% 0.26/0.46      ! [A: rat,B: rat] :
% 0.26/0.46        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.46       => ( ( ord_less_eq_rat @ B @ A )
% 0.26/0.46         => ( A = B ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % antisym
% 0.26/0.46  thf(fact_253_antisym,axiom,
% 0.26/0.46      ! [A: num,B: num] :
% 0.26/0.46        ( ( ord_less_eq_num @ A @ B )
% 0.26/0.46       => ( ( ord_less_eq_num @ B @ A )
% 0.26/0.46         => ( A = B ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % antisym
% 0.26/0.46  thf(fact_254_antisym,axiom,
% 0.26/0.46      ! [A: nat,B: nat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.46       => ( ( ord_less_eq_nat @ B @ A )
% 0.26/0.46         => ( A = B ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % antisym
% 0.26/0.46  thf(fact_255_antisym,axiom,
% 0.26/0.46      ! [A: int,B: int] :
% 0.26/0.46        ( ( ord_less_eq_int @ A @ B )
% 0.26/0.46       => ( ( ord_less_eq_int @ B @ A )
% 0.26/0.46         => ( A = B ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % antisym
% 0.26/0.46  thf(fact_256_dual__order_Otrans,axiom,
% 0.26/0.46      ! [B: set_nat,A: set_nat,C: set_nat] :
% 0.26/0.46        ( ( ord_less_eq_set_nat @ B @ A )
% 0.26/0.46       => ( ( ord_less_eq_set_nat @ C @ B )
% 0.26/0.46         => ( ord_less_eq_set_nat @ C @ A ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.trans
% 0.26/0.46  thf(fact_257_dual__order_Otrans,axiom,
% 0.26/0.46      ! [B: rat,A: rat,C: rat] :
% 0.26/0.46        ( ( ord_less_eq_rat @ B @ A )
% 0.26/0.46       => ( ( ord_less_eq_rat @ C @ B )
% 0.26/0.46         => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.trans
% 0.26/0.46  thf(fact_258_dual__order_Otrans,axiom,
% 0.26/0.46      ! [B: num,A: num,C: num] :
% 0.26/0.46        ( ( ord_less_eq_num @ B @ A )
% 0.26/0.46       => ( ( ord_less_eq_num @ C @ B )
% 0.26/0.46         => ( ord_less_eq_num @ C @ A ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.trans
% 0.26/0.46  thf(fact_259_dual__order_Otrans,axiom,
% 0.26/0.46      ! [B: nat,A: nat,C: nat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ B @ A )
% 0.26/0.46       => ( ( ord_less_eq_nat @ C @ B )
% 0.26/0.46         => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.trans
% 0.26/0.46  thf(fact_260_dual__order_Otrans,axiom,
% 0.26/0.46      ! [B: int,A: int,C: int] :
% 0.26/0.46        ( ( ord_less_eq_int @ B @ A )
% 0.26/0.46       => ( ( ord_less_eq_int @ C @ B )
% 0.26/0.46         => ( ord_less_eq_int @ C @ A ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.trans
% 0.26/0.46  thf(fact_261_dual__order_Oantisym,axiom,
% 0.26/0.46      ! [B: set_nat,A: set_nat] :
% 0.26/0.46        ( ( ord_less_eq_set_nat @ B @ A )
% 0.26/0.46       => ( ( ord_less_eq_set_nat @ A @ B )
% 0.26/0.46         => ( A = B ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.antisym
% 0.26/0.46  thf(fact_262_dual__order_Oantisym,axiom,
% 0.26/0.46      ! [B: rat,A: rat] :
% 0.26/0.46        ( ( ord_less_eq_rat @ B @ A )
% 0.26/0.46       => ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.46         => ( A = B ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.antisym
% 0.26/0.46  thf(fact_263_dual__order_Oantisym,axiom,
% 0.26/0.46      ! [B: num,A: num] :
% 0.26/0.46        ( ( ord_less_eq_num @ B @ A )
% 0.26/0.46       => ( ( ord_less_eq_num @ A @ B )
% 0.26/0.46         => ( A = B ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.antisym
% 0.26/0.46  thf(fact_264_dual__order_Oantisym,axiom,
% 0.26/0.46      ! [B: nat,A: nat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ B @ A )
% 0.26/0.46       => ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.46         => ( A = B ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.antisym
% 0.26/0.46  thf(fact_265_dual__order_Oantisym,axiom,
% 0.26/0.46      ! [B: int,A: int] :
% 0.26/0.46        ( ( ord_less_eq_int @ B @ A )
% 0.26/0.46       => ( ( ord_less_eq_int @ A @ B )
% 0.26/0.46         => ( A = B ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.antisym
% 0.26/0.46  thf(fact_266_dual__order_Oeq__iff,axiom,
% 0.26/0.46      ( ( ^ [Y5: set_nat,Z2: set_nat] : ( Y5 = Z2 ) )
% 0.26/0.46      = ( ^ [A4: set_nat,B3: set_nat] :
% 0.26/0.46            ( ( ord_less_eq_set_nat @ B3 @ A4 )
% 0.26/0.46            & ( ord_less_eq_set_nat @ A4 @ B3 ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.eq_iff
% 0.26/0.46  thf(fact_267_dual__order_Oeq__iff,axiom,
% 0.26/0.46      ( ( ^ [Y5: rat,Z2: rat] : ( Y5 = Z2 ) )
% 0.26/0.46      = ( ^ [A4: rat,B3: rat] :
% 0.26/0.46            ( ( ord_less_eq_rat @ B3 @ A4 )
% 0.26/0.46            & ( ord_less_eq_rat @ A4 @ B3 ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.eq_iff
% 0.26/0.46  thf(fact_268_dual__order_Oeq__iff,axiom,
% 0.26/0.46      ( ( ^ [Y5: num,Z2: num] : ( Y5 = Z2 ) )
% 0.26/0.46      = ( ^ [A4: num,B3: num] :
% 0.26/0.46            ( ( ord_less_eq_num @ B3 @ A4 )
% 0.26/0.46            & ( ord_less_eq_num @ A4 @ B3 ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.eq_iff
% 0.26/0.46  thf(fact_269_dual__order_Oeq__iff,axiom,
% 0.26/0.46      ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 0.26/0.46      = ( ^ [A4: nat,B3: nat] :
% 0.26/0.46            ( ( ord_less_eq_nat @ B3 @ A4 )
% 0.26/0.46            & ( ord_less_eq_nat @ A4 @ B3 ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.eq_iff
% 0.26/0.46  thf(fact_270_dual__order_Oeq__iff,axiom,
% 0.26/0.46      ( ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 0.26/0.46      = ( ^ [A4: int,B3: int] :
% 0.26/0.46            ( ( ord_less_eq_int @ B3 @ A4 )
% 0.26/0.46            & ( ord_less_eq_int @ A4 @ B3 ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.eq_iff
% 0.26/0.46  thf(fact_271_linorder__wlog,axiom,
% 0.26/0.46      ! [P: rat > rat > $o,A: rat,B: rat] :
% 0.26/0.46        ( ! [A5: rat,B4: rat] :
% 0.26/0.46            ( ( ord_less_eq_rat @ A5 @ B4 )
% 0.26/0.46           => ( P @ A5 @ B4 ) )
% 0.26/0.46       => ( ! [A5: rat,B4: rat] :
% 0.26/0.46              ( ( P @ B4 @ A5 )
% 0.26/0.46             => ( P @ A5 @ B4 ) )
% 0.26/0.46         => ( P @ A @ B ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % linorder_wlog
% 0.26/0.46  thf(fact_272_linorder__wlog,axiom,
% 0.26/0.46      ! [P: num > num > $o,A: num,B: num] :
% 0.26/0.46        ( ! [A5: num,B4: num] :
% 0.26/0.46            ( ( ord_less_eq_num @ A5 @ B4 )
% 0.26/0.46           => ( P @ A5 @ B4 ) )
% 0.26/0.46       => ( ! [A5: num,B4: num] :
% 0.26/0.46              ( ( P @ B4 @ A5 )
% 0.26/0.46             => ( P @ A5 @ B4 ) )
% 0.26/0.46         => ( P @ A @ B ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % linorder_wlog
% 0.26/0.46  thf(fact_273_linorder__wlog,axiom,
% 0.26/0.46      ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.26/0.46        ( ! [A5: nat,B4: nat] :
% 0.26/0.46            ( ( ord_less_eq_nat @ A5 @ B4 )
% 0.26/0.46           => ( P @ A5 @ B4 ) )
% 0.26/0.46       => ( ! [A5: nat,B4: nat] :
% 0.26/0.46              ( ( P @ B4 @ A5 )
% 0.26/0.46             => ( P @ A5 @ B4 ) )
% 0.26/0.46         => ( P @ A @ B ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % linorder_wlog
% 0.26/0.46  thf(fact_274_linorder__wlog,axiom,
% 0.26/0.46      ! [P: int > int > $o,A: int,B: int] :
% 0.26/0.46        ( ! [A5: int,B4: int] :
% 0.26/0.46            ( ( ord_less_eq_int @ A5 @ B4 )
% 0.26/0.46           => ( P @ A5 @ B4 ) )
% 0.26/0.46       => ( ! [A5: int,B4: int] :
% 0.26/0.46              ( ( P @ B4 @ A5 )
% 0.26/0.46             => ( P @ A5 @ B4 ) )
% 0.26/0.46         => ( P @ A @ B ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % linorder_wlog
% 0.26/0.46  thf(fact_275_order__trans,axiom,
% 0.26/0.46      ! [X3: set_nat,Y3: set_nat,Z: set_nat] :
% 0.26/0.46        ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 0.26/0.46       => ( ( ord_less_eq_set_nat @ Y3 @ Z )
% 0.26/0.46         => ( ord_less_eq_set_nat @ X3 @ Z ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_trans
% 0.26/0.46  thf(fact_276_order__trans,axiom,
% 0.26/0.46      ! [X3: rat,Y3: rat,Z: rat] :
% 0.26/0.46        ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.26/0.46       => ( ( ord_less_eq_rat @ Y3 @ Z )
% 0.26/0.46         => ( ord_less_eq_rat @ X3 @ Z ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_trans
% 0.26/0.46  thf(fact_277_order__trans,axiom,
% 0.26/0.46      ! [X3: num,Y3: num,Z: num] :
% 0.26/0.46        ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.26/0.46       => ( ( ord_less_eq_num @ Y3 @ Z )
% 0.26/0.46         => ( ord_less_eq_num @ X3 @ Z ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_trans
% 0.26/0.46  thf(fact_278_order__trans,axiom,
% 0.26/0.46      ! [X3: nat,Y3: nat,Z: nat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.26/0.46       => ( ( ord_less_eq_nat @ Y3 @ Z )
% 0.26/0.46         => ( ord_less_eq_nat @ X3 @ Z ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_trans
% 0.26/0.46  thf(fact_279_order__trans,axiom,
% 0.26/0.46      ! [X3: int,Y3: int,Z: int] :
% 0.26/0.46        ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.26/0.46       => ( ( ord_less_eq_int @ Y3 @ Z )
% 0.26/0.46         => ( ord_less_eq_int @ X3 @ Z ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_trans
% 0.26/0.46  thf(fact_280_order_Otrans,axiom,
% 0.26/0.46      ! [A: set_nat,B: set_nat,C: set_nat] :
% 0.26/0.46        ( ( ord_less_eq_set_nat @ A @ B )
% 0.26/0.46       => ( ( ord_less_eq_set_nat @ B @ C )
% 0.26/0.46         => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order.trans
% 0.26/0.46  thf(fact_281_order_Otrans,axiom,
% 0.26/0.46      ! [A: rat,B: rat,C: rat] :
% 0.26/0.46        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.46       => ( ( ord_less_eq_rat @ B @ C )
% 0.26/0.46         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order.trans
% 0.26/0.46  thf(fact_282_order_Otrans,axiom,
% 0.26/0.46      ! [A: num,B: num,C: num] :
% 0.26/0.46        ( ( ord_less_eq_num @ A @ B )
% 0.26/0.46       => ( ( ord_less_eq_num @ B @ C )
% 0.26/0.46         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order.trans
% 0.26/0.46  thf(fact_283_order_Otrans,axiom,
% 0.26/0.46      ! [A: nat,B: nat,C: nat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.46       => ( ( ord_less_eq_nat @ B @ C )
% 0.26/0.46         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order.trans
% 0.26/0.46  thf(fact_284_order_Otrans,axiom,
% 0.26/0.46      ! [A: int,B: int,C: int] :
% 0.26/0.46        ( ( ord_less_eq_int @ A @ B )
% 0.26/0.46       => ( ( ord_less_eq_int @ B @ C )
% 0.26/0.46         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order.trans
% 0.26/0.46  thf(fact_285_order__antisym,axiom,
% 0.26/0.46      ! [X3: set_nat,Y3: set_nat] :
% 0.26/0.46        ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 0.26/0.46       => ( ( ord_less_eq_set_nat @ Y3 @ X3 )
% 0.26/0.46         => ( X3 = Y3 ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_antisym
% 0.26/0.46  thf(fact_286_order__antisym,axiom,
% 0.26/0.46      ! [X3: rat,Y3: rat] :
% 0.26/0.46        ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.26/0.46       => ( ( ord_less_eq_rat @ Y3 @ X3 )
% 0.26/0.46         => ( X3 = Y3 ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_antisym
% 0.26/0.46  thf(fact_287_order__antisym,axiom,
% 0.26/0.46      ! [X3: num,Y3: num] :
% 0.26/0.46        ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.26/0.46       => ( ( ord_less_eq_num @ Y3 @ X3 )
% 0.26/0.46         => ( X3 = Y3 ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_antisym
% 0.26/0.46  thf(fact_288_order__antisym,axiom,
% 0.26/0.46      ! [X3: nat,Y3: nat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.26/0.46       => ( ( ord_less_eq_nat @ Y3 @ X3 )
% 0.26/0.46         => ( X3 = Y3 ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_antisym
% 0.26/0.46  thf(fact_289_order__antisym,axiom,
% 0.26/0.46      ! [X3: int,Y3: int] :
% 0.26/0.46        ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.26/0.46       => ( ( ord_less_eq_int @ Y3 @ X3 )
% 0.26/0.46         => ( X3 = Y3 ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_antisym
% 0.26/0.46  thf(fact_290_ord__le__eq__trans,axiom,
% 0.26/0.46      ! [A: set_nat,B: set_nat,C: set_nat] :
% 0.26/0.46        ( ( ord_less_eq_set_nat @ A @ B )
% 0.26/0.46       => ( ( B = C )
% 0.26/0.46         => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_le_eq_trans
% 0.26/0.46  thf(fact_291_ord__le__eq__trans,axiom,
% 0.26/0.46      ! [A: rat,B: rat,C: rat] :
% 0.26/0.46        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.46       => ( ( B = C )
% 0.26/0.46         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_le_eq_trans
% 0.26/0.46  thf(fact_292_ord__le__eq__trans,axiom,
% 0.26/0.46      ! [A: num,B: num,C: num] :
% 0.26/0.46        ( ( ord_less_eq_num @ A @ B )
% 0.26/0.46       => ( ( B = C )
% 0.26/0.46         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_le_eq_trans
% 0.26/0.46  thf(fact_293_ord__le__eq__trans,axiom,
% 0.26/0.46      ! [A: nat,B: nat,C: nat] :
% 0.26/0.46        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.46       => ( ( B = C )
% 0.26/0.46         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_le_eq_trans
% 0.26/0.46  thf(fact_294_ord__le__eq__trans,axiom,
% 0.26/0.46      ! [A: int,B: int,C: int] :
% 0.26/0.46        ( ( ord_less_eq_int @ A @ B )
% 0.26/0.46       => ( ( B = C )
% 0.26/0.46         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_le_eq_trans
% 0.26/0.46  thf(fact_295_ord__eq__le__trans,axiom,
% 0.26/0.46      ! [A: set_nat,B: set_nat,C: set_nat] :
% 0.26/0.46        ( ( A = B )
% 0.26/0.46       => ( ( ord_less_eq_set_nat @ B @ C )
% 0.26/0.46         => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_eq_le_trans
% 0.26/0.46  thf(fact_296_ord__eq__le__trans,axiom,
% 0.26/0.46      ! [A: rat,B: rat,C: rat] :
% 0.26/0.46        ( ( A = B )
% 0.26/0.46       => ( ( ord_less_eq_rat @ B @ C )
% 0.26/0.46         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_eq_le_trans
% 0.26/0.46  thf(fact_297_ord__eq__le__trans,axiom,
% 0.26/0.46      ! [A: num,B: num,C: num] :
% 0.26/0.46        ( ( A = B )
% 0.26/0.46       => ( ( ord_less_eq_num @ B @ C )
% 0.26/0.46         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_eq_le_trans
% 0.26/0.46  thf(fact_298_ord__eq__le__trans,axiom,
% 0.26/0.46      ! [A: nat,B: nat,C: nat] :
% 0.26/0.46        ( ( A = B )
% 0.26/0.46       => ( ( ord_less_eq_nat @ B @ C )
% 0.26/0.46         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_eq_le_trans
% 0.26/0.46  thf(fact_299_ord__eq__le__trans,axiom,
% 0.26/0.46      ! [A: int,B: int,C: int] :
% 0.26/0.46        ( ( A = B )
% 0.26/0.46       => ( ( ord_less_eq_int @ B @ C )
% 0.26/0.46         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_eq_le_trans
% 0.26/0.46  thf(fact_300_order__class_Oorder__eq__iff,axiom,
% 0.26/0.46      ( ( ^ [Y5: set_nat,Z2: set_nat] : ( Y5 = Z2 ) )
% 0.26/0.46      = ( ^ [X: set_nat,Y: set_nat] :
% 0.26/0.46            ( ( ord_less_eq_set_nat @ X @ Y )
% 0.26/0.46            & ( ord_less_eq_set_nat @ Y @ X ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_class.order_eq_iff
% 0.26/0.46  thf(fact_301_order__class_Oorder__eq__iff,axiom,
% 0.26/0.46      ( ( ^ [Y5: rat,Z2: rat] : ( Y5 = Z2 ) )
% 0.26/0.46      = ( ^ [X: rat,Y: rat] :
% 0.26/0.46            ( ( ord_less_eq_rat @ X @ Y )
% 0.26/0.46            & ( ord_less_eq_rat @ Y @ X ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_class.order_eq_iff
% 0.26/0.46  thf(fact_302_order__class_Oorder__eq__iff,axiom,
% 0.26/0.46      ( ( ^ [Y5: num,Z2: num] : ( Y5 = Z2 ) )
% 0.26/0.46      = ( ^ [X: num,Y: num] :
% 0.26/0.46            ( ( ord_less_eq_num @ X @ Y )
% 0.26/0.46            & ( ord_less_eq_num @ Y @ X ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_class.order_eq_iff
% 0.26/0.46  thf(fact_303_order__class_Oorder__eq__iff,axiom,
% 0.26/0.46      ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 0.26/0.46      = ( ^ [X: nat,Y: nat] :
% 0.26/0.46            ( ( ord_less_eq_nat @ X @ Y )
% 0.26/0.46            & ( ord_less_eq_nat @ Y @ X ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_class.order_eq_iff
% 0.26/0.46  thf(fact_304_order__class_Oorder__eq__iff,axiom,
% 0.26/0.46      ( ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 0.26/0.46      = ( ^ [X: int,Y: int] :
% 0.26/0.46            ( ( ord_less_eq_int @ X @ Y )
% 0.26/0.46            & ( ord_less_eq_int @ Y @ X ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order_class.order_eq_iff
% 0.26/0.46  thf(fact_305_le__cases3,axiom,
% 0.26/0.46      ! [X3: rat,Y3: rat,Z: rat] :
% 0.26/0.46        ( ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.26/0.46         => ~ ( ord_less_eq_rat @ Y3 @ Z ) )
% 0.26/0.46       => ( ( ( ord_less_eq_rat @ Y3 @ X3 )
% 0.26/0.46           => ~ ( ord_less_eq_rat @ X3 @ Z ) )
% 0.26/0.46         => ( ( ( ord_less_eq_rat @ X3 @ Z )
% 0.26/0.46             => ~ ( ord_less_eq_rat @ Z @ Y3 ) )
% 0.26/0.46           => ( ( ( ord_less_eq_rat @ Z @ Y3 )
% 0.26/0.46               => ~ ( ord_less_eq_rat @ Y3 @ X3 ) )
% 0.26/0.46             => ( ( ( ord_less_eq_rat @ Y3 @ Z )
% 0.26/0.46                 => ~ ( ord_less_eq_rat @ Z @ X3 ) )
% 0.26/0.46               => ~ ( ( ord_less_eq_rat @ Z @ X3 )
% 0.26/0.46                   => ~ ( ord_less_eq_rat @ X3 @ Y3 ) ) ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % le_cases3
% 0.26/0.46  thf(fact_306_le__cases3,axiom,
% 0.26/0.46      ! [X3: num,Y3: num,Z: num] :
% 0.26/0.46        ( ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.26/0.46         => ~ ( ord_less_eq_num @ Y3 @ Z ) )
% 0.26/0.46       => ( ( ( ord_less_eq_num @ Y3 @ X3 )
% 0.26/0.46           => ~ ( ord_less_eq_num @ X3 @ Z ) )
% 0.26/0.46         => ( ( ( ord_less_eq_num @ X3 @ Z )
% 0.26/0.46             => ~ ( ord_less_eq_num @ Z @ Y3 ) )
% 0.26/0.46           => ( ( ( ord_less_eq_num @ Z @ Y3 )
% 0.26/0.46               => ~ ( ord_less_eq_num @ Y3 @ X3 ) )
% 0.26/0.46             => ( ( ( ord_less_eq_num @ Y3 @ Z )
% 0.26/0.46                 => ~ ( ord_less_eq_num @ Z @ X3 ) )
% 0.26/0.46               => ~ ( ( ord_less_eq_num @ Z @ X3 )
% 0.26/0.46                   => ~ ( ord_less_eq_num @ X3 @ Y3 ) ) ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % le_cases3
% 0.26/0.46  thf(fact_307_le__cases3,axiom,
% 0.26/0.46      ! [X3: nat,Y3: nat,Z: nat] :
% 0.26/0.46        ( ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.26/0.46         => ~ ( ord_less_eq_nat @ Y3 @ Z ) )
% 0.26/0.46       => ( ( ( ord_less_eq_nat @ Y3 @ X3 )
% 0.26/0.46           => ~ ( ord_less_eq_nat @ X3 @ Z ) )
% 0.26/0.46         => ( ( ( ord_less_eq_nat @ X3 @ Z )
% 0.26/0.46             => ~ ( ord_less_eq_nat @ Z @ Y3 ) )
% 0.26/0.46           => ( ( ( ord_less_eq_nat @ Z @ Y3 )
% 0.26/0.46               => ~ ( ord_less_eq_nat @ Y3 @ X3 ) )
% 0.26/0.46             => ( ( ( ord_less_eq_nat @ Y3 @ Z )
% 0.26/0.46                 => ~ ( ord_less_eq_nat @ Z @ X3 ) )
% 0.26/0.46               => ~ ( ( ord_less_eq_nat @ Z @ X3 )
% 0.26/0.46                   => ~ ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % le_cases3
% 0.26/0.46  thf(fact_308_le__cases3,axiom,
% 0.26/0.46      ! [X3: int,Y3: int,Z: int] :
% 0.26/0.46        ( ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.26/0.46         => ~ ( ord_less_eq_int @ Y3 @ Z ) )
% 0.26/0.46       => ( ( ( ord_less_eq_int @ Y3 @ X3 )
% 0.26/0.46           => ~ ( ord_less_eq_int @ X3 @ Z ) )
% 0.26/0.46         => ( ( ( ord_less_eq_int @ X3 @ Z )
% 0.26/0.46             => ~ ( ord_less_eq_int @ Z @ Y3 ) )
% 0.26/0.46           => ( ( ( ord_less_eq_int @ Z @ Y3 )
% 0.26/0.46               => ~ ( ord_less_eq_int @ Y3 @ X3 ) )
% 0.26/0.46             => ( ( ( ord_less_eq_int @ Y3 @ Z )
% 0.26/0.46                 => ~ ( ord_less_eq_int @ Z @ X3 ) )
% 0.26/0.46               => ~ ( ( ord_less_eq_int @ Z @ X3 )
% 0.26/0.46                   => ~ ( ord_less_eq_int @ X3 @ Y3 ) ) ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % le_cases3
% 0.26/0.46  thf(fact_309_nle__le,axiom,
% 0.26/0.46      ! [A: rat,B: rat] :
% 0.26/0.46        ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 0.26/0.46        = ( ( ord_less_eq_rat @ B @ A )
% 0.26/0.46          & ( B != A ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % nle_le
% 0.26/0.46  thf(fact_310_nle__le,axiom,
% 0.26/0.46      ! [A: num,B: num] :
% 0.26/0.46        ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 0.26/0.46        = ( ( ord_less_eq_num @ B @ A )
% 0.26/0.46          & ( B != A ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % nle_le
% 0.26/0.46  thf(fact_311_nle__le,axiom,
% 0.26/0.46      ! [A: nat,B: nat] :
% 0.26/0.46        ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 0.26/0.46        = ( ( ord_less_eq_nat @ B @ A )
% 0.26/0.46          & ( B != A ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % nle_le
% 0.26/0.46  thf(fact_312_nle__le,axiom,
% 0.26/0.46      ! [A: int,B: int] :
% 0.26/0.46        ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 0.26/0.46        = ( ( ord_less_eq_int @ B @ A )
% 0.26/0.46          & ( B != A ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % nle_le
% 0.26/0.46  thf(fact_313_lt__ex,axiom,
% 0.26/0.46      ! [X3: real] :
% 0.26/0.46      ? [Y4: real] : ( ord_less_real @ Y4 @ X3 ) ).
% 0.26/0.46  
% 0.26/0.46  % lt_ex
% 0.26/0.46  thf(fact_314_lt__ex,axiom,
% 0.26/0.46      ! [X3: rat] :
% 0.26/0.46      ? [Y4: rat] : ( ord_less_rat @ Y4 @ X3 ) ).
% 0.26/0.46  
% 0.26/0.46  % lt_ex
% 0.26/0.46  thf(fact_315_lt__ex,axiom,
% 0.26/0.46      ! [X3: int] :
% 0.26/0.46      ? [Y4: int] : ( ord_less_int @ Y4 @ X3 ) ).
% 0.26/0.46  
% 0.26/0.46  % lt_ex
% 0.26/0.46  thf(fact_316_gt__ex,axiom,
% 0.26/0.46      ! [X3: real] :
% 0.26/0.46      ? [X_1: real] : ( ord_less_real @ X3 @ X_1 ) ).
% 0.26/0.46  
% 0.26/0.46  % gt_ex
% 0.26/0.46  thf(fact_317_gt__ex,axiom,
% 0.26/0.46      ! [X3: rat] :
% 0.26/0.46      ? [X_1: rat] : ( ord_less_rat @ X3 @ X_1 ) ).
% 0.26/0.46  
% 0.26/0.46  % gt_ex
% 0.26/0.46  thf(fact_318_gt__ex,axiom,
% 0.26/0.46      ! [X3: nat] :
% 0.26/0.46      ? [X_1: nat] : ( ord_less_nat @ X3 @ X_1 ) ).
% 0.26/0.46  
% 0.26/0.46  % gt_ex
% 0.26/0.46  thf(fact_319_gt__ex,axiom,
% 0.26/0.46      ! [X3: int] :
% 0.26/0.46      ? [X_1: int] : ( ord_less_int @ X3 @ X_1 ) ).
% 0.26/0.46  
% 0.26/0.46  % gt_ex
% 0.26/0.46  thf(fact_320_dense,axiom,
% 0.26/0.46      ! [X3: real,Y3: real] :
% 0.26/0.46        ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.46       => ? [Z3: real] :
% 0.26/0.46            ( ( ord_less_real @ X3 @ Z3 )
% 0.26/0.46            & ( ord_less_real @ Z3 @ Y3 ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % dense
% 0.26/0.46  thf(fact_321_dense,axiom,
% 0.26/0.46      ! [X3: rat,Y3: rat] :
% 0.26/0.46        ( ( ord_less_rat @ X3 @ Y3 )
% 0.26/0.46       => ? [Z3: rat] :
% 0.26/0.46            ( ( ord_less_rat @ X3 @ Z3 )
% 0.26/0.46            & ( ord_less_rat @ Z3 @ Y3 ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % dense
% 0.26/0.46  thf(fact_322_less__imp__neq,axiom,
% 0.26/0.46      ! [X3: real,Y3: real] :
% 0.26/0.46        ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.46       => ( X3 != Y3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % less_imp_neq
% 0.26/0.46  thf(fact_323_less__imp__neq,axiom,
% 0.26/0.46      ! [X3: rat,Y3: rat] :
% 0.26/0.46        ( ( ord_less_rat @ X3 @ Y3 )
% 0.26/0.46       => ( X3 != Y3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % less_imp_neq
% 0.26/0.46  thf(fact_324_less__imp__neq,axiom,
% 0.26/0.46      ! [X3: num,Y3: num] :
% 0.26/0.46        ( ( ord_less_num @ X3 @ Y3 )
% 0.26/0.46       => ( X3 != Y3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % less_imp_neq
% 0.26/0.46  thf(fact_325_less__imp__neq,axiom,
% 0.26/0.46      ! [X3: nat,Y3: nat] :
% 0.26/0.46        ( ( ord_less_nat @ X3 @ Y3 )
% 0.26/0.46       => ( X3 != Y3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % less_imp_neq
% 0.26/0.46  thf(fact_326_less__imp__neq,axiom,
% 0.26/0.46      ! [X3: int,Y3: int] :
% 0.26/0.46        ( ( ord_less_int @ X3 @ Y3 )
% 0.26/0.46       => ( X3 != Y3 ) ) ).
% 0.26/0.46  
% 0.26/0.46  % less_imp_neq
% 0.26/0.46  thf(fact_327_order_Oasym,axiom,
% 0.26/0.46      ! [A: real,B: real] :
% 0.26/0.46        ( ( ord_less_real @ A @ B )
% 0.26/0.46       => ~ ( ord_less_real @ B @ A ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order.asym
% 0.26/0.46  thf(fact_328_order_Oasym,axiom,
% 0.26/0.46      ! [A: rat,B: rat] :
% 0.26/0.46        ( ( ord_less_rat @ A @ B )
% 0.26/0.46       => ~ ( ord_less_rat @ B @ A ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order.asym
% 0.26/0.46  thf(fact_329_order_Oasym,axiom,
% 0.26/0.46      ! [A: num,B: num] :
% 0.26/0.46        ( ( ord_less_num @ A @ B )
% 0.26/0.46       => ~ ( ord_less_num @ B @ A ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order.asym
% 0.26/0.46  thf(fact_330_order_Oasym,axiom,
% 0.26/0.46      ! [A: nat,B: nat] :
% 0.26/0.46        ( ( ord_less_nat @ A @ B )
% 0.26/0.46       => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order.asym
% 0.26/0.46  thf(fact_331_order_Oasym,axiom,
% 0.26/0.46      ! [A: int,B: int] :
% 0.26/0.46        ( ( ord_less_int @ A @ B )
% 0.26/0.46       => ~ ( ord_less_int @ B @ A ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order.asym
% 0.26/0.46  thf(fact_332_ord__eq__less__trans,axiom,
% 0.26/0.46      ! [A: real,B: real,C: real] :
% 0.26/0.46        ( ( A = B )
% 0.26/0.46       => ( ( ord_less_real @ B @ C )
% 0.26/0.46         => ( ord_less_real @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_eq_less_trans
% 0.26/0.46  thf(fact_333_ord__eq__less__trans,axiom,
% 0.26/0.46      ! [A: rat,B: rat,C: rat] :
% 0.26/0.46        ( ( A = B )
% 0.26/0.46       => ( ( ord_less_rat @ B @ C )
% 0.26/0.46         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_eq_less_trans
% 0.26/0.46  thf(fact_334_ord__eq__less__trans,axiom,
% 0.26/0.46      ! [A: num,B: num,C: num] :
% 0.26/0.46        ( ( A = B )
% 0.26/0.46       => ( ( ord_less_num @ B @ C )
% 0.26/0.46         => ( ord_less_num @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_eq_less_trans
% 0.26/0.46  thf(fact_335_ord__eq__less__trans,axiom,
% 0.26/0.46      ! [A: nat,B: nat,C: nat] :
% 0.26/0.46        ( ( A = B )
% 0.26/0.46       => ( ( ord_less_nat @ B @ C )
% 0.26/0.46         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_eq_less_trans
% 0.26/0.46  thf(fact_336_ord__eq__less__trans,axiom,
% 0.26/0.46      ! [A: int,B: int,C: int] :
% 0.26/0.46        ( ( A = B )
% 0.26/0.46       => ( ( ord_less_int @ B @ C )
% 0.26/0.46         => ( ord_less_int @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_eq_less_trans
% 0.26/0.46  thf(fact_337_ord__less__eq__trans,axiom,
% 0.26/0.46      ! [A: real,B: real,C: real] :
% 0.26/0.46        ( ( ord_less_real @ A @ B )
% 0.26/0.46       => ( ( B = C )
% 0.26/0.46         => ( ord_less_real @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_less_eq_trans
% 0.26/0.46  thf(fact_338_ord__less__eq__trans,axiom,
% 0.26/0.46      ! [A: rat,B: rat,C: rat] :
% 0.26/0.46        ( ( ord_less_rat @ A @ B )
% 0.26/0.46       => ( ( B = C )
% 0.26/0.46         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_less_eq_trans
% 0.26/0.46  thf(fact_339_ord__less__eq__trans,axiom,
% 0.26/0.46      ! [A: num,B: num,C: num] :
% 0.26/0.46        ( ( ord_less_num @ A @ B )
% 0.26/0.46       => ( ( B = C )
% 0.26/0.46         => ( ord_less_num @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_less_eq_trans
% 0.26/0.46  thf(fact_340_ord__less__eq__trans,axiom,
% 0.26/0.46      ! [A: nat,B: nat,C: nat] :
% 0.26/0.46        ( ( ord_less_nat @ A @ B )
% 0.26/0.46       => ( ( B = C )
% 0.26/0.46         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_less_eq_trans
% 0.26/0.46  thf(fact_341_ord__less__eq__trans,axiom,
% 0.26/0.46      ! [A: int,B: int,C: int] :
% 0.26/0.46        ( ( ord_less_int @ A @ B )
% 0.26/0.46       => ( ( B = C )
% 0.26/0.46         => ( ord_less_int @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % ord_less_eq_trans
% 0.26/0.46  thf(fact_342_less__induct,axiom,
% 0.26/0.46      ! [P: nat > $o,A: nat] :
% 0.26/0.46        ( ! [X4: nat] :
% 0.26/0.46            ( ! [Y6: nat] :
% 0.26/0.46                ( ( ord_less_nat @ Y6 @ X4 )
% 0.26/0.46               => ( P @ Y6 ) )
% 0.26/0.46           => ( P @ X4 ) )
% 0.26/0.46       => ( P @ A ) ) ).
% 0.26/0.46  
% 0.26/0.46  % less_induct
% 0.26/0.46  thf(fact_343_antisym__conv3,axiom,
% 0.26/0.46      ! [Y3: real,X3: real] :
% 0.26/0.46        ( ~ ( ord_less_real @ Y3 @ X3 )
% 0.26/0.46       => ( ( ~ ( ord_less_real @ X3 @ Y3 ) )
% 0.26/0.46          = ( X3 = Y3 ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % antisym_conv3
% 0.26/0.46  thf(fact_344_antisym__conv3,axiom,
% 0.26/0.46      ! [Y3: rat,X3: rat] :
% 0.26/0.46        ( ~ ( ord_less_rat @ Y3 @ X3 )
% 0.26/0.46       => ( ( ~ ( ord_less_rat @ X3 @ Y3 ) )
% 0.26/0.46          = ( X3 = Y3 ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % antisym_conv3
% 0.26/0.46  thf(fact_345_antisym__conv3,axiom,
% 0.26/0.46      ! [Y3: num,X3: num] :
% 0.26/0.46        ( ~ ( ord_less_num @ Y3 @ X3 )
% 0.26/0.46       => ( ( ~ ( ord_less_num @ X3 @ Y3 ) )
% 0.26/0.46          = ( X3 = Y3 ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % antisym_conv3
% 0.26/0.46  thf(fact_346_antisym__conv3,axiom,
% 0.26/0.46      ! [Y3: nat,X3: nat] :
% 0.26/0.46        ( ~ ( ord_less_nat @ Y3 @ X3 )
% 0.26/0.46       => ( ( ~ ( ord_less_nat @ X3 @ Y3 ) )
% 0.26/0.46          = ( X3 = Y3 ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % antisym_conv3
% 0.26/0.46  thf(fact_347_antisym__conv3,axiom,
% 0.26/0.46      ! [Y3: int,X3: int] :
% 0.26/0.46        ( ~ ( ord_less_int @ Y3 @ X3 )
% 0.26/0.46       => ( ( ~ ( ord_less_int @ X3 @ Y3 ) )
% 0.26/0.46          = ( X3 = Y3 ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % antisym_conv3
% 0.26/0.46  thf(fact_348_linorder__cases,axiom,
% 0.26/0.46      ! [X3: real,Y3: real] :
% 0.26/0.46        ( ~ ( ord_less_real @ X3 @ Y3 )
% 0.26/0.46       => ( ( X3 != Y3 )
% 0.26/0.46         => ( ord_less_real @ Y3 @ X3 ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % linorder_cases
% 0.26/0.46  thf(fact_349_linorder__cases,axiom,
% 0.26/0.46      ! [X3: rat,Y3: rat] :
% 0.26/0.46        ( ~ ( ord_less_rat @ X3 @ Y3 )
% 0.26/0.46       => ( ( X3 != Y3 )
% 0.26/0.46         => ( ord_less_rat @ Y3 @ X3 ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % linorder_cases
% 0.26/0.46  thf(fact_350_linorder__cases,axiom,
% 0.26/0.46      ! [X3: num,Y3: num] :
% 0.26/0.46        ( ~ ( ord_less_num @ X3 @ Y3 )
% 0.26/0.46       => ( ( X3 != Y3 )
% 0.26/0.46         => ( ord_less_num @ Y3 @ X3 ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % linorder_cases
% 0.26/0.46  thf(fact_351_linorder__cases,axiom,
% 0.26/0.46      ! [X3: nat,Y3: nat] :
% 0.26/0.46        ( ~ ( ord_less_nat @ X3 @ Y3 )
% 0.26/0.46       => ( ( X3 != Y3 )
% 0.26/0.46         => ( ord_less_nat @ Y3 @ X3 ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % linorder_cases
% 0.26/0.46  thf(fact_352_linorder__cases,axiom,
% 0.26/0.46      ! [X3: int,Y3: int] :
% 0.26/0.46        ( ~ ( ord_less_int @ X3 @ Y3 )
% 0.26/0.46       => ( ( X3 != Y3 )
% 0.26/0.46         => ( ord_less_int @ Y3 @ X3 ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % linorder_cases
% 0.26/0.46  thf(fact_353_dual__order_Oasym,axiom,
% 0.26/0.46      ! [B: real,A: real] :
% 0.26/0.46        ( ( ord_less_real @ B @ A )
% 0.26/0.46       => ~ ( ord_less_real @ A @ B ) ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.asym
% 0.26/0.46  thf(fact_354_dual__order_Oasym,axiom,
% 0.26/0.46      ! [B: rat,A: rat] :
% 0.26/0.46        ( ( ord_less_rat @ B @ A )
% 0.26/0.46       => ~ ( ord_less_rat @ A @ B ) ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.asym
% 0.26/0.46  thf(fact_355_dual__order_Oasym,axiom,
% 0.26/0.46      ! [B: num,A: num] :
% 0.26/0.46        ( ( ord_less_num @ B @ A )
% 0.26/0.46       => ~ ( ord_less_num @ A @ B ) ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.asym
% 0.26/0.46  thf(fact_356_dual__order_Oasym,axiom,
% 0.26/0.46      ! [B: nat,A: nat] :
% 0.26/0.46        ( ( ord_less_nat @ B @ A )
% 0.26/0.46       => ~ ( ord_less_nat @ A @ B ) ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.asym
% 0.26/0.46  thf(fact_357_dual__order_Oasym,axiom,
% 0.26/0.46      ! [B: int,A: int] :
% 0.26/0.46        ( ( ord_less_int @ B @ A )
% 0.26/0.46       => ~ ( ord_less_int @ A @ B ) ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.asym
% 0.26/0.46  thf(fact_358_dual__order_Oirrefl,axiom,
% 0.26/0.46      ! [A: real] :
% 0.26/0.46        ~ ( ord_less_real @ A @ A ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.irrefl
% 0.26/0.46  thf(fact_359_dual__order_Oirrefl,axiom,
% 0.26/0.46      ! [A: rat] :
% 0.26/0.46        ~ ( ord_less_rat @ A @ A ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.irrefl
% 0.26/0.46  thf(fact_360_dual__order_Oirrefl,axiom,
% 0.26/0.46      ! [A: num] :
% 0.26/0.46        ~ ( ord_less_num @ A @ A ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.irrefl
% 0.26/0.46  thf(fact_361_dual__order_Oirrefl,axiom,
% 0.26/0.46      ! [A: nat] :
% 0.26/0.46        ~ ( ord_less_nat @ A @ A ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.irrefl
% 0.26/0.46  thf(fact_362_dual__order_Oirrefl,axiom,
% 0.26/0.46      ! [A: int] :
% 0.26/0.46        ~ ( ord_less_int @ A @ A ) ).
% 0.26/0.46  
% 0.26/0.46  % dual_order.irrefl
% 0.26/0.46  thf(fact_363_exists__least__iff,axiom,
% 0.26/0.46      ( ( ^ [P2: nat > $o] :
% 0.26/0.46          ? [X5: nat] : ( P2 @ X5 ) )
% 0.26/0.46      = ( ^ [P3: nat > $o] :
% 0.26/0.46          ? [N3: nat] :
% 0.26/0.46            ( ( P3 @ N3 )
% 0.26/0.46            & ! [M3: nat] :
% 0.26/0.46                ( ( ord_less_nat @ M3 @ N3 )
% 0.26/0.46               => ~ ( P3 @ M3 ) ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % exists_least_iff
% 0.26/0.46  thf(fact_364_linorder__less__wlog,axiom,
% 0.26/0.46      ! [P: real > real > $o,A: real,B: real] :
% 0.26/0.46        ( ! [A5: real,B4: real] :
% 0.26/0.46            ( ( ord_less_real @ A5 @ B4 )
% 0.26/0.46           => ( P @ A5 @ B4 ) )
% 0.26/0.46       => ( ! [A5: real] : ( P @ A5 @ A5 )
% 0.26/0.46         => ( ! [A5: real,B4: real] :
% 0.26/0.46                ( ( P @ B4 @ A5 )
% 0.26/0.46               => ( P @ A5 @ B4 ) )
% 0.26/0.46           => ( P @ A @ B ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % linorder_less_wlog
% 0.26/0.46  thf(fact_365_linorder__less__wlog,axiom,
% 0.26/0.46      ! [P: rat > rat > $o,A: rat,B: rat] :
% 0.26/0.46        ( ! [A5: rat,B4: rat] :
% 0.26/0.46            ( ( ord_less_rat @ A5 @ B4 )
% 0.26/0.46           => ( P @ A5 @ B4 ) )
% 0.26/0.46       => ( ! [A5: rat] : ( P @ A5 @ A5 )
% 0.26/0.46         => ( ! [A5: rat,B4: rat] :
% 0.26/0.46                ( ( P @ B4 @ A5 )
% 0.26/0.46               => ( P @ A5 @ B4 ) )
% 0.26/0.46           => ( P @ A @ B ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % linorder_less_wlog
% 0.26/0.46  thf(fact_366_linorder__less__wlog,axiom,
% 0.26/0.46      ! [P: num > num > $o,A: num,B: num] :
% 0.26/0.46        ( ! [A5: num,B4: num] :
% 0.26/0.46            ( ( ord_less_num @ A5 @ B4 )
% 0.26/0.46           => ( P @ A5 @ B4 ) )
% 0.26/0.46       => ( ! [A5: num] : ( P @ A5 @ A5 )
% 0.26/0.46         => ( ! [A5: num,B4: num] :
% 0.26/0.46                ( ( P @ B4 @ A5 )
% 0.26/0.46               => ( P @ A5 @ B4 ) )
% 0.26/0.46           => ( P @ A @ B ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % linorder_less_wlog
% 0.26/0.46  thf(fact_367_linorder__less__wlog,axiom,
% 0.26/0.46      ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.26/0.46        ( ! [A5: nat,B4: nat] :
% 0.26/0.46            ( ( ord_less_nat @ A5 @ B4 )
% 0.26/0.46           => ( P @ A5 @ B4 ) )
% 0.26/0.46       => ( ! [A5: nat] : ( P @ A5 @ A5 )
% 0.26/0.46         => ( ! [A5: nat,B4: nat] :
% 0.26/0.46                ( ( P @ B4 @ A5 )
% 0.26/0.46               => ( P @ A5 @ B4 ) )
% 0.26/0.46           => ( P @ A @ B ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % linorder_less_wlog
% 0.26/0.46  thf(fact_368_linorder__less__wlog,axiom,
% 0.26/0.46      ! [P: int > int > $o,A: int,B: int] :
% 0.26/0.46        ( ! [A5: int,B4: int] :
% 0.26/0.46            ( ( ord_less_int @ A5 @ B4 )
% 0.26/0.46           => ( P @ A5 @ B4 ) )
% 0.26/0.46       => ( ! [A5: int] : ( P @ A5 @ A5 )
% 0.26/0.46         => ( ! [A5: int,B4: int] :
% 0.26/0.46                ( ( P @ B4 @ A5 )
% 0.26/0.46               => ( P @ A5 @ B4 ) )
% 0.26/0.46           => ( P @ A @ B ) ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % linorder_less_wlog
% 0.26/0.46  thf(fact_369_order_Ostrict__trans,axiom,
% 0.26/0.46      ! [A: real,B: real,C: real] :
% 0.26/0.46        ( ( ord_less_real @ A @ B )
% 0.26/0.46       => ( ( ord_less_real @ B @ C )
% 0.26/0.46         => ( ord_less_real @ A @ C ) ) ) ).
% 0.26/0.46  
% 0.26/0.46  % order.strict_trans
% 0.26/0.46  thf(fact_370_order_Ostrict__trans,axiom,
% 0.26/0.46      ! [A: rat,B: rat,C: rat] :
% 0.26/0.46        ( ( ord_less_rat @ A @ B )
% 0.26/0.46       => ( ( ord_less_rat @ B @ C )
% 0.26/0.46         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_trans
% 0.26/0.47  thf(fact_371_order_Ostrict__trans,axiom,
% 0.26/0.47      ! [A: num,B: num,C: num] :
% 0.26/0.47        ( ( ord_less_num @ A @ B )
% 0.26/0.47       => ( ( ord_less_num @ B @ C )
% 0.26/0.47         => ( ord_less_num @ A @ C ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_trans
% 0.26/0.47  thf(fact_372_order_Ostrict__trans,axiom,
% 0.26/0.47      ! [A: nat,B: nat,C: nat] :
% 0.26/0.47        ( ( ord_less_nat @ A @ B )
% 0.26/0.47       => ( ( ord_less_nat @ B @ C )
% 0.26/0.47         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_trans
% 0.26/0.47  thf(fact_373_order_Ostrict__trans,axiom,
% 0.26/0.47      ! [A: int,B: int,C: int] :
% 0.26/0.47        ( ( ord_less_int @ A @ B )
% 0.26/0.47       => ( ( ord_less_int @ B @ C )
% 0.26/0.47         => ( ord_less_int @ A @ C ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_trans
% 0.26/0.47  thf(fact_374_not__less__iff__gr__or__eq,axiom,
% 0.26/0.47      ! [X3: real,Y3: real] :
% 0.26/0.47        ( ( ~ ( ord_less_real @ X3 @ Y3 ) )
% 0.26/0.47        = ( ( ord_less_real @ Y3 @ X3 )
% 0.26/0.47          | ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % not_less_iff_gr_or_eq
% 0.26/0.47  thf(fact_375_not__less__iff__gr__or__eq,axiom,
% 0.26/0.47      ! [X3: rat,Y3: rat] :
% 0.26/0.47        ( ( ~ ( ord_less_rat @ X3 @ Y3 ) )
% 0.26/0.47        = ( ( ord_less_rat @ Y3 @ X3 )
% 0.26/0.47          | ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % not_less_iff_gr_or_eq
% 0.26/0.47  thf(fact_376_not__less__iff__gr__or__eq,axiom,
% 0.26/0.47      ! [X3: num,Y3: num] :
% 0.26/0.47        ( ( ~ ( ord_less_num @ X3 @ Y3 ) )
% 0.26/0.47        = ( ( ord_less_num @ Y3 @ X3 )
% 0.26/0.47          | ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % not_less_iff_gr_or_eq
% 0.26/0.47  thf(fact_377_not__less__iff__gr__or__eq,axiom,
% 0.26/0.47      ! [X3: nat,Y3: nat] :
% 0.26/0.47        ( ( ~ ( ord_less_nat @ X3 @ Y3 ) )
% 0.26/0.47        = ( ( ord_less_nat @ Y3 @ X3 )
% 0.26/0.47          | ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % not_less_iff_gr_or_eq
% 0.26/0.47  thf(fact_378_not__less__iff__gr__or__eq,axiom,
% 0.26/0.47      ! [X3: int,Y3: int] :
% 0.26/0.47        ( ( ~ ( ord_less_int @ X3 @ Y3 ) )
% 0.26/0.47        = ( ( ord_less_int @ Y3 @ X3 )
% 0.26/0.47          | ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % not_less_iff_gr_or_eq
% 0.26/0.47  thf(fact_379_dual__order_Ostrict__trans,axiom,
% 0.26/0.47      ! [B: real,A: real,C: real] :
% 0.26/0.47        ( ( ord_less_real @ B @ A )
% 0.26/0.47       => ( ( ord_less_real @ C @ B )
% 0.26/0.47         => ( ord_less_real @ C @ A ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_trans
% 0.26/0.47  thf(fact_380_dual__order_Ostrict__trans,axiom,
% 0.26/0.47      ! [B: rat,A: rat,C: rat] :
% 0.26/0.47        ( ( ord_less_rat @ B @ A )
% 0.26/0.47       => ( ( ord_less_rat @ C @ B )
% 0.26/0.47         => ( ord_less_rat @ C @ A ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_trans
% 0.26/0.47  thf(fact_381_dual__order_Ostrict__trans,axiom,
% 0.26/0.47      ! [B: num,A: num,C: num] :
% 0.26/0.47        ( ( ord_less_num @ B @ A )
% 0.26/0.47       => ( ( ord_less_num @ C @ B )
% 0.26/0.47         => ( ord_less_num @ C @ A ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_trans
% 0.26/0.47  thf(fact_382_dual__order_Ostrict__trans,axiom,
% 0.26/0.47      ! [B: nat,A: nat,C: nat] :
% 0.26/0.47        ( ( ord_less_nat @ B @ A )
% 0.26/0.47       => ( ( ord_less_nat @ C @ B )
% 0.26/0.47         => ( ord_less_nat @ C @ A ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_trans
% 0.26/0.47  thf(fact_383_dual__order_Ostrict__trans,axiom,
% 0.26/0.47      ! [B: int,A: int,C: int] :
% 0.26/0.47        ( ( ord_less_int @ B @ A )
% 0.26/0.47       => ( ( ord_less_int @ C @ B )
% 0.26/0.47         => ( ord_less_int @ C @ A ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_trans
% 0.26/0.47  thf(fact_384_order_Ostrict__implies__not__eq,axiom,
% 0.26/0.47      ! [A: real,B: real] :
% 0.26/0.47        ( ( ord_less_real @ A @ B )
% 0.26/0.47       => ( A != B ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_implies_not_eq
% 0.26/0.47  thf(fact_385_order_Ostrict__implies__not__eq,axiom,
% 0.26/0.47      ! [A: rat,B: rat] :
% 0.26/0.47        ( ( ord_less_rat @ A @ B )
% 0.26/0.47       => ( A != B ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_implies_not_eq
% 0.26/0.47  thf(fact_386_order_Ostrict__implies__not__eq,axiom,
% 0.26/0.47      ! [A: num,B: num] :
% 0.26/0.47        ( ( ord_less_num @ A @ B )
% 0.26/0.47       => ( A != B ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_implies_not_eq
% 0.26/0.47  thf(fact_387_order_Ostrict__implies__not__eq,axiom,
% 0.26/0.47      ! [A: nat,B: nat] :
% 0.26/0.47        ( ( ord_less_nat @ A @ B )
% 0.26/0.47       => ( A != B ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_implies_not_eq
% 0.26/0.47  thf(fact_388_order_Ostrict__implies__not__eq,axiom,
% 0.26/0.47      ! [A: int,B: int] :
% 0.26/0.47        ( ( ord_less_int @ A @ B )
% 0.26/0.47       => ( A != B ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_implies_not_eq
% 0.26/0.47  thf(fact_389_dual__order_Ostrict__implies__not__eq,axiom,
% 0.26/0.47      ! [B: real,A: real] :
% 0.26/0.47        ( ( ord_less_real @ B @ A )
% 0.26/0.47       => ( A != B ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_implies_not_eq
% 0.26/0.47  thf(fact_390_dual__order_Ostrict__implies__not__eq,axiom,
% 0.26/0.47      ! [B: rat,A: rat] :
% 0.26/0.47        ( ( ord_less_rat @ B @ A )
% 0.26/0.47       => ( A != B ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_implies_not_eq
% 0.26/0.47  thf(fact_391_dual__order_Ostrict__implies__not__eq,axiom,
% 0.26/0.47      ! [B: num,A: num] :
% 0.26/0.47        ( ( ord_less_num @ B @ A )
% 0.26/0.47       => ( A != B ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_implies_not_eq
% 0.26/0.47  thf(fact_392_dual__order_Ostrict__implies__not__eq,axiom,
% 0.26/0.47      ! [B: nat,A: nat] :
% 0.26/0.47        ( ( ord_less_nat @ B @ A )
% 0.26/0.47       => ( A != B ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_implies_not_eq
% 0.26/0.47  thf(fact_393_dual__order_Ostrict__implies__not__eq,axiom,
% 0.26/0.47      ! [B: int,A: int] :
% 0.26/0.47        ( ( ord_less_int @ B @ A )
% 0.26/0.47       => ( A != B ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_implies_not_eq
% 0.26/0.47  thf(fact_394_linorder__neqE,axiom,
% 0.26/0.47      ! [X3: real,Y3: real] :
% 0.26/0.47        ( ( X3 != Y3 )
% 0.26/0.47       => ( ~ ( ord_less_real @ X3 @ Y3 )
% 0.26/0.47         => ( ord_less_real @ Y3 @ X3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_neqE
% 0.26/0.47  thf(fact_395_linorder__neqE,axiom,
% 0.26/0.47      ! [X3: rat,Y3: rat] :
% 0.26/0.47        ( ( X3 != Y3 )
% 0.26/0.47       => ( ~ ( ord_less_rat @ X3 @ Y3 )
% 0.26/0.47         => ( ord_less_rat @ Y3 @ X3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_neqE
% 0.26/0.47  thf(fact_396_linorder__neqE,axiom,
% 0.26/0.47      ! [X3: num,Y3: num] :
% 0.26/0.47        ( ( X3 != Y3 )
% 0.26/0.47       => ( ~ ( ord_less_num @ X3 @ Y3 )
% 0.26/0.47         => ( ord_less_num @ Y3 @ X3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_neqE
% 0.26/0.47  thf(fact_397_linorder__neqE,axiom,
% 0.26/0.47      ! [X3: nat,Y3: nat] :
% 0.26/0.47        ( ( X3 != Y3 )
% 0.26/0.47       => ( ~ ( ord_less_nat @ X3 @ Y3 )
% 0.26/0.47         => ( ord_less_nat @ Y3 @ X3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_neqE
% 0.26/0.47  thf(fact_398_linorder__neqE,axiom,
% 0.26/0.47      ! [X3: int,Y3: int] :
% 0.26/0.47        ( ( X3 != Y3 )
% 0.26/0.47       => ( ~ ( ord_less_int @ X3 @ Y3 )
% 0.26/0.47         => ( ord_less_int @ Y3 @ X3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_neqE
% 0.26/0.47  thf(fact_399_order__less__asym,axiom,
% 0.26/0.47      ! [X3: real,Y3: real] :
% 0.26/0.47        ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.47       => ~ ( ord_less_real @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_asym
% 0.26/0.47  thf(fact_400_order__less__asym,axiom,
% 0.26/0.47      ! [X3: rat,Y3: rat] :
% 0.26/0.47        ( ( ord_less_rat @ X3 @ Y3 )
% 0.26/0.47       => ~ ( ord_less_rat @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_asym
% 0.26/0.47  thf(fact_401_order__less__asym,axiom,
% 0.26/0.47      ! [X3: num,Y3: num] :
% 0.26/0.47        ( ( ord_less_num @ X3 @ Y3 )
% 0.26/0.47       => ~ ( ord_less_num @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_asym
% 0.26/0.47  thf(fact_402_order__less__asym,axiom,
% 0.26/0.47      ! [X3: nat,Y3: nat] :
% 0.26/0.47        ( ( ord_less_nat @ X3 @ Y3 )
% 0.26/0.47       => ~ ( ord_less_nat @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_asym
% 0.26/0.47  thf(fact_403_order__less__asym,axiom,
% 0.26/0.47      ! [X3: int,Y3: int] :
% 0.26/0.47        ( ( ord_less_int @ X3 @ Y3 )
% 0.26/0.47       => ~ ( ord_less_int @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_asym
% 0.26/0.47  thf(fact_404_linorder__neq__iff,axiom,
% 0.26/0.47      ! [X3: real,Y3: real] :
% 0.26/0.47        ( ( X3 != Y3 )
% 0.26/0.47        = ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.47          | ( ord_less_real @ Y3 @ X3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_neq_iff
% 0.26/0.47  thf(fact_405_linorder__neq__iff,axiom,
% 0.26/0.47      ! [X3: rat,Y3: rat] :
% 0.26/0.47        ( ( X3 != Y3 )
% 0.26/0.47        = ( ( ord_less_rat @ X3 @ Y3 )
% 0.26/0.47          | ( ord_less_rat @ Y3 @ X3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_neq_iff
% 0.26/0.47  thf(fact_406_linorder__neq__iff,axiom,
% 0.26/0.47      ! [X3: num,Y3: num] :
% 0.26/0.47        ( ( X3 != Y3 )
% 0.26/0.47        = ( ( ord_less_num @ X3 @ Y3 )
% 0.26/0.47          | ( ord_less_num @ Y3 @ X3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_neq_iff
% 0.26/0.47  thf(fact_407_linorder__neq__iff,axiom,
% 0.26/0.47      ! [X3: nat,Y3: nat] :
% 0.26/0.47        ( ( X3 != Y3 )
% 0.26/0.47        = ( ( ord_less_nat @ X3 @ Y3 )
% 0.26/0.47          | ( ord_less_nat @ Y3 @ X3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_neq_iff
% 0.26/0.47  thf(fact_408_linorder__neq__iff,axiom,
% 0.26/0.47      ! [X3: int,Y3: int] :
% 0.26/0.47        ( ( X3 != Y3 )
% 0.26/0.47        = ( ( ord_less_int @ X3 @ Y3 )
% 0.26/0.47          | ( ord_less_int @ Y3 @ X3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_neq_iff
% 0.26/0.47  thf(fact_409_order__less__asym_H,axiom,
% 0.26/0.47      ! [A: real,B: real] :
% 0.26/0.47        ( ( ord_less_real @ A @ B )
% 0.26/0.47       => ~ ( ord_less_real @ B @ A ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_asym'
% 0.26/0.47  thf(fact_410_order__less__asym_H,axiom,
% 0.26/0.47      ! [A: rat,B: rat] :
% 0.26/0.47        ( ( ord_less_rat @ A @ B )
% 0.26/0.47       => ~ ( ord_less_rat @ B @ A ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_asym'
% 0.26/0.47  thf(fact_411_order__less__asym_H,axiom,
% 0.26/0.47      ! [A: num,B: num] :
% 0.26/0.47        ( ( ord_less_num @ A @ B )
% 0.26/0.47       => ~ ( ord_less_num @ B @ A ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_asym'
% 0.26/0.47  thf(fact_412_order__less__asym_H,axiom,
% 0.26/0.47      ! [A: nat,B: nat] :
% 0.26/0.47        ( ( ord_less_nat @ A @ B )
% 0.26/0.47       => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_asym'
% 0.26/0.47  thf(fact_413_order__less__asym_H,axiom,
% 0.26/0.47      ! [A: int,B: int] :
% 0.26/0.47        ( ( ord_less_int @ A @ B )
% 0.26/0.47       => ~ ( ord_less_int @ B @ A ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_asym'
% 0.26/0.47  thf(fact_414_order__less__trans,axiom,
% 0.26/0.47      ! [X3: real,Y3: real,Z: real] :
% 0.26/0.47        ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_real @ Y3 @ Z )
% 0.26/0.47         => ( ord_less_real @ X3 @ Z ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_trans
% 0.26/0.47  thf(fact_415_order__less__trans,axiom,
% 0.26/0.47      ! [X3: rat,Y3: rat,Z: rat] :
% 0.26/0.47        ( ( ord_less_rat @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_rat @ Y3 @ Z )
% 0.26/0.47         => ( ord_less_rat @ X3 @ Z ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_trans
% 0.26/0.47  thf(fact_416_order__less__trans,axiom,
% 0.26/0.47      ! [X3: num,Y3: num,Z: num] :
% 0.26/0.47        ( ( ord_less_num @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_num @ Y3 @ Z )
% 0.26/0.47         => ( ord_less_num @ X3 @ Z ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_trans
% 0.26/0.47  thf(fact_417_order__less__trans,axiom,
% 0.26/0.47      ! [X3: nat,Y3: nat,Z: nat] :
% 0.26/0.47        ( ( ord_less_nat @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_nat @ Y3 @ Z )
% 0.26/0.47         => ( ord_less_nat @ X3 @ Z ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_trans
% 0.26/0.47  thf(fact_418_order__less__trans,axiom,
% 0.26/0.47      ! [X3: int,Y3: int,Z: int] :
% 0.26/0.47        ( ( ord_less_int @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_int @ Y3 @ Z )
% 0.26/0.47         => ( ord_less_int @ X3 @ Z ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_trans
% 0.26/0.47  thf(fact_419_ord__eq__less__subst,axiom,
% 0.26/0.47      ! [A: real,F: real > real,B: real,C: real] :
% 0.26/0.47        ( ( A
% 0.26/0.47          = ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_real @ B @ C )
% 0.26/0.47         => ( ! [X4: real,Y4: real] :
% 0.26/0.47                ( ( ord_less_real @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % ord_eq_less_subst
% 0.26/0.47  thf(fact_420_ord__eq__less__subst,axiom,
% 0.26/0.47      ! [A: rat,F: real > rat,B: real,C: real] :
% 0.26/0.47        ( ( A
% 0.26/0.47          = ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_real @ B @ C )
% 0.26/0.47         => ( ! [X4: real,Y4: real] :
% 0.26/0.47                ( ( ord_less_real @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % ord_eq_less_subst
% 0.26/0.47  thf(fact_421_ord__eq__less__subst,axiom,
% 0.26/0.47      ! [A: num,F: real > num,B: real,C: real] :
% 0.26/0.47        ( ( A
% 0.26/0.47          = ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_real @ B @ C )
% 0.26/0.47         => ( ! [X4: real,Y4: real] :
% 0.26/0.47                ( ( ord_less_real @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % ord_eq_less_subst
% 0.26/0.47  thf(fact_422_ord__eq__less__subst,axiom,
% 0.26/0.47      ! [A: nat,F: real > nat,B: real,C: real] :
% 0.26/0.47        ( ( A
% 0.26/0.47          = ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_real @ B @ C )
% 0.26/0.47         => ( ! [X4: real,Y4: real] :
% 0.26/0.47                ( ( ord_less_real @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % ord_eq_less_subst
% 0.26/0.47  thf(fact_423_ord__eq__less__subst,axiom,
% 0.26/0.47      ! [A: int,F: real > int,B: real,C: real] :
% 0.26/0.47        ( ( A
% 0.26/0.47          = ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_real @ B @ C )
% 0.26/0.47         => ( ! [X4: real,Y4: real] :
% 0.26/0.47                ( ( ord_less_real @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % ord_eq_less_subst
% 0.26/0.47  thf(fact_424_ord__eq__less__subst,axiom,
% 0.26/0.47      ! [A: real,F: rat > real,B: rat,C: rat] :
% 0.26/0.47        ( ( A
% 0.26/0.47          = ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_rat @ B @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % ord_eq_less_subst
% 0.26/0.47  thf(fact_425_ord__eq__less__subst,axiom,
% 0.26/0.47      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.26/0.47        ( ( A
% 0.26/0.47          = ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_rat @ B @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % ord_eq_less_subst
% 0.26/0.47  thf(fact_426_ord__eq__less__subst,axiom,
% 0.26/0.47      ! [A: num,F: rat > num,B: rat,C: rat] :
% 0.26/0.47        ( ( A
% 0.26/0.47          = ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_rat @ B @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % ord_eq_less_subst
% 0.26/0.47  thf(fact_427_ord__eq__less__subst,axiom,
% 0.26/0.47      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 0.26/0.47        ( ( A
% 0.26/0.47          = ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_rat @ B @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % ord_eq_less_subst
% 0.26/0.47  thf(fact_428_ord__eq__less__subst,axiom,
% 0.26/0.47      ! [A: int,F: rat > int,B: rat,C: rat] :
% 0.26/0.47        ( ( A
% 0.26/0.47          = ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_rat @ B @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % ord_eq_less_subst
% 0.26/0.47  thf(fact_429_ord__less__eq__subst,axiom,
% 0.26/0.47      ! [A: real,B: real,F: real > real,C: real] :
% 0.26/0.47        ( ( ord_less_real @ A @ B )
% 0.26/0.47       => ( ( ( F @ B )
% 0.26/0.47            = C )
% 0.26/0.47         => ( ! [X4: real,Y4: real] :
% 0.26/0.47                ( ( ord_less_real @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % ord_less_eq_subst
% 0.26/0.47  thf(fact_430_ord__less__eq__subst,axiom,
% 0.26/0.47      ! [A: real,B: real,F: real > rat,C: rat] :
% 0.26/0.47        ( ( ord_less_real @ A @ B )
% 0.26/0.47       => ( ( ( F @ B )
% 0.26/0.47            = C )
% 0.26/0.47         => ( ! [X4: real,Y4: real] :
% 0.26/0.47                ( ( ord_less_real @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % ord_less_eq_subst
% 0.26/0.47  thf(fact_431_ord__less__eq__subst,axiom,
% 0.26/0.47      ! [A: real,B: real,F: real > num,C: num] :
% 0.26/0.47        ( ( ord_less_real @ A @ B )
% 0.26/0.47       => ( ( ( F @ B )
% 0.26/0.47            = C )
% 0.26/0.47         => ( ! [X4: real,Y4: real] :
% 0.26/0.47                ( ( ord_less_real @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % ord_less_eq_subst
% 0.26/0.47  thf(fact_432_ord__less__eq__subst,axiom,
% 0.26/0.47      ! [A: real,B: real,F: real > nat,C: nat] :
% 0.26/0.47        ( ( ord_less_real @ A @ B )
% 0.26/0.47       => ( ( ( F @ B )
% 0.26/0.47            = C )
% 0.26/0.47         => ( ! [X4: real,Y4: real] :
% 0.26/0.47                ( ( ord_less_real @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % ord_less_eq_subst
% 0.26/0.47  thf(fact_433_ord__less__eq__subst,axiom,
% 0.26/0.47      ! [A: real,B: real,F: real > int,C: int] :
% 0.26/0.47        ( ( ord_less_real @ A @ B )
% 0.26/0.47       => ( ( ( F @ B )
% 0.26/0.47            = C )
% 0.26/0.47         => ( ! [X4: real,Y4: real] :
% 0.26/0.47                ( ( ord_less_real @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % ord_less_eq_subst
% 0.26/0.47  thf(fact_434_ord__less__eq__subst,axiom,
% 0.26/0.47      ! [A: rat,B: rat,F: rat > real,C: real] :
% 0.26/0.47        ( ( ord_less_rat @ A @ B )
% 0.26/0.47       => ( ( ( F @ B )
% 0.26/0.47            = C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % ord_less_eq_subst
% 0.26/0.47  thf(fact_435_ord__less__eq__subst,axiom,
% 0.26/0.47      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.26/0.47        ( ( ord_less_rat @ A @ B )
% 0.26/0.47       => ( ( ( F @ B )
% 0.26/0.47            = C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % ord_less_eq_subst
% 0.26/0.47  thf(fact_436_ord__less__eq__subst,axiom,
% 0.26/0.47      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.26/0.47        ( ( ord_less_rat @ A @ B )
% 0.26/0.47       => ( ( ( F @ B )
% 0.26/0.47            = C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % ord_less_eq_subst
% 0.26/0.47  thf(fact_437_ord__less__eq__subst,axiom,
% 0.26/0.47      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.26/0.47        ( ( ord_less_rat @ A @ B )
% 0.26/0.47       => ( ( ( F @ B )
% 0.26/0.47            = C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % ord_less_eq_subst
% 0.26/0.47  thf(fact_438_ord__less__eq__subst,axiom,
% 0.26/0.47      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.26/0.47        ( ( ord_less_rat @ A @ B )
% 0.26/0.47       => ( ( ( F @ B )
% 0.26/0.47            = C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % ord_less_eq_subst
% 0.26/0.47  thf(fact_439_order__less__irrefl,axiom,
% 0.26/0.47      ! [X3: real] :
% 0.26/0.47        ~ ( ord_less_real @ X3 @ X3 ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_irrefl
% 0.26/0.47  thf(fact_440_order__less__irrefl,axiom,
% 0.26/0.47      ! [X3: rat] :
% 0.26/0.47        ~ ( ord_less_rat @ X3 @ X3 ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_irrefl
% 0.26/0.47  thf(fact_441_order__less__irrefl,axiom,
% 0.26/0.47      ! [X3: num] :
% 0.26/0.47        ~ ( ord_less_num @ X3 @ X3 ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_irrefl
% 0.26/0.47  thf(fact_442_order__less__irrefl,axiom,
% 0.26/0.47      ! [X3: nat] :
% 0.26/0.47        ~ ( ord_less_nat @ X3 @ X3 ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_irrefl
% 0.26/0.47  thf(fact_443_order__less__irrefl,axiom,
% 0.26/0.47      ! [X3: int] :
% 0.26/0.47        ~ ( ord_less_int @ X3 @ X3 ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_irrefl
% 0.26/0.47  thf(fact_444_order__less__subst1,axiom,
% 0.26/0.47      ! [A: real,F: real > real,B: real,C: real] :
% 0.26/0.47        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_real @ B @ C )
% 0.26/0.47         => ( ! [X4: real,Y4: real] :
% 0.26/0.47                ( ( ord_less_real @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_subst1
% 0.26/0.47  thf(fact_445_order__less__subst1,axiom,
% 0.26/0.47      ! [A: real,F: rat > real,B: rat,C: rat] :
% 0.26/0.47        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_rat @ B @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_subst1
% 0.26/0.47  thf(fact_446_order__less__subst1,axiom,
% 0.26/0.47      ! [A: real,F: num > real,B: num,C: num] :
% 0.26/0.47        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_num @ B @ C )
% 0.26/0.47         => ( ! [X4: num,Y4: num] :
% 0.26/0.47                ( ( ord_less_num @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_subst1
% 0.26/0.47  thf(fact_447_order__less__subst1,axiom,
% 0.26/0.47      ! [A: real,F: nat > real,B: nat,C: nat] :
% 0.26/0.47        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_nat @ B @ C )
% 0.26/0.47         => ( ! [X4: nat,Y4: nat] :
% 0.26/0.47                ( ( ord_less_nat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_subst1
% 0.26/0.47  thf(fact_448_order__less__subst1,axiom,
% 0.26/0.47      ! [A: real,F: int > real,B: int,C: int] :
% 0.26/0.47        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_int @ B @ C )
% 0.26/0.47         => ( ! [X4: int,Y4: int] :
% 0.26/0.47                ( ( ord_less_int @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_subst1
% 0.26/0.47  thf(fact_449_order__less__subst1,axiom,
% 0.26/0.47      ! [A: rat,F: real > rat,B: real,C: real] :
% 0.26/0.47        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_real @ B @ C )
% 0.26/0.47         => ( ! [X4: real,Y4: real] :
% 0.26/0.47                ( ( ord_less_real @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_subst1
% 0.26/0.47  thf(fact_450_order__less__subst1,axiom,
% 0.26/0.47      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.26/0.47        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_rat @ B @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_subst1
% 0.26/0.47  thf(fact_451_order__less__subst1,axiom,
% 0.26/0.47      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.26/0.47        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_num @ B @ C )
% 0.26/0.47         => ( ! [X4: num,Y4: num] :
% 0.26/0.47                ( ( ord_less_num @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_subst1
% 0.26/0.47  thf(fact_452_order__less__subst1,axiom,
% 0.26/0.47      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 0.26/0.47        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_nat @ B @ C )
% 0.26/0.47         => ( ! [X4: nat,Y4: nat] :
% 0.26/0.47                ( ( ord_less_nat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_subst1
% 0.26/0.47  thf(fact_453_order__less__subst1,axiom,
% 0.26/0.47      ! [A: rat,F: int > rat,B: int,C: int] :
% 0.26/0.47        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_int @ B @ C )
% 0.26/0.47         => ( ! [X4: int,Y4: int] :
% 0.26/0.47                ( ( ord_less_int @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_subst1
% 0.26/0.47  thf(fact_454_order__less__subst2,axiom,
% 0.26/0.47      ! [A: real,B: real,F: real > real,C: real] :
% 0.26/0.47        ( ( ord_less_real @ A @ B )
% 0.26/0.47       => ( ( ord_less_real @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: real,Y4: real] :
% 0.26/0.47                ( ( ord_less_real @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_subst2
% 0.26/0.47  thf(fact_455_order__less__subst2,axiom,
% 0.26/0.47      ! [A: real,B: real,F: real > rat,C: rat] :
% 0.26/0.47        ( ( ord_less_real @ A @ B )
% 0.26/0.47       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: real,Y4: real] :
% 0.26/0.47                ( ( ord_less_real @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_subst2
% 0.26/0.47  thf(fact_456_order__less__subst2,axiom,
% 0.26/0.47      ! [A: real,B: real,F: real > num,C: num] :
% 0.26/0.47        ( ( ord_less_real @ A @ B )
% 0.26/0.47       => ( ( ord_less_num @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: real,Y4: real] :
% 0.26/0.47                ( ( ord_less_real @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_subst2
% 0.26/0.47  thf(fact_457_order__less__subst2,axiom,
% 0.26/0.47      ! [A: real,B: real,F: real > nat,C: nat] :
% 0.26/0.47        ( ( ord_less_real @ A @ B )
% 0.26/0.47       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: real,Y4: real] :
% 0.26/0.47                ( ( ord_less_real @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_subst2
% 0.26/0.47  thf(fact_458_order__less__subst2,axiom,
% 0.26/0.47      ! [A: real,B: real,F: real > int,C: int] :
% 0.26/0.47        ( ( ord_less_real @ A @ B )
% 0.26/0.47       => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: real,Y4: real] :
% 0.26/0.47                ( ( ord_less_real @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_subst2
% 0.26/0.47  thf(fact_459_order__less__subst2,axiom,
% 0.26/0.47      ! [A: rat,B: rat,F: rat > real,C: real] :
% 0.26/0.47        ( ( ord_less_rat @ A @ B )
% 0.26/0.47       => ( ( ord_less_real @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_subst2
% 0.26/0.47  thf(fact_460_order__less__subst2,axiom,
% 0.26/0.47      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.26/0.47        ( ( ord_less_rat @ A @ B )
% 0.26/0.47       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_subst2
% 0.26/0.47  thf(fact_461_order__less__subst2,axiom,
% 0.26/0.47      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.26/0.47        ( ( ord_less_rat @ A @ B )
% 0.26/0.47       => ( ( ord_less_num @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_subst2
% 0.26/0.47  thf(fact_462_order__less__subst2,axiom,
% 0.26/0.47      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.26/0.47        ( ( ord_less_rat @ A @ B )
% 0.26/0.47       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_subst2
% 0.26/0.47  thf(fact_463_order__less__subst2,axiom,
% 0.26/0.47      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.26/0.47        ( ( ord_less_rat @ A @ B )
% 0.26/0.47       => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_subst2
% 0.26/0.47  thf(fact_464_order__less__not__sym,axiom,
% 0.26/0.47      ! [X3: real,Y3: real] :
% 0.26/0.47        ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.47       => ~ ( ord_less_real @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_not_sym
% 0.26/0.47  thf(fact_465_order__less__not__sym,axiom,
% 0.26/0.47      ! [X3: rat,Y3: rat] :
% 0.26/0.47        ( ( ord_less_rat @ X3 @ Y3 )
% 0.26/0.47       => ~ ( ord_less_rat @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_not_sym
% 0.26/0.47  thf(fact_466_order__less__not__sym,axiom,
% 0.26/0.47      ! [X3: num,Y3: num] :
% 0.26/0.47        ( ( ord_less_num @ X3 @ Y3 )
% 0.26/0.47       => ~ ( ord_less_num @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_not_sym
% 0.26/0.47  thf(fact_467_order__less__not__sym,axiom,
% 0.26/0.47      ! [X3: nat,Y3: nat] :
% 0.26/0.47        ( ( ord_less_nat @ X3 @ Y3 )
% 0.26/0.47       => ~ ( ord_less_nat @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_not_sym
% 0.26/0.47  thf(fact_468_order__less__not__sym,axiom,
% 0.26/0.47      ! [X3: int,Y3: int] :
% 0.26/0.47        ( ( ord_less_int @ X3 @ Y3 )
% 0.26/0.47       => ~ ( ord_less_int @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_not_sym
% 0.26/0.47  thf(fact_469_order__less__imp__triv,axiom,
% 0.26/0.47      ! [X3: real,Y3: real,P: $o] :
% 0.26/0.47        ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_real @ Y3 @ X3 )
% 0.26/0.47         => P ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_triv
% 0.26/0.47  thf(fact_470_order__less__imp__triv,axiom,
% 0.26/0.47      ! [X3: rat,Y3: rat,P: $o] :
% 0.26/0.47        ( ( ord_less_rat @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_rat @ Y3 @ X3 )
% 0.26/0.47         => P ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_triv
% 0.26/0.47  thf(fact_471_order__less__imp__triv,axiom,
% 0.26/0.47      ! [X3: num,Y3: num,P: $o] :
% 0.26/0.47        ( ( ord_less_num @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_num @ Y3 @ X3 )
% 0.26/0.47         => P ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_triv
% 0.26/0.47  thf(fact_472_order__less__imp__triv,axiom,
% 0.26/0.47      ! [X3: nat,Y3: nat,P: $o] :
% 0.26/0.47        ( ( ord_less_nat @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_nat @ Y3 @ X3 )
% 0.26/0.47         => P ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_triv
% 0.26/0.47  thf(fact_473_order__less__imp__triv,axiom,
% 0.26/0.47      ! [X3: int,Y3: int,P: $o] :
% 0.26/0.47        ( ( ord_less_int @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_int @ Y3 @ X3 )
% 0.26/0.47         => P ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_triv
% 0.26/0.47  thf(fact_474_linorder__less__linear,axiom,
% 0.26/0.47      ! [X3: real,Y3: real] :
% 0.26/0.47        ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.47        | ( X3 = Y3 )
% 0.26/0.47        | ( ord_less_real @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_less_linear
% 0.26/0.47  thf(fact_475_linorder__less__linear,axiom,
% 0.26/0.47      ! [X3: rat,Y3: rat] :
% 0.26/0.47        ( ( ord_less_rat @ X3 @ Y3 )
% 0.26/0.47        | ( X3 = Y3 )
% 0.26/0.47        | ( ord_less_rat @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_less_linear
% 0.26/0.47  thf(fact_476_linorder__less__linear,axiom,
% 0.26/0.47      ! [X3: num,Y3: num] :
% 0.26/0.47        ( ( ord_less_num @ X3 @ Y3 )
% 0.26/0.47        | ( X3 = Y3 )
% 0.26/0.47        | ( ord_less_num @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_less_linear
% 0.26/0.47  thf(fact_477_linorder__less__linear,axiom,
% 0.26/0.47      ! [X3: nat,Y3: nat] :
% 0.26/0.47        ( ( ord_less_nat @ X3 @ Y3 )
% 0.26/0.47        | ( X3 = Y3 )
% 0.26/0.47        | ( ord_less_nat @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_less_linear
% 0.26/0.47  thf(fact_478_linorder__less__linear,axiom,
% 0.26/0.47      ! [X3: int,Y3: int] :
% 0.26/0.47        ( ( ord_less_int @ X3 @ Y3 )
% 0.26/0.47        | ( X3 = Y3 )
% 0.26/0.47        | ( ord_less_int @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_less_linear
% 0.26/0.47  thf(fact_479_order__less__imp__not__eq,axiom,
% 0.26/0.47      ! [X3: real,Y3: real] :
% 0.26/0.47        ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.47       => ( X3 != Y3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_not_eq
% 0.26/0.47  thf(fact_480_order__less__imp__not__eq,axiom,
% 0.26/0.47      ! [X3: rat,Y3: rat] :
% 0.26/0.47        ( ( ord_less_rat @ X3 @ Y3 )
% 0.26/0.47       => ( X3 != Y3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_not_eq
% 0.26/0.47  thf(fact_481_order__less__imp__not__eq,axiom,
% 0.26/0.47      ! [X3: num,Y3: num] :
% 0.26/0.47        ( ( ord_less_num @ X3 @ Y3 )
% 0.26/0.47       => ( X3 != Y3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_not_eq
% 0.26/0.47  thf(fact_482_order__less__imp__not__eq,axiom,
% 0.26/0.47      ! [X3: nat,Y3: nat] :
% 0.26/0.47        ( ( ord_less_nat @ X3 @ Y3 )
% 0.26/0.47       => ( X3 != Y3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_not_eq
% 0.26/0.47  thf(fact_483_order__less__imp__not__eq,axiom,
% 0.26/0.47      ! [X3: int,Y3: int] :
% 0.26/0.47        ( ( ord_less_int @ X3 @ Y3 )
% 0.26/0.47       => ( X3 != Y3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_not_eq
% 0.26/0.47  thf(fact_484_order__less__imp__not__eq2,axiom,
% 0.26/0.47      ! [X3: real,Y3: real] :
% 0.26/0.47        ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.47       => ( Y3 != X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_not_eq2
% 0.26/0.47  thf(fact_485_order__less__imp__not__eq2,axiom,
% 0.26/0.47      ! [X3: rat,Y3: rat] :
% 0.26/0.47        ( ( ord_less_rat @ X3 @ Y3 )
% 0.26/0.47       => ( Y3 != X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_not_eq2
% 0.26/0.47  thf(fact_486_order__less__imp__not__eq2,axiom,
% 0.26/0.47      ! [X3: num,Y3: num] :
% 0.26/0.47        ( ( ord_less_num @ X3 @ Y3 )
% 0.26/0.47       => ( Y3 != X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_not_eq2
% 0.26/0.47  thf(fact_487_order__less__imp__not__eq2,axiom,
% 0.26/0.47      ! [X3: nat,Y3: nat] :
% 0.26/0.47        ( ( ord_less_nat @ X3 @ Y3 )
% 0.26/0.47       => ( Y3 != X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_not_eq2
% 0.26/0.47  thf(fact_488_order__less__imp__not__eq2,axiom,
% 0.26/0.47      ! [X3: int,Y3: int] :
% 0.26/0.47        ( ( ord_less_int @ X3 @ Y3 )
% 0.26/0.47       => ( Y3 != X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_not_eq2
% 0.26/0.47  thf(fact_489_order__less__imp__not__less,axiom,
% 0.26/0.47      ! [X3: real,Y3: real] :
% 0.26/0.47        ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.47       => ~ ( ord_less_real @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_not_less
% 0.26/0.47  thf(fact_490_order__less__imp__not__less,axiom,
% 0.26/0.47      ! [X3: rat,Y3: rat] :
% 0.26/0.47        ( ( ord_less_rat @ X3 @ Y3 )
% 0.26/0.47       => ~ ( ord_less_rat @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_not_less
% 0.26/0.47  thf(fact_491_order__less__imp__not__less,axiom,
% 0.26/0.47      ! [X3: num,Y3: num] :
% 0.26/0.47        ( ( ord_less_num @ X3 @ Y3 )
% 0.26/0.47       => ~ ( ord_less_num @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_not_less
% 0.26/0.47  thf(fact_492_order__less__imp__not__less,axiom,
% 0.26/0.47      ! [X3: nat,Y3: nat] :
% 0.26/0.47        ( ( ord_less_nat @ X3 @ Y3 )
% 0.26/0.47       => ~ ( ord_less_nat @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_not_less
% 0.26/0.47  thf(fact_493_order__less__imp__not__less,axiom,
% 0.26/0.47      ! [X3: int,Y3: int] :
% 0.26/0.47        ( ( ord_less_int @ X3 @ Y3 )
% 0.26/0.47       => ~ ( ord_less_int @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_not_less
% 0.26/0.47  thf(fact_494_nat__neq__iff,axiom,
% 0.26/0.47      ! [M: nat,N: nat] :
% 0.26/0.47        ( ( M != N )
% 0.26/0.47        = ( ( ord_less_nat @ M @ N )
% 0.26/0.47          | ( ord_less_nat @ N @ M ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % nat_neq_iff
% 0.26/0.47  thf(fact_495_less__not__refl,axiom,
% 0.26/0.47      ! [N: nat] :
% 0.26/0.47        ~ ( ord_less_nat @ N @ N ) ).
% 0.26/0.47  
% 0.26/0.47  % less_not_refl
% 0.26/0.47  thf(fact_496_less__not__refl2,axiom,
% 0.26/0.47      ! [N: nat,M: nat] :
% 0.26/0.47        ( ( ord_less_nat @ N @ M )
% 0.26/0.47       => ( M != N ) ) ).
% 0.26/0.47  
% 0.26/0.47  % less_not_refl2
% 0.26/0.47  thf(fact_497_less__not__refl3,axiom,
% 0.26/0.47      ! [S: nat,T: nat] :
% 0.26/0.47        ( ( ord_less_nat @ S @ T )
% 0.26/0.47       => ( S != T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % less_not_refl3
% 0.26/0.47  thf(fact_498_less__irrefl__nat,axiom,
% 0.26/0.47      ! [N: nat] :
% 0.26/0.47        ~ ( ord_less_nat @ N @ N ) ).
% 0.26/0.47  
% 0.26/0.47  % less_irrefl_nat
% 0.26/0.47  thf(fact_499_nat__less__induct,axiom,
% 0.26/0.47      ! [P: nat > $o,N: nat] :
% 0.26/0.47        ( ! [N2: nat] :
% 0.26/0.47            ( ! [M2: nat] :
% 0.26/0.47                ( ( ord_less_nat @ M2 @ N2 )
% 0.26/0.47               => ( P @ M2 ) )
% 0.26/0.47           => ( P @ N2 ) )
% 0.26/0.47       => ( P @ N ) ) ).
% 0.26/0.47  
% 0.26/0.47  % nat_less_induct
% 0.26/0.47  thf(fact_500_infinite__descent,axiom,
% 0.26/0.47      ! [P: nat > $o,N: nat] :
% 0.26/0.47        ( ! [N2: nat] :
% 0.26/0.47            ( ~ ( P @ N2 )
% 0.26/0.47           => ? [M2: nat] :
% 0.26/0.47                ( ( ord_less_nat @ M2 @ N2 )
% 0.26/0.47                & ~ ( P @ M2 ) ) )
% 0.26/0.47       => ( P @ N ) ) ).
% 0.26/0.47  
% 0.26/0.47  % infinite_descent
% 0.26/0.47  thf(fact_501_linorder__neqE__nat,axiom,
% 0.26/0.47      ! [X3: nat,Y3: nat] :
% 0.26/0.47        ( ( X3 != Y3 )
% 0.26/0.47       => ( ~ ( ord_less_nat @ X3 @ Y3 )
% 0.26/0.47         => ( ord_less_nat @ Y3 @ X3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_neqE_nat
% 0.26/0.47  thf(fact_502_Nat_Oex__has__greatest__nat,axiom,
% 0.26/0.47      ! [P: nat > $o,K: nat,B: nat] :
% 0.26/0.47        ( ( P @ K )
% 0.26/0.47       => ( ! [Y4: nat] :
% 0.26/0.47              ( ( P @ Y4 )
% 0.26/0.47             => ( ord_less_eq_nat @ Y4 @ B ) )
% 0.26/0.47         => ? [X4: nat] :
% 0.26/0.47              ( ( P @ X4 )
% 0.26/0.47              & ! [Y6: nat] :
% 0.26/0.47                  ( ( P @ Y6 )
% 0.26/0.47                 => ( ord_less_eq_nat @ Y6 @ X4 ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % Nat.ex_has_greatest_nat
% 0.26/0.47  thf(fact_503_nat__le__linear,axiom,
% 0.26/0.47      ! [M: nat,N: nat] :
% 0.26/0.47        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.47        | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.26/0.47  
% 0.26/0.47  % nat_le_linear
% 0.26/0.47  thf(fact_504_le__antisym,axiom,
% 0.26/0.47      ! [M: nat,N: nat] :
% 0.26/0.47        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.47       => ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.47         => ( M = N ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % le_antisym
% 0.26/0.47  thf(fact_505_eq__imp__le,axiom,
% 0.26/0.47      ! [M: nat,N: nat] :
% 0.26/0.47        ( ( M = N )
% 0.26/0.47       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.47  
% 0.26/0.47  % eq_imp_le
% 0.26/0.47  thf(fact_506_le__trans,axiom,
% 0.26/0.47      ! [I: nat,J: nat,K: nat] :
% 0.26/0.47        ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.47       => ( ( ord_less_eq_nat @ J @ K )
% 0.26/0.47         => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % le_trans
% 0.26/0.47  thf(fact_507_le__refl,axiom,
% 0.26/0.47      ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.26/0.47  
% 0.26/0.47  % le_refl
% 0.26/0.47  thf(fact_508_leD,axiom,
% 0.26/0.47      ! [Y3: real,X3: real] :
% 0.26/0.47        ( ( ord_less_eq_real @ Y3 @ X3 )
% 0.26/0.47       => ~ ( ord_less_real @ X3 @ Y3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % leD
% 0.26/0.47  thf(fact_509_leD,axiom,
% 0.26/0.47      ! [Y3: set_nat,X3: set_nat] :
% 0.26/0.47        ( ( ord_less_eq_set_nat @ Y3 @ X3 )
% 0.26/0.47       => ~ ( ord_less_set_nat @ X3 @ Y3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % leD
% 0.26/0.47  thf(fact_510_leD,axiom,
% 0.26/0.47      ! [Y3: rat,X3: rat] :
% 0.26/0.47        ( ( ord_less_eq_rat @ Y3 @ X3 )
% 0.26/0.47       => ~ ( ord_less_rat @ X3 @ Y3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % leD
% 0.26/0.47  thf(fact_511_leD,axiom,
% 0.26/0.47      ! [Y3: num,X3: num] :
% 0.26/0.47        ( ( ord_less_eq_num @ Y3 @ X3 )
% 0.26/0.47       => ~ ( ord_less_num @ X3 @ Y3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % leD
% 0.26/0.47  thf(fact_512_leD,axiom,
% 0.26/0.47      ! [Y3: nat,X3: nat] :
% 0.26/0.47        ( ( ord_less_eq_nat @ Y3 @ X3 )
% 0.26/0.47       => ~ ( ord_less_nat @ X3 @ Y3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % leD
% 0.26/0.47  thf(fact_513_leD,axiom,
% 0.26/0.47      ! [Y3: int,X3: int] :
% 0.26/0.47        ( ( ord_less_eq_int @ Y3 @ X3 )
% 0.26/0.47       => ~ ( ord_less_int @ X3 @ Y3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % leD
% 0.26/0.47  thf(fact_514_leI,axiom,
% 0.26/0.47      ! [X3: real,Y3: real] :
% 0.26/0.47        ( ~ ( ord_less_real @ X3 @ Y3 )
% 0.26/0.47       => ( ord_less_eq_real @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % leI
% 0.26/0.47  thf(fact_515_leI,axiom,
% 0.26/0.47      ! [X3: rat,Y3: rat] :
% 0.26/0.47        ( ~ ( ord_less_rat @ X3 @ Y3 )
% 0.26/0.47       => ( ord_less_eq_rat @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % leI
% 0.26/0.47  thf(fact_516_leI,axiom,
% 0.26/0.47      ! [X3: num,Y3: num] :
% 0.26/0.47        ( ~ ( ord_less_num @ X3 @ Y3 )
% 0.26/0.47       => ( ord_less_eq_num @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % leI
% 0.26/0.47  thf(fact_517_leI,axiom,
% 0.26/0.47      ! [X3: nat,Y3: nat] :
% 0.26/0.47        ( ~ ( ord_less_nat @ X3 @ Y3 )
% 0.26/0.47       => ( ord_less_eq_nat @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % leI
% 0.26/0.47  thf(fact_518_leI,axiom,
% 0.26/0.47      ! [X3: int,Y3: int] :
% 0.26/0.47        ( ~ ( ord_less_int @ X3 @ Y3 )
% 0.26/0.47       => ( ord_less_eq_int @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % leI
% 0.26/0.47  thf(fact_519_nless__le,axiom,
% 0.26/0.47      ! [A: real,B: real] :
% 0.26/0.47        ( ( ~ ( ord_less_real @ A @ B ) )
% 0.26/0.47        = ( ~ ( ord_less_eq_real @ A @ B )
% 0.26/0.47          | ( A = B ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % nless_le
% 0.26/0.47  thf(fact_520_nless__le,axiom,
% 0.26/0.47      ! [A: set_nat,B: set_nat] :
% 0.26/0.47        ( ( ~ ( ord_less_set_nat @ A @ B ) )
% 0.26/0.47        = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 0.26/0.47          | ( A = B ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % nless_le
% 0.26/0.47  thf(fact_521_nless__le,axiom,
% 0.26/0.47      ! [A: rat,B: rat] :
% 0.26/0.47        ( ( ~ ( ord_less_rat @ A @ B ) )
% 0.26/0.47        = ( ~ ( ord_less_eq_rat @ A @ B )
% 0.26/0.47          | ( A = B ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % nless_le
% 0.26/0.47  thf(fact_522_nless__le,axiom,
% 0.26/0.47      ! [A: num,B: num] :
% 0.26/0.47        ( ( ~ ( ord_less_num @ A @ B ) )
% 0.26/0.47        = ( ~ ( ord_less_eq_num @ A @ B )
% 0.26/0.47          | ( A = B ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % nless_le
% 0.26/0.47  thf(fact_523_nless__le,axiom,
% 0.26/0.47      ! [A: nat,B: nat] :
% 0.26/0.47        ( ( ~ ( ord_less_nat @ A @ B ) )
% 0.26/0.47        = ( ~ ( ord_less_eq_nat @ A @ B )
% 0.26/0.47          | ( A = B ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % nless_le
% 0.26/0.47  thf(fact_524_nless__le,axiom,
% 0.26/0.47      ! [A: int,B: int] :
% 0.26/0.47        ( ( ~ ( ord_less_int @ A @ B ) )
% 0.26/0.47        = ( ~ ( ord_less_eq_int @ A @ B )
% 0.26/0.47          | ( A = B ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % nless_le
% 0.26/0.47  thf(fact_525_antisym__conv1,axiom,
% 0.26/0.47      ! [X3: real,Y3: real] :
% 0.26/0.47        ( ~ ( ord_less_real @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.26/0.47          = ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % antisym_conv1
% 0.26/0.47  thf(fact_526_antisym__conv1,axiom,
% 0.26/0.47      ! [X3: set_nat,Y3: set_nat] :
% 0.26/0.47        ( ~ ( ord_less_set_nat @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 0.26/0.47          = ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % antisym_conv1
% 0.26/0.47  thf(fact_527_antisym__conv1,axiom,
% 0.26/0.47      ! [X3: rat,Y3: rat] :
% 0.26/0.47        ( ~ ( ord_less_rat @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.26/0.47          = ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % antisym_conv1
% 0.26/0.47  thf(fact_528_antisym__conv1,axiom,
% 0.26/0.47      ! [X3: num,Y3: num] :
% 0.26/0.47        ( ~ ( ord_less_num @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.26/0.47          = ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % antisym_conv1
% 0.26/0.47  thf(fact_529_antisym__conv1,axiom,
% 0.26/0.47      ! [X3: nat,Y3: nat] :
% 0.26/0.47        ( ~ ( ord_less_nat @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.26/0.47          = ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % antisym_conv1
% 0.26/0.47  thf(fact_530_antisym__conv1,axiom,
% 0.26/0.47      ! [X3: int,Y3: int] :
% 0.26/0.47        ( ~ ( ord_less_int @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.26/0.47          = ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % antisym_conv1
% 0.26/0.47  thf(fact_531_antisym__conv2,axiom,
% 0.26/0.47      ! [X3: real,Y3: real] :
% 0.26/0.47        ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.26/0.47       => ( ( ~ ( ord_less_real @ X3 @ Y3 ) )
% 0.26/0.47          = ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % antisym_conv2
% 0.26/0.47  thf(fact_532_antisym__conv2,axiom,
% 0.26/0.47      ! [X3: set_nat,Y3: set_nat] :
% 0.26/0.47        ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 0.26/0.47       => ( ( ~ ( ord_less_set_nat @ X3 @ Y3 ) )
% 0.26/0.47          = ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % antisym_conv2
% 0.26/0.47  thf(fact_533_antisym__conv2,axiom,
% 0.26/0.47      ! [X3: rat,Y3: rat] :
% 0.26/0.47        ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.26/0.47       => ( ( ~ ( ord_less_rat @ X3 @ Y3 ) )
% 0.26/0.47          = ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % antisym_conv2
% 0.26/0.47  thf(fact_534_antisym__conv2,axiom,
% 0.26/0.47      ! [X3: num,Y3: num] :
% 0.26/0.47        ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.26/0.47       => ( ( ~ ( ord_less_num @ X3 @ Y3 ) )
% 0.26/0.47          = ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % antisym_conv2
% 0.26/0.47  thf(fact_535_antisym__conv2,axiom,
% 0.26/0.47      ! [X3: nat,Y3: nat] :
% 0.26/0.47        ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.26/0.47       => ( ( ~ ( ord_less_nat @ X3 @ Y3 ) )
% 0.26/0.47          = ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % antisym_conv2
% 0.26/0.47  thf(fact_536_antisym__conv2,axiom,
% 0.26/0.47      ! [X3: int,Y3: int] :
% 0.26/0.47        ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.26/0.47       => ( ( ~ ( ord_less_int @ X3 @ Y3 ) )
% 0.26/0.47          = ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % antisym_conv2
% 0.26/0.47  thf(fact_537_dense__ge,axiom,
% 0.26/0.47      ! [Z: real,Y3: real] :
% 0.26/0.47        ( ! [X4: real] :
% 0.26/0.47            ( ( ord_less_real @ Z @ X4 )
% 0.26/0.47           => ( ord_less_eq_real @ Y3 @ X4 ) )
% 0.26/0.47       => ( ord_less_eq_real @ Y3 @ Z ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dense_ge
% 0.26/0.47  thf(fact_538_dense__ge,axiom,
% 0.26/0.47      ! [Z: rat,Y3: rat] :
% 0.26/0.47        ( ! [X4: rat] :
% 0.26/0.47            ( ( ord_less_rat @ Z @ X4 )
% 0.26/0.47           => ( ord_less_eq_rat @ Y3 @ X4 ) )
% 0.26/0.47       => ( ord_less_eq_rat @ Y3 @ Z ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dense_ge
% 0.26/0.47  thf(fact_539_dense__le,axiom,
% 0.26/0.47      ! [Y3: real,Z: real] :
% 0.26/0.47        ( ! [X4: real] :
% 0.26/0.47            ( ( ord_less_real @ X4 @ Y3 )
% 0.26/0.47           => ( ord_less_eq_real @ X4 @ Z ) )
% 0.26/0.47       => ( ord_less_eq_real @ Y3 @ Z ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dense_le
% 0.26/0.47  thf(fact_540_dense__le,axiom,
% 0.26/0.47      ! [Y3: rat,Z: rat] :
% 0.26/0.47        ( ! [X4: rat] :
% 0.26/0.47            ( ( ord_less_rat @ X4 @ Y3 )
% 0.26/0.47           => ( ord_less_eq_rat @ X4 @ Z ) )
% 0.26/0.47       => ( ord_less_eq_rat @ Y3 @ Z ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dense_le
% 0.26/0.47  thf(fact_541_less__le__not__le,axiom,
% 0.26/0.47      ( ord_less_real
% 0.26/0.47      = ( ^ [X: real,Y: real] :
% 0.26/0.47            ( ( ord_less_eq_real @ X @ Y )
% 0.26/0.47            & ~ ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % less_le_not_le
% 0.26/0.47  thf(fact_542_less__le__not__le,axiom,
% 0.26/0.47      ( ord_less_set_nat
% 0.26/0.47      = ( ^ [X: set_nat,Y: set_nat] :
% 0.26/0.47            ( ( ord_less_eq_set_nat @ X @ Y )
% 0.26/0.47            & ~ ( ord_less_eq_set_nat @ Y @ X ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % less_le_not_le
% 0.26/0.47  thf(fact_543_less__le__not__le,axiom,
% 0.26/0.47      ( ord_less_rat
% 0.26/0.47      = ( ^ [X: rat,Y: rat] :
% 0.26/0.47            ( ( ord_less_eq_rat @ X @ Y )
% 0.26/0.47            & ~ ( ord_less_eq_rat @ Y @ X ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % less_le_not_le
% 0.26/0.47  thf(fact_544_less__le__not__le,axiom,
% 0.26/0.47      ( ord_less_num
% 0.26/0.47      = ( ^ [X: num,Y: num] :
% 0.26/0.47            ( ( ord_less_eq_num @ X @ Y )
% 0.26/0.47            & ~ ( ord_less_eq_num @ Y @ X ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % less_le_not_le
% 0.26/0.47  thf(fact_545_less__le__not__le,axiom,
% 0.26/0.47      ( ord_less_nat
% 0.26/0.47      = ( ^ [X: nat,Y: nat] :
% 0.26/0.47            ( ( ord_less_eq_nat @ X @ Y )
% 0.26/0.47            & ~ ( ord_less_eq_nat @ Y @ X ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % less_le_not_le
% 0.26/0.47  thf(fact_546_less__le__not__le,axiom,
% 0.26/0.47      ( ord_less_int
% 0.26/0.47      = ( ^ [X: int,Y: int] :
% 0.26/0.47            ( ( ord_less_eq_int @ X @ Y )
% 0.26/0.47            & ~ ( ord_less_eq_int @ Y @ X ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % less_le_not_le
% 0.26/0.47  thf(fact_547_not__le__imp__less,axiom,
% 0.26/0.47      ! [Y3: real,X3: real] :
% 0.26/0.47        ( ~ ( ord_less_eq_real @ Y3 @ X3 )
% 0.26/0.47       => ( ord_less_real @ X3 @ Y3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % not_le_imp_less
% 0.26/0.47  thf(fact_548_not__le__imp__less,axiom,
% 0.26/0.47      ! [Y3: rat,X3: rat] :
% 0.26/0.47        ( ~ ( ord_less_eq_rat @ Y3 @ X3 )
% 0.26/0.47       => ( ord_less_rat @ X3 @ Y3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % not_le_imp_less
% 0.26/0.47  thf(fact_549_not__le__imp__less,axiom,
% 0.26/0.47      ! [Y3: num,X3: num] :
% 0.26/0.47        ( ~ ( ord_less_eq_num @ Y3 @ X3 )
% 0.26/0.47       => ( ord_less_num @ X3 @ Y3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % not_le_imp_less
% 0.26/0.47  thf(fact_550_not__le__imp__less,axiom,
% 0.26/0.47      ! [Y3: nat,X3: nat] :
% 0.26/0.47        ( ~ ( ord_less_eq_nat @ Y3 @ X3 )
% 0.26/0.47       => ( ord_less_nat @ X3 @ Y3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % not_le_imp_less
% 0.26/0.47  thf(fact_551_not__le__imp__less,axiom,
% 0.26/0.47      ! [Y3: int,X3: int] :
% 0.26/0.47        ( ~ ( ord_less_eq_int @ Y3 @ X3 )
% 0.26/0.47       => ( ord_less_int @ X3 @ Y3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % not_le_imp_less
% 0.26/0.47  thf(fact_552_order_Oorder__iff__strict,axiom,
% 0.26/0.47      ( ord_less_eq_real
% 0.26/0.47      = ( ^ [A4: real,B3: real] :
% 0.26/0.47            ( ( ord_less_real @ A4 @ B3 )
% 0.26/0.47            | ( A4 = B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.order_iff_strict
% 0.26/0.47  thf(fact_553_order_Oorder__iff__strict,axiom,
% 0.26/0.47      ( ord_less_eq_set_nat
% 0.26/0.47      = ( ^ [A4: set_nat,B3: set_nat] :
% 0.26/0.47            ( ( ord_less_set_nat @ A4 @ B3 )
% 0.26/0.47            | ( A4 = B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.order_iff_strict
% 0.26/0.47  thf(fact_554_order_Oorder__iff__strict,axiom,
% 0.26/0.47      ( ord_less_eq_rat
% 0.26/0.47      = ( ^ [A4: rat,B3: rat] :
% 0.26/0.47            ( ( ord_less_rat @ A4 @ B3 )
% 0.26/0.47            | ( A4 = B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.order_iff_strict
% 0.26/0.47  thf(fact_555_order_Oorder__iff__strict,axiom,
% 0.26/0.47      ( ord_less_eq_num
% 0.26/0.47      = ( ^ [A4: num,B3: num] :
% 0.26/0.47            ( ( ord_less_num @ A4 @ B3 )
% 0.26/0.47            | ( A4 = B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.order_iff_strict
% 0.26/0.47  thf(fact_556_order_Oorder__iff__strict,axiom,
% 0.26/0.47      ( ord_less_eq_nat
% 0.26/0.47      = ( ^ [A4: nat,B3: nat] :
% 0.26/0.47            ( ( ord_less_nat @ A4 @ B3 )
% 0.26/0.47            | ( A4 = B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.order_iff_strict
% 0.26/0.47  thf(fact_557_order_Oorder__iff__strict,axiom,
% 0.26/0.47      ( ord_less_eq_int
% 0.26/0.47      = ( ^ [A4: int,B3: int] :
% 0.26/0.47            ( ( ord_less_int @ A4 @ B3 )
% 0.26/0.47            | ( A4 = B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.order_iff_strict
% 0.26/0.47  thf(fact_558_order_Ostrict__iff__order,axiom,
% 0.26/0.47      ( ord_less_real
% 0.26/0.47      = ( ^ [A4: real,B3: real] :
% 0.26/0.47            ( ( ord_less_eq_real @ A4 @ B3 )
% 0.26/0.47            & ( A4 != B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_iff_order
% 0.26/0.47  thf(fact_559_order_Ostrict__iff__order,axiom,
% 0.26/0.47      ( ord_less_set_nat
% 0.26/0.47      = ( ^ [A4: set_nat,B3: set_nat] :
% 0.26/0.47            ( ( ord_less_eq_set_nat @ A4 @ B3 )
% 0.26/0.47            & ( A4 != B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_iff_order
% 0.26/0.47  thf(fact_560_order_Ostrict__iff__order,axiom,
% 0.26/0.47      ( ord_less_rat
% 0.26/0.47      = ( ^ [A4: rat,B3: rat] :
% 0.26/0.47            ( ( ord_less_eq_rat @ A4 @ B3 )
% 0.26/0.47            & ( A4 != B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_iff_order
% 0.26/0.47  thf(fact_561_order_Ostrict__iff__order,axiom,
% 0.26/0.47      ( ord_less_num
% 0.26/0.47      = ( ^ [A4: num,B3: num] :
% 0.26/0.47            ( ( ord_less_eq_num @ A4 @ B3 )
% 0.26/0.47            & ( A4 != B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_iff_order
% 0.26/0.47  thf(fact_562_order_Ostrict__iff__order,axiom,
% 0.26/0.47      ( ord_less_nat
% 0.26/0.47      = ( ^ [A4: nat,B3: nat] :
% 0.26/0.47            ( ( ord_less_eq_nat @ A4 @ B3 )
% 0.26/0.47            & ( A4 != B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_iff_order
% 0.26/0.47  thf(fact_563_order_Ostrict__iff__order,axiom,
% 0.26/0.47      ( ord_less_int
% 0.26/0.47      = ( ^ [A4: int,B3: int] :
% 0.26/0.47            ( ( ord_less_eq_int @ A4 @ B3 )
% 0.26/0.47            & ( A4 != B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_iff_order
% 0.26/0.47  thf(fact_564_order_Ostrict__trans1,axiom,
% 0.26/0.47      ! [A: real,B: real,C: real] :
% 0.26/0.47        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.47       => ( ( ord_less_real @ B @ C )
% 0.26/0.47         => ( ord_less_real @ A @ C ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_trans1
% 0.26/0.47  thf(fact_565_order_Ostrict__trans1,axiom,
% 0.26/0.47      ! [A: set_nat,B: set_nat,C: set_nat] :
% 0.26/0.47        ( ( ord_less_eq_set_nat @ A @ B )
% 0.26/0.47       => ( ( ord_less_set_nat @ B @ C )
% 0.26/0.47         => ( ord_less_set_nat @ A @ C ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_trans1
% 0.26/0.47  thf(fact_566_order_Ostrict__trans1,axiom,
% 0.26/0.47      ! [A: rat,B: rat,C: rat] :
% 0.26/0.47        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.47       => ( ( ord_less_rat @ B @ C )
% 0.26/0.47         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_trans1
% 0.26/0.47  thf(fact_567_order_Ostrict__trans1,axiom,
% 0.26/0.47      ! [A: num,B: num,C: num] :
% 0.26/0.47        ( ( ord_less_eq_num @ A @ B )
% 0.26/0.47       => ( ( ord_less_num @ B @ C )
% 0.26/0.47         => ( ord_less_num @ A @ C ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_trans1
% 0.26/0.47  thf(fact_568_order_Ostrict__trans1,axiom,
% 0.26/0.47      ! [A: nat,B: nat,C: nat] :
% 0.26/0.47        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.47       => ( ( ord_less_nat @ B @ C )
% 0.26/0.47         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_trans1
% 0.26/0.47  thf(fact_569_order_Ostrict__trans1,axiom,
% 0.26/0.47      ! [A: int,B: int,C: int] :
% 0.26/0.47        ( ( ord_less_eq_int @ A @ B )
% 0.26/0.47       => ( ( ord_less_int @ B @ C )
% 0.26/0.47         => ( ord_less_int @ A @ C ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_trans1
% 0.26/0.47  thf(fact_570_order_Ostrict__trans2,axiom,
% 0.26/0.47      ! [A: real,B: real,C: real] :
% 0.26/0.47        ( ( ord_less_real @ A @ B )
% 0.26/0.47       => ( ( ord_less_eq_real @ B @ C )
% 0.26/0.47         => ( ord_less_real @ A @ C ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_trans2
% 0.26/0.47  thf(fact_571_order_Ostrict__trans2,axiom,
% 0.26/0.47      ! [A: set_nat,B: set_nat,C: set_nat] :
% 0.26/0.47        ( ( ord_less_set_nat @ A @ B )
% 0.26/0.47       => ( ( ord_less_eq_set_nat @ B @ C )
% 0.26/0.47         => ( ord_less_set_nat @ A @ C ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_trans2
% 0.26/0.47  thf(fact_572_order_Ostrict__trans2,axiom,
% 0.26/0.47      ! [A: rat,B: rat,C: rat] :
% 0.26/0.47        ( ( ord_less_rat @ A @ B )
% 0.26/0.47       => ( ( ord_less_eq_rat @ B @ C )
% 0.26/0.47         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_trans2
% 0.26/0.47  thf(fact_573_order_Ostrict__trans2,axiom,
% 0.26/0.47      ! [A: num,B: num,C: num] :
% 0.26/0.47        ( ( ord_less_num @ A @ B )
% 0.26/0.47       => ( ( ord_less_eq_num @ B @ C )
% 0.26/0.47         => ( ord_less_num @ A @ C ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_trans2
% 0.26/0.47  thf(fact_574_order_Ostrict__trans2,axiom,
% 0.26/0.47      ! [A: nat,B: nat,C: nat] :
% 0.26/0.47        ( ( ord_less_nat @ A @ B )
% 0.26/0.47       => ( ( ord_less_eq_nat @ B @ C )
% 0.26/0.47         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_trans2
% 0.26/0.47  thf(fact_575_order_Ostrict__trans2,axiom,
% 0.26/0.47      ! [A: int,B: int,C: int] :
% 0.26/0.47        ( ( ord_less_int @ A @ B )
% 0.26/0.47       => ( ( ord_less_eq_int @ B @ C )
% 0.26/0.47         => ( ord_less_int @ A @ C ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_trans2
% 0.26/0.47  thf(fact_576_order_Ostrict__iff__not,axiom,
% 0.26/0.47      ( ord_less_real
% 0.26/0.47      = ( ^ [A4: real,B3: real] :
% 0.26/0.47            ( ( ord_less_eq_real @ A4 @ B3 )
% 0.26/0.47            & ~ ( ord_less_eq_real @ B3 @ A4 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_iff_not
% 0.26/0.47  thf(fact_577_order_Ostrict__iff__not,axiom,
% 0.26/0.47      ( ord_less_set_nat
% 0.26/0.47      = ( ^ [A4: set_nat,B3: set_nat] :
% 0.26/0.47            ( ( ord_less_eq_set_nat @ A4 @ B3 )
% 0.26/0.47            & ~ ( ord_less_eq_set_nat @ B3 @ A4 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_iff_not
% 0.26/0.47  thf(fact_578_order_Ostrict__iff__not,axiom,
% 0.26/0.47      ( ord_less_rat
% 0.26/0.47      = ( ^ [A4: rat,B3: rat] :
% 0.26/0.47            ( ( ord_less_eq_rat @ A4 @ B3 )
% 0.26/0.47            & ~ ( ord_less_eq_rat @ B3 @ A4 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_iff_not
% 0.26/0.47  thf(fact_579_order_Ostrict__iff__not,axiom,
% 0.26/0.47      ( ord_less_num
% 0.26/0.47      = ( ^ [A4: num,B3: num] :
% 0.26/0.47            ( ( ord_less_eq_num @ A4 @ B3 )
% 0.26/0.47            & ~ ( ord_less_eq_num @ B3 @ A4 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_iff_not
% 0.26/0.47  thf(fact_580_order_Ostrict__iff__not,axiom,
% 0.26/0.47      ( ord_less_nat
% 0.26/0.47      = ( ^ [A4: nat,B3: nat] :
% 0.26/0.47            ( ( ord_less_eq_nat @ A4 @ B3 )
% 0.26/0.47            & ~ ( ord_less_eq_nat @ B3 @ A4 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_iff_not
% 0.26/0.47  thf(fact_581_order_Ostrict__iff__not,axiom,
% 0.26/0.47      ( ord_less_int
% 0.26/0.47      = ( ^ [A4: int,B3: int] :
% 0.26/0.47            ( ( ord_less_eq_int @ A4 @ B3 )
% 0.26/0.47            & ~ ( ord_less_eq_int @ B3 @ A4 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_iff_not
% 0.26/0.47  thf(fact_582_dense__ge__bounded,axiom,
% 0.26/0.47      ! [Z: real,X3: real,Y3: real] :
% 0.26/0.47        ( ( ord_less_real @ Z @ X3 )
% 0.26/0.47       => ( ! [W2: real] :
% 0.26/0.47              ( ( ord_less_real @ Z @ W2 )
% 0.26/0.47             => ( ( ord_less_real @ W2 @ X3 )
% 0.26/0.47               => ( ord_less_eq_real @ Y3 @ W2 ) ) )
% 0.26/0.47         => ( ord_less_eq_real @ Y3 @ Z ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dense_ge_bounded
% 0.26/0.47  thf(fact_583_dense__ge__bounded,axiom,
% 0.26/0.47      ! [Z: rat,X3: rat,Y3: rat] :
% 0.26/0.47        ( ( ord_less_rat @ Z @ X3 )
% 0.26/0.47       => ( ! [W2: rat] :
% 0.26/0.47              ( ( ord_less_rat @ Z @ W2 )
% 0.26/0.47             => ( ( ord_less_rat @ W2 @ X3 )
% 0.26/0.47               => ( ord_less_eq_rat @ Y3 @ W2 ) ) )
% 0.26/0.47         => ( ord_less_eq_rat @ Y3 @ Z ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dense_ge_bounded
% 0.26/0.47  thf(fact_584_dense__le__bounded,axiom,
% 0.26/0.47      ! [X3: real,Y3: real,Z: real] :
% 0.26/0.47        ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.47       => ( ! [W2: real] :
% 0.26/0.47              ( ( ord_less_real @ X3 @ W2 )
% 0.26/0.47             => ( ( ord_less_real @ W2 @ Y3 )
% 0.26/0.47               => ( ord_less_eq_real @ W2 @ Z ) ) )
% 0.26/0.47         => ( ord_less_eq_real @ Y3 @ Z ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dense_le_bounded
% 0.26/0.47  thf(fact_585_dense__le__bounded,axiom,
% 0.26/0.47      ! [X3: rat,Y3: rat,Z: rat] :
% 0.26/0.47        ( ( ord_less_rat @ X3 @ Y3 )
% 0.26/0.47       => ( ! [W2: rat] :
% 0.26/0.47              ( ( ord_less_rat @ X3 @ W2 )
% 0.26/0.47             => ( ( ord_less_rat @ W2 @ Y3 )
% 0.26/0.47               => ( ord_less_eq_rat @ W2 @ Z ) ) )
% 0.26/0.47         => ( ord_less_eq_rat @ Y3 @ Z ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dense_le_bounded
% 0.26/0.47  thf(fact_586_dual__order_Oorder__iff__strict,axiom,
% 0.26/0.47      ( ord_less_eq_real
% 0.26/0.47      = ( ^ [B3: real,A4: real] :
% 0.26/0.47            ( ( ord_less_real @ B3 @ A4 )
% 0.26/0.47            | ( A4 = B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.order_iff_strict
% 0.26/0.47  thf(fact_587_dual__order_Oorder__iff__strict,axiom,
% 0.26/0.47      ( ord_less_eq_set_nat
% 0.26/0.47      = ( ^ [B3: set_nat,A4: set_nat] :
% 0.26/0.47            ( ( ord_less_set_nat @ B3 @ A4 )
% 0.26/0.47            | ( A4 = B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.order_iff_strict
% 0.26/0.47  thf(fact_588_dual__order_Oorder__iff__strict,axiom,
% 0.26/0.47      ( ord_less_eq_rat
% 0.26/0.47      = ( ^ [B3: rat,A4: rat] :
% 0.26/0.47            ( ( ord_less_rat @ B3 @ A4 )
% 0.26/0.47            | ( A4 = B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.order_iff_strict
% 0.26/0.47  thf(fact_589_dual__order_Oorder__iff__strict,axiom,
% 0.26/0.47      ( ord_less_eq_num
% 0.26/0.47      = ( ^ [B3: num,A4: num] :
% 0.26/0.47            ( ( ord_less_num @ B3 @ A4 )
% 0.26/0.47            | ( A4 = B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.order_iff_strict
% 0.26/0.47  thf(fact_590_dual__order_Oorder__iff__strict,axiom,
% 0.26/0.47      ( ord_less_eq_nat
% 0.26/0.47      = ( ^ [B3: nat,A4: nat] :
% 0.26/0.47            ( ( ord_less_nat @ B3 @ A4 )
% 0.26/0.47            | ( A4 = B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.order_iff_strict
% 0.26/0.47  thf(fact_591_dual__order_Oorder__iff__strict,axiom,
% 0.26/0.47      ( ord_less_eq_int
% 0.26/0.47      = ( ^ [B3: int,A4: int] :
% 0.26/0.47            ( ( ord_less_int @ B3 @ A4 )
% 0.26/0.47            | ( A4 = B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.order_iff_strict
% 0.26/0.47  thf(fact_592_dual__order_Ostrict__iff__order,axiom,
% 0.26/0.47      ( ord_less_real
% 0.26/0.47      = ( ^ [B3: real,A4: real] :
% 0.26/0.47            ( ( ord_less_eq_real @ B3 @ A4 )
% 0.26/0.47            & ( A4 != B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_iff_order
% 0.26/0.47  thf(fact_593_dual__order_Ostrict__iff__order,axiom,
% 0.26/0.47      ( ord_less_set_nat
% 0.26/0.47      = ( ^ [B3: set_nat,A4: set_nat] :
% 0.26/0.47            ( ( ord_less_eq_set_nat @ B3 @ A4 )
% 0.26/0.47            & ( A4 != B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_iff_order
% 0.26/0.47  thf(fact_594_dual__order_Ostrict__iff__order,axiom,
% 0.26/0.47      ( ord_less_rat
% 0.26/0.47      = ( ^ [B3: rat,A4: rat] :
% 0.26/0.47            ( ( ord_less_eq_rat @ B3 @ A4 )
% 0.26/0.47            & ( A4 != B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_iff_order
% 0.26/0.47  thf(fact_595_dual__order_Ostrict__iff__order,axiom,
% 0.26/0.47      ( ord_less_num
% 0.26/0.47      = ( ^ [B3: num,A4: num] :
% 0.26/0.47            ( ( ord_less_eq_num @ B3 @ A4 )
% 0.26/0.47            & ( A4 != B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_iff_order
% 0.26/0.47  thf(fact_596_dual__order_Ostrict__iff__order,axiom,
% 0.26/0.47      ( ord_less_nat
% 0.26/0.47      = ( ^ [B3: nat,A4: nat] :
% 0.26/0.47            ( ( ord_less_eq_nat @ B3 @ A4 )
% 0.26/0.47            & ( A4 != B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_iff_order
% 0.26/0.47  thf(fact_597_dual__order_Ostrict__iff__order,axiom,
% 0.26/0.47      ( ord_less_int
% 0.26/0.47      = ( ^ [B3: int,A4: int] :
% 0.26/0.47            ( ( ord_less_eq_int @ B3 @ A4 )
% 0.26/0.47            & ( A4 != B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_iff_order
% 0.26/0.47  thf(fact_598_dual__order_Ostrict__trans1,axiom,
% 0.26/0.47      ! [B: real,A: real,C: real] :
% 0.26/0.47        ( ( ord_less_eq_real @ B @ A )
% 0.26/0.47       => ( ( ord_less_real @ C @ B )
% 0.26/0.47         => ( ord_less_real @ C @ A ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_trans1
% 0.26/0.47  thf(fact_599_dual__order_Ostrict__trans1,axiom,
% 0.26/0.47      ! [B: set_nat,A: set_nat,C: set_nat] :
% 0.26/0.47        ( ( ord_less_eq_set_nat @ B @ A )
% 0.26/0.47       => ( ( ord_less_set_nat @ C @ B )
% 0.26/0.47         => ( ord_less_set_nat @ C @ A ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_trans1
% 0.26/0.47  thf(fact_600_dual__order_Ostrict__trans1,axiom,
% 0.26/0.47      ! [B: rat,A: rat,C: rat] :
% 0.26/0.47        ( ( ord_less_eq_rat @ B @ A )
% 0.26/0.47       => ( ( ord_less_rat @ C @ B )
% 0.26/0.47         => ( ord_less_rat @ C @ A ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_trans1
% 0.26/0.47  thf(fact_601_dual__order_Ostrict__trans1,axiom,
% 0.26/0.47      ! [B: num,A: num,C: num] :
% 0.26/0.47        ( ( ord_less_eq_num @ B @ A )
% 0.26/0.47       => ( ( ord_less_num @ C @ B )
% 0.26/0.47         => ( ord_less_num @ C @ A ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_trans1
% 0.26/0.47  thf(fact_602_dual__order_Ostrict__trans1,axiom,
% 0.26/0.47      ! [B: nat,A: nat,C: nat] :
% 0.26/0.47        ( ( ord_less_eq_nat @ B @ A )
% 0.26/0.47       => ( ( ord_less_nat @ C @ B )
% 0.26/0.47         => ( ord_less_nat @ C @ A ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_trans1
% 0.26/0.47  thf(fact_603_dual__order_Ostrict__trans1,axiom,
% 0.26/0.47      ! [B: int,A: int,C: int] :
% 0.26/0.47        ( ( ord_less_eq_int @ B @ A )
% 0.26/0.47       => ( ( ord_less_int @ C @ B )
% 0.26/0.47         => ( ord_less_int @ C @ A ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_trans1
% 0.26/0.47  thf(fact_604_dual__order_Ostrict__trans2,axiom,
% 0.26/0.47      ! [B: real,A: real,C: real] :
% 0.26/0.47        ( ( ord_less_real @ B @ A )
% 0.26/0.47       => ( ( ord_less_eq_real @ C @ B )
% 0.26/0.47         => ( ord_less_real @ C @ A ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_trans2
% 0.26/0.47  thf(fact_605_dual__order_Ostrict__trans2,axiom,
% 0.26/0.47      ! [B: set_nat,A: set_nat,C: set_nat] :
% 0.26/0.47        ( ( ord_less_set_nat @ B @ A )
% 0.26/0.47       => ( ( ord_less_eq_set_nat @ C @ B )
% 0.26/0.47         => ( ord_less_set_nat @ C @ A ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_trans2
% 0.26/0.47  thf(fact_606_dual__order_Ostrict__trans2,axiom,
% 0.26/0.47      ! [B: rat,A: rat,C: rat] :
% 0.26/0.47        ( ( ord_less_rat @ B @ A )
% 0.26/0.47       => ( ( ord_less_eq_rat @ C @ B )
% 0.26/0.47         => ( ord_less_rat @ C @ A ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_trans2
% 0.26/0.47  thf(fact_607_dual__order_Ostrict__trans2,axiom,
% 0.26/0.47      ! [B: num,A: num,C: num] :
% 0.26/0.47        ( ( ord_less_num @ B @ A )
% 0.26/0.47       => ( ( ord_less_eq_num @ C @ B )
% 0.26/0.47         => ( ord_less_num @ C @ A ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_trans2
% 0.26/0.47  thf(fact_608_dual__order_Ostrict__trans2,axiom,
% 0.26/0.47      ! [B: nat,A: nat,C: nat] :
% 0.26/0.47        ( ( ord_less_nat @ B @ A )
% 0.26/0.47       => ( ( ord_less_eq_nat @ C @ B )
% 0.26/0.47         => ( ord_less_nat @ C @ A ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_trans2
% 0.26/0.47  thf(fact_609_dual__order_Ostrict__trans2,axiom,
% 0.26/0.47      ! [B: int,A: int,C: int] :
% 0.26/0.47        ( ( ord_less_int @ B @ A )
% 0.26/0.47       => ( ( ord_less_eq_int @ C @ B )
% 0.26/0.47         => ( ord_less_int @ C @ A ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_trans2
% 0.26/0.47  thf(fact_610_dual__order_Ostrict__iff__not,axiom,
% 0.26/0.47      ( ord_less_real
% 0.26/0.47      = ( ^ [B3: real,A4: real] :
% 0.26/0.47            ( ( ord_less_eq_real @ B3 @ A4 )
% 0.26/0.47            & ~ ( ord_less_eq_real @ A4 @ B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_iff_not
% 0.26/0.47  thf(fact_611_dual__order_Ostrict__iff__not,axiom,
% 0.26/0.47      ( ord_less_set_nat
% 0.26/0.47      = ( ^ [B3: set_nat,A4: set_nat] :
% 0.26/0.47            ( ( ord_less_eq_set_nat @ B3 @ A4 )
% 0.26/0.47            & ~ ( ord_less_eq_set_nat @ A4 @ B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_iff_not
% 0.26/0.47  thf(fact_612_dual__order_Ostrict__iff__not,axiom,
% 0.26/0.47      ( ord_less_rat
% 0.26/0.47      = ( ^ [B3: rat,A4: rat] :
% 0.26/0.47            ( ( ord_less_eq_rat @ B3 @ A4 )
% 0.26/0.47            & ~ ( ord_less_eq_rat @ A4 @ B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_iff_not
% 0.26/0.47  thf(fact_613_dual__order_Ostrict__iff__not,axiom,
% 0.26/0.47      ( ord_less_num
% 0.26/0.47      = ( ^ [B3: num,A4: num] :
% 0.26/0.47            ( ( ord_less_eq_num @ B3 @ A4 )
% 0.26/0.47            & ~ ( ord_less_eq_num @ A4 @ B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_iff_not
% 0.26/0.47  thf(fact_614_dual__order_Ostrict__iff__not,axiom,
% 0.26/0.47      ( ord_less_nat
% 0.26/0.47      = ( ^ [B3: nat,A4: nat] :
% 0.26/0.47            ( ( ord_less_eq_nat @ B3 @ A4 )
% 0.26/0.47            & ~ ( ord_less_eq_nat @ A4 @ B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_iff_not
% 0.26/0.47  thf(fact_615_dual__order_Ostrict__iff__not,axiom,
% 0.26/0.47      ( ord_less_int
% 0.26/0.47      = ( ^ [B3: int,A4: int] :
% 0.26/0.47            ( ( ord_less_eq_int @ B3 @ A4 )
% 0.26/0.47            & ~ ( ord_less_eq_int @ A4 @ B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_iff_not
% 0.26/0.47  thf(fact_616_order_Ostrict__implies__order,axiom,
% 0.26/0.47      ! [A: real,B: real] :
% 0.26/0.47        ( ( ord_less_real @ A @ B )
% 0.26/0.47       => ( ord_less_eq_real @ A @ B ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_implies_order
% 0.26/0.47  thf(fact_617_order_Ostrict__implies__order,axiom,
% 0.26/0.47      ! [A: set_nat,B: set_nat] :
% 0.26/0.47        ( ( ord_less_set_nat @ A @ B )
% 0.26/0.47       => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_implies_order
% 0.26/0.47  thf(fact_618_order_Ostrict__implies__order,axiom,
% 0.26/0.47      ! [A: rat,B: rat] :
% 0.26/0.47        ( ( ord_less_rat @ A @ B )
% 0.26/0.47       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_implies_order
% 0.26/0.47  thf(fact_619_order_Ostrict__implies__order,axiom,
% 0.26/0.47      ! [A: num,B: num] :
% 0.26/0.47        ( ( ord_less_num @ A @ B )
% 0.26/0.47       => ( ord_less_eq_num @ A @ B ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_implies_order
% 0.26/0.47  thf(fact_620_order_Ostrict__implies__order,axiom,
% 0.26/0.47      ! [A: nat,B: nat] :
% 0.26/0.47        ( ( ord_less_nat @ A @ B )
% 0.26/0.47       => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_implies_order
% 0.26/0.47  thf(fact_621_order_Ostrict__implies__order,axiom,
% 0.26/0.47      ! [A: int,B: int] :
% 0.26/0.47        ( ( ord_less_int @ A @ B )
% 0.26/0.47       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order.strict_implies_order
% 0.26/0.47  thf(fact_622_dual__order_Ostrict__implies__order,axiom,
% 0.26/0.47      ! [B: real,A: real] :
% 0.26/0.47        ( ( ord_less_real @ B @ A )
% 0.26/0.47       => ( ord_less_eq_real @ B @ A ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_implies_order
% 0.26/0.47  thf(fact_623_dual__order_Ostrict__implies__order,axiom,
% 0.26/0.47      ! [B: set_nat,A: set_nat] :
% 0.26/0.47        ( ( ord_less_set_nat @ B @ A )
% 0.26/0.47       => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_implies_order
% 0.26/0.47  thf(fact_624_dual__order_Ostrict__implies__order,axiom,
% 0.26/0.47      ! [B: rat,A: rat] :
% 0.26/0.47        ( ( ord_less_rat @ B @ A )
% 0.26/0.47       => ( ord_less_eq_rat @ B @ A ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_implies_order
% 0.26/0.47  thf(fact_625_dual__order_Ostrict__implies__order,axiom,
% 0.26/0.47      ! [B: num,A: num] :
% 0.26/0.47        ( ( ord_less_num @ B @ A )
% 0.26/0.47       => ( ord_less_eq_num @ B @ A ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_implies_order
% 0.26/0.47  thf(fact_626_dual__order_Ostrict__implies__order,axiom,
% 0.26/0.47      ! [B: nat,A: nat] :
% 0.26/0.47        ( ( ord_less_nat @ B @ A )
% 0.26/0.47       => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_implies_order
% 0.26/0.47  thf(fact_627_dual__order_Ostrict__implies__order,axiom,
% 0.26/0.47      ! [B: int,A: int] :
% 0.26/0.47        ( ( ord_less_int @ B @ A )
% 0.26/0.47       => ( ord_less_eq_int @ B @ A ) ) ).
% 0.26/0.47  
% 0.26/0.47  % dual_order.strict_implies_order
% 0.26/0.47  thf(fact_628_order__le__less,axiom,
% 0.26/0.47      ( ord_less_eq_real
% 0.26/0.47      = ( ^ [X: real,Y: real] :
% 0.26/0.47            ( ( ord_less_real @ X @ Y )
% 0.26/0.47            | ( X = Y ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less
% 0.26/0.47  thf(fact_629_order__le__less,axiom,
% 0.26/0.47      ( ord_less_eq_set_nat
% 0.26/0.47      = ( ^ [X: set_nat,Y: set_nat] :
% 0.26/0.47            ( ( ord_less_set_nat @ X @ Y )
% 0.26/0.47            | ( X = Y ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less
% 0.26/0.47  thf(fact_630_order__le__less,axiom,
% 0.26/0.47      ( ord_less_eq_rat
% 0.26/0.47      = ( ^ [X: rat,Y: rat] :
% 0.26/0.47            ( ( ord_less_rat @ X @ Y )
% 0.26/0.47            | ( X = Y ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less
% 0.26/0.47  thf(fact_631_order__le__less,axiom,
% 0.26/0.47      ( ord_less_eq_num
% 0.26/0.47      = ( ^ [X: num,Y: num] :
% 0.26/0.47            ( ( ord_less_num @ X @ Y )
% 0.26/0.47            | ( X = Y ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less
% 0.26/0.47  thf(fact_632_order__le__less,axiom,
% 0.26/0.47      ( ord_less_eq_nat
% 0.26/0.47      = ( ^ [X: nat,Y: nat] :
% 0.26/0.47            ( ( ord_less_nat @ X @ Y )
% 0.26/0.47            | ( X = Y ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less
% 0.26/0.47  thf(fact_633_order__le__less,axiom,
% 0.26/0.47      ( ord_less_eq_int
% 0.26/0.47      = ( ^ [X: int,Y: int] :
% 0.26/0.47            ( ( ord_less_int @ X @ Y )
% 0.26/0.47            | ( X = Y ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less
% 0.26/0.47  thf(fact_634_order__less__le,axiom,
% 0.26/0.47      ( ord_less_real
% 0.26/0.47      = ( ^ [X: real,Y: real] :
% 0.26/0.47            ( ( ord_less_eq_real @ X @ Y )
% 0.26/0.47            & ( X != Y ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le
% 0.26/0.47  thf(fact_635_order__less__le,axiom,
% 0.26/0.47      ( ord_less_set_nat
% 0.26/0.47      = ( ^ [X: set_nat,Y: set_nat] :
% 0.26/0.47            ( ( ord_less_eq_set_nat @ X @ Y )
% 0.26/0.47            & ( X != Y ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le
% 0.26/0.47  thf(fact_636_order__less__le,axiom,
% 0.26/0.47      ( ord_less_rat
% 0.26/0.47      = ( ^ [X: rat,Y: rat] :
% 0.26/0.47            ( ( ord_less_eq_rat @ X @ Y )
% 0.26/0.47            & ( X != Y ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le
% 0.26/0.47  thf(fact_637_order__less__le,axiom,
% 0.26/0.47      ( ord_less_num
% 0.26/0.47      = ( ^ [X: num,Y: num] :
% 0.26/0.47            ( ( ord_less_eq_num @ X @ Y )
% 0.26/0.47            & ( X != Y ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le
% 0.26/0.47  thf(fact_638_order__less__le,axiom,
% 0.26/0.47      ( ord_less_nat
% 0.26/0.47      = ( ^ [X: nat,Y: nat] :
% 0.26/0.47            ( ( ord_less_eq_nat @ X @ Y )
% 0.26/0.47            & ( X != Y ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le
% 0.26/0.47  thf(fact_639_order__less__le,axiom,
% 0.26/0.47      ( ord_less_int
% 0.26/0.47      = ( ^ [X: int,Y: int] :
% 0.26/0.47            ( ( ord_less_eq_int @ X @ Y )
% 0.26/0.47            & ( X != Y ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le
% 0.26/0.47  thf(fact_640_linorder__not__le,axiom,
% 0.26/0.47      ! [X3: real,Y3: real] :
% 0.26/0.47        ( ( ~ ( ord_less_eq_real @ X3 @ Y3 ) )
% 0.26/0.47        = ( ord_less_real @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_not_le
% 0.26/0.47  thf(fact_641_linorder__not__le,axiom,
% 0.26/0.47      ! [X3: rat,Y3: rat] :
% 0.26/0.47        ( ( ~ ( ord_less_eq_rat @ X3 @ Y3 ) )
% 0.26/0.47        = ( ord_less_rat @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_not_le
% 0.26/0.47  thf(fact_642_linorder__not__le,axiom,
% 0.26/0.47      ! [X3: num,Y3: num] :
% 0.26/0.47        ( ( ~ ( ord_less_eq_num @ X3 @ Y3 ) )
% 0.26/0.47        = ( ord_less_num @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_not_le
% 0.26/0.47  thf(fact_643_linorder__not__le,axiom,
% 0.26/0.47      ! [X3: nat,Y3: nat] :
% 0.26/0.47        ( ( ~ ( ord_less_eq_nat @ X3 @ Y3 ) )
% 0.26/0.47        = ( ord_less_nat @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_not_le
% 0.26/0.47  thf(fact_644_linorder__not__le,axiom,
% 0.26/0.47      ! [X3: int,Y3: int] :
% 0.26/0.47        ( ( ~ ( ord_less_eq_int @ X3 @ Y3 ) )
% 0.26/0.47        = ( ord_less_int @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_not_le
% 0.26/0.47  thf(fact_645_linorder__not__less,axiom,
% 0.26/0.47      ! [X3: real,Y3: real] :
% 0.26/0.47        ( ( ~ ( ord_less_real @ X3 @ Y3 ) )
% 0.26/0.47        = ( ord_less_eq_real @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_not_less
% 0.26/0.47  thf(fact_646_linorder__not__less,axiom,
% 0.26/0.47      ! [X3: rat,Y3: rat] :
% 0.26/0.47        ( ( ~ ( ord_less_rat @ X3 @ Y3 ) )
% 0.26/0.47        = ( ord_less_eq_rat @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_not_less
% 0.26/0.47  thf(fact_647_linorder__not__less,axiom,
% 0.26/0.47      ! [X3: num,Y3: num] :
% 0.26/0.47        ( ( ~ ( ord_less_num @ X3 @ Y3 ) )
% 0.26/0.47        = ( ord_less_eq_num @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_not_less
% 0.26/0.47  thf(fact_648_linorder__not__less,axiom,
% 0.26/0.47      ! [X3: nat,Y3: nat] :
% 0.26/0.47        ( ( ~ ( ord_less_nat @ X3 @ Y3 ) )
% 0.26/0.47        = ( ord_less_eq_nat @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_not_less
% 0.26/0.47  thf(fact_649_linorder__not__less,axiom,
% 0.26/0.47      ! [X3: int,Y3: int] :
% 0.26/0.47        ( ( ~ ( ord_less_int @ X3 @ Y3 ) )
% 0.26/0.47        = ( ord_less_eq_int @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_not_less
% 0.26/0.47  thf(fact_650_order__less__imp__le,axiom,
% 0.26/0.47      ! [X3: real,Y3: real] :
% 0.26/0.47        ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.47       => ( ord_less_eq_real @ X3 @ Y3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_le
% 0.26/0.47  thf(fact_651_order__less__imp__le,axiom,
% 0.26/0.47      ! [X3: set_nat,Y3: set_nat] :
% 0.26/0.47        ( ( ord_less_set_nat @ X3 @ Y3 )
% 0.26/0.47       => ( ord_less_eq_set_nat @ X3 @ Y3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_le
% 0.26/0.47  thf(fact_652_order__less__imp__le,axiom,
% 0.26/0.47      ! [X3: rat,Y3: rat] :
% 0.26/0.47        ( ( ord_less_rat @ X3 @ Y3 )
% 0.26/0.47       => ( ord_less_eq_rat @ X3 @ Y3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_le
% 0.26/0.47  thf(fact_653_order__less__imp__le,axiom,
% 0.26/0.47      ! [X3: num,Y3: num] :
% 0.26/0.47        ( ( ord_less_num @ X3 @ Y3 )
% 0.26/0.47       => ( ord_less_eq_num @ X3 @ Y3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_le
% 0.26/0.47  thf(fact_654_order__less__imp__le,axiom,
% 0.26/0.47      ! [X3: nat,Y3: nat] :
% 0.26/0.47        ( ( ord_less_nat @ X3 @ Y3 )
% 0.26/0.47       => ( ord_less_eq_nat @ X3 @ Y3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_le
% 0.26/0.47  thf(fact_655_order__less__imp__le,axiom,
% 0.26/0.47      ! [X3: int,Y3: int] :
% 0.26/0.47        ( ( ord_less_int @ X3 @ Y3 )
% 0.26/0.47       => ( ord_less_eq_int @ X3 @ Y3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_imp_le
% 0.26/0.47  thf(fact_656_order__le__neq__trans,axiom,
% 0.26/0.47      ! [A: real,B: real] :
% 0.26/0.47        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.47       => ( ( A != B )
% 0.26/0.47         => ( ord_less_real @ A @ B ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_neq_trans
% 0.26/0.47  thf(fact_657_order__le__neq__trans,axiom,
% 0.26/0.47      ! [A: set_nat,B: set_nat] :
% 0.26/0.47        ( ( ord_less_eq_set_nat @ A @ B )
% 0.26/0.47       => ( ( A != B )
% 0.26/0.47         => ( ord_less_set_nat @ A @ B ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_neq_trans
% 0.26/0.47  thf(fact_658_order__le__neq__trans,axiom,
% 0.26/0.47      ! [A: rat,B: rat] :
% 0.26/0.47        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.47       => ( ( A != B )
% 0.26/0.47         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_neq_trans
% 0.26/0.47  thf(fact_659_order__le__neq__trans,axiom,
% 0.26/0.47      ! [A: num,B: num] :
% 0.26/0.47        ( ( ord_less_eq_num @ A @ B )
% 0.26/0.47       => ( ( A != B )
% 0.26/0.47         => ( ord_less_num @ A @ B ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_neq_trans
% 0.26/0.47  thf(fact_660_order__le__neq__trans,axiom,
% 0.26/0.47      ! [A: nat,B: nat] :
% 0.26/0.47        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.47       => ( ( A != B )
% 0.26/0.47         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_neq_trans
% 0.26/0.47  thf(fact_661_order__le__neq__trans,axiom,
% 0.26/0.47      ! [A: int,B: int] :
% 0.26/0.47        ( ( ord_less_eq_int @ A @ B )
% 0.26/0.47       => ( ( A != B )
% 0.26/0.47         => ( ord_less_int @ A @ B ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_neq_trans
% 0.26/0.47  thf(fact_662_order__neq__le__trans,axiom,
% 0.26/0.47      ! [A: real,B: real] :
% 0.26/0.47        ( ( A != B )
% 0.26/0.47       => ( ( ord_less_eq_real @ A @ B )
% 0.26/0.47         => ( ord_less_real @ A @ B ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_neq_le_trans
% 0.26/0.47  thf(fact_663_order__neq__le__trans,axiom,
% 0.26/0.47      ! [A: set_nat,B: set_nat] :
% 0.26/0.47        ( ( A != B )
% 0.26/0.47       => ( ( ord_less_eq_set_nat @ A @ B )
% 0.26/0.47         => ( ord_less_set_nat @ A @ B ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_neq_le_trans
% 0.26/0.47  thf(fact_664_order__neq__le__trans,axiom,
% 0.26/0.47      ! [A: rat,B: rat] :
% 0.26/0.47        ( ( A != B )
% 0.26/0.47       => ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.47         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_neq_le_trans
% 0.26/0.47  thf(fact_665_order__neq__le__trans,axiom,
% 0.26/0.47      ! [A: num,B: num] :
% 0.26/0.47        ( ( A != B )
% 0.26/0.47       => ( ( ord_less_eq_num @ A @ B )
% 0.26/0.47         => ( ord_less_num @ A @ B ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_neq_le_trans
% 0.26/0.47  thf(fact_666_order__neq__le__trans,axiom,
% 0.26/0.47      ! [A: nat,B: nat] :
% 0.26/0.47        ( ( A != B )
% 0.26/0.47       => ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.47         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_neq_le_trans
% 0.26/0.47  thf(fact_667_order__neq__le__trans,axiom,
% 0.26/0.47      ! [A: int,B: int] :
% 0.26/0.47        ( ( A != B )
% 0.26/0.47       => ( ( ord_less_eq_int @ A @ B )
% 0.26/0.47         => ( ord_less_int @ A @ B ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_neq_le_trans
% 0.26/0.47  thf(fact_668_order__le__less__trans,axiom,
% 0.26/0.47      ! [X3: real,Y3: real,Z: real] :
% 0.26/0.47        ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_real @ Y3 @ Z )
% 0.26/0.47         => ( ord_less_real @ X3 @ Z ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_trans
% 0.26/0.47  thf(fact_669_order__le__less__trans,axiom,
% 0.26/0.47      ! [X3: set_nat,Y3: set_nat,Z: set_nat] :
% 0.26/0.47        ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_set_nat @ Y3 @ Z )
% 0.26/0.47         => ( ord_less_set_nat @ X3 @ Z ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_trans
% 0.26/0.47  thf(fact_670_order__le__less__trans,axiom,
% 0.26/0.47      ! [X3: rat,Y3: rat,Z: rat] :
% 0.26/0.47        ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_rat @ Y3 @ Z )
% 0.26/0.47         => ( ord_less_rat @ X3 @ Z ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_trans
% 0.26/0.47  thf(fact_671_order__le__less__trans,axiom,
% 0.26/0.47      ! [X3: num,Y3: num,Z: num] :
% 0.26/0.47        ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_num @ Y3 @ Z )
% 0.26/0.47         => ( ord_less_num @ X3 @ Z ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_trans
% 0.26/0.47  thf(fact_672_order__le__less__trans,axiom,
% 0.26/0.47      ! [X3: nat,Y3: nat,Z: nat] :
% 0.26/0.47        ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_nat @ Y3 @ Z )
% 0.26/0.47         => ( ord_less_nat @ X3 @ Z ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_trans
% 0.26/0.47  thf(fact_673_order__le__less__trans,axiom,
% 0.26/0.47      ! [X3: int,Y3: int,Z: int] :
% 0.26/0.47        ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_int @ Y3 @ Z )
% 0.26/0.47         => ( ord_less_int @ X3 @ Z ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_trans
% 0.26/0.47  thf(fact_674_order__less__le__trans,axiom,
% 0.26/0.47      ! [X3: real,Y3: real,Z: real] :
% 0.26/0.47        ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_eq_real @ Y3 @ Z )
% 0.26/0.47         => ( ord_less_real @ X3 @ Z ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_trans
% 0.26/0.47  thf(fact_675_order__less__le__trans,axiom,
% 0.26/0.47      ! [X3: set_nat,Y3: set_nat,Z: set_nat] :
% 0.26/0.47        ( ( ord_less_set_nat @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_eq_set_nat @ Y3 @ Z )
% 0.26/0.47         => ( ord_less_set_nat @ X3 @ Z ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_trans
% 0.26/0.47  thf(fact_676_order__less__le__trans,axiom,
% 0.26/0.47      ! [X3: rat,Y3: rat,Z: rat] :
% 0.26/0.47        ( ( ord_less_rat @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_eq_rat @ Y3 @ Z )
% 0.26/0.47         => ( ord_less_rat @ X3 @ Z ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_trans
% 0.26/0.47  thf(fact_677_order__less__le__trans,axiom,
% 0.26/0.47      ! [X3: num,Y3: num,Z: num] :
% 0.26/0.47        ( ( ord_less_num @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_eq_num @ Y3 @ Z )
% 0.26/0.47         => ( ord_less_num @ X3 @ Z ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_trans
% 0.26/0.47  thf(fact_678_order__less__le__trans,axiom,
% 0.26/0.47      ! [X3: nat,Y3: nat,Z: nat] :
% 0.26/0.47        ( ( ord_less_nat @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_eq_nat @ Y3 @ Z )
% 0.26/0.47         => ( ord_less_nat @ X3 @ Z ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_trans
% 0.26/0.47  thf(fact_679_order__less__le__trans,axiom,
% 0.26/0.47      ! [X3: int,Y3: int,Z: int] :
% 0.26/0.47        ( ( ord_less_int @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_eq_int @ Y3 @ Z )
% 0.26/0.47         => ( ord_less_int @ X3 @ Z ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_trans
% 0.26/0.47  thf(fact_680_order__le__less__subst1,axiom,
% 0.26/0.47      ! [A: real,F: real > real,B: real,C: real] :
% 0.26/0.47        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_real @ B @ C )
% 0.26/0.47         => ( ! [X4: real,Y4: real] :
% 0.26/0.47                ( ( ord_less_real @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_subst1
% 0.26/0.47  thf(fact_681_order__le__less__subst1,axiom,
% 0.26/0.47      ! [A: real,F: rat > real,B: rat,C: rat] :
% 0.26/0.47        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_rat @ B @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_subst1
% 0.26/0.47  thf(fact_682_order__le__less__subst1,axiom,
% 0.26/0.47      ! [A: real,F: num > real,B: num,C: num] :
% 0.26/0.47        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_num @ B @ C )
% 0.26/0.47         => ( ! [X4: num,Y4: num] :
% 0.26/0.47                ( ( ord_less_num @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_subst1
% 0.26/0.47  thf(fact_683_order__le__less__subst1,axiom,
% 0.26/0.47      ! [A: real,F: nat > real,B: nat,C: nat] :
% 0.26/0.47        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_nat @ B @ C )
% 0.26/0.47         => ( ! [X4: nat,Y4: nat] :
% 0.26/0.47                ( ( ord_less_nat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_subst1
% 0.26/0.47  thf(fact_684_order__le__less__subst1,axiom,
% 0.26/0.47      ! [A: real,F: int > real,B: int,C: int] :
% 0.26/0.47        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_int @ B @ C )
% 0.26/0.47         => ( ! [X4: int,Y4: int] :
% 0.26/0.47                ( ( ord_less_int @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_subst1
% 0.26/0.47  thf(fact_685_order__le__less__subst1,axiom,
% 0.26/0.47      ! [A: rat,F: real > rat,B: real,C: real] :
% 0.26/0.47        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_real @ B @ C )
% 0.26/0.47         => ( ! [X4: real,Y4: real] :
% 0.26/0.47                ( ( ord_less_real @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_subst1
% 0.26/0.47  thf(fact_686_order__le__less__subst1,axiom,
% 0.26/0.47      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.26/0.47        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_rat @ B @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_subst1
% 0.26/0.47  thf(fact_687_order__le__less__subst1,axiom,
% 0.26/0.47      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.26/0.47        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_num @ B @ C )
% 0.26/0.47         => ( ! [X4: num,Y4: num] :
% 0.26/0.47                ( ( ord_less_num @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_subst1
% 0.26/0.47  thf(fact_688_order__le__less__subst1,axiom,
% 0.26/0.47      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 0.26/0.47        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_nat @ B @ C )
% 0.26/0.47         => ( ! [X4: nat,Y4: nat] :
% 0.26/0.47                ( ( ord_less_nat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_subst1
% 0.26/0.47  thf(fact_689_order__le__less__subst1,axiom,
% 0.26/0.47      ! [A: rat,F: int > rat,B: int,C: int] :
% 0.26/0.47        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_int @ B @ C )
% 0.26/0.47         => ( ! [X4: int,Y4: int] :
% 0.26/0.47                ( ( ord_less_int @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_subst1
% 0.26/0.47  thf(fact_690_order__le__less__subst2,axiom,
% 0.26/0.47      ! [A: rat,B: rat,F: rat > real,C: real] :
% 0.26/0.47        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.47       => ( ( ord_less_real @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_subst2
% 0.26/0.47  thf(fact_691_order__le__less__subst2,axiom,
% 0.26/0.47      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.26/0.47        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.47       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_subst2
% 0.26/0.47  thf(fact_692_order__le__less__subst2,axiom,
% 0.26/0.47      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.26/0.47        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.47       => ( ( ord_less_num @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_subst2
% 0.26/0.47  thf(fact_693_order__le__less__subst2,axiom,
% 0.26/0.47      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.26/0.47        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.47       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_subst2
% 0.26/0.47  thf(fact_694_order__le__less__subst2,axiom,
% 0.26/0.47      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.26/0.47        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.47       => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_subst2
% 0.26/0.47  thf(fact_695_order__le__less__subst2,axiom,
% 0.26/0.47      ! [A: num,B: num,F: num > real,C: real] :
% 0.26/0.47        ( ( ord_less_eq_num @ A @ B )
% 0.26/0.47       => ( ( ord_less_real @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: num,Y4: num] :
% 0.26/0.47                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_subst2
% 0.26/0.47  thf(fact_696_order__le__less__subst2,axiom,
% 0.26/0.47      ! [A: num,B: num,F: num > rat,C: rat] :
% 0.26/0.47        ( ( ord_less_eq_num @ A @ B )
% 0.26/0.47       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: num,Y4: num] :
% 0.26/0.47                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_subst2
% 0.26/0.47  thf(fact_697_order__le__less__subst2,axiom,
% 0.26/0.47      ! [A: num,B: num,F: num > num,C: num] :
% 0.26/0.47        ( ( ord_less_eq_num @ A @ B )
% 0.26/0.47       => ( ( ord_less_num @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: num,Y4: num] :
% 0.26/0.47                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_subst2
% 0.26/0.47  thf(fact_698_order__le__less__subst2,axiom,
% 0.26/0.47      ! [A: num,B: num,F: num > nat,C: nat] :
% 0.26/0.47        ( ( ord_less_eq_num @ A @ B )
% 0.26/0.47       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: num,Y4: num] :
% 0.26/0.47                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_subst2
% 0.26/0.47  thf(fact_699_order__le__less__subst2,axiom,
% 0.26/0.47      ! [A: num,B: num,F: num > int,C: int] :
% 0.26/0.47        ( ( ord_less_eq_num @ A @ B )
% 0.26/0.47       => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: num,Y4: num] :
% 0.26/0.47                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_less_subst2
% 0.26/0.47  thf(fact_700_order__less__le__subst1,axiom,
% 0.26/0.47      ! [A: real,F: rat > real,B: rat,C: rat] :
% 0.26/0.47        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_eq_rat @ B @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_subst1
% 0.26/0.47  thf(fact_701_order__less__le__subst1,axiom,
% 0.26/0.47      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.26/0.47        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_eq_rat @ B @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_subst1
% 0.26/0.47  thf(fact_702_order__less__le__subst1,axiom,
% 0.26/0.47      ! [A: num,F: rat > num,B: rat,C: rat] :
% 0.26/0.47        ( ( ord_less_num @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_eq_rat @ B @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_subst1
% 0.26/0.47  thf(fact_703_order__less__le__subst1,axiom,
% 0.26/0.47      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 0.26/0.47        ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_eq_rat @ B @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_subst1
% 0.26/0.47  thf(fact_704_order__less__le__subst1,axiom,
% 0.26/0.47      ! [A: int,F: rat > int,B: rat,C: rat] :
% 0.26/0.47        ( ( ord_less_int @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_eq_rat @ B @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_subst1
% 0.26/0.47  thf(fact_705_order__less__le__subst1,axiom,
% 0.26/0.47      ! [A: real,F: num > real,B: num,C: num] :
% 0.26/0.47        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_eq_num @ B @ C )
% 0.26/0.47         => ( ! [X4: num,Y4: num] :
% 0.26/0.47                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_subst1
% 0.26/0.47  thf(fact_706_order__less__le__subst1,axiom,
% 0.26/0.47      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.26/0.47        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_eq_num @ B @ C )
% 0.26/0.47         => ( ! [X4: num,Y4: num] :
% 0.26/0.47                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_subst1
% 0.26/0.47  thf(fact_707_order__less__le__subst1,axiom,
% 0.26/0.47      ! [A: num,F: num > num,B: num,C: num] :
% 0.26/0.47        ( ( ord_less_num @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_eq_num @ B @ C )
% 0.26/0.47         => ( ! [X4: num,Y4: num] :
% 0.26/0.47                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_subst1
% 0.26/0.47  thf(fact_708_order__less__le__subst1,axiom,
% 0.26/0.47      ! [A: nat,F: num > nat,B: num,C: num] :
% 0.26/0.47        ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_eq_num @ B @ C )
% 0.26/0.47         => ( ! [X4: num,Y4: num] :
% 0.26/0.47                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_subst1
% 0.26/0.47  thf(fact_709_order__less__le__subst1,axiom,
% 0.26/0.47      ! [A: int,F: num > int,B: num,C: num] :
% 0.26/0.47        ( ( ord_less_int @ A @ ( F @ B ) )
% 0.26/0.47       => ( ( ord_less_eq_num @ B @ C )
% 0.26/0.47         => ( ! [X4: num,Y4: num] :
% 0.26/0.47                ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_subst1
% 0.26/0.47  thf(fact_710_order__less__le__subst2,axiom,
% 0.26/0.47      ! [A: real,B: real,F: real > real,C: real] :
% 0.26/0.47        ( ( ord_less_real @ A @ B )
% 0.26/0.47       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: real,Y4: real] :
% 0.26/0.47                ( ( ord_less_real @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_subst2
% 0.26/0.47  thf(fact_711_order__less__le__subst2,axiom,
% 0.26/0.47      ! [A: rat,B: rat,F: rat > real,C: real] :
% 0.26/0.47        ( ( ord_less_rat @ A @ B )
% 0.26/0.47       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_subst2
% 0.26/0.47  thf(fact_712_order__less__le__subst2,axiom,
% 0.26/0.47      ! [A: num,B: num,F: num > real,C: real] :
% 0.26/0.47        ( ( ord_less_num @ A @ B )
% 0.26/0.47       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: num,Y4: num] :
% 0.26/0.47                ( ( ord_less_num @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_subst2
% 0.26/0.47  thf(fact_713_order__less__le__subst2,axiom,
% 0.26/0.47      ! [A: nat,B: nat,F: nat > real,C: real] :
% 0.26/0.47        ( ( ord_less_nat @ A @ B )
% 0.26/0.47       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: nat,Y4: nat] :
% 0.26/0.47                ( ( ord_less_nat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_subst2
% 0.26/0.47  thf(fact_714_order__less__le__subst2,axiom,
% 0.26/0.47      ! [A: int,B: int,F: int > real,C: real] :
% 0.26/0.47        ( ( ord_less_int @ A @ B )
% 0.26/0.47       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: int,Y4: int] :
% 0.26/0.47                ( ( ord_less_int @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_subst2
% 0.26/0.47  thf(fact_715_order__less__le__subst2,axiom,
% 0.26/0.47      ! [A: real,B: real,F: real > rat,C: rat] :
% 0.26/0.47        ( ( ord_less_real @ A @ B )
% 0.26/0.47       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: real,Y4: real] :
% 0.26/0.47                ( ( ord_less_real @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_subst2
% 0.26/0.47  thf(fact_716_order__less__le__subst2,axiom,
% 0.26/0.47      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.26/0.47        ( ( ord_less_rat @ A @ B )
% 0.26/0.47       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: rat,Y4: rat] :
% 0.26/0.47                ( ( ord_less_rat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_subst2
% 0.26/0.47  thf(fact_717_order__less__le__subst2,axiom,
% 0.26/0.47      ! [A: num,B: num,F: num > rat,C: rat] :
% 0.26/0.47        ( ( ord_less_num @ A @ B )
% 0.26/0.47       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: num,Y4: num] :
% 0.26/0.47                ( ( ord_less_num @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_subst2
% 0.26/0.47  thf(fact_718_order__less__le__subst2,axiom,
% 0.26/0.47      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 0.26/0.47        ( ( ord_less_nat @ A @ B )
% 0.26/0.47       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: nat,Y4: nat] :
% 0.26/0.47                ( ( ord_less_nat @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_subst2
% 0.26/0.47  thf(fact_719_order__less__le__subst2,axiom,
% 0.26/0.47      ! [A: int,B: int,F: int > rat,C: rat] :
% 0.26/0.47        ( ( ord_less_int @ A @ B )
% 0.26/0.47       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.26/0.47         => ( ! [X4: int,Y4: int] :
% 0.26/0.47                ( ( ord_less_int @ X4 @ Y4 )
% 0.26/0.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.26/0.47           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_less_le_subst2
% 0.26/0.47  thf(fact_720_linorder__le__less__linear,axiom,
% 0.26/0.47      ! [X3: real,Y3: real] :
% 0.26/0.47        ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.26/0.47        | ( ord_less_real @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_le_less_linear
% 0.26/0.47  thf(fact_721_linorder__le__less__linear,axiom,
% 0.26/0.47      ! [X3: rat,Y3: rat] :
% 0.26/0.47        ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.26/0.47        | ( ord_less_rat @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_le_less_linear
% 0.26/0.47  thf(fact_722_linorder__le__less__linear,axiom,
% 0.26/0.47      ! [X3: num,Y3: num] :
% 0.26/0.47        ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.26/0.47        | ( ord_less_num @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_le_less_linear
% 0.26/0.47  thf(fact_723_linorder__le__less__linear,axiom,
% 0.26/0.47      ! [X3: nat,Y3: nat] :
% 0.26/0.47        ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.26/0.47        | ( ord_less_nat @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_le_less_linear
% 0.26/0.47  thf(fact_724_linorder__le__less__linear,axiom,
% 0.26/0.47      ! [X3: int,Y3: int] :
% 0.26/0.47        ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.26/0.47        | ( ord_less_int @ Y3 @ X3 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % linorder_le_less_linear
% 0.26/0.47  thf(fact_725_order__le__imp__less__or__eq,axiom,
% 0.26/0.47      ! [X3: real,Y3: real] :
% 0.26/0.47        ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.47          | ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_imp_less_or_eq
% 0.26/0.47  thf(fact_726_order__le__imp__less__or__eq,axiom,
% 0.26/0.47      ! [X3: set_nat,Y3: set_nat] :
% 0.26/0.47        ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_set_nat @ X3 @ Y3 )
% 0.26/0.47          | ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_imp_less_or_eq
% 0.26/0.47  thf(fact_727_order__le__imp__less__or__eq,axiom,
% 0.26/0.47      ! [X3: rat,Y3: rat] :
% 0.26/0.47        ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_rat @ X3 @ Y3 )
% 0.26/0.47          | ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_imp_less_or_eq
% 0.26/0.47  thf(fact_728_order__le__imp__less__or__eq,axiom,
% 0.26/0.47      ! [X3: num,Y3: num] :
% 0.26/0.47        ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_num @ X3 @ Y3 )
% 0.26/0.47          | ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_imp_less_or_eq
% 0.26/0.47  thf(fact_729_order__le__imp__less__or__eq,axiom,
% 0.26/0.47      ! [X3: nat,Y3: nat] :
% 0.26/0.47        ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_nat @ X3 @ Y3 )
% 0.26/0.47          | ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_imp_less_or_eq
% 0.26/0.47  thf(fact_730_order__le__imp__less__or__eq,axiom,
% 0.26/0.47      ! [X3: int,Y3: int] :
% 0.26/0.47        ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.26/0.47       => ( ( ord_less_int @ X3 @ Y3 )
% 0.26/0.47          | ( X3 = Y3 ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % order_le_imp_less_or_eq
% 0.26/0.47  thf(fact_731_nat__less__le,axiom,
% 0.26/0.47      ( ord_less_nat
% 0.26/0.47      = ( ^ [M3: nat,N3: nat] :
% 0.26/0.47            ( ( ord_less_eq_nat @ M3 @ N3 )
% 0.26/0.47            & ( M3 != N3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % nat_less_le
% 0.26/0.47  thf(fact_732_less__imp__le__nat,axiom,
% 0.26/0.47      ! [M: nat,N: nat] :
% 0.26/0.47        ( ( ord_less_nat @ M @ N )
% 0.26/0.47       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.47  
% 0.26/0.47  % less_imp_le_nat
% 0.26/0.47  thf(fact_733_le__eq__less__or__eq,axiom,
% 0.26/0.47      ( ord_less_eq_nat
% 0.26/0.47      = ( ^ [M3: nat,N3: nat] :
% 0.26/0.47            ( ( ord_less_nat @ M3 @ N3 )
% 0.26/0.47            | ( M3 = N3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % le_eq_less_or_eq
% 0.26/0.47  thf(fact_734_less__or__eq__imp__le,axiom,
% 0.26/0.47      ! [M: nat,N: nat] :
% 0.26/0.47        ( ( ( ord_less_nat @ M @ N )
% 0.26/0.47          | ( M = N ) )
% 0.26/0.47       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.47  
% 0.26/0.47  % less_or_eq_imp_le
% 0.26/0.47  thf(fact_735_le__neq__implies__less,axiom,
% 0.26/0.47      ! [M: nat,N: nat] :
% 0.26/0.47        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.47       => ( ( M != N )
% 0.26/0.47         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % le_neq_implies_less
% 0.26/0.47  thf(fact_736_of__nat__less__two__power,axiom,
% 0.26/0.47      ! [N: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 0.26/0.47  
% 0.26/0.47  % of_nat_less_two_power
% 0.26/0.47  thf(fact_737_of__nat__less__two__power,axiom,
% 0.26/0.47      ! [N: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.26/0.47  
% 0.26/0.47  % of_nat_less_two_power
% 0.26/0.47  thf(fact_738_of__nat__less__two__power,axiom,
% 0.26/0.47      ! [N: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 0.26/0.47  
% 0.26/0.47  % of_nat_less_two_power
% 0.26/0.47  thf(fact_739_numeral__le__real__of__nat__iff,axiom,
% 0.26/0.47      ! [N: num,M: nat] :
% 0.26/0.47        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M ) )
% 0.26/0.47        = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M ) ) ).
% 0.26/0.47  
% 0.26/0.47  % numeral_le_real_of_nat_iff
% 0.26/0.47  thf(fact_740_numeral__less__real__of__nat__iff,axiom,
% 0.26/0.47      ! [W: num,N: nat] :
% 0.26/0.47        ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N ) )
% 0.26/0.47        = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N ) ) ).
% 0.26/0.47  
% 0.26/0.47  % numeral_less_real_of_nat_iff
% 0.26/0.47  thf(fact_741_real__of__nat__less__numeral__iff,axiom,
% 0.26/0.47      ! [N: nat,W: num] :
% 0.26/0.47        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W ) )
% 0.26/0.47        = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % real_of_nat_less_numeral_iff
% 0.26/0.47  thf(fact_742_greater__shift,axiom,
% 0.26/0.47      ( ord_less_nat
% 0.26/0.47      = ( ^ [Y: nat,X: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X ) @ ( some_nat @ Y ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % greater_shift
% 0.26/0.47  thf(fact_743_less__shift,axiom,
% 0.26/0.47      ( ord_less_nat
% 0.26/0.47      = ( ^ [X: nat,Y: nat] : ( vEBT_VEBT_less @ ( some_nat @ X ) @ ( some_nat @ Y ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % less_shift
% 0.26/0.47  thf(fact_744_option_Oinject,axiom,
% 0.26/0.47      ! [X2: nat,Y2: nat] :
% 0.26/0.47        ( ( ( some_nat @ X2 )
% 0.26/0.47          = ( some_nat @ Y2 ) )
% 0.26/0.47        = ( X2 = Y2 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % option.inject
% 0.26/0.47  thf(fact_745_option_Oinject,axiom,
% 0.26/0.47      ! [X2: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 0.26/0.47        ( ( ( some_P7363390416028606310at_nat @ X2 )
% 0.26/0.47          = ( some_P7363390416028606310at_nat @ Y2 ) )
% 0.26/0.47        = ( X2 = Y2 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % option.inject
% 0.26/0.47  thf(fact_746_option_Oinject,axiom,
% 0.26/0.47      ! [X2: num,Y2: num] :
% 0.26/0.47        ( ( ( some_num @ X2 )
% 0.26/0.47          = ( some_num @ Y2 ) )
% 0.26/0.47        = ( X2 = Y2 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % option.inject
% 0.26/0.47  thf(fact_747_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 0.26/0.47      ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 0.26/0.47        ( ( vEBT_V1502963449132264192at_nat @ F @ ( some_P7363390416028606310at_nat @ A ) @ ( some_P7363390416028606310at_nat @ B ) )
% 0.26/0.47        = ( some_P7363390416028606310at_nat @ ( F @ A @ B ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % VEBT_internal.option_shift.simps(3)
% 0.26/0.47  thf(fact_748_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 0.26/0.47      ! [F: num > num > num,A: num,B: num] :
% 0.26/0.47        ( ( vEBT_V819420779217536731ft_num @ F @ ( some_num @ A ) @ ( some_num @ B ) )
% 0.26/0.47        = ( some_num @ ( F @ A @ B ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % VEBT_internal.option_shift.simps(3)
% 0.26/0.47  thf(fact_749_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 0.26/0.47      ! [F: nat > nat > nat,A: nat,B: nat] :
% 0.26/0.47        ( ( vEBT_V4262088993061758097ft_nat @ F @ ( some_nat @ A ) @ ( some_nat @ B ) )
% 0.26/0.47        = ( some_nat @ ( F @ A @ B ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % VEBT_internal.option_shift.simps(3)
% 0.26/0.47  thf(fact_750_int__eq__iff__numeral,axiom,
% 0.26/0.47      ! [M: nat,V: num] :
% 0.26/0.47        ( ( ( semiri1314217659103216013at_int @ M )
% 0.26/0.47          = ( numeral_numeral_int @ V ) )
% 0.26/0.47        = ( M
% 0.26/0.47          = ( numeral_numeral_nat @ V ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % int_eq_iff_numeral
% 0.26/0.47  thf(fact_751_reals__Archimedean2,axiom,
% 0.26/0.47      ! [X3: real] :
% 0.26/0.47      ? [N2: nat] : ( ord_less_real @ X3 @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % reals_Archimedean2
% 0.26/0.47  thf(fact_752_reals__Archimedean2,axiom,
% 0.26/0.47      ! [X3: rat] :
% 0.26/0.47      ? [N2: nat] : ( ord_less_rat @ X3 @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % reals_Archimedean2
% 0.26/0.47  thf(fact_753_real__arch__simple,axiom,
% 0.26/0.47      ! [X3: real] :
% 0.26/0.47      ? [N2: nat] : ( ord_less_eq_real @ X3 @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % real_arch_simple
% 0.26/0.47  thf(fact_754_real__arch__simple,axiom,
% 0.26/0.47      ! [X3: rat] :
% 0.26/0.47      ? [N2: nat] : ( ord_less_eq_rat @ X3 @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % real_arch_simple
% 0.26/0.47  thf(fact_755_minf_I8_J,axiom,
% 0.26/0.47      ! [T: real] :
% 0.26/0.47      ? [Z3: real] :
% 0.26/0.47      ! [X6: real] :
% 0.26/0.47        ( ( ord_less_real @ X6 @ Z3 )
% 0.26/0.47       => ~ ( ord_less_eq_real @ T @ X6 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(8)
% 0.26/0.47  thf(fact_756_minf_I8_J,axiom,
% 0.26/0.47      ! [T: rat] :
% 0.26/0.47      ? [Z3: rat] :
% 0.26/0.47      ! [X6: rat] :
% 0.26/0.47        ( ( ord_less_rat @ X6 @ Z3 )
% 0.26/0.47       => ~ ( ord_less_eq_rat @ T @ X6 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(8)
% 0.26/0.47  thf(fact_757_minf_I8_J,axiom,
% 0.26/0.47      ! [T: num] :
% 0.26/0.47      ? [Z3: num] :
% 0.26/0.47      ! [X6: num] :
% 0.26/0.47        ( ( ord_less_num @ X6 @ Z3 )
% 0.26/0.47       => ~ ( ord_less_eq_num @ T @ X6 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(8)
% 0.26/0.47  thf(fact_758_minf_I8_J,axiom,
% 0.26/0.47      ! [T: nat] :
% 0.26/0.47      ? [Z3: nat] :
% 0.26/0.47      ! [X6: nat] :
% 0.26/0.47        ( ( ord_less_nat @ X6 @ Z3 )
% 0.26/0.47       => ~ ( ord_less_eq_nat @ T @ X6 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(8)
% 0.26/0.47  thf(fact_759_minf_I8_J,axiom,
% 0.26/0.47      ! [T: int] :
% 0.26/0.47      ? [Z3: int] :
% 0.26/0.47      ! [X6: int] :
% 0.26/0.47        ( ( ord_less_int @ X6 @ Z3 )
% 0.26/0.47       => ~ ( ord_less_eq_int @ T @ X6 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(8)
% 0.26/0.47  thf(fact_760_nat__int__comparison_I1_J,axiom,
% 0.26/0.47      ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 0.26/0.47      = ( ^ [A4: nat,B3: nat] :
% 0.26/0.47            ( ( semiri1314217659103216013at_int @ A4 )
% 0.26/0.47            = ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % nat_int_comparison(1)
% 0.26/0.47  thf(fact_761_int__if,axiom,
% 0.26/0.47      ! [P: $o,A: nat,B: nat] :
% 0.26/0.47        ( ( P
% 0.26/0.47         => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 0.26/0.47            = ( semiri1314217659103216013at_int @ A ) ) )
% 0.26/0.47        & ( ~ P
% 0.26/0.47         => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 0.26/0.47            = ( semiri1314217659103216013at_int @ B ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % int_if
% 0.26/0.47  thf(fact_762_complete__real,axiom,
% 0.26/0.47      ! [S2: set_real] :
% 0.26/0.47        ( ? [X6: real] : ( member_real @ X6 @ S2 )
% 0.26/0.47       => ( ? [Z4: real] :
% 0.26/0.47            ! [X4: real] :
% 0.26/0.47              ( ( member_real @ X4 @ S2 )
% 0.26/0.47             => ( ord_less_eq_real @ X4 @ Z4 ) )
% 0.26/0.47         => ? [Y4: real] :
% 0.26/0.47              ( ! [X6: real] :
% 0.26/0.47                  ( ( member_real @ X6 @ S2 )
% 0.26/0.47                 => ( ord_less_eq_real @ X6 @ Y4 ) )
% 0.26/0.47              & ! [Z4: real] :
% 0.26/0.47                  ( ! [X4: real] :
% 0.26/0.47                      ( ( member_real @ X4 @ S2 )
% 0.26/0.47                     => ( ord_less_eq_real @ X4 @ Z4 ) )
% 0.26/0.47                 => ( ord_less_eq_real @ Y4 @ Z4 ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % complete_real
% 0.26/0.47  thf(fact_763_verit__la__generic,axiom,
% 0.26/0.47      ! [A: int,X3: int] :
% 0.26/0.47        ( ( ord_less_eq_int @ A @ X3 )
% 0.26/0.47        | ( A = X3 )
% 0.26/0.47        | ( ord_less_eq_int @ X3 @ A ) ) ).
% 0.26/0.47  
% 0.26/0.47  % verit_la_generic
% 0.26/0.47  thf(fact_764_less__eq__real__def,axiom,
% 0.26/0.47      ( ord_less_eq_real
% 0.26/0.47      = ( ^ [X: real,Y: real] :
% 0.26/0.47            ( ( ord_less_real @ X @ Y )
% 0.26/0.47            | ( X = Y ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % less_eq_real_def
% 0.26/0.47  thf(fact_765_int__int__eq,axiom,
% 0.26/0.47      ! [M: nat,N: nat] :
% 0.26/0.47        ( ( ( semiri1314217659103216013at_int @ M )
% 0.26/0.47          = ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.47        = ( M = N ) ) ).
% 0.26/0.47  
% 0.26/0.47  % int_int_eq
% 0.26/0.47  thf(fact_766_pinf_I1_J,axiom,
% 0.26/0.47      ! [P: real > $o,P4: real > $o,Q: real > $o,Q2: real > $o] :
% 0.26/0.47        ( ? [Z4: real] :
% 0.26/0.47          ! [X4: real] :
% 0.26/0.47            ( ( ord_less_real @ Z4 @ X4 )
% 0.26/0.47           => ( ( P @ X4 )
% 0.26/0.47              = ( P4 @ X4 ) ) )
% 0.26/0.47       => ( ? [Z4: real] :
% 0.26/0.47            ! [X4: real] :
% 0.26/0.47              ( ( ord_less_real @ Z4 @ X4 )
% 0.26/0.47             => ( ( Q @ X4 )
% 0.26/0.47                = ( Q2 @ X4 ) ) )
% 0.26/0.47         => ? [Z3: real] :
% 0.26/0.47            ! [X6: real] :
% 0.26/0.47              ( ( ord_less_real @ Z3 @ X6 )
% 0.26/0.47             => ( ( ( P @ X6 )
% 0.26/0.47                  & ( Q @ X6 ) )
% 0.26/0.47                = ( ( P4 @ X6 )
% 0.26/0.47                  & ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(1)
% 0.26/0.47  thf(fact_767_pinf_I1_J,axiom,
% 0.26/0.47      ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 0.26/0.47        ( ? [Z4: rat] :
% 0.26/0.47          ! [X4: rat] :
% 0.26/0.47            ( ( ord_less_rat @ Z4 @ X4 )
% 0.26/0.47           => ( ( P @ X4 )
% 0.26/0.47              = ( P4 @ X4 ) ) )
% 0.26/0.47       => ( ? [Z4: rat] :
% 0.26/0.47            ! [X4: rat] :
% 0.26/0.47              ( ( ord_less_rat @ Z4 @ X4 )
% 0.26/0.47             => ( ( Q @ X4 )
% 0.26/0.47                = ( Q2 @ X4 ) ) )
% 0.26/0.47         => ? [Z3: rat] :
% 0.26/0.47            ! [X6: rat] :
% 0.26/0.47              ( ( ord_less_rat @ Z3 @ X6 )
% 0.26/0.47             => ( ( ( P @ X6 )
% 0.26/0.47                  & ( Q @ X6 ) )
% 0.26/0.47                = ( ( P4 @ X6 )
% 0.26/0.47                  & ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(1)
% 0.26/0.47  thf(fact_768_pinf_I1_J,axiom,
% 0.26/0.47      ! [P: num > $o,P4: num > $o,Q: num > $o,Q2: num > $o] :
% 0.26/0.47        ( ? [Z4: num] :
% 0.26/0.47          ! [X4: num] :
% 0.26/0.47            ( ( ord_less_num @ Z4 @ X4 )
% 0.26/0.47           => ( ( P @ X4 )
% 0.26/0.47              = ( P4 @ X4 ) ) )
% 0.26/0.47       => ( ? [Z4: num] :
% 0.26/0.47            ! [X4: num] :
% 0.26/0.47              ( ( ord_less_num @ Z4 @ X4 )
% 0.26/0.47             => ( ( Q @ X4 )
% 0.26/0.47                = ( Q2 @ X4 ) ) )
% 0.26/0.47         => ? [Z3: num] :
% 0.26/0.47            ! [X6: num] :
% 0.26/0.47              ( ( ord_less_num @ Z3 @ X6 )
% 0.26/0.47             => ( ( ( P @ X6 )
% 0.26/0.47                  & ( Q @ X6 ) )
% 0.26/0.47                = ( ( P4 @ X6 )
% 0.26/0.47                  & ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(1)
% 0.26/0.47  thf(fact_769_pinf_I1_J,axiom,
% 0.26/0.47      ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.26/0.47        ( ? [Z4: nat] :
% 0.26/0.47          ! [X4: nat] :
% 0.26/0.47            ( ( ord_less_nat @ Z4 @ X4 )
% 0.26/0.47           => ( ( P @ X4 )
% 0.26/0.47              = ( P4 @ X4 ) ) )
% 0.26/0.47       => ( ? [Z4: nat] :
% 0.26/0.47            ! [X4: nat] :
% 0.26/0.47              ( ( ord_less_nat @ Z4 @ X4 )
% 0.26/0.47             => ( ( Q @ X4 )
% 0.26/0.47                = ( Q2 @ X4 ) ) )
% 0.26/0.47         => ? [Z3: nat] :
% 0.26/0.47            ! [X6: nat] :
% 0.26/0.47              ( ( ord_less_nat @ Z3 @ X6 )
% 0.26/0.47             => ( ( ( P @ X6 )
% 0.26/0.47                  & ( Q @ X6 ) )
% 0.26/0.47                = ( ( P4 @ X6 )
% 0.26/0.47                  & ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(1)
% 0.26/0.47  thf(fact_770_pinf_I1_J,axiom,
% 0.26/0.47      ! [P: int > $o,P4: int > $o,Q: int > $o,Q2: int > $o] :
% 0.26/0.47        ( ? [Z4: int] :
% 0.26/0.47          ! [X4: int] :
% 0.26/0.47            ( ( ord_less_int @ Z4 @ X4 )
% 0.26/0.47           => ( ( P @ X4 )
% 0.26/0.47              = ( P4 @ X4 ) ) )
% 0.26/0.47       => ( ? [Z4: int] :
% 0.26/0.47            ! [X4: int] :
% 0.26/0.47              ( ( ord_less_int @ Z4 @ X4 )
% 0.26/0.47             => ( ( Q @ X4 )
% 0.26/0.47                = ( Q2 @ X4 ) ) )
% 0.26/0.47         => ? [Z3: int] :
% 0.26/0.47            ! [X6: int] :
% 0.26/0.47              ( ( ord_less_int @ Z3 @ X6 )
% 0.26/0.47             => ( ( ( P @ X6 )
% 0.26/0.47                  & ( Q @ X6 ) )
% 0.26/0.47                = ( ( P4 @ X6 )
% 0.26/0.47                  & ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(1)
% 0.26/0.47  thf(fact_771_pinf_I2_J,axiom,
% 0.26/0.47      ! [P: real > $o,P4: real > $o,Q: real > $o,Q2: real > $o] :
% 0.26/0.47        ( ? [Z4: real] :
% 0.26/0.47          ! [X4: real] :
% 0.26/0.47            ( ( ord_less_real @ Z4 @ X4 )
% 0.26/0.47           => ( ( P @ X4 )
% 0.26/0.47              = ( P4 @ X4 ) ) )
% 0.26/0.47       => ( ? [Z4: real] :
% 0.26/0.47            ! [X4: real] :
% 0.26/0.47              ( ( ord_less_real @ Z4 @ X4 )
% 0.26/0.47             => ( ( Q @ X4 )
% 0.26/0.47                = ( Q2 @ X4 ) ) )
% 0.26/0.47         => ? [Z3: real] :
% 0.26/0.47            ! [X6: real] :
% 0.26/0.47              ( ( ord_less_real @ Z3 @ X6 )
% 0.26/0.47             => ( ( ( P @ X6 )
% 0.26/0.47                  | ( Q @ X6 ) )
% 0.26/0.47                = ( ( P4 @ X6 )
% 0.26/0.47                  | ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(2)
% 0.26/0.47  thf(fact_772_pinf_I2_J,axiom,
% 0.26/0.47      ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 0.26/0.47        ( ? [Z4: rat] :
% 0.26/0.47          ! [X4: rat] :
% 0.26/0.47            ( ( ord_less_rat @ Z4 @ X4 )
% 0.26/0.47           => ( ( P @ X4 )
% 0.26/0.47              = ( P4 @ X4 ) ) )
% 0.26/0.47       => ( ? [Z4: rat] :
% 0.26/0.47            ! [X4: rat] :
% 0.26/0.47              ( ( ord_less_rat @ Z4 @ X4 )
% 0.26/0.47             => ( ( Q @ X4 )
% 0.26/0.47                = ( Q2 @ X4 ) ) )
% 0.26/0.47         => ? [Z3: rat] :
% 0.26/0.47            ! [X6: rat] :
% 0.26/0.47              ( ( ord_less_rat @ Z3 @ X6 )
% 0.26/0.47             => ( ( ( P @ X6 )
% 0.26/0.47                  | ( Q @ X6 ) )
% 0.26/0.47                = ( ( P4 @ X6 )
% 0.26/0.47                  | ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(2)
% 0.26/0.47  thf(fact_773_pinf_I2_J,axiom,
% 0.26/0.47      ! [P: num > $o,P4: num > $o,Q: num > $o,Q2: num > $o] :
% 0.26/0.47        ( ? [Z4: num] :
% 0.26/0.47          ! [X4: num] :
% 0.26/0.47            ( ( ord_less_num @ Z4 @ X4 )
% 0.26/0.47           => ( ( P @ X4 )
% 0.26/0.47              = ( P4 @ X4 ) ) )
% 0.26/0.47       => ( ? [Z4: num] :
% 0.26/0.47            ! [X4: num] :
% 0.26/0.47              ( ( ord_less_num @ Z4 @ X4 )
% 0.26/0.47             => ( ( Q @ X4 )
% 0.26/0.47                = ( Q2 @ X4 ) ) )
% 0.26/0.47         => ? [Z3: num] :
% 0.26/0.47            ! [X6: num] :
% 0.26/0.47              ( ( ord_less_num @ Z3 @ X6 )
% 0.26/0.47             => ( ( ( P @ X6 )
% 0.26/0.47                  | ( Q @ X6 ) )
% 0.26/0.47                = ( ( P4 @ X6 )
% 0.26/0.47                  | ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(2)
% 0.26/0.47  thf(fact_774_pinf_I2_J,axiom,
% 0.26/0.47      ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.26/0.47        ( ? [Z4: nat] :
% 0.26/0.47          ! [X4: nat] :
% 0.26/0.47            ( ( ord_less_nat @ Z4 @ X4 )
% 0.26/0.47           => ( ( P @ X4 )
% 0.26/0.47              = ( P4 @ X4 ) ) )
% 0.26/0.47       => ( ? [Z4: nat] :
% 0.26/0.47            ! [X4: nat] :
% 0.26/0.47              ( ( ord_less_nat @ Z4 @ X4 )
% 0.26/0.47             => ( ( Q @ X4 )
% 0.26/0.47                = ( Q2 @ X4 ) ) )
% 0.26/0.47         => ? [Z3: nat] :
% 0.26/0.47            ! [X6: nat] :
% 0.26/0.47              ( ( ord_less_nat @ Z3 @ X6 )
% 0.26/0.47             => ( ( ( P @ X6 )
% 0.26/0.47                  | ( Q @ X6 ) )
% 0.26/0.47                = ( ( P4 @ X6 )
% 0.26/0.47                  | ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(2)
% 0.26/0.47  thf(fact_775_pinf_I2_J,axiom,
% 0.26/0.47      ! [P: int > $o,P4: int > $o,Q: int > $o,Q2: int > $o] :
% 0.26/0.47        ( ? [Z4: int] :
% 0.26/0.47          ! [X4: int] :
% 0.26/0.47            ( ( ord_less_int @ Z4 @ X4 )
% 0.26/0.47           => ( ( P @ X4 )
% 0.26/0.47              = ( P4 @ X4 ) ) )
% 0.26/0.47       => ( ? [Z4: int] :
% 0.26/0.47            ! [X4: int] :
% 0.26/0.47              ( ( ord_less_int @ Z4 @ X4 )
% 0.26/0.47             => ( ( Q @ X4 )
% 0.26/0.47                = ( Q2 @ X4 ) ) )
% 0.26/0.47         => ? [Z3: int] :
% 0.26/0.47            ! [X6: int] :
% 0.26/0.47              ( ( ord_less_int @ Z3 @ X6 )
% 0.26/0.47             => ( ( ( P @ X6 )
% 0.26/0.47                  | ( Q @ X6 ) )
% 0.26/0.47                = ( ( P4 @ X6 )
% 0.26/0.47                  | ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(2)
% 0.26/0.47  thf(fact_776_pinf_I3_J,axiom,
% 0.26/0.47      ! [T: real] :
% 0.26/0.47      ? [Z3: real] :
% 0.26/0.47      ! [X6: real] :
% 0.26/0.47        ( ( ord_less_real @ Z3 @ X6 )
% 0.26/0.47       => ( X6 != T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(3)
% 0.26/0.47  thf(fact_777_pinf_I3_J,axiom,
% 0.26/0.47      ! [T: rat] :
% 0.26/0.47      ? [Z3: rat] :
% 0.26/0.47      ! [X6: rat] :
% 0.26/0.47        ( ( ord_less_rat @ Z3 @ X6 )
% 0.26/0.47       => ( X6 != T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(3)
% 0.26/0.47  thf(fact_778_pinf_I3_J,axiom,
% 0.26/0.47      ! [T: num] :
% 0.26/0.47      ? [Z3: num] :
% 0.26/0.47      ! [X6: num] :
% 0.26/0.47        ( ( ord_less_num @ Z3 @ X6 )
% 0.26/0.47       => ( X6 != T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(3)
% 0.26/0.47  thf(fact_779_pinf_I3_J,axiom,
% 0.26/0.47      ! [T: nat] :
% 0.26/0.47      ? [Z3: nat] :
% 0.26/0.47      ! [X6: nat] :
% 0.26/0.47        ( ( ord_less_nat @ Z3 @ X6 )
% 0.26/0.47       => ( X6 != T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(3)
% 0.26/0.47  thf(fact_780_pinf_I3_J,axiom,
% 0.26/0.47      ! [T: int] :
% 0.26/0.47      ? [Z3: int] :
% 0.26/0.47      ! [X6: int] :
% 0.26/0.47        ( ( ord_less_int @ Z3 @ X6 )
% 0.26/0.47       => ( X6 != T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(3)
% 0.26/0.47  thf(fact_781_pinf_I4_J,axiom,
% 0.26/0.47      ! [T: real] :
% 0.26/0.47      ? [Z3: real] :
% 0.26/0.47      ! [X6: real] :
% 0.26/0.47        ( ( ord_less_real @ Z3 @ X6 )
% 0.26/0.47       => ( X6 != T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(4)
% 0.26/0.47  thf(fact_782_pinf_I4_J,axiom,
% 0.26/0.47      ! [T: rat] :
% 0.26/0.47      ? [Z3: rat] :
% 0.26/0.47      ! [X6: rat] :
% 0.26/0.47        ( ( ord_less_rat @ Z3 @ X6 )
% 0.26/0.47       => ( X6 != T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(4)
% 0.26/0.47  thf(fact_783_pinf_I4_J,axiom,
% 0.26/0.47      ! [T: num] :
% 0.26/0.47      ? [Z3: num] :
% 0.26/0.47      ! [X6: num] :
% 0.26/0.47        ( ( ord_less_num @ Z3 @ X6 )
% 0.26/0.47       => ( X6 != T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(4)
% 0.26/0.47  thf(fact_784_pinf_I4_J,axiom,
% 0.26/0.47      ! [T: nat] :
% 0.26/0.47      ? [Z3: nat] :
% 0.26/0.47      ! [X6: nat] :
% 0.26/0.47        ( ( ord_less_nat @ Z3 @ X6 )
% 0.26/0.47       => ( X6 != T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(4)
% 0.26/0.47  thf(fact_785_pinf_I4_J,axiom,
% 0.26/0.47      ! [T: int] :
% 0.26/0.47      ? [Z3: int] :
% 0.26/0.47      ! [X6: int] :
% 0.26/0.47        ( ( ord_less_int @ Z3 @ X6 )
% 0.26/0.47       => ( X6 != T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(4)
% 0.26/0.47  thf(fact_786_pinf_I5_J,axiom,
% 0.26/0.47      ! [T: real] :
% 0.26/0.47      ? [Z3: real] :
% 0.26/0.47      ! [X6: real] :
% 0.26/0.47        ( ( ord_less_real @ Z3 @ X6 )
% 0.26/0.47       => ~ ( ord_less_real @ X6 @ T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(5)
% 0.26/0.47  thf(fact_787_pinf_I5_J,axiom,
% 0.26/0.47      ! [T: rat] :
% 0.26/0.47      ? [Z3: rat] :
% 0.26/0.47      ! [X6: rat] :
% 0.26/0.47        ( ( ord_less_rat @ Z3 @ X6 )
% 0.26/0.47       => ~ ( ord_less_rat @ X6 @ T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(5)
% 0.26/0.47  thf(fact_788_pinf_I5_J,axiom,
% 0.26/0.47      ! [T: num] :
% 0.26/0.47      ? [Z3: num] :
% 0.26/0.47      ! [X6: num] :
% 0.26/0.47        ( ( ord_less_num @ Z3 @ X6 )
% 0.26/0.47       => ~ ( ord_less_num @ X6 @ T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(5)
% 0.26/0.47  thf(fact_789_pinf_I5_J,axiom,
% 0.26/0.47      ! [T: nat] :
% 0.26/0.47      ? [Z3: nat] :
% 0.26/0.47      ! [X6: nat] :
% 0.26/0.47        ( ( ord_less_nat @ Z3 @ X6 )
% 0.26/0.47       => ~ ( ord_less_nat @ X6 @ T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(5)
% 0.26/0.47  thf(fact_790_pinf_I5_J,axiom,
% 0.26/0.47      ! [T: int] :
% 0.26/0.47      ? [Z3: int] :
% 0.26/0.47      ! [X6: int] :
% 0.26/0.47        ( ( ord_less_int @ Z3 @ X6 )
% 0.26/0.47       => ~ ( ord_less_int @ X6 @ T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(5)
% 0.26/0.47  thf(fact_791_pinf_I7_J,axiom,
% 0.26/0.47      ! [T: real] :
% 0.26/0.47      ? [Z3: real] :
% 0.26/0.47      ! [X6: real] :
% 0.26/0.47        ( ( ord_less_real @ Z3 @ X6 )
% 0.26/0.47       => ( ord_less_real @ T @ X6 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(7)
% 0.26/0.47  thf(fact_792_pinf_I7_J,axiom,
% 0.26/0.47      ! [T: rat] :
% 0.26/0.47      ? [Z3: rat] :
% 0.26/0.47      ! [X6: rat] :
% 0.26/0.47        ( ( ord_less_rat @ Z3 @ X6 )
% 0.26/0.47       => ( ord_less_rat @ T @ X6 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(7)
% 0.26/0.47  thf(fact_793_pinf_I7_J,axiom,
% 0.26/0.47      ! [T: num] :
% 0.26/0.47      ? [Z3: num] :
% 0.26/0.47      ! [X6: num] :
% 0.26/0.47        ( ( ord_less_num @ Z3 @ X6 )
% 0.26/0.47       => ( ord_less_num @ T @ X6 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(7)
% 0.26/0.47  thf(fact_794_pinf_I7_J,axiom,
% 0.26/0.47      ! [T: nat] :
% 0.26/0.47      ? [Z3: nat] :
% 0.26/0.47      ! [X6: nat] :
% 0.26/0.47        ( ( ord_less_nat @ Z3 @ X6 )
% 0.26/0.47       => ( ord_less_nat @ T @ X6 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(7)
% 0.26/0.47  thf(fact_795_pinf_I7_J,axiom,
% 0.26/0.47      ! [T: int] :
% 0.26/0.47      ? [Z3: int] :
% 0.26/0.47      ! [X6: int] :
% 0.26/0.47        ( ( ord_less_int @ Z3 @ X6 )
% 0.26/0.47       => ( ord_less_int @ T @ X6 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(7)
% 0.26/0.47  thf(fact_796_minf_I1_J,axiom,
% 0.26/0.47      ! [P: real > $o,P4: real > $o,Q: real > $o,Q2: real > $o] :
% 0.26/0.47        ( ? [Z4: real] :
% 0.26/0.47          ! [X4: real] :
% 0.26/0.47            ( ( ord_less_real @ X4 @ Z4 )
% 0.26/0.47           => ( ( P @ X4 )
% 0.26/0.47              = ( P4 @ X4 ) ) )
% 0.26/0.47       => ( ? [Z4: real] :
% 0.26/0.47            ! [X4: real] :
% 0.26/0.47              ( ( ord_less_real @ X4 @ Z4 )
% 0.26/0.47             => ( ( Q @ X4 )
% 0.26/0.47                = ( Q2 @ X4 ) ) )
% 0.26/0.47         => ? [Z3: real] :
% 0.26/0.47            ! [X6: real] :
% 0.26/0.47              ( ( ord_less_real @ X6 @ Z3 )
% 0.26/0.47             => ( ( ( P @ X6 )
% 0.26/0.47                  & ( Q @ X6 ) )
% 0.26/0.47                = ( ( P4 @ X6 )
% 0.26/0.47                  & ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(1)
% 0.26/0.47  thf(fact_797_minf_I1_J,axiom,
% 0.26/0.47      ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 0.26/0.47        ( ? [Z4: rat] :
% 0.26/0.47          ! [X4: rat] :
% 0.26/0.47            ( ( ord_less_rat @ X4 @ Z4 )
% 0.26/0.47           => ( ( P @ X4 )
% 0.26/0.47              = ( P4 @ X4 ) ) )
% 0.26/0.47       => ( ? [Z4: rat] :
% 0.26/0.47            ! [X4: rat] :
% 0.26/0.47              ( ( ord_less_rat @ X4 @ Z4 )
% 0.26/0.47             => ( ( Q @ X4 )
% 0.26/0.47                = ( Q2 @ X4 ) ) )
% 0.26/0.47         => ? [Z3: rat] :
% 0.26/0.47            ! [X6: rat] :
% 0.26/0.47              ( ( ord_less_rat @ X6 @ Z3 )
% 0.26/0.47             => ( ( ( P @ X6 )
% 0.26/0.47                  & ( Q @ X6 ) )
% 0.26/0.47                = ( ( P4 @ X6 )
% 0.26/0.47                  & ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(1)
% 0.26/0.47  thf(fact_798_minf_I1_J,axiom,
% 0.26/0.47      ! [P: num > $o,P4: num > $o,Q: num > $o,Q2: num > $o] :
% 0.26/0.47        ( ? [Z4: num] :
% 0.26/0.47          ! [X4: num] :
% 0.26/0.47            ( ( ord_less_num @ X4 @ Z4 )
% 0.26/0.47           => ( ( P @ X4 )
% 0.26/0.47              = ( P4 @ X4 ) ) )
% 0.26/0.47       => ( ? [Z4: num] :
% 0.26/0.47            ! [X4: num] :
% 0.26/0.47              ( ( ord_less_num @ X4 @ Z4 )
% 0.26/0.47             => ( ( Q @ X4 )
% 0.26/0.47                = ( Q2 @ X4 ) ) )
% 0.26/0.47         => ? [Z3: num] :
% 0.26/0.47            ! [X6: num] :
% 0.26/0.47              ( ( ord_less_num @ X6 @ Z3 )
% 0.26/0.47             => ( ( ( P @ X6 )
% 0.26/0.47                  & ( Q @ X6 ) )
% 0.26/0.47                = ( ( P4 @ X6 )
% 0.26/0.47                  & ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(1)
% 0.26/0.47  thf(fact_799_minf_I1_J,axiom,
% 0.26/0.47      ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.26/0.47        ( ? [Z4: nat] :
% 0.26/0.47          ! [X4: nat] :
% 0.26/0.47            ( ( ord_less_nat @ X4 @ Z4 )
% 0.26/0.47           => ( ( P @ X4 )
% 0.26/0.47              = ( P4 @ X4 ) ) )
% 0.26/0.47       => ( ? [Z4: nat] :
% 0.26/0.47            ! [X4: nat] :
% 0.26/0.47              ( ( ord_less_nat @ X4 @ Z4 )
% 0.26/0.47             => ( ( Q @ X4 )
% 0.26/0.47                = ( Q2 @ X4 ) ) )
% 0.26/0.47         => ? [Z3: nat] :
% 0.26/0.47            ! [X6: nat] :
% 0.26/0.47              ( ( ord_less_nat @ X6 @ Z3 )
% 0.26/0.47             => ( ( ( P @ X6 )
% 0.26/0.47                  & ( Q @ X6 ) )
% 0.26/0.47                = ( ( P4 @ X6 )
% 0.26/0.47                  & ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(1)
% 0.26/0.47  thf(fact_800_minf_I1_J,axiom,
% 0.26/0.47      ! [P: int > $o,P4: int > $o,Q: int > $o,Q2: int > $o] :
% 0.26/0.47        ( ? [Z4: int] :
% 0.26/0.47          ! [X4: int] :
% 0.26/0.47            ( ( ord_less_int @ X4 @ Z4 )
% 0.26/0.47           => ( ( P @ X4 )
% 0.26/0.47              = ( P4 @ X4 ) ) )
% 0.26/0.47       => ( ? [Z4: int] :
% 0.26/0.47            ! [X4: int] :
% 0.26/0.47              ( ( ord_less_int @ X4 @ Z4 )
% 0.26/0.47             => ( ( Q @ X4 )
% 0.26/0.47                = ( Q2 @ X4 ) ) )
% 0.26/0.47         => ? [Z3: int] :
% 0.26/0.47            ! [X6: int] :
% 0.26/0.47              ( ( ord_less_int @ X6 @ Z3 )
% 0.26/0.47             => ( ( ( P @ X6 )
% 0.26/0.47                  & ( Q @ X6 ) )
% 0.26/0.47                = ( ( P4 @ X6 )
% 0.26/0.47                  & ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(1)
% 0.26/0.47  thf(fact_801_minf_I2_J,axiom,
% 0.26/0.47      ! [P: real > $o,P4: real > $o,Q: real > $o,Q2: real > $o] :
% 0.26/0.47        ( ? [Z4: real] :
% 0.26/0.47          ! [X4: real] :
% 0.26/0.47            ( ( ord_less_real @ X4 @ Z4 )
% 0.26/0.47           => ( ( P @ X4 )
% 0.26/0.47              = ( P4 @ X4 ) ) )
% 0.26/0.47       => ( ? [Z4: real] :
% 0.26/0.47            ! [X4: real] :
% 0.26/0.47              ( ( ord_less_real @ X4 @ Z4 )
% 0.26/0.47             => ( ( Q @ X4 )
% 0.26/0.47                = ( Q2 @ X4 ) ) )
% 0.26/0.47         => ? [Z3: real] :
% 0.26/0.47            ! [X6: real] :
% 0.26/0.47              ( ( ord_less_real @ X6 @ Z3 )
% 0.26/0.47             => ( ( ( P @ X6 )
% 0.26/0.47                  | ( Q @ X6 ) )
% 0.26/0.47                = ( ( P4 @ X6 )
% 0.26/0.47                  | ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(2)
% 0.26/0.47  thf(fact_802_minf_I2_J,axiom,
% 0.26/0.47      ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 0.26/0.47        ( ? [Z4: rat] :
% 0.26/0.47          ! [X4: rat] :
% 0.26/0.47            ( ( ord_less_rat @ X4 @ Z4 )
% 0.26/0.47           => ( ( P @ X4 )
% 0.26/0.47              = ( P4 @ X4 ) ) )
% 0.26/0.47       => ( ? [Z4: rat] :
% 0.26/0.47            ! [X4: rat] :
% 0.26/0.47              ( ( ord_less_rat @ X4 @ Z4 )
% 0.26/0.47             => ( ( Q @ X4 )
% 0.26/0.47                = ( Q2 @ X4 ) ) )
% 0.26/0.47         => ? [Z3: rat] :
% 0.26/0.47            ! [X6: rat] :
% 0.26/0.47              ( ( ord_less_rat @ X6 @ Z3 )
% 0.26/0.47             => ( ( ( P @ X6 )
% 0.26/0.47                  | ( Q @ X6 ) )
% 0.26/0.47                = ( ( P4 @ X6 )
% 0.26/0.47                  | ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(2)
% 0.26/0.47  thf(fact_803_minf_I2_J,axiom,
% 0.26/0.47      ! [P: num > $o,P4: num > $o,Q: num > $o,Q2: num > $o] :
% 0.26/0.47        ( ? [Z4: num] :
% 0.26/0.47          ! [X4: num] :
% 0.26/0.47            ( ( ord_less_num @ X4 @ Z4 )
% 0.26/0.47           => ( ( P @ X4 )
% 0.26/0.47              = ( P4 @ X4 ) ) )
% 0.26/0.47       => ( ? [Z4: num] :
% 0.26/0.47            ! [X4: num] :
% 0.26/0.47              ( ( ord_less_num @ X4 @ Z4 )
% 0.26/0.47             => ( ( Q @ X4 )
% 0.26/0.47                = ( Q2 @ X4 ) ) )
% 0.26/0.47         => ? [Z3: num] :
% 0.26/0.47            ! [X6: num] :
% 0.26/0.47              ( ( ord_less_num @ X6 @ Z3 )
% 0.26/0.47             => ( ( ( P @ X6 )
% 0.26/0.47                  | ( Q @ X6 ) )
% 0.26/0.47                = ( ( P4 @ X6 )
% 0.26/0.47                  | ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(2)
% 0.26/0.47  thf(fact_804_minf_I2_J,axiom,
% 0.26/0.47      ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.26/0.47        ( ? [Z4: nat] :
% 0.26/0.47          ! [X4: nat] :
% 0.26/0.47            ( ( ord_less_nat @ X4 @ Z4 )
% 0.26/0.47           => ( ( P @ X4 )
% 0.26/0.47              = ( P4 @ X4 ) ) )
% 0.26/0.47       => ( ? [Z4: nat] :
% 0.26/0.47            ! [X4: nat] :
% 0.26/0.47              ( ( ord_less_nat @ X4 @ Z4 )
% 0.26/0.47             => ( ( Q @ X4 )
% 0.26/0.47                = ( Q2 @ X4 ) ) )
% 0.26/0.47         => ? [Z3: nat] :
% 0.26/0.47            ! [X6: nat] :
% 0.26/0.47              ( ( ord_less_nat @ X6 @ Z3 )
% 0.26/0.47             => ( ( ( P @ X6 )
% 0.26/0.47                  | ( Q @ X6 ) )
% 0.26/0.47                = ( ( P4 @ X6 )
% 0.26/0.47                  | ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(2)
% 0.26/0.47  thf(fact_805_minf_I2_J,axiom,
% 0.26/0.47      ! [P: int > $o,P4: int > $o,Q: int > $o,Q2: int > $o] :
% 0.26/0.47        ( ? [Z4: int] :
% 0.26/0.47          ! [X4: int] :
% 0.26/0.47            ( ( ord_less_int @ X4 @ Z4 )
% 0.26/0.47           => ( ( P @ X4 )
% 0.26/0.47              = ( P4 @ X4 ) ) )
% 0.26/0.47       => ( ? [Z4: int] :
% 0.26/0.47            ! [X4: int] :
% 0.26/0.47              ( ( ord_less_int @ X4 @ Z4 )
% 0.26/0.47             => ( ( Q @ X4 )
% 0.26/0.47                = ( Q2 @ X4 ) ) )
% 0.26/0.47         => ? [Z3: int] :
% 0.26/0.47            ! [X6: int] :
% 0.26/0.47              ( ( ord_less_int @ X6 @ Z3 )
% 0.26/0.47             => ( ( ( P @ X6 )
% 0.26/0.47                  | ( Q @ X6 ) )
% 0.26/0.47                = ( ( P4 @ X6 )
% 0.26/0.47                  | ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(2)
% 0.26/0.47  thf(fact_806_minf_I3_J,axiom,
% 0.26/0.47      ! [T: real] :
% 0.26/0.47      ? [Z3: real] :
% 0.26/0.47      ! [X6: real] :
% 0.26/0.47        ( ( ord_less_real @ X6 @ Z3 )
% 0.26/0.47       => ( X6 != T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(3)
% 0.26/0.47  thf(fact_807_minf_I3_J,axiom,
% 0.26/0.47      ! [T: rat] :
% 0.26/0.47      ? [Z3: rat] :
% 0.26/0.47      ! [X6: rat] :
% 0.26/0.47        ( ( ord_less_rat @ X6 @ Z3 )
% 0.26/0.47       => ( X6 != T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(3)
% 0.26/0.47  thf(fact_808_minf_I3_J,axiom,
% 0.26/0.47      ! [T: num] :
% 0.26/0.47      ? [Z3: num] :
% 0.26/0.47      ! [X6: num] :
% 0.26/0.47        ( ( ord_less_num @ X6 @ Z3 )
% 0.26/0.47       => ( X6 != T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(3)
% 0.26/0.47  thf(fact_809_minf_I3_J,axiom,
% 0.26/0.47      ! [T: nat] :
% 0.26/0.47      ? [Z3: nat] :
% 0.26/0.47      ! [X6: nat] :
% 0.26/0.47        ( ( ord_less_nat @ X6 @ Z3 )
% 0.26/0.47       => ( X6 != T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(3)
% 0.26/0.47  thf(fact_810_minf_I3_J,axiom,
% 0.26/0.47      ! [T: int] :
% 0.26/0.47      ? [Z3: int] :
% 0.26/0.47      ! [X6: int] :
% 0.26/0.47        ( ( ord_less_int @ X6 @ Z3 )
% 0.26/0.47       => ( X6 != T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(3)
% 0.26/0.47  thf(fact_811_minf_I4_J,axiom,
% 0.26/0.47      ! [T: real] :
% 0.26/0.47      ? [Z3: real] :
% 0.26/0.47      ! [X6: real] :
% 0.26/0.47        ( ( ord_less_real @ X6 @ Z3 )
% 0.26/0.47       => ( X6 != T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(4)
% 0.26/0.47  thf(fact_812_minf_I4_J,axiom,
% 0.26/0.47      ! [T: rat] :
% 0.26/0.47      ? [Z3: rat] :
% 0.26/0.47      ! [X6: rat] :
% 0.26/0.47        ( ( ord_less_rat @ X6 @ Z3 )
% 0.26/0.47       => ( X6 != T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(4)
% 0.26/0.47  thf(fact_813_minf_I4_J,axiom,
% 0.26/0.47      ! [T: num] :
% 0.26/0.47      ? [Z3: num] :
% 0.26/0.47      ! [X6: num] :
% 0.26/0.47        ( ( ord_less_num @ X6 @ Z3 )
% 0.26/0.47       => ( X6 != T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(4)
% 0.26/0.47  thf(fact_814_minf_I4_J,axiom,
% 0.26/0.47      ! [T: nat] :
% 0.26/0.47      ? [Z3: nat] :
% 0.26/0.47      ! [X6: nat] :
% 0.26/0.47        ( ( ord_less_nat @ X6 @ Z3 )
% 0.26/0.47       => ( X6 != T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(4)
% 0.26/0.47  thf(fact_815_minf_I4_J,axiom,
% 0.26/0.47      ! [T: int] :
% 0.26/0.47      ? [Z3: int] :
% 0.26/0.47      ! [X6: int] :
% 0.26/0.47        ( ( ord_less_int @ X6 @ Z3 )
% 0.26/0.47       => ( X6 != T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(4)
% 0.26/0.47  thf(fact_816_minf_I5_J,axiom,
% 0.26/0.47      ! [T: real] :
% 0.26/0.47      ? [Z3: real] :
% 0.26/0.47      ! [X6: real] :
% 0.26/0.47        ( ( ord_less_real @ X6 @ Z3 )
% 0.26/0.47       => ( ord_less_real @ X6 @ T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(5)
% 0.26/0.47  thf(fact_817_minf_I5_J,axiom,
% 0.26/0.47      ! [T: rat] :
% 0.26/0.47      ? [Z3: rat] :
% 0.26/0.47      ! [X6: rat] :
% 0.26/0.47        ( ( ord_less_rat @ X6 @ Z3 )
% 0.26/0.47       => ( ord_less_rat @ X6 @ T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(5)
% 0.26/0.47  thf(fact_818_minf_I5_J,axiom,
% 0.26/0.47      ! [T: num] :
% 0.26/0.47      ? [Z3: num] :
% 0.26/0.47      ! [X6: num] :
% 0.26/0.47        ( ( ord_less_num @ X6 @ Z3 )
% 0.26/0.47       => ( ord_less_num @ X6 @ T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(5)
% 0.26/0.47  thf(fact_819_minf_I5_J,axiom,
% 0.26/0.47      ! [T: nat] :
% 0.26/0.47      ? [Z3: nat] :
% 0.26/0.47      ! [X6: nat] :
% 0.26/0.47        ( ( ord_less_nat @ X6 @ Z3 )
% 0.26/0.47       => ( ord_less_nat @ X6 @ T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(5)
% 0.26/0.47  thf(fact_820_minf_I5_J,axiom,
% 0.26/0.47      ! [T: int] :
% 0.26/0.47      ? [Z3: int] :
% 0.26/0.47      ! [X6: int] :
% 0.26/0.47        ( ( ord_less_int @ X6 @ Z3 )
% 0.26/0.47       => ( ord_less_int @ X6 @ T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(5)
% 0.26/0.47  thf(fact_821_minf_I7_J,axiom,
% 0.26/0.47      ! [T: real] :
% 0.26/0.47      ? [Z3: real] :
% 0.26/0.47      ! [X6: real] :
% 0.26/0.47        ( ( ord_less_real @ X6 @ Z3 )
% 0.26/0.47       => ~ ( ord_less_real @ T @ X6 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(7)
% 0.26/0.47  thf(fact_822_minf_I7_J,axiom,
% 0.26/0.47      ! [T: rat] :
% 0.26/0.47      ? [Z3: rat] :
% 0.26/0.47      ! [X6: rat] :
% 0.26/0.47        ( ( ord_less_rat @ X6 @ Z3 )
% 0.26/0.47       => ~ ( ord_less_rat @ T @ X6 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(7)
% 0.26/0.47  thf(fact_823_minf_I7_J,axiom,
% 0.26/0.47      ! [T: num] :
% 0.26/0.47      ? [Z3: num] :
% 0.26/0.47      ! [X6: num] :
% 0.26/0.47        ( ( ord_less_num @ X6 @ Z3 )
% 0.26/0.47       => ~ ( ord_less_num @ T @ X6 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(7)
% 0.26/0.47  thf(fact_824_minf_I7_J,axiom,
% 0.26/0.47      ! [T: nat] :
% 0.26/0.47      ? [Z3: nat] :
% 0.26/0.47      ! [X6: nat] :
% 0.26/0.47        ( ( ord_less_nat @ X6 @ Z3 )
% 0.26/0.47       => ~ ( ord_less_nat @ T @ X6 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(7)
% 0.26/0.47  thf(fact_825_minf_I7_J,axiom,
% 0.26/0.47      ! [T: int] :
% 0.26/0.47      ? [Z3: int] :
% 0.26/0.47      ! [X6: int] :
% 0.26/0.47        ( ( ord_less_int @ X6 @ Z3 )
% 0.26/0.47       => ~ ( ord_less_int @ T @ X6 ) ) ).
% 0.26/0.47  
% 0.26/0.47  % minf(7)
% 0.26/0.47  thf(fact_826_zle__int,axiom,
% 0.26/0.47      ! [M: nat,N: nat] :
% 0.26/0.47        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.47        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.47  
% 0.26/0.47  % zle_int
% 0.26/0.47  thf(fact_827_pinf_I6_J,axiom,
% 0.26/0.47      ! [T: real] :
% 0.26/0.47      ? [Z3: real] :
% 0.26/0.47      ! [X6: real] :
% 0.26/0.47        ( ( ord_less_real @ Z3 @ X6 )
% 0.26/0.47       => ~ ( ord_less_eq_real @ X6 @ T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(6)
% 0.26/0.47  thf(fact_828_pinf_I6_J,axiom,
% 0.26/0.47      ! [T: rat] :
% 0.26/0.47      ? [Z3: rat] :
% 0.26/0.47      ! [X6: rat] :
% 0.26/0.47        ( ( ord_less_rat @ Z3 @ X6 )
% 0.26/0.47       => ~ ( ord_less_eq_rat @ X6 @ T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(6)
% 0.26/0.47  thf(fact_829_pinf_I6_J,axiom,
% 0.26/0.47      ! [T: num] :
% 0.26/0.47      ? [Z3: num] :
% 0.26/0.47      ! [X6: num] :
% 0.26/0.47        ( ( ord_less_num @ Z3 @ X6 )
% 0.26/0.47       => ~ ( ord_less_eq_num @ X6 @ T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(6)
% 0.26/0.47  thf(fact_830_pinf_I6_J,axiom,
% 0.26/0.47      ! [T: nat] :
% 0.26/0.47      ? [Z3: nat] :
% 0.26/0.47      ! [X6: nat] :
% 0.26/0.47        ( ( ord_less_nat @ Z3 @ X6 )
% 0.26/0.47       => ~ ( ord_less_eq_nat @ X6 @ T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(6)
% 0.26/0.47  thf(fact_831_pinf_I6_J,axiom,
% 0.26/0.47      ! [T: int] :
% 0.26/0.47      ? [Z3: int] :
% 0.26/0.47      ! [X6: int] :
% 0.26/0.47        ( ( ord_less_int @ Z3 @ X6 )
% 0.26/0.47       => ~ ( ord_less_eq_int @ X6 @ T ) ) ).
% 0.26/0.47  
% 0.26/0.47  % pinf(6)
% 0.26/0.47  thf(fact_832_pinf_I8_J,axiom,
% 0.26/0.47      ! [T: real] :
% 0.26/0.47      ? [Z3: real] :
% 0.26/0.47      ! [X6: real] :
% 0.26/0.47        ( ( ord_less_real @ Z3 @ X6 )
% 0.26/0.47       => ( ord_less_eq_real @ T @ X6 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % pinf(8)
% 0.26/0.48  thf(fact_833_pinf_I8_J,axiom,
% 0.26/0.48      ! [T: rat] :
% 0.26/0.48      ? [Z3: rat] :
% 0.26/0.48      ! [X6: rat] :
% 0.26/0.48        ( ( ord_less_rat @ Z3 @ X6 )
% 0.26/0.48       => ( ord_less_eq_rat @ T @ X6 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % pinf(8)
% 0.26/0.48  thf(fact_834_pinf_I8_J,axiom,
% 0.26/0.48      ! [T: num] :
% 0.26/0.48      ? [Z3: num] :
% 0.26/0.48      ! [X6: num] :
% 0.26/0.48        ( ( ord_less_num @ Z3 @ X6 )
% 0.26/0.48       => ( ord_less_eq_num @ T @ X6 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % pinf(8)
% 0.26/0.48  thf(fact_835_pinf_I8_J,axiom,
% 0.26/0.48      ! [T: nat] :
% 0.26/0.48      ? [Z3: nat] :
% 0.26/0.48      ! [X6: nat] :
% 0.26/0.48        ( ( ord_less_nat @ Z3 @ X6 )
% 0.26/0.48       => ( ord_less_eq_nat @ T @ X6 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % pinf(8)
% 0.26/0.48  thf(fact_836_pinf_I8_J,axiom,
% 0.26/0.48      ! [T: int] :
% 0.26/0.48      ? [Z3: int] :
% 0.26/0.48      ! [X6: int] :
% 0.26/0.48        ( ( ord_less_int @ Z3 @ X6 )
% 0.26/0.48       => ( ord_less_eq_int @ T @ X6 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % pinf(8)
% 0.26/0.48  thf(fact_837_minf_I6_J,axiom,
% 0.26/0.48      ! [T: real] :
% 0.26/0.48      ? [Z3: real] :
% 0.26/0.48      ! [X6: real] :
% 0.26/0.48        ( ( ord_less_real @ X6 @ Z3 )
% 0.26/0.48       => ( ord_less_eq_real @ X6 @ T ) ) ).
% 0.26/0.48  
% 0.26/0.48  % minf(6)
% 0.26/0.48  thf(fact_838_minf_I6_J,axiom,
% 0.26/0.48      ! [T: rat] :
% 0.26/0.48      ? [Z3: rat] :
% 0.26/0.48      ! [X6: rat] :
% 0.26/0.48        ( ( ord_less_rat @ X6 @ Z3 )
% 0.26/0.48       => ( ord_less_eq_rat @ X6 @ T ) ) ).
% 0.26/0.48  
% 0.26/0.48  % minf(6)
% 0.26/0.48  thf(fact_839_minf_I6_J,axiom,
% 0.26/0.48      ! [T: num] :
% 0.26/0.48      ? [Z3: num] :
% 0.26/0.48      ! [X6: num] :
% 0.26/0.48        ( ( ord_less_num @ X6 @ Z3 )
% 0.26/0.48       => ( ord_less_eq_num @ X6 @ T ) ) ).
% 0.26/0.48  
% 0.26/0.48  % minf(6)
% 0.26/0.48  thf(fact_840_minf_I6_J,axiom,
% 0.26/0.48      ! [T: nat] :
% 0.26/0.48      ? [Z3: nat] :
% 0.26/0.48      ! [X6: nat] :
% 0.26/0.48        ( ( ord_less_nat @ X6 @ Z3 )
% 0.26/0.48       => ( ord_less_eq_nat @ X6 @ T ) ) ).
% 0.26/0.48  
% 0.26/0.48  % minf(6)
% 0.26/0.48  thf(fact_841_minf_I6_J,axiom,
% 0.26/0.48      ! [T: int] :
% 0.26/0.48      ? [Z3: int] :
% 0.26/0.48      ! [X6: int] :
% 0.26/0.48        ( ( ord_less_int @ X6 @ Z3 )
% 0.26/0.48       => ( ord_less_eq_int @ X6 @ T ) ) ).
% 0.26/0.48  
% 0.26/0.48  % minf(6)
% 0.26/0.48  thf(fact_842_complete__interval,axiom,
% 0.26/0.48      ! [A: real,B: real,P: real > $o] :
% 0.26/0.48        ( ( ord_less_real @ A @ B )
% 0.26/0.48       => ( ( P @ A )
% 0.26/0.48         => ( ~ ( P @ B )
% 0.26/0.48           => ? [C2: real] :
% 0.26/0.48                ( ( ord_less_eq_real @ A @ C2 )
% 0.26/0.48                & ( ord_less_eq_real @ C2 @ B )
% 0.26/0.48                & ! [X6: real] :
% 0.26/0.48                    ( ( ( ord_less_eq_real @ A @ X6 )
% 0.26/0.48                      & ( ord_less_real @ X6 @ C2 ) )
% 0.26/0.48                   => ( P @ X6 ) )
% 0.26/0.48                & ! [D: real] :
% 0.26/0.48                    ( ! [X4: real] :
% 0.26/0.48                        ( ( ( ord_less_eq_real @ A @ X4 )
% 0.26/0.48                          & ( ord_less_real @ X4 @ D ) )
% 0.26/0.48                       => ( P @ X4 ) )
% 0.26/0.48                   => ( ord_less_eq_real @ D @ C2 ) ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % complete_interval
% 0.26/0.48  thf(fact_843_complete__interval,axiom,
% 0.26/0.48      ! [A: nat,B: nat,P: nat > $o] :
% 0.26/0.48        ( ( ord_less_nat @ A @ B )
% 0.26/0.48       => ( ( P @ A )
% 0.26/0.48         => ( ~ ( P @ B )
% 0.26/0.48           => ? [C2: nat] :
% 0.26/0.48                ( ( ord_less_eq_nat @ A @ C2 )
% 0.26/0.48                & ( ord_less_eq_nat @ C2 @ B )
% 0.26/0.48                & ! [X6: nat] :
% 0.26/0.48                    ( ( ( ord_less_eq_nat @ A @ X6 )
% 0.26/0.48                      & ( ord_less_nat @ X6 @ C2 ) )
% 0.26/0.48                   => ( P @ X6 ) )
% 0.26/0.48                & ! [D: nat] :
% 0.26/0.48                    ( ! [X4: nat] :
% 0.26/0.48                        ( ( ( ord_less_eq_nat @ A @ X4 )
% 0.26/0.48                          & ( ord_less_nat @ X4 @ D ) )
% 0.26/0.48                       => ( P @ X4 ) )
% 0.26/0.48                   => ( ord_less_eq_nat @ D @ C2 ) ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % complete_interval
% 0.26/0.48  thf(fact_844_complete__interval,axiom,
% 0.26/0.48      ! [A: int,B: int,P: int > $o] :
% 0.26/0.48        ( ( ord_less_int @ A @ B )
% 0.26/0.48       => ( ( P @ A )
% 0.26/0.48         => ( ~ ( P @ B )
% 0.26/0.48           => ? [C2: int] :
% 0.26/0.48                ( ( ord_less_eq_int @ A @ C2 )
% 0.26/0.48                & ( ord_less_eq_int @ C2 @ B )
% 0.26/0.48                & ! [X6: int] :
% 0.26/0.48                    ( ( ( ord_less_eq_int @ A @ X6 )
% 0.26/0.48                      & ( ord_less_int @ X6 @ C2 ) )
% 0.26/0.48                   => ( P @ X6 ) )
% 0.26/0.48                & ! [D: int] :
% 0.26/0.48                    ( ! [X4: int] :
% 0.26/0.48                        ( ( ( ord_less_eq_int @ A @ X4 )
% 0.26/0.48                          & ( ord_less_int @ X4 @ D ) )
% 0.26/0.48                       => ( P @ X4 ) )
% 0.26/0.48                   => ( ord_less_eq_int @ D @ C2 ) ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % complete_interval
% 0.26/0.48  thf(fact_845_zero__less__power2,axiom,
% 0.26/0.48      ! [A: real] :
% 0.26/0.48        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.48        = ( A != zero_zero_real ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_less_power2
% 0.26/0.48  thf(fact_846_zero__less__power2,axiom,
% 0.26/0.48      ! [A: rat] :
% 0.26/0.48        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.48        = ( A != zero_zero_rat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_less_power2
% 0.26/0.48  thf(fact_847_zero__less__power2,axiom,
% 0.26/0.48      ! [A: int] :
% 0.26/0.48        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.48        = ( A != zero_zero_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_less_power2
% 0.26/0.48  thf(fact_848_power2__eq__iff__nonneg,axiom,
% 0.26/0.48      ! [X3: real,Y3: real] :
% 0.26/0.48        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.48       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.48         => ( ( ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.48              = ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.48            = ( X3 = Y3 ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power2_eq_iff_nonneg
% 0.26/0.48  thf(fact_849_power2__eq__iff__nonneg,axiom,
% 0.26/0.48      ! [X3: rat,Y3: rat] :
% 0.26/0.48        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.26/0.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 0.26/0.48         => ( ( ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.48              = ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.48            = ( X3 = Y3 ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power2_eq_iff_nonneg
% 0.26/0.48  thf(fact_850_power2__eq__iff__nonneg,axiom,
% 0.26/0.48      ! [X3: nat,Y3: nat] :
% 0.26/0.48        ( ( ord_less_eq_nat @ zero_zero_nat @ X3 )
% 0.26/0.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 0.26/0.48         => ( ( ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.48              = ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.48            = ( X3 = Y3 ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power2_eq_iff_nonneg
% 0.26/0.48  thf(fact_851_power2__eq__iff__nonneg,axiom,
% 0.26/0.48      ! [X3: int,Y3: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.26/0.48       => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 0.26/0.48         => ( ( ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.48              = ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.48            = ( X3 = Y3 ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power2_eq_iff_nonneg
% 0.26/0.48  thf(fact_852_power2__less__eq__zero__iff,axiom,
% 0.26/0.48      ! [A: real] :
% 0.26/0.48        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 0.26/0.48        = ( A = zero_zero_real ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power2_less_eq_zero_iff
% 0.26/0.48  thf(fact_853_power2__less__eq__zero__iff,axiom,
% 0.26/0.48      ! [A: rat] :
% 0.26/0.48        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 0.26/0.48        = ( A = zero_zero_rat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power2_less_eq_zero_iff
% 0.26/0.48  thf(fact_854_power2__less__eq__zero__iff,axiom,
% 0.26/0.48      ! [A: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 0.26/0.48        = ( A = zero_zero_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power2_less_eq_zero_iff
% 0.26/0.48  thf(fact_855_power2__less__imp__less,axiom,
% 0.26/0.48      ! [X3: real,Y3: real] :
% 0.26/0.48        ( ( ord_less_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.48       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.48         => ( ord_less_real @ X3 @ Y3 ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power2_less_imp_less
% 0.26/0.48  thf(fact_856_power2__less__imp__less,axiom,
% 0.26/0.48      ! [X3: rat,Y3: rat] :
% 0.26/0.48        ( ( ord_less_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 0.26/0.48         => ( ord_less_rat @ X3 @ Y3 ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power2_less_imp_less
% 0.26/0.48  thf(fact_857_power2__less__imp__less,axiom,
% 0.26/0.48      ! [X3: nat,Y3: nat] :
% 0.26/0.48        ( ( ord_less_nat @ ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 0.26/0.48         => ( ord_less_nat @ X3 @ Y3 ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power2_less_imp_less
% 0.26/0.48  thf(fact_858_power2__less__imp__less,axiom,
% 0.26/0.48      ! [X3: int,Y3: int] :
% 0.26/0.48        ( ( ord_less_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.48       => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 0.26/0.48         => ( ord_less_int @ X3 @ Y3 ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power2_less_imp_less
% 0.26/0.48  thf(fact_859_nat__le__numeral__power__cancel__iff,axiom,
% 0.26/0.48      ! [A: int,X3: num,N: nat] :
% 0.26/0.48        ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) )
% 0.26/0.48        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % nat_le_numeral_power_cancel_iff
% 0.26/0.48  thf(fact_860_numeral__power__le__nat__cancel__iff,axiom,
% 0.26/0.48      ! [X3: num,N: nat,A: int] :
% 0.26/0.48        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) @ ( nat2 @ A ) )
% 0.26/0.48        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 0.26/0.48  
% 0.26/0.48  % numeral_power_le_nat_cancel_iff
% 0.26/0.48  thf(fact_861_numeral__power__less__nat__cancel__iff,axiom,
% 0.26/0.48      ! [X3: num,N: nat,A: int] :
% 0.26/0.48        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) @ ( nat2 @ A ) )
% 0.26/0.48        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 0.26/0.48  
% 0.26/0.48  % numeral_power_less_nat_cancel_iff
% 0.26/0.48  thf(fact_862_nat__less__numeral__power__cancel__iff,axiom,
% 0.26/0.48      ! [A: int,X3: num,N: nat] :
% 0.26/0.48        ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) )
% 0.26/0.48        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % nat_less_numeral_power_cancel_iff
% 0.26/0.48  thf(fact_863_of__int__less__numeral__power__cancel__iff,axiom,
% 0.26/0.48      ! [A: int,X3: num,N: nat] :
% 0.26/0.48        ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N ) )
% 0.26/0.48        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_less_numeral_power_cancel_iff
% 0.26/0.48  thf(fact_864_of__int__less__numeral__power__cancel__iff,axiom,
% 0.26/0.48      ! [A: int,X3: num,N: nat] :
% 0.26/0.48        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N ) )
% 0.26/0.48        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_less_numeral_power_cancel_iff
% 0.26/0.48  thf(fact_865_of__int__less__numeral__power__cancel__iff,axiom,
% 0.26/0.48      ! [A: int,X3: num,N: nat] :
% 0.26/0.48        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) )
% 0.26/0.48        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_less_numeral_power_cancel_iff
% 0.26/0.48  thf(fact_866_numeral__power__less__of__int__cancel__iff,axiom,
% 0.26/0.48      ! [X3: num,N: nat,A: int] :
% 0.26/0.48        ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 0.26/0.48        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 0.26/0.48  
% 0.26/0.48  % numeral_power_less_of_int_cancel_iff
% 0.26/0.48  thf(fact_867_numeral__power__less__of__int__cancel__iff,axiom,
% 0.26/0.48      ! [X3: num,N: nat,A: int] :
% 0.26/0.48        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 0.26/0.48        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 0.26/0.48  
% 0.26/0.48  % numeral_power_less_of_int_cancel_iff
% 0.26/0.48  thf(fact_868_numeral__power__less__of__int__cancel__iff,axiom,
% 0.26/0.48      ! [X3: num,N: nat,A: int] :
% 0.26/0.48        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 0.26/0.48        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 0.26/0.48  
% 0.26/0.48  % numeral_power_less_of_int_cancel_iff
% 0.26/0.48  thf(fact_869_bot__nat__0_Onot__eq__extremum,axiom,
% 0.26/0.48      ! [A: nat] :
% 0.26/0.48        ( ( A != zero_zero_nat )
% 0.26/0.48        = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 0.26/0.48  
% 0.26/0.48  % bot_nat_0.not_eq_extremum
% 0.26/0.48  thf(fact_870_neq0__conv,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( N != zero_zero_nat )
% 0.26/0.48        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % neq0_conv
% 0.26/0.48  thf(fact_871_less__nat__zero__code,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.26/0.48  
% 0.26/0.48  % less_nat_zero_code
% 0.26/0.48  thf(fact_872_le0,axiom,
% 0.26/0.48      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.26/0.48  
% 0.26/0.48  % le0
% 0.26/0.48  thf(fact_873_bot__nat__0_Oextremum,axiom,
% 0.26/0.48      ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 0.26/0.48  
% 0.26/0.48  % bot_nat_0.extremum
% 0.26/0.48  thf(fact_874_of__int__eq__iff,axiom,
% 0.26/0.48      ! [W: int,Z: int] :
% 0.26/0.48        ( ( ( ring_1_of_int_real @ W )
% 0.26/0.48          = ( ring_1_of_int_real @ Z ) )
% 0.26/0.48        = ( W = Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_iff
% 0.26/0.48  thf(fact_875_of__int__eq__iff,axiom,
% 0.26/0.48      ! [W: int,Z: int] :
% 0.26/0.48        ( ( ( ring_17405671764205052669omplex @ W )
% 0.26/0.48          = ( ring_17405671764205052669omplex @ Z ) )
% 0.26/0.48        = ( W = Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_iff
% 0.26/0.48  thf(fact_876_of__int__eq__iff,axiom,
% 0.26/0.48      ! [W: int,Z: int] :
% 0.26/0.48        ( ( ( ring_1_of_int_rat @ W )
% 0.26/0.48          = ( ring_1_of_int_rat @ Z ) )
% 0.26/0.48        = ( W = Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_iff
% 0.26/0.48  thf(fact_877_i0__less,axiom,
% 0.26/0.48      ! [N: extended_enat] :
% 0.26/0.48        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 0.26/0.48        = ( N != zero_z5237406670263579293d_enat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % i0_less
% 0.26/0.48  thf(fact_878_of__nat__eq__0__iff,axiom,
% 0.26/0.48      ! [M: nat] :
% 0.26/0.48        ( ( ( semiri8010041392384452111omplex @ M )
% 0.26/0.48          = zero_zero_complex )
% 0.26/0.48        = ( M = zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_eq_0_iff
% 0.26/0.48  thf(fact_879_of__nat__eq__0__iff,axiom,
% 0.26/0.48      ! [M: nat] :
% 0.26/0.48        ( ( ( semiri5074537144036343181t_real @ M )
% 0.26/0.48          = zero_zero_real )
% 0.26/0.48        = ( M = zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_eq_0_iff
% 0.26/0.48  thf(fact_880_of__nat__eq__0__iff,axiom,
% 0.26/0.48      ! [M: nat] :
% 0.26/0.48        ( ( ( semiri681578069525770553at_rat @ M )
% 0.26/0.48          = zero_zero_rat )
% 0.26/0.48        = ( M = zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_eq_0_iff
% 0.26/0.48  thf(fact_881_of__nat__eq__0__iff,axiom,
% 0.26/0.48      ! [M: nat] :
% 0.26/0.48        ( ( ( semiri1316708129612266289at_nat @ M )
% 0.26/0.48          = zero_zero_nat )
% 0.26/0.48        = ( M = zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_eq_0_iff
% 0.26/0.48  thf(fact_882_of__nat__eq__0__iff,axiom,
% 0.26/0.48      ! [M: nat] :
% 0.26/0.48        ( ( ( semiri1314217659103216013at_int @ M )
% 0.26/0.48          = zero_zero_int )
% 0.26/0.48        = ( M = zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_eq_0_iff
% 0.26/0.48  thf(fact_883_of__nat__0__eq__iff,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( zero_zero_complex
% 0.26/0.48          = ( semiri8010041392384452111omplex @ N ) )
% 0.26/0.48        = ( zero_zero_nat = N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_0_eq_iff
% 0.26/0.48  thf(fact_884_of__nat__0__eq__iff,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( zero_zero_real
% 0.26/0.48          = ( semiri5074537144036343181t_real @ N ) )
% 0.26/0.48        = ( zero_zero_nat = N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_0_eq_iff
% 0.26/0.48  thf(fact_885_of__nat__0__eq__iff,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( zero_zero_rat
% 0.26/0.48          = ( semiri681578069525770553at_rat @ N ) )
% 0.26/0.48        = ( zero_zero_nat = N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_0_eq_iff
% 0.26/0.48  thf(fact_886_of__nat__0__eq__iff,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( zero_zero_nat
% 0.26/0.48          = ( semiri1316708129612266289at_nat @ N ) )
% 0.26/0.48        = ( zero_zero_nat = N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_0_eq_iff
% 0.26/0.48  thf(fact_887_of__nat__0__eq__iff,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( zero_zero_int
% 0.26/0.48          = ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.48        = ( zero_zero_nat = N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_0_eq_iff
% 0.26/0.48  thf(fact_888_of__nat__0,axiom,
% 0.26/0.48      ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 0.26/0.48      = zero_zero_complex ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_0
% 0.26/0.48  thf(fact_889_of__nat__0,axiom,
% 0.26/0.48      ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 0.26/0.48      = zero_zero_real ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_0
% 0.26/0.48  thf(fact_890_of__nat__0,axiom,
% 0.26/0.48      ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 0.26/0.48      = zero_zero_rat ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_0
% 0.26/0.48  thf(fact_891_of__nat__0,axiom,
% 0.26/0.48      ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 0.26/0.48      = zero_zero_nat ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_0
% 0.26/0.48  thf(fact_892_of__nat__0,axiom,
% 0.26/0.48      ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 0.26/0.48      = zero_zero_int ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_0
% 0.26/0.48  thf(fact_893_of__int__0,axiom,
% 0.26/0.48      ( ( ring_1_of_int_int @ zero_zero_int )
% 0.26/0.48      = zero_zero_int ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_0
% 0.26/0.48  thf(fact_894_of__int__0,axiom,
% 0.26/0.48      ( ( ring_1_of_int_real @ zero_zero_int )
% 0.26/0.48      = zero_zero_real ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_0
% 0.26/0.48  thf(fact_895_of__int__0,axiom,
% 0.26/0.48      ( ( ring_17405671764205052669omplex @ zero_zero_int )
% 0.26/0.48      = zero_zero_complex ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_0
% 0.26/0.48  thf(fact_896_of__int__0,axiom,
% 0.26/0.48      ( ( ring_1_of_int_rat @ zero_zero_int )
% 0.26/0.48      = zero_zero_rat ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_0
% 0.26/0.48  thf(fact_897_of__int__0__eq__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( zero_zero_int
% 0.26/0.48          = ( ring_1_of_int_int @ Z ) )
% 0.26/0.48        = ( Z = zero_zero_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_0_eq_iff
% 0.26/0.48  thf(fact_898_of__int__0__eq__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( zero_zero_real
% 0.26/0.48          = ( ring_1_of_int_real @ Z ) )
% 0.26/0.48        = ( Z = zero_zero_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_0_eq_iff
% 0.26/0.48  thf(fact_899_of__int__0__eq__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( zero_zero_complex
% 0.26/0.48          = ( ring_17405671764205052669omplex @ Z ) )
% 0.26/0.48        = ( Z = zero_zero_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_0_eq_iff
% 0.26/0.48  thf(fact_900_of__int__0__eq__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( zero_zero_rat
% 0.26/0.48          = ( ring_1_of_int_rat @ Z ) )
% 0.26/0.48        = ( Z = zero_zero_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_0_eq_iff
% 0.26/0.48  thf(fact_901_of__int__eq__0__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ( ring_1_of_int_int @ Z )
% 0.26/0.48          = zero_zero_int )
% 0.26/0.48        = ( Z = zero_zero_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_0_iff
% 0.26/0.48  thf(fact_902_of__int__eq__0__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ( ring_1_of_int_real @ Z )
% 0.26/0.48          = zero_zero_real )
% 0.26/0.48        = ( Z = zero_zero_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_0_iff
% 0.26/0.48  thf(fact_903_of__int__eq__0__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ( ring_17405671764205052669omplex @ Z )
% 0.26/0.48          = zero_zero_complex )
% 0.26/0.48        = ( Z = zero_zero_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_0_iff
% 0.26/0.48  thf(fact_904_of__int__eq__0__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ( ring_1_of_int_rat @ Z )
% 0.26/0.48          = zero_zero_rat )
% 0.26/0.48        = ( Z = zero_zero_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_0_iff
% 0.26/0.48  thf(fact_905_nat__zero__less__power__iff,axiom,
% 0.26/0.48      ! [X3: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X3 @ N ) )
% 0.26/0.48        = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 0.26/0.48          | ( N = zero_zero_nat ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % nat_zero_less_power_iff
% 0.26/0.48  thf(fact_906_nat__le__0,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 0.26/0.48       => ( ( nat2 @ Z )
% 0.26/0.48          = zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % nat_le_0
% 0.26/0.48  thf(fact_907_nat__0__iff,axiom,
% 0.26/0.48      ! [I: int] :
% 0.26/0.48        ( ( ( nat2 @ I )
% 0.26/0.48          = zero_zero_nat )
% 0.26/0.48        = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % nat_0_iff
% 0.26/0.48  thf(fact_908_nat__int,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( nat2 @ ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.48        = N ) ).
% 0.26/0.48  
% 0.26/0.48  % nat_int
% 0.26/0.48  thf(fact_909_of__nat__le__0__iff,axiom,
% 0.26/0.48      ! [M: nat] :
% 0.26/0.48        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 0.26/0.48        = ( M = zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_le_0_iff
% 0.26/0.48  thf(fact_910_of__nat__le__0__iff,axiom,
% 0.26/0.48      ! [M: nat] :
% 0.26/0.48        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 0.26/0.48        = ( M = zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_le_0_iff
% 0.26/0.48  thf(fact_911_of__nat__le__0__iff,axiom,
% 0.26/0.48      ! [M: nat] :
% 0.26/0.48        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 0.26/0.48        = ( M = zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_le_0_iff
% 0.26/0.48  thf(fact_912_of__nat__le__0__iff,axiom,
% 0.26/0.48      ! [M: nat] :
% 0.26/0.48        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 0.26/0.48        = ( M = zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_le_0_iff
% 0.26/0.48  thf(fact_913_power__zero__numeral,axiom,
% 0.26/0.48      ! [K: num] :
% 0.26/0.48        ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 0.26/0.48        = zero_zero_rat ) ).
% 0.26/0.48  
% 0.26/0.48  % power_zero_numeral
% 0.26/0.48  thf(fact_914_power__zero__numeral,axiom,
% 0.26/0.48      ! [K: num] :
% 0.26/0.48        ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 0.26/0.48        = zero_zero_nat ) ).
% 0.26/0.48  
% 0.26/0.48  % power_zero_numeral
% 0.26/0.48  thf(fact_915_power__zero__numeral,axiom,
% 0.26/0.48      ! [K: num] :
% 0.26/0.48        ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 0.26/0.48        = zero_zero_int ) ).
% 0.26/0.48  
% 0.26/0.48  % power_zero_numeral
% 0.26/0.48  thf(fact_916_power__zero__numeral,axiom,
% 0.26/0.48      ! [K: num] :
% 0.26/0.48        ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 0.26/0.48        = zero_zero_real ) ).
% 0.26/0.48  
% 0.26/0.48  % power_zero_numeral
% 0.26/0.48  thf(fact_917_power__zero__numeral,axiom,
% 0.26/0.48      ! [K: num] :
% 0.26/0.48        ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 0.26/0.48        = zero_zero_complex ) ).
% 0.26/0.48  
% 0.26/0.48  % power_zero_numeral
% 0.26/0.48  thf(fact_918_power__eq__0__iff,axiom,
% 0.26/0.48      ! [A: rat,N: nat] :
% 0.26/0.48        ( ( ( power_power_rat @ A @ N )
% 0.26/0.48          = zero_zero_rat )
% 0.26/0.48        = ( ( A = zero_zero_rat )
% 0.26/0.48          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_eq_0_iff
% 0.26/0.48  thf(fact_919_power__eq__0__iff,axiom,
% 0.26/0.48      ! [A: nat,N: nat] :
% 0.26/0.48        ( ( ( power_power_nat @ A @ N )
% 0.26/0.48          = zero_zero_nat )
% 0.26/0.48        = ( ( A = zero_zero_nat )
% 0.26/0.48          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_eq_0_iff
% 0.26/0.48  thf(fact_920_power__eq__0__iff,axiom,
% 0.26/0.48      ! [A: int,N: nat] :
% 0.26/0.48        ( ( ( power_power_int @ A @ N )
% 0.26/0.48          = zero_zero_int )
% 0.26/0.48        = ( ( A = zero_zero_int )
% 0.26/0.48          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_eq_0_iff
% 0.26/0.48  thf(fact_921_power__eq__0__iff,axiom,
% 0.26/0.48      ! [A: real,N: nat] :
% 0.26/0.48        ( ( ( power_power_real @ A @ N )
% 0.26/0.48          = zero_zero_real )
% 0.26/0.48        = ( ( A = zero_zero_real )
% 0.26/0.48          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_eq_0_iff
% 0.26/0.48  thf(fact_922_power__eq__0__iff,axiom,
% 0.26/0.48      ! [A: complex,N: nat] :
% 0.26/0.48        ( ( ( power_power_complex @ A @ N )
% 0.26/0.48          = zero_zero_complex )
% 0.26/0.48        = ( ( A = zero_zero_complex )
% 0.26/0.48          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_eq_0_iff
% 0.26/0.48  thf(fact_923_of__int__numeral,axiom,
% 0.26/0.48      ! [K: num] :
% 0.26/0.48        ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 0.26/0.48        = ( numera6690914467698888265omplex @ K ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_numeral
% 0.26/0.48  thf(fact_924_of__int__numeral,axiom,
% 0.26/0.48      ! [K: num] :
% 0.26/0.48        ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 0.26/0.48        = ( numeral_numeral_real @ K ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_numeral
% 0.26/0.48  thf(fact_925_of__int__numeral,axiom,
% 0.26/0.48      ! [K: num] :
% 0.26/0.48        ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 0.26/0.48        = ( numeral_numeral_rat @ K ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_numeral
% 0.26/0.48  thf(fact_926_of__int__numeral,axiom,
% 0.26/0.48      ! [K: num] :
% 0.26/0.48        ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 0.26/0.48        = ( numeral_numeral_int @ K ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_numeral
% 0.26/0.48  thf(fact_927_of__int__eq__numeral__iff,axiom,
% 0.26/0.48      ! [Z: int,N: num] :
% 0.26/0.48        ( ( ( ring_17405671764205052669omplex @ Z )
% 0.26/0.48          = ( numera6690914467698888265omplex @ N ) )
% 0.26/0.48        = ( Z
% 0.26/0.48          = ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_numeral_iff
% 0.26/0.48  thf(fact_928_of__int__eq__numeral__iff,axiom,
% 0.26/0.48      ! [Z: int,N: num] :
% 0.26/0.48        ( ( ( ring_1_of_int_real @ Z )
% 0.26/0.48          = ( numeral_numeral_real @ N ) )
% 0.26/0.48        = ( Z
% 0.26/0.48          = ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_numeral_iff
% 0.26/0.48  thf(fact_929_of__int__eq__numeral__iff,axiom,
% 0.26/0.48      ! [Z: int,N: num] :
% 0.26/0.48        ( ( ( ring_1_of_int_rat @ Z )
% 0.26/0.48          = ( numeral_numeral_rat @ N ) )
% 0.26/0.48        = ( Z
% 0.26/0.48          = ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_numeral_iff
% 0.26/0.48  thf(fact_930_of__int__eq__numeral__iff,axiom,
% 0.26/0.48      ! [Z: int,N: num] :
% 0.26/0.48        ( ( ( ring_1_of_int_int @ Z )
% 0.26/0.48          = ( numeral_numeral_int @ N ) )
% 0.26/0.48        = ( Z
% 0.26/0.48          = ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_numeral_iff
% 0.26/0.48  thf(fact_931_of__int__le__iff,axiom,
% 0.26/0.48      ! [W: int,Z: int] :
% 0.26/0.48        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 0.26/0.48        = ( ord_less_eq_int @ W @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_le_iff
% 0.26/0.48  thf(fact_932_of__int__le__iff,axiom,
% 0.26/0.48      ! [W: int,Z: int] :
% 0.26/0.48        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 0.26/0.48        = ( ord_less_eq_int @ W @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_le_iff
% 0.26/0.48  thf(fact_933_of__int__le__iff,axiom,
% 0.26/0.48      ! [W: int,Z: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 0.26/0.48        = ( ord_less_eq_int @ W @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_le_iff
% 0.26/0.48  thf(fact_934_of__int__less__iff,axiom,
% 0.26/0.48      ! [W: int,Z: int] :
% 0.26/0.48        ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 0.26/0.48        = ( ord_less_int @ W @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_less_iff
% 0.26/0.48  thf(fact_935_of__int__less__iff,axiom,
% 0.26/0.48      ! [W: int,Z: int] :
% 0.26/0.48        ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 0.26/0.48        = ( ord_less_int @ W @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_less_iff
% 0.26/0.48  thf(fact_936_of__int__less__iff,axiom,
% 0.26/0.48      ! [W: int,Z: int] :
% 0.26/0.48        ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 0.26/0.48        = ( ord_less_int @ W @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_less_iff
% 0.26/0.48  thf(fact_937_nat__numeral,axiom,
% 0.26/0.48      ! [K: num] :
% 0.26/0.48        ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 0.26/0.48        = ( numeral_numeral_nat @ K ) ) ).
% 0.26/0.48  
% 0.26/0.48  % nat_numeral
% 0.26/0.48  thf(fact_938_zero__less__nat__eq,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 0.26/0.48        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_less_nat_eq
% 0.26/0.48  thf(fact_939_zless__nat__conj,axiom,
% 0.26/0.48      ! [W: int,Z: int] :
% 0.26/0.48        ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 0.26/0.48        = ( ( ord_less_int @ zero_zero_int @ Z )
% 0.26/0.48          & ( ord_less_int @ W @ Z ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zless_nat_conj
% 0.26/0.48  thf(fact_940_of__int__of__nat__eq,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ring_17405671764205052669omplex @ ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.48        = ( semiri8010041392384452111omplex @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_of_nat_eq
% 0.26/0.48  thf(fact_941_of__int__of__nat__eq,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ring_1_of_int_real @ ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.48        = ( semiri5074537144036343181t_real @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_of_nat_eq
% 0.26/0.48  thf(fact_942_of__int__of__nat__eq,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ring_1_of_int_rat @ ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.48        = ( semiri681578069525770553at_rat @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_of_nat_eq
% 0.26/0.48  thf(fact_943_of__int__of__nat__eq,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ring_1_of_int_int @ ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.48        = ( semiri1314217659103216013at_int @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_of_nat_eq
% 0.26/0.48  thf(fact_944_int__nat__eq,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.26/0.48         => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 0.26/0.48            = Z ) )
% 0.26/0.48        & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.26/0.48         => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 0.26/0.48            = zero_zero_int ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % int_nat_eq
% 0.26/0.48  thf(fact_945_of__int__power,axiom,
% 0.26/0.48      ! [Z: int,N: nat] :
% 0.26/0.48        ( ( ring_1_of_int_rat @ ( power_power_int @ Z @ N ) )
% 0.26/0.48        = ( power_power_rat @ ( ring_1_of_int_rat @ Z ) @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_power
% 0.26/0.48  thf(fact_946_of__int__power,axiom,
% 0.26/0.48      ! [Z: int,N: nat] :
% 0.26/0.48        ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N ) )
% 0.26/0.48        = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_power
% 0.26/0.48  thf(fact_947_of__int__power,axiom,
% 0.26/0.48      ! [Z: int,N: nat] :
% 0.26/0.48        ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N ) )
% 0.26/0.48        = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_power
% 0.26/0.48  thf(fact_948_of__int__power,axiom,
% 0.26/0.48      ! [Z: int,N: nat] :
% 0.26/0.48        ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N ) )
% 0.26/0.48        = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_power
% 0.26/0.48  thf(fact_949_of__int__eq__of__int__power__cancel__iff,axiom,
% 0.26/0.48      ! [B: int,W: nat,X3: int] :
% 0.26/0.48        ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W )
% 0.26/0.48          = ( ring_1_of_int_rat @ X3 ) )
% 0.26/0.48        = ( ( power_power_int @ B @ W )
% 0.26/0.48          = X3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_of_int_power_cancel_iff
% 0.26/0.48  thf(fact_950_of__int__eq__of__int__power__cancel__iff,axiom,
% 0.26/0.48      ! [B: int,W: nat,X3: int] :
% 0.26/0.48        ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W )
% 0.26/0.48          = ( ring_1_of_int_int @ X3 ) )
% 0.26/0.48        = ( ( power_power_int @ B @ W )
% 0.26/0.48          = X3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_of_int_power_cancel_iff
% 0.26/0.48  thf(fact_951_of__int__eq__of__int__power__cancel__iff,axiom,
% 0.26/0.48      ! [B: int,W: nat,X3: int] :
% 0.26/0.48        ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
% 0.26/0.48          = ( ring_1_of_int_real @ X3 ) )
% 0.26/0.48        = ( ( power_power_int @ B @ W )
% 0.26/0.48          = X3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_of_int_power_cancel_iff
% 0.26/0.48  thf(fact_952_of__int__eq__of__int__power__cancel__iff,axiom,
% 0.26/0.48      ! [B: int,W: nat,X3: int] :
% 0.26/0.48        ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W )
% 0.26/0.48          = ( ring_17405671764205052669omplex @ X3 ) )
% 0.26/0.48        = ( ( power_power_int @ B @ W )
% 0.26/0.48          = X3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_of_int_power_cancel_iff
% 0.26/0.48  thf(fact_953_of__int__power__eq__of__int__cancel__iff,axiom,
% 0.26/0.48      ! [X3: int,B: int,W: nat] :
% 0.26/0.48        ( ( ( ring_1_of_int_rat @ X3 )
% 0.26/0.48          = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 0.26/0.48        = ( X3
% 0.26/0.48          = ( power_power_int @ B @ W ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_power_eq_of_int_cancel_iff
% 0.26/0.48  thf(fact_954_of__int__power__eq__of__int__cancel__iff,axiom,
% 0.26/0.48      ! [X3: int,B: int,W: nat] :
% 0.26/0.48        ( ( ( ring_1_of_int_int @ X3 )
% 0.26/0.48          = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 0.26/0.48        = ( X3
% 0.26/0.48          = ( power_power_int @ B @ W ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_power_eq_of_int_cancel_iff
% 0.26/0.48  thf(fact_955_of__int__power__eq__of__int__cancel__iff,axiom,
% 0.26/0.48      ! [X3: int,B: int,W: nat] :
% 0.26/0.48        ( ( ( ring_1_of_int_real @ X3 )
% 0.26/0.48          = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 0.26/0.48        = ( X3
% 0.26/0.48          = ( power_power_int @ B @ W ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_power_eq_of_int_cancel_iff
% 0.26/0.48  thf(fact_956_of__int__power__eq__of__int__cancel__iff,axiom,
% 0.26/0.48      ! [X3: int,B: int,W: nat] :
% 0.26/0.48        ( ( ( ring_17405671764205052669omplex @ X3 )
% 0.26/0.48          = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W ) )
% 0.26/0.48        = ( X3
% 0.26/0.48          = ( power_power_int @ B @ W ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_power_eq_of_int_cancel_iff
% 0.26/0.48  thf(fact_957_power__mono__iff,axiom,
% 0.26/0.48      ! [A: real,B: real,N: nat] :
% 0.26/0.48        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.48       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.26/0.48         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48           => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 0.26/0.48              = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_mono_iff
% 0.26/0.48  thf(fact_958_power__mono__iff,axiom,
% 0.26/0.48      ! [A: rat,B: rat,N: nat] :
% 0.26/0.48        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.26/0.48         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48           => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 0.26/0.48              = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_mono_iff
% 0.26/0.48  thf(fact_959_power__mono__iff,axiom,
% 0.26/0.48      ! [A: nat,B: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.26/0.48         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48           => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 0.26/0.48              = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_mono_iff
% 0.26/0.48  thf(fact_960_power__mono__iff,axiom,
% 0.26/0.48      ! [A: int,B: int,N: nat] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.48       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.26/0.48         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48           => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 0.26/0.48              = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_mono_iff
% 0.26/0.48  thf(fact_961_of__nat__0__less__iff,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 0.26/0.48        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_0_less_iff
% 0.26/0.48  thf(fact_962_of__nat__0__less__iff,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 0.26/0.48        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_0_less_iff
% 0.26/0.48  thf(fact_963_of__nat__0__less__iff,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 0.26/0.48        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_0_less_iff
% 0.26/0.48  thf(fact_964_of__nat__0__less__iff,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.48        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_0_less_iff
% 0.26/0.48  thf(fact_965_of__int__le__0__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 0.26/0.48        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_le_0_iff
% 0.26/0.48  thf(fact_966_of__int__le__0__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 0.26/0.48        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_le_0_iff
% 0.26/0.48  thf(fact_967_of__int__le__0__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 0.26/0.48        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_le_0_iff
% 0.26/0.48  thf(fact_968_of__int__0__le__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 0.26/0.48        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_0_le_iff
% 0.26/0.48  thf(fact_969_of__int__0__le__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.26/0.48        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_0_le_iff
% 0.26/0.48  thf(fact_970_of__int__0__le__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 0.26/0.48        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_0_le_iff
% 0.26/0.48  thf(fact_971_of__int__less__0__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 0.26/0.48        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_less_0_iff
% 0.26/0.48  thf(fact_972_of__int__less__0__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 0.26/0.48        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_less_0_iff
% 0.26/0.48  thf(fact_973_of__int__less__0__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 0.26/0.48        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_less_0_iff
% 0.26/0.48  thf(fact_974_of__int__0__less__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 0.26/0.48        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_0_less_iff
% 0.26/0.48  thf(fact_975_of__int__0__less__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.26/0.48        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_0_less_iff
% 0.26/0.48  thf(fact_976_of__int__0__less__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 0.26/0.48        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_0_less_iff
% 0.26/0.48  thf(fact_977_of__nat__nat,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.26/0.48       => ( ( semiri8010041392384452111omplex @ ( nat2 @ Z ) )
% 0.26/0.48          = ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_nat
% 0.26/0.48  thf(fact_978_of__nat__nat,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.26/0.48       => ( ( semiri5074537144036343181t_real @ ( nat2 @ Z ) )
% 0.26/0.48          = ( ring_1_of_int_real @ Z ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_nat
% 0.26/0.48  thf(fact_979_of__nat__nat,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.26/0.48       => ( ( semiri681578069525770553at_rat @ ( nat2 @ Z ) )
% 0.26/0.48          = ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_nat
% 0.26/0.48  thf(fact_980_of__nat__nat,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.26/0.48       => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 0.26/0.48          = ( ring_1_of_int_int @ Z ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_nat
% 0.26/0.48  thf(fact_981_zero__eq__power2,axiom,
% 0.26/0.48      ! [A: rat] :
% 0.26/0.48        ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.48          = zero_zero_rat )
% 0.26/0.48        = ( A = zero_zero_rat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_eq_power2
% 0.26/0.48  thf(fact_982_zero__eq__power2,axiom,
% 0.26/0.48      ! [A: nat] :
% 0.26/0.48        ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.48          = zero_zero_nat )
% 0.26/0.48        = ( A = zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_eq_power2
% 0.26/0.48  thf(fact_983_zero__eq__power2,axiom,
% 0.26/0.48      ! [A: int] :
% 0.26/0.48        ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.48          = zero_zero_int )
% 0.26/0.48        = ( A = zero_zero_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_eq_power2
% 0.26/0.48  thf(fact_984_zero__eq__power2,axiom,
% 0.26/0.48      ! [A: real] :
% 0.26/0.48        ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.48          = zero_zero_real )
% 0.26/0.48        = ( A = zero_zero_real ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_eq_power2
% 0.26/0.48  thf(fact_985_zero__eq__power2,axiom,
% 0.26/0.48      ! [A: complex] :
% 0.26/0.48        ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.48          = zero_zero_complex )
% 0.26/0.48        = ( A = zero_zero_complex ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_eq_power2
% 0.26/0.48  thf(fact_986_of__nat__zero__less__power__iff,axiom,
% 0.26/0.48      ! [X3: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X3 ) @ N ) )
% 0.26/0.48        = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 0.26/0.48          | ( N = zero_zero_nat ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_zero_less_power_iff
% 0.26/0.48  thf(fact_987_of__nat__zero__less__power__iff,axiom,
% 0.26/0.48      ! [X3: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X3 ) @ N ) )
% 0.26/0.48        = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 0.26/0.48          | ( N = zero_zero_nat ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_zero_less_power_iff
% 0.26/0.48  thf(fact_988_of__nat__zero__less__power__iff,axiom,
% 0.26/0.48      ! [X3: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ N ) )
% 0.26/0.48        = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 0.26/0.48          | ( N = zero_zero_nat ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_zero_less_power_iff
% 0.26/0.48  thf(fact_989_of__nat__zero__less__power__iff,axiom,
% 0.26/0.48      ! [X3: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X3 ) @ N ) )
% 0.26/0.48        = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 0.26/0.48          | ( N = zero_zero_nat ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_zero_less_power_iff
% 0.26/0.48  thf(fact_990_of__int__numeral__le__iff,axiom,
% 0.26/0.48      ! [N: num,Z: int] :
% 0.26/0.48        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 0.26/0.48        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_numeral_le_iff
% 0.26/0.48  thf(fact_991_of__int__numeral__le__iff,axiom,
% 0.26/0.48      ! [N: num,Z: int] :
% 0.26/0.48        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 0.26/0.48        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_numeral_le_iff
% 0.26/0.48  thf(fact_992_of__int__numeral__le__iff,axiom,
% 0.26/0.48      ! [N: num,Z: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 0.26/0.48        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_numeral_le_iff
% 0.26/0.48  thf(fact_993_of__int__le__numeral__iff,axiom,
% 0.26/0.48      ! [Z: int,N: num] :
% 0.26/0.48        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 0.26/0.48        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_le_numeral_iff
% 0.26/0.48  thf(fact_994_of__int__le__numeral__iff,axiom,
% 0.26/0.48      ! [Z: int,N: num] :
% 0.26/0.48        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 0.26/0.48        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_le_numeral_iff
% 0.26/0.48  thf(fact_995_of__int__le__numeral__iff,axiom,
% 0.26/0.48      ! [Z: int,N: num] :
% 0.26/0.48        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.48        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_le_numeral_iff
% 0.26/0.48  thf(fact_996_of__int__less__numeral__iff,axiom,
% 0.26/0.48      ! [Z: int,N: num] :
% 0.26/0.48        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 0.26/0.48        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_less_numeral_iff
% 0.26/0.48  thf(fact_997_of__int__less__numeral__iff,axiom,
% 0.26/0.48      ! [Z: int,N: num] :
% 0.26/0.48        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 0.26/0.48        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_less_numeral_iff
% 0.26/0.48  thf(fact_998_of__int__less__numeral__iff,axiom,
% 0.26/0.48      ! [Z: int,N: num] :
% 0.26/0.48        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.48        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_less_numeral_iff
% 0.26/0.48  thf(fact_999_of__int__numeral__less__iff,axiom,
% 0.26/0.48      ! [N: num,Z: int] :
% 0.26/0.48        ( ( ord_less_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 0.26/0.48        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_numeral_less_iff
% 0.26/0.48  thf(fact_1000_of__int__numeral__less__iff,axiom,
% 0.26/0.48      ! [N: num,Z: int] :
% 0.26/0.48        ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 0.26/0.48        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_numeral_less_iff
% 0.26/0.48  thf(fact_1001_of__int__numeral__less__iff,axiom,
% 0.26/0.48      ! [N: num,Z: int] :
% 0.26/0.48        ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 0.26/0.48        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_numeral_less_iff
% 0.26/0.48  thf(fact_1002_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.26/0.48      ! [X3: num,N: nat,Y3: int] :
% 0.26/0.48        ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X3 ) @ N )
% 0.26/0.48          = ( ring_17405671764205052669omplex @ Y3 ) )
% 0.26/0.48        = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N )
% 0.26/0.48          = Y3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % numeral_power_eq_of_int_cancel_iff
% 0.26/0.48  thf(fact_1003_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.26/0.48      ! [X3: num,N: nat,Y3: int] :
% 0.26/0.48        ( ( ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N )
% 0.26/0.48          = ( ring_1_of_int_real @ Y3 ) )
% 0.26/0.48        = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N )
% 0.26/0.48          = Y3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % numeral_power_eq_of_int_cancel_iff
% 0.26/0.48  thf(fact_1004_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.26/0.48      ! [X3: num,N: nat,Y3: int] :
% 0.26/0.48        ( ( ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N )
% 0.26/0.48          = ( ring_1_of_int_rat @ Y3 ) )
% 0.26/0.48        = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N )
% 0.26/0.48          = Y3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % numeral_power_eq_of_int_cancel_iff
% 0.26/0.48  thf(fact_1005_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.26/0.48      ! [X3: num,N: nat,Y3: int] :
% 0.26/0.48        ( ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N )
% 0.26/0.48          = ( ring_1_of_int_int @ Y3 ) )
% 0.26/0.48        = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N )
% 0.26/0.48          = Y3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % numeral_power_eq_of_int_cancel_iff
% 0.26/0.48  thf(fact_1006_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.26/0.48      ! [Y3: int,X3: num,N: nat] :
% 0.26/0.48        ( ( ( ring_17405671764205052669omplex @ Y3 )
% 0.26/0.48          = ( power_power_complex @ ( numera6690914467698888265omplex @ X3 ) @ N ) )
% 0.26/0.48        = ( Y3
% 0.26/0.48          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_numeral_power_cancel_iff
% 0.26/0.48  thf(fact_1007_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.26/0.48      ! [Y3: int,X3: num,N: nat] :
% 0.26/0.48        ( ( ( ring_1_of_int_real @ Y3 )
% 0.26/0.48          = ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N ) )
% 0.26/0.48        = ( Y3
% 0.26/0.48          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_numeral_power_cancel_iff
% 0.26/0.48  thf(fact_1008_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.26/0.48      ! [Y3: int,X3: num,N: nat] :
% 0.26/0.48        ( ( ( ring_1_of_int_rat @ Y3 )
% 0.26/0.48          = ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N ) )
% 0.26/0.48        = ( Y3
% 0.26/0.48          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_numeral_power_cancel_iff
% 0.26/0.48  thf(fact_1009_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.26/0.48      ! [Y3: int,X3: num,N: nat] :
% 0.26/0.48        ( ( ( ring_1_of_int_int @ Y3 )
% 0.26/0.48          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) )
% 0.26/0.48        = ( Y3
% 0.26/0.48          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_numeral_power_cancel_iff
% 0.26/0.48  thf(fact_1010_of__int__power__le__of__int__cancel__iff,axiom,
% 0.26/0.48      ! [X3: int,B: int,W: nat] :
% 0.26/0.48        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X3 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 0.26/0.48        = ( ord_less_eq_int @ X3 @ ( power_power_int @ B @ W ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_power_le_of_int_cancel_iff
% 0.26/0.48  thf(fact_1011_of__int__power__le__of__int__cancel__iff,axiom,
% 0.26/0.48      ! [X3: int,B: int,W: nat] :
% 0.26/0.48        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X3 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 0.26/0.48        = ( ord_less_eq_int @ X3 @ ( power_power_int @ B @ W ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_power_le_of_int_cancel_iff
% 0.26/0.48  thf(fact_1012_of__int__power__le__of__int__cancel__iff,axiom,
% 0.26/0.48      ! [X3: int,B: int,W: nat] :
% 0.26/0.48        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X3 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 0.26/0.48        = ( ord_less_eq_int @ X3 @ ( power_power_int @ B @ W ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_power_le_of_int_cancel_iff
% 0.26/0.48  thf(fact_1013_of__int__le__of__int__power__cancel__iff,axiom,
% 0.26/0.48      ! [B: int,W: nat,X3: int] :
% 0.26/0.48        ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X3 ) )
% 0.26/0.48        = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_le_of_int_power_cancel_iff
% 0.26/0.48  thf(fact_1014_of__int__le__of__int__power__cancel__iff,axiom,
% 0.26/0.48      ! [B: int,W: nat,X3: int] :
% 0.26/0.48        ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X3 ) )
% 0.26/0.48        = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_le_of_int_power_cancel_iff
% 0.26/0.48  thf(fact_1015_of__int__le__of__int__power__cancel__iff,axiom,
% 0.26/0.48      ! [B: int,W: nat,X3: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X3 ) )
% 0.26/0.48        = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_le_of_int_power_cancel_iff
% 0.26/0.48  thf(fact_1016_of__int__less__of__int__power__cancel__iff,axiom,
% 0.26/0.48      ! [B: int,W: nat,X3: int] :
% 0.26/0.48        ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X3 ) )
% 0.26/0.48        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_less_of_int_power_cancel_iff
% 0.26/0.48  thf(fact_1017_of__int__less__of__int__power__cancel__iff,axiom,
% 0.26/0.48      ! [B: int,W: nat,X3: int] :
% 0.26/0.48        ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X3 ) )
% 0.26/0.48        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_less_of_int_power_cancel_iff
% 0.26/0.48  thf(fact_1018_of__int__less__of__int__power__cancel__iff,axiom,
% 0.26/0.48      ! [B: int,W: nat,X3: int] :
% 0.26/0.48        ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X3 ) )
% 0.26/0.48        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_less_of_int_power_cancel_iff
% 0.26/0.48  thf(fact_1019_of__int__power__less__of__int__cancel__iff,axiom,
% 0.26/0.48      ! [X3: int,B: int,W: nat] :
% 0.26/0.48        ( ( ord_less_real @ ( ring_1_of_int_real @ X3 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 0.26/0.48        = ( ord_less_int @ X3 @ ( power_power_int @ B @ W ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_power_less_of_int_cancel_iff
% 0.26/0.48  thf(fact_1020_of__int__power__less__of__int__cancel__iff,axiom,
% 0.26/0.48      ! [X3: int,B: int,W: nat] :
% 0.26/0.48        ( ( ord_less_rat @ ( ring_1_of_int_rat @ X3 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 0.26/0.48        = ( ord_less_int @ X3 @ ( power_power_int @ B @ W ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_power_less_of_int_cancel_iff
% 0.26/0.48  thf(fact_1021_of__int__power__less__of__int__cancel__iff,axiom,
% 0.26/0.48      ! [X3: int,B: int,W: nat] :
% 0.26/0.48        ( ( ord_less_int @ ( ring_1_of_int_int @ X3 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 0.26/0.48        = ( ord_less_int @ X3 @ ( power_power_int @ B @ W ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_power_less_of_int_cancel_iff
% 0.26/0.48  thf(fact_1022_nat__eq__numeral__power__cancel__iff,axiom,
% 0.26/0.48      ! [Y3: int,X3: num,N: nat] :
% 0.26/0.48        ( ( ( nat2 @ Y3 )
% 0.26/0.48          = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) )
% 0.26/0.48        = ( Y3
% 0.26/0.48          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % nat_eq_numeral_power_cancel_iff
% 0.26/0.48  thf(fact_1023_numeral__power__eq__nat__cancel__iff,axiom,
% 0.26/0.48      ! [X3: num,N: nat,Y3: int] :
% 0.26/0.48        ( ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N )
% 0.26/0.48          = ( nat2 @ Y3 ) )
% 0.26/0.48        = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N )
% 0.26/0.48          = Y3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % numeral_power_eq_nat_cancel_iff
% 0.26/0.48  thf(fact_1024_numeral__power__le__of__int__cancel__iff,axiom,
% 0.26/0.48      ! [X3: num,N: nat,A: int] :
% 0.26/0.48        ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 0.26/0.48        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 0.26/0.48  
% 0.26/0.48  % numeral_power_le_of_int_cancel_iff
% 0.26/0.48  thf(fact_1025_numeral__power__le__of__int__cancel__iff,axiom,
% 0.26/0.48      ! [X3: num,N: nat,A: int] :
% 0.26/0.48        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 0.26/0.48        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 0.26/0.48  
% 0.26/0.48  % numeral_power_le_of_int_cancel_iff
% 0.26/0.48  thf(fact_1026_numeral__power__le__of__int__cancel__iff,axiom,
% 0.26/0.48      ! [X3: num,N: nat,A: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 0.26/0.48        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 0.26/0.48  
% 0.26/0.48  % numeral_power_le_of_int_cancel_iff
% 0.26/0.48  thf(fact_1027_of__int__le__numeral__power__cancel__iff,axiom,
% 0.26/0.48      ! [A: int,X3: num,N: nat] :
% 0.26/0.48        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N ) )
% 0.26/0.48        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_le_numeral_power_cancel_iff
% 0.26/0.48  thf(fact_1028_of__int__le__numeral__power__cancel__iff,axiom,
% 0.26/0.48      ! [A: int,X3: num,N: nat] :
% 0.26/0.48        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N ) )
% 0.26/0.48        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_le_numeral_power_cancel_iff
% 0.26/0.48  thf(fact_1029_of__int__le__numeral__power__cancel__iff,axiom,
% 0.26/0.48      ! [A: int,X3: num,N: nat] :
% 0.26/0.48        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) )
% 0.26/0.48        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_le_numeral_power_cancel_iff
% 0.26/0.48  thf(fact_1030_nat__zero__as__int,axiom,
% 0.26/0.48      ( zero_zero_nat
% 0.26/0.48      = ( nat2 @ zero_zero_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % nat_zero_as_int
% 0.26/0.48  thf(fact_1031_eq__nat__nat__iff,axiom,
% 0.26/0.48      ! [Z: int,Z5: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.26/0.48       => ( ( ord_less_eq_int @ zero_zero_int @ Z5 )
% 0.26/0.48         => ( ( ( nat2 @ Z )
% 0.26/0.48              = ( nat2 @ Z5 ) )
% 0.26/0.48            = ( Z = Z5 ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % eq_nat_nat_iff
% 0.26/0.48  thf(fact_1032_all__nat,axiom,
% 0.26/0.48      ( ( ^ [P2: nat > $o] :
% 0.26/0.48          ! [X5: nat] : ( P2 @ X5 ) )
% 0.26/0.48      = ( ^ [P3: nat > $o] :
% 0.26/0.48          ! [X: int] :
% 0.26/0.48            ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.26/0.48           => ( P3 @ ( nat2 @ X ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % all_nat
% 0.26/0.48  thf(fact_1033_ex__nat,axiom,
% 0.26/0.48      ( ( ^ [P2: nat > $o] :
% 0.26/0.48          ? [X5: nat] : ( P2 @ X5 ) )
% 0.26/0.48      = ( ^ [P3: nat > $o] :
% 0.26/0.48          ? [X: int] :
% 0.26/0.48            ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.26/0.48            & ( P3 @ ( nat2 @ X ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % ex_nat
% 0.26/0.48  thf(fact_1034_int__ops_I1_J,axiom,
% 0.26/0.48      ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 0.26/0.48      = zero_zero_int ) ).
% 0.26/0.48  
% 0.26/0.48  % int_ops(1)
% 0.26/0.48  thf(fact_1035_of__int__nonneg,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.26/0.48       => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_nonneg
% 0.26/0.48  thf(fact_1036_of__int__nonneg,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.26/0.48       => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_nonneg
% 0.26/0.48  thf(fact_1037_of__int__nonneg,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.26/0.48       => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_nonneg
% 0.26/0.48  thf(fact_1038_of__int__pos,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.26/0.48       => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_pos
% 0.26/0.48  thf(fact_1039_of__int__pos,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.26/0.48       => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_pos
% 0.26/0.48  thf(fact_1040_of__int__pos,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.26/0.48       => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_pos
% 0.26/0.48  thf(fact_1041_nat__eq__iff2,axiom,
% 0.26/0.48      ! [M: nat,W: int] :
% 0.26/0.48        ( ( M
% 0.26/0.48          = ( nat2 @ W ) )
% 0.26/0.48        = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 0.26/0.48           => ( W
% 0.26/0.48              = ( semiri1314217659103216013at_int @ M ) ) )
% 0.26/0.48          & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 0.26/0.48           => ( M = zero_zero_nat ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % nat_eq_iff2
% 0.26/0.48  thf(fact_1042_nat__eq__iff,axiom,
% 0.26/0.48      ! [W: int,M: nat] :
% 0.26/0.48        ( ( ( nat2 @ W )
% 0.26/0.48          = M )
% 0.26/0.48        = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 0.26/0.48           => ( W
% 0.26/0.48              = ( semiri1314217659103216013at_int @ M ) ) )
% 0.26/0.48          & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 0.26/0.48           => ( M = zero_zero_nat ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % nat_eq_iff
% 0.26/0.48  thf(fact_1043_split__nat,axiom,
% 0.26/0.48      ! [P: nat > $o,I: int] :
% 0.26/0.48        ( ( P @ ( nat2 @ I ) )
% 0.26/0.48        = ( ! [N3: nat] :
% 0.26/0.48              ( ( I
% 0.26/0.48                = ( semiri1314217659103216013at_int @ N3 ) )
% 0.26/0.48             => ( P @ N3 ) )
% 0.26/0.48          & ( ( ord_less_int @ I @ zero_zero_int )
% 0.26/0.48           => ( P @ zero_zero_nat ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % split_nat
% 0.26/0.48  thf(fact_1044_nat__mono__iff,axiom,
% 0.26/0.48      ! [Z: int,W: int] :
% 0.26/0.48        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.26/0.48       => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 0.26/0.48          = ( ord_less_int @ W @ Z ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % nat_mono_iff
% 0.26/0.48  thf(fact_1045_nat__power__eq,axiom,
% 0.26/0.48      ! [Z: int,N: nat] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.26/0.48       => ( ( nat2 @ ( power_power_int @ Z @ N ) )
% 0.26/0.48          = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % nat_power_eq
% 0.26/0.48  thf(fact_1046_int__eq__iff,axiom,
% 0.26/0.48      ! [M: nat,Z: int] :
% 0.26/0.48        ( ( ( semiri1314217659103216013at_int @ M )
% 0.26/0.48          = Z )
% 0.26/0.48        = ( ( M
% 0.26/0.48            = ( nat2 @ Z ) )
% 0.26/0.48          & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % int_eq_iff
% 0.26/0.48  thf(fact_1047_nat__0__le,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.26/0.48       => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 0.26/0.48          = Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % nat_0_le
% 0.26/0.48  thf(fact_1048_ex__le__of__int,axiom,
% 0.26/0.48      ! [X3: real] :
% 0.26/0.48      ? [Z3: int] : ( ord_less_eq_real @ X3 @ ( ring_1_of_int_real @ Z3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % ex_le_of_int
% 0.26/0.48  thf(fact_1049_ex__le__of__int,axiom,
% 0.26/0.48      ! [X3: rat] :
% 0.26/0.48      ? [Z3: int] : ( ord_less_eq_rat @ X3 @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % ex_le_of_int
% 0.26/0.48  thf(fact_1050_ex__less__of__int,axiom,
% 0.26/0.48      ! [X3: real] :
% 0.26/0.48      ? [Z3: int] : ( ord_less_real @ X3 @ ( ring_1_of_int_real @ Z3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % ex_less_of_int
% 0.26/0.48  thf(fact_1051_ex__less__of__int,axiom,
% 0.26/0.48      ! [X3: rat] :
% 0.26/0.48      ? [Z3: int] : ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % ex_less_of_int
% 0.26/0.48  thf(fact_1052_ex__of__int__less,axiom,
% 0.26/0.48      ! [X3: real] :
% 0.26/0.48      ? [Z3: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z3 ) @ X3 ) ).
% 0.26/0.48  
% 0.26/0.48  % ex_of_int_less
% 0.26/0.48  thf(fact_1053_ex__of__int__less,axiom,
% 0.26/0.48      ! [X3: rat] :
% 0.26/0.48      ? [Z3: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z3 ) @ X3 ) ).
% 0.26/0.48  
% 0.26/0.48  % ex_of_int_less
% 0.26/0.48  thf(fact_1054_zero__power,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48       => ( ( power_power_rat @ zero_zero_rat @ N )
% 0.26/0.48          = zero_zero_rat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_power
% 0.26/0.48  thf(fact_1055_zero__power,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48       => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.26/0.48          = zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_power
% 0.26/0.48  thf(fact_1056_zero__power,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48       => ( ( power_power_int @ zero_zero_int @ N )
% 0.26/0.48          = zero_zero_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_power
% 0.26/0.48  thf(fact_1057_zero__power,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48       => ( ( power_power_real @ zero_zero_real @ N )
% 0.26/0.48          = zero_zero_real ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_power
% 0.26/0.48  thf(fact_1058_zero__power,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48       => ( ( power_power_complex @ zero_zero_complex @ N )
% 0.26/0.48          = zero_zero_complex ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_power
% 0.26/0.48  thf(fact_1059_le__numeral__extra_I3_J,axiom,
% 0.26/0.48      ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 0.26/0.48  
% 0.26/0.48  % le_numeral_extra(3)
% 0.26/0.48  thf(fact_1060_le__numeral__extra_I3_J,axiom,
% 0.26/0.48      ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 0.26/0.48  
% 0.26/0.48  % le_numeral_extra(3)
% 0.26/0.48  thf(fact_1061_le__numeral__extra_I3_J,axiom,
% 0.26/0.48      ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 0.26/0.48  
% 0.26/0.48  % le_numeral_extra(3)
% 0.26/0.48  thf(fact_1062_le__numeral__extra_I3_J,axiom,
% 0.26/0.48      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.26/0.48  
% 0.26/0.48  % le_numeral_extra(3)
% 0.26/0.48  thf(fact_1063_less__numeral__extra_I3_J,axiom,
% 0.26/0.48      ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 0.26/0.48  
% 0.26/0.48  % less_numeral_extra(3)
% 0.26/0.48  thf(fact_1064_less__numeral__extra_I3_J,axiom,
% 0.26/0.48      ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 0.26/0.48  
% 0.26/0.48  % less_numeral_extra(3)
% 0.26/0.48  thf(fact_1065_less__numeral__extra_I3_J,axiom,
% 0.26/0.48      ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.26/0.48  
% 0.26/0.48  % less_numeral_extra(3)
% 0.26/0.48  thf(fact_1066_less__numeral__extra_I3_J,axiom,
% 0.26/0.48      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.26/0.48  
% 0.26/0.48  % less_numeral_extra(3)
% 0.26/0.48  thf(fact_1067_field__lbound__gt__zero,axiom,
% 0.26/0.48      ! [D1: real,D2: real] :
% 0.26/0.48        ( ( ord_less_real @ zero_zero_real @ D1 )
% 0.26/0.48       => ( ( ord_less_real @ zero_zero_real @ D2 )
% 0.26/0.48         => ? [E: real] :
% 0.26/0.48              ( ( ord_less_real @ zero_zero_real @ E )
% 0.26/0.48              & ( ord_less_real @ E @ D1 )
% 0.26/0.48              & ( ord_less_real @ E @ D2 ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % field_lbound_gt_zero
% 0.26/0.48  thf(fact_1068_field__lbound__gt__zero,axiom,
% 0.26/0.48      ! [D1: rat,D2: rat] :
% 0.26/0.48        ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 0.26/0.48       => ( ( ord_less_rat @ zero_zero_rat @ D2 )
% 0.26/0.48         => ? [E: rat] :
% 0.26/0.48              ( ( ord_less_rat @ zero_zero_rat @ E )
% 0.26/0.48              & ( ord_less_rat @ E @ D1 )
% 0.26/0.48              & ( ord_less_rat @ E @ D2 ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % field_lbound_gt_zero
% 0.26/0.48  thf(fact_1069_zero__neq__numeral,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( zero_zero_complex
% 0.26/0.48       != ( numera6690914467698888265omplex @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_neq_numeral
% 0.26/0.48  thf(fact_1070_zero__neq__numeral,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( zero_zero_real
% 0.26/0.48       != ( numeral_numeral_real @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_neq_numeral
% 0.26/0.48  thf(fact_1071_zero__neq__numeral,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( zero_zero_rat
% 0.26/0.48       != ( numeral_numeral_rat @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_neq_numeral
% 0.26/0.48  thf(fact_1072_zero__neq__numeral,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( zero_zero_nat
% 0.26/0.48       != ( numeral_numeral_nat @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_neq_numeral
% 0.26/0.48  thf(fact_1073_zero__neq__numeral,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( zero_zero_int
% 0.26/0.48       != ( numeral_numeral_int @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_neq_numeral
% 0.26/0.48  thf(fact_1074_power__not__zero,axiom,
% 0.26/0.48      ! [A: rat,N: nat] :
% 0.26/0.48        ( ( A != zero_zero_rat )
% 0.26/0.48       => ( ( power_power_rat @ A @ N )
% 0.26/0.48         != zero_zero_rat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_not_zero
% 0.26/0.48  thf(fact_1075_power__not__zero,axiom,
% 0.26/0.48      ! [A: nat,N: nat] :
% 0.26/0.48        ( ( A != zero_zero_nat )
% 0.26/0.48       => ( ( power_power_nat @ A @ N )
% 0.26/0.48         != zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_not_zero
% 0.26/0.48  thf(fact_1076_power__not__zero,axiom,
% 0.26/0.48      ! [A: int,N: nat] :
% 0.26/0.48        ( ( A != zero_zero_int )
% 0.26/0.48       => ( ( power_power_int @ A @ N )
% 0.26/0.48         != zero_zero_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_not_zero
% 0.26/0.48  thf(fact_1077_power__not__zero,axiom,
% 0.26/0.48      ! [A: real,N: nat] :
% 0.26/0.48        ( ( A != zero_zero_real )
% 0.26/0.48       => ( ( power_power_real @ A @ N )
% 0.26/0.48         != zero_zero_real ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_not_zero
% 0.26/0.48  thf(fact_1078_power__not__zero,axiom,
% 0.26/0.48      ! [A: complex,N: nat] :
% 0.26/0.48        ( ( A != zero_zero_complex )
% 0.26/0.48       => ( ( power_power_complex @ A @ N )
% 0.26/0.48         != zero_zero_complex ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_not_zero
% 0.26/0.48  thf(fact_1079_bot__nat__0_Oextremum__strict,axiom,
% 0.26/0.48      ! [A: nat] :
% 0.26/0.48        ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 0.26/0.48  
% 0.26/0.48  % bot_nat_0.extremum_strict
% 0.26/0.48  thf(fact_1080_gr0I,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( N != zero_zero_nat )
% 0.26/0.48       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % gr0I
% 0.26/0.48  thf(fact_1081_not__gr0,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.26/0.48        = ( N = zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % not_gr0
% 0.26/0.48  thf(fact_1082_not__less0,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.26/0.48  
% 0.26/0.48  % not_less0
% 0.26/0.48  thf(fact_1083_less__zeroE,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.26/0.48  
% 0.26/0.48  % less_zeroE
% 0.26/0.48  thf(fact_1084_gr__implies__not0,axiom,
% 0.26/0.48      ! [M: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_nat @ M @ N )
% 0.26/0.48       => ( N != zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % gr_implies_not0
% 0.26/0.48  thf(fact_1085_infinite__descent0,axiom,
% 0.26/0.48      ! [P: nat > $o,N: nat] :
% 0.26/0.48        ( ( P @ zero_zero_nat )
% 0.26/0.48       => ( ! [N2: nat] :
% 0.26/0.48              ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.26/0.48             => ( ~ ( P @ N2 )
% 0.26/0.48               => ? [M2: nat] :
% 0.26/0.48                    ( ( ord_less_nat @ M2 @ N2 )
% 0.26/0.48                    & ~ ( P @ M2 ) ) ) )
% 0.26/0.48         => ( P @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % infinite_descent0
% 0.26/0.48  thf(fact_1086_le__0__eq,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.26/0.48        = ( N = zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % le_0_eq
% 0.26/0.48  thf(fact_1087_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.26/0.48      ! [A: nat] :
% 0.26/0.48        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.26/0.48       => ( A = zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % bot_nat_0.extremum_uniqueI
% 0.26/0.48  thf(fact_1088_bot__nat__0_Oextremum__unique,axiom,
% 0.26/0.48      ! [A: nat] :
% 0.26/0.48        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.26/0.48        = ( A = zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % bot_nat_0.extremum_unique
% 0.26/0.48  thf(fact_1089_less__eq__nat_Osimps_I1_J,axiom,
% 0.26/0.48      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.26/0.48  
% 0.26/0.48  % less_eq_nat.simps(1)
% 0.26/0.48  thf(fact_1090_conj__le__cong,axiom,
% 0.26/0.48      ! [X3: int,X7: int,P: $o,P4: $o] :
% 0.26/0.48        ( ( X3 = X7 )
% 0.26/0.48       => ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 0.26/0.48           => ( P = P4 ) )
% 0.26/0.48         => ( ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.26/0.48              & P )
% 0.26/0.48            = ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 0.26/0.48              & P4 ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % conj_le_cong
% 0.26/0.48  thf(fact_1091_imp__le__cong,axiom,
% 0.26/0.48      ! [X3: int,X7: int,P: $o,P4: $o] :
% 0.26/0.48        ( ( X3 = X7 )
% 0.26/0.48       => ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 0.26/0.48           => ( P = P4 ) )
% 0.26/0.48         => ( ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.26/0.48             => P )
% 0.26/0.48            = ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 0.26/0.48             => P4 ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % imp_le_cong
% 0.26/0.48  thf(fact_1092_less__eq__int__code_I1_J,axiom,
% 0.26/0.48      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.26/0.48  
% 0.26/0.48  % less_eq_int_code(1)
% 0.26/0.48  thf(fact_1093_less__int__code_I1_J,axiom,
% 0.26/0.48      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.26/0.48  
% 0.26/0.48  % less_int_code(1)
% 0.26/0.48  thf(fact_1094_not__iless0,axiom,
% 0.26/0.48      ! [N: extended_enat] :
% 0.26/0.48        ~ ( ord_le72135733267957522d_enat @ N @ zero_z5237406670263579293d_enat ) ).
% 0.26/0.48  
% 0.26/0.48  % not_iless0
% 0.26/0.48  thf(fact_1095_nat__less__eq__zless,axiom,
% 0.26/0.48      ! [W: int,Z: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ W )
% 0.26/0.48       => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 0.26/0.48          = ( ord_less_int @ W @ Z ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % nat_less_eq_zless
% 0.26/0.48  thf(fact_1096_nat__le__eq__zle,axiom,
% 0.26/0.48      ! [W: int,Z: int] :
% 0.26/0.48        ( ( ( ord_less_int @ zero_zero_int @ W )
% 0.26/0.48          | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 0.26/0.48       => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 0.26/0.48          = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % nat_le_eq_zle
% 0.26/0.48  thf(fact_1097_le__nat__iff,axiom,
% 0.26/0.48      ! [K: int,N: nat] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.26/0.48       => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 0.26/0.48          = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % le_nat_iff
% 0.26/0.48  thf(fact_1098_ile0__eq,axiom,
% 0.26/0.48      ! [N: extended_enat] :
% 0.26/0.48        ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 0.26/0.48        = ( N = zero_z5237406670263579293d_enat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % ile0_eq
% 0.26/0.48  thf(fact_1099_i0__lb,axiom,
% 0.26/0.48      ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 0.26/0.48  
% 0.26/0.48  % i0_lb
% 0.26/0.48  thf(fact_1100_power__eq__iff__eq__base,axiom,
% 0.26/0.48      ! [N: nat,A: real,B: real] :
% 0.26/0.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.48         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.26/0.48           => ( ( ( power_power_real @ A @ N )
% 0.26/0.48                = ( power_power_real @ B @ N ) )
% 0.26/0.48              = ( A = B ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_eq_iff_eq_base
% 0.26/0.48  thf(fact_1101_power__eq__iff__eq__base,axiom,
% 0.26/0.48      ! [N: nat,A: rat,B: rat] :
% 0.26/0.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.48         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.26/0.48           => ( ( ( power_power_rat @ A @ N )
% 0.26/0.48                = ( power_power_rat @ B @ N ) )
% 0.26/0.48              = ( A = B ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_eq_iff_eq_base
% 0.26/0.48  thf(fact_1102_power__eq__iff__eq__base,axiom,
% 0.26/0.48      ! [N: nat,A: nat,B: nat] :
% 0.26/0.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.48         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.26/0.48           => ( ( ( power_power_nat @ A @ N )
% 0.26/0.48                = ( power_power_nat @ B @ N ) )
% 0.26/0.48              = ( A = B ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_eq_iff_eq_base
% 0.26/0.48  thf(fact_1103_power__eq__iff__eq__base,axiom,
% 0.26/0.48      ! [N: nat,A: int,B: int] :
% 0.26/0.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.48         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.26/0.48           => ( ( ( power_power_int @ A @ N )
% 0.26/0.48                = ( power_power_int @ B @ N ) )
% 0.26/0.48              = ( A = B ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_eq_iff_eq_base
% 0.26/0.48  thf(fact_1104_power__eq__imp__eq__base,axiom,
% 0.26/0.48      ! [A: real,N: nat,B: real] :
% 0.26/0.48        ( ( ( power_power_real @ A @ N )
% 0.26/0.48          = ( power_power_real @ B @ N ) )
% 0.26/0.48       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.48         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.26/0.48           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48             => ( A = B ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_eq_imp_eq_base
% 0.26/0.48  thf(fact_1105_power__eq__imp__eq__base,axiom,
% 0.26/0.48      ! [A: rat,N: nat,B: rat] :
% 0.26/0.48        ( ( ( power_power_rat @ A @ N )
% 0.26/0.48          = ( power_power_rat @ B @ N ) )
% 0.26/0.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.48         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.26/0.48           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48             => ( A = B ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_eq_imp_eq_base
% 0.26/0.48  thf(fact_1106_power__eq__imp__eq__base,axiom,
% 0.26/0.48      ! [A: nat,N: nat,B: nat] :
% 0.26/0.48        ( ( ( power_power_nat @ A @ N )
% 0.26/0.48          = ( power_power_nat @ B @ N ) )
% 0.26/0.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.48         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.26/0.48           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48             => ( A = B ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_eq_imp_eq_base
% 0.26/0.48  thf(fact_1107_power__eq__imp__eq__base,axiom,
% 0.26/0.48      ! [A: int,N: nat,B: int] :
% 0.26/0.48        ( ( ( power_power_int @ A @ N )
% 0.26/0.48          = ( power_power_int @ B @ N ) )
% 0.26/0.48       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.48         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.26/0.48           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48             => ( A = B ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_eq_imp_eq_base
% 0.26/0.48  thf(fact_1108_zero__less__imp__eq__int,axiom,
% 0.26/0.48      ! [K: int] :
% 0.26/0.48        ( ( ord_less_int @ zero_zero_int @ K )
% 0.26/0.48       => ? [N2: nat] :
% 0.26/0.48            ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.26/0.48            & ( K
% 0.26/0.48              = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_less_imp_eq_int
% 0.26/0.48  thf(fact_1109_pos__int__cases,axiom,
% 0.26/0.48      ! [K: int] :
% 0.26/0.48        ( ( ord_less_int @ zero_zero_int @ K )
% 0.26/0.48       => ~ ! [N2: nat] :
% 0.26/0.48              ( ( K
% 0.26/0.48                = ( semiri1314217659103216013at_int @ N2 ) )
% 0.26/0.48             => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % pos_int_cases
% 0.26/0.48  thf(fact_1110_nat__numeral__as__int,axiom,
% 0.26/0.48      ( numeral_numeral_nat
% 0.26/0.48      = ( ^ [I4: num] : ( nat2 @ ( numeral_numeral_int @ I4 ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % nat_numeral_as_int
% 0.26/0.48  thf(fact_1111_nat__less__iff,axiom,
% 0.26/0.48      ! [W: int,M: nat] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ W )
% 0.26/0.48       => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 0.26/0.48          = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % nat_less_iff
% 0.26/0.48  thf(fact_1112_nat__mono,axiom,
% 0.26/0.48      ! [X3: int,Y3: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.26/0.48       => ( ord_less_eq_nat @ ( nat2 @ X3 ) @ ( nat2 @ Y3 ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % nat_mono
% 0.26/0.48  thf(fact_1113_power__strict__mono,axiom,
% 0.26/0.48      ! [A: real,B: real,N: nat] :
% 0.26/0.48        ( ( ord_less_real @ A @ B )
% 0.26/0.48       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.48         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48           => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_strict_mono
% 0.26/0.48  thf(fact_1114_power__strict__mono,axiom,
% 0.26/0.48      ! [A: rat,B: rat,N: nat] :
% 0.26/0.48        ( ( ord_less_rat @ A @ B )
% 0.26/0.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.48         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48           => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_strict_mono
% 0.26/0.48  thf(fact_1115_power__strict__mono,axiom,
% 0.26/0.48      ! [A: nat,B: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_nat @ A @ B )
% 0.26/0.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.48         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48           => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_strict_mono
% 0.26/0.48  thf(fact_1116_power__strict__mono,axiom,
% 0.26/0.48      ! [A: int,B: int,N: nat] :
% 0.26/0.48        ( ( ord_less_int @ A @ B )
% 0.26/0.48       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.48         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48           => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_strict_mono
% 0.26/0.48  thf(fact_1117_not__numeral__le__zero,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 0.26/0.48  
% 0.26/0.48  % not_numeral_le_zero
% 0.26/0.48  thf(fact_1118_not__numeral__le__zero,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 0.26/0.48  
% 0.26/0.48  % not_numeral_le_zero
% 0.26/0.48  thf(fact_1119_not__numeral__le__zero,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 0.26/0.48  
% 0.26/0.48  % not_numeral_le_zero
% 0.26/0.48  thf(fact_1120_not__numeral__le__zero,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 0.26/0.48  
% 0.26/0.48  % not_numeral_le_zero
% 0.26/0.48  thf(fact_1121_zero__le__numeral,axiom,
% 0.26/0.48      ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_le_numeral
% 0.26/0.48  thf(fact_1122_zero__le__numeral,axiom,
% 0.26/0.48      ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_le_numeral
% 0.26/0.48  thf(fact_1123_zero__le__numeral,axiom,
% 0.26/0.48      ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_le_numeral
% 0.26/0.48  thf(fact_1124_zero__le__numeral,axiom,
% 0.26/0.48      ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_le_numeral
% 0.26/0.48  thf(fact_1125_zero__less__numeral,axiom,
% 0.26/0.48      ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_less_numeral
% 0.26/0.48  thf(fact_1126_zero__less__numeral,axiom,
% 0.26/0.48      ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_less_numeral
% 0.26/0.48  thf(fact_1127_zero__less__numeral,axiom,
% 0.26/0.48      ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_less_numeral
% 0.26/0.48  thf(fact_1128_zero__less__numeral,axiom,
% 0.26/0.48      ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_less_numeral
% 0.26/0.48  thf(fact_1129_not__numeral__less__zero,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 0.26/0.48  
% 0.26/0.48  % not_numeral_less_zero
% 0.26/0.48  thf(fact_1130_not__numeral__less__zero,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 0.26/0.48  
% 0.26/0.48  % not_numeral_less_zero
% 0.26/0.48  thf(fact_1131_not__numeral__less__zero,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 0.26/0.48  
% 0.26/0.48  % not_numeral_less_zero
% 0.26/0.48  thf(fact_1132_not__numeral__less__zero,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 0.26/0.48  
% 0.26/0.48  % not_numeral_less_zero
% 0.26/0.48  thf(fact_1133_zero__le__power,axiom,
% 0.26/0.48      ! [A: real,N: nat] :
% 0.26/0.48        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.48       => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_le_power
% 0.26/0.48  thf(fact_1134_zero__le__power,axiom,
% 0.26/0.48      ! [A: rat,N: nat] :
% 0.26/0.48        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.48       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_le_power
% 0.26/0.48  thf(fact_1135_zero__le__power,axiom,
% 0.26/0.48      ! [A: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.48       => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_le_power
% 0.26/0.48  thf(fact_1136_zero__le__power,axiom,
% 0.26/0.48      ! [A: int,N: nat] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.48       => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_le_power
% 0.26/0.48  thf(fact_1137_power__mono,axiom,
% 0.26/0.48      ! [A: real,B: real,N: nat] :
% 0.26/0.48        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.48       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.48         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_mono
% 0.26/0.48  thf(fact_1138_power__mono,axiom,
% 0.26/0.48      ! [A: rat,B: rat,N: nat] :
% 0.26/0.48        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.48         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_mono
% 0.26/0.48  thf(fact_1139_power__mono,axiom,
% 0.26/0.48      ! [A: nat,B: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.48         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_mono
% 0.26/0.48  thf(fact_1140_power__mono,axiom,
% 0.26/0.48      ! [A: int,B: int,N: nat] :
% 0.26/0.48        ( ( ord_less_eq_int @ A @ B )
% 0.26/0.48       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.48         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_mono
% 0.26/0.48  thf(fact_1141_zero__less__power,axiom,
% 0.26/0.48      ! [A: real,N: nat] :
% 0.26/0.48        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.48       => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_less_power
% 0.26/0.48  thf(fact_1142_zero__less__power,axiom,
% 0.26/0.48      ! [A: rat,N: nat] :
% 0.26/0.48        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.48       => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_less_power
% 0.26/0.48  thf(fact_1143_zero__less__power,axiom,
% 0.26/0.48      ! [A: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.26/0.48       => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_less_power
% 0.26/0.48  thf(fact_1144_zero__less__power,axiom,
% 0.26/0.48      ! [A: int,N: nat] :
% 0.26/0.48        ( ( ord_less_int @ zero_zero_int @ A )
% 0.26/0.48       => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_less_power
% 0.26/0.48  thf(fact_1145_of__nat__0__le__iff,axiom,
% 0.26/0.48      ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_0_le_iff
% 0.26/0.48  thf(fact_1146_of__nat__0__le__iff,axiom,
% 0.26/0.48      ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_0_le_iff
% 0.26/0.48  thf(fact_1147_of__nat__0__le__iff,axiom,
% 0.26/0.48      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_0_le_iff
% 0.26/0.48  thf(fact_1148_of__nat__0__le__iff,axiom,
% 0.26/0.48      ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_0_le_iff
% 0.26/0.48  thf(fact_1149_of__nat__less__0__iff,axiom,
% 0.26/0.48      ! [M: nat] :
% 0.26/0.48        ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_less_0_iff
% 0.26/0.48  thf(fact_1150_of__nat__less__0__iff,axiom,
% 0.26/0.48      ! [M: nat] :
% 0.26/0.48        ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_less_0_iff
% 0.26/0.48  thf(fact_1151_of__nat__less__0__iff,axiom,
% 0.26/0.48      ! [M: nat] :
% 0.26/0.48        ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_less_0_iff
% 0.26/0.48  thf(fact_1152_of__nat__less__0__iff,axiom,
% 0.26/0.48      ! [M: nat] :
% 0.26/0.48        ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_less_0_iff
% 0.26/0.48  thf(fact_1153_ex__least__nat__le,axiom,
% 0.26/0.48      ! [P: nat > $o,N: nat] :
% 0.26/0.48        ( ( P @ N )
% 0.26/0.48       => ( ~ ( P @ zero_zero_nat )
% 0.26/0.48         => ? [K2: nat] :
% 0.26/0.48              ( ( ord_less_eq_nat @ K2 @ N )
% 0.26/0.48              & ! [I2: nat] :
% 0.26/0.48                  ( ( ord_less_nat @ I2 @ K2 )
% 0.26/0.48                 => ~ ( P @ I2 ) )
% 0.26/0.48              & ( P @ K2 ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % ex_least_nat_le
% 0.26/0.48  thf(fact_1154_nat__power__less__imp__less,axiom,
% 0.26/0.48      ! [I: nat,M: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_nat @ zero_zero_nat @ I )
% 0.26/0.48       => ( ( ord_less_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 0.26/0.48         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % nat_power_less_imp_less
% 0.26/0.48  thf(fact_1155_zero__le__imp__eq__int,axiom,
% 0.26/0.48      ! [K: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.26/0.48       => ? [N2: nat] :
% 0.26/0.48            ( K
% 0.26/0.48            = ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_le_imp_eq_int
% 0.26/0.48  thf(fact_1156_nonneg__int__cases,axiom,
% 0.26/0.48      ! [K: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.26/0.48       => ~ ! [N2: nat] :
% 0.26/0.48              ( K
% 0.26/0.48             != ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % nonneg_int_cases
% 0.26/0.48  thf(fact_1157_zless__nat__eq__int__zless,axiom,
% 0.26/0.48      ! [M: nat,Z: int] :
% 0.26/0.48        ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 0.26/0.48        = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zless_nat_eq_int_zless
% 0.26/0.48  thf(fact_1158_nat__le__iff,axiom,
% 0.26/0.48      ! [X3: int,N: nat] :
% 0.26/0.48        ( ( ord_less_eq_nat @ ( nat2 @ X3 ) @ N )
% 0.26/0.48        = ( ord_less_eq_int @ X3 @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % nat_le_iff
% 0.26/0.48  thf(fact_1159_ex__gt__or__lt,axiom,
% 0.26/0.48      ! [A: real] :
% 0.26/0.48      ? [B4: real] :
% 0.26/0.48        ( ( ord_less_real @ A @ B4 )
% 0.26/0.48        | ( ord_less_real @ B4 @ A ) ) ).
% 0.26/0.48  
% 0.26/0.48  % ex_gt_or_lt
% 0.26/0.48  thf(fact_1160_power__less__imp__less__base,axiom,
% 0.26/0.48      ! [A: real,N: nat,B: real] :
% 0.26/0.48        ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 0.26/0.48       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.26/0.48         => ( ord_less_real @ A @ B ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_less_imp_less_base
% 0.26/0.48  thf(fact_1161_power__less__imp__less__base,axiom,
% 0.26/0.48      ! [A: rat,N: nat,B: rat] :
% 0.26/0.48        ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 0.26/0.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.26/0.48         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_less_imp_less_base
% 0.26/0.48  thf(fact_1162_power__less__imp__less__base,axiom,
% 0.26/0.48      ! [A: nat,N: nat,B: nat] :
% 0.26/0.48        ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 0.26/0.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.26/0.48         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_less_imp_less_base
% 0.26/0.48  thf(fact_1163_power__less__imp__less__base,axiom,
% 0.26/0.48      ! [A: int,N: nat,B: int] :
% 0.26/0.48        ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 0.26/0.48       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.26/0.48         => ( ord_less_int @ A @ B ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_less_imp_less_base
% 0.26/0.48  thf(fact_1164_of__nat__less__of__int__iff,axiom,
% 0.26/0.48      ! [N: nat,X3: int] :
% 0.26/0.48        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( ring_1_of_int_real @ X3 ) )
% 0.26/0.48        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_less_of_int_iff
% 0.26/0.48  thf(fact_1165_of__nat__less__of__int__iff,axiom,
% 0.26/0.48      ! [N: nat,X3: int] :
% 0.26/0.48        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X3 ) )
% 0.26/0.48        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_less_of_int_iff
% 0.26/0.48  thf(fact_1166_of__nat__less__of__int__iff,axiom,
% 0.26/0.48      ! [N: nat,X3: int] :
% 0.26/0.48        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X3 ) )
% 0.26/0.48        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_less_of_int_iff
% 0.26/0.48  thf(fact_1167_zero__power2,axiom,
% 0.26/0.48      ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.48      = zero_zero_rat ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_power2
% 0.26/0.48  thf(fact_1168_zero__power2,axiom,
% 0.26/0.48      ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.48      = zero_zero_nat ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_power2
% 0.26/0.48  thf(fact_1169_zero__power2,axiom,
% 0.26/0.48      ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.48      = zero_zero_int ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_power2
% 0.26/0.48  thf(fact_1170_zero__power2,axiom,
% 0.26/0.48      ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.48      = zero_zero_real ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_power2
% 0.26/0.48  thf(fact_1171_zero__power2,axiom,
% 0.26/0.48      ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.48      = zero_zero_complex ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_power2
% 0.26/0.48  thf(fact_1172_zero__le__power2,axiom,
% 0.26/0.48      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_le_power2
% 0.26/0.48  thf(fact_1173_zero__le__power2,axiom,
% 0.26/0.48      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_le_power2
% 0.26/0.48  thf(fact_1174_zero__le__power2,axiom,
% 0.26/0.48      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_le_power2
% 0.26/0.48  thf(fact_1175_power2__eq__imp__eq,axiom,
% 0.26/0.48      ! [X3: real,Y3: real] :
% 0.26/0.48        ( ( ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.48          = ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.48       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.48         => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.48           => ( X3 = Y3 ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power2_eq_imp_eq
% 0.26/0.48  thf(fact_1176_power2__eq__imp__eq,axiom,
% 0.26/0.48      ! [X3: rat,Y3: rat] :
% 0.26/0.48        ( ( ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.48          = ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.26/0.48         => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 0.26/0.48           => ( X3 = Y3 ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power2_eq_imp_eq
% 0.26/0.48  thf(fact_1177_power2__eq__imp__eq,axiom,
% 0.26/0.48      ! [X3: nat,Y3: nat] :
% 0.26/0.48        ( ( ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.48          = ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ X3 )
% 0.26/0.48         => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 0.26/0.48           => ( X3 = Y3 ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power2_eq_imp_eq
% 0.26/0.48  thf(fact_1178_power2__eq__imp__eq,axiom,
% 0.26/0.48      ! [X3: int,Y3: int] :
% 0.26/0.48        ( ( ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.48          = ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.48       => ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.26/0.48         => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 0.26/0.48           => ( X3 = Y3 ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power2_eq_imp_eq
% 0.26/0.48  thf(fact_1179_power2__le__imp__le,axiom,
% 0.26/0.48      ! [X3: real,Y3: real] :
% 0.26/0.48        ( ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.48       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.48         => ( ord_less_eq_real @ X3 @ Y3 ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power2_le_imp_le
% 0.26/0.48  thf(fact_1180_power2__le__imp__le,axiom,
% 0.26/0.48      ! [X3: rat,Y3: rat] :
% 0.26/0.48        ( ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 0.26/0.48         => ( ord_less_eq_rat @ X3 @ Y3 ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power2_le_imp_le
% 0.26/0.48  thf(fact_1181_power2__le__imp__le,axiom,
% 0.26/0.48      ! [X3: nat,Y3: nat] :
% 0.26/0.48        ( ( ord_less_eq_nat @ ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 0.26/0.48         => ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power2_le_imp_le
% 0.26/0.48  thf(fact_1182_power2__le__imp__le,axiom,
% 0.26/0.48      ! [X3: int,Y3: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.48       => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 0.26/0.48         => ( ord_less_eq_int @ X3 @ Y3 ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power2_le_imp_le
% 0.26/0.48  thf(fact_1183_power2__less__0,axiom,
% 0.26/0.48      ! [A: real] :
% 0.26/0.48        ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 0.26/0.48  
% 0.26/0.48  % power2_less_0
% 0.26/0.48  thf(fact_1184_power2__less__0,axiom,
% 0.26/0.48      ! [A: rat] :
% 0.26/0.48        ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 0.26/0.48  
% 0.26/0.48  % power2_less_0
% 0.26/0.48  thf(fact_1185_power2__less__0,axiom,
% 0.26/0.48      ! [A: int] :
% 0.26/0.48        ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 0.26/0.48  
% 0.26/0.48  % power2_less_0
% 0.26/0.48  thf(fact_1186_not__exp__less__eq__0__int,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 0.26/0.48  
% 0.26/0.48  % not_exp_less_eq_0_int
% 0.26/0.48  thf(fact_1187_not__gr__zero,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.26/0.48        = ( N = zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % not_gr_zero
% 0.26/0.48  thf(fact_1188_le__zero__eq,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.26/0.48        = ( N = zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % le_zero_eq
% 0.26/0.48  thf(fact_1189_pos2,axiom,
% 0.26/0.48      ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 0.26/0.48  
% 0.26/0.48  % pos2
% 0.26/0.48  thf(fact_1190_realpow__pos__nth__unique,axiom,
% 0.26/0.48      ! [N: nat,A: real] :
% 0.26/0.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.48         => ? [X4: real] :
% 0.26/0.48              ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.26/0.48              & ( ( power_power_real @ X4 @ N )
% 0.26/0.48                = A )
% 0.26/0.48              & ! [Y6: real] :
% 0.26/0.48                  ( ( ( ord_less_real @ zero_zero_real @ Y6 )
% 0.26/0.48                    & ( ( power_power_real @ Y6 @ N )
% 0.26/0.48                      = A ) )
% 0.26/0.48                 => ( Y6 = X4 ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % realpow_pos_nth_unique
% 0.26/0.48  thf(fact_1191_realpow__pos__nth,axiom,
% 0.26/0.48      ! [N: nat,A: real] :
% 0.26/0.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.48         => ? [R: real] :
% 0.26/0.48              ( ( ord_less_real @ zero_zero_real @ R )
% 0.26/0.48              & ( ( power_power_real @ R @ N )
% 0.26/0.48                = A ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % realpow_pos_nth
% 0.26/0.48  thf(fact_1192_gr__zeroI,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( N != zero_zero_nat )
% 0.26/0.48       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % gr_zeroI
% 0.26/0.48  thf(fact_1193_not__less__zero,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.26/0.48  
% 0.26/0.48  % not_less_zero
% 0.26/0.48  thf(fact_1194_gr__implies__not__zero,axiom,
% 0.26/0.48      ! [M: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_nat @ M @ N )
% 0.26/0.48       => ( N != zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % gr_implies_not_zero
% 0.26/0.48  thf(fact_1195_zero__less__iff__neq__zero,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.48        = ( N != zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_less_iff_neq_zero
% 0.26/0.48  thf(fact_1196_zero__reorient,axiom,
% 0.26/0.48      ! [X3: literal] :
% 0.26/0.48        ( ( zero_zero_literal = X3 )
% 0.26/0.48        = ( X3 = zero_zero_literal ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_reorient
% 0.26/0.48  thf(fact_1197_zero__reorient,axiom,
% 0.26/0.48      ! [X3: real] :
% 0.26/0.48        ( ( zero_zero_real = X3 )
% 0.26/0.48        = ( X3 = zero_zero_real ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_reorient
% 0.26/0.48  thf(fact_1198_zero__reorient,axiom,
% 0.26/0.48      ! [X3: rat] :
% 0.26/0.48        ( ( zero_zero_rat = X3 )
% 0.26/0.48        = ( X3 = zero_zero_rat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_reorient
% 0.26/0.48  thf(fact_1199_zero__reorient,axiom,
% 0.26/0.48      ! [X3: nat] :
% 0.26/0.48        ( ( zero_zero_nat = X3 )
% 0.26/0.48        = ( X3 = zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_reorient
% 0.26/0.48  thf(fact_1200_zero__reorient,axiom,
% 0.26/0.48      ! [X3: int] :
% 0.26/0.48        ( ( zero_zero_int = X3 )
% 0.26/0.48        = ( X3 = zero_zero_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_reorient
% 0.26/0.48  thf(fact_1201_zero__le,axiom,
% 0.26/0.48      ! [X3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X3 ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_le
% 0.26/0.48  thf(fact_1202_log2__of__power__le,axiom,
% 0.26/0.48      ! [M: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.48       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.48         => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % log2_of_power_le
% 0.26/0.48  thf(fact_1203_take__bit__int__eq__self__iff,axiom,
% 0.26/0.48      ! [N: nat,K: int] :
% 0.26/0.48        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.26/0.48          = K )
% 0.26/0.48        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.26/0.48          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % take_bit_int_eq_self_iff
% 0.26/0.48  thf(fact_1204_take__bit__int__eq__self,axiom,
% 0.26/0.48      ! [K: int,N: nat] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.26/0.48       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.48         => ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.26/0.48            = K ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % take_bit_int_eq_self
% 0.26/0.48  thf(fact_1205_XOR__upper,axiom,
% 0.26/0.48      ! [X3: int,N: nat,Y3: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.26/0.48       => ( ( ord_less_int @ X3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.48         => ( ( ord_less_int @ Y3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.48           => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X3 @ Y3 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % XOR_upper
% 0.26/0.48  thf(fact_1206_power__le__zero__eq__numeral,axiom,
% 0.26/0.48      ! [A: real,W: num] :
% 0.26/0.48        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 0.26/0.48        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 0.26/0.48          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.48              & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 0.26/0.48            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.48              & ( A = zero_zero_real ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_le_zero_eq_numeral
% 0.26/0.48  thf(fact_1207_power__le__zero__eq__numeral,axiom,
% 0.26/0.48      ! [A: rat,W: num] :
% 0.26/0.48        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 0.26/0.48        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 0.26/0.48          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.48              & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 0.26/0.48            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.48              & ( A = zero_zero_rat ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_le_zero_eq_numeral
% 0.26/0.48  thf(fact_1208_power__le__zero__eq__numeral,axiom,
% 0.26/0.48      ! [A: int,W: num] :
% 0.26/0.48        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 0.26/0.48        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 0.26/0.48          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.48              & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 0.26/0.48            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.48              & ( A = zero_zero_int ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_le_zero_eq_numeral
% 0.26/0.48  thf(fact_1209_OR__upper,axiom,
% 0.26/0.48      ! [X3: int,N: nat,Y3: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.26/0.48       => ( ( ord_less_int @ X3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.48         => ( ( ord_less_int @ Y3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.48           => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X3 @ Y3 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % OR_upper
% 0.26/0.48  thf(fact_1210_real__sqrt__pow2__iff,axiom,
% 0.26/0.48      ! [X3: real] :
% 0.26/0.48        ( ( ( power_power_real @ ( sqrt @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.48          = X3 )
% 0.26/0.48        = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % real_sqrt_pow2_iff
% 0.26/0.48  thf(fact_1211_real__sqrt__pow2,axiom,
% 0.26/0.48      ! [X3: real] :
% 0.26/0.48        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.48       => ( ( power_power_real @ ( sqrt @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.48          = X3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % real_sqrt_pow2
% 0.26/0.48  thf(fact_1212_real__less__lsqrt,axiom,
% 0.26/0.48      ! [X3: real,Y3: real] :
% 0.26/0.48        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.48       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.48         => ( ( ord_less_real @ X3 @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.48           => ( ord_less_real @ ( sqrt @ X3 ) @ Y3 ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % real_less_lsqrt
% 0.26/0.48  thf(fact_1213_power__decreasing__iff,axiom,
% 0.26/0.48      ! [B: real,M: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_real @ zero_zero_real @ B )
% 0.26/0.48       => ( ( ord_less_real @ B @ one_one_real )
% 0.26/0.48         => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 0.26/0.48            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_decreasing_iff
% 0.26/0.48  thf(fact_1214_power__decreasing__iff,axiom,
% 0.26/0.48      ! [B: rat,M: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.26/0.48       => ( ( ord_less_rat @ B @ one_one_rat )
% 0.26/0.48         => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 0.26/0.48            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_decreasing_iff
% 0.26/0.48  thf(fact_1215_power__decreasing__iff,axiom,
% 0.26/0.48      ! [B: nat,M: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.26/0.48       => ( ( ord_less_nat @ B @ one_one_nat )
% 0.26/0.48         => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 0.26/0.48            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_decreasing_iff
% 0.26/0.48  thf(fact_1216_power__decreasing__iff,axiom,
% 0.26/0.48      ! [B: int,M: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.48       => ( ( ord_less_int @ B @ one_one_int )
% 0.26/0.48         => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 0.26/0.48            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_decreasing_iff
% 0.26/0.48  thf(fact_1217_log2__of__power__less,axiom,
% 0.26/0.48      ! [M: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.48       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.48         => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % log2_of_power_less
% 0.26/0.48  thf(fact_1218_power__one__right,axiom,
% 0.26/0.48      ! [A: nat] :
% 0.26/0.48        ( ( power_power_nat @ A @ one_one_nat )
% 0.26/0.48        = A ) ).
% 0.26/0.48  
% 0.26/0.48  % power_one_right
% 0.26/0.48  thf(fact_1219_power__one__right,axiom,
% 0.26/0.48      ! [A: int] :
% 0.26/0.48        ( ( power_power_int @ A @ one_one_nat )
% 0.26/0.48        = A ) ).
% 0.26/0.48  
% 0.26/0.48  % power_one_right
% 0.26/0.48  thf(fact_1220_power__one__right,axiom,
% 0.26/0.48      ! [A: real] :
% 0.26/0.48        ( ( power_power_real @ A @ one_one_nat )
% 0.26/0.48        = A ) ).
% 0.26/0.48  
% 0.26/0.48  % power_one_right
% 0.26/0.48  thf(fact_1221_power__one__right,axiom,
% 0.26/0.48      ! [A: complex] :
% 0.26/0.48        ( ( power_power_complex @ A @ one_one_nat )
% 0.26/0.48        = A ) ).
% 0.26/0.48  
% 0.26/0.48  % power_one_right
% 0.26/0.48  thf(fact_1222_nat__dvd__1__iff__1,axiom,
% 0.26/0.48      ! [M: nat] :
% 0.26/0.48        ( ( dvd_dvd_nat @ M @ one_one_nat )
% 0.26/0.48        = ( M = one_one_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % nat_dvd_1_iff_1
% 0.26/0.48  thf(fact_1223_or_Oidem,axiom,
% 0.26/0.48      ! [A: int] :
% 0.26/0.48        ( ( bit_se1409905431419307370or_int @ A @ A )
% 0.26/0.48        = A ) ).
% 0.26/0.48  
% 0.26/0.48  % or.idem
% 0.26/0.48  thf(fact_1224_or_Oidem,axiom,
% 0.26/0.48      ! [A: nat] :
% 0.26/0.48        ( ( bit_se1412395901928357646or_nat @ A @ A )
% 0.26/0.48        = A ) ).
% 0.26/0.48  
% 0.26/0.48  % or.idem
% 0.26/0.48  thf(fact_1225_or_Oleft__idem,axiom,
% 0.26/0.48      ! [A: int,B: int] :
% 0.26/0.48        ( ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 0.26/0.48        = ( bit_se1409905431419307370or_int @ A @ B ) ) ).
% 0.26/0.48  
% 0.26/0.48  % or.left_idem
% 0.26/0.48  thf(fact_1226_or_Oleft__idem,axiom,
% 0.26/0.48      ! [A: nat,B: nat] :
% 0.26/0.48        ( ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 0.26/0.48        = ( bit_se1412395901928357646or_nat @ A @ B ) ) ).
% 0.26/0.48  
% 0.26/0.48  % or.left_idem
% 0.26/0.48  thf(fact_1227_or_Oright__idem,axiom,
% 0.26/0.48      ! [A: int,B: int] :
% 0.26/0.48        ( ( bit_se1409905431419307370or_int @ ( bit_se1409905431419307370or_int @ A @ B ) @ B )
% 0.26/0.48        = ( bit_se1409905431419307370or_int @ A @ B ) ) ).
% 0.26/0.48  
% 0.26/0.48  % or.right_idem
% 0.26/0.48  thf(fact_1228_or_Oright__idem,axiom,
% 0.26/0.48      ! [A: nat,B: nat] :
% 0.26/0.48        ( ( bit_se1412395901928357646or_nat @ ( bit_se1412395901928357646or_nat @ A @ B ) @ B )
% 0.26/0.48        = ( bit_se1412395901928357646or_nat @ A @ B ) ) ).
% 0.26/0.48  
% 0.26/0.48  % or.right_idem
% 0.26/0.48  thf(fact_1229_real__sqrt__one,axiom,
% 0.26/0.48      ( ( sqrt @ one_one_real )
% 0.26/0.48      = one_one_real ) ).
% 0.26/0.48  
% 0.26/0.48  % real_sqrt_one
% 0.26/0.48  thf(fact_1230_real__sqrt__eq__iff,axiom,
% 0.26/0.48      ! [X3: real,Y3: real] :
% 0.26/0.48        ( ( ( sqrt @ X3 )
% 0.26/0.48          = ( sqrt @ Y3 ) )
% 0.26/0.48        = ( X3 = Y3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % real_sqrt_eq_iff
% 0.26/0.48  thf(fact_1231_real__sqrt__eq__1__iff,axiom,
% 0.26/0.48      ! [X3: real] :
% 0.26/0.48        ( ( ( sqrt @ X3 )
% 0.26/0.48          = one_one_real )
% 0.26/0.48        = ( X3 = one_one_real ) ) ).
% 0.26/0.48  
% 0.26/0.48  % real_sqrt_eq_1_iff
% 0.26/0.48  thf(fact_1232_bit_Oxor__left__self,axiom,
% 0.26/0.48      ! [X3: int,Y3: int] :
% 0.26/0.48        ( ( bit_se6526347334894502574or_int @ X3 @ ( bit_se6526347334894502574or_int @ X3 @ Y3 ) )
% 0.26/0.48        = Y3 ) ).
% 0.26/0.48  
% 0.26/0.48  % bit.xor_left_self
% 0.26/0.48  thf(fact_1233_power__one,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( power_power_rat @ one_one_rat @ N )
% 0.26/0.48        = one_one_rat ) ).
% 0.26/0.48  
% 0.26/0.48  % power_one
% 0.26/0.48  thf(fact_1234_power__one,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( power_power_nat @ one_one_nat @ N )
% 0.26/0.48        = one_one_nat ) ).
% 0.26/0.48  
% 0.26/0.48  % power_one
% 0.26/0.48  thf(fact_1235_power__one,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( power_power_int @ one_one_int @ N )
% 0.26/0.48        = one_one_int ) ).
% 0.26/0.48  
% 0.26/0.48  % power_one
% 0.26/0.48  thf(fact_1236_power__one,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( power_power_real @ one_one_real @ N )
% 0.26/0.48        = one_one_real ) ).
% 0.26/0.48  
% 0.26/0.48  % power_one
% 0.26/0.48  thf(fact_1237_power__one,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( power_power_complex @ one_one_complex @ N )
% 0.26/0.48        = one_one_complex ) ).
% 0.26/0.48  
% 0.26/0.48  % power_one
% 0.26/0.48  thf(fact_1238_of__nat__eq__1__iff,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ( semiri8010041392384452111omplex @ N )
% 0.26/0.48          = one_one_complex )
% 0.26/0.48        = ( N = one_one_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_eq_1_iff
% 0.26/0.48  thf(fact_1239_of__nat__eq__1__iff,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ( semiri5074537144036343181t_real @ N )
% 0.26/0.48          = one_one_real )
% 0.26/0.48        = ( N = one_one_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_eq_1_iff
% 0.26/0.48  thf(fact_1240_of__nat__eq__1__iff,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ( semiri681578069525770553at_rat @ N )
% 0.26/0.48          = one_one_rat )
% 0.26/0.48        = ( N = one_one_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_eq_1_iff
% 0.26/0.48  thf(fact_1241_of__nat__eq__1__iff,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ( semiri1316708129612266289at_nat @ N )
% 0.26/0.48          = one_one_nat )
% 0.26/0.48        = ( N = one_one_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_eq_1_iff
% 0.26/0.48  thf(fact_1242_of__nat__eq__1__iff,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ( semiri1314217659103216013at_int @ N )
% 0.26/0.48          = one_one_int )
% 0.26/0.48        = ( N = one_one_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_eq_1_iff
% 0.26/0.48  thf(fact_1243_of__nat__1__eq__iff,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( one_one_complex
% 0.26/0.48          = ( semiri8010041392384452111omplex @ N ) )
% 0.26/0.48        = ( N = one_one_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_1_eq_iff
% 0.26/0.48  thf(fact_1244_of__nat__1__eq__iff,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( one_one_real
% 0.26/0.48          = ( semiri5074537144036343181t_real @ N ) )
% 0.26/0.48        = ( N = one_one_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_1_eq_iff
% 0.26/0.48  thf(fact_1245_of__nat__1__eq__iff,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( one_one_rat
% 0.26/0.48          = ( semiri681578069525770553at_rat @ N ) )
% 0.26/0.48        = ( N = one_one_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_1_eq_iff
% 0.26/0.48  thf(fact_1246_of__nat__1__eq__iff,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( one_one_nat
% 0.26/0.48          = ( semiri1316708129612266289at_nat @ N ) )
% 0.26/0.48        = ( N = one_one_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_1_eq_iff
% 0.26/0.48  thf(fact_1247_of__nat__1__eq__iff,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( one_one_int
% 0.26/0.48          = ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.48        = ( N = one_one_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_1_eq_iff
% 0.26/0.48  thf(fact_1248_of__nat__1,axiom,
% 0.26/0.48      ( ( semiri8010041392384452111omplex @ one_one_nat )
% 0.26/0.48      = one_one_complex ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_1
% 0.26/0.48  thf(fact_1249_of__nat__1,axiom,
% 0.26/0.48      ( ( semiri5074537144036343181t_real @ one_one_nat )
% 0.26/0.48      = one_one_real ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_1
% 0.26/0.48  thf(fact_1250_of__nat__1,axiom,
% 0.26/0.48      ( ( semiri681578069525770553at_rat @ one_one_nat )
% 0.26/0.48      = one_one_rat ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_1
% 0.26/0.48  thf(fact_1251_of__nat__1,axiom,
% 0.26/0.48      ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 0.26/0.48      = one_one_nat ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_1
% 0.26/0.48  thf(fact_1252_of__nat__1,axiom,
% 0.26/0.48      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 0.26/0.48      = one_one_int ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_1
% 0.26/0.48  thf(fact_1253_less__one,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ord_less_nat @ N @ one_one_nat )
% 0.26/0.48        = ( N = zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % less_one
% 0.26/0.48  thf(fact_1254_of__int__1,axiom,
% 0.26/0.48      ( ( ring_1_of_int_int @ one_one_int )
% 0.26/0.48      = one_one_int ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_1
% 0.26/0.48  thf(fact_1255_of__int__1,axiom,
% 0.26/0.48      ( ( ring_1_of_int_real @ one_one_int )
% 0.26/0.48      = one_one_real ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_1
% 0.26/0.48  thf(fact_1256_of__int__1,axiom,
% 0.26/0.48      ( ( ring_17405671764205052669omplex @ one_one_int )
% 0.26/0.48      = one_one_complex ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_1
% 0.26/0.48  thf(fact_1257_of__int__1,axiom,
% 0.26/0.48      ( ( ring_1_of_int_rat @ one_one_int )
% 0.26/0.48      = one_one_rat ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_1
% 0.26/0.48  thf(fact_1258_of__int__eq__1__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ( ring_1_of_int_int @ Z )
% 0.26/0.48          = one_one_int )
% 0.26/0.48        = ( Z = one_one_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_1_iff
% 0.26/0.48  thf(fact_1259_of__int__eq__1__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ( ring_1_of_int_real @ Z )
% 0.26/0.48          = one_one_real )
% 0.26/0.48        = ( Z = one_one_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_1_iff
% 0.26/0.48  thf(fact_1260_of__int__eq__1__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ( ring_17405671764205052669omplex @ Z )
% 0.26/0.48          = one_one_complex )
% 0.26/0.48        = ( Z = one_one_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_1_iff
% 0.26/0.48  thf(fact_1261_of__int__eq__1__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ( ring_1_of_int_rat @ Z )
% 0.26/0.48          = one_one_rat )
% 0.26/0.48        = ( Z = one_one_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_eq_1_iff
% 0.26/0.48  thf(fact_1262_take__bit__of__0,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( bit_se2923211474154528505it_int @ N @ zero_zero_int )
% 0.26/0.48        = zero_zero_int ) ).
% 0.26/0.48  
% 0.26/0.48  % take_bit_of_0
% 0.26/0.48  thf(fact_1263_take__bit__of__0,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( bit_se2925701944663578781it_nat @ N @ zero_zero_nat )
% 0.26/0.48        = zero_zero_nat ) ).
% 0.26/0.48  
% 0.26/0.48  % take_bit_of_0
% 0.26/0.48  thf(fact_1264_or_Oright__neutral,axiom,
% 0.26/0.48      ! [A: int] :
% 0.26/0.48        ( ( bit_se1409905431419307370or_int @ A @ zero_zero_int )
% 0.26/0.48        = A ) ).
% 0.26/0.48  
% 0.26/0.48  % or.right_neutral
% 0.26/0.48  thf(fact_1265_or_Oright__neutral,axiom,
% 0.26/0.48      ! [A: nat] :
% 0.26/0.48        ( ( bit_se1412395901928357646or_nat @ A @ zero_zero_nat )
% 0.26/0.48        = A ) ).
% 0.26/0.48  
% 0.26/0.48  % or.right_neutral
% 0.26/0.48  thf(fact_1266_or_Oleft__neutral,axiom,
% 0.26/0.48      ! [A: int] :
% 0.26/0.48        ( ( bit_se1409905431419307370or_int @ zero_zero_int @ A )
% 0.26/0.48        = A ) ).
% 0.26/0.48  
% 0.26/0.48  % or.left_neutral
% 0.26/0.48  thf(fact_1267_or_Oleft__neutral,axiom,
% 0.26/0.48      ! [A: nat] :
% 0.26/0.48        ( ( bit_se1412395901928357646or_nat @ zero_zero_nat @ A )
% 0.26/0.48        = A ) ).
% 0.26/0.48  
% 0.26/0.48  % or.left_neutral
% 0.26/0.48  thf(fact_1268_xor_Oright__neutral,axiom,
% 0.26/0.48      ! [A: int] :
% 0.26/0.48        ( ( bit_se6526347334894502574or_int @ A @ zero_zero_int )
% 0.26/0.48        = A ) ).
% 0.26/0.48  
% 0.26/0.48  % xor.right_neutral
% 0.26/0.48  thf(fact_1269_xor_Oright__neutral,axiom,
% 0.26/0.48      ! [A: nat] :
% 0.26/0.48        ( ( bit_se6528837805403552850or_nat @ A @ zero_zero_nat )
% 0.26/0.48        = A ) ).
% 0.26/0.48  
% 0.26/0.48  % xor.right_neutral
% 0.26/0.48  thf(fact_1270_xor_Oleft__neutral,axiom,
% 0.26/0.48      ! [A: int] :
% 0.26/0.48        ( ( bit_se6526347334894502574or_int @ zero_zero_int @ A )
% 0.26/0.48        = A ) ).
% 0.26/0.48  
% 0.26/0.48  % xor.left_neutral
% 0.26/0.48  thf(fact_1271_xor_Oleft__neutral,axiom,
% 0.26/0.48      ! [A: nat] :
% 0.26/0.48        ( ( bit_se6528837805403552850or_nat @ zero_zero_nat @ A )
% 0.26/0.48        = A ) ).
% 0.26/0.48  
% 0.26/0.48  % xor.left_neutral
% 0.26/0.48  thf(fact_1272_xor__self__eq,axiom,
% 0.26/0.48      ! [A: int] :
% 0.26/0.48        ( ( bit_se6526347334894502574or_int @ A @ A )
% 0.26/0.48        = zero_zero_int ) ).
% 0.26/0.48  
% 0.26/0.48  % xor_self_eq
% 0.26/0.48  thf(fact_1273_xor__self__eq,axiom,
% 0.26/0.48      ! [A: nat] :
% 0.26/0.48        ( ( bit_se6528837805403552850or_nat @ A @ A )
% 0.26/0.48        = zero_zero_nat ) ).
% 0.26/0.48  
% 0.26/0.48  % xor_self_eq
% 0.26/0.48  thf(fact_1274_bit_Oxor__self,axiom,
% 0.26/0.48      ! [X3: int] :
% 0.26/0.48        ( ( bit_se6526347334894502574or_int @ X3 @ X3 )
% 0.26/0.48        = zero_zero_int ) ).
% 0.26/0.48  
% 0.26/0.48  % bit.xor_self
% 0.26/0.48  thf(fact_1275_real__sqrt__zero,axiom,
% 0.26/0.48      ( ( sqrt @ zero_zero_real )
% 0.26/0.48      = zero_zero_real ) ).
% 0.26/0.48  
% 0.26/0.48  % real_sqrt_zero
% 0.26/0.48  thf(fact_1276_real__sqrt__eq__zero__cancel__iff,axiom,
% 0.26/0.48      ! [X3: real] :
% 0.26/0.48        ( ( ( sqrt @ X3 )
% 0.26/0.48          = zero_zero_real )
% 0.26/0.48        = ( X3 = zero_zero_real ) ) ).
% 0.26/0.48  
% 0.26/0.48  % real_sqrt_eq_zero_cancel_iff
% 0.26/0.48  thf(fact_1277_real__sqrt__lt__1__iff,axiom,
% 0.26/0.48      ! [X3: real] :
% 0.26/0.48        ( ( ord_less_real @ ( sqrt @ X3 ) @ one_one_real )
% 0.26/0.48        = ( ord_less_real @ X3 @ one_one_real ) ) ).
% 0.26/0.48  
% 0.26/0.48  % real_sqrt_lt_1_iff
% 0.26/0.48  thf(fact_1278_real__sqrt__gt__1__iff,axiom,
% 0.26/0.48      ! [Y3: real] :
% 0.26/0.48        ( ( ord_less_real @ one_one_real @ ( sqrt @ Y3 ) )
% 0.26/0.48        = ( ord_less_real @ one_one_real @ Y3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % real_sqrt_gt_1_iff
% 0.26/0.48  thf(fact_1279_real__sqrt__less__iff,axiom,
% 0.26/0.48      ! [X3: real,Y3: real] :
% 0.26/0.48        ( ( ord_less_real @ ( sqrt @ X3 ) @ ( sqrt @ Y3 ) )
% 0.26/0.48        = ( ord_less_real @ X3 @ Y3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % real_sqrt_less_iff
% 0.26/0.48  thf(fact_1280_real__sqrt__ge__1__iff,axiom,
% 0.26/0.48      ! [Y3: real] :
% 0.26/0.48        ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y3 ) )
% 0.26/0.48        = ( ord_less_eq_real @ one_one_real @ Y3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % real_sqrt_ge_1_iff
% 0.26/0.48  thf(fact_1281_real__sqrt__le__1__iff,axiom,
% 0.26/0.48      ! [X3: real] :
% 0.26/0.48        ( ( ord_less_eq_real @ ( sqrt @ X3 ) @ one_one_real )
% 0.26/0.48        = ( ord_less_eq_real @ X3 @ one_one_real ) ) ).
% 0.26/0.48  
% 0.26/0.48  % real_sqrt_le_1_iff
% 0.26/0.48  thf(fact_1282_real__sqrt__le__iff,axiom,
% 0.26/0.48      ! [X3: real,Y3: real] :
% 0.26/0.48        ( ( ord_less_eq_real @ ( sqrt @ X3 ) @ ( sqrt @ Y3 ) )
% 0.26/0.48        = ( ord_less_eq_real @ X3 @ Y3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % real_sqrt_le_iff
% 0.26/0.48  thf(fact_1283_log__one,axiom,
% 0.26/0.48      ! [A: real] :
% 0.26/0.48        ( ( log @ A @ one_one_real )
% 0.26/0.48        = zero_zero_real ) ).
% 0.26/0.48  
% 0.26/0.48  % log_one
% 0.26/0.48  thf(fact_1284_take__bit__or,axiom,
% 0.26/0.48      ! [N: nat,A: int,B: int] :
% 0.26/0.48        ( ( bit_se2923211474154528505it_int @ N @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 0.26/0.48        = ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % take_bit_or
% 0.26/0.48  thf(fact_1285_take__bit__or,axiom,
% 0.26/0.48      ! [N: nat,A: nat,B: nat] :
% 0.26/0.48        ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 0.26/0.48        = ( bit_se1412395901928357646or_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % take_bit_or
% 0.26/0.48  thf(fact_1286_take__bit__xor,axiom,
% 0.26/0.48      ! [N: nat,A: int,B: int] :
% 0.26/0.48        ( ( bit_se2923211474154528505it_int @ N @ ( bit_se6526347334894502574or_int @ A @ B ) )
% 0.26/0.48        = ( bit_se6526347334894502574or_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % take_bit_xor
% 0.26/0.48  thf(fact_1287_take__bit__xor,axiom,
% 0.26/0.48      ! [N: nat,A: nat,B: nat] :
% 0.26/0.48        ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se6528837805403552850or_nat @ A @ B ) )
% 0.26/0.48        = ( bit_se6528837805403552850or_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % take_bit_xor
% 0.26/0.48  thf(fact_1288_numeral__eq__one__iff,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( ( ( numera6690914467698888265omplex @ N )
% 0.26/0.48          = one_one_complex )
% 0.26/0.48        = ( N = one ) ) ).
% 0.26/0.48  
% 0.26/0.48  % numeral_eq_one_iff
% 0.26/0.48  thf(fact_1289_numeral__eq__one__iff,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( ( ( numeral_numeral_real @ N )
% 0.26/0.48          = one_one_real )
% 0.26/0.48        = ( N = one ) ) ).
% 0.26/0.48  
% 0.26/0.48  % numeral_eq_one_iff
% 0.26/0.48  thf(fact_1290_numeral__eq__one__iff,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( ( ( numeral_numeral_rat @ N )
% 0.26/0.48          = one_one_rat )
% 0.26/0.48        = ( N = one ) ) ).
% 0.26/0.48  
% 0.26/0.48  % numeral_eq_one_iff
% 0.26/0.48  thf(fact_1291_numeral__eq__one__iff,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( ( ( numeral_numeral_nat @ N )
% 0.26/0.48          = one_one_nat )
% 0.26/0.48        = ( N = one ) ) ).
% 0.26/0.48  
% 0.26/0.48  % numeral_eq_one_iff
% 0.26/0.48  thf(fact_1292_numeral__eq__one__iff,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( ( ( numeral_numeral_int @ N )
% 0.26/0.48          = one_one_int )
% 0.26/0.48        = ( N = one ) ) ).
% 0.26/0.48  
% 0.26/0.48  % numeral_eq_one_iff
% 0.26/0.48  thf(fact_1293_one__eq__numeral__iff,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( ( one_one_complex
% 0.26/0.48          = ( numera6690914467698888265omplex @ N ) )
% 0.26/0.48        = ( one = N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % one_eq_numeral_iff
% 0.26/0.48  thf(fact_1294_one__eq__numeral__iff,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( ( one_one_real
% 0.26/0.48          = ( numeral_numeral_real @ N ) )
% 0.26/0.48        = ( one = N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % one_eq_numeral_iff
% 0.26/0.48  thf(fact_1295_one__eq__numeral__iff,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( ( one_one_rat
% 0.26/0.48          = ( numeral_numeral_rat @ N ) )
% 0.26/0.48        = ( one = N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % one_eq_numeral_iff
% 0.26/0.48  thf(fact_1296_one__eq__numeral__iff,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( ( one_one_nat
% 0.26/0.48          = ( numeral_numeral_nat @ N ) )
% 0.26/0.48        = ( one = N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % one_eq_numeral_iff
% 0.26/0.48  thf(fact_1297_one__eq__numeral__iff,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( ( one_one_int
% 0.26/0.48          = ( numeral_numeral_int @ N ) )
% 0.26/0.48        = ( one = N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % one_eq_numeral_iff
% 0.26/0.48  thf(fact_1298_power__inject__exp,axiom,
% 0.26/0.48      ! [A: real,M: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_real @ one_one_real @ A )
% 0.26/0.48       => ( ( ( power_power_real @ A @ M )
% 0.26/0.48            = ( power_power_real @ A @ N ) )
% 0.26/0.48          = ( M = N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_inject_exp
% 0.26/0.48  thf(fact_1299_power__inject__exp,axiom,
% 0.26/0.48      ! [A: rat,M: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_rat @ one_one_rat @ A )
% 0.26/0.48       => ( ( ( power_power_rat @ A @ M )
% 0.26/0.48            = ( power_power_rat @ A @ N ) )
% 0.26/0.48          = ( M = N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_inject_exp
% 0.26/0.48  thf(fact_1300_power__inject__exp,axiom,
% 0.26/0.48      ! [A: nat,M: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_nat @ one_one_nat @ A )
% 0.26/0.48       => ( ( ( power_power_nat @ A @ M )
% 0.26/0.48            = ( power_power_nat @ A @ N ) )
% 0.26/0.48          = ( M = N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_inject_exp
% 0.26/0.48  thf(fact_1301_power__inject__exp,axiom,
% 0.26/0.48      ! [A: int,M: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_int @ one_one_int @ A )
% 0.26/0.48       => ( ( ( power_power_int @ A @ M )
% 0.26/0.48            = ( power_power_int @ A @ N ) )
% 0.26/0.48          = ( M = N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_inject_exp
% 0.26/0.48  thf(fact_1302_take__bit__0,axiom,
% 0.26/0.48      ! [A: int] :
% 0.26/0.48        ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 0.26/0.48        = zero_zero_int ) ).
% 0.26/0.48  
% 0.26/0.48  % take_bit_0
% 0.26/0.48  thf(fact_1303_take__bit__0,axiom,
% 0.26/0.48      ! [A: nat] :
% 0.26/0.48        ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 0.26/0.48        = zero_zero_nat ) ).
% 0.26/0.48  
% 0.26/0.48  % take_bit_0
% 0.26/0.48  thf(fact_1304_take__bit__numeral__1,axiom,
% 0.26/0.48      ! [L: num] :
% 0.26/0.48        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ one_one_int )
% 0.26/0.48        = one_one_int ) ).
% 0.26/0.48  
% 0.26/0.48  % take_bit_numeral_1
% 0.26/0.48  thf(fact_1305_take__bit__numeral__1,axiom,
% 0.26/0.48      ! [L: num] :
% 0.26/0.48        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ one_one_nat )
% 0.26/0.48        = one_one_nat ) ).
% 0.26/0.48  
% 0.26/0.48  % take_bit_numeral_1
% 0.26/0.48  thf(fact_1306_real__sqrt__gt__0__iff,axiom,
% 0.26/0.48      ! [Y3: real] :
% 0.26/0.48        ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y3 ) )
% 0.26/0.48        = ( ord_less_real @ zero_zero_real @ Y3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % real_sqrt_gt_0_iff
% 0.26/0.48  thf(fact_1307_real__sqrt__lt__0__iff,axiom,
% 0.26/0.48      ! [X3: real] :
% 0.26/0.48        ( ( ord_less_real @ ( sqrt @ X3 ) @ zero_zero_real )
% 0.26/0.48        = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 0.26/0.48  
% 0.26/0.48  % real_sqrt_lt_0_iff
% 0.26/0.48  thf(fact_1308_real__sqrt__ge__0__iff,axiom,
% 0.26/0.48      ! [Y3: real] :
% 0.26/0.48        ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y3 ) )
% 0.26/0.48        = ( ord_less_eq_real @ zero_zero_real @ Y3 ) ) ).
% 0.26/0.48  
% 0.26/0.48  % real_sqrt_ge_0_iff
% 0.26/0.48  thf(fact_1309_real__sqrt__le__0__iff,axiom,
% 0.26/0.48      ! [X3: real] :
% 0.26/0.48        ( ( ord_less_eq_real @ ( sqrt @ X3 ) @ zero_zero_real )
% 0.26/0.48        = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ).
% 0.26/0.48  
% 0.26/0.48  % real_sqrt_le_0_iff
% 0.26/0.48  thf(fact_1310_zero__less__log__cancel__iff,axiom,
% 0.26/0.48      ! [A: real,X3: real] :
% 0.26/0.48        ( ( ord_less_real @ one_one_real @ A )
% 0.26/0.48       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.48         => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X3 ) )
% 0.26/0.48            = ( ord_less_real @ one_one_real @ X3 ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_less_log_cancel_iff
% 0.26/0.48  thf(fact_1311_log__less__zero__cancel__iff,axiom,
% 0.26/0.48      ! [A: real,X3: real] :
% 0.26/0.48        ( ( ord_less_real @ one_one_real @ A )
% 0.26/0.48       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.48         => ( ( ord_less_real @ ( log @ A @ X3 ) @ zero_zero_real )
% 0.26/0.48            = ( ord_less_real @ X3 @ one_one_real ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % log_less_zero_cancel_iff
% 0.26/0.48  thf(fact_1312_one__less__log__cancel__iff,axiom,
% 0.26/0.48      ! [A: real,X3: real] :
% 0.26/0.48        ( ( ord_less_real @ one_one_real @ A )
% 0.26/0.48       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.48         => ( ( ord_less_real @ one_one_real @ ( log @ A @ X3 ) )
% 0.26/0.48            = ( ord_less_real @ A @ X3 ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % one_less_log_cancel_iff
% 0.26/0.48  thf(fact_1313_log__less__one__cancel__iff,axiom,
% 0.26/0.48      ! [A: real,X3: real] :
% 0.26/0.48        ( ( ord_less_real @ one_one_real @ A )
% 0.26/0.48       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.48         => ( ( ord_less_real @ ( log @ A @ X3 ) @ one_one_real )
% 0.26/0.48            = ( ord_less_real @ X3 @ A ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % log_less_one_cancel_iff
% 0.26/0.48  thf(fact_1314_log__less__cancel__iff,axiom,
% 0.26/0.48      ! [A: real,X3: real,Y3: real] :
% 0.26/0.48        ( ( ord_less_real @ one_one_real @ A )
% 0.26/0.48       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.48         => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.48           => ( ( ord_less_real @ ( log @ A @ X3 ) @ ( log @ A @ Y3 ) )
% 0.26/0.48              = ( ord_less_real @ X3 @ Y3 ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % log_less_cancel_iff
% 0.26/0.48  thf(fact_1315_log__eq__one,axiom,
% 0.26/0.48      ! [A: real] :
% 0.26/0.48        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.48       => ( ( A != one_one_real )
% 0.26/0.48         => ( ( log @ A @ A )
% 0.26/0.48            = one_one_real ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % log_eq_one
% 0.26/0.48  thf(fact_1316_or__nonnegative__int__iff,axiom,
% 0.26/0.48      ! [K: int,L: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 0.26/0.48        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.26/0.48          & ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % or_nonnegative_int_iff
% 0.26/0.48  thf(fact_1317_or__negative__int__iff,axiom,
% 0.26/0.48      ! [K: int,L: int] :
% 0.26/0.48        ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ zero_zero_int )
% 0.26/0.48        = ( ( ord_less_int @ K @ zero_zero_int )
% 0.26/0.48          | ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % or_negative_int_iff
% 0.26/0.48  thf(fact_1318_xor__nonnegative__int__iff,axiom,
% 0.26/0.48      ! [K: int,L: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 0.26/0.48        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.26/0.48          = ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % xor_nonnegative_int_iff
% 0.26/0.48  thf(fact_1319_xor__negative__int__iff,axiom,
% 0.26/0.48      ! [K: int,L: int] :
% 0.26/0.48        ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ zero_zero_int )
% 0.26/0.48        = ( ( ord_less_int @ K @ zero_zero_int )
% 0.26/0.48         != ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % xor_negative_int_iff
% 0.26/0.48  thf(fact_1320_power__strict__increasing__iff,axiom,
% 0.26/0.48      ! [B: real,X3: nat,Y3: nat] :
% 0.26/0.48        ( ( ord_less_real @ one_one_real @ B )
% 0.26/0.48       => ( ( ord_less_real @ ( power_power_real @ B @ X3 ) @ ( power_power_real @ B @ Y3 ) )
% 0.26/0.48          = ( ord_less_nat @ X3 @ Y3 ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_strict_increasing_iff
% 0.26/0.48  thf(fact_1321_power__strict__increasing__iff,axiom,
% 0.26/0.48      ! [B: rat,X3: nat,Y3: nat] :
% 0.26/0.48        ( ( ord_less_rat @ one_one_rat @ B )
% 0.26/0.48       => ( ( ord_less_rat @ ( power_power_rat @ B @ X3 ) @ ( power_power_rat @ B @ Y3 ) )
% 0.26/0.48          = ( ord_less_nat @ X3 @ Y3 ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_strict_increasing_iff
% 0.26/0.48  thf(fact_1322_power__strict__increasing__iff,axiom,
% 0.26/0.48      ! [B: nat,X3: nat,Y3: nat] :
% 0.26/0.48        ( ( ord_less_nat @ one_one_nat @ B )
% 0.26/0.48       => ( ( ord_less_nat @ ( power_power_nat @ B @ X3 ) @ ( power_power_nat @ B @ Y3 ) )
% 0.26/0.48          = ( ord_less_nat @ X3 @ Y3 ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_strict_increasing_iff
% 0.26/0.48  thf(fact_1323_power__strict__increasing__iff,axiom,
% 0.26/0.48      ! [B: int,X3: nat,Y3: nat] :
% 0.26/0.48        ( ( ord_less_int @ one_one_int @ B )
% 0.26/0.48       => ( ( ord_less_int @ ( power_power_int @ B @ X3 ) @ ( power_power_int @ B @ Y3 ) )
% 0.26/0.48          = ( ord_less_nat @ X3 @ Y3 ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_strict_increasing_iff
% 0.26/0.48  thf(fact_1324_take__bit__of__1__eq__0__iff,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 0.26/0.48          = zero_zero_int )
% 0.26/0.48        = ( N = zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % take_bit_of_1_eq_0_iff
% 0.26/0.48  thf(fact_1325_take__bit__of__1__eq__0__iff,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 0.26/0.48          = zero_zero_nat )
% 0.26/0.48        = ( N = zero_zero_nat ) ) ).
% 0.26/0.48  
% 0.26/0.48  % take_bit_of_1_eq_0_iff
% 0.26/0.48  thf(fact_1326_of__int__le__1__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 0.26/0.48        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_le_1_iff
% 0.26/0.48  thf(fact_1327_of__int__le__1__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 0.26/0.48        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_le_1_iff
% 0.26/0.48  thf(fact_1328_of__int__le__1__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 0.26/0.48        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_le_1_iff
% 0.26/0.48  thf(fact_1329_of__int__1__le__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 0.26/0.48        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_1_le_iff
% 0.26/0.48  thf(fact_1330_of__int__1__le__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.26/0.48        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_1_le_iff
% 0.26/0.48  thf(fact_1331_of__int__1__le__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 0.26/0.48        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_1_le_iff
% 0.26/0.48  thf(fact_1332_of__int__less__1__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 0.26/0.48        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_less_1_iff
% 0.26/0.48  thf(fact_1333_of__int__less__1__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 0.26/0.48        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_less_1_iff
% 0.26/0.48  thf(fact_1334_of__int__less__1__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 0.26/0.48        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_less_1_iff
% 0.26/0.48  thf(fact_1335_of__int__1__less__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 0.26/0.48        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_1_less_iff
% 0.26/0.48  thf(fact_1336_of__int__1__less__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.26/0.48        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_1_less_iff
% 0.26/0.48  thf(fact_1337_of__int__1__less__iff,axiom,
% 0.26/0.48      ! [Z: int] :
% 0.26/0.48        ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 0.26/0.48        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_int_1_less_iff
% 0.26/0.48  thf(fact_1338_real__sqrt__four,axiom,
% 0.26/0.48      ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.26/0.48      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % real_sqrt_four
% 0.26/0.48  thf(fact_1339_zero__le__log__cancel__iff,axiom,
% 0.26/0.48      ! [A: real,X3: real] :
% 0.26/0.48        ( ( ord_less_real @ one_one_real @ A )
% 0.26/0.48       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.48         => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X3 ) )
% 0.26/0.48            = ( ord_less_eq_real @ one_one_real @ X3 ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_le_log_cancel_iff
% 0.26/0.48  thf(fact_1340_log__le__zero__cancel__iff,axiom,
% 0.26/0.48      ! [A: real,X3: real] :
% 0.26/0.48        ( ( ord_less_real @ one_one_real @ A )
% 0.26/0.48       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.48         => ( ( ord_less_eq_real @ ( log @ A @ X3 ) @ zero_zero_real )
% 0.26/0.48            = ( ord_less_eq_real @ X3 @ one_one_real ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % log_le_zero_cancel_iff
% 0.26/0.48  thf(fact_1341_one__le__log__cancel__iff,axiom,
% 0.26/0.48      ! [A: real,X3: real] :
% 0.26/0.48        ( ( ord_less_real @ one_one_real @ A )
% 0.26/0.48       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.48         => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X3 ) )
% 0.26/0.48            = ( ord_less_eq_real @ A @ X3 ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % one_le_log_cancel_iff
% 0.26/0.48  thf(fact_1342_log__le__one__cancel__iff,axiom,
% 0.26/0.48      ! [A: real,X3: real] :
% 0.26/0.48        ( ( ord_less_real @ one_one_real @ A )
% 0.26/0.48       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.48         => ( ( ord_less_eq_real @ ( log @ A @ X3 ) @ one_one_real )
% 0.26/0.48            = ( ord_less_eq_real @ X3 @ A ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % log_le_one_cancel_iff
% 0.26/0.48  thf(fact_1343_log__le__cancel__iff,axiom,
% 0.26/0.48      ! [A: real,X3: real,Y3: real] :
% 0.26/0.48        ( ( ord_less_real @ one_one_real @ A )
% 0.26/0.48       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.48         => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.48           => ( ( ord_less_eq_real @ ( log @ A @ X3 ) @ ( log @ A @ Y3 ) )
% 0.26/0.48              = ( ord_less_eq_real @ X3 @ Y3 ) ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % log_le_cancel_iff
% 0.26/0.48  thf(fact_1344_of__nat__nat__take__bit__eq,axiom,
% 0.26/0.48      ! [N: nat,K: int] :
% 0.26/0.48        ( ( semiri8010041392384452111omplex @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 0.26/0.48        = ( ring_17405671764205052669omplex @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_nat_take_bit_eq
% 0.26/0.48  thf(fact_1345_of__nat__nat__take__bit__eq,axiom,
% 0.26/0.48      ! [N: nat,K: int] :
% 0.26/0.48        ( ( semiri5074537144036343181t_real @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 0.26/0.48        = ( ring_1_of_int_real @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_nat_take_bit_eq
% 0.26/0.48  thf(fact_1346_of__nat__nat__take__bit__eq,axiom,
% 0.26/0.48      ! [N: nat,K: int] :
% 0.26/0.48        ( ( semiri681578069525770553at_rat @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 0.26/0.48        = ( ring_1_of_int_rat @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_nat_take_bit_eq
% 0.26/0.48  thf(fact_1347_of__nat__nat__take__bit__eq,axiom,
% 0.26/0.48      ! [N: nat,K: int] :
% 0.26/0.48        ( ( semiri1314217659103216013at_int @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 0.26/0.48        = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % of_nat_nat_take_bit_eq
% 0.26/0.48  thf(fact_1348_power__strict__decreasing__iff,axiom,
% 0.26/0.48      ! [B: real,M: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_real @ zero_zero_real @ B )
% 0.26/0.48       => ( ( ord_less_real @ B @ one_one_real )
% 0.26/0.48         => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 0.26/0.48            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_strict_decreasing_iff
% 0.26/0.48  thf(fact_1349_power__strict__decreasing__iff,axiom,
% 0.26/0.48      ! [B: rat,M: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.26/0.48       => ( ( ord_less_rat @ B @ one_one_rat )
% 0.26/0.48         => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 0.26/0.48            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_strict_decreasing_iff
% 0.26/0.48  thf(fact_1350_power__strict__decreasing__iff,axiom,
% 0.26/0.48      ! [B: nat,M: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.26/0.48       => ( ( ord_less_nat @ B @ one_one_nat )
% 0.26/0.48         => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 0.26/0.48            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_strict_decreasing_iff
% 0.26/0.48  thf(fact_1351_power__strict__decreasing__iff,axiom,
% 0.26/0.48      ! [B: int,M: nat,N: nat] :
% 0.26/0.48        ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.48       => ( ( ord_less_int @ B @ one_one_int )
% 0.26/0.48         => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 0.26/0.48            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_strict_decreasing_iff
% 0.26/0.48  thf(fact_1352_power__increasing__iff,axiom,
% 0.26/0.48      ! [B: real,X3: nat,Y3: nat] :
% 0.26/0.48        ( ( ord_less_real @ one_one_real @ B )
% 0.26/0.48       => ( ( ord_less_eq_real @ ( power_power_real @ B @ X3 ) @ ( power_power_real @ B @ Y3 ) )
% 0.26/0.48          = ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_increasing_iff
% 0.26/0.48  thf(fact_1353_power__increasing__iff,axiom,
% 0.26/0.48      ! [B: rat,X3: nat,Y3: nat] :
% 0.26/0.48        ( ( ord_less_rat @ one_one_rat @ B )
% 0.26/0.48       => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X3 ) @ ( power_power_rat @ B @ Y3 ) )
% 0.26/0.48          = ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_increasing_iff
% 0.26/0.48  thf(fact_1354_power__increasing__iff,axiom,
% 0.26/0.48      ! [B: nat,X3: nat,Y3: nat] :
% 0.26/0.48        ( ( ord_less_nat @ one_one_nat @ B )
% 0.26/0.48       => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X3 ) @ ( power_power_nat @ B @ Y3 ) )
% 0.26/0.48          = ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_increasing_iff
% 0.26/0.48  thf(fact_1355_power__increasing__iff,axiom,
% 0.26/0.48      ! [B: int,X3: nat,Y3: nat] :
% 0.26/0.48        ( ( ord_less_int @ one_one_int @ B )
% 0.26/0.48       => ( ( ord_less_eq_int @ ( power_power_int @ B @ X3 ) @ ( power_power_int @ B @ Y3 ) )
% 0.26/0.48          = ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_increasing_iff
% 0.26/0.48  thf(fact_1356_numeral__le__one__iff,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 0.26/0.48        = ( ord_less_eq_num @ N @ one ) ) ).
% 0.26/0.48  
% 0.26/0.48  % numeral_le_one_iff
% 0.26/0.48  thf(fact_1357_numeral__le__one__iff,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 0.26/0.48        = ( ord_less_eq_num @ N @ one ) ) ).
% 0.26/0.48  
% 0.26/0.48  % numeral_le_one_iff
% 0.26/0.48  thf(fact_1358_numeral__le__one__iff,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 0.26/0.48        = ( ord_less_eq_num @ N @ one ) ) ).
% 0.26/0.48  
% 0.26/0.48  % numeral_le_one_iff
% 0.26/0.48  thf(fact_1359_numeral__le__one__iff,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 0.26/0.48        = ( ord_less_eq_num @ N @ one ) ) ).
% 0.26/0.48  
% 0.26/0.48  % numeral_le_one_iff
% 0.26/0.48  thf(fact_1360_one__less__numeral__iff,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 0.26/0.48        = ( ord_less_num @ one @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % one_less_numeral_iff
% 0.26/0.48  thf(fact_1361_one__less__numeral__iff,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 0.26/0.48        = ( ord_less_num @ one @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % one_less_numeral_iff
% 0.26/0.48  thf(fact_1362_one__less__numeral__iff,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 0.26/0.48        = ( ord_less_num @ one @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % one_less_numeral_iff
% 0.26/0.48  thf(fact_1363_one__less__numeral__iff,axiom,
% 0.26/0.48      ! [N: num] :
% 0.26/0.48        ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 0.26/0.48        = ( ord_less_num @ one @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % one_less_numeral_iff
% 0.26/0.48  thf(fact_1364_log__pow__cancel,axiom,
% 0.26/0.48      ! [A: real,B: nat] :
% 0.26/0.48        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.48       => ( ( A != one_one_real )
% 0.26/0.48         => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 0.26/0.48            = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % log_pow_cancel
% 0.26/0.48  thf(fact_1365_even__take__bit__eq,axiom,
% 0.26/0.48      ! [N: nat,A: code_integer] :
% 0.26/0.48        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N @ A ) )
% 0.26/0.48        = ( ( N = zero_zero_nat )
% 0.26/0.48          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % even_take_bit_eq
% 0.26/0.48  thf(fact_1366_even__take__bit__eq,axiom,
% 0.26/0.48      ! [N: nat,A: int] :
% 0.26/0.48        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 0.26/0.48        = ( ( N = zero_zero_nat )
% 0.26/0.48          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % even_take_bit_eq
% 0.26/0.48  thf(fact_1367_even__take__bit__eq,axiom,
% 0.26/0.48      ! [N: nat,A: nat] :
% 0.26/0.48        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N @ A ) )
% 0.26/0.48        = ( ( N = zero_zero_nat )
% 0.26/0.48          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % even_take_bit_eq
% 0.26/0.48  thf(fact_1368_even__power,axiom,
% 0.26/0.48      ! [A: code_integer,N: nat] :
% 0.26/0.48        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 0.26/0.48        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.48          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % even_power
% 0.26/0.48  thf(fact_1369_even__power,axiom,
% 0.26/0.48      ! [A: nat,N: nat] :
% 0.26/0.48        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N ) )
% 0.26/0.48        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.48          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % even_power
% 0.26/0.48  thf(fact_1370_even__power,axiom,
% 0.26/0.48      ! [A: int,N: nat] :
% 0.26/0.48        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N ) )
% 0.26/0.48        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.48          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % even_power
% 0.26/0.48  thf(fact_1371_zero__le__power__eq__numeral,axiom,
% 0.26/0.48      ! [A: real,W: num] :
% 0.26/0.48        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.26/0.48        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.48          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.48            & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_le_power_eq_numeral
% 0.26/0.48  thf(fact_1372_zero__le__power__eq__numeral,axiom,
% 0.26/0.48      ! [A: rat,W: num] :
% 0.26/0.48        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.26/0.48        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.48          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.48            & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_le_power_eq_numeral
% 0.26/0.48  thf(fact_1373_zero__le__power__eq__numeral,axiom,
% 0.26/0.48      ! [A: int,W: num] :
% 0.26/0.48        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.26/0.48        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.48          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.48            & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_le_power_eq_numeral
% 0.26/0.48  thf(fact_1374_power__less__zero__eq,axiom,
% 0.26/0.48      ! [A: real,N: nat] :
% 0.26/0.48        ( ( ord_less_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 0.26/0.48        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.48          & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_less_zero_eq
% 0.26/0.48  thf(fact_1375_power__less__zero__eq,axiom,
% 0.26/0.48      ! [A: rat,N: nat] :
% 0.26/0.48        ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 0.26/0.48        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.48          & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_less_zero_eq
% 0.26/0.48  thf(fact_1376_power__less__zero__eq,axiom,
% 0.26/0.48      ! [A: int,N: nat] :
% 0.26/0.48        ( ( ord_less_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 0.26/0.48        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.48          & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_less_zero_eq
% 0.26/0.48  thf(fact_1377_power__less__zero__eq__numeral,axiom,
% 0.26/0.48      ! [A: real,W: num] :
% 0.26/0.48        ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 0.26/0.48        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.48          & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_less_zero_eq_numeral
% 0.26/0.48  thf(fact_1378_power__less__zero__eq__numeral,axiom,
% 0.26/0.48      ! [A: rat,W: num] :
% 0.26/0.48        ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 0.26/0.48        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.48          & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_less_zero_eq_numeral
% 0.26/0.48  thf(fact_1379_power__less__zero__eq__numeral,axiom,
% 0.26/0.48      ! [A: int,W: num] :
% 0.26/0.48        ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 0.26/0.48        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.48          & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % power_less_zero_eq_numeral
% 0.26/0.48  thf(fact_1380_even__of__nat,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N ) )
% 0.26/0.48        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % even_of_nat
% 0.26/0.48  thf(fact_1381_even__of__nat,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.26/0.48        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % even_of_nat
% 0.26/0.48  thf(fact_1382_even__of__nat,axiom,
% 0.26/0.48      ! [N: nat] :
% 0.26/0.48        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.48        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.26/0.48  
% 0.26/0.48  % even_of_nat
% 0.26/0.48  thf(fact_1383_zero__less__power__eq__numeral,axiom,
% 0.26/0.48      ! [A: real,W: num] :
% 0.26/0.48        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.26/0.48        = ( ( ( numeral_numeral_nat @ W )
% 0.26/0.48            = zero_zero_nat )
% 0.26/0.48          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.48            & ( A != zero_zero_real ) )
% 0.26/0.48          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.48            & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 0.26/0.48  
% 0.26/0.48  % zero_less_power_eq_numeral
% 0.26/0.48  thf(fact_1384_zero__less__power__eq__numeral,axiom,
% 0.26/0.48      ! [A: rat,W: num] :
% 0.26/0.48        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.26/0.48        = ( ( ( numeral_numeral_nat @ W )
% 0.26/0.48            = zero_zero_nat )
% 0.26/0.48          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.48            & ( A != zero_zero_rat ) )
% 0.26/0.48          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.48            & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_less_power_eq_numeral
% 0.26/0.49  thf(fact_1385_zero__less__power__eq__numeral,axiom,
% 0.26/0.49      ! [A: int,W: num] :
% 0.26/0.49        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.26/0.49        = ( ( ( numeral_numeral_nat @ W )
% 0.26/0.49            = zero_zero_nat )
% 0.26/0.49          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.49            & ( A != zero_zero_int ) )
% 0.26/0.49          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.49            & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_less_power_eq_numeral
% 0.26/0.49  thf(fact_1386_or_Oassoc,axiom,
% 0.26/0.49      ! [A: int,B: int,C: int] :
% 0.26/0.49        ( ( bit_se1409905431419307370or_int @ ( bit_se1409905431419307370or_int @ A @ B ) @ C )
% 0.26/0.49        = ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ B @ C ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % or.assoc
% 0.26/0.49  thf(fact_1387_or_Oassoc,axiom,
% 0.26/0.49      ! [A: nat,B: nat,C: nat] :
% 0.26/0.49        ( ( bit_se1412395901928357646or_nat @ ( bit_se1412395901928357646or_nat @ A @ B ) @ C )
% 0.26/0.49        = ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ B @ C ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % or.assoc
% 0.26/0.49  thf(fact_1388_xor_Oassoc,axiom,
% 0.26/0.49      ! [A: int,B: int,C: int] :
% 0.26/0.49        ( ( bit_se6526347334894502574or_int @ ( bit_se6526347334894502574or_int @ A @ B ) @ C )
% 0.26/0.49        = ( bit_se6526347334894502574or_int @ A @ ( bit_se6526347334894502574or_int @ B @ C ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % xor.assoc
% 0.26/0.49  thf(fact_1389_xor_Oassoc,axiom,
% 0.26/0.49      ! [A: nat,B: nat,C: nat] :
% 0.26/0.49        ( ( bit_se6528837805403552850or_nat @ ( bit_se6528837805403552850or_nat @ A @ B ) @ C )
% 0.26/0.49        = ( bit_se6528837805403552850or_nat @ A @ ( bit_se6528837805403552850or_nat @ B @ C ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % xor.assoc
% 0.26/0.49  thf(fact_1390_or_Ocommute,axiom,
% 0.26/0.49      ( bit_se1409905431419307370or_int
% 0.26/0.49      = ( ^ [A4: int,B3: int] : ( bit_se1409905431419307370or_int @ B3 @ A4 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % or.commute
% 0.26/0.49  thf(fact_1391_or_Ocommute,axiom,
% 0.26/0.49      ( bit_se1412395901928357646or_nat
% 0.26/0.49      = ( ^ [A4: nat,B3: nat] : ( bit_se1412395901928357646or_nat @ B3 @ A4 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % or.commute
% 0.26/0.49  thf(fact_1392_xor_Ocommute,axiom,
% 0.26/0.49      ( bit_se6526347334894502574or_int
% 0.26/0.49      = ( ^ [A4: int,B3: int] : ( bit_se6526347334894502574or_int @ B3 @ A4 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % xor.commute
% 0.26/0.49  thf(fact_1393_xor_Ocommute,axiom,
% 0.26/0.49      ( bit_se6528837805403552850or_nat
% 0.26/0.49      = ( ^ [A4: nat,B3: nat] : ( bit_se6528837805403552850or_nat @ B3 @ A4 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % xor.commute
% 0.26/0.49  thf(fact_1394_or_Oleft__commute,axiom,
% 0.26/0.49      ! [B: int,A: int,C: int] :
% 0.26/0.49        ( ( bit_se1409905431419307370or_int @ B @ ( bit_se1409905431419307370or_int @ A @ C ) )
% 0.26/0.49        = ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ B @ C ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % or.left_commute
% 0.26/0.49  thf(fact_1395_or_Oleft__commute,axiom,
% 0.26/0.49      ! [B: nat,A: nat,C: nat] :
% 0.26/0.49        ( ( bit_se1412395901928357646or_nat @ B @ ( bit_se1412395901928357646or_nat @ A @ C ) )
% 0.26/0.49        = ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ B @ C ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % or.left_commute
% 0.26/0.49  thf(fact_1396_xor_Oleft__commute,axiom,
% 0.26/0.49      ! [B: int,A: int,C: int] :
% 0.26/0.49        ( ( bit_se6526347334894502574or_int @ B @ ( bit_se6526347334894502574or_int @ A @ C ) )
% 0.26/0.49        = ( bit_se6526347334894502574or_int @ A @ ( bit_se6526347334894502574or_int @ B @ C ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % xor.left_commute
% 0.26/0.49  thf(fact_1397_xor_Oleft__commute,axiom,
% 0.26/0.49      ! [B: nat,A: nat,C: nat] :
% 0.26/0.49        ( ( bit_se6528837805403552850or_nat @ B @ ( bit_se6528837805403552850or_nat @ A @ C ) )
% 0.26/0.49        = ( bit_se6528837805403552850or_nat @ A @ ( bit_se6528837805403552850or_nat @ B @ C ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % xor.left_commute
% 0.26/0.49  thf(fact_1398_one__reorient,axiom,
% 0.26/0.49      ! [X3: complex] :
% 0.26/0.49        ( ( one_one_complex = X3 )
% 0.26/0.49        = ( X3 = one_one_complex ) ) ).
% 0.26/0.49  
% 0.26/0.49  % one_reorient
% 0.26/0.49  thf(fact_1399_one__reorient,axiom,
% 0.26/0.49      ! [X3: real] :
% 0.26/0.49        ( ( one_one_real = X3 )
% 0.26/0.49        = ( X3 = one_one_real ) ) ).
% 0.26/0.49  
% 0.26/0.49  % one_reorient
% 0.26/0.49  thf(fact_1400_one__reorient,axiom,
% 0.26/0.49      ! [X3: rat] :
% 0.26/0.49        ( ( one_one_rat = X3 )
% 0.26/0.49        = ( X3 = one_one_rat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % one_reorient
% 0.26/0.49  thf(fact_1401_one__reorient,axiom,
% 0.26/0.49      ! [X3: nat] :
% 0.26/0.49        ( ( one_one_nat = X3 )
% 0.26/0.49        = ( X3 = one_one_nat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % one_reorient
% 0.26/0.49  thf(fact_1402_one__reorient,axiom,
% 0.26/0.49      ! [X3: int] :
% 0.26/0.49        ( ( one_one_int = X3 )
% 0.26/0.49        = ( X3 = one_one_int ) ) ).
% 0.26/0.49  
% 0.26/0.49  % one_reorient
% 0.26/0.49  thf(fact_1403_of__nat__or__eq,axiom,
% 0.26/0.49      ! [M: nat,N: nat] :
% 0.26/0.49        ( ( semiri1314217659103216013at_int @ ( bit_se1412395901928357646or_nat @ M @ N ) )
% 0.26/0.49        = ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % of_nat_or_eq
% 0.26/0.49  thf(fact_1404_of__nat__or__eq,axiom,
% 0.26/0.49      ! [M: nat,N: nat] :
% 0.26/0.49        ( ( semiri1316708129612266289at_nat @ ( bit_se1412395901928357646or_nat @ M @ N ) )
% 0.26/0.49        = ( bit_se1412395901928357646or_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % of_nat_or_eq
% 0.26/0.49  thf(fact_1405_take__bit__of__nat,axiom,
% 0.26/0.49      ! [N: nat,M: nat] :
% 0.26/0.49        ( ( bit_se2923211474154528505it_int @ N @ ( semiri1314217659103216013at_int @ M ) )
% 0.26/0.49        = ( semiri1314217659103216013at_int @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_of_nat
% 0.26/0.49  thf(fact_1406_take__bit__of__nat,axiom,
% 0.26/0.49      ! [N: nat,M: nat] :
% 0.26/0.49        ( ( bit_se2925701944663578781it_nat @ N @ ( semiri1316708129612266289at_nat @ M ) )
% 0.26/0.49        = ( semiri1316708129612266289at_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_of_nat
% 0.26/0.49  thf(fact_1407_dvd__antisym,axiom,
% 0.26/0.49      ! [M: nat,N: nat] :
% 0.26/0.49        ( ( dvd_dvd_nat @ M @ N )
% 0.26/0.49       => ( ( dvd_dvd_nat @ N @ M )
% 0.26/0.49         => ( M = N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_antisym
% 0.26/0.49  thf(fact_1408_take__bit__of__int,axiom,
% 0.26/0.49      ! [N: nat,K: int] :
% 0.26/0.49        ( ( bit_se2923211474154528505it_int @ N @ ( ring_1_of_int_int @ K ) )
% 0.26/0.49        = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_of_int
% 0.26/0.49  thf(fact_1409_of__int__or__eq,axiom,
% 0.26/0.49      ! [K: int,L: int] :
% 0.26/0.49        ( ( ring_1_of_int_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 0.26/0.49        = ( bit_se1409905431419307370or_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % of_int_or_eq
% 0.26/0.49  thf(fact_1410_of__nat__xor__eq,axiom,
% 0.26/0.49      ! [M: nat,N: nat] :
% 0.26/0.49        ( ( semiri1314217659103216013at_int @ ( bit_se6528837805403552850or_nat @ M @ N ) )
% 0.26/0.49        = ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % of_nat_xor_eq
% 0.26/0.49  thf(fact_1411_of__nat__xor__eq,axiom,
% 0.26/0.49      ! [M: nat,N: nat] :
% 0.26/0.49        ( ( semiri1316708129612266289at_nat @ ( bit_se6528837805403552850or_nat @ M @ N ) )
% 0.26/0.49        = ( bit_se6528837805403552850or_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % of_nat_xor_eq
% 0.26/0.49  thf(fact_1412_real__sqrt__ge__one,axiom,
% 0.26/0.49      ! [X3: real] :
% 0.26/0.49        ( ( ord_less_eq_real @ one_one_real @ X3 )
% 0.26/0.49       => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X3 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % real_sqrt_ge_one
% 0.26/0.49  thf(fact_1413_of__int__xor__eq,axiom,
% 0.26/0.49      ! [K: int,L: int] :
% 0.26/0.49        ( ( ring_1_of_int_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 0.26/0.49        = ( bit_se6526347334894502574or_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % of_int_xor_eq
% 0.26/0.49  thf(fact_1414_int__ops_I2_J,axiom,
% 0.26/0.49      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 0.26/0.49      = one_one_int ) ).
% 0.26/0.49  
% 0.26/0.49  % int_ops(2)
% 0.26/0.49  thf(fact_1415_nat__one__as__int,axiom,
% 0.26/0.49      ( one_one_nat
% 0.26/0.49      = ( nat2 @ one_one_int ) ) ).
% 0.26/0.49  
% 0.26/0.49  % nat_one_as_int
% 0.26/0.49  thf(fact_1416_is__unit__power__iff,axiom,
% 0.26/0.49      ! [A: code_integer,N: nat] :
% 0.26/0.49        ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 0.26/0.49        = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.26/0.49          | ( N = zero_zero_nat ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % is_unit_power_iff
% 0.26/0.49  thf(fact_1417_is__unit__power__iff,axiom,
% 0.26/0.49      ! [A: nat,N: nat] :
% 0.26/0.49        ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 0.26/0.49        = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.26/0.49          | ( N = zero_zero_nat ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % is_unit_power_iff
% 0.26/0.49  thf(fact_1418_is__unit__power__iff,axiom,
% 0.26/0.49      ! [A: int,N: nat] :
% 0.26/0.49        ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 0.26/0.49        = ( ( dvd_dvd_int @ A @ one_one_int )
% 0.26/0.49          | ( N = zero_zero_nat ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % is_unit_power_iff
% 0.26/0.49  thf(fact_1419_bit_Odisj__zero__right,axiom,
% 0.26/0.49      ! [X3: int] :
% 0.26/0.49        ( ( bit_se1409905431419307370or_int @ X3 @ zero_zero_int )
% 0.26/0.49        = X3 ) ).
% 0.26/0.49  
% 0.26/0.49  % bit.disj_zero_right
% 0.26/0.49  thf(fact_1420_or__eq__0__iff,axiom,
% 0.26/0.49      ! [A: int,B: int] :
% 0.26/0.49        ( ( ( bit_se1409905431419307370or_int @ A @ B )
% 0.26/0.49          = zero_zero_int )
% 0.26/0.49        = ( ( A = zero_zero_int )
% 0.26/0.49          & ( B = zero_zero_int ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % or_eq_0_iff
% 0.26/0.49  thf(fact_1421_or__eq__0__iff,axiom,
% 0.26/0.49      ! [A: nat,B: nat] :
% 0.26/0.49        ( ( ( bit_se1412395901928357646or_nat @ A @ B )
% 0.26/0.49          = zero_zero_nat )
% 0.26/0.49        = ( ( A = zero_zero_nat )
% 0.26/0.49          & ( B = zero_zero_nat ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % or_eq_0_iff
% 0.26/0.49  thf(fact_1422_take__bit__tightened,axiom,
% 0.26/0.49      ! [N: nat,A: int,B: int,M: nat] :
% 0.26/0.49        ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 0.26/0.49          = ( bit_se2923211474154528505it_int @ N @ B ) )
% 0.26/0.49       => ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.49         => ( ( bit_se2923211474154528505it_int @ M @ A )
% 0.26/0.49            = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_tightened
% 0.26/0.49  thf(fact_1423_take__bit__tightened,axiom,
% 0.26/0.49      ! [N: nat,A: nat,B: nat,M: nat] :
% 0.26/0.49        ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 0.26/0.49          = ( bit_se2925701944663578781it_nat @ N @ B ) )
% 0.26/0.49       => ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.49         => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 0.26/0.49            = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_tightened
% 0.26/0.49  thf(fact_1424_real__sqrt__less__mono,axiom,
% 0.26/0.49      ! [X3: real,Y3: real] :
% 0.26/0.49        ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.49       => ( ord_less_real @ ( sqrt @ X3 ) @ ( sqrt @ Y3 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % real_sqrt_less_mono
% 0.26/0.49  thf(fact_1425_real__sqrt__le__mono,axiom,
% 0.26/0.49      ! [X3: real,Y3: real] :
% 0.26/0.49        ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.26/0.49       => ( ord_less_eq_real @ ( sqrt @ X3 ) @ ( sqrt @ Y3 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % real_sqrt_le_mono
% 0.26/0.49  thf(fact_1426_odd__one,axiom,
% 0.26/0.49      ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 0.26/0.49  
% 0.26/0.49  % odd_one
% 0.26/0.49  thf(fact_1427_odd__one,axiom,
% 0.26/0.49      ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 0.26/0.49  
% 0.26/0.49  % odd_one
% 0.26/0.49  thf(fact_1428_odd__one,axiom,
% 0.26/0.49      ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 0.26/0.49  
% 0.26/0.49  % odd_one
% 0.26/0.49  thf(fact_1429_real__sqrt__power,axiom,
% 0.26/0.49      ! [X3: real,K: nat] :
% 0.26/0.49        ( ( sqrt @ ( power_power_real @ X3 @ K ) )
% 0.26/0.49        = ( power_power_real @ ( sqrt @ X3 ) @ K ) ) ).
% 0.26/0.49  
% 0.26/0.49  % real_sqrt_power
% 0.26/0.49  thf(fact_1430_less__log__of__power,axiom,
% 0.26/0.49      ! [B: real,N: nat,M: real] :
% 0.26/0.49        ( ( ord_less_real @ ( power_power_real @ B @ N ) @ M )
% 0.26/0.49       => ( ( ord_less_real @ one_one_real @ B )
% 0.26/0.49         => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % less_log_of_power
% 0.26/0.49  thf(fact_1431_log__of__power__eq,axiom,
% 0.26/0.49      ! [M: nat,B: real,N: nat] :
% 0.26/0.49        ( ( ( semiri5074537144036343181t_real @ M )
% 0.26/0.49          = ( power_power_real @ B @ N ) )
% 0.26/0.49       => ( ( ord_less_real @ one_one_real @ B )
% 0.26/0.49         => ( ( semiri5074537144036343181t_real @ N )
% 0.26/0.49            = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % log_of_power_eq
% 0.26/0.49  thf(fact_1432_dvd__power__same,axiom,
% 0.26/0.49      ! [X3: code_integer,Y3: code_integer,N: nat] :
% 0.26/0.49        ( ( dvd_dvd_Code_integer @ X3 @ Y3 )
% 0.26/0.49       => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X3 @ N ) @ ( power_8256067586552552935nteger @ Y3 @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_power_same
% 0.26/0.49  thf(fact_1433_dvd__power__same,axiom,
% 0.26/0.49      ! [X3: nat,Y3: nat,N: nat] :
% 0.26/0.49        ( ( dvd_dvd_nat @ X3 @ Y3 )
% 0.26/0.49       => ( dvd_dvd_nat @ ( power_power_nat @ X3 @ N ) @ ( power_power_nat @ Y3 @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_power_same
% 0.26/0.49  thf(fact_1434_dvd__power__same,axiom,
% 0.26/0.49      ! [X3: int,Y3: int,N: nat] :
% 0.26/0.49        ( ( dvd_dvd_int @ X3 @ Y3 )
% 0.26/0.49       => ( dvd_dvd_int @ ( power_power_int @ X3 @ N ) @ ( power_power_int @ Y3 @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_power_same
% 0.26/0.49  thf(fact_1435_dvd__power__same,axiom,
% 0.26/0.49      ! [X3: real,Y3: real,N: nat] :
% 0.26/0.49        ( ( dvd_dvd_real @ X3 @ Y3 )
% 0.26/0.49       => ( dvd_dvd_real @ ( power_power_real @ X3 @ N ) @ ( power_power_real @ Y3 @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_power_same
% 0.26/0.49  thf(fact_1436_dvd__power__same,axiom,
% 0.26/0.49      ! [X3: complex,Y3: complex,N: nat] :
% 0.26/0.49        ( ( dvd_dvd_complex @ X3 @ Y3 )
% 0.26/0.49       => ( dvd_dvd_complex @ ( power_power_complex @ X3 @ N ) @ ( power_power_complex @ Y3 @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_power_same
% 0.26/0.49  thf(fact_1437_le__numeral__extra_I4_J,axiom,
% 0.26/0.49      ord_less_eq_real @ one_one_real @ one_one_real ).
% 0.26/0.49  
% 0.26/0.49  % le_numeral_extra(4)
% 0.26/0.49  thf(fact_1438_le__numeral__extra_I4_J,axiom,
% 0.26/0.49      ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 0.26/0.49  
% 0.26/0.49  % le_numeral_extra(4)
% 0.26/0.49  thf(fact_1439_le__numeral__extra_I4_J,axiom,
% 0.26/0.49      ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 0.26/0.49  
% 0.26/0.49  % le_numeral_extra(4)
% 0.26/0.49  thf(fact_1440_le__numeral__extra_I4_J,axiom,
% 0.26/0.49      ord_less_eq_int @ one_one_int @ one_one_int ).
% 0.26/0.49  
% 0.26/0.49  % le_numeral_extra(4)
% 0.26/0.49  thf(fact_1441_less__numeral__extra_I4_J,axiom,
% 0.26/0.49      ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 0.26/0.49  
% 0.26/0.49  % less_numeral_extra(4)
% 0.26/0.49  thf(fact_1442_less__numeral__extra_I4_J,axiom,
% 0.26/0.49      ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 0.26/0.49  
% 0.26/0.49  % less_numeral_extra(4)
% 0.26/0.49  thf(fact_1443_less__numeral__extra_I4_J,axiom,
% 0.26/0.49      ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 0.26/0.49  
% 0.26/0.49  % less_numeral_extra(4)
% 0.26/0.49  thf(fact_1444_less__numeral__extra_I4_J,axiom,
% 0.26/0.49      ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 0.26/0.49  
% 0.26/0.49  % less_numeral_extra(4)
% 0.26/0.49  thf(fact_1445_even__or__iff,axiom,
% 0.26/0.49      ! [A: code_integer,B: code_integer] :
% 0.26/0.49        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1080825931792720795nteger @ A @ B ) )
% 0.26/0.49        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.49          & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % even_or_iff
% 0.26/0.49  thf(fact_1446_even__or__iff,axiom,
% 0.26/0.49      ! [A: int,B: int] :
% 0.26/0.49        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 0.26/0.49        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.49          & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % even_or_iff
% 0.26/0.49  thf(fact_1447_even__or__iff,axiom,
% 0.26/0.49      ! [A: nat,B: nat] :
% 0.26/0.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 0.26/0.49        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.49          & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % even_or_iff
% 0.26/0.49  thf(fact_1448_even__xor__iff,axiom,
% 0.26/0.49      ! [A: code_integer,B: code_integer] :
% 0.26/0.49        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ A @ B ) )
% 0.26/0.49        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.49          = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % even_xor_iff
% 0.26/0.49  thf(fact_1449_even__xor__iff,axiom,
% 0.26/0.49      ! [A: int,B: int] :
% 0.26/0.49        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ A @ B ) )
% 0.26/0.49        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.49          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % even_xor_iff
% 0.26/0.49  thf(fact_1450_even__xor__iff,axiom,
% 0.26/0.49      ! [A: nat,B: nat] :
% 0.26/0.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ A @ B ) )
% 0.26/0.49        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.49          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % even_xor_iff
% 0.26/0.49  thf(fact_1451_zero__one__enat__neq_I1_J,axiom,
% 0.26/0.49      zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 0.26/0.49  
% 0.26/0.49  % zero_one_enat_neq(1)
% 0.26/0.49  thf(fact_1452_dvd__power__iff,axiom,
% 0.26/0.49      ! [X3: code_integer,M: nat,N: nat] :
% 0.26/0.49        ( ( X3 != zero_z3403309356797280102nteger )
% 0.26/0.49       => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X3 @ M ) @ ( power_8256067586552552935nteger @ X3 @ N ) )
% 0.26/0.49          = ( ( dvd_dvd_Code_integer @ X3 @ one_one_Code_integer )
% 0.26/0.49            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_power_iff
% 0.26/0.49  thf(fact_1453_dvd__power__iff,axiom,
% 0.26/0.49      ! [X3: nat,M: nat,N: nat] :
% 0.26/0.49        ( ( X3 != zero_zero_nat )
% 0.26/0.49       => ( ( dvd_dvd_nat @ ( power_power_nat @ X3 @ M ) @ ( power_power_nat @ X3 @ N ) )
% 0.26/0.49          = ( ( dvd_dvd_nat @ X3 @ one_one_nat )
% 0.26/0.49            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_power_iff
% 0.26/0.49  thf(fact_1454_dvd__power__iff,axiom,
% 0.26/0.49      ! [X3: int,M: nat,N: nat] :
% 0.26/0.49        ( ( X3 != zero_zero_int )
% 0.26/0.49       => ( ( dvd_dvd_int @ ( power_power_int @ X3 @ M ) @ ( power_power_int @ X3 @ N ) )
% 0.26/0.49          = ( ( dvd_dvd_int @ X3 @ one_one_int )
% 0.26/0.49            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_power_iff
% 0.26/0.49  thf(fact_1455_dvd__power,axiom,
% 0.26/0.49      ! [N: nat,X3: code_integer] :
% 0.26/0.49        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.49          | ( X3 = one_one_Code_integer ) )
% 0.26/0.49       => ( dvd_dvd_Code_integer @ X3 @ ( power_8256067586552552935nteger @ X3 @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_power
% 0.26/0.49  thf(fact_1456_dvd__power,axiom,
% 0.26/0.49      ! [N: nat,X3: rat] :
% 0.26/0.49        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.49          | ( X3 = one_one_rat ) )
% 0.26/0.49       => ( dvd_dvd_rat @ X3 @ ( power_power_rat @ X3 @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_power
% 0.26/0.49  thf(fact_1457_dvd__power,axiom,
% 0.26/0.49      ! [N: nat,X3: nat] :
% 0.26/0.49        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.49          | ( X3 = one_one_nat ) )
% 0.26/0.49       => ( dvd_dvd_nat @ X3 @ ( power_power_nat @ X3 @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_power
% 0.26/0.49  thf(fact_1458_dvd__power,axiom,
% 0.26/0.49      ! [N: nat,X3: int] :
% 0.26/0.49        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.49          | ( X3 = one_one_int ) )
% 0.26/0.49       => ( dvd_dvd_int @ X3 @ ( power_power_int @ X3 @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_power
% 0.26/0.49  thf(fact_1459_dvd__power,axiom,
% 0.26/0.49      ! [N: nat,X3: real] :
% 0.26/0.49        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.49          | ( X3 = one_one_real ) )
% 0.26/0.49       => ( dvd_dvd_real @ X3 @ ( power_power_real @ X3 @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_power
% 0.26/0.49  thf(fact_1460_dvd__power,axiom,
% 0.26/0.49      ! [N: nat,X3: complex] :
% 0.26/0.49        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.49          | ( X3 = one_one_complex ) )
% 0.26/0.49       => ( dvd_dvd_complex @ X3 @ ( power_power_complex @ X3 @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_power
% 0.26/0.49  thf(fact_1461_power__dvd__imp__le,axiom,
% 0.26/0.49      ! [I: nat,M: nat,N: nat] :
% 0.26/0.49        ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 0.26/0.49       => ( ( ord_less_nat @ one_one_nat @ I )
% 0.26/0.49         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_dvd_imp_le
% 0.26/0.49  thf(fact_1462_le__log__of__power,axiom,
% 0.26/0.49      ! [B: real,N: nat,M: real] :
% 0.26/0.49        ( ( ord_less_eq_real @ ( power_power_real @ B @ N ) @ M )
% 0.26/0.49       => ( ( ord_less_real @ one_one_real @ B )
% 0.26/0.49         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_log_of_power
% 0.26/0.49  thf(fact_1463_real__sqrt__gt__zero,axiom,
% 0.26/0.49      ! [X3: real] :
% 0.26/0.49        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.49       => ( ord_less_real @ zero_zero_real @ ( sqrt @ X3 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % real_sqrt_gt_zero
% 0.26/0.49  thf(fact_1464_real__sqrt__ge__zero,axiom,
% 0.26/0.49      ! [X3: real] :
% 0.26/0.49        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.49       => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X3 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % real_sqrt_ge_zero
% 0.26/0.49  thf(fact_1465_real__sqrt__eq__zero__cancel,axiom,
% 0.26/0.49      ! [X3: real] :
% 0.26/0.49        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.49       => ( ( ( sqrt @ X3 )
% 0.26/0.49            = zero_zero_real )
% 0.26/0.49         => ( X3 = zero_zero_real ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % real_sqrt_eq_zero_cancel
% 0.26/0.49  thf(fact_1466_log__of__power__less,axiom,
% 0.26/0.49      ! [M: nat,B: real,N: nat] :
% 0.26/0.49        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 0.26/0.49       => ( ( ord_less_real @ one_one_real @ B )
% 0.26/0.49         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.49           => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % log_of_power_less
% 0.26/0.49  thf(fact_1467_OR__lower,axiom,
% 0.26/0.49      ! [X3: int,Y3: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.26/0.49       => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 0.26/0.49         => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % OR_lower
% 0.26/0.49  thf(fact_1468_or__greater__eq,axiom,
% 0.26/0.49      ! [L: int,K: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ zero_zero_int @ L )
% 0.26/0.49       => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % or_greater_eq
% 0.26/0.49  thf(fact_1469_even__numeral,axiom,
% 0.26/0.49      ! [N: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % even_numeral
% 0.26/0.49  thf(fact_1470_even__numeral,axiom,
% 0.26/0.49      ! [N: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % even_numeral
% 0.26/0.49  thf(fact_1471_even__numeral,axiom,
% 0.26/0.49      ! [N: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % even_numeral
% 0.26/0.49  thf(fact_1472_take__bit__tightened__less__eq__int,axiom,
% 0.26/0.49      ! [M: nat,N: nat,K: int] :
% 0.26/0.49        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.49       => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_tightened_less_eq_int
% 0.26/0.49  thf(fact_1473_XOR__lower,axiom,
% 0.26/0.49      ! [X3: int,Y3: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.26/0.49       => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 0.26/0.49         => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % XOR_lower
% 0.26/0.49  thf(fact_1474_take__bit__nonnegative,axiom,
% 0.26/0.49      ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_nonnegative
% 0.26/0.49  thf(fact_1475_take__bit__int__less__eq__self__iff,axiom,
% 0.26/0.49      ! [N: nat,K: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 0.26/0.49        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_int_less_eq_self_iff
% 0.26/0.49  thf(fact_1476_not__take__bit__negative,axiom,
% 0.26/0.49      ! [N: nat,K: int] :
% 0.26/0.49        ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 0.26/0.49  
% 0.26/0.49  % not_take_bit_negative
% 0.26/0.49  thf(fact_1477_take__bit__int__greater__self__iff,axiom,
% 0.26/0.49      ! [K: int,N: nat] :
% 0.26/0.49        ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 0.26/0.49        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_int_greater_self_iff
% 0.26/0.49  thf(fact_1478_le__imp__power__dvd,axiom,
% 0.26/0.49      ! [M: nat,N: nat,A: code_integer] :
% 0.26/0.49        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.49       => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_imp_power_dvd
% 0.26/0.49  thf(fact_1479_le__imp__power__dvd,axiom,
% 0.26/0.49      ! [M: nat,N: nat,A: nat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.49       => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_imp_power_dvd
% 0.26/0.49  thf(fact_1480_le__imp__power__dvd,axiom,
% 0.26/0.49      ! [M: nat,N: nat,A: int] :
% 0.26/0.49        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.49       => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_imp_power_dvd
% 0.26/0.49  thf(fact_1481_le__imp__power__dvd,axiom,
% 0.26/0.49      ! [M: nat,N: nat,A: real] :
% 0.26/0.49        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.49       => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_imp_power_dvd
% 0.26/0.49  thf(fact_1482_le__imp__power__dvd,axiom,
% 0.26/0.49      ! [M: nat,N: nat,A: complex] :
% 0.26/0.49        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.49       => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_imp_power_dvd
% 0.26/0.49  thf(fact_1483_power__le__dvd,axiom,
% 0.26/0.49      ! [A: code_integer,N: nat,B: code_integer,M: nat] :
% 0.26/0.49        ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ B )
% 0.26/0.49       => ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.49         => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_le_dvd
% 0.26/0.49  thf(fact_1484_power__le__dvd,axiom,
% 0.26/0.49      ! [A: nat,N: nat,B: nat,M: nat] :
% 0.26/0.49        ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ B )
% 0.26/0.49       => ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.49         => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_le_dvd
% 0.26/0.49  thf(fact_1485_power__le__dvd,axiom,
% 0.26/0.49      ! [A: int,N: nat,B: int,M: nat] :
% 0.26/0.49        ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ B )
% 0.26/0.49       => ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.49         => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_le_dvd
% 0.26/0.49  thf(fact_1486_power__le__dvd,axiom,
% 0.26/0.49      ! [A: real,N: nat,B: real,M: nat] :
% 0.26/0.49        ( ( dvd_dvd_real @ ( power_power_real @ A @ N ) @ B )
% 0.26/0.49       => ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.49         => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_le_dvd
% 0.26/0.49  thf(fact_1487_power__le__dvd,axiom,
% 0.26/0.49      ! [A: complex,N: nat,B: complex,M: nat] :
% 0.26/0.49        ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N ) @ B )
% 0.26/0.49       => ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.49         => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_le_dvd
% 0.26/0.49  thf(fact_1488_dvd__power__le,axiom,
% 0.26/0.49      ! [X3: code_integer,Y3: code_integer,N: nat,M: nat] :
% 0.26/0.49        ( ( dvd_dvd_Code_integer @ X3 @ Y3 )
% 0.26/0.49       => ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.49         => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X3 @ N ) @ ( power_8256067586552552935nteger @ Y3 @ M ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_power_le
% 0.26/0.49  thf(fact_1489_dvd__power__le,axiom,
% 0.26/0.49      ! [X3: nat,Y3: nat,N: nat,M: nat] :
% 0.26/0.49        ( ( dvd_dvd_nat @ X3 @ Y3 )
% 0.26/0.49       => ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.49         => ( dvd_dvd_nat @ ( power_power_nat @ X3 @ N ) @ ( power_power_nat @ Y3 @ M ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_power_le
% 0.26/0.49  thf(fact_1490_dvd__power__le,axiom,
% 0.26/0.49      ! [X3: int,Y3: int,N: nat,M: nat] :
% 0.26/0.49        ( ( dvd_dvd_int @ X3 @ Y3 )
% 0.26/0.49       => ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.49         => ( dvd_dvd_int @ ( power_power_int @ X3 @ N ) @ ( power_power_int @ Y3 @ M ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_power_le
% 0.26/0.49  thf(fact_1491_dvd__power__le,axiom,
% 0.26/0.49      ! [X3: real,Y3: real,N: nat,M: nat] :
% 0.26/0.49        ( ( dvd_dvd_real @ X3 @ Y3 )
% 0.26/0.49       => ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.49         => ( dvd_dvd_real @ ( power_power_real @ X3 @ N ) @ ( power_power_real @ Y3 @ M ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_power_le
% 0.26/0.49  thf(fact_1492_dvd__power__le,axiom,
% 0.26/0.49      ! [X3: complex,Y3: complex,N: nat,M: nat] :
% 0.26/0.49        ( ( dvd_dvd_complex @ X3 @ Y3 )
% 0.26/0.49       => ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.49         => ( dvd_dvd_complex @ ( power_power_complex @ X3 @ N ) @ ( power_power_complex @ Y3 @ M ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_power_le
% 0.26/0.49  thf(fact_1493_nat__dvd__not__less,axiom,
% 0.26/0.49      ! [M: nat,N: nat] :
% 0.26/0.49        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.49       => ( ( ord_less_nat @ M @ N )
% 0.26/0.49         => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % nat_dvd_not_less
% 0.26/0.49  thf(fact_1494_less__numeral__extra_I1_J,axiom,
% 0.26/0.49      ord_less_real @ zero_zero_real @ one_one_real ).
% 0.26/0.49  
% 0.26/0.49  % less_numeral_extra(1)
% 0.26/0.49  thf(fact_1495_less__numeral__extra_I1_J,axiom,
% 0.26/0.49      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 0.26/0.49  
% 0.26/0.49  % less_numeral_extra(1)
% 0.26/0.49  thf(fact_1496_less__numeral__extra_I1_J,axiom,
% 0.26/0.49      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.26/0.49  
% 0.26/0.49  % less_numeral_extra(1)
% 0.26/0.49  thf(fact_1497_less__numeral__extra_I1_J,axiom,
% 0.26/0.49      ord_less_int @ zero_zero_int @ one_one_int ).
% 0.26/0.49  
% 0.26/0.49  % less_numeral_extra(1)
% 0.26/0.49  thf(fact_1498_one__le__numeral,axiom,
% 0.26/0.49      ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 0.26/0.49  
% 0.26/0.49  % one_le_numeral
% 0.26/0.49  thf(fact_1499_one__le__numeral,axiom,
% 0.26/0.49      ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 0.26/0.49  
% 0.26/0.49  % one_le_numeral
% 0.26/0.49  thf(fact_1500_one__le__numeral,axiom,
% 0.26/0.49      ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 0.26/0.49  
% 0.26/0.49  % one_le_numeral
% 0.26/0.49  thf(fact_1501_one__le__numeral,axiom,
% 0.26/0.49      ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 0.26/0.49  
% 0.26/0.49  % one_le_numeral
% 0.26/0.49  thf(fact_1502_not__numeral__less__one,axiom,
% 0.26/0.49      ! [N: num] :
% 0.26/0.49        ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 0.26/0.49  
% 0.26/0.49  % not_numeral_less_one
% 0.26/0.49  thf(fact_1503_not__numeral__less__one,axiom,
% 0.26/0.49      ! [N: num] :
% 0.26/0.49        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 0.26/0.49  
% 0.26/0.49  % not_numeral_less_one
% 0.26/0.49  thf(fact_1504_not__numeral__less__one,axiom,
% 0.26/0.49      ! [N: num] :
% 0.26/0.49        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 0.26/0.49  
% 0.26/0.49  % not_numeral_less_one
% 0.26/0.49  thf(fact_1505_not__numeral__less__one,axiom,
% 0.26/0.49      ! [N: num] :
% 0.26/0.49        ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 0.26/0.49  
% 0.26/0.49  % not_numeral_less_one
% 0.26/0.49  thf(fact_1506_numeral__One,axiom,
% 0.26/0.49      ( ( numera6690914467698888265omplex @ one )
% 0.26/0.49      = one_one_complex ) ).
% 0.26/0.49  
% 0.26/0.49  % numeral_One
% 0.26/0.49  thf(fact_1507_numeral__One,axiom,
% 0.26/0.49      ( ( numeral_numeral_real @ one )
% 0.26/0.49      = one_one_real ) ).
% 0.26/0.49  
% 0.26/0.49  % numeral_One
% 0.26/0.49  thf(fact_1508_numeral__One,axiom,
% 0.26/0.49      ( ( numeral_numeral_rat @ one )
% 0.26/0.49      = one_one_rat ) ).
% 0.26/0.49  
% 0.26/0.49  % numeral_One
% 0.26/0.49  thf(fact_1509_numeral__One,axiom,
% 0.26/0.49      ( ( numeral_numeral_nat @ one )
% 0.26/0.49      = one_one_nat ) ).
% 0.26/0.49  
% 0.26/0.49  % numeral_One
% 0.26/0.49  thf(fact_1510_numeral__One,axiom,
% 0.26/0.49      ( ( numeral_numeral_int @ one )
% 0.26/0.49      = one_one_int ) ).
% 0.26/0.49  
% 0.26/0.49  % numeral_One
% 0.26/0.49  thf(fact_1511_one__le__power,axiom,
% 0.26/0.49      ! [A: real,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_real @ one_one_real @ A )
% 0.26/0.49       => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % one_le_power
% 0.26/0.49  thf(fact_1512_one__le__power,axiom,
% 0.26/0.49      ! [A: rat,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.26/0.49       => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % one_le_power
% 0.26/0.49  thf(fact_1513_one__le__power,axiom,
% 0.26/0.49      ! [A: nat,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.26/0.49       => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % one_le_power
% 0.26/0.49  thf(fact_1514_one__le__power,axiom,
% 0.26/0.49      ! [A: int,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_int @ one_one_int @ A )
% 0.26/0.49       => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % one_le_power
% 0.26/0.49  thf(fact_1515_take__bit__eq__0__iff,axiom,
% 0.26/0.49      ! [N: nat,A: code_integer] :
% 0.26/0.49        ( ( ( bit_se1745604003318907178nteger @ N @ A )
% 0.26/0.49          = zero_z3403309356797280102nteger )
% 0.26/0.49        = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_eq_0_iff
% 0.26/0.49  thf(fact_1516_take__bit__eq__0__iff,axiom,
% 0.26/0.49      ! [N: nat,A: int] :
% 0.26/0.49        ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 0.26/0.49          = zero_zero_int )
% 0.26/0.49        = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_eq_0_iff
% 0.26/0.49  thf(fact_1517_take__bit__eq__0__iff,axiom,
% 0.26/0.49      ! [N: nat,A: nat] :
% 0.26/0.49        ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 0.26/0.49          = zero_zero_nat )
% 0.26/0.49        = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_eq_0_iff
% 0.26/0.49  thf(fact_1518_power__0,axiom,
% 0.26/0.49      ! [A: rat] :
% 0.26/0.49        ( ( power_power_rat @ A @ zero_zero_nat )
% 0.26/0.49        = one_one_rat ) ).
% 0.26/0.49  
% 0.26/0.49  % power_0
% 0.26/0.49  thf(fact_1519_power__0,axiom,
% 0.26/0.49      ! [A: nat] :
% 0.26/0.49        ( ( power_power_nat @ A @ zero_zero_nat )
% 0.26/0.49        = one_one_nat ) ).
% 0.26/0.49  
% 0.26/0.49  % power_0
% 0.26/0.49  thf(fact_1520_power__0,axiom,
% 0.26/0.49      ! [A: int] :
% 0.26/0.49        ( ( power_power_int @ A @ zero_zero_nat )
% 0.26/0.49        = one_one_int ) ).
% 0.26/0.49  
% 0.26/0.49  % power_0
% 0.26/0.49  thf(fact_1521_power__0,axiom,
% 0.26/0.49      ! [A: real] :
% 0.26/0.49        ( ( power_power_real @ A @ zero_zero_nat )
% 0.26/0.49        = one_one_real ) ).
% 0.26/0.49  
% 0.26/0.49  % power_0
% 0.26/0.49  thf(fact_1522_power__0,axiom,
% 0.26/0.49      ! [A: complex] :
% 0.26/0.49        ( ( power_power_complex @ A @ zero_zero_nat )
% 0.26/0.49        = one_one_complex ) ).
% 0.26/0.49  
% 0.26/0.49  % power_0
% 0.26/0.49  thf(fact_1523_numerals_I1_J,axiom,
% 0.26/0.49      ( ( numeral_numeral_nat @ one )
% 0.26/0.49      = one_one_nat ) ).
% 0.26/0.49  
% 0.26/0.49  % numerals(1)
% 0.26/0.49  thf(fact_1524_real__arch__pow,axiom,
% 0.26/0.49      ! [X3: real,Y3: real] :
% 0.26/0.49        ( ( ord_less_real @ one_one_real @ X3 )
% 0.26/0.49       => ? [N2: nat] : ( ord_less_real @ Y3 @ ( power_power_real @ X3 @ N2 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % real_arch_pow
% 0.26/0.49  thf(fact_1525_log__of__power__le,axiom,
% 0.26/0.49      ! [M: nat,B: real,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 0.26/0.49       => ( ( ord_less_real @ one_one_real @ B )
% 0.26/0.49         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.49           => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % log_of_power_le
% 0.26/0.49  thf(fact_1526_even__of__int__iff,axiom,
% 0.26/0.49      ! [K: int] :
% 0.26/0.49        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ K ) )
% 0.26/0.49        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 0.26/0.49  
% 0.26/0.49  % even_of_int_iff
% 0.26/0.49  thf(fact_1527_even__of__int__iff,axiom,
% 0.26/0.49      ! [K: int] :
% 0.26/0.49        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 0.26/0.49        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 0.26/0.49  
% 0.26/0.49  % even_of_int_iff
% 0.26/0.49  thf(fact_1528_even__zero,axiom,
% 0.26/0.49      dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 0.26/0.49  
% 0.26/0.49  % even_zero
% 0.26/0.49  thf(fact_1529_even__zero,axiom,
% 0.26/0.49      dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 0.26/0.49  
% 0.26/0.49  % even_zero
% 0.26/0.49  thf(fact_1530_even__zero,axiom,
% 0.26/0.49      dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 0.26/0.49  
% 0.26/0.49  % even_zero
% 0.26/0.49  thf(fact_1531_dvd__imp__le,axiom,
% 0.26/0.49      ! [K: nat,N: nat] :
% 0.26/0.49        ( ( dvd_dvd_nat @ K @ N )
% 0.26/0.49       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.49         => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_imp_le
% 0.26/0.49  thf(fact_1532_power__le__one,axiom,
% 0.26/0.49      ! [A: real,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.49       => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.26/0.49         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_le_one
% 0.26/0.49  thf(fact_1533_power__le__one,axiom,
% 0.26/0.49      ! [A: rat,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.49       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.26/0.49         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_le_one
% 0.26/0.49  thf(fact_1534_power__le__one,axiom,
% 0.26/0.49      ! [A: nat,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.49       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.26/0.49         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_le_one
% 0.26/0.49  thf(fact_1535_power__le__one,axiom,
% 0.26/0.49      ! [A: int,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.49       => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.26/0.49         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_le_one
% 0.26/0.49  thf(fact_1536_power__0__left,axiom,
% 0.26/0.49      ! [N: nat] :
% 0.26/0.49        ( ( ( N = zero_zero_nat )
% 0.26/0.49         => ( ( power_power_rat @ zero_zero_rat @ N )
% 0.26/0.49            = one_one_rat ) )
% 0.26/0.49        & ( ( N != zero_zero_nat )
% 0.26/0.49         => ( ( power_power_rat @ zero_zero_rat @ N )
% 0.26/0.49            = zero_zero_rat ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_0_left
% 0.26/0.49  thf(fact_1537_power__0__left,axiom,
% 0.26/0.49      ! [N: nat] :
% 0.26/0.49        ( ( ( N = zero_zero_nat )
% 0.26/0.49         => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.26/0.49            = one_one_nat ) )
% 0.26/0.49        & ( ( N != zero_zero_nat )
% 0.26/0.49         => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.26/0.49            = zero_zero_nat ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_0_left
% 0.26/0.49  thf(fact_1538_power__0__left,axiom,
% 0.26/0.49      ! [N: nat] :
% 0.26/0.49        ( ( ( N = zero_zero_nat )
% 0.26/0.49         => ( ( power_power_int @ zero_zero_int @ N )
% 0.26/0.49            = one_one_int ) )
% 0.26/0.49        & ( ( N != zero_zero_nat )
% 0.26/0.49         => ( ( power_power_int @ zero_zero_int @ N )
% 0.26/0.49            = zero_zero_int ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_0_left
% 0.26/0.49  thf(fact_1539_power__0__left,axiom,
% 0.26/0.49      ! [N: nat] :
% 0.26/0.49        ( ( ( N = zero_zero_nat )
% 0.26/0.49         => ( ( power_power_real @ zero_zero_real @ N )
% 0.26/0.49            = one_one_real ) )
% 0.26/0.49        & ( ( N != zero_zero_nat )
% 0.26/0.49         => ( ( power_power_real @ zero_zero_real @ N )
% 0.26/0.49            = zero_zero_real ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_0_left
% 0.26/0.49  thf(fact_1540_power__0__left,axiom,
% 0.26/0.49      ! [N: nat] :
% 0.26/0.49        ( ( ( N = zero_zero_nat )
% 0.26/0.49         => ( ( power_power_complex @ zero_zero_complex @ N )
% 0.26/0.49            = one_one_complex ) )
% 0.26/0.49        & ( ( N != zero_zero_nat )
% 0.26/0.49         => ( ( power_power_complex @ zero_zero_complex @ N )
% 0.26/0.49            = zero_zero_complex ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_0_left
% 0.26/0.49  thf(fact_1541_power__less__imp__less__exp,axiom,
% 0.26/0.49      ! [A: real,M: nat,N: nat] :
% 0.26/0.49        ( ( ord_less_real @ one_one_real @ A )
% 0.26/0.49       => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 0.26/0.49         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_less_imp_less_exp
% 0.26/0.49  thf(fact_1542_power__less__imp__less__exp,axiom,
% 0.26/0.49      ! [A: rat,M: nat,N: nat] :
% 0.26/0.49        ( ( ord_less_rat @ one_one_rat @ A )
% 0.26/0.49       => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 0.26/0.49         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_less_imp_less_exp
% 0.26/0.49  thf(fact_1543_power__less__imp__less__exp,axiom,
% 0.26/0.49      ! [A: nat,M: nat,N: nat] :
% 0.26/0.49        ( ( ord_less_nat @ one_one_nat @ A )
% 0.26/0.49       => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 0.26/0.49         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_less_imp_less_exp
% 0.26/0.49  thf(fact_1544_power__less__imp__less__exp,axiom,
% 0.26/0.49      ! [A: int,M: nat,N: nat] :
% 0.26/0.49        ( ( ord_less_int @ one_one_int @ A )
% 0.26/0.49       => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 0.26/0.49         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_less_imp_less_exp
% 0.26/0.49  thf(fact_1545_power__strict__increasing,axiom,
% 0.26/0.49      ! [N: nat,N4: nat,A: real] :
% 0.26/0.49        ( ( ord_less_nat @ N @ N4 )
% 0.26/0.49       => ( ( ord_less_real @ one_one_real @ A )
% 0.26/0.49         => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_strict_increasing
% 0.26/0.49  thf(fact_1546_power__strict__increasing,axiom,
% 0.26/0.49      ! [N: nat,N4: nat,A: rat] :
% 0.26/0.49        ( ( ord_less_nat @ N @ N4 )
% 0.26/0.49       => ( ( ord_less_rat @ one_one_rat @ A )
% 0.26/0.49         => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_strict_increasing
% 0.26/0.49  thf(fact_1547_power__strict__increasing,axiom,
% 0.26/0.49      ! [N: nat,N4: nat,A: nat] :
% 0.26/0.49        ( ( ord_less_nat @ N @ N4 )
% 0.26/0.49       => ( ( ord_less_nat @ one_one_nat @ A )
% 0.26/0.49         => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_strict_increasing
% 0.26/0.49  thf(fact_1548_power__strict__increasing,axiom,
% 0.26/0.49      ! [N: nat,N4: nat,A: int] :
% 0.26/0.49        ( ( ord_less_nat @ N @ N4 )
% 0.26/0.49       => ( ( ord_less_int @ one_one_int @ A )
% 0.26/0.49         => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_strict_increasing
% 0.26/0.49  thf(fact_1549_power__increasing,axiom,
% 0.26/0.49      ! [N: nat,N4: nat,A: real] :
% 0.26/0.49        ( ( ord_less_eq_nat @ N @ N4 )
% 0.26/0.49       => ( ( ord_less_eq_real @ one_one_real @ A )
% 0.26/0.49         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_increasing
% 0.26/0.49  thf(fact_1550_power__increasing,axiom,
% 0.26/0.49      ! [N: nat,N4: nat,A: rat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ N @ N4 )
% 0.26/0.49       => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.26/0.49         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_increasing
% 0.26/0.49  thf(fact_1551_power__increasing,axiom,
% 0.26/0.49      ! [N: nat,N4: nat,A: nat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ N @ N4 )
% 0.26/0.49       => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.26/0.49         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_increasing
% 0.26/0.49  thf(fact_1552_power__increasing,axiom,
% 0.26/0.49      ! [N: nat,N4: nat,A: int] :
% 0.26/0.49        ( ( ord_less_eq_nat @ N @ N4 )
% 0.26/0.49       => ( ( ord_less_eq_int @ one_one_int @ A )
% 0.26/0.49         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_increasing
% 0.26/0.49  thf(fact_1553_real__arch__pow__inv,axiom,
% 0.26/0.49      ! [Y3: real,X3: real] :
% 0.26/0.49        ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.49       => ( ( ord_less_real @ X3 @ one_one_real )
% 0.26/0.49         => ? [N2: nat] : ( ord_less_real @ ( power_power_real @ X3 @ N2 ) @ Y3 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % real_arch_pow_inv
% 0.26/0.49  thf(fact_1554_int__one__le__iff__zero__less,axiom,
% 0.26/0.49      ! [Z: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ one_one_int @ Z )
% 0.26/0.49        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.26/0.49  
% 0.26/0.49  % int_one_le_iff_zero_less
% 0.26/0.49  thf(fact_1555_power__mono__odd,axiom,
% 0.26/0.49      ! [N: nat,A: real,B: real] :
% 0.26/0.49        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49       => ( ( ord_less_eq_real @ A @ B )
% 0.26/0.49         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_mono_odd
% 0.26/0.49  thf(fact_1556_power__mono__odd,axiom,
% 0.26/0.49      ! [N: nat,A: rat,B: rat] :
% 0.26/0.49        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49       => ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.49         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_mono_odd
% 0.26/0.49  thf(fact_1557_power__mono__odd,axiom,
% 0.26/0.49      ! [N: nat,A: int,B: int] :
% 0.26/0.49        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49       => ( ( ord_less_eq_int @ A @ B )
% 0.26/0.49         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_mono_odd
% 0.26/0.49  thf(fact_1558_odd__pos,axiom,
% 0.26/0.49      ! [N: nat] :
% 0.26/0.49        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.26/0.49  
% 0.26/0.49  % odd_pos
% 0.26/0.49  thf(fact_1559_sqrt2__less__2,axiom,
% 0.26/0.49      ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 0.26/0.49  
% 0.26/0.49  % sqrt2_less_2
% 0.26/0.49  thf(fact_1560_log2__of__power__eq,axiom,
% 0.26/0.49      ! [M: nat,N: nat] :
% 0.26/0.49        ( ( M
% 0.26/0.49          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.49       => ( ( semiri5074537144036343181t_real @ N )
% 0.26/0.49          = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % log2_of_power_eq
% 0.26/0.49  thf(fact_1561_power__strict__decreasing,axiom,
% 0.26/0.49      ! [N: nat,N4: nat,A: real] :
% 0.26/0.49        ( ( ord_less_nat @ N @ N4 )
% 0.26/0.49       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.49         => ( ( ord_less_real @ A @ one_one_real )
% 0.26/0.49           => ( ord_less_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_strict_decreasing
% 0.26/0.49  thf(fact_1562_power__strict__decreasing,axiom,
% 0.26/0.49      ! [N: nat,N4: nat,A: rat] :
% 0.26/0.49        ( ( ord_less_nat @ N @ N4 )
% 0.26/0.49       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.49         => ( ( ord_less_rat @ A @ one_one_rat )
% 0.26/0.49           => ( ord_less_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_strict_decreasing
% 0.26/0.49  thf(fact_1563_power__strict__decreasing,axiom,
% 0.26/0.49      ! [N: nat,N4: nat,A: nat] :
% 0.26/0.49        ( ( ord_less_nat @ N @ N4 )
% 0.26/0.49       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.26/0.49         => ( ( ord_less_nat @ A @ one_one_nat )
% 0.26/0.49           => ( ord_less_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_strict_decreasing
% 0.26/0.49  thf(fact_1564_power__strict__decreasing,axiom,
% 0.26/0.49      ! [N: nat,N4: nat,A: int] :
% 0.26/0.49        ( ( ord_less_nat @ N @ N4 )
% 0.26/0.49       => ( ( ord_less_int @ zero_zero_int @ A )
% 0.26/0.49         => ( ( ord_less_int @ A @ one_one_int )
% 0.26/0.49           => ( ord_less_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_strict_decreasing
% 0.26/0.49  thf(fact_1565_power__decreasing,axiom,
% 0.26/0.49      ! [N: nat,N4: nat,A: real] :
% 0.26/0.49        ( ( ord_less_eq_nat @ N @ N4 )
% 0.26/0.49       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.49         => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.26/0.49           => ( ord_less_eq_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_decreasing
% 0.26/0.49  thf(fact_1566_power__decreasing,axiom,
% 0.26/0.49      ! [N: nat,N4: nat,A: rat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ N @ N4 )
% 0.26/0.49       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.49         => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.26/0.49           => ( ord_less_eq_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_decreasing
% 0.26/0.49  thf(fact_1567_power__decreasing,axiom,
% 0.26/0.49      ! [N: nat,N4: nat,A: nat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ N @ N4 )
% 0.26/0.49       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.49         => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.26/0.49           => ( ord_less_eq_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_decreasing
% 0.26/0.49  thf(fact_1568_power__decreasing,axiom,
% 0.26/0.49      ! [N: nat,N4: nat,A: int] :
% 0.26/0.49        ( ( ord_less_eq_nat @ N @ N4 )
% 0.26/0.49       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.49         => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.26/0.49           => ( ord_less_eq_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_decreasing
% 0.26/0.49  thf(fact_1569_power__le__imp__le__exp,axiom,
% 0.26/0.49      ! [A: real,M: nat,N: nat] :
% 0.26/0.49        ( ( ord_less_real @ one_one_real @ A )
% 0.26/0.49       => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 0.26/0.49         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_le_imp_le_exp
% 0.26/0.49  thf(fact_1570_power__le__imp__le__exp,axiom,
% 0.26/0.49      ! [A: rat,M: nat,N: nat] :
% 0.26/0.49        ( ( ord_less_rat @ one_one_rat @ A )
% 0.26/0.49       => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 0.26/0.49         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_le_imp_le_exp
% 0.26/0.49  thf(fact_1571_power__le__imp__le__exp,axiom,
% 0.26/0.49      ! [A: nat,M: nat,N: nat] :
% 0.26/0.49        ( ( ord_less_nat @ one_one_nat @ A )
% 0.26/0.49       => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 0.26/0.49         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_le_imp_le_exp
% 0.26/0.49  thf(fact_1572_power__le__imp__le__exp,axiom,
% 0.26/0.49      ! [A: int,M: nat,N: nat] :
% 0.26/0.49        ( ( ord_less_int @ one_one_int @ A )
% 0.26/0.49       => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 0.26/0.49         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_le_imp_le_exp
% 0.26/0.49  thf(fact_1573_one__power2,axiom,
% 0.26/0.49      ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.49      = one_one_rat ) ).
% 0.26/0.49  
% 0.26/0.49  % one_power2
% 0.26/0.49  thf(fact_1574_one__power2,axiom,
% 0.26/0.49      ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.49      = one_one_nat ) ).
% 0.26/0.49  
% 0.26/0.49  % one_power2
% 0.26/0.49  thf(fact_1575_one__power2,axiom,
% 0.26/0.49      ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.49      = one_one_int ) ).
% 0.26/0.49  
% 0.26/0.49  % one_power2
% 0.26/0.49  thf(fact_1576_one__power2,axiom,
% 0.26/0.49      ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.49      = one_one_real ) ).
% 0.26/0.49  
% 0.26/0.49  % one_power2
% 0.26/0.49  thf(fact_1577_one__power2,axiom,
% 0.26/0.49      ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.49      = one_one_complex ) ).
% 0.26/0.49  
% 0.26/0.49  % one_power2
% 0.26/0.49  thf(fact_1578_self__le__power,axiom,
% 0.26/0.49      ! [A: real,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_real @ one_one_real @ A )
% 0.26/0.49       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.49         => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % self_le_power
% 0.26/0.49  thf(fact_1579_self__le__power,axiom,
% 0.26/0.49      ! [A: rat,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.26/0.49       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.49         => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % self_le_power
% 0.26/0.49  thf(fact_1580_self__le__power,axiom,
% 0.26/0.49      ! [A: nat,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.26/0.49       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.49         => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % self_le_power
% 0.26/0.49  thf(fact_1581_self__le__power,axiom,
% 0.26/0.49      ! [A: int,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_int @ one_one_int @ A )
% 0.26/0.49       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.49         => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % self_le_power
% 0.26/0.49  thf(fact_1582_one__less__power,axiom,
% 0.26/0.49      ! [A: real,N: nat] :
% 0.26/0.49        ( ( ord_less_real @ one_one_real @ A )
% 0.26/0.49       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.49         => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % one_less_power
% 0.26/0.49  thf(fact_1583_one__less__power,axiom,
% 0.26/0.49      ! [A: rat,N: nat] :
% 0.26/0.49        ( ( ord_less_rat @ one_one_rat @ A )
% 0.26/0.49       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.49         => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % one_less_power
% 0.26/0.49  thf(fact_1584_one__less__power,axiom,
% 0.26/0.49      ! [A: nat,N: nat] :
% 0.26/0.49        ( ( ord_less_nat @ one_one_nat @ A )
% 0.26/0.49       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.49         => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % one_less_power
% 0.26/0.49  thf(fact_1585_one__less__power,axiom,
% 0.26/0.49      ! [A: int,N: nat] :
% 0.26/0.49        ( ( ord_less_int @ one_one_int @ A )
% 0.26/0.49       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.49         => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % one_less_power
% 0.26/0.49  thf(fact_1586_zero__le__power__eq,axiom,
% 0.26/0.49      ! [A: real,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 0.26/0.49        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49            & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_le_power_eq
% 0.26/0.49  thf(fact_1587_zero__le__power__eq,axiom,
% 0.26/0.49      ! [A: rat,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 0.26/0.49        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49            & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_le_power_eq
% 0.26/0.49  thf(fact_1588_zero__le__power__eq,axiom,
% 0.26/0.49      ! [A: int,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 0.26/0.49        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49            & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_le_power_eq
% 0.26/0.49  thf(fact_1589_zero__le__odd__power,axiom,
% 0.26/0.49      ! [N: nat,A: real] :
% 0.26/0.49        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49       => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 0.26/0.49          = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_le_odd_power
% 0.26/0.49  thf(fact_1590_zero__le__odd__power,axiom,
% 0.26/0.49      ! [N: nat,A: rat] :
% 0.26/0.49        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49       => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 0.26/0.49          = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_le_odd_power
% 0.26/0.49  thf(fact_1591_zero__le__odd__power,axiom,
% 0.26/0.49      ! [N: nat,A: int] :
% 0.26/0.49        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49       => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 0.26/0.49          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_le_odd_power
% 0.26/0.49  thf(fact_1592_zero__le__even__power,axiom,
% 0.26/0.49      ! [N: nat,A: real] :
% 0.26/0.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49       => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_le_even_power
% 0.26/0.49  thf(fact_1593_zero__le__even__power,axiom,
% 0.26/0.49      ! [N: nat,A: rat] :
% 0.26/0.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_le_even_power
% 0.26/0.49  thf(fact_1594_zero__le__even__power,axiom,
% 0.26/0.49      ! [N: nat,A: int] :
% 0.26/0.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49       => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_le_even_power
% 0.26/0.49  thf(fact_1595_real__less__rsqrt,axiom,
% 0.26/0.49      ! [X3: real,Y3: real] :
% 0.26/0.49        ( ( ord_less_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y3 )
% 0.26/0.49       => ( ord_less_real @ X3 @ ( sqrt @ Y3 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % real_less_rsqrt
% 0.26/0.49  thf(fact_1596_sqrt__le__D,axiom,
% 0.26/0.49      ! [X3: real,Y3: real] :
% 0.26/0.49        ( ( ord_less_eq_real @ ( sqrt @ X3 ) @ Y3 )
% 0.26/0.49       => ( ord_less_eq_real @ X3 @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % sqrt_le_D
% 0.26/0.49  thf(fact_1597_real__le__rsqrt,axiom,
% 0.26/0.49      ! [X3: real,Y3: real] :
% 0.26/0.49        ( ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y3 )
% 0.26/0.49       => ( ord_less_eq_real @ X3 @ ( sqrt @ Y3 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % real_le_rsqrt
% 0.26/0.49  thf(fact_1598_take__bit__int__less__exp,axiom,
% 0.26/0.49      ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_int_less_exp
% 0.26/0.49  thf(fact_1599_zero__less__power__eq,axiom,
% 0.26/0.49      ! [A: real,N: nat] :
% 0.26/0.49        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 0.26/0.49        = ( ( N = zero_zero_nat )
% 0.26/0.49          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49            & ( A != zero_zero_real ) )
% 0.26/0.49          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49            & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_less_power_eq
% 0.26/0.49  thf(fact_1600_zero__less__power__eq,axiom,
% 0.26/0.49      ! [A: rat,N: nat] :
% 0.26/0.49        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 0.26/0.49        = ( ( N = zero_zero_nat )
% 0.26/0.49          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49            & ( A != zero_zero_rat ) )
% 0.26/0.49          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49            & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_less_power_eq
% 0.26/0.49  thf(fact_1601_zero__less__power__eq,axiom,
% 0.26/0.49      ! [A: int,N: nat] :
% 0.26/0.49        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 0.26/0.49        = ( ( N = zero_zero_nat )
% 0.26/0.49          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49            & ( A != zero_zero_int ) )
% 0.26/0.49          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49            & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_less_power_eq
% 0.26/0.49  thf(fact_1602_dvd__power__iff__le,axiom,
% 0.26/0.49      ! [K: nat,M: nat,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.26/0.49       => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 0.26/0.49          = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_power_iff_le
% 0.26/0.49  thf(fact_1603_two__realpow__ge__one,axiom,
% 0.26/0.49      ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 0.26/0.49  
% 0.26/0.49  % two_realpow_ge_one
% 0.26/0.49  thf(fact_1604_real__le__lsqrt,axiom,
% 0.26/0.49      ! [X3: real,Y3: real] :
% 0.26/0.49        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.49       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.49         => ( ( ord_less_eq_real @ X3 @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.49           => ( ord_less_eq_real @ ( sqrt @ X3 ) @ Y3 ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % real_le_lsqrt
% 0.26/0.49  thf(fact_1605_real__sqrt__unique,axiom,
% 0.26/0.49      ! [Y3: real,X3: real] :
% 0.26/0.49        ( ( ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.49          = X3 )
% 0.26/0.49       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.49         => ( ( sqrt @ X3 )
% 0.26/0.49            = Y3 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % real_sqrt_unique
% 0.26/0.49  thf(fact_1606_less__log2__of__power,axiom,
% 0.26/0.49      ! [N: nat,M: nat] :
% 0.26/0.49        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 0.26/0.49       => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % less_log2_of_power
% 0.26/0.49  thf(fact_1607_le__log2__of__power,axiom,
% 0.26/0.49      ! [N: nat,M: nat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 0.26/0.49       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_log2_of_power
% 0.26/0.49  thf(fact_1608_take__bit__int__greater__eq__self__iff,axiom,
% 0.26/0.49      ! [K: int,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 0.26/0.49        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_int_greater_eq_self_iff
% 0.26/0.49  thf(fact_1609_take__bit__int__less__self__iff,axiom,
% 0.26/0.49      ! [N: nat,K: int] :
% 0.26/0.49        ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 0.26/0.49        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_int_less_self_iff
% 0.26/0.49  thf(fact_1610_power__le__zero__eq,axiom,
% 0.26/0.49      ! [A: real,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 0.26/0.49        = ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.49          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49              & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 0.26/0.49            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49              & ( A = zero_zero_real ) ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_le_zero_eq
% 0.26/0.49  thf(fact_1611_power__le__zero__eq,axiom,
% 0.26/0.49      ! [A: rat,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 0.26/0.49        = ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.49          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49              & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 0.26/0.49            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49              & ( A = zero_zero_rat ) ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_le_zero_eq
% 0.26/0.49  thf(fact_1612_power__le__zero__eq,axiom,
% 0.26/0.49      ! [A: int,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 0.26/0.49        = ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.49          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49              & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 0.26/0.49            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49              & ( A = zero_zero_int ) ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_le_zero_eq
% 0.26/0.49  thf(fact_1613_pow__divides__pow__iff,axiom,
% 0.26/0.49      ! [N: nat,A: nat,B: nat] :
% 0.26/0.49        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.49       => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 0.26/0.49          = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % pow_divides_pow_iff
% 0.26/0.49  thf(fact_1614_pow__divides__pow__iff,axiom,
% 0.26/0.49      ! [N: nat,A: int,B: int] :
% 0.26/0.49        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.49       => ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 0.26/0.49          = ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % pow_divides_pow_iff
% 0.26/0.49  thf(fact_1615_arcosh__1,axiom,
% 0.26/0.49      ( ( arcosh_real @ one_one_real )
% 0.26/0.49      = zero_zero_real ) ).
% 0.26/0.49  
% 0.26/0.49  % arcosh_1
% 0.26/0.49  thf(fact_1616_dvd__0__left__iff,axiom,
% 0.26/0.49      ! [A: code_integer] :
% 0.26/0.49        ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 0.26/0.49        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_0_left_iff
% 0.26/0.49  thf(fact_1617_dvd__0__left__iff,axiom,
% 0.26/0.49      ! [A: real] :
% 0.26/0.49        ( ( dvd_dvd_real @ zero_zero_real @ A )
% 0.26/0.49        = ( A = zero_zero_real ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_0_left_iff
% 0.26/0.49  thf(fact_1618_dvd__0__left__iff,axiom,
% 0.26/0.49      ! [A: rat] :
% 0.26/0.49        ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 0.26/0.49        = ( A = zero_zero_rat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_0_left_iff
% 0.26/0.49  thf(fact_1619_dvd__0__left__iff,axiom,
% 0.26/0.49      ! [A: nat] :
% 0.26/0.49        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.26/0.49        = ( A = zero_zero_nat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_0_left_iff
% 0.26/0.49  thf(fact_1620_dvd__0__left__iff,axiom,
% 0.26/0.49      ! [A: int] :
% 0.26/0.49        ( ( dvd_dvd_int @ zero_zero_int @ A )
% 0.26/0.49        = ( A = zero_zero_int ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_0_left_iff
% 0.26/0.49  thf(fact_1621_dvd__0__right,axiom,
% 0.26/0.49      ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ zero_z3403309356797280102nteger ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_0_right
% 0.26/0.49  thf(fact_1622_dvd__0__right,axiom,
% 0.26/0.49      ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_0_right
% 0.26/0.49  thf(fact_1623_dvd__0__right,axiom,
% 0.26/0.49      ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_0_right
% 0.26/0.49  thf(fact_1624_dvd__0__right,axiom,
% 0.26/0.49      ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_0_right
% 0.26/0.49  thf(fact_1625_dvd__0__right,axiom,
% 0.26/0.49      ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_0_right
% 0.26/0.49  thf(fact_1626_artanh__0,axiom,
% 0.26/0.49      ( ( artanh_real @ zero_zero_real )
% 0.26/0.49      = zero_zero_real ) ).
% 0.26/0.49  
% 0.26/0.49  % artanh_0
% 0.26/0.49  thf(fact_1627_arsinh__0,axiom,
% 0.26/0.49      ( ( arsinh_real @ zero_zero_real )
% 0.26/0.49      = zero_zero_real ) ).
% 0.26/0.49  
% 0.26/0.49  % arsinh_0
% 0.26/0.49  thf(fact_1628_of__nat__dvd__iff,axiom,
% 0.26/0.49      ! [M: nat,N: nat] :
% 0.26/0.49        ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 0.26/0.49        = ( dvd_dvd_nat @ M @ N ) ) ).
% 0.26/0.49  
% 0.26/0.49  % of_nat_dvd_iff
% 0.26/0.49  thf(fact_1629_of__nat__dvd__iff,axiom,
% 0.26/0.49      ! [M: nat,N: nat] :
% 0.26/0.49        ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.26/0.49        = ( dvd_dvd_nat @ M @ N ) ) ).
% 0.26/0.49  
% 0.26/0.49  % of_nat_dvd_iff
% 0.26/0.49  thf(fact_1630_of__nat__dvd__iff,axiom,
% 0.26/0.49      ! [M: nat,N: nat] :
% 0.26/0.49        ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.49        = ( dvd_dvd_nat @ M @ N ) ) ).
% 0.26/0.49  
% 0.26/0.49  % of_nat_dvd_iff
% 0.26/0.49  thf(fact_1631_log__ceil__idem,axiom,
% 0.26/0.49      ! [X3: real] :
% 0.26/0.49        ( ( ord_less_eq_real @ one_one_real @ X3 )
% 0.26/0.49       => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) )
% 0.26/0.49          = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X3 ) ) ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % log_ceil_idem
% 0.26/0.49  thf(fact_1632_dbl__simps_I3_J,axiom,
% 0.26/0.49      ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 0.26/0.49      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dbl_simps(3)
% 0.26/0.49  thf(fact_1633_dbl__simps_I3_J,axiom,
% 0.26/0.49      ( ( neg_numeral_dbl_real @ one_one_real )
% 0.26/0.49      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dbl_simps(3)
% 0.26/0.49  thf(fact_1634_dbl__simps_I3_J,axiom,
% 0.26/0.49      ( ( neg_numeral_dbl_rat @ one_one_rat )
% 0.26/0.49      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dbl_simps(3)
% 0.26/0.49  thf(fact_1635_dbl__simps_I3_J,axiom,
% 0.26/0.49      ( ( neg_numeral_dbl_int @ one_one_int )
% 0.26/0.49      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dbl_simps(3)
% 0.26/0.49  thf(fact_1636_dvd__pos__nat,axiom,
% 0.26/0.49      ! [N: nat,M: nat] :
% 0.26/0.49        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.49       => ( ( dvd_dvd_nat @ M @ N )
% 0.26/0.49         => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_pos_nat
% 0.26/0.49  thf(fact_1637_not__is__unit__0,axiom,
% 0.26/0.49      ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 0.26/0.49  
% 0.26/0.49  % not_is_unit_0
% 0.26/0.49  thf(fact_1638_not__is__unit__0,axiom,
% 0.26/0.49      ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 0.26/0.49  
% 0.26/0.49  % not_is_unit_0
% 0.26/0.49  thf(fact_1639_not__is__unit__0,axiom,
% 0.26/0.49      ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 0.26/0.49  
% 0.26/0.49  % not_is_unit_0
% 0.26/0.49  thf(fact_1640_ceiling__of__int,axiom,
% 0.26/0.49      ! [Z: int] :
% 0.26/0.49        ( ( archim2889992004027027881ng_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.26/0.49        = Z ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_of_int
% 0.26/0.49  thf(fact_1641_ceiling__of__int,axiom,
% 0.26/0.49      ! [Z: int] :
% 0.26/0.49        ( ( archim7802044766580827645g_real @ ( ring_1_of_int_real @ Z ) )
% 0.26/0.49        = Z ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_of_int
% 0.26/0.49  thf(fact_1642_of__int__ceiling__cancel,axiom,
% 0.26/0.49      ! [X3: rat] :
% 0.26/0.49        ( ( ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X3 ) )
% 0.26/0.49          = X3 )
% 0.26/0.49        = ( ? [N3: int] :
% 0.26/0.49              ( X3
% 0.26/0.49              = ( ring_1_of_int_rat @ N3 ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % of_int_ceiling_cancel
% 0.26/0.49  thf(fact_1643_of__int__ceiling__cancel,axiom,
% 0.26/0.49      ! [X3: real] :
% 0.26/0.49        ( ( ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X3 ) )
% 0.26/0.49          = X3 )
% 0.26/0.49        = ( ? [N3: int] :
% 0.26/0.49              ( X3
% 0.26/0.49              = ( ring_1_of_int_real @ N3 ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % of_int_ceiling_cancel
% 0.26/0.49  thf(fact_1644_dbl__simps_I2_J,axiom,
% 0.26/0.49      ( ( neg_numeral_dbl_real @ zero_zero_real )
% 0.26/0.49      = zero_zero_real ) ).
% 0.26/0.49  
% 0.26/0.49  % dbl_simps(2)
% 0.26/0.49  thf(fact_1645_dbl__simps_I2_J,axiom,
% 0.26/0.49      ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 0.26/0.49      = zero_zero_rat ) ).
% 0.26/0.49  
% 0.26/0.49  % dbl_simps(2)
% 0.26/0.49  thf(fact_1646_dbl__simps_I2_J,axiom,
% 0.26/0.49      ( ( neg_numeral_dbl_int @ zero_zero_int )
% 0.26/0.49      = zero_zero_int ) ).
% 0.26/0.49  
% 0.26/0.49  % dbl_simps(2)
% 0.26/0.49  thf(fact_1647_ceiling__zero,axiom,
% 0.26/0.49      ( ( archim2889992004027027881ng_rat @ zero_zero_rat )
% 0.26/0.49      = zero_zero_int ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_zero
% 0.26/0.49  thf(fact_1648_ceiling__zero,axiom,
% 0.26/0.49      ( ( archim7802044766580827645g_real @ zero_zero_real )
% 0.26/0.49      = zero_zero_int ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_zero
% 0.26/0.49  thf(fact_1649_ceiling__numeral,axiom,
% 0.26/0.49      ! [V: num] :
% 0.26/0.49        ( ( archim7802044766580827645g_real @ ( numeral_numeral_real @ V ) )
% 0.26/0.49        = ( numeral_numeral_int @ V ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_numeral
% 0.26/0.49  thf(fact_1650_ceiling__numeral,axiom,
% 0.26/0.49      ! [V: num] :
% 0.26/0.49        ( ( archim2889992004027027881ng_rat @ ( numeral_numeral_rat @ V ) )
% 0.26/0.49        = ( numeral_numeral_int @ V ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_numeral
% 0.26/0.49  thf(fact_1651_ceiling__one,axiom,
% 0.26/0.49      ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 0.26/0.49      = one_one_int ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_one
% 0.26/0.49  thf(fact_1652_ceiling__one,axiom,
% 0.26/0.49      ( ( archim7802044766580827645g_real @ one_one_real )
% 0.26/0.49      = one_one_int ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_one
% 0.26/0.49  thf(fact_1653_ceiling__of__nat,axiom,
% 0.26/0.49      ! [N: nat] :
% 0.26/0.49        ( ( archim7802044766580827645g_real @ ( semiri5074537144036343181t_real @ N ) )
% 0.26/0.49        = ( semiri1314217659103216013at_int @ N ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_of_nat
% 0.26/0.49  thf(fact_1654_ceiling__of__nat,axiom,
% 0.26/0.49      ! [N: nat] :
% 0.26/0.49        ( ( archim2889992004027027881ng_rat @ ( semiri681578069525770553at_rat @ N ) )
% 0.26/0.49        = ( semiri1314217659103216013at_int @ N ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_of_nat
% 0.26/0.49  thf(fact_1655_int__dvd__int__iff,axiom,
% 0.26/0.49      ! [M: nat,N: nat] :
% 0.26/0.49        ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.49        = ( dvd_dvd_nat @ M @ N ) ) ).
% 0.26/0.49  
% 0.26/0.49  % int_dvd_int_iff
% 0.26/0.49  thf(fact_1656_dbl__simps_I5_J,axiom,
% 0.26/0.49      ! [K: num] :
% 0.26/0.49        ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 0.26/0.49        = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dbl_simps(5)
% 0.26/0.49  thf(fact_1657_dbl__simps_I5_J,axiom,
% 0.26/0.49      ! [K: num] :
% 0.26/0.49        ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 0.26/0.49        = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dbl_simps(5)
% 0.26/0.49  thf(fact_1658_dbl__simps_I5_J,axiom,
% 0.26/0.49      ! [K: num] :
% 0.26/0.49        ( ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) )
% 0.26/0.49        = ( numeral_numeral_rat @ ( bit0 @ K ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dbl_simps(5)
% 0.26/0.49  thf(fact_1659_dbl__simps_I5_J,axiom,
% 0.26/0.49      ! [K: num] :
% 0.26/0.49        ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 0.26/0.49        = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dbl_simps(5)
% 0.26/0.49  thf(fact_1660_ceiling__le__zero,axiom,
% 0.26/0.49      ! [X3: real] :
% 0.26/0.49        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X3 ) @ zero_zero_int )
% 0.26/0.49        = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_le_zero
% 0.26/0.49  thf(fact_1661_ceiling__le__zero,axiom,
% 0.26/0.49      ! [X3: rat] :
% 0.26/0.49        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X3 ) @ zero_zero_int )
% 0.26/0.49        = ( ord_less_eq_rat @ X3 @ zero_zero_rat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_le_zero
% 0.26/0.49  thf(fact_1662_zero__less__ceiling,axiom,
% 0.26/0.49      ! [X3: rat] :
% 0.26/0.49        ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X3 ) )
% 0.26/0.49        = ( ord_less_rat @ zero_zero_rat @ X3 ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_less_ceiling
% 0.26/0.49  thf(fact_1663_zero__less__ceiling,axiom,
% 0.26/0.49      ! [X3: real] :
% 0.26/0.49        ( ( ord_less_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X3 ) )
% 0.26/0.49        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_less_ceiling
% 0.26/0.49  thf(fact_1664_ceiling__le__numeral,axiom,
% 0.26/0.49      ! [X3: real,V: num] :
% 0.26/0.49        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X3 ) @ ( numeral_numeral_int @ V ) )
% 0.26/0.49        = ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ V ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_le_numeral
% 0.26/0.49  thf(fact_1665_ceiling__le__numeral,axiom,
% 0.26/0.49      ! [X3: rat,V: num] :
% 0.26/0.49        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X3 ) @ ( numeral_numeral_int @ V ) )
% 0.26/0.49        = ( ord_less_eq_rat @ X3 @ ( numeral_numeral_rat @ V ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_le_numeral
% 0.26/0.49  thf(fact_1666_ceiling__less__one,axiom,
% 0.26/0.49      ! [X3: real] :
% 0.26/0.49        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X3 ) @ one_one_int )
% 0.26/0.49        = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_less_one
% 0.26/0.49  thf(fact_1667_ceiling__less__one,axiom,
% 0.26/0.49      ! [X3: rat] :
% 0.26/0.49        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X3 ) @ one_one_int )
% 0.26/0.49        = ( ord_less_eq_rat @ X3 @ zero_zero_rat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_less_one
% 0.26/0.49  thf(fact_1668_numeral__less__ceiling,axiom,
% 0.26/0.49      ! [V: num,X3: real] :
% 0.26/0.49        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X3 ) )
% 0.26/0.49        = ( ord_less_real @ ( numeral_numeral_real @ V ) @ X3 ) ) ).
% 0.26/0.49  
% 0.26/0.49  % numeral_less_ceiling
% 0.26/0.49  thf(fact_1669_numeral__less__ceiling,axiom,
% 0.26/0.49      ! [V: num,X3: rat] :
% 0.26/0.49        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X3 ) )
% 0.26/0.49        = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X3 ) ) ).
% 0.26/0.49  
% 0.26/0.49  % numeral_less_ceiling
% 0.26/0.49  thf(fact_1670_one__le__ceiling,axiom,
% 0.26/0.49      ! [X3: rat] :
% 0.26/0.49        ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X3 ) )
% 0.26/0.49        = ( ord_less_rat @ zero_zero_rat @ X3 ) ) ).
% 0.26/0.49  
% 0.26/0.49  % one_le_ceiling
% 0.26/0.49  thf(fact_1671_one__le__ceiling,axiom,
% 0.26/0.49      ! [X3: real] :
% 0.26/0.49        ( ( ord_less_eq_int @ one_one_int @ ( archim7802044766580827645g_real @ X3 ) )
% 0.26/0.49        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 0.26/0.49  
% 0.26/0.49  % one_le_ceiling
% 0.26/0.49  thf(fact_1672_ceiling__le__one,axiom,
% 0.26/0.49      ! [X3: real] :
% 0.26/0.49        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X3 ) @ one_one_int )
% 0.26/0.49        = ( ord_less_eq_real @ X3 @ one_one_real ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_le_one
% 0.26/0.49  thf(fact_1673_ceiling__le__one,axiom,
% 0.26/0.49      ! [X3: rat] :
% 0.26/0.49        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X3 ) @ one_one_int )
% 0.26/0.49        = ( ord_less_eq_rat @ X3 @ one_one_rat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_le_one
% 0.26/0.49  thf(fact_1674_one__less__ceiling,axiom,
% 0.26/0.49      ! [X3: rat] :
% 0.26/0.49        ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X3 ) )
% 0.26/0.49        = ( ord_less_rat @ one_one_rat @ X3 ) ) ).
% 0.26/0.49  
% 0.26/0.49  % one_less_ceiling
% 0.26/0.49  thf(fact_1675_one__less__ceiling,axiom,
% 0.26/0.49      ! [X3: real] :
% 0.26/0.49        ( ( ord_less_int @ one_one_int @ ( archim7802044766580827645g_real @ X3 ) )
% 0.26/0.49        = ( ord_less_real @ one_one_real @ X3 ) ) ).
% 0.26/0.49  
% 0.26/0.49  % one_less_ceiling
% 0.26/0.49  thf(fact_1676_ceiling__numeral__power,axiom,
% 0.26/0.49      ! [X3: num,N: nat] :
% 0.26/0.49        ( ( archim7802044766580827645g_real @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N ) )
% 0.26/0.49        = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_numeral_power
% 0.26/0.49  thf(fact_1677_ceiling__numeral__power,axiom,
% 0.26/0.49      ! [X3: num,N: nat] :
% 0.26/0.49        ( ( archim2889992004027027881ng_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N ) )
% 0.26/0.49        = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_numeral_power
% 0.26/0.49  thf(fact_1678_nat__ceiling__le__eq,axiom,
% 0.26/0.49      ! [X3: real,A: nat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X3 ) ) @ A )
% 0.26/0.49        = ( ord_less_eq_real @ X3 @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % nat_ceiling_le_eq
% 0.26/0.49  thf(fact_1679_take__bit__nat__less__eq__self,axiom,
% 0.26/0.49      ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_nat_less_eq_self
% 0.26/0.49  thf(fact_1680_take__bit__tightened__less__eq__nat,axiom,
% 0.26/0.49      ! [M: nat,N: nat,Q3: nat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.49       => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q3 ) @ ( bit_se2925701944663578781it_nat @ N @ Q3 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_tightened_less_eq_nat
% 0.26/0.49  thf(fact_1681_ceiling__mono,axiom,
% 0.26/0.49      ! [Y3: real,X3: real] :
% 0.26/0.49        ( ( ord_less_eq_real @ Y3 @ X3 )
% 0.26/0.49       => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ Y3 ) @ ( archim7802044766580827645g_real @ X3 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_mono
% 0.26/0.49  thf(fact_1682_ceiling__mono,axiom,
% 0.26/0.49      ! [Y3: rat,X3: rat] :
% 0.26/0.49        ( ( ord_less_eq_rat @ Y3 @ X3 )
% 0.26/0.49       => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ Y3 ) @ ( archim2889992004027027881ng_rat @ X3 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_mono
% 0.26/0.49  thf(fact_1683_le__of__int__ceiling,axiom,
% 0.26/0.49      ! [X3: real] : ( ord_less_eq_real @ X3 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X3 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_of_int_ceiling
% 0.26/0.49  thf(fact_1684_le__of__int__ceiling,axiom,
% 0.26/0.49      ! [X3: rat] : ( ord_less_eq_rat @ X3 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X3 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_of_int_ceiling
% 0.26/0.49  thf(fact_1685_ceiling__less__cancel,axiom,
% 0.26/0.49      ! [X3: rat,Y3: rat] :
% 0.26/0.49        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X3 ) @ ( archim2889992004027027881ng_rat @ Y3 ) )
% 0.26/0.49       => ( ord_less_rat @ X3 @ Y3 ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_less_cancel
% 0.26/0.49  thf(fact_1686_ceiling__less__cancel,axiom,
% 0.26/0.49      ! [X3: real,Y3: real] :
% 0.26/0.49        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X3 ) @ ( archim7802044766580827645g_real @ Y3 ) )
% 0.26/0.49       => ( ord_less_real @ X3 @ Y3 ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_less_cancel
% 0.26/0.49  thf(fact_1687_zdvd__antisym__nonneg,axiom,
% 0.26/0.49      ! [M: int,N: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ zero_zero_int @ M )
% 0.26/0.49       => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 0.26/0.49         => ( ( dvd_dvd_int @ M @ N )
% 0.26/0.49           => ( ( dvd_dvd_int @ N @ M )
% 0.26/0.49             => ( M = N ) ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zdvd_antisym_nonneg
% 0.26/0.49  thf(fact_1688_zdvd__not__zless,axiom,
% 0.26/0.49      ! [M: int,N: int] :
% 0.26/0.49        ( ( ord_less_int @ zero_zero_int @ M )
% 0.26/0.49       => ( ( ord_less_int @ M @ N )
% 0.26/0.49         => ~ ( dvd_dvd_int @ N @ M ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zdvd_not_zless
% 0.26/0.49  thf(fact_1689_real__nat__ceiling__ge,axiom,
% 0.26/0.49      ! [X3: real] : ( ord_less_eq_real @ X3 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X3 ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % real_nat_ceiling_ge
% 0.26/0.49  thf(fact_1690_of__nat__ceiling,axiom,
% 0.26/0.49      ! [R2: real] : ( ord_less_eq_real @ R2 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ R2 ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % of_nat_ceiling
% 0.26/0.49  thf(fact_1691_of__nat__ceiling,axiom,
% 0.26/0.49      ! [R2: rat] : ( ord_less_eq_rat @ R2 @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim2889992004027027881ng_rat @ R2 ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % of_nat_ceiling
% 0.26/0.49  thf(fact_1692_ceiling__le,axiom,
% 0.26/0.49      ! [X3: real,A: int] :
% 0.26/0.49        ( ( ord_less_eq_real @ X3 @ ( ring_1_of_int_real @ A ) )
% 0.26/0.49       => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X3 ) @ A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_le
% 0.26/0.49  thf(fact_1693_ceiling__le,axiom,
% 0.26/0.49      ! [X3: rat,A: int] :
% 0.26/0.49        ( ( ord_less_eq_rat @ X3 @ ( ring_1_of_int_rat @ A ) )
% 0.26/0.49       => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X3 ) @ A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_le
% 0.26/0.49  thf(fact_1694_ceiling__le__iff,axiom,
% 0.26/0.49      ! [X3: real,Z: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X3 ) @ Z )
% 0.26/0.49        = ( ord_less_eq_real @ X3 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_le_iff
% 0.26/0.49  thf(fact_1695_ceiling__le__iff,axiom,
% 0.26/0.49      ! [X3: rat,Z: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X3 ) @ Z )
% 0.26/0.49        = ( ord_less_eq_rat @ X3 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ceiling_le_iff
% 0.26/0.49  thf(fact_1696_less__ceiling__iff,axiom,
% 0.26/0.49      ! [Z: int,X3: rat] :
% 0.26/0.49        ( ( ord_less_int @ Z @ ( archim2889992004027027881ng_rat @ X3 ) )
% 0.26/0.49        = ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ X3 ) ) ).
% 0.26/0.49  
% 0.26/0.49  % less_ceiling_iff
% 0.26/0.49  thf(fact_1697_less__ceiling__iff,axiom,
% 0.26/0.49      ! [Z: int,X3: real] :
% 0.26/0.49        ( ( ord_less_int @ Z @ ( archim7802044766580827645g_real @ X3 ) )
% 0.26/0.49        = ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ X3 ) ) ).
% 0.26/0.49  
% 0.26/0.49  % less_ceiling_iff
% 0.26/0.49  thf(fact_1698_or__nat__def,axiom,
% 0.26/0.49      ( bit_se1412395901928357646or_nat
% 0.26/0.49      = ( ^ [M3: nat,N3: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % or_nat_def
% 0.26/0.49  thf(fact_1699_zdvd__imp__le,axiom,
% 0.26/0.49      ! [Z: int,N: int] :
% 0.26/0.49        ( ( dvd_dvd_int @ Z @ N )
% 0.26/0.49       => ( ( ord_less_int @ zero_zero_int @ N )
% 0.26/0.49         => ( ord_less_eq_int @ Z @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zdvd_imp_le
% 0.26/0.49  thf(fact_1700_linorder__neqE__linordered__idom,axiom,
% 0.26/0.49      ! [X3: real,Y3: real] :
% 0.26/0.49        ( ( X3 != Y3 )
% 0.26/0.49       => ( ~ ( ord_less_real @ X3 @ Y3 )
% 0.26/0.49         => ( ord_less_real @ Y3 @ X3 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % linorder_neqE_linordered_idom
% 0.26/0.49  thf(fact_1701_linorder__neqE__linordered__idom,axiom,
% 0.26/0.49      ! [X3: rat,Y3: rat] :
% 0.26/0.49        ( ( X3 != Y3 )
% 0.26/0.49       => ( ~ ( ord_less_rat @ X3 @ Y3 )
% 0.26/0.49         => ( ord_less_rat @ Y3 @ X3 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % linorder_neqE_linordered_idom
% 0.26/0.49  thf(fact_1702_linorder__neqE__linordered__idom,axiom,
% 0.26/0.49      ! [X3: int,Y3: int] :
% 0.26/0.49        ( ( X3 != Y3 )
% 0.26/0.49       => ( ~ ( ord_less_int @ X3 @ Y3 )
% 0.26/0.49         => ( ord_less_int @ Y3 @ X3 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % linorder_neqE_linordered_idom
% 0.26/0.49  thf(fact_1703_xor__nat__def,axiom,
% 0.26/0.49      ( bit_se6528837805403552850or_nat
% 0.26/0.49      = ( ^ [M3: nat,N3: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % xor_nat_def
% 0.26/0.49  thf(fact_1704_take__bit__nat__eq,axiom,
% 0.26/0.49      ! [K: int,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.26/0.49       => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 0.26/0.49          = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_nat_eq
% 0.26/0.49  thf(fact_1705_nat__take__bit__eq,axiom,
% 0.26/0.49      ! [K: int,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.26/0.49       => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 0.26/0.49          = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % nat_take_bit_eq
% 0.26/0.49  thf(fact_1706_take__bit__nat__eq__self__iff,axiom,
% 0.26/0.49      ! [N: nat,M: nat] :
% 0.26/0.49        ( ( ( bit_se2925701944663578781it_nat @ N @ M )
% 0.26/0.49          = M )
% 0.26/0.49        = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_nat_eq_self_iff
% 0.26/0.49  thf(fact_1707_take__bit__nat__less__exp,axiom,
% 0.26/0.49      ! [N: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_nat_less_exp
% 0.26/0.49  thf(fact_1708_take__bit__nat__eq__self,axiom,
% 0.26/0.49      ! [M: nat,N: nat] :
% 0.26/0.49        ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.49       => ( ( bit_se2925701944663578781it_nat @ N @ M )
% 0.26/0.49          = M ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_nat_eq_self
% 0.26/0.49  thf(fact_1709_take__bit__nat__less__self__iff,axiom,
% 0.26/0.49      ! [N: nat,M: nat] :
% 0.26/0.49        ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 0.26/0.49        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_nat_less_self_iff
% 0.26/0.49  thf(fact_1710_nat__dvd__iff,axiom,
% 0.26/0.49      ! [Z: int,M: nat] :
% 0.26/0.49        ( ( dvd_dvd_nat @ ( nat2 @ Z ) @ M )
% 0.26/0.49        = ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.26/0.49           => ( dvd_dvd_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) )
% 0.26/0.49          & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.26/0.49           => ( M = zero_zero_nat ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % nat_dvd_iff
% 0.26/0.49  thf(fact_1711_zero__neq__one,axiom,
% 0.26/0.49      zero_zero_complex != one_one_complex ).
% 0.26/0.49  
% 0.26/0.49  % zero_neq_one
% 0.26/0.49  thf(fact_1712_zero__neq__one,axiom,
% 0.26/0.49      zero_zero_real != one_one_real ).
% 0.26/0.49  
% 0.26/0.49  % zero_neq_one
% 0.26/0.49  thf(fact_1713_zero__neq__one,axiom,
% 0.26/0.49      zero_zero_rat != one_one_rat ).
% 0.26/0.49  
% 0.26/0.49  % zero_neq_one
% 0.26/0.49  thf(fact_1714_zero__neq__one,axiom,
% 0.26/0.49      zero_zero_nat != one_one_nat ).
% 0.26/0.49  
% 0.26/0.49  % zero_neq_one
% 0.26/0.49  thf(fact_1715_zero__neq__one,axiom,
% 0.26/0.49      zero_zero_int != one_one_int ).
% 0.26/0.49  
% 0.26/0.49  % zero_neq_one
% 0.26/0.49  thf(fact_1716_dvd__0__left,axiom,
% 0.26/0.49      ! [A: code_integer] :
% 0.26/0.49        ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 0.26/0.49       => ( A = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_0_left
% 0.26/0.49  thf(fact_1717_dvd__0__left,axiom,
% 0.26/0.49      ! [A: real] :
% 0.26/0.49        ( ( dvd_dvd_real @ zero_zero_real @ A )
% 0.26/0.49       => ( A = zero_zero_real ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_0_left
% 0.26/0.49  thf(fact_1718_dvd__0__left,axiom,
% 0.26/0.49      ! [A: rat] :
% 0.26/0.49        ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 0.26/0.49       => ( A = zero_zero_rat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_0_left
% 0.26/0.49  thf(fact_1719_dvd__0__left,axiom,
% 0.26/0.49      ! [A: nat] :
% 0.26/0.49        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.26/0.49       => ( A = zero_zero_nat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_0_left
% 0.26/0.49  thf(fact_1720_dvd__0__left,axiom,
% 0.26/0.49      ! [A: int] :
% 0.26/0.49        ( ( dvd_dvd_int @ zero_zero_int @ A )
% 0.26/0.49       => ( A = zero_zero_int ) ) ).
% 0.26/0.49  
% 0.26/0.49  % dvd_0_left
% 0.26/0.49  thf(fact_1721_gcd__nat_Oextremum__uniqueI,axiom,
% 0.26/0.49      ! [A: nat] :
% 0.26/0.49        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.26/0.49       => ( A = zero_zero_nat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % gcd_nat.extremum_uniqueI
% 0.26/0.49  thf(fact_1722_gcd__nat_Onot__eq__extremum,axiom,
% 0.26/0.49      ! [A: nat] :
% 0.26/0.49        ( ( A != zero_zero_nat )
% 0.26/0.49        = ( ( dvd_dvd_nat @ A @ zero_zero_nat )
% 0.26/0.49          & ( A != zero_zero_nat ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % gcd_nat.not_eq_extremum
% 0.26/0.49  thf(fact_1723_gcd__nat_Oextremum__unique,axiom,
% 0.26/0.49      ! [A: nat] :
% 0.26/0.49        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.26/0.49        = ( A = zero_zero_nat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % gcd_nat.extremum_unique
% 0.26/0.49  thf(fact_1724_gcd__nat_Oextremum__strict,axiom,
% 0.26/0.49      ! [A: nat] :
% 0.26/0.49        ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.26/0.49          & ( zero_zero_nat != A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % gcd_nat.extremum_strict
% 0.26/0.49  thf(fact_1725_gcd__nat_Oextremum,axiom,
% 0.26/0.49      ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 0.26/0.49  
% 0.26/0.49  % gcd_nat.extremum
% 0.26/0.49  thf(fact_1726_even__nat__iff,axiom,
% 0.26/0.49      ! [K: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.26/0.49       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 0.26/0.49          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % even_nat_iff
% 0.26/0.49  thf(fact_1727_not__one__le__zero,axiom,
% 0.26/0.49      ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 0.26/0.49  
% 0.26/0.49  % not_one_le_zero
% 0.26/0.49  thf(fact_1728_not__one__le__zero,axiom,
% 0.26/0.49      ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 0.26/0.49  
% 0.26/0.49  % not_one_le_zero
% 0.26/0.49  thf(fact_1729_not__one__le__zero,axiom,
% 0.26/0.49      ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.26/0.49  
% 0.26/0.49  % not_one_le_zero
% 0.26/0.49  thf(fact_1730_not__one__le__zero,axiom,
% 0.26/0.49      ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 0.26/0.49  
% 0.26/0.49  % not_one_le_zero
% 0.26/0.49  thf(fact_1731_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.26/0.49      ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 0.26/0.49  
% 0.26/0.49  % linordered_nonzero_semiring_class.zero_le_one
% 0.26/0.49  thf(fact_1732_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.26/0.49      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 0.26/0.49  
% 0.26/0.49  % linordered_nonzero_semiring_class.zero_le_one
% 0.26/0.49  thf(fact_1733_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.26/0.49      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 0.26/0.49  
% 0.26/0.49  % linordered_nonzero_semiring_class.zero_le_one
% 0.26/0.49  thf(fact_1734_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.26/0.49      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.26/0.49  
% 0.26/0.49  % linordered_nonzero_semiring_class.zero_le_one
% 0.26/0.49  thf(fact_1735_zero__less__one__class_Ozero__le__one,axiom,
% 0.26/0.49      ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 0.26/0.49  
% 0.26/0.49  % zero_less_one_class.zero_le_one
% 0.26/0.49  thf(fact_1736_zero__less__one__class_Ozero__le__one,axiom,
% 0.26/0.49      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 0.26/0.49  
% 0.26/0.49  % zero_less_one_class.zero_le_one
% 0.26/0.49  thf(fact_1737_zero__less__one__class_Ozero__le__one,axiom,
% 0.26/0.49      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 0.26/0.49  
% 0.26/0.49  % zero_less_one_class.zero_le_one
% 0.26/0.49  thf(fact_1738_zero__less__one__class_Ozero__le__one,axiom,
% 0.26/0.49      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.26/0.49  
% 0.26/0.49  % zero_less_one_class.zero_le_one
% 0.26/0.49  thf(fact_1739_not__one__less__zero,axiom,
% 0.26/0.49      ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 0.26/0.49  
% 0.26/0.49  % not_one_less_zero
% 0.26/0.49  thf(fact_1740_not__one__less__zero,axiom,
% 0.26/0.49      ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 0.26/0.49  
% 0.26/0.49  % not_one_less_zero
% 0.26/0.49  thf(fact_1741_not__one__less__zero,axiom,
% 0.26/0.49      ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.26/0.49  
% 0.26/0.49  % not_one_less_zero
% 0.26/0.49  thf(fact_1742_not__one__less__zero,axiom,
% 0.26/0.49      ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 0.26/0.49  
% 0.26/0.49  % not_one_less_zero
% 0.26/0.49  thf(fact_1743_zero__less__one,axiom,
% 0.26/0.49      ord_less_real @ zero_zero_real @ one_one_real ).
% 0.26/0.49  
% 0.26/0.49  % zero_less_one
% 0.26/0.49  thf(fact_1744_zero__less__one,axiom,
% 0.26/0.49      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 0.26/0.49  
% 0.26/0.49  % zero_less_one
% 0.26/0.49  thf(fact_1745_zero__less__one,axiom,
% 0.26/0.49      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.26/0.49  
% 0.26/0.49  % zero_less_one
% 0.26/0.49  thf(fact_1746_zero__less__one,axiom,
% 0.26/0.49      ord_less_int @ zero_zero_int @ one_one_int ).
% 0.26/0.49  
% 0.26/0.49  % zero_less_one
% 0.26/0.49  thf(fact_1747_even__unset__bit__iff,axiom,
% 0.26/0.49      ! [M: nat,A: code_integer] :
% 0.26/0.49        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 0.26/0.49        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.49          | ( M = zero_zero_nat ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % even_unset_bit_iff
% 0.26/0.49  thf(fact_1748_even__unset__bit__iff,axiom,
% 0.26/0.49      ! [M: nat,A: int] :
% 0.26/0.49        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 0.26/0.49        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.49          | ( M = zero_zero_nat ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % even_unset_bit_iff
% 0.26/0.49  thf(fact_1749_even__unset__bit__iff,axiom,
% 0.26/0.49      ! [M: nat,A: nat] :
% 0.26/0.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 0.26/0.49        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.49          | ( M = zero_zero_nat ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % even_unset_bit_iff
% 0.26/0.49  thf(fact_1750_even__flip__bit__iff,axiom,
% 0.26/0.49      ! [M: nat,A: code_integer] :
% 0.26/0.49        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 0.26/0.49        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.49         != ( M = zero_zero_nat ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % even_flip_bit_iff
% 0.26/0.49  thf(fact_1751_even__flip__bit__iff,axiom,
% 0.26/0.49      ! [M: nat,A: int] :
% 0.26/0.49        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 0.26/0.49        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.49         != ( M = zero_zero_nat ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % even_flip_bit_iff
% 0.26/0.49  thf(fact_1752_even__flip__bit__iff,axiom,
% 0.26/0.49      ! [M: nat,A: nat] :
% 0.26/0.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 0.26/0.49        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.49         != ( M = zero_zero_nat ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % even_flip_bit_iff
% 0.26/0.49  thf(fact_1753_even__set__bit__iff,axiom,
% 0.26/0.49      ! [M: nat,A: code_integer] :
% 0.26/0.49        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 0.26/0.49        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.49          & ( M != zero_zero_nat ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % even_set_bit_iff
% 0.26/0.49  thf(fact_1754_even__set__bit__iff,axiom,
% 0.26/0.49      ! [M: nat,A: int] :
% 0.26/0.49        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 0.26/0.49        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.49          & ( M != zero_zero_nat ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % even_set_bit_iff
% 0.26/0.49  thf(fact_1755_even__set__bit__iff,axiom,
% 0.26/0.49      ! [M: nat,A: nat] :
% 0.26/0.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 0.26/0.49        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.49          & ( M != zero_zero_nat ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % even_set_bit_iff
% 0.26/0.49  thf(fact_1756_take__bit__int__greater__eq,axiom,
% 0.26/0.49      ! [K: int,N: nat] :
% 0.26/0.49        ( ( ord_less_int @ K @ zero_zero_int )
% 0.26/0.49       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_int_greater_eq
% 0.26/0.49  thf(fact_1757_ln__one,axiom,
% 0.26/0.49      ( ( ln_ln_real @ one_one_real )
% 0.26/0.49      = zero_zero_real ) ).
% 0.26/0.49  
% 0.26/0.49  % ln_one
% 0.26/0.49  thf(fact_1758_take__bit__int__less__eq,axiom,
% 0.26/0.49      ! [N: nat,K: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 0.26/0.49       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.49         => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % take_bit_int_less_eq
% 0.26/0.49  thf(fact_1759_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.26/0.49      ! [N: nat] :
% 0.26/0.49        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 0.26/0.49        = ( N = zero_zero_nat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % semiring_parity_class.even_mask_iff
% 0.26/0.49  thf(fact_1760_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.26/0.49      ! [N: nat] :
% 0.26/0.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 0.26/0.49        = ( N = zero_zero_nat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % semiring_parity_class.even_mask_iff
% 0.26/0.49  thf(fact_1761_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.26/0.49      ! [N: nat] :
% 0.26/0.49        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 0.26/0.49        = ( N = zero_zero_nat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % semiring_parity_class.even_mask_iff
% 0.26/0.49  thf(fact_1762_real__sqrt__power__even,axiom,
% 0.26/0.49      ! [N: nat,X3: real] :
% 0.26/0.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.49       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.49         => ( ( power_power_real @ ( sqrt @ X3 ) @ N )
% 0.26/0.49            = ( power_power_real @ X3 @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % real_sqrt_power_even
% 0.26/0.49  thf(fact_1763_arsinh__real__aux,axiom,
% 0.26/0.49      ! [X3: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X3 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % arsinh_real_aux
% 0.26/0.49  thf(fact_1764_numeral__le__ceiling,axiom,
% 0.26/0.49      ! [V: num,X3: real] :
% 0.26/0.49        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X3 ) )
% 0.26/0.49        = ( ord_less_real @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X3 ) ) ).
% 0.26/0.49  
% 0.26/0.49  % numeral_le_ceiling
% 0.26/0.49  thf(fact_1765_numeral__le__ceiling,axiom,
% 0.26/0.49      ! [V: num,X3: rat] :
% 0.26/0.49        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X3 ) )
% 0.26/0.49        = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X3 ) ) ).
% 0.26/0.49  
% 0.26/0.49  % numeral_le_ceiling
% 0.26/0.49  thf(fact_1766_add__left__cancel,axiom,
% 0.26/0.49      ! [A: real,B: real,C: real] :
% 0.26/0.49        ( ( ( plus_plus_real @ A @ B )
% 0.26/0.49          = ( plus_plus_real @ A @ C ) )
% 0.26/0.49        = ( B = C ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_left_cancel
% 0.26/0.49  thf(fact_1767_add__left__cancel,axiom,
% 0.26/0.49      ! [A: rat,B: rat,C: rat] :
% 0.26/0.49        ( ( ( plus_plus_rat @ A @ B )
% 0.26/0.49          = ( plus_plus_rat @ A @ C ) )
% 0.26/0.49        = ( B = C ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_left_cancel
% 0.26/0.49  thf(fact_1768_add__left__cancel,axiom,
% 0.26/0.49      ! [A: nat,B: nat,C: nat] :
% 0.26/0.49        ( ( ( plus_plus_nat @ A @ B )
% 0.26/0.49          = ( plus_plus_nat @ A @ C ) )
% 0.26/0.49        = ( B = C ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_left_cancel
% 0.26/0.49  thf(fact_1769_add__left__cancel,axiom,
% 0.26/0.49      ! [A: int,B: int,C: int] :
% 0.26/0.49        ( ( ( plus_plus_int @ A @ B )
% 0.26/0.49          = ( plus_plus_int @ A @ C ) )
% 0.26/0.49        = ( B = C ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_left_cancel
% 0.26/0.49  thf(fact_1770_add__right__cancel,axiom,
% 0.26/0.49      ! [B: real,A: real,C: real] :
% 0.26/0.49        ( ( ( plus_plus_real @ B @ A )
% 0.26/0.49          = ( plus_plus_real @ C @ A ) )
% 0.26/0.49        = ( B = C ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_right_cancel
% 0.26/0.49  thf(fact_1771_add__right__cancel,axiom,
% 0.26/0.49      ! [B: rat,A: rat,C: rat] :
% 0.26/0.49        ( ( ( plus_plus_rat @ B @ A )
% 0.26/0.49          = ( plus_plus_rat @ C @ A ) )
% 0.26/0.49        = ( B = C ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_right_cancel
% 0.26/0.49  thf(fact_1772_add__right__cancel,axiom,
% 0.26/0.49      ! [B: nat,A: nat,C: nat] :
% 0.26/0.49        ( ( ( plus_plus_nat @ B @ A )
% 0.26/0.49          = ( plus_plus_nat @ C @ A ) )
% 0.26/0.49        = ( B = C ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_right_cancel
% 0.26/0.49  thf(fact_1773_add__right__cancel,axiom,
% 0.26/0.49      ! [B: int,A: int,C: int] :
% 0.26/0.49        ( ( ( plus_plus_int @ B @ A )
% 0.26/0.49          = ( plus_plus_int @ C @ A ) )
% 0.26/0.49        = ( B = C ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_right_cancel
% 0.26/0.49  thf(fact_1774_diff__self__eq__0,axiom,
% 0.26/0.49      ! [M: nat] :
% 0.26/0.49        ( ( minus_minus_nat @ M @ M )
% 0.26/0.49        = zero_zero_nat ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_self_eq_0
% 0.26/0.49  thf(fact_1775_diff__0__eq__0,axiom,
% 0.26/0.49      ! [N: nat] :
% 0.26/0.49        ( ( minus_minus_nat @ zero_zero_nat @ N )
% 0.26/0.49        = zero_zero_nat ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_0_eq_0
% 0.26/0.49  thf(fact_1776_diff__diff__cancel,axiom,
% 0.26/0.49      ! [I: nat,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ I @ N )
% 0.26/0.49       => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 0.26/0.49          = I ) ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_diff_cancel
% 0.26/0.49  thf(fact_1777_idiff__0__right,axiom,
% 0.26/0.49      ! [N: extended_enat] :
% 0.26/0.49        ( ( minus_3235023915231533773d_enat @ N @ zero_z5237406670263579293d_enat )
% 0.26/0.49        = N ) ).
% 0.26/0.49  
% 0.26/0.49  % idiff_0_right
% 0.26/0.49  thf(fact_1778_idiff__0,axiom,
% 0.26/0.49      ! [N: extended_enat] :
% 0.26/0.49        ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N )
% 0.26/0.49        = zero_z5237406670263579293d_enat ) ).
% 0.26/0.49  
% 0.26/0.49  % idiff_0
% 0.26/0.49  thf(fact_1779_power__minus__is__div,axiom,
% 0.26/0.49      ! [B: nat,A: nat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ B @ A )
% 0.26/0.49       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B ) )
% 0.26/0.49          = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % power_minus_is_div
% 0.26/0.49  thf(fact_1780_add__le__cancel__right,axiom,
% 0.26/0.49      ! [A: real,C: real,B: real] :
% 0.26/0.49        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.26/0.49        = ( ord_less_eq_real @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_le_cancel_right
% 0.26/0.49  thf(fact_1781_add__le__cancel__right,axiom,
% 0.26/0.49      ! [A: rat,C: rat,B: rat] :
% 0.26/0.49        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.26/0.49        = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_le_cancel_right
% 0.26/0.49  thf(fact_1782_add__le__cancel__right,axiom,
% 0.26/0.49      ! [A: nat,C: nat,B: nat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.26/0.49        = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_le_cancel_right
% 0.26/0.49  thf(fact_1783_add__le__cancel__right,axiom,
% 0.26/0.49      ! [A: int,C: int,B: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.26/0.49        = ( ord_less_eq_int @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_le_cancel_right
% 0.26/0.49  thf(fact_1784_add__le__cancel__left,axiom,
% 0.26/0.49      ! [C: real,A: real,B: real] :
% 0.26/0.49        ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.26/0.49        = ( ord_less_eq_real @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_le_cancel_left
% 0.26/0.49  thf(fact_1785_add__le__cancel__left,axiom,
% 0.26/0.49      ! [C: rat,A: rat,B: rat] :
% 0.26/0.49        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.26/0.49        = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_le_cancel_left
% 0.26/0.49  thf(fact_1786_add__le__cancel__left,axiom,
% 0.26/0.49      ! [C: nat,A: nat,B: nat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.26/0.49        = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_le_cancel_left
% 0.26/0.49  thf(fact_1787_add__le__cancel__left,axiom,
% 0.26/0.49      ! [C: int,A: int,B: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.26/0.49        = ( ord_less_eq_int @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_le_cancel_left
% 0.26/0.49  thf(fact_1788_double__eq__0__iff,axiom,
% 0.26/0.49      ! [A: real] :
% 0.26/0.49        ( ( ( plus_plus_real @ A @ A )
% 0.26/0.49          = zero_zero_real )
% 0.26/0.49        = ( A = zero_zero_real ) ) ).
% 0.26/0.49  
% 0.26/0.49  % double_eq_0_iff
% 0.26/0.49  thf(fact_1789_double__eq__0__iff,axiom,
% 0.26/0.49      ! [A: rat] :
% 0.26/0.49        ( ( ( plus_plus_rat @ A @ A )
% 0.26/0.49          = zero_zero_rat )
% 0.26/0.49        = ( A = zero_zero_rat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % double_eq_0_iff
% 0.26/0.49  thf(fact_1790_double__eq__0__iff,axiom,
% 0.26/0.49      ! [A: int] :
% 0.26/0.49        ( ( ( plus_plus_int @ A @ A )
% 0.26/0.49          = zero_zero_int )
% 0.26/0.49        = ( A = zero_zero_int ) ) ).
% 0.26/0.49  
% 0.26/0.49  % double_eq_0_iff
% 0.26/0.49  thf(fact_1791_add__0,axiom,
% 0.26/0.49      ! [A: literal] :
% 0.26/0.49        ( ( plus_plus_literal @ zero_zero_literal @ A )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % add_0
% 0.26/0.49  thf(fact_1792_add__0,axiom,
% 0.26/0.49      ! [A: real] :
% 0.26/0.49        ( ( plus_plus_real @ zero_zero_real @ A )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % add_0
% 0.26/0.49  thf(fact_1793_add__0,axiom,
% 0.26/0.49      ! [A: rat] :
% 0.26/0.49        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % add_0
% 0.26/0.49  thf(fact_1794_add__0,axiom,
% 0.26/0.49      ! [A: nat] :
% 0.26/0.49        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % add_0
% 0.26/0.49  thf(fact_1795_add__0,axiom,
% 0.26/0.49      ! [A: int] :
% 0.26/0.49        ( ( plus_plus_int @ zero_zero_int @ A )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % add_0
% 0.26/0.49  thf(fact_1796_zero__eq__add__iff__both__eq__0,axiom,
% 0.26/0.49      ! [X3: nat,Y3: nat] :
% 0.26/0.49        ( ( zero_zero_nat
% 0.26/0.49          = ( plus_plus_nat @ X3 @ Y3 ) )
% 0.26/0.49        = ( ( X3 = zero_zero_nat )
% 0.26/0.49          & ( Y3 = zero_zero_nat ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_eq_add_iff_both_eq_0
% 0.26/0.49  thf(fact_1797_add__eq__0__iff__both__eq__0,axiom,
% 0.26/0.49      ! [X3: nat,Y3: nat] :
% 0.26/0.49        ( ( ( plus_plus_nat @ X3 @ Y3 )
% 0.26/0.49          = zero_zero_nat )
% 0.26/0.49        = ( ( X3 = zero_zero_nat )
% 0.26/0.49          & ( Y3 = zero_zero_nat ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_eq_0_iff_both_eq_0
% 0.26/0.49  thf(fact_1798_add__cancel__right__right,axiom,
% 0.26/0.49      ! [A: real,B: real] :
% 0.26/0.49        ( ( A
% 0.26/0.49          = ( plus_plus_real @ A @ B ) )
% 0.26/0.49        = ( B = zero_zero_real ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_cancel_right_right
% 0.26/0.49  thf(fact_1799_add__cancel__right__right,axiom,
% 0.26/0.49      ! [A: rat,B: rat] :
% 0.26/0.49        ( ( A
% 0.26/0.49          = ( plus_plus_rat @ A @ B ) )
% 0.26/0.49        = ( B = zero_zero_rat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_cancel_right_right
% 0.26/0.49  thf(fact_1800_add__cancel__right__right,axiom,
% 0.26/0.49      ! [A: nat,B: nat] :
% 0.26/0.49        ( ( A
% 0.26/0.49          = ( plus_plus_nat @ A @ B ) )
% 0.26/0.49        = ( B = zero_zero_nat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_cancel_right_right
% 0.26/0.49  thf(fact_1801_add__cancel__right__right,axiom,
% 0.26/0.49      ! [A: int,B: int] :
% 0.26/0.49        ( ( A
% 0.26/0.49          = ( plus_plus_int @ A @ B ) )
% 0.26/0.49        = ( B = zero_zero_int ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_cancel_right_right
% 0.26/0.49  thf(fact_1802_add__cancel__right__left,axiom,
% 0.26/0.49      ! [A: real,B: real] :
% 0.26/0.49        ( ( A
% 0.26/0.49          = ( plus_plus_real @ B @ A ) )
% 0.26/0.49        = ( B = zero_zero_real ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_cancel_right_left
% 0.26/0.49  thf(fact_1803_add__cancel__right__left,axiom,
% 0.26/0.49      ! [A: rat,B: rat] :
% 0.26/0.49        ( ( A
% 0.26/0.49          = ( plus_plus_rat @ B @ A ) )
% 0.26/0.49        = ( B = zero_zero_rat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_cancel_right_left
% 0.26/0.49  thf(fact_1804_add__cancel__right__left,axiom,
% 0.26/0.49      ! [A: nat,B: nat] :
% 0.26/0.49        ( ( A
% 0.26/0.49          = ( plus_plus_nat @ B @ A ) )
% 0.26/0.49        = ( B = zero_zero_nat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_cancel_right_left
% 0.26/0.49  thf(fact_1805_add__cancel__right__left,axiom,
% 0.26/0.49      ! [A: int,B: int] :
% 0.26/0.49        ( ( A
% 0.26/0.49          = ( plus_plus_int @ B @ A ) )
% 0.26/0.49        = ( B = zero_zero_int ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_cancel_right_left
% 0.26/0.49  thf(fact_1806_add__cancel__left__right,axiom,
% 0.26/0.49      ! [A: real,B: real] :
% 0.26/0.49        ( ( ( plus_plus_real @ A @ B )
% 0.26/0.49          = A )
% 0.26/0.49        = ( B = zero_zero_real ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_cancel_left_right
% 0.26/0.49  thf(fact_1807_add__cancel__left__right,axiom,
% 0.26/0.49      ! [A: rat,B: rat] :
% 0.26/0.49        ( ( ( plus_plus_rat @ A @ B )
% 0.26/0.49          = A )
% 0.26/0.49        = ( B = zero_zero_rat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_cancel_left_right
% 0.26/0.49  thf(fact_1808_add__cancel__left__right,axiom,
% 0.26/0.49      ! [A: nat,B: nat] :
% 0.26/0.49        ( ( ( plus_plus_nat @ A @ B )
% 0.26/0.49          = A )
% 0.26/0.49        = ( B = zero_zero_nat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_cancel_left_right
% 0.26/0.49  thf(fact_1809_add__cancel__left__right,axiom,
% 0.26/0.49      ! [A: int,B: int] :
% 0.26/0.49        ( ( ( plus_plus_int @ A @ B )
% 0.26/0.49          = A )
% 0.26/0.49        = ( B = zero_zero_int ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_cancel_left_right
% 0.26/0.49  thf(fact_1810_add__cancel__left__left,axiom,
% 0.26/0.49      ! [B: real,A: real] :
% 0.26/0.49        ( ( ( plus_plus_real @ B @ A )
% 0.26/0.49          = A )
% 0.26/0.49        = ( B = zero_zero_real ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_cancel_left_left
% 0.26/0.49  thf(fact_1811_add__cancel__left__left,axiom,
% 0.26/0.49      ! [B: rat,A: rat] :
% 0.26/0.49        ( ( ( plus_plus_rat @ B @ A )
% 0.26/0.49          = A )
% 0.26/0.49        = ( B = zero_zero_rat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_cancel_left_left
% 0.26/0.49  thf(fact_1812_add__cancel__left__left,axiom,
% 0.26/0.49      ! [B: nat,A: nat] :
% 0.26/0.49        ( ( ( plus_plus_nat @ B @ A )
% 0.26/0.49          = A )
% 0.26/0.49        = ( B = zero_zero_nat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_cancel_left_left
% 0.26/0.49  thf(fact_1813_add__cancel__left__left,axiom,
% 0.26/0.49      ! [B: int,A: int] :
% 0.26/0.49        ( ( ( plus_plus_int @ B @ A )
% 0.26/0.49          = A )
% 0.26/0.49        = ( B = zero_zero_int ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_cancel_left_left
% 0.26/0.49  thf(fact_1814_double__zero__sym,axiom,
% 0.26/0.49      ! [A: real] :
% 0.26/0.49        ( ( zero_zero_real
% 0.26/0.49          = ( plus_plus_real @ A @ A ) )
% 0.26/0.49        = ( A = zero_zero_real ) ) ).
% 0.26/0.49  
% 0.26/0.49  % double_zero_sym
% 0.26/0.49  thf(fact_1815_double__zero__sym,axiom,
% 0.26/0.49      ! [A: rat] :
% 0.26/0.49        ( ( zero_zero_rat
% 0.26/0.49          = ( plus_plus_rat @ A @ A ) )
% 0.26/0.49        = ( A = zero_zero_rat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % double_zero_sym
% 0.26/0.49  thf(fact_1816_double__zero__sym,axiom,
% 0.26/0.49      ! [A: int] :
% 0.26/0.49        ( ( zero_zero_int
% 0.26/0.49          = ( plus_plus_int @ A @ A ) )
% 0.26/0.49        = ( A = zero_zero_int ) ) ).
% 0.26/0.49  
% 0.26/0.49  % double_zero_sym
% 0.26/0.49  thf(fact_1817_add_Oright__neutral,axiom,
% 0.26/0.49      ! [A: literal] :
% 0.26/0.49        ( ( plus_plus_literal @ A @ zero_zero_literal )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % add.right_neutral
% 0.26/0.49  thf(fact_1818_add_Oright__neutral,axiom,
% 0.26/0.49      ! [A: real] :
% 0.26/0.49        ( ( plus_plus_real @ A @ zero_zero_real )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % add.right_neutral
% 0.26/0.49  thf(fact_1819_add_Oright__neutral,axiom,
% 0.26/0.49      ! [A: rat] :
% 0.26/0.49        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % add.right_neutral
% 0.26/0.49  thf(fact_1820_add_Oright__neutral,axiom,
% 0.26/0.49      ! [A: nat] :
% 0.26/0.49        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % add.right_neutral
% 0.26/0.49  thf(fact_1821_add_Oright__neutral,axiom,
% 0.26/0.49      ! [A: int] :
% 0.26/0.49        ( ( plus_plus_int @ A @ zero_zero_int )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % add.right_neutral
% 0.26/0.49  thf(fact_1822_add__less__cancel__left,axiom,
% 0.26/0.49      ! [C: real,A: real,B: real] :
% 0.26/0.49        ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.26/0.49        = ( ord_less_real @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_less_cancel_left
% 0.26/0.49  thf(fact_1823_add__less__cancel__left,axiom,
% 0.26/0.49      ! [C: rat,A: rat,B: rat] :
% 0.26/0.49        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.26/0.49        = ( ord_less_rat @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_less_cancel_left
% 0.26/0.49  thf(fact_1824_add__less__cancel__left,axiom,
% 0.26/0.49      ! [C: nat,A: nat,B: nat] :
% 0.26/0.49        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.26/0.49        = ( ord_less_nat @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_less_cancel_left
% 0.26/0.49  thf(fact_1825_add__less__cancel__left,axiom,
% 0.26/0.49      ! [C: int,A: int,B: int] :
% 0.26/0.49        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.26/0.49        = ( ord_less_int @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_less_cancel_left
% 0.26/0.49  thf(fact_1826_add__less__cancel__right,axiom,
% 0.26/0.49      ! [A: real,C: real,B: real] :
% 0.26/0.49        ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.26/0.49        = ( ord_less_real @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_less_cancel_right
% 0.26/0.49  thf(fact_1827_add__less__cancel__right,axiom,
% 0.26/0.49      ! [A: rat,C: rat,B: rat] :
% 0.26/0.49        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.26/0.49        = ( ord_less_rat @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_less_cancel_right
% 0.26/0.49  thf(fact_1828_add__less__cancel__right,axiom,
% 0.26/0.49      ! [A: nat,C: nat,B: nat] :
% 0.26/0.49        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.26/0.49        = ( ord_less_nat @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_less_cancel_right
% 0.26/0.49  thf(fact_1829_add__less__cancel__right,axiom,
% 0.26/0.49      ! [A: int,C: int,B: int] :
% 0.26/0.49        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.26/0.49        = ( ord_less_int @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_less_cancel_right
% 0.26/0.49  thf(fact_1830_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.26/0.49      ! [A: real] :
% 0.26/0.49        ( ( minus_minus_real @ A @ A )
% 0.26/0.49        = zero_zero_real ) ).
% 0.26/0.49  
% 0.26/0.49  % cancel_comm_monoid_add_class.diff_cancel
% 0.26/0.49  thf(fact_1831_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.26/0.49      ! [A: rat] :
% 0.26/0.49        ( ( minus_minus_rat @ A @ A )
% 0.26/0.49        = zero_zero_rat ) ).
% 0.26/0.49  
% 0.26/0.49  % cancel_comm_monoid_add_class.diff_cancel
% 0.26/0.49  thf(fact_1832_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.26/0.49      ! [A: nat] :
% 0.26/0.49        ( ( minus_minus_nat @ A @ A )
% 0.26/0.49        = zero_zero_nat ) ).
% 0.26/0.49  
% 0.26/0.49  % cancel_comm_monoid_add_class.diff_cancel
% 0.26/0.49  thf(fact_1833_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.26/0.49      ! [A: int] :
% 0.26/0.49        ( ( minus_minus_int @ A @ A )
% 0.26/0.49        = zero_zero_int ) ).
% 0.26/0.49  
% 0.26/0.49  % cancel_comm_monoid_add_class.diff_cancel
% 0.26/0.49  thf(fact_1834_diff__zero,axiom,
% 0.26/0.49      ! [A: real] :
% 0.26/0.49        ( ( minus_minus_real @ A @ zero_zero_real )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_zero
% 0.26/0.49  thf(fact_1835_diff__zero,axiom,
% 0.26/0.49      ! [A: rat] :
% 0.26/0.49        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_zero
% 0.26/0.49  thf(fact_1836_diff__zero,axiom,
% 0.26/0.49      ! [A: nat] :
% 0.26/0.49        ( ( minus_minus_nat @ A @ zero_zero_nat )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_zero
% 0.26/0.49  thf(fact_1837_diff__zero,axiom,
% 0.26/0.49      ! [A: int] :
% 0.26/0.49        ( ( minus_minus_int @ A @ zero_zero_int )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_zero
% 0.26/0.49  thf(fact_1838_zero__diff,axiom,
% 0.26/0.49      ! [A: nat] :
% 0.26/0.49        ( ( minus_minus_nat @ zero_zero_nat @ A )
% 0.26/0.49        = zero_zero_nat ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_diff
% 0.26/0.49  thf(fact_1839_diff__0__right,axiom,
% 0.26/0.49      ! [A: real] :
% 0.26/0.49        ( ( minus_minus_real @ A @ zero_zero_real )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_0_right
% 0.26/0.49  thf(fact_1840_diff__0__right,axiom,
% 0.26/0.49      ! [A: rat] :
% 0.26/0.49        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_0_right
% 0.26/0.49  thf(fact_1841_diff__0__right,axiom,
% 0.26/0.49      ! [A: int] :
% 0.26/0.49        ( ( minus_minus_int @ A @ zero_zero_int )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_0_right
% 0.26/0.49  thf(fact_1842_diff__self,axiom,
% 0.26/0.49      ! [A: real] :
% 0.26/0.49        ( ( minus_minus_real @ A @ A )
% 0.26/0.49        = zero_zero_real ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_self
% 0.26/0.49  thf(fact_1843_diff__self,axiom,
% 0.26/0.49      ! [A: rat] :
% 0.26/0.49        ( ( minus_minus_rat @ A @ A )
% 0.26/0.49        = zero_zero_rat ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_self
% 0.26/0.49  thf(fact_1844_diff__self,axiom,
% 0.26/0.49      ! [A: int] :
% 0.26/0.49        ( ( minus_minus_int @ A @ A )
% 0.26/0.49        = zero_zero_int ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_self
% 0.26/0.49  thf(fact_1845_bits__div__by__0,axiom,
% 0.26/0.49      ! [A: nat] :
% 0.26/0.49        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 0.26/0.49        = zero_zero_nat ) ).
% 0.26/0.49  
% 0.26/0.49  % bits_div_by_0
% 0.26/0.49  thf(fact_1846_bits__div__by__0,axiom,
% 0.26/0.49      ! [A: int] :
% 0.26/0.49        ( ( divide_divide_int @ A @ zero_zero_int )
% 0.26/0.49        = zero_zero_int ) ).
% 0.26/0.49  
% 0.26/0.49  % bits_div_by_0
% 0.26/0.49  thf(fact_1847_bits__div__0,axiom,
% 0.26/0.49      ! [A: nat] :
% 0.26/0.49        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 0.26/0.49        = zero_zero_nat ) ).
% 0.26/0.49  
% 0.26/0.49  % bits_div_0
% 0.26/0.49  thf(fact_1848_bits__div__0,axiom,
% 0.26/0.49      ! [A: int] :
% 0.26/0.49        ( ( divide_divide_int @ zero_zero_int @ A )
% 0.26/0.49        = zero_zero_int ) ).
% 0.26/0.49  
% 0.26/0.49  % bits_div_0
% 0.26/0.49  thf(fact_1849_div__by__0,axiom,
% 0.26/0.49      ! [A: complex] :
% 0.26/0.49        ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 0.26/0.49        = zero_zero_complex ) ).
% 0.26/0.49  
% 0.26/0.49  % div_by_0
% 0.26/0.49  thf(fact_1850_div__by__0,axiom,
% 0.26/0.49      ! [A: real] :
% 0.26/0.49        ( ( divide_divide_real @ A @ zero_zero_real )
% 0.26/0.49        = zero_zero_real ) ).
% 0.26/0.49  
% 0.26/0.49  % div_by_0
% 0.26/0.49  thf(fact_1851_div__by__0,axiom,
% 0.26/0.49      ! [A: rat] :
% 0.26/0.49        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 0.26/0.49        = zero_zero_rat ) ).
% 0.26/0.49  
% 0.26/0.49  % div_by_0
% 0.26/0.49  thf(fact_1852_div__by__0,axiom,
% 0.26/0.49      ! [A: nat] :
% 0.26/0.49        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 0.26/0.49        = zero_zero_nat ) ).
% 0.26/0.49  
% 0.26/0.49  % div_by_0
% 0.26/0.49  thf(fact_1853_div__by__0,axiom,
% 0.26/0.49      ! [A: int] :
% 0.26/0.49        ( ( divide_divide_int @ A @ zero_zero_int )
% 0.26/0.49        = zero_zero_int ) ).
% 0.26/0.49  
% 0.26/0.49  % div_by_0
% 0.26/0.49  thf(fact_1854_div__0,axiom,
% 0.26/0.49      ! [A: complex] :
% 0.26/0.49        ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 0.26/0.49        = zero_zero_complex ) ).
% 0.26/0.49  
% 0.26/0.49  % div_0
% 0.26/0.49  thf(fact_1855_div__0,axiom,
% 0.26/0.49      ! [A: real] :
% 0.26/0.49        ( ( divide_divide_real @ zero_zero_real @ A )
% 0.26/0.49        = zero_zero_real ) ).
% 0.26/0.49  
% 0.26/0.49  % div_0
% 0.26/0.49  thf(fact_1856_div__0,axiom,
% 0.26/0.49      ! [A: rat] :
% 0.26/0.49        ( ( divide_divide_rat @ zero_zero_rat @ A )
% 0.26/0.49        = zero_zero_rat ) ).
% 0.26/0.49  
% 0.26/0.49  % div_0
% 0.26/0.49  thf(fact_1857_div__0,axiom,
% 0.26/0.49      ! [A: nat] :
% 0.26/0.49        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 0.26/0.49        = zero_zero_nat ) ).
% 0.26/0.49  
% 0.26/0.49  % div_0
% 0.26/0.49  thf(fact_1858_div__0,axiom,
% 0.26/0.49      ! [A: int] :
% 0.26/0.49        ( ( divide_divide_int @ zero_zero_int @ A )
% 0.26/0.49        = zero_zero_int ) ).
% 0.26/0.49  
% 0.26/0.49  % div_0
% 0.26/0.49  thf(fact_1859_add__numeral__left,axiom,
% 0.26/0.49      ! [V: num,W: num,Z: complex] :
% 0.26/0.49        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 0.26/0.49        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_numeral_left
% 0.26/0.49  thf(fact_1860_add__numeral__left,axiom,
% 0.26/0.49      ! [V: num,W: num,Z: real] :
% 0.26/0.49        ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 0.26/0.49        = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_numeral_left
% 0.26/0.49  thf(fact_1861_add__numeral__left,axiom,
% 0.26/0.49      ! [V: num,W: num,Z: rat] :
% 0.26/0.49        ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 0.26/0.49        = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_numeral_left
% 0.26/0.49  thf(fact_1862_add__numeral__left,axiom,
% 0.26/0.49      ! [V: num,W: num,Z: nat] :
% 0.26/0.49        ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 0.26/0.49        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_numeral_left
% 0.26/0.49  thf(fact_1863_add__numeral__left,axiom,
% 0.26/0.49      ! [V: num,W: num,Z: int] :
% 0.26/0.49        ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 0.26/0.49        = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_numeral_left
% 0.26/0.49  thf(fact_1864_numeral__plus__numeral,axiom,
% 0.26/0.49      ! [M: num,N: num] :
% 0.26/0.49        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 0.26/0.49        = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % numeral_plus_numeral
% 0.26/0.49  thf(fact_1865_numeral__plus__numeral,axiom,
% 0.26/0.49      ! [M: num,N: num] :
% 0.26/0.49        ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 0.26/0.49        = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % numeral_plus_numeral
% 0.26/0.49  thf(fact_1866_numeral__plus__numeral,axiom,
% 0.26/0.49      ! [M: num,N: num] :
% 0.26/0.49        ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 0.26/0.49        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % numeral_plus_numeral
% 0.26/0.49  thf(fact_1867_numeral__plus__numeral,axiom,
% 0.26/0.49      ! [M: num,N: num] :
% 0.26/0.49        ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.26/0.49        = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % numeral_plus_numeral
% 0.26/0.49  thf(fact_1868_numeral__plus__numeral,axiom,
% 0.26/0.49      ! [M: num,N: num] :
% 0.26/0.49        ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.49        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % numeral_plus_numeral
% 0.26/0.49  thf(fact_1869_add__diff__cancel,axiom,
% 0.26/0.49      ! [A: real,B: real] :
% 0.26/0.49        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % add_diff_cancel
% 0.26/0.49  thf(fact_1870_add__diff__cancel,axiom,
% 0.26/0.49      ! [A: rat,B: rat] :
% 0.26/0.49        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % add_diff_cancel
% 0.26/0.49  thf(fact_1871_add__diff__cancel,axiom,
% 0.26/0.49      ! [A: int,B: int] :
% 0.26/0.49        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % add_diff_cancel
% 0.26/0.49  thf(fact_1872_diff__add__cancel,axiom,
% 0.26/0.49      ! [A: real,B: real] :
% 0.26/0.49        ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_add_cancel
% 0.26/0.49  thf(fact_1873_diff__add__cancel,axiom,
% 0.26/0.49      ! [A: rat,B: rat] :
% 0.26/0.49        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_add_cancel
% 0.26/0.49  thf(fact_1874_diff__add__cancel,axiom,
% 0.26/0.49      ! [A: int,B: int] :
% 0.26/0.49        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_add_cancel
% 0.26/0.49  thf(fact_1875_add__diff__cancel__left,axiom,
% 0.26/0.49      ! [C: real,A: real,B: real] :
% 0.26/0.49        ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.26/0.49        = ( minus_minus_real @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_diff_cancel_left
% 0.26/0.49  thf(fact_1876_add__diff__cancel__left,axiom,
% 0.26/0.49      ! [C: rat,A: rat,B: rat] :
% 0.26/0.49        ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.26/0.49        = ( minus_minus_rat @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_diff_cancel_left
% 0.26/0.49  thf(fact_1877_add__diff__cancel__left,axiom,
% 0.26/0.49      ! [C: nat,A: nat,B: nat] :
% 0.26/0.49        ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.26/0.49        = ( minus_minus_nat @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_diff_cancel_left
% 0.26/0.49  thf(fact_1878_add__diff__cancel__left,axiom,
% 0.26/0.49      ! [C: int,A: int,B: int] :
% 0.26/0.49        ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.26/0.49        = ( minus_minus_int @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_diff_cancel_left
% 0.26/0.49  thf(fact_1879_add__diff__cancel__left_H,axiom,
% 0.26/0.49      ! [A: real,B: real] :
% 0.26/0.49        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 0.26/0.49        = B ) ).
% 0.26/0.49  
% 0.26/0.49  % add_diff_cancel_left'
% 0.26/0.49  thf(fact_1880_add__diff__cancel__left_H,axiom,
% 0.26/0.49      ! [A: rat,B: rat] :
% 0.26/0.49        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 0.26/0.49        = B ) ).
% 0.26/0.49  
% 0.26/0.49  % add_diff_cancel_left'
% 0.26/0.49  thf(fact_1881_add__diff__cancel__left_H,axiom,
% 0.26/0.49      ! [A: nat,B: nat] :
% 0.26/0.49        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 0.26/0.49        = B ) ).
% 0.26/0.49  
% 0.26/0.49  % add_diff_cancel_left'
% 0.26/0.49  thf(fact_1882_add__diff__cancel__left_H,axiom,
% 0.26/0.49      ! [A: int,B: int] :
% 0.26/0.49        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 0.26/0.49        = B ) ).
% 0.26/0.49  
% 0.26/0.49  % add_diff_cancel_left'
% 0.26/0.49  thf(fact_1883_add__diff__cancel__right,axiom,
% 0.26/0.49      ! [A: real,C: real,B: real] :
% 0.26/0.49        ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.26/0.49        = ( minus_minus_real @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_diff_cancel_right
% 0.26/0.49  thf(fact_1884_add__diff__cancel__right,axiom,
% 0.26/0.49      ! [A: rat,C: rat,B: rat] :
% 0.26/0.49        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.26/0.49        = ( minus_minus_rat @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_diff_cancel_right
% 0.26/0.49  thf(fact_1885_add__diff__cancel__right,axiom,
% 0.26/0.49      ! [A: nat,C: nat,B: nat] :
% 0.26/0.49        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.26/0.49        = ( minus_minus_nat @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_diff_cancel_right
% 0.26/0.49  thf(fact_1886_add__diff__cancel__right,axiom,
% 0.26/0.49      ! [A: int,C: int,B: int] :
% 0.26/0.49        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.26/0.49        = ( minus_minus_int @ A @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_diff_cancel_right
% 0.26/0.49  thf(fact_1887_add__diff__cancel__right_H,axiom,
% 0.26/0.49      ! [A: real,B: real] :
% 0.26/0.49        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % add_diff_cancel_right'
% 0.26/0.49  thf(fact_1888_add__diff__cancel__right_H,axiom,
% 0.26/0.49      ! [A: rat,B: rat] :
% 0.26/0.49        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % add_diff_cancel_right'
% 0.26/0.49  thf(fact_1889_add__diff__cancel__right_H,axiom,
% 0.26/0.49      ! [A: nat,B: nat] :
% 0.26/0.49        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % add_diff_cancel_right'
% 0.26/0.49  thf(fact_1890_add__diff__cancel__right_H,axiom,
% 0.26/0.49      ! [A: int,B: int] :
% 0.26/0.49        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % add_diff_cancel_right'
% 0.26/0.49  thf(fact_1891_bits__div__by__1,axiom,
% 0.26/0.49      ! [A: nat] :
% 0.26/0.49        ( ( divide_divide_nat @ A @ one_one_nat )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % bits_div_by_1
% 0.26/0.49  thf(fact_1892_bits__div__by__1,axiom,
% 0.26/0.49      ! [A: int] :
% 0.26/0.49        ( ( divide_divide_int @ A @ one_one_int )
% 0.26/0.49        = A ) ).
% 0.26/0.49  
% 0.26/0.49  % bits_div_by_1
% 0.26/0.49  thf(fact_1893_of__nat__add,axiom,
% 0.26/0.49      ! [M: nat,N: nat] :
% 0.26/0.49        ( ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ N ) )
% 0.26/0.49        = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % of_nat_add
% 0.26/0.49  thf(fact_1894_of__nat__add,axiom,
% 0.26/0.49      ! [M: nat,N: nat] :
% 0.26/0.49        ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N ) )
% 0.26/0.49        = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % of_nat_add
% 0.26/0.49  thf(fact_1895_of__nat__add,axiom,
% 0.26/0.49      ! [M: nat,N: nat] :
% 0.26/0.49        ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 0.26/0.49        = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % of_nat_add
% 0.26/0.49  thf(fact_1896_of__nat__add,axiom,
% 0.26/0.49      ! [M: nat,N: nat] :
% 0.26/0.49        ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 0.26/0.49        = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % of_nat_add
% 0.26/0.49  thf(fact_1897_of__nat__add,axiom,
% 0.26/0.49      ! [M: nat,N: nat] :
% 0.26/0.49        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 0.26/0.49        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % of_nat_add
% 0.26/0.49  thf(fact_1898_zero__less__diff,axiom,
% 0.26/0.49      ! [N: nat,M: nat] :
% 0.26/0.49        ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 0.26/0.49        = ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_less_diff
% 0.26/0.49  thf(fact_1899_diff__is__0__eq,axiom,
% 0.26/0.49      ! [M: nat,N: nat] :
% 0.26/0.49        ( ( ( minus_minus_nat @ M @ N )
% 0.26/0.49          = zero_zero_nat )
% 0.26/0.49        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_is_0_eq
% 0.26/0.49  thf(fact_1900_diff__is__0__eq_H,axiom,
% 0.26/0.49      ! [M: nat,N: nat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.49       => ( ( minus_minus_nat @ M @ N )
% 0.26/0.49          = zero_zero_nat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_is_0_eq'
% 0.26/0.49  thf(fact_1901_ln__inj__iff,axiom,
% 0.26/0.49      ! [X3: real,Y3: real] :
% 0.26/0.49        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.49       => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.49         => ( ( ( ln_ln_real @ X3 )
% 0.26/0.49              = ( ln_ln_real @ Y3 ) )
% 0.26/0.49            = ( X3 = Y3 ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ln_inj_iff
% 0.26/0.49  thf(fact_1902_ln__less__cancel__iff,axiom,
% 0.26/0.49      ! [X3: real,Y3: real] :
% 0.26/0.49        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.49       => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.49         => ( ( ord_less_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y3 ) )
% 0.26/0.49            = ( ord_less_real @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ln_less_cancel_iff
% 0.26/0.49  thf(fact_1903_unset__bit__nonnegative__int__iff,axiom,
% 0.26/0.49      ! [N: nat,K: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 0.26/0.49        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.26/0.49  
% 0.26/0.49  % unset_bit_nonnegative_int_iff
% 0.26/0.49  thf(fact_1904_set__bit__nonnegative__int__iff,axiom,
% 0.26/0.49      ! [N: nat,K: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 0.26/0.49        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.26/0.49  
% 0.26/0.49  % set_bit_nonnegative_int_iff
% 0.26/0.49  thf(fact_1905_flip__bit__nonnegative__int__iff,axiom,
% 0.26/0.49      ! [N: nat,K: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 0.26/0.49        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.26/0.49  
% 0.26/0.49  % flip_bit_nonnegative_int_iff
% 0.26/0.49  thf(fact_1906_unset__bit__negative__int__iff,axiom,
% 0.26/0.49      ! [N: nat,K: int] :
% 0.26/0.49        ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 0.26/0.49        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.26/0.49  
% 0.26/0.49  % unset_bit_negative_int_iff
% 0.26/0.49  thf(fact_1907_set__bit__negative__int__iff,axiom,
% 0.26/0.49      ! [N: nat,K: int] :
% 0.26/0.49        ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 0.26/0.49        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.26/0.49  
% 0.26/0.49  % set_bit_negative_int_iff
% 0.26/0.49  thf(fact_1908_flip__bit__negative__int__iff,axiom,
% 0.26/0.49      ! [N: nat,K: int] :
% 0.26/0.49        ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 0.26/0.49        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.26/0.49  
% 0.26/0.49  % flip_bit_negative_int_iff
% 0.26/0.49  thf(fact_1909_add__le__same__cancel1,axiom,
% 0.26/0.49      ! [B: real,A: real] :
% 0.26/0.49        ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 0.26/0.49        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_le_same_cancel1
% 0.26/0.49  thf(fact_1910_add__le__same__cancel1,axiom,
% 0.26/0.49      ! [B: rat,A: rat] :
% 0.26/0.49        ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 0.26/0.49        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_le_same_cancel1
% 0.26/0.49  thf(fact_1911_add__le__same__cancel1,axiom,
% 0.26/0.49      ! [B: nat,A: nat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.26/0.49        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_le_same_cancel1
% 0.26/0.49  thf(fact_1912_add__le__same__cancel1,axiom,
% 0.26/0.49      ! [B: int,A: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.26/0.49        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_le_same_cancel1
% 0.26/0.49  thf(fact_1913_add__le__same__cancel2,axiom,
% 0.26/0.49      ! [A: real,B: real] :
% 0.26/0.49        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.26/0.49        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_le_same_cancel2
% 0.26/0.49  thf(fact_1914_add__le__same__cancel2,axiom,
% 0.26/0.49      ! [A: rat,B: rat] :
% 0.26/0.49        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.26/0.49        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_le_same_cancel2
% 0.26/0.49  thf(fact_1915_add__le__same__cancel2,axiom,
% 0.26/0.49      ! [A: nat,B: nat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.26/0.49        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_le_same_cancel2
% 0.26/0.49  thf(fact_1916_add__le__same__cancel2,axiom,
% 0.26/0.49      ! [A: int,B: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.26/0.49        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_le_same_cancel2
% 0.26/0.49  thf(fact_1917_le__add__same__cancel1,axiom,
% 0.26/0.49      ! [A: real,B: real] :
% 0.26/0.49        ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.26/0.49        = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_add_same_cancel1
% 0.26/0.49  thf(fact_1918_le__add__same__cancel1,axiom,
% 0.26/0.49      ! [A: rat,B: rat] :
% 0.26/0.49        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.26/0.49        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_add_same_cancel1
% 0.26/0.49  thf(fact_1919_le__add__same__cancel1,axiom,
% 0.26/0.49      ! [A: nat,B: nat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.26/0.49        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_add_same_cancel1
% 0.26/0.49  thf(fact_1920_le__add__same__cancel1,axiom,
% 0.26/0.49      ! [A: int,B: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.26/0.49        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_add_same_cancel1
% 0.26/0.49  thf(fact_1921_le__add__same__cancel2,axiom,
% 0.26/0.49      ! [A: real,B: real] :
% 0.26/0.49        ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.26/0.49        = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_add_same_cancel2
% 0.26/0.49  thf(fact_1922_le__add__same__cancel2,axiom,
% 0.26/0.49      ! [A: rat,B: rat] :
% 0.26/0.49        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.26/0.49        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_add_same_cancel2
% 0.26/0.49  thf(fact_1923_le__add__same__cancel2,axiom,
% 0.26/0.49      ! [A: nat,B: nat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.26/0.49        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_add_same_cancel2
% 0.26/0.49  thf(fact_1924_le__add__same__cancel2,axiom,
% 0.26/0.49      ! [A: int,B: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.26/0.49        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_add_same_cancel2
% 0.26/0.49  thf(fact_1925_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.26/0.49      ! [A: real] :
% 0.26/0.49        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 0.26/0.49        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.26/0.49  
% 0.26/0.49  % double_add_le_zero_iff_single_add_le_zero
% 0.26/0.49  thf(fact_1926_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.26/0.49      ! [A: rat] :
% 0.26/0.49        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 0.26/0.49        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % double_add_le_zero_iff_single_add_le_zero
% 0.26/0.49  thf(fact_1927_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.26/0.49      ! [A: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 0.26/0.49        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.26/0.49  
% 0.26/0.49  % double_add_le_zero_iff_single_add_le_zero
% 0.26/0.49  thf(fact_1928_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.26/0.49      ! [A: real] :
% 0.26/0.49        ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 0.26/0.49        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_le_double_add_iff_zero_le_single_add
% 0.26/0.49  thf(fact_1929_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.26/0.49      ! [A: rat] :
% 0.26/0.49        ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 0.26/0.49        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_le_double_add_iff_zero_le_single_add
% 0.26/0.49  thf(fact_1930_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.26/0.49      ! [A: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 0.26/0.49        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_le_double_add_iff_zero_le_single_add
% 0.26/0.49  thf(fact_1931_add__less__same__cancel1,axiom,
% 0.26/0.49      ! [B: real,A: real] :
% 0.26/0.49        ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 0.26/0.49        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_less_same_cancel1
% 0.26/0.49  thf(fact_1932_add__less__same__cancel1,axiom,
% 0.26/0.49      ! [B: rat,A: rat] :
% 0.26/0.49        ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 0.26/0.49        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_less_same_cancel1
% 0.26/0.49  thf(fact_1933_add__less__same__cancel1,axiom,
% 0.26/0.49      ! [B: nat,A: nat] :
% 0.26/0.49        ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.26/0.49        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_less_same_cancel1
% 0.26/0.49  thf(fact_1934_add__less__same__cancel1,axiom,
% 0.26/0.49      ! [B: int,A: int] :
% 0.26/0.49        ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.26/0.49        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_less_same_cancel1
% 0.26/0.49  thf(fact_1935_add__less__same__cancel2,axiom,
% 0.26/0.49      ! [A: real,B: real] :
% 0.26/0.49        ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.26/0.49        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_less_same_cancel2
% 0.26/0.49  thf(fact_1936_add__less__same__cancel2,axiom,
% 0.26/0.49      ! [A: rat,B: rat] :
% 0.26/0.49        ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.26/0.49        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_less_same_cancel2
% 0.26/0.49  thf(fact_1937_add__less__same__cancel2,axiom,
% 0.26/0.49      ! [A: nat,B: nat] :
% 0.26/0.49        ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.26/0.49        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_less_same_cancel2
% 0.26/0.49  thf(fact_1938_add__less__same__cancel2,axiom,
% 0.26/0.49      ! [A: int,B: int] :
% 0.26/0.49        ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.26/0.49        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.26/0.49  
% 0.26/0.49  % add_less_same_cancel2
% 0.26/0.49  thf(fact_1939_less__add__same__cancel1,axiom,
% 0.26/0.49      ! [A: real,B: real] :
% 0.26/0.49        ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.26/0.49        = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % less_add_same_cancel1
% 0.26/0.49  thf(fact_1940_less__add__same__cancel1,axiom,
% 0.26/0.49      ! [A: rat,B: rat] :
% 0.26/0.49        ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.26/0.49        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % less_add_same_cancel1
% 0.26/0.49  thf(fact_1941_less__add__same__cancel1,axiom,
% 0.26/0.49      ! [A: nat,B: nat] :
% 0.26/0.49        ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.26/0.49        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % less_add_same_cancel1
% 0.26/0.49  thf(fact_1942_less__add__same__cancel1,axiom,
% 0.26/0.49      ! [A: int,B: int] :
% 0.26/0.49        ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.26/0.49        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % less_add_same_cancel1
% 0.26/0.49  thf(fact_1943_less__add__same__cancel2,axiom,
% 0.26/0.49      ! [A: real,B: real] :
% 0.26/0.49        ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.26/0.49        = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % less_add_same_cancel2
% 0.26/0.49  thf(fact_1944_less__add__same__cancel2,axiom,
% 0.26/0.49      ! [A: rat,B: rat] :
% 0.26/0.49        ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.26/0.49        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % less_add_same_cancel2
% 0.26/0.49  thf(fact_1945_less__add__same__cancel2,axiom,
% 0.26/0.49      ! [A: nat,B: nat] :
% 0.26/0.49        ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.26/0.49        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % less_add_same_cancel2
% 0.26/0.49  thf(fact_1946_less__add__same__cancel2,axiom,
% 0.26/0.49      ! [A: int,B: int] :
% 0.26/0.49        ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.26/0.49        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 0.26/0.49  
% 0.26/0.49  % less_add_same_cancel2
% 0.26/0.49  thf(fact_1947_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.26/0.49      ! [A: real] :
% 0.26/0.49        ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 0.26/0.49        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.26/0.49  
% 0.26/0.49  % double_add_less_zero_iff_single_add_less_zero
% 0.26/0.49  thf(fact_1948_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.26/0.49      ! [A: rat] :
% 0.26/0.49        ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 0.26/0.49        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % double_add_less_zero_iff_single_add_less_zero
% 0.26/0.49  thf(fact_1949_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.26/0.49      ! [A: int] :
% 0.26/0.49        ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 0.26/0.49        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.26/0.49  
% 0.26/0.49  % double_add_less_zero_iff_single_add_less_zero
% 0.26/0.49  thf(fact_1950_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.26/0.49      ! [A: real] :
% 0.26/0.49        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 0.26/0.49        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_less_double_add_iff_zero_less_single_add
% 0.26/0.49  thf(fact_1951_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.26/0.49      ! [A: rat] :
% 0.26/0.49        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 0.26/0.49        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_less_double_add_iff_zero_less_single_add
% 0.26/0.49  thf(fact_1952_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.26/0.49      ! [A: int] :
% 0.26/0.49        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 0.26/0.49        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % zero_less_double_add_iff_zero_less_single_add
% 0.26/0.49  thf(fact_1953_diff__ge__0__iff__ge,axiom,
% 0.26/0.49      ! [A: real,B: real] :
% 0.26/0.49        ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 0.26/0.49        = ( ord_less_eq_real @ B @ A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_ge_0_iff_ge
% 0.26/0.49  thf(fact_1954_diff__ge__0__iff__ge,axiom,
% 0.26/0.49      ! [A: rat,B: rat] :
% 0.26/0.49        ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.26/0.49        = ( ord_less_eq_rat @ B @ A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_ge_0_iff_ge
% 0.26/0.49  thf(fact_1955_diff__ge__0__iff__ge,axiom,
% 0.26/0.49      ! [A: int,B: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.26/0.49        = ( ord_less_eq_int @ B @ A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_ge_0_iff_ge
% 0.26/0.49  thf(fact_1956_diff__gt__0__iff__gt,axiom,
% 0.26/0.49      ! [A: real,B: real] :
% 0.26/0.49        ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 0.26/0.49        = ( ord_less_real @ B @ A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_gt_0_iff_gt
% 0.26/0.49  thf(fact_1957_diff__gt__0__iff__gt,axiom,
% 0.26/0.49      ! [A: rat,B: rat] :
% 0.26/0.49        ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.26/0.49        = ( ord_less_rat @ B @ A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_gt_0_iff_gt
% 0.26/0.49  thf(fact_1958_diff__gt__0__iff__gt,axiom,
% 0.26/0.49      ! [A: int,B: int] :
% 0.26/0.49        ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.26/0.49        = ( ord_less_int @ B @ A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_gt_0_iff_gt
% 0.26/0.49  thf(fact_1959_diff__numeral__special_I9_J,axiom,
% 0.26/0.49      ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 0.26/0.49      = zero_zero_complex ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_numeral_special(9)
% 0.26/0.49  thf(fact_1960_diff__numeral__special_I9_J,axiom,
% 0.26/0.49      ( ( minus_minus_real @ one_one_real @ one_one_real )
% 0.26/0.49      = zero_zero_real ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_numeral_special(9)
% 0.26/0.49  thf(fact_1961_diff__numeral__special_I9_J,axiom,
% 0.26/0.49      ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 0.26/0.49      = zero_zero_rat ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_numeral_special(9)
% 0.26/0.49  thf(fact_1962_diff__numeral__special_I9_J,axiom,
% 0.26/0.49      ( ( minus_minus_int @ one_one_int @ one_one_int )
% 0.26/0.49      = zero_zero_int ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_numeral_special(9)
% 0.26/0.49  thf(fact_1963_le__add__diff__inverse,axiom,
% 0.26/0.49      ! [B: real,A: real] :
% 0.26/0.49        ( ( ord_less_eq_real @ B @ A )
% 0.26/0.49       => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 0.26/0.49          = A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_add_diff_inverse
% 0.26/0.49  thf(fact_1964_le__add__diff__inverse,axiom,
% 0.26/0.49      ! [B: rat,A: rat] :
% 0.26/0.49        ( ( ord_less_eq_rat @ B @ A )
% 0.26/0.49       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 0.26/0.49          = A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_add_diff_inverse
% 0.26/0.49  thf(fact_1965_le__add__diff__inverse,axiom,
% 0.26/0.49      ! [B: nat,A: nat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ B @ A )
% 0.26/0.49       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 0.26/0.49          = A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_add_diff_inverse
% 0.26/0.49  thf(fact_1966_le__add__diff__inverse,axiom,
% 0.26/0.49      ! [B: int,A: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ B @ A )
% 0.26/0.49       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 0.26/0.49          = A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_add_diff_inverse
% 0.26/0.49  thf(fact_1967_le__add__diff__inverse2,axiom,
% 0.26/0.49      ! [B: real,A: real] :
% 0.26/0.49        ( ( ord_less_eq_real @ B @ A )
% 0.26/0.49       => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 0.26/0.49          = A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_add_diff_inverse2
% 0.26/0.49  thf(fact_1968_le__add__diff__inverse2,axiom,
% 0.26/0.49      ! [B: rat,A: rat] :
% 0.26/0.49        ( ( ord_less_eq_rat @ B @ A )
% 0.26/0.49       => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 0.26/0.49          = A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_add_diff_inverse2
% 0.26/0.49  thf(fact_1969_le__add__diff__inverse2,axiom,
% 0.26/0.49      ! [B: nat,A: nat] :
% 0.26/0.49        ( ( ord_less_eq_nat @ B @ A )
% 0.26/0.49       => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 0.26/0.49          = A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_add_diff_inverse2
% 0.26/0.49  thf(fact_1970_le__add__diff__inverse2,axiom,
% 0.26/0.49      ! [B: int,A: int] :
% 0.26/0.49        ( ( ord_less_eq_int @ B @ A )
% 0.26/0.49       => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 0.26/0.49          = A ) ) ).
% 0.26/0.49  
% 0.26/0.49  % le_add_diff_inverse2
% 0.26/0.49  thf(fact_1971_diff__add__zero,axiom,
% 0.26/0.49      ! [A: nat,B: nat] :
% 0.26/0.49        ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.26/0.49        = zero_zero_nat ) ).
% 0.26/0.49  
% 0.26/0.49  % diff_add_zero
% 0.26/0.49  thf(fact_1972_div__self,axiom,
% 0.26/0.49      ! [A: complex] :
% 0.26/0.49        ( ( A != zero_zero_complex )
% 0.26/0.49       => ( ( divide1717551699836669952omplex @ A @ A )
% 0.26/0.49          = one_one_complex ) ) ).
% 0.26/0.49  
% 0.26/0.49  % div_self
% 0.26/0.49  thf(fact_1973_div__self,axiom,
% 0.26/0.49      ! [A: real] :
% 0.26/0.49        ( ( A != zero_zero_real )
% 0.26/0.49       => ( ( divide_divide_real @ A @ A )
% 0.26/0.49          = one_one_real ) ) ).
% 0.26/0.49  
% 0.26/0.49  % div_self
% 0.26/0.49  thf(fact_1974_div__self,axiom,
% 0.26/0.49      ! [A: rat] :
% 0.26/0.49        ( ( A != zero_zero_rat )
% 0.26/0.49       => ( ( divide_divide_rat @ A @ A )
% 0.26/0.49          = one_one_rat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % div_self
% 0.26/0.49  thf(fact_1975_div__self,axiom,
% 0.26/0.49      ! [A: nat] :
% 0.26/0.49        ( ( A != zero_zero_nat )
% 0.26/0.49       => ( ( divide_divide_nat @ A @ A )
% 0.26/0.49          = one_one_nat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % div_self
% 0.26/0.49  thf(fact_1976_div__self,axiom,
% 0.26/0.49      ! [A: int] :
% 0.26/0.49        ( ( A != zero_zero_int )
% 0.26/0.49       => ( ( divide_divide_int @ A @ A )
% 0.26/0.49          = one_one_int ) ) ).
% 0.26/0.49  
% 0.26/0.49  % div_self
% 0.26/0.49  thf(fact_1977_ln__le__cancel__iff,axiom,
% 0.26/0.49      ! [X3: real,Y3: real] :
% 0.26/0.49        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.49       => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.49         => ( ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y3 ) )
% 0.26/0.49            = ( ord_less_eq_real @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ln_le_cancel_iff
% 0.26/0.49  thf(fact_1978_div__less,axiom,
% 0.26/0.49      ! [M: nat,N: nat] :
% 0.26/0.49        ( ( ord_less_nat @ M @ N )
% 0.26/0.49       => ( ( divide_divide_nat @ M @ N )
% 0.26/0.49          = zero_zero_nat ) ) ).
% 0.26/0.49  
% 0.26/0.49  % div_less
% 0.26/0.49  thf(fact_1979_ln__less__zero__iff,axiom,
% 0.26/0.49      ! [X3: real] :
% 0.26/0.49        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.49       => ( ( ord_less_real @ ( ln_ln_real @ X3 ) @ zero_zero_real )
% 0.26/0.49          = ( ord_less_real @ X3 @ one_one_real ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ln_less_zero_iff
% 0.26/0.49  thf(fact_1980_ln__gt__zero__iff,axiom,
% 0.26/0.49      ! [X3: real] :
% 0.26/0.49        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.49       => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X3 ) )
% 0.26/0.49          = ( ord_less_real @ one_one_real @ X3 ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ln_gt_zero_iff
% 0.26/0.49  thf(fact_1981_ln__eq__zero__iff,axiom,
% 0.26/0.49      ! [X3: real] :
% 0.26/0.49        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.49       => ( ( ( ln_ln_real @ X3 )
% 0.26/0.49            = zero_zero_real )
% 0.26/0.49          = ( X3 = one_one_real ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % ln_eq_zero_iff
% 0.26/0.49  thf(fact_1982_of__int__add,axiom,
% 0.26/0.49      ! [W: int,Z: int] :
% 0.26/0.49        ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 0.26/0.49        = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 0.26/0.49  
% 0.26/0.49  % of_int_add
% 0.26/0.49  thf(fact_1983_of__int__add,axiom,
% 0.26/0.49      ! [W: int,Z: int] :
% 0.26/0.49        ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 0.26/0.50        = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % of_int_add
% 0.26/0.50  thf(fact_1984_of__int__add,axiom,
% 0.26/0.50      ! [W: int,Z: int] :
% 0.26/0.50        ( ( ring_17405671764205052669omplex @ ( plus_plus_int @ W @ Z ) )
% 0.26/0.50        = ( plus_plus_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % of_int_add
% 0.26/0.50  thf(fact_1985_of__int__add,axiom,
% 0.26/0.50      ! [W: int,Z: int] :
% 0.26/0.50        ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 0.26/0.50        = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % of_int_add
% 0.26/0.50  thf(fact_1986_of__int__diff,axiom,
% 0.26/0.50      ! [W: int,Z: int] :
% 0.26/0.50        ( ( ring_17405671764205052669omplex @ ( minus_minus_int @ W @ Z ) )
% 0.26/0.50        = ( minus_minus_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % of_int_diff
% 0.26/0.50  thf(fact_1987_of__int__diff,axiom,
% 0.26/0.50      ! [W: int,Z: int] :
% 0.26/0.50        ( ( ring_1_of_int_real @ ( minus_minus_int @ W @ Z ) )
% 0.26/0.50        = ( minus_minus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % of_int_diff
% 0.26/0.50  thf(fact_1988_of__int__diff,axiom,
% 0.26/0.50      ! [W: int,Z: int] :
% 0.26/0.50        ( ( ring_1_of_int_rat @ ( minus_minus_int @ W @ Z ) )
% 0.26/0.50        = ( minus_minus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % of_int_diff
% 0.26/0.50  thf(fact_1989_of__int__diff,axiom,
% 0.26/0.50      ! [W: int,Z: int] :
% 0.26/0.50        ( ( ring_1_of_int_int @ ( minus_minus_int @ W @ Z ) )
% 0.26/0.50        = ( minus_minus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % of_int_diff
% 0.26/0.50  thf(fact_1990_numeral__plus__one,axiom,
% 0.26/0.50      ! [N: num] :
% 0.26/0.50        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 0.26/0.50        = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % numeral_plus_one
% 0.26/0.50  thf(fact_1991_numeral__plus__one,axiom,
% 0.26/0.50      ! [N: num] :
% 0.26/0.50        ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 0.26/0.50        = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % numeral_plus_one
% 0.26/0.50  thf(fact_1992_numeral__plus__one,axiom,
% 0.26/0.50      ! [N: num] :
% 0.26/0.50        ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 0.26/0.50        = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % numeral_plus_one
% 0.26/0.50  thf(fact_1993_numeral__plus__one,axiom,
% 0.26/0.50      ! [N: num] :
% 0.26/0.50        ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 0.26/0.50        = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % numeral_plus_one
% 0.26/0.50  thf(fact_1994_numeral__plus__one,axiom,
% 0.26/0.50      ! [N: num] :
% 0.26/0.50        ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 0.26/0.50        = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % numeral_plus_one
% 0.26/0.50  thf(fact_1995_one__plus__numeral,axiom,
% 0.26/0.50      ! [N: num] :
% 0.26/0.50        ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 0.26/0.50        = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % one_plus_numeral
% 0.26/0.50  thf(fact_1996_one__plus__numeral,axiom,
% 0.26/0.50      ! [N: num] :
% 0.26/0.50        ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 0.26/0.50        = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % one_plus_numeral
% 0.26/0.50  thf(fact_1997_one__plus__numeral,axiom,
% 0.26/0.50      ! [N: num] :
% 0.26/0.50        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 0.26/0.50        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % one_plus_numeral
% 0.26/0.50  thf(fact_1998_one__plus__numeral,axiom,
% 0.26/0.50      ! [N: num] :
% 0.26/0.50        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 0.26/0.50        = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % one_plus_numeral
% 0.26/0.50  thf(fact_1999_one__plus__numeral,axiom,
% 0.26/0.50      ! [N: num] :
% 0.26/0.50        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 0.26/0.50        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % one_plus_numeral
% 0.26/0.50  thf(fact_2000_ln__le__zero__iff,axiom,
% 0.26/0.50      ! [X3: real] :
% 0.26/0.50        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.50       => ( ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ zero_zero_real )
% 0.26/0.50          = ( ord_less_eq_real @ X3 @ one_one_real ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ln_le_zero_iff
% 0.26/0.50  thf(fact_2001_ln__ge__zero__iff,axiom,
% 0.26/0.50      ! [X3: real] :
% 0.26/0.50        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.50       => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X3 ) )
% 0.26/0.50          = ( ord_less_eq_real @ one_one_real @ X3 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ln_ge_zero_iff
% 0.26/0.50  thf(fact_2002_diff__nat__numeral,axiom,
% 0.26/0.50      ! [V: num,V2: num] :
% 0.26/0.50        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V2 ) )
% 0.26/0.50        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V2 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_nat_numeral
% 0.26/0.50  thf(fact_2003_zle__add1__eq__le,axiom,
% 0.26/0.50      ! [W: int,Z: int] :
% 0.26/0.50        ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 0.26/0.50        = ( ord_less_eq_int @ W @ Z ) ) ).
% 0.26/0.50  
% 0.26/0.50  % zle_add1_eq_le
% 0.26/0.50  thf(fact_2004_ceiling__add__of__int,axiom,
% 0.26/0.50      ! [X3: rat,Z: int] :
% 0.26/0.50        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X3 @ ( ring_1_of_int_rat @ Z ) ) )
% 0.26/0.50        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X3 ) @ Z ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ceiling_add_of_int
% 0.26/0.50  thf(fact_2005_ceiling__add__of__int,axiom,
% 0.26/0.50      ! [X3: real,Z: int] :
% 0.26/0.50        ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X3 @ ( ring_1_of_int_real @ Z ) ) )
% 0.26/0.50        = ( plus_plus_int @ ( archim7802044766580827645g_real @ X3 ) @ Z ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ceiling_add_of_int
% 0.26/0.50  thf(fact_2006_zle__diff1__eq,axiom,
% 0.26/0.50      ! [W: int,Z: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 0.26/0.50        = ( ord_less_int @ W @ Z ) ) ).
% 0.26/0.50  
% 0.26/0.50  % zle_diff1_eq
% 0.26/0.50  thf(fact_2007_ceiling__diff__of__int,axiom,
% 0.26/0.50      ! [X3: rat,Z: int] :
% 0.26/0.50        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X3 @ ( ring_1_of_int_rat @ Z ) ) )
% 0.26/0.50        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X3 ) @ Z ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ceiling_diff_of_int
% 0.26/0.50  thf(fact_2008_ceiling__diff__of__int,axiom,
% 0.26/0.50      ! [X3: real,Z: int] :
% 0.26/0.50        ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X3 @ ( ring_1_of_int_real @ Z ) ) )
% 0.26/0.50        = ( minus_minus_int @ ( archim7802044766580827645g_real @ X3 ) @ Z ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ceiling_diff_of_int
% 0.26/0.50  thf(fact_2009_one__add__one,axiom,
% 0.26/0.50      ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 0.26/0.50      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % one_add_one
% 0.26/0.50  thf(fact_2010_one__add__one,axiom,
% 0.26/0.50      ( ( plus_plus_real @ one_one_real @ one_one_real )
% 0.26/0.50      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % one_add_one
% 0.26/0.50  thf(fact_2011_one__add__one,axiom,
% 0.26/0.50      ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 0.26/0.50      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % one_add_one
% 0.26/0.50  thf(fact_2012_one__add__one,axiom,
% 0.26/0.50      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.26/0.50      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % one_add_one
% 0.26/0.50  thf(fact_2013_one__add__one,axiom,
% 0.26/0.50      ( ( plus_plus_int @ one_one_int @ one_one_int )
% 0.26/0.50      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % one_add_one
% 0.26/0.50  thf(fact_2014_odd__add,axiom,
% 0.26/0.50      ! [A: code_integer,B: code_integer] :
% 0.26/0.50        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 0.26/0.50        = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 0.26/0.50         != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % odd_add
% 0.26/0.50  thf(fact_2015_odd__add,axiom,
% 0.26/0.50      ! [A: nat,B: nat] :
% 0.26/0.50        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 0.26/0.50        = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 0.26/0.50         != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % odd_add
% 0.26/0.50  thf(fact_2016_odd__add,axiom,
% 0.26/0.50      ! [A: int,B: int] :
% 0.26/0.50        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 0.26/0.50        = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.26/0.50         != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % odd_add
% 0.26/0.50  thf(fact_2017_even__add,axiom,
% 0.26/0.50      ! [A: code_integer,B: code_integer] :
% 0.26/0.50        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.26/0.50        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.50          = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_add
% 0.26/0.50  thf(fact_2018_even__add,axiom,
% 0.26/0.50      ! [A: nat,B: nat] :
% 0.26/0.50        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 0.26/0.50        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.50          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_add
% 0.26/0.50  thf(fact_2019_even__add,axiom,
% 0.26/0.50      ! [A: int,B: int] :
% 0.26/0.50        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 0.26/0.50        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.50          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_add
% 0.26/0.50  thf(fact_2020_ceiling__add__numeral,axiom,
% 0.26/0.50      ! [X3: real,V: num] :
% 0.26/0.50        ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X3 @ ( numeral_numeral_real @ V ) ) )
% 0.26/0.50        = ( plus_plus_int @ ( archim7802044766580827645g_real @ X3 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ceiling_add_numeral
% 0.26/0.50  thf(fact_2021_ceiling__add__numeral,axiom,
% 0.26/0.50      ! [X3: rat,V: num] :
% 0.26/0.50        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X3 @ ( numeral_numeral_rat @ V ) ) )
% 0.26/0.50        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X3 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ceiling_add_numeral
% 0.26/0.50  thf(fact_2022_ceiling__add__one,axiom,
% 0.26/0.50      ! [X3: rat] :
% 0.26/0.50        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X3 @ one_one_rat ) )
% 0.26/0.50        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X3 ) @ one_one_int ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ceiling_add_one
% 0.26/0.50  thf(fact_2023_ceiling__add__one,axiom,
% 0.26/0.50      ! [X3: real] :
% 0.26/0.50        ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X3 @ one_one_real ) )
% 0.26/0.50        = ( plus_plus_int @ ( archim7802044766580827645g_real @ X3 ) @ one_one_int ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ceiling_add_one
% 0.26/0.50  thf(fact_2024_ceiling__diff__numeral,axiom,
% 0.26/0.50      ! [X3: real,V: num] :
% 0.26/0.50        ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X3 @ ( numeral_numeral_real @ V ) ) )
% 0.26/0.50        = ( minus_minus_int @ ( archim7802044766580827645g_real @ X3 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ceiling_diff_numeral
% 0.26/0.50  thf(fact_2025_ceiling__diff__numeral,axiom,
% 0.26/0.50      ! [X3: rat,V: num] :
% 0.26/0.50        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X3 @ ( numeral_numeral_rat @ V ) ) )
% 0.26/0.50        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X3 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ceiling_diff_numeral
% 0.26/0.50  thf(fact_2026_ceiling__diff__one,axiom,
% 0.26/0.50      ! [X3: rat] :
% 0.26/0.50        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X3 @ one_one_rat ) )
% 0.26/0.50        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X3 ) @ one_one_int ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ceiling_diff_one
% 0.26/0.50  thf(fact_2027_ceiling__diff__one,axiom,
% 0.26/0.50      ! [X3: real] :
% 0.26/0.50        ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X3 @ one_one_real ) )
% 0.26/0.50        = ( minus_minus_int @ ( archim7802044766580827645g_real @ X3 ) @ one_one_int ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ceiling_diff_one
% 0.26/0.50  thf(fact_2028_bits__1__div__2,axiom,
% 0.26/0.50      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.50      = zero_zero_nat ) ).
% 0.26/0.50  
% 0.26/0.50  % bits_1_div_2
% 0.26/0.50  thf(fact_2029_bits__1__div__2,axiom,
% 0.26/0.50      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.50      = zero_zero_int ) ).
% 0.26/0.50  
% 0.26/0.50  % bits_1_div_2
% 0.26/0.50  thf(fact_2030_one__div__two__eq__zero,axiom,
% 0.26/0.50      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.50      = zero_zero_nat ) ).
% 0.26/0.50  
% 0.26/0.50  % one_div_two_eq_zero
% 0.26/0.50  thf(fact_2031_one__div__two__eq__zero,axiom,
% 0.26/0.50      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.50      = zero_zero_int ) ).
% 0.26/0.50  
% 0.26/0.50  % one_div_two_eq_zero
% 0.26/0.50  thf(fact_2032_sum__power2__eq__zero__iff,axiom,
% 0.26/0.50      ! [X3: rat,Y3: rat] :
% 0.26/0.50        ( ( ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.50          = zero_zero_rat )
% 0.26/0.50        = ( ( X3 = zero_zero_rat )
% 0.26/0.50          & ( Y3 = zero_zero_rat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % sum_power2_eq_zero_iff
% 0.26/0.50  thf(fact_2033_sum__power2__eq__zero__iff,axiom,
% 0.26/0.50      ! [X3: int,Y3: int] :
% 0.26/0.50        ( ( ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.50          = zero_zero_int )
% 0.26/0.50        = ( ( X3 = zero_zero_int )
% 0.26/0.50          & ( Y3 = zero_zero_int ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % sum_power2_eq_zero_iff
% 0.26/0.50  thf(fact_2034_sum__power2__eq__zero__iff,axiom,
% 0.26/0.50      ! [X3: real,Y3: real] :
% 0.26/0.50        ( ( ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.50          = zero_zero_real )
% 0.26/0.50        = ( ( X3 = zero_zero_real )
% 0.26/0.50          & ( Y3 = zero_zero_real ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % sum_power2_eq_zero_iff
% 0.26/0.50  thf(fact_2035_even__plus__one__iff,axiom,
% 0.26/0.50      ! [A: code_integer] :
% 0.26/0.50        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 0.26/0.50        = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_plus_one_iff
% 0.26/0.50  thf(fact_2036_even__plus__one__iff,axiom,
% 0.26/0.50      ! [A: nat] :
% 0.26/0.50        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 0.26/0.50        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_plus_one_iff
% 0.26/0.50  thf(fact_2037_even__plus__one__iff,axiom,
% 0.26/0.50      ! [A: int] :
% 0.26/0.50        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 0.26/0.50        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_plus_one_iff
% 0.26/0.50  thf(fact_2038_even__diff,axiom,
% 0.26/0.50      ! [A: code_integer,B: code_integer] :
% 0.26/0.50        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.26/0.50        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_diff
% 0.26/0.50  thf(fact_2039_even__diff,axiom,
% 0.26/0.50      ! [A: int,B: int] :
% 0.26/0.50        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 0.26/0.50        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_diff
% 0.26/0.50  thf(fact_2040_nat__numeral__diff__1,axiom,
% 0.26/0.50      ! [V: num] :
% 0.26/0.50        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 0.26/0.50        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % nat_numeral_diff_1
% 0.26/0.50  thf(fact_2041_even__succ__div__2,axiom,
% 0.26/0.50      ! [A: code_integer] :
% 0.26/0.50        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.50       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.26/0.50          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_succ_div_2
% 0.26/0.50  thf(fact_2042_even__succ__div__2,axiom,
% 0.26/0.50      ! [A: nat] :
% 0.26/0.50        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.50       => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.50          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_succ_div_2
% 0.26/0.50  thf(fact_2043_even__succ__div__2,axiom,
% 0.26/0.50      ! [A: int] :
% 0.26/0.50        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.50       => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.50          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_succ_div_2
% 0.26/0.50  thf(fact_2044_odd__succ__div__two,axiom,
% 0.26/0.50      ! [A: code_integer] :
% 0.26/0.50        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.50       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.26/0.50          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % odd_succ_div_two
% 0.26/0.50  thf(fact_2045_odd__succ__div__two,axiom,
% 0.26/0.50      ! [A: nat] :
% 0.26/0.50        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.50       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.50          = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % odd_succ_div_two
% 0.26/0.50  thf(fact_2046_odd__succ__div__two,axiom,
% 0.26/0.50      ! [A: int] :
% 0.26/0.50        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.50       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.50          = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % odd_succ_div_two
% 0.26/0.50  thf(fact_2047_even__succ__div__two,axiom,
% 0.26/0.50      ! [A: code_integer] :
% 0.26/0.50        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.50       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.26/0.50          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_succ_div_two
% 0.26/0.50  thf(fact_2048_even__succ__div__two,axiom,
% 0.26/0.50      ! [A: nat] :
% 0.26/0.50        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.50       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.50          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_succ_div_two
% 0.26/0.50  thf(fact_2049_even__succ__div__two,axiom,
% 0.26/0.50      ! [A: int] :
% 0.26/0.50        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.50       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.50          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_succ_div_two
% 0.26/0.50  thf(fact_2050_ceiling__less__numeral,axiom,
% 0.26/0.50      ! [X3: real,V: num] :
% 0.26/0.50        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X3 ) @ ( numeral_numeral_int @ V ) )
% 0.26/0.50        = ( ord_less_eq_real @ X3 @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ceiling_less_numeral
% 0.26/0.50  thf(fact_2051_ceiling__less__numeral,axiom,
% 0.26/0.50      ! [X3: rat,V: num] :
% 0.26/0.50        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X3 ) @ ( numeral_numeral_int @ V ) )
% 0.26/0.50        = ( ord_less_eq_rat @ X3 @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ceiling_less_numeral
% 0.26/0.50  thf(fact_2052_even__succ__div__exp,axiom,
% 0.26/0.50      ! [A: code_integer,N: nat] :
% 0.26/0.50        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.50       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.50         => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.50            = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_succ_div_exp
% 0.26/0.50  thf(fact_2053_even__succ__div__exp,axiom,
% 0.26/0.50      ! [A: nat,N: nat] :
% 0.26/0.50        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.50       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.50         => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.50            = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_succ_div_exp
% 0.26/0.50  thf(fact_2054_even__succ__div__exp,axiom,
% 0.26/0.50      ! [A: int,N: nat] :
% 0.26/0.50        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.50       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.50         => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.50            = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_succ_div_exp
% 0.26/0.50  thf(fact_2055_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.26/0.50      ! [A: real,B: real] :
% 0.26/0.50        ( ~ ( ord_less_real @ A @ B )
% 0.26/0.50       => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 0.26/0.50          = A ) ) ).
% 0.26/0.50  
% 0.26/0.50  % linordered_semidom_class.add_diff_inverse
% 0.26/0.50  thf(fact_2056_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.26/0.50      ! [A: rat,B: rat] :
% 0.26/0.50        ( ~ ( ord_less_rat @ A @ B )
% 0.26/0.50       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 0.26/0.50          = A ) ) ).
% 0.26/0.50  
% 0.26/0.50  % linordered_semidom_class.add_diff_inverse
% 0.26/0.50  thf(fact_2057_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.26/0.50      ! [A: nat,B: nat] :
% 0.26/0.50        ( ~ ( ord_less_nat @ A @ B )
% 0.26/0.50       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 0.26/0.50          = A ) ) ).
% 0.26/0.50  
% 0.26/0.50  % linordered_semidom_class.add_diff_inverse
% 0.26/0.50  thf(fact_2058_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.26/0.50      ! [A: int,B: int] :
% 0.26/0.50        ( ~ ( ord_less_int @ A @ B )
% 0.26/0.50       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 0.26/0.50          = A ) ) ).
% 0.26/0.50  
% 0.26/0.50  % linordered_semidom_class.add_diff_inverse
% 0.26/0.50  thf(fact_2059_add__le__add__imp__diff__le,axiom,
% 0.26/0.50      ! [I: real,K: real,N: real,J: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 0.26/0.50       => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 0.26/0.50         => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 0.26/0.50           => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 0.26/0.50             => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_le_add_imp_diff_le
% 0.26/0.50  thf(fact_2060_add__le__add__imp__diff__le,axiom,
% 0.26/0.50      ! [I: rat,K: rat,N: rat,J: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 0.26/0.50       => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 0.26/0.50         => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 0.26/0.50           => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 0.26/0.50             => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_le_add_imp_diff_le
% 0.26/0.50  thf(fact_2061_add__le__add__imp__diff__le,axiom,
% 0.26/0.50      ! [I: nat,K: nat,N: nat,J: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 0.26/0.50       => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 0.26/0.50         => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 0.26/0.50           => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 0.26/0.50             => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_le_add_imp_diff_le
% 0.26/0.50  thf(fact_2062_add__le__add__imp__diff__le,axiom,
% 0.26/0.50      ! [I: int,K: int,N: int,J: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 0.26/0.50       => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 0.26/0.50         => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 0.26/0.50           => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 0.26/0.50             => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_le_add_imp_diff_le
% 0.26/0.50  thf(fact_2063_add__le__imp__le__diff,axiom,
% 0.26/0.50      ! [I: real,K: real,N: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 0.26/0.50       => ( ord_less_eq_real @ I @ ( minus_minus_real @ N @ K ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_le_imp_le_diff
% 0.26/0.50  thf(fact_2064_add__le__imp__le__diff,axiom,
% 0.26/0.50      ! [I: rat,K: rat,N: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 0.26/0.50       => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N @ K ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_le_imp_le_diff
% 0.26/0.50  thf(fact_2065_add__le__imp__le__diff,axiom,
% 0.26/0.50      ! [I: nat,K: nat,N: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 0.26/0.50       => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_le_imp_le_diff
% 0.26/0.50  thf(fact_2066_add__le__imp__le__diff,axiom,
% 0.26/0.50      ! [I: int,K: int,N: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 0.26/0.50       => ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_le_imp_le_diff
% 0.26/0.50  thf(fact_2067_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.50       => ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.50         => ( ( ( minus_minus_nat @ B @ A )
% 0.26/0.50              = C )
% 0.26/0.50            = ( B
% 0.26/0.50              = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 0.26/0.50  thf(fact_2068_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 0.26/0.50      ! [A: nat,B: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.50       => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 0.26/0.50          = B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 0.26/0.50  thf(fact_2069_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.50       => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.26/0.50          = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 0.26/0.50  thf(fact_2070_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.50       => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 0.26/0.50          = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 0.26/0.50  thf(fact_2071_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.50       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 0.26/0.50          = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 0.26/0.50  thf(fact_2072_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.50       => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 0.26/0.50          = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 0.26/0.50  thf(fact_2073_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.50       => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.26/0.50          = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 0.26/0.50  thf(fact_2074_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.50       => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.26/0.50          = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 0.26/0.50  thf(fact_2075_le__add__diff,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.50       => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % le_add_diff
% 0.26/0.50  thf(fact_2076_diff__add,axiom,
% 0.26/0.50      ! [A: nat,B: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.50       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 0.26/0.50          = B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_add
% 0.26/0.50  thf(fact_2077_le__diff__eq,axiom,
% 0.26/0.50      ! [A: real,C: real,B: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 0.26/0.50        = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % le_diff_eq
% 0.26/0.50  thf(fact_2078_le__diff__eq,axiom,
% 0.26/0.50      ! [A: rat,C: rat,B: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 0.26/0.50        = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % le_diff_eq
% 0.26/0.50  thf(fact_2079_le__diff__eq,axiom,
% 0.26/0.50      ! [A: int,C: int,B: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 0.26/0.50        = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % le_diff_eq
% 0.26/0.50  thf(fact_2080_diff__le__eq,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.26/0.50        = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_le_eq
% 0.26/0.50  thf(fact_2081_diff__le__eq,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.26/0.50        = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_le_eq
% 0.26/0.50  thf(fact_2082_diff__le__eq,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.26/0.50        = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_le_eq
% 0.26/0.50  thf(fact_2083_diff__less__eq,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.26/0.50        = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_less_eq
% 0.26/0.50  thf(fact_2084_diff__less__eq,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.26/0.50        = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_less_eq
% 0.26/0.50  thf(fact_2085_diff__less__eq,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.26/0.50        = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_less_eq
% 0.26/0.50  thf(fact_2086_less__diff__eq,axiom,
% 0.26/0.50      ! [A: real,C: real,B: real] :
% 0.26/0.50        ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 0.26/0.50        = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % less_diff_eq
% 0.26/0.50  thf(fact_2087_less__diff__eq,axiom,
% 0.26/0.50      ! [A: rat,C: rat,B: rat] :
% 0.26/0.50        ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 0.26/0.50        = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % less_diff_eq
% 0.26/0.50  thf(fact_2088_less__diff__eq,axiom,
% 0.26/0.50      ! [A: int,C: int,B: int] :
% 0.26/0.50        ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 0.26/0.50        = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % less_diff_eq
% 0.26/0.50  thf(fact_2089_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.26/0.50        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ab_semigroup_add_class.add_ac(1)
% 0.26/0.50  thf(fact_2090_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.26/0.50        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ab_semigroup_add_class.add_ac(1)
% 0.26/0.50  thf(fact_2091_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat] :
% 0.26/0.50        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.26/0.50        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ab_semigroup_add_class.add_ac(1)
% 0.26/0.50  thf(fact_2092_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.26/0.50        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ab_semigroup_add_class.add_ac(1)
% 0.26/0.50  thf(fact_2093_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.26/0.50      ! [I: real,J: real,K: real,L: real] :
% 0.26/0.50        ( ( ( I = J )
% 0.26/0.50          & ( K = L ) )
% 0.26/0.50       => ( ( plus_plus_real @ I @ K )
% 0.26/0.50          = ( plus_plus_real @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_semiring(4)
% 0.26/0.50  thf(fact_2094_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.26/0.50      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.26/0.50        ( ( ( I = J )
% 0.26/0.50          & ( K = L ) )
% 0.26/0.50       => ( ( plus_plus_rat @ I @ K )
% 0.26/0.50          = ( plus_plus_rat @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_semiring(4)
% 0.26/0.50  thf(fact_2095_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.26/0.50      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.26/0.50        ( ( ( I = J )
% 0.26/0.50          & ( K = L ) )
% 0.26/0.50       => ( ( plus_plus_nat @ I @ K )
% 0.26/0.50          = ( plus_plus_nat @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_semiring(4)
% 0.26/0.50  thf(fact_2096_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.26/0.50      ! [I: int,J: int,K: int,L: int] :
% 0.26/0.50        ( ( ( I = J )
% 0.26/0.50          & ( K = L ) )
% 0.26/0.50       => ( ( plus_plus_int @ I @ K )
% 0.26/0.50          = ( plus_plus_int @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_semiring(4)
% 0.26/0.50  thf(fact_2097_group__cancel_Oadd1,axiom,
% 0.26/0.50      ! [A3: real,K: real,A: real,B: real] :
% 0.26/0.50        ( ( A3
% 0.26/0.50          = ( plus_plus_real @ K @ A ) )
% 0.26/0.50       => ( ( plus_plus_real @ A3 @ B )
% 0.26/0.50          = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % group_cancel.add1
% 0.26/0.50  thf(fact_2098_group__cancel_Oadd1,axiom,
% 0.26/0.50      ! [A3: rat,K: rat,A: rat,B: rat] :
% 0.26/0.50        ( ( A3
% 0.26/0.50          = ( plus_plus_rat @ K @ A ) )
% 0.26/0.50       => ( ( plus_plus_rat @ A3 @ B )
% 0.26/0.50          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % group_cancel.add1
% 0.26/0.50  thf(fact_2099_group__cancel_Oadd1,axiom,
% 0.26/0.50      ! [A3: nat,K: nat,A: nat,B: nat] :
% 0.26/0.50        ( ( A3
% 0.26/0.50          = ( plus_plus_nat @ K @ A ) )
% 0.26/0.50       => ( ( plus_plus_nat @ A3 @ B )
% 0.26/0.50          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % group_cancel.add1
% 0.26/0.50  thf(fact_2100_group__cancel_Oadd1,axiom,
% 0.26/0.50      ! [A3: int,K: int,A: int,B: int] :
% 0.26/0.50        ( ( A3
% 0.26/0.50          = ( plus_plus_int @ K @ A ) )
% 0.26/0.50       => ( ( plus_plus_int @ A3 @ B )
% 0.26/0.50          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % group_cancel.add1
% 0.26/0.50  thf(fact_2101_group__cancel_Oadd2,axiom,
% 0.26/0.50      ! [B5: real,K: real,B: real,A: real] :
% 0.26/0.50        ( ( B5
% 0.26/0.50          = ( plus_plus_real @ K @ B ) )
% 0.26/0.50       => ( ( plus_plus_real @ A @ B5 )
% 0.26/0.50          = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % group_cancel.add2
% 0.26/0.50  thf(fact_2102_group__cancel_Oadd2,axiom,
% 0.26/0.50      ! [B5: rat,K: rat,B: rat,A: rat] :
% 0.26/0.50        ( ( B5
% 0.26/0.50          = ( plus_plus_rat @ K @ B ) )
% 0.26/0.50       => ( ( plus_plus_rat @ A @ B5 )
% 0.26/0.50          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % group_cancel.add2
% 0.26/0.50  thf(fact_2103_group__cancel_Oadd2,axiom,
% 0.26/0.50      ! [B5: nat,K: nat,B: nat,A: nat] :
% 0.26/0.50        ( ( B5
% 0.26/0.50          = ( plus_plus_nat @ K @ B ) )
% 0.26/0.50       => ( ( plus_plus_nat @ A @ B5 )
% 0.26/0.50          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % group_cancel.add2
% 0.26/0.50  thf(fact_2104_group__cancel_Oadd2,axiom,
% 0.26/0.50      ! [B5: int,K: int,B: int,A: int] :
% 0.26/0.50        ( ( B5
% 0.26/0.50          = ( plus_plus_int @ K @ B ) )
% 0.26/0.50       => ( ( plus_plus_int @ A @ B5 )
% 0.26/0.50          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % group_cancel.add2
% 0.26/0.50  thf(fact_2105_group__cancel_Osub1,axiom,
% 0.26/0.50      ! [A3: real,K: real,A: real,B: real] :
% 0.26/0.50        ( ( A3
% 0.26/0.50          = ( plus_plus_real @ K @ A ) )
% 0.26/0.50       => ( ( minus_minus_real @ A3 @ B )
% 0.26/0.50          = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % group_cancel.sub1
% 0.26/0.50  thf(fact_2106_group__cancel_Osub1,axiom,
% 0.26/0.50      ! [A3: rat,K: rat,A: rat,B: rat] :
% 0.26/0.50        ( ( A3
% 0.26/0.50          = ( plus_plus_rat @ K @ A ) )
% 0.26/0.50       => ( ( minus_minus_rat @ A3 @ B )
% 0.26/0.50          = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % group_cancel.sub1
% 0.26/0.50  thf(fact_2107_group__cancel_Osub1,axiom,
% 0.26/0.50      ! [A3: int,K: int,A: int,B: int] :
% 0.26/0.50        ( ( A3
% 0.26/0.50          = ( plus_plus_int @ K @ A ) )
% 0.26/0.50       => ( ( minus_minus_int @ A3 @ B )
% 0.26/0.50          = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % group_cancel.sub1
% 0.26/0.50  thf(fact_2108_diff__eq__eq,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( ( minus_minus_real @ A @ B )
% 0.26/0.50          = C )
% 0.26/0.50        = ( A
% 0.26/0.50          = ( plus_plus_real @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_eq_eq
% 0.26/0.50  thf(fact_2109_diff__eq__eq,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( ( minus_minus_rat @ A @ B )
% 0.26/0.50          = C )
% 0.26/0.50        = ( A
% 0.26/0.50          = ( plus_plus_rat @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_eq_eq
% 0.26/0.50  thf(fact_2110_diff__eq__eq,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( ( minus_minus_int @ A @ B )
% 0.26/0.50          = C )
% 0.26/0.50        = ( A
% 0.26/0.50          = ( plus_plus_int @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_eq_eq
% 0.26/0.50  thf(fact_2111_eq__diff__eq,axiom,
% 0.26/0.50      ! [A: real,C: real,B: real] :
% 0.26/0.50        ( ( A
% 0.26/0.50          = ( minus_minus_real @ C @ B ) )
% 0.26/0.50        = ( ( plus_plus_real @ A @ B )
% 0.26/0.50          = C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % eq_diff_eq
% 0.26/0.50  thf(fact_2112_eq__diff__eq,axiom,
% 0.26/0.50      ! [A: rat,C: rat,B: rat] :
% 0.26/0.50        ( ( A
% 0.26/0.50          = ( minus_minus_rat @ C @ B ) )
% 0.26/0.50        = ( ( plus_plus_rat @ A @ B )
% 0.26/0.50          = C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % eq_diff_eq
% 0.26/0.50  thf(fact_2113_eq__diff__eq,axiom,
% 0.26/0.50      ! [A: int,C: int,B: int] :
% 0.26/0.50        ( ( A
% 0.26/0.50          = ( minus_minus_int @ C @ B ) )
% 0.26/0.50        = ( ( plus_plus_int @ A @ B )
% 0.26/0.50          = C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % eq_diff_eq
% 0.26/0.50  thf(fact_2114_add__diff__eq,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.26/0.50        = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_diff_eq
% 0.26/0.50  thf(fact_2115_add__diff__eq,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.26/0.50        = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_diff_eq
% 0.26/0.50  thf(fact_2116_add__diff__eq,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.26/0.50        = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_diff_eq
% 0.26/0.50  thf(fact_2117_diff__diff__eq2,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.26/0.50        = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_diff_eq2
% 0.26/0.50  thf(fact_2118_diff__diff__eq2,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.26/0.50        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_diff_eq2
% 0.26/0.50  thf(fact_2119_diff__diff__eq2,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.26/0.50        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_diff_eq2
% 0.26/0.50  thf(fact_2120_add_Oassoc,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.26/0.50        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add.assoc
% 0.26/0.50  thf(fact_2121_add_Oassoc,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.26/0.50        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add.assoc
% 0.26/0.50  thf(fact_2122_add_Oassoc,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat] :
% 0.26/0.50        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.26/0.50        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add.assoc
% 0.26/0.50  thf(fact_2123_add_Oassoc,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.26/0.50        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add.assoc
% 0.26/0.50  thf(fact_2124_diff__add__eq,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.26/0.50        = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_add_eq
% 0.26/0.50  thf(fact_2125_diff__add__eq,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.26/0.50        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_add_eq
% 0.26/0.50  thf(fact_2126_diff__add__eq,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.26/0.50        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_add_eq
% 0.26/0.50  thf(fact_2127_add_Oleft__cancel,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( ( plus_plus_real @ A @ B )
% 0.26/0.50          = ( plus_plus_real @ A @ C ) )
% 0.26/0.50        = ( B = C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add.left_cancel
% 0.26/0.50  thf(fact_2128_add_Oleft__cancel,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( ( plus_plus_rat @ A @ B )
% 0.26/0.50          = ( plus_plus_rat @ A @ C ) )
% 0.26/0.50        = ( B = C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add.left_cancel
% 0.26/0.50  thf(fact_2129_add_Oleft__cancel,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( ( plus_plus_int @ A @ B )
% 0.26/0.50          = ( plus_plus_int @ A @ C ) )
% 0.26/0.50        = ( B = C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add.left_cancel
% 0.26/0.50  thf(fact_2130_diff__eq__diff__eq,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real,D3: real] :
% 0.26/0.50        ( ( ( minus_minus_real @ A @ B )
% 0.26/0.50          = ( minus_minus_real @ C @ D3 ) )
% 0.26/0.50       => ( ( A = B )
% 0.26/0.50          = ( C = D3 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_eq_diff_eq
% 0.26/0.50  thf(fact_2131_diff__eq__diff__eq,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat,D3: rat] :
% 0.26/0.50        ( ( ( minus_minus_rat @ A @ B )
% 0.26/0.50          = ( minus_minus_rat @ C @ D3 ) )
% 0.26/0.50       => ( ( A = B )
% 0.26/0.50          = ( C = D3 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_eq_diff_eq
% 0.26/0.50  thf(fact_2132_diff__eq__diff__eq,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int,D3: int] :
% 0.26/0.50        ( ( ( minus_minus_int @ A @ B )
% 0.26/0.50          = ( minus_minus_int @ C @ D3 ) )
% 0.26/0.50       => ( ( A = B )
% 0.26/0.50          = ( C = D3 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_eq_diff_eq
% 0.26/0.50  thf(fact_2133_add_Oright__cancel,axiom,
% 0.26/0.50      ! [B: real,A: real,C: real] :
% 0.26/0.50        ( ( ( plus_plus_real @ B @ A )
% 0.26/0.50          = ( plus_plus_real @ C @ A ) )
% 0.26/0.50        = ( B = C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add.right_cancel
% 0.26/0.50  thf(fact_2134_add_Oright__cancel,axiom,
% 0.26/0.50      ! [B: rat,A: rat,C: rat] :
% 0.26/0.50        ( ( ( plus_plus_rat @ B @ A )
% 0.26/0.50          = ( plus_plus_rat @ C @ A ) )
% 0.26/0.50        = ( B = C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add.right_cancel
% 0.26/0.50  thf(fact_2135_add_Oright__cancel,axiom,
% 0.26/0.50      ! [B: int,A: int,C: int] :
% 0.26/0.50        ( ( ( plus_plus_int @ B @ A )
% 0.26/0.50          = ( plus_plus_int @ C @ A ) )
% 0.26/0.50        = ( B = C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add.right_cancel
% 0.26/0.50  thf(fact_2136_add_Ocommute,axiom,
% 0.26/0.50      ( plus_plus_real
% 0.26/0.50      = ( ^ [A4: real,B3: real] : ( plus_plus_real @ B3 @ A4 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add.commute
% 0.26/0.50  thf(fact_2137_add_Ocommute,axiom,
% 0.26/0.50      ( plus_plus_rat
% 0.26/0.50      = ( ^ [A4: rat,B3: rat] : ( plus_plus_rat @ B3 @ A4 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add.commute
% 0.26/0.50  thf(fact_2138_add_Ocommute,axiom,
% 0.26/0.50      ( plus_plus_nat
% 0.26/0.50      = ( ^ [A4: nat,B3: nat] : ( plus_plus_nat @ B3 @ A4 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add.commute
% 0.26/0.50  thf(fact_2139_add_Ocommute,axiom,
% 0.26/0.50      ( plus_plus_int
% 0.26/0.50      = ( ^ [A4: int,B3: int] : ( plus_plus_int @ B3 @ A4 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add.commute
% 0.26/0.50  thf(fact_2140_add_Oleft__commute,axiom,
% 0.26/0.50      ! [B: real,A: real,C: real] :
% 0.26/0.50        ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 0.26/0.50        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add.left_commute
% 0.26/0.50  thf(fact_2141_add_Oleft__commute,axiom,
% 0.26/0.50      ! [B: rat,A: rat,C: rat] :
% 0.26/0.50        ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 0.26/0.50        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add.left_commute
% 0.26/0.50  thf(fact_2142_add_Oleft__commute,axiom,
% 0.26/0.50      ! [B: nat,A: nat,C: nat] :
% 0.26/0.50        ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 0.26/0.50        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add.left_commute
% 0.26/0.50  thf(fact_2143_add_Oleft__commute,axiom,
% 0.26/0.50      ! [B: int,A: int,C: int] :
% 0.26/0.50        ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 0.26/0.50        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add.left_commute
% 0.26/0.50  thf(fact_2144_add__left__imp__eq,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( ( plus_plus_real @ A @ B )
% 0.26/0.50          = ( plus_plus_real @ A @ C ) )
% 0.26/0.50       => ( B = C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_left_imp_eq
% 0.26/0.50  thf(fact_2145_add__left__imp__eq,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( ( plus_plus_rat @ A @ B )
% 0.26/0.50          = ( plus_plus_rat @ A @ C ) )
% 0.26/0.50       => ( B = C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_left_imp_eq
% 0.26/0.50  thf(fact_2146_add__left__imp__eq,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat] :
% 0.26/0.50        ( ( ( plus_plus_nat @ A @ B )
% 0.26/0.50          = ( plus_plus_nat @ A @ C ) )
% 0.26/0.50       => ( B = C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_left_imp_eq
% 0.26/0.50  thf(fact_2147_add__left__imp__eq,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( ( plus_plus_int @ A @ B )
% 0.26/0.50          = ( plus_plus_int @ A @ C ) )
% 0.26/0.50       => ( B = C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_left_imp_eq
% 0.26/0.50  thf(fact_2148_diff__add__eq__diff__diff__swap,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.26/0.50        = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_add_eq_diff_diff_swap
% 0.26/0.50  thf(fact_2149_diff__add__eq__diff__diff__swap,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.26/0.50        = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_add_eq_diff_diff_swap
% 0.26/0.50  thf(fact_2150_diff__add__eq__diff__diff__swap,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.26/0.50        = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_add_eq_diff_diff_swap
% 0.26/0.50  thf(fact_2151_add__right__imp__eq,axiom,
% 0.26/0.50      ! [B: real,A: real,C: real] :
% 0.26/0.50        ( ( ( plus_plus_real @ B @ A )
% 0.26/0.50          = ( plus_plus_real @ C @ A ) )
% 0.26/0.50       => ( B = C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_right_imp_eq
% 0.26/0.50  thf(fact_2152_add__right__imp__eq,axiom,
% 0.26/0.50      ! [B: rat,A: rat,C: rat] :
% 0.26/0.50        ( ( ( plus_plus_rat @ B @ A )
% 0.26/0.50          = ( plus_plus_rat @ C @ A ) )
% 0.26/0.50       => ( B = C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_right_imp_eq
% 0.26/0.50  thf(fact_2153_add__right__imp__eq,axiom,
% 0.26/0.50      ! [B: nat,A: nat,C: nat] :
% 0.26/0.50        ( ( ( plus_plus_nat @ B @ A )
% 0.26/0.50          = ( plus_plus_nat @ C @ A ) )
% 0.26/0.50       => ( B = C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_right_imp_eq
% 0.26/0.50  thf(fact_2154_add__right__imp__eq,axiom,
% 0.26/0.50      ! [B: int,A: int,C: int] :
% 0.26/0.50        ( ( ( plus_plus_int @ B @ A )
% 0.26/0.50          = ( plus_plus_int @ C @ A ) )
% 0.26/0.50       => ( B = C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_right_imp_eq
% 0.26/0.50  thf(fact_2155_add__implies__diff,axiom,
% 0.26/0.50      ! [C: real,B: real,A: real] :
% 0.26/0.50        ( ( ( plus_plus_real @ C @ B )
% 0.26/0.50          = A )
% 0.26/0.50       => ( C
% 0.26/0.50          = ( minus_minus_real @ A @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_implies_diff
% 0.26/0.50  thf(fact_2156_add__implies__diff,axiom,
% 0.26/0.50      ! [C: rat,B: rat,A: rat] :
% 0.26/0.50        ( ( ( plus_plus_rat @ C @ B )
% 0.26/0.50          = A )
% 0.26/0.50       => ( C
% 0.26/0.50          = ( minus_minus_rat @ A @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_implies_diff
% 0.26/0.50  thf(fact_2157_add__implies__diff,axiom,
% 0.26/0.50      ! [C: nat,B: nat,A: nat] :
% 0.26/0.50        ( ( ( plus_plus_nat @ C @ B )
% 0.26/0.50          = A )
% 0.26/0.50       => ( C
% 0.26/0.50          = ( minus_minus_nat @ A @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_implies_diff
% 0.26/0.50  thf(fact_2158_add__implies__diff,axiom,
% 0.26/0.50      ! [C: int,B: int,A: int] :
% 0.26/0.50        ( ( ( plus_plus_int @ C @ B )
% 0.26/0.50          = A )
% 0.26/0.50       => ( C
% 0.26/0.50          = ( minus_minus_int @ A @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_implies_diff
% 0.26/0.50  thf(fact_2159_diff__right__commute,axiom,
% 0.26/0.50      ! [A: real,C: real,B: real] :
% 0.26/0.50        ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 0.26/0.50        = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_right_commute
% 0.26/0.50  thf(fact_2160_diff__right__commute,axiom,
% 0.26/0.50      ! [A: rat,C: rat,B: rat] :
% 0.26/0.50        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 0.26/0.50        = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_right_commute
% 0.26/0.50  thf(fact_2161_diff__right__commute,axiom,
% 0.26/0.50      ! [A: nat,C: nat,B: nat] :
% 0.26/0.50        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 0.26/0.50        = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_right_commute
% 0.26/0.50  thf(fact_2162_diff__right__commute,axiom,
% 0.26/0.50      ! [A: int,C: int,B: int] :
% 0.26/0.50        ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 0.26/0.50        = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_right_commute
% 0.26/0.50  thf(fact_2163_diff__diff__eq,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.26/0.50        = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_diff_eq
% 0.26/0.50  thf(fact_2164_diff__diff__eq,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.26/0.50        = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_diff_eq
% 0.26/0.50  thf(fact_2165_diff__diff__eq,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat] :
% 0.26/0.50        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 0.26/0.50        = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_diff_eq
% 0.26/0.50  thf(fact_2166_diff__diff__eq,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.26/0.50        = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_diff_eq
% 0.26/0.50  thf(fact_2167_add__diff__add,axiom,
% 0.26/0.50      ! [A: real,C: real,B: real,D3: real] :
% 0.26/0.50        ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D3 ) )
% 0.26/0.50        = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D3 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_diff_add
% 0.26/0.50  thf(fact_2168_add__diff__add,axiom,
% 0.26/0.50      ! [A: rat,C: rat,B: rat,D3: rat] :
% 0.26/0.50        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D3 ) )
% 0.26/0.50        = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D3 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_diff_add
% 0.26/0.50  thf(fact_2169_add__diff__add,axiom,
% 0.26/0.50      ! [A: int,C: int,B: int,D3: int] :
% 0.26/0.50        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D3 ) )
% 0.26/0.50        = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D3 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_diff_add
% 0.26/0.50  thf(fact_2170_is__num__normalize_I1_J,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.26/0.50        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % is_num_normalize(1)
% 0.26/0.50  thf(fact_2171_is__num__normalize_I1_J,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.26/0.50        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % is_num_normalize(1)
% 0.26/0.50  thf(fact_2172_is__num__normalize_I1_J,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.26/0.50        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % is_num_normalize(1)
% 0.26/0.50  thf(fact_2173_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 0.26/0.50      ! [M: nat,N: nat] :
% 0.26/0.50        ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N ) )
% 0.26/0.50        = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % unique_euclidean_semiring_with_nat_class.of_nat_div
% 0.26/0.50  thf(fact_2174_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 0.26/0.50      ! [M: nat,N: nat] :
% 0.26/0.50        ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) )
% 0.26/0.50        = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % unique_euclidean_semiring_with_nat_class.of_nat_div
% 0.26/0.50  thf(fact_2175_div__add__self2,axiom,
% 0.26/0.50      ! [B: nat,A: nat] :
% 0.26/0.50        ( ( B != zero_zero_nat )
% 0.26/0.50       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.26/0.50          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % div_add_self2
% 0.26/0.50  thf(fact_2176_div__add__self2,axiom,
% 0.26/0.50      ! [B: int,A: int] :
% 0.26/0.50        ( ( B != zero_zero_int )
% 0.26/0.50       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.26/0.50          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % div_add_self2
% 0.26/0.50  thf(fact_2177_div__add__self1,axiom,
% 0.26/0.50      ! [B: nat,A: nat] :
% 0.26/0.50        ( ( B != zero_zero_nat )
% 0.26/0.50       => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.26/0.50          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % div_add_self1
% 0.26/0.50  thf(fact_2178_div__add__self1,axiom,
% 0.26/0.50      ! [B: int,A: int] :
% 0.26/0.50        ( ( B != zero_zero_int )
% 0.26/0.50       => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.26/0.50          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % div_add_self1
% 0.26/0.50  thf(fact_2179_of__nat__diff,axiom,
% 0.26/0.50      ! [N: nat,M: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.50       => ( ( semiri8010041392384452111omplex @ ( minus_minus_nat @ M @ N ) )
% 0.26/0.50          = ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % of_nat_diff
% 0.26/0.50  thf(fact_2180_of__nat__diff,axiom,
% 0.26/0.50      ! [N: nat,M: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.50       => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N ) )
% 0.26/0.50          = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % of_nat_diff
% 0.26/0.50  thf(fact_2181_of__nat__diff,axiom,
% 0.26/0.50      ! [N: nat,M: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.50       => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N ) )
% 0.26/0.50          = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % of_nat_diff
% 0.26/0.50  thf(fact_2182_of__nat__diff,axiom,
% 0.26/0.50      ! [N: nat,M: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.50       => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 0.26/0.50          = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % of_nat_diff
% 0.26/0.50  thf(fact_2183_of__nat__diff,axiom,
% 0.26/0.50      ! [N: nat,M: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.50       => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 0.26/0.50          = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % of_nat_diff
% 0.26/0.50  thf(fact_2184_int__induct,axiom,
% 0.26/0.50      ! [P: int > $o,K: int,I: int] :
% 0.26/0.50        ( ( P @ K )
% 0.26/0.50       => ( ! [I3: int] :
% 0.26/0.50              ( ( ord_less_eq_int @ K @ I3 )
% 0.26/0.50             => ( ( P @ I3 )
% 0.26/0.50               => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 0.26/0.50         => ( ! [I3: int] :
% 0.26/0.50                ( ( ord_less_eq_int @ I3 @ K )
% 0.26/0.50               => ( ( P @ I3 )
% 0.26/0.50                 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 0.26/0.50           => ( P @ I ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % int_induct
% 0.26/0.50  thf(fact_2185_int__minus,axiom,
% 0.26/0.50      ! [N: nat,M: nat] :
% 0.26/0.50        ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ M ) )
% 0.26/0.50        = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % int_minus
% 0.26/0.50  thf(fact_2186_ceiling__add__le,axiom,
% 0.26/0.50      ! [X3: rat,Y3: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X3 @ Y3 ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X3 ) @ ( archim2889992004027027881ng_rat @ Y3 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ceiling_add_le
% 0.26/0.50  thf(fact_2187_ceiling__add__le,axiom,
% 0.26/0.50      ! [X3: real,Y3: real] : ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( plus_plus_real @ X3 @ Y3 ) ) @ ( plus_plus_int @ ( archim7802044766580827645g_real @ X3 ) @ ( archim7802044766580827645g_real @ Y3 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ceiling_add_le
% 0.26/0.50  thf(fact_2188_diff__eq__diff__less__eq,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real,D3: real] :
% 0.26/0.50        ( ( ( minus_minus_real @ A @ B )
% 0.26/0.50          = ( minus_minus_real @ C @ D3 ) )
% 0.26/0.50       => ( ( ord_less_eq_real @ A @ B )
% 0.26/0.50          = ( ord_less_eq_real @ C @ D3 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_eq_diff_less_eq
% 0.26/0.50  thf(fact_2189_diff__eq__diff__less__eq,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat,D3: rat] :
% 0.26/0.50        ( ( ( minus_minus_rat @ A @ B )
% 0.26/0.50          = ( minus_minus_rat @ C @ D3 ) )
% 0.26/0.50       => ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.50          = ( ord_less_eq_rat @ C @ D3 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_eq_diff_less_eq
% 0.26/0.50  thf(fact_2190_diff__eq__diff__less__eq,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int,D3: int] :
% 0.26/0.50        ( ( ( minus_minus_int @ A @ B )
% 0.26/0.50          = ( minus_minus_int @ C @ D3 ) )
% 0.26/0.50       => ( ( ord_less_eq_int @ A @ B )
% 0.26/0.50          = ( ord_less_eq_int @ C @ D3 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_eq_diff_less_eq
% 0.26/0.50  thf(fact_2191_diff__right__mono,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.50       => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_right_mono
% 0.26/0.50  thf(fact_2192_diff__right__mono,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.50       => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_right_mono
% 0.26/0.50  thf(fact_2193_diff__right__mono,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ A @ B )
% 0.26/0.50       => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_right_mono
% 0.26/0.50  thf(fact_2194_diff__left__mono,axiom,
% 0.26/0.50      ! [B: real,A: real,C: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ B @ A )
% 0.26/0.50       => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_left_mono
% 0.26/0.50  thf(fact_2195_diff__left__mono,axiom,
% 0.26/0.50      ! [B: rat,A: rat,C: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ B @ A )
% 0.26/0.50       => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_left_mono
% 0.26/0.50  thf(fact_2196_diff__left__mono,axiom,
% 0.26/0.50      ! [B: int,A: int,C: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ B @ A )
% 0.26/0.50       => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_left_mono
% 0.26/0.50  thf(fact_2197_diff__mono,axiom,
% 0.26/0.50      ! [A: real,B: real,D3: real,C: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.50       => ( ( ord_less_eq_real @ D3 @ C )
% 0.26/0.50         => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_mono
% 0.26/0.50  thf(fact_2198_diff__mono,axiom,
% 0.26/0.50      ! [A: rat,B: rat,D3: rat,C: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.50       => ( ( ord_less_eq_rat @ D3 @ C )
% 0.26/0.50         => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_mono
% 0.26/0.50  thf(fact_2199_diff__mono,axiom,
% 0.26/0.50      ! [A: int,B: int,D3: int,C: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ A @ B )
% 0.26/0.50       => ( ( ord_less_eq_int @ D3 @ C )
% 0.26/0.50         => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_mono
% 0.26/0.50  thf(fact_2200_eq__iff__diff__eq__0,axiom,
% 0.26/0.50      ( ( ^ [Y5: real,Z2: real] : ( Y5 = Z2 ) )
% 0.26/0.50      = ( ^ [A4: real,B3: real] :
% 0.26/0.50            ( ( minus_minus_real @ A4 @ B3 )
% 0.26/0.50            = zero_zero_real ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % eq_iff_diff_eq_0
% 0.26/0.50  thf(fact_2201_eq__iff__diff__eq__0,axiom,
% 0.26/0.50      ( ( ^ [Y5: rat,Z2: rat] : ( Y5 = Z2 ) )
% 0.26/0.50      = ( ^ [A4: rat,B3: rat] :
% 0.26/0.50            ( ( minus_minus_rat @ A4 @ B3 )
% 0.26/0.50            = zero_zero_rat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % eq_iff_diff_eq_0
% 0.26/0.50  thf(fact_2202_eq__iff__diff__eq__0,axiom,
% 0.26/0.50      ( ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 0.26/0.50      = ( ^ [A4: int,B3: int] :
% 0.26/0.50            ( ( minus_minus_int @ A4 @ B3 )
% 0.26/0.50            = zero_zero_int ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % eq_iff_diff_eq_0
% 0.26/0.50  thf(fact_2203_diff__strict__mono,axiom,
% 0.26/0.50      ! [A: real,B: real,D3: real,C: real] :
% 0.26/0.50        ( ( ord_less_real @ A @ B )
% 0.26/0.50       => ( ( ord_less_real @ D3 @ C )
% 0.26/0.50         => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_strict_mono
% 0.26/0.50  thf(fact_2204_diff__strict__mono,axiom,
% 0.26/0.50      ! [A: rat,B: rat,D3: rat,C: rat] :
% 0.26/0.50        ( ( ord_less_rat @ A @ B )
% 0.26/0.50       => ( ( ord_less_rat @ D3 @ C )
% 0.26/0.50         => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_strict_mono
% 0.26/0.50  thf(fact_2205_diff__strict__mono,axiom,
% 0.26/0.50      ! [A: int,B: int,D3: int,C: int] :
% 0.26/0.50        ( ( ord_less_int @ A @ B )
% 0.26/0.50       => ( ( ord_less_int @ D3 @ C )
% 0.26/0.50         => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_strict_mono
% 0.26/0.50  thf(fact_2206_diff__eq__diff__less,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real,D3: real] :
% 0.26/0.50        ( ( ( minus_minus_real @ A @ B )
% 0.26/0.50          = ( minus_minus_real @ C @ D3 ) )
% 0.26/0.50       => ( ( ord_less_real @ A @ B )
% 0.26/0.50          = ( ord_less_real @ C @ D3 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_eq_diff_less
% 0.26/0.50  thf(fact_2207_diff__eq__diff__less,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat,D3: rat] :
% 0.26/0.50        ( ( ( minus_minus_rat @ A @ B )
% 0.26/0.50          = ( minus_minus_rat @ C @ D3 ) )
% 0.26/0.50       => ( ( ord_less_rat @ A @ B )
% 0.26/0.50          = ( ord_less_rat @ C @ D3 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_eq_diff_less
% 0.26/0.50  thf(fact_2208_diff__eq__diff__less,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int,D3: int] :
% 0.26/0.50        ( ( ( minus_minus_int @ A @ B )
% 0.26/0.50          = ( minus_minus_int @ C @ D3 ) )
% 0.26/0.50       => ( ( ord_less_int @ A @ B )
% 0.26/0.50          = ( ord_less_int @ C @ D3 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_eq_diff_less
% 0.26/0.50  thf(fact_2209_diff__strict__left__mono,axiom,
% 0.26/0.50      ! [B: real,A: real,C: real] :
% 0.26/0.50        ( ( ord_less_real @ B @ A )
% 0.26/0.50       => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_strict_left_mono
% 0.26/0.50  thf(fact_2210_diff__strict__left__mono,axiom,
% 0.26/0.50      ! [B: rat,A: rat,C: rat] :
% 0.26/0.50        ( ( ord_less_rat @ B @ A )
% 0.26/0.50       => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_strict_left_mono
% 0.26/0.50  thf(fact_2211_diff__strict__left__mono,axiom,
% 0.26/0.50      ! [B: int,A: int,C: int] :
% 0.26/0.50        ( ( ord_less_int @ B @ A )
% 0.26/0.50       => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_strict_left_mono
% 0.26/0.50  thf(fact_2212_diff__strict__right__mono,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( ord_less_real @ A @ B )
% 0.26/0.50       => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_strict_right_mono
% 0.26/0.50  thf(fact_2213_diff__strict__right__mono,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( ord_less_rat @ A @ B )
% 0.26/0.50       => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_strict_right_mono
% 0.26/0.50  thf(fact_2214_diff__strict__right__mono,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( ord_less_int @ A @ B )
% 0.26/0.50       => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_strict_right_mono
% 0.26/0.50  thf(fact_2215_add__le__imp__le__right,axiom,
% 0.26/0.50      ! [A: real,C: real,B: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.26/0.50       => ( ord_less_eq_real @ A @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_le_imp_le_right
% 0.26/0.50  thf(fact_2216_add__le__imp__le__right,axiom,
% 0.26/0.50      ! [A: rat,C: rat,B: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.26/0.50       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_le_imp_le_right
% 0.26/0.50  thf(fact_2217_add__le__imp__le__right,axiom,
% 0.26/0.50      ! [A: nat,C: nat,B: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.26/0.50       => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_le_imp_le_right
% 0.26/0.50  thf(fact_2218_add__le__imp__le__right,axiom,
% 0.26/0.50      ! [A: int,C: int,B: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.26/0.50       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_le_imp_le_right
% 0.26/0.50  thf(fact_2219_add__le__imp__le__left,axiom,
% 0.26/0.50      ! [C: real,A: real,B: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.26/0.50       => ( ord_less_eq_real @ A @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_le_imp_le_left
% 0.26/0.50  thf(fact_2220_add__le__imp__le__left,axiom,
% 0.26/0.50      ! [C: rat,A: rat,B: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.26/0.50       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_le_imp_le_left
% 0.26/0.50  thf(fact_2221_add__le__imp__le__left,axiom,
% 0.26/0.50      ! [C: nat,A: nat,B: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.26/0.50       => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_le_imp_le_left
% 0.26/0.50  thf(fact_2222_add__le__imp__le__left,axiom,
% 0.26/0.50      ! [C: int,A: int,B: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.26/0.50       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_le_imp_le_left
% 0.26/0.50  thf(fact_2223_le__iff__add,axiom,
% 0.26/0.50      ( ord_less_eq_nat
% 0.26/0.50      = ( ^ [A4: nat,B3: nat] :
% 0.26/0.50          ? [C3: nat] :
% 0.26/0.50            ( B3
% 0.26/0.50            = ( plus_plus_nat @ A4 @ C3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % le_iff_add
% 0.26/0.50  thf(fact_2224_add__right__mono,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.50       => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_right_mono
% 0.26/0.50  thf(fact_2225_add__right__mono,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.50       => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_right_mono
% 0.26/0.50  thf(fact_2226_add__right__mono,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.50       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_right_mono
% 0.26/0.50  thf(fact_2227_add__right__mono,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ A @ B )
% 0.26/0.50       => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_right_mono
% 0.26/0.50  thf(fact_2228_less__eqE,axiom,
% 0.26/0.50      ! [A: nat,B: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.50       => ~ ! [C2: nat] :
% 0.26/0.50              ( B
% 0.26/0.50             != ( plus_plus_nat @ A @ C2 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % less_eqE
% 0.26/0.50  thf(fact_2229_add__left__mono,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.50       => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_left_mono
% 0.26/0.50  thf(fact_2230_add__left__mono,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.50       => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_left_mono
% 0.26/0.50  thf(fact_2231_add__left__mono,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.50       => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_left_mono
% 0.26/0.50  thf(fact_2232_add__left__mono,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ A @ B )
% 0.26/0.50       => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_left_mono
% 0.26/0.50  thf(fact_2233_add__mono,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real,D3: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.50       => ( ( ord_less_eq_real @ C @ D3 )
% 0.26/0.50         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono
% 0.26/0.50  thf(fact_2234_add__mono,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat,D3: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.50       => ( ( ord_less_eq_rat @ C @ D3 )
% 0.26/0.50         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono
% 0.26/0.50  thf(fact_2235_add__mono,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat,D3: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.50       => ( ( ord_less_eq_nat @ C @ D3 )
% 0.26/0.50         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono
% 0.26/0.50  thf(fact_2236_add__mono,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int,D3: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ A @ B )
% 0.26/0.50       => ( ( ord_less_eq_int @ C @ D3 )
% 0.26/0.50         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono
% 0.26/0.50  thf(fact_2237_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.26/0.50      ! [I: real,J: real,K: real,L: real] :
% 0.26/0.50        ( ( ( ord_less_eq_real @ I @ J )
% 0.26/0.50          & ( ord_less_eq_real @ K @ L ) )
% 0.26/0.50       => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_semiring(1)
% 0.26/0.50  thf(fact_2238_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.26/0.50      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.26/0.50        ( ( ( ord_less_eq_rat @ I @ J )
% 0.26/0.50          & ( ord_less_eq_rat @ K @ L ) )
% 0.26/0.50       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_semiring(1)
% 0.26/0.50  thf(fact_2239_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.26/0.50      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.26/0.50        ( ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.50          & ( ord_less_eq_nat @ K @ L ) )
% 0.26/0.50       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_semiring(1)
% 0.26/0.50  thf(fact_2240_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.26/0.50      ! [I: int,J: int,K: int,L: int] :
% 0.26/0.50        ( ( ( ord_less_eq_int @ I @ J )
% 0.26/0.50          & ( ord_less_eq_int @ K @ L ) )
% 0.26/0.50       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_semiring(1)
% 0.26/0.50  thf(fact_2241_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.26/0.50      ! [I: real,J: real,K: real,L: real] :
% 0.26/0.50        ( ( ( I = J )
% 0.26/0.50          & ( ord_less_eq_real @ K @ L ) )
% 0.26/0.50       => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_semiring(2)
% 0.26/0.50  thf(fact_2242_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.26/0.50      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.26/0.50        ( ( ( I = J )
% 0.26/0.50          & ( ord_less_eq_rat @ K @ L ) )
% 0.26/0.50       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_semiring(2)
% 0.26/0.50  thf(fact_2243_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.26/0.50      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.26/0.50        ( ( ( I = J )
% 0.26/0.50          & ( ord_less_eq_nat @ K @ L ) )
% 0.26/0.50       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_semiring(2)
% 0.26/0.50  thf(fact_2244_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.26/0.50      ! [I: int,J: int,K: int,L: int] :
% 0.26/0.50        ( ( ( I = J )
% 0.26/0.50          & ( ord_less_eq_int @ K @ L ) )
% 0.26/0.50       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_semiring(2)
% 0.26/0.50  thf(fact_2245_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.26/0.50      ! [I: real,J: real,K: real,L: real] :
% 0.26/0.50        ( ( ( ord_less_eq_real @ I @ J )
% 0.26/0.50          & ( K = L ) )
% 0.26/0.50       => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_semiring(3)
% 0.26/0.50  thf(fact_2246_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.26/0.50      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.26/0.50        ( ( ( ord_less_eq_rat @ I @ J )
% 0.26/0.50          & ( K = L ) )
% 0.26/0.50       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_semiring(3)
% 0.26/0.50  thf(fact_2247_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.26/0.50      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.26/0.50        ( ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.50          & ( K = L ) )
% 0.26/0.50       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_semiring(3)
% 0.26/0.50  thf(fact_2248_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.26/0.50      ! [I: int,J: int,K: int,L: int] :
% 0.26/0.50        ( ( ( ord_less_eq_int @ I @ J )
% 0.26/0.50          & ( K = L ) )
% 0.26/0.50       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_semiring(3)
% 0.26/0.50  thf(fact_2249_verit__sum__simplify,axiom,
% 0.26/0.50      ! [A: real] :
% 0.26/0.50        ( ( plus_plus_real @ A @ zero_zero_real )
% 0.26/0.50        = A ) ).
% 0.26/0.50  
% 0.26/0.50  % verit_sum_simplify
% 0.26/0.50  thf(fact_2250_verit__sum__simplify,axiom,
% 0.26/0.50      ! [A: rat] :
% 0.26/0.50        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.26/0.50        = A ) ).
% 0.26/0.50  
% 0.26/0.50  % verit_sum_simplify
% 0.26/0.50  thf(fact_2251_verit__sum__simplify,axiom,
% 0.26/0.50      ! [A: nat] :
% 0.26/0.50        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.26/0.50        = A ) ).
% 0.26/0.50  
% 0.26/0.50  % verit_sum_simplify
% 0.26/0.50  thf(fact_2252_verit__sum__simplify,axiom,
% 0.26/0.50      ! [A: int] :
% 0.26/0.50        ( ( plus_plus_int @ A @ zero_zero_int )
% 0.26/0.50        = A ) ).
% 0.26/0.50  
% 0.26/0.50  % verit_sum_simplify
% 0.26/0.50  thf(fact_2253_add_Ogroup__left__neutral,axiom,
% 0.26/0.50      ! [A: real] :
% 0.26/0.50        ( ( plus_plus_real @ zero_zero_real @ A )
% 0.26/0.50        = A ) ).
% 0.26/0.50  
% 0.26/0.50  % add.group_left_neutral
% 0.26/0.50  thf(fact_2254_add_Ogroup__left__neutral,axiom,
% 0.26/0.50      ! [A: rat] :
% 0.26/0.50        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.26/0.50        = A ) ).
% 0.26/0.50  
% 0.26/0.50  % add.group_left_neutral
% 0.26/0.50  thf(fact_2255_add_Ogroup__left__neutral,axiom,
% 0.26/0.50      ! [A: int] :
% 0.26/0.50        ( ( plus_plus_int @ zero_zero_int @ A )
% 0.26/0.50        = A ) ).
% 0.26/0.50  
% 0.26/0.50  % add.group_left_neutral
% 0.26/0.50  thf(fact_2256_add_Ocomm__neutral,axiom,
% 0.26/0.50      ! [A: real] :
% 0.26/0.50        ( ( plus_plus_real @ A @ zero_zero_real )
% 0.26/0.50        = A ) ).
% 0.26/0.50  
% 0.26/0.50  % add.comm_neutral
% 0.26/0.50  thf(fact_2257_add_Ocomm__neutral,axiom,
% 0.26/0.50      ! [A: rat] :
% 0.26/0.50        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.26/0.50        = A ) ).
% 0.26/0.50  
% 0.26/0.50  % add.comm_neutral
% 0.26/0.50  thf(fact_2258_add_Ocomm__neutral,axiom,
% 0.26/0.50      ! [A: nat] :
% 0.26/0.50        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.26/0.50        = A ) ).
% 0.26/0.50  
% 0.26/0.50  % add.comm_neutral
% 0.26/0.50  thf(fact_2259_add_Ocomm__neutral,axiom,
% 0.26/0.50      ! [A: int] :
% 0.26/0.50        ( ( plus_plus_int @ A @ zero_zero_int )
% 0.26/0.50        = A ) ).
% 0.26/0.50  
% 0.26/0.50  % add.comm_neutral
% 0.26/0.50  thf(fact_2260_comm__monoid__add__class_Oadd__0,axiom,
% 0.26/0.50      ! [A: real] :
% 0.26/0.50        ( ( plus_plus_real @ zero_zero_real @ A )
% 0.26/0.50        = A ) ).
% 0.26/0.50  
% 0.26/0.50  % comm_monoid_add_class.add_0
% 0.26/0.50  thf(fact_2261_comm__monoid__add__class_Oadd__0,axiom,
% 0.26/0.50      ! [A: rat] :
% 0.26/0.50        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.26/0.50        = A ) ).
% 0.26/0.50  
% 0.26/0.50  % comm_monoid_add_class.add_0
% 0.26/0.50  thf(fact_2262_comm__monoid__add__class_Oadd__0,axiom,
% 0.26/0.50      ! [A: nat] :
% 0.26/0.50        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.26/0.50        = A ) ).
% 0.26/0.50  
% 0.26/0.50  % comm_monoid_add_class.add_0
% 0.26/0.50  thf(fact_2263_comm__monoid__add__class_Oadd__0,axiom,
% 0.26/0.50      ! [A: int] :
% 0.26/0.50        ( ( plus_plus_int @ zero_zero_int @ A )
% 0.26/0.50        = A ) ).
% 0.26/0.50  
% 0.26/0.50  % comm_monoid_add_class.add_0
% 0.26/0.50  thf(fact_2264_add__mono__thms__linordered__field_I5_J,axiom,
% 0.26/0.50      ! [I: real,J: real,K: real,L: real] :
% 0.26/0.50        ( ( ( ord_less_real @ I @ J )
% 0.26/0.50          & ( ord_less_real @ K @ L ) )
% 0.26/0.50       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_field(5)
% 0.26/0.50  thf(fact_2265_add__mono__thms__linordered__field_I5_J,axiom,
% 0.26/0.50      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.26/0.50        ( ( ( ord_less_rat @ I @ J )
% 0.26/0.50          & ( ord_less_rat @ K @ L ) )
% 0.26/0.50       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_field(5)
% 0.26/0.50  thf(fact_2266_add__mono__thms__linordered__field_I5_J,axiom,
% 0.26/0.50      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.26/0.50        ( ( ( ord_less_nat @ I @ J )
% 0.26/0.50          & ( ord_less_nat @ K @ L ) )
% 0.26/0.50       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_field(5)
% 0.26/0.50  thf(fact_2267_add__mono__thms__linordered__field_I5_J,axiom,
% 0.26/0.50      ! [I: int,J: int,K: int,L: int] :
% 0.26/0.50        ( ( ( ord_less_int @ I @ J )
% 0.26/0.50          & ( ord_less_int @ K @ L ) )
% 0.26/0.50       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_field(5)
% 0.26/0.50  thf(fact_2268_add__mono__thms__linordered__field_I2_J,axiom,
% 0.26/0.50      ! [I: real,J: real,K: real,L: real] :
% 0.26/0.50        ( ( ( I = J )
% 0.26/0.50          & ( ord_less_real @ K @ L ) )
% 0.26/0.50       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_field(2)
% 0.26/0.50  thf(fact_2269_add__mono__thms__linordered__field_I2_J,axiom,
% 0.26/0.50      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.26/0.50        ( ( ( I = J )
% 0.26/0.50          & ( ord_less_rat @ K @ L ) )
% 0.26/0.50       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_field(2)
% 0.26/0.50  thf(fact_2270_add__mono__thms__linordered__field_I2_J,axiom,
% 0.26/0.50      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.26/0.50        ( ( ( I = J )
% 0.26/0.50          & ( ord_less_nat @ K @ L ) )
% 0.26/0.50       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_field(2)
% 0.26/0.50  thf(fact_2271_add__mono__thms__linordered__field_I2_J,axiom,
% 0.26/0.50      ! [I: int,J: int,K: int,L: int] :
% 0.26/0.50        ( ( ( I = J )
% 0.26/0.50          & ( ord_less_int @ K @ L ) )
% 0.26/0.50       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_field(2)
% 0.26/0.50  thf(fact_2272_add__mono__thms__linordered__field_I1_J,axiom,
% 0.26/0.50      ! [I: real,J: real,K: real,L: real] :
% 0.26/0.50        ( ( ( ord_less_real @ I @ J )
% 0.26/0.50          & ( K = L ) )
% 0.26/0.50       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_field(1)
% 0.26/0.50  thf(fact_2273_add__mono__thms__linordered__field_I1_J,axiom,
% 0.26/0.50      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.26/0.50        ( ( ( ord_less_rat @ I @ J )
% 0.26/0.50          & ( K = L ) )
% 0.26/0.50       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_field(1)
% 0.26/0.50  thf(fact_2274_add__mono__thms__linordered__field_I1_J,axiom,
% 0.26/0.50      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.26/0.50        ( ( ( ord_less_nat @ I @ J )
% 0.26/0.50          & ( K = L ) )
% 0.26/0.50       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_field(1)
% 0.26/0.50  thf(fact_2275_add__mono__thms__linordered__field_I1_J,axiom,
% 0.26/0.50      ! [I: int,J: int,K: int,L: int] :
% 0.26/0.50        ( ( ( ord_less_int @ I @ J )
% 0.26/0.50          & ( K = L ) )
% 0.26/0.50       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_field(1)
% 0.26/0.50  thf(fact_2276_add__strict__mono,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real,D3: real] :
% 0.26/0.50        ( ( ord_less_real @ A @ B )
% 0.26/0.50       => ( ( ord_less_real @ C @ D3 )
% 0.26/0.50         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_strict_mono
% 0.26/0.50  thf(fact_2277_add__strict__mono,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat,D3: rat] :
% 0.26/0.50        ( ( ord_less_rat @ A @ B )
% 0.26/0.50       => ( ( ord_less_rat @ C @ D3 )
% 0.26/0.50         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_strict_mono
% 0.26/0.50  thf(fact_2278_add__strict__mono,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat,D3: nat] :
% 0.26/0.50        ( ( ord_less_nat @ A @ B )
% 0.26/0.50       => ( ( ord_less_nat @ C @ D3 )
% 0.26/0.50         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_strict_mono
% 0.26/0.50  thf(fact_2279_add__strict__mono,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int,D3: int] :
% 0.26/0.50        ( ( ord_less_int @ A @ B )
% 0.26/0.50       => ( ( ord_less_int @ C @ D3 )
% 0.26/0.50         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_strict_mono
% 0.26/0.50  thf(fact_2280_add__strict__left__mono,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( ord_less_real @ A @ B )
% 0.26/0.50       => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_strict_left_mono
% 0.26/0.50  thf(fact_2281_add__strict__left__mono,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( ord_less_rat @ A @ B )
% 0.26/0.50       => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_strict_left_mono
% 0.26/0.50  thf(fact_2282_add__strict__left__mono,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat] :
% 0.26/0.50        ( ( ord_less_nat @ A @ B )
% 0.26/0.50       => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_strict_left_mono
% 0.26/0.50  thf(fact_2283_add__strict__left__mono,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( ord_less_int @ A @ B )
% 0.26/0.50       => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_strict_left_mono
% 0.26/0.50  thf(fact_2284_add__strict__right__mono,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( ord_less_real @ A @ B )
% 0.26/0.50       => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_strict_right_mono
% 0.26/0.50  thf(fact_2285_add__strict__right__mono,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( ord_less_rat @ A @ B )
% 0.26/0.50       => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_strict_right_mono
% 0.26/0.50  thf(fact_2286_add__strict__right__mono,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat] :
% 0.26/0.50        ( ( ord_less_nat @ A @ B )
% 0.26/0.50       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_strict_right_mono
% 0.26/0.50  thf(fact_2287_add__strict__right__mono,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( ord_less_int @ A @ B )
% 0.26/0.50       => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_strict_right_mono
% 0.26/0.50  thf(fact_2288_add__less__imp__less__left,axiom,
% 0.26/0.50      ! [C: real,A: real,B: real] :
% 0.26/0.50        ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.26/0.50       => ( ord_less_real @ A @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_less_imp_less_left
% 0.26/0.50  thf(fact_2289_add__less__imp__less__left,axiom,
% 0.26/0.50      ! [C: rat,A: rat,B: rat] :
% 0.26/0.50        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.26/0.50       => ( ord_less_rat @ A @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_less_imp_less_left
% 0.26/0.50  thf(fact_2290_add__less__imp__less__left,axiom,
% 0.26/0.50      ! [C: nat,A: nat,B: nat] :
% 0.26/0.50        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.26/0.50       => ( ord_less_nat @ A @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_less_imp_less_left
% 0.26/0.50  thf(fact_2291_add__less__imp__less__left,axiom,
% 0.26/0.50      ! [C: int,A: int,B: int] :
% 0.26/0.50        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.26/0.50       => ( ord_less_int @ A @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_less_imp_less_left
% 0.26/0.50  thf(fact_2292_add__less__imp__less__right,axiom,
% 0.26/0.50      ! [A: real,C: real,B: real] :
% 0.26/0.50        ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.26/0.50       => ( ord_less_real @ A @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_less_imp_less_right
% 0.26/0.50  thf(fact_2293_add__less__imp__less__right,axiom,
% 0.26/0.50      ! [A: rat,C: rat,B: rat] :
% 0.26/0.50        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.26/0.50       => ( ord_less_rat @ A @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_less_imp_less_right
% 0.26/0.50  thf(fact_2294_add__less__imp__less__right,axiom,
% 0.26/0.50      ! [A: nat,C: nat,B: nat] :
% 0.26/0.50        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.26/0.50       => ( ord_less_nat @ A @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_less_imp_less_right
% 0.26/0.50  thf(fact_2295_add__less__imp__less__right,axiom,
% 0.26/0.50      ! [A: int,C: int,B: int] :
% 0.26/0.50        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.26/0.50       => ( ord_less_int @ A @ B ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_less_imp_less_right
% 0.26/0.50  thf(fact_2296_power__divide,axiom,
% 0.26/0.50      ! [A: complex,B: complex,N: nat] :
% 0.26/0.50        ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N )
% 0.26/0.50        = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % power_divide
% 0.26/0.50  thf(fact_2297_power__divide,axiom,
% 0.26/0.50      ! [A: real,B: real,N: nat] :
% 0.26/0.50        ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N )
% 0.26/0.50        = ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % power_divide
% 0.26/0.50  thf(fact_2298_power__divide,axiom,
% 0.26/0.50      ! [A: rat,B: rat,N: nat] :
% 0.26/0.50        ( ( power_power_rat @ ( divide_divide_rat @ A @ B ) @ N )
% 0.26/0.50        = ( divide_divide_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % power_divide
% 0.26/0.50  thf(fact_2299_diffs0__imp__equal,axiom,
% 0.26/0.50      ! [M: nat,N: nat] :
% 0.26/0.50        ( ( ( minus_minus_nat @ M @ N )
% 0.26/0.50          = zero_zero_nat )
% 0.26/0.50       => ( ( ( minus_minus_nat @ N @ M )
% 0.26/0.50            = zero_zero_nat )
% 0.26/0.50         => ( M = N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diffs0_imp_equal
% 0.26/0.50  thf(fact_2300_minus__nat_Odiff__0,axiom,
% 0.26/0.50      ! [M: nat] :
% 0.26/0.50        ( ( minus_minus_nat @ M @ zero_zero_nat )
% 0.26/0.50        = M ) ).
% 0.26/0.50  
% 0.26/0.50  % minus_nat.diff_0
% 0.26/0.50  thf(fact_2301_diff__less__mono2,axiom,
% 0.26/0.50      ! [M: nat,N: nat,L: nat] :
% 0.26/0.50        ( ( ord_less_nat @ M @ N )
% 0.26/0.50       => ( ( ord_less_nat @ M @ L )
% 0.26/0.50         => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_less_mono2
% 0.26/0.50  thf(fact_2302_less__imp__diff__less,axiom,
% 0.26/0.50      ! [J: nat,K: nat,N: nat] :
% 0.26/0.50        ( ( ord_less_nat @ J @ K )
% 0.26/0.50       => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 0.26/0.50  
% 0.26/0.50  % less_imp_diff_less
% 0.26/0.50  thf(fact_2303_minus__int__code_I1_J,axiom,
% 0.26/0.50      ! [K: int] :
% 0.26/0.50        ( ( minus_minus_int @ K @ zero_zero_int )
% 0.26/0.50        = K ) ).
% 0.26/0.50  
% 0.26/0.50  % minus_int_code(1)
% 0.26/0.50  thf(fact_2304_diff__le__mono2,axiom,
% 0.26/0.50      ! [M: nat,N: nat,L: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.50       => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_le_mono2
% 0.26/0.50  thf(fact_2305_le__diff__iff_H,axiom,
% 0.26/0.50      ! [A: nat,C: nat,B: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ A @ C )
% 0.26/0.50       => ( ( ord_less_eq_nat @ B @ C )
% 0.26/0.50         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 0.26/0.50            = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % le_diff_iff'
% 0.26/0.50  thf(fact_2306_diff__le__self,axiom,
% 0.26/0.50      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_le_self
% 0.26/0.50  thf(fact_2307_diff__le__mono,axiom,
% 0.26/0.50      ! [M: nat,N: nat,L: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.50       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_le_mono
% 0.26/0.50  thf(fact_2308_Nat_Odiff__diff__eq,axiom,
% 0.26/0.50      ! [K: nat,M: nat,N: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ K @ M )
% 0.26/0.50       => ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.50         => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.26/0.50            = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % Nat.diff_diff_eq
% 0.26/0.50  thf(fact_2309_le__diff__iff,axiom,
% 0.26/0.50      ! [K: nat,M: nat,N: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ K @ M )
% 0.26/0.50       => ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.50         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.26/0.50            = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % le_diff_iff
% 0.26/0.50  thf(fact_2310_eq__diff__iff,axiom,
% 0.26/0.50      ! [K: nat,M: nat,N: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ K @ M )
% 0.26/0.50       => ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.50         => ( ( ( minus_minus_nat @ M @ K )
% 0.26/0.50              = ( minus_minus_nat @ N @ K ) )
% 0.26/0.50            = ( M = N ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % eq_diff_iff
% 0.26/0.50  thf(fact_2311_div__le__dividend,axiom,
% 0.26/0.50      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 0.26/0.50  
% 0.26/0.50  % div_le_dividend
% 0.26/0.50  thf(fact_2312_div__le__mono,axiom,
% 0.26/0.50      ! [M: nat,N: nat,K: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.50       => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % div_le_mono
% 0.26/0.50  thf(fact_2313_plus__int__code_I1_J,axiom,
% 0.26/0.50      ! [K: int] :
% 0.26/0.50        ( ( plus_plus_int @ K @ zero_zero_int )
% 0.26/0.50        = K ) ).
% 0.26/0.50  
% 0.26/0.50  % plus_int_code(1)
% 0.26/0.50  thf(fact_2314_plus__int__code_I2_J,axiom,
% 0.26/0.50      ! [L: int] :
% 0.26/0.50        ( ( plus_plus_int @ zero_zero_int @ L )
% 0.26/0.50        = L ) ).
% 0.26/0.50  
% 0.26/0.50  % plus_int_code(2)
% 0.26/0.50  thf(fact_2315_int__diff__cases,axiom,
% 0.26/0.50      ! [Z: int] :
% 0.26/0.50        ~ ! [M4: nat,N2: nat] :
% 0.26/0.50            ( Z
% 0.26/0.50           != ( minus_minus_int @ ( semiri1314217659103216013at_int @ M4 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % int_diff_cases
% 0.26/0.50  thf(fact_2316_dvd__diff__nat,axiom,
% 0.26/0.50      ! [K: nat,M: nat,N: nat] :
% 0.26/0.50        ( ( dvd_dvd_nat @ K @ M )
% 0.26/0.50       => ( ( dvd_dvd_nat @ K @ N )
% 0.26/0.50         => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % dvd_diff_nat
% 0.26/0.50  thf(fact_2317_take__bit__add,axiom,
% 0.26/0.50      ! [N: nat,A: int,B: int] :
% 0.26/0.50        ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) )
% 0.26/0.50        = ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ A @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % take_bit_add
% 0.26/0.50  thf(fact_2318_take__bit__add,axiom,
% 0.26/0.50      ! [N: nat,A: nat,B: nat] :
% 0.26/0.50        ( ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) )
% 0.26/0.50        = ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ A @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % take_bit_add
% 0.26/0.50  thf(fact_2319_zdvd__zdiffD,axiom,
% 0.26/0.50      ! [K: int,M: int,N: int] :
% 0.26/0.50        ( ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N ) )
% 0.26/0.50       => ( ( dvd_dvd_int @ K @ N )
% 0.26/0.50         => ( dvd_dvd_int @ K @ M ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % zdvd_zdiffD
% 0.26/0.50  thf(fact_2320_take__bit__diff,axiom,
% 0.26/0.50      ! [N: nat,K: int,L: int] :
% 0.26/0.50        ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L ) ) )
% 0.26/0.50        = ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % take_bit_diff
% 0.26/0.50  thf(fact_2321_ln__eq__minus__one,axiom,
% 0.26/0.50      ! [X3: real] :
% 0.26/0.50        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.50       => ( ( ( ln_ln_real @ X3 )
% 0.26/0.50            = ( minus_minus_real @ X3 @ one_one_real ) )
% 0.26/0.50         => ( X3 = one_one_real ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ln_eq_minus_one
% 0.26/0.50  thf(fact_2322_ln__add__one__self__le__self,axiom,
% 0.26/0.50      ! [X3: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.50       => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X3 ) ) @ X3 ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ln_add_one_self_le_self
% 0.26/0.50  thf(fact_2323_artanh__def,axiom,
% 0.26/0.50      ( artanh_real
% 0.26/0.50      = ( ^ [X: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X ) @ ( minus_minus_real @ one_one_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % artanh_def
% 0.26/0.50  thf(fact_2324_field__sum__of__halves,axiom,
% 0.26/0.50      ! [X3: real] :
% 0.26/0.50        ( ( plus_plus_real @ ( divide_divide_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.50        = X3 ) ).
% 0.26/0.50  
% 0.26/0.50  % field_sum_of_halves
% 0.26/0.50  thf(fact_2325_field__sum__of__halves,axiom,
% 0.26/0.50      ! [X3: rat] :
% 0.26/0.50        ( ( plus_plus_rat @ ( divide_divide_rat @ X3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.26/0.50        = X3 ) ).
% 0.26/0.50  
% 0.26/0.50  % field_sum_of_halves
% 0.26/0.50  thf(fact_2326_power__diff,axiom,
% 0.26/0.50      ! [A: complex,N: nat,M: nat] :
% 0.26/0.50        ( ( A != zero_zero_complex )
% 0.26/0.50       => ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.50         => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N ) )
% 0.26/0.50            = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % power_diff
% 0.26/0.50  thf(fact_2327_power__diff,axiom,
% 0.26/0.50      ! [A: real,N: nat,M: nat] :
% 0.26/0.50        ( ( A != zero_zero_real )
% 0.26/0.50       => ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.50         => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N ) )
% 0.26/0.50            = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % power_diff
% 0.26/0.50  thf(fact_2328_power__diff,axiom,
% 0.26/0.50      ! [A: rat,N: nat,M: nat] :
% 0.26/0.50        ( ( A != zero_zero_rat )
% 0.26/0.50       => ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.50         => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N ) )
% 0.26/0.50            = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % power_diff
% 0.26/0.50  thf(fact_2329_power__diff,axiom,
% 0.26/0.50      ! [A: nat,N: nat,M: nat] :
% 0.26/0.50        ( ( A != zero_zero_nat )
% 0.26/0.50       => ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.50         => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) )
% 0.26/0.50            = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % power_diff
% 0.26/0.50  thf(fact_2330_power__diff,axiom,
% 0.26/0.50      ! [A: int,N: nat,M: nat] :
% 0.26/0.50        ( ( A != zero_zero_int )
% 0.26/0.50       => ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.50         => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) )
% 0.26/0.50            = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % power_diff
% 0.26/0.50  thf(fact_2331_int__ops_I6_J,axiom,
% 0.26/0.50      ! [A: nat,B: nat] :
% 0.26/0.50        ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 0.26/0.50         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 0.26/0.50            = zero_zero_int ) )
% 0.26/0.50        & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 0.26/0.50         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 0.26/0.50            = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % int_ops(6)
% 0.26/0.50  thf(fact_2332_nat__diff__distrib,axiom,
% 0.26/0.50      ! [Z5: int,Z: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ zero_zero_int @ Z5 )
% 0.26/0.50       => ( ( ord_less_eq_int @ Z5 @ Z )
% 0.26/0.50         => ( ( nat2 @ ( minus_minus_int @ Z @ Z5 ) )
% 0.26/0.50            = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z5 ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % nat_diff_distrib
% 0.26/0.50  thf(fact_2333_nat__diff__distrib_H,axiom,
% 0.26/0.50      ! [X3: int,Y3: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.26/0.50       => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 0.26/0.50         => ( ( nat2 @ ( minus_minus_int @ X3 @ Y3 ) )
% 0.26/0.50            = ( minus_minus_nat @ ( nat2 @ X3 ) @ ( nat2 @ Y3 ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % nat_diff_distrib'
% 0.26/0.50  thf(fact_2334_unset__bit__nat__def,axiom,
% 0.26/0.50      ( bit_se4205575877204974255it_nat
% 0.26/0.50      = ( ^ [M3: nat,N3: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M3 @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % unset_bit_nat_def
% 0.26/0.50  thf(fact_2335_dbl__def,axiom,
% 0.26/0.50      ( neg_numeral_dbl_real
% 0.26/0.50      = ( ^ [X: real] : ( plus_plus_real @ X @ X ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % dbl_def
% 0.26/0.50  thf(fact_2336_dbl__def,axiom,
% 0.26/0.50      ( neg_numeral_dbl_rat
% 0.26/0.50      = ( ^ [X: rat] : ( plus_plus_rat @ X @ X ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % dbl_def
% 0.26/0.50  thf(fact_2337_dbl__def,axiom,
% 0.26/0.50      ( neg_numeral_dbl_int
% 0.26/0.50      = ( ^ [X: int] : ( plus_plus_int @ X @ X ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % dbl_def
% 0.26/0.50  thf(fact_2338_unset__bit__less__eq,axiom,
% 0.26/0.50      ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 0.26/0.50  
% 0.26/0.50  % unset_bit_less_eq
% 0.26/0.50  thf(fact_2339_set__bit__greater__eq,axiom,
% 0.26/0.50      ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 0.26/0.50  
% 0.26/0.50  % set_bit_greater_eq
% 0.26/0.50  thf(fact_2340_ln__le__minus__one,axiom,
% 0.26/0.50      ! [X3: real] :
% 0.26/0.50        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.50       => ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ ( minus_minus_real @ X3 @ one_one_real ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ln_le_minus_one
% 0.26/0.50  thf(fact_2341_field__less__half__sum,axiom,
% 0.26/0.50      ! [X3: real,Y3: real] :
% 0.26/0.50        ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.50       => ( ord_less_real @ X3 @ ( divide_divide_real @ ( plus_plus_real @ X3 @ Y3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % field_less_half_sum
% 0.26/0.50  thf(fact_2342_field__less__half__sum,axiom,
% 0.26/0.50      ! [X3: rat,Y3: rat] :
% 0.26/0.50        ( ( ord_less_rat @ X3 @ Y3 )
% 0.26/0.50       => ( ord_less_rat @ X3 @ ( divide_divide_rat @ ( plus_plus_rat @ X3 @ Y3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % field_less_half_sum
% 0.26/0.50  thf(fact_2343_power__diff__power__eq,axiom,
% 0.26/0.50      ! [A: nat,N: nat,M: nat] :
% 0.26/0.50        ( ( A != zero_zero_nat )
% 0.26/0.50       => ( ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.50           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 0.26/0.50              = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 0.26/0.50          & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.26/0.50           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 0.26/0.50              = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % power_diff_power_eq
% 0.26/0.50  thf(fact_2344_power__diff__power__eq,axiom,
% 0.26/0.50      ! [A: int,N: nat,M: nat] :
% 0.26/0.50        ( ( A != zero_zero_int )
% 0.26/0.50       => ( ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.50           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 0.26/0.50              = ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 0.26/0.50          & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.26/0.50           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 0.26/0.50              = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % power_diff_power_eq
% 0.26/0.50  thf(fact_2345_ln__less__self,axiom,
% 0.26/0.50      ! [X3: real] :
% 0.26/0.50        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.50       => ( ord_less_real @ ( ln_ln_real @ X3 ) @ X3 ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ln_less_self
% 0.26/0.50  thf(fact_2346_zdiff__int__split,axiom,
% 0.26/0.50      ! [P: int > $o,X3: nat,Y3: nat] :
% 0.26/0.50        ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X3 @ Y3 ) ) )
% 0.26/0.50        = ( ( ( ord_less_eq_nat @ Y3 @ X3 )
% 0.26/0.50           => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( semiri1314217659103216013at_int @ Y3 ) ) ) )
% 0.26/0.50          & ( ( ord_less_nat @ X3 @ Y3 )
% 0.26/0.50           => ( P @ zero_zero_int ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % zdiff_int_split
% 0.26/0.50  thf(fact_2347_even__diff__iff,axiom,
% 0.26/0.50      ! [K: int,L: int] :
% 0.26/0.50        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L ) )
% 0.26/0.50        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_diff_iff
% 0.26/0.50  thf(fact_2348_le__iff__diff__le__0,axiom,
% 0.26/0.50      ( ord_less_eq_real
% 0.26/0.50      = ( ^ [A4: real,B3: real] : ( ord_less_eq_real @ ( minus_minus_real @ A4 @ B3 ) @ zero_zero_real ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % le_iff_diff_le_0
% 0.26/0.50  thf(fact_2349_le__iff__diff__le__0,axiom,
% 0.26/0.50      ( ord_less_eq_rat
% 0.26/0.50      = ( ^ [A4: rat,B3: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A4 @ B3 ) @ zero_zero_rat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % le_iff_diff_le_0
% 0.26/0.50  thf(fact_2350_le__iff__diff__le__0,axiom,
% 0.26/0.50      ( ord_less_eq_int
% 0.26/0.50      = ( ^ [A4: int,B3: int] : ( ord_less_eq_int @ ( minus_minus_int @ A4 @ B3 ) @ zero_zero_int ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % le_iff_diff_le_0
% 0.26/0.50  thf(fact_2351_less__iff__diff__less__0,axiom,
% 0.26/0.50      ( ord_less_real
% 0.26/0.50      = ( ^ [A4: real,B3: real] : ( ord_less_real @ ( minus_minus_real @ A4 @ B3 ) @ zero_zero_real ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % less_iff_diff_less_0
% 0.26/0.50  thf(fact_2352_less__iff__diff__less__0,axiom,
% 0.26/0.50      ( ord_less_rat
% 0.26/0.50      = ( ^ [A4: rat,B3: rat] : ( ord_less_rat @ ( minus_minus_rat @ A4 @ B3 ) @ zero_zero_rat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % less_iff_diff_less_0
% 0.26/0.50  thf(fact_2353_less__iff__diff__less__0,axiom,
% 0.26/0.50      ( ord_less_int
% 0.26/0.50      = ( ^ [A4: int,B3: int] : ( ord_less_int @ ( minus_minus_int @ A4 @ B3 ) @ zero_zero_int ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % less_iff_diff_less_0
% 0.26/0.50  thf(fact_2354_divide__numeral__1,axiom,
% 0.26/0.50      ! [A: complex] :
% 0.26/0.50        ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 0.26/0.50        = A ) ).
% 0.26/0.50  
% 0.26/0.50  % divide_numeral_1
% 0.26/0.50  thf(fact_2355_divide__numeral__1,axiom,
% 0.26/0.50      ! [A: real] :
% 0.26/0.50        ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 0.26/0.50        = A ) ).
% 0.26/0.50  
% 0.26/0.50  % divide_numeral_1
% 0.26/0.50  thf(fact_2356_divide__numeral__1,axiom,
% 0.26/0.50      ! [A: rat] :
% 0.26/0.50        ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 0.26/0.50        = A ) ).
% 0.26/0.50  
% 0.26/0.50  % divide_numeral_1
% 0.26/0.50  thf(fact_2357_add__decreasing,axiom,
% 0.26/0.50      ! [A: real,C: real,B: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.26/0.50       => ( ( ord_less_eq_real @ C @ B )
% 0.26/0.50         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_decreasing
% 0.26/0.50  thf(fact_2358_add__decreasing,axiom,
% 0.26/0.50      ! [A: rat,C: rat,B: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.26/0.50       => ( ( ord_less_eq_rat @ C @ B )
% 0.26/0.50         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_decreasing
% 0.26/0.50  thf(fact_2359_add__decreasing,axiom,
% 0.26/0.50      ! [A: nat,C: nat,B: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.26/0.50       => ( ( ord_less_eq_nat @ C @ B )
% 0.26/0.50         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_decreasing
% 0.26/0.50  thf(fact_2360_add__decreasing,axiom,
% 0.26/0.50      ! [A: int,C: int,B: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.26/0.50       => ( ( ord_less_eq_int @ C @ B )
% 0.26/0.50         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_decreasing
% 0.26/0.50  thf(fact_2361_add__increasing,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.50       => ( ( ord_less_eq_real @ B @ C )
% 0.26/0.50         => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_increasing
% 0.26/0.50  thf(fact_2362_add__increasing,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.50       => ( ( ord_less_eq_rat @ B @ C )
% 0.26/0.50         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_increasing
% 0.26/0.50  thf(fact_2363_add__increasing,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.50       => ( ( ord_less_eq_nat @ B @ C )
% 0.26/0.50         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_increasing
% 0.26/0.50  thf(fact_2364_add__increasing,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.50       => ( ( ord_less_eq_int @ B @ C )
% 0.26/0.50         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_increasing
% 0.26/0.50  thf(fact_2365_add__decreasing2,axiom,
% 0.26/0.50      ! [C: real,A: real,B: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.26/0.50       => ( ( ord_less_eq_real @ A @ B )
% 0.26/0.50         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_decreasing2
% 0.26/0.50  thf(fact_2366_add__decreasing2,axiom,
% 0.26/0.50      ! [C: rat,A: rat,B: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.26/0.50       => ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.50         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_decreasing2
% 0.26/0.50  thf(fact_2367_add__decreasing2,axiom,
% 0.26/0.50      ! [C: nat,A: nat,B: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 0.26/0.50       => ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.50         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_decreasing2
% 0.26/0.50  thf(fact_2368_add__decreasing2,axiom,
% 0.26/0.50      ! [C: int,A: int,B: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.26/0.50       => ( ( ord_less_eq_int @ A @ B )
% 0.26/0.50         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_decreasing2
% 0.26/0.50  thf(fact_2369_add__increasing2,axiom,
% 0.26/0.50      ! [C: real,B: real,A: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.26/0.50       => ( ( ord_less_eq_real @ B @ A )
% 0.26/0.50         => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_increasing2
% 0.26/0.50  thf(fact_2370_add__increasing2,axiom,
% 0.26/0.50      ! [C: rat,B: rat,A: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.26/0.50       => ( ( ord_less_eq_rat @ B @ A )
% 0.26/0.50         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_increasing2
% 0.26/0.50  thf(fact_2371_add__increasing2,axiom,
% 0.26/0.50      ! [C: nat,B: nat,A: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.26/0.50       => ( ( ord_less_eq_nat @ B @ A )
% 0.26/0.50         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_increasing2
% 0.26/0.50  thf(fact_2372_add__increasing2,axiom,
% 0.26/0.50      ! [C: int,B: int,A: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.26/0.50       => ( ( ord_less_eq_int @ B @ A )
% 0.26/0.50         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_increasing2
% 0.26/0.50  thf(fact_2373_add__nonneg__nonneg,axiom,
% 0.26/0.50      ! [A: real,B: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.50       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.26/0.50         => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonneg_nonneg
% 0.26/0.50  thf(fact_2374_add__nonneg__nonneg,axiom,
% 0.26/0.50      ! [A: rat,B: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.50       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.26/0.50         => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonneg_nonneg
% 0.26/0.50  thf(fact_2375_add__nonneg__nonneg,axiom,
% 0.26/0.50      ! [A: nat,B: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.50       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.26/0.50         => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonneg_nonneg
% 0.26/0.50  thf(fact_2376_add__nonneg__nonneg,axiom,
% 0.26/0.50      ! [A: int,B: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.50       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.26/0.50         => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonneg_nonneg
% 0.26/0.50  thf(fact_2377_add__nonpos__nonpos,axiom,
% 0.26/0.50      ! [A: real,B: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.26/0.50       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.26/0.50         => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonpos_nonpos
% 0.26/0.50  thf(fact_2378_add__nonpos__nonpos,axiom,
% 0.26/0.50      ! [A: rat,B: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.26/0.50       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.26/0.50         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonpos_nonpos
% 0.26/0.50  thf(fact_2379_add__nonpos__nonpos,axiom,
% 0.26/0.50      ! [A: nat,B: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.26/0.50       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.26/0.50         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonpos_nonpos
% 0.26/0.50  thf(fact_2380_add__nonpos__nonpos,axiom,
% 0.26/0.50      ! [A: int,B: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.26/0.50       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.26/0.50         => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonpos_nonpos
% 0.26/0.50  thf(fact_2381_add__nonneg__eq__0__iff,axiom,
% 0.26/0.50      ! [X3: real,Y3: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.50       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.50         => ( ( ( plus_plus_real @ X3 @ Y3 )
% 0.26/0.50              = zero_zero_real )
% 0.26/0.50            = ( ( X3 = zero_zero_real )
% 0.26/0.50              & ( Y3 = zero_zero_real ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonneg_eq_0_iff
% 0.26/0.50  thf(fact_2382_add__nonneg__eq__0__iff,axiom,
% 0.26/0.50      ! [X3: rat,Y3: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.26/0.50       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 0.26/0.50         => ( ( ( plus_plus_rat @ X3 @ Y3 )
% 0.26/0.50              = zero_zero_rat )
% 0.26/0.50            = ( ( X3 = zero_zero_rat )
% 0.26/0.50              & ( Y3 = zero_zero_rat ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonneg_eq_0_iff
% 0.26/0.50  thf(fact_2383_add__nonneg__eq__0__iff,axiom,
% 0.26/0.50      ! [X3: nat,Y3: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ zero_zero_nat @ X3 )
% 0.26/0.50       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 0.26/0.50         => ( ( ( plus_plus_nat @ X3 @ Y3 )
% 0.26/0.50              = zero_zero_nat )
% 0.26/0.50            = ( ( X3 = zero_zero_nat )
% 0.26/0.50              & ( Y3 = zero_zero_nat ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonneg_eq_0_iff
% 0.26/0.50  thf(fact_2384_add__nonneg__eq__0__iff,axiom,
% 0.26/0.50      ! [X3: int,Y3: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.26/0.50       => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 0.26/0.50         => ( ( ( plus_plus_int @ X3 @ Y3 )
% 0.26/0.50              = zero_zero_int )
% 0.26/0.50            = ( ( X3 = zero_zero_int )
% 0.26/0.50              & ( Y3 = zero_zero_int ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonneg_eq_0_iff
% 0.26/0.50  thf(fact_2385_add__nonpos__eq__0__iff,axiom,
% 0.26/0.50      ! [X3: real,Y3: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 0.26/0.50       => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 0.26/0.50         => ( ( ( plus_plus_real @ X3 @ Y3 )
% 0.26/0.50              = zero_zero_real )
% 0.26/0.50            = ( ( X3 = zero_zero_real )
% 0.26/0.50              & ( Y3 = zero_zero_real ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonpos_eq_0_iff
% 0.26/0.50  thf(fact_2386_add__nonpos__eq__0__iff,axiom,
% 0.26/0.50      ! [X3: rat,Y3: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 0.26/0.50       => ( ( ord_less_eq_rat @ Y3 @ zero_zero_rat )
% 0.26/0.50         => ( ( ( plus_plus_rat @ X3 @ Y3 )
% 0.26/0.50              = zero_zero_rat )
% 0.26/0.50            = ( ( X3 = zero_zero_rat )
% 0.26/0.50              & ( Y3 = zero_zero_rat ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonpos_eq_0_iff
% 0.26/0.50  thf(fact_2387_add__nonpos__eq__0__iff,axiom,
% 0.26/0.50      ! [X3: nat,Y3: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ X3 @ zero_zero_nat )
% 0.26/0.50       => ( ( ord_less_eq_nat @ Y3 @ zero_zero_nat )
% 0.26/0.50         => ( ( ( plus_plus_nat @ X3 @ Y3 )
% 0.26/0.50              = zero_zero_nat )
% 0.26/0.50            = ( ( X3 = zero_zero_nat )
% 0.26/0.50              & ( Y3 = zero_zero_nat ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonpos_eq_0_iff
% 0.26/0.50  thf(fact_2388_add__nonpos__eq__0__iff,axiom,
% 0.26/0.50      ! [X3: int,Y3: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ X3 @ zero_zero_int )
% 0.26/0.50       => ( ( ord_less_eq_int @ Y3 @ zero_zero_int )
% 0.26/0.50         => ( ( ( plus_plus_int @ X3 @ Y3 )
% 0.26/0.50              = zero_zero_int )
% 0.26/0.50            = ( ( X3 = zero_zero_int )
% 0.26/0.50              & ( Y3 = zero_zero_int ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonpos_eq_0_iff
% 0.26/0.50  thf(fact_2389_add__less__le__mono,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real,D3: real] :
% 0.26/0.50        ( ( ord_less_real @ A @ B )
% 0.26/0.50       => ( ( ord_less_eq_real @ C @ D3 )
% 0.26/0.50         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_less_le_mono
% 0.26/0.50  thf(fact_2390_add__less__le__mono,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat,D3: rat] :
% 0.26/0.50        ( ( ord_less_rat @ A @ B )
% 0.26/0.50       => ( ( ord_less_eq_rat @ C @ D3 )
% 0.26/0.50         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_less_le_mono
% 0.26/0.50  thf(fact_2391_add__less__le__mono,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat,D3: nat] :
% 0.26/0.50        ( ( ord_less_nat @ A @ B )
% 0.26/0.50       => ( ( ord_less_eq_nat @ C @ D3 )
% 0.26/0.50         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_less_le_mono
% 0.26/0.50  thf(fact_2392_add__less__le__mono,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int,D3: int] :
% 0.26/0.50        ( ( ord_less_int @ A @ B )
% 0.26/0.50       => ( ( ord_less_eq_int @ C @ D3 )
% 0.26/0.50         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_less_le_mono
% 0.26/0.50  thf(fact_2393_add__le__less__mono,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real,D3: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.50       => ( ( ord_less_real @ C @ D3 )
% 0.26/0.50         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_le_less_mono
% 0.26/0.50  thf(fact_2394_add__le__less__mono,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat,D3: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.50       => ( ( ord_less_rat @ C @ D3 )
% 0.26/0.50         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_le_less_mono
% 0.26/0.50  thf(fact_2395_add__le__less__mono,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat,D3: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.50       => ( ( ord_less_nat @ C @ D3 )
% 0.26/0.50         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_le_less_mono
% 0.26/0.50  thf(fact_2396_add__le__less__mono,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int,D3: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ A @ B )
% 0.26/0.50       => ( ( ord_less_int @ C @ D3 )
% 0.26/0.50         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D3 ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_le_less_mono
% 0.26/0.50  thf(fact_2397_add__mono__thms__linordered__field_I3_J,axiom,
% 0.26/0.50      ! [I: real,J: real,K: real,L: real] :
% 0.26/0.50        ( ( ( ord_less_real @ I @ J )
% 0.26/0.50          & ( ord_less_eq_real @ K @ L ) )
% 0.26/0.50       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_field(3)
% 0.26/0.50  thf(fact_2398_add__mono__thms__linordered__field_I3_J,axiom,
% 0.26/0.50      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.26/0.50        ( ( ( ord_less_rat @ I @ J )
% 0.26/0.50          & ( ord_less_eq_rat @ K @ L ) )
% 0.26/0.50       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_field(3)
% 0.26/0.50  thf(fact_2399_add__mono__thms__linordered__field_I3_J,axiom,
% 0.26/0.50      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.26/0.50        ( ( ( ord_less_nat @ I @ J )
% 0.26/0.50          & ( ord_less_eq_nat @ K @ L ) )
% 0.26/0.50       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_field(3)
% 0.26/0.50  thf(fact_2400_add__mono__thms__linordered__field_I3_J,axiom,
% 0.26/0.50      ! [I: int,J: int,K: int,L: int] :
% 0.26/0.50        ( ( ( ord_less_int @ I @ J )
% 0.26/0.50          & ( ord_less_eq_int @ K @ L ) )
% 0.26/0.50       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_field(3)
% 0.26/0.50  thf(fact_2401_add__mono__thms__linordered__field_I4_J,axiom,
% 0.26/0.50      ! [I: real,J: real,K: real,L: real] :
% 0.26/0.50        ( ( ( ord_less_eq_real @ I @ J )
% 0.26/0.50          & ( ord_less_real @ K @ L ) )
% 0.26/0.50       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_field(4)
% 0.26/0.50  thf(fact_2402_add__mono__thms__linordered__field_I4_J,axiom,
% 0.26/0.50      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.26/0.50        ( ( ( ord_less_eq_rat @ I @ J )
% 0.26/0.50          & ( ord_less_rat @ K @ L ) )
% 0.26/0.50       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_field(4)
% 0.26/0.50  thf(fact_2403_add__mono__thms__linordered__field_I4_J,axiom,
% 0.26/0.50      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.26/0.50        ( ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.50          & ( ord_less_nat @ K @ L ) )
% 0.26/0.50       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_field(4)
% 0.26/0.50  thf(fact_2404_add__mono__thms__linordered__field_I4_J,axiom,
% 0.26/0.50      ! [I: int,J: int,K: int,L: int] :
% 0.26/0.50        ( ( ( ord_less_eq_int @ I @ J )
% 0.26/0.50          & ( ord_less_int @ K @ L ) )
% 0.26/0.50       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono_thms_linordered_field(4)
% 0.26/0.50  thf(fact_2405_add__neg__neg,axiom,
% 0.26/0.50      ! [A: real,B: real] :
% 0.26/0.50        ( ( ord_less_real @ A @ zero_zero_real )
% 0.26/0.50       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.26/0.50         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_neg_neg
% 0.26/0.50  thf(fact_2406_add__neg__neg,axiom,
% 0.26/0.50      ! [A: rat,B: rat] :
% 0.26/0.50        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.26/0.50       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.26/0.50         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_neg_neg
% 0.26/0.50  thf(fact_2407_add__neg__neg,axiom,
% 0.26/0.50      ! [A: nat,B: nat] :
% 0.26/0.50        ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.26/0.50       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.26/0.50         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_neg_neg
% 0.26/0.50  thf(fact_2408_add__neg__neg,axiom,
% 0.26/0.50      ! [A: int,B: int] :
% 0.26/0.50        ( ( ord_less_int @ A @ zero_zero_int )
% 0.26/0.50       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.26/0.50         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_neg_neg
% 0.26/0.50  thf(fact_2409_add__pos__pos,axiom,
% 0.26/0.50      ! [A: real,B: real] :
% 0.26/0.50        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.50       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.26/0.50         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_pos_pos
% 0.26/0.50  thf(fact_2410_add__pos__pos,axiom,
% 0.26/0.50      ! [A: rat,B: rat] :
% 0.26/0.50        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.50       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.26/0.50         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_pos_pos
% 0.26/0.50  thf(fact_2411_add__pos__pos,axiom,
% 0.26/0.50      ! [A: nat,B: nat] :
% 0.26/0.50        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.26/0.50       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.26/0.50         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_pos_pos
% 0.26/0.50  thf(fact_2412_add__pos__pos,axiom,
% 0.26/0.50      ! [A: int,B: int] :
% 0.26/0.50        ( ( ord_less_int @ zero_zero_int @ A )
% 0.26/0.50       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.50         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_pos_pos
% 0.26/0.50  thf(fact_2413_canonically__ordered__monoid__add__class_OlessE,axiom,
% 0.26/0.50      ! [A: nat,B: nat] :
% 0.26/0.50        ( ( ord_less_nat @ A @ B )
% 0.26/0.50       => ~ ! [C2: nat] :
% 0.26/0.50              ( ( B
% 0.26/0.50                = ( plus_plus_nat @ A @ C2 ) )
% 0.26/0.50             => ( C2 = zero_zero_nat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % canonically_ordered_monoid_add_class.lessE
% 0.26/0.50  thf(fact_2414_pos__add__strict,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.50       => ( ( ord_less_real @ B @ C )
% 0.26/0.50         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % pos_add_strict
% 0.26/0.50  thf(fact_2415_pos__add__strict,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.50       => ( ( ord_less_rat @ B @ C )
% 0.26/0.50         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % pos_add_strict
% 0.26/0.50  thf(fact_2416_pos__add__strict,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat] :
% 0.26/0.50        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.26/0.50       => ( ( ord_less_nat @ B @ C )
% 0.26/0.50         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % pos_add_strict
% 0.26/0.50  thf(fact_2417_pos__add__strict,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( ord_less_int @ zero_zero_int @ A )
% 0.26/0.50       => ( ( ord_less_int @ B @ C )
% 0.26/0.50         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % pos_add_strict
% 0.26/0.50  thf(fact_2418_add__less__zeroD,axiom,
% 0.26/0.50      ! [X3: real,Y3: real] :
% 0.26/0.50        ( ( ord_less_real @ ( plus_plus_real @ X3 @ Y3 ) @ zero_zero_real )
% 0.26/0.50       => ( ( ord_less_real @ X3 @ zero_zero_real )
% 0.26/0.50          | ( ord_less_real @ Y3 @ zero_zero_real ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_less_zeroD
% 0.26/0.50  thf(fact_2419_add__less__zeroD,axiom,
% 0.26/0.50      ! [X3: rat,Y3: rat] :
% 0.26/0.50        ( ( ord_less_rat @ ( plus_plus_rat @ X3 @ Y3 ) @ zero_zero_rat )
% 0.26/0.50       => ( ( ord_less_rat @ X3 @ zero_zero_rat )
% 0.26/0.50          | ( ord_less_rat @ Y3 @ zero_zero_rat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_less_zeroD
% 0.26/0.50  thf(fact_2420_add__less__zeroD,axiom,
% 0.26/0.50      ! [X3: int,Y3: int] :
% 0.26/0.50        ( ( ord_less_int @ ( plus_plus_int @ X3 @ Y3 ) @ zero_zero_int )
% 0.26/0.50       => ( ( ord_less_int @ X3 @ zero_zero_int )
% 0.26/0.50          | ( ord_less_int @ Y3 @ zero_zero_int ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_less_zeroD
% 0.26/0.50  thf(fact_2421_dvd__div__eq__0__iff,axiom,
% 0.26/0.50      ! [B: code_integer,A: code_integer] :
% 0.26/0.50        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.26/0.50       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 0.26/0.50            = zero_z3403309356797280102nteger )
% 0.26/0.50          = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % dvd_div_eq_0_iff
% 0.26/0.50  thf(fact_2422_dvd__div__eq__0__iff,axiom,
% 0.26/0.50      ! [B: complex,A: complex] :
% 0.26/0.50        ( ( dvd_dvd_complex @ B @ A )
% 0.26/0.50       => ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.26/0.50            = zero_zero_complex )
% 0.26/0.50          = ( A = zero_zero_complex ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % dvd_div_eq_0_iff
% 0.26/0.50  thf(fact_2423_dvd__div__eq__0__iff,axiom,
% 0.26/0.50      ! [B: real,A: real] :
% 0.26/0.50        ( ( dvd_dvd_real @ B @ A )
% 0.26/0.50       => ( ( ( divide_divide_real @ A @ B )
% 0.26/0.50            = zero_zero_real )
% 0.26/0.50          = ( A = zero_zero_real ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % dvd_div_eq_0_iff
% 0.26/0.50  thf(fact_2424_dvd__div__eq__0__iff,axiom,
% 0.26/0.50      ! [B: rat,A: rat] :
% 0.26/0.50        ( ( dvd_dvd_rat @ B @ A )
% 0.26/0.50       => ( ( ( divide_divide_rat @ A @ B )
% 0.26/0.50            = zero_zero_rat )
% 0.26/0.50          = ( A = zero_zero_rat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % dvd_div_eq_0_iff
% 0.26/0.50  thf(fact_2425_dvd__div__eq__0__iff,axiom,
% 0.26/0.50      ! [B: nat,A: nat] :
% 0.26/0.50        ( ( dvd_dvd_nat @ B @ A )
% 0.26/0.50       => ( ( ( divide_divide_nat @ A @ B )
% 0.26/0.50            = zero_zero_nat )
% 0.26/0.50          = ( A = zero_zero_nat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % dvd_div_eq_0_iff
% 0.26/0.50  thf(fact_2426_dvd__div__eq__0__iff,axiom,
% 0.26/0.50      ! [B: int,A: int] :
% 0.26/0.50        ( ( dvd_dvd_int @ B @ A )
% 0.26/0.50       => ( ( ( divide_divide_int @ A @ B )
% 0.26/0.50            = zero_zero_int )
% 0.26/0.50          = ( A = zero_zero_int ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % dvd_div_eq_0_iff
% 0.26/0.50  thf(fact_2427_power__one__over,axiom,
% 0.26/0.50      ! [A: complex,N: nat] :
% 0.26/0.50        ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N )
% 0.26/0.50        = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % power_one_over
% 0.26/0.50  thf(fact_2428_power__one__over,axiom,
% 0.26/0.50      ! [A: real,N: nat] :
% 0.26/0.50        ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N )
% 0.26/0.50        = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % power_one_over
% 0.26/0.50  thf(fact_2429_power__one__over,axiom,
% 0.26/0.50      ! [A: rat,N: nat] :
% 0.26/0.50        ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 0.26/0.50        = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % power_one_over
% 0.26/0.50  thf(fact_2430_add__mono1,axiom,
% 0.26/0.50      ! [A: real,B: real] :
% 0.26/0.50        ( ( ord_less_real @ A @ B )
% 0.26/0.50       => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono1
% 0.26/0.50  thf(fact_2431_add__mono1,axiom,
% 0.26/0.50      ! [A: rat,B: rat] :
% 0.26/0.50        ( ( ord_less_rat @ A @ B )
% 0.26/0.50       => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono1
% 0.26/0.50  thf(fact_2432_add__mono1,axiom,
% 0.26/0.50      ! [A: nat,B: nat] :
% 0.26/0.50        ( ( ord_less_nat @ A @ B )
% 0.26/0.50       => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono1
% 0.26/0.50  thf(fact_2433_add__mono1,axiom,
% 0.26/0.50      ! [A: int,B: int] :
% 0.26/0.50        ( ( ord_less_int @ A @ B )
% 0.26/0.50       => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_mono1
% 0.26/0.50  thf(fact_2434_less__add__one,axiom,
% 0.26/0.50      ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 0.26/0.50  
% 0.26/0.50  % less_add_one
% 0.26/0.50  thf(fact_2435_less__add__one,axiom,
% 0.26/0.50      ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 0.26/0.50  
% 0.26/0.50  % less_add_one
% 0.26/0.50  thf(fact_2436_less__add__one,axiom,
% 0.26/0.50      ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 0.26/0.50  
% 0.26/0.50  % less_add_one
% 0.26/0.50  thf(fact_2437_less__add__one,axiom,
% 0.26/0.50      ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 0.26/0.50  
% 0.26/0.50  % less_add_one
% 0.26/0.50  thf(fact_2438_numeral__Bit0,axiom,
% 0.26/0.50      ! [N: num] :
% 0.26/0.50        ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 0.26/0.50        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % numeral_Bit0
% 0.26/0.50  thf(fact_2439_numeral__Bit0,axiom,
% 0.26/0.50      ! [N: num] :
% 0.26/0.50        ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 0.26/0.50        = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % numeral_Bit0
% 0.26/0.50  thf(fact_2440_numeral__Bit0,axiom,
% 0.26/0.50      ! [N: num] :
% 0.26/0.50        ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 0.26/0.50        = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % numeral_Bit0
% 0.26/0.50  thf(fact_2441_numeral__Bit0,axiom,
% 0.26/0.50      ! [N: num] :
% 0.26/0.50        ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 0.26/0.50        = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % numeral_Bit0
% 0.26/0.50  thf(fact_2442_numeral__Bit0,axiom,
% 0.26/0.50      ! [N: num] :
% 0.26/0.50        ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 0.26/0.50        = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % numeral_Bit0
% 0.26/0.50  thf(fact_2443_one__plus__numeral__commute,axiom,
% 0.26/0.50      ! [X3: num] :
% 0.26/0.50        ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X3 ) )
% 0.26/0.50        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X3 ) @ one_one_complex ) ) ).
% 0.26/0.50  
% 0.26/0.50  % one_plus_numeral_commute
% 0.26/0.50  thf(fact_2444_one__plus__numeral__commute,axiom,
% 0.26/0.50      ! [X3: num] :
% 0.26/0.50        ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X3 ) )
% 0.26/0.50        = ( plus_plus_real @ ( numeral_numeral_real @ X3 ) @ one_one_real ) ) ).
% 0.26/0.50  
% 0.26/0.50  % one_plus_numeral_commute
% 0.26/0.50  thf(fact_2445_one__plus__numeral__commute,axiom,
% 0.26/0.50      ! [X3: num] :
% 0.26/0.50        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X3 ) )
% 0.26/0.50        = ( plus_plus_rat @ ( numeral_numeral_rat @ X3 ) @ one_one_rat ) ) ).
% 0.26/0.50  
% 0.26/0.50  % one_plus_numeral_commute
% 0.26/0.50  thf(fact_2446_one__plus__numeral__commute,axiom,
% 0.26/0.50      ! [X3: num] :
% 0.26/0.50        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X3 ) )
% 0.26/0.50        = ( plus_plus_nat @ ( numeral_numeral_nat @ X3 ) @ one_one_nat ) ) ).
% 0.26/0.50  
% 0.26/0.50  % one_plus_numeral_commute
% 0.26/0.50  thf(fact_2447_one__plus__numeral__commute,axiom,
% 0.26/0.50      ! [X3: num] :
% 0.26/0.50        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X3 ) )
% 0.26/0.50        = ( plus_plus_int @ ( numeral_numeral_int @ X3 ) @ one_one_int ) ) ).
% 0.26/0.50  
% 0.26/0.50  % one_plus_numeral_commute
% 0.26/0.50  thf(fact_2448_div__power,axiom,
% 0.26/0.50      ! [B: code_integer,A: code_integer,N: nat] :
% 0.26/0.50        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.26/0.50       => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N )
% 0.26/0.50          = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % div_power
% 0.26/0.50  thf(fact_2449_div__power,axiom,
% 0.26/0.50      ! [B: nat,A: nat,N: nat] :
% 0.26/0.50        ( ( dvd_dvd_nat @ B @ A )
% 0.26/0.50       => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N )
% 0.26/0.50          = ( divide_divide_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % div_power
% 0.26/0.50  thf(fact_2450_div__power,axiom,
% 0.26/0.50      ! [B: int,A: int,N: nat] :
% 0.26/0.50        ( ( dvd_dvd_int @ B @ A )
% 0.26/0.50       => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N )
% 0.26/0.50          = ( divide_divide_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % div_power
% 0.26/0.50  thf(fact_2451_pinf_I9_J,axiom,
% 0.26/0.50      ! [D3: code_integer,S: code_integer] :
% 0.26/0.50      ? [Z3: code_integer] :
% 0.26/0.50      ! [X6: code_integer] :
% 0.26/0.50        ( ( ord_le6747313008572928689nteger @ Z3 @ X6 )
% 0.26/0.50       => ( ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ X6 @ S ) )
% 0.26/0.50          = ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ X6 @ S ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % pinf(9)
% 0.26/0.50  thf(fact_2452_pinf_I9_J,axiom,
% 0.26/0.50      ! [D3: real,S: real] :
% 0.26/0.50      ? [Z3: real] :
% 0.26/0.50      ! [X6: real] :
% 0.26/0.50        ( ( ord_less_real @ Z3 @ X6 )
% 0.26/0.50       => ( ( dvd_dvd_real @ D3 @ ( plus_plus_real @ X6 @ S ) )
% 0.26/0.50          = ( dvd_dvd_real @ D3 @ ( plus_plus_real @ X6 @ S ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % pinf(9)
% 0.26/0.50  thf(fact_2453_pinf_I9_J,axiom,
% 0.26/0.50      ! [D3: rat,S: rat] :
% 0.26/0.50      ? [Z3: rat] :
% 0.26/0.50      ! [X6: rat] :
% 0.26/0.50        ( ( ord_less_rat @ Z3 @ X6 )
% 0.26/0.50       => ( ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ X6 @ S ) )
% 0.26/0.50          = ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ X6 @ S ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % pinf(9)
% 0.26/0.50  thf(fact_2454_pinf_I9_J,axiom,
% 0.26/0.50      ! [D3: nat,S: nat] :
% 0.26/0.50      ? [Z3: nat] :
% 0.26/0.50      ! [X6: nat] :
% 0.26/0.50        ( ( ord_less_nat @ Z3 @ X6 )
% 0.26/0.50       => ( ( dvd_dvd_nat @ D3 @ ( plus_plus_nat @ X6 @ S ) )
% 0.26/0.50          = ( dvd_dvd_nat @ D3 @ ( plus_plus_nat @ X6 @ S ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % pinf(9)
% 0.26/0.50  thf(fact_2455_pinf_I9_J,axiom,
% 0.26/0.50      ! [D3: int,S: int] :
% 0.26/0.50      ? [Z3: int] :
% 0.26/0.50      ! [X6: int] :
% 0.26/0.50        ( ( ord_less_int @ Z3 @ X6 )
% 0.26/0.50       => ( ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ S ) )
% 0.26/0.50          = ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ S ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % pinf(9)
% 0.26/0.50  thf(fact_2456_pinf_I10_J,axiom,
% 0.26/0.50      ! [D3: code_integer,S: code_integer] :
% 0.26/0.50      ? [Z3: code_integer] :
% 0.26/0.50      ! [X6: code_integer] :
% 0.26/0.50        ( ( ord_le6747313008572928689nteger @ Z3 @ X6 )
% 0.26/0.50       => ( ( ~ ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ X6 @ S ) ) )
% 0.26/0.50          = ( ~ ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ X6 @ S ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % pinf(10)
% 0.26/0.50  thf(fact_2457_pinf_I10_J,axiom,
% 0.26/0.50      ! [D3: real,S: real] :
% 0.26/0.50      ? [Z3: real] :
% 0.26/0.50      ! [X6: real] :
% 0.26/0.50        ( ( ord_less_real @ Z3 @ X6 )
% 0.26/0.50       => ( ( ~ ( dvd_dvd_real @ D3 @ ( plus_plus_real @ X6 @ S ) ) )
% 0.26/0.50          = ( ~ ( dvd_dvd_real @ D3 @ ( plus_plus_real @ X6 @ S ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % pinf(10)
% 0.26/0.50  thf(fact_2458_pinf_I10_J,axiom,
% 0.26/0.50      ! [D3: rat,S: rat] :
% 0.26/0.50      ? [Z3: rat] :
% 0.26/0.50      ! [X6: rat] :
% 0.26/0.50        ( ( ord_less_rat @ Z3 @ X6 )
% 0.26/0.50       => ( ( ~ ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ X6 @ S ) ) )
% 0.26/0.50          = ( ~ ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ X6 @ S ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % pinf(10)
% 0.26/0.50  thf(fact_2459_pinf_I10_J,axiom,
% 0.26/0.50      ! [D3: nat,S: nat] :
% 0.26/0.50      ? [Z3: nat] :
% 0.26/0.50      ! [X6: nat] :
% 0.26/0.50        ( ( ord_less_nat @ Z3 @ X6 )
% 0.26/0.50       => ( ( ~ ( dvd_dvd_nat @ D3 @ ( plus_plus_nat @ X6 @ S ) ) )
% 0.26/0.50          = ( ~ ( dvd_dvd_nat @ D3 @ ( plus_plus_nat @ X6 @ S ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % pinf(10)
% 0.26/0.50  thf(fact_2460_pinf_I10_J,axiom,
% 0.26/0.50      ! [D3: int,S: int] :
% 0.26/0.50      ? [Z3: int] :
% 0.26/0.50      ! [X6: int] :
% 0.26/0.50        ( ( ord_less_int @ Z3 @ X6 )
% 0.26/0.50       => ( ( ~ ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ S ) ) )
% 0.26/0.50          = ( ~ ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ S ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % pinf(10)
% 0.26/0.50  thf(fact_2461_minf_I9_J,axiom,
% 0.26/0.50      ! [D3: code_integer,S: code_integer] :
% 0.26/0.50      ? [Z3: code_integer] :
% 0.26/0.50      ! [X6: code_integer] :
% 0.26/0.50        ( ( ord_le6747313008572928689nteger @ X6 @ Z3 )
% 0.26/0.50       => ( ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ X6 @ S ) )
% 0.26/0.50          = ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ X6 @ S ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % minf(9)
% 0.26/0.50  thf(fact_2462_minf_I9_J,axiom,
% 0.26/0.50      ! [D3: real,S: real] :
% 0.26/0.50      ? [Z3: real] :
% 0.26/0.50      ! [X6: real] :
% 0.26/0.50        ( ( ord_less_real @ X6 @ Z3 )
% 0.26/0.50       => ( ( dvd_dvd_real @ D3 @ ( plus_plus_real @ X6 @ S ) )
% 0.26/0.50          = ( dvd_dvd_real @ D3 @ ( plus_plus_real @ X6 @ S ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % minf(9)
% 0.26/0.50  thf(fact_2463_minf_I9_J,axiom,
% 0.26/0.50      ! [D3: rat,S: rat] :
% 0.26/0.50      ? [Z3: rat] :
% 0.26/0.50      ! [X6: rat] :
% 0.26/0.50        ( ( ord_less_rat @ X6 @ Z3 )
% 0.26/0.50       => ( ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ X6 @ S ) )
% 0.26/0.50          = ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ X6 @ S ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % minf(9)
% 0.26/0.50  thf(fact_2464_minf_I9_J,axiom,
% 0.26/0.50      ! [D3: nat,S: nat] :
% 0.26/0.50      ? [Z3: nat] :
% 0.26/0.50      ! [X6: nat] :
% 0.26/0.50        ( ( ord_less_nat @ X6 @ Z3 )
% 0.26/0.50       => ( ( dvd_dvd_nat @ D3 @ ( plus_plus_nat @ X6 @ S ) )
% 0.26/0.50          = ( dvd_dvd_nat @ D3 @ ( plus_plus_nat @ X6 @ S ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % minf(9)
% 0.26/0.50  thf(fact_2465_minf_I9_J,axiom,
% 0.26/0.50      ! [D3: int,S: int] :
% 0.26/0.50      ? [Z3: int] :
% 0.26/0.50      ! [X6: int] :
% 0.26/0.50        ( ( ord_less_int @ X6 @ Z3 )
% 0.26/0.50       => ( ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ S ) )
% 0.26/0.50          = ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ S ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % minf(9)
% 0.26/0.50  thf(fact_2466_minf_I10_J,axiom,
% 0.26/0.50      ! [D3: code_integer,S: code_integer] :
% 0.26/0.50      ? [Z3: code_integer] :
% 0.26/0.50      ! [X6: code_integer] :
% 0.26/0.50        ( ( ord_le6747313008572928689nteger @ X6 @ Z3 )
% 0.26/0.50       => ( ( ~ ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ X6 @ S ) ) )
% 0.26/0.50          = ( ~ ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ X6 @ S ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % minf(10)
% 0.26/0.50  thf(fact_2467_minf_I10_J,axiom,
% 0.26/0.50      ! [D3: real,S: real] :
% 0.26/0.50      ? [Z3: real] :
% 0.26/0.50      ! [X6: real] :
% 0.26/0.50        ( ( ord_less_real @ X6 @ Z3 )
% 0.26/0.50       => ( ( ~ ( dvd_dvd_real @ D3 @ ( plus_plus_real @ X6 @ S ) ) )
% 0.26/0.50          = ( ~ ( dvd_dvd_real @ D3 @ ( plus_plus_real @ X6 @ S ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % minf(10)
% 0.26/0.50  thf(fact_2468_minf_I10_J,axiom,
% 0.26/0.50      ! [D3: rat,S: rat] :
% 0.26/0.50      ? [Z3: rat] :
% 0.26/0.50      ! [X6: rat] :
% 0.26/0.50        ( ( ord_less_rat @ X6 @ Z3 )
% 0.26/0.50       => ( ( ~ ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ X6 @ S ) ) )
% 0.26/0.50          = ( ~ ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ X6 @ S ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % minf(10)
% 0.26/0.50  thf(fact_2469_minf_I10_J,axiom,
% 0.26/0.50      ! [D3: nat,S: nat] :
% 0.26/0.50      ? [Z3: nat] :
% 0.26/0.50      ! [X6: nat] :
% 0.26/0.50        ( ( ord_less_nat @ X6 @ Z3 )
% 0.26/0.50       => ( ( ~ ( dvd_dvd_nat @ D3 @ ( plus_plus_nat @ X6 @ S ) ) )
% 0.26/0.50          = ( ~ ( dvd_dvd_nat @ D3 @ ( plus_plus_nat @ X6 @ S ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % minf(10)
% 0.26/0.50  thf(fact_2470_minf_I10_J,axiom,
% 0.26/0.50      ! [D3: int,S: int] :
% 0.26/0.50      ? [Z3: int] :
% 0.26/0.50      ! [X6: int] :
% 0.26/0.50        ( ( ord_less_int @ X6 @ Z3 )
% 0.26/0.50       => ( ( ~ ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ S ) ) )
% 0.26/0.50          = ( ~ ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ S ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % minf(10)
% 0.26/0.50  thf(fact_2471_ln__one__plus__pos__lower__bound,axiom,
% 0.26/0.50      ! [X3: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.50       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 0.26/0.50         => ( ord_less_eq_real @ ( minus_minus_real @ X3 @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X3 ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ln_one_plus_pos_lower_bound
% 0.26/0.50  thf(fact_2472_diff__less,axiom,
% 0.26/0.50      ! [N: nat,M: nat] :
% 0.26/0.50        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.50       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.50         => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_less
% 0.26/0.50  thf(fact_2473_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 0.26/0.50      ! [M: nat,N: nat] :
% 0.26/0.50        ( ( ( divide_divide_nat @ M @ N )
% 0.26/0.50          = zero_zero_nat )
% 0.26/0.50        = ( ( ord_less_nat @ M @ N )
% 0.26/0.50          | ( N = zero_zero_nat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % Euclidean_Division.div_eq_0_iff
% 0.26/0.50  thf(fact_2474_diff__less__mono,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat] :
% 0.26/0.50        ( ( ord_less_nat @ A @ B )
% 0.26/0.50       => ( ( ord_less_eq_nat @ C @ A )
% 0.26/0.50         => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % diff_less_mono
% 0.26/0.50  thf(fact_2475_less__diff__iff,axiom,
% 0.26/0.50      ! [K: nat,M: nat,N: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ K @ M )
% 0.26/0.50       => ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.50         => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.26/0.50            = ( ord_less_nat @ M @ N ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % less_diff_iff
% 0.26/0.50  thf(fact_2476_arcosh__real__def,axiom,
% 0.26/0.50      ! [X3: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ one_one_real @ X3 )
% 0.26/0.50       => ( ( arcosh_real @ X3 )
% 0.26/0.50          = ( ln_ln_real @ ( plus_plus_real @ X3 @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % arcosh_real_def
% 0.26/0.50  thf(fact_2477_dvd__minus__self,axiom,
% 0.26/0.50      ! [M: nat,N: nat] :
% 0.26/0.50        ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 0.26/0.50        = ( ( ord_less_nat @ N @ M )
% 0.26/0.50          | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % dvd_minus_self
% 0.26/0.50  thf(fact_2478_int__le__induct,axiom,
% 0.26/0.50      ! [I: int,K: int,P: int > $o] :
% 0.26/0.50        ( ( ord_less_eq_int @ I @ K )
% 0.26/0.50       => ( ( P @ K )
% 0.26/0.50         => ( ! [I3: int] :
% 0.26/0.50                ( ( ord_less_eq_int @ I3 @ K )
% 0.26/0.50               => ( ( P @ I3 )
% 0.26/0.50                 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 0.26/0.50           => ( P @ I ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % int_le_induct
% 0.26/0.50  thf(fact_2479_int__less__induct,axiom,
% 0.26/0.50      ! [I: int,K: int,P: int > $o] :
% 0.26/0.50        ( ( ord_less_int @ I @ K )
% 0.26/0.50       => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 0.26/0.50         => ( ! [I3: int] :
% 0.26/0.50                ( ( ord_less_int @ I3 @ K )
% 0.26/0.50               => ( ( P @ I3 )
% 0.26/0.50                 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 0.26/0.50           => ( P @ I ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % int_less_induct
% 0.26/0.50  thf(fact_2480_dvd__diffD,axiom,
% 0.26/0.50      ! [K: nat,M: nat,N: nat] :
% 0.26/0.50        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.26/0.50       => ( ( dvd_dvd_nat @ K @ N )
% 0.26/0.50         => ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.50           => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % dvd_diffD
% 0.26/0.50  thf(fact_2481_dvd__diffD1,axiom,
% 0.26/0.50      ! [K: nat,M: nat,N: nat] :
% 0.26/0.50        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.26/0.50       => ( ( dvd_dvd_nat @ K @ M )
% 0.26/0.50         => ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.50           => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % dvd_diffD1
% 0.26/0.50  thf(fact_2482_less__eq__dvd__minus,axiom,
% 0.26/0.50      ! [M: nat,N: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.50       => ( ( dvd_dvd_nat @ M @ N )
% 0.26/0.50          = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % less_eq_dvd_minus
% 0.26/0.50  thf(fact_2483_odd__nonzero,axiom,
% 0.26/0.50      ! [Z: int] :
% 0.26/0.50        ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 0.26/0.50       != zero_zero_int ) ).
% 0.26/0.50  
% 0.26/0.50  % odd_nonzero
% 0.26/0.50  thf(fact_2484_int__ge__induct,axiom,
% 0.26/0.50      ! [K: int,I: int,P: int > $o] :
% 0.26/0.50        ( ( ord_less_eq_int @ K @ I )
% 0.26/0.50       => ( ( P @ K )
% 0.26/0.50         => ( ! [I3: int] :
% 0.26/0.50                ( ( ord_less_eq_int @ K @ I3 )
% 0.26/0.50               => ( ( P @ I3 )
% 0.26/0.50                 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 0.26/0.50           => ( P @ I ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % int_ge_induct
% 0.26/0.50  thf(fact_2485_zless__add1__eq,axiom,
% 0.26/0.50      ! [W: int,Z: int] :
% 0.26/0.50        ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 0.26/0.50        = ( ( ord_less_int @ W @ Z )
% 0.26/0.50          | ( W = Z ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % zless_add1_eq
% 0.26/0.50  thf(fact_2486_int__gr__induct,axiom,
% 0.26/0.50      ! [K: int,I: int,P: int > $o] :
% 0.26/0.50        ( ( ord_less_int @ K @ I )
% 0.26/0.50       => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 0.26/0.50         => ( ! [I3: int] :
% 0.26/0.50                ( ( ord_less_int @ K @ I3 )
% 0.26/0.50               => ( ( P @ I3 )
% 0.26/0.50                 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 0.26/0.50           => ( P @ I ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % int_gr_induct
% 0.26/0.50  thf(fact_2487_zle__iff__zadd,axiom,
% 0.26/0.50      ( ord_less_eq_int
% 0.26/0.50      = ( ^ [W3: int,Z6: int] :
% 0.26/0.50          ? [N3: nat] :
% 0.26/0.50            ( Z6
% 0.26/0.50            = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % zle_iff_zadd
% 0.26/0.50  thf(fact_2488_ln__bound,axiom,
% 0.26/0.50      ! [X3: real] :
% 0.26/0.50        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.50       => ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ X3 ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ln_bound
% 0.26/0.50  thf(fact_2489_ln__gt__zero__imp__gt__one,axiom,
% 0.26/0.50      ! [X3: real] :
% 0.26/0.50        ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X3 ) )
% 0.26/0.50       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.50         => ( ord_less_real @ one_one_real @ X3 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ln_gt_zero_imp_gt_one
% 0.26/0.50  thf(fact_2490_ln__less__zero,axiom,
% 0.26/0.50      ! [X3: real] :
% 0.26/0.50        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.50       => ( ( ord_less_real @ X3 @ one_one_real )
% 0.26/0.50         => ( ord_less_real @ ( ln_ln_real @ X3 ) @ zero_zero_real ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ln_less_zero
% 0.26/0.50  thf(fact_2491_ln__gt__zero,axiom,
% 0.26/0.50      ! [X3: real] :
% 0.26/0.50        ( ( ord_less_real @ one_one_real @ X3 )
% 0.26/0.50       => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X3 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ln_gt_zero
% 0.26/0.50  thf(fact_2492_ln__ge__zero,axiom,
% 0.26/0.50      ! [X3: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ one_one_real @ X3 )
% 0.26/0.50       => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X3 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ln_ge_zero
% 0.26/0.50  thf(fact_2493_arsinh__real__def,axiom,
% 0.26/0.50      ( arsinh_real
% 0.26/0.50      = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % arsinh_real_def
% 0.26/0.50  thf(fact_2494_ceiling__eq,axiom,
% 0.26/0.50      ! [N: int,X3: real] :
% 0.26/0.50        ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X3 )
% 0.26/0.50       => ( ( ord_less_eq_real @ X3 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 0.26/0.50         => ( ( archim7802044766580827645g_real @ X3 )
% 0.26/0.50            = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ceiling_eq
% 0.26/0.50  thf(fact_2495_ceiling__eq,axiom,
% 0.26/0.50      ! [N: int,X3: rat] :
% 0.26/0.50        ( ( ord_less_rat @ ( ring_1_of_int_rat @ N ) @ X3 )
% 0.26/0.50       => ( ( ord_less_eq_rat @ X3 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ N ) @ one_one_rat ) )
% 0.26/0.50         => ( ( archim2889992004027027881ng_rat @ X3 )
% 0.26/0.50            = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ceiling_eq
% 0.26/0.50  thf(fact_2496_numeral__Bit0__div__2,axiom,
% 0.26/0.50      ! [N: num] :
% 0.26/0.50        ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.50        = ( numeral_numeral_nat @ N ) ) ).
% 0.26/0.50  
% 0.26/0.50  % numeral_Bit0_div_2
% 0.26/0.50  thf(fact_2497_numeral__Bit0__div__2,axiom,
% 0.26/0.50      ! [N: num] :
% 0.26/0.50        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.50        = ( numeral_numeral_int @ N ) ) ).
% 0.26/0.50  
% 0.26/0.50  % numeral_Bit0_div_2
% 0.26/0.50  thf(fact_2498_add__strict__increasing2,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.50       => ( ( ord_less_real @ B @ C )
% 0.26/0.50         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_strict_increasing2
% 0.26/0.50  thf(fact_2499_add__strict__increasing2,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.50       => ( ( ord_less_rat @ B @ C )
% 0.26/0.50         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_strict_increasing2
% 0.26/0.50  thf(fact_2500_add__strict__increasing2,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.50       => ( ( ord_less_nat @ B @ C )
% 0.26/0.50         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_strict_increasing2
% 0.26/0.50  thf(fact_2501_add__strict__increasing2,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.50       => ( ( ord_less_int @ B @ C )
% 0.26/0.50         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_strict_increasing2
% 0.26/0.50  thf(fact_2502_add__strict__increasing,axiom,
% 0.26/0.50      ! [A: real,B: real,C: real] :
% 0.26/0.50        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.50       => ( ( ord_less_eq_real @ B @ C )
% 0.26/0.50         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_strict_increasing
% 0.26/0.50  thf(fact_2503_add__strict__increasing,axiom,
% 0.26/0.50      ! [A: rat,B: rat,C: rat] :
% 0.26/0.50        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.50       => ( ( ord_less_eq_rat @ B @ C )
% 0.26/0.50         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_strict_increasing
% 0.26/0.50  thf(fact_2504_add__strict__increasing,axiom,
% 0.26/0.50      ! [A: nat,B: nat,C: nat] :
% 0.26/0.50        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.26/0.50       => ( ( ord_less_eq_nat @ B @ C )
% 0.26/0.50         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_strict_increasing
% 0.26/0.50  thf(fact_2505_add__strict__increasing,axiom,
% 0.26/0.50      ! [A: int,B: int,C: int] :
% 0.26/0.50        ( ( ord_less_int @ zero_zero_int @ A )
% 0.26/0.50       => ( ( ord_less_eq_int @ B @ C )
% 0.26/0.50         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_strict_increasing
% 0.26/0.50  thf(fact_2506_add__pos__nonneg,axiom,
% 0.26/0.50      ! [A: real,B: real] :
% 0.26/0.50        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.50       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.26/0.50         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_pos_nonneg
% 0.26/0.50  thf(fact_2507_add__pos__nonneg,axiom,
% 0.26/0.50      ! [A: rat,B: rat] :
% 0.26/0.50        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.50       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.26/0.50         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_pos_nonneg
% 0.26/0.50  thf(fact_2508_add__pos__nonneg,axiom,
% 0.26/0.50      ! [A: nat,B: nat] :
% 0.26/0.50        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.26/0.50       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.26/0.50         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_pos_nonneg
% 0.26/0.50  thf(fact_2509_add__pos__nonneg,axiom,
% 0.26/0.50      ! [A: int,B: int] :
% 0.26/0.50        ( ( ord_less_int @ zero_zero_int @ A )
% 0.26/0.50       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.26/0.50         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_pos_nonneg
% 0.26/0.50  thf(fact_2510_add__nonpos__neg,axiom,
% 0.26/0.50      ! [A: real,B: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.26/0.50       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.26/0.50         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonpos_neg
% 0.26/0.50  thf(fact_2511_add__nonpos__neg,axiom,
% 0.26/0.50      ! [A: rat,B: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.26/0.50       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.26/0.50         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonpos_neg
% 0.26/0.50  thf(fact_2512_add__nonpos__neg,axiom,
% 0.26/0.50      ! [A: nat,B: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.26/0.50       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.26/0.50         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonpos_neg
% 0.26/0.50  thf(fact_2513_add__nonpos__neg,axiom,
% 0.26/0.50      ! [A: int,B: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.26/0.50       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.26/0.50         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonpos_neg
% 0.26/0.50  thf(fact_2514_add__nonneg__pos,axiom,
% 0.26/0.50      ! [A: real,B: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.50       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.26/0.50         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonneg_pos
% 0.26/0.50  thf(fact_2515_add__nonneg__pos,axiom,
% 0.26/0.50      ! [A: rat,B: rat] :
% 0.26/0.50        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.50       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.26/0.50         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonneg_pos
% 0.26/0.50  thf(fact_2516_add__nonneg__pos,axiom,
% 0.26/0.50      ! [A: nat,B: nat] :
% 0.26/0.50        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.50       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.26/0.50         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonneg_pos
% 0.26/0.50  thf(fact_2517_add__nonneg__pos,axiom,
% 0.26/0.50      ! [A: int,B: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.50       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.50         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_nonneg_pos
% 0.26/0.50  thf(fact_2518_add__neg__nonpos,axiom,
% 0.26/0.50      ! [A: real,B: real] :
% 0.26/0.50        ( ( ord_less_real @ A @ zero_zero_real )
% 0.26/0.50       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.26/0.50         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_neg_nonpos
% 0.26/0.50  thf(fact_2519_add__neg__nonpos,axiom,
% 0.26/0.50      ! [A: rat,B: rat] :
% 0.26/0.50        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.26/0.50       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.26/0.50         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_neg_nonpos
% 0.26/0.50  thf(fact_2520_add__neg__nonpos,axiom,
% 0.26/0.50      ! [A: nat,B: nat] :
% 0.26/0.50        ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.26/0.50       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.26/0.50         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_neg_nonpos
% 0.26/0.50  thf(fact_2521_add__neg__nonpos,axiom,
% 0.26/0.50      ! [A: int,B: int] :
% 0.26/0.50        ( ( ord_less_int @ A @ zero_zero_int )
% 0.26/0.50       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.26/0.50         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add_neg_nonpos
% 0.26/0.50  thf(fact_2522_unit__div__eq__0__iff,axiom,
% 0.26/0.50      ! [B: code_integer,A: code_integer] :
% 0.26/0.50        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.26/0.50       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 0.26/0.50            = zero_z3403309356797280102nteger )
% 0.26/0.50          = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % unit_div_eq_0_iff
% 0.26/0.50  thf(fact_2523_unit__div__eq__0__iff,axiom,
% 0.26/0.50      ! [B: nat,A: nat] :
% 0.26/0.50        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.26/0.50       => ( ( ( divide_divide_nat @ A @ B )
% 0.26/0.50            = zero_zero_nat )
% 0.26/0.50          = ( A = zero_zero_nat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % unit_div_eq_0_iff
% 0.26/0.50  thf(fact_2524_unit__div__eq__0__iff,axiom,
% 0.26/0.50      ! [B: int,A: int] :
% 0.26/0.50        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.26/0.50       => ( ( ( divide_divide_int @ A @ B )
% 0.26/0.50            = zero_zero_int )
% 0.26/0.50          = ( A = zero_zero_int ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % unit_div_eq_0_iff
% 0.26/0.50  thf(fact_2525_zero__less__two,axiom,
% 0.26/0.50      ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 0.26/0.50  
% 0.26/0.50  % zero_less_two
% 0.26/0.50  thf(fact_2526_zero__less__two,axiom,
% 0.26/0.50      ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 0.26/0.50  
% 0.26/0.50  % zero_less_two
% 0.26/0.50  thf(fact_2527_zero__less__two,axiom,
% 0.26/0.50      ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 0.26/0.50  
% 0.26/0.50  % zero_less_two
% 0.26/0.50  thf(fact_2528_zero__less__two,axiom,
% 0.26/0.50      ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 0.26/0.50  
% 0.26/0.50  % zero_less_two
% 0.26/0.50  thf(fact_2529_take__bit__incr__eq,axiom,
% 0.26/0.50      ! [N: nat,K: int] :
% 0.26/0.50        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.26/0.50         != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 0.26/0.50       => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 0.26/0.50          = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % take_bit_incr_eq
% 0.26/0.50  thf(fact_2530_div__greater__zero__iff,axiom,
% 0.26/0.50      ! [M: nat,N: nat] :
% 0.26/0.50        ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 0.26/0.50        = ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.50          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % div_greater_zero_iff
% 0.26/0.50  thf(fact_2531_div__le__mono2,axiom,
% 0.26/0.50      ! [M: nat,N: nat,K: nat] :
% 0.26/0.50        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.50       => ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.50         => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % div_le_mono2
% 0.26/0.50  thf(fact_2532_div__eq__dividend__iff,axiom,
% 0.26/0.50      ! [M: nat,N: nat] :
% 0.26/0.50        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.50       => ( ( ( divide_divide_nat @ M @ N )
% 0.26/0.50            = M )
% 0.26/0.50          = ( N = one_one_nat ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % div_eq_dividend_iff
% 0.26/0.50  thf(fact_2533_div__less__dividend,axiom,
% 0.26/0.50      ! [N: nat,M: nat] :
% 0.26/0.50        ( ( ord_less_nat @ one_one_nat @ N )
% 0.26/0.50       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.50         => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % div_less_dividend
% 0.26/0.50  thf(fact_2534_odd__less__0__iff,axiom,
% 0.26/0.50      ! [Z: int] :
% 0.26/0.50        ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 0.26/0.50        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 0.26/0.50  
% 0.26/0.50  % odd_less_0_iff
% 0.26/0.50  thf(fact_2535_sqrt__add__le__add__sqrt,axiom,
% 0.26/0.50      ! [X3: real,Y3: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.50       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.50         => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X3 @ Y3 ) ) @ ( plus_plus_real @ ( sqrt @ X3 ) @ ( sqrt @ Y3 ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % sqrt_add_le_add_sqrt
% 0.26/0.50  thf(fact_2536_zless__imp__add1__zle,axiom,
% 0.26/0.50      ! [W: int,Z: int] :
% 0.26/0.50        ( ( ord_less_int @ W @ Z )
% 0.26/0.50       => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 0.26/0.50  
% 0.26/0.50  % zless_imp_add1_zle
% 0.26/0.50  thf(fact_2537_add1__zle__eq,axiom,
% 0.26/0.50      ! [W: int,Z: int] :
% 0.26/0.50        ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 0.26/0.50        = ( ord_less_int @ W @ Z ) ) ).
% 0.26/0.50  
% 0.26/0.50  % add1_zle_eq
% 0.26/0.50  thf(fact_2538_take__bit__decr__eq,axiom,
% 0.26/0.50      ! [N: nat,K: int] :
% 0.26/0.50        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.26/0.50         != zero_zero_int )
% 0.26/0.50       => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 0.26/0.50          = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % take_bit_decr_eq
% 0.26/0.50  thf(fact_2539_even__mask__div__iff_H,axiom,
% 0.26/0.50      ! [M: nat,N: nat] :
% 0.26/0.50        ( ( 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 ) ) )
% 0.26/0.50        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_mask_div_iff'
% 0.26/0.50  thf(fact_2540_even__mask__div__iff_H,axiom,
% 0.26/0.50      ! [M: nat,N: nat] :
% 0.26/0.50        ( ( 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 ) ) )
% 0.26/0.50        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_mask_div_iff'
% 0.26/0.50  thf(fact_2541_even__mask__div__iff_H,axiom,
% 0.26/0.50      ! [M: nat,N: nat] :
% 0.26/0.50        ( ( 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 ) ) )
% 0.26/0.50        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_mask_div_iff'
% 0.26/0.50  thf(fact_2542_ln__ge__zero__imp__ge__one,axiom,
% 0.26/0.50      ! [X3: real] :
% 0.26/0.50        ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X3 ) )
% 0.26/0.50       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.50         => ( ord_less_eq_real @ one_one_real @ X3 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % ln_ge_zero_imp_ge_one
% 0.26/0.50  thf(fact_2543_even__mask__div__iff,axiom,
% 0.26/0.50      ! [M: nat,N: nat] :
% 0.26/0.50        ( ( 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 ) ) )
% 0.26/0.50        = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 0.26/0.50            = zero_z3403309356797280102nteger )
% 0.26/0.50          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_mask_div_iff
% 0.26/0.50  thf(fact_2544_even__mask__div__iff,axiom,
% 0.26/0.50      ! [M: nat,N: nat] :
% 0.26/0.50        ( ( 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 ) ) )
% 0.26/0.50        = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.50            = zero_zero_nat )
% 0.26/0.50          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_mask_div_iff
% 0.26/0.50  thf(fact_2545_even__mask__div__iff,axiom,
% 0.26/0.50      ! [M: nat,N: nat] :
% 0.26/0.50        ( ( 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 ) ) )
% 0.26/0.50        = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.26/0.50            = zero_zero_int )
% 0.26/0.50          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % even_mask_div_iff
% 0.26/0.50  thf(fact_2546_stable__imp__take__bit__eq,axiom,
% 0.26/0.50      ! [A: code_integer,N: nat] :
% 0.26/0.50        ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.26/0.50          = A )
% 0.26/0.50       => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.50           => ( ( bit_se1745604003318907178nteger @ N @ A )
% 0.26/0.50              = zero_z3403309356797280102nteger ) )
% 0.26/0.50          & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.50           => ( ( bit_se1745604003318907178nteger @ N @ A )
% 0.26/0.50              = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % stable_imp_take_bit_eq
% 0.26/0.50  thf(fact_2547_stable__imp__take__bit__eq,axiom,
% 0.26/0.50      ! [A: int,N: nat] :
% 0.26/0.50        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.50          = A )
% 0.26/0.50       => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.50           => ( ( bit_se2923211474154528505it_int @ N @ A )
% 0.26/0.50              = zero_zero_int ) )
% 0.26/0.50          & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.50           => ( ( bit_se2923211474154528505it_int @ N @ A )
% 0.26/0.50              = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % stable_imp_take_bit_eq
% 0.26/0.50  thf(fact_2548_stable__imp__take__bit__eq,axiom,
% 0.26/0.50      ! [A: nat,N: nat] :
% 0.26/0.50        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.50          = A )
% 0.26/0.50       => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.50           => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 0.26/0.50              = zero_zero_nat ) )
% 0.26/0.50          & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.50           => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 0.26/0.50              = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % stable_imp_take_bit_eq
% 0.26/0.50  thf(fact_2549_bit__eq__rec,axiom,
% 0.26/0.50      ( ( ^ [Y5: code_integer,Z2: code_integer] : ( Y5 = Z2 ) )
% 0.26/0.50      = ( ^ [A4: code_integer,B3: code_integer] :
% 0.26/0.50            ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 )
% 0.26/0.50              = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) )
% 0.26/0.50            & ( ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.26/0.50              = ( divide6298287555418463151nteger @ B3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % bit_eq_rec
% 0.26/0.50  thf(fact_2550_bit__eq__rec,axiom,
% 0.26/0.50      ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 0.26/0.50      = ( ^ [A4: nat,B3: nat] :
% 0.26/0.50            ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 )
% 0.26/0.50              = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) )
% 0.26/0.50            & ( ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.50              = ( divide_divide_nat @ B3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % bit_eq_rec
% 0.26/0.50  thf(fact_2551_bit__eq__rec,axiom,
% 0.26/0.50      ( ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 0.26/0.50      = ( ^ [A4: int,B3: int] :
% 0.26/0.50            ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 )
% 0.26/0.50              = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) )
% 0.26/0.50            & ( ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.50              = ( divide_divide_int @ B3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % bit_eq_rec
% 0.26/0.50  thf(fact_2552_power2__commute,axiom,
% 0.26/0.50      ! [X3: complex,Y3: complex] :
% 0.26/0.50        ( ( power_power_complex @ ( minus_minus_complex @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.50        = ( power_power_complex @ ( minus_minus_complex @ Y3 @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % power2_commute
% 0.26/0.50  thf(fact_2553_power2__commute,axiom,
% 0.26/0.50      ! [X3: real,Y3: real] :
% 0.26/0.50        ( ( power_power_real @ ( minus_minus_real @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.50        = ( power_power_real @ ( minus_minus_real @ Y3 @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % power2_commute
% 0.26/0.50  thf(fact_2554_power2__commute,axiom,
% 0.26/0.50      ! [X3: rat,Y3: rat] :
% 0.26/0.50        ( ( power_power_rat @ ( minus_minus_rat @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.50        = ( power_power_rat @ ( minus_minus_rat @ Y3 @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % power2_commute
% 0.26/0.50  thf(fact_2555_power2__commute,axiom,
% 0.26/0.50      ! [X3: int,Y3: int] :
% 0.26/0.50        ( ( power_power_int @ ( minus_minus_int @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.50        = ( power_power_int @ ( minus_minus_int @ Y3 @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % power2_commute
% 0.26/0.50  thf(fact_2556_odd__even__add,axiom,
% 0.26/0.50      ! [A: code_integer,B: code_integer] :
% 0.26/0.50        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.50       => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 0.26/0.50         => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % odd_even_add
% 0.26/0.50  thf(fact_2557_odd__even__add,axiom,
% 0.26/0.50      ! [A: nat,B: nat] :
% 0.26/0.50        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.50       => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.26/0.50         => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % odd_even_add
% 0.26/0.50  thf(fact_2558_odd__even__add,axiom,
% 0.26/0.50      ! [A: int,B: int] :
% 0.26/0.50        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.50       => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 0.26/0.50         => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % odd_even_add
% 0.26/0.50  thf(fact_2559_of__int__ceiling__diff__one__le,axiom,
% 0.26/0.50      ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R2 ) ) @ one_one_real ) @ R2 ) ).
% 0.26/0.50  
% 0.26/0.50  % of_int_ceiling_diff_one_le
% 0.26/0.50  thf(fact_2560_of__int__ceiling__diff__one__le,axiom,
% 0.26/0.50      ! [R2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R2 ) ) @ one_one_rat ) @ R2 ) ).
% 0.26/0.50  
% 0.26/0.50  % of_int_ceiling_diff_one_le
% 0.26/0.50  thf(fact_2561_floor__exists1,axiom,
% 0.26/0.50      ! [X3: real] :
% 0.26/0.50      ? [X4: int] :
% 0.26/0.50        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X4 ) @ X3 )
% 0.26/0.50        & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ X4 @ one_one_int ) ) )
% 0.26/0.50        & ! [Y6: int] :
% 0.26/0.50            ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y6 ) @ X3 )
% 0.26/0.50              & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ Y6 @ one_one_int ) ) ) )
% 0.26/0.50           => ( Y6 = X4 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % floor_exists1
% 0.26/0.50  thf(fact_2562_floor__exists1,axiom,
% 0.26/0.50      ! [X3: rat] :
% 0.26/0.50      ? [X4: int] :
% 0.26/0.50        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X4 ) @ X3 )
% 0.26/0.50        & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ X4 @ one_one_int ) ) )
% 0.26/0.50        & ! [Y6: int] :
% 0.26/0.50            ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y6 ) @ X3 )
% 0.26/0.50              & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y6 @ one_one_int ) ) ) )
% 0.26/0.50           => ( Y6 = X4 ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % floor_exists1
% 0.26/0.50  thf(fact_2563_floor__exists,axiom,
% 0.26/0.50      ! [X3: real] :
% 0.26/0.50      ? [Z3: int] :
% 0.26/0.50        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z3 ) @ X3 )
% 0.26/0.50        & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % floor_exists
% 0.26/0.50  thf(fact_2564_floor__exists,axiom,
% 0.26/0.50      ! [X3: rat] :
% 0.26/0.50      ? [Z3: int] :
% 0.26/0.50        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X3 )
% 0.26/0.50        & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % floor_exists
% 0.26/0.50  thf(fact_2565_take__bit__set__bit__eq,axiom,
% 0.26/0.50      ! [N: nat,M: nat,A: int] :
% 0.26/0.50        ( ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.50         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 0.26/0.50            = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 0.26/0.50        & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.26/0.50         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 0.26/0.50            = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 0.26/0.50  
% 0.26/0.50  % take_bit_set_bit_eq
% 0.26/0.50  thf(fact_2566_take__bit__set__bit__eq,axiom,
% 0.26/0.50      ! [N: nat,M: nat,A: nat] :
% 0.26/0.50        ( ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.50         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 0.26/0.50            = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 0.26/0.50        & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.26/0.50         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 0.26/0.50            = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % take_bit_set_bit_eq
% 0.26/0.51  thf(fact_2567_take__bit__flip__bit__eq,axiom,
% 0.26/0.51      ! [N: nat,M: nat,A: int] :
% 0.26/0.51        ( ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.51         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 0.26/0.51            = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 0.26/0.51        & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.26/0.51         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 0.26/0.51            = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % take_bit_flip_bit_eq
% 0.26/0.51  thf(fact_2568_take__bit__flip__bit__eq,axiom,
% 0.26/0.51      ! [N: nat,M: nat,A: nat] :
% 0.26/0.51        ( ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.51         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 0.26/0.51            = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 0.26/0.51        & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.26/0.51         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 0.26/0.51            = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % take_bit_flip_bit_eq
% 0.26/0.51  thf(fact_2569_take__bit__unset__bit__eq,axiom,
% 0.26/0.51      ! [N: nat,M: nat,A: int] :
% 0.26/0.51        ( ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.51         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 0.26/0.51            = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 0.26/0.51        & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.26/0.51         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 0.26/0.51            = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % take_bit_unset_bit_eq
% 0.26/0.51  thf(fact_2570_take__bit__unset__bit__eq,axiom,
% 0.26/0.51      ! [N: nat,M: nat,A: nat] :
% 0.26/0.51        ( ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.51         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 0.26/0.51            = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 0.26/0.51        & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.26/0.51         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 0.26/0.51            = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % take_bit_unset_bit_eq
% 0.26/0.51  thf(fact_2571_of__int__ceiling__le__add__one,axiom,
% 0.26/0.51      ! [R2: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R2 ) ) @ ( plus_plus_real @ R2 @ one_one_real ) ) ).
% 0.26/0.51  
% 0.26/0.51  % of_int_ceiling_le_add_one
% 0.26/0.51  thf(fact_2572_of__int__ceiling__le__add__one,axiom,
% 0.26/0.51      ! [R2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R2 ) ) @ ( plus_plus_rat @ R2 @ one_one_rat ) ) ).
% 0.26/0.51  
% 0.26/0.51  % of_int_ceiling_le_add_one
% 0.26/0.51  thf(fact_2573_nat__less__real__le,axiom,
% 0.26/0.51      ( ord_less_nat
% 0.26/0.51      = ( ^ [N3: nat,M3: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N3 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % nat_less_real_le
% 0.26/0.51  thf(fact_2574_nat__le__real__less,axiom,
% 0.26/0.51      ( ord_less_eq_nat
% 0.26/0.51      = ( ^ [N3: nat,M3: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M3 ) @ one_one_real ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % nat_le_real_less
% 0.26/0.51  thf(fact_2575_le__imp__0__less,axiom,
% 0.26/0.51      ! [Z: int] :
% 0.26/0.51        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.26/0.51       => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % le_imp_0_less
% 0.26/0.51  thf(fact_2576_int__le__real__less,axiom,
% 0.26/0.51      ( ord_less_eq_int
% 0.26/0.51      = ( ^ [N3: int,M3: int] : ( ord_less_real @ ( ring_1_of_int_real @ N3 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M3 ) @ one_one_real ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % int_le_real_less
% 0.26/0.51  thf(fact_2577_int__less__real__le,axiom,
% 0.26/0.51      ( ord_less_int
% 0.26/0.51      = ( ^ [N3: int,M3: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N3 ) @ one_one_real ) @ ( ring_1_of_int_real @ M3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % int_less_real_le
% 0.26/0.51  thf(fact_2578_half__gt__zero,axiom,
% 0.26/0.51      ! [A: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.51       => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % half_gt_zero
% 0.26/0.51  thf(fact_2579_half__gt__zero,axiom,
% 0.26/0.51      ! [A: rat] :
% 0.26/0.51        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.51       => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % half_gt_zero
% 0.26/0.51  thf(fact_2580_half__gt__zero__iff,axiom,
% 0.26/0.51      ! [A: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.51        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.26/0.51  
% 0.26/0.51  % half_gt_zero_iff
% 0.26/0.51  thf(fact_2581_half__gt__zero__iff,axiom,
% 0.26/0.51      ! [A: rat] :
% 0.26/0.51        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.26/0.51        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.26/0.51  
% 0.26/0.51  % half_gt_zero_iff
% 0.26/0.51  thf(fact_2582_inverse__of__nat__le,axiom,
% 0.26/0.51      ! [N: nat,M: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.51       => ( ( N != zero_zero_nat )
% 0.26/0.51         => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % inverse_of_nat_le
% 0.26/0.51  thf(fact_2583_inverse__of__nat__le,axiom,
% 0.26/0.51      ! [N: nat,M: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.51       => ( ( N != zero_zero_nat )
% 0.26/0.51         => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % inverse_of_nat_le
% 0.26/0.51  thf(fact_2584_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 0.26/0.51      ! [N: nat,M: nat] :
% 0.26/0.51        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.51         != zero_zero_nat )
% 0.26/0.51       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 0.26/0.51         != zero_zero_nat ) ) ).
% 0.26/0.51  
% 0.26/0.51  % exp_not_zero_imp_exp_diff_not_zero
% 0.26/0.51  thf(fact_2585_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 0.26/0.51      ! [N: nat,M: nat] :
% 0.26/0.51        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.26/0.51         != zero_zero_int )
% 0.26/0.51       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 0.26/0.51         != zero_zero_int ) ) ).
% 0.26/0.51  
% 0.26/0.51  % exp_not_zero_imp_exp_diff_not_zero
% 0.26/0.51  thf(fact_2586_ceiling__split,axiom,
% 0.26/0.51      ! [P: int > $o,T: real] :
% 0.26/0.51        ( ( P @ ( archim7802044766580827645g_real @ T ) )
% 0.26/0.51        = ( ! [I4: int] :
% 0.26/0.51              ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ I4 ) @ one_one_real ) @ T )
% 0.26/0.51                & ( ord_less_eq_real @ T @ ( ring_1_of_int_real @ I4 ) ) )
% 0.26/0.51             => ( P @ I4 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % ceiling_split
% 0.26/0.51  thf(fact_2587_ceiling__split,axiom,
% 0.26/0.51      ! [P: int > $o,T: rat] :
% 0.26/0.51        ( ( P @ ( archim2889992004027027881ng_rat @ T ) )
% 0.26/0.51        = ( ! [I4: int] :
% 0.26/0.51              ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I4 ) @ one_one_rat ) @ T )
% 0.26/0.51                & ( ord_less_eq_rat @ T @ ( ring_1_of_int_rat @ I4 ) ) )
% 0.26/0.51             => ( P @ I4 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % ceiling_split
% 0.26/0.51  thf(fact_2588_ceiling__eq__iff,axiom,
% 0.26/0.51      ! [X3: real,A: int] :
% 0.26/0.51        ( ( ( archim7802044766580827645g_real @ X3 )
% 0.26/0.51          = A )
% 0.26/0.51        = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ X3 )
% 0.26/0.51          & ( ord_less_eq_real @ X3 @ ( ring_1_of_int_real @ A ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % ceiling_eq_iff
% 0.26/0.51  thf(fact_2589_ceiling__eq__iff,axiom,
% 0.26/0.51      ! [X3: rat,A: int] :
% 0.26/0.51        ( ( ( archim2889992004027027881ng_rat @ X3 )
% 0.26/0.51          = A )
% 0.26/0.51        = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X3 )
% 0.26/0.51          & ( ord_less_eq_rat @ X3 @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % ceiling_eq_iff
% 0.26/0.51  thf(fact_2590_ceiling__unique,axiom,
% 0.26/0.51      ! [Z: int,X3: real] :
% 0.26/0.51        ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X3 )
% 0.26/0.51       => ( ( ord_less_eq_real @ X3 @ ( ring_1_of_int_real @ Z ) )
% 0.26/0.51         => ( ( archim7802044766580827645g_real @ X3 )
% 0.26/0.51            = Z ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % ceiling_unique
% 0.26/0.51  thf(fact_2591_ceiling__unique,axiom,
% 0.26/0.51      ! [Z: int,X3: rat] :
% 0.26/0.51        ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X3 )
% 0.26/0.51       => ( ( ord_less_eq_rat @ X3 @ ( ring_1_of_int_rat @ Z ) )
% 0.26/0.51         => ( ( archim2889992004027027881ng_rat @ X3 )
% 0.26/0.51            = Z ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % ceiling_unique
% 0.26/0.51  thf(fact_2592_ceiling__correct,axiom,
% 0.26/0.51      ! [X3: real] :
% 0.26/0.51        ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X3 ) ) @ one_one_real ) @ X3 )
% 0.26/0.51        & ( ord_less_eq_real @ X3 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % ceiling_correct
% 0.26/0.51  thf(fact_2593_ceiling__correct,axiom,
% 0.26/0.51      ! [X3: rat] :
% 0.26/0.51        ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X3 ) ) @ one_one_rat ) @ X3 )
% 0.26/0.51        & ( ord_less_eq_rat @ X3 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % ceiling_correct
% 0.26/0.51  thf(fact_2594_diff__le__diff__pow,axiom,
% 0.26/0.51      ! [K: nat,M: nat,N: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.26/0.51       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % diff_le_diff_pow
% 0.26/0.51  thf(fact_2595_ceiling__less__iff,axiom,
% 0.26/0.51      ! [X3: real,Z: int] :
% 0.26/0.51        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X3 ) @ Z )
% 0.26/0.51        = ( ord_less_eq_real @ X3 @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % ceiling_less_iff
% 0.26/0.51  thf(fact_2596_ceiling__less__iff,axiom,
% 0.26/0.51      ! [X3: rat,Z: int] :
% 0.26/0.51        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X3 ) @ Z )
% 0.26/0.51        = ( ord_less_eq_rat @ X3 @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % ceiling_less_iff
% 0.26/0.51  thf(fact_2597_le__ceiling__iff,axiom,
% 0.26/0.51      ! [Z: int,X3: rat] :
% 0.26/0.51        ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X3 ) )
% 0.26/0.51        = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % le_ceiling_iff
% 0.26/0.51  thf(fact_2598_le__ceiling__iff,axiom,
% 0.26/0.51      ! [Z: int,X3: real] :
% 0.26/0.51        ( ( ord_less_eq_int @ Z @ ( archim7802044766580827645g_real @ X3 ) )
% 0.26/0.51        = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % le_ceiling_iff
% 0.26/0.51  thf(fact_2599_sum__power2__ge__zero,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % sum_power2_ge_zero
% 0.26/0.51  thf(fact_2600_sum__power2__ge__zero,axiom,
% 0.26/0.51      ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % sum_power2_ge_zero
% 0.26/0.51  thf(fact_2601_sum__power2__ge__zero,axiom,
% 0.26/0.51      ! [X3: int,Y3: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % sum_power2_ge_zero
% 0.26/0.51  thf(fact_2602_sum__power2__le__zero__iff,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 0.26/0.51        = ( ( X3 = zero_zero_real )
% 0.26/0.51          & ( Y3 = zero_zero_real ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % sum_power2_le_zero_iff
% 0.26/0.51  thf(fact_2603_sum__power2__le__zero__iff,axiom,
% 0.26/0.51      ! [X3: rat,Y3: rat] :
% 0.26/0.51        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 0.26/0.51        = ( ( X3 = zero_zero_rat )
% 0.26/0.51          & ( Y3 = zero_zero_rat ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % sum_power2_le_zero_iff
% 0.26/0.51  thf(fact_2604_sum__power2__le__zero__iff,axiom,
% 0.26/0.51      ! [X3: int,Y3: int] :
% 0.26/0.51        ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 0.26/0.51        = ( ( X3 = zero_zero_int )
% 0.26/0.51          & ( Y3 = zero_zero_int ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % sum_power2_le_zero_iff
% 0.26/0.51  thf(fact_2605_not__sum__power2__lt__zero,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 0.26/0.51  
% 0.26/0.51  % not_sum_power2_lt_zero
% 0.26/0.51  thf(fact_2606_not__sum__power2__lt__zero,axiom,
% 0.26/0.51      ! [X3: rat,Y3: rat] :
% 0.26/0.51        ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 0.26/0.51  
% 0.26/0.51  % not_sum_power2_lt_zero
% 0.26/0.51  thf(fact_2607_not__sum__power2__lt__zero,axiom,
% 0.26/0.51      ! [X3: int,Y3: int] :
% 0.26/0.51        ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 0.26/0.51  
% 0.26/0.51  % not_sum_power2_lt_zero
% 0.26/0.51  thf(fact_2608_sum__power2__gt__zero__iff,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.51        = ( ( X3 != zero_zero_real )
% 0.26/0.51          | ( Y3 != zero_zero_real ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % sum_power2_gt_zero_iff
% 0.26/0.51  thf(fact_2609_sum__power2__gt__zero__iff,axiom,
% 0.26/0.51      ! [X3: rat,Y3: rat] :
% 0.26/0.51        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.51        = ( ( X3 != zero_zero_rat )
% 0.26/0.51          | ( Y3 != zero_zero_rat ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % sum_power2_gt_zero_iff
% 0.26/0.51  thf(fact_2610_sum__power2__gt__zero__iff,axiom,
% 0.26/0.51      ! [X3: int,Y3: int] :
% 0.26/0.51        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.51        = ( ( X3 != zero_zero_int )
% 0.26/0.51          | ( Y3 != zero_zero_int ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % sum_power2_gt_zero_iff
% 0.26/0.51  thf(fact_2611_real__sqrt__sum__squares__eq__cancel,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.51          = X3 )
% 0.26/0.51       => ( Y3 = zero_zero_real ) ) ).
% 0.26/0.51  
% 0.26/0.51  % real_sqrt_sum_squares_eq_cancel
% 0.26/0.51  thf(fact_2612_real__sqrt__sum__squares__eq__cancel2,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.51          = Y3 )
% 0.26/0.51       => ( X3 = zero_zero_real ) ) ).
% 0.26/0.51  
% 0.26/0.51  % real_sqrt_sum_squares_eq_cancel2
% 0.26/0.51  thf(fact_2613_real__sqrt__sum__squares__ge1,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] : ( ord_less_eq_real @ X3 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % real_sqrt_sum_squares_ge1
% 0.26/0.51  thf(fact_2614_real__sqrt__sum__squares__ge2,axiom,
% 0.26/0.51      ! [Y3: real,X3: real] : ( ord_less_eq_real @ Y3 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % real_sqrt_sum_squares_ge2
% 0.26/0.51  thf(fact_2615_real__sqrt__sum__squares__triangle__ineq,axiom,
% 0.26/0.51      ! [A: real,C: real,B: real,D3: 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 @ D3 ) @ ( 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 @ D3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % real_sqrt_sum_squares_triangle_ineq
% 0.26/0.51  thf(fact_2616_sqrt__sum__squares__le__sum,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.51       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.51         => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % sqrt_sum_squares_le_sum
% 0.26/0.51  thf(fact_2617_sqrt__even__pow2,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.51       => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.51          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % sqrt_even_pow2
% 0.26/0.51  thf(fact_2618_le__divide__eq__1__pos,axiom,
% 0.26/0.51      ! [A: real,B: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.51       => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.26/0.51          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % le_divide_eq_1_pos
% 0.26/0.51  thf(fact_2619_le__divide__eq__1__pos,axiom,
% 0.26/0.51      ! [A: rat,B: rat] :
% 0.26/0.51        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.51       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.26/0.51          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % le_divide_eq_1_pos
% 0.26/0.51  thf(fact_2620_le__divide__eq__1__neg,axiom,
% 0.26/0.51      ! [A: real,B: real] :
% 0.26/0.51        ( ( ord_less_real @ A @ zero_zero_real )
% 0.26/0.51       => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.26/0.51          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % le_divide_eq_1_neg
% 0.26/0.51  thf(fact_2621_le__divide__eq__1__neg,axiom,
% 0.26/0.51      ! [A: rat,B: rat] :
% 0.26/0.51        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.26/0.51       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.26/0.51          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % le_divide_eq_1_neg
% 0.26/0.51  thf(fact_2622_divide__le__eq__1__pos,axiom,
% 0.26/0.51      ! [A: real,B: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.51       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.26/0.51          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_le_eq_1_pos
% 0.26/0.51  thf(fact_2623_divide__le__eq__1__pos,axiom,
% 0.26/0.51      ! [A: rat,B: rat] :
% 0.26/0.51        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.51       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.26/0.51          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_le_eq_1_pos
% 0.26/0.51  thf(fact_2624_divide__le__eq__1__neg,axiom,
% 0.26/0.51      ! [A: real,B: real] :
% 0.26/0.51        ( ( ord_less_real @ A @ zero_zero_real )
% 0.26/0.51       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.26/0.51          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_le_eq_1_neg
% 0.26/0.51  thf(fact_2625_divide__le__eq__1__neg,axiom,
% 0.26/0.51      ! [A: rat,B: rat] :
% 0.26/0.51        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.26/0.51       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.26/0.51          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_le_eq_1_neg
% 0.26/0.51  thf(fact_2626_divide__less__0__1__iff,axiom,
% 0.26/0.51      ! [A: real] :
% 0.26/0.51        ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 0.26/0.51        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_less_0_1_iff
% 0.26/0.51  thf(fact_2627_divide__less__0__1__iff,axiom,
% 0.26/0.51      ! [A: rat] :
% 0.26/0.51        ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 0.26/0.51        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_less_0_1_iff
% 0.26/0.51  thf(fact_2628_divide__less__eq__1__neg,axiom,
% 0.26/0.51      ! [A: real,B: real] :
% 0.26/0.51        ( ( ord_less_real @ A @ zero_zero_real )
% 0.26/0.51       => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.26/0.51          = ( ord_less_real @ A @ B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_less_eq_1_neg
% 0.26/0.51  thf(fact_2629_divide__less__eq__1__neg,axiom,
% 0.26/0.51      ! [A: rat,B: rat] :
% 0.26/0.51        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.26/0.51       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.26/0.51          = ( ord_less_rat @ A @ B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_less_eq_1_neg
% 0.26/0.51  thf(fact_2630_divide__less__eq__1__pos,axiom,
% 0.26/0.51      ! [A: real,B: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.51       => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.26/0.51          = ( ord_less_real @ B @ A ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_less_eq_1_pos
% 0.26/0.51  thf(fact_2631_divide__less__eq__1__pos,axiom,
% 0.26/0.51      ! [A: rat,B: rat] :
% 0.26/0.51        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.51       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.26/0.51          = ( ord_less_rat @ B @ A ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_less_eq_1_pos
% 0.26/0.51  thf(fact_2632_less__divide__eq__1__neg,axiom,
% 0.26/0.51      ! [A: real,B: real] :
% 0.26/0.51        ( ( ord_less_real @ A @ zero_zero_real )
% 0.26/0.51       => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.26/0.51          = ( ord_less_real @ B @ A ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % less_divide_eq_1_neg
% 0.26/0.51  thf(fact_2633_less__divide__eq__1__neg,axiom,
% 0.26/0.51      ! [A: rat,B: rat] :
% 0.26/0.51        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.26/0.51       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.26/0.51          = ( ord_less_rat @ B @ A ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % less_divide_eq_1_neg
% 0.26/0.51  thf(fact_2634_less__divide__eq__1__pos,axiom,
% 0.26/0.51      ! [A: real,B: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.51       => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.26/0.51          = ( ord_less_real @ A @ B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % less_divide_eq_1_pos
% 0.26/0.51  thf(fact_2635_less__divide__eq__1__pos,axiom,
% 0.26/0.51      ! [A: rat,B: rat] :
% 0.26/0.51        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.51       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.26/0.51          = ( ord_less_rat @ A @ B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % less_divide_eq_1_pos
% 0.26/0.51  thf(fact_2636_zero__less__divide__1__iff,axiom,
% 0.26/0.51      ! [A: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 0.26/0.51        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zero_less_divide_1_iff
% 0.26/0.51  thf(fact_2637_zero__less__divide__1__iff,axiom,
% 0.26/0.51      ! [A: rat] :
% 0.26/0.51        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 0.26/0.51        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zero_less_divide_1_iff
% 0.26/0.51  thf(fact_2638_pow__sum,axiom,
% 0.26/0.51      ! [A: nat,B: nat] :
% 0.26/0.51        ( ( 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 ) )
% 0.26/0.51        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 0.26/0.51  
% 0.26/0.51  % pow_sum
% 0.26/0.51  thf(fact_2639_divide__eq__0__iff,axiom,
% 0.26/0.51      ! [A: complex,B: complex] :
% 0.26/0.51        ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.26/0.51          = zero_zero_complex )
% 0.26/0.51        = ( ( A = zero_zero_complex )
% 0.26/0.51          | ( B = zero_zero_complex ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_eq_0_iff
% 0.26/0.51  thf(fact_2640_divide__eq__0__iff,axiom,
% 0.26/0.51      ! [A: real,B: real] :
% 0.26/0.51        ( ( ( divide_divide_real @ A @ B )
% 0.26/0.51          = zero_zero_real )
% 0.26/0.51        = ( ( A = zero_zero_real )
% 0.26/0.51          | ( B = zero_zero_real ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_eq_0_iff
% 0.26/0.51  thf(fact_2641_divide__eq__0__iff,axiom,
% 0.26/0.51      ! [A: rat,B: rat] :
% 0.26/0.51        ( ( ( divide_divide_rat @ A @ B )
% 0.26/0.51          = zero_zero_rat )
% 0.26/0.51        = ( ( A = zero_zero_rat )
% 0.26/0.51          | ( B = zero_zero_rat ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_eq_0_iff
% 0.26/0.51  thf(fact_2642_divide__cancel__left,axiom,
% 0.26/0.51      ! [C: complex,A: complex,B: complex] :
% 0.26/0.51        ( ( ( divide1717551699836669952omplex @ C @ A )
% 0.26/0.51          = ( divide1717551699836669952omplex @ C @ B ) )
% 0.26/0.51        = ( ( C = zero_zero_complex )
% 0.26/0.51          | ( A = B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_cancel_left
% 0.26/0.51  thf(fact_2643_divide__cancel__left,axiom,
% 0.26/0.51      ! [C: real,A: real,B: real] :
% 0.26/0.51        ( ( ( divide_divide_real @ C @ A )
% 0.26/0.51          = ( divide_divide_real @ C @ B ) )
% 0.26/0.51        = ( ( C = zero_zero_real )
% 0.26/0.51          | ( A = B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_cancel_left
% 0.26/0.51  thf(fact_2644_divide__cancel__left,axiom,
% 0.26/0.51      ! [C: rat,A: rat,B: rat] :
% 0.26/0.51        ( ( ( divide_divide_rat @ C @ A )
% 0.26/0.51          = ( divide_divide_rat @ C @ B ) )
% 0.26/0.51        = ( ( C = zero_zero_rat )
% 0.26/0.51          | ( A = B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_cancel_left
% 0.26/0.51  thf(fact_2645_divide__cancel__right,axiom,
% 0.26/0.51      ! [A: complex,C: complex,B: complex] :
% 0.26/0.51        ( ( ( divide1717551699836669952omplex @ A @ C )
% 0.26/0.51          = ( divide1717551699836669952omplex @ B @ C ) )
% 0.26/0.51        = ( ( C = zero_zero_complex )
% 0.26/0.51          | ( A = B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_cancel_right
% 0.26/0.51  thf(fact_2646_divide__cancel__right,axiom,
% 0.26/0.51      ! [A: real,C: real,B: real] :
% 0.26/0.51        ( ( ( divide_divide_real @ A @ C )
% 0.26/0.51          = ( divide_divide_real @ B @ C ) )
% 0.26/0.51        = ( ( C = zero_zero_real )
% 0.26/0.51          | ( A = B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_cancel_right
% 0.26/0.51  thf(fact_2647_divide__cancel__right,axiom,
% 0.26/0.51      ! [A: rat,C: rat,B: rat] :
% 0.26/0.51        ( ( ( divide_divide_rat @ A @ C )
% 0.26/0.51          = ( divide_divide_rat @ B @ C ) )
% 0.26/0.51        = ( ( C = zero_zero_rat )
% 0.26/0.51          | ( A = B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_cancel_right
% 0.26/0.51  thf(fact_2648_division__ring__divide__zero,axiom,
% 0.26/0.51      ! [A: complex] :
% 0.26/0.51        ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 0.26/0.51        = zero_zero_complex ) ).
% 0.26/0.51  
% 0.26/0.51  % division_ring_divide_zero
% 0.26/0.51  thf(fact_2649_division__ring__divide__zero,axiom,
% 0.26/0.51      ! [A: real] :
% 0.26/0.51        ( ( divide_divide_real @ A @ zero_zero_real )
% 0.26/0.51        = zero_zero_real ) ).
% 0.26/0.51  
% 0.26/0.51  % division_ring_divide_zero
% 0.26/0.51  thf(fact_2650_division__ring__divide__zero,axiom,
% 0.26/0.51      ! [A: rat] :
% 0.26/0.51        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 0.26/0.51        = zero_zero_rat ) ).
% 0.26/0.51  
% 0.26/0.51  % division_ring_divide_zero
% 0.26/0.51  thf(fact_2651_add__is__0,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( ( plus_plus_nat @ M @ N )
% 0.26/0.51          = zero_zero_nat )
% 0.26/0.51        = ( ( M = zero_zero_nat )
% 0.26/0.51          & ( N = zero_zero_nat ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % add_is_0
% 0.26/0.51  thf(fact_2652_Nat_Oadd__0__right,axiom,
% 0.26/0.51      ! [M: nat] :
% 0.26/0.51        ( ( plus_plus_nat @ M @ zero_zero_nat )
% 0.26/0.51        = M ) ).
% 0.26/0.51  
% 0.26/0.51  % Nat.add_0_right
% 0.26/0.51  thf(fact_2653_nat__add__left__cancel__less,axiom,
% 0.26/0.51      ! [K: nat,M: nat,N: nat] :
% 0.26/0.51        ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.26/0.51        = ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % nat_add_left_cancel_less
% 0.26/0.51  thf(fact_2654_nat__add__left__cancel__le,axiom,
% 0.26/0.51      ! [K: nat,M: nat,N: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.26/0.51        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % nat_add_left_cancel_le
% 0.26/0.51  thf(fact_2655_diff__diff__left,axiom,
% 0.26/0.51      ! [I: nat,J: nat,K: nat] :
% 0.26/0.51        ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 0.26/0.51        = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % diff_diff_left
% 0.26/0.51  thf(fact_2656_semiring__norm_I6_J,axiom,
% 0.26/0.51      ! [M: num,N: num] :
% 0.26/0.51        ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.26/0.51        = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % semiring_norm(6)
% 0.26/0.51  thf(fact_2657_divide__eq__1__iff,axiom,
% 0.26/0.51      ! [A: complex,B: complex] :
% 0.26/0.51        ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.26/0.51          = one_one_complex )
% 0.26/0.51        = ( ( B != zero_zero_complex )
% 0.26/0.51          & ( A = B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_eq_1_iff
% 0.26/0.51  thf(fact_2658_divide__eq__1__iff,axiom,
% 0.26/0.51      ! [A: real,B: real] :
% 0.26/0.51        ( ( ( divide_divide_real @ A @ B )
% 0.26/0.51          = one_one_real )
% 0.26/0.51        = ( ( B != zero_zero_real )
% 0.26/0.51          & ( A = B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_eq_1_iff
% 0.26/0.51  thf(fact_2659_divide__eq__1__iff,axiom,
% 0.26/0.51      ! [A: rat,B: rat] :
% 0.26/0.51        ( ( ( divide_divide_rat @ A @ B )
% 0.26/0.51          = one_one_rat )
% 0.26/0.51        = ( ( B != zero_zero_rat )
% 0.26/0.51          & ( A = B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_eq_1_iff
% 0.26/0.51  thf(fact_2660_one__eq__divide__iff,axiom,
% 0.26/0.51      ! [A: complex,B: complex] :
% 0.26/0.51        ( ( one_one_complex
% 0.26/0.51          = ( divide1717551699836669952omplex @ A @ B ) )
% 0.26/0.51        = ( ( B != zero_zero_complex )
% 0.26/0.51          & ( A = B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % one_eq_divide_iff
% 0.26/0.51  thf(fact_2661_one__eq__divide__iff,axiom,
% 0.26/0.51      ! [A: real,B: real] :
% 0.26/0.51        ( ( one_one_real
% 0.26/0.51          = ( divide_divide_real @ A @ B ) )
% 0.26/0.51        = ( ( B != zero_zero_real )
% 0.26/0.51          & ( A = B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % one_eq_divide_iff
% 0.26/0.51  thf(fact_2662_one__eq__divide__iff,axiom,
% 0.26/0.51      ! [A: rat,B: rat] :
% 0.26/0.51        ( ( one_one_rat
% 0.26/0.51          = ( divide_divide_rat @ A @ B ) )
% 0.26/0.51        = ( ( B != zero_zero_rat )
% 0.26/0.51          & ( A = B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % one_eq_divide_iff
% 0.26/0.51  thf(fact_2663_divide__self,axiom,
% 0.26/0.51      ! [A: complex] :
% 0.26/0.51        ( ( A != zero_zero_complex )
% 0.26/0.51       => ( ( divide1717551699836669952omplex @ A @ A )
% 0.26/0.51          = one_one_complex ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_self
% 0.26/0.51  thf(fact_2664_divide__self,axiom,
% 0.26/0.51      ! [A: real] :
% 0.26/0.51        ( ( A != zero_zero_real )
% 0.26/0.51       => ( ( divide_divide_real @ A @ A )
% 0.26/0.51          = one_one_real ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_self
% 0.26/0.51  thf(fact_2665_divide__self,axiom,
% 0.26/0.51      ! [A: rat] :
% 0.26/0.51        ( ( A != zero_zero_rat )
% 0.26/0.51       => ( ( divide_divide_rat @ A @ A )
% 0.26/0.51          = one_one_rat ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_self
% 0.26/0.51  thf(fact_2666_divide__self__if,axiom,
% 0.26/0.51      ! [A: complex] :
% 0.26/0.51        ( ( ( A = zero_zero_complex )
% 0.26/0.51         => ( ( divide1717551699836669952omplex @ A @ A )
% 0.26/0.51            = zero_zero_complex ) )
% 0.26/0.51        & ( ( A != zero_zero_complex )
% 0.26/0.51         => ( ( divide1717551699836669952omplex @ A @ A )
% 0.26/0.51            = one_one_complex ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_self_if
% 0.26/0.51  thf(fact_2667_divide__self__if,axiom,
% 0.26/0.51      ! [A: real] :
% 0.26/0.51        ( ( ( A = zero_zero_real )
% 0.26/0.51         => ( ( divide_divide_real @ A @ A )
% 0.26/0.51            = zero_zero_real ) )
% 0.26/0.51        & ( ( A != zero_zero_real )
% 0.26/0.51         => ( ( divide_divide_real @ A @ A )
% 0.26/0.51            = one_one_real ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_self_if
% 0.26/0.51  thf(fact_2668_divide__self__if,axiom,
% 0.26/0.51      ! [A: rat] :
% 0.26/0.51        ( ( ( A = zero_zero_rat )
% 0.26/0.51         => ( ( divide_divide_rat @ A @ A )
% 0.26/0.51            = zero_zero_rat ) )
% 0.26/0.51        & ( ( A != zero_zero_rat )
% 0.26/0.51         => ( ( divide_divide_rat @ A @ A )
% 0.26/0.51            = one_one_rat ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_self_if
% 0.26/0.51  thf(fact_2669_divide__eq__eq__1,axiom,
% 0.26/0.51      ! [B: real,A: real] :
% 0.26/0.51        ( ( ( divide_divide_real @ B @ A )
% 0.26/0.51          = one_one_real )
% 0.26/0.51        = ( ( A != zero_zero_real )
% 0.26/0.51          & ( A = B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_eq_eq_1
% 0.26/0.51  thf(fact_2670_divide__eq__eq__1,axiom,
% 0.26/0.51      ! [B: rat,A: rat] :
% 0.26/0.51        ( ( ( divide_divide_rat @ B @ A )
% 0.26/0.51          = one_one_rat )
% 0.26/0.51        = ( ( A != zero_zero_rat )
% 0.26/0.51          & ( A = B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_eq_eq_1
% 0.26/0.51  thf(fact_2671_eq__divide__eq__1,axiom,
% 0.26/0.51      ! [B: real,A: real] :
% 0.26/0.51        ( ( one_one_real
% 0.26/0.51          = ( divide_divide_real @ B @ A ) )
% 0.26/0.51        = ( ( A != zero_zero_real )
% 0.26/0.51          & ( A = B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % eq_divide_eq_1
% 0.26/0.51  thf(fact_2672_eq__divide__eq__1,axiom,
% 0.26/0.51      ! [B: rat,A: rat] :
% 0.26/0.51        ( ( one_one_rat
% 0.26/0.51          = ( divide_divide_rat @ B @ A ) )
% 0.26/0.51        = ( ( A != zero_zero_rat )
% 0.26/0.51          & ( A = B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % eq_divide_eq_1
% 0.26/0.51  thf(fact_2673_one__divide__eq__0__iff,axiom,
% 0.26/0.51      ! [A: real] :
% 0.26/0.51        ( ( ( divide_divide_real @ one_one_real @ A )
% 0.26/0.51          = zero_zero_real )
% 0.26/0.51        = ( A = zero_zero_real ) ) ).
% 0.26/0.51  
% 0.26/0.51  % one_divide_eq_0_iff
% 0.26/0.51  thf(fact_2674_one__divide__eq__0__iff,axiom,
% 0.26/0.51      ! [A: rat] :
% 0.26/0.51        ( ( ( divide_divide_rat @ one_one_rat @ A )
% 0.26/0.51          = zero_zero_rat )
% 0.26/0.51        = ( A = zero_zero_rat ) ) ).
% 0.26/0.51  
% 0.26/0.51  % one_divide_eq_0_iff
% 0.26/0.51  thf(fact_2675_zero__eq__1__divide__iff,axiom,
% 0.26/0.51      ! [A: real] :
% 0.26/0.51        ( ( zero_zero_real
% 0.26/0.51          = ( divide_divide_real @ one_one_real @ A ) )
% 0.26/0.51        = ( A = zero_zero_real ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zero_eq_1_divide_iff
% 0.26/0.51  thf(fact_2676_zero__eq__1__divide__iff,axiom,
% 0.26/0.51      ! [A: rat] :
% 0.26/0.51        ( ( zero_zero_rat
% 0.26/0.51          = ( divide_divide_rat @ one_one_rat @ A ) )
% 0.26/0.51        = ( A = zero_zero_rat ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zero_eq_1_divide_iff
% 0.26/0.51  thf(fact_2677_add__gr__0,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 0.26/0.51        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.51          | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % add_gr_0
% 0.26/0.51  thf(fact_2678_Nat_Odiff__diff__right,axiom,
% 0.26/0.51      ! [K: nat,J: nat,I: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ K @ J )
% 0.26/0.51       => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.26/0.51          = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Nat.diff_diff_right
% 0.26/0.51  thf(fact_2679_Nat_Oadd__diff__assoc2,axiom,
% 0.26/0.51      ! [K: nat,J: nat,I: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ K @ J )
% 0.26/0.51       => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 0.26/0.51          = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Nat.add_diff_assoc2
% 0.26/0.51  thf(fact_2680_Nat_Oadd__diff__assoc,axiom,
% 0.26/0.51      ! [K: nat,J: nat,I: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ K @ J )
% 0.26/0.51       => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.26/0.51          = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Nat.add_diff_assoc
% 0.26/0.51  thf(fact_2681_div__neg__neg__trivial,axiom,
% 0.26/0.51      ! [K: int,L: int] :
% 0.26/0.51        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 0.26/0.51       => ( ( ord_less_int @ L @ K )
% 0.26/0.51         => ( ( divide_divide_int @ K @ L )
% 0.26/0.51            = zero_zero_int ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % div_neg_neg_trivial
% 0.26/0.51  thf(fact_2682_div__pos__pos__trivial,axiom,
% 0.26/0.51      ! [K: int,L: int] :
% 0.26/0.51        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.26/0.51       => ( ( ord_less_int @ K @ L )
% 0.26/0.51         => ( ( divide_divide_int @ K @ L )
% 0.26/0.51            = zero_zero_int ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % div_pos_pos_trivial
% 0.26/0.51  thf(fact_2683_semiring__norm_I2_J,axiom,
% 0.26/0.51      ( ( plus_plus_num @ one @ one )
% 0.26/0.51      = ( bit0 @ one ) ) ).
% 0.26/0.51  
% 0.26/0.51  % semiring_norm(2)
% 0.26/0.51  thf(fact_2684_zero__le__divide__1__iff,axiom,
% 0.26/0.51      ! [A: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 0.26/0.51        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zero_le_divide_1_iff
% 0.26/0.51  thf(fact_2685_zero__le__divide__1__iff,axiom,
% 0.26/0.51      ! [A: rat] :
% 0.26/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 0.26/0.51        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zero_le_divide_1_iff
% 0.26/0.51  thf(fact_2686_divide__le__0__1__iff,axiom,
% 0.26/0.51      ! [A: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 0.26/0.51        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_le_0_1_iff
% 0.26/0.51  thf(fact_2687_divide__le__0__1__iff,axiom,
% 0.26/0.51      ! [A: rat] :
% 0.26/0.51        ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 0.26/0.51        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_le_0_1_iff
% 0.26/0.51  thf(fact_2688_add__self__div__2,axiom,
% 0.26/0.51      ! [M: nat] :
% 0.26/0.51        ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.51        = M ) ).
% 0.26/0.51  
% 0.26/0.51  % add_self_div_2
% 0.26/0.51  thf(fact_2689_half__nonnegative__int__iff,axiom,
% 0.26/0.51      ! [K: int] :
% 0.26/0.51        ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.26/0.51        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.26/0.51  
% 0.26/0.51  % half_nonnegative_int_iff
% 0.26/0.51  thf(fact_2690_half__negative__int__iff,axiom,
% 0.26/0.51      ! [K: int] :
% 0.26/0.51        ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 0.26/0.51        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.26/0.51  
% 0.26/0.51  % half_negative_int_iff
% 0.26/0.51  thf(fact_2691_even__diff__nat,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 0.26/0.51        = ( ( ord_less_nat @ M @ N )
% 0.26/0.51          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % even_diff_nat
% 0.26/0.51  thf(fact_2692_Nat_Odiff__cancel,axiom,
% 0.26/0.51      ! [K: nat,M: nat,N: nat] :
% 0.26/0.51        ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.26/0.51        = ( minus_minus_nat @ M @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Nat.diff_cancel
% 0.26/0.51  thf(fact_2693_diff__cancel2,axiom,
% 0.26/0.51      ! [M: nat,K: nat,N: nat] :
% 0.26/0.51        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 0.26/0.51        = ( minus_minus_nat @ M @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % diff_cancel2
% 0.26/0.51  thf(fact_2694_diff__commute,axiom,
% 0.26/0.51      ! [I: nat,J: nat,K: nat] :
% 0.26/0.51        ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 0.26/0.51        = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 0.26/0.51  
% 0.26/0.51  % diff_commute
% 0.26/0.51  thf(fact_2695_diff__add__inverse,axiom,
% 0.26/0.51      ! [N: nat,M: nat] :
% 0.26/0.51        ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 0.26/0.51        = M ) ).
% 0.26/0.51  
% 0.26/0.51  % diff_add_inverse
% 0.26/0.51  thf(fact_2696_diff__add__inverse2,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 0.26/0.51        = M ) ).
% 0.26/0.51  
% 0.26/0.51  % diff_add_inverse2
% 0.26/0.51  thf(fact_2697_real__of__int__div4,axiom,
% 0.26/0.51      ! [N: int,X3: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X3 ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X3 ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % real_of_int_div4
% 0.26/0.51  thf(fact_2698_real__of__int__div,axiom,
% 0.26/0.51      ! [D3: int,N: int] :
% 0.26/0.51        ( ( dvd_dvd_int @ D3 @ N )
% 0.26/0.51       => ( ( ring_1_of_int_real @ ( divide_divide_int @ N @ D3 ) )
% 0.26/0.51          = ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ D3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % real_of_int_div
% 0.26/0.51  thf(fact_2699_add__One__commute,axiom,
% 0.26/0.51      ! [N: num] :
% 0.26/0.51        ( ( plus_plus_num @ one @ N )
% 0.26/0.51        = ( plus_plus_num @ N @ one ) ) ).
% 0.26/0.51  
% 0.26/0.51  % add_One_commute
% 0.26/0.51  thf(fact_2700_Euclid__induct,axiom,
% 0.26/0.51      ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.26/0.51        ( ! [A5: nat,B4: nat] :
% 0.26/0.51            ( ( P @ A5 @ B4 )
% 0.26/0.51            = ( P @ B4 @ A5 ) )
% 0.26/0.51       => ( ! [A5: nat] : ( P @ A5 @ zero_zero_nat )
% 0.26/0.51         => ( ! [A5: nat,B4: nat] :
% 0.26/0.51                ( ( P @ A5 @ B4 )
% 0.26/0.51               => ( P @ A5 @ ( plus_plus_nat @ A5 @ B4 ) ) )
% 0.26/0.51           => ( P @ A @ B ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Euclid_induct
% 0.26/0.51  thf(fact_2701_plus__nat_Oadd__0,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( plus_plus_nat @ zero_zero_nat @ N )
% 0.26/0.51        = N ) ).
% 0.26/0.51  
% 0.26/0.51  % plus_nat.add_0
% 0.26/0.51  thf(fact_2702_add__eq__self__zero,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( ( plus_plus_nat @ M @ N )
% 0.26/0.51          = M )
% 0.26/0.51       => ( N = zero_zero_nat ) ) ).
% 0.26/0.51  
% 0.26/0.51  % add_eq_self_zero
% 0.26/0.51  thf(fact_2703_diff__add__0,axiom,
% 0.26/0.51      ! [N: nat,M: nat] :
% 0.26/0.51        ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 0.26/0.51        = zero_zero_nat ) ).
% 0.26/0.51  
% 0.26/0.51  % diff_add_0
% 0.26/0.51  thf(fact_2704_less__add__eq__less,axiom,
% 0.26/0.51      ! [K: nat,L: nat,M: nat,N: nat] :
% 0.26/0.51        ( ( ord_less_nat @ K @ L )
% 0.26/0.51       => ( ( ( plus_plus_nat @ M @ L )
% 0.26/0.51            = ( plus_plus_nat @ K @ N ) )
% 0.26/0.51         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % less_add_eq_less
% 0.26/0.51  thf(fact_2705_trans__less__add2,axiom,
% 0.26/0.51      ! [I: nat,J: nat,M: nat] :
% 0.26/0.51        ( ( ord_less_nat @ I @ J )
% 0.26/0.51       => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % trans_less_add2
% 0.26/0.51  thf(fact_2706_trans__less__add1,axiom,
% 0.26/0.51      ! [I: nat,J: nat,M: nat] :
% 0.26/0.51        ( ( ord_less_nat @ I @ J )
% 0.26/0.51       => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % trans_less_add1
% 0.26/0.51  thf(fact_2707_add__less__mono1,axiom,
% 0.26/0.51      ! [I: nat,J: nat,K: nat] :
% 0.26/0.51        ( ( ord_less_nat @ I @ J )
% 0.26/0.51       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % add_less_mono1
% 0.26/0.51  thf(fact_2708_not__add__less2,axiom,
% 0.26/0.51      ! [J: nat,I: nat] :
% 0.26/0.51        ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 0.26/0.51  
% 0.26/0.51  % not_add_less2
% 0.26/0.51  thf(fact_2709_not__add__less1,axiom,
% 0.26/0.51      ! [I: nat,J: nat] :
% 0.26/0.51        ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 0.26/0.51  
% 0.26/0.51  % not_add_less1
% 0.26/0.51  thf(fact_2710_add__less__mono,axiom,
% 0.26/0.51      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.26/0.51        ( ( ord_less_nat @ I @ J )
% 0.26/0.51       => ( ( ord_less_nat @ K @ L )
% 0.26/0.51         => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % add_less_mono
% 0.26/0.51  thf(fact_2711_add__lessD1,axiom,
% 0.26/0.51      ! [I: nat,J: nat,K: nat] :
% 0.26/0.51        ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 0.26/0.51       => ( ord_less_nat @ I @ K ) ) ).
% 0.26/0.51  
% 0.26/0.51  % add_lessD1
% 0.26/0.51  thf(fact_2712_add__diff__inverse__nat,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ~ ( ord_less_nat @ M @ N )
% 0.26/0.51       => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 0.26/0.51          = M ) ) ).
% 0.26/0.51  
% 0.26/0.51  % add_diff_inverse_nat
% 0.26/0.51  thf(fact_2713_less__diff__conv,axiom,
% 0.26/0.51      ! [I: nat,J: nat,K: nat] :
% 0.26/0.51        ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.26/0.51        = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 0.26/0.51  
% 0.26/0.51  % less_diff_conv
% 0.26/0.51  thf(fact_2714_add__leE,axiom,
% 0.26/0.51      ! [M: nat,K: nat,N: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.26/0.51       => ~ ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.51           => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % add_leE
% 0.26/0.51  thf(fact_2715_le__add1,axiom,
% 0.26/0.51      ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 0.26/0.51  
% 0.26/0.51  % le_add1
% 0.26/0.51  thf(fact_2716_le__add2,axiom,
% 0.26/0.51      ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % le_add2
% 0.26/0.51  thf(fact_2717_add__leD1,axiom,
% 0.26/0.51      ! [M: nat,K: nat,N: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.26/0.51       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % add_leD1
% 0.26/0.51  thf(fact_2718_add__leD2,axiom,
% 0.26/0.51      ! [M: nat,K: nat,N: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.26/0.51       => ( ord_less_eq_nat @ K @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % add_leD2
% 0.26/0.51  thf(fact_2719_le__Suc__ex,axiom,
% 0.26/0.51      ! [K: nat,L: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ K @ L )
% 0.26/0.51       => ? [N2: nat] :
% 0.26/0.51            ( L
% 0.26/0.51            = ( plus_plus_nat @ K @ N2 ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % le_Suc_ex
% 0.26/0.51  thf(fact_2720_add__le__mono,axiom,
% 0.26/0.51      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.51       => ( ( ord_less_eq_nat @ K @ L )
% 0.26/0.51         => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % add_le_mono
% 0.26/0.51  thf(fact_2721_add__le__mono1,axiom,
% 0.26/0.51      ! [I: nat,J: nat,K: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.51       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % add_le_mono1
% 0.26/0.51  thf(fact_2722_trans__le__add1,axiom,
% 0.26/0.51      ! [I: nat,J: nat,M: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.51       => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % trans_le_add1
% 0.26/0.51  thf(fact_2723_trans__le__add2,axiom,
% 0.26/0.51      ! [I: nat,J: nat,M: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.51       => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % trans_le_add2
% 0.26/0.51  thf(fact_2724_nat__le__iff__add,axiom,
% 0.26/0.51      ( ord_less_eq_nat
% 0.26/0.51      = ( ^ [M3: nat,N3: nat] :
% 0.26/0.51          ? [K3: nat] :
% 0.26/0.51            ( N3
% 0.26/0.51            = ( plus_plus_nat @ M3 @ K3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % nat_le_iff_add
% 0.26/0.51  thf(fact_2725_Nat_Ole__imp__diff__is__add,axiom,
% 0.26/0.51      ! [I: nat,J: nat,K: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.51       => ( ( ( minus_minus_nat @ J @ I )
% 0.26/0.51            = K )
% 0.26/0.51          = ( J
% 0.26/0.51            = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Nat.le_imp_diff_is_add
% 0.26/0.51  thf(fact_2726_Nat_Odiff__add__assoc2,axiom,
% 0.26/0.51      ! [K: nat,J: nat,I: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ K @ J )
% 0.26/0.51       => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 0.26/0.51          = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Nat.diff_add_assoc2
% 0.26/0.51  thf(fact_2727_Nat_Odiff__add__assoc,axiom,
% 0.26/0.51      ! [K: nat,J: nat,I: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ K @ J )
% 0.26/0.51       => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 0.26/0.51          = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Nat.diff_add_assoc
% 0.26/0.51  thf(fact_2728_Nat_Ole__diff__conv2,axiom,
% 0.26/0.51      ! [K: nat,J: nat,I: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ K @ J )
% 0.26/0.51       => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.26/0.51          = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Nat.le_diff_conv2
% 0.26/0.51  thf(fact_2729_le__diff__conv,axiom,
% 0.26/0.51      ! [J: nat,K: nat,I: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 0.26/0.51        = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % le_diff_conv
% 0.26/0.51  thf(fact_2730_real__sqrt__divide,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( sqrt @ ( divide_divide_real @ X3 @ Y3 ) )
% 0.26/0.51        = ( divide_divide_real @ ( sqrt @ X3 ) @ ( sqrt @ Y3 ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % real_sqrt_divide
% 0.26/0.51  thf(fact_2731_iadd__is__0,axiom,
% 0.26/0.51      ! [M: extended_enat,N: extended_enat] :
% 0.26/0.51        ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 0.26/0.51          = zero_z5237406670263579293d_enat )
% 0.26/0.51        = ( ( M = zero_z5237406670263579293d_enat )
% 0.26/0.51          & ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % iadd_is_0
% 0.26/0.51  thf(fact_2732_add__diff__assoc__enat,axiom,
% 0.26/0.51      ! [Z: extended_enat,Y3: extended_enat,X3: extended_enat] :
% 0.26/0.51        ( ( ord_le2932123472753598470d_enat @ Z @ Y3 )
% 0.26/0.51       => ( ( plus_p3455044024723400733d_enat @ X3 @ ( minus_3235023915231533773d_enat @ Y3 @ Z ) )
% 0.26/0.51          = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X3 @ Y3 ) @ Z ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % add_diff_assoc_enat
% 0.26/0.51  thf(fact_2733_real__of__int__div2,axiom,
% 0.26/0.51      ! [N: int,X3: 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 @ X3 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % real_of_int_div2
% 0.26/0.51  thf(fact_2734_real__of__int__div3,axiom,
% 0.26/0.51      ! [N: int,X3: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X3 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X3 ) ) ) @ one_one_real ) ).
% 0.26/0.51  
% 0.26/0.51  % real_of_int_div3
% 0.26/0.51  thf(fact_2735_ln__div,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.51       => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.51         => ( ( ln_ln_real @ ( divide_divide_real @ X3 @ Y3 ) )
% 0.26/0.51            = ( minus_minus_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y3 ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % ln_div
% 0.26/0.51  thf(fact_2736_less__imp__add__positive,axiom,
% 0.26/0.51      ! [I: nat,J: nat] :
% 0.26/0.51        ( ( ord_less_nat @ I @ J )
% 0.26/0.51       => ? [K2: nat] :
% 0.26/0.51            ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.26/0.51            & ( ( plus_plus_nat @ I @ K2 )
% 0.26/0.51              = J ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % less_imp_add_positive
% 0.26/0.51  thf(fact_2737_nat__diff__split__asm,axiom,
% 0.26/0.51      ! [P: nat > $o,A: nat,B: nat] :
% 0.26/0.51        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 0.26/0.51        = ( ~ ( ( ( ord_less_nat @ A @ B )
% 0.26/0.51                & ~ ( P @ zero_zero_nat ) )
% 0.26/0.51              | ? [D4: nat] :
% 0.26/0.51                  ( ( A
% 0.26/0.51                    = ( plus_plus_nat @ B @ D4 ) )
% 0.26/0.51                  & ~ ( P @ D4 ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % nat_diff_split_asm
% 0.26/0.51  thf(fact_2738_nat__diff__split,axiom,
% 0.26/0.51      ! [P: nat > $o,A: nat,B: nat] :
% 0.26/0.51        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 0.26/0.51        = ( ( ( ord_less_nat @ A @ B )
% 0.26/0.51           => ( P @ zero_zero_nat ) )
% 0.26/0.51          & ! [D4: nat] :
% 0.26/0.51              ( ( A
% 0.26/0.51                = ( plus_plus_nat @ B @ D4 ) )
% 0.26/0.51             => ( P @ D4 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % nat_diff_split
% 0.26/0.51  thf(fact_2739_mono__nat__linear__lb,axiom,
% 0.26/0.51      ! [F: nat > nat,M: nat,K: nat] :
% 0.26/0.51        ( ! [M4: nat,N2: nat] :
% 0.26/0.51            ( ( ord_less_nat @ M4 @ N2 )
% 0.26/0.51           => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N2 ) ) )
% 0.26/0.51       => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % mono_nat_linear_lb
% 0.26/0.51  thf(fact_2740_less__diff__conv2,axiom,
% 0.26/0.51      ! [K: nat,J: nat,I: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ K @ J )
% 0.26/0.51       => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 0.26/0.51          = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % less_diff_conv2
% 0.26/0.51  thf(fact_2741_int__ops_I5_J,axiom,
% 0.26/0.51      ! [A: nat,B: nat] :
% 0.26/0.51        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 0.26/0.51        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % int_ops(5)
% 0.26/0.51  thf(fact_2742_int__plus,axiom,
% 0.26/0.51      ! [N: nat,M: nat] :
% 0.26/0.51        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
% 0.26/0.51        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % int_plus
% 0.26/0.51  thf(fact_2743_zadd__int__left,axiom,
% 0.26/0.51      ! [M: nat,N: nat,Z: int] :
% 0.26/0.51        ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z ) )
% 0.26/0.51        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zadd_int_left
% 0.26/0.51  thf(fact_2744_ln__diff__le,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.51       => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.51         => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y3 ) ) @ ( divide_divide_real @ ( minus_minus_real @ X3 @ Y3 ) @ Y3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % ln_diff_le
% 0.26/0.51  thf(fact_2745_linordered__field__no__ub,axiom,
% 0.26/0.51      ! [X6: real] :
% 0.26/0.51      ? [X_1: real] : ( ord_less_real @ X6 @ X_1 ) ).
% 0.26/0.51  
% 0.26/0.51  % linordered_field_no_ub
% 0.26/0.51  thf(fact_2746_linordered__field__no__ub,axiom,
% 0.26/0.51      ! [X6: rat] :
% 0.26/0.51      ? [X_1: rat] : ( ord_less_rat @ X6 @ X_1 ) ).
% 0.26/0.51  
% 0.26/0.51  % linordered_field_no_ub
% 0.26/0.51  thf(fact_2747_linordered__field__no__lb,axiom,
% 0.26/0.51      ! [X6: real] :
% 0.26/0.51      ? [Y4: real] : ( ord_less_real @ Y4 @ X6 ) ).
% 0.26/0.51  
% 0.26/0.51  % linordered_field_no_lb
% 0.26/0.51  thf(fact_2748_linordered__field__no__lb,axiom,
% 0.26/0.51      ! [X6: rat] :
% 0.26/0.51      ? [Y4: rat] : ( ord_less_rat @ Y4 @ X6 ) ).
% 0.26/0.51  
% 0.26/0.51  % linordered_field_no_lb
% 0.26/0.51  thf(fact_2749_real__div__sqrt,axiom,
% 0.26/0.51      ! [X3: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.51       => ( ( divide_divide_real @ X3 @ ( sqrt @ X3 ) )
% 0.26/0.51          = ( sqrt @ X3 ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % real_div_sqrt
% 0.26/0.51  thf(fact_2750_real__of__nat__div4,axiom,
% 0.26/0.51      ! [N: nat,X3: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X3 ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X3 ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % real_of_nat_div4
% 0.26/0.51  thf(fact_2751_real__of__nat__div,axiom,
% 0.26/0.51      ! [D3: nat,N: nat] :
% 0.26/0.51        ( ( dvd_dvd_nat @ D3 @ N )
% 0.26/0.51       => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ D3 ) )
% 0.26/0.51          = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ D3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % real_of_nat_div
% 0.26/0.51  thf(fact_2752_nat__int__add,axiom,
% 0.26/0.51      ! [A: nat,B: nat] :
% 0.26/0.51        ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 0.26/0.51        = ( plus_plus_nat @ A @ B ) ) ).
% 0.26/0.51  
% 0.26/0.51  % nat_int_add
% 0.26/0.51  thf(fact_2753_nat__1__add__1,axiom,
% 0.26/0.51      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.26/0.51      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % nat_1_add_1
% 0.26/0.51  thf(fact_2754_real__of__nat__div2,axiom,
% 0.26/0.51      ! [N: nat,X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X3 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % real_of_nat_div2
% 0.26/0.51  thf(fact_2755_nat__div__distrib_H,axiom,
% 0.26/0.51      ! [Y3: int,X3: int] :
% 0.26/0.51        ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 0.26/0.51       => ( ( nat2 @ ( divide_divide_int @ X3 @ Y3 ) )
% 0.26/0.51          = ( divide_divide_nat @ ( nat2 @ X3 ) @ ( nat2 @ Y3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % nat_div_distrib'
% 0.26/0.51  thf(fact_2756_nat__div__distrib,axiom,
% 0.26/0.51      ! [X3: int,Y3: int] :
% 0.26/0.51        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.26/0.51       => ( ( nat2 @ ( divide_divide_int @ X3 @ Y3 ) )
% 0.26/0.51          = ( divide_divide_nat @ ( nat2 @ X3 ) @ ( nat2 @ Y3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % nat_div_distrib
% 0.26/0.51  thf(fact_2757_real__of__nat__div3,axiom,
% 0.26/0.51      ! [N: nat,X3: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X3 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X3 ) ) ) @ one_one_real ) ).
% 0.26/0.51  
% 0.26/0.51  % real_of_nat_div3
% 0.26/0.51  thf(fact_2758_log__base__change,axiom,
% 0.26/0.51      ! [A: real,B: real,X3: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.51       => ( ( A != one_one_real )
% 0.26/0.51         => ( ( log @ B @ X3 )
% 0.26/0.51            = ( divide_divide_real @ ( log @ A @ X3 ) @ ( log @ A @ B ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % log_base_change
% 0.26/0.51  thf(fact_2759_log__divide,axiom,
% 0.26/0.51      ! [A: real,X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.51       => ( ( A != one_one_real )
% 0.26/0.51         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.51           => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.51             => ( ( log @ A @ ( divide_divide_real @ X3 @ Y3 ) )
% 0.26/0.51                = ( minus_minus_real @ ( log @ A @ X3 ) @ ( log @ A @ Y3 ) ) ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % log_divide
% 0.26/0.51  thf(fact_2760_nat__add__distrib,axiom,
% 0.26/0.51      ! [Z: int,Z5: int] :
% 0.26/0.51        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.26/0.51       => ( ( ord_less_eq_int @ zero_zero_int @ Z5 )
% 0.26/0.51         => ( ( nat2 @ ( plus_plus_int @ Z @ Z5 ) )
% 0.26/0.51            = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z5 ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % nat_add_distrib
% 0.26/0.51  thf(fact_2761_exp__add__not__zero__imp__right,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 0.26/0.51         != zero_zero_nat )
% 0.26/0.51       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.51         != zero_zero_nat ) ) ).
% 0.26/0.51  
% 0.26/0.51  % exp_add_not_zero_imp_right
% 0.26/0.51  thf(fact_2762_exp__add__not__zero__imp__right,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 0.26/0.51         != zero_zero_int )
% 0.26/0.51       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.26/0.51         != zero_zero_int ) ) ).
% 0.26/0.51  
% 0.26/0.51  % exp_add_not_zero_imp_right
% 0.26/0.51  thf(fact_2763_exp__add__not__zero__imp__left,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 0.26/0.51         != zero_zero_nat )
% 0.26/0.51       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 0.26/0.51         != zero_zero_nat ) ) ).
% 0.26/0.51  
% 0.26/0.51  % exp_add_not_zero_imp_left
% 0.26/0.51  thf(fact_2764_exp__add__not__zero__imp__left,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 0.26/0.51         != zero_zero_int )
% 0.26/0.51       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 0.26/0.51         != zero_zero_int ) ) ).
% 0.26/0.51  
% 0.26/0.51  % exp_add_not_zero_imp_left
% 0.26/0.51  thf(fact_2765_div__exp__eq,axiom,
% 0.26/0.51      ! [A: nat,M: nat,N: nat] :
% 0.26/0.51        ( ( 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 ) )
% 0.26/0.51        = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % div_exp_eq
% 0.26/0.51  thf(fact_2766_div__exp__eq,axiom,
% 0.26/0.51      ! [A: int,M: nat,N: nat] :
% 0.26/0.51        ( ( 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 ) )
% 0.26/0.51        = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % div_exp_eq
% 0.26/0.51  thf(fact_2767_nat__induct2,axiom,
% 0.26/0.51      ! [P: nat > $o,N: nat] :
% 0.26/0.51        ( ( P @ zero_zero_nat )
% 0.26/0.51       => ( ( P @ one_one_nat )
% 0.26/0.51         => ( ! [N2: nat] :
% 0.26/0.51                ( ( P @ N2 )
% 0.26/0.51               => ( P @ ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.51           => ( P @ N ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % nat_induct2
% 0.26/0.51  thf(fact_2768_log__base__pow,axiom,
% 0.26/0.51      ! [A: real,N: nat,X3: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.51       => ( ( log @ ( power_power_real @ A @ N ) @ X3 )
% 0.26/0.51          = ( divide_divide_real @ ( log @ A @ X3 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % log_base_pow
% 0.26/0.51  thf(fact_2769_lemma__real__divide__sqrt__less,axiom,
% 0.26/0.51      ! [U: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ U )
% 0.26/0.51       => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 0.26/0.51  
% 0.26/0.51  % lemma_real_divide_sqrt_less
% 0.26/0.51  thf(fact_2770_ln__sqrt,axiom,
% 0.26/0.51      ! [X3: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.51       => ( ( ln_ln_real @ ( sqrt @ X3 ) )
% 0.26/0.51          = ( divide_divide_real @ ( ln_ln_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % ln_sqrt
% 0.26/0.51  thf(fact_2771_dvd__field__iff,axiom,
% 0.26/0.51      ( dvd_dvd_real
% 0.26/0.51      = ( ^ [A4: real,B3: real] :
% 0.26/0.51            ( ( A4 = zero_zero_real )
% 0.26/0.51           => ( B3 = zero_zero_real ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % dvd_field_iff
% 0.26/0.51  thf(fact_2772_dvd__field__iff,axiom,
% 0.26/0.51      ( dvd_dvd_rat
% 0.26/0.51      = ( ^ [A4: rat,B3: rat] :
% 0.26/0.51            ( ( A4 = zero_zero_rat )
% 0.26/0.51           => ( B3 = zero_zero_rat ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % dvd_field_iff
% 0.26/0.51  thf(fact_2773_ex__power__ivl2,axiom,
% 0.26/0.51      ! [B: nat,K: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.26/0.51       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.26/0.51         => ? [N2: nat] :
% 0.26/0.51              ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 0.26/0.51              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % ex_power_ivl2
% 0.26/0.51  thf(fact_2774_ex__power__ivl1,axiom,
% 0.26/0.51      ! [B: nat,K: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.26/0.51       => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 0.26/0.51         => ? [N2: nat] :
% 0.26/0.51              ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 0.26/0.51              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % ex_power_ivl1
% 0.26/0.51  thf(fact_2775_divide__right__mono__neg,axiom,
% 0.26/0.51      ! [A: real,B: real,C: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.51       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.26/0.51         => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_right_mono_neg
% 0.26/0.51  thf(fact_2776_divide__right__mono__neg,axiom,
% 0.26/0.51      ! [A: rat,B: rat,C: rat] :
% 0.26/0.51        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.51       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.26/0.51         => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_right_mono_neg
% 0.26/0.51  thf(fact_2777_divide__nonpos__nonpos,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 0.26/0.51       => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 0.26/0.51         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_nonpos_nonpos
% 0.26/0.51  thf(fact_2778_divide__nonpos__nonpos,axiom,
% 0.26/0.51      ! [X3: rat,Y3: rat] :
% 0.26/0.51        ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 0.26/0.51       => ( ( ord_less_eq_rat @ Y3 @ zero_zero_rat )
% 0.26/0.51         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_nonpos_nonpos
% 0.26/0.51  thf(fact_2779_divide__nonpos__nonneg,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 0.26/0.51       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.51         => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y3 ) @ zero_zero_real ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_nonpos_nonneg
% 0.26/0.51  thf(fact_2780_divide__nonpos__nonneg,axiom,
% 0.26/0.51      ! [X3: rat,Y3: rat] :
% 0.26/0.51        ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 0.26/0.51       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 0.26/0.51         => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_nonpos_nonneg
% 0.26/0.51  thf(fact_2781_divide__nonneg__nonpos,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.51       => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 0.26/0.51         => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y3 ) @ zero_zero_real ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_nonneg_nonpos
% 0.26/0.51  thf(fact_2782_divide__nonneg__nonpos,axiom,
% 0.26/0.51      ! [X3: rat,Y3: rat] :
% 0.26/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.26/0.51       => ( ( ord_less_eq_rat @ Y3 @ zero_zero_rat )
% 0.26/0.51         => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_nonneg_nonpos
% 0.26/0.51  thf(fact_2783_divide__nonneg__nonneg,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.51       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.51         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_nonneg_nonneg
% 0.26/0.51  thf(fact_2784_divide__nonneg__nonneg,axiom,
% 0.26/0.51      ! [X3: rat,Y3: rat] :
% 0.26/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.26/0.51       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 0.26/0.51         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_nonneg_nonneg
% 0.26/0.51  thf(fact_2785_zero__le__divide__iff,axiom,
% 0.26/0.51      ! [A: real,B: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 0.26/0.51        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.51            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 0.26/0.51          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.26/0.51            & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zero_le_divide_iff
% 0.26/0.51  thf(fact_2786_zero__le__divide__iff,axiom,
% 0.26/0.51      ! [A: rat,B: rat] :
% 0.26/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 0.26/0.51        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.51            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.26/0.51          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.26/0.51            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zero_le_divide_iff
% 0.26/0.51  thf(fact_2787_divide__right__mono,axiom,
% 0.26/0.51      ! [A: real,B: real,C: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.51       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.26/0.51         => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_right_mono
% 0.26/0.51  thf(fact_2788_divide__right__mono,axiom,
% 0.26/0.51      ! [A: rat,B: rat,C: rat] :
% 0.26/0.51        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.51       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.26/0.51         => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_right_mono
% 0.26/0.51  thf(fact_2789_divide__le__0__iff,axiom,
% 0.26/0.51      ! [A: real,B: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 0.26/0.51        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.51            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.26/0.51          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.26/0.51            & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_le_0_iff
% 0.26/0.51  thf(fact_2790_divide__le__0__iff,axiom,
% 0.26/0.51      ! [A: rat,B: rat] :
% 0.26/0.51        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 0.26/0.51        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.51            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.26/0.51          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.26/0.51            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_le_0_iff
% 0.26/0.51  thf(fact_2791_divide__strict__right__mono__neg,axiom,
% 0.26/0.51      ! [B: real,A: real,C: real] :
% 0.26/0.51        ( ( ord_less_real @ B @ A )
% 0.26/0.51       => ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.51         => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_strict_right_mono_neg
% 0.26/0.51  thf(fact_2792_divide__strict__right__mono__neg,axiom,
% 0.26/0.51      ! [B: rat,A: rat,C: rat] :
% 0.26/0.51        ( ( ord_less_rat @ B @ A )
% 0.26/0.51       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.51         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_strict_right_mono_neg
% 0.26/0.51  thf(fact_2793_divide__strict__right__mono,axiom,
% 0.26/0.51      ! [A: real,B: real,C: real] :
% 0.26/0.51        ( ( ord_less_real @ A @ B )
% 0.26/0.51       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.51         => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_strict_right_mono
% 0.26/0.51  thf(fact_2794_divide__strict__right__mono,axiom,
% 0.26/0.51      ! [A: rat,B: rat,C: rat] :
% 0.26/0.51        ( ( ord_less_rat @ A @ B )
% 0.26/0.51       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.51         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_strict_right_mono
% 0.26/0.51  thf(fact_2795_zero__less__divide__iff,axiom,
% 0.26/0.51      ! [A: real,B: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 0.26/0.51        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.51            & ( ord_less_real @ zero_zero_real @ B ) )
% 0.26/0.51          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.26/0.51            & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zero_less_divide_iff
% 0.26/0.51  thf(fact_2796_zero__less__divide__iff,axiom,
% 0.26/0.51      ! [A: rat,B: rat] :
% 0.26/0.51        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 0.26/0.51        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.51            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 0.26/0.51          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.26/0.51            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zero_less_divide_iff
% 0.26/0.51  thf(fact_2797_divide__less__cancel,axiom,
% 0.26/0.51      ! [A: real,C: real,B: real] :
% 0.26/0.51        ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 0.26/0.51        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.51           => ( ord_less_real @ A @ B ) )
% 0.26/0.51          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.51           => ( ord_less_real @ B @ A ) )
% 0.26/0.51          & ( C != zero_zero_real ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_less_cancel
% 0.26/0.51  thf(fact_2798_divide__less__cancel,axiom,
% 0.26/0.51      ! [A: rat,C: rat,B: rat] :
% 0.26/0.51        ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 0.26/0.51        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.51           => ( ord_less_rat @ A @ B ) )
% 0.26/0.51          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.51           => ( ord_less_rat @ B @ A ) )
% 0.26/0.51          & ( C != zero_zero_rat ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_less_cancel
% 0.26/0.51  thf(fact_2799_divide__less__0__iff,axiom,
% 0.26/0.51      ! [A: real,B: real] :
% 0.26/0.51        ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 0.26/0.51        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.51            & ( ord_less_real @ B @ zero_zero_real ) )
% 0.26/0.51          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.26/0.51            & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_less_0_iff
% 0.26/0.51  thf(fact_2800_divide__less__0__iff,axiom,
% 0.26/0.51      ! [A: rat,B: rat] :
% 0.26/0.51        ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 0.26/0.51        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.51            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 0.26/0.51          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.26/0.51            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_less_0_iff
% 0.26/0.51  thf(fact_2801_divide__pos__pos,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.51       => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.51         => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_pos_pos
% 0.26/0.51  thf(fact_2802_divide__pos__pos,axiom,
% 0.26/0.51      ! [X3: rat,Y3: rat] :
% 0.26/0.51        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 0.26/0.51       => ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 0.26/0.51         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_pos_pos
% 0.26/0.51  thf(fact_2803_divide__pos__neg,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.51       => ( ( ord_less_real @ Y3 @ zero_zero_real )
% 0.26/0.51         => ( ord_less_real @ ( divide_divide_real @ X3 @ Y3 ) @ zero_zero_real ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_pos_neg
% 0.26/0.51  thf(fact_2804_divide__pos__neg,axiom,
% 0.26/0.51      ! [X3: rat,Y3: rat] :
% 0.26/0.51        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 0.26/0.51       => ( ( ord_less_rat @ Y3 @ zero_zero_rat )
% 0.26/0.51         => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_pos_neg
% 0.26/0.51  thf(fact_2805_divide__neg__pos,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_real @ X3 @ zero_zero_real )
% 0.26/0.51       => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.51         => ( ord_less_real @ ( divide_divide_real @ X3 @ Y3 ) @ zero_zero_real ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_neg_pos
% 0.26/0.51  thf(fact_2806_divide__neg__pos,axiom,
% 0.26/0.51      ! [X3: rat,Y3: rat] :
% 0.26/0.51        ( ( ord_less_rat @ X3 @ zero_zero_rat )
% 0.26/0.51       => ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 0.26/0.51         => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_neg_pos
% 0.26/0.51  thf(fact_2807_divide__neg__neg,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_real @ X3 @ zero_zero_real )
% 0.26/0.51       => ( ( ord_less_real @ Y3 @ zero_zero_real )
% 0.26/0.51         => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_neg_neg
% 0.26/0.51  thf(fact_2808_divide__neg__neg,axiom,
% 0.26/0.51      ! [X3: rat,Y3: rat] :
% 0.26/0.51        ( ( ord_less_rat @ X3 @ zero_zero_rat )
% 0.26/0.51       => ( ( ord_less_rat @ Y3 @ zero_zero_rat )
% 0.26/0.51         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_neg_neg
% 0.26/0.51  thf(fact_2809_right__inverse__eq,axiom,
% 0.26/0.51      ! [B: complex,A: complex] :
% 0.26/0.51        ( ( B != zero_zero_complex )
% 0.26/0.51       => ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.26/0.51            = one_one_complex )
% 0.26/0.51          = ( A = B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % right_inverse_eq
% 0.26/0.51  thf(fact_2810_right__inverse__eq,axiom,
% 0.26/0.51      ! [B: real,A: real] :
% 0.26/0.51        ( ( B != zero_zero_real )
% 0.26/0.51       => ( ( ( divide_divide_real @ A @ B )
% 0.26/0.51            = one_one_real )
% 0.26/0.51          = ( A = B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % right_inverse_eq
% 0.26/0.51  thf(fact_2811_right__inverse__eq,axiom,
% 0.26/0.51      ! [B: rat,A: rat] :
% 0.26/0.51        ( ( B != zero_zero_rat )
% 0.26/0.51       => ( ( ( divide_divide_rat @ A @ B )
% 0.26/0.51            = one_one_rat )
% 0.26/0.51          = ( A = B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % right_inverse_eq
% 0.26/0.51  thf(fact_2812_sqrt__sum__squares__half__less,axiom,
% 0.26/0.51      ! [X3: real,U: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_real @ X3 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.51       => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.51         => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.51           => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.51             => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % sqrt_sum_squares_half_less
% 0.26/0.51  thf(fact_2813_ceiling__log2__div2,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.51       => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.26/0.51          = ( 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 ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % ceiling_log2_div2
% 0.26/0.51  thf(fact_2814_field__le__epsilon,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ! [E: real] :
% 0.26/0.51            ( ( ord_less_real @ zero_zero_real @ E )
% 0.26/0.51           => ( ord_less_eq_real @ X3 @ ( plus_plus_real @ Y3 @ E ) ) )
% 0.26/0.51       => ( ord_less_eq_real @ X3 @ Y3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % field_le_epsilon
% 0.26/0.51  thf(fact_2815_field__le__epsilon,axiom,
% 0.26/0.51      ! [X3: rat,Y3: rat] :
% 0.26/0.51        ( ! [E: rat] :
% 0.26/0.51            ( ( ord_less_rat @ zero_zero_rat @ E )
% 0.26/0.51           => ( ord_less_eq_rat @ X3 @ ( plus_plus_rat @ Y3 @ E ) ) )
% 0.26/0.51       => ( ord_less_eq_rat @ X3 @ Y3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % field_le_epsilon
% 0.26/0.51  thf(fact_2816_frac__le,axiom,
% 0.26/0.51      ! [Y3: real,X3: real,W: real,Z: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.51       => ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.26/0.51         => ( ( ord_less_real @ zero_zero_real @ W )
% 0.26/0.51           => ( ( ord_less_eq_real @ W @ Z )
% 0.26/0.51             => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Z ) @ ( divide_divide_real @ Y3 @ W ) ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % frac_le
% 0.26/0.51  thf(fact_2817_frac__le,axiom,
% 0.26/0.51      ! [Y3: rat,X3: rat,W: rat,Z: rat] :
% 0.26/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 0.26/0.51       => ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.26/0.51         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 0.26/0.51           => ( ( ord_less_eq_rat @ W @ Z )
% 0.26/0.51             => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Z ) @ ( divide_divide_rat @ Y3 @ W ) ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % frac_le
% 0.26/0.51  thf(fact_2818_frac__less,axiom,
% 0.26/0.51      ! [X3: real,Y3: real,W: real,Z: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.51       => ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.51         => ( ( ord_less_real @ zero_zero_real @ W )
% 0.26/0.51           => ( ( ord_less_eq_real @ W @ Z )
% 0.26/0.51             => ( ord_less_real @ ( divide_divide_real @ X3 @ Z ) @ ( divide_divide_real @ Y3 @ W ) ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % frac_less
% 0.26/0.51  thf(fact_2819_frac__less,axiom,
% 0.26/0.51      ! [X3: rat,Y3: rat,W: rat,Z: rat] :
% 0.26/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.26/0.51       => ( ( ord_less_rat @ X3 @ Y3 )
% 0.26/0.51         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 0.26/0.51           => ( ( ord_less_eq_rat @ W @ Z )
% 0.26/0.51             => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Z ) @ ( divide_divide_rat @ Y3 @ W ) ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % frac_less
% 0.26/0.51  thf(fact_2820_frac__less2,axiom,
% 0.26/0.51      ! [X3: real,Y3: real,W: real,Z: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.51       => ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.26/0.51         => ( ( ord_less_real @ zero_zero_real @ W )
% 0.26/0.51           => ( ( ord_less_real @ W @ Z )
% 0.26/0.51             => ( ord_less_real @ ( divide_divide_real @ X3 @ Z ) @ ( divide_divide_real @ Y3 @ W ) ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % frac_less2
% 0.26/0.51  thf(fact_2821_frac__less2,axiom,
% 0.26/0.51      ! [X3: rat,Y3: rat,W: rat,Z: rat] :
% 0.26/0.51        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 0.26/0.51       => ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.26/0.51         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 0.26/0.51           => ( ( ord_less_rat @ W @ Z )
% 0.26/0.51             => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Z ) @ ( divide_divide_rat @ Y3 @ W ) ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % frac_less2
% 0.26/0.51  thf(fact_2822_divide__le__cancel,axiom,
% 0.26/0.51      ! [A: real,C: real,B: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 0.26/0.51        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.51           => ( ord_less_eq_real @ A @ B ) )
% 0.26/0.51          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.51           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_le_cancel
% 0.26/0.51  thf(fact_2823_divide__le__cancel,axiom,
% 0.26/0.51      ! [A: rat,C: rat,B: rat] :
% 0.26/0.51        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 0.26/0.51        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.51           => ( ord_less_eq_rat @ A @ B ) )
% 0.26/0.51          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.51           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_le_cancel
% 0.26/0.51  thf(fact_2824_divide__nonneg__neg,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.51       => ( ( ord_less_real @ Y3 @ zero_zero_real )
% 0.26/0.51         => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y3 ) @ zero_zero_real ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_nonneg_neg
% 0.26/0.51  thf(fact_2825_divide__nonneg__neg,axiom,
% 0.26/0.51      ! [X3: rat,Y3: rat] :
% 0.26/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.26/0.51       => ( ( ord_less_rat @ Y3 @ zero_zero_rat )
% 0.26/0.51         => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_nonneg_neg
% 0.26/0.51  thf(fact_2826_divide__nonneg__pos,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.51       => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.51         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_nonneg_pos
% 0.26/0.51  thf(fact_2827_divide__nonneg__pos,axiom,
% 0.26/0.51      ! [X3: rat,Y3: rat] :
% 0.26/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.26/0.51       => ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 0.26/0.51         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_nonneg_pos
% 0.26/0.51  thf(fact_2828_divide__nonpos__neg,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 0.26/0.51       => ( ( ord_less_real @ Y3 @ zero_zero_real )
% 0.26/0.51         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_nonpos_neg
% 0.26/0.51  thf(fact_2829_divide__nonpos__neg,axiom,
% 0.26/0.51      ! [X3: rat,Y3: rat] :
% 0.26/0.51        ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 0.26/0.51       => ( ( ord_less_rat @ Y3 @ zero_zero_rat )
% 0.26/0.51         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_nonpos_neg
% 0.26/0.51  thf(fact_2830_divide__nonpos__pos,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 0.26/0.51       => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.51         => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y3 ) @ zero_zero_real ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_nonpos_pos
% 0.26/0.51  thf(fact_2831_divide__nonpos__pos,axiom,
% 0.26/0.51      ! [X3: rat,Y3: rat] :
% 0.26/0.51        ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 0.26/0.51       => ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 0.26/0.51         => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_nonpos_pos
% 0.26/0.51  thf(fact_2832_less__divide__eq__1,axiom,
% 0.26/0.51      ! [B: real,A: real] :
% 0.26/0.51        ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.26/0.51        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.51            & ( ord_less_real @ A @ B ) )
% 0.26/0.51          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.26/0.51            & ( ord_less_real @ B @ A ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % less_divide_eq_1
% 0.26/0.51  thf(fact_2833_less__divide__eq__1,axiom,
% 0.26/0.51      ! [B: rat,A: rat] :
% 0.26/0.51        ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.26/0.51        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.51            & ( ord_less_rat @ A @ B ) )
% 0.26/0.51          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.26/0.51            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % less_divide_eq_1
% 0.26/0.51  thf(fact_2834_divide__less__eq__1,axiom,
% 0.26/0.51      ! [B: real,A: real] :
% 0.26/0.51        ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.26/0.51        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.51            & ( ord_less_real @ B @ A ) )
% 0.26/0.51          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.26/0.51            & ( ord_less_real @ A @ B ) )
% 0.26/0.51          | ( A = zero_zero_real ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_less_eq_1
% 0.26/0.51  thf(fact_2835_divide__less__eq__1,axiom,
% 0.26/0.51      ! [B: rat,A: rat] :
% 0.26/0.51        ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.26/0.51        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.51            & ( ord_less_rat @ B @ A ) )
% 0.26/0.51          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.26/0.51            & ( ord_less_rat @ A @ B ) )
% 0.26/0.51          | ( A = zero_zero_rat ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_less_eq_1
% 0.26/0.51  thf(fact_2836_gt__half__sum,axiom,
% 0.26/0.51      ! [A: real,B: real] :
% 0.26/0.51        ( ( ord_less_real @ A @ B )
% 0.26/0.51       => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 0.26/0.51  
% 0.26/0.51  % gt_half_sum
% 0.26/0.51  thf(fact_2837_gt__half__sum,axiom,
% 0.26/0.51      ! [A: rat,B: rat] :
% 0.26/0.51        ( ( ord_less_rat @ A @ B )
% 0.26/0.51       => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 0.26/0.51  
% 0.26/0.51  % gt_half_sum
% 0.26/0.51  thf(fact_2838_less__half__sum,axiom,
% 0.26/0.51      ! [A: real,B: real] :
% 0.26/0.51        ( ( ord_less_real @ A @ B )
% 0.26/0.51       => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % less_half_sum
% 0.26/0.51  thf(fact_2839_less__half__sum,axiom,
% 0.26/0.51      ! [A: rat,B: rat] :
% 0.26/0.51        ( ( ord_less_rat @ A @ B )
% 0.26/0.51       => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % less_half_sum
% 0.26/0.51  thf(fact_2840_ceiling__log__nat__eq__if,axiom,
% 0.26/0.51      ! [B: nat,N: nat,K: nat] :
% 0.26/0.51        ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 0.26/0.51       => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 0.26/0.51         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.26/0.51           => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.26/0.51              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % ceiling_log_nat_eq_if
% 0.26/0.51  thf(fact_2841_ceiling__log__nat__eq__powr__iff,axiom,
% 0.26/0.51      ! [B: nat,K: nat,N: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.26/0.51       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.26/0.51         => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.26/0.51              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 0.26/0.51            = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 0.26/0.51              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % ceiling_log_nat_eq_powr_iff
% 0.26/0.51  thf(fact_2842_le__divide__eq__1,axiom,
% 0.26/0.51      ! [B: real,A: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.26/0.51        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.51            & ( ord_less_eq_real @ A @ B ) )
% 0.26/0.51          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.26/0.51            & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % le_divide_eq_1
% 0.26/0.51  thf(fact_2843_le__divide__eq__1,axiom,
% 0.26/0.51      ! [B: rat,A: rat] :
% 0.26/0.51        ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.26/0.51        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.51            & ( ord_less_eq_rat @ A @ B ) )
% 0.26/0.51          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.26/0.51            & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % le_divide_eq_1
% 0.26/0.51  thf(fact_2844_divide__le__eq__1,axiom,
% 0.26/0.51      ! [B: real,A: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.26/0.51        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.51            & ( ord_less_eq_real @ B @ A ) )
% 0.26/0.51          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.26/0.51            & ( ord_less_eq_real @ A @ B ) )
% 0.26/0.51          | ( A = zero_zero_real ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_le_eq_1
% 0.26/0.51  thf(fact_2845_divide__le__eq__1,axiom,
% 0.26/0.51      ! [B: rat,A: rat] :
% 0.26/0.51        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.26/0.51        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.51            & ( ord_less_eq_rat @ B @ A ) )
% 0.26/0.51          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.26/0.51            & ( ord_less_eq_rat @ A @ B ) )
% 0.26/0.51          | ( A = zero_zero_rat ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % divide_le_eq_1
% 0.26/0.51  thf(fact_2846_real__average__minus__first,axiom,
% 0.26/0.51      ! [A: real,B: real] :
% 0.26/0.51        ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 0.26/0.51        = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % real_average_minus_first
% 0.26/0.51  thf(fact_2847_real__average__minus__second,axiom,
% 0.26/0.51      ! [B: real,A: real] :
% 0.26/0.51        ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 0.26/0.51        = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % real_average_minus_second
% 0.26/0.51  thf(fact_2848_add__def,axiom,
% 0.26/0.51      ( vEBT_VEBT_add
% 0.26/0.51      = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 0.26/0.51  
% 0.26/0.51  % add_def
% 0.26/0.51  thf(fact_2849_div__pos__geq,axiom,
% 0.26/0.51      ! [L: int,K: int] :
% 0.26/0.51        ( ( ord_less_int @ zero_zero_int @ L )
% 0.26/0.51       => ( ( ord_less_eq_int @ L @ K )
% 0.26/0.51         => ( ( divide_divide_int @ K @ L )
% 0.26/0.51            = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % div_pos_geq
% 0.26/0.51  thf(fact_2850_ln__2__less__1,axiom,
% 0.26/0.51      ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 0.26/0.51  
% 0.26/0.51  % ln_2_less_1
% 0.26/0.51  thf(fact_2851__C5_Ohyps_C_I4_J,axiom,
% 0.26/0.51      ( deg
% 0.26/0.51      = ( plus_plus_nat @ na @ m ) ) ).
% 0.26/0.51  
% 0.26/0.51  % "5.hyps"(4)
% 0.26/0.51  thf(fact_2852_div2__even__ext__nat,axiom,
% 0.26/0.51      ! [X3: nat,Y3: nat] :
% 0.26/0.51        ( ( ( divide_divide_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.51          = ( divide_divide_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.51       => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X3 )
% 0.26/0.51            = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y3 ) )
% 0.26/0.51         => ( X3 = Y3 ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % div2_even_ext_nat
% 0.26/0.51  thf(fact_2853_zdiv__numeral__Bit0,axiom,
% 0.26/0.51      ! [V: num,W: num] :
% 0.26/0.51        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 0.26/0.51        = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zdiv_numeral_Bit0
% 0.26/0.51  thf(fact_2854_add__shift,axiom,
% 0.26/0.51      ! [X3: nat,Y3: nat,Z: nat] :
% 0.26/0.51        ( ( ( plus_plus_nat @ X3 @ Y3 )
% 0.26/0.51          = Z )
% 0.26/0.51        = ( ( vEBT_VEBT_add @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) )
% 0.26/0.51          = ( some_nat @ Z ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % add_shift
% 0.26/0.51  thf(fact_2855__C5_Ohyps_C_I3_J,axiom,
% 0.26/0.51      ( m
% 0.26/0.51      = ( suc @ na ) ) ).
% 0.26/0.51  
% 0.26/0.51  % "5.hyps"(3)
% 0.26/0.51  thf(fact_2856_div__neg__pos__less0,axiom,
% 0.26/0.51      ! [A: int,B: int] :
% 0.26/0.51        ( ( ord_less_int @ A @ zero_zero_int )
% 0.26/0.51       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.51         => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % div_neg_pos_less0
% 0.26/0.51  thf(fact_2857_neg__imp__zdiv__neg__iff,axiom,
% 0.26/0.51      ! [B: int,A: int] :
% 0.26/0.51        ( ( ord_less_int @ B @ zero_zero_int )
% 0.26/0.51       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 0.26/0.51          = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % neg_imp_zdiv_neg_iff
% 0.26/0.51  thf(fact_2858_pos__imp__zdiv__neg__iff,axiom,
% 0.26/0.51      ! [B: int,A: int] :
% 0.26/0.51        ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.51       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 0.26/0.51          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % pos_imp_zdiv_neg_iff
% 0.26/0.51  thf(fact_2859_zdiv__int,axiom,
% 0.26/0.51      ! [A: nat,B: nat] :
% 0.26/0.51        ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 0.26/0.51        = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zdiv_int
% 0.26/0.51  thf(fact_2860_nonneg1__imp__zdiv__pos__iff,axiom,
% 0.26/0.51      ! [A: int,B: int] :
% 0.26/0.51        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.51       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.26/0.51          = ( ( ord_less_eq_int @ B @ A )
% 0.26/0.51            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % nonneg1_imp_zdiv_pos_iff
% 0.26/0.51  thf(fact_2861_pos__imp__zdiv__nonneg__iff,axiom,
% 0.26/0.51      ! [B: int,A: int] :
% 0.26/0.51        ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.51       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.26/0.51          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % pos_imp_zdiv_nonneg_iff
% 0.26/0.51  thf(fact_2862_neg__imp__zdiv__nonneg__iff,axiom,
% 0.26/0.51      ! [B: int,A: int] :
% 0.26/0.51        ( ( ord_less_int @ B @ zero_zero_int )
% 0.26/0.51       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.26/0.51          = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % neg_imp_zdiv_nonneg_iff
% 0.26/0.51  thf(fact_2863_pos__imp__zdiv__pos__iff,axiom,
% 0.26/0.51      ! [K: int,I: int] :
% 0.26/0.51        ( ( ord_less_int @ zero_zero_int @ K )
% 0.26/0.51       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 0.26/0.51          = ( ord_less_eq_int @ K @ I ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % pos_imp_zdiv_pos_iff
% 0.26/0.51  thf(fact_2864_div__nonpos__pos__le0,axiom,
% 0.26/0.51      ! [A: int,B: int] :
% 0.26/0.51        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.26/0.51       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.51         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % div_nonpos_pos_le0
% 0.26/0.51  thf(fact_2865_div__nonneg__neg__le0,axiom,
% 0.26/0.51      ! [A: int,B: int] :
% 0.26/0.51        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.51       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.26/0.51         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % div_nonneg_neg_le0
% 0.26/0.51  thf(fact_2866_div__positive__int,axiom,
% 0.26/0.51      ! [L: int,K: int] :
% 0.26/0.51        ( ( ord_less_eq_int @ L @ K )
% 0.26/0.51       => ( ( ord_less_int @ zero_zero_int @ L )
% 0.26/0.51         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % div_positive_int
% 0.26/0.51  thf(fact_2867_div__int__pos__iff,axiom,
% 0.26/0.51      ! [K: int,L: int] :
% 0.26/0.51        ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 0.26/0.51        = ( ( K = zero_zero_int )
% 0.26/0.51          | ( L = zero_zero_int )
% 0.26/0.51          | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.26/0.51            & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 0.26/0.51          | ( ( ord_less_int @ K @ zero_zero_int )
% 0.26/0.51            & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % div_int_pos_iff
% 0.26/0.51  thf(fact_2868_zdiv__mono2__neg,axiom,
% 0.26/0.51      ! [A: int,B2: int,B: int] :
% 0.26/0.51        ( ( ord_less_int @ A @ zero_zero_int )
% 0.26/0.51       => ( ( ord_less_int @ zero_zero_int @ B2 )
% 0.26/0.51         => ( ( ord_less_eq_int @ B2 @ B )
% 0.26/0.51           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B2 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zdiv_mono2_neg
% 0.26/0.51  thf(fact_2869_zdiv__mono1__neg,axiom,
% 0.26/0.51      ! [A: int,A2: int,B: int] :
% 0.26/0.51        ( ( ord_less_eq_int @ A @ A2 )
% 0.26/0.51       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.26/0.51         => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zdiv_mono1_neg
% 0.26/0.51  thf(fact_2870_zdiv__eq__0__iff,axiom,
% 0.26/0.51      ! [I: int,K: int] :
% 0.26/0.51        ( ( ( divide_divide_int @ I @ K )
% 0.26/0.51          = zero_zero_int )
% 0.26/0.51        = ( ( K = zero_zero_int )
% 0.26/0.51          | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 0.26/0.51            & ( ord_less_int @ I @ K ) )
% 0.26/0.51          | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 0.26/0.51            & ( ord_less_int @ K @ I ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zdiv_eq_0_iff
% 0.26/0.51  thf(fact_2871_zdiv__mono2,axiom,
% 0.26/0.51      ! [A: int,B2: int,B: int] :
% 0.26/0.51        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.51       => ( ( ord_less_int @ zero_zero_int @ B2 )
% 0.26/0.51         => ( ( ord_less_eq_int @ B2 @ B )
% 0.26/0.51           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B2 ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zdiv_mono2
% 0.26/0.51  thf(fact_2872_zdiv__mono1,axiom,
% 0.26/0.51      ! [A: int,A2: int,B: int] :
% 0.26/0.51        ( ( ord_less_eq_int @ A @ A2 )
% 0.26/0.51       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.51         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A2 @ B ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zdiv_mono1
% 0.26/0.51  thf(fact_2873_int__div__less__self,axiom,
% 0.26/0.51      ! [X3: int,K: int] :
% 0.26/0.51        ( ( ord_less_int @ zero_zero_int @ X3 )
% 0.26/0.51       => ( ( ord_less_int @ one_one_int @ K )
% 0.26/0.51         => ( ord_less_int @ ( divide_divide_int @ X3 @ K ) @ X3 ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % int_div_less_self
% 0.26/0.51  thf(fact_2874_div__positive,axiom,
% 0.26/0.51      ! [B: nat,A: nat] :
% 0.26/0.51        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.26/0.51       => ( ( ord_less_eq_nat @ B @ A )
% 0.26/0.51         => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % div_positive
% 0.26/0.51  thf(fact_2875_div__positive,axiom,
% 0.26/0.51      ! [B: int,A: int] :
% 0.26/0.51        ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.51       => ( ( ord_less_eq_int @ B @ A )
% 0.26/0.51         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % div_positive
% 0.26/0.51  thf(fact_2876_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 0.26/0.51      ! [A: nat,B: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.51       => ( ( ord_less_nat @ A @ B )
% 0.26/0.51         => ( ( divide_divide_nat @ A @ B )
% 0.26/0.51            = zero_zero_nat ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % unique_euclidean_semiring_numeral_class.div_less
% 0.26/0.51  thf(fact_2877_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 0.26/0.51      ! [A: int,B: int] :
% 0.26/0.51        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.51       => ( ( ord_less_int @ A @ B )
% 0.26/0.51         => ( ( divide_divide_int @ A @ B )
% 0.26/0.51            = zero_zero_int ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % unique_euclidean_semiring_numeral_class.div_less
% 0.26/0.51  thf(fact_2878_discrete,axiom,
% 0.26/0.51      ( ord_less_nat
% 0.26/0.51      = ( ^ [A4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A4 @ one_one_nat ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % discrete
% 0.26/0.51  thf(fact_2879_discrete,axiom,
% 0.26/0.51      ( ord_less_int
% 0.26/0.51      = ( ^ [A4: int] : ( ord_less_eq_int @ ( plus_plus_int @ A4 @ one_one_int ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % discrete
% 0.26/0.51  thf(fact_2880_Bolzano,axiom,
% 0.26/0.51      ! [A: real,B: real,P: real > real > $o] :
% 0.26/0.51        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.51       => ( ! [A5: real,B4: real,C2: real] :
% 0.26/0.51              ( ( P @ A5 @ B4 )
% 0.26/0.51             => ( ( P @ B4 @ C2 )
% 0.26/0.51               => ( ( ord_less_eq_real @ A5 @ B4 )
% 0.26/0.51                 => ( ( ord_less_eq_real @ B4 @ C2 )
% 0.26/0.51                   => ( P @ A5 @ C2 ) ) ) ) )
% 0.26/0.51         => ( ! [X4: real] :
% 0.26/0.51                ( ( ord_less_eq_real @ A @ X4 )
% 0.26/0.51               => ( ( ord_less_eq_real @ X4 @ B )
% 0.26/0.51                 => ? [D: real] :
% 0.26/0.51                      ( ( ord_less_real @ zero_zero_real @ D )
% 0.26/0.51                      & ! [A5: real,B4: real] :
% 0.26/0.51                          ( ( ( ord_less_eq_real @ A5 @ X4 )
% 0.26/0.51                            & ( ord_less_eq_real @ X4 @ B4 )
% 0.26/0.51                            & ( ord_less_real @ ( minus_minus_real @ B4 @ A5 ) @ D ) )
% 0.26/0.51                         => ( P @ A5 @ B4 ) ) ) ) )
% 0.26/0.51           => ( P @ A @ B ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Bolzano
% 0.26/0.51  thf(fact_2881_round__unique,axiom,
% 0.26/0.51      ! [X3: real,Y3: int] :
% 0.26/0.51        ( ( ord_less_real @ ( minus_minus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y3 ) )
% 0.26/0.51       => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y3 ) @ ( plus_plus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.26/0.51         => ( ( archim8280529875227126926d_real @ X3 )
% 0.26/0.51            = Y3 ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % round_unique
% 0.26/0.51  thf(fact_2882_round__unique,axiom,
% 0.26/0.51      ! [X3: rat,Y3: int] :
% 0.26/0.51        ( ( ord_less_rat @ ( minus_minus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y3 ) )
% 0.26/0.51       => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y3 ) @ ( plus_plus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.51         => ( ( archim7778729529865785530nd_rat @ X3 )
% 0.26/0.51            = Y3 ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % round_unique
% 0.26/0.51  thf(fact_2883_high__bound__aux,axiom,
% 0.26/0.51      ! [Ma: nat,N: nat,M: nat] :
% 0.26/0.51        ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 0.26/0.51       => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % high_bound_aux
% 0.26/0.51  thf(fact_2884_tanh__ln__real,axiom,
% 0.26/0.51      ! [X3: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.51       => ( ( tanh_real @ ( ln_ln_real @ X3 ) )
% 0.26/0.51          = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % tanh_ln_real
% 0.26/0.51  thf(fact_2885_ceiling__log__eq__powr__iff,axiom,
% 0.26/0.51      ! [X3: real,B: real,K: nat] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.51       => ( ( ord_less_real @ one_one_real @ B )
% 0.26/0.51         => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X3 ) )
% 0.26/0.51              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 0.26/0.51            = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X3 )
% 0.26/0.51              & ( ord_less_eq_real @ X3 @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % ceiling_log_eq_powr_iff
% 0.26/0.51  thf(fact_2886__C5_Ohyps_C_I2_J,axiom,
% 0.26/0.51      ( ( size_s6755466524823107622T_VEBT @ treeList )
% 0.26/0.51      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 0.26/0.51  
% 0.26/0.51  % "5.hyps"(2)
% 0.26/0.51  thf(fact_2887_floor__log__nat__eq__powr__iff,axiom,
% 0.26/0.51      ! [B: nat,K: nat,N: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.26/0.51       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.26/0.51         => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.26/0.51              = ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.51            = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 0.26/0.51              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_log_nat_eq_powr_iff
% 0.26/0.51  thf(fact_2888_high__def,axiom,
% 0.26/0.51      ( vEBT_VEBT_high
% 0.26/0.51      = ( ^ [X: nat,N3: nat] : ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % high_def
% 0.26/0.51  thf(fact_2889_even__odd__cases,axiom,
% 0.26/0.51      ! [X3: nat] :
% 0.26/0.51        ( ! [N2: nat] :
% 0.26/0.51            ( X3
% 0.26/0.51           != ( plus_plus_nat @ N2 @ N2 ) )
% 0.26/0.51       => ~ ! [N2: nat] :
% 0.26/0.51              ( X3
% 0.26/0.51             != ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % even_odd_cases
% 0.26/0.51  thf(fact_2890_old_Onat_Oinject,axiom,
% 0.26/0.51      ! [Nat: nat,Nat2: nat] :
% 0.26/0.51        ( ( ( suc @ Nat )
% 0.26/0.51          = ( suc @ Nat2 ) )
% 0.26/0.51        = ( Nat = Nat2 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % old.nat.inject
% 0.26/0.51  thf(fact_2891_nat_Oinject,axiom,
% 0.26/0.51      ! [X2: nat,Y2: nat] :
% 0.26/0.51        ( ( ( suc @ X2 )
% 0.26/0.51          = ( suc @ Y2 ) )
% 0.26/0.51        = ( X2 = Y2 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % nat.inject
% 0.26/0.51  thf(fact_2892_Suc__less__eq,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.26/0.51        = ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Suc_less_eq
% 0.26/0.51  thf(fact_2893_Suc__mono,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( ord_less_nat @ M @ N )
% 0.26/0.51       => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Suc_mono
% 0.26/0.51  thf(fact_2894_lessI,axiom,
% 0.26/0.51      ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % lessI
% 0.26/0.51  thf(fact_2895_add__Suc__right,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 0.26/0.51        = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % add_Suc_right
% 0.26/0.51  thf(fact_2896_Suc__le__mono,axiom,
% 0.26/0.51      ! [N: nat,M: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 0.26/0.51        = ( ord_less_eq_nat @ N @ M ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Suc_le_mono
% 0.26/0.51  thf(fact_2897_diff__Suc__Suc,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.26/0.51        = ( minus_minus_nat @ M @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % diff_Suc_Suc
% 0.26/0.51  thf(fact_2898_Suc__diff__diff,axiom,
% 0.26/0.51      ! [M: nat,N: nat,K: nat] :
% 0.26/0.51        ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 0.26/0.51        = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Suc_diff_diff
% 0.26/0.51  thf(fact_2899_powr__0,axiom,
% 0.26/0.51      ! [Z: real] :
% 0.26/0.51        ( ( powr_real @ zero_zero_real @ Z )
% 0.26/0.51        = zero_zero_real ) ).
% 0.26/0.51  
% 0.26/0.51  % powr_0
% 0.26/0.51  thf(fact_2900_powr__eq__0__iff,axiom,
% 0.26/0.51      ! [W: real,Z: real] :
% 0.26/0.51        ( ( ( powr_real @ W @ Z )
% 0.26/0.51          = zero_zero_real )
% 0.26/0.51        = ( W = zero_zero_real ) ) ).
% 0.26/0.51  
% 0.26/0.51  % powr_eq_0_iff
% 0.26/0.51  thf(fact_2901_floor__of__int,axiom,
% 0.26/0.51      ! [Z: int] :
% 0.26/0.51        ( ( archim3151403230148437115or_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.26/0.51        = Z ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_of_int
% 0.26/0.51  thf(fact_2902_floor__of__int,axiom,
% 0.26/0.51      ! [Z: int] :
% 0.26/0.51        ( ( archim6058952711729229775r_real @ ( ring_1_of_int_real @ Z ) )
% 0.26/0.51        = Z ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_of_int
% 0.26/0.51  thf(fact_2903_of__int__floor__cancel,axiom,
% 0.26/0.51      ! [X3: rat] :
% 0.26/0.51        ( ( ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X3 ) )
% 0.26/0.51          = X3 )
% 0.26/0.51        = ( ? [N3: int] :
% 0.26/0.51              ( X3
% 0.26/0.51              = ( ring_1_of_int_rat @ N3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % of_int_floor_cancel
% 0.26/0.51  thf(fact_2904_of__int__floor__cancel,axiom,
% 0.26/0.51      ! [X3: real] :
% 0.26/0.51        ( ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X3 ) )
% 0.26/0.51          = X3 )
% 0.26/0.51        = ( ? [N3: int] :
% 0.26/0.51              ( X3
% 0.26/0.51              = ( ring_1_of_int_real @ N3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % of_int_floor_cancel
% 0.26/0.51  thf(fact_2905_tanh__0,axiom,
% 0.26/0.51      ( ( tanh_real @ zero_zero_real )
% 0.26/0.51      = zero_zero_real ) ).
% 0.26/0.51  
% 0.26/0.51  % tanh_0
% 0.26/0.51  thf(fact_2906_tanh__real__zero__iff,axiom,
% 0.26/0.51      ! [X3: real] :
% 0.26/0.51        ( ( ( tanh_real @ X3 )
% 0.26/0.51          = zero_zero_real )
% 0.26/0.51        = ( X3 = zero_zero_real ) ) ).
% 0.26/0.51  
% 0.26/0.51  % tanh_real_zero_iff
% 0.26/0.51  thf(fact_2907_tanh__real__less__iff,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_real @ ( tanh_real @ X3 ) @ ( tanh_real @ Y3 ) )
% 0.26/0.51        = ( ord_less_real @ X3 @ Y3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % tanh_real_less_iff
% 0.26/0.51  thf(fact_2908_tanh__real__le__iff,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ ( tanh_real @ X3 ) @ ( tanh_real @ Y3 ) )
% 0.26/0.51        = ( ord_less_eq_real @ X3 @ Y3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % tanh_real_le_iff
% 0.26/0.51  thf(fact_2909_round__of__int,axiom,
% 0.26/0.51      ! [N: int] :
% 0.26/0.51        ( ( archim8280529875227126926d_real @ ( ring_1_of_int_real @ N ) )
% 0.26/0.51        = N ) ).
% 0.26/0.51  
% 0.26/0.51  % round_of_int
% 0.26/0.51  thf(fact_2910_round__of__int,axiom,
% 0.26/0.51      ! [N: int] :
% 0.26/0.51        ( ( archim7778729529865785530nd_rat @ ( ring_1_of_int_rat @ N ) )
% 0.26/0.51        = N ) ).
% 0.26/0.51  
% 0.26/0.51  % round_of_int
% 0.26/0.51  thf(fact_2911_power__0__Suc,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 0.26/0.51        = zero_zero_rat ) ).
% 0.26/0.51  
% 0.26/0.51  % power_0_Suc
% 0.26/0.51  thf(fact_2912_power__0__Suc,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.26/0.51        = zero_zero_nat ) ).
% 0.26/0.51  
% 0.26/0.51  % power_0_Suc
% 0.26/0.51  thf(fact_2913_power__0__Suc,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 0.26/0.51        = zero_zero_int ) ).
% 0.26/0.51  
% 0.26/0.51  % power_0_Suc
% 0.26/0.51  thf(fact_2914_power__0__Suc,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 0.26/0.51        = zero_zero_real ) ).
% 0.26/0.51  
% 0.26/0.51  % power_0_Suc
% 0.26/0.51  thf(fact_2915_power__0__Suc,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 0.26/0.51        = zero_zero_complex ) ).
% 0.26/0.51  
% 0.26/0.51  % power_0_Suc
% 0.26/0.51  thf(fact_2916_power__Suc0__right,axiom,
% 0.26/0.51      ! [A: nat] :
% 0.26/0.51        ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 0.26/0.51        = A ) ).
% 0.26/0.51  
% 0.26/0.51  % power_Suc0_right
% 0.26/0.51  thf(fact_2917_power__Suc0__right,axiom,
% 0.26/0.51      ! [A: int] :
% 0.26/0.51        ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 0.26/0.51        = A ) ).
% 0.26/0.51  
% 0.26/0.51  % power_Suc0_right
% 0.26/0.51  thf(fact_2918_power__Suc0__right,axiom,
% 0.26/0.51      ! [A: real] :
% 0.26/0.51        ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 0.26/0.51        = A ) ).
% 0.26/0.51  
% 0.26/0.51  % power_Suc0_right
% 0.26/0.51  thf(fact_2919_power__Suc0__right,axiom,
% 0.26/0.51      ! [A: complex] :
% 0.26/0.51        ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 0.26/0.51        = A ) ).
% 0.26/0.51  
% 0.26/0.51  % power_Suc0_right
% 0.26/0.51  thf(fact_2920_zero__less__Suc,axiom,
% 0.26/0.51      ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zero_less_Suc
% 0.26/0.51  thf(fact_2921_less__Suc0,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.26/0.51        = ( N = zero_zero_nat ) ) ).
% 0.26/0.51  
% 0.26/0.51  % less_Suc0
% 0.26/0.51  thf(fact_2922_div__by__Suc__0,axiom,
% 0.26/0.51      ! [M: nat] :
% 0.26/0.51        ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.26/0.51        = M ) ).
% 0.26/0.51  
% 0.26/0.51  % div_by_Suc_0
% 0.26/0.51  thf(fact_2923_power__Suc__0,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.26/0.51        = ( suc @ zero_zero_nat ) ) ).
% 0.26/0.51  
% 0.26/0.51  % power_Suc_0
% 0.26/0.51  thf(fact_2924_nat__power__eq__Suc__0__iff,axiom,
% 0.26/0.51      ! [X3: nat,M: nat] :
% 0.26/0.51        ( ( ( power_power_nat @ X3 @ M )
% 0.26/0.51          = ( suc @ zero_zero_nat ) )
% 0.26/0.51        = ( ( M = zero_zero_nat )
% 0.26/0.51          | ( X3
% 0.26/0.51            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % nat_power_eq_Suc_0_iff
% 0.26/0.51  thf(fact_2925_dvd__1__left,axiom,
% 0.26/0.51      ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 0.26/0.51  
% 0.26/0.51  % dvd_1_left
% 0.26/0.51  thf(fact_2926_dvd__1__iff__1,axiom,
% 0.26/0.51      ! [M: nat] :
% 0.26/0.51        ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.26/0.51        = ( M
% 0.26/0.51          = ( suc @ zero_zero_nat ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % dvd_1_iff_1
% 0.26/0.51  thf(fact_2927_diff__Suc__1,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 0.26/0.51        = N ) ).
% 0.26/0.51  
% 0.26/0.51  % diff_Suc_1
% 0.26/0.51  thf(fact_2928_take__bit__Suc__1,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ one_one_int )
% 0.26/0.51        = one_one_int ) ).
% 0.26/0.51  
% 0.26/0.51  % take_bit_Suc_1
% 0.26/0.51  thf(fact_2929_take__bit__Suc__1,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ one_one_nat )
% 0.26/0.51        = one_one_nat ) ).
% 0.26/0.51  
% 0.26/0.51  % take_bit_Suc_1
% 0.26/0.51  thf(fact_2930_powr__zero__eq__one,axiom,
% 0.26/0.51      ! [X3: real] :
% 0.26/0.51        ( ( ( X3 = zero_zero_real )
% 0.26/0.51         => ( ( powr_real @ X3 @ zero_zero_real )
% 0.26/0.51            = zero_zero_real ) )
% 0.26/0.51        & ( ( X3 != zero_zero_real )
% 0.26/0.51         => ( ( powr_real @ X3 @ zero_zero_real )
% 0.26/0.51            = one_one_real ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % powr_zero_eq_one
% 0.26/0.51  thf(fact_2931_floor__zero,axiom,
% 0.26/0.51      ( ( archim3151403230148437115or_rat @ zero_zero_rat )
% 0.26/0.51      = zero_zero_int ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_zero
% 0.26/0.51  thf(fact_2932_floor__zero,axiom,
% 0.26/0.51      ( ( archim6058952711729229775r_real @ zero_zero_real )
% 0.26/0.51      = zero_zero_int ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_zero
% 0.26/0.51  thf(fact_2933_floor__numeral,axiom,
% 0.26/0.51      ! [V: num] :
% 0.26/0.51        ( ( archim3151403230148437115or_rat @ ( numeral_numeral_rat @ V ) )
% 0.26/0.51        = ( numeral_numeral_int @ V ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_numeral
% 0.26/0.51  thf(fact_2934_floor__numeral,axiom,
% 0.26/0.51      ! [V: num] :
% 0.26/0.51        ( ( archim6058952711729229775r_real @ ( numeral_numeral_real @ V ) )
% 0.26/0.51        = ( numeral_numeral_int @ V ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_numeral
% 0.26/0.51  thf(fact_2935_floor__one,axiom,
% 0.26/0.51      ( ( archim3151403230148437115or_rat @ one_one_rat )
% 0.26/0.51      = one_one_int ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_one
% 0.26/0.51  thf(fact_2936_floor__one,axiom,
% 0.26/0.51      ( ( archim6058952711729229775r_real @ one_one_real )
% 0.26/0.51      = one_one_int ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_one
% 0.26/0.51  thf(fact_2937_powr__gt__zero,axiom,
% 0.26/0.51      ! [X3: real,A: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X3 @ A ) )
% 0.26/0.51        = ( X3 != zero_zero_real ) ) ).
% 0.26/0.51  
% 0.26/0.51  % powr_gt_zero
% 0.26/0.51  thf(fact_2938_powr__nonneg__iff,axiom,
% 0.26/0.51      ! [A: real,X3: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ ( powr_real @ A @ X3 ) @ zero_zero_real )
% 0.26/0.51        = ( A = zero_zero_real ) ) ).
% 0.26/0.51  
% 0.26/0.51  % powr_nonneg_iff
% 0.26/0.51  thf(fact_2939_powr__less__cancel__iff,axiom,
% 0.26/0.51      ! [X3: real,A: real,B: real] :
% 0.26/0.51        ( ( ord_less_real @ one_one_real @ X3 )
% 0.26/0.51       => ( ( ord_less_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) )
% 0.26/0.51          = ( ord_less_real @ A @ B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % powr_less_cancel_iff
% 0.26/0.51  thf(fact_2940_floor__of__nat,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( archim3151403230148437115or_rat @ ( semiri681578069525770553at_rat @ N ) )
% 0.26/0.51        = ( semiri1314217659103216013at_int @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_of_nat
% 0.26/0.51  thf(fact_2941_floor__of__nat,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( archim6058952711729229775r_real @ ( semiri5074537144036343181t_real @ N ) )
% 0.26/0.51        = ( semiri1314217659103216013at_int @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_of_nat
% 0.26/0.51  thf(fact_2942_round__0,axiom,
% 0.26/0.51      ( ( archim8280529875227126926d_real @ zero_zero_real )
% 0.26/0.51      = zero_zero_int ) ).
% 0.26/0.51  
% 0.26/0.51  % round_0
% 0.26/0.51  thf(fact_2943_round__0,axiom,
% 0.26/0.51      ( ( archim7778729529865785530nd_rat @ zero_zero_rat )
% 0.26/0.51      = zero_zero_int ) ).
% 0.26/0.51  
% 0.26/0.51  % round_0
% 0.26/0.51  thf(fact_2944_tanh__real__pos__iff,axiom,
% 0.26/0.51      ! [X3: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X3 ) )
% 0.26/0.51        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % tanh_real_pos_iff
% 0.26/0.51  thf(fact_2945_tanh__real__neg__iff,axiom,
% 0.26/0.51      ! [X3: real] :
% 0.26/0.51        ( ( ord_less_real @ ( tanh_real @ X3 ) @ zero_zero_real )
% 0.26/0.51        = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 0.26/0.51  
% 0.26/0.51  % tanh_real_neg_iff
% 0.26/0.51  thf(fact_2946_tanh__real__nonpos__iff,axiom,
% 0.26/0.51      ! [X3: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ ( tanh_real @ X3 ) @ zero_zero_real )
% 0.26/0.51        = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ).
% 0.26/0.51  
% 0.26/0.51  % tanh_real_nonpos_iff
% 0.26/0.51  thf(fact_2947_tanh__real__nonneg__iff,axiom,
% 0.26/0.51      ! [X3: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X3 ) )
% 0.26/0.51        = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % tanh_real_nonneg_iff
% 0.26/0.51  thf(fact_2948_round__numeral,axiom,
% 0.26/0.51      ! [N: num] :
% 0.26/0.51        ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N ) )
% 0.26/0.51        = ( numeral_numeral_int @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % round_numeral
% 0.26/0.51  thf(fact_2949_round__numeral,axiom,
% 0.26/0.51      ! [N: num] :
% 0.26/0.51        ( ( archim7778729529865785530nd_rat @ ( numeral_numeral_rat @ N ) )
% 0.26/0.51        = ( numeral_numeral_int @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % round_numeral
% 0.26/0.51  thf(fact_2950_round__1,axiom,
% 0.26/0.51      ( ( archim8280529875227126926d_real @ one_one_real )
% 0.26/0.51      = one_one_int ) ).
% 0.26/0.51  
% 0.26/0.51  % round_1
% 0.26/0.51  thf(fact_2951_round__1,axiom,
% 0.26/0.51      ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 0.26/0.51      = one_one_int ) ).
% 0.26/0.51  
% 0.26/0.51  % round_1
% 0.26/0.51  thf(fact_2952_round__of__nat,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( archim8280529875227126926d_real @ ( semiri5074537144036343181t_real @ N ) )
% 0.26/0.51        = ( semiri1314217659103216013at_int @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % round_of_nat
% 0.26/0.51  thf(fact_2953_round__of__nat,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( archim7778729529865785530nd_rat @ ( semiri681578069525770553at_rat @ N ) )
% 0.26/0.51        = ( semiri1314217659103216013at_int @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % round_of_nat
% 0.26/0.51  thf(fact_2954_of__nat__Suc,axiom,
% 0.26/0.51      ! [M: nat] :
% 0.26/0.51        ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 0.26/0.51        = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % of_nat_Suc
% 0.26/0.51  thf(fact_2955_of__nat__Suc,axiom,
% 0.26/0.51      ! [M: nat] :
% 0.26/0.51        ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 0.26/0.51        = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % of_nat_Suc
% 0.26/0.51  thf(fact_2956_of__nat__Suc,axiom,
% 0.26/0.51      ! [M: nat] :
% 0.26/0.51        ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 0.26/0.51        = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % of_nat_Suc
% 0.26/0.51  thf(fact_2957_of__nat__Suc,axiom,
% 0.26/0.51      ! [M: nat] :
% 0.26/0.51        ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 0.26/0.51        = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % of_nat_Suc
% 0.26/0.51  thf(fact_2958_of__nat__Suc,axiom,
% 0.26/0.51      ! [M: nat] :
% 0.26/0.51        ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 0.26/0.51        = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % of_nat_Suc
% 0.26/0.51  thf(fact_2959_Suc__pred,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.51       => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 0.26/0.51          = N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Suc_pred
% 0.26/0.51  thf(fact_2960_diff__Suc__diff__eq2,axiom,
% 0.26/0.51      ! [K: nat,J: nat,I: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ K @ J )
% 0.26/0.51       => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 0.26/0.51          = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % diff_Suc_diff_eq2
% 0.26/0.51  thf(fact_2961_diff__Suc__diff__eq1,axiom,
% 0.26/0.51      ! [K: nat,J: nat,I: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ K @ J )
% 0.26/0.51       => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 0.26/0.51          = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % diff_Suc_diff_eq1
% 0.26/0.51  thf(fact_2962_nat__1,axiom,
% 0.26/0.51      ( ( nat2 @ one_one_int )
% 0.26/0.51      = ( suc @ zero_zero_nat ) ) ).
% 0.26/0.51  
% 0.26/0.51  % nat_1
% 0.26/0.51  thf(fact_2963_Suc__numeral,axiom,
% 0.26/0.51      ! [N: num] :
% 0.26/0.51        ( ( suc @ ( numeral_numeral_nat @ N ) )
% 0.26/0.51        = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Suc_numeral
% 0.26/0.51  thf(fact_2964_powr__eq__one__iff,axiom,
% 0.26/0.51      ! [A: real,X3: real] :
% 0.26/0.51        ( ( ord_less_real @ one_one_real @ A )
% 0.26/0.51       => ( ( ( powr_real @ A @ X3 )
% 0.26/0.51            = one_one_real )
% 0.26/0.51          = ( X3 = zero_zero_real ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % powr_eq_one_iff
% 0.26/0.51  thf(fact_2965_powr__one,axiom,
% 0.26/0.51      ! [X3: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.51       => ( ( powr_real @ X3 @ one_one_real )
% 0.26/0.51          = X3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % powr_one
% 0.26/0.51  thf(fact_2966_powr__one__gt__zero__iff,axiom,
% 0.26/0.51      ! [X3: real] :
% 0.26/0.51        ( ( ( powr_real @ X3 @ one_one_real )
% 0.26/0.51          = X3 )
% 0.26/0.51        = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % powr_one_gt_zero_iff
% 0.26/0.51  thf(fact_2967_powr__le__cancel__iff,axiom,
% 0.26/0.51      ! [X3: real,A: real,B: real] :
% 0.26/0.51        ( ( ord_less_real @ one_one_real @ X3 )
% 0.26/0.51       => ( ( ord_less_eq_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) )
% 0.26/0.51          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % powr_le_cancel_iff
% 0.26/0.51  thf(fact_2968_numeral__powr__numeral__real,axiom,
% 0.26/0.51      ! [M: num,N: num] :
% 0.26/0.51        ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 0.26/0.51        = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % numeral_powr_numeral_real
% 0.26/0.51  thf(fact_2969_floor__diff__of__int,axiom,
% 0.26/0.51      ! [X3: rat,Z: int] :
% 0.26/0.51        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X3 @ ( ring_1_of_int_rat @ Z ) ) )
% 0.26/0.51        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X3 ) @ Z ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_diff_of_int
% 0.26/0.51  thf(fact_2970_floor__diff__of__int,axiom,
% 0.26/0.51      ! [X3: real,Z: int] :
% 0.26/0.51        ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X3 @ ( ring_1_of_int_real @ Z ) ) )
% 0.26/0.51        = ( minus_minus_int @ ( archim6058952711729229775r_real @ X3 ) @ Z ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_diff_of_int
% 0.26/0.51  thf(fact_2971_add__2__eq__Suc_H,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.51        = ( suc @ ( suc @ N ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % add_2_eq_Suc'
% 0.26/0.51  thf(fact_2972_add__2__eq__Suc,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.51        = ( suc @ ( suc @ N ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % add_2_eq_Suc
% 0.26/0.51  thf(fact_2973_Suc__1,axiom,
% 0.26/0.51      ( ( suc @ one_one_nat )
% 0.26/0.51      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Suc_1
% 0.26/0.51  thf(fact_2974_div2__Suc__Suc,axiom,
% 0.26/0.51      ! [M: nat] :
% 0.26/0.51        ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.51        = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % div2_Suc_Suc
% 0.26/0.51  thf(fact_2975_even__Suc__Suc__iff,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 0.26/0.51        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % even_Suc_Suc_iff
% 0.26/0.51  thf(fact_2976_even__Suc,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 0.26/0.51        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % even_Suc
% 0.26/0.51  thf(fact_2977_Suc__diff__1,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.51       => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.26/0.51          = N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Suc_diff_1
% 0.26/0.51  thf(fact_2978_zero__le__floor,axiom,
% 0.26/0.51      ! [X3: rat] :
% 0.26/0.51        ( ( ord_less_eq_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X3 ) )
% 0.26/0.51        = ( ord_less_eq_rat @ zero_zero_rat @ X3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zero_le_floor
% 0.26/0.51  thf(fact_2979_zero__le__floor,axiom,
% 0.26/0.51      ! [X3: real] :
% 0.26/0.51        ( ( ord_less_eq_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X3 ) )
% 0.26/0.51        = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zero_le_floor
% 0.26/0.51  thf(fact_2980_floor__less__zero,axiom,
% 0.26/0.51      ! [X3: rat] :
% 0.26/0.51        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X3 ) @ zero_zero_int )
% 0.26/0.51        = ( ord_less_rat @ X3 @ zero_zero_rat ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_less_zero
% 0.26/0.51  thf(fact_2981_floor__less__zero,axiom,
% 0.26/0.51      ! [X3: real] :
% 0.26/0.51        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X3 ) @ zero_zero_int )
% 0.26/0.51        = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_less_zero
% 0.26/0.51  thf(fact_2982_numeral__le__floor,axiom,
% 0.26/0.51      ! [V: num,X3: rat] :
% 0.26/0.51        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X3 ) )
% 0.26/0.51        = ( ord_less_eq_rat @ ( numeral_numeral_rat @ V ) @ X3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % numeral_le_floor
% 0.26/0.51  thf(fact_2983_numeral__le__floor,axiom,
% 0.26/0.51      ! [V: num,X3: real] :
% 0.26/0.51        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X3 ) )
% 0.26/0.51        = ( ord_less_eq_real @ ( numeral_numeral_real @ V ) @ X3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % numeral_le_floor
% 0.26/0.51  thf(fact_2984_zero__less__floor,axiom,
% 0.26/0.51      ! [X3: rat] :
% 0.26/0.51        ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X3 ) )
% 0.26/0.51        = ( ord_less_eq_rat @ one_one_rat @ X3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zero_less_floor
% 0.26/0.51  thf(fact_2985_zero__less__floor,axiom,
% 0.26/0.51      ! [X3: real] :
% 0.26/0.51        ( ( ord_less_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X3 ) )
% 0.26/0.51        = ( ord_less_eq_real @ one_one_real @ X3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zero_less_floor
% 0.26/0.51  thf(fact_2986_floor__le__zero,axiom,
% 0.26/0.51      ! [X3: rat] :
% 0.26/0.51        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X3 ) @ zero_zero_int )
% 0.26/0.51        = ( ord_less_rat @ X3 @ one_one_rat ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_le_zero
% 0.26/0.51  thf(fact_2987_floor__le__zero,axiom,
% 0.26/0.51      ! [X3: real] :
% 0.26/0.51        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X3 ) @ zero_zero_int )
% 0.26/0.51        = ( ord_less_real @ X3 @ one_one_real ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_le_zero
% 0.26/0.51  thf(fact_2988_floor__less__numeral,axiom,
% 0.26/0.51      ! [X3: rat,V: num] :
% 0.26/0.51        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X3 ) @ ( numeral_numeral_int @ V ) )
% 0.26/0.51        = ( ord_less_rat @ X3 @ ( numeral_numeral_rat @ V ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_less_numeral
% 0.26/0.51  thf(fact_2989_floor__less__numeral,axiom,
% 0.26/0.51      ! [X3: real,V: num] :
% 0.26/0.51        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X3 ) @ ( numeral_numeral_int @ V ) )
% 0.26/0.51        = ( ord_less_real @ X3 @ ( numeral_numeral_real @ V ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_less_numeral
% 0.26/0.51  thf(fact_2990_one__le__floor,axiom,
% 0.26/0.51      ! [X3: rat] :
% 0.26/0.51        ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X3 ) )
% 0.26/0.51        = ( ord_less_eq_rat @ one_one_rat @ X3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % one_le_floor
% 0.26/0.51  thf(fact_2991_one__le__floor,axiom,
% 0.26/0.51      ! [X3: real] :
% 0.26/0.51        ( ( ord_less_eq_int @ one_one_int @ ( archim6058952711729229775r_real @ X3 ) )
% 0.26/0.51        = ( ord_less_eq_real @ one_one_real @ X3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % one_le_floor
% 0.26/0.51  thf(fact_2992_floor__less__one,axiom,
% 0.26/0.51      ! [X3: rat] :
% 0.26/0.51        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X3 ) @ one_one_int )
% 0.26/0.51        = ( ord_less_rat @ X3 @ one_one_rat ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_less_one
% 0.26/0.51  thf(fact_2993_floor__less__one,axiom,
% 0.26/0.51      ! [X3: real] :
% 0.26/0.51        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X3 ) @ one_one_int )
% 0.26/0.51        = ( ord_less_real @ X3 @ one_one_real ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_less_one
% 0.26/0.51  thf(fact_2994_floor__diff__numeral,axiom,
% 0.26/0.51      ! [X3: rat,V: num] :
% 0.26/0.51        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X3 @ ( numeral_numeral_rat @ V ) ) )
% 0.26/0.51        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X3 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_diff_numeral
% 0.26/0.51  thf(fact_2995_floor__diff__numeral,axiom,
% 0.26/0.51      ! [X3: real,V: num] :
% 0.26/0.51        ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X3 @ ( numeral_numeral_real @ V ) ) )
% 0.26/0.51        = ( minus_minus_int @ ( archim6058952711729229775r_real @ X3 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_diff_numeral
% 0.26/0.51  thf(fact_2996_floor__diff__one,axiom,
% 0.26/0.51      ! [X3: rat] :
% 0.26/0.51        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X3 @ one_one_rat ) )
% 0.26/0.51        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X3 ) @ one_one_int ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_diff_one
% 0.26/0.51  thf(fact_2997_floor__diff__one,axiom,
% 0.26/0.51      ! [X3: real] :
% 0.26/0.51        ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X3 @ one_one_real ) )
% 0.26/0.51        = ( minus_minus_int @ ( archim6058952711729229775r_real @ X3 ) @ one_one_int ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_diff_one
% 0.26/0.51  thf(fact_2998_floor__numeral__power,axiom,
% 0.26/0.51      ! [X3: num,N: nat] :
% 0.26/0.51        ( ( archim3151403230148437115or_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N ) )
% 0.26/0.51        = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_numeral_power
% 0.26/0.51  thf(fact_2999_floor__numeral__power,axiom,
% 0.26/0.51      ! [X3: num,N: nat] :
% 0.26/0.51        ( ( archim6058952711729229775r_real @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N ) )
% 0.26/0.51        = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_numeral_power
% 0.26/0.51  thf(fact_3000_powr__log__cancel,axiom,
% 0.26/0.51      ! [A: real,X3: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.51       => ( ( A != one_one_real )
% 0.26/0.51         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.51           => ( ( powr_real @ A @ ( log @ A @ X3 ) )
% 0.26/0.51              = X3 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % powr_log_cancel
% 0.26/0.51  thf(fact_3001_log__powr__cancel,axiom,
% 0.26/0.51      ! [A: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.51       => ( ( A != one_one_real )
% 0.26/0.51         => ( ( log @ A @ ( powr_real @ A @ Y3 ) )
% 0.26/0.51            = Y3 ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % log_powr_cancel
% 0.26/0.51  thf(fact_3002_floor__divide__eq__div__numeral,axiom,
% 0.26/0.51      ! [A: num,B: num] :
% 0.26/0.51        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 0.26/0.51        = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_divide_eq_div_numeral
% 0.26/0.51  thf(fact_3003_even__Suc__div__two,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.51       => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.51          = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % even_Suc_div_two
% 0.26/0.51  thf(fact_3004_odd__Suc__div__two,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.51       => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.51          = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % odd_Suc_div_two
% 0.26/0.51  thf(fact_3005_one__less__nat__eq,axiom,
% 0.26/0.51      ! [Z: int] :
% 0.26/0.51        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 0.26/0.51        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.26/0.51  
% 0.26/0.51  % one_less_nat_eq
% 0.26/0.51  thf(fact_3006_powr__numeral,axiom,
% 0.26/0.51      ! [X3: real,N: num] :
% 0.26/0.51        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.51       => ( ( powr_real @ X3 @ ( numeral_numeral_real @ N ) )
% 0.26/0.51          = ( power_power_real @ X3 @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % powr_numeral
% 0.26/0.51  thf(fact_3007_odd__Suc__minus__one,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.51       => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 0.26/0.51          = N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % odd_Suc_minus_one
% 0.26/0.51  thf(fact_3008_numeral__less__floor,axiom,
% 0.26/0.51      ! [V: num,X3: rat] :
% 0.26/0.51        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X3 ) )
% 0.26/0.51        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % numeral_less_floor
% 0.26/0.51  thf(fact_3009_numeral__less__floor,axiom,
% 0.26/0.51      ! [V: num,X3: real] :
% 0.26/0.51        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X3 ) )
% 0.26/0.51        = ( ord_less_eq_real @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % numeral_less_floor
% 0.26/0.51  thf(fact_3010_floor__le__numeral,axiom,
% 0.26/0.51      ! [X3: rat,V: num] :
% 0.26/0.51        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X3 ) @ ( numeral_numeral_int @ V ) )
% 0.26/0.51        = ( ord_less_rat @ X3 @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_le_numeral
% 0.26/0.51  thf(fact_3011_floor__le__numeral,axiom,
% 0.26/0.51      ! [X3: real,V: num] :
% 0.26/0.51        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X3 ) @ ( numeral_numeral_int @ V ) )
% 0.26/0.51        = ( ord_less_real @ X3 @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_le_numeral
% 0.26/0.51  thf(fact_3012_one__less__floor,axiom,
% 0.26/0.51      ! [X3: rat] :
% 0.26/0.51        ( ( ord_less_int @ one_one_int @ ( archim3151403230148437115or_rat @ X3 ) )
% 0.26/0.51        = ( ord_less_eq_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % one_less_floor
% 0.26/0.51  thf(fact_3013_one__less__floor,axiom,
% 0.26/0.51      ! [X3: real] :
% 0.26/0.51        ( ( ord_less_int @ one_one_int @ ( archim6058952711729229775r_real @ X3 ) )
% 0.26/0.51        = ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % one_less_floor
% 0.26/0.51  thf(fact_3014_floor__le__one,axiom,
% 0.26/0.51      ! [X3: rat] :
% 0.26/0.51        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X3 ) @ one_one_int )
% 0.26/0.51        = ( ord_less_rat @ X3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_le_one
% 0.26/0.51  thf(fact_3015_floor__le__one,axiom,
% 0.26/0.51      ! [X3: real] :
% 0.26/0.51        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X3 ) @ one_one_int )
% 0.26/0.51        = ( ord_less_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_le_one
% 0.26/0.51  thf(fact_3016_floor__one__divide__eq__div__numeral,axiom,
% 0.26/0.51      ! [B: num] :
% 0.26/0.51        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 0.26/0.51        = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_one_divide_eq_div_numeral
% 0.26/0.51  thf(fact_3017_n__not__Suc__n,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( N
% 0.26/0.51       != ( suc @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % n_not_Suc_n
% 0.26/0.51  thf(fact_3018_Suc__inject,axiom,
% 0.26/0.51      ! [X3: nat,Y3: nat] :
% 0.26/0.51        ( ( ( suc @ X3 )
% 0.26/0.51          = ( suc @ Y3 ) )
% 0.26/0.51       => ( X3 = Y3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Suc_inject
% 0.26/0.51  thf(fact_3019_floor__le__round,axiom,
% 0.26/0.51      ! [X3: real] : ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X3 ) @ ( archim8280529875227126926d_real @ X3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_le_round
% 0.26/0.51  thf(fact_3020_size__neq__size__imp__neq,axiom,
% 0.26/0.51      ! [X3: list_VEBT_VEBT,Y3: list_VEBT_VEBT] :
% 0.26/0.51        ( ( ( size_s6755466524823107622T_VEBT @ X3 )
% 0.26/0.51         != ( size_s6755466524823107622T_VEBT @ Y3 ) )
% 0.26/0.51       => ( X3 != Y3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % size_neq_size_imp_neq
% 0.26/0.51  thf(fact_3021_size__neq__size__imp__neq,axiom,
% 0.26/0.51      ! [X3: list_o,Y3: list_o] :
% 0.26/0.51        ( ( ( size_size_list_o @ X3 )
% 0.26/0.51         != ( size_size_list_o @ Y3 ) )
% 0.26/0.51       => ( X3 != Y3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % size_neq_size_imp_neq
% 0.26/0.51  thf(fact_3022_size__neq__size__imp__neq,axiom,
% 0.26/0.51      ! [X3: list_nat,Y3: list_nat] :
% 0.26/0.51        ( ( ( size_size_list_nat @ X3 )
% 0.26/0.51         != ( size_size_list_nat @ Y3 ) )
% 0.26/0.51       => ( X3 != Y3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % size_neq_size_imp_neq
% 0.26/0.51  thf(fact_3023_size__neq__size__imp__neq,axiom,
% 0.26/0.51      ! [X3: list_int,Y3: list_int] :
% 0.26/0.51        ( ( ( size_size_list_int @ X3 )
% 0.26/0.51         != ( size_size_list_int @ Y3 ) )
% 0.26/0.51       => ( X3 != Y3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % size_neq_size_imp_neq
% 0.26/0.51  thf(fact_3024_size__neq__size__imp__neq,axiom,
% 0.26/0.51      ! [X3: num,Y3: num] :
% 0.26/0.51        ( ( ( size_size_num @ X3 )
% 0.26/0.51         != ( size_size_num @ Y3 ) )
% 0.26/0.51       => ( X3 != Y3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % size_neq_size_imp_neq
% 0.26/0.51  thf(fact_3025_exists__least__lemma,axiom,
% 0.26/0.51      ! [P: nat > $o] :
% 0.26/0.51        ( ~ ( P @ zero_zero_nat )
% 0.26/0.51       => ( ? [X_12: nat] : ( P @ X_12 )
% 0.26/0.51         => ? [N2: nat] :
% 0.26/0.51              ( ~ ( P @ N2 )
% 0.26/0.51              & ( P @ ( suc @ N2 ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % exists_least_lemma
% 0.26/0.51  thf(fact_3026_nat_Odistinct_I1_J,axiom,
% 0.26/0.51      ! [X2: nat] :
% 0.26/0.51        ( zero_zero_nat
% 0.26/0.51       != ( suc @ X2 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % nat.distinct(1)
% 0.26/0.51  thf(fact_3027_old_Onat_Odistinct_I2_J,axiom,
% 0.26/0.51      ! [Nat2: nat] :
% 0.26/0.51        ( ( suc @ Nat2 )
% 0.26/0.51       != zero_zero_nat ) ).
% 0.26/0.51  
% 0.26/0.51  % old.nat.distinct(2)
% 0.26/0.51  thf(fact_3028_old_Onat_Odistinct_I1_J,axiom,
% 0.26/0.51      ! [Nat2: nat] :
% 0.26/0.51        ( zero_zero_nat
% 0.26/0.51       != ( suc @ Nat2 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % old.nat.distinct(1)
% 0.26/0.51  thf(fact_3029_nat_OdiscI,axiom,
% 0.26/0.51      ! [Nat: nat,X2: nat] :
% 0.26/0.51        ( ( Nat
% 0.26/0.51          = ( suc @ X2 ) )
% 0.26/0.51       => ( Nat != zero_zero_nat ) ) ).
% 0.26/0.51  
% 0.26/0.51  % nat.discI
% 0.26/0.51  thf(fact_3030_old_Onat_Oexhaust,axiom,
% 0.26/0.51      ! [Y3: nat] :
% 0.26/0.51        ( ( Y3 != zero_zero_nat )
% 0.26/0.51       => ~ ! [Nat3: nat] :
% 0.26/0.51              ( Y3
% 0.26/0.51             != ( suc @ Nat3 ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % old.nat.exhaust
% 0.26/0.51  thf(fact_3031_nat__induct,axiom,
% 0.26/0.51      ! [P: nat > $o,N: nat] :
% 0.26/0.51        ( ( P @ zero_zero_nat )
% 0.26/0.51       => ( ! [N2: nat] :
% 0.26/0.51              ( ( P @ N2 )
% 0.26/0.51             => ( P @ ( suc @ N2 ) ) )
% 0.26/0.51         => ( P @ N ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % nat_induct
% 0.26/0.51  thf(fact_3032_diff__induct,axiom,
% 0.26/0.51      ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.26/0.51        ( ! [X4: nat] : ( P @ X4 @ zero_zero_nat )
% 0.26/0.51       => ( ! [Y4: nat] : ( P @ zero_zero_nat @ ( suc @ Y4 ) )
% 0.26/0.51         => ( ! [X4: nat,Y4: nat] :
% 0.26/0.51                ( ( P @ X4 @ Y4 )
% 0.26/0.51               => ( P @ ( suc @ X4 ) @ ( suc @ Y4 ) ) )
% 0.26/0.51           => ( P @ M @ N ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % diff_induct
% 0.26/0.51  thf(fact_3033_zero__induct,axiom,
% 0.26/0.51      ! [P: nat > $o,K: nat] :
% 0.26/0.51        ( ( P @ K )
% 0.26/0.51       => ( ! [N2: nat] :
% 0.26/0.51              ( ( P @ ( suc @ N2 ) )
% 0.26/0.51             => ( P @ N2 ) )
% 0.26/0.51         => ( P @ zero_zero_nat ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zero_induct
% 0.26/0.51  thf(fact_3034_Suc__neq__Zero,axiom,
% 0.26/0.51      ! [M: nat] :
% 0.26/0.51        ( ( suc @ M )
% 0.26/0.51       != zero_zero_nat ) ).
% 0.26/0.51  
% 0.26/0.51  % Suc_neq_Zero
% 0.26/0.51  thf(fact_3035_Zero__neq__Suc,axiom,
% 0.26/0.51      ! [M: nat] :
% 0.26/0.51        ( zero_zero_nat
% 0.26/0.51       != ( suc @ M ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Zero_neq_Suc
% 0.26/0.51  thf(fact_3036_Zero__not__Suc,axiom,
% 0.26/0.51      ! [M: nat] :
% 0.26/0.51        ( zero_zero_nat
% 0.26/0.51       != ( suc @ M ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Zero_not_Suc
% 0.26/0.51  thf(fact_3037_not0__implies__Suc,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ( ( N != zero_zero_nat )
% 0.26/0.51       => ? [M4: nat] :
% 0.26/0.51            ( N
% 0.26/0.51            = ( suc @ M4 ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % not0_implies_Suc
% 0.26/0.51  thf(fact_3038_list__decode_Ocases,axiom,
% 0.26/0.51      ! [X3: nat] :
% 0.26/0.51        ( ( X3 != zero_zero_nat )
% 0.26/0.51       => ~ ! [N2: nat] :
% 0.26/0.51              ( X3
% 0.26/0.51             != ( suc @ N2 ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % list_decode.cases
% 0.26/0.51  thf(fact_3039_not__less__less__Suc__eq,axiom,
% 0.26/0.51      ! [N: nat,M: nat] :
% 0.26/0.51        ( ~ ( ord_less_nat @ N @ M )
% 0.26/0.51       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.26/0.51          = ( N = M ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % not_less_less_Suc_eq
% 0.26/0.51  thf(fact_3040_strict__inc__induct,axiom,
% 0.26/0.51      ! [I: nat,J: nat,P: nat > $o] :
% 0.26/0.51        ( ( ord_less_nat @ I @ J )
% 0.26/0.51       => ( ! [I3: nat] :
% 0.26/0.51              ( ( J
% 0.26/0.51                = ( suc @ I3 ) )
% 0.26/0.51             => ( P @ I3 ) )
% 0.26/0.51         => ( ! [I3: nat] :
% 0.26/0.51                ( ( ord_less_nat @ I3 @ J )
% 0.26/0.51               => ( ( P @ ( suc @ I3 ) )
% 0.26/0.51                 => ( P @ I3 ) ) )
% 0.26/0.51           => ( P @ I ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % strict_inc_induct
% 0.26/0.51  thf(fact_3041_less__Suc__induct,axiom,
% 0.26/0.51      ! [I: nat,J: nat,P: nat > nat > $o] :
% 0.26/0.51        ( ( ord_less_nat @ I @ J )
% 0.26/0.51       => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 0.26/0.51         => ( ! [I3: nat,J2: nat,K2: nat] :
% 0.26/0.51                ( ( ord_less_nat @ I3 @ J2 )
% 0.26/0.51               => ( ( ord_less_nat @ J2 @ K2 )
% 0.26/0.51                 => ( ( P @ I3 @ J2 )
% 0.26/0.51                   => ( ( P @ J2 @ K2 )
% 0.26/0.51                     => ( P @ I3 @ K2 ) ) ) ) )
% 0.26/0.51           => ( P @ I @ J ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % less_Suc_induct
% 0.26/0.51  thf(fact_3042_less__trans__Suc,axiom,
% 0.26/0.51      ! [I: nat,J: nat,K: nat] :
% 0.26/0.51        ( ( ord_less_nat @ I @ J )
% 0.26/0.51       => ( ( ord_less_nat @ J @ K )
% 0.26/0.51         => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % less_trans_Suc
% 0.26/0.51  thf(fact_3043_Suc__less__SucD,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.26/0.51       => ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Suc_less_SucD
% 0.26/0.51  thf(fact_3044_less__antisym,axiom,
% 0.26/0.51      ! [N: nat,M: nat] :
% 0.26/0.51        ( ~ ( ord_less_nat @ N @ M )
% 0.26/0.51       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.26/0.51         => ( M = N ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % less_antisym
% 0.26/0.51  thf(fact_3045_Suc__less__eq2,axiom,
% 0.26/0.51      ! [N: nat,M: nat] :
% 0.26/0.51        ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.26/0.51        = ( ? [M5: nat] :
% 0.26/0.51              ( ( M
% 0.26/0.51                = ( suc @ M5 ) )
% 0.26/0.51              & ( ord_less_nat @ N @ M5 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Suc_less_eq2
% 0.26/0.51  thf(fact_3046_All__less__Suc,axiom,
% 0.26/0.51      ! [N: nat,P: nat > $o] :
% 0.26/0.51        ( ( ! [I4: nat] :
% 0.26/0.51              ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 0.26/0.51             => ( P @ I4 ) ) )
% 0.26/0.51        = ( ( P @ N )
% 0.26/0.51          & ! [I4: nat] :
% 0.26/0.51              ( ( ord_less_nat @ I4 @ N )
% 0.26/0.51             => ( P @ I4 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % All_less_Suc
% 0.26/0.51  thf(fact_3047_not__less__eq,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( ~ ( ord_less_nat @ M @ N ) )
% 0.26/0.51        = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % not_less_eq
% 0.26/0.51  thf(fact_3048_less__Suc__eq,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.26/0.51        = ( ( ord_less_nat @ M @ N )
% 0.26/0.51          | ( M = N ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % less_Suc_eq
% 0.26/0.51  thf(fact_3049_Ex__less__Suc,axiom,
% 0.26/0.51      ! [N: nat,P: nat > $o] :
% 0.26/0.51        ( ( ? [I4: nat] :
% 0.26/0.51              ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 0.26/0.51              & ( P @ I4 ) ) )
% 0.26/0.51        = ( ( P @ N )
% 0.26/0.51          | ? [I4: nat] :
% 0.26/0.51              ( ( ord_less_nat @ I4 @ N )
% 0.26/0.51              & ( P @ I4 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Ex_less_Suc
% 0.26/0.51  thf(fact_3050_less__SucI,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( ord_less_nat @ M @ N )
% 0.26/0.51       => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % less_SucI
% 0.26/0.51  thf(fact_3051_less__SucE,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.26/0.51       => ( ~ ( ord_less_nat @ M @ N )
% 0.26/0.51         => ( M = N ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % less_SucE
% 0.26/0.51  thf(fact_3052_Suc__lessI,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( ord_less_nat @ M @ N )
% 0.26/0.51       => ( ( ( suc @ M )
% 0.26/0.51           != N )
% 0.26/0.51         => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Suc_lessI
% 0.26/0.51  thf(fact_3053_Suc__lessE,axiom,
% 0.26/0.51      ! [I: nat,K: nat] :
% 0.26/0.51        ( ( ord_less_nat @ ( suc @ I ) @ K )
% 0.26/0.51       => ~ ! [J2: nat] :
% 0.26/0.51              ( ( ord_less_nat @ I @ J2 )
% 0.26/0.51             => ( K
% 0.26/0.51               != ( suc @ J2 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Suc_lessE
% 0.26/0.51  thf(fact_3054_Suc__lessD,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( ord_less_nat @ ( suc @ M ) @ N )
% 0.26/0.51       => ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Suc_lessD
% 0.26/0.51  thf(fact_3055_Nat_OlessE,axiom,
% 0.26/0.51      ! [I: nat,K: nat] :
% 0.26/0.51        ( ( ord_less_nat @ I @ K )
% 0.26/0.51       => ( ( K
% 0.26/0.51           != ( suc @ I ) )
% 0.26/0.51         => ~ ! [J2: nat] :
% 0.26/0.51                ( ( ord_less_nat @ I @ J2 )
% 0.26/0.51               => ( K
% 0.26/0.51                 != ( suc @ J2 ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Nat.lessE
% 0.26/0.51  thf(fact_3056_nat__arith_Osuc1,axiom,
% 0.26/0.51      ! [A3: nat,K: nat,A: nat] :
% 0.26/0.51        ( ( A3
% 0.26/0.51          = ( plus_plus_nat @ K @ A ) )
% 0.26/0.51       => ( ( suc @ A3 )
% 0.26/0.51          = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % nat_arith.suc1
% 0.26/0.51  thf(fact_3057_add__Suc,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.26/0.51        = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % add_Suc
% 0.26/0.51  thf(fact_3058_add__Suc__shift,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.26/0.51        = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % add_Suc_shift
% 0.26/0.51  thf(fact_3059_Suc__leD,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.26/0.51       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Suc_leD
% 0.26/0.51  thf(fact_3060_le__SucE,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.26/0.51       => ( ~ ( ord_less_eq_nat @ M @ N )
% 0.26/0.51         => ( M
% 0.26/0.51            = ( suc @ N ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % le_SucE
% 0.26/0.51  thf(fact_3061_le__SucI,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.51       => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % le_SucI
% 0.26/0.51  thf(fact_3062_Suc__le__D,axiom,
% 0.26/0.51      ! [N: nat,M6: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ ( suc @ N ) @ M6 )
% 0.26/0.51       => ? [M4: nat] :
% 0.26/0.51            ( M6
% 0.26/0.51            = ( suc @ M4 ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % Suc_le_D
% 0.26/0.51  thf(fact_3063_le__Suc__eq,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.26/0.51        = ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.51          | ( M
% 0.26/0.51            = ( suc @ N ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % le_Suc_eq
% 0.26/0.51  thf(fact_3064_Suc__n__not__le__n,axiom,
% 0.26/0.51      ! [N: nat] :
% 0.26/0.51        ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 0.26/0.51  
% 0.26/0.51  % Suc_n_not_le_n
% 0.26/0.51  thf(fact_3065_not__less__eq__eq,axiom,
% 0.26/0.51      ! [M: nat,N: nat] :
% 0.26/0.51        ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 0.26/0.51        = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 0.26/0.51  
% 0.26/0.51  % not_less_eq_eq
% 0.26/0.51  thf(fact_3066_full__nat__induct,axiom,
% 0.26/0.51      ! [P: nat > $o,N: nat] :
% 0.26/0.51        ( ! [N2: nat] :
% 0.26/0.51            ( ! [M2: nat] :
% 0.26/0.51                ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N2 )
% 0.26/0.51               => ( P @ M2 ) )
% 0.26/0.51           => ( P @ N2 ) )
% 0.26/0.51       => ( P @ N ) ) ).
% 0.26/0.51  
% 0.26/0.51  % full_nat_induct
% 0.26/0.51  thf(fact_3067_nat__induct__at__least,axiom,
% 0.26/0.51      ! [M: nat,N: nat,P: nat > $o] :
% 0.26/0.51        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.51       => ( ( P @ M )
% 0.26/0.51         => ( ! [N2: nat] :
% 0.26/0.51                ( ( ord_less_eq_nat @ M @ N2 )
% 0.26/0.51               => ( ( P @ N2 )
% 0.26/0.51                 => ( P @ ( suc @ N2 ) ) ) )
% 0.26/0.51           => ( P @ N ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % nat_induct_at_least
% 0.26/0.51  thf(fact_3068_transitive__stepwise__le,axiom,
% 0.26/0.51      ! [M: nat,N: nat,R3: nat > nat > $o] :
% 0.26/0.51        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.51       => ( ! [X4: nat] : ( R3 @ X4 @ X4 )
% 0.26/0.51         => ( ! [X4: nat,Y4: nat,Z3: nat] :
% 0.26/0.51                ( ( R3 @ X4 @ Y4 )
% 0.26/0.51               => ( ( R3 @ Y4 @ Z3 )
% 0.26/0.51                 => ( R3 @ X4 @ Z3 ) ) )
% 0.26/0.51           => ( ! [N2: nat] : ( R3 @ N2 @ ( suc @ N2 ) )
% 0.26/0.51             => ( R3 @ M @ N ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % transitive_stepwise_le
% 0.26/0.51  thf(fact_3069_zero__induct__lemma,axiom,
% 0.26/0.51      ! [P: nat > $o,K: nat,I: nat] :
% 0.26/0.51        ( ( P @ K )
% 0.26/0.51       => ( ! [N2: nat] :
% 0.26/0.51              ( ( P @ ( suc @ N2 ) )
% 0.26/0.51             => ( P @ N2 ) )
% 0.26/0.51         => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % zero_induct_lemma
% 0.26/0.51  thf(fact_3070_floor__eq3,axiom,
% 0.26/0.51      ! [N: nat,X3: real] :
% 0.26/0.51        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X3 )
% 0.26/0.51       => ( ( ord_less_real @ X3 @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 0.26/0.51         => ( ( nat2 @ ( archim6058952711729229775r_real @ X3 ) )
% 0.26/0.51            = N ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_eq3
% 0.26/0.51  thf(fact_3071_floor__mono,axiom,
% 0.26/0.51      ! [X3: rat,Y3: rat] :
% 0.26/0.51        ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.26/0.51       => ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X3 ) @ ( archim3151403230148437115or_rat @ Y3 ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_mono
% 0.26/0.51  thf(fact_3072_floor__mono,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.26/0.51       => ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X3 ) @ ( archim6058952711729229775r_real @ Y3 ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_mono
% 0.26/0.51  thf(fact_3073_of__int__floor__le,axiom,
% 0.26/0.51      ! [X3: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X3 ) ) @ X3 ) ).
% 0.26/0.51  
% 0.26/0.51  % of_int_floor_le
% 0.26/0.51  thf(fact_3074_of__int__floor__le,axiom,
% 0.26/0.51      ! [X3: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X3 ) ) @ X3 ) ).
% 0.26/0.51  
% 0.26/0.51  % of_int_floor_le
% 0.26/0.51  thf(fact_3075_floor__less__cancel,axiom,
% 0.26/0.51      ! [X3: rat,Y3: rat] :
% 0.26/0.51        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X3 ) @ ( archim3151403230148437115or_rat @ Y3 ) )
% 0.26/0.51       => ( ord_less_rat @ X3 @ Y3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_less_cancel
% 0.26/0.51  thf(fact_3076_floor__less__cancel,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X3 ) @ ( archim6058952711729229775r_real @ Y3 ) )
% 0.26/0.51       => ( ord_less_real @ X3 @ Y3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_less_cancel
% 0.26/0.51  thf(fact_3077_powr__less__mono2__neg,axiom,
% 0.26/0.51      ! [A: real,X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_real @ A @ zero_zero_real )
% 0.26/0.51       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.51         => ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.51           => ( ord_less_real @ ( powr_real @ Y3 @ A ) @ ( powr_real @ X3 @ A ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % powr_less_mono2_neg
% 0.26/0.51  thf(fact_3078_powr__non__neg,axiom,
% 0.26/0.51      ! [A: real,X3: real] :
% 0.26/0.51        ~ ( ord_less_real @ ( powr_real @ A @ X3 ) @ zero_zero_real ) ).
% 0.26/0.51  
% 0.26/0.51  % powr_non_neg
% 0.26/0.51  thf(fact_3079_powr__ge__pzero,axiom,
% 0.26/0.51      ! [X3: real,Y3: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X3 @ Y3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % powr_ge_pzero
% 0.26/0.51  thf(fact_3080_powr__mono2,axiom,
% 0.26/0.51      ! [A: real,X3: real,Y3: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.51       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.51         => ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.26/0.51           => ( ord_less_eq_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ Y3 @ A ) ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % powr_mono2
% 0.26/0.51  thf(fact_3081_floor__eq4,axiom,
% 0.26/0.51      ! [N: nat,X3: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X3 )
% 0.26/0.51       => ( ( ord_less_real @ X3 @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 0.26/0.51         => ( ( nat2 @ ( archim6058952711729229775r_real @ X3 ) )
% 0.26/0.51            = N ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_eq4
% 0.26/0.51  thf(fact_3082_powr__less__mono,axiom,
% 0.26/0.51      ! [A: real,B: real,X3: real] :
% 0.26/0.51        ( ( ord_less_real @ A @ B )
% 0.26/0.51       => ( ( ord_less_real @ one_one_real @ X3 )
% 0.26/0.51         => ( ord_less_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % powr_less_mono
% 0.26/0.51  thf(fact_3083_powr__less__cancel,axiom,
% 0.26/0.51      ! [X3: real,A: real,B: real] :
% 0.26/0.51        ( ( ord_less_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) )
% 0.26/0.51       => ( ( ord_less_real @ one_one_real @ X3 )
% 0.26/0.51         => ( ord_less_real @ A @ B ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % powr_less_cancel
% 0.26/0.51  thf(fact_3084_powr__mono,axiom,
% 0.26/0.51      ! [A: real,B: real,X3: real] :
% 0.26/0.51        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.51       => ( ( ord_less_eq_real @ one_one_real @ X3 )
% 0.26/0.51         => ( ord_less_eq_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % powr_mono
% 0.26/0.51  thf(fact_3085_floor__le__ceiling,axiom,
% 0.26/0.51      ! [X3: real] : ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X3 ) @ ( archim7802044766580827645g_real @ X3 ) ) ).
% 0.26/0.51  
% 0.26/0.51  % floor_le_ceiling
% 0.26/0.51  thf(fact_3086_lift__Suc__mono__less__iff,axiom,
% 0.26/0.51      ! [F: nat > real,N: nat,M: nat] :
% 0.26/0.51        ( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.51       => ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
% 0.26/0.51          = ( ord_less_nat @ N @ M ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % lift_Suc_mono_less_iff
% 0.26/0.51  thf(fact_3087_lift__Suc__mono__less__iff,axiom,
% 0.26/0.51      ! [F: nat > rat,N: nat,M: nat] :
% 0.26/0.51        ( ! [N2: nat] : ( ord_less_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.51       => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 0.26/0.51          = ( ord_less_nat @ N @ M ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % lift_Suc_mono_less_iff
% 0.26/0.51  thf(fact_3088_lift__Suc__mono__less__iff,axiom,
% 0.26/0.51      ! [F: nat > num,N: nat,M: nat] :
% 0.26/0.51        ( ! [N2: nat] : ( ord_less_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.51       => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 0.26/0.51          = ( ord_less_nat @ N @ M ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % lift_Suc_mono_less_iff
% 0.26/0.51  thf(fact_3089_lift__Suc__mono__less__iff,axiom,
% 0.26/0.51      ! [F: nat > nat,N: nat,M: nat] :
% 0.26/0.51        ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.51       => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 0.26/0.51          = ( ord_less_nat @ N @ M ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % lift_Suc_mono_less_iff
% 0.26/0.51  thf(fact_3090_lift__Suc__mono__less__iff,axiom,
% 0.26/0.51      ! [F: nat > int,N: nat,M: nat] :
% 0.26/0.51        ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.51       => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 0.26/0.51          = ( ord_less_nat @ N @ M ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % lift_Suc_mono_less_iff
% 0.26/0.51  thf(fact_3091_lift__Suc__mono__less,axiom,
% 0.26/0.51      ! [F: nat > real,N: nat,N5: nat] :
% 0.26/0.51        ( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.51       => ( ( ord_less_nat @ N @ N5 )
% 0.26/0.51         => ( ord_less_real @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % lift_Suc_mono_less
% 0.26/0.51  thf(fact_3092_lift__Suc__mono__less,axiom,
% 0.26/0.51      ! [F: nat > rat,N: nat,N5: nat] :
% 0.26/0.51        ( ! [N2: nat] : ( ord_less_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.51       => ( ( ord_less_nat @ N @ N5 )
% 0.26/0.51         => ( ord_less_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % lift_Suc_mono_less
% 0.26/0.51  thf(fact_3093_lift__Suc__mono__less,axiom,
% 0.26/0.51      ! [F: nat > num,N: nat,N5: nat] :
% 0.26/0.51        ( ! [N2: nat] : ( ord_less_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.51       => ( ( ord_less_nat @ N @ N5 )
% 0.26/0.51         => ( ord_less_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % lift_Suc_mono_less
% 0.26/0.51  thf(fact_3094_lift__Suc__mono__less,axiom,
% 0.26/0.51      ! [F: nat > nat,N: nat,N5: nat] :
% 0.26/0.51        ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.51       => ( ( ord_less_nat @ N @ N5 )
% 0.26/0.51         => ( ord_less_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % lift_Suc_mono_less
% 0.26/0.51  thf(fact_3095_lift__Suc__mono__less,axiom,
% 0.26/0.51      ! [F: nat > int,N: nat,N5: nat] :
% 0.26/0.51        ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.51       => ( ( ord_less_nat @ N @ N5 )
% 0.26/0.51         => ( ord_less_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % lift_Suc_mono_less
% 0.26/0.51  thf(fact_3096_lift__Suc__mono__le,axiom,
% 0.26/0.51      ! [F: nat > set_nat,N: nat,N5: nat] :
% 0.26/0.51        ( ! [N2: nat] : ( ord_less_eq_set_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.51       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.26/0.51         => ( ord_less_eq_set_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % lift_Suc_mono_le
% 0.26/0.51  thf(fact_3097_lift__Suc__mono__le,axiom,
% 0.26/0.51      ! [F: nat > rat,N: nat,N5: nat] :
% 0.26/0.51        ( ! [N2: nat] : ( ord_less_eq_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.51       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.26/0.51         => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % lift_Suc_mono_le
% 0.26/0.51  thf(fact_3098_lift__Suc__mono__le,axiom,
% 0.26/0.51      ! [F: nat > num,N: nat,N5: nat] :
% 0.26/0.51        ( ! [N2: nat] : ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.51       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.26/0.51         => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % lift_Suc_mono_le
% 0.26/0.51  thf(fact_3099_lift__Suc__mono__le,axiom,
% 0.26/0.51      ! [F: nat > nat,N: nat,N5: nat] :
% 0.26/0.51        ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.51       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.26/0.51         => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % lift_Suc_mono_le
% 0.26/0.51  thf(fact_3100_lift__Suc__mono__le,axiom,
% 0.26/0.51      ! [F: nat > int,N: nat,N5: nat] :
% 0.26/0.51        ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.51       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.26/0.51         => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % lift_Suc_mono_le
% 0.26/0.51  thf(fact_3101_lift__Suc__antimono__le,axiom,
% 0.26/0.51      ! [F: nat > set_nat,N: nat,N5: nat] :
% 0.26/0.51        ( ! [N2: nat] : ( ord_less_eq_set_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.26/0.51       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.26/0.51         => ( ord_less_eq_set_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % lift_Suc_antimono_le
% 0.26/0.51  thf(fact_3102_lift__Suc__antimono__le,axiom,
% 0.26/0.51      ! [F: nat > rat,N: nat,N5: nat] :
% 0.26/0.51        ( ! [N2: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.26/0.51       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.26/0.51         => ( ord_less_eq_rat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % lift_Suc_antimono_le
% 0.26/0.51  thf(fact_3103_lift__Suc__antimono__le,axiom,
% 0.26/0.51      ! [F: nat > num,N: nat,N5: nat] :
% 0.26/0.51        ( ! [N2: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.26/0.51       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.26/0.51         => ( ord_less_eq_num @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 0.26/0.51  
% 0.26/0.51  % lift_Suc_antimono_le
% 0.26/0.51  thf(fact_3104_lift__Suc__antimono__le,axiom,
% 0.26/0.51      ! [F: nat > nat,N: nat,N5: nat] :
% 0.26/0.52        ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.26/0.52       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.26/0.52         => ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % lift_Suc_antimono_le
% 0.26/0.52  thf(fact_3105_lift__Suc__antimono__le,axiom,
% 0.26/0.52      ! [F: nat > int,N: nat,N5: nat] :
% 0.26/0.52        ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.26/0.52       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.26/0.52         => ( ord_less_eq_int @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % lift_Suc_antimono_le
% 0.26/0.52  thf(fact_3106_of__nat__neq__0,axiom,
% 0.26/0.52      ! [N: nat] :
% 0.26/0.52        ( ( semiri8010041392384452111omplex @ ( suc @ N ) )
% 0.26/0.52       != zero_zero_complex ) ).
% 0.26/0.52  
% 0.26/0.52  % of_nat_neq_0
% 0.26/0.52  thf(fact_3107_of__nat__neq__0,axiom,
% 0.26/0.52      ! [N: nat] :
% 0.26/0.52        ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 0.26/0.52       != zero_zero_real ) ).
% 0.26/0.52  
% 0.26/0.52  % of_nat_neq_0
% 0.26/0.52  thf(fact_3108_of__nat__neq__0,axiom,
% 0.26/0.52      ! [N: nat] :
% 0.26/0.52        ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 0.26/0.52       != zero_zero_rat ) ).
% 0.26/0.52  
% 0.26/0.52  % of_nat_neq_0
% 0.26/0.52  thf(fact_3109_of__nat__neq__0,axiom,
% 0.26/0.52      ! [N: nat] :
% 0.26/0.52        ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 0.26/0.52       != zero_zero_nat ) ).
% 0.26/0.52  
% 0.26/0.52  % of_nat_neq_0
% 0.26/0.52  thf(fact_3110_of__nat__neq__0,axiom,
% 0.26/0.52      ! [N: nat] :
% 0.26/0.52        ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 0.26/0.52       != zero_zero_int ) ).
% 0.26/0.52  
% 0.26/0.52  % of_nat_neq_0
% 0.26/0.52  thf(fact_3111_less__Suc__eq__0__disj,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.26/0.52        = ( ( M = zero_zero_nat )
% 0.26/0.52          | ? [J3: nat] :
% 0.26/0.52              ( ( M
% 0.26/0.52                = ( suc @ J3 ) )
% 0.26/0.52              & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % less_Suc_eq_0_disj
% 0.26/0.52  thf(fact_3112_gr0__implies__Suc,axiom,
% 0.26/0.52      ! [N: nat] :
% 0.26/0.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.52       => ? [M4: nat] :
% 0.26/0.52            ( N
% 0.26/0.52            = ( suc @ M4 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % gr0_implies_Suc
% 0.26/0.52  thf(fact_3113_All__less__Suc2,axiom,
% 0.26/0.52      ! [N: nat,P: nat > $o] :
% 0.26/0.52        ( ( ! [I4: nat] :
% 0.26/0.52              ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 0.26/0.52             => ( P @ I4 ) ) )
% 0.26/0.52        = ( ( P @ zero_zero_nat )
% 0.26/0.52          & ! [I4: nat] :
% 0.26/0.52              ( ( ord_less_nat @ I4 @ N )
% 0.26/0.52             => ( P @ ( suc @ I4 ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % All_less_Suc2
% 0.26/0.52  thf(fact_3114_gr0__conv__Suc,axiom,
% 0.26/0.52      ! [N: nat] :
% 0.26/0.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.52        = ( ? [M3: nat] :
% 0.26/0.52              ( N
% 0.26/0.52              = ( suc @ M3 ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % gr0_conv_Suc
% 0.26/0.52  thf(fact_3115_Ex__less__Suc2,axiom,
% 0.26/0.52      ! [N: nat,P: nat > $o] :
% 0.26/0.52        ( ( ? [I4: nat] :
% 0.26/0.52              ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 0.26/0.52              & ( P @ I4 ) ) )
% 0.26/0.52        = ( ( P @ zero_zero_nat )
% 0.26/0.52          | ? [I4: nat] :
% 0.26/0.52              ( ( ord_less_nat @ I4 @ N )
% 0.26/0.52              & ( P @ ( suc @ I4 ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % Ex_less_Suc2
% 0.26/0.52  thf(fact_3116_one__is__add,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( ( suc @ zero_zero_nat )
% 0.26/0.52          = ( plus_plus_nat @ M @ N ) )
% 0.26/0.52        = ( ( ( M
% 0.26/0.52              = ( suc @ zero_zero_nat ) )
% 0.26/0.52            & ( N = zero_zero_nat ) )
% 0.26/0.52          | ( ( M = zero_zero_nat )
% 0.26/0.52            & ( N
% 0.26/0.52              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % one_is_add
% 0.26/0.52  thf(fact_3117_add__is__1,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( ( plus_plus_nat @ M @ N )
% 0.26/0.52          = ( suc @ zero_zero_nat ) )
% 0.26/0.52        = ( ( ( M
% 0.26/0.52              = ( suc @ zero_zero_nat ) )
% 0.26/0.52            & ( N = zero_zero_nat ) )
% 0.26/0.52          | ( ( M = zero_zero_nat )
% 0.26/0.52            & ( N
% 0.26/0.52              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % add_is_1
% 0.26/0.52  thf(fact_3118_less__natE,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( ord_less_nat @ M @ N )
% 0.26/0.52       => ~ ! [Q4: nat] :
% 0.26/0.52              ( N
% 0.26/0.52             != ( suc @ ( plus_plus_nat @ M @ Q4 ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % less_natE
% 0.26/0.52  thf(fact_3119_less__add__Suc1,axiom,
% 0.26/0.52      ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % less_add_Suc1
% 0.26/0.52  thf(fact_3120_less__add__Suc2,axiom,
% 0.26/0.52      ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % less_add_Suc2
% 0.26/0.52  thf(fact_3121_less__iff__Suc__add,axiom,
% 0.26/0.52      ( ord_less_nat
% 0.26/0.52      = ( ^ [M3: nat,N3: nat] :
% 0.26/0.52          ? [K3: nat] :
% 0.26/0.52            ( N3
% 0.26/0.52            = ( suc @ ( plus_plus_nat @ M3 @ K3 ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % less_iff_Suc_add
% 0.26/0.52  thf(fact_3122_less__imp__Suc__add,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( ord_less_nat @ M @ N )
% 0.26/0.52       => ? [K2: nat] :
% 0.26/0.52            ( N
% 0.26/0.52            = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % less_imp_Suc_add
% 0.26/0.52  thf(fact_3123_Suc__leI,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( ord_less_nat @ M @ N )
% 0.26/0.52       => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 0.26/0.52  
% 0.26/0.52  % Suc_leI
% 0.26/0.52  thf(fact_3124_Suc__le__eq,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.26/0.52        = ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.52  
% 0.26/0.52  % Suc_le_eq
% 0.26/0.52  thf(fact_3125_dec__induct,axiom,
% 0.26/0.52      ! [I: nat,J: nat,P: nat > $o] :
% 0.26/0.52        ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.52       => ( ( P @ I )
% 0.26/0.52         => ( ! [N2: nat] :
% 0.26/0.52                ( ( ord_less_eq_nat @ I @ N2 )
% 0.26/0.52               => ( ( ord_less_nat @ N2 @ J )
% 0.26/0.52                 => ( ( P @ N2 )
% 0.26/0.52                   => ( P @ ( suc @ N2 ) ) ) ) )
% 0.26/0.52           => ( P @ J ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % dec_induct
% 0.26/0.52  thf(fact_3126_inc__induct,axiom,
% 0.26/0.52      ! [I: nat,J: nat,P: nat > $o] :
% 0.26/0.52        ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.52       => ( ( P @ J )
% 0.26/0.52         => ( ! [N2: nat] :
% 0.26/0.52                ( ( ord_less_eq_nat @ I @ N2 )
% 0.26/0.52               => ( ( ord_less_nat @ N2 @ J )
% 0.26/0.52                 => ( ( P @ ( suc @ N2 ) )
% 0.26/0.52                   => ( P @ N2 ) ) ) )
% 0.26/0.52           => ( P @ I ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % inc_induct
% 0.26/0.52  thf(fact_3127_Suc__le__lessD,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.26/0.52       => ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.52  
% 0.26/0.52  % Suc_le_lessD
% 0.26/0.52  thf(fact_3128_le__less__Suc__eq,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.52       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.26/0.52          = ( N = M ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % le_less_Suc_eq
% 0.26/0.52  thf(fact_3129_less__Suc__eq__le,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.26/0.52        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.52  
% 0.26/0.52  % less_Suc_eq_le
% 0.26/0.52  thf(fact_3130_less__eq__Suc__le,axiom,
% 0.26/0.52      ( ord_less_nat
% 0.26/0.52      = ( ^ [N3: nat] : ( ord_less_eq_nat @ ( suc @ N3 ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % less_eq_Suc_le
% 0.26/0.52  thf(fact_3131_le__imp__less__Suc,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.52       => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % le_imp_less_Suc
% 0.26/0.52  thf(fact_3132_One__nat__def,axiom,
% 0.26/0.52      ( one_one_nat
% 0.26/0.52      = ( suc @ zero_zero_nat ) ) ).
% 0.26/0.52  
% 0.26/0.52  % One_nat_def
% 0.26/0.52  thf(fact_3133_Suc__eq__plus1,axiom,
% 0.26/0.52      ( suc
% 0.26/0.52      = ( ^ [N3: nat] : ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % Suc_eq_plus1
% 0.26/0.52  thf(fact_3134_plus__1__eq__Suc,axiom,
% 0.26/0.52      ( ( plus_plus_nat @ one_one_nat )
% 0.26/0.52      = suc ) ).
% 0.26/0.52  
% 0.26/0.52  % plus_1_eq_Suc
% 0.26/0.52  thf(fact_3135_Suc__eq__plus1__left,axiom,
% 0.26/0.52      ( suc
% 0.26/0.52      = ( plus_plus_nat @ one_one_nat ) ) ).
% 0.26/0.52  
% 0.26/0.52  % Suc_eq_plus1_left
% 0.26/0.52  thf(fact_3136_diff__less__Suc,axiom,
% 0.26/0.52      ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 0.26/0.52  
% 0.26/0.52  % diff_less_Suc
% 0.26/0.52  thf(fact_3137_Suc__diff__Suc,axiom,
% 0.26/0.52      ! [N: nat,M: nat] :
% 0.26/0.52        ( ( ord_less_nat @ N @ M )
% 0.26/0.52       => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 0.26/0.52          = ( minus_minus_nat @ M @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % Suc_diff_Suc
% 0.26/0.52  thf(fact_3138_Suc__div__le__mono,axiom,
% 0.26/0.52      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 0.26/0.52  
% 0.26/0.52  % Suc_div_le_mono
% 0.26/0.52  thf(fact_3139_Suc__diff__le,axiom,
% 0.26/0.52      ! [N: nat,M: nat] :
% 0.26/0.52        ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.52       => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 0.26/0.52          = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % Suc_diff_le
% 0.26/0.52  thf(fact_3140_diff__Suc__eq__diff__pred,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 0.26/0.52        = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 0.26/0.52  
% 0.26/0.52  % diff_Suc_eq_diff_pred
% 0.26/0.52  thf(fact_3141_tanh__real__lt__1,axiom,
% 0.26/0.52      ! [X3: real] : ( ord_less_real @ ( tanh_real @ X3 ) @ one_one_real ) ).
% 0.26/0.52  
% 0.26/0.52  % tanh_real_lt_1
% 0.26/0.52  thf(fact_3142_le__floor__iff,axiom,
% 0.26/0.52      ! [Z: int,X3: rat] :
% 0.26/0.52        ( ( ord_less_eq_int @ Z @ ( archim3151403230148437115or_rat @ X3 ) )
% 0.26/0.52        = ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X3 ) ) ).
% 0.26/0.52  
% 0.26/0.52  % le_floor_iff
% 0.26/0.52  thf(fact_3143_le__floor__iff,axiom,
% 0.26/0.52      ! [Z: int,X3: real] :
% 0.26/0.52        ( ( ord_less_eq_int @ Z @ ( archim6058952711729229775r_real @ X3 ) )
% 0.26/0.52        = ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X3 ) ) ).
% 0.26/0.52  
% 0.26/0.52  % le_floor_iff
% 0.26/0.52  thf(fact_3144_floor__less__iff,axiom,
% 0.26/0.52      ! [X3: rat,Z: int] :
% 0.26/0.52        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X3 ) @ Z )
% 0.26/0.52        = ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_less_iff
% 0.26/0.52  thf(fact_3145_floor__less__iff,axiom,
% 0.26/0.52      ! [X3: real,Z: int] :
% 0.26/0.52        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X3 ) @ Z )
% 0.26/0.52        = ( ord_less_real @ X3 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_less_iff
% 0.26/0.52  thf(fact_3146_powr__mono2_H,axiom,
% 0.26/0.52      ! [A: real,X3: real,Y3: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.26/0.52       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.52         => ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.26/0.52           => ( ord_less_eq_real @ ( powr_real @ Y3 @ A ) @ ( powr_real @ X3 @ A ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % powr_mono2'
% 0.26/0.52  thf(fact_3147_powr__less__mono2,axiom,
% 0.26/0.52      ! [A: real,X3: real,Y3: real] :
% 0.26/0.52        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.52         => ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.52           => ( ord_less_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ Y3 @ A ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % powr_less_mono2
% 0.26/0.52  thf(fact_3148_le__floor__add,axiom,
% 0.26/0.52      ! [X3: rat,Y3: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X3 ) @ ( archim3151403230148437115or_rat @ Y3 ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X3 @ Y3 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % le_floor_add
% 0.26/0.52  thf(fact_3149_le__floor__add,axiom,
% 0.26/0.52      ! [X3: real,Y3: real] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X3 ) @ ( archim6058952711729229775r_real @ Y3 ) ) @ ( archim6058952711729229775r_real @ ( plus_plus_real @ X3 @ Y3 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % le_floor_add
% 0.26/0.52  thf(fact_3150_int__add__floor,axiom,
% 0.26/0.52      ! [Z: int,X3: rat] :
% 0.26/0.52        ( ( plus_plus_int @ Z @ ( archim3151403230148437115or_rat @ X3 ) )
% 0.26/0.52        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ X3 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % int_add_floor
% 0.26/0.52  thf(fact_3151_int__add__floor,axiom,
% 0.26/0.52      ! [Z: int,X3: real] :
% 0.26/0.52        ( ( plus_plus_int @ Z @ ( archim6058952711729229775r_real @ X3 ) )
% 0.26/0.52        = ( archim6058952711729229775r_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ X3 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % int_add_floor
% 0.26/0.52  thf(fact_3152_floor__add__int,axiom,
% 0.26/0.52      ! [X3: rat,Z: int] :
% 0.26/0.52        ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X3 ) @ Z )
% 0.26/0.52        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X3 @ ( ring_1_of_int_rat @ Z ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_add_int
% 0.26/0.52  thf(fact_3153_floor__add__int,axiom,
% 0.26/0.52      ! [X3: real,Z: int] :
% 0.26/0.52        ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X3 ) @ Z )
% 0.26/0.52        = ( archim6058952711729229775r_real @ ( plus_plus_real @ X3 @ ( ring_1_of_int_real @ Z ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_add_int
% 0.26/0.52  thf(fact_3154_powr__inj,axiom,
% 0.26/0.52      ! [A: real,X3: real,Y3: real] :
% 0.26/0.52        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.52       => ( ( A != one_one_real )
% 0.26/0.52         => ( ( ( powr_real @ A @ X3 )
% 0.26/0.52              = ( powr_real @ A @ Y3 ) )
% 0.26/0.52            = ( X3 = Y3 ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % powr_inj
% 0.26/0.52  thf(fact_3155_gr__one__powr,axiom,
% 0.26/0.52      ! [X3: real,Y3: real] :
% 0.26/0.52        ( ( ord_less_real @ one_one_real @ X3 )
% 0.26/0.52       => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.52         => ( ord_less_real @ one_one_real @ ( powr_real @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % gr_one_powr
% 0.26/0.52  thf(fact_3156_powr__le1,axiom,
% 0.26/0.52      ! [A: real,X3: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.52         => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 0.26/0.52           => ( ord_less_eq_real @ ( powr_real @ X3 @ A ) @ one_one_real ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % powr_le1
% 0.26/0.52  thf(fact_3157_powr__mono__both,axiom,
% 0.26/0.52      ! [A: real,B: real,X3: real,Y3: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.52       => ( ( ord_less_eq_real @ A @ B )
% 0.26/0.52         => ( ( ord_less_eq_real @ one_one_real @ X3 )
% 0.26/0.52           => ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.26/0.52             => ( ord_less_eq_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ Y3 @ B ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % powr_mono_both
% 0.26/0.52  thf(fact_3158_ge__one__powr__ge__zero,axiom,
% 0.26/0.52      ! [X3: real,A: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ one_one_real @ X3 )
% 0.26/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.52         => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X3 @ A ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % ge_one_powr_ge_zero
% 0.26/0.52  thf(fact_3159_powr__divide,axiom,
% 0.26/0.52      ! [X3: real,Y3: real,A: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.52         => ( ( powr_real @ ( divide_divide_real @ X3 @ Y3 ) @ A )
% 0.26/0.52            = ( divide_divide_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ Y3 @ A ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % powr_divide
% 0.26/0.52  thf(fact_3160_floor__divide__of__int__eq,axiom,
% 0.26/0.52      ! [K: int,L: int] :
% 0.26/0.52        ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ K ) @ ( ring_1_of_int_rat @ L ) ) )
% 0.26/0.52        = ( divide_divide_int @ K @ L ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_divide_of_int_eq
% 0.26/0.52  thf(fact_3161_floor__divide__of__int__eq,axiom,
% 0.26/0.52      ! [K: int,L: int] :
% 0.26/0.52        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( ring_1_of_int_real @ K ) @ ( ring_1_of_int_real @ L ) ) )
% 0.26/0.52        = ( divide_divide_int @ K @ L ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_divide_of_int_eq
% 0.26/0.52  thf(fact_3162_floor__power,axiom,
% 0.26/0.52      ! [X3: rat,N: nat] :
% 0.26/0.52        ( ( X3
% 0.26/0.52          = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X3 ) ) )
% 0.26/0.52       => ( ( archim3151403230148437115or_rat @ ( power_power_rat @ X3 @ N ) )
% 0.26/0.52          = ( power_power_int @ ( archim3151403230148437115or_rat @ X3 ) @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_power
% 0.26/0.52  thf(fact_3163_floor__power,axiom,
% 0.26/0.52      ! [X3: real,N: nat] :
% 0.26/0.52        ( ( X3
% 0.26/0.52          = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X3 ) ) )
% 0.26/0.52       => ( ( archim6058952711729229775r_real @ ( power_power_real @ X3 @ N ) )
% 0.26/0.52          = ( power_power_int @ ( archim6058952711729229775r_real @ X3 ) @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_power
% 0.26/0.52  thf(fact_3164_log__base__powr,axiom,
% 0.26/0.52      ! [A: real,B: real,X3: real] :
% 0.26/0.52        ( ( A != zero_zero_real )
% 0.26/0.52       => ( ( log @ ( powr_real @ A @ B ) @ X3 )
% 0.26/0.52          = ( divide_divide_real @ ( log @ A @ X3 ) @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % log_base_powr
% 0.26/0.52  thf(fact_3165_round__mono,axiom,
% 0.26/0.52      ! [X3: rat,Y3: rat] :
% 0.26/0.52        ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.26/0.52       => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X3 ) @ ( archim7778729529865785530nd_rat @ Y3 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % round_mono
% 0.26/0.52  thf(fact_3166_power__inject__base,axiom,
% 0.26/0.52      ! [A: real,N: nat,B: real] :
% 0.26/0.52        ( ( ( power_power_real @ A @ ( suc @ N ) )
% 0.26/0.52          = ( power_power_real @ B @ ( suc @ N ) ) )
% 0.26/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.52         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.26/0.52           => ( A = B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_inject_base
% 0.26/0.52  thf(fact_3167_power__inject__base,axiom,
% 0.26/0.52      ! [A: rat,N: nat,B: rat] :
% 0.26/0.52        ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 0.26/0.52          = ( power_power_rat @ B @ ( suc @ N ) ) )
% 0.26/0.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.52         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.26/0.52           => ( A = B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_inject_base
% 0.26/0.52  thf(fact_3168_power__inject__base,axiom,
% 0.26/0.52      ! [A: nat,N: nat,B: nat] :
% 0.26/0.52        ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 0.26/0.52          = ( power_power_nat @ B @ ( suc @ N ) ) )
% 0.26/0.52       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.52         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.26/0.52           => ( A = B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_inject_base
% 0.26/0.52  thf(fact_3169_power__inject__base,axiom,
% 0.26/0.52      ! [A: int,N: nat,B: int] :
% 0.26/0.52        ( ( ( power_power_int @ A @ ( suc @ N ) )
% 0.26/0.52          = ( power_power_int @ B @ ( suc @ N ) ) )
% 0.26/0.52       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.52         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.26/0.52           => ( A = B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_inject_base
% 0.26/0.52  thf(fact_3170_power__le__imp__le__base,axiom,
% 0.26/0.52      ! [A: real,N: nat,B: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 0.26/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.26/0.52         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_le_imp_le_base
% 0.26/0.52  thf(fact_3171_power__le__imp__le__base,axiom,
% 0.26/0.52      ! [A: rat,N: nat,B: rat] :
% 0.26/0.52        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 0.26/0.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.26/0.52         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_le_imp_le_base
% 0.26/0.52  thf(fact_3172_power__le__imp__le__base,axiom,
% 0.26/0.52      ! [A: nat,N: nat,B: nat] :
% 0.26/0.52        ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 0.26/0.52       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.26/0.52         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_le_imp_le_base
% 0.26/0.52  thf(fact_3173_power__le__imp__le__base,axiom,
% 0.26/0.52      ! [A: int,N: nat,B: int] :
% 0.26/0.52        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 0.26/0.52       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.26/0.52         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_le_imp_le_base
% 0.26/0.52  thf(fact_3174_power__gt1,axiom,
% 0.26/0.52      ! [A: real,N: nat] :
% 0.26/0.52        ( ( ord_less_real @ one_one_real @ A )
% 0.26/0.52       => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_gt1
% 0.26/0.52  thf(fact_3175_power__gt1,axiom,
% 0.26/0.52      ! [A: rat,N: nat] :
% 0.26/0.52        ( ( ord_less_rat @ one_one_rat @ A )
% 0.26/0.52       => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_gt1
% 0.26/0.52  thf(fact_3176_power__gt1,axiom,
% 0.26/0.52      ! [A: nat,N: nat] :
% 0.26/0.52        ( ( ord_less_nat @ one_one_nat @ A )
% 0.26/0.52       => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_gt1
% 0.26/0.52  thf(fact_3177_power__gt1,axiom,
% 0.26/0.52      ! [A: int,N: nat] :
% 0.26/0.52        ( ( ord_less_int @ one_one_int @ A )
% 0.26/0.52       => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_gt1
% 0.26/0.52  thf(fact_3178_round__def,axiom,
% 0.26/0.52      ( archim7778729529865785530nd_rat
% 0.26/0.52      = ( ^ [X: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % round_def
% 0.26/0.52  thf(fact_3179_round__def,axiom,
% 0.26/0.52      ( archim8280529875227126926d_real
% 0.26/0.52      = ( ^ [X: real] : ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % round_def
% 0.26/0.52  thf(fact_3180_numeral__1__eq__Suc__0,axiom,
% 0.26/0.52      ( ( numeral_numeral_nat @ one )
% 0.26/0.52      = ( suc @ zero_zero_nat ) ) ).
% 0.26/0.52  
% 0.26/0.52  % numeral_1_eq_Suc_0
% 0.26/0.52  thf(fact_3181_ex__least__nat__less,axiom,
% 0.26/0.52      ! [P: nat > $o,N: nat] :
% 0.26/0.52        ( ( P @ N )
% 0.26/0.52       => ( ~ ( P @ zero_zero_nat )
% 0.26/0.52         => ? [K2: nat] :
% 0.26/0.52              ( ( ord_less_nat @ K2 @ N )
% 0.26/0.52              & ! [I2: nat] :
% 0.26/0.52                  ( ( ord_less_eq_nat @ I2 @ K2 )
% 0.26/0.52                 => ~ ( P @ I2 ) )
% 0.26/0.52              & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % ex_least_nat_less
% 0.26/0.52  thf(fact_3182_nat__induct__non__zero,axiom,
% 0.26/0.52      ! [N: nat,P: nat > $o] :
% 0.26/0.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.52       => ( ( P @ one_one_nat )
% 0.26/0.52         => ( ! [N2: nat] :
% 0.26/0.52                ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.26/0.52               => ( ( P @ N2 )
% 0.26/0.52                 => ( P @ ( suc @ N2 ) ) ) )
% 0.26/0.52           => ( P @ N ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nat_induct_non_zero
% 0.26/0.52  thf(fact_3183_diff__Suc__less,axiom,
% 0.26/0.52      ! [N: nat,I: nat] :
% 0.26/0.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.52       => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% 0.26/0.52  
% 0.26/0.52  % diff_Suc_less
% 0.26/0.52  thf(fact_3184_power__gt__expt,axiom,
% 0.26/0.52      ! [N: nat,K: nat] :
% 0.26/0.52        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.26/0.52       => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_gt_expt
% 0.26/0.52  thf(fact_3185_realpow__pos__nth2,axiom,
% 0.26/0.52      ! [A: real,N: nat] :
% 0.26/0.52        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.52       => ? [R: real] :
% 0.26/0.52            ( ( ord_less_real @ zero_zero_real @ R )
% 0.26/0.52            & ( ( power_power_real @ R @ ( suc @ N ) )
% 0.26/0.52              = A ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % realpow_pos_nth2
% 0.26/0.52  thf(fact_3186_nat__one__le__power,axiom,
% 0.26/0.52      ! [I: nat,N: nat] :
% 0.26/0.52        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 0.26/0.52       => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nat_one_le_power
% 0.26/0.52  thf(fact_3187_ceiling__ge__round,axiom,
% 0.26/0.52      ! [X3: real] : ( ord_less_eq_int @ ( archim8280529875227126926d_real @ X3 ) @ ( archim7802044766580827645g_real @ X3 ) ) ).
% 0.26/0.52  
% 0.26/0.52  % ceiling_ge_round
% 0.26/0.52  thf(fact_3188_int__Suc,axiom,
% 0.26/0.52      ! [N: nat] :
% 0.26/0.52        ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 0.26/0.52        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 0.26/0.52  
% 0.26/0.52  % int_Suc
% 0.26/0.52  thf(fact_3189_int__ops_I4_J,axiom,
% 0.26/0.52      ! [A: nat] :
% 0.26/0.52        ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 0.26/0.52        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 0.26/0.52  
% 0.26/0.52  % int_ops(4)
% 0.26/0.52  thf(fact_3190_zless__iff__Suc__zadd,axiom,
% 0.26/0.52      ( ord_less_int
% 0.26/0.52      = ( ^ [W3: int,Z6: int] :
% 0.26/0.52          ? [N3: nat] :
% 0.26/0.52            ( Z6
% 0.26/0.52            = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % zless_iff_Suc_zadd
% 0.26/0.52  thf(fact_3191_of__nat__floor,axiom,
% 0.26/0.52      ! [R2: rat] :
% 0.26/0.52        ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 0.26/0.52       => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim3151403230148437115or_rat @ R2 ) ) ) @ R2 ) ) ).
% 0.26/0.52  
% 0.26/0.52  % of_nat_floor
% 0.26/0.52  thf(fact_3192_of__nat__floor,axiom,
% 0.26/0.52      ! [R2: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 0.26/0.52       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim6058952711729229775r_real @ R2 ) ) ) @ R2 ) ) ).
% 0.26/0.52  
% 0.26/0.52  % of_nat_floor
% 0.26/0.52  thf(fact_3193_one__add__floor,axiom,
% 0.26/0.52      ! [X3: rat] :
% 0.26/0.52        ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X3 ) @ one_one_int )
% 0.26/0.52        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X3 @ one_one_rat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % one_add_floor
% 0.26/0.52  thf(fact_3194_one__add__floor,axiom,
% 0.26/0.52      ! [X3: real] :
% 0.26/0.52        ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X3 ) @ one_one_int )
% 0.26/0.52        = ( archim6058952711729229775r_real @ ( plus_plus_real @ X3 @ one_one_real ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % one_add_floor
% 0.26/0.52  thf(fact_3195_floor__log__eq__powr__iff,axiom,
% 0.26/0.52      ! [X3: real,B: real,K: int] :
% 0.26/0.52        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.52       => ( ( ord_less_real @ one_one_real @ B )
% 0.26/0.52         => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X3 ) )
% 0.26/0.52              = K )
% 0.26/0.52            = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X3 )
% 0.26/0.52              & ( ord_less_real @ X3 @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_log_eq_powr_iff
% 0.26/0.52  thf(fact_3196_floor__divide__of__nat__eq,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) )
% 0.26/0.52        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_divide_of_nat_eq
% 0.26/0.52  thf(fact_3197_floor__divide__of__nat__eq,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.26/0.52        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_divide_of_nat_eq
% 0.26/0.52  thf(fact_3198_nat__floor__neg,axiom,
% 0.26/0.52      ! [X3: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 0.26/0.52       => ( ( nat2 @ ( archim6058952711729229775r_real @ X3 ) )
% 0.26/0.52          = zero_zero_nat ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nat_floor_neg
% 0.26/0.52  thf(fact_3199_powr__realpow,axiom,
% 0.26/0.52      ! [X3: real,N: nat] :
% 0.26/0.52        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.52       => ( ( powr_real @ X3 @ ( semiri5074537144036343181t_real @ N ) )
% 0.26/0.52          = ( power_power_real @ X3 @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % powr_realpow
% 0.26/0.52  thf(fact_3200_powr__less__iff,axiom,
% 0.26/0.52      ! [B: real,X3: real,Y3: real] :
% 0.26/0.52        ( ( ord_less_real @ one_one_real @ B )
% 0.26/0.52       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.52         => ( ( ord_less_real @ ( powr_real @ B @ Y3 ) @ X3 )
% 0.26/0.52            = ( ord_less_real @ Y3 @ ( log @ B @ X3 ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % powr_less_iff
% 0.26/0.52  thf(fact_3201_less__powr__iff,axiom,
% 0.26/0.52      ! [B: real,X3: real,Y3: real] :
% 0.26/0.52        ( ( ord_less_real @ one_one_real @ B )
% 0.26/0.52       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.52         => ( ( ord_less_real @ X3 @ ( powr_real @ B @ Y3 ) )
% 0.26/0.52            = ( ord_less_real @ ( log @ B @ X3 ) @ Y3 ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % less_powr_iff
% 0.26/0.52  thf(fact_3202_log__less__iff,axiom,
% 0.26/0.52      ! [B: real,X3: real,Y3: real] :
% 0.26/0.52        ( ( ord_less_real @ one_one_real @ B )
% 0.26/0.52       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.52         => ( ( ord_less_real @ ( log @ B @ X3 ) @ Y3 )
% 0.26/0.52            = ( ord_less_real @ X3 @ ( powr_real @ B @ Y3 ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % log_less_iff
% 0.26/0.52  thf(fact_3203_less__log__iff,axiom,
% 0.26/0.52      ! [B: real,X3: real,Y3: real] :
% 0.26/0.52        ( ( ord_less_real @ one_one_real @ B )
% 0.26/0.52       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.52         => ( ( ord_less_real @ Y3 @ ( log @ B @ X3 ) )
% 0.26/0.52            = ( ord_less_real @ ( powr_real @ B @ Y3 ) @ X3 ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % less_log_iff
% 0.26/0.52  thf(fact_3204_le__nat__floor,axiom,
% 0.26/0.52      ! [X3: nat,A: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X3 ) @ A )
% 0.26/0.52       => ( ord_less_eq_nat @ X3 @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % le_nat_floor
% 0.26/0.52  thf(fact_3205_ceiling__altdef,axiom,
% 0.26/0.52      ( archim2889992004027027881ng_rat
% 0.26/0.52      = ( ^ [X: rat] :
% 0.26/0.52            ( if_int
% 0.26/0.52            @ ( X
% 0.26/0.52              = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) )
% 0.26/0.52            @ ( archim3151403230148437115or_rat @ X )
% 0.26/0.52            @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % ceiling_altdef
% 0.26/0.52  thf(fact_3206_ceiling__altdef,axiom,
% 0.26/0.52      ( archim7802044766580827645g_real
% 0.26/0.52      = ( ^ [X: real] :
% 0.26/0.52            ( if_int
% 0.26/0.52            @ ( X
% 0.26/0.52              = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) )
% 0.26/0.52            @ ( archim6058952711729229775r_real @ X )
% 0.26/0.52            @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % ceiling_altdef
% 0.26/0.52  thf(fact_3207_ceiling__diff__floor__le__1,axiom,
% 0.26/0.52      ! [X3: real] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim7802044766580827645g_real @ X3 ) @ ( archim6058952711729229775r_real @ X3 ) ) @ one_one_int ) ).
% 0.26/0.52  
% 0.26/0.52  % ceiling_diff_floor_le_1
% 0.26/0.52  thf(fact_3208_floor__eq,axiom,
% 0.26/0.52      ! [N: int,X3: real] :
% 0.26/0.52        ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X3 )
% 0.26/0.52       => ( ( ord_less_real @ X3 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 0.26/0.52         => ( ( archim6058952711729229775r_real @ X3 )
% 0.26/0.52            = N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_eq
% 0.26/0.52  thf(fact_3209_real__of__int__floor__add__one__gt,axiom,
% 0.26/0.52      ! [R2: real] : ( ord_less_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 0.26/0.52  
% 0.26/0.52  % real_of_int_floor_add_one_gt
% 0.26/0.52  thf(fact_3210_real__of__int__floor__add__one__ge,axiom,
% 0.26/0.52      ! [R2: real] : ( ord_less_eq_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 0.26/0.52  
% 0.26/0.52  % real_of_int_floor_add_one_ge
% 0.26/0.52  thf(fact_3211_real__of__int__floor__gt__diff__one,axiom,
% 0.26/0.52      ! [R2: real] : ( ord_less_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % real_of_int_floor_gt_diff_one
% 0.26/0.52  thf(fact_3212_real__of__int__floor__ge__diff__one,axiom,
% 0.26/0.52      ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % real_of_int_floor_ge_diff_one
% 0.26/0.52  thf(fact_3213_power__Suc__le__self,axiom,
% 0.26/0.52      ! [A: real,N: nat] :
% 0.26/0.52        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.52       => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.26/0.52         => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_Suc_le_self
% 0.26/0.52  thf(fact_3214_power__Suc__le__self,axiom,
% 0.26/0.52      ! [A: rat,N: nat] :
% 0.26/0.52        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.52       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.26/0.52         => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_Suc_le_self
% 0.26/0.52  thf(fact_3215_power__Suc__le__self,axiom,
% 0.26/0.52      ! [A: nat,N: nat] :
% 0.26/0.52        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.52       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.26/0.52         => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_Suc_le_self
% 0.26/0.52  thf(fact_3216_power__Suc__le__self,axiom,
% 0.26/0.52      ! [A: int,N: nat] :
% 0.26/0.52        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.52       => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.26/0.52         => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_Suc_le_self
% 0.26/0.52  thf(fact_3217_power__Suc__less__one,axiom,
% 0.26/0.52      ! [A: real,N: nat] :
% 0.26/0.52        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.52       => ( ( ord_less_real @ A @ one_one_real )
% 0.26/0.52         => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_Suc_less_one
% 0.26/0.52  thf(fact_3218_power__Suc__less__one,axiom,
% 0.26/0.52      ! [A: rat,N: nat] :
% 0.26/0.52        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.52       => ( ( ord_less_rat @ A @ one_one_rat )
% 0.26/0.52         => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_Suc_less_one
% 0.26/0.52  thf(fact_3219_power__Suc__less__one,axiom,
% 0.26/0.52      ! [A: nat,N: nat] :
% 0.26/0.52        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.26/0.52       => ( ( ord_less_nat @ A @ one_one_nat )
% 0.26/0.52         => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_Suc_less_one
% 0.26/0.52  thf(fact_3220_power__Suc__less__one,axiom,
% 0.26/0.52      ! [A: int,N: nat] :
% 0.26/0.52        ( ( ord_less_int @ zero_zero_int @ A )
% 0.26/0.52       => ( ( ord_less_int @ A @ one_one_int )
% 0.26/0.52         => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_Suc_less_one
% 0.26/0.52  thf(fact_3221_numeral__2__eq__2,axiom,
% 0.26/0.52      ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.26/0.52      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % numeral_2_eq_2
% 0.26/0.52  thf(fact_3222_Suc__pred_H,axiom,
% 0.26/0.52      ! [N: nat] :
% 0.26/0.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.52       => ( N
% 0.26/0.52          = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % Suc_pred'
% 0.26/0.52  thf(fact_3223_Suc__diff__eq__diff__pred,axiom,
% 0.26/0.52      ! [N: nat,M: nat] :
% 0.26/0.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.52       => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 0.26/0.52          = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % Suc_diff_eq_diff_pred
% 0.26/0.52  thf(fact_3224_add__eq__if,axiom,
% 0.26/0.52      ( plus_plus_nat
% 0.26/0.52      = ( ^ [M3: nat,N3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N3 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N3 ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % add_eq_if
% 0.26/0.52  thf(fact_3225_div__if,axiom,
% 0.26/0.52      ( divide_divide_nat
% 0.26/0.52      = ( ^ [M3: nat,N3: nat] :
% 0.26/0.52            ( if_nat
% 0.26/0.52            @ ( ( ord_less_nat @ M3 @ N3 )
% 0.26/0.52              | ( N3 = zero_zero_nat ) )
% 0.26/0.52            @ zero_zero_nat
% 0.26/0.52            @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M3 @ N3 ) @ N3 ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % div_if
% 0.26/0.52  thf(fact_3226_div__geq,axiom,
% 0.26/0.52      ! [N: nat,M: nat] :
% 0.26/0.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.52       => ( ~ ( ord_less_nat @ M @ N )
% 0.26/0.52         => ( ( divide_divide_nat @ M @ N )
% 0.26/0.52            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % div_geq
% 0.26/0.52  thf(fact_3227_Suc__nat__number__of__add,axiom,
% 0.26/0.52      ! [V: num,N: nat] :
% 0.26/0.52        ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 0.26/0.52        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 0.26/0.52  
% 0.26/0.52  % Suc_nat_number_of_add
% 0.26/0.52  thf(fact_3228_Suc__as__int,axiom,
% 0.26/0.52      ( suc
% 0.26/0.52      = ( ^ [A4: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A4 ) @ one_one_int ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % Suc_as_int
% 0.26/0.52  thf(fact_3229_floor__unique,axiom,
% 0.26/0.52      ! [Z: int,X3: rat] :
% 0.26/0.52        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X3 )
% 0.26/0.52       => ( ( ord_less_rat @ X3 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) )
% 0.26/0.52         => ( ( archim3151403230148437115or_rat @ X3 )
% 0.26/0.52            = Z ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_unique
% 0.26/0.52  thf(fact_3230_floor__unique,axiom,
% 0.26/0.52      ! [Z: int,X3: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X3 )
% 0.26/0.52       => ( ( ord_less_real @ X3 @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) )
% 0.26/0.52         => ( ( archim6058952711729229775r_real @ X3 )
% 0.26/0.52            = Z ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_unique
% 0.26/0.52  thf(fact_3231_floor__eq__iff,axiom,
% 0.26/0.52      ! [X3: rat,A: int] :
% 0.26/0.52        ( ( ( archim3151403230148437115or_rat @ X3 )
% 0.26/0.52          = A )
% 0.26/0.52        = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X3 )
% 0.26/0.52          & ( ord_less_rat @ X3 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_eq_iff
% 0.26/0.52  thf(fact_3232_floor__eq__iff,axiom,
% 0.26/0.52      ! [X3: real,A: int] :
% 0.26/0.52        ( ( ( archim6058952711729229775r_real @ X3 )
% 0.26/0.52          = A )
% 0.26/0.52        = ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ X3 )
% 0.26/0.52          & ( ord_less_real @ X3 @ ( plus_plus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_eq_iff
% 0.26/0.52  thf(fact_3233_floor__split,axiom,
% 0.26/0.52      ! [P: int > $o,T: rat] :
% 0.26/0.52        ( ( P @ ( archim3151403230148437115or_rat @ T ) )
% 0.26/0.52        = ( ! [I4: int] :
% 0.26/0.52              ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I4 ) @ T )
% 0.26/0.52                & ( ord_less_rat @ T @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I4 ) @ one_one_rat ) ) )
% 0.26/0.52             => ( P @ I4 ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_split
% 0.26/0.52  thf(fact_3234_floor__split,axiom,
% 0.26/0.52      ! [P: int > $o,T: real] :
% 0.26/0.52        ( ( P @ ( archim6058952711729229775r_real @ T ) )
% 0.26/0.52        = ( ! [I4: int] :
% 0.26/0.52              ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ I4 ) @ T )
% 0.26/0.52                & ( ord_less_real @ T @ ( plus_plus_real @ ( ring_1_of_int_real @ I4 ) @ one_one_real ) ) )
% 0.26/0.52             => ( P @ I4 ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_split
% 0.26/0.52  thf(fact_3235_less__floor__iff,axiom,
% 0.26/0.52      ! [Z: int,X3: rat] :
% 0.26/0.52        ( ( ord_less_int @ Z @ ( archim3151403230148437115or_rat @ X3 ) )
% 0.26/0.52        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X3 ) ) ).
% 0.26/0.52  
% 0.26/0.52  % less_floor_iff
% 0.26/0.52  thf(fact_3236_less__floor__iff,axiom,
% 0.26/0.52      ! [Z: int,X3: real] :
% 0.26/0.52        ( ( ord_less_int @ Z @ ( archim6058952711729229775r_real @ X3 ) )
% 0.26/0.52        = ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X3 ) ) ).
% 0.26/0.52  
% 0.26/0.52  % less_floor_iff
% 0.26/0.52  thf(fact_3237_floor__le__iff,axiom,
% 0.26/0.52      ! [X3: rat,Z: int] :
% 0.26/0.52        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X3 ) @ Z )
% 0.26/0.52        = ( ord_less_rat @ X3 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_le_iff
% 0.26/0.52  thf(fact_3238_floor__le__iff,axiom,
% 0.26/0.52      ! [X3: real,Z: int] :
% 0.26/0.52        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X3 ) @ Z )
% 0.26/0.52        = ( ord_less_real @ X3 @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_le_iff
% 0.26/0.52  thf(fact_3239_floor__correct,axiom,
% 0.26/0.52      ! [X3: rat] :
% 0.26/0.52        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X3 ) ) @ X3 )
% 0.26/0.52        & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X3 ) @ one_one_int ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_correct
% 0.26/0.52  thf(fact_3240_floor__correct,axiom,
% 0.26/0.52      ! [X3: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X3 ) ) @ X3 )
% 0.26/0.52        & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X3 ) @ one_one_int ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_correct
% 0.26/0.52  thf(fact_3241_le__log__iff,axiom,
% 0.26/0.52      ! [B: real,X3: real,Y3: real] :
% 0.26/0.52        ( ( ord_less_real @ one_one_real @ B )
% 0.26/0.52       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.52         => ( ( ord_less_eq_real @ Y3 @ ( log @ B @ X3 ) )
% 0.26/0.52            = ( ord_less_eq_real @ ( powr_real @ B @ Y3 ) @ X3 ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % le_log_iff
% 0.26/0.52  thf(fact_3242_log__le__iff,axiom,
% 0.26/0.52      ! [B: real,X3: real,Y3: real] :
% 0.26/0.52        ( ( ord_less_real @ one_one_real @ B )
% 0.26/0.52       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.52         => ( ( ord_less_eq_real @ ( log @ B @ X3 ) @ Y3 )
% 0.26/0.52            = ( ord_less_eq_real @ X3 @ ( powr_real @ B @ Y3 ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % log_le_iff
% 0.26/0.52  thf(fact_3243_le__powr__iff,axiom,
% 0.26/0.52      ! [B: real,X3: real,Y3: real] :
% 0.26/0.52        ( ( ord_less_real @ one_one_real @ B )
% 0.26/0.52       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.52         => ( ( ord_less_eq_real @ X3 @ ( powr_real @ B @ Y3 ) )
% 0.26/0.52            = ( ord_less_eq_real @ ( log @ B @ X3 ) @ Y3 ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % le_powr_iff
% 0.26/0.52  thf(fact_3244_powr__le__iff,axiom,
% 0.26/0.52      ! [B: real,X3: real,Y3: real] :
% 0.26/0.52        ( ( ord_less_real @ one_one_real @ B )
% 0.26/0.52       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.52         => ( ( ord_less_eq_real @ ( powr_real @ B @ Y3 ) @ X3 )
% 0.26/0.52            = ( ord_less_eq_real @ Y3 @ ( log @ B @ X3 ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % powr_le_iff
% 0.26/0.52  thf(fact_3245_floor__eq2,axiom,
% 0.26/0.52      ! [N: int,X3: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X3 )
% 0.26/0.52       => ( ( ord_less_real @ X3 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 0.26/0.52         => ( ( archim6058952711729229775r_real @ X3 )
% 0.26/0.52            = N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_eq2
% 0.26/0.52  thf(fact_3246_floor__divide__real__eq__div,axiom,
% 0.26/0.52      ! [B: int,A: real] :
% 0.26/0.52        ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.26/0.52       => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 0.26/0.52          = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_divide_real_eq_div
% 0.26/0.52  thf(fact_3247_nat__approx__posE,axiom,
% 0.26/0.52      ! [E2: real] :
% 0.26/0.52        ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.26/0.52       => ~ ! [N2: nat] :
% 0.26/0.52              ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ E2 ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nat_approx_posE
% 0.26/0.52  thf(fact_3248_nat__approx__posE,axiom,
% 0.26/0.52      ! [E2: rat] :
% 0.26/0.52        ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 0.26/0.52       => ~ ! [N2: nat] :
% 0.26/0.52              ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N2 ) ) ) @ E2 ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nat_approx_posE
% 0.26/0.52  thf(fact_3249_less__2__cases__iff,axiom,
% 0.26/0.52      ! [N: nat] :
% 0.26/0.52        ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.52        = ( ( N = zero_zero_nat )
% 0.26/0.52          | ( N
% 0.26/0.52            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % less_2_cases_iff
% 0.26/0.52  thf(fact_3250_less__2__cases,axiom,
% 0.26/0.52      ! [N: nat] :
% 0.26/0.52        ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.52       => ( ( N = zero_zero_nat )
% 0.26/0.52          | ( N
% 0.26/0.52            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % less_2_cases
% 0.26/0.52  thf(fact_3251_nat__2,axiom,
% 0.26/0.52      ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.52      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nat_2
% 0.26/0.52  thf(fact_3252_le__div__geq,axiom,
% 0.26/0.52      ! [N: nat,M: nat] :
% 0.26/0.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.52       => ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.52         => ( ( divide_divide_nat @ M @ N )
% 0.26/0.52            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % le_div_geq
% 0.26/0.52  thf(fact_3253_Suc__nat__eq__nat__zadd1,axiom,
% 0.26/0.52      ! [Z: int] :
% 0.26/0.52        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.26/0.52       => ( ( suc @ ( nat2 @ Z ) )
% 0.26/0.52          = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % Suc_nat_eq_nat_zadd1
% 0.26/0.52  thf(fact_3254_ln__powr__bound,axiom,
% 0.26/0.52      ! [X3: real,A: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ one_one_real @ X3 )
% 0.26/0.52       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.52         => ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ ( divide_divide_real @ ( powr_real @ X3 @ A ) @ A ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % ln_powr_bound
% 0.26/0.52  thf(fact_3255_minus__log__eq__powr,axiom,
% 0.26/0.52      ! [B: real,X3: real,Y3: real] :
% 0.26/0.52        ( ( ord_less_real @ zero_zero_real @ B )
% 0.26/0.52       => ( ( B != one_one_real )
% 0.26/0.52         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.52           => ( ( minus_minus_real @ Y3 @ ( log @ B @ X3 ) )
% 0.26/0.52              = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y3 ) @ X3 ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % minus_log_eq_powr
% 0.26/0.52  thf(fact_3256_Suc__n__div__2__gt__zero,axiom,
% 0.26/0.52      ! [N: nat] :
% 0.26/0.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.52       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % Suc_n_div_2_gt_zero
% 0.26/0.52  thf(fact_3257_div__2__gt__zero,axiom,
% 0.26/0.52      ! [N: nat] :
% 0.26/0.52        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.26/0.52       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % div_2_gt_zero
% 0.26/0.52  thf(fact_3258_powr__half__sqrt,axiom,
% 0.26/0.52      ! [X3: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.52       => ( ( powr_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.52          = ( sqrt @ X3 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % powr_half_sqrt
% 0.26/0.52  thf(fact_3259_int__power__div__base,axiom,
% 0.26/0.52      ! [M: nat,K: int] :
% 0.26/0.52        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.52       => ( ( ord_less_int @ zero_zero_int @ K )
% 0.26/0.52         => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 0.26/0.52            = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % int_power_div_base
% 0.26/0.52  thf(fact_3260_floor__log2__div2,axiom,
% 0.26/0.52      ! [N: nat] :
% 0.26/0.52        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.52       => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.26/0.52          = ( 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 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_log2_div2
% 0.26/0.52  thf(fact_3261_floor__log__nat__eq__if,axiom,
% 0.26/0.52      ! [B: nat,N: nat,K: nat] :
% 0.26/0.52        ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 0.26/0.52       => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 0.26/0.52         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.26/0.52           => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.26/0.52              = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % floor_log_nat_eq_if
% 0.26/0.52  thf(fact_3262_of__int__round__le,axiom,
% 0.26/0.52      ! [X3: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X3 ) ) @ ( plus_plus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % of_int_round_le
% 0.26/0.52  thf(fact_3263_of__int__round__le,axiom,
% 0.26/0.52      ! [X3: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X3 ) ) @ ( plus_plus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % of_int_round_le
% 0.26/0.52  thf(fact_3264_of__int__round__ge,axiom,
% 0.26/0.52      ! [X3: real] : ( ord_less_eq_real @ ( minus_minus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X3 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % of_int_round_ge
% 0.26/0.52  thf(fact_3265_of__int__round__ge,axiom,
% 0.26/0.52      ! [X3: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X3 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % of_int_round_ge
% 0.26/0.52  thf(fact_3266_of__int__round__gt,axiom,
% 0.26/0.52      ! [X3: real] : ( ord_less_real @ ( minus_minus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X3 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % of_int_round_gt
% 0.26/0.52  thf(fact_3267_of__int__round__gt,axiom,
% 0.26/0.52      ! [X3: rat] : ( ord_less_rat @ ( minus_minus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X3 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % of_int_round_gt
% 0.26/0.52  thf(fact_3268_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 0.26/0.52      ! [X3: nat,N: nat,M: nat] :
% 0.26/0.52        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 0.26/0.52       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.52         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.52           => ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % VEBT_internal.exp_split_high_low(1)
% 0.26/0.52  thf(fact_3269_high__inv,axiom,
% 0.26/0.52      ! [X3: nat,N: nat,Y3: nat] :
% 0.26/0.52        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.52       => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X3 ) @ N )
% 0.26/0.52          = Y3 ) ) ).
% 0.26/0.52  
% 0.26/0.52  % high_inv
% 0.26/0.52  thf(fact_3270_arcosh__def,axiom,
% 0.26/0.52      ( arcosh_real
% 0.26/0.52      = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( powr_real @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % arcosh_def
% 0.26/0.52  thf(fact_3271_round__altdef,axiom,
% 0.26/0.52      ( archim7778729529865785530nd_rat
% 0.26/0.52      = ( ^ [X: rat] : ( if_int @ ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( archimedean_frac_rat @ X ) ) @ ( archim2889992004027027881ng_rat @ X ) @ ( archim3151403230148437115or_rat @ X ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % round_altdef
% 0.26/0.52  thf(fact_3272_round__altdef,axiom,
% 0.26/0.52      ( archim8280529875227126926d_real
% 0.26/0.52      = ( ^ [X: real] : ( if_int @ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( archim2898591450579166408c_real @ X ) ) @ ( archim7802044766580827645g_real @ X ) @ ( archim6058952711729229775r_real @ X ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % round_altdef
% 0.26/0.52  thf(fact_3273_arsinh__def,axiom,
% 0.26/0.52      ( arsinh_real
% 0.26/0.52      = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( powr_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % arsinh_def
% 0.26/0.52  thf(fact_3274_mult__cancel__right,axiom,
% 0.26/0.52      ! [A: real,C: real,B: real] :
% 0.26/0.52        ( ( ( times_times_real @ A @ C )
% 0.26/0.52          = ( times_times_real @ B @ C ) )
% 0.26/0.52        = ( ( C = zero_zero_real )
% 0.26/0.52          | ( A = B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_right
% 0.26/0.52  thf(fact_3275_mult__cancel__right,axiom,
% 0.26/0.52      ! [A: rat,C: rat,B: rat] :
% 0.26/0.52        ( ( ( times_times_rat @ A @ C )
% 0.26/0.52          = ( times_times_rat @ B @ C ) )
% 0.26/0.52        = ( ( C = zero_zero_rat )
% 0.26/0.52          | ( A = B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_right
% 0.26/0.52  thf(fact_3276_mult__cancel__right,axiom,
% 0.26/0.52      ! [A: nat,C: nat,B: nat] :
% 0.26/0.52        ( ( ( times_times_nat @ A @ C )
% 0.26/0.52          = ( times_times_nat @ B @ C ) )
% 0.26/0.52        = ( ( C = zero_zero_nat )
% 0.26/0.52          | ( A = B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_right
% 0.26/0.52  thf(fact_3277_mult__cancel__right,axiom,
% 0.26/0.52      ! [A: int,C: int,B: int] :
% 0.26/0.52        ( ( ( times_times_int @ A @ C )
% 0.26/0.52          = ( times_times_int @ B @ C ) )
% 0.26/0.52        = ( ( C = zero_zero_int )
% 0.26/0.52          | ( A = B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_right
% 0.26/0.52  thf(fact_3278_mult__cancel__left,axiom,
% 0.26/0.52      ! [C: real,A: real,B: real] :
% 0.26/0.52        ( ( ( times_times_real @ C @ A )
% 0.26/0.52          = ( times_times_real @ C @ B ) )
% 0.26/0.52        = ( ( C = zero_zero_real )
% 0.26/0.52          | ( A = B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_left
% 0.26/0.52  thf(fact_3279_mult__cancel__left,axiom,
% 0.26/0.52      ! [C: rat,A: rat,B: rat] :
% 0.26/0.52        ( ( ( times_times_rat @ C @ A )
% 0.26/0.52          = ( times_times_rat @ C @ B ) )
% 0.26/0.52        = ( ( C = zero_zero_rat )
% 0.26/0.52          | ( A = B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_left
% 0.26/0.52  thf(fact_3280_mult__cancel__left,axiom,
% 0.26/0.52      ! [C: nat,A: nat,B: nat] :
% 0.26/0.52        ( ( ( times_times_nat @ C @ A )
% 0.26/0.52          = ( times_times_nat @ C @ B ) )
% 0.26/0.52        = ( ( C = zero_zero_nat )
% 0.26/0.52          | ( A = B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_left
% 0.26/0.52  thf(fact_3281_mult__cancel__left,axiom,
% 0.26/0.52      ! [C: int,A: int,B: int] :
% 0.26/0.52        ( ( ( times_times_int @ C @ A )
% 0.26/0.52          = ( times_times_int @ C @ B ) )
% 0.26/0.52        = ( ( C = zero_zero_int )
% 0.26/0.52          | ( A = B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_left
% 0.26/0.52  thf(fact_3282_mult__eq__0__iff,axiom,
% 0.26/0.52      ! [A: real,B: real] :
% 0.26/0.52        ( ( ( times_times_real @ A @ B )
% 0.26/0.52          = zero_zero_real )
% 0.26/0.52        = ( ( A = zero_zero_real )
% 0.26/0.52          | ( B = zero_zero_real ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_eq_0_iff
% 0.26/0.52  thf(fact_3283_mult__eq__0__iff,axiom,
% 0.26/0.52      ! [A: rat,B: rat] :
% 0.26/0.52        ( ( ( times_times_rat @ A @ B )
% 0.26/0.52          = zero_zero_rat )
% 0.26/0.52        = ( ( A = zero_zero_rat )
% 0.26/0.52          | ( B = zero_zero_rat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_eq_0_iff
% 0.26/0.52  thf(fact_3284_mult__eq__0__iff,axiom,
% 0.26/0.52      ! [A: nat,B: nat] :
% 0.26/0.52        ( ( ( times_times_nat @ A @ B )
% 0.26/0.52          = zero_zero_nat )
% 0.26/0.52        = ( ( A = zero_zero_nat )
% 0.26/0.52          | ( B = zero_zero_nat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_eq_0_iff
% 0.26/0.52  thf(fact_3285_mult__eq__0__iff,axiom,
% 0.26/0.52      ! [A: int,B: int] :
% 0.26/0.52        ( ( ( times_times_int @ A @ B )
% 0.26/0.52          = zero_zero_int )
% 0.26/0.52        = ( ( A = zero_zero_int )
% 0.26/0.52          | ( B = zero_zero_int ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_eq_0_iff
% 0.26/0.52  thf(fact_3286_mult__zero__right,axiom,
% 0.26/0.52      ! [A: real] :
% 0.26/0.52        ( ( times_times_real @ A @ zero_zero_real )
% 0.26/0.52        = zero_zero_real ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_zero_right
% 0.26/0.52  thf(fact_3287_mult__zero__right,axiom,
% 0.26/0.52      ! [A: rat] :
% 0.26/0.52        ( ( times_times_rat @ A @ zero_zero_rat )
% 0.26/0.52        = zero_zero_rat ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_zero_right
% 0.26/0.52  thf(fact_3288_mult__zero__right,axiom,
% 0.26/0.52      ! [A: nat] :
% 0.26/0.52        ( ( times_times_nat @ A @ zero_zero_nat )
% 0.26/0.52        = zero_zero_nat ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_zero_right
% 0.26/0.52  thf(fact_3289_mult__zero__right,axiom,
% 0.26/0.52      ! [A: int] :
% 0.26/0.52        ( ( times_times_int @ A @ zero_zero_int )
% 0.26/0.52        = zero_zero_int ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_zero_right
% 0.26/0.52  thf(fact_3290_mult__zero__left,axiom,
% 0.26/0.52      ! [A: real] :
% 0.26/0.52        ( ( times_times_real @ zero_zero_real @ A )
% 0.26/0.52        = zero_zero_real ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_zero_left
% 0.26/0.52  thf(fact_3291_mult__zero__left,axiom,
% 0.26/0.52      ! [A: rat] :
% 0.26/0.52        ( ( times_times_rat @ zero_zero_rat @ A )
% 0.26/0.52        = zero_zero_rat ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_zero_left
% 0.26/0.52  thf(fact_3292_mult__zero__left,axiom,
% 0.26/0.52      ! [A: nat] :
% 0.26/0.52        ( ( times_times_nat @ zero_zero_nat @ A )
% 0.26/0.52        = zero_zero_nat ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_zero_left
% 0.26/0.52  thf(fact_3293_mult__zero__left,axiom,
% 0.26/0.52      ! [A: int] :
% 0.26/0.52        ( ( times_times_int @ zero_zero_int @ A )
% 0.26/0.52        = zero_zero_int ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_zero_left
% 0.26/0.52  thf(fact_3294_numeral__times__numeral,axiom,
% 0.26/0.52      ! [M: num,N: num] :
% 0.26/0.52        ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 0.26/0.52        = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % numeral_times_numeral
% 0.26/0.52  thf(fact_3295_numeral__times__numeral,axiom,
% 0.26/0.52      ! [M: num,N: num] :
% 0.26/0.52        ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 0.26/0.52        = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % numeral_times_numeral
% 0.26/0.52  thf(fact_3296_numeral__times__numeral,axiom,
% 0.26/0.52      ! [M: num,N: num] :
% 0.26/0.52        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 0.26/0.52        = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % numeral_times_numeral
% 0.26/0.52  thf(fact_3297_numeral__times__numeral,axiom,
% 0.26/0.52      ! [M: num,N: num] :
% 0.26/0.52        ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.26/0.52        = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % numeral_times_numeral
% 0.26/0.52  thf(fact_3298_numeral__times__numeral,axiom,
% 0.26/0.52      ! [M: num,N: num] :
% 0.26/0.52        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.52        = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % numeral_times_numeral
% 0.26/0.52  thf(fact_3299_mult__numeral__left__semiring__numeral,axiom,
% 0.26/0.52      ! [V: num,W: num,Z: complex] :
% 0.26/0.52        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 0.26/0.52        = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_numeral_left_semiring_numeral
% 0.26/0.52  thf(fact_3300_mult__numeral__left__semiring__numeral,axiom,
% 0.26/0.52      ! [V: num,W: num,Z: real] :
% 0.26/0.52        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 0.26/0.52        = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_numeral_left_semiring_numeral
% 0.26/0.52  thf(fact_3301_mult__numeral__left__semiring__numeral,axiom,
% 0.26/0.52      ! [V: num,W: num,Z: rat] :
% 0.26/0.52        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 0.26/0.52        = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_numeral_left_semiring_numeral
% 0.26/0.52  thf(fact_3302_mult__numeral__left__semiring__numeral,axiom,
% 0.26/0.52      ! [V: num,W: num,Z: nat] :
% 0.26/0.52        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 0.26/0.52        = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_numeral_left_semiring_numeral
% 0.26/0.52  thf(fact_3303_mult__numeral__left__semiring__numeral,axiom,
% 0.26/0.52      ! [V: num,W: num,Z: int] :
% 0.26/0.52        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 0.26/0.52        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_numeral_left_semiring_numeral
% 0.26/0.52  thf(fact_3304_mult_Oright__neutral,axiom,
% 0.26/0.52      ! [A: complex] :
% 0.26/0.52        ( ( times_times_complex @ A @ one_one_complex )
% 0.26/0.52        = A ) ).
% 0.26/0.52  
% 0.26/0.52  % mult.right_neutral
% 0.26/0.52  thf(fact_3305_mult_Oright__neutral,axiom,
% 0.26/0.52      ! [A: real] :
% 0.26/0.52        ( ( times_times_real @ A @ one_one_real )
% 0.26/0.52        = A ) ).
% 0.26/0.52  
% 0.26/0.52  % mult.right_neutral
% 0.26/0.52  thf(fact_3306_mult_Oright__neutral,axiom,
% 0.26/0.52      ! [A: rat] :
% 0.26/0.52        ( ( times_times_rat @ A @ one_one_rat )
% 0.26/0.52        = A ) ).
% 0.26/0.52  
% 0.26/0.52  % mult.right_neutral
% 0.26/0.52  thf(fact_3307_mult_Oright__neutral,axiom,
% 0.26/0.52      ! [A: nat] :
% 0.26/0.52        ( ( times_times_nat @ A @ one_one_nat )
% 0.26/0.52        = A ) ).
% 0.26/0.52  
% 0.26/0.52  % mult.right_neutral
% 0.26/0.52  thf(fact_3308_mult_Oright__neutral,axiom,
% 0.26/0.52      ! [A: int] :
% 0.26/0.52        ( ( times_times_int @ A @ one_one_int )
% 0.26/0.52        = A ) ).
% 0.26/0.52  
% 0.26/0.52  % mult.right_neutral
% 0.26/0.52  thf(fact_3309_mult__1,axiom,
% 0.26/0.52      ! [A: complex] :
% 0.26/0.52        ( ( times_times_complex @ one_one_complex @ A )
% 0.26/0.52        = A ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_1
% 0.26/0.52  thf(fact_3310_mult__1,axiom,
% 0.26/0.52      ! [A: real] :
% 0.26/0.52        ( ( times_times_real @ one_one_real @ A )
% 0.26/0.52        = A ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_1
% 0.26/0.52  thf(fact_3311_mult__1,axiom,
% 0.26/0.52      ! [A: rat] :
% 0.26/0.52        ( ( times_times_rat @ one_one_rat @ A )
% 0.26/0.52        = A ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_1
% 0.26/0.52  thf(fact_3312_mult__1,axiom,
% 0.26/0.52      ! [A: nat] :
% 0.26/0.52        ( ( times_times_nat @ one_one_nat @ A )
% 0.26/0.52        = A ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_1
% 0.26/0.52  thf(fact_3313_mult__1,axiom,
% 0.26/0.52      ! [A: int] :
% 0.26/0.52        ( ( times_times_int @ one_one_int @ A )
% 0.26/0.52        = A ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_1
% 0.26/0.52  thf(fact_3314_of__int__mult,axiom,
% 0.26/0.52      ! [W: int,Z: int] :
% 0.26/0.52        ( ( ring_17405671764205052669omplex @ ( times_times_int @ W @ Z ) )
% 0.26/0.52        = ( times_times_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % of_int_mult
% 0.26/0.52  thf(fact_3315_of__int__mult,axiom,
% 0.26/0.52      ! [W: int,Z: int] :
% 0.26/0.52        ( ( ring_1_of_int_real @ ( times_times_int @ W @ Z ) )
% 0.26/0.52        = ( times_times_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % of_int_mult
% 0.26/0.52  thf(fact_3316_of__int__mult,axiom,
% 0.26/0.52      ! [W: int,Z: int] :
% 0.26/0.52        ( ( ring_1_of_int_rat @ ( times_times_int @ W @ Z ) )
% 0.26/0.52        = ( times_times_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % of_int_mult
% 0.26/0.52  thf(fact_3317_of__int__mult,axiom,
% 0.26/0.52      ! [W: int,Z: int] :
% 0.26/0.52        ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z ) )
% 0.26/0.52        = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % of_int_mult
% 0.26/0.52  thf(fact_3318_mult__cancel2,axiom,
% 0.26/0.52      ! [M: nat,K: nat,N: nat] :
% 0.26/0.52        ( ( ( times_times_nat @ M @ K )
% 0.26/0.52          = ( times_times_nat @ N @ K ) )
% 0.26/0.52        = ( ( M = N )
% 0.26/0.52          | ( K = zero_zero_nat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel2
% 0.26/0.52  thf(fact_3319_mult__cancel1,axiom,
% 0.26/0.52      ! [K: nat,M: nat,N: nat] :
% 0.26/0.52        ( ( ( times_times_nat @ K @ M )
% 0.26/0.52          = ( times_times_nat @ K @ N ) )
% 0.26/0.52        = ( ( M = N )
% 0.26/0.52          | ( K = zero_zero_nat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel1
% 0.26/0.52  thf(fact_3320_mult__0__right,axiom,
% 0.26/0.52      ! [M: nat] :
% 0.26/0.52        ( ( times_times_nat @ M @ zero_zero_nat )
% 0.26/0.52        = zero_zero_nat ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_0_right
% 0.26/0.52  thf(fact_3321_mult__is__0,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( ( times_times_nat @ M @ N )
% 0.26/0.52          = zero_zero_nat )
% 0.26/0.52        = ( ( M = zero_zero_nat )
% 0.26/0.52          | ( N = zero_zero_nat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_is_0
% 0.26/0.52  thf(fact_3322_nat__mult__eq__1__iff,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( ( times_times_nat @ M @ N )
% 0.26/0.52          = one_one_nat )
% 0.26/0.52        = ( ( M = one_one_nat )
% 0.26/0.52          & ( N = one_one_nat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nat_mult_eq_1_iff
% 0.26/0.52  thf(fact_3323_nat__1__eq__mult__iff,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( one_one_nat
% 0.26/0.52          = ( times_times_nat @ M @ N ) )
% 0.26/0.52        = ( ( M = one_one_nat )
% 0.26/0.52          & ( N = one_one_nat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nat_1_eq_mult_iff
% 0.26/0.52  thf(fact_3324_bit__concat__def,axiom,
% 0.26/0.52      ( vEBT_VEBT_bit_concat
% 0.26/0.52      = ( ^ [H: nat,L2: nat,D4: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D4 ) ) @ L2 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % bit_concat_def
% 0.26/0.52  thf(fact_3325_mult__cancel__right2,axiom,
% 0.26/0.52      ! [A: complex,C: complex] :
% 0.26/0.52        ( ( ( times_times_complex @ A @ C )
% 0.26/0.52          = C )
% 0.26/0.52        = ( ( C = zero_zero_complex )
% 0.26/0.52          | ( A = one_one_complex ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_right2
% 0.26/0.52  thf(fact_3326_mult__cancel__right2,axiom,
% 0.26/0.52      ! [A: real,C: real] :
% 0.26/0.52        ( ( ( times_times_real @ A @ C )
% 0.26/0.52          = C )
% 0.26/0.52        = ( ( C = zero_zero_real )
% 0.26/0.52          | ( A = one_one_real ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_right2
% 0.26/0.52  thf(fact_3327_mult__cancel__right2,axiom,
% 0.26/0.52      ! [A: rat,C: rat] :
% 0.26/0.52        ( ( ( times_times_rat @ A @ C )
% 0.26/0.52          = C )
% 0.26/0.52        = ( ( C = zero_zero_rat )
% 0.26/0.52          | ( A = one_one_rat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_right2
% 0.26/0.52  thf(fact_3328_mult__cancel__right2,axiom,
% 0.26/0.52      ! [A: int,C: int] :
% 0.26/0.52        ( ( ( times_times_int @ A @ C )
% 0.26/0.52          = C )
% 0.26/0.52        = ( ( C = zero_zero_int )
% 0.26/0.52          | ( A = one_one_int ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_right2
% 0.26/0.52  thf(fact_3329_mult__cancel__right1,axiom,
% 0.26/0.52      ! [C: complex,B: complex] :
% 0.26/0.52        ( ( C
% 0.26/0.52          = ( times_times_complex @ B @ C ) )
% 0.26/0.52        = ( ( C = zero_zero_complex )
% 0.26/0.52          | ( B = one_one_complex ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_right1
% 0.26/0.52  thf(fact_3330_mult__cancel__right1,axiom,
% 0.26/0.52      ! [C: real,B: real] :
% 0.26/0.52        ( ( C
% 0.26/0.52          = ( times_times_real @ B @ C ) )
% 0.26/0.52        = ( ( C = zero_zero_real )
% 0.26/0.52          | ( B = one_one_real ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_right1
% 0.26/0.52  thf(fact_3331_mult__cancel__right1,axiom,
% 0.26/0.52      ! [C: rat,B: rat] :
% 0.26/0.52        ( ( C
% 0.26/0.52          = ( times_times_rat @ B @ C ) )
% 0.26/0.52        = ( ( C = zero_zero_rat )
% 0.26/0.52          | ( B = one_one_rat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_right1
% 0.26/0.52  thf(fact_3332_mult__cancel__right1,axiom,
% 0.26/0.52      ! [C: int,B: int] :
% 0.26/0.52        ( ( C
% 0.26/0.52          = ( times_times_int @ B @ C ) )
% 0.26/0.52        = ( ( C = zero_zero_int )
% 0.26/0.52          | ( B = one_one_int ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_right1
% 0.26/0.52  thf(fact_3333_mult__cancel__left2,axiom,
% 0.26/0.52      ! [C: complex,A: complex] :
% 0.26/0.52        ( ( ( times_times_complex @ C @ A )
% 0.26/0.52          = C )
% 0.26/0.52        = ( ( C = zero_zero_complex )
% 0.26/0.52          | ( A = one_one_complex ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_left2
% 0.26/0.52  thf(fact_3334_mult__cancel__left2,axiom,
% 0.26/0.52      ! [C: real,A: real] :
% 0.26/0.52        ( ( ( times_times_real @ C @ A )
% 0.26/0.52          = C )
% 0.26/0.52        = ( ( C = zero_zero_real )
% 0.26/0.52          | ( A = one_one_real ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_left2
% 0.26/0.52  thf(fact_3335_mult__cancel__left2,axiom,
% 0.26/0.52      ! [C: rat,A: rat] :
% 0.26/0.52        ( ( ( times_times_rat @ C @ A )
% 0.26/0.52          = C )
% 0.26/0.52        = ( ( C = zero_zero_rat )
% 0.26/0.52          | ( A = one_one_rat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_left2
% 0.26/0.52  thf(fact_3336_mult__cancel__left2,axiom,
% 0.26/0.52      ! [C: int,A: int] :
% 0.26/0.52        ( ( ( times_times_int @ C @ A )
% 0.26/0.52          = C )
% 0.26/0.52        = ( ( C = zero_zero_int )
% 0.26/0.52          | ( A = one_one_int ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_left2
% 0.26/0.52  thf(fact_3337_mult__cancel__left1,axiom,
% 0.26/0.52      ! [C: complex,B: complex] :
% 0.26/0.52        ( ( C
% 0.26/0.52          = ( times_times_complex @ C @ B ) )
% 0.26/0.52        = ( ( C = zero_zero_complex )
% 0.26/0.52          | ( B = one_one_complex ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_left1
% 0.26/0.52  thf(fact_3338_mult__cancel__left1,axiom,
% 0.26/0.52      ! [C: real,B: real] :
% 0.26/0.52        ( ( C
% 0.26/0.52          = ( times_times_real @ C @ B ) )
% 0.26/0.52        = ( ( C = zero_zero_real )
% 0.26/0.52          | ( B = one_one_real ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_left1
% 0.26/0.52  thf(fact_3339_mult__cancel__left1,axiom,
% 0.26/0.52      ! [C: rat,B: rat] :
% 0.26/0.52        ( ( C
% 0.26/0.52          = ( times_times_rat @ C @ B ) )
% 0.26/0.52        = ( ( C = zero_zero_rat )
% 0.26/0.52          | ( B = one_one_rat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_left1
% 0.26/0.52  thf(fact_3340_mult__cancel__left1,axiom,
% 0.26/0.52      ! [C: int,B: int] :
% 0.26/0.52        ( ( C
% 0.26/0.52          = ( times_times_int @ C @ B ) )
% 0.26/0.52        = ( ( C = zero_zero_int )
% 0.26/0.52          | ( B = one_one_int ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_cancel_left1
% 0.26/0.52  thf(fact_3341_sum__squares__eq__zero__iff,axiom,
% 0.26/0.52      ! [X3: real,Y3: real] :
% 0.26/0.52        ( ( ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y3 @ Y3 ) )
% 0.26/0.52          = zero_zero_real )
% 0.26/0.52        = ( ( X3 = zero_zero_real )
% 0.26/0.52          & ( Y3 = zero_zero_real ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % sum_squares_eq_zero_iff
% 0.26/0.52  thf(fact_3342_sum__squares__eq__zero__iff,axiom,
% 0.26/0.52      ! [X3: rat,Y3: rat] :
% 0.26/0.52        ( ( ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y3 @ Y3 ) )
% 0.26/0.52          = zero_zero_rat )
% 0.26/0.52        = ( ( X3 = zero_zero_rat )
% 0.26/0.52          & ( Y3 = zero_zero_rat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % sum_squares_eq_zero_iff
% 0.26/0.52  thf(fact_3343_sum__squares__eq__zero__iff,axiom,
% 0.26/0.52      ! [X3: int,Y3: int] :
% 0.26/0.52        ( ( ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y3 @ Y3 ) )
% 0.26/0.52          = zero_zero_int )
% 0.26/0.52        = ( ( X3 = zero_zero_int )
% 0.26/0.52          & ( Y3 = zero_zero_int ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % sum_squares_eq_zero_iff
% 0.26/0.52  thf(fact_3344_div__mult__mult1__if,axiom,
% 0.26/0.52      ! [C: nat,A: nat,B: nat] :
% 0.26/0.52        ( ( ( C = zero_zero_nat )
% 0.26/0.52         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.26/0.52            = zero_zero_nat ) )
% 0.26/0.52        & ( ( C != zero_zero_nat )
% 0.26/0.52         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.26/0.52            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % div_mult_mult1_if
% 0.26/0.52  thf(fact_3345_div__mult__mult1__if,axiom,
% 0.26/0.52      ! [C: int,A: int,B: int] :
% 0.26/0.52        ( ( ( C = zero_zero_int )
% 0.26/0.52         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.26/0.52            = zero_zero_int ) )
% 0.26/0.52        & ( ( C != zero_zero_int )
% 0.26/0.52         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.26/0.52            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % div_mult_mult1_if
% 0.26/0.52  thf(fact_3346_div__mult__mult2,axiom,
% 0.26/0.52      ! [C: nat,A: nat,B: nat] :
% 0.26/0.52        ( ( C != zero_zero_nat )
% 0.26/0.52       => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.26/0.52          = ( divide_divide_nat @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % div_mult_mult2
% 0.26/0.52  thf(fact_3347_div__mult__mult2,axiom,
% 0.26/0.52      ! [C: int,A: int,B: int] :
% 0.26/0.52        ( ( C != zero_zero_int )
% 0.26/0.52       => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.26/0.52          = ( divide_divide_int @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % div_mult_mult2
% 0.26/0.52  thf(fact_3348_div__mult__mult1,axiom,
% 0.26/0.52      ! [C: nat,A: nat,B: nat] :
% 0.26/0.52        ( ( C != zero_zero_nat )
% 0.26/0.52       => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.26/0.52          = ( divide_divide_nat @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % div_mult_mult1
% 0.26/0.52  thf(fact_3349_div__mult__mult1,axiom,
% 0.26/0.52      ! [C: int,A: int,B: int] :
% 0.26/0.52        ( ( C != zero_zero_int )
% 0.26/0.52       => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.26/0.52          = ( divide_divide_int @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % div_mult_mult1
% 0.26/0.52  thf(fact_3350_nonzero__mult__div__cancel__right,axiom,
% 0.26/0.52      ! [B: complex,A: complex] :
% 0.26/0.52        ( ( B != zero_zero_complex )
% 0.26/0.52       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 0.26/0.52          = A ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_mult_div_cancel_right
% 0.26/0.52  thf(fact_3351_nonzero__mult__div__cancel__right,axiom,
% 0.26/0.52      ! [B: real,A: real] :
% 0.26/0.52        ( ( B != zero_zero_real )
% 0.26/0.52       => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 0.26/0.52          = A ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_mult_div_cancel_right
% 0.26/0.52  thf(fact_3352_nonzero__mult__div__cancel__right,axiom,
% 0.26/0.52      ! [B: rat,A: rat] :
% 0.26/0.52        ( ( B != zero_zero_rat )
% 0.26/0.52       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 0.26/0.52          = A ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_mult_div_cancel_right
% 0.26/0.52  thf(fact_3353_nonzero__mult__div__cancel__right,axiom,
% 0.26/0.52      ! [B: nat,A: nat] :
% 0.26/0.52        ( ( B != zero_zero_nat )
% 0.26/0.52       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 0.26/0.52          = A ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_mult_div_cancel_right
% 0.26/0.52  thf(fact_3354_nonzero__mult__div__cancel__right,axiom,
% 0.26/0.52      ! [B: int,A: int] :
% 0.26/0.52        ( ( B != zero_zero_int )
% 0.26/0.52       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 0.26/0.52          = A ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_mult_div_cancel_right
% 0.26/0.52  thf(fact_3355_nonzero__mult__div__cancel__left,axiom,
% 0.26/0.52      ! [A: complex,B: complex] :
% 0.26/0.52        ( ( A != zero_zero_complex )
% 0.26/0.52       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 0.26/0.52          = B ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_mult_div_cancel_left
% 0.26/0.52  thf(fact_3356_nonzero__mult__div__cancel__left,axiom,
% 0.26/0.52      ! [A: real,B: real] :
% 0.26/0.52        ( ( A != zero_zero_real )
% 0.26/0.52       => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 0.26/0.52          = B ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_mult_div_cancel_left
% 0.26/0.52  thf(fact_3357_nonzero__mult__div__cancel__left,axiom,
% 0.26/0.52      ! [A: rat,B: rat] :
% 0.26/0.52        ( ( A != zero_zero_rat )
% 0.26/0.52       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 0.26/0.52          = B ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_mult_div_cancel_left
% 0.26/0.52  thf(fact_3358_nonzero__mult__div__cancel__left,axiom,
% 0.26/0.52      ! [A: nat,B: nat] :
% 0.26/0.52        ( ( A != zero_zero_nat )
% 0.26/0.52       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 0.26/0.52          = B ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_mult_div_cancel_left
% 0.26/0.52  thf(fact_3359_nonzero__mult__div__cancel__left,axiom,
% 0.26/0.52      ! [A: int,B: int] :
% 0.26/0.52        ( ( A != zero_zero_int )
% 0.26/0.52       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 0.26/0.52          = B ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_mult_div_cancel_left
% 0.26/0.52  thf(fact_3360_nonzero__mult__divide__mult__cancel__right2,axiom,
% 0.26/0.52      ! [C: complex,A: complex,B: complex] :
% 0.26/0.52        ( ( C != zero_zero_complex )
% 0.26/0.52       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 0.26/0.52          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_mult_divide_mult_cancel_right2
% 0.26/0.52  thf(fact_3361_nonzero__mult__divide__mult__cancel__right2,axiom,
% 0.26/0.52      ! [C: real,A: real,B: real] :
% 0.26/0.52        ( ( C != zero_zero_real )
% 0.26/0.52       => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 0.26/0.52          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_mult_divide_mult_cancel_right2
% 0.26/0.52  thf(fact_3362_nonzero__mult__divide__mult__cancel__right2,axiom,
% 0.26/0.52      ! [C: rat,A: rat,B: rat] :
% 0.26/0.52        ( ( C != zero_zero_rat )
% 0.26/0.52       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 0.26/0.52          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_mult_divide_mult_cancel_right2
% 0.26/0.52  thf(fact_3363_nonzero__mult__divide__mult__cancel__right,axiom,
% 0.26/0.52      ! [C: complex,A: complex,B: complex] :
% 0.26/0.52        ( ( C != zero_zero_complex )
% 0.26/0.52       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 0.26/0.52          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_mult_divide_mult_cancel_right
% 0.26/0.52  thf(fact_3364_nonzero__mult__divide__mult__cancel__right,axiom,
% 0.26/0.52      ! [C: real,A: real,B: real] :
% 0.26/0.52        ( ( C != zero_zero_real )
% 0.26/0.52       => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.26/0.52          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_mult_divide_mult_cancel_right
% 0.26/0.52  thf(fact_3365_nonzero__mult__divide__mult__cancel__right,axiom,
% 0.26/0.52      ! [C: rat,A: rat,B: rat] :
% 0.26/0.52        ( ( C != zero_zero_rat )
% 0.26/0.52       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.26/0.52          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_mult_divide_mult_cancel_right
% 0.26/0.52  thf(fact_3366_nonzero__mult__divide__mult__cancel__left2,axiom,
% 0.26/0.52      ! [C: complex,A: complex,B: complex] :
% 0.26/0.52        ( ( C != zero_zero_complex )
% 0.26/0.52       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 0.26/0.52          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_mult_divide_mult_cancel_left2
% 0.26/0.52  thf(fact_3367_nonzero__mult__divide__mult__cancel__left2,axiom,
% 0.26/0.52      ! [C: real,A: real,B: real] :
% 0.26/0.52        ( ( C != zero_zero_real )
% 0.26/0.52       => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 0.26/0.52          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_mult_divide_mult_cancel_left2
% 0.26/0.52  thf(fact_3368_nonzero__mult__divide__mult__cancel__left2,axiom,
% 0.26/0.52      ! [C: rat,A: rat,B: rat] :
% 0.26/0.52        ( ( C != zero_zero_rat )
% 0.26/0.52       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 0.26/0.52          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_mult_divide_mult_cancel_left2
% 0.26/0.52  thf(fact_3369_nonzero__mult__divide__mult__cancel__left,axiom,
% 0.26/0.52      ! [C: complex,A: complex,B: complex] :
% 0.26/0.52        ( ( C != zero_zero_complex )
% 0.26/0.52       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 0.26/0.52          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_mult_divide_mult_cancel_left
% 0.26/0.52  thf(fact_3370_nonzero__mult__divide__mult__cancel__left,axiom,
% 0.26/0.52      ! [C: real,A: real,B: real] :
% 0.26/0.52        ( ( C != zero_zero_real )
% 0.26/0.52       => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.26/0.52          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_mult_divide_mult_cancel_left
% 0.26/0.52  thf(fact_3371_nonzero__mult__divide__mult__cancel__left,axiom,
% 0.26/0.52      ! [C: rat,A: rat,B: rat] :
% 0.26/0.52        ( ( C != zero_zero_rat )
% 0.26/0.52       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.26/0.52          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_mult_divide_mult_cancel_left
% 0.26/0.52  thf(fact_3372_mult__divide__mult__cancel__left__if,axiom,
% 0.26/0.52      ! [C: complex,A: complex,B: complex] :
% 0.26/0.52        ( ( ( C = zero_zero_complex )
% 0.26/0.52         => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 0.26/0.52            = zero_zero_complex ) )
% 0.26/0.52        & ( ( C != zero_zero_complex )
% 0.26/0.52         => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 0.26/0.52            = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_divide_mult_cancel_left_if
% 0.26/0.52  thf(fact_3373_mult__divide__mult__cancel__left__if,axiom,
% 0.26/0.52      ! [C: real,A: real,B: real] :
% 0.26/0.52        ( ( ( C = zero_zero_real )
% 0.26/0.52         => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.26/0.52            = zero_zero_real ) )
% 0.26/0.52        & ( ( C != zero_zero_real )
% 0.26/0.52         => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.26/0.52            = ( divide_divide_real @ A @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_divide_mult_cancel_left_if
% 0.26/0.52  thf(fact_3374_mult__divide__mult__cancel__left__if,axiom,
% 0.26/0.52      ! [C: rat,A: rat,B: rat] :
% 0.26/0.52        ( ( ( C = zero_zero_rat )
% 0.26/0.52         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.26/0.52            = zero_zero_rat ) )
% 0.26/0.52        & ( ( C != zero_zero_rat )
% 0.26/0.52         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.26/0.52            = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_divide_mult_cancel_left_if
% 0.26/0.52  thf(fact_3375_distrib__right__numeral,axiom,
% 0.26/0.52      ! [A: complex,B: complex,V: num] :
% 0.26/0.52        ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 0.26/0.52        = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % distrib_right_numeral
% 0.26/0.52  thf(fact_3376_distrib__right__numeral,axiom,
% 0.26/0.52      ! [A: real,B: real,V: num] :
% 0.26/0.52        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 0.26/0.52        = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % distrib_right_numeral
% 0.26/0.52  thf(fact_3377_distrib__right__numeral,axiom,
% 0.26/0.52      ! [A: rat,B: rat,V: num] :
% 0.26/0.52        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 0.26/0.52        = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % distrib_right_numeral
% 0.26/0.52  thf(fact_3378_distrib__right__numeral,axiom,
% 0.26/0.52      ! [A: nat,B: nat,V: num] :
% 0.26/0.52        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 0.26/0.52        = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % distrib_right_numeral
% 0.26/0.52  thf(fact_3379_distrib__right__numeral,axiom,
% 0.26/0.52      ! [A: int,B: int,V: num] :
% 0.26/0.52        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 0.26/0.52        = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % distrib_right_numeral
% 0.26/0.52  thf(fact_3380_distrib__left__numeral,axiom,
% 0.26/0.52      ! [V: num,B: complex,C: complex] :
% 0.26/0.52        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 0.26/0.52        = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % distrib_left_numeral
% 0.26/0.52  thf(fact_3381_distrib__left__numeral,axiom,
% 0.26/0.52      ! [V: num,B: real,C: real] :
% 0.26/0.52        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 0.26/0.52        = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % distrib_left_numeral
% 0.26/0.52  thf(fact_3382_distrib__left__numeral,axiom,
% 0.26/0.52      ! [V: num,B: rat,C: rat] :
% 0.26/0.52        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 0.26/0.52        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % distrib_left_numeral
% 0.26/0.52  thf(fact_3383_distrib__left__numeral,axiom,
% 0.26/0.52      ! [V: num,B: nat,C: nat] :
% 0.26/0.52        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 0.26/0.52        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % distrib_left_numeral
% 0.26/0.52  thf(fact_3384_distrib__left__numeral,axiom,
% 0.26/0.52      ! [V: num,B: int,C: int] :
% 0.26/0.52        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 0.26/0.52        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % distrib_left_numeral
% 0.26/0.52  thf(fact_3385_right__diff__distrib__numeral,axiom,
% 0.26/0.52      ! [V: num,B: complex,C: complex] :
% 0.26/0.52        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 0.26/0.52        = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % right_diff_distrib_numeral
% 0.26/0.52  thf(fact_3386_right__diff__distrib__numeral,axiom,
% 0.26/0.52      ! [V: num,B: real,C: real] :
% 0.26/0.52        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 0.26/0.52        = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % right_diff_distrib_numeral
% 0.26/0.52  thf(fact_3387_right__diff__distrib__numeral,axiom,
% 0.26/0.52      ! [V: num,B: rat,C: rat] :
% 0.26/0.52        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 0.26/0.52        = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % right_diff_distrib_numeral
% 0.26/0.52  thf(fact_3388_right__diff__distrib__numeral,axiom,
% 0.26/0.52      ! [V: num,B: int,C: int] :
% 0.26/0.52        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 0.26/0.52        = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % right_diff_distrib_numeral
% 0.26/0.52  thf(fact_3389_left__diff__distrib__numeral,axiom,
% 0.26/0.52      ! [A: complex,B: complex,V: num] :
% 0.26/0.52        ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 0.26/0.52        = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % left_diff_distrib_numeral
% 0.26/0.52  thf(fact_3390_left__diff__distrib__numeral,axiom,
% 0.26/0.52      ! [A: real,B: real,V: num] :
% 0.26/0.52        ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 0.26/0.52        = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % left_diff_distrib_numeral
% 0.26/0.52  thf(fact_3391_left__diff__distrib__numeral,axiom,
% 0.26/0.52      ! [A: rat,B: rat,V: num] :
% 0.26/0.52        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 0.26/0.52        = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % left_diff_distrib_numeral
% 0.26/0.52  thf(fact_3392_left__diff__distrib__numeral,axiom,
% 0.26/0.52      ! [A: int,B: int,V: num] :
% 0.26/0.52        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 0.26/0.52        = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % left_diff_distrib_numeral
% 0.26/0.52  thf(fact_3393_dvd__times__right__cancel__iff,axiom,
% 0.26/0.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.26/0.52        ( ( A != zero_z3403309356797280102nteger )
% 0.26/0.52       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 0.26/0.52          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % dvd_times_right_cancel_iff
% 0.26/0.52  thf(fact_3394_dvd__times__right__cancel__iff,axiom,
% 0.26/0.52      ! [A: nat,B: nat,C: nat] :
% 0.26/0.52        ( ( A != zero_zero_nat )
% 0.26/0.52       => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 0.26/0.52          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % dvd_times_right_cancel_iff
% 0.26/0.52  thf(fact_3395_dvd__times__right__cancel__iff,axiom,
% 0.26/0.52      ! [A: int,B: int,C: int] :
% 0.26/0.52        ( ( A != zero_zero_int )
% 0.26/0.52       => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 0.26/0.52          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % dvd_times_right_cancel_iff
% 0.26/0.52  thf(fact_3396_dvd__times__left__cancel__iff,axiom,
% 0.26/0.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.26/0.52        ( ( A != zero_z3403309356797280102nteger )
% 0.26/0.52       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 0.26/0.52          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % dvd_times_left_cancel_iff
% 0.26/0.52  thf(fact_3397_dvd__times__left__cancel__iff,axiom,
% 0.26/0.52      ! [A: nat,B: nat,C: nat] :
% 0.26/0.52        ( ( A != zero_zero_nat )
% 0.26/0.52       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 0.26/0.52          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % dvd_times_left_cancel_iff
% 0.26/0.52  thf(fact_3398_dvd__times__left__cancel__iff,axiom,
% 0.26/0.52      ! [A: int,B: int,C: int] :
% 0.26/0.52        ( ( A != zero_zero_int )
% 0.26/0.52       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 0.26/0.52          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % dvd_times_left_cancel_iff
% 0.26/0.52  thf(fact_3399_dvd__mult__cancel__right,axiom,
% 0.26/0.52      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.26/0.52        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.26/0.52        = ( ( C = zero_z3403309356797280102nteger )
% 0.26/0.52          | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % dvd_mult_cancel_right
% 0.26/0.52  thf(fact_3400_dvd__mult__cancel__right,axiom,
% 0.26/0.52      ! [A: real,C: real,B: real] :
% 0.26/0.52        ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.26/0.52        = ( ( C = zero_zero_real )
% 0.26/0.52          | ( dvd_dvd_real @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % dvd_mult_cancel_right
% 0.26/0.52  thf(fact_3401_dvd__mult__cancel__right,axiom,
% 0.26/0.52      ! [A: rat,C: rat,B: rat] :
% 0.26/0.52        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.26/0.52        = ( ( C = zero_zero_rat )
% 0.26/0.52          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % dvd_mult_cancel_right
% 0.26/0.52  thf(fact_3402_dvd__mult__cancel__right,axiom,
% 0.26/0.52      ! [A: int,C: int,B: int] :
% 0.26/0.52        ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.26/0.52        = ( ( C = zero_zero_int )
% 0.26/0.52          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % dvd_mult_cancel_right
% 0.26/0.52  thf(fact_3403_dvd__mult__cancel__left,axiom,
% 0.26/0.52      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.26/0.52        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.26/0.52        = ( ( C = zero_z3403309356797280102nteger )
% 0.26/0.52          | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % dvd_mult_cancel_left
% 0.26/0.52  thf(fact_3404_dvd__mult__cancel__left,axiom,
% 0.26/0.52      ! [C: real,A: real,B: real] :
% 0.26/0.52        ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.26/0.52        = ( ( C = zero_zero_real )
% 0.26/0.52          | ( dvd_dvd_real @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % dvd_mult_cancel_left
% 0.26/0.52  thf(fact_3405_dvd__mult__cancel__left,axiom,
% 0.26/0.52      ! [C: rat,A: rat,B: rat] :
% 0.26/0.52        ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.26/0.52        = ( ( C = zero_zero_rat )
% 0.26/0.52          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % dvd_mult_cancel_left
% 0.26/0.52  thf(fact_3406_dvd__mult__cancel__left,axiom,
% 0.26/0.52      ! [C: int,A: int,B: int] :
% 0.26/0.52        ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.26/0.52        = ( ( C = zero_zero_int )
% 0.26/0.52          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % dvd_mult_cancel_left
% 0.26/0.52  thf(fact_3407_mult__eq__1__iff,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( ( times_times_nat @ M @ N )
% 0.26/0.52          = ( suc @ zero_zero_nat ) )
% 0.26/0.52        = ( ( M
% 0.26/0.52            = ( suc @ zero_zero_nat ) )
% 0.26/0.52          & ( N
% 0.26/0.52            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_eq_1_iff
% 0.26/0.52  thf(fact_3408_one__eq__mult__iff,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( ( suc @ zero_zero_nat )
% 0.26/0.52          = ( times_times_nat @ M @ N ) )
% 0.26/0.52        = ( ( M
% 0.26/0.52            = ( suc @ zero_zero_nat ) )
% 0.26/0.52          & ( N
% 0.26/0.52            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % one_eq_mult_iff
% 0.26/0.52  thf(fact_3409_of__nat__mult,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( semiri8010041392384452111omplex @ ( times_times_nat @ M @ N ) )
% 0.26/0.52        = ( times_times_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % of_nat_mult
% 0.26/0.52  thf(fact_3410_of__nat__mult,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N ) )
% 0.26/0.52        = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % of_nat_mult
% 0.26/0.52  thf(fact_3411_of__nat__mult,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N ) )
% 0.26/0.52        = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % of_nat_mult
% 0.26/0.52  thf(fact_3412_of__nat__mult,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 0.26/0.52        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % of_nat_mult
% 0.26/0.52  thf(fact_3413_of__nat__mult,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 0.26/0.52        = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % of_nat_mult
% 0.26/0.52  thf(fact_3414_mult__less__cancel2,axiom,
% 0.26/0.52      ! [M: nat,K: nat,N: nat] :
% 0.26/0.52        ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 0.26/0.52        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.26/0.52          & ( ord_less_nat @ M @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_less_cancel2
% 0.26/0.52  thf(fact_3415_nat__0__less__mult__iff,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 0.26/0.52        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.52          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nat_0_less_mult_iff
% 0.26/0.52  thf(fact_3416_nat__mult__less__cancel__disj,axiom,
% 0.26/0.52      ! [K: nat,M: nat,N: nat] :
% 0.26/0.52        ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.26/0.52        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.26/0.52          & ( ord_less_nat @ M @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nat_mult_less_cancel_disj
% 0.26/0.52  thf(fact_3417_mult__Suc__right,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( times_times_nat @ M @ ( suc @ N ) )
% 0.26/0.52        = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_Suc_right
% 0.26/0.52  thf(fact_3418_nat__mult__div__cancel__disj,axiom,
% 0.26/0.52      ! [K: nat,M: nat,N: nat] :
% 0.26/0.52        ( ( ( K = zero_zero_nat )
% 0.26/0.52         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.26/0.52            = zero_zero_nat ) )
% 0.26/0.52        & ( ( K != zero_zero_nat )
% 0.26/0.52         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.26/0.52            = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nat_mult_div_cancel_disj
% 0.26/0.52  thf(fact_3419_nat__mult__dvd__cancel__disj,axiom,
% 0.26/0.52      ! [K: nat,M: nat,N: nat] :
% 0.26/0.52        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.26/0.52        = ( ( K = zero_zero_nat )
% 0.26/0.52          | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nat_mult_dvd_cancel_disj
% 0.26/0.52  thf(fact_3420_frac__of__int,axiom,
% 0.26/0.52      ! [Z: int] :
% 0.26/0.52        ( ( archim2898591450579166408c_real @ ( ring_1_of_int_real @ Z ) )
% 0.26/0.52        = zero_zero_real ) ).
% 0.26/0.52  
% 0.26/0.52  % frac_of_int
% 0.26/0.52  thf(fact_3421_frac__of__int,axiom,
% 0.26/0.52      ! [Z: int] :
% 0.26/0.52        ( ( archimedean_frac_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.26/0.52        = zero_zero_rat ) ).
% 0.26/0.52  
% 0.26/0.52  % frac_of_int
% 0.26/0.52  thf(fact_3422_le__divide__eq__numeral1_I1_J,axiom,
% 0.26/0.52      ! [A: real,B: real,W: num] :
% 0.26/0.52        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 0.26/0.52        = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 0.26/0.52  
% 0.26/0.52  % le_divide_eq_numeral1(1)
% 0.26/0.52  thf(fact_3423_le__divide__eq__numeral1_I1_J,axiom,
% 0.26/0.52      ! [A: rat,B: rat,W: num] :
% 0.26/0.52        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 0.26/0.52        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 0.26/0.52  
% 0.26/0.52  % le_divide_eq_numeral1(1)
% 0.26/0.52  thf(fact_3424_divide__le__eq__numeral1_I1_J,axiom,
% 0.26/0.52      ! [B: real,W: num,A: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 0.26/0.52        = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % divide_le_eq_numeral1(1)
% 0.26/0.52  thf(fact_3425_divide__le__eq__numeral1_I1_J,axiom,
% 0.26/0.52      ! [B: rat,W: num,A: rat] :
% 0.26/0.52        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 0.26/0.52        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % divide_le_eq_numeral1(1)
% 0.26/0.52  thf(fact_3426_divide__eq__eq__numeral1_I1_J,axiom,
% 0.26/0.52      ! [B: complex,W: num,A: complex] :
% 0.26/0.52        ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 0.26/0.52          = A )
% 0.26/0.52        = ( ( ( ( numera6690914467698888265omplex @ W )
% 0.26/0.52             != zero_zero_complex )
% 0.26/0.52           => ( B
% 0.26/0.52              = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 0.26/0.52          & ( ( ( numera6690914467698888265omplex @ W )
% 0.26/0.52              = zero_zero_complex )
% 0.26/0.52           => ( A = zero_zero_complex ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % divide_eq_eq_numeral1(1)
% 0.26/0.52  thf(fact_3427_divide__eq__eq__numeral1_I1_J,axiom,
% 0.26/0.52      ! [B: real,W: num,A: real] :
% 0.26/0.52        ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 0.26/0.52          = A )
% 0.26/0.52        = ( ( ( ( numeral_numeral_real @ W )
% 0.26/0.52             != zero_zero_real )
% 0.26/0.52           => ( B
% 0.26/0.52              = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 0.26/0.52          & ( ( ( numeral_numeral_real @ W )
% 0.26/0.52              = zero_zero_real )
% 0.26/0.52           => ( A = zero_zero_real ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % divide_eq_eq_numeral1(1)
% 0.26/0.52  thf(fact_3428_divide__eq__eq__numeral1_I1_J,axiom,
% 0.26/0.52      ! [B: rat,W: num,A: rat] :
% 0.26/0.52        ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 0.26/0.52          = A )
% 0.26/0.52        = ( ( ( ( numeral_numeral_rat @ W )
% 0.26/0.52             != zero_zero_rat )
% 0.26/0.52           => ( B
% 0.26/0.52              = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 0.26/0.52          & ( ( ( numeral_numeral_rat @ W )
% 0.26/0.52              = zero_zero_rat )
% 0.26/0.52           => ( A = zero_zero_rat ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % divide_eq_eq_numeral1(1)
% 0.26/0.52  thf(fact_3429_eq__divide__eq__numeral1_I1_J,axiom,
% 0.26/0.52      ! [A: complex,B: complex,W: num] :
% 0.26/0.52        ( ( A
% 0.26/0.52          = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 0.26/0.52        = ( ( ( ( numera6690914467698888265omplex @ W )
% 0.26/0.52             != zero_zero_complex )
% 0.26/0.52           => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 0.26/0.52              = B ) )
% 0.26/0.52          & ( ( ( numera6690914467698888265omplex @ W )
% 0.26/0.52              = zero_zero_complex )
% 0.26/0.52           => ( A = zero_zero_complex ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % eq_divide_eq_numeral1(1)
% 0.26/0.52  thf(fact_3430_eq__divide__eq__numeral1_I1_J,axiom,
% 0.26/0.52      ! [A: real,B: real,W: num] :
% 0.26/0.52        ( ( A
% 0.26/0.52          = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 0.26/0.52        = ( ( ( ( numeral_numeral_real @ W )
% 0.26/0.52             != zero_zero_real )
% 0.26/0.52           => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 0.26/0.52              = B ) )
% 0.26/0.52          & ( ( ( numeral_numeral_real @ W )
% 0.26/0.52              = zero_zero_real )
% 0.26/0.52           => ( A = zero_zero_real ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % eq_divide_eq_numeral1(1)
% 0.26/0.52  thf(fact_3431_eq__divide__eq__numeral1_I1_J,axiom,
% 0.26/0.52      ! [A: rat,B: rat,W: num] :
% 0.26/0.52        ( ( A
% 0.26/0.52          = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 0.26/0.52        = ( ( ( ( numeral_numeral_rat @ W )
% 0.26/0.52             != zero_zero_rat )
% 0.26/0.52           => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 0.26/0.52              = B ) )
% 0.26/0.52          & ( ( ( numeral_numeral_rat @ W )
% 0.26/0.52              = zero_zero_rat )
% 0.26/0.52           => ( A = zero_zero_rat ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % eq_divide_eq_numeral1(1)
% 0.26/0.52  thf(fact_3432_divide__less__eq__numeral1_I1_J,axiom,
% 0.26/0.52      ! [B: real,W: num,A: real] :
% 0.26/0.52        ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 0.26/0.52        = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % divide_less_eq_numeral1(1)
% 0.26/0.52  thf(fact_3433_divide__less__eq__numeral1_I1_J,axiom,
% 0.26/0.52      ! [B: rat,W: num,A: rat] :
% 0.26/0.52        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 0.26/0.52        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % divide_less_eq_numeral1(1)
% 0.26/0.52  thf(fact_3434_less__divide__eq__numeral1_I1_J,axiom,
% 0.26/0.52      ! [A: real,B: real,W: num] :
% 0.26/0.52        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 0.26/0.52        = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 0.26/0.52  
% 0.26/0.52  % less_divide_eq_numeral1(1)
% 0.26/0.52  thf(fact_3435_less__divide__eq__numeral1_I1_J,axiom,
% 0.26/0.52      ! [A: rat,B: rat,W: num] :
% 0.26/0.52        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 0.26/0.52        = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 0.26/0.52  
% 0.26/0.52  % less_divide_eq_numeral1(1)
% 0.26/0.52  thf(fact_3436_nonzero__divide__mult__cancel__right,axiom,
% 0.26/0.52      ! [B: complex,A: complex] :
% 0.26/0.52        ( ( B != zero_zero_complex )
% 0.26/0.52       => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 0.26/0.52          = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_divide_mult_cancel_right
% 0.26/0.52  thf(fact_3437_nonzero__divide__mult__cancel__right,axiom,
% 0.26/0.52      ! [B: real,A: real] :
% 0.26/0.52        ( ( B != zero_zero_real )
% 0.26/0.52       => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 0.26/0.52          = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_divide_mult_cancel_right
% 0.26/0.52  thf(fact_3438_nonzero__divide__mult__cancel__right,axiom,
% 0.26/0.52      ! [B: rat,A: rat] :
% 0.26/0.52        ( ( B != zero_zero_rat )
% 0.26/0.52       => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 0.26/0.52          = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_divide_mult_cancel_right
% 0.26/0.52  thf(fact_3439_nonzero__divide__mult__cancel__left,axiom,
% 0.26/0.52      ! [A: complex,B: complex] :
% 0.26/0.52        ( ( A != zero_zero_complex )
% 0.26/0.52       => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 0.26/0.52          = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_divide_mult_cancel_left
% 0.26/0.52  thf(fact_3440_nonzero__divide__mult__cancel__left,axiom,
% 0.26/0.52      ! [A: real,B: real] :
% 0.26/0.52        ( ( A != zero_zero_real )
% 0.26/0.52       => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 0.26/0.52          = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_divide_mult_cancel_left
% 0.26/0.52  thf(fact_3441_nonzero__divide__mult__cancel__left,axiom,
% 0.26/0.52      ! [A: rat,B: rat] :
% 0.26/0.52        ( ( A != zero_zero_rat )
% 0.26/0.52       => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 0.26/0.52          = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nonzero_divide_mult_cancel_left
% 0.26/0.52  thf(fact_3442_div__mult__self1,axiom,
% 0.26/0.52      ! [B: nat,A: nat,C: nat] :
% 0.26/0.52        ( ( B != zero_zero_nat )
% 0.26/0.52       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 0.26/0.52          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % div_mult_self1
% 0.26/0.52  thf(fact_3443_div__mult__self1,axiom,
% 0.26/0.52      ! [B: int,A: int,C: int] :
% 0.26/0.52        ( ( B != zero_zero_int )
% 0.26/0.52       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 0.26/0.52          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % div_mult_self1
% 0.26/0.52  thf(fact_3444_div__mult__self2,axiom,
% 0.26/0.52      ! [B: nat,A: nat,C: nat] :
% 0.26/0.52        ( ( B != zero_zero_nat )
% 0.26/0.52       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 0.26/0.52          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % div_mult_self2
% 0.26/0.52  thf(fact_3445_div__mult__self2,axiom,
% 0.26/0.52      ! [B: int,A: int,C: int] :
% 0.26/0.52        ( ( B != zero_zero_int )
% 0.26/0.52       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 0.26/0.52          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % div_mult_self2
% 0.26/0.52  thf(fact_3446_div__mult__self3,axiom,
% 0.26/0.52      ! [B: nat,C: nat,A: nat] :
% 0.26/0.52        ( ( B != zero_zero_nat )
% 0.26/0.52       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 0.26/0.52          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % div_mult_self3
% 0.26/0.52  thf(fact_3447_div__mult__self3,axiom,
% 0.26/0.52      ! [B: int,C: int,A: int] :
% 0.26/0.52        ( ( B != zero_zero_int )
% 0.26/0.52       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 0.26/0.52          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % div_mult_self3
% 0.26/0.52  thf(fact_3448_div__mult__self4,axiom,
% 0.26/0.52      ! [B: nat,C: nat,A: nat] :
% 0.26/0.52        ( ( B != zero_zero_nat )
% 0.26/0.52       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 0.26/0.52          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % div_mult_self4
% 0.26/0.52  thf(fact_3449_div__mult__self4,axiom,
% 0.26/0.52      ! [B: int,C: int,A: int] :
% 0.26/0.52        ( ( B != zero_zero_int )
% 0.26/0.52       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 0.26/0.52          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % div_mult_self4
% 0.26/0.52  thf(fact_3450_one__le__mult__iff,axiom,
% 0.26/0.52      ! [M: nat,N: nat] :
% 0.26/0.52        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 0.26/0.52        = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.26/0.52          & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % one_le_mult_iff
% 0.26/0.52  thf(fact_3451_mult__le__cancel2,axiom,
% 0.26/0.52      ! [M: nat,K: nat,N: nat] :
% 0.26/0.52        ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 0.26/0.52        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.26/0.52         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_le_cancel2
% 0.26/0.52  thf(fact_3452_nat__mult__le__cancel__disj,axiom,
% 0.26/0.52      ! [K: nat,M: nat,N: nat] :
% 0.26/0.52        ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.26/0.52        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.26/0.52         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nat_mult_le_cancel_disj
% 0.26/0.52  thf(fact_3453_div__mult__self1__is__m,axiom,
% 0.26/0.52      ! [N: nat,M: nat] :
% 0.26/0.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.52       => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 0.26/0.52          = M ) ) ).
% 0.26/0.52  
% 0.26/0.52  % div_mult_self1_is_m
% 0.26/0.52  thf(fact_3454_div__mult__self__is__m,axiom,
% 0.26/0.52      ! [N: nat,M: nat] :
% 0.26/0.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.52       => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 0.26/0.52          = M ) ) ).
% 0.26/0.52  
% 0.26/0.52  % div_mult_self_is_m
% 0.26/0.52  thf(fact_3455_power__add__numeral,axiom,
% 0.26/0.52      ! [A: complex,M: num,N: num] :
% 0.26/0.52        ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.26/0.52        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_add_numeral
% 0.26/0.52  thf(fact_3456_power__add__numeral,axiom,
% 0.26/0.52      ! [A: real,M: num,N: num] :
% 0.26/0.52        ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.26/0.52        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_add_numeral
% 0.26/0.52  thf(fact_3457_power__add__numeral,axiom,
% 0.26/0.52      ! [A: rat,M: num,N: num] :
% 0.26/0.52        ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.26/0.52        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_add_numeral
% 0.26/0.52  thf(fact_3458_power__add__numeral,axiom,
% 0.26/0.52      ! [A: nat,M: num,N: num] :
% 0.26/0.52        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.26/0.52        = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_add_numeral
% 0.26/0.52  thf(fact_3459_power__add__numeral,axiom,
% 0.26/0.52      ! [A: int,M: num,N: num] :
% 0.26/0.52        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.26/0.52        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_add_numeral
% 0.26/0.52  thf(fact_3460_power__add__numeral2,axiom,
% 0.26/0.52      ! [A: complex,M: num,N: num,B: complex] :
% 0.26/0.52        ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.26/0.52        = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_add_numeral2
% 0.26/0.52  thf(fact_3461_power__add__numeral2,axiom,
% 0.26/0.52      ! [A: real,M: num,N: num,B: real] :
% 0.26/0.52        ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.26/0.52        = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_add_numeral2
% 0.26/0.52  thf(fact_3462_power__add__numeral2,axiom,
% 0.26/0.52      ! [A: rat,M: num,N: num,B: rat] :
% 0.26/0.52        ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.26/0.52        = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_add_numeral2
% 0.26/0.52  thf(fact_3463_power__add__numeral2,axiom,
% 0.26/0.52      ! [A: nat,M: num,N: num,B: nat] :
% 0.26/0.52        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.26/0.52        = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_add_numeral2
% 0.26/0.52  thf(fact_3464_power__add__numeral2,axiom,
% 0.26/0.52      ! [A: int,M: num,N: num,B: int] :
% 0.26/0.52        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.26/0.52        = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_add_numeral2
% 0.26/0.52  thf(fact_3465_even__mult__iff,axiom,
% 0.26/0.52      ! [A: code_integer,B: code_integer] :
% 0.26/0.52        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.26/0.52        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.52          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % even_mult_iff
% 0.26/0.52  thf(fact_3466_even__mult__iff,axiom,
% 0.26/0.52      ! [A: nat,B: nat] :
% 0.26/0.52        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 0.26/0.52        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.52          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % even_mult_iff
% 0.26/0.52  thf(fact_3467_even__mult__iff,axiom,
% 0.26/0.52      ! [A: int,B: int] :
% 0.26/0.52        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 0.26/0.52        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.52          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % even_mult_iff
% 0.26/0.52  thf(fact_3468_or__numerals_I3_J,axiom,
% 0.26/0.52      ! [X3: num,Y3: num] :
% 0.26/0.52        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X3 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y3 ) ) )
% 0.26/0.52        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % or_numerals(3)
% 0.26/0.52  thf(fact_3469_or__numerals_I3_J,axiom,
% 0.26/0.52      ! [X3: num,Y3: num] :
% 0.26/0.52        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 0.26/0.52        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X3 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % or_numerals(3)
% 0.26/0.52  thf(fact_3470_xor__numerals_I3_J,axiom,
% 0.26/0.52      ! [X3: num,Y3: num] :
% 0.26/0.52        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X3 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y3 ) ) )
% 0.26/0.52        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % xor_numerals(3)
% 0.26/0.52  thf(fact_3471_xor__numerals_I3_J,axiom,
% 0.26/0.52      ! [X3: num,Y3: num] :
% 0.26/0.52        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 0.26/0.52        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X3 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % xor_numerals(3)
% 0.26/0.52  thf(fact_3472_unset__bit__0,axiom,
% 0.26/0.52      ! [A: int] :
% 0.26/0.52        ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 0.26/0.52        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % unset_bit_0
% 0.26/0.52  thf(fact_3473_unset__bit__0,axiom,
% 0.26/0.52      ! [A: nat] :
% 0.26/0.52        ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 0.26/0.52        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % unset_bit_0
% 0.26/0.52  thf(fact_3474_odd__two__times__div__two__succ,axiom,
% 0.26/0.52      ! [A: code_integer] :
% 0.26/0.52        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.52       => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 0.26/0.52          = A ) ) ).
% 0.26/0.52  
% 0.26/0.52  % odd_two_times_div_two_succ
% 0.26/0.52  thf(fact_3475_odd__two__times__div__two__succ,axiom,
% 0.26/0.52      ! [A: nat] :
% 0.26/0.52        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.52       => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 0.26/0.52          = A ) ) ).
% 0.26/0.52  
% 0.26/0.52  % odd_two_times_div_two_succ
% 0.26/0.52  thf(fact_3476_odd__two__times__div__two__succ,axiom,
% 0.26/0.52      ! [A: int] :
% 0.26/0.52        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.52       => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 0.26/0.52          = A ) ) ).
% 0.26/0.52  
% 0.26/0.52  % odd_two_times_div_two_succ
% 0.26/0.52  thf(fact_3477_odd__two__times__div__two__nat,axiom,
% 0.26/0.52      ! [N: nat] :
% 0.26/0.52        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.52       => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.52          = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % odd_two_times_div_two_nat
% 0.26/0.52  thf(fact_3478_set__bit__0,axiom,
% 0.26/0.52      ! [A: int] :
% 0.26/0.52        ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 0.26/0.52        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % set_bit_0
% 0.26/0.52  thf(fact_3479_set__bit__0,axiom,
% 0.26/0.52      ! [A: nat] :
% 0.26/0.52        ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 0.26/0.52        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % set_bit_0
% 0.26/0.52  thf(fact_3480_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.26/0.52      ! [A: real,B: real,C: real] :
% 0.26/0.52        ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 0.26/0.52        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % ab_semigroup_mult_class.mult_ac(1)
% 0.26/0.52  thf(fact_3481_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.26/0.52      ! [A: rat,B: rat,C: rat] :
% 0.26/0.52        ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 0.26/0.52        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % ab_semigroup_mult_class.mult_ac(1)
% 0.26/0.52  thf(fact_3482_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.26/0.52      ! [A: nat,B: nat,C: nat] :
% 0.26/0.52        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.26/0.52        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % ab_semigroup_mult_class.mult_ac(1)
% 0.26/0.52  thf(fact_3483_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.26/0.52      ! [A: int,B: int,C: int] :
% 0.26/0.52        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 0.26/0.52        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % ab_semigroup_mult_class.mult_ac(1)
% 0.26/0.52  thf(fact_3484_mult_Oassoc,axiom,
% 0.26/0.52      ! [A: real,B: real,C: real] :
% 0.26/0.52        ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 0.26/0.52        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult.assoc
% 0.26/0.52  thf(fact_3485_mult_Oassoc,axiom,
% 0.26/0.52      ! [A: rat,B: rat,C: rat] :
% 0.26/0.52        ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 0.26/0.52        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult.assoc
% 0.26/0.52  thf(fact_3486_mult_Oassoc,axiom,
% 0.26/0.52      ! [A: nat,B: nat,C: nat] :
% 0.26/0.52        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.26/0.52        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult.assoc
% 0.26/0.52  thf(fact_3487_mult_Oassoc,axiom,
% 0.26/0.52      ! [A: int,B: int,C: int] :
% 0.26/0.52        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 0.26/0.52        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult.assoc
% 0.26/0.52  thf(fact_3488_mult_Ocommute,axiom,
% 0.26/0.52      ( times_times_real
% 0.26/0.52      = ( ^ [A4: real,B3: real] : ( times_times_real @ B3 @ A4 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult.commute
% 0.26/0.52  thf(fact_3489_mult_Ocommute,axiom,
% 0.26/0.52      ( times_times_rat
% 0.26/0.52      = ( ^ [A4: rat,B3: rat] : ( times_times_rat @ B3 @ A4 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult.commute
% 0.26/0.52  thf(fact_3490_mult_Ocommute,axiom,
% 0.26/0.52      ( times_times_nat
% 0.26/0.52      = ( ^ [A4: nat,B3: nat] : ( times_times_nat @ B3 @ A4 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult.commute
% 0.26/0.52  thf(fact_3491_mult_Ocommute,axiom,
% 0.26/0.52      ( times_times_int
% 0.26/0.52      = ( ^ [A4: int,B3: int] : ( times_times_int @ B3 @ A4 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult.commute
% 0.26/0.52  thf(fact_3492_mult_Oleft__commute,axiom,
% 0.26/0.52      ! [B: real,A: real,C: real] :
% 0.26/0.52        ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 0.26/0.52        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult.left_commute
% 0.26/0.52  thf(fact_3493_mult_Oleft__commute,axiom,
% 0.26/0.52      ! [B: rat,A: rat,C: rat] :
% 0.26/0.52        ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 0.26/0.52        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult.left_commute
% 0.26/0.52  thf(fact_3494_mult_Oleft__commute,axiom,
% 0.26/0.52      ! [B: nat,A: nat,C: nat] :
% 0.26/0.52        ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 0.26/0.52        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult.left_commute
% 0.26/0.52  thf(fact_3495_mult_Oleft__commute,axiom,
% 0.26/0.52      ! [B: int,A: int,C: int] :
% 0.26/0.52        ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 0.26/0.52        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult.left_commute
% 0.26/0.52  thf(fact_3496_mult__right__cancel,axiom,
% 0.26/0.52      ! [C: real,A: real,B: real] :
% 0.26/0.52        ( ( C != zero_zero_real )
% 0.26/0.52       => ( ( ( times_times_real @ A @ C )
% 0.26/0.52            = ( times_times_real @ B @ C ) )
% 0.26/0.52          = ( A = B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_right_cancel
% 0.26/0.52  thf(fact_3497_mult__right__cancel,axiom,
% 0.26/0.52      ! [C: rat,A: rat,B: rat] :
% 0.26/0.52        ( ( C != zero_zero_rat )
% 0.26/0.52       => ( ( ( times_times_rat @ A @ C )
% 0.26/0.52            = ( times_times_rat @ B @ C ) )
% 0.26/0.52          = ( A = B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_right_cancel
% 0.26/0.52  thf(fact_3498_mult__right__cancel,axiom,
% 0.26/0.52      ! [C: nat,A: nat,B: nat] :
% 0.26/0.52        ( ( C != zero_zero_nat )
% 0.26/0.52       => ( ( ( times_times_nat @ A @ C )
% 0.26/0.52            = ( times_times_nat @ B @ C ) )
% 0.26/0.52          = ( A = B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_right_cancel
% 0.26/0.52  thf(fact_3499_mult__right__cancel,axiom,
% 0.26/0.52      ! [C: int,A: int,B: int] :
% 0.26/0.52        ( ( C != zero_zero_int )
% 0.26/0.52       => ( ( ( times_times_int @ A @ C )
% 0.26/0.52            = ( times_times_int @ B @ C ) )
% 0.26/0.52          = ( A = B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_right_cancel
% 0.26/0.52  thf(fact_3500_mult__left__cancel,axiom,
% 0.26/0.52      ! [C: real,A: real,B: real] :
% 0.26/0.52        ( ( C != zero_zero_real )
% 0.26/0.52       => ( ( ( times_times_real @ C @ A )
% 0.26/0.52            = ( times_times_real @ C @ B ) )
% 0.26/0.52          = ( A = B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_left_cancel
% 0.26/0.52  thf(fact_3501_mult__left__cancel,axiom,
% 0.26/0.52      ! [C: rat,A: rat,B: rat] :
% 0.26/0.52        ( ( C != zero_zero_rat )
% 0.26/0.52       => ( ( ( times_times_rat @ C @ A )
% 0.26/0.52            = ( times_times_rat @ C @ B ) )
% 0.26/0.52          = ( A = B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_left_cancel
% 0.26/0.52  thf(fact_3502_mult__left__cancel,axiom,
% 0.26/0.52      ! [C: nat,A: nat,B: nat] :
% 0.26/0.52        ( ( C != zero_zero_nat )
% 0.26/0.52       => ( ( ( times_times_nat @ C @ A )
% 0.26/0.52            = ( times_times_nat @ C @ B ) )
% 0.26/0.52          = ( A = B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_left_cancel
% 0.26/0.52  thf(fact_3503_mult__left__cancel,axiom,
% 0.26/0.52      ! [C: int,A: int,B: int] :
% 0.26/0.52        ( ( C != zero_zero_int )
% 0.26/0.52       => ( ( ( times_times_int @ C @ A )
% 0.26/0.52            = ( times_times_int @ C @ B ) )
% 0.26/0.52          = ( A = B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_left_cancel
% 0.26/0.52  thf(fact_3504_no__zero__divisors,axiom,
% 0.26/0.52      ! [A: real,B: real] :
% 0.26/0.52        ( ( A != zero_zero_real )
% 0.26/0.52       => ( ( B != zero_zero_real )
% 0.26/0.52         => ( ( times_times_real @ A @ B )
% 0.26/0.52           != zero_zero_real ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % no_zero_divisors
% 0.26/0.52  thf(fact_3505_no__zero__divisors,axiom,
% 0.26/0.52      ! [A: rat,B: rat] :
% 0.26/0.52        ( ( A != zero_zero_rat )
% 0.26/0.52       => ( ( B != zero_zero_rat )
% 0.26/0.52         => ( ( times_times_rat @ A @ B )
% 0.26/0.52           != zero_zero_rat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % no_zero_divisors
% 0.26/0.52  thf(fact_3506_no__zero__divisors,axiom,
% 0.26/0.52      ! [A: nat,B: nat] :
% 0.26/0.52        ( ( A != zero_zero_nat )
% 0.26/0.52       => ( ( B != zero_zero_nat )
% 0.26/0.52         => ( ( times_times_nat @ A @ B )
% 0.26/0.52           != zero_zero_nat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % no_zero_divisors
% 0.26/0.52  thf(fact_3507_no__zero__divisors,axiom,
% 0.26/0.52      ! [A: int,B: int] :
% 0.26/0.52        ( ( A != zero_zero_int )
% 0.26/0.52       => ( ( B != zero_zero_int )
% 0.26/0.52         => ( ( times_times_int @ A @ B )
% 0.26/0.52           != zero_zero_int ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % no_zero_divisors
% 0.26/0.52  thf(fact_3508_divisors__zero,axiom,
% 0.26/0.52      ! [A: real,B: real] :
% 0.26/0.52        ( ( ( times_times_real @ A @ B )
% 0.26/0.52          = zero_zero_real )
% 0.26/0.52       => ( ( A = zero_zero_real )
% 0.26/0.52          | ( B = zero_zero_real ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % divisors_zero
% 0.26/0.52  thf(fact_3509_divisors__zero,axiom,
% 0.26/0.52      ! [A: rat,B: rat] :
% 0.26/0.52        ( ( ( times_times_rat @ A @ B )
% 0.26/0.52          = zero_zero_rat )
% 0.26/0.52       => ( ( A = zero_zero_rat )
% 0.26/0.52          | ( B = zero_zero_rat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % divisors_zero
% 0.26/0.52  thf(fact_3510_divisors__zero,axiom,
% 0.26/0.52      ! [A: nat,B: nat] :
% 0.26/0.52        ( ( ( times_times_nat @ A @ B )
% 0.26/0.52          = zero_zero_nat )
% 0.26/0.52       => ( ( A = zero_zero_nat )
% 0.26/0.52          | ( B = zero_zero_nat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % divisors_zero
% 0.26/0.52  thf(fact_3511_divisors__zero,axiom,
% 0.26/0.52      ! [A: int,B: int] :
% 0.26/0.52        ( ( ( times_times_int @ A @ B )
% 0.26/0.52          = zero_zero_int )
% 0.26/0.52       => ( ( A = zero_zero_int )
% 0.26/0.52          | ( B = zero_zero_int ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % divisors_zero
% 0.26/0.52  thf(fact_3512_mult__not__zero,axiom,
% 0.26/0.52      ! [A: real,B: real] :
% 0.26/0.52        ( ( ( times_times_real @ A @ B )
% 0.26/0.52         != zero_zero_real )
% 0.26/0.52       => ( ( A != zero_zero_real )
% 0.26/0.52          & ( B != zero_zero_real ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_not_zero
% 0.26/0.52  thf(fact_3513_mult__not__zero,axiom,
% 0.26/0.52      ! [A: rat,B: rat] :
% 0.26/0.52        ( ( ( times_times_rat @ A @ B )
% 0.26/0.52         != zero_zero_rat )
% 0.26/0.52       => ( ( A != zero_zero_rat )
% 0.26/0.52          & ( B != zero_zero_rat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_not_zero
% 0.26/0.52  thf(fact_3514_mult__not__zero,axiom,
% 0.26/0.52      ! [A: nat,B: nat] :
% 0.26/0.52        ( ( ( times_times_nat @ A @ B )
% 0.26/0.52         != zero_zero_nat )
% 0.26/0.52       => ( ( A != zero_zero_nat )
% 0.26/0.52          & ( B != zero_zero_nat ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_not_zero
% 0.26/0.52  thf(fact_3515_mult__not__zero,axiom,
% 0.26/0.52      ! [A: int,B: int] :
% 0.26/0.52        ( ( ( times_times_int @ A @ B )
% 0.26/0.52         != zero_zero_int )
% 0.26/0.52       => ( ( A != zero_zero_int )
% 0.26/0.52          & ( B != zero_zero_int ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_not_zero
% 0.26/0.52  thf(fact_3516_comm__monoid__mult__class_Omult__1,axiom,
% 0.26/0.52      ! [A: complex] :
% 0.26/0.52        ( ( times_times_complex @ one_one_complex @ A )
% 0.26/0.52        = A ) ).
% 0.26/0.52  
% 0.26/0.52  % comm_monoid_mult_class.mult_1
% 0.26/0.52  thf(fact_3517_comm__monoid__mult__class_Omult__1,axiom,
% 0.26/0.52      ! [A: real] :
% 0.26/0.52        ( ( times_times_real @ one_one_real @ A )
% 0.26/0.52        = A ) ).
% 0.26/0.52  
% 0.26/0.52  % comm_monoid_mult_class.mult_1
% 0.26/0.52  thf(fact_3518_comm__monoid__mult__class_Omult__1,axiom,
% 0.26/0.52      ! [A: rat] :
% 0.26/0.52        ( ( times_times_rat @ one_one_rat @ A )
% 0.26/0.52        = A ) ).
% 0.26/0.52  
% 0.26/0.52  % comm_monoid_mult_class.mult_1
% 0.26/0.52  thf(fact_3519_comm__monoid__mult__class_Omult__1,axiom,
% 0.26/0.52      ! [A: nat] :
% 0.26/0.52        ( ( times_times_nat @ one_one_nat @ A )
% 0.26/0.52        = A ) ).
% 0.26/0.52  
% 0.26/0.52  % comm_monoid_mult_class.mult_1
% 0.26/0.52  thf(fact_3520_comm__monoid__mult__class_Omult__1,axiom,
% 0.26/0.52      ! [A: int] :
% 0.26/0.52        ( ( times_times_int @ one_one_int @ A )
% 0.26/0.52        = A ) ).
% 0.26/0.52  
% 0.26/0.52  % comm_monoid_mult_class.mult_1
% 0.26/0.52  thf(fact_3521_mult_Ocomm__neutral,axiom,
% 0.26/0.52      ! [A: complex] :
% 0.26/0.52        ( ( times_times_complex @ A @ one_one_complex )
% 0.26/0.52        = A ) ).
% 0.26/0.52  
% 0.26/0.52  % mult.comm_neutral
% 0.26/0.52  thf(fact_3522_mult_Ocomm__neutral,axiom,
% 0.26/0.52      ! [A: real] :
% 0.26/0.52        ( ( times_times_real @ A @ one_one_real )
% 0.26/0.52        = A ) ).
% 0.26/0.52  
% 0.26/0.52  % mult.comm_neutral
% 0.26/0.52  thf(fact_3523_mult_Ocomm__neutral,axiom,
% 0.26/0.52      ! [A: rat] :
% 0.26/0.52        ( ( times_times_rat @ A @ one_one_rat )
% 0.26/0.52        = A ) ).
% 0.26/0.52  
% 0.26/0.52  % mult.comm_neutral
% 0.26/0.52  thf(fact_3524_mult_Ocomm__neutral,axiom,
% 0.26/0.52      ! [A: nat] :
% 0.26/0.52        ( ( times_times_nat @ A @ one_one_nat )
% 0.26/0.52        = A ) ).
% 0.26/0.52  
% 0.26/0.52  % mult.comm_neutral
% 0.26/0.52  thf(fact_3525_mult_Ocomm__neutral,axiom,
% 0.26/0.52      ! [A: int] :
% 0.26/0.52        ( ( times_times_int @ A @ one_one_int )
% 0.26/0.52        = A ) ).
% 0.26/0.52  
% 0.26/0.52  % mult.comm_neutral
% 0.26/0.52  thf(fact_3526_inf__period_I2_J,axiom,
% 0.26/0.52      ! [P: real > $o,D5: real,Q: real > $o] :
% 0.26/0.52        ( ! [X4: real,K2: real] :
% 0.26/0.52            ( ( P @ X4 )
% 0.26/0.52            = ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K2 @ D5 ) ) ) )
% 0.26/0.52       => ( ! [X4: real,K2: real] :
% 0.26/0.52              ( ( Q @ X4 )
% 0.26/0.52              = ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K2 @ D5 ) ) ) )
% 0.26/0.52         => ! [X6: real,K4: real] :
% 0.26/0.52              ( ( ( P @ X6 )
% 0.26/0.52                | ( Q @ X6 ) )
% 0.26/0.52              = ( ( P @ ( minus_minus_real @ X6 @ ( times_times_real @ K4 @ D5 ) ) )
% 0.26/0.52                | ( Q @ ( minus_minus_real @ X6 @ ( times_times_real @ K4 @ D5 ) ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % inf_period(2)
% 0.26/0.52  thf(fact_3527_inf__period_I2_J,axiom,
% 0.26/0.52      ! [P: rat > $o,D5: rat,Q: rat > $o] :
% 0.26/0.52        ( ! [X4: rat,K2: rat] :
% 0.26/0.52            ( ( P @ X4 )
% 0.26/0.52            = ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K2 @ D5 ) ) ) )
% 0.26/0.52       => ( ! [X4: rat,K2: rat] :
% 0.26/0.52              ( ( Q @ X4 )
% 0.26/0.52              = ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K2 @ D5 ) ) ) )
% 0.26/0.52         => ! [X6: rat,K4: rat] :
% 0.26/0.52              ( ( ( P @ X6 )
% 0.26/0.52                | ( Q @ X6 ) )
% 0.26/0.52              = ( ( P @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D5 ) ) )
% 0.26/0.52                | ( Q @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D5 ) ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % inf_period(2)
% 0.26/0.52  thf(fact_3528_inf__period_I2_J,axiom,
% 0.26/0.52      ! [P: int > $o,D5: int,Q: int > $o] :
% 0.26/0.52        ( ! [X4: int,K2: int] :
% 0.26/0.52            ( ( P @ X4 )
% 0.26/0.52            = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D5 ) ) ) )
% 0.26/0.52       => ( ! [X4: int,K2: int] :
% 0.26/0.52              ( ( Q @ X4 )
% 0.26/0.52              = ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D5 ) ) ) )
% 0.26/0.52         => ! [X6: int,K4: int] :
% 0.26/0.52              ( ( ( P @ X6 )
% 0.26/0.52                | ( Q @ X6 ) )
% 0.26/0.52              = ( ( P @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D5 ) ) )
% 0.26/0.52                | ( Q @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D5 ) ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % inf_period(2)
% 0.26/0.52  thf(fact_3529_inf__period_I1_J,axiom,
% 0.26/0.52      ! [P: real > $o,D5: real,Q: real > $o] :
% 0.26/0.52        ( ! [X4: real,K2: real] :
% 0.26/0.52            ( ( P @ X4 )
% 0.26/0.52            = ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K2 @ D5 ) ) ) )
% 0.26/0.52       => ( ! [X4: real,K2: real] :
% 0.26/0.52              ( ( Q @ X4 )
% 0.26/0.52              = ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K2 @ D5 ) ) ) )
% 0.26/0.52         => ! [X6: real,K4: real] :
% 0.26/0.52              ( ( ( P @ X6 )
% 0.26/0.52                & ( Q @ X6 ) )
% 0.26/0.52              = ( ( P @ ( minus_minus_real @ X6 @ ( times_times_real @ K4 @ D5 ) ) )
% 0.26/0.52                & ( Q @ ( minus_minus_real @ X6 @ ( times_times_real @ K4 @ D5 ) ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % inf_period(1)
% 0.26/0.52  thf(fact_3530_inf__period_I1_J,axiom,
% 0.26/0.52      ! [P: rat > $o,D5: rat,Q: rat > $o] :
% 0.26/0.52        ( ! [X4: rat,K2: rat] :
% 0.26/0.52            ( ( P @ X4 )
% 0.26/0.52            = ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K2 @ D5 ) ) ) )
% 0.26/0.52       => ( ! [X4: rat,K2: rat] :
% 0.26/0.52              ( ( Q @ X4 )
% 0.26/0.52              = ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K2 @ D5 ) ) ) )
% 0.26/0.52         => ! [X6: rat,K4: rat] :
% 0.26/0.52              ( ( ( P @ X6 )
% 0.26/0.52                & ( Q @ X6 ) )
% 0.26/0.52              = ( ( P @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D5 ) ) )
% 0.26/0.52                & ( Q @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D5 ) ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % inf_period(1)
% 0.26/0.52  thf(fact_3531_inf__period_I1_J,axiom,
% 0.26/0.52      ! [P: int > $o,D5: int,Q: int > $o] :
% 0.26/0.52        ( ! [X4: int,K2: int] :
% 0.26/0.52            ( ( P @ X4 )
% 0.26/0.52            = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D5 ) ) ) )
% 0.26/0.52       => ( ! [X4: int,K2: int] :
% 0.26/0.52              ( ( Q @ X4 )
% 0.26/0.52              = ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D5 ) ) ) )
% 0.26/0.52         => ! [X6: int,K4: int] :
% 0.26/0.52              ( ( ( P @ X6 )
% 0.26/0.52                & ( Q @ X6 ) )
% 0.26/0.52              = ( ( P @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D5 ) ) )
% 0.26/0.52                & ( Q @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D5 ) ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % inf_period(1)
% 0.26/0.52  thf(fact_3532_power__commutes,axiom,
% 0.26/0.52      ! [A: complex,N: nat] :
% 0.26/0.52        ( ( times_times_complex @ ( power_power_complex @ A @ N ) @ A )
% 0.26/0.52        = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_commutes
% 0.26/0.52  thf(fact_3533_power__commutes,axiom,
% 0.26/0.52      ! [A: real,N: nat] :
% 0.26/0.52        ( ( times_times_real @ ( power_power_real @ A @ N ) @ A )
% 0.26/0.52        = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_commutes
% 0.26/0.52  thf(fact_3534_power__commutes,axiom,
% 0.26/0.52      ! [A: rat,N: nat] :
% 0.26/0.52        ( ( times_times_rat @ ( power_power_rat @ A @ N ) @ A )
% 0.26/0.52        = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_commutes
% 0.26/0.52  thf(fact_3535_power__commutes,axiom,
% 0.26/0.52      ! [A: nat,N: nat] :
% 0.26/0.52        ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 0.26/0.52        = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_commutes
% 0.26/0.52  thf(fact_3536_power__commutes,axiom,
% 0.26/0.52      ! [A: int,N: nat] :
% 0.26/0.52        ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 0.26/0.52        = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_commutes
% 0.26/0.52  thf(fact_3537_power__mult__distrib,axiom,
% 0.26/0.52      ! [A: complex,B: complex,N: nat] :
% 0.26/0.52        ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N )
% 0.26/0.52        = ( times_times_complex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_mult_distrib
% 0.26/0.52  thf(fact_3538_power__mult__distrib,axiom,
% 0.26/0.52      ! [A: real,B: real,N: nat] :
% 0.26/0.52        ( ( power_power_real @ ( times_times_real @ A @ B ) @ N )
% 0.26/0.52        = ( times_times_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_mult_distrib
% 0.26/0.52  thf(fact_3539_power__mult__distrib,axiom,
% 0.26/0.52      ! [A: rat,B: rat,N: nat] :
% 0.26/0.52        ( ( power_power_rat @ ( times_times_rat @ A @ B ) @ N )
% 0.26/0.52        = ( times_times_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_mult_distrib
% 0.26/0.52  thf(fact_3540_power__mult__distrib,axiom,
% 0.26/0.52      ! [A: nat,B: nat,N: nat] :
% 0.26/0.52        ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 0.26/0.52        = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_mult_distrib
% 0.26/0.52  thf(fact_3541_power__mult__distrib,axiom,
% 0.26/0.52      ! [A: int,B: int,N: nat] :
% 0.26/0.52        ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 0.26/0.52        = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_mult_distrib
% 0.26/0.52  thf(fact_3542_power__commuting__commutes,axiom,
% 0.26/0.52      ! [X3: complex,Y3: complex,N: nat] :
% 0.26/0.52        ( ( ( times_times_complex @ X3 @ Y3 )
% 0.26/0.52          = ( times_times_complex @ Y3 @ X3 ) )
% 0.26/0.52       => ( ( times_times_complex @ ( power_power_complex @ X3 @ N ) @ Y3 )
% 0.26/0.52          = ( times_times_complex @ Y3 @ ( power_power_complex @ X3 @ N ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_commuting_commutes
% 0.26/0.52  thf(fact_3543_power__commuting__commutes,axiom,
% 0.26/0.52      ! [X3: real,Y3: real,N: nat] :
% 0.26/0.52        ( ( ( times_times_real @ X3 @ Y3 )
% 0.26/0.52          = ( times_times_real @ Y3 @ X3 ) )
% 0.26/0.52       => ( ( times_times_real @ ( power_power_real @ X3 @ N ) @ Y3 )
% 0.26/0.52          = ( times_times_real @ Y3 @ ( power_power_real @ X3 @ N ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_commuting_commutes
% 0.26/0.52  thf(fact_3544_power__commuting__commutes,axiom,
% 0.26/0.52      ! [X3: rat,Y3: rat,N: nat] :
% 0.26/0.52        ( ( ( times_times_rat @ X3 @ Y3 )
% 0.26/0.52          = ( times_times_rat @ Y3 @ X3 ) )
% 0.26/0.52       => ( ( times_times_rat @ ( power_power_rat @ X3 @ N ) @ Y3 )
% 0.26/0.52          = ( times_times_rat @ Y3 @ ( power_power_rat @ X3 @ N ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_commuting_commutes
% 0.26/0.52  thf(fact_3545_power__commuting__commutes,axiom,
% 0.26/0.52      ! [X3: nat,Y3: nat,N: nat] :
% 0.26/0.52        ( ( ( times_times_nat @ X3 @ Y3 )
% 0.26/0.52          = ( times_times_nat @ Y3 @ X3 ) )
% 0.26/0.52       => ( ( times_times_nat @ ( power_power_nat @ X3 @ N ) @ Y3 )
% 0.26/0.52          = ( times_times_nat @ Y3 @ ( power_power_nat @ X3 @ N ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_commuting_commutes
% 0.26/0.52  thf(fact_3546_power__commuting__commutes,axiom,
% 0.26/0.52      ! [X3: int,Y3: int,N: nat] :
% 0.26/0.52        ( ( ( times_times_int @ X3 @ Y3 )
% 0.26/0.52          = ( times_times_int @ Y3 @ X3 ) )
% 0.26/0.52       => ( ( times_times_int @ ( power_power_int @ X3 @ N ) @ Y3 )
% 0.26/0.52          = ( times_times_int @ Y3 @ ( power_power_int @ X3 @ N ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_commuting_commutes
% 0.26/0.52  thf(fact_3547_Suc__mult__cancel1,axiom,
% 0.26/0.52      ! [K: nat,M: nat,N: nat] :
% 0.26/0.52        ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 0.26/0.52          = ( times_times_nat @ ( suc @ K ) @ N ) )
% 0.26/0.52        = ( M = N ) ) ).
% 0.26/0.52  
% 0.26/0.52  % Suc_mult_cancel1
% 0.26/0.52  thf(fact_3548_mult__0,axiom,
% 0.26/0.52      ! [N: nat] :
% 0.26/0.52        ( ( times_times_nat @ zero_zero_nat @ N )
% 0.26/0.52        = zero_zero_nat ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_0
% 0.26/0.52  thf(fact_3549_nat__mult__eq__cancel__disj,axiom,
% 0.26/0.52      ! [K: nat,M: nat,N: nat] :
% 0.26/0.52        ( ( ( times_times_nat @ K @ M )
% 0.26/0.52          = ( times_times_nat @ K @ N ) )
% 0.26/0.52        = ( ( K = zero_zero_nat )
% 0.26/0.52          | ( M = N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % nat_mult_eq_cancel_disj
% 0.26/0.52  thf(fact_3550_power__mult,axiom,
% 0.26/0.52      ! [A: nat,M: nat,N: nat] :
% 0.26/0.52        ( ( power_power_nat @ A @ ( times_times_nat @ M @ N ) )
% 0.26/0.52        = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_mult
% 0.26/0.52  thf(fact_3551_power__mult,axiom,
% 0.26/0.52      ! [A: int,M: nat,N: nat] :
% 0.26/0.52        ( ( power_power_int @ A @ ( times_times_nat @ M @ N ) )
% 0.26/0.52        = ( power_power_int @ ( power_power_int @ A @ M ) @ N ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_mult
% 0.26/0.52  thf(fact_3552_power__mult,axiom,
% 0.26/0.52      ! [A: real,M: nat,N: nat] :
% 0.26/0.52        ( ( power_power_real @ A @ ( times_times_nat @ M @ N ) )
% 0.26/0.52        = ( power_power_real @ ( power_power_real @ A @ M ) @ N ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_mult
% 0.26/0.52  thf(fact_3553_power__mult,axiom,
% 0.26/0.52      ! [A: complex,M: nat,N: nat] :
% 0.26/0.52        ( ( power_power_complex @ A @ ( times_times_nat @ M @ N ) )
% 0.26/0.52        = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N ) ) ).
% 0.26/0.52  
% 0.26/0.52  % power_mult
% 0.26/0.52  thf(fact_3554_mult__of__nat__commute,axiom,
% 0.26/0.52      ! [X3: nat,Y3: complex] :
% 0.26/0.52        ( ( times_times_complex @ ( semiri8010041392384452111omplex @ X3 ) @ Y3 )
% 0.26/0.52        = ( times_times_complex @ Y3 @ ( semiri8010041392384452111omplex @ X3 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_of_nat_commute
% 0.26/0.52  thf(fact_3555_mult__of__nat__commute,axiom,
% 0.26/0.52      ! [X3: nat,Y3: real] :
% 0.26/0.52        ( ( times_times_real @ ( semiri5074537144036343181t_real @ X3 ) @ Y3 )
% 0.26/0.52        = ( times_times_real @ Y3 @ ( semiri5074537144036343181t_real @ X3 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_of_nat_commute
% 0.26/0.52  thf(fact_3556_mult__of__nat__commute,axiom,
% 0.26/0.52      ! [X3: nat,Y3: rat] :
% 0.26/0.52        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X3 ) @ Y3 )
% 0.26/0.52        = ( times_times_rat @ Y3 @ ( semiri681578069525770553at_rat @ X3 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_of_nat_commute
% 0.26/0.52  thf(fact_3557_mult__of__nat__commute,axiom,
% 0.26/0.52      ! [X3: nat,Y3: nat] :
% 0.26/0.52        ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ Y3 )
% 0.26/0.52        = ( times_times_nat @ Y3 @ ( semiri1316708129612266289at_nat @ X3 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_of_nat_commute
% 0.26/0.52  thf(fact_3558_mult__of__nat__commute,axiom,
% 0.26/0.52      ! [X3: nat,Y3: int] :
% 0.26/0.52        ( ( times_times_int @ ( semiri1314217659103216013at_int @ X3 ) @ Y3 )
% 0.26/0.52        = ( times_times_int @ Y3 @ ( semiri1314217659103216013at_int @ X3 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_of_nat_commute
% 0.26/0.52  thf(fact_3559_add__mult__distrib2,axiom,
% 0.26/0.52      ! [K: nat,M: nat,N: nat] :
% 0.26/0.52        ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 0.26/0.52        = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % add_mult_distrib2
% 0.26/0.52  thf(fact_3560_add__mult__distrib,axiom,
% 0.26/0.52      ! [M: nat,N: nat,K: nat] :
% 0.26/0.52        ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 0.26/0.52        = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % add_mult_distrib
% 0.26/0.52  thf(fact_3561_left__add__mult__distrib,axiom,
% 0.26/0.52      ! [I: nat,U: nat,J: nat,K: nat] :
% 0.26/0.52        ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 0.26/0.52        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 0.26/0.52  
% 0.26/0.52  % left_add_mult_distrib
% 0.26/0.52  thf(fact_3562_mult__le__mono2,axiom,
% 0.26/0.52      ! [I: nat,J: nat,K: nat] :
% 0.26/0.52        ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.52       => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_le_mono2
% 0.26/0.52  thf(fact_3563_mult__le__mono1,axiom,
% 0.26/0.52      ! [I: nat,J: nat,K: nat] :
% 0.26/0.52        ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.52       => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_le_mono1
% 0.26/0.52  thf(fact_3564_mult__le__mono,axiom,
% 0.26/0.52      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.26/0.52        ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.52       => ( ( ord_less_eq_nat @ K @ L )
% 0.26/0.52         => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_le_mono
% 0.26/0.52  thf(fact_3565_le__square,axiom,
% 0.26/0.52      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 0.26/0.52  
% 0.26/0.52  % le_square
% 0.26/0.52  thf(fact_3566_le__cube,axiom,
% 0.26/0.52      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % le_cube
% 0.26/0.52  thf(fact_3567_nat__mult__1__right,axiom,
% 0.26/0.52      ! [N: nat] :
% 0.26/0.52        ( ( times_times_nat @ N @ one_one_nat )
% 0.26/0.52        = N ) ).
% 0.26/0.52  
% 0.26/0.52  % nat_mult_1_right
% 0.26/0.52  thf(fact_3568_nat__mult__1,axiom,
% 0.26/0.52      ! [N: nat] :
% 0.26/0.52        ( ( times_times_nat @ one_one_nat @ N )
% 0.26/0.52        = N ) ).
% 0.26/0.52  
% 0.26/0.52  % nat_mult_1
% 0.26/0.52  thf(fact_3569_diff__mult__distrib2,axiom,
% 0.26/0.52      ! [K: nat,M: nat,N: nat] :
% 0.26/0.52        ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.26/0.52        = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % diff_mult_distrib2
% 0.26/0.52  thf(fact_3570_diff__mult__distrib,axiom,
% 0.26/0.52      ! [M: nat,N: nat,K: nat] :
% 0.26/0.52        ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 0.26/0.52        = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % diff_mult_distrib
% 0.26/0.52  thf(fact_3571_mult__of__int__commute,axiom,
% 0.26/0.52      ! [X3: int,Y3: complex] :
% 0.26/0.52        ( ( times_times_complex @ ( ring_17405671764205052669omplex @ X3 ) @ Y3 )
% 0.26/0.52        = ( times_times_complex @ Y3 @ ( ring_17405671764205052669omplex @ X3 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_of_int_commute
% 0.26/0.52  thf(fact_3572_mult__of__int__commute,axiom,
% 0.26/0.52      ! [X3: int,Y3: real] :
% 0.26/0.52        ( ( times_times_real @ ( ring_1_of_int_real @ X3 ) @ Y3 )
% 0.26/0.52        = ( times_times_real @ Y3 @ ( ring_1_of_int_real @ X3 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_of_int_commute
% 0.26/0.52  thf(fact_3573_mult__of__int__commute,axiom,
% 0.26/0.52      ! [X3: int,Y3: rat] :
% 0.26/0.52        ( ( times_times_rat @ ( ring_1_of_int_rat @ X3 ) @ Y3 )
% 0.26/0.52        = ( times_times_rat @ Y3 @ ( ring_1_of_int_rat @ X3 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_of_int_commute
% 0.26/0.52  thf(fact_3574_mult__of__int__commute,axiom,
% 0.26/0.52      ! [X3: int,Y3: int] :
% 0.26/0.52        ( ( times_times_int @ ( ring_1_of_int_int @ X3 ) @ Y3 )
% 0.26/0.52        = ( times_times_int @ Y3 @ ( ring_1_of_int_int @ X3 ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_of_int_commute
% 0.26/0.52  thf(fact_3575_le__mult__nat__floor,axiom,
% 0.26/0.52      ! [A: rat,B: rat] : ( ord_less_eq_nat @ ( times_times_nat @ ( nat2 @ ( archim3151403230148437115or_rat @ A ) ) @ ( nat2 @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( nat2 @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % le_mult_nat_floor
% 0.26/0.52  thf(fact_3576_le__mult__nat__floor,axiom,
% 0.26/0.52      ! [A: real,B: real] : ( ord_less_eq_nat @ ( times_times_nat @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) @ ( nat2 @ ( archim6058952711729229775r_real @ B ) ) ) @ ( nat2 @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % le_mult_nat_floor
% 0.26/0.52  thf(fact_3577_le__mult__floor,axiom,
% 0.26/0.52      ! [A: rat,B: rat] :
% 0.26/0.52        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.26/0.52         => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % le_mult_floor
% 0.26/0.52  thf(fact_3578_le__mult__floor,axiom,
% 0.26/0.52      ! [A: real,B: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.26/0.52         => ( ord_less_eq_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % le_mult_floor
% 0.26/0.52  thf(fact_3579_mult__ceiling__le,axiom,
% 0.26/0.52      ! [A: real,B: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.26/0.52         => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_ceiling_le
% 0.26/0.52  thf(fact_3580_mult__ceiling__le,axiom,
% 0.26/0.52      ! [A: rat,B: rat] :
% 0.26/0.52        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.26/0.52         => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_ceiling_le
% 0.26/0.52  thf(fact_3581_mult__mono,axiom,
% 0.26/0.52      ! [A: real,B: real,C: real,D3: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.52       => ( ( ord_less_eq_real @ C @ D3 )
% 0.26/0.52         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.26/0.52           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.26/0.52             => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_mono
% 0.26/0.52  thf(fact_3582_mult__mono,axiom,
% 0.26/0.52      ! [A: rat,B: rat,C: rat,D3: rat] :
% 0.26/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.52       => ( ( ord_less_eq_rat @ C @ D3 )
% 0.26/0.52         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.26/0.52           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.26/0.52             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_mono
% 0.26/0.52  thf(fact_3583_mult__mono,axiom,
% 0.26/0.52      ! [A: nat,B: nat,C: nat,D3: nat] :
% 0.26/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.52       => ( ( ord_less_eq_nat @ C @ D3 )
% 0.26/0.52         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.26/0.52           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.26/0.52             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_mono
% 0.26/0.52  thf(fact_3584_mult__mono,axiom,
% 0.26/0.52      ! [A: int,B: int,C: int,D3: int] :
% 0.26/0.52        ( ( ord_less_eq_int @ A @ B )
% 0.26/0.52       => ( ( ord_less_eq_int @ C @ D3 )
% 0.26/0.52         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.26/0.52           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.26/0.52             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_mono
% 0.26/0.52  thf(fact_3585_mult__mono_H,axiom,
% 0.26/0.52      ! [A: real,B: real,C: real,D3: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.52       => ( ( ord_less_eq_real @ C @ D3 )
% 0.26/0.52         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.52           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.26/0.52             => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_mono'
% 0.26/0.52  thf(fact_3586_mult__mono_H,axiom,
% 0.26/0.52      ! [A: rat,B: rat,C: rat,D3: rat] :
% 0.26/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.52       => ( ( ord_less_eq_rat @ C @ D3 )
% 0.26/0.52         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.52           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.26/0.52             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_mono'
% 0.26/0.52  thf(fact_3587_mult__mono_H,axiom,
% 0.26/0.52      ! [A: nat,B: nat,C: nat,D3: nat] :
% 0.26/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.52       => ( ( ord_less_eq_nat @ C @ D3 )
% 0.26/0.52         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.52           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.26/0.52             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_mono'
% 0.26/0.52  thf(fact_3588_mult__mono_H,axiom,
% 0.26/0.52      ! [A: int,B: int,C: int,D3: int] :
% 0.26/0.52        ( ( ord_less_eq_int @ A @ B )
% 0.26/0.52       => ( ( ord_less_eq_int @ C @ D3 )
% 0.26/0.52         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.52           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.26/0.52             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_mono'
% 0.26/0.52  thf(fact_3589_zero__le__square,axiom,
% 0.26/0.52      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 0.26/0.52  
% 0.26/0.52  % zero_le_square
% 0.26/0.52  thf(fact_3590_zero__le__square,axiom,
% 0.26/0.52      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 0.26/0.52  
% 0.26/0.52  % zero_le_square
% 0.26/0.52  thf(fact_3591_zero__le__square,axiom,
% 0.26/0.52      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 0.26/0.52  
% 0.26/0.52  % zero_le_square
% 0.26/0.52  thf(fact_3592_split__mult__pos__le,axiom,
% 0.26/0.52      ! [A: real,B: real] :
% 0.26/0.52        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.52            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 0.26/0.52          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.26/0.52            & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 0.26/0.52       => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % split_mult_pos_le
% 0.26/0.52  thf(fact_3593_split__mult__pos__le,axiom,
% 0.26/0.52      ! [A: rat,B: rat] :
% 0.26/0.52        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.52            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.26/0.52          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.26/0.52            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 0.26/0.52       => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % split_mult_pos_le
% 0.26/0.52  thf(fact_3594_split__mult__pos__le,axiom,
% 0.26/0.52      ! [A: int,B: int] :
% 0.26/0.52        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.52            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 0.26/0.52          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.26/0.52            & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 0.26/0.52       => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % split_mult_pos_le
% 0.26/0.52  thf(fact_3595_mult__left__mono__neg,axiom,
% 0.26/0.52      ! [B: real,A: real,C: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ B @ A )
% 0.26/0.52       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.26/0.52         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_left_mono_neg
% 0.26/0.52  thf(fact_3596_mult__left__mono__neg,axiom,
% 0.26/0.52      ! [B: rat,A: rat,C: rat] :
% 0.26/0.52        ( ( ord_less_eq_rat @ B @ A )
% 0.26/0.52       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.26/0.52         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_left_mono_neg
% 0.26/0.52  thf(fact_3597_mult__left__mono__neg,axiom,
% 0.26/0.52      ! [B: int,A: int,C: int] :
% 0.26/0.52        ( ( ord_less_eq_int @ B @ A )
% 0.26/0.52       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.26/0.52         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_left_mono_neg
% 0.26/0.52  thf(fact_3598_mult__nonpos__nonpos,axiom,
% 0.26/0.52      ! [A: real,B: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.26/0.52       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.26/0.52         => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_nonpos_nonpos
% 0.26/0.52  thf(fact_3599_mult__nonpos__nonpos,axiom,
% 0.26/0.52      ! [A: rat,B: rat] :
% 0.26/0.52        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.26/0.52       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.26/0.52         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_nonpos_nonpos
% 0.26/0.52  thf(fact_3600_mult__nonpos__nonpos,axiom,
% 0.26/0.52      ! [A: int,B: int] :
% 0.26/0.52        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.26/0.52       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.26/0.52         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_nonpos_nonpos
% 0.26/0.52  thf(fact_3601_mult__left__mono,axiom,
% 0.26/0.52      ! [A: real,B: real,C: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.26/0.52         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_left_mono
% 0.26/0.52  thf(fact_3602_mult__left__mono,axiom,
% 0.26/0.52      ! [A: rat,B: rat,C: rat] :
% 0.26/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.26/0.52         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_left_mono
% 0.26/0.52  thf(fact_3603_mult__left__mono,axiom,
% 0.26/0.52      ! [A: nat,B: nat,C: nat] :
% 0.26/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.52       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.26/0.52         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_left_mono
% 0.26/0.52  thf(fact_3604_mult__left__mono,axiom,
% 0.26/0.52      ! [A: int,B: int,C: int] :
% 0.26/0.52        ( ( ord_less_eq_int @ A @ B )
% 0.26/0.52       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.26/0.52         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_left_mono
% 0.26/0.52  thf(fact_3605_mult__right__mono__neg,axiom,
% 0.26/0.52      ! [B: real,A: real,C: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ B @ A )
% 0.26/0.52       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.26/0.52         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_right_mono_neg
% 0.26/0.52  thf(fact_3606_mult__right__mono__neg,axiom,
% 0.26/0.52      ! [B: rat,A: rat,C: rat] :
% 0.26/0.52        ( ( ord_less_eq_rat @ B @ A )
% 0.26/0.52       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.26/0.52         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_right_mono_neg
% 0.26/0.52  thf(fact_3607_mult__right__mono__neg,axiom,
% 0.26/0.52      ! [B: int,A: int,C: int] :
% 0.26/0.52        ( ( ord_less_eq_int @ B @ A )
% 0.26/0.52       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.26/0.52         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_right_mono_neg
% 0.26/0.52  thf(fact_3608_mult__right__mono,axiom,
% 0.26/0.52      ! [A: real,B: real,C: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.26/0.52         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_right_mono
% 0.26/0.52  thf(fact_3609_mult__right__mono,axiom,
% 0.26/0.52      ! [A: rat,B: rat,C: rat] :
% 0.26/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.26/0.52         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_right_mono
% 0.26/0.52  thf(fact_3610_mult__right__mono,axiom,
% 0.26/0.52      ! [A: nat,B: nat,C: nat] :
% 0.26/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.52       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.26/0.52         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_right_mono
% 0.26/0.52  thf(fact_3611_mult__right__mono,axiom,
% 0.26/0.52      ! [A: int,B: int,C: int] :
% 0.26/0.52        ( ( ord_less_eq_int @ A @ B )
% 0.26/0.52       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.26/0.52         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_right_mono
% 0.26/0.52  thf(fact_3612_mult__le__0__iff,axiom,
% 0.26/0.52      ! [A: real,B: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 0.26/0.52        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.52            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.26/0.52          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.26/0.52            & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_le_0_iff
% 0.26/0.52  thf(fact_3613_mult__le__0__iff,axiom,
% 0.26/0.52      ! [A: rat,B: rat] :
% 0.26/0.52        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 0.26/0.52        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.52            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.26/0.52          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.26/0.52            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_le_0_iff
% 0.26/0.52  thf(fact_3614_mult__le__0__iff,axiom,
% 0.26/0.52      ! [A: int,B: int] :
% 0.26/0.52        ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 0.26/0.52        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.52            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 0.26/0.52          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.26/0.52            & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_le_0_iff
% 0.26/0.52  thf(fact_3615_split__mult__neg__le,axiom,
% 0.26/0.52      ! [A: real,B: real] :
% 0.26/0.52        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.52            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.26/0.52          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.26/0.52            & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 0.26/0.52       => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 0.26/0.52  
% 0.26/0.52  % split_mult_neg_le
% 0.26/0.52  thf(fact_3616_split__mult__neg__le,axiom,
% 0.26/0.52      ! [A: rat,B: rat] :
% 0.26/0.52        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.52            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.26/0.52          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.26/0.52            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 0.26/0.52       => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 0.26/0.52  
% 0.26/0.52  % split_mult_neg_le
% 0.26/0.52  thf(fact_3617_split__mult__neg__le,axiom,
% 0.26/0.52      ! [A: nat,B: nat] :
% 0.26/0.52        ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.52            & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 0.26/0.52          | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.26/0.52            & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 0.26/0.52       => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 0.26/0.52  
% 0.26/0.52  % split_mult_neg_le
% 0.26/0.52  thf(fact_3618_split__mult__neg__le,axiom,
% 0.26/0.52      ! [A: int,B: int] :
% 0.26/0.52        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.52            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 0.26/0.52          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.26/0.52            & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 0.26/0.52       => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 0.26/0.52  
% 0.26/0.52  % split_mult_neg_le
% 0.26/0.52  thf(fact_3619_mult__nonneg__nonneg,axiom,
% 0.26/0.52      ! [A: real,B: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.26/0.52         => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_nonneg_nonneg
% 0.26/0.52  thf(fact_3620_mult__nonneg__nonneg,axiom,
% 0.26/0.52      ! [A: rat,B: rat] :
% 0.26/0.52        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.26/0.52         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_nonneg_nonneg
% 0.26/0.52  thf(fact_3621_mult__nonneg__nonneg,axiom,
% 0.26/0.52      ! [A: nat,B: nat] :
% 0.26/0.52        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.52       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.26/0.52         => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_nonneg_nonneg
% 0.26/0.52  thf(fact_3622_mult__nonneg__nonneg,axiom,
% 0.26/0.52      ! [A: int,B: int] :
% 0.26/0.52        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.52       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.26/0.52         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_nonneg_nonneg
% 0.26/0.52  thf(fact_3623_mult__nonneg__nonpos,axiom,
% 0.26/0.52      ! [A: real,B: real] :
% 0.26/0.52        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.52       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.26/0.52         => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.26/0.52  
% 0.26/0.52  % mult_nonneg_nonpos
% 0.26/0.53  thf(fact_3624_mult__nonneg__nonpos,axiom,
% 0.26/0.53      ! [A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.53       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.26/0.53         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_nonneg_nonpos
% 0.26/0.53  thf(fact_3625_mult__nonneg__nonpos,axiom,
% 0.26/0.53      ! [A: nat,B: nat] :
% 0.26/0.53        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.53       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.26/0.53         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_nonneg_nonpos
% 0.26/0.53  thf(fact_3626_mult__nonneg__nonpos,axiom,
% 0.26/0.53      ! [A: int,B: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.53       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.26/0.53         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_nonneg_nonpos
% 0.26/0.53  thf(fact_3627_mult__nonpos__nonneg,axiom,
% 0.26/0.53      ! [A: real,B: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.26/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.26/0.53         => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_nonpos_nonneg
% 0.26/0.53  thf(fact_3628_mult__nonpos__nonneg,axiom,
% 0.26/0.53      ! [A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.26/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.26/0.53         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_nonpos_nonneg
% 0.26/0.53  thf(fact_3629_mult__nonpos__nonneg,axiom,
% 0.26/0.53      ! [A: nat,B: nat] :
% 0.26/0.53        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.26/0.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.26/0.53         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_nonpos_nonneg
% 0.26/0.53  thf(fact_3630_mult__nonpos__nonneg,axiom,
% 0.26/0.53      ! [A: int,B: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.26/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.26/0.53         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_nonpos_nonneg
% 0.26/0.53  thf(fact_3631_mult__nonneg__nonpos2,axiom,
% 0.26/0.53      ! [A: real,B: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.53       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.26/0.53         => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_nonneg_nonpos2
% 0.26/0.53  thf(fact_3632_mult__nonneg__nonpos2,axiom,
% 0.26/0.53      ! [A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.53       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.26/0.53         => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_nonneg_nonpos2
% 0.26/0.53  thf(fact_3633_mult__nonneg__nonpos2,axiom,
% 0.26/0.53      ! [A: nat,B: nat] :
% 0.26/0.53        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.53       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.26/0.53         => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_nonneg_nonpos2
% 0.26/0.53  thf(fact_3634_mult__nonneg__nonpos2,axiom,
% 0.26/0.53      ! [A: int,B: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.53       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.26/0.53         => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_nonneg_nonpos2
% 0.26/0.53  thf(fact_3635_zero__le__mult__iff,axiom,
% 0.26/0.53      ! [A: real,B: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.26/0.53        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.53            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 0.26/0.53          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.26/0.53            & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % zero_le_mult_iff
% 0.26/0.53  thf(fact_3636_zero__le__mult__iff,axiom,
% 0.26/0.53      ! [A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.26/0.53        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.53            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.26/0.53          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.26/0.53            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % zero_le_mult_iff
% 0.26/0.53  thf(fact_3637_zero__le__mult__iff,axiom,
% 0.26/0.53      ! [A: int,B: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.26/0.53        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.53            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 0.26/0.53          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.26/0.53            & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % zero_le_mult_iff
% 0.26/0.53  thf(fact_3638_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.26/0.53      ! [A: real,B: real,C: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.26/0.53         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.26/0.53  thf(fact_3639_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.26/0.53      ! [A: rat,B: rat,C: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.26/0.53         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.26/0.53  thf(fact_3640_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.26/0.53      ! [A: nat,B: nat,C: nat] :
% 0.26/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.26/0.53         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.26/0.53  thf(fact_3641_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.26/0.53      ! [A: int,B: int,C: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ A @ B )
% 0.26/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.26/0.53         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.26/0.53  thf(fact_3642_mult__neg__neg,axiom,
% 0.26/0.53      ! [A: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ A @ zero_zero_real )
% 0.26/0.53       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.26/0.53         => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_neg_neg
% 0.26/0.53  thf(fact_3643_mult__neg__neg,axiom,
% 0.26/0.53      ! [A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.26/0.53       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.26/0.53         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_neg_neg
% 0.26/0.53  thf(fact_3644_mult__neg__neg,axiom,
% 0.26/0.53      ! [A: int,B: int] :
% 0.26/0.53        ( ( ord_less_int @ A @ zero_zero_int )
% 0.26/0.53       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.26/0.53         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_neg_neg
% 0.26/0.53  thf(fact_3645_not__square__less__zero,axiom,
% 0.26/0.53      ! [A: real] :
% 0.26/0.53        ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 0.26/0.53  
% 0.26/0.53  % not_square_less_zero
% 0.26/0.53  thf(fact_3646_not__square__less__zero,axiom,
% 0.26/0.53      ! [A: rat] :
% 0.26/0.53        ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 0.26/0.53  
% 0.26/0.53  % not_square_less_zero
% 0.26/0.53  thf(fact_3647_not__square__less__zero,axiom,
% 0.26/0.53      ! [A: int] :
% 0.26/0.53        ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 0.26/0.53  
% 0.26/0.53  % not_square_less_zero
% 0.26/0.53  thf(fact_3648_mult__less__0__iff,axiom,
% 0.26/0.53      ! [A: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 0.26/0.53        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.53            & ( ord_less_real @ B @ zero_zero_real ) )
% 0.26/0.53          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.26/0.53            & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_0_iff
% 0.26/0.53  thf(fact_3649_mult__less__0__iff,axiom,
% 0.26/0.53      ! [A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 0.26/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.53            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 0.26/0.53          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.26/0.53            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_0_iff
% 0.26/0.53  thf(fact_3650_mult__less__0__iff,axiom,
% 0.26/0.53      ! [A: int,B: int] :
% 0.26/0.53        ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 0.26/0.53        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 0.26/0.53            & ( ord_less_int @ B @ zero_zero_int ) )
% 0.26/0.53          | ( ( ord_less_int @ A @ zero_zero_int )
% 0.26/0.53            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_0_iff
% 0.26/0.53  thf(fact_3651_mult__neg__pos,axiom,
% 0.26/0.53      ! [A: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ A @ zero_zero_real )
% 0.26/0.53       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.26/0.53         => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_neg_pos
% 0.26/0.53  thf(fact_3652_mult__neg__pos,axiom,
% 0.26/0.53      ! [A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.26/0.53       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.26/0.53         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_neg_pos
% 0.26/0.53  thf(fact_3653_mult__neg__pos,axiom,
% 0.26/0.53      ! [A: nat,B: nat] :
% 0.26/0.53        ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.26/0.53       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.26/0.53         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_neg_pos
% 0.26/0.53  thf(fact_3654_mult__neg__pos,axiom,
% 0.26/0.53      ! [A: int,B: int] :
% 0.26/0.53        ( ( ord_less_int @ A @ zero_zero_int )
% 0.26/0.53       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.53         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_neg_pos
% 0.26/0.53  thf(fact_3655_mult__pos__neg,axiom,
% 0.26/0.53      ! [A: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.53       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.26/0.53         => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_pos_neg
% 0.26/0.53  thf(fact_3656_mult__pos__neg,axiom,
% 0.26/0.53      ! [A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.53       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.26/0.53         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_pos_neg
% 0.26/0.53  thf(fact_3657_mult__pos__neg,axiom,
% 0.26/0.53      ! [A: nat,B: nat] :
% 0.26/0.53        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.26/0.53       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.26/0.53         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_pos_neg
% 0.26/0.53  thf(fact_3658_mult__pos__neg,axiom,
% 0.26/0.53      ! [A: int,B: int] :
% 0.26/0.53        ( ( ord_less_int @ zero_zero_int @ A )
% 0.26/0.53       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.26/0.53         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_pos_neg
% 0.26/0.53  thf(fact_3659_mult__pos__pos,axiom,
% 0.26/0.53      ! [A: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.53       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.26/0.53         => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_pos_pos
% 0.26/0.53  thf(fact_3660_mult__pos__pos,axiom,
% 0.26/0.53      ! [A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.53       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.26/0.53         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_pos_pos
% 0.26/0.53  thf(fact_3661_mult__pos__pos,axiom,
% 0.26/0.53      ! [A: nat,B: nat] :
% 0.26/0.53        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.26/0.53       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.26/0.53         => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_pos_pos
% 0.26/0.53  thf(fact_3662_mult__pos__pos,axiom,
% 0.26/0.53      ! [A: int,B: int] :
% 0.26/0.53        ( ( ord_less_int @ zero_zero_int @ A )
% 0.26/0.53       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.53         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_pos_pos
% 0.26/0.53  thf(fact_3663_mult__pos__neg2,axiom,
% 0.26/0.53      ! [A: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.53       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.26/0.53         => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_pos_neg2
% 0.26/0.53  thf(fact_3664_mult__pos__neg2,axiom,
% 0.26/0.53      ! [A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.53       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.26/0.53         => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_pos_neg2
% 0.26/0.53  thf(fact_3665_mult__pos__neg2,axiom,
% 0.26/0.53      ! [A: nat,B: nat] :
% 0.26/0.53        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.26/0.53       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.26/0.53         => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_pos_neg2
% 0.26/0.53  thf(fact_3666_mult__pos__neg2,axiom,
% 0.26/0.53      ! [A: int,B: int] :
% 0.26/0.53        ( ( ord_less_int @ zero_zero_int @ A )
% 0.26/0.53       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.26/0.53         => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_pos_neg2
% 0.26/0.53  thf(fact_3667_zero__less__mult__iff,axiom,
% 0.26/0.53      ! [A: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.26/0.53        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.53            & ( ord_less_real @ zero_zero_real @ B ) )
% 0.26/0.53          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.26/0.53            & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % zero_less_mult_iff
% 0.26/0.53  thf(fact_3668_zero__less__mult__iff,axiom,
% 0.26/0.53      ! [A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.26/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.53            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 0.26/0.53          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.26/0.53            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % zero_less_mult_iff
% 0.26/0.53  thf(fact_3669_zero__less__mult__iff,axiom,
% 0.26/0.53      ! [A: int,B: int] :
% 0.26/0.53        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.26/0.53        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 0.26/0.53            & ( ord_less_int @ zero_zero_int @ B ) )
% 0.26/0.53          | ( ( ord_less_int @ A @ zero_zero_int )
% 0.26/0.53            & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % zero_less_mult_iff
% 0.26/0.53  thf(fact_3670_zero__less__mult__pos,axiom,
% 0.26/0.53      ! [A: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.26/0.53       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.53         => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % zero_less_mult_pos
% 0.26/0.53  thf(fact_3671_zero__less__mult__pos,axiom,
% 0.26/0.53      ! [A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.26/0.53       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.53         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % zero_less_mult_pos
% 0.26/0.53  thf(fact_3672_zero__less__mult__pos,axiom,
% 0.26/0.53      ! [A: nat,B: nat] :
% 0.26/0.53        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 0.26/0.53       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.26/0.53         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % zero_less_mult_pos
% 0.26/0.53  thf(fact_3673_zero__less__mult__pos,axiom,
% 0.26/0.53      ! [A: int,B: int] :
% 0.26/0.53        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.26/0.53       => ( ( ord_less_int @ zero_zero_int @ A )
% 0.26/0.53         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % zero_less_mult_pos
% 0.26/0.53  thf(fact_3674_zero__less__mult__pos2,axiom,
% 0.26/0.53      ! [B: real,A: real] :
% 0.26/0.53        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 0.26/0.53       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.53         => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % zero_less_mult_pos2
% 0.26/0.53  thf(fact_3675_zero__less__mult__pos2,axiom,
% 0.26/0.53      ! [B: rat,A: rat] :
% 0.26/0.53        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 0.26/0.53       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.53         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % zero_less_mult_pos2
% 0.26/0.53  thf(fact_3676_zero__less__mult__pos2,axiom,
% 0.26/0.53      ! [B: nat,A: nat] :
% 0.26/0.53        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 0.26/0.53       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.26/0.53         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % zero_less_mult_pos2
% 0.26/0.53  thf(fact_3677_zero__less__mult__pos2,axiom,
% 0.26/0.53      ! [B: int,A: int] :
% 0.26/0.53        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 0.26/0.53       => ( ( ord_less_int @ zero_zero_int @ A )
% 0.26/0.53         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % zero_less_mult_pos2
% 0.26/0.53  thf(fact_3678_mult__less__cancel__left__neg,axiom,
% 0.26/0.53      ! [C: real,A: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53       => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.26/0.53          = ( ord_less_real @ B @ A ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_left_neg
% 0.26/0.53  thf(fact_3679_mult__less__cancel__left__neg,axiom,
% 0.26/0.53      ! [C: rat,A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.26/0.53          = ( ord_less_rat @ B @ A ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_left_neg
% 0.26/0.53  thf(fact_3680_mult__less__cancel__left__neg,axiom,
% 0.26/0.53      ! [C: int,A: int,B: int] :
% 0.26/0.53        ( ( ord_less_int @ C @ zero_zero_int )
% 0.26/0.53       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.26/0.53          = ( ord_less_int @ B @ A ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_left_neg
% 0.26/0.53  thf(fact_3681_mult__less__cancel__left__pos,axiom,
% 0.26/0.53      ! [C: real,A: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53       => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.26/0.53          = ( ord_less_real @ A @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_left_pos
% 0.26/0.53  thf(fact_3682_mult__less__cancel__left__pos,axiom,
% 0.26/0.53      ! [C: rat,A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.26/0.53          = ( ord_less_rat @ A @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_left_pos
% 0.26/0.53  thf(fact_3683_mult__less__cancel__left__pos,axiom,
% 0.26/0.53      ! [C: int,A: int,B: int] :
% 0.26/0.53        ( ( ord_less_int @ zero_zero_int @ C )
% 0.26/0.53       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.26/0.53          = ( ord_less_int @ A @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_left_pos
% 0.26/0.53  thf(fact_3684_mult__strict__left__mono__neg,axiom,
% 0.26/0.53      ! [B: real,A: real,C: real] :
% 0.26/0.53        ( ( ord_less_real @ B @ A )
% 0.26/0.53       => ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_strict_left_mono_neg
% 0.26/0.53  thf(fact_3685_mult__strict__left__mono__neg,axiom,
% 0.26/0.53      ! [B: rat,A: rat,C: rat] :
% 0.26/0.53        ( ( ord_less_rat @ B @ A )
% 0.26/0.53       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_strict_left_mono_neg
% 0.26/0.53  thf(fact_3686_mult__strict__left__mono__neg,axiom,
% 0.26/0.53      ! [B: int,A: int,C: int] :
% 0.26/0.53        ( ( ord_less_int @ B @ A )
% 0.26/0.53       => ( ( ord_less_int @ C @ zero_zero_int )
% 0.26/0.53         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_strict_left_mono_neg
% 0.26/0.53  thf(fact_3687_mult__strict__left__mono,axiom,
% 0.26/0.53      ! [A: real,B: real,C: real] :
% 0.26/0.53        ( ( ord_less_real @ A @ B )
% 0.26/0.53       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_strict_left_mono
% 0.26/0.53  thf(fact_3688_mult__strict__left__mono,axiom,
% 0.26/0.53      ! [A: rat,B: rat,C: rat] :
% 0.26/0.53        ( ( ord_less_rat @ A @ B )
% 0.26/0.53       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_strict_left_mono
% 0.26/0.53  thf(fact_3689_mult__strict__left__mono,axiom,
% 0.26/0.53      ! [A: nat,B: nat,C: nat] :
% 0.26/0.53        ( ( ord_less_nat @ A @ B )
% 0.26/0.53       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.26/0.53         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_strict_left_mono
% 0.26/0.53  thf(fact_3690_mult__strict__left__mono,axiom,
% 0.26/0.53      ! [A: int,B: int,C: int] :
% 0.26/0.53        ( ( ord_less_int @ A @ B )
% 0.26/0.53       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.26/0.53         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_strict_left_mono
% 0.26/0.53  thf(fact_3691_mult__less__cancel__left__disj,axiom,
% 0.26/0.53      ! [C: real,A: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.26/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53            & ( ord_less_real @ A @ B ) )
% 0.26/0.53          | ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53            & ( ord_less_real @ B @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_left_disj
% 0.26/0.53  thf(fact_3692_mult__less__cancel__left__disj,axiom,
% 0.26/0.53      ! [C: rat,A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.26/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53            & ( ord_less_rat @ A @ B ) )
% 0.26/0.53          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_left_disj
% 0.26/0.53  thf(fact_3693_mult__less__cancel__left__disj,axiom,
% 0.26/0.53      ! [C: int,A: int,B: int] :
% 0.26/0.53        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.26/0.53        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.26/0.53            & ( ord_less_int @ A @ B ) )
% 0.26/0.53          | ( ( ord_less_int @ C @ zero_zero_int )
% 0.26/0.53            & ( ord_less_int @ B @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_left_disj
% 0.26/0.53  thf(fact_3694_mult__strict__right__mono__neg,axiom,
% 0.26/0.53      ! [B: real,A: real,C: real] :
% 0.26/0.53        ( ( ord_less_real @ B @ A )
% 0.26/0.53       => ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53         => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_strict_right_mono_neg
% 0.26/0.53  thf(fact_3695_mult__strict__right__mono__neg,axiom,
% 0.26/0.53      ! [B: rat,A: rat,C: rat] :
% 0.26/0.53        ( ( ord_less_rat @ B @ A )
% 0.26/0.53       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_strict_right_mono_neg
% 0.26/0.53  thf(fact_3696_mult__strict__right__mono__neg,axiom,
% 0.26/0.53      ! [B: int,A: int,C: int] :
% 0.26/0.53        ( ( ord_less_int @ B @ A )
% 0.26/0.53       => ( ( ord_less_int @ C @ zero_zero_int )
% 0.26/0.53         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_strict_right_mono_neg
% 0.26/0.53  thf(fact_3697_mult__strict__right__mono,axiom,
% 0.26/0.53      ! [A: real,B: real,C: real] :
% 0.26/0.53        ( ( ord_less_real @ A @ B )
% 0.26/0.53       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53         => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_strict_right_mono
% 0.26/0.53  thf(fact_3698_mult__strict__right__mono,axiom,
% 0.26/0.53      ! [A: rat,B: rat,C: rat] :
% 0.26/0.53        ( ( ord_less_rat @ A @ B )
% 0.26/0.53       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_strict_right_mono
% 0.26/0.53  thf(fact_3699_mult__strict__right__mono,axiom,
% 0.26/0.53      ! [A: nat,B: nat,C: nat] :
% 0.26/0.53        ( ( ord_less_nat @ A @ B )
% 0.26/0.53       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.26/0.53         => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_strict_right_mono
% 0.26/0.53  thf(fact_3700_mult__strict__right__mono,axiom,
% 0.26/0.53      ! [A: int,B: int,C: int] :
% 0.26/0.53        ( ( ord_less_int @ A @ B )
% 0.26/0.53       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.26/0.53         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_strict_right_mono
% 0.26/0.53  thf(fact_3701_mult__less__cancel__right__disj,axiom,
% 0.26/0.53      ! [A: real,C: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.26/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53            & ( ord_less_real @ A @ B ) )
% 0.26/0.53          | ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53            & ( ord_less_real @ B @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_right_disj
% 0.26/0.53  thf(fact_3702_mult__less__cancel__right__disj,axiom,
% 0.26/0.53      ! [A: rat,C: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.26/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53            & ( ord_less_rat @ A @ B ) )
% 0.26/0.53          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_right_disj
% 0.26/0.53  thf(fact_3703_mult__less__cancel__right__disj,axiom,
% 0.26/0.53      ! [A: int,C: int,B: int] :
% 0.26/0.53        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.26/0.53        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.26/0.53            & ( ord_less_int @ A @ B ) )
% 0.26/0.53          | ( ( ord_less_int @ C @ zero_zero_int )
% 0.26/0.53            & ( ord_less_int @ B @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_right_disj
% 0.26/0.53  thf(fact_3704_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.26/0.53      ! [A: real,B: real,C: real] :
% 0.26/0.53        ( ( ord_less_real @ A @ B )
% 0.26/0.53       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.26/0.53  thf(fact_3705_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.26/0.53      ! [A: rat,B: rat,C: rat] :
% 0.26/0.53        ( ( ord_less_rat @ A @ B )
% 0.26/0.53       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.26/0.53  thf(fact_3706_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.26/0.53      ! [A: nat,B: nat,C: nat] :
% 0.26/0.53        ( ( ord_less_nat @ A @ B )
% 0.26/0.53       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.26/0.53         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.26/0.53  thf(fact_3707_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.26/0.53      ! [A: int,B: int,C: int] :
% 0.26/0.53        ( ( ord_less_int @ A @ B )
% 0.26/0.53       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.26/0.53         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.26/0.53  thf(fact_3708_less__1__mult,axiom,
% 0.26/0.53      ! [M: real,N: real] :
% 0.26/0.53        ( ( ord_less_real @ one_one_real @ M )
% 0.26/0.53       => ( ( ord_less_real @ one_one_real @ N )
% 0.26/0.53         => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % less_1_mult
% 0.26/0.53  thf(fact_3709_less__1__mult,axiom,
% 0.26/0.53      ! [M: rat,N: rat] :
% 0.26/0.53        ( ( ord_less_rat @ one_one_rat @ M )
% 0.26/0.53       => ( ( ord_less_rat @ one_one_rat @ N )
% 0.26/0.53         => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % less_1_mult
% 0.26/0.53  thf(fact_3710_less__1__mult,axiom,
% 0.26/0.53      ! [M: nat,N: nat] :
% 0.26/0.53        ( ( ord_less_nat @ one_one_nat @ M )
% 0.26/0.53       => ( ( ord_less_nat @ one_one_nat @ N )
% 0.26/0.53         => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % less_1_mult
% 0.26/0.53  thf(fact_3711_less__1__mult,axiom,
% 0.26/0.53      ! [M: int,N: int] :
% 0.26/0.53        ( ( ord_less_int @ one_one_int @ M )
% 0.26/0.53       => ( ( ord_less_int @ one_one_int @ N )
% 0.26/0.53         => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % less_1_mult
% 0.26/0.53  thf(fact_3712_nonzero__eq__divide__eq,axiom,
% 0.26/0.53      ! [C: complex,A: complex,B: complex] :
% 0.26/0.53        ( ( C != zero_zero_complex )
% 0.26/0.53       => ( ( A
% 0.26/0.53            = ( divide1717551699836669952omplex @ B @ C ) )
% 0.26/0.53          = ( ( times_times_complex @ A @ C )
% 0.26/0.53            = B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % nonzero_eq_divide_eq
% 0.26/0.53  thf(fact_3713_nonzero__eq__divide__eq,axiom,
% 0.26/0.53      ! [C: real,A: real,B: real] :
% 0.26/0.53        ( ( C != zero_zero_real )
% 0.26/0.53       => ( ( A
% 0.26/0.53            = ( divide_divide_real @ B @ C ) )
% 0.26/0.53          = ( ( times_times_real @ A @ C )
% 0.26/0.53            = B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % nonzero_eq_divide_eq
% 0.26/0.53  thf(fact_3714_nonzero__eq__divide__eq,axiom,
% 0.26/0.53      ! [C: rat,A: rat,B: rat] :
% 0.26/0.53        ( ( C != zero_zero_rat )
% 0.26/0.53       => ( ( A
% 0.26/0.53            = ( divide_divide_rat @ B @ C ) )
% 0.26/0.53          = ( ( times_times_rat @ A @ C )
% 0.26/0.53            = B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % nonzero_eq_divide_eq
% 0.26/0.53  thf(fact_3715_nonzero__divide__eq__eq,axiom,
% 0.26/0.53      ! [C: complex,B: complex,A: complex] :
% 0.26/0.53        ( ( C != zero_zero_complex )
% 0.26/0.53       => ( ( ( divide1717551699836669952omplex @ B @ C )
% 0.26/0.53            = A )
% 0.26/0.53          = ( B
% 0.26/0.53            = ( times_times_complex @ A @ C ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % nonzero_divide_eq_eq
% 0.26/0.53  thf(fact_3716_nonzero__divide__eq__eq,axiom,
% 0.26/0.53      ! [C: real,B: real,A: real] :
% 0.26/0.53        ( ( C != zero_zero_real )
% 0.26/0.53       => ( ( ( divide_divide_real @ B @ C )
% 0.26/0.53            = A )
% 0.26/0.53          = ( B
% 0.26/0.53            = ( times_times_real @ A @ C ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % nonzero_divide_eq_eq
% 0.26/0.53  thf(fact_3717_nonzero__divide__eq__eq,axiom,
% 0.26/0.53      ! [C: rat,B: rat,A: rat] :
% 0.26/0.53        ( ( C != zero_zero_rat )
% 0.26/0.53       => ( ( ( divide_divide_rat @ B @ C )
% 0.26/0.53            = A )
% 0.26/0.53          = ( B
% 0.26/0.53            = ( times_times_rat @ A @ C ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % nonzero_divide_eq_eq
% 0.26/0.53  thf(fact_3718_eq__divide__imp,axiom,
% 0.26/0.53      ! [C: complex,A: complex,B: complex] :
% 0.26/0.53        ( ( C != zero_zero_complex )
% 0.26/0.53       => ( ( ( times_times_complex @ A @ C )
% 0.26/0.53            = B )
% 0.26/0.53         => ( A
% 0.26/0.53            = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % eq_divide_imp
% 0.26/0.53  thf(fact_3719_eq__divide__imp,axiom,
% 0.26/0.53      ! [C: real,A: real,B: real] :
% 0.26/0.53        ( ( C != zero_zero_real )
% 0.26/0.53       => ( ( ( times_times_real @ A @ C )
% 0.26/0.53            = B )
% 0.26/0.53         => ( A
% 0.26/0.53            = ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % eq_divide_imp
% 0.26/0.53  thf(fact_3720_eq__divide__imp,axiom,
% 0.26/0.53      ! [C: rat,A: rat,B: rat] :
% 0.26/0.53        ( ( C != zero_zero_rat )
% 0.26/0.53       => ( ( ( times_times_rat @ A @ C )
% 0.26/0.53            = B )
% 0.26/0.53         => ( A
% 0.26/0.53            = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % eq_divide_imp
% 0.26/0.53  thf(fact_3721_divide__eq__imp,axiom,
% 0.26/0.53      ! [C: complex,B: complex,A: complex] :
% 0.26/0.53        ( ( C != zero_zero_complex )
% 0.26/0.53       => ( ( B
% 0.26/0.53            = ( times_times_complex @ A @ C ) )
% 0.26/0.53         => ( ( divide1717551699836669952omplex @ B @ C )
% 0.26/0.53            = A ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_eq_imp
% 0.26/0.53  thf(fact_3722_divide__eq__imp,axiom,
% 0.26/0.53      ! [C: real,B: real,A: real] :
% 0.26/0.53        ( ( C != zero_zero_real )
% 0.26/0.53       => ( ( B
% 0.26/0.53            = ( times_times_real @ A @ C ) )
% 0.26/0.53         => ( ( divide_divide_real @ B @ C )
% 0.26/0.53            = A ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_eq_imp
% 0.26/0.53  thf(fact_3723_divide__eq__imp,axiom,
% 0.26/0.53      ! [C: rat,B: rat,A: rat] :
% 0.26/0.53        ( ( C != zero_zero_rat )
% 0.26/0.53       => ( ( B
% 0.26/0.53            = ( times_times_rat @ A @ C ) )
% 0.26/0.53         => ( ( divide_divide_rat @ B @ C )
% 0.26/0.53            = A ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_eq_imp
% 0.26/0.53  thf(fact_3724_eq__divide__eq,axiom,
% 0.26/0.53      ! [A: complex,B: complex,C: complex] :
% 0.26/0.53        ( ( A
% 0.26/0.53          = ( divide1717551699836669952omplex @ B @ C ) )
% 0.26/0.53        = ( ( ( C != zero_zero_complex )
% 0.26/0.53           => ( ( times_times_complex @ A @ C )
% 0.26/0.53              = B ) )
% 0.26/0.53          & ( ( C = zero_zero_complex )
% 0.26/0.53           => ( A = zero_zero_complex ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % eq_divide_eq
% 0.26/0.53  thf(fact_3725_eq__divide__eq,axiom,
% 0.26/0.53      ! [A: real,B: real,C: real] :
% 0.26/0.53        ( ( A
% 0.26/0.53          = ( divide_divide_real @ B @ C ) )
% 0.26/0.53        = ( ( ( C != zero_zero_real )
% 0.26/0.53           => ( ( times_times_real @ A @ C )
% 0.26/0.53              = B ) )
% 0.26/0.53          & ( ( C = zero_zero_real )
% 0.26/0.53           => ( A = zero_zero_real ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % eq_divide_eq
% 0.26/0.53  thf(fact_3726_eq__divide__eq,axiom,
% 0.26/0.53      ! [A: rat,B: rat,C: rat] :
% 0.26/0.53        ( ( A
% 0.26/0.53          = ( divide_divide_rat @ B @ C ) )
% 0.26/0.53        = ( ( ( C != zero_zero_rat )
% 0.26/0.53           => ( ( times_times_rat @ A @ C )
% 0.26/0.53              = B ) )
% 0.26/0.53          & ( ( C = zero_zero_rat )
% 0.26/0.53           => ( A = zero_zero_rat ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % eq_divide_eq
% 0.26/0.53  thf(fact_3727_divide__eq__eq,axiom,
% 0.26/0.53      ! [B: complex,C: complex,A: complex] :
% 0.26/0.53        ( ( ( divide1717551699836669952omplex @ B @ C )
% 0.26/0.53          = A )
% 0.26/0.53        = ( ( ( C != zero_zero_complex )
% 0.26/0.53           => ( B
% 0.26/0.53              = ( times_times_complex @ A @ C ) ) )
% 0.26/0.53          & ( ( C = zero_zero_complex )
% 0.26/0.53           => ( A = zero_zero_complex ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_eq_eq
% 0.26/0.53  thf(fact_3728_divide__eq__eq,axiom,
% 0.26/0.53      ! [B: real,C: real,A: real] :
% 0.26/0.53        ( ( ( divide_divide_real @ B @ C )
% 0.26/0.53          = A )
% 0.26/0.53        = ( ( ( C != zero_zero_real )
% 0.26/0.53           => ( B
% 0.26/0.53              = ( times_times_real @ A @ C ) ) )
% 0.26/0.53          & ( ( C = zero_zero_real )
% 0.26/0.53           => ( A = zero_zero_real ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_eq_eq
% 0.26/0.53  thf(fact_3729_divide__eq__eq,axiom,
% 0.26/0.53      ! [B: rat,C: rat,A: rat] :
% 0.26/0.53        ( ( ( divide_divide_rat @ B @ C )
% 0.26/0.53          = A )
% 0.26/0.53        = ( ( ( C != zero_zero_rat )
% 0.26/0.53           => ( B
% 0.26/0.53              = ( times_times_rat @ A @ C ) ) )
% 0.26/0.53          & ( ( C = zero_zero_rat )
% 0.26/0.53           => ( A = zero_zero_rat ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_eq_eq
% 0.26/0.53  thf(fact_3730_frac__eq__eq,axiom,
% 0.26/0.53      ! [Y3: complex,Z: complex,X3: complex,W: complex] :
% 0.26/0.53        ( ( Y3 != zero_zero_complex )
% 0.26/0.53       => ( ( Z != zero_zero_complex )
% 0.26/0.53         => ( ( ( divide1717551699836669952omplex @ X3 @ Y3 )
% 0.26/0.53              = ( divide1717551699836669952omplex @ W @ Z ) )
% 0.26/0.53            = ( ( times_times_complex @ X3 @ Z )
% 0.26/0.53              = ( times_times_complex @ W @ Y3 ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % frac_eq_eq
% 0.26/0.53  thf(fact_3731_frac__eq__eq,axiom,
% 0.26/0.53      ! [Y3: real,Z: real,X3: real,W: real] :
% 0.26/0.53        ( ( Y3 != zero_zero_real )
% 0.26/0.53       => ( ( Z != zero_zero_real )
% 0.26/0.53         => ( ( ( divide_divide_real @ X3 @ Y3 )
% 0.26/0.53              = ( divide_divide_real @ W @ Z ) )
% 0.26/0.53            = ( ( times_times_real @ X3 @ Z )
% 0.26/0.53              = ( times_times_real @ W @ Y3 ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % frac_eq_eq
% 0.26/0.53  thf(fact_3732_frac__eq__eq,axiom,
% 0.26/0.53      ! [Y3: rat,Z: rat,X3: rat,W: rat] :
% 0.26/0.53        ( ( Y3 != zero_zero_rat )
% 0.26/0.53       => ( ( Z != zero_zero_rat )
% 0.26/0.53         => ( ( ( divide_divide_rat @ X3 @ Y3 )
% 0.26/0.53              = ( divide_divide_rat @ W @ Z ) )
% 0.26/0.53            = ( ( times_times_rat @ X3 @ Z )
% 0.26/0.53              = ( times_times_rat @ W @ Y3 ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % frac_eq_eq
% 0.26/0.53  thf(fact_3733_mult__numeral__1,axiom,
% 0.26/0.53      ! [A: complex] :
% 0.26/0.53        ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 0.26/0.53        = A ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_numeral_1
% 0.26/0.53  thf(fact_3734_mult__numeral__1,axiom,
% 0.26/0.53      ! [A: real] :
% 0.26/0.53        ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 0.26/0.53        = A ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_numeral_1
% 0.26/0.53  thf(fact_3735_mult__numeral__1,axiom,
% 0.26/0.53      ! [A: rat] :
% 0.26/0.53        ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 0.26/0.53        = A ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_numeral_1
% 0.26/0.53  thf(fact_3736_mult__numeral__1,axiom,
% 0.26/0.53      ! [A: nat] :
% 0.26/0.53        ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 0.26/0.53        = A ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_numeral_1
% 0.26/0.53  thf(fact_3737_mult__numeral__1,axiom,
% 0.26/0.53      ! [A: int] :
% 0.26/0.53        ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 0.26/0.53        = A ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_numeral_1
% 0.26/0.53  thf(fact_3738_mult__numeral__1__right,axiom,
% 0.26/0.53      ! [A: complex] :
% 0.26/0.53        ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 0.26/0.53        = A ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_numeral_1_right
% 0.26/0.53  thf(fact_3739_mult__numeral__1__right,axiom,
% 0.26/0.53      ! [A: real] :
% 0.26/0.53        ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 0.26/0.53        = A ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_numeral_1_right
% 0.26/0.53  thf(fact_3740_mult__numeral__1__right,axiom,
% 0.26/0.53      ! [A: rat] :
% 0.26/0.53        ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 0.26/0.53        = A ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_numeral_1_right
% 0.26/0.53  thf(fact_3741_mult__numeral__1__right,axiom,
% 0.26/0.53      ! [A: nat] :
% 0.26/0.53        ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 0.26/0.53        = A ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_numeral_1_right
% 0.26/0.53  thf(fact_3742_mult__numeral__1__right,axiom,
% 0.26/0.53      ! [A: int] :
% 0.26/0.53        ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 0.26/0.53        = A ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_numeral_1_right
% 0.26/0.53  thf(fact_3743_mult__diff__mult,axiom,
% 0.26/0.53      ! [X3: real,Y3: real,A: real,B: real] :
% 0.26/0.53        ( ( minus_minus_real @ ( times_times_real @ X3 @ Y3 ) @ ( times_times_real @ A @ B ) )
% 0.26/0.53        = ( plus_plus_real @ ( times_times_real @ X3 @ ( minus_minus_real @ Y3 @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X3 @ A ) @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_diff_mult
% 0.26/0.53  thf(fact_3744_mult__diff__mult,axiom,
% 0.26/0.53      ! [X3: rat,Y3: rat,A: rat,B: rat] :
% 0.26/0.53        ( ( minus_minus_rat @ ( times_times_rat @ X3 @ Y3 ) @ ( times_times_rat @ A @ B ) )
% 0.26/0.53        = ( plus_plus_rat @ ( times_times_rat @ X3 @ ( minus_minus_rat @ Y3 @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X3 @ A ) @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_diff_mult
% 0.26/0.53  thf(fact_3745_mult__diff__mult,axiom,
% 0.26/0.53      ! [X3: int,Y3: int,A: int,B: int] :
% 0.26/0.53        ( ( minus_minus_int @ ( times_times_int @ X3 @ Y3 ) @ ( times_times_int @ A @ B ) )
% 0.26/0.53        = ( plus_plus_int @ ( times_times_int @ X3 @ ( minus_minus_int @ Y3 @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X3 @ A ) @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_diff_mult
% 0.26/0.53  thf(fact_3746_left__right__inverse__power,axiom,
% 0.26/0.53      ! [X3: complex,Y3: complex,N: nat] :
% 0.26/0.53        ( ( ( times_times_complex @ X3 @ Y3 )
% 0.26/0.53          = one_one_complex )
% 0.26/0.53       => ( ( times_times_complex @ ( power_power_complex @ X3 @ N ) @ ( power_power_complex @ Y3 @ N ) )
% 0.26/0.53          = one_one_complex ) ) ).
% 0.26/0.53  
% 0.26/0.53  % left_right_inverse_power
% 0.26/0.53  thf(fact_3747_left__right__inverse__power,axiom,
% 0.26/0.53      ! [X3: real,Y3: real,N: nat] :
% 0.26/0.53        ( ( ( times_times_real @ X3 @ Y3 )
% 0.26/0.53          = one_one_real )
% 0.26/0.53       => ( ( times_times_real @ ( power_power_real @ X3 @ N ) @ ( power_power_real @ Y3 @ N ) )
% 0.26/0.53          = one_one_real ) ) ).
% 0.26/0.53  
% 0.26/0.53  % left_right_inverse_power
% 0.26/0.53  thf(fact_3748_left__right__inverse__power,axiom,
% 0.26/0.53      ! [X3: rat,Y3: rat,N: nat] :
% 0.26/0.53        ( ( ( times_times_rat @ X3 @ Y3 )
% 0.26/0.53          = one_one_rat )
% 0.26/0.53       => ( ( times_times_rat @ ( power_power_rat @ X3 @ N ) @ ( power_power_rat @ Y3 @ N ) )
% 0.26/0.53          = one_one_rat ) ) ).
% 0.26/0.53  
% 0.26/0.53  % left_right_inverse_power
% 0.26/0.53  thf(fact_3749_left__right__inverse__power,axiom,
% 0.26/0.53      ! [X3: nat,Y3: nat,N: nat] :
% 0.26/0.53        ( ( ( times_times_nat @ X3 @ Y3 )
% 0.26/0.53          = one_one_nat )
% 0.26/0.53       => ( ( times_times_nat @ ( power_power_nat @ X3 @ N ) @ ( power_power_nat @ Y3 @ N ) )
% 0.26/0.53          = one_one_nat ) ) ).
% 0.26/0.53  
% 0.26/0.53  % left_right_inverse_power
% 0.26/0.53  thf(fact_3750_left__right__inverse__power,axiom,
% 0.26/0.53      ! [X3: int,Y3: int,N: nat] :
% 0.26/0.53        ( ( ( times_times_int @ X3 @ Y3 )
% 0.26/0.53          = one_one_int )
% 0.26/0.53       => ( ( times_times_int @ ( power_power_int @ X3 @ N ) @ ( power_power_int @ Y3 @ N ) )
% 0.26/0.53          = one_one_int ) ) ).
% 0.26/0.53  
% 0.26/0.53  % left_right_inverse_power
% 0.26/0.53  thf(fact_3751_power__Suc,axiom,
% 0.26/0.53      ! [A: complex,N: nat] :
% 0.26/0.53        ( ( power_power_complex @ A @ ( suc @ N ) )
% 0.26/0.53        = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_Suc
% 0.26/0.53  thf(fact_3752_power__Suc,axiom,
% 0.26/0.53      ! [A: real,N: nat] :
% 0.26/0.53        ( ( power_power_real @ A @ ( suc @ N ) )
% 0.26/0.53        = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_Suc
% 0.26/0.53  thf(fact_3753_power__Suc,axiom,
% 0.26/0.53      ! [A: rat,N: nat] :
% 0.26/0.53        ( ( power_power_rat @ A @ ( suc @ N ) )
% 0.26/0.53        = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_Suc
% 0.26/0.53  thf(fact_3754_power__Suc,axiom,
% 0.26/0.53      ! [A: nat,N: nat] :
% 0.26/0.53        ( ( power_power_nat @ A @ ( suc @ N ) )
% 0.26/0.53        = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_Suc
% 0.26/0.53  thf(fact_3755_power__Suc,axiom,
% 0.26/0.53      ! [A: int,N: nat] :
% 0.26/0.53        ( ( power_power_int @ A @ ( suc @ N ) )
% 0.26/0.53        = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_Suc
% 0.26/0.53  thf(fact_3756_power__Suc2,axiom,
% 0.26/0.53      ! [A: complex,N: nat] :
% 0.26/0.53        ( ( power_power_complex @ A @ ( suc @ N ) )
% 0.26/0.53        = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_Suc2
% 0.26/0.53  thf(fact_3757_power__Suc2,axiom,
% 0.26/0.53      ! [A: real,N: nat] :
% 0.26/0.53        ( ( power_power_real @ A @ ( suc @ N ) )
% 0.26/0.53        = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_Suc2
% 0.26/0.53  thf(fact_3758_power__Suc2,axiom,
% 0.26/0.53      ! [A: rat,N: nat] :
% 0.26/0.53        ( ( power_power_rat @ A @ ( suc @ N ) )
% 0.26/0.53        = ( times_times_rat @ ( power_power_rat @ A @ N ) @ A ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_Suc2
% 0.26/0.53  thf(fact_3759_power__Suc2,axiom,
% 0.26/0.53      ! [A: nat,N: nat] :
% 0.26/0.53        ( ( power_power_nat @ A @ ( suc @ N ) )
% 0.26/0.53        = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_Suc2
% 0.26/0.53  thf(fact_3760_power__Suc2,axiom,
% 0.26/0.53      ! [A: int,N: nat] :
% 0.26/0.53        ( ( power_power_int @ A @ ( suc @ N ) )
% 0.26/0.53        = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_Suc2
% 0.26/0.53  thf(fact_3761_div__mult2__eq_H,axiom,
% 0.26/0.53      ! [A: nat,M: nat,N: nat] :
% 0.26/0.53        ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 0.26/0.53        = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % div_mult2_eq'
% 0.26/0.53  thf(fact_3762_div__mult2__eq_H,axiom,
% 0.26/0.53      ! [A: int,M: nat,N: nat] :
% 0.26/0.53        ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.26/0.53        = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % div_mult2_eq'
% 0.26/0.53  thf(fact_3763_Suc__mult__less__cancel1,axiom,
% 0.26/0.53      ! [K: nat,M: nat,N: nat] :
% 0.26/0.53        ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 0.26/0.53        = ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.53  
% 0.26/0.53  % Suc_mult_less_cancel1
% 0.26/0.53  thf(fact_3764_power__add,axiom,
% 0.26/0.53      ! [A: complex,M: nat,N: nat] :
% 0.26/0.53        ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N ) )
% 0.26/0.53        = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_add
% 0.26/0.53  thf(fact_3765_power__add,axiom,
% 0.26/0.53      ! [A: real,M: nat,N: nat] :
% 0.26/0.53        ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N ) )
% 0.26/0.53        = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_add
% 0.26/0.53  thf(fact_3766_power__add,axiom,
% 0.26/0.53      ! [A: rat,M: nat,N: nat] :
% 0.26/0.53        ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N ) )
% 0.26/0.53        = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_add
% 0.26/0.53  thf(fact_3767_power__add,axiom,
% 0.26/0.53      ! [A: nat,M: nat,N: nat] :
% 0.26/0.53        ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 0.26/0.53        = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_add
% 0.26/0.53  thf(fact_3768_power__add,axiom,
% 0.26/0.53      ! [A: int,M: nat,N: nat] :
% 0.26/0.53        ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 0.26/0.53        = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_add
% 0.26/0.53  thf(fact_3769_mult__less__mono1,axiom,
% 0.26/0.53      ! [I: nat,J: nat,K: nat] :
% 0.26/0.53        ( ( ord_less_nat @ I @ J )
% 0.26/0.53       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.26/0.53         => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_mono1
% 0.26/0.53  thf(fact_3770_mult__less__mono2,axiom,
% 0.26/0.53      ! [I: nat,J: nat,K: nat] :
% 0.26/0.53        ( ( ord_less_nat @ I @ J )
% 0.26/0.53       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.26/0.53         => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_mono2
% 0.26/0.53  thf(fact_3771_nat__mult__less__cancel1,axiom,
% 0.26/0.53      ! [K: nat,M: nat,N: nat] :
% 0.26/0.53        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.26/0.53       => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.26/0.53          = ( ord_less_nat @ M @ N ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % nat_mult_less_cancel1
% 0.26/0.53  thf(fact_3772_nat__mult__eq__cancel1,axiom,
% 0.26/0.53      ! [K: nat,M: nat,N: nat] :
% 0.26/0.53        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.26/0.53       => ( ( ( times_times_nat @ K @ M )
% 0.26/0.53            = ( times_times_nat @ K @ N ) )
% 0.26/0.53          = ( M = N ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % nat_mult_eq_cancel1
% 0.26/0.53  thf(fact_3773_mult__Suc,axiom,
% 0.26/0.53      ! [M: nat,N: nat] :
% 0.26/0.53        ( ( times_times_nat @ ( suc @ M ) @ N )
% 0.26/0.53        = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_Suc
% 0.26/0.53  thf(fact_3774_Suc__mult__le__cancel1,axiom,
% 0.26/0.53      ! [K: nat,M: nat,N: nat] :
% 0.26/0.53        ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 0.26/0.53        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.53  
% 0.26/0.53  % Suc_mult_le_cancel1
% 0.26/0.53  thf(fact_3775_mult__eq__self__implies__10,axiom,
% 0.26/0.53      ! [M: nat,N: nat] :
% 0.26/0.53        ( ( M
% 0.26/0.53          = ( times_times_nat @ M @ N ) )
% 0.26/0.53       => ( ( N = one_one_nat )
% 0.26/0.53          | ( M = zero_zero_nat ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_eq_self_implies_10
% 0.26/0.53  thf(fact_3776_less__mult__imp__div__less,axiom,
% 0.26/0.53      ! [M: nat,I: nat,N: nat] :
% 0.26/0.53        ( ( ord_less_nat @ M @ ( times_times_nat @ I @ N ) )
% 0.26/0.53       => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ I ) ) ).
% 0.26/0.53  
% 0.26/0.53  % less_mult_imp_div_less
% 0.26/0.53  thf(fact_3777_div__times__less__eq__dividend,axiom,
% 0.26/0.53      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 0.26/0.53  
% 0.26/0.53  % div_times_less_eq_dividend
% 0.26/0.53  thf(fact_3778_times__div__less__eq__dividend,axiom,
% 0.26/0.53      ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 0.26/0.53  
% 0.26/0.53  % times_div_less_eq_dividend
% 0.26/0.53  thf(fact_3779_power__odd__eq,axiom,
% 0.26/0.53      ! [A: complex,N: nat] :
% 0.26/0.53        ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.26/0.53        = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_odd_eq
% 0.26/0.53  thf(fact_3780_power__odd__eq,axiom,
% 0.26/0.53      ! [A: real,N: nat] :
% 0.26/0.53        ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.26/0.53        = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_odd_eq
% 0.26/0.53  thf(fact_3781_power__odd__eq,axiom,
% 0.26/0.53      ! [A: rat,N: nat] :
% 0.26/0.53        ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.26/0.53        = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_odd_eq
% 0.26/0.53  thf(fact_3782_power__odd__eq,axiom,
% 0.26/0.53      ! [A: nat,N: nat] :
% 0.26/0.53        ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.26/0.53        = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_odd_eq
% 0.26/0.53  thf(fact_3783_power__odd__eq,axiom,
% 0.26/0.53      ! [A: int,N: nat] :
% 0.26/0.53        ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.26/0.53        = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_odd_eq
% 0.26/0.53  thf(fact_3784_frac__ge__0,axiom,
% 0.26/0.53      ! [X3: real] : ( ord_less_eq_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X3 ) ) ).
% 0.26/0.53  
% 0.26/0.53  % frac_ge_0
% 0.26/0.53  thf(fact_3785_frac__ge__0,axiom,
% 0.26/0.53      ! [X3: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X3 ) ) ).
% 0.26/0.53  
% 0.26/0.53  % frac_ge_0
% 0.26/0.53  thf(fact_3786_frac__lt__1,axiom,
% 0.26/0.53      ! [X3: real] : ( ord_less_real @ ( archim2898591450579166408c_real @ X3 ) @ one_one_real ) ).
% 0.26/0.53  
% 0.26/0.53  % frac_lt_1
% 0.26/0.53  thf(fact_3787_frac__lt__1,axiom,
% 0.26/0.53      ! [X3: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X3 ) @ one_one_rat ) ).
% 0.26/0.53  
% 0.26/0.53  % frac_lt_1
% 0.26/0.53  thf(fact_3788_frac__1__eq,axiom,
% 0.26/0.53      ! [X3: real] :
% 0.26/0.53        ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X3 @ one_one_real ) )
% 0.26/0.53        = ( archim2898591450579166408c_real @ X3 ) ) ).
% 0.26/0.53  
% 0.26/0.53  % frac_1_eq
% 0.26/0.53  thf(fact_3789_frac__1__eq,axiom,
% 0.26/0.53      ! [X3: rat] :
% 0.26/0.53        ( ( archimedean_frac_rat @ ( plus_plus_rat @ X3 @ one_one_rat ) )
% 0.26/0.53        = ( archimedean_frac_rat @ X3 ) ) ).
% 0.26/0.53  
% 0.26/0.53  % frac_1_eq
% 0.26/0.53  thf(fact_3790_mult__less__le__imp__less,axiom,
% 0.26/0.53      ! [A: real,B: real,C: real,D3: real] :
% 0.26/0.53        ( ( ord_less_real @ A @ B )
% 0.26/0.53       => ( ( ord_less_eq_real @ C @ D3 )
% 0.26/0.53         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.53           => ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_le_imp_less
% 0.26/0.53  thf(fact_3791_mult__less__le__imp__less,axiom,
% 0.26/0.53      ! [A: rat,B: rat,C: rat,D3: rat] :
% 0.26/0.53        ( ( ord_less_rat @ A @ B )
% 0.26/0.53       => ( ( ord_less_eq_rat @ C @ D3 )
% 0.26/0.53         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.53           => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_le_imp_less
% 0.26/0.53  thf(fact_3792_mult__less__le__imp__less,axiom,
% 0.26/0.53      ! [A: nat,B: nat,C: nat,D3: nat] :
% 0.26/0.53        ( ( ord_less_nat @ A @ B )
% 0.26/0.53       => ( ( ord_less_eq_nat @ C @ D3 )
% 0.26/0.53         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.53           => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.26/0.53             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_le_imp_less
% 0.26/0.53  thf(fact_3793_mult__less__le__imp__less,axiom,
% 0.26/0.53      ! [A: int,B: int,C: int,D3: int] :
% 0.26/0.53        ( ( ord_less_int @ A @ B )
% 0.26/0.53       => ( ( ord_less_eq_int @ C @ D3 )
% 0.26/0.53         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.53           => ( ( ord_less_int @ zero_zero_int @ C )
% 0.26/0.53             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_le_imp_less
% 0.26/0.53  thf(fact_3794_mult__le__less__imp__less,axiom,
% 0.26/0.53      ! [A: real,B: real,C: real,D3: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.53       => ( ( ord_less_real @ C @ D3 )
% 0.26/0.53         => ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.53           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.26/0.53             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_less_imp_less
% 0.26/0.53  thf(fact_3795_mult__le__less__imp__less,axiom,
% 0.26/0.53      ! [A: rat,B: rat,C: rat,D3: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.53       => ( ( ord_less_rat @ C @ D3 )
% 0.26/0.53         => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.53           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.26/0.53             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_less_imp_less
% 0.26/0.53  thf(fact_3796_mult__le__less__imp__less,axiom,
% 0.26/0.53      ! [A: nat,B: nat,C: nat,D3: nat] :
% 0.26/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.53       => ( ( ord_less_nat @ C @ D3 )
% 0.26/0.53         => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.26/0.53           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.26/0.53             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_less_imp_less
% 0.26/0.53  thf(fact_3797_mult__le__less__imp__less,axiom,
% 0.26/0.53      ! [A: int,B: int,C: int,D3: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ A @ B )
% 0.26/0.53       => ( ( ord_less_int @ C @ D3 )
% 0.26/0.53         => ( ( ord_less_int @ zero_zero_int @ A )
% 0.26/0.53           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.26/0.53             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_less_imp_less
% 0.26/0.53  thf(fact_3798_mult__right__le__imp__le,axiom,
% 0.26/0.53      ! [A: real,C: real,B: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.26/0.53       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_right_le_imp_le
% 0.26/0.53  thf(fact_3799_mult__right__le__imp__le,axiom,
% 0.26/0.53      ! [A: rat,C: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.26/0.53       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_right_le_imp_le
% 0.26/0.53  thf(fact_3800_mult__right__le__imp__le,axiom,
% 0.26/0.53      ! [A: nat,C: nat,B: nat] :
% 0.26/0.53        ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.26/0.53       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.26/0.53         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_right_le_imp_le
% 0.26/0.53  thf(fact_3801_mult__right__le__imp__le,axiom,
% 0.26/0.53      ! [A: int,C: int,B: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.26/0.53       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.26/0.53         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_right_le_imp_le
% 0.26/0.53  thf(fact_3802_mult__left__le__imp__le,axiom,
% 0.26/0.53      ! [C: real,A: real,B: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.26/0.53       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_left_le_imp_le
% 0.26/0.53  thf(fact_3803_mult__left__le__imp__le,axiom,
% 0.26/0.53      ! [C: rat,A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.26/0.53       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_left_le_imp_le
% 0.26/0.53  thf(fact_3804_mult__left__le__imp__le,axiom,
% 0.26/0.53      ! [C: nat,A: nat,B: nat] :
% 0.26/0.53        ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.26/0.53       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.26/0.53         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_left_le_imp_le
% 0.26/0.53  thf(fact_3805_mult__left__le__imp__le,axiom,
% 0.26/0.53      ! [C: int,A: int,B: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.26/0.53       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.26/0.53         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_left_le_imp_le
% 0.26/0.53  thf(fact_3806_mult__le__cancel__left__pos,axiom,
% 0.26/0.53      ! [C: real,A: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53       => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.26/0.53          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_left_pos
% 0.26/0.53  thf(fact_3807_mult__le__cancel__left__pos,axiom,
% 0.26/0.53      ! [C: rat,A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.26/0.53          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_left_pos
% 0.26/0.53  thf(fact_3808_mult__le__cancel__left__pos,axiom,
% 0.26/0.53      ! [C: int,A: int,B: int] :
% 0.26/0.53        ( ( ord_less_int @ zero_zero_int @ C )
% 0.26/0.53       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.26/0.53          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_left_pos
% 0.26/0.53  thf(fact_3809_mult__le__cancel__left__neg,axiom,
% 0.26/0.53      ! [C: real,A: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53       => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.26/0.53          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_left_neg
% 0.26/0.53  thf(fact_3810_mult__le__cancel__left__neg,axiom,
% 0.26/0.53      ! [C: rat,A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.26/0.53          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_left_neg
% 0.26/0.53  thf(fact_3811_mult__le__cancel__left__neg,axiom,
% 0.26/0.53      ! [C: int,A: int,B: int] :
% 0.26/0.53        ( ( ord_less_int @ C @ zero_zero_int )
% 0.26/0.53       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.26/0.53          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_left_neg
% 0.26/0.53  thf(fact_3812_mult__less__cancel__right,axiom,
% 0.26/0.53      ! [A: real,C: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.26/0.53        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ord_less_real @ A @ B ) )
% 0.26/0.53          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.26/0.53           => ( ord_less_real @ B @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_right
% 0.26/0.53  thf(fact_3813_mult__less__cancel__right,axiom,
% 0.26/0.53      ! [A: rat,C: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.26/0.53        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ord_less_rat @ A @ B ) )
% 0.26/0.53          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.26/0.53           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_right
% 0.26/0.53  thf(fact_3814_mult__less__cancel__right,axiom,
% 0.26/0.53      ! [A: int,C: int,B: int] :
% 0.26/0.53        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.26/0.53        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.26/0.53           => ( ord_less_int @ A @ B ) )
% 0.26/0.53          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.26/0.53           => ( ord_less_int @ B @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_right
% 0.26/0.53  thf(fact_3815_mult__strict__mono_H,axiom,
% 0.26/0.53      ! [A: real,B: real,C: real,D3: real] :
% 0.26/0.53        ( ( ord_less_real @ A @ B )
% 0.26/0.53       => ( ( ord_less_real @ C @ D3 )
% 0.26/0.53         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.53           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.26/0.53             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_strict_mono'
% 0.26/0.53  thf(fact_3816_mult__strict__mono_H,axiom,
% 0.26/0.53      ! [A: rat,B: rat,C: rat,D3: rat] :
% 0.26/0.53        ( ( ord_less_rat @ A @ B )
% 0.26/0.53       => ( ( ord_less_rat @ C @ D3 )
% 0.26/0.53         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.53           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.26/0.53             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_strict_mono'
% 0.26/0.53  thf(fact_3817_mult__strict__mono_H,axiom,
% 0.26/0.53      ! [A: nat,B: nat,C: nat,D3: nat] :
% 0.26/0.53        ( ( ord_less_nat @ A @ B )
% 0.26/0.53       => ( ( ord_less_nat @ C @ D3 )
% 0.26/0.53         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.53           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.26/0.53             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_strict_mono'
% 0.26/0.53  thf(fact_3818_mult__strict__mono_H,axiom,
% 0.26/0.53      ! [A: int,B: int,C: int,D3: int] :
% 0.26/0.53        ( ( ord_less_int @ A @ B )
% 0.26/0.53       => ( ( ord_less_int @ C @ D3 )
% 0.26/0.53         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.53           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.26/0.53             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_strict_mono'
% 0.26/0.53  thf(fact_3819_mult__right__less__imp__less,axiom,
% 0.26/0.53      ! [A: real,C: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.26/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.26/0.53         => ( ord_less_real @ A @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_right_less_imp_less
% 0.26/0.53  thf(fact_3820_mult__right__less__imp__less,axiom,
% 0.26/0.53      ! [A: rat,C: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.26/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.26/0.53         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_right_less_imp_less
% 0.26/0.53  thf(fact_3821_mult__right__less__imp__less,axiom,
% 0.26/0.53      ! [A: nat,C: nat,B: nat] :
% 0.26/0.53        ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.26/0.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.26/0.53         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_right_less_imp_less
% 0.26/0.53  thf(fact_3822_mult__right__less__imp__less,axiom,
% 0.26/0.53      ! [A: int,C: int,B: int] :
% 0.26/0.53        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.26/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.26/0.53         => ( ord_less_int @ A @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_right_less_imp_less
% 0.26/0.53  thf(fact_3823_mult__less__cancel__left,axiom,
% 0.26/0.53      ! [C: real,A: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.26/0.53        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ord_less_real @ A @ B ) )
% 0.26/0.53          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.26/0.53           => ( ord_less_real @ B @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_left
% 0.26/0.53  thf(fact_3824_mult__less__cancel__left,axiom,
% 0.26/0.53      ! [C: rat,A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.26/0.53        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ord_less_rat @ A @ B ) )
% 0.26/0.53          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.26/0.53           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_left
% 0.26/0.53  thf(fact_3825_mult__less__cancel__left,axiom,
% 0.26/0.53      ! [C: int,A: int,B: int] :
% 0.26/0.53        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.26/0.53        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.26/0.53           => ( ord_less_int @ A @ B ) )
% 0.26/0.53          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.26/0.53           => ( ord_less_int @ B @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_left
% 0.26/0.53  thf(fact_3826_mult__strict__mono,axiom,
% 0.26/0.53      ! [A: real,B: real,C: real,D3: real] :
% 0.26/0.53        ( ( ord_less_real @ A @ B )
% 0.26/0.53       => ( ( ord_less_real @ C @ D3 )
% 0.26/0.53         => ( ( ord_less_real @ zero_zero_real @ B )
% 0.26/0.53           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.26/0.53             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_strict_mono
% 0.26/0.53  thf(fact_3827_mult__strict__mono,axiom,
% 0.26/0.53      ! [A: rat,B: rat,C: rat,D3: rat] :
% 0.26/0.53        ( ( ord_less_rat @ A @ B )
% 0.26/0.53       => ( ( ord_less_rat @ C @ D3 )
% 0.26/0.53         => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.26/0.53           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.26/0.53             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_strict_mono
% 0.26/0.53  thf(fact_3828_mult__strict__mono,axiom,
% 0.26/0.53      ! [A: nat,B: nat,C: nat,D3: nat] :
% 0.26/0.53        ( ( ord_less_nat @ A @ B )
% 0.26/0.53       => ( ( ord_less_nat @ C @ D3 )
% 0.26/0.53         => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.26/0.53           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.26/0.53             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_strict_mono
% 0.26/0.53  thf(fact_3829_mult__strict__mono,axiom,
% 0.26/0.53      ! [A: int,B: int,C: int,D3: int] :
% 0.26/0.53        ( ( ord_less_int @ A @ B )
% 0.26/0.53       => ( ( ord_less_int @ C @ D3 )
% 0.26/0.53         => ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.53           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.26/0.53             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_strict_mono
% 0.26/0.53  thf(fact_3830_mult__left__less__imp__less,axiom,
% 0.26/0.53      ! [C: real,A: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.26/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.26/0.53         => ( ord_less_real @ A @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_left_less_imp_less
% 0.26/0.53  thf(fact_3831_mult__left__less__imp__less,axiom,
% 0.26/0.53      ! [C: rat,A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.26/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.26/0.53         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_left_less_imp_less
% 0.26/0.53  thf(fact_3832_mult__left__less__imp__less,axiom,
% 0.26/0.53      ! [C: nat,A: nat,B: nat] :
% 0.26/0.53        ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.26/0.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.26/0.53         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_left_less_imp_less
% 0.26/0.53  thf(fact_3833_mult__left__less__imp__less,axiom,
% 0.26/0.53      ! [C: int,A: int,B: int] :
% 0.26/0.53        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.26/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.26/0.53         => ( ord_less_int @ A @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_left_less_imp_less
% 0.26/0.53  thf(fact_3834_mult__le__cancel__right,axiom,
% 0.26/0.53      ! [A: real,C: real,B: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.26/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ord_less_eq_real @ A @ B ) )
% 0.26/0.53          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_right
% 0.26/0.53  thf(fact_3835_mult__le__cancel__right,axiom,
% 0.26/0.53      ! [A: rat,C: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.26/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ord_less_eq_rat @ A @ B ) )
% 0.26/0.53          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_right
% 0.26/0.53  thf(fact_3836_mult__le__cancel__right,axiom,
% 0.26/0.53      ! [A: int,C: int,B: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.26/0.53        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.26/0.53           => ( ord_less_eq_int @ A @ B ) )
% 0.26/0.53          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.26/0.53           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_right
% 0.26/0.53  thf(fact_3837_mult__le__cancel__left,axiom,
% 0.26/0.53      ! [C: real,A: real,B: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.26/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ord_less_eq_real @ A @ B ) )
% 0.26/0.53          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_left
% 0.26/0.53  thf(fact_3838_mult__le__cancel__left,axiom,
% 0.26/0.53      ! [C: rat,A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.26/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ord_less_eq_rat @ A @ B ) )
% 0.26/0.53          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_left
% 0.26/0.53  thf(fact_3839_mult__le__cancel__left,axiom,
% 0.26/0.53      ! [C: int,A: int,B: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.26/0.53        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.26/0.53           => ( ord_less_eq_int @ A @ B ) )
% 0.26/0.53          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.26/0.53           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_left
% 0.26/0.53  thf(fact_3840_mult__left__le__one__le,axiom,
% 0.26/0.53      ! [X3: real,Y3: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.53         => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 0.26/0.53           => ( ord_less_eq_real @ ( times_times_real @ Y3 @ X3 ) @ X3 ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_left_le_one_le
% 0.26/0.53  thf(fact_3841_mult__left__le__one__le,axiom,
% 0.26/0.53      ! [X3: rat,Y3: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.26/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 0.26/0.53         => ( ( ord_less_eq_rat @ Y3 @ one_one_rat )
% 0.26/0.53           => ( ord_less_eq_rat @ ( times_times_rat @ Y3 @ X3 ) @ X3 ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_left_le_one_le
% 0.26/0.53  thf(fact_3842_mult__left__le__one__le,axiom,
% 0.26/0.53      ! [X3: int,Y3: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.26/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 0.26/0.53         => ( ( ord_less_eq_int @ Y3 @ one_one_int )
% 0.26/0.53           => ( ord_less_eq_int @ ( times_times_int @ Y3 @ X3 ) @ X3 ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_left_le_one_le
% 0.26/0.53  thf(fact_3843_mult__right__le__one__le,axiom,
% 0.26/0.53      ! [X3: real,Y3: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.53         => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 0.26/0.53           => ( ord_less_eq_real @ ( times_times_real @ X3 @ Y3 ) @ X3 ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_right_le_one_le
% 0.26/0.53  thf(fact_3844_mult__right__le__one__le,axiom,
% 0.26/0.53      ! [X3: rat,Y3: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.26/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 0.26/0.53         => ( ( ord_less_eq_rat @ Y3 @ one_one_rat )
% 0.26/0.53           => ( ord_less_eq_rat @ ( times_times_rat @ X3 @ Y3 ) @ X3 ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_right_le_one_le
% 0.26/0.53  thf(fact_3845_mult__right__le__one__le,axiom,
% 0.26/0.53      ! [X3: int,Y3: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.26/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 0.26/0.53         => ( ( ord_less_eq_int @ Y3 @ one_one_int )
% 0.26/0.53           => ( ord_less_eq_int @ ( times_times_int @ X3 @ Y3 ) @ X3 ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_right_le_one_le
% 0.26/0.53  thf(fact_3846_mult__le__one,axiom,
% 0.26/0.53      ! [A: real,B: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ A @ one_one_real )
% 0.26/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.26/0.53         => ( ( ord_less_eq_real @ B @ one_one_real )
% 0.26/0.53           => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_one
% 0.26/0.53  thf(fact_3847_mult__le__one,axiom,
% 0.26/0.53      ! [A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.26/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.26/0.53         => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 0.26/0.53           => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_one
% 0.26/0.53  thf(fact_3848_mult__le__one,axiom,
% 0.26/0.53      ! [A: nat,B: nat] :
% 0.26/0.53        ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.26/0.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.26/0.53         => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 0.26/0.53           => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_one
% 0.26/0.53  thf(fact_3849_mult__le__one,axiom,
% 0.26/0.53      ! [A: int,B: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ A @ one_one_int )
% 0.26/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.26/0.53         => ( ( ord_less_eq_int @ B @ one_one_int )
% 0.26/0.53           => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_one
% 0.26/0.53  thf(fact_3850_mult__left__le,axiom,
% 0.26/0.53      ! [C: real,A: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ C @ one_one_real )
% 0.26/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.53         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_left_le
% 0.26/0.53  thf(fact_3851_mult__left__le,axiom,
% 0.26/0.53      ! [C: rat,A: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ C @ one_one_rat )
% 0.26/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.53         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_left_le
% 0.26/0.53  thf(fact_3852_mult__left__le,axiom,
% 0.26/0.53      ! [C: nat,A: nat] :
% 0.26/0.53        ( ( ord_less_eq_nat @ C @ one_one_nat )
% 0.26/0.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.53         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_left_le
% 0.26/0.53  thf(fact_3853_mult__left__le,axiom,
% 0.26/0.53      ! [C: int,A: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ C @ one_one_int )
% 0.26/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.53         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_left_le
% 0.26/0.53  thf(fact_3854_sum__squares__le__zero__iff,axiom,
% 0.26/0.53      ! [X3: real,Y3: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y3 @ Y3 ) ) @ zero_zero_real )
% 0.26/0.53        = ( ( X3 = zero_zero_real )
% 0.26/0.53          & ( Y3 = zero_zero_real ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % sum_squares_le_zero_iff
% 0.26/0.53  thf(fact_3855_sum__squares__le__zero__iff,axiom,
% 0.26/0.53      ! [X3: rat,Y3: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y3 @ Y3 ) ) @ zero_zero_rat )
% 0.26/0.53        = ( ( X3 = zero_zero_rat )
% 0.26/0.53          & ( Y3 = zero_zero_rat ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % sum_squares_le_zero_iff
% 0.26/0.53  thf(fact_3856_sum__squares__le__zero__iff,axiom,
% 0.26/0.53      ! [X3: int,Y3: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y3 @ Y3 ) ) @ zero_zero_int )
% 0.26/0.53        = ( ( X3 = zero_zero_int )
% 0.26/0.53          & ( Y3 = zero_zero_int ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % sum_squares_le_zero_iff
% 0.26/0.53  thf(fact_3857_sum__squares__ge__zero,axiom,
% 0.26/0.53      ! [X3: real,Y3: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y3 @ Y3 ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % sum_squares_ge_zero
% 0.26/0.53  thf(fact_3858_sum__squares__ge__zero,axiom,
% 0.26/0.53      ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y3 @ Y3 ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % sum_squares_ge_zero
% 0.26/0.53  thf(fact_3859_sum__squares__ge__zero,axiom,
% 0.26/0.53      ! [X3: int,Y3: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y3 @ Y3 ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % sum_squares_ge_zero
% 0.26/0.53  thf(fact_3860_sum__squares__gt__zero__iff,axiom,
% 0.26/0.53      ! [X3: real,Y3: real] :
% 0.26/0.53        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y3 @ Y3 ) ) )
% 0.26/0.53        = ( ( X3 != zero_zero_real )
% 0.26/0.53          | ( Y3 != zero_zero_real ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % sum_squares_gt_zero_iff
% 0.26/0.53  thf(fact_3861_sum__squares__gt__zero__iff,axiom,
% 0.26/0.53      ! [X3: rat,Y3: rat] :
% 0.26/0.53        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y3 @ Y3 ) ) )
% 0.26/0.53        = ( ( X3 != zero_zero_rat )
% 0.26/0.53          | ( Y3 != zero_zero_rat ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % sum_squares_gt_zero_iff
% 0.26/0.53  thf(fact_3862_sum__squares__gt__zero__iff,axiom,
% 0.26/0.53      ! [X3: int,Y3: int] :
% 0.26/0.53        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y3 @ Y3 ) ) )
% 0.26/0.53        = ( ( X3 != zero_zero_int )
% 0.26/0.53          | ( Y3 != zero_zero_int ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % sum_squares_gt_zero_iff
% 0.26/0.53  thf(fact_3863_not__sum__squares__lt__zero,axiom,
% 0.26/0.53      ! [X3: real,Y3: real] :
% 0.26/0.53        ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y3 @ Y3 ) ) @ zero_zero_real ) ).
% 0.26/0.53  
% 0.26/0.53  % not_sum_squares_lt_zero
% 0.26/0.53  thf(fact_3864_not__sum__squares__lt__zero,axiom,
% 0.26/0.53      ! [X3: rat,Y3: rat] :
% 0.26/0.53        ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y3 @ Y3 ) ) @ zero_zero_rat ) ).
% 0.26/0.53  
% 0.26/0.53  % not_sum_squares_lt_zero
% 0.26/0.53  thf(fact_3865_not__sum__squares__lt__zero,axiom,
% 0.26/0.53      ! [X3: int,Y3: int] :
% 0.26/0.53        ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y3 @ Y3 ) ) @ zero_zero_int ) ).
% 0.26/0.53  
% 0.26/0.53  % not_sum_squares_lt_zero
% 0.26/0.53  thf(fact_3866_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 0.26/0.53      ! [C: nat,A: nat,B: nat] :
% 0.26/0.53        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.26/0.53       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.26/0.53          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 0.26/0.53  thf(fact_3867_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 0.26/0.53      ! [C: int,A: int,B: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.26/0.53       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.26/0.53          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 0.26/0.53  thf(fact_3868_divide__less__eq,axiom,
% 0.26/0.53      ! [B: real,C: real,A: real] :
% 0.26/0.53        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.26/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 0.26/0.53          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53               => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 0.26/0.53              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53               => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_less_eq
% 0.26/0.53  thf(fact_3869_divide__less__eq,axiom,
% 0.26/0.53      ! [B: rat,C: rat,A: rat] :
% 0.26/0.53        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.26/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.26/0.53          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.26/0.53              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_less_eq
% 0.26/0.53  thf(fact_3870_less__divide__eq,axiom,
% 0.26/0.53      ! [A: real,B: real,C: real] :
% 0.26/0.53        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.26/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 0.26/0.53          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53               => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 0.26/0.53              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53               => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % less_divide_eq
% 0.26/0.53  thf(fact_3871_less__divide__eq,axiom,
% 0.26/0.53      ! [A: rat,B: rat,C: rat] :
% 0.26/0.53        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.26/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.26/0.53          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53               => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.26/0.53              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % less_divide_eq
% 0.26/0.53  thf(fact_3872_neg__divide__less__eq,axiom,
% 0.26/0.53      ! [C: real,B: real,A: real] :
% 0.26/0.53        ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53       => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.26/0.53          = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % neg_divide_less_eq
% 0.26/0.53  thf(fact_3873_neg__divide__less__eq,axiom,
% 0.26/0.53      ! [C: rat,B: rat,A: rat] :
% 0.26/0.53        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.26/0.53          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % neg_divide_less_eq
% 0.26/0.53  thf(fact_3874_neg__less__divide__eq,axiom,
% 0.26/0.53      ! [C: real,A: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53       => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.26/0.53          = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % neg_less_divide_eq
% 0.26/0.53  thf(fact_3875_neg__less__divide__eq,axiom,
% 0.26/0.53      ! [C: rat,A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.26/0.53          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % neg_less_divide_eq
% 0.26/0.53  thf(fact_3876_pos__divide__less__eq,axiom,
% 0.26/0.53      ! [C: real,B: real,A: real] :
% 0.26/0.53        ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53       => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.26/0.53          = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % pos_divide_less_eq
% 0.26/0.53  thf(fact_3877_pos__divide__less__eq,axiom,
% 0.26/0.53      ! [C: rat,B: rat,A: rat] :
% 0.26/0.53        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.26/0.53          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % pos_divide_less_eq
% 0.26/0.53  thf(fact_3878_pos__less__divide__eq,axiom,
% 0.26/0.53      ! [C: real,A: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53       => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.26/0.53          = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % pos_less_divide_eq
% 0.26/0.53  thf(fact_3879_pos__less__divide__eq,axiom,
% 0.26/0.53      ! [C: rat,A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.26/0.53          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % pos_less_divide_eq
% 0.26/0.53  thf(fact_3880_mult__imp__div__pos__less,axiom,
% 0.26/0.53      ! [Y3: real,X3: real,Z: real] :
% 0.26/0.53        ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.53       => ( ( ord_less_real @ X3 @ ( times_times_real @ Z @ Y3 ) )
% 0.26/0.53         => ( ord_less_real @ ( divide_divide_real @ X3 @ Y3 ) @ Z ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_imp_div_pos_less
% 0.26/0.53  thf(fact_3881_mult__imp__div__pos__less,axiom,
% 0.26/0.53      ! [Y3: rat,X3: rat,Z: rat] :
% 0.26/0.53        ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 0.26/0.53       => ( ( ord_less_rat @ X3 @ ( times_times_rat @ Z @ Y3 ) )
% 0.26/0.53         => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ Z ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_imp_div_pos_less
% 0.26/0.53  thf(fact_3882_mult__imp__less__div__pos,axiom,
% 0.26/0.53      ! [Y3: real,Z: real,X3: real] :
% 0.26/0.53        ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.53       => ( ( ord_less_real @ ( times_times_real @ Z @ Y3 ) @ X3 )
% 0.26/0.53         => ( ord_less_real @ Z @ ( divide_divide_real @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_imp_less_div_pos
% 0.26/0.53  thf(fact_3883_mult__imp__less__div__pos,axiom,
% 0.26/0.53      ! [Y3: rat,Z: rat,X3: rat] :
% 0.26/0.53        ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 0.26/0.53       => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y3 ) @ X3 )
% 0.26/0.53         => ( ord_less_rat @ Z @ ( divide_divide_rat @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_imp_less_div_pos
% 0.26/0.53  thf(fact_3884_divide__strict__left__mono,axiom,
% 0.26/0.53      ! [B: real,A: real,C: real] :
% 0.26/0.53        ( ( ord_less_real @ B @ A )
% 0.26/0.53       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.26/0.53           => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_strict_left_mono
% 0.26/0.53  thf(fact_3885_divide__strict__left__mono,axiom,
% 0.26/0.53      ! [B: rat,A: rat,C: rat] :
% 0.26/0.53        ( ( ord_less_rat @ B @ A )
% 0.26/0.53       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.26/0.53           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_strict_left_mono
% 0.26/0.53  thf(fact_3886_divide__strict__left__mono__neg,axiom,
% 0.26/0.53      ! [A: real,B: real,C: real] :
% 0.26/0.53        ( ( ord_less_real @ A @ B )
% 0.26/0.53       => ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.26/0.53           => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_strict_left_mono_neg
% 0.26/0.53  thf(fact_3887_divide__strict__left__mono__neg,axiom,
% 0.26/0.53      ! [A: rat,B: rat,C: rat] :
% 0.26/0.53        ( ( ord_less_rat @ A @ B )
% 0.26/0.53       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.26/0.53           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_strict_left_mono_neg
% 0.26/0.53  thf(fact_3888_divide__eq__eq__numeral_I1_J,axiom,
% 0.26/0.53      ! [B: complex,C: complex,W: num] :
% 0.26/0.53        ( ( ( divide1717551699836669952omplex @ B @ C )
% 0.26/0.53          = ( numera6690914467698888265omplex @ W ) )
% 0.26/0.53        = ( ( ( C != zero_zero_complex )
% 0.26/0.53           => ( B
% 0.26/0.53              = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 0.26/0.53          & ( ( C = zero_zero_complex )
% 0.26/0.53           => ( ( numera6690914467698888265omplex @ W )
% 0.26/0.53              = zero_zero_complex ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_eq_eq_numeral(1)
% 0.26/0.53  thf(fact_3889_divide__eq__eq__numeral_I1_J,axiom,
% 0.26/0.53      ! [B: real,C: real,W: num] :
% 0.26/0.53        ( ( ( divide_divide_real @ B @ C )
% 0.26/0.53          = ( numeral_numeral_real @ W ) )
% 0.26/0.53        = ( ( ( C != zero_zero_real )
% 0.26/0.53           => ( B
% 0.26/0.53              = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 0.26/0.53          & ( ( C = zero_zero_real )
% 0.26/0.53           => ( ( numeral_numeral_real @ W )
% 0.26/0.53              = zero_zero_real ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_eq_eq_numeral(1)
% 0.26/0.53  thf(fact_3890_divide__eq__eq__numeral_I1_J,axiom,
% 0.26/0.53      ! [B: rat,C: rat,W: num] :
% 0.26/0.53        ( ( ( divide_divide_rat @ B @ C )
% 0.26/0.53          = ( numeral_numeral_rat @ W ) )
% 0.26/0.53        = ( ( ( C != zero_zero_rat )
% 0.26/0.53           => ( B
% 0.26/0.53              = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.26/0.53          & ( ( C = zero_zero_rat )
% 0.26/0.53           => ( ( numeral_numeral_rat @ W )
% 0.26/0.53              = zero_zero_rat ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_eq_eq_numeral(1)
% 0.26/0.53  thf(fact_3891_eq__divide__eq__numeral_I1_J,axiom,
% 0.26/0.53      ! [W: num,B: complex,C: complex] :
% 0.26/0.53        ( ( ( numera6690914467698888265omplex @ W )
% 0.26/0.53          = ( divide1717551699836669952omplex @ B @ C ) )
% 0.26/0.53        = ( ( ( C != zero_zero_complex )
% 0.26/0.53           => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 0.26/0.53              = B ) )
% 0.26/0.53          & ( ( C = zero_zero_complex )
% 0.26/0.53           => ( ( numera6690914467698888265omplex @ W )
% 0.26/0.53              = zero_zero_complex ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % eq_divide_eq_numeral(1)
% 0.26/0.53  thf(fact_3892_eq__divide__eq__numeral_I1_J,axiom,
% 0.26/0.53      ! [W: num,B: real,C: real] :
% 0.26/0.53        ( ( ( numeral_numeral_real @ W )
% 0.26/0.53          = ( divide_divide_real @ B @ C ) )
% 0.26/0.53        = ( ( ( C != zero_zero_real )
% 0.26/0.53           => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 0.26/0.53              = B ) )
% 0.26/0.53          & ( ( C = zero_zero_real )
% 0.26/0.53           => ( ( numeral_numeral_real @ W )
% 0.26/0.53              = zero_zero_real ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % eq_divide_eq_numeral(1)
% 0.26/0.53  thf(fact_3893_eq__divide__eq__numeral_I1_J,axiom,
% 0.26/0.53      ! [W: num,B: rat,C: rat] :
% 0.26/0.53        ( ( ( numeral_numeral_rat @ W )
% 0.26/0.53          = ( divide_divide_rat @ B @ C ) )
% 0.26/0.53        = ( ( ( C != zero_zero_rat )
% 0.26/0.53           => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 0.26/0.53              = B ) )
% 0.26/0.53          & ( ( C = zero_zero_rat )
% 0.26/0.53           => ( ( numeral_numeral_rat @ W )
% 0.26/0.53              = zero_zero_rat ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % eq_divide_eq_numeral(1)
% 0.26/0.53  thf(fact_3894_ordered__ring__class_Ole__add__iff2,axiom,
% 0.26/0.53      ! [A: real,E2: real,C: real,B: real,D3: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D3 ) )
% 0.26/0.53        = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D3 ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % ordered_ring_class.le_add_iff2
% 0.26/0.53  thf(fact_3895_ordered__ring__class_Ole__add__iff2,axiom,
% 0.26/0.53      ! [A: rat,E2: rat,C: rat,B: rat,D3: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D3 ) )
% 0.26/0.53        = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D3 ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % ordered_ring_class.le_add_iff2
% 0.26/0.53  thf(fact_3896_ordered__ring__class_Ole__add__iff2,axiom,
% 0.26/0.53      ! [A: int,E2: int,C: int,B: int,D3: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D3 ) )
% 0.26/0.53        = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D3 ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % ordered_ring_class.le_add_iff2
% 0.26/0.53  thf(fact_3897_ordered__ring__class_Ole__add__iff1,axiom,
% 0.26/0.53      ! [A: real,E2: real,C: real,B: real,D3: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D3 ) )
% 0.26/0.53        = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D3 ) ) ).
% 0.26/0.53  
% 0.26/0.53  % ordered_ring_class.le_add_iff1
% 0.26/0.53  thf(fact_3898_ordered__ring__class_Ole__add__iff1,axiom,
% 0.26/0.53      ! [A: rat,E2: rat,C: rat,B: rat,D3: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D3 ) )
% 0.26/0.53        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D3 ) ) ).
% 0.26/0.53  
% 0.26/0.53  % ordered_ring_class.le_add_iff1
% 0.26/0.53  thf(fact_3899_ordered__ring__class_Ole__add__iff1,axiom,
% 0.26/0.53      ! [A: int,E2: int,C: int,B: int,D3: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D3 ) )
% 0.26/0.53        = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D3 ) ) ).
% 0.26/0.53  
% 0.26/0.53  % ordered_ring_class.le_add_iff1
% 0.26/0.53  thf(fact_3900_divide__add__eq__iff,axiom,
% 0.26/0.53      ! [Z: complex,X3: complex,Y3: complex] :
% 0.26/0.53        ( ( Z != zero_zero_complex )
% 0.26/0.53       => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X3 @ Z ) @ Y3 )
% 0.26/0.53          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X3 @ ( times_times_complex @ Y3 @ Z ) ) @ Z ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_add_eq_iff
% 0.26/0.53  thf(fact_3901_divide__add__eq__iff,axiom,
% 0.26/0.53      ! [Z: real,X3: real,Y3: real] :
% 0.26/0.53        ( ( Z != zero_zero_real )
% 0.26/0.53       => ( ( plus_plus_real @ ( divide_divide_real @ X3 @ Z ) @ Y3 )
% 0.26/0.53          = ( divide_divide_real @ ( plus_plus_real @ X3 @ ( times_times_real @ Y3 @ Z ) ) @ Z ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_add_eq_iff
% 0.26/0.53  thf(fact_3902_divide__add__eq__iff,axiom,
% 0.26/0.53      ! [Z: rat,X3: rat,Y3: rat] :
% 0.26/0.53        ( ( Z != zero_zero_rat )
% 0.26/0.53       => ( ( plus_plus_rat @ ( divide_divide_rat @ X3 @ Z ) @ Y3 )
% 0.26/0.53          = ( divide_divide_rat @ ( plus_plus_rat @ X3 @ ( times_times_rat @ Y3 @ Z ) ) @ Z ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_add_eq_iff
% 0.26/0.53  thf(fact_3903_add__divide__eq__iff,axiom,
% 0.26/0.53      ! [Z: complex,X3: complex,Y3: complex] :
% 0.26/0.53        ( ( Z != zero_zero_complex )
% 0.26/0.53       => ( ( plus_plus_complex @ X3 @ ( divide1717551699836669952omplex @ Y3 @ Z ) )
% 0.26/0.53          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X3 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % add_divide_eq_iff
% 0.26/0.53  thf(fact_3904_add__divide__eq__iff,axiom,
% 0.26/0.53      ! [Z: real,X3: real,Y3: real] :
% 0.26/0.53        ( ( Z != zero_zero_real )
% 0.26/0.53       => ( ( plus_plus_real @ X3 @ ( divide_divide_real @ Y3 @ Z ) )
% 0.26/0.53          = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X3 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % add_divide_eq_iff
% 0.26/0.53  thf(fact_3905_add__divide__eq__iff,axiom,
% 0.26/0.53      ! [Z: rat,X3: rat,Y3: rat] :
% 0.26/0.53        ( ( Z != zero_zero_rat )
% 0.26/0.53       => ( ( plus_plus_rat @ X3 @ ( divide_divide_rat @ Y3 @ Z ) )
% 0.26/0.53          = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % add_divide_eq_iff
% 0.26/0.53  thf(fact_3906_add__num__frac,axiom,
% 0.26/0.53      ! [Y3: complex,Z: complex,X3: complex] :
% 0.26/0.53        ( ( Y3 != zero_zero_complex )
% 0.26/0.53       => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X3 @ Y3 ) )
% 0.26/0.53          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X3 @ ( times_times_complex @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % add_num_frac
% 0.26/0.53  thf(fact_3907_add__num__frac,axiom,
% 0.26/0.53      ! [Y3: real,Z: real,X3: real] :
% 0.26/0.53        ( ( Y3 != zero_zero_real )
% 0.26/0.53       => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X3 @ Y3 ) )
% 0.26/0.53          = ( divide_divide_real @ ( plus_plus_real @ X3 @ ( times_times_real @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % add_num_frac
% 0.26/0.53  thf(fact_3908_add__num__frac,axiom,
% 0.26/0.53      ! [Y3: rat,Z: rat,X3: rat] :
% 0.26/0.53        ( ( Y3 != zero_zero_rat )
% 0.26/0.53       => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X3 @ Y3 ) )
% 0.26/0.53          = ( divide_divide_rat @ ( plus_plus_rat @ X3 @ ( times_times_rat @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % add_num_frac
% 0.26/0.53  thf(fact_3909_add__frac__num,axiom,
% 0.26/0.53      ! [Y3: complex,X3: complex,Z: complex] :
% 0.26/0.53        ( ( Y3 != zero_zero_complex )
% 0.26/0.53       => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X3 @ Y3 ) @ Z )
% 0.26/0.53          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X3 @ ( times_times_complex @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % add_frac_num
% 0.26/0.53  thf(fact_3910_add__frac__num,axiom,
% 0.26/0.53      ! [Y3: real,X3: real,Z: real] :
% 0.26/0.53        ( ( Y3 != zero_zero_real )
% 0.26/0.53       => ( ( plus_plus_real @ ( divide_divide_real @ X3 @ Y3 ) @ Z )
% 0.26/0.53          = ( divide_divide_real @ ( plus_plus_real @ X3 @ ( times_times_real @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % add_frac_num
% 0.26/0.53  thf(fact_3911_add__frac__num,axiom,
% 0.26/0.53      ! [Y3: rat,X3: rat,Z: rat] :
% 0.26/0.53        ( ( Y3 != zero_zero_rat )
% 0.26/0.53       => ( ( plus_plus_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ Z )
% 0.26/0.53          = ( divide_divide_rat @ ( plus_plus_rat @ X3 @ ( times_times_rat @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % add_frac_num
% 0.26/0.53  thf(fact_3912_add__frac__eq,axiom,
% 0.26/0.53      ! [Y3: complex,Z: complex,X3: complex,W: complex] :
% 0.26/0.53        ( ( Y3 != zero_zero_complex )
% 0.26/0.53       => ( ( Z != zero_zero_complex )
% 0.26/0.53         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X3 @ Y3 ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 0.26/0.53            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X3 @ Z ) @ ( times_times_complex @ W @ Y3 ) ) @ ( times_times_complex @ Y3 @ Z ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % add_frac_eq
% 0.26/0.53  thf(fact_3913_add__frac__eq,axiom,
% 0.26/0.53      ! [Y3: real,Z: real,X3: real,W: real] :
% 0.26/0.53        ( ( Y3 != zero_zero_real )
% 0.26/0.53       => ( ( Z != zero_zero_real )
% 0.26/0.53         => ( ( plus_plus_real @ ( divide_divide_real @ X3 @ Y3 ) @ ( divide_divide_real @ W @ Z ) )
% 0.26/0.53            = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X3 @ Z ) @ ( times_times_real @ W @ Y3 ) ) @ ( times_times_real @ Y3 @ Z ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % add_frac_eq
% 0.26/0.53  thf(fact_3914_add__frac__eq,axiom,
% 0.26/0.53      ! [Y3: rat,Z: rat,X3: rat,W: rat] :
% 0.26/0.53        ( ( Y3 != zero_zero_rat )
% 0.26/0.53       => ( ( Z != zero_zero_rat )
% 0.26/0.53         => ( ( plus_plus_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ ( divide_divide_rat @ W @ Z ) )
% 0.26/0.53            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ Z ) @ ( times_times_rat @ W @ Y3 ) ) @ ( times_times_rat @ Y3 @ Z ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % add_frac_eq
% 0.26/0.53  thf(fact_3915_add__divide__eq__if__simps_I1_J,axiom,
% 0.26/0.53      ! [Z: complex,A: complex,B: complex] :
% 0.26/0.53        ( ( ( Z = zero_zero_complex )
% 0.26/0.53         => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 0.26/0.53            = A ) )
% 0.26/0.53        & ( ( Z != zero_zero_complex )
% 0.26/0.53         => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 0.26/0.53            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % add_divide_eq_if_simps(1)
% 0.26/0.53  thf(fact_3916_add__divide__eq__if__simps_I1_J,axiom,
% 0.26/0.53      ! [Z: real,A: real,B: real] :
% 0.26/0.53        ( ( ( Z = zero_zero_real )
% 0.26/0.53         => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 0.26/0.53            = A ) )
% 0.26/0.53        & ( ( Z != zero_zero_real )
% 0.26/0.53         => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 0.26/0.53            = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % add_divide_eq_if_simps(1)
% 0.26/0.53  thf(fact_3917_add__divide__eq__if__simps_I1_J,axiom,
% 0.26/0.53      ! [Z: rat,A: rat,B: rat] :
% 0.26/0.53        ( ( ( Z = zero_zero_rat )
% 0.26/0.53         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 0.26/0.53            = A ) )
% 0.26/0.53        & ( ( Z != zero_zero_rat )
% 0.26/0.53         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 0.26/0.53            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % add_divide_eq_if_simps(1)
% 0.26/0.53  thf(fact_3918_add__divide__eq__if__simps_I2_J,axiom,
% 0.26/0.53      ! [Z: complex,A: complex,B: complex] :
% 0.26/0.53        ( ( ( Z = zero_zero_complex )
% 0.26/0.53         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 0.26/0.53            = B ) )
% 0.26/0.53        & ( ( Z != zero_zero_complex )
% 0.26/0.53         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 0.26/0.53            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % add_divide_eq_if_simps(2)
% 0.26/0.53  thf(fact_3919_add__divide__eq__if__simps_I2_J,axiom,
% 0.26/0.53      ! [Z: real,A: real,B: real] :
% 0.26/0.53        ( ( ( Z = zero_zero_real )
% 0.26/0.53         => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 0.26/0.53            = B ) )
% 0.26/0.53        & ( ( Z != zero_zero_real )
% 0.26/0.53         => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 0.26/0.53            = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % add_divide_eq_if_simps(2)
% 0.26/0.53  thf(fact_3920_add__divide__eq__if__simps_I2_J,axiom,
% 0.26/0.53      ! [Z: rat,A: rat,B: rat] :
% 0.26/0.53        ( ( ( Z = zero_zero_rat )
% 0.26/0.53         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 0.26/0.53            = B ) )
% 0.26/0.53        & ( ( Z != zero_zero_rat )
% 0.26/0.53         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 0.26/0.53            = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % add_divide_eq_if_simps(2)
% 0.26/0.53  thf(fact_3921_less__add__iff1,axiom,
% 0.26/0.53      ! [A: real,E2: real,C: real,B: real,D3: real] :
% 0.26/0.53        ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D3 ) )
% 0.26/0.53        = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D3 ) ) ).
% 0.26/0.53  
% 0.26/0.53  % less_add_iff1
% 0.26/0.53  thf(fact_3922_less__add__iff1,axiom,
% 0.26/0.53      ! [A: rat,E2: rat,C: rat,B: rat,D3: rat] :
% 0.26/0.53        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D3 ) )
% 0.26/0.53        = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D3 ) ) ).
% 0.26/0.53  
% 0.26/0.53  % less_add_iff1
% 0.26/0.53  thf(fact_3923_less__add__iff1,axiom,
% 0.26/0.53      ! [A: int,E2: int,C: int,B: int,D3: int] :
% 0.26/0.53        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D3 ) )
% 0.26/0.53        = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D3 ) ) ).
% 0.26/0.53  
% 0.26/0.53  % less_add_iff1
% 0.26/0.53  thf(fact_3924_less__add__iff2,axiom,
% 0.26/0.53      ! [A: real,E2: real,C: real,B: real,D3: real] :
% 0.26/0.53        ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D3 ) )
% 0.26/0.53        = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D3 ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % less_add_iff2
% 0.26/0.53  thf(fact_3925_less__add__iff2,axiom,
% 0.26/0.53      ! [A: rat,E2: rat,C: rat,B: rat,D3: rat] :
% 0.26/0.53        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D3 ) )
% 0.26/0.53        = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D3 ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % less_add_iff2
% 0.26/0.53  thf(fact_3926_less__add__iff2,axiom,
% 0.26/0.53      ! [A: int,E2: int,C: int,B: int,D3: int] :
% 0.26/0.53        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D3 ) )
% 0.26/0.53        = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D3 ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % less_add_iff2
% 0.26/0.53  thf(fact_3927_divide__diff__eq__iff,axiom,
% 0.26/0.53      ! [Z: complex,X3: complex,Y3: complex] :
% 0.26/0.53        ( ( Z != zero_zero_complex )
% 0.26/0.53       => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X3 @ Z ) @ Y3 )
% 0.26/0.53          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X3 @ ( times_times_complex @ Y3 @ Z ) ) @ Z ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_diff_eq_iff
% 0.26/0.53  thf(fact_3928_divide__diff__eq__iff,axiom,
% 0.26/0.53      ! [Z: real,X3: real,Y3: real] :
% 0.26/0.53        ( ( Z != zero_zero_real )
% 0.26/0.53       => ( ( minus_minus_real @ ( divide_divide_real @ X3 @ Z ) @ Y3 )
% 0.26/0.53          = ( divide_divide_real @ ( minus_minus_real @ X3 @ ( times_times_real @ Y3 @ Z ) ) @ Z ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_diff_eq_iff
% 0.26/0.53  thf(fact_3929_divide__diff__eq__iff,axiom,
% 0.26/0.53      ! [Z: rat,X3: rat,Y3: rat] :
% 0.26/0.53        ( ( Z != zero_zero_rat )
% 0.26/0.53       => ( ( minus_minus_rat @ ( divide_divide_rat @ X3 @ Z ) @ Y3 )
% 0.26/0.53          = ( divide_divide_rat @ ( minus_minus_rat @ X3 @ ( times_times_rat @ Y3 @ Z ) ) @ Z ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_diff_eq_iff
% 0.26/0.53  thf(fact_3930_diff__divide__eq__iff,axiom,
% 0.26/0.53      ! [Z: complex,X3: complex,Y3: complex] :
% 0.26/0.53        ( ( Z != zero_zero_complex )
% 0.26/0.53       => ( ( minus_minus_complex @ X3 @ ( divide1717551699836669952omplex @ Y3 @ Z ) )
% 0.26/0.53          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X3 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % diff_divide_eq_iff
% 0.26/0.53  thf(fact_3931_diff__divide__eq__iff,axiom,
% 0.26/0.53      ! [Z: real,X3: real,Y3: real] :
% 0.26/0.53        ( ( Z != zero_zero_real )
% 0.26/0.53       => ( ( minus_minus_real @ X3 @ ( divide_divide_real @ Y3 @ Z ) )
% 0.26/0.53          = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X3 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % diff_divide_eq_iff
% 0.26/0.53  thf(fact_3932_diff__divide__eq__iff,axiom,
% 0.26/0.53      ! [Z: rat,X3: rat,Y3: rat] :
% 0.26/0.53        ( ( Z != zero_zero_rat )
% 0.26/0.53       => ( ( minus_minus_rat @ X3 @ ( divide_divide_rat @ Y3 @ Z ) )
% 0.26/0.53          = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X3 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % diff_divide_eq_iff
% 0.26/0.53  thf(fact_3933_diff__frac__eq,axiom,
% 0.26/0.53      ! [Y3: complex,Z: complex,X3: complex,W: complex] :
% 0.26/0.53        ( ( Y3 != zero_zero_complex )
% 0.26/0.53       => ( ( Z != zero_zero_complex )
% 0.26/0.53         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X3 @ Y3 ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 0.26/0.53            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X3 @ Z ) @ ( times_times_complex @ W @ Y3 ) ) @ ( times_times_complex @ Y3 @ Z ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % diff_frac_eq
% 0.26/0.53  thf(fact_3934_diff__frac__eq,axiom,
% 0.26/0.53      ! [Y3: real,Z: real,X3: real,W: real] :
% 0.26/0.53        ( ( Y3 != zero_zero_real )
% 0.26/0.53       => ( ( Z != zero_zero_real )
% 0.26/0.53         => ( ( minus_minus_real @ ( divide_divide_real @ X3 @ Y3 ) @ ( divide_divide_real @ W @ Z ) )
% 0.26/0.53            = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X3 @ Z ) @ ( times_times_real @ W @ Y3 ) ) @ ( times_times_real @ Y3 @ Z ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % diff_frac_eq
% 0.26/0.53  thf(fact_3935_diff__frac__eq,axiom,
% 0.26/0.53      ! [Y3: rat,Z: rat,X3: rat,W: rat] :
% 0.26/0.53        ( ( Y3 != zero_zero_rat )
% 0.26/0.53       => ( ( Z != zero_zero_rat )
% 0.26/0.53         => ( ( minus_minus_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ ( divide_divide_rat @ W @ Z ) )
% 0.26/0.53            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X3 @ Z ) @ ( times_times_rat @ W @ Y3 ) ) @ ( times_times_rat @ Y3 @ Z ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % diff_frac_eq
% 0.26/0.53  thf(fact_3936_add__divide__eq__if__simps_I4_J,axiom,
% 0.26/0.53      ! [Z: complex,A: complex,B: complex] :
% 0.26/0.53        ( ( ( Z = zero_zero_complex )
% 0.26/0.53         => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 0.26/0.53            = A ) )
% 0.26/0.53        & ( ( Z != zero_zero_complex )
% 0.26/0.53         => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 0.26/0.53            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % add_divide_eq_if_simps(4)
% 0.26/0.53  thf(fact_3937_add__divide__eq__if__simps_I4_J,axiom,
% 0.26/0.53      ! [Z: real,A: real,B: real] :
% 0.26/0.53        ( ( ( Z = zero_zero_real )
% 0.26/0.53         => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 0.26/0.53            = A ) )
% 0.26/0.53        & ( ( Z != zero_zero_real )
% 0.26/0.53         => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 0.26/0.53            = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % add_divide_eq_if_simps(4)
% 0.26/0.53  thf(fact_3938_add__divide__eq__if__simps_I4_J,axiom,
% 0.26/0.53      ! [Z: rat,A: rat,B: rat] :
% 0.26/0.53        ( ( ( Z = zero_zero_rat )
% 0.26/0.53         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 0.26/0.53            = A ) )
% 0.26/0.53        & ( ( Z != zero_zero_rat )
% 0.26/0.53         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 0.26/0.53            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % add_divide_eq_if_simps(4)
% 0.26/0.53  thf(fact_3939_power__gt1__lemma,axiom,
% 0.26/0.53      ! [A: real,N: nat] :
% 0.26/0.53        ( ( ord_less_real @ one_one_real @ A )
% 0.26/0.53       => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_gt1_lemma
% 0.26/0.53  thf(fact_3940_power__gt1__lemma,axiom,
% 0.26/0.53      ! [A: rat,N: nat] :
% 0.26/0.53        ( ( ord_less_rat @ one_one_rat @ A )
% 0.26/0.53       => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_gt1_lemma
% 0.26/0.53  thf(fact_3941_power__gt1__lemma,axiom,
% 0.26/0.53      ! [A: nat,N: nat] :
% 0.26/0.53        ( ( ord_less_nat @ one_one_nat @ A )
% 0.26/0.53       => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_gt1_lemma
% 0.26/0.53  thf(fact_3942_power__gt1__lemma,axiom,
% 0.26/0.53      ! [A: int,N: nat] :
% 0.26/0.53        ( ( ord_less_int @ one_one_int @ A )
% 0.26/0.53       => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_gt1_lemma
% 0.26/0.53  thf(fact_3943_power__less__power__Suc,axiom,
% 0.26/0.53      ! [A: real,N: nat] :
% 0.26/0.53        ( ( ord_less_real @ one_one_real @ A )
% 0.26/0.53       => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_less_power_Suc
% 0.26/0.53  thf(fact_3944_power__less__power__Suc,axiom,
% 0.26/0.53      ! [A: rat,N: nat] :
% 0.26/0.53        ( ( ord_less_rat @ one_one_rat @ A )
% 0.26/0.53       => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_less_power_Suc
% 0.26/0.53  thf(fact_3945_power__less__power__Suc,axiom,
% 0.26/0.53      ! [A: nat,N: nat] :
% 0.26/0.53        ( ( ord_less_nat @ one_one_nat @ A )
% 0.26/0.53       => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_less_power_Suc
% 0.26/0.53  thf(fact_3946_power__less__power__Suc,axiom,
% 0.26/0.53      ! [A: int,N: nat] :
% 0.26/0.53        ( ( ord_less_int @ one_one_int @ A )
% 0.26/0.53       => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_less_power_Suc
% 0.26/0.53  thf(fact_3947_ex__less__of__nat__mult,axiom,
% 0.26/0.53      ! [X3: real,Y3: real] :
% 0.26/0.53        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.53       => ? [N2: nat] : ( ord_less_real @ Y3 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X3 ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % ex_less_of_nat_mult
% 0.26/0.53  thf(fact_3948_ex__less__of__nat__mult,axiom,
% 0.26/0.53      ! [X3: rat,Y3: rat] :
% 0.26/0.53        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 0.26/0.53       => ? [N2: nat] : ( ord_less_rat @ Y3 @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ X3 ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % ex_less_of_nat_mult
% 0.26/0.53  thf(fact_3949_unit__dvdE,axiom,
% 0.26/0.53      ! [A: code_integer,B: code_integer] :
% 0.26/0.53        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.26/0.53       => ~ ( ( A != zero_z3403309356797280102nteger )
% 0.26/0.53           => ! [C2: code_integer] :
% 0.26/0.53                ( B
% 0.26/0.53               != ( times_3573771949741848930nteger @ A @ C2 ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % unit_dvdE
% 0.26/0.53  thf(fact_3950_unit__dvdE,axiom,
% 0.26/0.53      ! [A: nat,B: nat] :
% 0.26/0.53        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.26/0.53       => ~ ( ( A != zero_zero_nat )
% 0.26/0.53           => ! [C2: nat] :
% 0.26/0.53                ( B
% 0.26/0.53               != ( times_times_nat @ A @ C2 ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % unit_dvdE
% 0.26/0.53  thf(fact_3951_unit__dvdE,axiom,
% 0.26/0.53      ! [A: int,B: int] :
% 0.26/0.53        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.26/0.53       => ~ ( ( A != zero_zero_int )
% 0.26/0.53           => ! [C2: int] :
% 0.26/0.53                ( B
% 0.26/0.53               != ( times_times_int @ A @ C2 ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % unit_dvdE
% 0.26/0.53  thf(fact_3952_unity__coeff__ex,axiom,
% 0.26/0.53      ! [P: code_integer > $o,L: code_integer] :
% 0.26/0.53        ( ( ? [X: code_integer] : ( P @ ( times_3573771949741848930nteger @ L @ X ) ) )
% 0.26/0.53        = ( ? [X: code_integer] :
% 0.26/0.53              ( ( dvd_dvd_Code_integer @ L @ ( plus_p5714425477246183910nteger @ X @ zero_z3403309356797280102nteger ) )
% 0.26/0.53              & ( P @ X ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % unity_coeff_ex
% 0.26/0.53  thf(fact_3953_unity__coeff__ex,axiom,
% 0.26/0.53      ! [P: real > $o,L: real] :
% 0.26/0.53        ( ( ? [X: real] : ( P @ ( times_times_real @ L @ X ) ) )
% 0.26/0.53        = ( ? [X: real] :
% 0.26/0.53              ( ( dvd_dvd_real @ L @ ( plus_plus_real @ X @ zero_zero_real ) )
% 0.26/0.53              & ( P @ X ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % unity_coeff_ex
% 0.26/0.53  thf(fact_3954_unity__coeff__ex,axiom,
% 0.26/0.53      ! [P: rat > $o,L: rat] :
% 0.26/0.53        ( ( ? [X: rat] : ( P @ ( times_times_rat @ L @ X ) ) )
% 0.26/0.53        = ( ? [X: rat] :
% 0.26/0.53              ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X @ zero_zero_rat ) )
% 0.26/0.53              & ( P @ X ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % unity_coeff_ex
% 0.26/0.53  thf(fact_3955_unity__coeff__ex,axiom,
% 0.26/0.53      ! [P: nat > $o,L: nat] :
% 0.26/0.53        ( ( ? [X: nat] : ( P @ ( times_times_nat @ L @ X ) ) )
% 0.26/0.53        = ( ? [X: nat] :
% 0.26/0.53              ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X @ zero_zero_nat ) )
% 0.26/0.53              & ( P @ X ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % unity_coeff_ex
% 0.26/0.53  thf(fact_3956_unity__coeff__ex,axiom,
% 0.26/0.53      ! [P: int > $o,L: int] :
% 0.26/0.53        ( ( ? [X: int] : ( P @ ( times_times_int @ L @ X ) ) )
% 0.26/0.53        = ( ? [X: int] :
% 0.26/0.53              ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X @ zero_zero_int ) )
% 0.26/0.53              & ( P @ X ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % unity_coeff_ex
% 0.26/0.53  thf(fact_3957_dvd__div__div__eq__mult,axiom,
% 0.26/0.53      ! [A: code_integer,C: code_integer,B: code_integer,D3: code_integer] :
% 0.26/0.53        ( ( A != zero_z3403309356797280102nteger )
% 0.26/0.53       => ( ( C != zero_z3403309356797280102nteger )
% 0.26/0.53         => ( ( dvd_dvd_Code_integer @ A @ B )
% 0.26/0.53           => ( ( dvd_dvd_Code_integer @ C @ D3 )
% 0.26/0.53             => ( ( ( divide6298287555418463151nteger @ B @ A )
% 0.26/0.53                  = ( divide6298287555418463151nteger @ D3 @ C ) )
% 0.26/0.53                = ( ( times_3573771949741848930nteger @ B @ C )
% 0.26/0.53                  = ( times_3573771949741848930nteger @ A @ D3 ) ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % dvd_div_div_eq_mult
% 0.26/0.53  thf(fact_3958_dvd__div__div__eq__mult,axiom,
% 0.26/0.53      ! [A: nat,C: nat,B: nat,D3: nat] :
% 0.26/0.53        ( ( A != zero_zero_nat )
% 0.26/0.53       => ( ( C != zero_zero_nat )
% 0.26/0.53         => ( ( dvd_dvd_nat @ A @ B )
% 0.26/0.53           => ( ( dvd_dvd_nat @ C @ D3 )
% 0.26/0.53             => ( ( ( divide_divide_nat @ B @ A )
% 0.26/0.53                  = ( divide_divide_nat @ D3 @ C ) )
% 0.26/0.53                = ( ( times_times_nat @ B @ C )
% 0.26/0.53                  = ( times_times_nat @ A @ D3 ) ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % dvd_div_div_eq_mult
% 0.26/0.53  thf(fact_3959_dvd__div__div__eq__mult,axiom,
% 0.26/0.53      ! [A: int,C: int,B: int,D3: int] :
% 0.26/0.53        ( ( A != zero_zero_int )
% 0.26/0.53       => ( ( C != zero_zero_int )
% 0.26/0.53         => ( ( dvd_dvd_int @ A @ B )
% 0.26/0.53           => ( ( dvd_dvd_int @ C @ D3 )
% 0.26/0.53             => ( ( ( divide_divide_int @ B @ A )
% 0.26/0.53                  = ( divide_divide_int @ D3 @ C ) )
% 0.26/0.53                = ( ( times_times_int @ B @ C )
% 0.26/0.53                  = ( times_times_int @ A @ D3 ) ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % dvd_div_div_eq_mult
% 0.26/0.53  thf(fact_3960_dvd__div__iff__mult,axiom,
% 0.26/0.53      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.26/0.53        ( ( C != zero_z3403309356797280102nteger )
% 0.26/0.53       => ( ( dvd_dvd_Code_integer @ C @ B )
% 0.26/0.53         => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 0.26/0.53            = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % dvd_div_iff_mult
% 0.26/0.53  thf(fact_3961_dvd__div__iff__mult,axiom,
% 0.26/0.53      ! [C: nat,B: nat,A: nat] :
% 0.26/0.53        ( ( C != zero_zero_nat )
% 0.26/0.53       => ( ( dvd_dvd_nat @ C @ B )
% 0.26/0.53         => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 0.26/0.53            = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % dvd_div_iff_mult
% 0.26/0.53  thf(fact_3962_dvd__div__iff__mult,axiom,
% 0.26/0.53      ! [C: int,B: int,A: int] :
% 0.26/0.53        ( ( C != zero_zero_int )
% 0.26/0.53       => ( ( dvd_dvd_int @ C @ B )
% 0.26/0.53         => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 0.26/0.53            = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % dvd_div_iff_mult
% 0.26/0.53  thf(fact_3963_div__dvd__iff__mult,axiom,
% 0.26/0.53      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.26/0.53        ( ( B != zero_z3403309356797280102nteger )
% 0.26/0.53       => ( ( dvd_dvd_Code_integer @ B @ A )
% 0.26/0.53         => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 0.26/0.53            = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % div_dvd_iff_mult
% 0.26/0.53  thf(fact_3964_div__dvd__iff__mult,axiom,
% 0.26/0.53      ! [B: nat,A: nat,C: nat] :
% 0.26/0.53        ( ( B != zero_zero_nat )
% 0.26/0.53       => ( ( dvd_dvd_nat @ B @ A )
% 0.26/0.53         => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 0.26/0.53            = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % div_dvd_iff_mult
% 0.26/0.53  thf(fact_3965_div__dvd__iff__mult,axiom,
% 0.26/0.53      ! [B: int,A: int,C: int] :
% 0.26/0.53        ( ( B != zero_zero_int )
% 0.26/0.53       => ( ( dvd_dvd_int @ B @ A )
% 0.26/0.53         => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 0.26/0.53            = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % div_dvd_iff_mult
% 0.26/0.53  thf(fact_3966_dvd__div__eq__mult,axiom,
% 0.26/0.53      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.26/0.53        ( ( A != zero_z3403309356797280102nteger )
% 0.26/0.53       => ( ( dvd_dvd_Code_integer @ A @ B )
% 0.26/0.53         => ( ( ( divide6298287555418463151nteger @ B @ A )
% 0.26/0.53              = C )
% 0.26/0.53            = ( B
% 0.26/0.53              = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % dvd_div_eq_mult
% 0.26/0.53  thf(fact_3967_dvd__div__eq__mult,axiom,
% 0.26/0.53      ! [A: nat,B: nat,C: nat] :
% 0.26/0.53        ( ( A != zero_zero_nat )
% 0.26/0.53       => ( ( dvd_dvd_nat @ A @ B )
% 0.26/0.53         => ( ( ( divide_divide_nat @ B @ A )
% 0.26/0.53              = C )
% 0.26/0.53            = ( B
% 0.26/0.53              = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % dvd_div_eq_mult
% 0.26/0.53  thf(fact_3968_dvd__div__eq__mult,axiom,
% 0.26/0.53      ! [A: int,B: int,C: int] :
% 0.26/0.53        ( ( A != zero_zero_int )
% 0.26/0.53       => ( ( dvd_dvd_int @ A @ B )
% 0.26/0.53         => ( ( ( divide_divide_int @ B @ A )
% 0.26/0.53              = C )
% 0.26/0.53            = ( B
% 0.26/0.53              = ( times_times_int @ C @ A ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % dvd_div_eq_mult
% 0.26/0.53  thf(fact_3969_inf__period_I4_J,axiom,
% 0.26/0.53      ! [D3: code_integer,D5: code_integer,T: code_integer] :
% 0.26/0.53        ( ( dvd_dvd_Code_integer @ D3 @ D5 )
% 0.26/0.53       => ! [X6: code_integer,K4: code_integer] :
% 0.26/0.53            ( ( ~ ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ X6 @ T ) ) )
% 0.26/0.53            = ( ~ ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X6 @ ( times_3573771949741848930nteger @ K4 @ D5 ) ) @ T ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % inf_period(4)
% 0.26/0.53  thf(fact_3970_inf__period_I4_J,axiom,
% 0.26/0.53      ! [D3: real,D5: real,T: real] :
% 0.26/0.53        ( ( dvd_dvd_real @ D3 @ D5 )
% 0.26/0.53       => ! [X6: real,K4: real] :
% 0.26/0.53            ( ( ~ ( dvd_dvd_real @ D3 @ ( plus_plus_real @ X6 @ T ) ) )
% 0.26/0.53            = ( ~ ( dvd_dvd_real @ D3 @ ( plus_plus_real @ ( minus_minus_real @ X6 @ ( times_times_real @ K4 @ D5 ) ) @ T ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % inf_period(4)
% 0.26/0.53  thf(fact_3971_inf__period_I4_J,axiom,
% 0.26/0.53      ! [D3: rat,D5: rat,T: rat] :
% 0.26/0.53        ( ( dvd_dvd_rat @ D3 @ D5 )
% 0.26/0.53       => ! [X6: rat,K4: rat] :
% 0.26/0.53            ( ( ~ ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ X6 @ T ) ) )
% 0.26/0.53            = ( ~ ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D5 ) ) @ T ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % inf_period(4)
% 0.26/0.53  thf(fact_3972_inf__period_I4_J,axiom,
% 0.26/0.53      ! [D3: int,D5: int,T: int] :
% 0.26/0.53        ( ( dvd_dvd_int @ D3 @ D5 )
% 0.26/0.53       => ! [X6: int,K4: int] :
% 0.26/0.53            ( ( ~ ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ T ) ) )
% 0.26/0.53            = ( ~ ( dvd_dvd_int @ D3 @ ( plus_plus_int @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D5 ) ) @ T ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % inf_period(4)
% 0.26/0.53  thf(fact_3973_inf__period_I3_J,axiom,
% 0.26/0.53      ! [D3: code_integer,D5: code_integer,T: code_integer] :
% 0.26/0.53        ( ( dvd_dvd_Code_integer @ D3 @ D5 )
% 0.26/0.53       => ! [X6: code_integer,K4: code_integer] :
% 0.26/0.53            ( ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ X6 @ T ) )
% 0.26/0.53            = ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X6 @ ( times_3573771949741848930nteger @ K4 @ D5 ) ) @ T ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % inf_period(3)
% 0.26/0.53  thf(fact_3974_inf__period_I3_J,axiom,
% 0.26/0.53      ! [D3: real,D5: real,T: real] :
% 0.26/0.53        ( ( dvd_dvd_real @ D3 @ D5 )
% 0.26/0.53       => ! [X6: real,K4: real] :
% 0.26/0.53            ( ( dvd_dvd_real @ D3 @ ( plus_plus_real @ X6 @ T ) )
% 0.26/0.53            = ( dvd_dvd_real @ D3 @ ( plus_plus_real @ ( minus_minus_real @ X6 @ ( times_times_real @ K4 @ D5 ) ) @ T ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % inf_period(3)
% 0.26/0.53  thf(fact_3975_inf__period_I3_J,axiom,
% 0.26/0.53      ! [D3: rat,D5: rat,T: rat] :
% 0.26/0.53        ( ( dvd_dvd_rat @ D3 @ D5 )
% 0.26/0.53       => ! [X6: rat,K4: rat] :
% 0.26/0.53            ( ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ X6 @ T ) )
% 0.26/0.53            = ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D5 ) ) @ T ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % inf_period(3)
% 0.26/0.53  thf(fact_3976_inf__period_I3_J,axiom,
% 0.26/0.53      ! [D3: int,D5: int,T: int] :
% 0.26/0.53        ( ( dvd_dvd_int @ D3 @ D5 )
% 0.26/0.53       => ! [X6: int,K4: int] :
% 0.26/0.53            ( ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ T ) )
% 0.26/0.53            = ( dvd_dvd_int @ D3 @ ( plus_plus_int @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D5 ) ) @ T ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % inf_period(3)
% 0.26/0.53  thf(fact_3977_one__less__mult,axiom,
% 0.26/0.53      ! [N: nat,M: nat] :
% 0.26/0.53        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.26/0.53       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.26/0.53         => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % one_less_mult
% 0.26/0.53  thf(fact_3978_n__less__m__mult__n,axiom,
% 0.26/0.53      ! [N: nat,M: nat] :
% 0.26/0.53        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.53       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.26/0.53         => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % n_less_m_mult_n
% 0.26/0.53  thf(fact_3979_n__less__n__mult__m,axiom,
% 0.26/0.53      ! [N: nat,M: nat] :
% 0.26/0.53        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.53       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.26/0.53         => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % n_less_n_mult_m
% 0.26/0.53  thf(fact_3980_nat__mult__le__cancel1,axiom,
% 0.26/0.53      ! [K: nat,M: nat,N: nat] :
% 0.26/0.53        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.26/0.53       => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.26/0.53          = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % nat_mult_le_cancel1
% 0.26/0.53  thf(fact_3981_nat__mult__div__cancel1,axiom,
% 0.26/0.53      ! [K: nat,M: nat,N: nat] :
% 0.26/0.53        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.26/0.53       => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.26/0.53          = ( divide_divide_nat @ M @ N ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % nat_mult_div_cancel1
% 0.26/0.53  thf(fact_3982_div__less__iff__less__mult,axiom,
% 0.26/0.53      ! [Q3: nat,M: nat,N: nat] :
% 0.26/0.53        ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 0.26/0.53       => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q3 ) @ N )
% 0.26/0.53          = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q3 ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % div_less_iff_less_mult
% 0.26/0.53  thf(fact_3983_dvd__mult__cancel,axiom,
% 0.26/0.53      ! [K: nat,M: nat,N: nat] :
% 0.26/0.53        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.26/0.53       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.26/0.53         => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % dvd_mult_cancel
% 0.26/0.53  thf(fact_3984_nat__mult__dvd__cancel1,axiom,
% 0.26/0.53      ! [K: nat,M: nat,N: nat] :
% 0.26/0.53        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.26/0.53       => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.26/0.53          = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % nat_mult_dvd_cancel1
% 0.26/0.53  thf(fact_3985_nat__eq__add__iff1,axiom,
% 0.26/0.53      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.26/0.53        ( ( ord_less_eq_nat @ J @ I )
% 0.26/0.53       => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 0.26/0.53            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.26/0.53          = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 0.26/0.53            = N ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % nat_eq_add_iff1
% 0.26/0.53  thf(fact_3986_nat__eq__add__iff2,axiom,
% 0.26/0.53      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.26/0.53        ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.53       => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 0.26/0.53            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.26/0.53          = ( M
% 0.26/0.53            = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % nat_eq_add_iff2
% 0.26/0.53  thf(fact_3987_nat__le__add__iff1,axiom,
% 0.26/0.53      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.26/0.53        ( ( ord_less_eq_nat @ J @ I )
% 0.26/0.53       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.26/0.53          = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % nat_le_add_iff1
% 0.26/0.53  thf(fact_3988_nat__le__add__iff2,axiom,
% 0.26/0.53      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.26/0.53        ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.53       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.26/0.53          = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % nat_le_add_iff2
% 0.26/0.53  thf(fact_3989_nat__diff__add__eq1,axiom,
% 0.26/0.53      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.26/0.53        ( ( ord_less_eq_nat @ J @ I )
% 0.26/0.53       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.26/0.53          = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % nat_diff_add_eq1
% 0.26/0.53  thf(fact_3990_nat__diff__add__eq2,axiom,
% 0.26/0.53      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.26/0.53        ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.53       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.26/0.53          = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % nat_diff_add_eq2
% 0.26/0.53  thf(fact_3991_bezout__add__strong__nat,axiom,
% 0.26/0.53      ! [A: nat,B: nat] :
% 0.26/0.53        ( ( A != zero_zero_nat )
% 0.26/0.53       => ? [D6: nat,X4: nat,Y4: nat] :
% 0.26/0.53            ( ( dvd_dvd_nat @ D6 @ A )
% 0.26/0.53            & ( dvd_dvd_nat @ D6 @ B )
% 0.26/0.53            & ( ( times_times_nat @ A @ X4 )
% 0.26/0.53              = ( plus_plus_nat @ ( times_times_nat @ B @ Y4 ) @ D6 ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % bezout_add_strong_nat
% 0.26/0.53  thf(fact_3992_mult__le__cancel__left1,axiom,
% 0.26/0.53      ! [C: real,B: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 0.26/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ord_less_eq_real @ one_one_real @ B ) )
% 0.26/0.53          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53           => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_left1
% 0.26/0.53  thf(fact_3993_mult__le__cancel__left1,axiom,
% 0.26/0.53      ! [C: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 0.26/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 0.26/0.53          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_left1
% 0.26/0.53  thf(fact_3994_mult__le__cancel__left1,axiom,
% 0.26/0.53      ! [C: int,B: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 0.26/0.53        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.26/0.53           => ( ord_less_eq_int @ one_one_int @ B ) )
% 0.26/0.53          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.26/0.53           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_left1
% 0.26/0.53  thf(fact_3995_mult__le__cancel__left2,axiom,
% 0.26/0.53      ! [C: real,A: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 0.26/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ord_less_eq_real @ A @ one_one_real ) )
% 0.26/0.53          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53           => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_left2
% 0.26/0.53  thf(fact_3996_mult__le__cancel__left2,axiom,
% 0.26/0.53      ! [C: rat,A: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 0.26/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 0.26/0.53          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_left2
% 0.26/0.53  thf(fact_3997_mult__le__cancel__left2,axiom,
% 0.26/0.53      ! [C: int,A: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 0.26/0.53        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.26/0.53           => ( ord_less_eq_int @ A @ one_one_int ) )
% 0.26/0.53          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.26/0.53           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_left2
% 0.26/0.53  thf(fact_3998_mult__le__cancel__right1,axiom,
% 0.26/0.53      ! [C: real,B: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 0.26/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ord_less_eq_real @ one_one_real @ B ) )
% 0.26/0.53          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53           => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_right1
% 0.26/0.53  thf(fact_3999_mult__le__cancel__right1,axiom,
% 0.26/0.53      ! [C: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 0.26/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 0.26/0.53          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_right1
% 0.26/0.53  thf(fact_4000_mult__le__cancel__right1,axiom,
% 0.26/0.53      ! [C: int,B: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 0.26/0.53        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.26/0.53           => ( ord_less_eq_int @ one_one_int @ B ) )
% 0.26/0.53          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.26/0.53           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_right1
% 0.26/0.53  thf(fact_4001_mult__le__cancel__right2,axiom,
% 0.26/0.53      ! [A: real,C: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 0.26/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ord_less_eq_real @ A @ one_one_real ) )
% 0.26/0.53          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53           => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_right2
% 0.26/0.53  thf(fact_4002_mult__le__cancel__right2,axiom,
% 0.26/0.53      ! [A: rat,C: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 0.26/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 0.26/0.53          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_right2
% 0.26/0.53  thf(fact_4003_mult__le__cancel__right2,axiom,
% 0.26/0.53      ! [A: int,C: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 0.26/0.53        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.26/0.53           => ( ord_less_eq_int @ A @ one_one_int ) )
% 0.26/0.53          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.26/0.53           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_le_cancel_right2
% 0.26/0.53  thf(fact_4004_mult__less__cancel__left1,axiom,
% 0.26/0.53      ! [C: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 0.26/0.53        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ord_less_real @ one_one_real @ B ) )
% 0.26/0.53          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.26/0.53           => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_left1
% 0.26/0.53  thf(fact_4005_mult__less__cancel__left1,axiom,
% 0.26/0.53      ! [C: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 0.26/0.53        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ord_less_rat @ one_one_rat @ B ) )
% 0.26/0.53          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.26/0.53           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_left1
% 0.26/0.53  thf(fact_4006_mult__less__cancel__left1,axiom,
% 0.26/0.53      ! [C: int,B: int] :
% 0.26/0.53        ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 0.26/0.53        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.26/0.53           => ( ord_less_int @ one_one_int @ B ) )
% 0.26/0.53          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.26/0.53           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_left1
% 0.26/0.53  thf(fact_4007_mult__less__cancel__left2,axiom,
% 0.26/0.53      ! [C: real,A: real] :
% 0.26/0.53        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 0.26/0.53        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ord_less_real @ A @ one_one_real ) )
% 0.26/0.53          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.26/0.53           => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_left2
% 0.26/0.53  thf(fact_4008_mult__less__cancel__left2,axiom,
% 0.26/0.53      ! [C: rat,A: rat] :
% 0.26/0.53        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 0.26/0.53        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ord_less_rat @ A @ one_one_rat ) )
% 0.26/0.53          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.26/0.53           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_left2
% 0.26/0.53  thf(fact_4009_mult__less__cancel__left2,axiom,
% 0.26/0.53      ! [C: int,A: int] :
% 0.26/0.53        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 0.26/0.53        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.26/0.53           => ( ord_less_int @ A @ one_one_int ) )
% 0.26/0.53          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.26/0.53           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_left2
% 0.26/0.53  thf(fact_4010_mult__less__cancel__right1,axiom,
% 0.26/0.53      ! [C: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 0.26/0.53        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ord_less_real @ one_one_real @ B ) )
% 0.26/0.53          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.26/0.53           => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_right1
% 0.26/0.53  thf(fact_4011_mult__less__cancel__right1,axiom,
% 0.26/0.53      ! [C: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 0.26/0.53        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ord_less_rat @ one_one_rat @ B ) )
% 0.26/0.53          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.26/0.53           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_right1
% 0.26/0.53  thf(fact_4012_mult__less__cancel__right1,axiom,
% 0.26/0.53      ! [C: int,B: int] :
% 0.26/0.53        ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 0.26/0.53        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.26/0.53           => ( ord_less_int @ one_one_int @ B ) )
% 0.26/0.53          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.26/0.53           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_right1
% 0.26/0.53  thf(fact_4013_mult__less__cancel__right2,axiom,
% 0.26/0.53      ! [A: real,C: real] :
% 0.26/0.53        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 0.26/0.53        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ord_less_real @ A @ one_one_real ) )
% 0.26/0.53          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.26/0.53           => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_right2
% 0.26/0.53  thf(fact_4014_mult__less__cancel__right2,axiom,
% 0.26/0.53      ! [A: rat,C: rat] :
% 0.26/0.53        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 0.26/0.53        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ord_less_rat @ A @ one_one_rat ) )
% 0.26/0.53          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.26/0.53           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_right2
% 0.26/0.53  thf(fact_4015_mult__less__cancel__right2,axiom,
% 0.26/0.53      ! [A: int,C: int] :
% 0.26/0.53        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 0.26/0.53        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.26/0.53           => ( ord_less_int @ A @ one_one_int ) )
% 0.26/0.53          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.26/0.53           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_less_cancel_right2
% 0.26/0.53  thf(fact_4016_field__le__mult__one__interval,axiom,
% 0.26/0.53      ! [X3: real,Y3: real] :
% 0.26/0.53        ( ! [Z3: real] :
% 0.26/0.53            ( ( ord_less_real @ zero_zero_real @ Z3 )
% 0.26/0.53           => ( ( ord_less_real @ Z3 @ one_one_real )
% 0.26/0.53             => ( ord_less_eq_real @ ( times_times_real @ Z3 @ X3 ) @ Y3 ) ) )
% 0.26/0.53       => ( ord_less_eq_real @ X3 @ Y3 ) ) ).
% 0.26/0.53  
% 0.26/0.53  % field_le_mult_one_interval
% 0.26/0.53  thf(fact_4017_field__le__mult__one__interval,axiom,
% 0.26/0.53      ! [X3: rat,Y3: rat] :
% 0.26/0.53        ( ! [Z3: rat] :
% 0.26/0.53            ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 0.26/0.53           => ( ( ord_less_rat @ Z3 @ one_one_rat )
% 0.26/0.53             => ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ X3 ) @ Y3 ) ) )
% 0.26/0.53       => ( ord_less_eq_rat @ X3 @ Y3 ) ) ).
% 0.26/0.53  
% 0.26/0.53  % field_le_mult_one_interval
% 0.26/0.53  thf(fact_4018_divide__le__eq,axiom,
% 0.26/0.53      ! [B: real,C: real,A: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.26/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 0.26/0.53          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53               => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 0.26/0.53              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53               => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_le_eq
% 0.26/0.53  thf(fact_4019_divide__le__eq,axiom,
% 0.26/0.53      ! [B: rat,C: rat,A: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.26/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.26/0.53          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.26/0.53              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_le_eq
% 0.26/0.53  thf(fact_4020_le__divide__eq,axiom,
% 0.26/0.53      ! [A: real,B: real,C: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.26/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 0.26/0.53          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53               => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 0.26/0.53              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53               => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % le_divide_eq
% 0.26/0.53  thf(fact_4021_le__divide__eq,axiom,
% 0.26/0.53      ! [A: rat,B: rat,C: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.26/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.26/0.53          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53               => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.26/0.53              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % le_divide_eq
% 0.26/0.53  thf(fact_4022_divide__left__mono,axiom,
% 0.26/0.53      ! [B: real,A: real,C: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ B @ A )
% 0.26/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.26/0.53         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.26/0.53           => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_left_mono
% 0.26/0.53  thf(fact_4023_divide__left__mono,axiom,
% 0.26/0.53      ! [B: rat,A: rat,C: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ B @ A )
% 0.26/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.26/0.53         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.26/0.53           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_left_mono
% 0.26/0.53  thf(fact_4024_neg__divide__le__eq,axiom,
% 0.26/0.53      ! [C: real,B: real,A: real] :
% 0.26/0.53        ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.26/0.53          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % neg_divide_le_eq
% 0.26/0.53  thf(fact_4025_neg__divide__le__eq,axiom,
% 0.26/0.53      ! [C: rat,B: rat,A: rat] :
% 0.26/0.53        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.26/0.53          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % neg_divide_le_eq
% 0.26/0.53  thf(fact_4026_neg__le__divide__eq,axiom,
% 0.26/0.53      ! [C: real,A: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53       => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.26/0.53          = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % neg_le_divide_eq
% 0.26/0.53  thf(fact_4027_neg__le__divide__eq,axiom,
% 0.26/0.53      ! [C: rat,A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.26/0.53          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % neg_le_divide_eq
% 0.26/0.53  thf(fact_4028_pos__divide__le__eq,axiom,
% 0.26/0.53      ! [C: real,B: real,A: real] :
% 0.26/0.53        ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.26/0.53          = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % pos_divide_le_eq
% 0.26/0.53  thf(fact_4029_pos__divide__le__eq,axiom,
% 0.26/0.53      ! [C: rat,B: rat,A: rat] :
% 0.26/0.53        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.26/0.53          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % pos_divide_le_eq
% 0.26/0.53  thf(fact_4030_pos__le__divide__eq,axiom,
% 0.26/0.53      ! [C: real,A: real,B: real] :
% 0.26/0.53        ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53       => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.26/0.53          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % pos_le_divide_eq
% 0.26/0.53  thf(fact_4031_pos__le__divide__eq,axiom,
% 0.26/0.53      ! [C: rat,A: rat,B: rat] :
% 0.26/0.53        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.26/0.53          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % pos_le_divide_eq
% 0.26/0.53  thf(fact_4032_mult__imp__div__pos__le,axiom,
% 0.26/0.53      ! [Y3: real,X3: real,Z: real] :
% 0.26/0.53        ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.53       => ( ( ord_less_eq_real @ X3 @ ( times_times_real @ Z @ Y3 ) )
% 0.26/0.53         => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y3 ) @ Z ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_imp_div_pos_le
% 0.26/0.53  thf(fact_4033_mult__imp__div__pos__le,axiom,
% 0.26/0.53      ! [Y3: rat,X3: rat,Z: rat] :
% 0.26/0.53        ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 0.26/0.53       => ( ( ord_less_eq_rat @ X3 @ ( times_times_rat @ Z @ Y3 ) )
% 0.26/0.53         => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ Z ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_imp_div_pos_le
% 0.26/0.53  thf(fact_4034_mult__imp__le__div__pos,axiom,
% 0.26/0.53      ! [Y3: real,Z: real,X3: real] :
% 0.26/0.53        ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.53       => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y3 ) @ X3 )
% 0.26/0.53         => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_imp_le_div_pos
% 0.26/0.53  thf(fact_4035_mult__imp__le__div__pos,axiom,
% 0.26/0.53      ! [Y3: rat,Z: rat,X3: rat] :
% 0.26/0.53        ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 0.26/0.53       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y3 ) @ X3 )
% 0.26/0.53         => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_imp_le_div_pos
% 0.26/0.53  thf(fact_4036_divide__left__mono__neg,axiom,
% 0.26/0.53      ! [A: real,B: real,C: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.53       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.26/0.53         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.26/0.53           => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_left_mono_neg
% 0.26/0.53  thf(fact_4037_divide__left__mono__neg,axiom,
% 0.26/0.53      ! [A: rat,B: rat,C: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.53       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.26/0.53         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.26/0.53           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_left_mono_neg
% 0.26/0.53  thf(fact_4038_convex__bound__le,axiom,
% 0.26/0.53      ! [X3: real,A: real,Y3: real,U: real,V: real] :
% 0.26/0.53        ( ( ord_less_eq_real @ X3 @ A )
% 0.26/0.53       => ( ( ord_less_eq_real @ Y3 @ A )
% 0.26/0.53         => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 0.26/0.53           => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 0.26/0.53             => ( ( ( plus_plus_real @ U @ V )
% 0.26/0.53                  = one_one_real )
% 0.26/0.53               => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X3 ) @ ( times_times_real @ V @ Y3 ) ) @ A ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % convex_bound_le
% 0.26/0.53  thf(fact_4039_convex__bound__le,axiom,
% 0.26/0.53      ! [X3: rat,A: rat,Y3: rat,U: rat,V: rat] :
% 0.26/0.53        ( ( ord_less_eq_rat @ X3 @ A )
% 0.26/0.53       => ( ( ord_less_eq_rat @ Y3 @ A )
% 0.26/0.53         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 0.26/0.53           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 0.26/0.53             => ( ( ( plus_plus_rat @ U @ V )
% 0.26/0.53                  = one_one_rat )
% 0.26/0.53               => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X3 ) @ ( times_times_rat @ V @ Y3 ) ) @ A ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % convex_bound_le
% 0.26/0.53  thf(fact_4040_convex__bound__le,axiom,
% 0.26/0.53      ! [X3: int,A: int,Y3: int,U: int,V: int] :
% 0.26/0.53        ( ( ord_less_eq_int @ X3 @ A )
% 0.26/0.53       => ( ( ord_less_eq_int @ Y3 @ A )
% 0.26/0.53         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.26/0.53           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 0.26/0.53             => ( ( ( plus_plus_int @ U @ V )
% 0.26/0.53                  = one_one_int )
% 0.26/0.53               => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X3 ) @ ( times_times_int @ V @ Y3 ) ) @ A ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % convex_bound_le
% 0.26/0.53  thf(fact_4041_divide__less__eq__numeral_I1_J,axiom,
% 0.26/0.53      ! [B: real,C: real,W: num] :
% 0.26/0.53        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 0.26/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 0.26/0.53          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53               => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 0.26/0.53              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53               => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_less_eq_numeral(1)
% 0.26/0.53  thf(fact_4042_divide__less__eq__numeral_I1_J,axiom,
% 0.26/0.53      ! [B: rat,C: rat,W: num] :
% 0.26/0.53        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 0.26/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.26/0.53          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53               => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 0.26/0.53              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53               => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % divide_less_eq_numeral(1)
% 0.26/0.53  thf(fact_4043_less__divide__eq__numeral_I1_J,axiom,
% 0.26/0.53      ! [W: num,B: real,C: real] :
% 0.26/0.53        ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 0.26/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 0.26/0.53          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.53           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53               => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 0.26/0.53              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.53               => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % less_divide_eq_numeral(1)
% 0.26/0.53  thf(fact_4044_less__divide__eq__numeral_I1_J,axiom,
% 0.26/0.53      ! [W: num,B: rat,C: rat] :
% 0.26/0.53        ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 0.26/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 0.26/0.53          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.53           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53               => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.26/0.53              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.53               => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % less_divide_eq_numeral(1)
% 0.26/0.53  thf(fact_4045_frac__le__eq,axiom,
% 0.26/0.53      ! [Y3: real,Z: real,X3: real,W: real] :
% 0.26/0.53        ( ( Y3 != zero_zero_real )
% 0.26/0.53       => ( ( Z != zero_zero_real )
% 0.26/0.53         => ( ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y3 ) @ ( divide_divide_real @ W @ Z ) )
% 0.26/0.53            = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X3 @ Z ) @ ( times_times_real @ W @ Y3 ) ) @ ( times_times_real @ Y3 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % frac_le_eq
% 0.26/0.53  thf(fact_4046_frac__le__eq,axiom,
% 0.26/0.53      ! [Y3: rat,Z: rat,X3: rat,W: rat] :
% 0.26/0.53        ( ( Y3 != zero_zero_rat )
% 0.26/0.53       => ( ( Z != zero_zero_rat )
% 0.26/0.53         => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ ( divide_divide_rat @ W @ Z ) )
% 0.26/0.53            = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X3 @ Z ) @ ( times_times_rat @ W @ Y3 ) ) @ ( times_times_rat @ Y3 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % frac_le_eq
% 0.26/0.53  thf(fact_4047_power__Suc__less,axiom,
% 0.26/0.53      ! [A: real,N: nat] :
% 0.26/0.53        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.53       => ( ( ord_less_real @ A @ one_one_real )
% 0.26/0.53         => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_Suc_less
% 0.26/0.53  thf(fact_4048_power__Suc__less,axiom,
% 0.26/0.53      ! [A: rat,N: nat] :
% 0.26/0.53        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.53       => ( ( ord_less_rat @ A @ one_one_rat )
% 0.26/0.53         => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_Suc_less
% 0.26/0.53  thf(fact_4049_power__Suc__less,axiom,
% 0.26/0.53      ! [A: nat,N: nat] :
% 0.26/0.53        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.26/0.53       => ( ( ord_less_nat @ A @ one_one_nat )
% 0.26/0.53         => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_Suc_less
% 0.26/0.53  thf(fact_4050_power__Suc__less,axiom,
% 0.26/0.53      ! [A: int,N: nat] :
% 0.26/0.53        ( ( ord_less_int @ zero_zero_int @ A )
% 0.26/0.53       => ( ( ord_less_int @ A @ one_one_int )
% 0.26/0.53         => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % power_Suc_less
% 0.26/0.53  thf(fact_4051_frac__less__eq,axiom,
% 0.26/0.53      ! [Y3: real,Z: real,X3: real,W: real] :
% 0.26/0.53        ( ( Y3 != zero_zero_real )
% 0.26/0.53       => ( ( Z != zero_zero_real )
% 0.26/0.53         => ( ( ord_less_real @ ( divide_divide_real @ X3 @ Y3 ) @ ( divide_divide_real @ W @ Z ) )
% 0.26/0.53            = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X3 @ Z ) @ ( times_times_real @ W @ Y3 ) ) @ ( times_times_real @ Y3 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % frac_less_eq
% 0.26/0.53  thf(fact_4052_frac__less__eq,axiom,
% 0.26/0.53      ! [Y3: rat,Z: rat,X3: rat,W: rat] :
% 0.26/0.53        ( ( Y3 != zero_zero_rat )
% 0.26/0.53       => ( ( Z != zero_zero_rat )
% 0.26/0.53         => ( ( ord_less_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ ( divide_divide_rat @ W @ Z ) )
% 0.26/0.53            = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X3 @ Z ) @ ( times_times_rat @ W @ Y3 ) ) @ ( times_times_rat @ Y3 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % frac_less_eq
% 0.26/0.53  thf(fact_4053_mult__2,axiom,
% 0.26/0.53      ! [Z: complex] :
% 0.26/0.53        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 0.26/0.53        = ( plus_plus_complex @ Z @ Z ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_2
% 0.26/0.53  thf(fact_4054_mult__2,axiom,
% 0.26/0.53      ! [Z: real] :
% 0.26/0.53        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 0.26/0.53        = ( plus_plus_real @ Z @ Z ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_2
% 0.26/0.53  thf(fact_4055_mult__2,axiom,
% 0.26/0.53      ! [Z: rat] :
% 0.26/0.53        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 0.26/0.53        = ( plus_plus_rat @ Z @ Z ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_2
% 0.26/0.53  thf(fact_4056_mult__2,axiom,
% 0.26/0.53      ! [Z: nat] :
% 0.26/0.53        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 0.26/0.53        = ( plus_plus_nat @ Z @ Z ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_2
% 0.26/0.53  thf(fact_4057_mult__2,axiom,
% 0.26/0.53      ! [Z: int] :
% 0.26/0.53        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 0.26/0.53        = ( plus_plus_int @ Z @ Z ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_2
% 0.26/0.53  thf(fact_4058_mult__2__right,axiom,
% 0.26/0.53      ! [Z: complex] :
% 0.26/0.53        ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 0.26/0.53        = ( plus_plus_complex @ Z @ Z ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_2_right
% 0.26/0.53  thf(fact_4059_mult__2__right,axiom,
% 0.26/0.53      ! [Z: real] :
% 0.26/0.53        ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.26/0.53        = ( plus_plus_real @ Z @ Z ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_2_right
% 0.26/0.53  thf(fact_4060_mult__2__right,axiom,
% 0.26/0.53      ! [Z: rat] :
% 0.26/0.53        ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 0.26/0.53        = ( plus_plus_rat @ Z @ Z ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_2_right
% 0.26/0.53  thf(fact_4061_mult__2__right,axiom,
% 0.26/0.53      ! [Z: nat] :
% 0.26/0.53        ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.53        = ( plus_plus_nat @ Z @ Z ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_2_right
% 0.26/0.53  thf(fact_4062_mult__2__right,axiom,
% 0.26/0.53      ! [Z: int] :
% 0.26/0.53        ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.53        = ( plus_plus_int @ Z @ Z ) ) ).
% 0.26/0.53  
% 0.26/0.53  % mult_2_right
% 0.26/0.53  thf(fact_4063_left__add__twice,axiom,
% 0.26/0.53      ! [A: complex,B: complex] :
% 0.26/0.53        ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 0.26/0.53        = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.26/0.53  
% 0.26/0.53  % left_add_twice
% 0.26/0.53  thf(fact_4064_left__add__twice,axiom,
% 0.26/0.53      ! [A: real,B: real] :
% 0.26/0.53        ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.26/0.53        = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.26/0.53  
% 0.26/0.53  % left_add_twice
% 0.26/0.53  thf(fact_4065_left__add__twice,axiom,
% 0.26/0.53      ! [A: rat,B: rat] :
% 0.26/0.53        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.26/0.53        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.26/0.53  
% 0.26/0.53  % left_add_twice
% 0.26/0.53  thf(fact_4066_left__add__twice,axiom,
% 0.26/0.53      ! [A: nat,B: nat] :
% 0.26/0.53        ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.26/0.53        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.26/0.53  
% 0.26/0.53  % left_add_twice
% 0.26/0.53  thf(fact_4067_left__add__twice,axiom,
% 0.26/0.53      ! [A: int,B: int] :
% 0.26/0.53        ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.26/0.53        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.26/0.53  
% 0.26/0.53  % left_add_twice
% 0.26/0.53  thf(fact_4068_is__unit__div__mult__cancel__right,axiom,
% 0.26/0.53      ! [A: code_integer,B: code_integer] :
% 0.26/0.53        ( ( A != zero_z3403309356797280102nteger )
% 0.26/0.53       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.26/0.53         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 0.26/0.53            = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % is_unit_div_mult_cancel_right
% 0.26/0.53  thf(fact_4069_is__unit__div__mult__cancel__right,axiom,
% 0.26/0.53      ! [A: nat,B: nat] :
% 0.26/0.53        ( ( A != zero_zero_nat )
% 0.26/0.53       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.26/0.53         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 0.26/0.53            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % is_unit_div_mult_cancel_right
% 0.26/0.53  thf(fact_4070_is__unit__div__mult__cancel__right,axiom,
% 0.26/0.53      ! [A: int,B: int] :
% 0.26/0.53        ( ( A != zero_zero_int )
% 0.26/0.53       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.26/0.53         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 0.26/0.53            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % is_unit_div_mult_cancel_right
% 0.26/0.53  thf(fact_4071_is__unit__div__mult__cancel__left,axiom,
% 0.26/0.53      ! [A: code_integer,B: code_integer] :
% 0.26/0.53        ( ( A != zero_z3403309356797280102nteger )
% 0.26/0.53       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.26/0.53         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.26/0.53            = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % is_unit_div_mult_cancel_left
% 0.26/0.53  thf(fact_4072_is__unit__div__mult__cancel__left,axiom,
% 0.26/0.53      ! [A: nat,B: nat] :
% 0.26/0.53        ( ( A != zero_zero_nat )
% 0.26/0.53       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.26/0.53         => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 0.26/0.53            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % is_unit_div_mult_cancel_left
% 0.26/0.53  thf(fact_4073_is__unit__div__mult__cancel__left,axiom,
% 0.26/0.53      ! [A: int,B: int] :
% 0.26/0.53        ( ( A != zero_zero_int )
% 0.26/0.53       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.26/0.53         => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 0.26/0.53            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % is_unit_div_mult_cancel_left
% 0.26/0.53  thf(fact_4074_is__unitE,axiom,
% 0.26/0.53      ! [A: code_integer,C: code_integer] :
% 0.26/0.53        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.26/0.53       => ~ ( ( A != zero_z3403309356797280102nteger )
% 0.26/0.53           => ! [B4: code_integer] :
% 0.26/0.53                ( ( B4 != zero_z3403309356797280102nteger )
% 0.26/0.53               => ( ( dvd_dvd_Code_integer @ B4 @ one_one_Code_integer )
% 0.26/0.53                 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 0.26/0.53                      = B4 )
% 0.26/0.53                   => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B4 )
% 0.26/0.53                        = A )
% 0.26/0.53                     => ( ( ( times_3573771949741848930nteger @ A @ B4 )
% 0.26/0.53                          = one_one_Code_integer )
% 0.26/0.53                       => ( ( divide6298287555418463151nteger @ C @ A )
% 0.26/0.53                         != ( times_3573771949741848930nteger @ C @ B4 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % is_unitE
% 0.26/0.53  thf(fact_4075_is__unitE,axiom,
% 0.26/0.53      ! [A: nat,C: nat] :
% 0.26/0.53        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.26/0.53       => ~ ( ( A != zero_zero_nat )
% 0.26/0.53           => ! [B4: nat] :
% 0.26/0.53                ( ( B4 != zero_zero_nat )
% 0.26/0.53               => ( ( dvd_dvd_nat @ B4 @ one_one_nat )
% 0.26/0.53                 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 0.26/0.53                      = B4 )
% 0.26/0.53                   => ( ( ( divide_divide_nat @ one_one_nat @ B4 )
% 0.26/0.53                        = A )
% 0.26/0.53                     => ( ( ( times_times_nat @ A @ B4 )
% 0.26/0.53                          = one_one_nat )
% 0.26/0.53                       => ( ( divide_divide_nat @ C @ A )
% 0.26/0.53                         != ( times_times_nat @ C @ B4 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % is_unitE
% 0.26/0.53  thf(fact_4076_is__unitE,axiom,
% 0.26/0.53      ! [A: int,C: int] :
% 0.26/0.53        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.26/0.53       => ~ ( ( A != zero_zero_int )
% 0.26/0.53           => ! [B4: int] :
% 0.26/0.53                ( ( B4 != zero_zero_int )
% 0.26/0.53               => ( ( dvd_dvd_int @ B4 @ one_one_int )
% 0.26/0.53                 => ( ( ( divide_divide_int @ one_one_int @ A )
% 0.26/0.53                      = B4 )
% 0.26/0.53                   => ( ( ( divide_divide_int @ one_one_int @ B4 )
% 0.26/0.53                        = A )
% 0.26/0.53                     => ( ( ( times_times_int @ A @ B4 )
% 0.26/0.53                          = one_one_int )
% 0.26/0.53                       => ( ( divide_divide_int @ C @ A )
% 0.26/0.53                         != ( times_times_int @ C @ B4 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.53  
% 0.26/0.53  % is_unitE
% 0.26/0.53  thf(fact_4077_evenE,axiom,
% 0.26/0.53      ! [A: code_integer] :
% 0.26/0.53        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.53       => ~ ! [B4: code_integer] :
% 0.26/0.53              ( A
% 0.26/0.53             != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B4 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % evenE
% 0.26/0.54  thf(fact_4078_evenE,axiom,
% 0.26/0.54      ! [A: nat] :
% 0.26/0.54        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.54       => ~ ! [B4: nat] :
% 0.26/0.54              ( A
% 0.26/0.54             != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B4 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % evenE
% 0.26/0.54  thf(fact_4079_evenE,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.54       => ~ ! [B4: int] :
% 0.26/0.54              ( A
% 0.26/0.54             != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B4 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % evenE
% 0.26/0.54  thf(fact_4080_power4__eq__xxxx,axiom,
% 0.26/0.54      ! [X3: complex] :
% 0.26/0.54        ( ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.26/0.54        = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X3 @ X3 ) @ X3 ) @ X3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power4_eq_xxxx
% 0.26/0.54  thf(fact_4081_power4__eq__xxxx,axiom,
% 0.26/0.54      ! [X3: real] :
% 0.26/0.54        ( ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.26/0.54        = ( times_times_real @ ( times_times_real @ ( times_times_real @ X3 @ X3 ) @ X3 ) @ X3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power4_eq_xxxx
% 0.26/0.54  thf(fact_4082_power4__eq__xxxx,axiom,
% 0.26/0.54      ! [X3: rat] :
% 0.26/0.54        ( ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.26/0.54        = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X3 @ X3 ) @ X3 ) @ X3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power4_eq_xxxx
% 0.26/0.54  thf(fact_4083_power4__eq__xxxx,axiom,
% 0.26/0.54      ! [X3: nat] :
% 0.26/0.54        ( ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.26/0.54        = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X3 @ X3 ) @ X3 ) @ X3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power4_eq_xxxx
% 0.26/0.54  thf(fact_4084_power4__eq__xxxx,axiom,
% 0.26/0.54      ! [X3: int] :
% 0.26/0.54        ( ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.26/0.54        = ( times_times_int @ ( times_times_int @ ( times_times_int @ X3 @ X3 ) @ X3 ) @ X3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power4_eq_xxxx
% 0.26/0.54  thf(fact_4085_power2__eq__square,axiom,
% 0.26/0.54      ! [A: complex] :
% 0.26/0.54        ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.54        = ( times_times_complex @ A @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power2_eq_square
% 0.26/0.54  thf(fact_4086_power2__eq__square,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.54        = ( times_times_real @ A @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power2_eq_square
% 0.26/0.54  thf(fact_4087_power2__eq__square,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.54        = ( times_times_rat @ A @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power2_eq_square
% 0.26/0.54  thf(fact_4088_power2__eq__square,axiom,
% 0.26/0.54      ! [A: nat] :
% 0.26/0.54        ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.54        = ( times_times_nat @ A @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power2_eq_square
% 0.26/0.54  thf(fact_4089_power2__eq__square,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.54        = ( times_times_int @ A @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power2_eq_square
% 0.26/0.54  thf(fact_4090_Suc__double__not__eq__double,axiom,
% 0.26/0.54      ! [M: nat,N: nat] :
% 0.26/0.54        ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.26/0.54       != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % Suc_double_not_eq_double
% 0.26/0.54  thf(fact_4091_double__not__eq__Suc__double,axiom,
% 0.26/0.54      ! [M: nat,N: nat] :
% 0.26/0.54        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 0.26/0.54       != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % double_not_eq_Suc_double
% 0.26/0.54  thf(fact_4092_power__even__eq,axiom,
% 0.26/0.54      ! [A: nat,N: nat] :
% 0.26/0.54        ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.54        = ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power_even_eq
% 0.26/0.54  thf(fact_4093_power__even__eq,axiom,
% 0.26/0.54      ! [A: int,N: nat] :
% 0.26/0.54        ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.54        = ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power_even_eq
% 0.26/0.54  thf(fact_4094_power__even__eq,axiom,
% 0.26/0.54      ! [A: real,N: nat] :
% 0.26/0.54        ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.54        = ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power_even_eq
% 0.26/0.54  thf(fact_4095_power__even__eq,axiom,
% 0.26/0.54      ! [A: complex,N: nat] :
% 0.26/0.54        ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.54        = ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power_even_eq
% 0.26/0.54  thf(fact_4096_frac__def,axiom,
% 0.26/0.54      ( archimedean_frac_rat
% 0.26/0.54      = ( ^ [X: rat] : ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % frac_def
% 0.26/0.54  thf(fact_4097_frac__def,axiom,
% 0.26/0.54      ( archim2898591450579166408c_real
% 0.26/0.54      = ( ^ [X: real] : ( minus_minus_real @ X @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % frac_def
% 0.26/0.54  thf(fact_4098_num_Osize_I4_J,axiom,
% 0.26/0.54      ( ( size_size_num @ one )
% 0.26/0.54      = zero_zero_nat ) ).
% 0.26/0.54  
% 0.26/0.54  % num.size(4)
% 0.26/0.54  thf(fact_4099_div__nat__eqI,axiom,
% 0.26/0.54      ! [N: nat,Q3: nat,M: nat] :
% 0.26/0.54        ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q3 ) @ M )
% 0.26/0.54       => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q3 ) ) )
% 0.26/0.54         => ( ( divide_divide_nat @ M @ N )
% 0.26/0.54            = Q3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % div_nat_eqI
% 0.26/0.54  thf(fact_4100_split__div,axiom,
% 0.26/0.54      ! [P: nat > $o,M: nat,N: nat] :
% 0.26/0.54        ( ( P @ ( divide_divide_nat @ M @ N ) )
% 0.26/0.54        = ( ( ( N = zero_zero_nat )
% 0.26/0.54           => ( P @ zero_zero_nat ) )
% 0.26/0.54          & ( ( N != zero_zero_nat )
% 0.26/0.54           => ! [I4: nat,J3: nat] :
% 0.26/0.54                ( ( ord_less_nat @ J3 @ N )
% 0.26/0.54               => ( ( M
% 0.26/0.54                    = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J3 ) )
% 0.26/0.54                 => ( P @ I4 ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % split_div
% 0.26/0.54  thf(fact_4101_dividend__less__div__times,axiom,
% 0.26/0.54      ! [N: nat,M: nat] :
% 0.26/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.54       => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % dividend_less_div_times
% 0.26/0.54  thf(fact_4102_dividend__less__times__div,axiom,
% 0.26/0.54      ! [N: nat,M: nat] :
% 0.26/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.54       => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % dividend_less_times_div
% 0.26/0.54  thf(fact_4103_less__eq__div__iff__mult__less__eq,axiom,
% 0.26/0.54      ! [Q3: nat,M: nat,N: nat] :
% 0.26/0.54        ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 0.26/0.54       => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q3 ) )
% 0.26/0.54          = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q3 ) @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % less_eq_div_iff_mult_less_eq
% 0.26/0.54  thf(fact_4104_nat__less__add__iff2,axiom,
% 0.26/0.54      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.26/0.54        ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.54       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.26/0.54          = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % nat_less_add_iff2
% 0.26/0.54  thf(fact_4105_nat__less__add__iff1,axiom,
% 0.26/0.54      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.26/0.54        ( ( ord_less_eq_nat @ J @ I )
% 0.26/0.54       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.26/0.54          = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % nat_less_add_iff1
% 0.26/0.54  thf(fact_4106_mult__eq__if,axiom,
% 0.26/0.54      ( times_times_nat
% 0.26/0.54      = ( ^ [M3: nat,N3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N3 @ ( times_times_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N3 ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_eq_if
% 0.26/0.54  thf(fact_4107_dvd__mult__cancel2,axiom,
% 0.26/0.54      ! [M: nat,N: nat] :
% 0.26/0.54        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.54       => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 0.26/0.54          = ( N = one_one_nat ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % dvd_mult_cancel2
% 0.26/0.54  thf(fact_4108_dvd__mult__cancel1,axiom,
% 0.26/0.54      ! [M: nat,N: nat] :
% 0.26/0.54        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.54       => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 0.26/0.54          = ( N = one_one_nat ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % dvd_mult_cancel1
% 0.26/0.54  thf(fact_4109_dvd__minus__add,axiom,
% 0.26/0.54      ! [Q3: nat,N: nat,R2: nat,M: nat] :
% 0.26/0.54        ( ( ord_less_eq_nat @ Q3 @ N )
% 0.26/0.54       => ( ( ord_less_eq_nat @ Q3 @ ( times_times_nat @ R2 @ M ) )
% 0.26/0.54         => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q3 ) )
% 0.26/0.54            = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M ) @ Q3 ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % dvd_minus_add
% 0.26/0.54  thf(fact_4110_convex__bound__lt,axiom,
% 0.26/0.54      ! [X3: real,A: real,Y3: real,U: real,V: real] :
% 0.26/0.54        ( ( ord_less_real @ X3 @ A )
% 0.26/0.54       => ( ( ord_less_real @ Y3 @ A )
% 0.26/0.54         => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 0.26/0.54           => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 0.26/0.54             => ( ( ( plus_plus_real @ U @ V )
% 0.26/0.54                  = one_one_real )
% 0.26/0.54               => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X3 ) @ ( times_times_real @ V @ Y3 ) ) @ A ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % convex_bound_lt
% 0.26/0.54  thf(fact_4111_convex__bound__lt,axiom,
% 0.26/0.54      ! [X3: rat,A: rat,Y3: rat,U: rat,V: rat] :
% 0.26/0.54        ( ( ord_less_rat @ X3 @ A )
% 0.26/0.54       => ( ( ord_less_rat @ Y3 @ A )
% 0.26/0.54         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 0.26/0.54           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 0.26/0.54             => ( ( ( plus_plus_rat @ U @ V )
% 0.26/0.54                  = one_one_rat )
% 0.26/0.54               => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X3 ) @ ( times_times_rat @ V @ Y3 ) ) @ A ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % convex_bound_lt
% 0.26/0.54  thf(fact_4112_convex__bound__lt,axiom,
% 0.26/0.54      ! [X3: int,A: int,Y3: int,U: int,V: int] :
% 0.26/0.54        ( ( ord_less_int @ X3 @ A )
% 0.26/0.54       => ( ( ord_less_int @ Y3 @ A )
% 0.26/0.54         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.26/0.54           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 0.26/0.54             => ( ( ( plus_plus_int @ U @ V )
% 0.26/0.54                  = one_one_int )
% 0.26/0.54               => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X3 ) @ ( times_times_int @ V @ Y3 ) ) @ A ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % convex_bound_lt
% 0.26/0.54  thf(fact_4113_le__divide__eq__numeral_I1_J,axiom,
% 0.26/0.54      ! [W: num,B: real,C: real] :
% 0.26/0.54        ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 0.26/0.54        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.54           => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 0.26/0.54          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.54           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.54               => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 0.26/0.54              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.54               => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % le_divide_eq_numeral(1)
% 0.26/0.54  thf(fact_4114_le__divide__eq__numeral_I1_J,axiom,
% 0.26/0.54      ! [W: num,B: rat,C: rat] :
% 0.26/0.54        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 0.26/0.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.54           => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 0.26/0.54          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.54           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.54               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.26/0.54              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.54               => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % le_divide_eq_numeral(1)
% 0.26/0.54  thf(fact_4115_divide__le__eq__numeral_I1_J,axiom,
% 0.26/0.54      ! [B: real,C: real,W: num] :
% 0.26/0.54        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 0.26/0.54        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.54           => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 0.26/0.54          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.54           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.54               => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 0.26/0.54              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.54               => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % divide_le_eq_numeral(1)
% 0.26/0.54  thf(fact_4116_divide__le__eq__numeral_I1_J,axiom,
% 0.26/0.54      ! [B: rat,C: rat,W: num] :
% 0.26/0.54        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 0.26/0.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.54           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.26/0.54          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.54           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.54               => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 0.26/0.54              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.54               => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % divide_le_eq_numeral(1)
% 0.26/0.54  thf(fact_4117_scaling__mono,axiom,
% 0.26/0.54      ! [U: real,V: real,R2: real,S: real] :
% 0.26/0.54        ( ( ord_less_eq_real @ U @ V )
% 0.26/0.54       => ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 0.26/0.54         => ( ( ord_less_eq_real @ R2 @ S )
% 0.26/0.54           => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R2 @ ( minus_minus_real @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % scaling_mono
% 0.26/0.54  thf(fact_4118_scaling__mono,axiom,
% 0.26/0.54      ! [U: rat,V: rat,R2: rat,S: rat] :
% 0.26/0.54        ( ( ord_less_eq_rat @ U @ V )
% 0.26/0.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 0.26/0.54         => ( ( ord_less_eq_rat @ R2 @ S )
% 0.26/0.54           => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R2 @ ( minus_minus_rat @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % scaling_mono
% 0.26/0.54  thf(fact_4119_frac__eq,axiom,
% 0.26/0.54      ! [X3: real] :
% 0.26/0.54        ( ( ( archim2898591450579166408c_real @ X3 )
% 0.26/0.54          = X3 )
% 0.26/0.54        = ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.54          & ( ord_less_real @ X3 @ one_one_real ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % frac_eq
% 0.26/0.54  thf(fact_4120_frac__eq,axiom,
% 0.26/0.54      ! [X3: rat] :
% 0.26/0.54        ( ( ( archimedean_frac_rat @ X3 )
% 0.26/0.54          = X3 )
% 0.26/0.54        = ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.26/0.54          & ( ord_less_rat @ X3 @ one_one_rat ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % frac_eq
% 0.26/0.54  thf(fact_4121_even__two__times__div__two,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.54       => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 0.26/0.54          = A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % even_two_times_div_two
% 0.26/0.54  thf(fact_4122_even__two__times__div__two,axiom,
% 0.26/0.54      ! [A: nat] :
% 0.26/0.54        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.54       => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.54          = A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % even_two_times_div_two
% 0.26/0.54  thf(fact_4123_even__two__times__div__two,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.54       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.26/0.54          = A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % even_two_times_div_two
% 0.26/0.54  thf(fact_4124_frac__add,axiom,
% 0.26/0.54      ! [X3: real,Y3: real] :
% 0.26/0.54        ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X3 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real )
% 0.26/0.54         => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X3 @ Y3 ) )
% 0.26/0.54            = ( plus_plus_real @ ( archim2898591450579166408c_real @ X3 ) @ ( archim2898591450579166408c_real @ Y3 ) ) ) )
% 0.26/0.54        & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X3 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real )
% 0.26/0.54         => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X3 @ Y3 ) )
% 0.26/0.54            = ( minus_minus_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X3 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % frac_add
% 0.26/0.54  thf(fact_4125_frac__add,axiom,
% 0.26/0.54      ! [X3: rat,Y3: rat] :
% 0.26/0.54        ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X3 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat )
% 0.26/0.54         => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X3 @ Y3 ) )
% 0.26/0.54            = ( plus_plus_rat @ ( archimedean_frac_rat @ X3 ) @ ( archimedean_frac_rat @ Y3 ) ) ) )
% 0.26/0.54        & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X3 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat )
% 0.26/0.54         => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X3 @ Y3 ) )
% 0.26/0.54            = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X3 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % frac_add
% 0.26/0.54  thf(fact_4126_take__bit__Suc__bit0,axiom,
% 0.26/0.54      ! [N: nat,K: num] :
% 0.26/0.54        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 0.26/0.54        = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % take_bit_Suc_bit0
% 0.26/0.54  thf(fact_4127_take__bit__Suc__bit0,axiom,
% 0.26/0.54      ! [N: nat,K: num] :
% 0.26/0.54        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.26/0.54        = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % take_bit_Suc_bit0
% 0.26/0.54  thf(fact_4128_power__eq__if,axiom,
% 0.26/0.54      ( power_power_complex
% 0.26/0.54      = ( ^ [P5: complex,M3: nat] : ( if_complex @ ( M3 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P5 @ ( power_power_complex @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power_eq_if
% 0.26/0.54  thf(fact_4129_power__eq__if,axiom,
% 0.26/0.54      ( power_power_real
% 0.26/0.54      = ( ^ [P5: real,M3: nat] : ( if_real @ ( M3 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P5 @ ( power_power_real @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power_eq_if
% 0.26/0.54  thf(fact_4130_power__eq__if,axiom,
% 0.26/0.54      ( power_power_rat
% 0.26/0.54      = ( ^ [P5: rat,M3: nat] : ( if_rat @ ( M3 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P5 @ ( power_power_rat @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power_eq_if
% 0.26/0.54  thf(fact_4131_power__eq__if,axiom,
% 0.26/0.54      ( power_power_nat
% 0.26/0.54      = ( ^ [P5: nat,M3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P5 @ ( power_power_nat @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power_eq_if
% 0.26/0.54  thf(fact_4132_power__eq__if,axiom,
% 0.26/0.54      ( power_power_int
% 0.26/0.54      = ( ^ [P5: int,M3: nat] : ( if_int @ ( M3 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P5 @ ( power_power_int @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power_eq_if
% 0.26/0.54  thf(fact_4133_power__minus__mult,axiom,
% 0.26/0.54      ! [N: nat,A: complex] :
% 0.26/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.54       => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.26/0.54          = ( power_power_complex @ A @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power_minus_mult
% 0.26/0.54  thf(fact_4134_power__minus__mult,axiom,
% 0.26/0.54      ! [N: nat,A: real] :
% 0.26/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.54       => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.26/0.54          = ( power_power_real @ A @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power_minus_mult
% 0.26/0.54  thf(fact_4135_power__minus__mult,axiom,
% 0.26/0.54      ! [N: nat,A: rat] :
% 0.26/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.54       => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.26/0.54          = ( power_power_rat @ A @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power_minus_mult
% 0.26/0.54  thf(fact_4136_power__minus__mult,axiom,
% 0.26/0.54      ! [N: nat,A: nat] :
% 0.26/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.54       => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.26/0.54          = ( power_power_nat @ A @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power_minus_mult
% 0.26/0.54  thf(fact_4137_power__minus__mult,axiom,
% 0.26/0.54      ! [N: nat,A: int] :
% 0.26/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.54       => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.26/0.54          = ( power_power_int @ A @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power_minus_mult
% 0.26/0.54  thf(fact_4138_split__div_H,axiom,
% 0.26/0.54      ! [P: nat > $o,M: nat,N: nat] :
% 0.26/0.54        ( ( P @ ( divide_divide_nat @ M @ N ) )
% 0.26/0.54        = ( ( ( N = zero_zero_nat )
% 0.26/0.54            & ( P @ zero_zero_nat ) )
% 0.26/0.54          | ? [Q5: nat] :
% 0.26/0.54              ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q5 ) @ M )
% 0.26/0.54              & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q5 ) ) )
% 0.26/0.54              & ( P @ Q5 ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % split_div'
% 0.26/0.54  thf(fact_4139_oddE,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.54       => ~ ! [B4: code_integer] :
% 0.26/0.54              ( A
% 0.26/0.54             != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B4 ) @ one_one_Code_integer ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % oddE
% 0.26/0.54  thf(fact_4140_oddE,axiom,
% 0.26/0.54      ! [A: nat] :
% 0.26/0.54        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.54       => ~ ! [B4: nat] :
% 0.26/0.54              ( A
% 0.26/0.54             != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B4 ) @ one_one_nat ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % oddE
% 0.26/0.54  thf(fact_4141_oddE,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.54       => ~ ! [B4: int] :
% 0.26/0.54              ( A
% 0.26/0.54             != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B4 ) @ one_one_int ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % oddE
% 0.26/0.54  thf(fact_4142_power2__sum,axiom,
% 0.26/0.54      ! [X3: complex,Y3: complex] :
% 0.26/0.54        ( ( power_power_complex @ ( plus_plus_complex @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.54        = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) @ Y3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power2_sum
% 0.26/0.54  thf(fact_4143_power2__sum,axiom,
% 0.26/0.54      ! [X3: real,Y3: real] :
% 0.26/0.54        ( ( power_power_real @ ( plus_plus_real @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.54        = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) @ Y3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power2_sum
% 0.26/0.54  thf(fact_4144_power2__sum,axiom,
% 0.26/0.54      ! [X3: rat,Y3: rat] :
% 0.26/0.54        ( ( power_power_rat @ ( plus_plus_rat @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.54        = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X3 ) @ Y3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power2_sum
% 0.26/0.54  thf(fact_4145_power2__sum,axiom,
% 0.26/0.54      ! [X3: nat,Y3: nat] :
% 0.26/0.54        ( ( power_power_nat @ ( plus_plus_nat @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.54        = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X3 ) @ Y3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power2_sum
% 0.26/0.54  thf(fact_4146_power2__sum,axiom,
% 0.26/0.54      ! [X3: int,Y3: int] :
% 0.26/0.54        ( ( power_power_int @ ( plus_plus_int @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.54        = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 ) @ Y3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power2_sum
% 0.26/0.54  thf(fact_4147_zero__le__even__power_H,axiom,
% 0.26/0.54      ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % zero_le_even_power'
% 0.26/0.54  thf(fact_4148_zero__le__even__power_H,axiom,
% 0.26/0.54      ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % zero_le_even_power'
% 0.26/0.54  thf(fact_4149_zero__le__even__power_H,axiom,
% 0.26/0.54      ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % zero_le_even_power'
% 0.26/0.54  thf(fact_4150_nat__bit__induct,axiom,
% 0.26/0.54      ! [P: nat > $o,N: nat] :
% 0.26/0.54        ( ( P @ zero_zero_nat )
% 0.26/0.54       => ( ! [N2: nat] :
% 0.26/0.54              ( ( P @ N2 )
% 0.26/0.54             => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.26/0.54               => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.26/0.54         => ( ! [N2: nat] :
% 0.26/0.54                ( ( P @ N2 )
% 0.26/0.54               => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.26/0.54           => ( P @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % nat_bit_induct
% 0.26/0.54  thf(fact_4151_floor__divide__lower,axiom,
% 0.26/0.54      ! [Q3: rat,P6: rat] :
% 0.26/0.54        ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 0.26/0.54       => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P6 @ Q3 ) ) ) @ Q3 ) @ P6 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % floor_divide_lower
% 0.26/0.54  thf(fact_4152_floor__divide__lower,axiom,
% 0.26/0.54      ! [Q3: real,P6: real] :
% 0.26/0.54        ( ( ord_less_real @ zero_zero_real @ Q3 )
% 0.26/0.54       => ( ord_less_eq_real @ ( times_times_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P6 @ Q3 ) ) ) @ Q3 ) @ P6 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % floor_divide_lower
% 0.26/0.54  thf(fact_4153_ceiling__divide__upper,axiom,
% 0.26/0.54      ! [Q3: real,P6: real] :
% 0.26/0.54        ( ( ord_less_real @ zero_zero_real @ Q3 )
% 0.26/0.54       => ( ord_less_eq_real @ P6 @ ( times_times_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P6 @ Q3 ) ) ) @ Q3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % ceiling_divide_upper
% 0.26/0.54  thf(fact_4154_ceiling__divide__upper,axiom,
% 0.26/0.54      ! [Q3: rat,P6: rat] :
% 0.26/0.54        ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 0.26/0.54       => ( ord_less_eq_rat @ P6 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P6 @ Q3 ) ) ) @ Q3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % ceiling_divide_upper
% 0.26/0.54  thf(fact_4155_vebt__buildup_Ocases,axiom,
% 0.26/0.54      ! [X3: nat] :
% 0.26/0.54        ( ( X3 != zero_zero_nat )
% 0.26/0.54       => ( ( X3
% 0.26/0.54           != ( suc @ zero_zero_nat ) )
% 0.26/0.54         => ~ ! [Va: nat] :
% 0.26/0.54                ( X3
% 0.26/0.54               != ( suc @ ( suc @ Va ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % vebt_buildup.cases
% 0.26/0.54  thf(fact_4156_option_Osize_I4_J,axiom,
% 0.26/0.54      ! [X2: nat] :
% 0.26/0.54        ( ( size_size_option_nat @ ( some_nat @ X2 ) )
% 0.26/0.54        = ( suc @ zero_zero_nat ) ) ).
% 0.26/0.54  
% 0.26/0.54  % option.size(4)
% 0.26/0.54  thf(fact_4157_option_Osize_I4_J,axiom,
% 0.26/0.54      ! [X2: product_prod_nat_nat] :
% 0.26/0.54        ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X2 ) )
% 0.26/0.54        = ( suc @ zero_zero_nat ) ) ).
% 0.26/0.54  
% 0.26/0.54  % option.size(4)
% 0.26/0.54  thf(fact_4158_option_Osize_I4_J,axiom,
% 0.26/0.54      ! [X2: num] :
% 0.26/0.54        ( ( size_size_option_num @ ( some_num @ X2 ) )
% 0.26/0.54        = ( suc @ zero_zero_nat ) ) ).
% 0.26/0.54  
% 0.26/0.54  % option.size(4)
% 0.26/0.54  thf(fact_4159_sum__squares__bound,axiom,
% 0.26/0.54      ! [X3: real,Y3: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) @ Y3 ) @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % sum_squares_bound
% 0.26/0.54  thf(fact_4160_sum__squares__bound,axiom,
% 0.26/0.54      ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X3 ) @ Y3 ) @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % sum_squares_bound
% 0.26/0.54  thf(fact_4161_power2__diff,axiom,
% 0.26/0.54      ! [X3: complex,Y3: complex] :
% 0.26/0.54        ( ( power_power_complex @ ( minus_minus_complex @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.54        = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) @ Y3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power2_diff
% 0.26/0.54  thf(fact_4162_power2__diff,axiom,
% 0.26/0.54      ! [X3: real,Y3: real] :
% 0.26/0.54        ( ( power_power_real @ ( minus_minus_real @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.54        = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) @ Y3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power2_diff
% 0.26/0.54  thf(fact_4163_power2__diff,axiom,
% 0.26/0.54      ! [X3: rat,Y3: rat] :
% 0.26/0.54        ( ( power_power_rat @ ( minus_minus_rat @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.54        = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X3 ) @ Y3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power2_diff
% 0.26/0.54  thf(fact_4164_power2__diff,axiom,
% 0.26/0.54      ! [X3: int,Y3: int] :
% 0.26/0.54        ( ( power_power_int @ ( minus_minus_int @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.54        = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 ) @ Y3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power2_diff
% 0.26/0.54  thf(fact_4165_odd__0__le__power__imp__0__le,axiom,
% 0.26/0.54      ! [A: real,N: nat] :
% 0.26/0.54        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.26/0.54       => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % odd_0_le_power_imp_0_le
% 0.26/0.54  thf(fact_4166_odd__0__le__power__imp__0__le,axiom,
% 0.26/0.54      ! [A: rat,N: nat] :
% 0.26/0.54        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.26/0.54       => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % odd_0_le_power_imp_0_le
% 0.26/0.54  thf(fact_4167_odd__0__le__power__imp__0__le,axiom,
% 0.26/0.54      ! [A: int,N: nat] :
% 0.26/0.54        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.26/0.54       => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % odd_0_le_power_imp_0_le
% 0.26/0.54  thf(fact_4168_odd__power__less__zero,axiom,
% 0.26/0.54      ! [A: real,N: nat] :
% 0.26/0.54        ( ( ord_less_real @ A @ zero_zero_real )
% 0.26/0.54       => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 0.26/0.54  
% 0.26/0.54  % odd_power_less_zero
% 0.26/0.54  thf(fact_4169_odd__power__less__zero,axiom,
% 0.26/0.54      ! [A: rat,N: nat] :
% 0.26/0.54        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.26/0.54       => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 0.26/0.54  
% 0.26/0.54  % odd_power_less_zero
% 0.26/0.54  thf(fact_4170_odd__power__less__zero,axiom,
% 0.26/0.54      ! [A: int,N: nat] :
% 0.26/0.54        ( ( ord_less_int @ A @ zero_zero_int )
% 0.26/0.54       => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 0.26/0.54  
% 0.26/0.54  % odd_power_less_zero
% 0.26/0.54  thf(fact_4171_floor__divide__upper,axiom,
% 0.26/0.54      ! [Q3: rat,P6: rat] :
% 0.26/0.54        ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 0.26/0.54       => ( ord_less_rat @ P6 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P6 @ Q3 ) ) ) @ one_one_rat ) @ Q3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % floor_divide_upper
% 0.26/0.54  thf(fact_4172_floor__divide__upper,axiom,
% 0.26/0.54      ! [Q3: real,P6: real] :
% 0.26/0.54        ( ( ord_less_real @ zero_zero_real @ Q3 )
% 0.26/0.54       => ( ord_less_real @ P6 @ ( times_times_real @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P6 @ Q3 ) ) ) @ one_one_real ) @ Q3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % floor_divide_upper
% 0.26/0.54  thf(fact_4173_ceiling__divide__lower,axiom,
% 0.26/0.54      ! [Q3: real,P6: real] :
% 0.26/0.54        ( ( ord_less_real @ zero_zero_real @ Q3 )
% 0.26/0.54       => ( ord_less_real @ ( times_times_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P6 @ Q3 ) ) ) @ one_one_real ) @ Q3 ) @ P6 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % ceiling_divide_lower
% 0.26/0.54  thf(fact_4174_ceiling__divide__lower,axiom,
% 0.26/0.54      ! [Q3: rat,P6: rat] :
% 0.26/0.54        ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 0.26/0.54       => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P6 @ Q3 ) ) ) @ one_one_rat ) @ Q3 ) @ P6 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % ceiling_divide_lower
% 0.26/0.54  thf(fact_4175_floor__add,axiom,
% 0.26/0.54      ! [X3: rat,Y3: rat] :
% 0.26/0.54        ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X3 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat )
% 0.26/0.54         => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X3 @ Y3 ) )
% 0.26/0.54            = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X3 ) @ ( archim3151403230148437115or_rat @ Y3 ) ) ) )
% 0.26/0.54        & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X3 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat )
% 0.26/0.54         => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X3 @ Y3 ) )
% 0.26/0.54            = ( plus_plus_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X3 ) @ ( archim3151403230148437115or_rat @ Y3 ) ) @ one_one_int ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % floor_add
% 0.26/0.54  thf(fact_4176_floor__add,axiom,
% 0.26/0.54      ! [X3: real,Y3: real] :
% 0.26/0.54        ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X3 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real )
% 0.26/0.54         => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X3 @ Y3 ) )
% 0.26/0.54            = ( plus_plus_int @ ( archim6058952711729229775r_real @ X3 ) @ ( archim6058952711729229775r_real @ Y3 ) ) ) )
% 0.26/0.54        & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X3 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real )
% 0.26/0.54         => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X3 @ Y3 ) )
% 0.26/0.54            = ( plus_plus_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X3 ) @ ( archim6058952711729229775r_real @ Y3 ) ) @ one_one_int ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % floor_add
% 0.26/0.54  thf(fact_4177_num_Osize_I5_J,axiom,
% 0.26/0.54      ! [X2: num] :
% 0.26/0.54        ( ( size_size_num @ ( bit0 @ X2 ) )
% 0.26/0.54        = ( plus_plus_nat @ ( size_size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % num.size(5)
% 0.26/0.54  thf(fact_4178_arith__geo__mean,axiom,
% 0.26/0.54      ! [U: real,X3: real,Y3: real] :
% 0.26/0.54        ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.54          = ( times_times_real @ X3 @ Y3 ) )
% 0.26/0.54       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.54         => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.54           => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X3 @ Y3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % arith_geo_mean
% 0.26/0.54  thf(fact_4179_arith__geo__mean,axiom,
% 0.26/0.54      ! [U: rat,X3: rat,Y3: rat] :
% 0.26/0.54        ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.54          = ( times_times_rat @ X3 @ Y3 ) )
% 0.26/0.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.26/0.54         => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 0.26/0.54           => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X3 @ Y3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % arith_geo_mean
% 0.26/0.54  thf(fact_4180_even__mult__exp__div__exp__iff,axiom,
% 0.26/0.54      ! [A: code_integer,M: nat,N: nat] :
% 0.26/0.54        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 0.26/0.54        = ( ( ord_less_nat @ N @ M )
% 0.26/0.54          | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 0.26/0.54            = zero_z3403309356797280102nteger )
% 0.26/0.54          | ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.54            & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % even_mult_exp_div_exp_iff
% 0.26/0.54  thf(fact_4181_even__mult__exp__div__exp__iff,axiom,
% 0.26/0.54      ! [A: nat,M: nat,N: nat] :
% 0.26/0.54        ( ( 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 ) ) )
% 0.26/0.54        = ( ( ord_less_nat @ N @ M )
% 0.26/0.54          | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.54            = zero_zero_nat )
% 0.26/0.54          | ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.54            & ( 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 ) ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % even_mult_exp_div_exp_iff
% 0.26/0.54  thf(fact_4182_even__mult__exp__div__exp__iff,axiom,
% 0.26/0.54      ! [A: int,M: nat,N: nat] :
% 0.26/0.54        ( ( 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 ) ) )
% 0.26/0.54        = ( ( ord_less_nat @ N @ M )
% 0.26/0.54          | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.26/0.54            = zero_zero_int )
% 0.26/0.54          | ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.54            & ( 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 ) ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % even_mult_exp_div_exp_iff
% 0.26/0.54  thf(fact_4183_of__real__of__int__eq,axiom,
% 0.26/0.54      ! [Z: int] :
% 0.26/0.54        ( ( real_V1803761363581548252l_real @ ( ring_1_of_int_real @ Z ) )
% 0.26/0.54        = ( ring_1_of_int_real @ Z ) ) ).
% 0.26/0.54  
% 0.26/0.54  % of_real_of_int_eq
% 0.26/0.54  thf(fact_4184_of__real__of__int__eq,axiom,
% 0.26/0.54      ! [Z: int] :
% 0.26/0.54        ( ( real_V4546457046886955230omplex @ ( ring_1_of_int_real @ Z ) )
% 0.26/0.54        = ( ring_17405671764205052669omplex @ Z ) ) ).
% 0.26/0.54  
% 0.26/0.54  % of_real_of_int_eq
% 0.26/0.54  thf(fact_4185_of__real__of__nat__eq,axiom,
% 0.26/0.54      ! [N: nat] :
% 0.26/0.54        ( ( real_V4546457046886955230omplex @ ( semiri5074537144036343181t_real @ N ) )
% 0.26/0.54        = ( semiri8010041392384452111omplex @ N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % of_real_of_nat_eq
% 0.26/0.54  thf(fact_4186_of__real__of__nat__eq,axiom,
% 0.26/0.54      ! [N: nat] :
% 0.26/0.54        ( ( real_V1803761363581548252l_real @ ( semiri5074537144036343181t_real @ N ) )
% 0.26/0.54        = ( semiri5074537144036343181t_real @ N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % of_real_of_nat_eq
% 0.26/0.54  thf(fact_4187_of__real__power,axiom,
% 0.26/0.54      ! [X3: real,N: nat] :
% 0.26/0.54        ( ( real_V1803761363581548252l_real @ ( power_power_real @ X3 @ N ) )
% 0.26/0.54        = ( power_power_real @ ( real_V1803761363581548252l_real @ X3 ) @ N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % of_real_power
% 0.26/0.54  thf(fact_4188_of__real__power,axiom,
% 0.26/0.54      ! [X3: real,N: nat] :
% 0.26/0.54        ( ( real_V4546457046886955230omplex @ ( power_power_real @ X3 @ N ) )
% 0.26/0.54        = ( power_power_complex @ ( real_V4546457046886955230omplex @ X3 ) @ N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % of_real_power
% 0.26/0.54  thf(fact_4189_of__real__numeral,axiom,
% 0.26/0.54      ! [W: num] :
% 0.26/0.54        ( ( real_V1803761363581548252l_real @ ( numeral_numeral_real @ W ) )
% 0.26/0.54        = ( numeral_numeral_real @ W ) ) ).
% 0.26/0.54  
% 0.26/0.54  % of_real_numeral
% 0.26/0.54  thf(fact_4190_of__real__numeral,axiom,
% 0.26/0.54      ! [W: num] :
% 0.26/0.54        ( ( real_V4546457046886955230omplex @ ( numeral_numeral_real @ W ) )
% 0.26/0.54        = ( numera6690914467698888265omplex @ W ) ) ).
% 0.26/0.54  
% 0.26/0.54  % of_real_numeral
% 0.26/0.54  thf(fact_4191_of__real__0,axiom,
% 0.26/0.54      ( ( real_V1803761363581548252l_real @ zero_zero_real )
% 0.26/0.54      = zero_zero_real ) ).
% 0.26/0.54  
% 0.26/0.54  % of_real_0
% 0.26/0.54  thf(fact_4192_of__real__0,axiom,
% 0.26/0.54      ( ( real_V4546457046886955230omplex @ zero_zero_real )
% 0.26/0.54      = zero_zero_complex ) ).
% 0.26/0.54  
% 0.26/0.54  % of_real_0
% 0.26/0.54  thf(fact_4193_of__real__eq__0__iff,axiom,
% 0.26/0.54      ! [X3: real] :
% 0.26/0.54        ( ( ( real_V1803761363581548252l_real @ X3 )
% 0.26/0.54          = zero_zero_real )
% 0.26/0.54        = ( X3 = zero_zero_real ) ) ).
% 0.26/0.54  
% 0.26/0.54  % of_real_eq_0_iff
% 0.26/0.54  thf(fact_4194_of__real__eq__0__iff,axiom,
% 0.26/0.54      ! [X3: real] :
% 0.26/0.54        ( ( ( real_V4546457046886955230omplex @ X3 )
% 0.26/0.54          = zero_zero_complex )
% 0.26/0.54        = ( X3 = zero_zero_real ) ) ).
% 0.26/0.54  
% 0.26/0.54  % of_real_eq_0_iff
% 0.26/0.54  thf(fact_4195_mul__def,axiom,
% 0.26/0.54      ( vEBT_VEBT_mul
% 0.26/0.54      = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mul_def
% 0.26/0.54  thf(fact_4196_mul__shift,axiom,
% 0.26/0.54      ! [X3: nat,Y3: nat,Z: nat] :
% 0.26/0.54        ( ( ( times_times_nat @ X3 @ Y3 )
% 0.26/0.54          = Z )
% 0.26/0.54        = ( ( vEBT_VEBT_mul @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) )
% 0.26/0.54          = ( some_nat @ Z ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mul_shift
% 0.26/0.54  thf(fact_4197_real__divide__square__eq,axiom,
% 0.26/0.54      ! [R2: real,A: real] :
% 0.26/0.54        ( ( divide_divide_real @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ R2 ) )
% 0.26/0.54        = ( divide_divide_real @ A @ R2 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % real_divide_square_eq
% 0.26/0.54  thf(fact_4198_not__real__square__gt__zero,axiom,
% 0.26/0.54      ! [X3: real] :
% 0.26/0.54        ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X3 @ X3 ) ) )
% 0.26/0.54        = ( X3 = zero_zero_real ) ) ).
% 0.26/0.54  
% 0.26/0.54  % not_real_square_gt_zero
% 0.26/0.54  thf(fact_4199_semiring__norm_I13_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.26/0.54        = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(13)
% 0.26/0.54  thf(fact_4200_semiring__norm_I11_J,axiom,
% 0.26/0.54      ! [M: num] :
% 0.26/0.54        ( ( times_times_num @ M @ one )
% 0.26/0.54        = M ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(11)
% 0.26/0.54  thf(fact_4201_semiring__norm_I12_J,axiom,
% 0.26/0.54      ! [N: num] :
% 0.26/0.54        ( ( times_times_num @ one @ N )
% 0.26/0.54        = N ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(12)
% 0.26/0.54  thf(fact_4202_num__double,axiom,
% 0.26/0.54      ! [N: num] :
% 0.26/0.54        ( ( times_times_num @ ( bit0 @ one ) @ N )
% 0.26/0.54        = ( bit0 @ N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % num_double
% 0.26/0.54  thf(fact_4203_power__mult__numeral,axiom,
% 0.26/0.54      ! [A: nat,M: num,N: num] :
% 0.26/0.54        ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 0.26/0.54        = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power_mult_numeral
% 0.26/0.54  thf(fact_4204_power__mult__numeral,axiom,
% 0.26/0.54      ! [A: int,M: num,N: num] :
% 0.26/0.54        ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 0.26/0.54        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power_mult_numeral
% 0.26/0.54  thf(fact_4205_power__mult__numeral,axiom,
% 0.26/0.54      ! [A: real,M: num,N: num] :
% 0.26/0.54        ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 0.26/0.54        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power_mult_numeral
% 0.26/0.54  thf(fact_4206_power__mult__numeral,axiom,
% 0.26/0.54      ! [A: complex,M: num,N: num] :
% 0.26/0.54        ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 0.26/0.54        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % power_mult_numeral
% 0.26/0.54  thf(fact_4207_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 0.26/0.54      ! [X3: real,Y3: real,Xa: real,Ya: real] :
% 0.26/0.54        ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.54        = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % real_sqrt_sum_squares_mult_squared_eq
% 0.26/0.54  thf(fact_4208_times__int__code_I2_J,axiom,
% 0.26/0.54      ! [L: int] :
% 0.26/0.54        ( ( times_times_int @ zero_zero_int @ L )
% 0.26/0.54        = zero_zero_int ) ).
% 0.26/0.54  
% 0.26/0.54  % times_int_code(2)
% 0.26/0.54  thf(fact_4209_times__int__code_I1_J,axiom,
% 0.26/0.54      ! [K: int] :
% 0.26/0.54        ( ( times_times_int @ K @ zero_zero_int )
% 0.26/0.54        = zero_zero_int ) ).
% 0.26/0.54  
% 0.26/0.54  % times_int_code(1)
% 0.26/0.54  thf(fact_4210_int__distrib_I1_J,axiom,
% 0.26/0.54      ! [Z1: int,Z22: int,W: int] :
% 0.26/0.54        ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W )
% 0.26/0.54        = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % int_distrib(1)
% 0.26/0.54  thf(fact_4211_int__distrib_I2_J,axiom,
% 0.26/0.54      ! [W: int,Z1: int,Z22: int] :
% 0.26/0.54        ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z22 ) )
% 0.26/0.54        = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % int_distrib(2)
% 0.26/0.54  thf(fact_4212_int__distrib_I3_J,axiom,
% 0.26/0.54      ! [Z1: int,Z22: int,W: int] :
% 0.26/0.54        ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W )
% 0.26/0.54        = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % int_distrib(3)
% 0.26/0.54  thf(fact_4213_int__distrib_I4_J,axiom,
% 0.26/0.54      ! [W: int,Z1: int,Z22: int] :
% 0.26/0.54        ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z22 ) )
% 0.26/0.54        = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % int_distrib(4)
% 0.26/0.54  thf(fact_4214_real__sqrt__mult,axiom,
% 0.26/0.54      ! [X3: real,Y3: real] :
% 0.26/0.54        ( ( sqrt @ ( times_times_real @ X3 @ Y3 ) )
% 0.26/0.54        = ( times_times_real @ ( sqrt @ X3 ) @ ( sqrt @ Y3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % real_sqrt_mult
% 0.26/0.54  thf(fact_4215_take__bit__mult,axiom,
% 0.26/0.54      ! [N: nat,K: int,L: int] :
% 0.26/0.54        ( ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L ) ) )
% 0.26/0.54        = ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ K @ L ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % take_bit_mult
% 0.26/0.54  thf(fact_4216_imult__is__0,axiom,
% 0.26/0.54      ! [M: extended_enat,N: extended_enat] :
% 0.26/0.54        ( ( ( times_7803423173614009249d_enat @ M @ N )
% 0.26/0.54          = zero_z5237406670263579293d_enat )
% 0.26/0.54        = ( ( M = zero_z5237406670263579293d_enat )
% 0.26/0.54          | ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % imult_is_0
% 0.26/0.54  thf(fact_4217_div__mult2__numeral__eq,axiom,
% 0.26/0.54      ! [A: nat,K: num,L: num] :
% 0.26/0.54        ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L ) )
% 0.26/0.54        = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % div_mult2_numeral_eq
% 0.26/0.54  thf(fact_4218_div__mult2__numeral__eq,axiom,
% 0.26/0.54      ! [A: int,K: num,L: num] :
% 0.26/0.54        ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L ) )
% 0.26/0.54        = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % div_mult2_numeral_eq
% 0.26/0.54  thf(fact_4219_zmult__zless__mono2,axiom,
% 0.26/0.54      ! [I: int,J: int,K: int] :
% 0.26/0.54        ( ( ord_less_int @ I @ J )
% 0.26/0.54       => ( ( ord_less_int @ zero_zero_int @ K )
% 0.26/0.54         => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % zmult_zless_mono2
% 0.26/0.54  thf(fact_4220_int__ops_I7_J,axiom,
% 0.26/0.54      ! [A: nat,B: nat] :
% 0.26/0.54        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 0.26/0.54        = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % int_ops(7)
% 0.26/0.54  thf(fact_4221_zdvd__mult__cancel,axiom,
% 0.26/0.54      ! [K: int,M: int,N: int] :
% 0.26/0.54        ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) )
% 0.26/0.54       => ( ( K != zero_zero_int )
% 0.26/0.54         => ( dvd_dvd_int @ M @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % zdvd_mult_cancel
% 0.26/0.54  thf(fact_4222_zdvd__mono,axiom,
% 0.26/0.54      ! [K: int,M: int,T: int] :
% 0.26/0.54        ( ( K != zero_zero_int )
% 0.26/0.54       => ( ( dvd_dvd_int @ M @ T )
% 0.26/0.54          = ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ T ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % zdvd_mono
% 0.26/0.54  thf(fact_4223_zdvd__period,axiom,
% 0.26/0.54      ! [A: int,D3: int,X3: int,T: int,C: int] :
% 0.26/0.54        ( ( dvd_dvd_int @ A @ D3 )
% 0.26/0.54       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X3 @ T ) )
% 0.26/0.54          = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X3 @ ( times_times_int @ C @ D3 ) ) @ T ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % zdvd_period
% 0.26/0.54  thf(fact_4224_zdvd__reduce,axiom,
% 0.26/0.54      ! [K: int,N: int,M: int] :
% 0.26/0.54        ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) )
% 0.26/0.54        = ( dvd_dvd_int @ K @ N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % zdvd_reduce
% 0.26/0.54  thf(fact_4225_enat__0__less__mult__iff,axiom,
% 0.26/0.54      ! [M: extended_enat,N: extended_enat] :
% 0.26/0.54        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N ) )
% 0.26/0.54        = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 0.26/0.54          & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % enat_0_less_mult_iff
% 0.26/0.54  thf(fact_4226_reals__Archimedean3,axiom,
% 0.26/0.54      ! [X3: real] :
% 0.26/0.54        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.54       => ! [Y6: real] :
% 0.26/0.54          ? [N2: nat] : ( ord_less_real @ Y6 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % reals_Archimedean3
% 0.26/0.54  thf(fact_4227_pos__zmult__eq__1__iff,axiom,
% 0.26/0.54      ! [M: int,N: int] :
% 0.26/0.54        ( ( ord_less_int @ zero_zero_int @ M )
% 0.26/0.54       => ( ( ( times_times_int @ M @ N )
% 0.26/0.54            = one_one_int )
% 0.26/0.54          = ( ( M = one_one_int )
% 0.26/0.54            & ( N = one_one_int ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % pos_zmult_eq_1_iff
% 0.26/0.54  thf(fact_4228_powr__mult,axiom,
% 0.26/0.54      ! [X3: real,Y3: real,A: real] :
% 0.26/0.54        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.54       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.54         => ( ( powr_real @ ( times_times_real @ X3 @ Y3 ) @ A )
% 0.26/0.54            = ( times_times_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ Y3 @ A ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % powr_mult
% 0.26/0.54  thf(fact_4229_minusinfinity,axiom,
% 0.26/0.54      ! [D3: int,P1: int > $o,P: int > $o] :
% 0.26/0.54        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.26/0.54       => ( ! [X4: int,K2: int] :
% 0.26/0.54              ( ( P1 @ X4 )
% 0.26/0.54              = ( P1 @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 0.26/0.54         => ( ? [Z4: int] :
% 0.26/0.54              ! [X4: int] :
% 0.26/0.54                ( ( ord_less_int @ X4 @ Z4 )
% 0.26/0.54               => ( ( P @ X4 )
% 0.26/0.54                  = ( P1 @ X4 ) ) )
% 0.26/0.54           => ( ? [X_12: int] : ( P1 @ X_12 )
% 0.26/0.54             => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % minusinfinity
% 0.26/0.54  thf(fact_4230_plusinfinity,axiom,
% 0.26/0.54      ! [D3: int,P4: int > $o,P: int > $o] :
% 0.26/0.54        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.26/0.54       => ( ! [X4: int,K2: int] :
% 0.26/0.54              ( ( P4 @ X4 )
% 0.26/0.54              = ( P4 @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 0.26/0.54         => ( ? [Z4: int] :
% 0.26/0.54              ! [X4: int] :
% 0.26/0.54                ( ( ord_less_int @ Z4 @ X4 )
% 0.26/0.54               => ( ( P @ X4 )
% 0.26/0.54                  = ( P4 @ X4 ) ) )
% 0.26/0.54           => ( ? [X_12: int] : ( P4 @ X_12 )
% 0.26/0.54             => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % plusinfinity
% 0.26/0.54  thf(fact_4231_zdiv__zmult2__eq,axiom,
% 0.26/0.54      ! [C: int,A: int,B: int] :
% 0.26/0.54        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.26/0.54       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.26/0.54          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % zdiv_zmult2_eq
% 0.26/0.54  thf(fact_4232_le__real__sqrt__sumsq,axiom,
% 0.26/0.54      ! [X3: real,Y3: real] : ( ord_less_eq_real @ X3 @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y3 @ Y3 ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % le_real_sqrt_sumsq
% 0.26/0.54  thf(fact_4233_log__powr,axiom,
% 0.26/0.54      ! [X3: real,B: real,Y3: real] :
% 0.26/0.54        ( ( X3 != zero_zero_real )
% 0.26/0.54       => ( ( log @ B @ ( powr_real @ X3 @ Y3 ) )
% 0.26/0.54          = ( times_times_real @ Y3 @ ( log @ B @ X3 ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % log_powr
% 0.26/0.54  thf(fact_4234_ln__powr,axiom,
% 0.26/0.54      ! [X3: real,Y3: real] :
% 0.26/0.54        ( ( X3 != zero_zero_real )
% 0.26/0.54       => ( ( ln_ln_real @ ( powr_real @ X3 @ Y3 ) )
% 0.26/0.54          = ( times_times_real @ Y3 @ ( ln_ln_real @ X3 ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % ln_powr
% 0.26/0.54  thf(fact_4235_zmult__zless__mono2__lemma,axiom,
% 0.26/0.54      ! [I: int,J: int,K: nat] :
% 0.26/0.54        ( ( ord_less_int @ I @ J )
% 0.26/0.54       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.26/0.54         => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % zmult_zless_mono2_lemma
% 0.26/0.54  thf(fact_4236_incr__mult__lemma,axiom,
% 0.26/0.54      ! [D3: int,P: int > $o,K: int] :
% 0.26/0.54        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.26/0.54       => ( ! [X4: int] :
% 0.26/0.54              ( ( P @ X4 )
% 0.26/0.54             => ( P @ ( plus_plus_int @ X4 @ D3 ) ) )
% 0.26/0.54         => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.26/0.54           => ! [X6: int] :
% 0.26/0.54                ( ( P @ X6 )
% 0.26/0.54               => ( P @ ( plus_plus_int @ X6 @ ( times_times_int @ K @ D3 ) ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % incr_mult_lemma
% 0.26/0.54  thf(fact_4237_q__pos__lemma,axiom,
% 0.26/0.54      ! [B2: int,Q6: int,R4: int] :
% 0.26/0.54        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q6 ) @ R4 ) )
% 0.26/0.54       => ( ( ord_less_int @ R4 @ B2 )
% 0.26/0.54         => ( ( ord_less_int @ zero_zero_int @ B2 )
% 0.26/0.54           => ( ord_less_eq_int @ zero_zero_int @ Q6 ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % q_pos_lemma
% 0.26/0.54  thf(fact_4238_zdiv__mono2__lemma,axiom,
% 0.26/0.54      ! [B: int,Q3: int,R2: int,B2: int,Q6: int,R4: int] :
% 0.26/0.54        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 )
% 0.26/0.54          = ( plus_plus_int @ ( times_times_int @ B2 @ Q6 ) @ R4 ) )
% 0.26/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q6 ) @ R4 ) )
% 0.26/0.54         => ( ( ord_less_int @ R4 @ B2 )
% 0.26/0.54           => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 0.26/0.54             => ( ( ord_less_int @ zero_zero_int @ B2 )
% 0.26/0.54               => ( ( ord_less_eq_int @ B2 @ B )
% 0.26/0.54                 => ( ord_less_eq_int @ Q3 @ Q6 ) ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % zdiv_mono2_lemma
% 0.26/0.54  thf(fact_4239_zdiv__mono2__neg__lemma,axiom,
% 0.26/0.54      ! [B: int,Q3: int,R2: int,B2: int,Q6: int,R4: int] :
% 0.26/0.54        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 )
% 0.26/0.54          = ( plus_plus_int @ ( times_times_int @ B2 @ Q6 ) @ R4 ) )
% 0.26/0.54       => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q6 ) @ R4 ) @ zero_zero_int )
% 0.26/0.54         => ( ( ord_less_int @ R2 @ B )
% 0.26/0.54           => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 0.26/0.54             => ( ( ord_less_int @ zero_zero_int @ B2 )
% 0.26/0.54               => ( ( ord_less_eq_int @ B2 @ B )
% 0.26/0.54                 => ( ord_less_eq_int @ Q6 @ Q3 ) ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % zdiv_mono2_neg_lemma
% 0.26/0.54  thf(fact_4240_unique__quotient__lemma,axiom,
% 0.26/0.54      ! [B: int,Q6: int,R4: int,Q3: int,R2: int] :
% 0.26/0.54        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 0.26/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 0.26/0.54         => ( ( ord_less_int @ R4 @ B )
% 0.26/0.54           => ( ( ord_less_int @ R2 @ B )
% 0.26/0.54             => ( ord_less_eq_int @ Q6 @ Q3 ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % unique_quotient_lemma
% 0.26/0.54  thf(fact_4241_unique__quotient__lemma__neg,axiom,
% 0.26/0.54      ! [B: int,Q6: int,R4: int,Q3: int,R2: int] :
% 0.26/0.54        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 0.26/0.54       => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 0.26/0.54         => ( ( ord_less_int @ B @ R2 )
% 0.26/0.54           => ( ( ord_less_int @ B @ R4 )
% 0.26/0.54             => ( ord_less_eq_int @ Q3 @ Q6 ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % unique_quotient_lemma_neg
% 0.26/0.54  thf(fact_4242_nat__mult__distrib,axiom,
% 0.26/0.54      ! [Z: int,Z5: int] :
% 0.26/0.54        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.26/0.54       => ( ( nat2 @ ( times_times_int @ Z @ Z5 ) )
% 0.26/0.54          = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z5 ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % nat_mult_distrib
% 0.26/0.54  thf(fact_4243_decr__mult__lemma,axiom,
% 0.26/0.54      ! [D3: int,P: int > $o,K: int] :
% 0.26/0.54        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.26/0.54       => ( ! [X4: int] :
% 0.26/0.54              ( ( P @ X4 )
% 0.26/0.54             => ( P @ ( minus_minus_int @ X4 @ D3 ) ) )
% 0.26/0.54         => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.26/0.54           => ! [X6: int] :
% 0.26/0.54                ( ( P @ X6 )
% 0.26/0.54               => ( P @ ( minus_minus_int @ X6 @ ( times_times_int @ K @ D3 ) ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % decr_mult_lemma
% 0.26/0.54  thf(fact_4244_ln__mult,axiom,
% 0.26/0.54      ! [X3: real,Y3: real] :
% 0.26/0.54        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.54       => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.54         => ( ( ln_ln_real @ ( times_times_real @ X3 @ Y3 ) )
% 0.26/0.54            = ( plus_plus_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y3 ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % ln_mult
% 0.26/0.54  thf(fact_4245_four__x__squared,axiom,
% 0.26/0.54      ! [X3: real] :
% 0.26/0.54        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.54        = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % four_x_squared
% 0.26/0.54  thf(fact_4246_real__archimedian__rdiv__eq__0,axiom,
% 0.26/0.54      ! [X3: real,C: real] :
% 0.26/0.54        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.54       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.26/0.54         => ( ! [M4: nat] :
% 0.26/0.54                ( ( ord_less_nat @ zero_zero_nat @ M4 )
% 0.26/0.54               => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M4 ) @ X3 ) @ C ) )
% 0.26/0.54           => ( X3 = zero_zero_real ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % real_archimedian_rdiv_eq_0
% 0.26/0.54  thf(fact_4247_log__mult,axiom,
% 0.26/0.54      ! [A: real,X3: real,Y3: real] :
% 0.26/0.54        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.54       => ( ( A != one_one_real )
% 0.26/0.54         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.54           => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.54             => ( ( log @ A @ ( times_times_real @ X3 @ Y3 ) )
% 0.26/0.54                = ( plus_plus_real @ ( log @ A @ X3 ) @ ( log @ A @ Y3 ) ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % log_mult
% 0.26/0.54  thf(fact_4248_powr__mult__base,axiom,
% 0.26/0.54      ! [X3: real,Y3: real] :
% 0.26/0.54        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.54       => ( ( times_times_real @ X3 @ ( powr_real @ X3 @ Y3 ) )
% 0.26/0.54          = ( powr_real @ X3 @ ( plus_plus_real @ one_one_real @ Y3 ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % powr_mult_base
% 0.26/0.54  thf(fact_4249_log__nat__power,axiom,
% 0.26/0.54      ! [X3: real,B: real,N: nat] :
% 0.26/0.54        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.54       => ( ( log @ B @ ( power_power_real @ X3 @ N ) )
% 0.26/0.54          = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X3 ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % log_nat_power
% 0.26/0.54  thf(fact_4250_int__div__pos__eq,axiom,
% 0.26/0.54      ! [A: int,B: int,Q3: int,R2: int] :
% 0.26/0.54        ( ( A
% 0.26/0.54          = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 0.26/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 0.26/0.54         => ( ( ord_less_int @ R2 @ B )
% 0.26/0.54           => ( ( divide_divide_int @ A @ B )
% 0.26/0.54              = Q3 ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % int_div_pos_eq
% 0.26/0.54  thf(fact_4251_int__div__neg__eq,axiom,
% 0.26/0.54      ! [A: int,B: int,Q3: int,R2: int] :
% 0.26/0.54        ( ( A
% 0.26/0.54          = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 0.26/0.54       => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 0.26/0.54         => ( ( ord_less_int @ B @ R2 )
% 0.26/0.54           => ( ( divide_divide_int @ A @ B )
% 0.26/0.54              = Q3 ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % int_div_neg_eq
% 0.26/0.54  thf(fact_4252_split__zdiv,axiom,
% 0.26/0.54      ! [P: int > $o,N: int,K: int] :
% 0.26/0.54        ( ( P @ ( divide_divide_int @ N @ K ) )
% 0.26/0.54        = ( ( ( K = zero_zero_int )
% 0.26/0.54           => ( P @ zero_zero_int ) )
% 0.26/0.54          & ( ( ord_less_int @ zero_zero_int @ K )
% 0.26/0.54           => ! [I4: int,J3: int] :
% 0.26/0.54                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 0.26/0.54                  & ( ord_less_int @ J3 @ K )
% 0.26/0.54                  & ( N
% 0.26/0.54                    = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 0.26/0.54               => ( P @ I4 ) ) )
% 0.26/0.54          & ( ( ord_less_int @ K @ zero_zero_int )
% 0.26/0.54           => ! [I4: int,J3: int] :
% 0.26/0.54                ( ( ( ord_less_int @ K @ J3 )
% 0.26/0.54                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 0.26/0.54                  & ( N
% 0.26/0.54                    = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 0.26/0.54               => ( P @ I4 ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % split_zdiv
% 0.26/0.54  thf(fact_4253_ln__realpow,axiom,
% 0.26/0.54      ! [X3: real,N: nat] :
% 0.26/0.54        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.54       => ( ( ln_ln_real @ ( power_power_real @ X3 @ N ) )
% 0.26/0.54          = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X3 ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % ln_realpow
% 0.26/0.54  thf(fact_4254_linear__plus__1__le__power,axiom,
% 0.26/0.54      ! [X3: real,N: nat] :
% 0.26/0.54        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.54       => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X3 ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X3 @ one_one_real ) @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % linear_plus_1_le_power
% 0.26/0.54  thf(fact_4255_ln__powr__bound2,axiom,
% 0.26/0.54      ! [X3: real,A: real] :
% 0.26/0.54        ( ( ord_less_real @ one_one_real @ X3 )
% 0.26/0.54       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.54         => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X3 ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X3 ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % ln_powr_bound2
% 0.26/0.54  thf(fact_4256_log__eq__div__ln__mult__log,axiom,
% 0.26/0.54      ! [A: real,B: real,X3: real] :
% 0.26/0.54        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.54       => ( ( A != one_one_real )
% 0.26/0.54         => ( ( ord_less_real @ zero_zero_real @ B )
% 0.26/0.54           => ( ( B != one_one_real )
% 0.26/0.54             => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.54               => ( ( log @ A @ X3 )
% 0.26/0.54                  = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X3 ) ) ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % log_eq_div_ln_mult_log
% 0.26/0.54  thf(fact_4257_log__add__eq__powr,axiom,
% 0.26/0.54      ! [B: real,X3: real,Y3: real] :
% 0.26/0.54        ( ( ord_less_real @ zero_zero_real @ B )
% 0.26/0.54       => ( ( B != one_one_real )
% 0.26/0.54         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.54           => ( ( plus_plus_real @ ( log @ B @ X3 ) @ Y3 )
% 0.26/0.54              = ( log @ B @ ( times_times_real @ X3 @ ( powr_real @ B @ Y3 ) ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % log_add_eq_powr
% 0.26/0.54  thf(fact_4258_add__log__eq__powr,axiom,
% 0.26/0.54      ! [B: real,X3: real,Y3: real] :
% 0.26/0.54        ( ( ord_less_real @ zero_zero_real @ B )
% 0.26/0.54       => ( ( B != one_one_real )
% 0.26/0.54         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.54           => ( ( plus_plus_real @ Y3 @ ( log @ B @ X3 ) )
% 0.26/0.54              = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y3 ) @ X3 ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % add_log_eq_powr
% 0.26/0.54  thf(fact_4259_L2__set__mult__ineq__lemma,axiom,
% 0.26/0.54      ! [A: real,C: real,B: real,D3: 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 @ D3 ) ) @ ( plus_plus_real @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D3 @ ( 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 ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % L2_set_mult_ineq_lemma
% 0.26/0.54  thf(fact_4260_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 0.26/0.54      ! [X3: real,Y3: real,Xa: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % real_sqrt_sum_squares_mult_ge_zero
% 0.26/0.54  thf(fact_4261_arith__geo__mean__sqrt,axiom,
% 0.26/0.54      ! [X3: real,Y3: real] :
% 0.26/0.54        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.54       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.54         => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X3 @ Y3 ) ) @ ( divide_divide_real @ ( plus_plus_real @ X3 @ Y3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % arith_geo_mean_sqrt
% 0.26/0.54  thf(fact_4262_neg__zdiv__mult__2,axiom,
% 0.26/0.54      ! [A: int,B: int] :
% 0.26/0.54        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.26/0.54       => ( ( 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 ) )
% 0.26/0.54          = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_zdiv_mult_2
% 0.26/0.54  thf(fact_4263_pos__zdiv__mult__2,axiom,
% 0.26/0.54      ! [A: int,B: int] :
% 0.26/0.54        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.54       => ( ( 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 ) )
% 0.26/0.54          = ( divide_divide_int @ B @ A ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % pos_zdiv_mult_2
% 0.26/0.54  thf(fact_4264_Bernoulli__inequality__even,axiom,
% 0.26/0.54      ! [N: nat,X3: real] :
% 0.26/0.54        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.54       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X3 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X3 ) @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % Bernoulli_inequality_even
% 0.26/0.54  thf(fact_4265_nonzero__of__real__divide,axiom,
% 0.26/0.54      ! [Y3: real,X3: real] :
% 0.26/0.54        ( ( Y3 != zero_zero_real )
% 0.26/0.54       => ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X3 @ Y3 ) )
% 0.26/0.54          = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X3 ) @ ( real_V1803761363581548252l_real @ Y3 ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % nonzero_of_real_divide
% 0.26/0.54  thf(fact_4266_nonzero__of__real__divide,axiom,
% 0.26/0.54      ! [Y3: real,X3: real] :
% 0.26/0.54        ( ( Y3 != zero_zero_real )
% 0.26/0.54       => ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X3 @ Y3 ) )
% 0.26/0.54          = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X3 ) @ ( real_V4546457046886955230omplex @ Y3 ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % nonzero_of_real_divide
% 0.26/0.54  thf(fact_4267_lemma__termdiff3,axiom,
% 0.26/0.54      ! [H2: real,Z: real,K5: real,N: nat] :
% 0.26/0.54        ( ( H2 != zero_zero_real )
% 0.26/0.54       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K5 )
% 0.26/0.54         => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H2 ) ) @ K5 )
% 0.26/0.54           => ( 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 ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % lemma_termdiff3
% 0.26/0.54  thf(fact_4268_lemma__termdiff3,axiom,
% 0.26/0.54      ! [H2: complex,Z: complex,K5: real,N: nat] :
% 0.26/0.54        ( ( H2 != zero_zero_complex )
% 0.26/0.54       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K5 )
% 0.26/0.54         => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H2 ) ) @ K5 )
% 0.26/0.54           => ( 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 ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % lemma_termdiff3
% 0.26/0.54  thf(fact_4269_low__inv,axiom,
% 0.26/0.54      ! [X3: nat,N: nat,Y3: nat] :
% 0.26/0.54        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.54       => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X3 ) @ N )
% 0.26/0.54          = X3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % low_inv
% 0.26/0.54  thf(fact_4270_mult__le__cancel__iff1,axiom,
% 0.26/0.54      ! [Z: real,X3: real,Y3: real] :
% 0.26/0.54        ( ( ord_less_real @ zero_zero_real @ Z )
% 0.26/0.54       => ( ( ord_less_eq_real @ ( times_times_real @ X3 @ Z ) @ ( times_times_real @ Y3 @ Z ) )
% 0.26/0.54          = ( ord_less_eq_real @ X3 @ Y3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_le_cancel_iff1
% 0.26/0.54  thf(fact_4271_mult__le__cancel__iff1,axiom,
% 0.26/0.54      ! [Z: rat,X3: rat,Y3: rat] :
% 0.26/0.54        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 0.26/0.54       => ( ( ord_less_eq_rat @ ( times_times_rat @ X3 @ Z ) @ ( times_times_rat @ Y3 @ Z ) )
% 0.26/0.54          = ( ord_less_eq_rat @ X3 @ Y3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_le_cancel_iff1
% 0.26/0.54  thf(fact_4272_mult__le__cancel__iff1,axiom,
% 0.26/0.54      ! [Z: int,X3: int,Y3: int] :
% 0.26/0.54        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.26/0.54       => ( ( ord_less_eq_int @ ( times_times_int @ X3 @ Z ) @ ( times_times_int @ Y3 @ Z ) )
% 0.26/0.54          = ( ord_less_eq_int @ X3 @ Y3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_le_cancel_iff1
% 0.26/0.54  thf(fact_4273_mult__le__cancel__iff2,axiom,
% 0.26/0.54      ! [Z: real,X3: real,Y3: real] :
% 0.26/0.54        ( ( ord_less_real @ zero_zero_real @ Z )
% 0.26/0.54       => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X3 ) @ ( times_times_real @ Z @ Y3 ) )
% 0.26/0.54          = ( ord_less_eq_real @ X3 @ Y3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_le_cancel_iff2
% 0.26/0.54  thf(fact_4274_mult__le__cancel__iff2,axiom,
% 0.26/0.54      ! [Z: rat,X3: rat,Y3: rat] :
% 0.26/0.54        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 0.26/0.54       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X3 ) @ ( times_times_rat @ Z @ Y3 ) )
% 0.26/0.54          = ( ord_less_eq_rat @ X3 @ Y3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_le_cancel_iff2
% 0.26/0.54  thf(fact_4275_mult__le__cancel__iff2,axiom,
% 0.26/0.54      ! [Z: int,X3: int,Y3: int] :
% 0.26/0.54        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.26/0.54       => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X3 ) @ ( times_times_int @ Z @ Y3 ) )
% 0.26/0.54          = ( ord_less_eq_int @ X3 @ Y3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_le_cancel_iff2
% 0.26/0.54  thf(fact_4276_triangle__def,axiom,
% 0.26/0.54      ( nat_triangle
% 0.26/0.54      = ( ^ [N3: nat] : ( divide_divide_nat @ ( times_times_nat @ N3 @ ( suc @ N3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % triangle_def
% 0.26/0.54  thf(fact_4277_ln__one__minus__pos__lower__bound,axiom,
% 0.26/0.54      ! [X3: real] :
% 0.26/0.54        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.54       => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.54         => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X3 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % ln_one_minus_pos_lower_bound
% 0.26/0.54  thf(fact_4278_abs__ln__one__plus__x__minus__x__bound,axiom,
% 0.26/0.54      ! [X3: real] :
% 0.26/0.54        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.54       => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X3 ) ) @ X3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_ln_one_plus_x_minus_x_bound
% 0.26/0.54  thf(fact_4279_bit__split__inv,axiom,
% 0.26/0.54      ! [X3: nat,D3: nat] :
% 0.26/0.54        ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X3 @ D3 ) @ ( vEBT_VEBT_low @ X3 @ D3 ) @ D3 )
% 0.26/0.54        = X3 ) ).
% 0.26/0.54  
% 0.26/0.54  % bit_split_inv
% 0.26/0.54  thf(fact_4280_add_Oinverse__inverse,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 0.26/0.54        = A ) ).
% 0.26/0.54  
% 0.26/0.54  % add.inverse_inverse
% 0.26/0.54  thf(fact_4281_add_Oinverse__inverse,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 0.26/0.54        = A ) ).
% 0.26/0.54  
% 0.26/0.54  % add.inverse_inverse
% 0.26/0.54  thf(fact_4282_add_Oinverse__inverse,axiom,
% 0.26/0.54      ! [A: complex] :
% 0.26/0.54        ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 0.26/0.54        = A ) ).
% 0.26/0.54  
% 0.26/0.54  % add.inverse_inverse
% 0.26/0.54  thf(fact_4283_add_Oinverse__inverse,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.26/0.54        = A ) ).
% 0.26/0.54  
% 0.26/0.54  % add.inverse_inverse
% 0.26/0.54  thf(fact_4284_add_Oinverse__inverse,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 0.26/0.54        = A ) ).
% 0.26/0.54  
% 0.26/0.54  % add.inverse_inverse
% 0.26/0.54  thf(fact_4285_neg__equal__iff__equal,axiom,
% 0.26/0.54      ! [A: real,B: real] :
% 0.26/0.54        ( ( ( uminus_uminus_real @ A )
% 0.26/0.54          = ( uminus_uminus_real @ B ) )
% 0.26/0.54        = ( A = B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_equal_iff_equal
% 0.26/0.54  thf(fact_4286_neg__equal__iff__equal,axiom,
% 0.26/0.54      ! [A: int,B: int] :
% 0.26/0.54        ( ( ( uminus_uminus_int @ A )
% 0.26/0.54          = ( uminus_uminus_int @ B ) )
% 0.26/0.54        = ( A = B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_equal_iff_equal
% 0.26/0.54  thf(fact_4287_neg__equal__iff__equal,axiom,
% 0.26/0.54      ! [A: complex,B: complex] :
% 0.26/0.54        ( ( ( uminus1482373934393186551omplex @ A )
% 0.26/0.54          = ( uminus1482373934393186551omplex @ B ) )
% 0.26/0.54        = ( A = B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_equal_iff_equal
% 0.26/0.54  thf(fact_4288_neg__equal__iff__equal,axiom,
% 0.26/0.54      ! [A: code_integer,B: code_integer] :
% 0.26/0.54        ( ( ( uminus1351360451143612070nteger @ A )
% 0.26/0.54          = ( uminus1351360451143612070nteger @ B ) )
% 0.26/0.54        = ( A = B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_equal_iff_equal
% 0.26/0.54  thf(fact_4289_neg__equal__iff__equal,axiom,
% 0.26/0.54      ! [A: rat,B: rat] :
% 0.26/0.54        ( ( ( uminus_uminus_rat @ A )
% 0.26/0.54          = ( uminus_uminus_rat @ B ) )
% 0.26/0.54        = ( A = B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_equal_iff_equal
% 0.26/0.54  thf(fact_4290_verit__minus__simplify_I4_J,axiom,
% 0.26/0.54      ! [B: real] :
% 0.26/0.54        ( ( uminus_uminus_real @ ( uminus_uminus_real @ B ) )
% 0.26/0.54        = B ) ).
% 0.26/0.54  
% 0.26/0.54  % verit_minus_simplify(4)
% 0.26/0.54  thf(fact_4291_verit__minus__simplify_I4_J,axiom,
% 0.26/0.54      ! [B: int] :
% 0.26/0.54        ( ( uminus_uminus_int @ ( uminus_uminus_int @ B ) )
% 0.26/0.54        = B ) ).
% 0.26/0.54  
% 0.26/0.54  % verit_minus_simplify(4)
% 0.26/0.54  thf(fact_4292_verit__minus__simplify_I4_J,axiom,
% 0.26/0.54      ! [B: complex] :
% 0.26/0.54        ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ B ) )
% 0.26/0.54        = B ) ).
% 0.26/0.54  
% 0.26/0.54  % verit_minus_simplify(4)
% 0.26/0.54  thf(fact_4293_verit__minus__simplify_I4_J,axiom,
% 0.26/0.54      ! [B: code_integer] :
% 0.26/0.54        ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ B ) )
% 0.26/0.54        = B ) ).
% 0.26/0.54  
% 0.26/0.54  % verit_minus_simplify(4)
% 0.26/0.54  thf(fact_4294_verit__minus__simplify_I4_J,axiom,
% 0.26/0.54      ! [B: rat] :
% 0.26/0.54        ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ B ) )
% 0.26/0.54        = B ) ).
% 0.26/0.54  
% 0.26/0.54  % verit_minus_simplify(4)
% 0.26/0.54  thf(fact_4295_abs__idempotent,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 0.26/0.54        = ( abs_abs_real @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_idempotent
% 0.26/0.54  thf(fact_4296_abs__idempotent,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 0.26/0.54        = ( abs_abs_int @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_idempotent
% 0.26/0.54  thf(fact_4297_abs__idempotent,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 0.26/0.54        = ( abs_abs_Code_integer @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_idempotent
% 0.26/0.54  thf(fact_4298_abs__idempotent,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 0.26/0.54        = ( abs_abs_rat @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_idempotent
% 0.26/0.54  thf(fact_4299_neg__le__iff__le,axiom,
% 0.26/0.54      ! [B: real,A: real] :
% 0.26/0.54        ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 0.26/0.54        = ( ord_less_eq_real @ A @ B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_le_iff_le
% 0.26/0.54  thf(fact_4300_neg__le__iff__le,axiom,
% 0.26/0.54      ! [B: code_integer,A: code_integer] :
% 0.26/0.54        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.26/0.54        = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_le_iff_le
% 0.26/0.54  thf(fact_4301_neg__le__iff__le,axiom,
% 0.26/0.54      ! [B: rat,A: rat] :
% 0.26/0.54        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 0.26/0.54        = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_le_iff_le
% 0.26/0.54  thf(fact_4302_neg__le__iff__le,axiom,
% 0.26/0.54      ! [B: int,A: int] :
% 0.26/0.54        ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 0.26/0.54        = ( ord_less_eq_int @ A @ B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_le_iff_le
% 0.26/0.54  thf(fact_4303_neg__equal__zero,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( ( uminus_uminus_real @ A )
% 0.26/0.54          = A )
% 0.26/0.54        = ( A = zero_zero_real ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_equal_zero
% 0.26/0.54  thf(fact_4304_neg__equal__zero,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( ( uminus_uminus_int @ A )
% 0.26/0.54          = A )
% 0.26/0.54        = ( A = zero_zero_int ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_equal_zero
% 0.26/0.54  thf(fact_4305_neg__equal__zero,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( ( uminus1351360451143612070nteger @ A )
% 0.26/0.54          = A )
% 0.26/0.54        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_equal_zero
% 0.26/0.54  thf(fact_4306_neg__equal__zero,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( ( uminus_uminus_rat @ A )
% 0.26/0.54          = A )
% 0.26/0.54        = ( A = zero_zero_rat ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_equal_zero
% 0.26/0.54  thf(fact_4307_equal__neg__zero,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( A
% 0.26/0.54          = ( uminus_uminus_real @ A ) )
% 0.26/0.54        = ( A = zero_zero_real ) ) ).
% 0.26/0.54  
% 0.26/0.54  % equal_neg_zero
% 0.26/0.54  thf(fact_4308_equal__neg__zero,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( A
% 0.26/0.54          = ( uminus_uminus_int @ A ) )
% 0.26/0.54        = ( A = zero_zero_int ) ) ).
% 0.26/0.54  
% 0.26/0.54  % equal_neg_zero
% 0.26/0.54  thf(fact_4309_equal__neg__zero,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( A
% 0.26/0.54          = ( uminus1351360451143612070nteger @ A ) )
% 0.26/0.54        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.54  
% 0.26/0.54  % equal_neg_zero
% 0.26/0.54  thf(fact_4310_equal__neg__zero,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( A
% 0.26/0.54          = ( uminus_uminus_rat @ A ) )
% 0.26/0.54        = ( A = zero_zero_rat ) ) ).
% 0.26/0.54  
% 0.26/0.54  % equal_neg_zero
% 0.26/0.54  thf(fact_4311_neg__equal__0__iff__equal,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( ( uminus_uminus_real @ A )
% 0.26/0.54          = zero_zero_real )
% 0.26/0.54        = ( A = zero_zero_real ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_equal_0_iff_equal
% 0.26/0.54  thf(fact_4312_neg__equal__0__iff__equal,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( ( uminus_uminus_int @ A )
% 0.26/0.54          = zero_zero_int )
% 0.26/0.54        = ( A = zero_zero_int ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_equal_0_iff_equal
% 0.26/0.54  thf(fact_4313_neg__equal__0__iff__equal,axiom,
% 0.26/0.54      ! [A: complex] :
% 0.26/0.54        ( ( ( uminus1482373934393186551omplex @ A )
% 0.26/0.54          = zero_zero_complex )
% 0.26/0.54        = ( A = zero_zero_complex ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_equal_0_iff_equal
% 0.26/0.54  thf(fact_4314_neg__equal__0__iff__equal,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( ( uminus1351360451143612070nteger @ A )
% 0.26/0.54          = zero_z3403309356797280102nteger )
% 0.26/0.54        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_equal_0_iff_equal
% 0.26/0.54  thf(fact_4315_neg__equal__0__iff__equal,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( ( uminus_uminus_rat @ A )
% 0.26/0.54          = zero_zero_rat )
% 0.26/0.54        = ( A = zero_zero_rat ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_equal_0_iff_equal
% 0.26/0.54  thf(fact_4316_neg__0__equal__iff__equal,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( zero_zero_real
% 0.26/0.54          = ( uminus_uminus_real @ A ) )
% 0.26/0.54        = ( zero_zero_real = A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_0_equal_iff_equal
% 0.26/0.54  thf(fact_4317_neg__0__equal__iff__equal,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( zero_zero_int
% 0.26/0.54          = ( uminus_uminus_int @ A ) )
% 0.26/0.54        = ( zero_zero_int = A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_0_equal_iff_equal
% 0.26/0.54  thf(fact_4318_neg__0__equal__iff__equal,axiom,
% 0.26/0.54      ! [A: complex] :
% 0.26/0.54        ( ( zero_zero_complex
% 0.26/0.54          = ( uminus1482373934393186551omplex @ A ) )
% 0.26/0.54        = ( zero_zero_complex = A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_0_equal_iff_equal
% 0.26/0.54  thf(fact_4319_neg__0__equal__iff__equal,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( zero_z3403309356797280102nteger
% 0.26/0.54          = ( uminus1351360451143612070nteger @ A ) )
% 0.26/0.54        = ( zero_z3403309356797280102nteger = A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_0_equal_iff_equal
% 0.26/0.54  thf(fact_4320_neg__0__equal__iff__equal,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( zero_zero_rat
% 0.26/0.54          = ( uminus_uminus_rat @ A ) )
% 0.26/0.54        = ( zero_zero_rat = A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_0_equal_iff_equal
% 0.26/0.54  thf(fact_4321_add_Oinverse__neutral,axiom,
% 0.26/0.54      ( ( uminus_uminus_real @ zero_zero_real )
% 0.26/0.54      = zero_zero_real ) ).
% 0.26/0.54  
% 0.26/0.54  % add.inverse_neutral
% 0.26/0.54  thf(fact_4322_add_Oinverse__neutral,axiom,
% 0.26/0.54      ( ( uminus_uminus_int @ zero_zero_int )
% 0.26/0.54      = zero_zero_int ) ).
% 0.26/0.54  
% 0.26/0.54  % add.inverse_neutral
% 0.26/0.54  thf(fact_4323_add_Oinverse__neutral,axiom,
% 0.26/0.54      ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 0.26/0.54      = zero_zero_complex ) ).
% 0.26/0.54  
% 0.26/0.54  % add.inverse_neutral
% 0.26/0.54  thf(fact_4324_add_Oinverse__neutral,axiom,
% 0.26/0.54      ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 0.26/0.54      = zero_z3403309356797280102nteger ) ).
% 0.26/0.54  
% 0.26/0.54  % add.inverse_neutral
% 0.26/0.54  thf(fact_4325_add_Oinverse__neutral,axiom,
% 0.26/0.54      ( ( uminus_uminus_rat @ zero_zero_rat )
% 0.26/0.54      = zero_zero_rat ) ).
% 0.26/0.54  
% 0.26/0.54  % add.inverse_neutral
% 0.26/0.54  thf(fact_4326_neg__less__iff__less,axiom,
% 0.26/0.54      ! [B: real,A: real] :
% 0.26/0.54        ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 0.26/0.54        = ( ord_less_real @ A @ B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_less_iff_less
% 0.26/0.54  thf(fact_4327_neg__less__iff__less,axiom,
% 0.26/0.54      ! [B: int,A: int] :
% 0.26/0.54        ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 0.26/0.54        = ( ord_less_int @ A @ B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_less_iff_less
% 0.26/0.54  thf(fact_4328_neg__less__iff__less,axiom,
% 0.26/0.54      ! [B: code_integer,A: code_integer] :
% 0.26/0.54        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.26/0.54        = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_less_iff_less
% 0.26/0.54  thf(fact_4329_neg__less__iff__less,axiom,
% 0.26/0.54      ! [B: rat,A: rat] :
% 0.26/0.54        ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 0.26/0.54        = ( ord_less_rat @ A @ B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_less_iff_less
% 0.26/0.54  thf(fact_4330_neg__numeral__eq__iff,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 0.26/0.54          = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.26/0.54        = ( M = N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_numeral_eq_iff
% 0.26/0.54  thf(fact_4331_neg__numeral__eq__iff,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 0.26/0.54          = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.54        = ( M = N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_numeral_eq_iff
% 0.26/0.54  thf(fact_4332_neg__numeral__eq__iff,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 0.26/0.54          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.26/0.54        = ( M = N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_numeral_eq_iff
% 0.26/0.54  thf(fact_4333_neg__numeral__eq__iff,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 0.26/0.54          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.26/0.54        = ( M = N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_numeral_eq_iff
% 0.26/0.54  thf(fact_4334_neg__numeral__eq__iff,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 0.26/0.54          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.26/0.54        = ( M = N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_numeral_eq_iff
% 0.26/0.54  thf(fact_4335_add__minus__cancel,axiom,
% 0.26/0.54      ! [A: real,B: real] :
% 0.26/0.54        ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 0.26/0.54        = B ) ).
% 0.26/0.54  
% 0.26/0.54  % add_minus_cancel
% 0.26/0.54  thf(fact_4336_add__minus__cancel,axiom,
% 0.26/0.54      ! [A: int,B: int] :
% 0.26/0.54        ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 0.26/0.54        = B ) ).
% 0.26/0.54  
% 0.26/0.54  % add_minus_cancel
% 0.26/0.54  thf(fact_4337_add__minus__cancel,axiom,
% 0.26/0.54      ! [A: complex,B: complex] :
% 0.26/0.54        ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 0.26/0.54        = B ) ).
% 0.26/0.54  
% 0.26/0.54  % add_minus_cancel
% 0.26/0.54  thf(fact_4338_add__minus__cancel,axiom,
% 0.26/0.54      ! [A: code_integer,B: code_integer] :
% 0.26/0.54        ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 0.26/0.54        = B ) ).
% 0.26/0.54  
% 0.26/0.54  % add_minus_cancel
% 0.26/0.54  thf(fact_4339_add__minus__cancel,axiom,
% 0.26/0.54      ! [A: rat,B: rat] :
% 0.26/0.54        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 0.26/0.54        = B ) ).
% 0.26/0.54  
% 0.26/0.54  % add_minus_cancel
% 0.26/0.54  thf(fact_4340_minus__add__cancel,axiom,
% 0.26/0.54      ! [A: real,B: real] :
% 0.26/0.54        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 0.26/0.54        = B ) ).
% 0.26/0.54  
% 0.26/0.54  % minus_add_cancel
% 0.26/0.54  thf(fact_4341_minus__add__cancel,axiom,
% 0.26/0.54      ! [A: int,B: int] :
% 0.26/0.54        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 0.26/0.54        = B ) ).
% 0.26/0.54  
% 0.26/0.54  % minus_add_cancel
% 0.26/0.54  thf(fact_4342_minus__add__cancel,axiom,
% 0.26/0.54      ! [A: complex,B: complex] :
% 0.26/0.54        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 0.26/0.54        = B ) ).
% 0.26/0.54  
% 0.26/0.54  % minus_add_cancel
% 0.26/0.54  thf(fact_4343_minus__add__cancel,axiom,
% 0.26/0.54      ! [A: code_integer,B: code_integer] :
% 0.26/0.54        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.26/0.54        = B ) ).
% 0.26/0.54  
% 0.26/0.54  % minus_add_cancel
% 0.26/0.54  thf(fact_4344_minus__add__cancel,axiom,
% 0.26/0.54      ! [A: rat,B: rat] :
% 0.26/0.54        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 0.26/0.54        = B ) ).
% 0.26/0.54  
% 0.26/0.54  % minus_add_cancel
% 0.26/0.54  thf(fact_4345_minus__add__distrib,axiom,
% 0.26/0.54      ! [A: real,B: real] :
% 0.26/0.54        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 0.26/0.54        = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % minus_add_distrib
% 0.26/0.54  thf(fact_4346_minus__add__distrib,axiom,
% 0.26/0.54      ! [A: int,B: int] :
% 0.26/0.54        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.26/0.54        = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % minus_add_distrib
% 0.26/0.54  thf(fact_4347_minus__add__distrib,axiom,
% 0.26/0.54      ! [A: complex,B: complex] :
% 0.26/0.54        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 0.26/0.54        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % minus_add_distrib
% 0.26/0.54  thf(fact_4348_minus__add__distrib,axiom,
% 0.26/0.54      ! [A: code_integer,B: code_integer] :
% 0.26/0.54        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.26/0.54        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % minus_add_distrib
% 0.26/0.54  thf(fact_4349_minus__add__distrib,axiom,
% 0.26/0.54      ! [A: rat,B: rat] :
% 0.26/0.54        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.26/0.54        = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % minus_add_distrib
% 0.26/0.54  thf(fact_4350_minus__diff__eq,axiom,
% 0.26/0.54      ! [A: real,B: real] :
% 0.26/0.54        ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 0.26/0.54        = ( minus_minus_real @ B @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % minus_diff_eq
% 0.26/0.54  thf(fact_4351_minus__diff__eq,axiom,
% 0.26/0.54      ! [A: int,B: int] :
% 0.26/0.54        ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 0.26/0.54        = ( minus_minus_int @ B @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % minus_diff_eq
% 0.26/0.54  thf(fact_4352_minus__diff__eq,axiom,
% 0.26/0.54      ! [A: complex,B: complex] :
% 0.26/0.54        ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 0.26/0.54        = ( minus_minus_complex @ B @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % minus_diff_eq
% 0.26/0.54  thf(fact_4353_minus__diff__eq,axiom,
% 0.26/0.54      ! [A: code_integer,B: code_integer] :
% 0.26/0.54        ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.26/0.54        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % minus_diff_eq
% 0.26/0.54  thf(fact_4354_minus__diff__eq,axiom,
% 0.26/0.54      ! [A: rat,B: rat] :
% 0.26/0.54        ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 0.26/0.54        = ( minus_minus_rat @ B @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % minus_diff_eq
% 0.26/0.54  thf(fact_4355_abs__zero,axiom,
% 0.26/0.54      ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 0.26/0.54      = zero_z3403309356797280102nteger ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_zero
% 0.26/0.54  thf(fact_4356_abs__zero,axiom,
% 0.26/0.54      ( ( abs_abs_real @ zero_zero_real )
% 0.26/0.54      = zero_zero_real ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_zero
% 0.26/0.54  thf(fact_4357_abs__zero,axiom,
% 0.26/0.54      ( ( abs_abs_rat @ zero_zero_rat )
% 0.26/0.54      = zero_zero_rat ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_zero
% 0.26/0.54  thf(fact_4358_abs__zero,axiom,
% 0.26/0.54      ( ( abs_abs_int @ zero_zero_int )
% 0.26/0.54      = zero_zero_int ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_zero
% 0.26/0.54  thf(fact_4359_abs__eq__0,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( ( abs_abs_Code_integer @ A )
% 0.26/0.54          = zero_z3403309356797280102nteger )
% 0.26/0.54        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_eq_0
% 0.26/0.54  thf(fact_4360_abs__eq__0,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( ( abs_abs_real @ A )
% 0.26/0.54          = zero_zero_real )
% 0.26/0.54        = ( A = zero_zero_real ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_eq_0
% 0.26/0.54  thf(fact_4361_abs__eq__0,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( ( abs_abs_rat @ A )
% 0.26/0.54          = zero_zero_rat )
% 0.26/0.54        = ( A = zero_zero_rat ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_eq_0
% 0.26/0.54  thf(fact_4362_abs__eq__0,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( ( abs_abs_int @ A )
% 0.26/0.54          = zero_zero_int )
% 0.26/0.54        = ( A = zero_zero_int ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_eq_0
% 0.26/0.54  thf(fact_4363_abs__0__eq,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( zero_z3403309356797280102nteger
% 0.26/0.54          = ( abs_abs_Code_integer @ A ) )
% 0.26/0.54        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_0_eq
% 0.26/0.54  thf(fact_4364_abs__0__eq,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( zero_zero_real
% 0.26/0.54          = ( abs_abs_real @ A ) )
% 0.26/0.54        = ( A = zero_zero_real ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_0_eq
% 0.26/0.54  thf(fact_4365_abs__0__eq,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( zero_zero_rat
% 0.26/0.54          = ( abs_abs_rat @ A ) )
% 0.26/0.54        = ( A = zero_zero_rat ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_0_eq
% 0.26/0.54  thf(fact_4366_abs__0__eq,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( zero_zero_int
% 0.26/0.54          = ( abs_abs_int @ A ) )
% 0.26/0.54        = ( A = zero_zero_int ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_0_eq
% 0.26/0.54  thf(fact_4367_abs__0,axiom,
% 0.26/0.54      ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 0.26/0.54      = zero_z3403309356797280102nteger ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_0
% 0.26/0.54  thf(fact_4368_abs__0,axiom,
% 0.26/0.54      ( ( abs_abs_real @ zero_zero_real )
% 0.26/0.54      = zero_zero_real ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_0
% 0.26/0.54  thf(fact_4369_abs__0,axiom,
% 0.26/0.54      ( ( abs_abs_rat @ zero_zero_rat )
% 0.26/0.54      = zero_zero_rat ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_0
% 0.26/0.54  thf(fact_4370_abs__0,axiom,
% 0.26/0.54      ( ( abs_abs_int @ zero_zero_int )
% 0.26/0.54      = zero_zero_int ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_0
% 0.26/0.54  thf(fact_4371_abs__numeral,axiom,
% 0.26/0.54      ! [N: num] :
% 0.26/0.54        ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 0.26/0.54        = ( numera6620942414471956472nteger @ N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_numeral
% 0.26/0.54  thf(fact_4372_abs__numeral,axiom,
% 0.26/0.54      ! [N: num] :
% 0.26/0.54        ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 0.26/0.54        = ( numeral_numeral_real @ N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_numeral
% 0.26/0.54  thf(fact_4373_abs__numeral,axiom,
% 0.26/0.54      ! [N: num] :
% 0.26/0.54        ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 0.26/0.54        = ( numeral_numeral_rat @ N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_numeral
% 0.26/0.54  thf(fact_4374_abs__numeral,axiom,
% 0.26/0.54      ! [N: num] :
% 0.26/0.54        ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 0.26/0.54        = ( numeral_numeral_int @ N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_numeral
% 0.26/0.54  thf(fact_4375_abs__add__abs,axiom,
% 0.26/0.54      ! [A: code_integer,B: code_integer] :
% 0.26/0.54        ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 0.26/0.54        = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_add_abs
% 0.26/0.54  thf(fact_4376_abs__add__abs,axiom,
% 0.26/0.54      ! [A: real,B: real] :
% 0.26/0.54        ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 0.26/0.54        = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_add_abs
% 0.26/0.54  thf(fact_4377_abs__add__abs,axiom,
% 0.26/0.54      ! [A: rat,B: rat] :
% 0.26/0.54        ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 0.26/0.54        = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_add_abs
% 0.26/0.54  thf(fact_4378_abs__add__abs,axiom,
% 0.26/0.54      ! [A: int,B: int] :
% 0.26/0.54        ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 0.26/0.54        = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_add_abs
% 0.26/0.54  thf(fact_4379_abs__minus__cancel,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 0.26/0.54        = ( abs_abs_real @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_minus_cancel
% 0.26/0.54  thf(fact_4380_abs__minus__cancel,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 0.26/0.54        = ( abs_abs_int @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_minus_cancel
% 0.26/0.54  thf(fact_4381_abs__minus__cancel,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 0.26/0.54        = ( abs_abs_Code_integer @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_minus_cancel
% 0.26/0.54  thf(fact_4382_abs__minus__cancel,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 0.26/0.54        = ( abs_abs_rat @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_minus_cancel
% 0.26/0.54  thf(fact_4383_of__int__minus,axiom,
% 0.26/0.54      ! [Z: int] :
% 0.26/0.54        ( ( ring_1_of_int_real @ ( uminus_uminus_int @ Z ) )
% 0.26/0.54        = ( uminus_uminus_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % of_int_minus
% 0.26/0.54  thf(fact_4384_of__int__minus,axiom,
% 0.26/0.54      ! [Z: int] :
% 0.26/0.54        ( ( ring_1_of_int_int @ ( uminus_uminus_int @ Z ) )
% 0.26/0.54        = ( uminus_uminus_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % of_int_minus
% 0.26/0.54  thf(fact_4385_of__int__minus,axiom,
% 0.26/0.54      ! [Z: int] :
% 0.26/0.54        ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ Z ) )
% 0.26/0.54        = ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % of_int_minus
% 0.26/0.54  thf(fact_4386_of__int__minus,axiom,
% 0.26/0.54      ! [Z: int] :
% 0.26/0.54        ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ Z ) )
% 0.26/0.54        = ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ Z ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % of_int_minus
% 0.26/0.54  thf(fact_4387_of__int__minus,axiom,
% 0.26/0.54      ! [Z: int] :
% 0.26/0.54        ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ Z ) )
% 0.26/0.54        = ( uminus_uminus_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % of_int_minus
% 0.26/0.54  thf(fact_4388_abs__of__nat,axiom,
% 0.26/0.54      ! [N: nat] :
% 0.26/0.54        ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 0.26/0.54        = ( semiri4939895301339042750nteger @ N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_of_nat
% 0.26/0.54  thf(fact_4389_abs__of__nat,axiom,
% 0.26/0.54      ! [N: nat] :
% 0.26/0.54        ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N ) )
% 0.26/0.54        = ( semiri5074537144036343181t_real @ N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_of_nat
% 0.26/0.54  thf(fact_4390_abs__of__nat,axiom,
% 0.26/0.54      ! [N: nat] :
% 0.26/0.54        ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N ) )
% 0.26/0.54        = ( semiri681578069525770553at_rat @ N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_of_nat
% 0.26/0.54  thf(fact_4391_abs__of__nat,axiom,
% 0.26/0.54      ! [N: nat] :
% 0.26/0.54        ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.54        = ( semiri1314217659103216013at_int @ N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_of_nat
% 0.26/0.54  thf(fact_4392_of__int__abs,axiom,
% 0.26/0.54      ! [X3: int] :
% 0.26/0.54        ( ( ring_1_of_int_int @ ( abs_abs_int @ X3 ) )
% 0.26/0.54        = ( abs_abs_int @ ( ring_1_of_int_int @ X3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % of_int_abs
% 0.26/0.54  thf(fact_4393_of__int__abs,axiom,
% 0.26/0.54      ! [X3: int] :
% 0.26/0.54        ( ( ring_18347121197199848620nteger @ ( abs_abs_int @ X3 ) )
% 0.26/0.54        = ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ X3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % of_int_abs
% 0.26/0.54  thf(fact_4394_of__int__abs,axiom,
% 0.26/0.54      ! [X3: int] :
% 0.26/0.54        ( ( ring_1_of_int_real @ ( abs_abs_int @ X3 ) )
% 0.26/0.54        = ( abs_abs_real @ ( ring_1_of_int_real @ X3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % of_int_abs
% 0.26/0.54  thf(fact_4395_of__int__abs,axiom,
% 0.26/0.54      ! [X3: int] :
% 0.26/0.54        ( ( ring_1_of_int_rat @ ( abs_abs_int @ X3 ) )
% 0.26/0.54        = ( abs_abs_rat @ ( ring_1_of_int_rat @ X3 ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % of_int_abs
% 0.26/0.54  thf(fact_4396_triangle__0,axiom,
% 0.26/0.54      ( ( nat_triangle @ zero_zero_nat )
% 0.26/0.54      = zero_zero_nat ) ).
% 0.26/0.54  
% 0.26/0.54  % triangle_0
% 0.26/0.54  thf(fact_4397_neg__0__le__iff__le,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 0.26/0.54        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_0_le_iff_le
% 0.26/0.54  thf(fact_4398_neg__0__le__iff__le,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.26/0.54        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_0_le_iff_le
% 0.26/0.54  thf(fact_4399_neg__0__le__iff__le,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 0.26/0.54        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_0_le_iff_le
% 0.26/0.54  thf(fact_4400_neg__0__le__iff__le,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.26/0.54        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_0_le_iff_le
% 0.26/0.54  thf(fact_4401_neg__le__0__iff__le,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 0.26/0.54        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_le_0_iff_le
% 0.26/0.54  thf(fact_4402_neg__le__0__iff__le,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 0.26/0.54        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_le_0_iff_le
% 0.26/0.54  thf(fact_4403_neg__le__0__iff__le,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 0.26/0.54        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_le_0_iff_le
% 0.26/0.54  thf(fact_4404_neg__le__0__iff__le,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.26/0.54        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_le_0_iff_le
% 0.26/0.54  thf(fact_4405_less__eq__neg__nonpos,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 0.26/0.54        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.26/0.54  
% 0.26/0.54  % less_eq_neg_nonpos
% 0.26/0.54  thf(fact_4406_less__eq__neg__nonpos,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.26/0.54        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.26/0.54  
% 0.26/0.54  % less_eq_neg_nonpos
% 0.26/0.54  thf(fact_4407_less__eq__neg__nonpos,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.26/0.54        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.26/0.54  
% 0.26/0.54  % less_eq_neg_nonpos
% 0.26/0.54  thf(fact_4408_less__eq__neg__nonpos,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 0.26/0.54        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.26/0.54  
% 0.26/0.54  % less_eq_neg_nonpos
% 0.26/0.54  thf(fact_4409_neg__less__eq__nonneg,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 0.26/0.54        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_less_eq_nonneg
% 0.26/0.54  thf(fact_4410_neg__less__eq__nonneg,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.26/0.54        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_less_eq_nonneg
% 0.26/0.54  thf(fact_4411_neg__less__eq__nonneg,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.26/0.54        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_less_eq_nonneg
% 0.26/0.54  thf(fact_4412_neg__less__eq__nonneg,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 0.26/0.54        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_less_eq_nonneg
% 0.26/0.54  thf(fact_4413_less__neg__neg,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 0.26/0.54        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.26/0.54  
% 0.26/0.54  % less_neg_neg
% 0.26/0.54  thf(fact_4414_less__neg__neg,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 0.26/0.54        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.26/0.54  
% 0.26/0.54  % less_neg_neg
% 0.26/0.54  thf(fact_4415_less__neg__neg,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.26/0.54        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.26/0.54  
% 0.26/0.54  % less_neg_neg
% 0.26/0.54  thf(fact_4416_less__neg__neg,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.26/0.54        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.26/0.54  
% 0.26/0.54  % less_neg_neg
% 0.26/0.54  thf(fact_4417_neg__less__pos,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 0.26/0.54        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_less_pos
% 0.26/0.54  thf(fact_4418_neg__less__pos,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 0.26/0.54        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_less_pos
% 0.26/0.54  thf(fact_4419_neg__less__pos,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.26/0.54        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_less_pos
% 0.26/0.54  thf(fact_4420_neg__less__pos,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.26/0.54        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_less_pos
% 0.26/0.54  thf(fact_4421_neg__0__less__iff__less,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 0.26/0.54        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_0_less_iff_less
% 0.26/0.54  thf(fact_4422_neg__0__less__iff__less,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.26/0.54        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_0_less_iff_less
% 0.26/0.54  thf(fact_4423_neg__0__less__iff__less,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.26/0.54        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_0_less_iff_less
% 0.26/0.54  thf(fact_4424_neg__0__less__iff__less,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 0.26/0.54        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_0_less_iff_less
% 0.26/0.54  thf(fact_4425_neg__less__0__iff__less,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 0.26/0.54        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_less_0_iff_less
% 0.26/0.54  thf(fact_4426_neg__less__0__iff__less,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.26/0.54        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_less_0_iff_less
% 0.26/0.54  thf(fact_4427_neg__less__0__iff__less,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 0.26/0.54        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_less_0_iff_less
% 0.26/0.54  thf(fact_4428_neg__less__0__iff__less,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 0.26/0.54        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_less_0_iff_less
% 0.26/0.54  thf(fact_4429_add_Oright__inverse,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 0.26/0.54        = zero_zero_real ) ).
% 0.26/0.54  
% 0.26/0.54  % add.right_inverse
% 0.26/0.54  thf(fact_4430_add_Oright__inverse,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 0.26/0.54        = zero_zero_int ) ).
% 0.26/0.54  
% 0.26/0.54  % add.right_inverse
% 0.26/0.54  thf(fact_4431_add_Oright__inverse,axiom,
% 0.26/0.54      ! [A: complex] :
% 0.26/0.54        ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 0.26/0.54        = zero_zero_complex ) ).
% 0.26/0.54  
% 0.26/0.54  % add.right_inverse
% 0.26/0.54  thf(fact_4432_add_Oright__inverse,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.26/0.54        = zero_z3403309356797280102nteger ) ).
% 0.26/0.54  
% 0.26/0.54  % add.right_inverse
% 0.26/0.54  thf(fact_4433_add_Oright__inverse,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.26/0.54        = zero_zero_rat ) ).
% 0.26/0.54  
% 0.26/0.54  % add.right_inverse
% 0.26/0.54  thf(fact_4434_ab__left__minus,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 0.26/0.54        = zero_zero_real ) ).
% 0.26/0.54  
% 0.26/0.54  % ab_left_minus
% 0.26/0.54  thf(fact_4435_ab__left__minus,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 0.26/0.54        = zero_zero_int ) ).
% 0.26/0.54  
% 0.26/0.54  % ab_left_minus
% 0.26/0.54  thf(fact_4436_ab__left__minus,axiom,
% 0.26/0.54      ! [A: complex] :
% 0.26/0.54        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 0.26/0.54        = zero_zero_complex ) ).
% 0.26/0.54  
% 0.26/0.54  % ab_left_minus
% 0.26/0.54  thf(fact_4437_ab__left__minus,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.26/0.54        = zero_z3403309356797280102nteger ) ).
% 0.26/0.54  
% 0.26/0.54  % ab_left_minus
% 0.26/0.54  thf(fact_4438_ab__left__minus,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.26/0.54        = zero_zero_rat ) ).
% 0.26/0.54  
% 0.26/0.54  % ab_left_minus
% 0.26/0.54  thf(fact_4439_verit__minus__simplify_I3_J,axiom,
% 0.26/0.54      ! [B: real] :
% 0.26/0.54        ( ( minus_minus_real @ zero_zero_real @ B )
% 0.26/0.54        = ( uminus_uminus_real @ B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % verit_minus_simplify(3)
% 0.26/0.54  thf(fact_4440_verit__minus__simplify_I3_J,axiom,
% 0.26/0.54      ! [B: int] :
% 0.26/0.54        ( ( minus_minus_int @ zero_zero_int @ B )
% 0.26/0.54        = ( uminus_uminus_int @ B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % verit_minus_simplify(3)
% 0.26/0.54  thf(fact_4441_verit__minus__simplify_I3_J,axiom,
% 0.26/0.54      ! [B: complex] :
% 0.26/0.54        ( ( minus_minus_complex @ zero_zero_complex @ B )
% 0.26/0.54        = ( uminus1482373934393186551omplex @ B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % verit_minus_simplify(3)
% 0.26/0.54  thf(fact_4442_verit__minus__simplify_I3_J,axiom,
% 0.26/0.54      ! [B: code_integer] :
% 0.26/0.54        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 0.26/0.54        = ( uminus1351360451143612070nteger @ B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % verit_minus_simplify(3)
% 0.26/0.54  thf(fact_4443_verit__minus__simplify_I3_J,axiom,
% 0.26/0.54      ! [B: rat] :
% 0.26/0.54        ( ( minus_minus_rat @ zero_zero_rat @ B )
% 0.26/0.54        = ( uminus_uminus_rat @ B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % verit_minus_simplify(3)
% 0.26/0.54  thf(fact_4444_diff__0,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( minus_minus_real @ zero_zero_real @ A )
% 0.26/0.54        = ( uminus_uminus_real @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_0
% 0.26/0.54  thf(fact_4445_diff__0,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( minus_minus_int @ zero_zero_int @ A )
% 0.26/0.54        = ( uminus_uminus_int @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_0
% 0.26/0.54  thf(fact_4446_diff__0,axiom,
% 0.26/0.54      ! [A: complex] :
% 0.26/0.54        ( ( minus_minus_complex @ zero_zero_complex @ A )
% 0.26/0.54        = ( uminus1482373934393186551omplex @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_0
% 0.26/0.54  thf(fact_4447_diff__0,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 0.26/0.54        = ( uminus1351360451143612070nteger @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_0
% 0.26/0.54  thf(fact_4448_diff__0,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( minus_minus_rat @ zero_zero_rat @ A )
% 0.26/0.54        = ( uminus_uminus_rat @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_0
% 0.26/0.54  thf(fact_4449_add__neg__numeral__simps_I3_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.26/0.54        = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % add_neg_numeral_simps(3)
% 0.26/0.54  thf(fact_4450_add__neg__numeral__simps_I3_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.54        = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % add_neg_numeral_simps(3)
% 0.26/0.54  thf(fact_4451_add__neg__numeral__simps_I3_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.26/0.54        = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % add_neg_numeral_simps(3)
% 0.26/0.54  thf(fact_4452_add__neg__numeral__simps_I3_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.26/0.54        = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % add_neg_numeral_simps(3)
% 0.26/0.54  thf(fact_4453_add__neg__numeral__simps_I3_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.26/0.54        = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % add_neg_numeral_simps(3)
% 0.26/0.54  thf(fact_4454_mult__minus1__right,axiom,
% 0.26/0.54      ! [Z: real] :
% 0.26/0.54        ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 0.26/0.54        = ( uminus_uminus_real @ Z ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_minus1_right
% 0.26/0.54  thf(fact_4455_mult__minus1__right,axiom,
% 0.26/0.54      ! [Z: int] :
% 0.26/0.54        ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.54        = ( uminus_uminus_int @ Z ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_minus1_right
% 0.26/0.54  thf(fact_4456_mult__minus1__right,axiom,
% 0.26/0.54      ! [Z: complex] :
% 0.26/0.54        ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.26/0.54        = ( uminus1482373934393186551omplex @ Z ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_minus1_right
% 0.26/0.54  thf(fact_4457_mult__minus1__right,axiom,
% 0.26/0.54      ! [Z: code_integer] :
% 0.26/0.54        ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.26/0.54        = ( uminus1351360451143612070nteger @ Z ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_minus1_right
% 0.26/0.54  thf(fact_4458_mult__minus1__right,axiom,
% 0.26/0.54      ! [Z: rat] :
% 0.26/0.54        ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.26/0.54        = ( uminus_uminus_rat @ Z ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_minus1_right
% 0.26/0.54  thf(fact_4459_mult__minus1,axiom,
% 0.26/0.54      ! [Z: real] :
% 0.26/0.54        ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 0.26/0.54        = ( uminus_uminus_real @ Z ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_minus1
% 0.26/0.54  thf(fact_4460_mult__minus1,axiom,
% 0.26/0.54      ! [Z: int] :
% 0.26/0.54        ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 0.26/0.54        = ( uminus_uminus_int @ Z ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_minus1
% 0.26/0.54  thf(fact_4461_mult__minus1,axiom,
% 0.26/0.54      ! [Z: complex] :
% 0.26/0.54        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 0.26/0.54        = ( uminus1482373934393186551omplex @ Z ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_minus1
% 0.26/0.54  thf(fact_4462_mult__minus1,axiom,
% 0.26/0.54      ! [Z: code_integer] :
% 0.26/0.54        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 0.26/0.54        = ( uminus1351360451143612070nteger @ Z ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_minus1
% 0.26/0.54  thf(fact_4463_mult__minus1,axiom,
% 0.26/0.54      ! [Z: rat] :
% 0.26/0.54        ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 0.26/0.54        = ( uminus_uminus_rat @ Z ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_minus1
% 0.26/0.54  thf(fact_4464_abs__of__nonneg,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.26/0.54       => ( ( abs_abs_Code_integer @ A )
% 0.26/0.54          = A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_of_nonneg
% 0.26/0.54  thf(fact_4465_abs__of__nonneg,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.54       => ( ( abs_abs_real @ A )
% 0.26/0.54          = A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_of_nonneg
% 0.26/0.54  thf(fact_4466_abs__of__nonneg,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.54       => ( ( abs_abs_rat @ A )
% 0.26/0.54          = A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_of_nonneg
% 0.26/0.54  thf(fact_4467_abs__of__nonneg,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.54       => ( ( abs_abs_int @ A )
% 0.26/0.54          = A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_of_nonneg
% 0.26/0.54  thf(fact_4468_abs__le__self__iff,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 0.26/0.54        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_le_self_iff
% 0.26/0.54  thf(fact_4469_abs__le__self__iff,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 0.26/0.54        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_le_self_iff
% 0.26/0.54  thf(fact_4470_abs__le__self__iff,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 0.26/0.54        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_le_self_iff
% 0.26/0.54  thf(fact_4471_abs__le__self__iff,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 0.26/0.54        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_le_self_iff
% 0.26/0.54  thf(fact_4472_abs__le__zero__iff,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 0.26/0.54        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_le_zero_iff
% 0.26/0.54  thf(fact_4473_abs__le__zero__iff,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 0.26/0.54        = ( A = zero_zero_real ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_le_zero_iff
% 0.26/0.54  thf(fact_4474_abs__le__zero__iff,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 0.26/0.54        = ( A = zero_zero_rat ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_le_zero_iff
% 0.26/0.54  thf(fact_4475_abs__le__zero__iff,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 0.26/0.54        = ( A = zero_zero_int ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_le_zero_iff
% 0.26/0.54  thf(fact_4476_diff__minus__eq__add,axiom,
% 0.26/0.54      ! [A: real,B: real] :
% 0.26/0.54        ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 0.26/0.54        = ( plus_plus_real @ A @ B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_minus_eq_add
% 0.26/0.54  thf(fact_4477_diff__minus__eq__add,axiom,
% 0.26/0.54      ! [A: int,B: int] :
% 0.26/0.54        ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 0.26/0.54        = ( plus_plus_int @ A @ B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_minus_eq_add
% 0.26/0.54  thf(fact_4478_diff__minus__eq__add,axiom,
% 0.26/0.54      ! [A: complex,B: complex] :
% 0.26/0.54        ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 0.26/0.54        = ( plus_plus_complex @ A @ B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_minus_eq_add
% 0.26/0.54  thf(fact_4479_diff__minus__eq__add,axiom,
% 0.26/0.54      ! [A: code_integer,B: code_integer] :
% 0.26/0.54        ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.26/0.54        = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_minus_eq_add
% 0.26/0.54  thf(fact_4480_diff__minus__eq__add,axiom,
% 0.26/0.54      ! [A: rat,B: rat] :
% 0.26/0.54        ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.26/0.54        = ( plus_plus_rat @ A @ B ) ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_minus_eq_add
% 0.26/0.54  thf(fact_4481_uminus__add__conv__diff,axiom,
% 0.26/0.54      ! [A: real,B: real] :
% 0.26/0.54        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 0.26/0.54        = ( minus_minus_real @ B @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % uminus_add_conv_diff
% 0.26/0.54  thf(fact_4482_uminus__add__conv__diff,axiom,
% 0.26/0.54      ! [A: int,B: int] :
% 0.26/0.54        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 0.26/0.54        = ( minus_minus_int @ B @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % uminus_add_conv_diff
% 0.26/0.54  thf(fact_4483_uminus__add__conv__diff,axiom,
% 0.26/0.54      ! [A: complex,B: complex] :
% 0.26/0.54        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 0.26/0.54        = ( minus_minus_complex @ B @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % uminus_add_conv_diff
% 0.26/0.54  thf(fact_4484_uminus__add__conv__diff,axiom,
% 0.26/0.54      ! [A: code_integer,B: code_integer] :
% 0.26/0.54        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.26/0.54        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % uminus_add_conv_diff
% 0.26/0.54  thf(fact_4485_uminus__add__conv__diff,axiom,
% 0.26/0.54      ! [A: rat,B: rat] :
% 0.26/0.54        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.26/0.54        = ( minus_minus_rat @ B @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % uminus_add_conv_diff
% 0.26/0.54  thf(fact_4486_zero__less__abs__iff,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 0.26/0.54        = ( A != zero_z3403309356797280102nteger ) ) ).
% 0.26/0.54  
% 0.26/0.54  % zero_less_abs_iff
% 0.26/0.54  thf(fact_4487_zero__less__abs__iff,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 0.26/0.54        = ( A != zero_zero_real ) ) ).
% 0.26/0.54  
% 0.26/0.54  % zero_less_abs_iff
% 0.26/0.54  thf(fact_4488_zero__less__abs__iff,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 0.26/0.54        = ( A != zero_zero_rat ) ) ).
% 0.26/0.54  
% 0.26/0.54  % zero_less_abs_iff
% 0.26/0.54  thf(fact_4489_zero__less__abs__iff,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 0.26/0.54        = ( A != zero_zero_int ) ) ).
% 0.26/0.54  
% 0.26/0.54  % zero_less_abs_iff
% 0.26/0.54  thf(fact_4490_abs__neg__numeral,axiom,
% 0.26/0.54      ! [N: num] :
% 0.26/0.54        ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.26/0.54        = ( numeral_numeral_real @ N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_neg_numeral
% 0.26/0.54  thf(fact_4491_abs__neg__numeral,axiom,
% 0.26/0.54      ! [N: num] :
% 0.26/0.54        ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.54        = ( numeral_numeral_int @ N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_neg_numeral
% 0.26/0.54  thf(fact_4492_abs__neg__numeral,axiom,
% 0.26/0.54      ! [N: num] :
% 0.26/0.54        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.26/0.54        = ( numera6620942414471956472nteger @ N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_neg_numeral
% 0.26/0.54  thf(fact_4493_abs__neg__numeral,axiom,
% 0.26/0.54      ! [N: num] :
% 0.26/0.54        ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.26/0.54        = ( numeral_numeral_rat @ N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_neg_numeral
% 0.26/0.54  thf(fact_4494_abs__neg__one,axiom,
% 0.26/0.54      ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.26/0.54      = one_one_real ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_neg_one
% 0.26/0.54  thf(fact_4495_abs__neg__one,axiom,
% 0.26/0.54      ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.54      = one_one_int ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_neg_one
% 0.26/0.54  thf(fact_4496_abs__neg__one,axiom,
% 0.26/0.54      ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.26/0.54      = one_one_Code_integer ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_neg_one
% 0.26/0.54  thf(fact_4497_abs__neg__one,axiom,
% 0.26/0.54      ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.26/0.54      = one_one_rat ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_neg_one
% 0.26/0.54  thf(fact_4498_norm__eq__zero,axiom,
% 0.26/0.54      ! [X3: real] :
% 0.26/0.54        ( ( ( real_V7735802525324610683m_real @ X3 )
% 0.26/0.54          = zero_zero_real )
% 0.26/0.54        = ( X3 = zero_zero_real ) ) ).
% 0.26/0.54  
% 0.26/0.54  % norm_eq_zero
% 0.26/0.54  thf(fact_4499_norm__eq__zero,axiom,
% 0.26/0.54      ! [X3: complex] :
% 0.26/0.54        ( ( ( real_V1022390504157884413omplex @ X3 )
% 0.26/0.54          = zero_zero_real )
% 0.26/0.54        = ( X3 = zero_zero_complex ) ) ).
% 0.26/0.54  
% 0.26/0.54  % norm_eq_zero
% 0.26/0.54  thf(fact_4500_norm__zero,axiom,
% 0.26/0.54      ( ( real_V7735802525324610683m_real @ zero_zero_real )
% 0.26/0.54      = zero_zero_real ) ).
% 0.26/0.54  
% 0.26/0.54  % norm_zero
% 0.26/0.54  thf(fact_4501_norm__zero,axiom,
% 0.26/0.54      ( ( real_V1022390504157884413omplex @ zero_zero_complex )
% 0.26/0.54      = zero_zero_real ) ).
% 0.26/0.54  
% 0.26/0.54  % norm_zero
% 0.26/0.54  thf(fact_4502_abs__power__minus,axiom,
% 0.26/0.54      ! [A: real,N: nat] :
% 0.26/0.54        ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 0.26/0.54        = ( abs_abs_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_power_minus
% 0.26/0.54  thf(fact_4503_abs__power__minus,axiom,
% 0.26/0.54      ! [A: int,N: nat] :
% 0.26/0.54        ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 0.26/0.54        = ( abs_abs_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_power_minus
% 0.26/0.54  thf(fact_4504_abs__power__minus,axiom,
% 0.26/0.54      ! [A: code_integer,N: nat] :
% 0.26/0.54        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 0.26/0.54        = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_power_minus
% 0.26/0.54  thf(fact_4505_abs__power__minus,axiom,
% 0.26/0.54      ! [A: rat,N: nat] :
% 0.26/0.54        ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 0.26/0.54        = ( abs_abs_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_power_minus
% 0.26/0.54  thf(fact_4506_norm__numeral,axiom,
% 0.26/0.54      ! [W: num] :
% 0.26/0.54        ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 0.26/0.54        = ( numeral_numeral_real @ W ) ) ).
% 0.26/0.54  
% 0.26/0.54  % norm_numeral
% 0.26/0.54  thf(fact_4507_norm__numeral,axiom,
% 0.26/0.54      ! [W: num] :
% 0.26/0.54        ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.26/0.54        = ( numeral_numeral_real @ W ) ) ).
% 0.26/0.54  
% 0.26/0.54  % norm_numeral
% 0.26/0.54  thf(fact_4508_bit_Odisj__one__left,axiom,
% 0.26/0.54      ! [X3: code_integer] :
% 0.26/0.54        ( ( bit_se1080825931792720795nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X3 )
% 0.26/0.54        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.54  
% 0.26/0.54  % bit.disj_one_left
% 0.26/0.54  thf(fact_4509_bit_Odisj__one__left,axiom,
% 0.26/0.54      ! [X3: int] :
% 0.26/0.54        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ one_one_int ) @ X3 )
% 0.26/0.54        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.54  
% 0.26/0.54  % bit.disj_one_left
% 0.26/0.54  thf(fact_4510_bit_Odisj__one__right,axiom,
% 0.26/0.54      ! [X3: code_integer] :
% 0.26/0.54        ( ( bit_se1080825931792720795nteger @ X3 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.26/0.54        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.54  
% 0.26/0.54  % bit.disj_one_right
% 0.26/0.54  thf(fact_4511_bit_Odisj__one__right,axiom,
% 0.26/0.54      ! [X3: int] :
% 0.26/0.54        ( ( bit_se1409905431419307370or_int @ X3 @ ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.54        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.54  
% 0.26/0.54  % bit.disj_one_right
% 0.26/0.54  thf(fact_4512_real__add__minus__iff,axiom,
% 0.26/0.54      ! [X3: real,A: real] :
% 0.26/0.54        ( ( ( plus_plus_real @ X3 @ ( uminus_uminus_real @ A ) )
% 0.26/0.54          = zero_zero_real )
% 0.26/0.54        = ( X3 = A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % real_add_minus_iff
% 0.26/0.54  thf(fact_4513_norm__of__nat,axiom,
% 0.26/0.54      ! [N: nat] :
% 0.26/0.54        ( ( real_V7735802525324610683m_real @ ( semiri5074537144036343181t_real @ N ) )
% 0.26/0.54        = ( semiri5074537144036343181t_real @ N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % norm_of_nat
% 0.26/0.54  thf(fact_4514_norm__of__nat,axiom,
% 0.26/0.54      ! [N: nat] :
% 0.26/0.54        ( ( real_V1022390504157884413omplex @ ( semiri8010041392384452111omplex @ N ) )
% 0.26/0.54        = ( semiri5074537144036343181t_real @ N ) ) ).
% 0.26/0.54  
% 0.26/0.54  % norm_of_nat
% 0.26/0.54  thf(fact_4515_floor__uminus__of__int,axiom,
% 0.26/0.54      ! [Z: int] :
% 0.26/0.54        ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ Z ) ) )
% 0.26/0.54        = ( uminus_uminus_int @ Z ) ) ).
% 0.26/0.54  
% 0.26/0.54  % floor_uminus_of_int
% 0.26/0.54  thf(fact_4516_floor__uminus__of__int,axiom,
% 0.26/0.54      ! [Z: int] :
% 0.26/0.54        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( ring_1_of_int_real @ Z ) ) )
% 0.26/0.54        = ( uminus_uminus_int @ Z ) ) ).
% 0.26/0.54  
% 0.26/0.54  % floor_uminus_of_int
% 0.26/0.54  thf(fact_4517_real__sqrt__abs2,axiom,
% 0.26/0.54      ! [X3: real] :
% 0.26/0.54        ( ( sqrt @ ( times_times_real @ X3 @ X3 ) )
% 0.26/0.54        = ( abs_abs_real @ X3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % real_sqrt_abs2
% 0.26/0.54  thf(fact_4518_real__sqrt__mult__self,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 0.26/0.54        = ( abs_abs_real @ A ) ) ).
% 0.26/0.54  
% 0.26/0.54  % real_sqrt_mult_self
% 0.26/0.54  thf(fact_4519_dbl__simps_I1_J,axiom,
% 0.26/0.54      ! [K: num] :
% 0.26/0.54        ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 0.26/0.54        = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % dbl_simps(1)
% 0.26/0.54  thf(fact_4520_dbl__simps_I1_J,axiom,
% 0.26/0.54      ! [K: num] :
% 0.26/0.54        ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.26/0.54        = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % dbl_simps(1)
% 0.26/0.54  thf(fact_4521_dbl__simps_I1_J,axiom,
% 0.26/0.54      ! [K: num] :
% 0.26/0.54        ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 0.26/0.54        = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % dbl_simps(1)
% 0.26/0.54  thf(fact_4522_dbl__simps_I1_J,axiom,
% 0.26/0.54      ! [K: num] :
% 0.26/0.54        ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.26/0.54        = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % dbl_simps(1)
% 0.26/0.54  thf(fact_4523_dbl__simps_I1_J,axiom,
% 0.26/0.54      ! [K: num] :
% 0.26/0.54        ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.26/0.54        = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % dbl_simps(1)
% 0.26/0.54  thf(fact_4524_add__neg__numeral__special_I8_J,axiom,
% 0.26/0.54      ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 0.26/0.54      = zero_zero_real ) ).
% 0.26/0.54  
% 0.26/0.54  % add_neg_numeral_special(8)
% 0.26/0.54  thf(fact_4525_add__neg__numeral__special_I8_J,axiom,
% 0.26/0.54      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 0.26/0.54      = zero_zero_int ) ).
% 0.26/0.54  
% 0.26/0.54  % add_neg_numeral_special(8)
% 0.26/0.54  thf(fact_4526_add__neg__numeral__special_I8_J,axiom,
% 0.26/0.54      ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 0.26/0.54      = zero_zero_complex ) ).
% 0.26/0.54  
% 0.26/0.54  % add_neg_numeral_special(8)
% 0.26/0.54  thf(fact_4527_add__neg__numeral__special_I8_J,axiom,
% 0.26/0.54      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 0.26/0.54      = zero_z3403309356797280102nteger ) ).
% 0.26/0.54  
% 0.26/0.54  % add_neg_numeral_special(8)
% 0.26/0.54  thf(fact_4528_add__neg__numeral__special_I8_J,axiom,
% 0.26/0.54      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 0.26/0.54      = zero_zero_rat ) ).
% 0.26/0.54  
% 0.26/0.54  % add_neg_numeral_special(8)
% 0.26/0.54  thf(fact_4529_add__neg__numeral__special_I7_J,axiom,
% 0.26/0.54      ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.26/0.54      = zero_zero_real ) ).
% 0.26/0.54  
% 0.26/0.54  % add_neg_numeral_special(7)
% 0.26/0.54  thf(fact_4530_add__neg__numeral__special_I7_J,axiom,
% 0.26/0.54      ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.54      = zero_zero_int ) ).
% 0.26/0.54  
% 0.26/0.54  % add_neg_numeral_special(7)
% 0.26/0.54  thf(fact_4531_add__neg__numeral__special_I7_J,axiom,
% 0.26/0.54      ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.26/0.54      = zero_zero_complex ) ).
% 0.26/0.54  
% 0.26/0.54  % add_neg_numeral_special(7)
% 0.26/0.54  thf(fact_4532_add__neg__numeral__special_I7_J,axiom,
% 0.26/0.54      ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.26/0.54      = zero_z3403309356797280102nteger ) ).
% 0.26/0.54  
% 0.26/0.54  % add_neg_numeral_special(7)
% 0.26/0.54  thf(fact_4533_add__neg__numeral__special_I7_J,axiom,
% 0.26/0.54      ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.26/0.54      = zero_zero_rat ) ).
% 0.26/0.54  
% 0.26/0.54  % add_neg_numeral_special(7)
% 0.26/0.54  thf(fact_4534_diff__numeral__special_I12_J,axiom,
% 0.26/0.54      ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.26/0.54      = zero_zero_real ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_numeral_special(12)
% 0.26/0.54  thf(fact_4535_diff__numeral__special_I12_J,axiom,
% 0.26/0.54      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.54      = zero_zero_int ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_numeral_special(12)
% 0.26/0.54  thf(fact_4536_diff__numeral__special_I12_J,axiom,
% 0.26/0.54      ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.26/0.54      = zero_zero_complex ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_numeral_special(12)
% 0.26/0.54  thf(fact_4537_diff__numeral__special_I12_J,axiom,
% 0.26/0.54      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.26/0.54      = zero_z3403309356797280102nteger ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_numeral_special(12)
% 0.26/0.54  thf(fact_4538_diff__numeral__special_I12_J,axiom,
% 0.26/0.54      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.26/0.54      = zero_zero_rat ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_numeral_special(12)
% 0.26/0.54  thf(fact_4539_neg__one__eq__numeral__iff,axiom,
% 0.26/0.54      ! [N: num] :
% 0.26/0.54        ( ( ( uminus_uminus_real @ one_one_real )
% 0.26/0.54          = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.26/0.54        = ( N = one ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_one_eq_numeral_iff
% 0.26/0.54  thf(fact_4540_neg__one__eq__numeral__iff,axiom,
% 0.26/0.54      ! [N: num] :
% 0.26/0.54        ( ( ( uminus_uminus_int @ one_one_int )
% 0.26/0.54          = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.54        = ( N = one ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_one_eq_numeral_iff
% 0.26/0.54  thf(fact_4541_neg__one__eq__numeral__iff,axiom,
% 0.26/0.54      ! [N: num] :
% 0.26/0.54        ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 0.26/0.54          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.26/0.54        = ( N = one ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_one_eq_numeral_iff
% 0.26/0.54  thf(fact_4542_neg__one__eq__numeral__iff,axiom,
% 0.26/0.54      ! [N: num] :
% 0.26/0.54        ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 0.26/0.54          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.26/0.54        = ( N = one ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_one_eq_numeral_iff
% 0.26/0.54  thf(fact_4543_neg__one__eq__numeral__iff,axiom,
% 0.26/0.54      ! [N: num] :
% 0.26/0.54        ( ( ( uminus_uminus_rat @ one_one_rat )
% 0.26/0.54          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.26/0.54        = ( N = one ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_one_eq_numeral_iff
% 0.26/0.54  thf(fact_4544_numeral__eq__neg__one__iff,axiom,
% 0.26/0.54      ! [N: num] :
% 0.26/0.54        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N ) )
% 0.26/0.54          = ( uminus_uminus_real @ one_one_real ) )
% 0.26/0.54        = ( N = one ) ) ).
% 0.26/0.54  
% 0.26/0.54  % numeral_eq_neg_one_iff
% 0.26/0.54  thf(fact_4545_numeral__eq__neg__one__iff,axiom,
% 0.26/0.54      ! [N: num] :
% 0.26/0.54        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 0.26/0.54          = ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.54        = ( N = one ) ) ).
% 0.26/0.54  
% 0.26/0.54  % numeral_eq_neg_one_iff
% 0.26/0.54  thf(fact_4546_numeral__eq__neg__one__iff,axiom,
% 0.26/0.54      ! [N: num] :
% 0.26/0.54        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) )
% 0.26/0.54          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.26/0.54        = ( N = one ) ) ).
% 0.26/0.54  
% 0.26/0.54  % numeral_eq_neg_one_iff
% 0.26/0.54  thf(fact_4547_numeral__eq__neg__one__iff,axiom,
% 0.26/0.54      ! [N: num] :
% 0.26/0.54        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 0.26/0.54          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.26/0.54        = ( N = one ) ) ).
% 0.26/0.54  
% 0.26/0.54  % numeral_eq_neg_one_iff
% 0.26/0.54  thf(fact_4548_numeral__eq__neg__one__iff,axiom,
% 0.26/0.54      ! [N: num] :
% 0.26/0.54        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 0.26/0.54          = ( uminus_uminus_rat @ one_one_rat ) )
% 0.26/0.54        = ( N = one ) ) ).
% 0.26/0.54  
% 0.26/0.54  % numeral_eq_neg_one_iff
% 0.26/0.54  thf(fact_4549_divide__le__0__abs__iff,axiom,
% 0.26/0.54      ! [A: real,B: real] :
% 0.26/0.54        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 0.26/0.54        = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.26/0.54          | ( B = zero_zero_real ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % divide_le_0_abs_iff
% 0.26/0.54  thf(fact_4550_divide__le__0__abs__iff,axiom,
% 0.26/0.54      ! [A: rat,B: rat] :
% 0.26/0.54        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 0.26/0.54        = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.26/0.54          | ( B = zero_zero_rat ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % divide_le_0_abs_iff
% 0.26/0.54  thf(fact_4551_zero__le__divide__abs__iff,axiom,
% 0.26/0.54      ! [A: real,B: real] :
% 0.26/0.54        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 0.26/0.54        = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.54          | ( B = zero_zero_real ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % zero_le_divide_abs_iff
% 0.26/0.54  thf(fact_4552_zero__le__divide__abs__iff,axiom,
% 0.26/0.54      ! [A: rat,B: rat] :
% 0.26/0.54        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 0.26/0.54        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.54          | ( B = zero_zero_rat ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % zero_le_divide_abs_iff
% 0.26/0.54  thf(fact_4553_left__minus__one__mult__self,axiom,
% 0.26/0.54      ! [N: nat,A: real] :
% 0.26/0.54        ( ( 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 ) )
% 0.26/0.54        = A ) ).
% 0.26/0.54  
% 0.26/0.54  % left_minus_one_mult_self
% 0.26/0.54  thf(fact_4554_left__minus__one__mult__self,axiom,
% 0.26/0.54      ! [N: nat,A: int] :
% 0.26/0.54        ( ( 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 ) )
% 0.26/0.54        = A ) ).
% 0.26/0.54  
% 0.26/0.54  % left_minus_one_mult_self
% 0.26/0.54  thf(fact_4555_left__minus__one__mult__self,axiom,
% 0.26/0.54      ! [N: nat,A: complex] :
% 0.26/0.54        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ A ) )
% 0.26/0.54        = A ) ).
% 0.26/0.54  
% 0.26/0.54  % left_minus_one_mult_self
% 0.26/0.54  thf(fact_4556_left__minus__one__mult__self,axiom,
% 0.26/0.54      ! [N: nat,A: code_integer] :
% 0.26/0.54        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 0.26/0.54        = A ) ).
% 0.26/0.54  
% 0.26/0.54  % left_minus_one_mult_self
% 0.26/0.54  thf(fact_4557_left__minus__one__mult__self,axiom,
% 0.26/0.54      ! [N: nat,A: rat] :
% 0.26/0.54        ( ( 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 ) )
% 0.26/0.54        = A ) ).
% 0.26/0.54  
% 0.26/0.54  % left_minus_one_mult_self
% 0.26/0.54  thf(fact_4558_minus__one__mult__self,axiom,
% 0.26/0.54      ! [N: nat] :
% 0.26/0.54        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) )
% 0.26/0.54        = one_one_real ) ).
% 0.26/0.54  
% 0.26/0.54  % minus_one_mult_self
% 0.26/0.54  thf(fact_4559_minus__one__mult__self,axiom,
% 0.26/0.54      ! [N: nat] :
% 0.26/0.54        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 0.26/0.54        = one_one_int ) ).
% 0.26/0.54  
% 0.26/0.54  % minus_one_mult_self
% 0.26/0.54  thf(fact_4560_minus__one__mult__self,axiom,
% 0.26/0.54      ! [N: nat] :
% 0.26/0.54        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) )
% 0.26/0.54        = one_one_complex ) ).
% 0.26/0.54  
% 0.26/0.54  % minus_one_mult_self
% 0.26/0.54  thf(fact_4561_minus__one__mult__self,axiom,
% 0.26/0.54      ! [N: nat] :
% 0.26/0.54        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 0.26/0.54        = one_one_Code_integer ) ).
% 0.26/0.54  
% 0.26/0.54  % minus_one_mult_self
% 0.26/0.54  thf(fact_4562_minus__one__mult__self,axiom,
% 0.26/0.54      ! [N: nat] :
% 0.26/0.54        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 0.26/0.54        = one_one_rat ) ).
% 0.26/0.54  
% 0.26/0.54  % minus_one_mult_self
% 0.26/0.54  thf(fact_4563_abs__of__nonpos,axiom,
% 0.26/0.54      ! [A: real] :
% 0.26/0.54        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.26/0.54       => ( ( abs_abs_real @ A )
% 0.26/0.54          = ( uminus_uminus_real @ A ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_of_nonpos
% 0.26/0.54  thf(fact_4564_abs__of__nonpos,axiom,
% 0.26/0.54      ! [A: code_integer] :
% 0.26/0.54        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.26/0.54       => ( ( abs_abs_Code_integer @ A )
% 0.26/0.54          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_of_nonpos
% 0.26/0.54  thf(fact_4565_abs__of__nonpos,axiom,
% 0.26/0.54      ! [A: rat] :
% 0.26/0.54        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.26/0.54       => ( ( abs_abs_rat @ A )
% 0.26/0.54          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_of_nonpos
% 0.26/0.54  thf(fact_4566_abs__of__nonpos,axiom,
% 0.26/0.54      ! [A: int] :
% 0.26/0.54        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.26/0.54       => ( ( abs_abs_int @ A )
% 0.26/0.54          = ( uminus_uminus_int @ A ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % abs_of_nonpos
% 0.26/0.54  thf(fact_4567_zero__less__norm__iff,axiom,
% 0.26/0.54      ! [X3: real] :
% 0.26/0.54        ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X3 ) )
% 0.26/0.54        = ( X3 != zero_zero_real ) ) ).
% 0.26/0.54  
% 0.26/0.54  % zero_less_norm_iff
% 0.26/0.54  thf(fact_4568_zero__less__norm__iff,axiom,
% 0.26/0.54      ! [X3: complex] :
% 0.26/0.54        ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X3 ) )
% 0.26/0.54        = ( X3 != zero_zero_complex ) ) ).
% 0.26/0.54  
% 0.26/0.54  % zero_less_norm_iff
% 0.26/0.54  thf(fact_4569_norm__le__zero__iff,axiom,
% 0.26/0.54      ! [X3: real] :
% 0.26/0.54        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X3 ) @ zero_zero_real )
% 0.26/0.54        = ( X3 = zero_zero_real ) ) ).
% 0.26/0.54  
% 0.26/0.54  % norm_le_zero_iff
% 0.26/0.54  thf(fact_4570_norm__le__zero__iff,axiom,
% 0.26/0.54      ! [X3: complex] :
% 0.26/0.54        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X3 ) @ zero_zero_real )
% 0.26/0.54        = ( X3 = zero_zero_complex ) ) ).
% 0.26/0.54  
% 0.26/0.54  % norm_le_zero_iff
% 0.26/0.54  thf(fact_4571_norm__neg__numeral,axiom,
% 0.26/0.54      ! [W: num] :
% 0.26/0.54        ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.26/0.54        = ( numeral_numeral_real @ W ) ) ).
% 0.26/0.54  
% 0.26/0.54  % norm_neg_numeral
% 0.26/0.54  thf(fact_4572_norm__neg__numeral,axiom,
% 0.26/0.54      ! [W: num] :
% 0.26/0.54        ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.26/0.54        = ( numeral_numeral_real @ W ) ) ).
% 0.26/0.54  
% 0.26/0.54  % norm_neg_numeral
% 0.26/0.54  thf(fact_4573_floor__neg__numeral,axiom,
% 0.26/0.54      ! [V: num] :
% 0.26/0.54        ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.26/0.54        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % floor_neg_numeral
% 0.26/0.54  thf(fact_4574_floor__neg__numeral,axiom,
% 0.26/0.54      ! [V: num] :
% 0.26/0.54        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.26/0.54        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % floor_neg_numeral
% 0.26/0.54  thf(fact_4575_semiring__norm_I168_J,axiom,
% 0.26/0.54      ! [V: num,W: num,Y3: real] :
% 0.26/0.54        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y3 ) )
% 0.26/0.54        = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(168)
% 0.26/0.54  thf(fact_4576_semiring__norm_I168_J,axiom,
% 0.26/0.54      ! [V: num,W: num,Y3: int] :
% 0.26/0.54        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y3 ) )
% 0.26/0.54        = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(168)
% 0.26/0.54  thf(fact_4577_semiring__norm_I168_J,axiom,
% 0.26/0.54      ! [V: num,W: num,Y3: complex] :
% 0.26/0.54        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y3 ) )
% 0.26/0.54        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(168)
% 0.26/0.54  thf(fact_4578_semiring__norm_I168_J,axiom,
% 0.26/0.54      ! [V: num,W: num,Y3: code_integer] :
% 0.26/0.54        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y3 ) )
% 0.26/0.54        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(168)
% 0.26/0.54  thf(fact_4579_semiring__norm_I168_J,axiom,
% 0.26/0.54      ! [V: num,W: num,Y3: rat] :
% 0.26/0.54        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y3 ) )
% 0.26/0.54        = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(168)
% 0.26/0.54  thf(fact_4580_diff__numeral__simps_I3_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 0.26/0.54        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_numeral_simps(3)
% 0.26/0.54  thf(fact_4581_diff__numeral__simps_I3_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.54        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_numeral_simps(3)
% 0.26/0.54  thf(fact_4582_diff__numeral__simps_I3_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 0.26/0.54        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_numeral_simps(3)
% 0.26/0.54  thf(fact_4583_diff__numeral__simps_I3_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 0.26/0.54        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_numeral_simps(3)
% 0.26/0.54  thf(fact_4584_diff__numeral__simps_I3_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 0.26/0.54        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_numeral_simps(3)
% 0.26/0.54  thf(fact_4585_diff__numeral__simps_I2_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.26/0.54        = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_numeral_simps(2)
% 0.26/0.54  thf(fact_4586_diff__numeral__simps_I2_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.54        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_numeral_simps(2)
% 0.26/0.54  thf(fact_4587_diff__numeral__simps_I2_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.26/0.54        = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_numeral_simps(2)
% 0.26/0.54  thf(fact_4588_diff__numeral__simps_I2_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.26/0.54        = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_numeral_simps(2)
% 0.26/0.54  thf(fact_4589_diff__numeral__simps_I2_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.26/0.54        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % diff_numeral_simps(2)
% 0.26/0.54  thf(fact_4590_ceiling__neg__numeral,axiom,
% 0.26/0.54      ! [V: num] :
% 0.26/0.54        ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.26/0.54        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % ceiling_neg_numeral
% 0.26/0.54  thf(fact_4591_ceiling__neg__numeral,axiom,
% 0.26/0.54      ! [V: num] :
% 0.26/0.54        ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.26/0.54        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % ceiling_neg_numeral
% 0.26/0.54  thf(fact_4592_semiring__norm_I172_J,axiom,
% 0.26/0.54      ! [V: num,W: num,Y3: real] :
% 0.26/0.54        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y3 ) )
% 0.26/0.54        = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(172)
% 0.26/0.54  thf(fact_4593_semiring__norm_I172_J,axiom,
% 0.26/0.54      ! [V: num,W: num,Y3: int] :
% 0.26/0.54        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y3 ) )
% 0.26/0.54        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(172)
% 0.26/0.54  thf(fact_4594_semiring__norm_I172_J,axiom,
% 0.26/0.54      ! [V: num,W: num,Y3: complex] :
% 0.26/0.54        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y3 ) )
% 0.26/0.54        = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(172)
% 0.26/0.54  thf(fact_4595_semiring__norm_I172_J,axiom,
% 0.26/0.54      ! [V: num,W: num,Y3: code_integer] :
% 0.26/0.54        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y3 ) )
% 0.26/0.54        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(172)
% 0.26/0.54  thf(fact_4596_semiring__norm_I172_J,axiom,
% 0.26/0.54      ! [V: num,W: num,Y3: rat] :
% 0.26/0.54        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y3 ) )
% 0.26/0.54        = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(172)
% 0.26/0.54  thf(fact_4597_semiring__norm_I171_J,axiom,
% 0.26/0.54      ! [V: num,W: num,Y3: real] :
% 0.26/0.54        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y3 ) )
% 0.26/0.54        = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(171)
% 0.26/0.54  thf(fact_4598_semiring__norm_I171_J,axiom,
% 0.26/0.54      ! [V: num,W: num,Y3: int] :
% 0.26/0.54        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y3 ) )
% 0.26/0.54        = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(171)
% 0.26/0.54  thf(fact_4599_semiring__norm_I171_J,axiom,
% 0.26/0.54      ! [V: num,W: num,Y3: complex] :
% 0.26/0.54        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y3 ) )
% 0.26/0.54        = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(171)
% 0.26/0.54  thf(fact_4600_semiring__norm_I171_J,axiom,
% 0.26/0.54      ! [V: num,W: num,Y3: code_integer] :
% 0.26/0.54        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y3 ) )
% 0.26/0.54        = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(171)
% 0.26/0.54  thf(fact_4601_semiring__norm_I171_J,axiom,
% 0.26/0.54      ! [V: num,W: num,Y3: rat] :
% 0.26/0.54        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y3 ) )
% 0.26/0.54        = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(171)
% 0.26/0.54  thf(fact_4602_semiring__norm_I170_J,axiom,
% 0.26/0.54      ! [V: num,W: num,Y3: real] :
% 0.26/0.54        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y3 ) )
% 0.26/0.54        = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(170)
% 0.26/0.54  thf(fact_4603_semiring__norm_I170_J,axiom,
% 0.26/0.54      ! [V: num,W: num,Y3: int] :
% 0.26/0.54        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y3 ) )
% 0.26/0.54        = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(170)
% 0.26/0.54  thf(fact_4604_semiring__norm_I170_J,axiom,
% 0.26/0.54      ! [V: num,W: num,Y3: complex] :
% 0.26/0.54        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y3 ) )
% 0.26/0.54        = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(170)
% 0.26/0.54  thf(fact_4605_semiring__norm_I170_J,axiom,
% 0.26/0.54      ! [V: num,W: num,Y3: code_integer] :
% 0.26/0.54        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y3 ) )
% 0.26/0.54        = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(170)
% 0.26/0.54  thf(fact_4606_semiring__norm_I170_J,axiom,
% 0.26/0.54      ! [V: num,W: num,Y3: rat] :
% 0.26/0.54        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y3 ) )
% 0.26/0.54        = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 0.26/0.54  
% 0.26/0.54  % semiring_norm(170)
% 0.26/0.54  thf(fact_4607_mult__neg__numeral__simps_I3_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.26/0.54        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_neg_numeral_simps(3)
% 0.26/0.54  thf(fact_4608_mult__neg__numeral__simps_I3_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.54        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_neg_numeral_simps(3)
% 0.26/0.54  thf(fact_4609_mult__neg__numeral__simps_I3_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.26/0.54        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_neg_numeral_simps(3)
% 0.26/0.54  thf(fact_4610_mult__neg__numeral__simps_I3_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.26/0.54        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_neg_numeral_simps(3)
% 0.26/0.54  thf(fact_4611_mult__neg__numeral__simps_I3_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.26/0.54        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_neg_numeral_simps(3)
% 0.26/0.54  thf(fact_4612_mult__neg__numeral__simps_I2_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 0.26/0.54        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_neg_numeral_simps(2)
% 0.26/0.54  thf(fact_4613_mult__neg__numeral__simps_I2_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.54        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_neg_numeral_simps(2)
% 0.26/0.54  thf(fact_4614_mult__neg__numeral__simps_I2_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 0.26/0.54        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_neg_numeral_simps(2)
% 0.26/0.54  thf(fact_4615_mult__neg__numeral__simps_I2_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 0.26/0.54        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_neg_numeral_simps(2)
% 0.26/0.54  thf(fact_4616_mult__neg__numeral__simps_I2_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 0.26/0.54        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_neg_numeral_simps(2)
% 0.26/0.54  thf(fact_4617_mult__neg__numeral__simps_I1_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.26/0.54        = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_neg_numeral_simps(1)
% 0.26/0.54  thf(fact_4618_mult__neg__numeral__simps_I1_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.54        = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_neg_numeral_simps(1)
% 0.26/0.54  thf(fact_4619_mult__neg__numeral__simps_I1_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.26/0.54        = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_neg_numeral_simps(1)
% 0.26/0.54  thf(fact_4620_mult__neg__numeral__simps_I1_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.26/0.54        = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_neg_numeral_simps(1)
% 0.26/0.54  thf(fact_4621_mult__neg__numeral__simps_I1_J,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.26/0.54        = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % mult_neg_numeral_simps(1)
% 0.26/0.54  thf(fact_4622_artanh__minus__real,axiom,
% 0.26/0.54      ! [X3: real] :
% 0.26/0.54        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.26/0.54       => ( ( artanh_real @ ( uminus_uminus_real @ X3 ) )
% 0.26/0.54          = ( uminus_uminus_real @ ( artanh_real @ X3 ) ) ) ) ).
% 0.26/0.54  
% 0.26/0.54  % artanh_minus_real
% 0.26/0.54  thf(fact_4623_neg__numeral__le__iff,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.26/0.54        = ( ord_less_eq_num @ N @ M ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_numeral_le_iff
% 0.26/0.54  thf(fact_4624_neg__numeral__le__iff,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.26/0.54        = ( ord_less_eq_num @ N @ M ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_numeral_le_iff
% 0.26/0.54  thf(fact_4625_neg__numeral__le__iff,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.26/0.54        = ( ord_less_eq_num @ N @ M ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_numeral_le_iff
% 0.26/0.54  thf(fact_4626_neg__numeral__le__iff,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.54        = ( ord_less_eq_num @ N @ M ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_numeral_le_iff
% 0.26/0.54  thf(fact_4627_neg__numeral__less__iff,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.26/0.54        = ( ord_less_num @ N @ M ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_numeral_less_iff
% 0.26/0.54  thf(fact_4628_neg__numeral__less__iff,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.54        = ( ord_less_num @ N @ M ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_numeral_less_iff
% 0.26/0.54  thf(fact_4629_neg__numeral__less__iff,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.26/0.54        = ( ord_less_num @ N @ M ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_numeral_less_iff
% 0.26/0.54  thf(fact_4630_neg__numeral__less__iff,axiom,
% 0.26/0.54      ! [M: num,N: num] :
% 0.26/0.54        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.26/0.54        = ( ord_less_num @ N @ M ) ) ).
% 0.26/0.54  
% 0.26/0.54  % neg_numeral_less_iff
% 0.26/0.54  thf(fact_4631_round__neg__numeral,axiom,
% 0.26/0.54      ! [N: num] :
% 0.26/0.54        ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.26/0.55        = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % round_neg_numeral
% 0.26/0.55  thf(fact_4632_round__neg__numeral,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.26/0.55        = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % round_neg_numeral
% 0.26/0.55  thf(fact_4633_norm__of__int,axiom,
% 0.26/0.55      ! [Z: int] :
% 0.26/0.55        ( ( real_V7735802525324610683m_real @ ( ring_1_of_int_real @ Z ) )
% 0.26/0.55        = ( abs_abs_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % norm_of_int
% 0.26/0.55  thf(fact_4634_norm__of__int,axiom,
% 0.26/0.55      ! [Z: int] :
% 0.26/0.55        ( ( real_V1022390504157884413omplex @ ( ring_17405671764205052669omplex @ Z ) )
% 0.26/0.55        = ( abs_abs_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % norm_of_int
% 0.26/0.55  thf(fact_4635_not__neg__one__le__neg__numeral__iff,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 0.26/0.55        = ( M != one ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_neg_one_le_neg_numeral_iff
% 0.26/0.55  thf(fact_4636_not__neg__one__le__neg__numeral__iff,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 0.26/0.55        = ( M != one ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_neg_one_le_neg_numeral_iff
% 0.26/0.55  thf(fact_4637_not__neg__one__le__neg__numeral__iff,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 0.26/0.55        = ( M != one ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_neg_one_le_neg_numeral_iff
% 0.26/0.55  thf(fact_4638_not__neg__one__le__neg__numeral__iff,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 0.26/0.55        = ( M != one ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_neg_one_le_neg_numeral_iff
% 0.26/0.55  thf(fact_4639_neg__numeral__less__neg__one__iff,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.26/0.55        = ( M != one ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_less_neg_one_iff
% 0.26/0.55  thf(fact_4640_neg__numeral__less__neg__one__iff,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.55        = ( M != one ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_less_neg_one_iff
% 0.26/0.55  thf(fact_4641_neg__numeral__less__neg__one__iff,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.26/0.55        = ( M != one ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_less_neg_one_iff
% 0.26/0.55  thf(fact_4642_neg__numeral__less__neg__one__iff,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.26/0.55        = ( M != one ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_less_neg_one_iff
% 0.26/0.55  thf(fact_4643_le__divide__eq__numeral1_I2_J,axiom,
% 0.26/0.55      ! [A: real,B: real,W: num] :
% 0.26/0.55        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 0.26/0.55        = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % le_divide_eq_numeral1(2)
% 0.26/0.55  thf(fact_4644_le__divide__eq__numeral1_I2_J,axiom,
% 0.26/0.55      ! [A: rat,B: rat,W: num] :
% 0.26/0.55        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 0.26/0.55        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % le_divide_eq_numeral1(2)
% 0.26/0.55  thf(fact_4645_divide__le__eq__numeral1_I2_J,axiom,
% 0.26/0.55      ! [B: real,W: num,A: real] :
% 0.26/0.55        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 0.26/0.55        = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 0.26/0.55  
% 0.26/0.55  % divide_le_eq_numeral1(2)
% 0.26/0.55  thf(fact_4646_divide__le__eq__numeral1_I2_J,axiom,
% 0.26/0.55      ! [B: rat,W: num,A: rat] :
% 0.26/0.55        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 0.26/0.55        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 0.26/0.55  
% 0.26/0.55  % divide_le_eq_numeral1(2)
% 0.26/0.55  thf(fact_4647_divide__eq__eq__numeral1_I2_J,axiom,
% 0.26/0.55      ! [B: real,W: num,A: real] :
% 0.26/0.55        ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.26/0.55          = A )
% 0.26/0.55        = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.26/0.55             != zero_zero_real )
% 0.26/0.55           => ( B
% 0.26/0.55              = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 0.26/0.55          & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.26/0.55              = zero_zero_real )
% 0.26/0.55           => ( A = zero_zero_real ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % divide_eq_eq_numeral1(2)
% 0.26/0.55  thf(fact_4648_divide__eq__eq__numeral1_I2_J,axiom,
% 0.26/0.55      ! [B: complex,W: num,A: complex] :
% 0.26/0.55        ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.26/0.55          = A )
% 0.26/0.55        = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.26/0.55             != zero_zero_complex )
% 0.26/0.55           => ( B
% 0.26/0.55              = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 0.26/0.55          & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.26/0.55              = zero_zero_complex )
% 0.26/0.55           => ( A = zero_zero_complex ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % divide_eq_eq_numeral1(2)
% 0.26/0.55  thf(fact_4649_divide__eq__eq__numeral1_I2_J,axiom,
% 0.26/0.55      ! [B: rat,W: num,A: rat] :
% 0.26/0.55        ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.26/0.55          = A )
% 0.26/0.55        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.26/0.55             != zero_zero_rat )
% 0.26/0.55           => ( B
% 0.26/0.55              = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 0.26/0.55          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.26/0.55              = zero_zero_rat )
% 0.26/0.55           => ( A = zero_zero_rat ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % divide_eq_eq_numeral1(2)
% 0.26/0.55  thf(fact_4650_eq__divide__eq__numeral1_I2_J,axiom,
% 0.26/0.55      ! [A: real,B: real,W: num] :
% 0.26/0.55        ( ( A
% 0.26/0.55          = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 0.26/0.55        = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.26/0.55             != zero_zero_real )
% 0.26/0.55           => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.26/0.55              = B ) )
% 0.26/0.55          & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.26/0.55              = zero_zero_real )
% 0.26/0.55           => ( A = zero_zero_real ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % eq_divide_eq_numeral1(2)
% 0.26/0.55  thf(fact_4651_eq__divide__eq__numeral1_I2_J,axiom,
% 0.26/0.55      ! [A: complex,B: complex,W: num] :
% 0.26/0.55        ( ( A
% 0.26/0.55          = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 0.26/0.55        = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.26/0.55             != zero_zero_complex )
% 0.26/0.55           => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.26/0.55              = B ) )
% 0.26/0.55          & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.26/0.55              = zero_zero_complex )
% 0.26/0.55           => ( A = zero_zero_complex ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % eq_divide_eq_numeral1(2)
% 0.26/0.55  thf(fact_4652_eq__divide__eq__numeral1_I2_J,axiom,
% 0.26/0.55      ! [A: rat,B: rat,W: num] :
% 0.26/0.55        ( ( A
% 0.26/0.55          = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 0.26/0.55        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.26/0.55             != zero_zero_rat )
% 0.26/0.55           => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.26/0.55              = B ) )
% 0.26/0.55          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.26/0.55              = zero_zero_rat )
% 0.26/0.55           => ( A = zero_zero_rat ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % eq_divide_eq_numeral1(2)
% 0.26/0.55  thf(fact_4653_divide__less__eq__numeral1_I2_J,axiom,
% 0.26/0.55      ! [B: real,W: num,A: real] :
% 0.26/0.55        ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 0.26/0.55        = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 0.26/0.55  
% 0.26/0.55  % divide_less_eq_numeral1(2)
% 0.26/0.55  thf(fact_4654_divide__less__eq__numeral1_I2_J,axiom,
% 0.26/0.55      ! [B: rat,W: num,A: rat] :
% 0.26/0.55        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 0.26/0.55        = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 0.26/0.55  
% 0.26/0.55  % divide_less_eq_numeral1(2)
% 0.26/0.55  thf(fact_4655_less__divide__eq__numeral1_I2_J,axiom,
% 0.26/0.55      ! [A: real,B: real,W: num] :
% 0.26/0.55        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 0.26/0.55        = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % less_divide_eq_numeral1(2)
% 0.26/0.55  thf(fact_4656_less__divide__eq__numeral1_I2_J,axiom,
% 0.26/0.55      ! [A: rat,B: rat,W: num] :
% 0.26/0.55        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 0.26/0.55        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % less_divide_eq_numeral1(2)
% 0.26/0.55  thf(fact_4657_power2__minus,axiom,
% 0.26/0.55      ! [A: real] :
% 0.26/0.55        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.55        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power2_minus
% 0.26/0.55  thf(fact_4658_power2__minus,axiom,
% 0.26/0.55      ! [A: int] :
% 0.26/0.55        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.55        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power2_minus
% 0.26/0.55  thf(fact_4659_power2__minus,axiom,
% 0.26/0.55      ! [A: complex] :
% 0.26/0.55        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.55        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power2_minus
% 0.26/0.55  thf(fact_4660_power2__minus,axiom,
% 0.26/0.55      ! [A: code_integer] :
% 0.26/0.55        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.55        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power2_minus
% 0.26/0.55  thf(fact_4661_power2__minus,axiom,
% 0.26/0.55      ! [A: rat] :
% 0.26/0.55        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.55        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power2_minus
% 0.26/0.55  thf(fact_4662_zero__less__power__abs__iff,axiom,
% 0.26/0.55      ! [A: code_integer,N: nat] :
% 0.26/0.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 0.26/0.55        = ( ( A != zero_z3403309356797280102nteger )
% 0.26/0.55          | ( N = zero_zero_nat ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % zero_less_power_abs_iff
% 0.26/0.55  thf(fact_4663_zero__less__power__abs__iff,axiom,
% 0.26/0.55      ! [A: real,N: nat] :
% 0.26/0.55        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 0.26/0.55        = ( ( A != zero_zero_real )
% 0.26/0.55          | ( N = zero_zero_nat ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % zero_less_power_abs_iff
% 0.26/0.55  thf(fact_4664_zero__less__power__abs__iff,axiom,
% 0.26/0.55      ! [A: rat,N: nat] :
% 0.26/0.55        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 0.26/0.55        = ( ( A != zero_zero_rat )
% 0.26/0.55          | ( N = zero_zero_nat ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % zero_less_power_abs_iff
% 0.26/0.55  thf(fact_4665_zero__less__power__abs__iff,axiom,
% 0.26/0.55      ! [A: int,N: nat] :
% 0.26/0.55        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 0.26/0.55        = ( ( A != zero_zero_int )
% 0.26/0.55          | ( N = zero_zero_nat ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % zero_less_power_abs_iff
% 0.26/0.55  thf(fact_4666_abs__power2,axiom,
% 0.26/0.55      ! [A: code_integer] :
% 0.26/0.55        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.55        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_power2
% 0.26/0.55  thf(fact_4667_abs__power2,axiom,
% 0.26/0.55      ! [A: rat] :
% 0.26/0.55        ( ( abs_abs_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.55        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_power2
% 0.26/0.55  thf(fact_4668_abs__power2,axiom,
% 0.26/0.55      ! [A: int] :
% 0.26/0.55        ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.55        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_power2
% 0.26/0.55  thf(fact_4669_abs__power2,axiom,
% 0.26/0.55      ! [A: real] :
% 0.26/0.55        ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.55        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_power2
% 0.26/0.55  thf(fact_4670_power2__abs,axiom,
% 0.26/0.55      ! [A: code_integer] :
% 0.26/0.55        ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.55        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power2_abs
% 0.26/0.55  thf(fact_4671_power2__abs,axiom,
% 0.26/0.55      ! [A: rat] :
% 0.26/0.55        ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.55        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power2_abs
% 0.26/0.55  thf(fact_4672_power2__abs,axiom,
% 0.26/0.55      ! [A: int] :
% 0.26/0.55        ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.55        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power2_abs
% 0.26/0.55  thf(fact_4673_power2__abs,axiom,
% 0.26/0.55      ! [A: real] :
% 0.26/0.55        ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.55        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power2_abs
% 0.26/0.55  thf(fact_4674_norm__mult__numeral1,axiom,
% 0.26/0.55      ! [W: num,A: real] :
% 0.26/0.55        ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 0.26/0.55        = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % norm_mult_numeral1
% 0.26/0.55  thf(fact_4675_norm__mult__numeral1,axiom,
% 0.26/0.55      ! [W: num,A: complex] :
% 0.26/0.55        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 0.26/0.55        = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % norm_mult_numeral1
% 0.26/0.55  thf(fact_4676_norm__mult__numeral2,axiom,
% 0.26/0.55      ! [A: real,W: num] :
% 0.26/0.55        ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 0.26/0.55        = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % norm_mult_numeral2
% 0.26/0.55  thf(fact_4677_norm__mult__numeral2,axiom,
% 0.26/0.55      ! [A: complex,W: num] :
% 0.26/0.55        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 0.26/0.55        = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % norm_mult_numeral2
% 0.26/0.55  thf(fact_4678_norm__divide__numeral,axiom,
% 0.26/0.55      ! [A: real,W: num] :
% 0.26/0.55        ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 0.26/0.55        = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % norm_divide_numeral
% 0.26/0.55  thf(fact_4679_norm__divide__numeral,axiom,
% 0.26/0.55      ! [A: complex,W: num] :
% 0.26/0.55        ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 0.26/0.55        = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % norm_divide_numeral
% 0.26/0.55  thf(fact_4680_of__real__neg__numeral,axiom,
% 0.26/0.55      ! [W: num] :
% 0.26/0.55        ( ( real_V1803761363581548252l_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.26/0.55        = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_real_neg_numeral
% 0.26/0.55  thf(fact_4681_of__real__neg__numeral,axiom,
% 0.26/0.55      ! [W: num] :
% 0.26/0.55        ( ( real_V4546457046886955230omplex @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.26/0.55        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_real_neg_numeral
% 0.26/0.55  thf(fact_4682_add__neg__numeral__special_I9_J,axiom,
% 0.26/0.55      ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.26/0.55      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % add_neg_numeral_special(9)
% 0.26/0.55  thf(fact_4683_add__neg__numeral__special_I9_J,axiom,
% 0.26/0.55      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.55      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % add_neg_numeral_special(9)
% 0.26/0.55  thf(fact_4684_add__neg__numeral__special_I9_J,axiom,
% 0.26/0.55      ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.26/0.55      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % add_neg_numeral_special(9)
% 0.26/0.55  thf(fact_4685_add__neg__numeral__special_I9_J,axiom,
% 0.26/0.55      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.26/0.55      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % add_neg_numeral_special(9)
% 0.26/0.55  thf(fact_4686_add__neg__numeral__special_I9_J,axiom,
% 0.26/0.55      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.26/0.55      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % add_neg_numeral_special(9)
% 0.26/0.55  thf(fact_4687_diff__numeral__special_I11_J,axiom,
% 0.26/0.55      ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.26/0.55      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_numeral_special(11)
% 0.26/0.55  thf(fact_4688_diff__numeral__special_I11_J,axiom,
% 0.26/0.55      ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.55      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_numeral_special(11)
% 0.26/0.55  thf(fact_4689_diff__numeral__special_I11_J,axiom,
% 0.26/0.55      ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.26/0.55      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_numeral_special(11)
% 0.26/0.55  thf(fact_4690_diff__numeral__special_I11_J,axiom,
% 0.26/0.55      ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.26/0.55      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_numeral_special(11)
% 0.26/0.55  thf(fact_4691_diff__numeral__special_I11_J,axiom,
% 0.26/0.55      ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.26/0.55      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_numeral_special(11)
% 0.26/0.55  thf(fact_4692_diff__numeral__special_I10_J,axiom,
% 0.26/0.55      ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 0.26/0.55      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_numeral_special(10)
% 0.26/0.55  thf(fact_4693_diff__numeral__special_I10_J,axiom,
% 0.26/0.55      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 0.26/0.55      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_numeral_special(10)
% 0.26/0.55  thf(fact_4694_diff__numeral__special_I10_J,axiom,
% 0.26/0.55      ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 0.26/0.55      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_numeral_special(10)
% 0.26/0.55  thf(fact_4695_diff__numeral__special_I10_J,axiom,
% 0.26/0.55      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 0.26/0.55      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_numeral_special(10)
% 0.26/0.55  thf(fact_4696_diff__numeral__special_I10_J,axiom,
% 0.26/0.55      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 0.26/0.55      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_numeral_special(10)
% 0.26/0.55  thf(fact_4697_minus__1__div__2__eq,axiom,
% 0.26/0.55      ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.55      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_1_div_2_eq
% 0.26/0.55  thf(fact_4698_minus__1__div__2__eq,axiom,
% 0.26/0.55      ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.26/0.55      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_1_div_2_eq
% 0.26/0.55  thf(fact_4699_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.26/0.55      ! [A: real,N: nat] :
% 0.26/0.55        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.55        = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % Power.ring_1_class.power_minus_even
% 0.26/0.55  thf(fact_4700_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.26/0.55      ! [A: int,N: nat] :
% 0.26/0.55        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.55        = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % Power.ring_1_class.power_minus_even
% 0.26/0.55  thf(fact_4701_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.26/0.55      ! [A: complex,N: nat] :
% 0.26/0.55        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.55        = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % Power.ring_1_class.power_minus_even
% 0.26/0.55  thf(fact_4702_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.26/0.55      ! [A: code_integer,N: nat] :
% 0.26/0.55        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.55        = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % Power.ring_1_class.power_minus_even
% 0.26/0.55  thf(fact_4703_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.26/0.55      ! [A: rat,N: nat] :
% 0.26/0.55        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.55        = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % Power.ring_1_class.power_minus_even
% 0.26/0.55  thf(fact_4704_power__minus__odd,axiom,
% 0.26/0.55      ! [N: nat,A: real] :
% 0.26/0.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.55       => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 0.26/0.55          = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power_minus_odd
% 0.26/0.55  thf(fact_4705_power__minus__odd,axiom,
% 0.26/0.55      ! [N: nat,A: int] :
% 0.26/0.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.55       => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 0.26/0.55          = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power_minus_odd
% 0.26/0.55  thf(fact_4706_power__minus__odd,axiom,
% 0.26/0.55      ! [N: nat,A: complex] :
% 0.26/0.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.55       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 0.26/0.55          = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power_minus_odd
% 0.26/0.55  thf(fact_4707_power__minus__odd,axiom,
% 0.26/0.55      ! [N: nat,A: code_integer] :
% 0.26/0.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.55       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 0.26/0.55          = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power_minus_odd
% 0.26/0.55  thf(fact_4708_power__minus__odd,axiom,
% 0.26/0.55      ! [N: nat,A: rat] :
% 0.26/0.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.55       => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 0.26/0.55          = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power_minus_odd
% 0.26/0.55  thf(fact_4709_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.26/0.55      ! [N: nat,A: real] :
% 0.26/0.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.55       => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 0.26/0.55          = ( power_power_real @ A @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % Parity.ring_1_class.power_minus_even
% 0.26/0.55  thf(fact_4710_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.26/0.55      ! [N: nat,A: int] :
% 0.26/0.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.55       => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 0.26/0.55          = ( power_power_int @ A @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % Parity.ring_1_class.power_minus_even
% 0.26/0.55  thf(fact_4711_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.26/0.55      ! [N: nat,A: complex] :
% 0.26/0.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.55       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 0.26/0.55          = ( power_power_complex @ A @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % Parity.ring_1_class.power_minus_even
% 0.26/0.55  thf(fact_4712_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.26/0.55      ! [N: nat,A: code_integer] :
% 0.26/0.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.55       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 0.26/0.55          = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % Parity.ring_1_class.power_minus_even
% 0.26/0.55  thf(fact_4713_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.26/0.55      ! [N: nat,A: rat] :
% 0.26/0.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.55       => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 0.26/0.55          = ( power_power_rat @ A @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % Parity.ring_1_class.power_minus_even
% 0.26/0.55  thf(fact_4714_power__even__abs__numeral,axiom,
% 0.26/0.55      ! [W: num,A: code_integer] :
% 0.26/0.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.55       => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.55          = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power_even_abs_numeral
% 0.26/0.55  thf(fact_4715_power__even__abs__numeral,axiom,
% 0.26/0.55      ! [W: num,A: rat] :
% 0.26/0.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.55       => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.55          = ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power_even_abs_numeral
% 0.26/0.55  thf(fact_4716_power__even__abs__numeral,axiom,
% 0.26/0.55      ! [W: num,A: int] :
% 0.26/0.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.55       => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.55          = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power_even_abs_numeral
% 0.26/0.55  thf(fact_4717_power__even__abs__numeral,axiom,
% 0.26/0.55      ! [W: num,A: real] :
% 0.26/0.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.55       => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 0.26/0.55          = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power_even_abs_numeral
% 0.26/0.55  thf(fact_4718_diff__numeral__special_I4_J,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 0.26/0.55        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_numeral_special(4)
% 0.26/0.55  thf(fact_4719_diff__numeral__special_I4_J,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 0.26/0.55        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_numeral_special(4)
% 0.26/0.55  thf(fact_4720_diff__numeral__special_I4_J,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 0.26/0.55        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_numeral_special(4)
% 0.26/0.55  thf(fact_4721_diff__numeral__special_I4_J,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 0.26/0.55        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_numeral_special(4)
% 0.26/0.55  thf(fact_4722_diff__numeral__special_I4_J,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 0.26/0.55        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_numeral_special(4)
% 0.26/0.55  thf(fact_4723_diff__numeral__special_I3_J,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.26/0.55        = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_numeral_special(3)
% 0.26/0.55  thf(fact_4724_diff__numeral__special_I3_J,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.55        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_numeral_special(3)
% 0.26/0.55  thf(fact_4725_diff__numeral__special_I3_J,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.26/0.55        = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_numeral_special(3)
% 0.26/0.55  thf(fact_4726_diff__numeral__special_I3_J,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.26/0.55        = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_numeral_special(3)
% 0.26/0.55  thf(fact_4727_diff__numeral__special_I3_J,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.26/0.55        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_numeral_special(3)
% 0.26/0.55  thf(fact_4728_neg__numeral__le__floor,axiom,
% 0.26/0.55      ! [V: num,X3: rat] :
% 0.26/0.55        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X3 ) )
% 0.26/0.55        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X3 ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_le_floor
% 0.26/0.55  thf(fact_4729_neg__numeral__le__floor,axiom,
% 0.26/0.55      ! [V: num,X3: real] :
% 0.26/0.55        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X3 ) )
% 0.26/0.55        = ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X3 ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_le_floor
% 0.26/0.55  thf(fact_4730_floor__less__neg__numeral,axiom,
% 0.26/0.55      ! [X3: rat,V: num] :
% 0.26/0.55        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X3 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.26/0.55        = ( ord_less_rat @ X3 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % floor_less_neg_numeral
% 0.26/0.55  thf(fact_4731_floor__less__neg__numeral,axiom,
% 0.26/0.55      ! [X3: real,V: num] :
% 0.26/0.55        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X3 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.26/0.55        = ( ord_less_real @ X3 @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % floor_less_neg_numeral
% 0.26/0.55  thf(fact_4732_ceiling__le__neg__numeral,axiom,
% 0.26/0.55      ! [X3: real,V: num] :
% 0.26/0.55        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X3 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.26/0.55        = ( ord_less_eq_real @ X3 @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % ceiling_le_neg_numeral
% 0.26/0.55  thf(fact_4733_ceiling__le__neg__numeral,axiom,
% 0.26/0.55      ! [X3: rat,V: num] :
% 0.26/0.55        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X3 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.26/0.55        = ( ord_less_eq_rat @ X3 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % ceiling_le_neg_numeral
% 0.26/0.55  thf(fact_4734_ceiling__less__zero,axiom,
% 0.26/0.55      ! [X3: real] :
% 0.26/0.55        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X3 ) @ zero_zero_int )
% 0.26/0.55        = ( ord_less_eq_real @ X3 @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % ceiling_less_zero
% 0.26/0.55  thf(fact_4735_ceiling__less__zero,axiom,
% 0.26/0.55      ! [X3: rat] :
% 0.26/0.55        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X3 ) @ zero_zero_int )
% 0.26/0.55        = ( ord_less_eq_rat @ X3 @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % ceiling_less_zero
% 0.26/0.55  thf(fact_4736_zero__le__ceiling,axiom,
% 0.26/0.55      ! [X3: real] :
% 0.26/0.55        ( ( ord_less_eq_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X3 ) )
% 0.26/0.55        = ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 ) ) ).
% 0.26/0.55  
% 0.26/0.55  % zero_le_ceiling
% 0.26/0.55  thf(fact_4737_zero__le__ceiling,axiom,
% 0.26/0.55      ! [X3: rat] :
% 0.26/0.55        ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X3 ) )
% 0.26/0.55        = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X3 ) ) ).
% 0.26/0.55  
% 0.26/0.55  % zero_le_ceiling
% 0.26/0.55  thf(fact_4738_neg__numeral__less__ceiling,axiom,
% 0.26/0.55      ! [V: num,X3: real] :
% 0.26/0.55        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X3 ) )
% 0.26/0.55        = ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X3 ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_less_ceiling
% 0.26/0.55  thf(fact_4739_neg__numeral__less__ceiling,axiom,
% 0.26/0.55      ! [V: num,X3: rat] :
% 0.26/0.55        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X3 ) )
% 0.26/0.55        = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X3 ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_less_ceiling
% 0.26/0.55  thf(fact_4740_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.26/0.55      ! [X3: num,N: nat,Y3: int] :
% 0.26/0.55        ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N )
% 0.26/0.55          = ( ring_1_of_int_real @ Y3 ) )
% 0.26/0.55        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N )
% 0.26/0.55          = Y3 ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_power_eq_of_int_cancel_iff
% 0.26/0.55  thf(fact_4741_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.26/0.55      ! [X3: num,N: nat,Y3: int] :
% 0.26/0.55        ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N )
% 0.26/0.55          = ( ring_1_of_int_int @ Y3 ) )
% 0.26/0.55        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N )
% 0.26/0.55          = Y3 ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_power_eq_of_int_cancel_iff
% 0.26/0.55  thf(fact_4742_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.26/0.55      ! [X3: num,N: nat,Y3: int] :
% 0.26/0.55        ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X3 ) ) @ N )
% 0.26/0.55          = ( ring_17405671764205052669omplex @ Y3 ) )
% 0.26/0.55        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N )
% 0.26/0.55          = Y3 ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_power_eq_of_int_cancel_iff
% 0.26/0.55  thf(fact_4743_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.26/0.55      ! [X3: num,N: nat,Y3: int] :
% 0.26/0.55        ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N )
% 0.26/0.55          = ( ring_18347121197199848620nteger @ Y3 ) )
% 0.26/0.55        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N )
% 0.26/0.55          = Y3 ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_power_eq_of_int_cancel_iff
% 0.26/0.55  thf(fact_4744_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.26/0.55      ! [X3: num,N: nat,Y3: int] :
% 0.26/0.55        ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N )
% 0.26/0.55          = ( ring_1_of_int_rat @ Y3 ) )
% 0.26/0.55        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N )
% 0.26/0.55          = Y3 ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_power_eq_of_int_cancel_iff
% 0.26/0.55  thf(fact_4745_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.26/0.55      ! [Y3: int,X3: num,N: nat] :
% 0.26/0.55        ( ( ( ring_1_of_int_real @ Y3 )
% 0.26/0.55          = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N ) )
% 0.26/0.55        = ( Y3
% 0.26/0.55          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_eq_neg_numeral_power_cancel_iff
% 0.26/0.55  thf(fact_4746_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.26/0.55      ! [Y3: int,X3: num,N: nat] :
% 0.26/0.55        ( ( ( ring_1_of_int_int @ Y3 )
% 0.26/0.55          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) )
% 0.26/0.55        = ( Y3
% 0.26/0.55          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_eq_neg_numeral_power_cancel_iff
% 0.26/0.55  thf(fact_4747_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.26/0.55      ! [Y3: int,X3: num,N: nat] :
% 0.26/0.55        ( ( ( ring_17405671764205052669omplex @ Y3 )
% 0.26/0.55          = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X3 ) ) @ N ) )
% 0.26/0.55        = ( Y3
% 0.26/0.55          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_eq_neg_numeral_power_cancel_iff
% 0.26/0.55  thf(fact_4748_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.26/0.55      ! [Y3: int,X3: num,N: nat] :
% 0.26/0.55        ( ( ( ring_18347121197199848620nteger @ Y3 )
% 0.26/0.55          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N ) )
% 0.26/0.55        = ( Y3
% 0.26/0.55          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_eq_neg_numeral_power_cancel_iff
% 0.26/0.55  thf(fact_4749_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.26/0.55      ! [Y3: int,X3: num,N: nat] :
% 0.26/0.55        ( ( ( ring_1_of_int_rat @ Y3 )
% 0.26/0.55          = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N ) )
% 0.26/0.55        = ( Y3
% 0.26/0.55          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_eq_neg_numeral_power_cancel_iff
% 0.26/0.55  thf(fact_4750_real__sqrt__abs,axiom,
% 0.26/0.55      ! [X3: real] :
% 0.26/0.55        ( ( sqrt @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.55        = ( abs_abs_real @ X3 ) ) ).
% 0.26/0.55  
% 0.26/0.55  % real_sqrt_abs
% 0.26/0.55  thf(fact_4751_dbl__simps_I4_J,axiom,
% 0.26/0.55      ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.26/0.55      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % dbl_simps(4)
% 0.26/0.55  thf(fact_4752_dbl__simps_I4_J,axiom,
% 0.26/0.55      ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.55      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % dbl_simps(4)
% 0.26/0.55  thf(fact_4753_dbl__simps_I4_J,axiom,
% 0.26/0.55      ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.26/0.55      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % dbl_simps(4)
% 0.26/0.55  thf(fact_4754_dbl__simps_I4_J,axiom,
% 0.26/0.55      ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.26/0.55      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % dbl_simps(4)
% 0.26/0.55  thf(fact_4755_dbl__simps_I4_J,axiom,
% 0.26/0.55      ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.26/0.55      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % dbl_simps(4)
% 0.26/0.55  thf(fact_4756_power__minus1__even,axiom,
% 0.26/0.55      ! [N: nat] :
% 0.26/0.55        ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.55        = one_one_real ) ).
% 0.26/0.55  
% 0.26/0.55  % power_minus1_even
% 0.26/0.55  thf(fact_4757_power__minus1__even,axiom,
% 0.26/0.55      ! [N: nat] :
% 0.26/0.55        ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.55        = one_one_int ) ).
% 0.26/0.55  
% 0.26/0.55  % power_minus1_even
% 0.26/0.55  thf(fact_4758_power__minus1__even,axiom,
% 0.26/0.55      ! [N: nat] :
% 0.26/0.55        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.55        = one_one_complex ) ).
% 0.26/0.55  
% 0.26/0.55  % power_minus1_even
% 0.26/0.55  thf(fact_4759_power__minus1__even,axiom,
% 0.26/0.55      ! [N: nat] :
% 0.26/0.55        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.55        = one_one_Code_integer ) ).
% 0.26/0.55  
% 0.26/0.55  % power_minus1_even
% 0.26/0.55  thf(fact_4760_power__minus1__even,axiom,
% 0.26/0.55      ! [N: nat] :
% 0.26/0.55        ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.55        = one_one_rat ) ).
% 0.26/0.55  
% 0.26/0.55  % power_minus1_even
% 0.26/0.55  thf(fact_4761_neg__one__odd__power,axiom,
% 0.26/0.55      ! [N: nat] :
% 0.26/0.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.55       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 0.26/0.55          = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_one_odd_power
% 0.26/0.55  thf(fact_4762_neg__one__odd__power,axiom,
% 0.26/0.55      ! [N: nat] :
% 0.26/0.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.55       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 0.26/0.55          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_one_odd_power
% 0.26/0.55  thf(fact_4763_neg__one__odd__power,axiom,
% 0.26/0.55      ! [N: nat] :
% 0.26/0.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.55       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 0.26/0.55          = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_one_odd_power
% 0.26/0.55  thf(fact_4764_neg__one__odd__power,axiom,
% 0.26/0.55      ! [N: nat] :
% 0.26/0.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.55       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 0.26/0.55          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_one_odd_power
% 0.26/0.55  thf(fact_4765_neg__one__odd__power,axiom,
% 0.26/0.55      ! [N: nat] :
% 0.26/0.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.55       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 0.26/0.55          = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_one_odd_power
% 0.26/0.55  thf(fact_4766_neg__one__even__power,axiom,
% 0.26/0.55      ! [N: nat] :
% 0.26/0.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.55       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 0.26/0.55          = one_one_real ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_one_even_power
% 0.26/0.55  thf(fact_4767_neg__one__even__power,axiom,
% 0.26/0.55      ! [N: nat] :
% 0.26/0.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.55       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 0.26/0.55          = one_one_int ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_one_even_power
% 0.26/0.55  thf(fact_4768_neg__one__even__power,axiom,
% 0.26/0.55      ! [N: nat] :
% 0.26/0.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.55       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 0.26/0.55          = one_one_complex ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_one_even_power
% 0.26/0.55  thf(fact_4769_neg__one__even__power,axiom,
% 0.26/0.55      ! [N: nat] :
% 0.26/0.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.55       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 0.26/0.55          = one_one_Code_integer ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_one_even_power
% 0.26/0.55  thf(fact_4770_neg__one__even__power,axiom,
% 0.26/0.55      ! [N: nat] :
% 0.26/0.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.55       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 0.26/0.55          = one_one_rat ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_one_even_power
% 0.26/0.55  thf(fact_4771_norm__of__real__addn,axiom,
% 0.26/0.55      ! [X3: real,B: num] :
% 0.26/0.55        ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X3 ) @ ( numeral_numeral_real @ B ) ) )
% 0.26/0.55        = ( abs_abs_real @ ( plus_plus_real @ X3 @ ( numeral_numeral_real @ B ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % norm_of_real_addn
% 0.26/0.55  thf(fact_4772_norm__of__real__addn,axiom,
% 0.26/0.55      ! [X3: real,B: num] :
% 0.26/0.55        ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X3 ) @ ( numera6690914467698888265omplex @ B ) ) )
% 0.26/0.55        = ( abs_abs_real @ ( plus_plus_real @ X3 @ ( numeral_numeral_real @ B ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % norm_of_real_addn
% 0.26/0.55  thf(fact_4773_neg__numeral__less__floor,axiom,
% 0.26/0.55      ! [V: num,X3: rat] :
% 0.26/0.55        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X3 ) )
% 0.26/0.55        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X3 ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_less_floor
% 0.26/0.55  thf(fact_4774_neg__numeral__less__floor,axiom,
% 0.26/0.55      ! [V: num,X3: real] :
% 0.26/0.55        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X3 ) )
% 0.26/0.55        = ( ord_less_eq_real @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X3 ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_less_floor
% 0.26/0.55  thf(fact_4775_floor__le__neg__numeral,axiom,
% 0.26/0.55      ! [X3: rat,V: num] :
% 0.26/0.55        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X3 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.26/0.55        = ( ord_less_rat @ X3 @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % floor_le_neg_numeral
% 0.26/0.55  thf(fact_4776_floor__le__neg__numeral,axiom,
% 0.26/0.55      ! [X3: real,V: num] :
% 0.26/0.55        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X3 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.26/0.55        = ( ord_less_real @ X3 @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % floor_le_neg_numeral
% 0.26/0.55  thf(fact_4777_ceiling__less__neg__numeral,axiom,
% 0.26/0.55      ! [X3: real,V: num] :
% 0.26/0.55        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X3 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.26/0.55        = ( ord_less_eq_real @ X3 @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % ceiling_less_neg_numeral
% 0.26/0.55  thf(fact_4778_ceiling__less__neg__numeral,axiom,
% 0.26/0.55      ! [X3: rat,V: num] :
% 0.26/0.55        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X3 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.26/0.55        = ( ord_less_eq_rat @ X3 @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % ceiling_less_neg_numeral
% 0.26/0.55  thf(fact_4779_neg__numeral__le__ceiling,axiom,
% 0.26/0.55      ! [V: num,X3: real] :
% 0.26/0.55        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X3 ) )
% 0.26/0.55        = ( ord_less_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X3 ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_le_ceiling
% 0.26/0.55  thf(fact_4780_neg__numeral__le__ceiling,axiom,
% 0.26/0.55      ! [V: num,X3: rat] :
% 0.26/0.55        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X3 ) )
% 0.26/0.55        = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X3 ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_le_ceiling
% 0.26/0.55  thf(fact_4781_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.26/0.55      ! [A: int,X3: num,N: nat] :
% 0.26/0.55        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N ) )
% 0.26/0.55        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_le_neg_numeral_power_cancel_iff
% 0.26/0.55  thf(fact_4782_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.26/0.55      ! [A: int,X3: num,N: nat] :
% 0.26/0.55        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N ) )
% 0.26/0.55        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_le_neg_numeral_power_cancel_iff
% 0.26/0.55  thf(fact_4783_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.26/0.55      ! [A: int,X3: num,N: nat] :
% 0.26/0.55        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N ) )
% 0.26/0.55        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_le_neg_numeral_power_cancel_iff
% 0.26/0.55  thf(fact_4784_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.26/0.55      ! [A: int,X3: num,N: nat] :
% 0.26/0.55        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) )
% 0.26/0.55        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_le_neg_numeral_power_cancel_iff
% 0.26/0.55  thf(fact_4785_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.26/0.55      ! [X3: num,N: nat,A: int] :
% 0.26/0.55        ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 0.26/0.55        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_power_le_of_int_cancel_iff
% 0.26/0.55  thf(fact_4786_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.26/0.55      ! [X3: num,N: nat,A: int] :
% 0.26/0.55        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 0.26/0.55        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_power_le_of_int_cancel_iff
% 0.26/0.55  thf(fact_4787_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.26/0.55      ! [X3: num,N: nat,A: int] :
% 0.26/0.55        ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 0.26/0.55        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_power_le_of_int_cancel_iff
% 0.26/0.55  thf(fact_4788_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.26/0.55      ! [X3: num,N: nat,A: int] :
% 0.26/0.55        ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 0.26/0.55        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_power_le_of_int_cancel_iff
% 0.26/0.55  thf(fact_4789_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.26/0.55      ! [X3: num,N: nat,A: int] :
% 0.26/0.55        ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 0.26/0.55        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_power_less_of_int_cancel_iff
% 0.26/0.55  thf(fact_4790_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.26/0.55      ! [X3: num,N: nat,A: int] :
% 0.26/0.55        ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 0.26/0.55        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_power_less_of_int_cancel_iff
% 0.26/0.55  thf(fact_4791_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.26/0.55      ! [X3: num,N: nat,A: int] :
% 0.26/0.55        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 0.26/0.55        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_power_less_of_int_cancel_iff
% 0.26/0.55  thf(fact_4792_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.26/0.55      ! [X3: num,N: nat,A: int] :
% 0.26/0.55        ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 0.26/0.55        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_power_less_of_int_cancel_iff
% 0.26/0.55  thf(fact_4793_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.26/0.55      ! [A: int,X3: num,N: nat] :
% 0.26/0.55        ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N ) )
% 0.26/0.55        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_less_neg_numeral_power_cancel_iff
% 0.26/0.55  thf(fact_4794_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.26/0.55      ! [A: int,X3: num,N: nat] :
% 0.26/0.55        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) )
% 0.26/0.55        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_less_neg_numeral_power_cancel_iff
% 0.26/0.55  thf(fact_4795_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.26/0.55      ! [A: int,X3: num,N: nat] :
% 0.26/0.55        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N ) )
% 0.26/0.55        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_less_neg_numeral_power_cancel_iff
% 0.26/0.55  thf(fact_4796_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.26/0.55      ! [A: int,X3: num,N: nat] :
% 0.26/0.55        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N ) )
% 0.26/0.55        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_less_neg_numeral_power_cancel_iff
% 0.26/0.55  thf(fact_4797_square__powr__half,axiom,
% 0.26/0.55      ! [X3: real] :
% 0.26/0.55        ( ( powr_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.55        = ( abs_abs_real @ X3 ) ) ).
% 0.26/0.55  
% 0.26/0.55  % square_powr_half
% 0.26/0.55  thf(fact_4798_abs__less__iff,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 0.26/0.55        = ( ( ord_less_real @ A @ B )
% 0.26/0.55          & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_less_iff
% 0.26/0.55  thf(fact_4799_abs__less__iff,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 0.26/0.55        = ( ( ord_less_int @ A @ B )
% 0.26/0.55          & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_less_iff
% 0.26/0.55  thf(fact_4800_abs__less__iff,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.26/0.55        = ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.26/0.55          & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_less_iff
% 0.26/0.55  thf(fact_4801_abs__less__iff,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 0.26/0.55        = ( ( ord_less_rat @ A @ B )
% 0.26/0.55          & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_less_iff
% 0.26/0.55  thf(fact_4802_equation__minus__iff,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( A
% 0.26/0.55          = ( uminus_uminus_real @ B ) )
% 0.26/0.55        = ( B
% 0.26/0.55          = ( uminus_uminus_real @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % equation_minus_iff
% 0.26/0.55  thf(fact_4803_equation__minus__iff,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( A
% 0.26/0.55          = ( uminus_uminus_int @ B ) )
% 0.26/0.55        = ( B
% 0.26/0.55          = ( uminus_uminus_int @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % equation_minus_iff
% 0.26/0.55  thf(fact_4804_equation__minus__iff,axiom,
% 0.26/0.55      ! [A: complex,B: complex] :
% 0.26/0.55        ( ( A
% 0.26/0.55          = ( uminus1482373934393186551omplex @ B ) )
% 0.26/0.55        = ( B
% 0.26/0.55          = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % equation_minus_iff
% 0.26/0.55  thf(fact_4805_equation__minus__iff,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( A
% 0.26/0.55          = ( uminus1351360451143612070nteger @ B ) )
% 0.26/0.55        = ( B
% 0.26/0.55          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % equation_minus_iff
% 0.26/0.55  thf(fact_4806_equation__minus__iff,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( A
% 0.26/0.55          = ( uminus_uminus_rat @ B ) )
% 0.26/0.55        = ( B
% 0.26/0.55          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % equation_minus_iff
% 0.26/0.55  thf(fact_4807_minus__equation__iff,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( ( uminus_uminus_real @ A )
% 0.26/0.55          = B )
% 0.26/0.55        = ( ( uminus_uminus_real @ B )
% 0.26/0.55          = A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_equation_iff
% 0.26/0.55  thf(fact_4808_minus__equation__iff,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( ( uminus_uminus_int @ A )
% 0.26/0.55          = B )
% 0.26/0.55        = ( ( uminus_uminus_int @ B )
% 0.26/0.55          = A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_equation_iff
% 0.26/0.55  thf(fact_4809_minus__equation__iff,axiom,
% 0.26/0.55      ! [A: complex,B: complex] :
% 0.26/0.55        ( ( ( uminus1482373934393186551omplex @ A )
% 0.26/0.55          = B )
% 0.26/0.55        = ( ( uminus1482373934393186551omplex @ B )
% 0.26/0.55          = A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_equation_iff
% 0.26/0.55  thf(fact_4810_minus__equation__iff,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( ( uminus1351360451143612070nteger @ A )
% 0.26/0.55          = B )
% 0.26/0.55        = ( ( uminus1351360451143612070nteger @ B )
% 0.26/0.55          = A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_equation_iff
% 0.26/0.55  thf(fact_4811_minus__equation__iff,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( ( uminus_uminus_rat @ A )
% 0.26/0.55          = B )
% 0.26/0.55        = ( ( uminus_uminus_rat @ B )
% 0.26/0.55          = A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_equation_iff
% 0.26/0.55  thf(fact_4812_abs__ge__minus__self,axiom,
% 0.26/0.55      ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_ge_minus_self
% 0.26/0.55  thf(fact_4813_abs__ge__minus__self,axiom,
% 0.26/0.55      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_ge_minus_self
% 0.26/0.55  thf(fact_4814_abs__ge__minus__self,axiom,
% 0.26/0.55      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_ge_minus_self
% 0.26/0.55  thf(fact_4815_abs__ge__minus__self,axiom,
% 0.26/0.55      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_ge_minus_self
% 0.26/0.55  thf(fact_4816_abs__le__iff,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 0.26/0.55        = ( ( ord_less_eq_real @ A @ B )
% 0.26/0.55          & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_le_iff
% 0.26/0.55  thf(fact_4817_abs__le__iff,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.26/0.55        = ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.26/0.55          & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_le_iff
% 0.26/0.55  thf(fact_4818_abs__le__iff,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.26/0.55        = ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.55          & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_le_iff
% 0.26/0.55  thf(fact_4819_abs__le__iff,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.26/0.55        = ( ( ord_less_eq_int @ A @ B )
% 0.26/0.55          & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_le_iff
% 0.26/0.55  thf(fact_4820_abs__le__D2,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 0.26/0.55       => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_le_D2
% 0.26/0.55  thf(fact_4821_abs__le__D2,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.26/0.55       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_le_D2
% 0.26/0.55  thf(fact_4822_abs__le__D2,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.26/0.55       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_le_D2
% 0.26/0.55  thf(fact_4823_abs__le__D2,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.26/0.55       => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_le_D2
% 0.26/0.55  thf(fact_4824_abs__leI,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.55       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 0.26/0.55         => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_leI
% 0.26/0.55  thf(fact_4825_abs__leI,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.26/0.55       => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.26/0.55         => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_leI
% 0.26/0.55  thf(fact_4826_abs__leI,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.55       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.26/0.55         => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_leI
% 0.26/0.55  thf(fact_4827_abs__leI,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( ord_less_eq_int @ A @ B )
% 0.26/0.55       => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 0.26/0.55         => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_leI
% 0.26/0.55  thf(fact_4828_verit__negate__coefficient_I3_J,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( A = B )
% 0.26/0.55       => ( ( uminus_uminus_real @ A )
% 0.26/0.55          = ( uminus_uminus_real @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % verit_negate_coefficient(3)
% 0.26/0.55  thf(fact_4829_verit__negate__coefficient_I3_J,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( A = B )
% 0.26/0.55       => ( ( uminus_uminus_int @ A )
% 0.26/0.55          = ( uminus_uminus_int @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % verit_negate_coefficient(3)
% 0.26/0.55  thf(fact_4830_verit__negate__coefficient_I3_J,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( A = B )
% 0.26/0.55       => ( ( uminus1351360451143612070nteger @ A )
% 0.26/0.55          = ( uminus1351360451143612070nteger @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % verit_negate_coefficient(3)
% 0.26/0.55  thf(fact_4831_verit__negate__coefficient_I3_J,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( A = B )
% 0.26/0.55       => ( ( uminus_uminus_rat @ A )
% 0.26/0.55          = ( uminus_uminus_rat @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % verit_negate_coefficient(3)
% 0.26/0.55  thf(fact_4832_abs__minus__le__zero,axiom,
% 0.26/0.55      ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_minus_le_zero
% 0.26/0.55  thf(fact_4833_abs__minus__le__zero,axiom,
% 0.26/0.55      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_minus_le_zero
% 0.26/0.55  thf(fact_4834_abs__minus__le__zero,axiom,
% 0.26/0.55      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_minus_le_zero
% 0.26/0.55  thf(fact_4835_abs__minus__le__zero,axiom,
% 0.26/0.55      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_minus_le_zero
% 0.26/0.55  thf(fact_4836_abs__eq__iff_H,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( ( abs_abs_real @ A )
% 0.26/0.55          = B )
% 0.26/0.55        = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.26/0.55          & ( ( A = B )
% 0.26/0.55            | ( A
% 0.26/0.55              = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_eq_iff'
% 0.26/0.55  thf(fact_4837_abs__eq__iff_H,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( ( abs_abs_Code_integer @ A )
% 0.26/0.55          = B )
% 0.26/0.55        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.26/0.55          & ( ( A = B )
% 0.26/0.55            | ( A
% 0.26/0.55              = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_eq_iff'
% 0.26/0.55  thf(fact_4838_abs__eq__iff_H,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( ( abs_abs_rat @ A )
% 0.26/0.55          = B )
% 0.26/0.55        = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.26/0.55          & ( ( A = B )
% 0.26/0.55            | ( A
% 0.26/0.55              = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_eq_iff'
% 0.26/0.55  thf(fact_4839_abs__eq__iff_H,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( ( abs_abs_int @ A )
% 0.26/0.55          = B )
% 0.26/0.55        = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.26/0.55          & ( ( A = B )
% 0.26/0.55            | ( A
% 0.26/0.55              = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_eq_iff'
% 0.26/0.55  thf(fact_4840_eq__abs__iff_H,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( A
% 0.26/0.55          = ( abs_abs_real @ B ) )
% 0.26/0.55        = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.55          & ( ( B = A )
% 0.26/0.55            | ( B
% 0.26/0.55              = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % eq_abs_iff'
% 0.26/0.55  thf(fact_4841_eq__abs__iff_H,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( A
% 0.26/0.55          = ( abs_abs_Code_integer @ B ) )
% 0.26/0.55        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.26/0.55          & ( ( B = A )
% 0.26/0.55            | ( B
% 0.26/0.55              = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % eq_abs_iff'
% 0.26/0.55  thf(fact_4842_eq__abs__iff_H,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( A
% 0.26/0.55          = ( abs_abs_rat @ B ) )
% 0.26/0.55        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.55          & ( ( B = A )
% 0.26/0.55            | ( B
% 0.26/0.55              = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % eq_abs_iff'
% 0.26/0.55  thf(fact_4843_eq__abs__iff_H,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( A
% 0.26/0.55          = ( abs_abs_int @ B ) )
% 0.26/0.55        = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.55          & ( ( B = A )
% 0.26/0.55            | ( B
% 0.26/0.55              = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % eq_abs_iff'
% 0.26/0.55  thf(fact_4844_abs__if__raw,axiom,
% 0.26/0.55      ( abs_abs_real
% 0.26/0.55      = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_if_raw
% 0.26/0.55  thf(fact_4845_abs__if__raw,axiom,
% 0.26/0.55      ( abs_abs_int
% 0.26/0.55      = ( ^ [A4: int] : ( if_int @ ( ord_less_int @ A4 @ zero_zero_int ) @ ( uminus_uminus_int @ A4 ) @ A4 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_if_raw
% 0.26/0.55  thf(fact_4846_abs__if__raw,axiom,
% 0.26/0.55      ( abs_abs_Code_integer
% 0.26/0.55      = ( ^ [A4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A4 ) @ A4 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_if_raw
% 0.26/0.55  thf(fact_4847_abs__if__raw,axiom,
% 0.26/0.55      ( abs_abs_rat
% 0.26/0.55      = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_if_raw
% 0.26/0.55  thf(fact_4848_abs__of__neg,axiom,
% 0.26/0.55      ! [A: real] :
% 0.26/0.55        ( ( ord_less_real @ A @ zero_zero_real )
% 0.26/0.55       => ( ( abs_abs_real @ A )
% 0.26/0.55          = ( uminus_uminus_real @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_of_neg
% 0.26/0.55  thf(fact_4849_abs__of__neg,axiom,
% 0.26/0.55      ! [A: int] :
% 0.26/0.55        ( ( ord_less_int @ A @ zero_zero_int )
% 0.26/0.55       => ( ( abs_abs_int @ A )
% 0.26/0.55          = ( uminus_uminus_int @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_of_neg
% 0.26/0.55  thf(fact_4850_abs__of__neg,axiom,
% 0.26/0.55      ! [A: code_integer] :
% 0.26/0.55        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.26/0.55       => ( ( abs_abs_Code_integer @ A )
% 0.26/0.55          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_of_neg
% 0.26/0.55  thf(fact_4851_abs__of__neg,axiom,
% 0.26/0.55      ! [A: rat] :
% 0.26/0.55        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.26/0.55       => ( ( abs_abs_rat @ A )
% 0.26/0.55          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_of_neg
% 0.26/0.55  thf(fact_4852_abs__if,axiom,
% 0.26/0.55      ( abs_abs_real
% 0.26/0.55      = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_if
% 0.26/0.55  thf(fact_4853_abs__if,axiom,
% 0.26/0.55      ( abs_abs_int
% 0.26/0.55      = ( ^ [A4: int] : ( if_int @ ( ord_less_int @ A4 @ zero_zero_int ) @ ( uminus_uminus_int @ A4 ) @ A4 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_if
% 0.26/0.55  thf(fact_4854_abs__if,axiom,
% 0.26/0.55      ( abs_abs_Code_integer
% 0.26/0.55      = ( ^ [A4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A4 ) @ A4 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_if
% 0.26/0.55  thf(fact_4855_abs__if,axiom,
% 0.26/0.55      ( abs_abs_rat
% 0.26/0.55      = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_if
% 0.26/0.55  thf(fact_4856_abs__real__def,axiom,
% 0.26/0.55      ( abs_abs_real
% 0.26/0.55      = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_real_def
% 0.26/0.55  thf(fact_4857_abs__ge__self,axiom,
% 0.26/0.55      ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_ge_self
% 0.26/0.55  thf(fact_4858_abs__ge__self,axiom,
% 0.26/0.55      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_ge_self
% 0.26/0.55  thf(fact_4859_abs__ge__self,axiom,
% 0.26/0.55      ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_ge_self
% 0.26/0.55  thf(fact_4860_abs__ge__self,axiom,
% 0.26/0.55      ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_ge_self
% 0.26/0.55  thf(fact_4861_abs__le__D1,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 0.26/0.55       => ( ord_less_eq_real @ A @ B ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_le_D1
% 0.26/0.55  thf(fact_4862_abs__le__D1,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.26/0.55       => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_le_D1
% 0.26/0.55  thf(fact_4863_abs__le__D1,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.26/0.55       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_le_D1
% 0.26/0.55  thf(fact_4864_abs__le__D1,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.26/0.55       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_le_D1
% 0.26/0.55  thf(fact_4865_abs__eq__0__iff,axiom,
% 0.26/0.55      ! [A: code_integer] :
% 0.26/0.55        ( ( ( abs_abs_Code_integer @ A )
% 0.26/0.55          = zero_z3403309356797280102nteger )
% 0.26/0.55        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_eq_0_iff
% 0.26/0.55  thf(fact_4866_abs__eq__0__iff,axiom,
% 0.26/0.55      ! [A: real] :
% 0.26/0.55        ( ( ( abs_abs_real @ A )
% 0.26/0.55          = zero_zero_real )
% 0.26/0.55        = ( A = zero_zero_real ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_eq_0_iff
% 0.26/0.55  thf(fact_4867_abs__eq__0__iff,axiom,
% 0.26/0.55      ! [A: rat] :
% 0.26/0.55        ( ( ( abs_abs_rat @ A )
% 0.26/0.55          = zero_zero_rat )
% 0.26/0.55        = ( A = zero_zero_rat ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_eq_0_iff
% 0.26/0.55  thf(fact_4868_abs__eq__0__iff,axiom,
% 0.26/0.55      ! [A: int] :
% 0.26/0.55        ( ( ( abs_abs_int @ A )
% 0.26/0.55          = zero_zero_int )
% 0.26/0.55        = ( A = zero_zero_int ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_eq_0_iff
% 0.26/0.55  thf(fact_4869_abs__minus__commute,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.26/0.55        = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_minus_commute
% 0.26/0.55  thf(fact_4870_abs__minus__commute,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 0.26/0.55        = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_minus_commute
% 0.26/0.55  thf(fact_4871_abs__minus__commute,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 0.26/0.55        = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_minus_commute
% 0.26/0.55  thf(fact_4872_abs__minus__commute,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 0.26/0.55        = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_minus_commute
% 0.26/0.55  thf(fact_4873_power__abs,axiom,
% 0.26/0.55      ! [A: code_integer,N: nat] :
% 0.26/0.55        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) )
% 0.26/0.55        = ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power_abs
% 0.26/0.55  thf(fact_4874_power__abs,axiom,
% 0.26/0.55      ! [A: rat,N: nat] :
% 0.26/0.55        ( ( abs_abs_rat @ ( power_power_rat @ A @ N ) )
% 0.26/0.55        = ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power_abs
% 0.26/0.55  thf(fact_4875_power__abs,axiom,
% 0.26/0.55      ! [A: int,N: nat] :
% 0.26/0.55        ( ( abs_abs_int @ ( power_power_int @ A @ N ) )
% 0.26/0.55        = ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power_abs
% 0.26/0.55  thf(fact_4876_power__abs,axiom,
% 0.26/0.55      ! [A: real,N: nat] :
% 0.26/0.55        ( ( abs_abs_real @ ( power_power_real @ A @ N ) )
% 0.26/0.55        = ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power_abs
% 0.26/0.55  thf(fact_4877_ceiling__def,axiom,
% 0.26/0.55      ( archim2889992004027027881ng_rat
% 0.26/0.55      = ( ^ [X: rat] : ( uminus_uminus_int @ ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ X ) ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % ceiling_def
% 0.26/0.55  thf(fact_4878_ceiling__def,axiom,
% 0.26/0.55      ( archim7802044766580827645g_real
% 0.26/0.55      = ( ^ [X: real] : ( uminus_uminus_int @ ( archim6058952711729229775r_real @ ( uminus_uminus_real @ X ) ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % ceiling_def
% 0.26/0.55  thf(fact_4879_floor__minus,axiom,
% 0.26/0.55      ! [X3: rat] :
% 0.26/0.55        ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ X3 ) )
% 0.26/0.55        = ( uminus_uminus_int @ ( archim2889992004027027881ng_rat @ X3 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % floor_minus
% 0.26/0.55  thf(fact_4880_floor__minus,axiom,
% 0.26/0.55      ! [X3: real] :
% 0.26/0.55        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ X3 ) )
% 0.26/0.55        = ( uminus_uminus_int @ ( archim7802044766580827645g_real @ X3 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % floor_minus
% 0.26/0.55  thf(fact_4881_ceiling__minus,axiom,
% 0.26/0.55      ! [X3: rat] :
% 0.26/0.55        ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ X3 ) )
% 0.26/0.55        = ( uminus_uminus_int @ ( archim3151403230148437115or_rat @ X3 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % ceiling_minus
% 0.26/0.55  thf(fact_4882_ceiling__minus,axiom,
% 0.26/0.55      ! [X3: real] :
% 0.26/0.55        ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ X3 ) )
% 0.26/0.55        = ( uminus_uminus_int @ ( archim6058952711729229775r_real @ X3 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % ceiling_minus
% 0.26/0.55  thf(fact_4883_le__imp__neg__le,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.55       => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % le_imp_neg_le
% 0.26/0.55  thf(fact_4884_le__imp__neg__le,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.26/0.55       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % le_imp_neg_le
% 0.26/0.55  thf(fact_4885_le__imp__neg__le,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.55       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % le_imp_neg_le
% 0.26/0.55  thf(fact_4886_le__imp__neg__le,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( ord_less_eq_int @ A @ B )
% 0.26/0.55       => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % le_imp_neg_le
% 0.26/0.55  thf(fact_4887_minus__le__iff,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 0.26/0.55        = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_le_iff
% 0.26/0.55  thf(fact_4888_minus__le__iff,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.26/0.55        = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_le_iff
% 0.26/0.55  thf(fact_4889_minus__le__iff,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.26/0.55        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_le_iff
% 0.26/0.55  thf(fact_4890_minus__le__iff,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 0.26/0.55        = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_le_iff
% 0.26/0.55  thf(fact_4891_le__minus__iff,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 0.26/0.55        = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % le_minus_iff
% 0.26/0.55  thf(fact_4892_le__minus__iff,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.26/0.55        = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % le_minus_iff
% 0.26/0.55  thf(fact_4893_le__minus__iff,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.26/0.55        = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % le_minus_iff
% 0.26/0.55  thf(fact_4894_le__minus__iff,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 0.26/0.55        = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % le_minus_iff
% 0.26/0.55  thf(fact_4895_verit__negate__coefficient_I2_J,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( ord_less_real @ A @ B )
% 0.26/0.55       => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % verit_negate_coefficient(2)
% 0.26/0.55  thf(fact_4896_verit__negate__coefficient_I2_J,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( ord_less_int @ A @ B )
% 0.26/0.55       => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % verit_negate_coefficient(2)
% 0.26/0.55  thf(fact_4897_verit__negate__coefficient_I2_J,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.26/0.55       => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % verit_negate_coefficient(2)
% 0.26/0.55  thf(fact_4898_verit__negate__coefficient_I2_J,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( ord_less_rat @ A @ B )
% 0.26/0.55       => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % verit_negate_coefficient(2)
% 0.26/0.55  thf(fact_4899_less__minus__iff,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 0.26/0.55        = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % less_minus_iff
% 0.26/0.55  thf(fact_4900_less__minus__iff,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 0.26/0.55        = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % less_minus_iff
% 0.26/0.55  thf(fact_4901_less__minus__iff,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.26/0.55        = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % less_minus_iff
% 0.26/0.55  thf(fact_4902_less__minus__iff,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.26/0.55        = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % less_minus_iff
% 0.26/0.55  thf(fact_4903_minus__less__iff,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 0.26/0.55        = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_less_iff
% 0.26/0.55  thf(fact_4904_minus__less__iff,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 0.26/0.55        = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_less_iff
% 0.26/0.55  thf(fact_4905_minus__less__iff,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.26/0.55        = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_less_iff
% 0.26/0.55  thf(fact_4906_minus__less__iff,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.26/0.55        = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_less_iff
% 0.26/0.55  thf(fact_4907_neg__numeral__neq__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] :
% 0.26/0.55        ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 0.26/0.55       != ( numeral_numeral_real @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_neq_numeral
% 0.26/0.55  thf(fact_4908_neg__numeral__neq__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] :
% 0.26/0.55        ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 0.26/0.55       != ( numeral_numeral_int @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_neq_numeral
% 0.26/0.55  thf(fact_4909_neg__numeral__neq__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] :
% 0.26/0.55        ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 0.26/0.55       != ( numera6690914467698888265omplex @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_neq_numeral
% 0.26/0.55  thf(fact_4910_neg__numeral__neq__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] :
% 0.26/0.55        ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 0.26/0.55       != ( numera6620942414471956472nteger @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_neq_numeral
% 0.26/0.55  thf(fact_4911_neg__numeral__neq__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] :
% 0.26/0.55        ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 0.26/0.55       != ( numeral_numeral_rat @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_neq_numeral
% 0.26/0.55  thf(fact_4912_numeral__neq__neg__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] :
% 0.26/0.55        ( ( numeral_numeral_real @ M )
% 0.26/0.55       != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % numeral_neq_neg_numeral
% 0.26/0.55  thf(fact_4913_numeral__neq__neg__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] :
% 0.26/0.55        ( ( numeral_numeral_int @ M )
% 0.26/0.55       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % numeral_neq_neg_numeral
% 0.26/0.55  thf(fact_4914_numeral__neq__neg__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] :
% 0.26/0.55        ( ( numera6690914467698888265omplex @ M )
% 0.26/0.55       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % numeral_neq_neg_numeral
% 0.26/0.55  thf(fact_4915_numeral__neq__neg__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] :
% 0.26/0.55        ( ( numera6620942414471956472nteger @ M )
% 0.26/0.55       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % numeral_neq_neg_numeral
% 0.26/0.55  thf(fact_4916_numeral__neq__neg__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] :
% 0.26/0.55        ( ( numeral_numeral_rat @ M )
% 0.26/0.55       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % numeral_neq_neg_numeral
% 0.26/0.55  thf(fact_4917_one__neq__neg__one,axiom,
% 0.26/0.55      ( one_one_real
% 0.26/0.55     != ( uminus_uminus_real @ one_one_real ) ) ).
% 0.26/0.55  
% 0.26/0.55  % one_neq_neg_one
% 0.26/0.55  thf(fact_4918_one__neq__neg__one,axiom,
% 0.26/0.55      ( one_one_int
% 0.26/0.55     != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.55  
% 0.26/0.55  % one_neq_neg_one
% 0.26/0.55  thf(fact_4919_one__neq__neg__one,axiom,
% 0.26/0.55      ( one_one_complex
% 0.26/0.55     != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.26/0.55  
% 0.26/0.55  % one_neq_neg_one
% 0.26/0.55  thf(fact_4920_one__neq__neg__one,axiom,
% 0.26/0.55      ( one_one_Code_integer
% 0.26/0.55     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.55  
% 0.26/0.55  % one_neq_neg_one
% 0.26/0.55  thf(fact_4921_one__neq__neg__one,axiom,
% 0.26/0.55      ( one_one_rat
% 0.26/0.55     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.26/0.55  
% 0.26/0.55  % one_neq_neg_one
% 0.26/0.55  thf(fact_4922_group__cancel_Oneg1,axiom,
% 0.26/0.55      ! [A3: real,K: real,A: real] :
% 0.26/0.55        ( ( A3
% 0.26/0.55          = ( plus_plus_real @ K @ A ) )
% 0.26/0.55       => ( ( uminus_uminus_real @ A3 )
% 0.26/0.55          = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % group_cancel.neg1
% 0.26/0.55  thf(fact_4923_group__cancel_Oneg1,axiom,
% 0.26/0.55      ! [A3: int,K: int,A: int] :
% 0.26/0.55        ( ( A3
% 0.26/0.55          = ( plus_plus_int @ K @ A ) )
% 0.26/0.55       => ( ( uminus_uminus_int @ A3 )
% 0.26/0.55          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % group_cancel.neg1
% 0.26/0.55  thf(fact_4924_group__cancel_Oneg1,axiom,
% 0.26/0.55      ! [A3: complex,K: complex,A: complex] :
% 0.26/0.55        ( ( A3
% 0.26/0.55          = ( plus_plus_complex @ K @ A ) )
% 0.26/0.55       => ( ( uminus1482373934393186551omplex @ A3 )
% 0.26/0.55          = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % group_cancel.neg1
% 0.26/0.55  thf(fact_4925_group__cancel_Oneg1,axiom,
% 0.26/0.55      ! [A3: code_integer,K: code_integer,A: code_integer] :
% 0.26/0.55        ( ( A3
% 0.26/0.55          = ( plus_p5714425477246183910nteger @ K @ A ) )
% 0.26/0.55       => ( ( uminus1351360451143612070nteger @ A3 )
% 0.26/0.55          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % group_cancel.neg1
% 0.26/0.55  thf(fact_4926_group__cancel_Oneg1,axiom,
% 0.26/0.55      ! [A3: rat,K: rat,A: rat] :
% 0.26/0.55        ( ( A3
% 0.26/0.55          = ( plus_plus_rat @ K @ A ) )
% 0.26/0.55       => ( ( uminus_uminus_rat @ A3 )
% 0.26/0.55          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % group_cancel.neg1
% 0.26/0.55  thf(fact_4927_add_Oinverse__distrib__swap,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 0.26/0.55        = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % add.inverse_distrib_swap
% 0.26/0.55  thf(fact_4928_add_Oinverse__distrib__swap,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.26/0.55        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % add.inverse_distrib_swap
% 0.26/0.55  thf(fact_4929_add_Oinverse__distrib__swap,axiom,
% 0.26/0.55      ! [A: complex,B: complex] :
% 0.26/0.55        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 0.26/0.55        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % add.inverse_distrib_swap
% 0.26/0.55  thf(fact_4930_add_Oinverse__distrib__swap,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.26/0.55        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % add.inverse_distrib_swap
% 0.26/0.55  thf(fact_4931_add_Oinverse__distrib__swap,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.26/0.55        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % add.inverse_distrib_swap
% 0.26/0.55  thf(fact_4932_is__num__normalize_I8_J,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 0.26/0.55        = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % is_num_normalize(8)
% 0.26/0.55  thf(fact_4933_is__num__normalize_I8_J,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.26/0.55        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % is_num_normalize(8)
% 0.26/0.55  thf(fact_4934_is__num__normalize_I8_J,axiom,
% 0.26/0.55      ! [A: complex,B: complex] :
% 0.26/0.55        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 0.26/0.55        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % is_num_normalize(8)
% 0.26/0.55  thf(fact_4935_is__num__normalize_I8_J,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.26/0.55        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % is_num_normalize(8)
% 0.26/0.55  thf(fact_4936_is__num__normalize_I8_J,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.26/0.55        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % is_num_normalize(8)
% 0.26/0.55  thf(fact_4937_minus__diff__commute,axiom,
% 0.26/0.55      ! [B: real,A: real] :
% 0.26/0.55        ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 0.26/0.55        = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_diff_commute
% 0.26/0.55  thf(fact_4938_minus__diff__commute,axiom,
% 0.26/0.55      ! [B: int,A: int] :
% 0.26/0.55        ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 0.26/0.55        = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_diff_commute
% 0.26/0.55  thf(fact_4939_minus__diff__commute,axiom,
% 0.26/0.55      ! [B: complex,A: complex] :
% 0.26/0.55        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 0.26/0.55        = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_diff_commute
% 0.26/0.55  thf(fact_4940_minus__diff__commute,axiom,
% 0.26/0.55      ! [B: code_integer,A: code_integer] :
% 0.26/0.55        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 0.26/0.55        = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_diff_commute
% 0.26/0.55  thf(fact_4941_minus__diff__commute,axiom,
% 0.26/0.55      ! [B: rat,A: rat] :
% 0.26/0.55        ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 0.26/0.55        = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_diff_commute
% 0.26/0.55  thf(fact_4942_minus__diff__minus,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 0.26/0.55        = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_diff_minus
% 0.26/0.55  thf(fact_4943_minus__diff__minus,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 0.26/0.55        = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_diff_minus
% 0.26/0.55  thf(fact_4944_minus__diff__minus,axiom,
% 0.26/0.55      ! [A: complex,B: complex] :
% 0.26/0.55        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 0.26/0.55        = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_diff_minus
% 0.26/0.55  thf(fact_4945_minus__diff__minus,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 0.26/0.55        = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_diff_minus
% 0.26/0.55  thf(fact_4946_minus__diff__minus,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.26/0.55        = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_diff_minus
% 0.26/0.55  thf(fact_4947_real__minus__mult__self__le,axiom,
% 0.26/0.55      ! [U: real,X3: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X3 @ X3 ) ) ).
% 0.26/0.55  
% 0.26/0.55  % real_minus_mult_self_le
% 0.26/0.55  thf(fact_4948_real__sqrt__minus,axiom,
% 0.26/0.55      ! [X3: real] :
% 0.26/0.55        ( ( sqrt @ ( uminus_uminus_real @ X3 ) )
% 0.26/0.55        = ( uminus_uminus_real @ ( sqrt @ X3 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % real_sqrt_minus
% 0.26/0.55  thf(fact_4949_norm__triangle__ineq3,axiom,
% 0.26/0.55      ! [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 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % norm_triangle_ineq3
% 0.26/0.55  thf(fact_4950_norm__triangle__ineq3,axiom,
% 0.26/0.55      ! [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 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % norm_triangle_ineq3
% 0.26/0.55  thf(fact_4951_of__int__neg__numeral,axiom,
% 0.26/0.55      ! [K: num] :
% 0.26/0.55        ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.26/0.55        = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_neg_numeral
% 0.26/0.55  thf(fact_4952_of__int__neg__numeral,axiom,
% 0.26/0.55      ! [K: num] :
% 0.26/0.55        ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.26/0.55        = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_neg_numeral
% 0.26/0.55  thf(fact_4953_of__int__neg__numeral,axiom,
% 0.26/0.55      ! [K: num] :
% 0.26/0.55        ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.26/0.55        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_neg_numeral
% 0.26/0.55  thf(fact_4954_of__int__neg__numeral,axiom,
% 0.26/0.55      ! [K: num] :
% 0.26/0.55        ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.26/0.55        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_neg_numeral
% 0.26/0.55  thf(fact_4955_of__int__neg__numeral,axiom,
% 0.26/0.55      ! [K: num] :
% 0.26/0.55        ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.26/0.55        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_neg_numeral
% 0.26/0.55  thf(fact_4956_abs__ge__zero,axiom,
% 0.26/0.55      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_ge_zero
% 0.26/0.55  thf(fact_4957_abs__ge__zero,axiom,
% 0.26/0.55      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_ge_zero
% 0.26/0.55  thf(fact_4958_abs__ge__zero,axiom,
% 0.26/0.55      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_ge_zero
% 0.26/0.55  thf(fact_4959_abs__ge__zero,axiom,
% 0.26/0.55      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_ge_zero
% 0.26/0.55  thf(fact_4960_abs__of__pos,axiom,
% 0.26/0.55      ! [A: code_integer] :
% 0.26/0.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.26/0.55       => ( ( abs_abs_Code_integer @ A )
% 0.26/0.55          = A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_of_pos
% 0.26/0.55  thf(fact_4961_abs__of__pos,axiom,
% 0.26/0.55      ! [A: real] :
% 0.26/0.55        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.55       => ( ( abs_abs_real @ A )
% 0.26/0.55          = A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_of_pos
% 0.26/0.55  thf(fact_4962_abs__of__pos,axiom,
% 0.26/0.55      ! [A: rat] :
% 0.26/0.55        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.26/0.55       => ( ( abs_abs_rat @ A )
% 0.26/0.55          = A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_of_pos
% 0.26/0.55  thf(fact_4963_abs__of__pos,axiom,
% 0.26/0.55      ! [A: int] :
% 0.26/0.55        ( ( ord_less_int @ zero_zero_int @ A )
% 0.26/0.55       => ( ( abs_abs_int @ A )
% 0.26/0.55          = A ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_of_pos
% 0.26/0.55  thf(fact_4964_abs__not__less__zero,axiom,
% 0.26/0.55      ! [A: code_integer] :
% 0.26/0.55        ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_not_less_zero
% 0.26/0.55  thf(fact_4965_abs__not__less__zero,axiom,
% 0.26/0.55      ! [A: real] :
% 0.26/0.55        ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_not_less_zero
% 0.26/0.55  thf(fact_4966_abs__not__less__zero,axiom,
% 0.26/0.55      ! [A: rat] :
% 0.26/0.55        ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_not_less_zero
% 0.26/0.55  thf(fact_4967_abs__not__less__zero,axiom,
% 0.26/0.55      ! [A: int] :
% 0.26/0.55        ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_not_less_zero
% 0.26/0.55  thf(fact_4968_abs__triangle__ineq,axiom,
% 0.26/0.55      ! [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 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_triangle_ineq
% 0.26/0.55  thf(fact_4969_abs__triangle__ineq,axiom,
% 0.26/0.55      ! [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 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_triangle_ineq
% 0.26/0.55  thf(fact_4970_abs__triangle__ineq,axiom,
% 0.26/0.55      ! [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 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_triangle_ineq
% 0.26/0.55  thf(fact_4971_abs__triangle__ineq,axiom,
% 0.26/0.55      ! [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 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_triangle_ineq
% 0.26/0.55  thf(fact_4972_abs__mult__less,axiom,
% 0.26/0.55      ! [A: code_integer,C: code_integer,B: code_integer,D3: code_integer] :
% 0.26/0.55        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 0.26/0.55       => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D3 )
% 0.26/0.55         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_mult_less
% 0.26/0.55  thf(fact_4973_abs__mult__less,axiom,
% 0.26/0.55      ! [A: real,C: real,B: real,D3: real] :
% 0.26/0.55        ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 0.26/0.55       => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D3 )
% 0.26/0.55         => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_mult_less
% 0.26/0.55  thf(fact_4974_abs__mult__less,axiom,
% 0.26/0.55      ! [A: rat,C: rat,B: rat,D3: rat] :
% 0.26/0.55        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 0.26/0.55       => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D3 )
% 0.26/0.55         => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_mult_less
% 0.26/0.55  thf(fact_4975_abs__mult__less,axiom,
% 0.26/0.55      ! [A: int,C: int,B: int,D3: int] :
% 0.26/0.55        ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 0.26/0.55       => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D3 )
% 0.26/0.55         => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_mult_less
% 0.26/0.55  thf(fact_4976_abs__triangle__ineq2__sym,axiom,
% 0.26/0.55      ! [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 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_triangle_ineq2_sym
% 0.26/0.55  thf(fact_4977_abs__triangle__ineq2__sym,axiom,
% 0.26/0.55      ! [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 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_triangle_ineq2_sym
% 0.26/0.55  thf(fact_4978_abs__triangle__ineq2__sym,axiom,
% 0.26/0.55      ! [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 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_triangle_ineq2_sym
% 0.26/0.55  thf(fact_4979_abs__triangle__ineq2__sym,axiom,
% 0.26/0.55      ! [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 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_triangle_ineq2_sym
% 0.26/0.55  thf(fact_4980_abs__triangle__ineq3,axiom,
% 0.26/0.55      ! [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 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_triangle_ineq3
% 0.26/0.55  thf(fact_4981_abs__triangle__ineq3,axiom,
% 0.26/0.55      ! [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 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_triangle_ineq3
% 0.26/0.55  thf(fact_4982_abs__triangle__ineq3,axiom,
% 0.26/0.55      ! [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 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_triangle_ineq3
% 0.26/0.55  thf(fact_4983_abs__triangle__ineq3,axiom,
% 0.26/0.55      ! [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 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_triangle_ineq3
% 0.26/0.55  thf(fact_4984_abs__triangle__ineq2,axiom,
% 0.26/0.55      ! [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 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_triangle_ineq2
% 0.26/0.55  thf(fact_4985_abs__triangle__ineq2,axiom,
% 0.26/0.55      ! [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 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_triangle_ineq2
% 0.26/0.55  thf(fact_4986_abs__triangle__ineq2,axiom,
% 0.26/0.55      ! [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 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_triangle_ineq2
% 0.26/0.55  thf(fact_4987_abs__triangle__ineq2,axiom,
% 0.26/0.55      ! [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 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_triangle_ineq2
% 0.26/0.55  thf(fact_4988_nonzero__abs__divide,axiom,
% 0.26/0.55      ! [B: real,A: real] :
% 0.26/0.55        ( ( B != zero_zero_real )
% 0.26/0.55       => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 0.26/0.55          = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % nonzero_abs_divide
% 0.26/0.55  thf(fact_4989_nonzero__abs__divide,axiom,
% 0.26/0.55      ! [B: rat,A: rat] :
% 0.26/0.55        ( ( B != zero_zero_rat )
% 0.26/0.55       => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 0.26/0.55          = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % nonzero_abs_divide
% 0.26/0.55  thf(fact_4990_norm__of__real__diff,axiom,
% 0.26/0.55      ! [B: real,A: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( real_V1803761363581548252l_real @ B ) @ ( real_V1803761363581548252l_real @ A ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % norm_of_real_diff
% 0.26/0.55  thf(fact_4991_norm__of__real__diff,axiom,
% 0.26/0.55      ! [B: real,A: real] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( real_V4546457046886955230omplex @ B ) @ ( real_V4546457046886955230omplex @ A ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % norm_of_real_diff
% 0.26/0.55  thf(fact_4992_norm__mult__less,axiom,
% 0.26/0.55      ! [X3: real,R2: real,Y3: real,S: real] :
% 0.26/0.55        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ R2 )
% 0.26/0.55       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y3 ) @ S )
% 0.26/0.55         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X3 @ Y3 ) ) @ ( times_times_real @ R2 @ S ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % norm_mult_less
% 0.26/0.55  thf(fact_4993_norm__mult__less,axiom,
% 0.26/0.55      ! [X3: complex,R2: real,Y3: complex,S: real] :
% 0.26/0.55        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ R2 )
% 0.26/0.55       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y3 ) @ S )
% 0.26/0.55         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X3 @ Y3 ) ) @ ( times_times_real @ R2 @ S ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % norm_mult_less
% 0.26/0.55  thf(fact_4994_norm__mult__ineq,axiom,
% 0.26/0.55      ! [X3: real,Y3: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X3 @ Y3 ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % norm_mult_ineq
% 0.26/0.55  thf(fact_4995_norm__mult__ineq,axiom,
% 0.26/0.55      ! [X3: complex,Y3: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X3 @ Y3 ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % norm_mult_ineq
% 0.26/0.55  thf(fact_4996_norm__not__less__zero,axiom,
% 0.26/0.55      ! [X3: complex] :
% 0.26/0.55        ~ ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ zero_zero_real ) ).
% 0.26/0.55  
% 0.26/0.55  % norm_not_less_zero
% 0.26/0.55  thf(fact_4997_norm__ge__zero,axiom,
% 0.26/0.55      ! [X3: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X3 ) ) ).
% 0.26/0.55  
% 0.26/0.55  % norm_ge_zero
% 0.26/0.55  thf(fact_4998_not__numeral__le__neg__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] :
% 0.26/0.55        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_numeral_le_neg_numeral
% 0.26/0.55  thf(fact_4999_not__numeral__le__neg__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] :
% 0.26/0.55        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_numeral_le_neg_numeral
% 0.26/0.55  thf(fact_5000_not__numeral__le__neg__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] :
% 0.26/0.55        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_numeral_le_neg_numeral
% 0.26/0.55  thf(fact_5001_not__numeral__le__neg__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] :
% 0.26/0.55        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_numeral_le_neg_numeral
% 0.26/0.55  thf(fact_5002_neg__numeral__le__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_le_numeral
% 0.26/0.55  thf(fact_5003_neg__numeral__le__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_le_numeral
% 0.26/0.55  thf(fact_5004_neg__numeral__le__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_le_numeral
% 0.26/0.55  thf(fact_5005_neg__numeral__le__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_le_numeral
% 0.26/0.55  thf(fact_5006_zero__neq__neg__numeral,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ( zero_zero_real
% 0.26/0.55       != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % zero_neq_neg_numeral
% 0.26/0.55  thf(fact_5007_zero__neq__neg__numeral,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ( zero_zero_int
% 0.26/0.55       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % zero_neq_neg_numeral
% 0.26/0.55  thf(fact_5008_zero__neq__neg__numeral,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ( zero_zero_complex
% 0.26/0.55       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % zero_neq_neg_numeral
% 0.26/0.55  thf(fact_5009_zero__neq__neg__numeral,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ( zero_z3403309356797280102nteger
% 0.26/0.55       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % zero_neq_neg_numeral
% 0.26/0.55  thf(fact_5010_zero__neq__neg__numeral,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ( zero_zero_rat
% 0.26/0.55       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % zero_neq_neg_numeral
% 0.26/0.55  thf(fact_5011_neg__numeral__less__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_less_numeral
% 0.26/0.55  thf(fact_5012_neg__numeral__less__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_less_numeral
% 0.26/0.55  thf(fact_5013_neg__numeral__less__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_less_numeral
% 0.26/0.55  thf(fact_5014_neg__numeral__less__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_less_numeral
% 0.26/0.55  thf(fact_5015_not__numeral__less__neg__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] :
% 0.26/0.55        ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_numeral_less_neg_numeral
% 0.26/0.55  thf(fact_5016_not__numeral__less__neg__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] :
% 0.26/0.55        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_numeral_less_neg_numeral
% 0.26/0.55  thf(fact_5017_not__numeral__less__neg__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] :
% 0.26/0.55        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_numeral_less_neg_numeral
% 0.26/0.55  thf(fact_5018_not__numeral__less__neg__numeral,axiom,
% 0.26/0.55      ! [M: num,N: num] :
% 0.26/0.55        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_numeral_less_neg_numeral
% 0.26/0.55  thf(fact_5019_le__minus__one__simps_I2_J,axiom,
% 0.26/0.55      ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 0.26/0.55  
% 0.26/0.55  % le_minus_one_simps(2)
% 0.26/0.55  thf(fact_5020_le__minus__one__simps_I2_J,axiom,
% 0.26/0.55      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 0.26/0.55  
% 0.26/0.55  % le_minus_one_simps(2)
% 0.26/0.55  thf(fact_5021_le__minus__one__simps_I2_J,axiom,
% 0.26/0.55      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 0.26/0.55  
% 0.26/0.55  % le_minus_one_simps(2)
% 0.26/0.55  thf(fact_5022_le__minus__one__simps_I2_J,axiom,
% 0.26/0.55      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 0.26/0.55  
% 0.26/0.55  % le_minus_one_simps(2)
% 0.26/0.55  thf(fact_5023_le__minus__one__simps_I4_J,axiom,
% 0.26/0.55      ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.26/0.55  
% 0.26/0.55  % le_minus_one_simps(4)
% 0.26/0.55  thf(fact_5024_le__minus__one__simps_I4_J,axiom,
% 0.26/0.55      ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.55  
% 0.26/0.55  % le_minus_one_simps(4)
% 0.26/0.55  thf(fact_5025_le__minus__one__simps_I4_J,axiom,
% 0.26/0.55      ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.26/0.55  
% 0.26/0.55  % le_minus_one_simps(4)
% 0.26/0.55  thf(fact_5026_le__minus__one__simps_I4_J,axiom,
% 0.26/0.55      ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.55  
% 0.26/0.55  % le_minus_one_simps(4)
% 0.26/0.55  thf(fact_5027_zero__neq__neg__one,axiom,
% 0.26/0.55      ( zero_zero_real
% 0.26/0.55     != ( uminus_uminus_real @ one_one_real ) ) ).
% 0.26/0.55  
% 0.26/0.55  % zero_neq_neg_one
% 0.26/0.55  thf(fact_5028_zero__neq__neg__one,axiom,
% 0.26/0.55      ( zero_zero_int
% 0.26/0.55     != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.55  
% 0.26/0.55  % zero_neq_neg_one
% 0.26/0.55  thf(fact_5029_zero__neq__neg__one,axiom,
% 0.26/0.55      ( zero_zero_complex
% 0.26/0.55     != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.26/0.55  
% 0.26/0.55  % zero_neq_neg_one
% 0.26/0.55  thf(fact_5030_zero__neq__neg__one,axiom,
% 0.26/0.55      ( zero_z3403309356797280102nteger
% 0.26/0.55     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.55  
% 0.26/0.55  % zero_neq_neg_one
% 0.26/0.55  thf(fact_5031_zero__neq__neg__one,axiom,
% 0.26/0.55      ( zero_zero_rat
% 0.26/0.55     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.26/0.55  
% 0.26/0.55  % zero_neq_neg_one
% 0.26/0.55  thf(fact_5032_neg__eq__iff__add__eq__0,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( ( uminus_uminus_real @ A )
% 0.26/0.55          = B )
% 0.26/0.55        = ( ( plus_plus_real @ A @ B )
% 0.26/0.55          = zero_zero_real ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_eq_iff_add_eq_0
% 0.26/0.55  thf(fact_5033_neg__eq__iff__add__eq__0,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( ( uminus_uminus_int @ A )
% 0.26/0.55          = B )
% 0.26/0.55        = ( ( plus_plus_int @ A @ B )
% 0.26/0.55          = zero_zero_int ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_eq_iff_add_eq_0
% 0.26/0.55  thf(fact_5034_neg__eq__iff__add__eq__0,axiom,
% 0.26/0.55      ! [A: complex,B: complex] :
% 0.26/0.55        ( ( ( uminus1482373934393186551omplex @ A )
% 0.26/0.55          = B )
% 0.26/0.55        = ( ( plus_plus_complex @ A @ B )
% 0.26/0.55          = zero_zero_complex ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_eq_iff_add_eq_0
% 0.26/0.55  thf(fact_5035_neg__eq__iff__add__eq__0,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( ( uminus1351360451143612070nteger @ A )
% 0.26/0.55          = B )
% 0.26/0.55        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.26/0.55          = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_eq_iff_add_eq_0
% 0.26/0.55  thf(fact_5036_neg__eq__iff__add__eq__0,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( ( uminus_uminus_rat @ A )
% 0.26/0.55          = B )
% 0.26/0.55        = ( ( plus_plus_rat @ A @ B )
% 0.26/0.55          = zero_zero_rat ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_eq_iff_add_eq_0
% 0.26/0.55  thf(fact_5037_eq__neg__iff__add__eq__0,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( A
% 0.26/0.55          = ( uminus_uminus_real @ B ) )
% 0.26/0.55        = ( ( plus_plus_real @ A @ B )
% 0.26/0.55          = zero_zero_real ) ) ).
% 0.26/0.55  
% 0.26/0.55  % eq_neg_iff_add_eq_0
% 0.26/0.55  thf(fact_5038_eq__neg__iff__add__eq__0,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( A
% 0.26/0.55          = ( uminus_uminus_int @ B ) )
% 0.26/0.55        = ( ( plus_plus_int @ A @ B )
% 0.26/0.55          = zero_zero_int ) ) ).
% 0.26/0.55  
% 0.26/0.55  % eq_neg_iff_add_eq_0
% 0.26/0.55  thf(fact_5039_eq__neg__iff__add__eq__0,axiom,
% 0.26/0.55      ! [A: complex,B: complex] :
% 0.26/0.55        ( ( A
% 0.26/0.55          = ( uminus1482373934393186551omplex @ B ) )
% 0.26/0.55        = ( ( plus_plus_complex @ A @ B )
% 0.26/0.55          = zero_zero_complex ) ) ).
% 0.26/0.55  
% 0.26/0.55  % eq_neg_iff_add_eq_0
% 0.26/0.55  thf(fact_5040_eq__neg__iff__add__eq__0,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( A
% 0.26/0.55          = ( uminus1351360451143612070nteger @ B ) )
% 0.26/0.55        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.26/0.55          = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.55  
% 0.26/0.55  % eq_neg_iff_add_eq_0
% 0.26/0.55  thf(fact_5041_eq__neg__iff__add__eq__0,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( A
% 0.26/0.55          = ( uminus_uminus_rat @ B ) )
% 0.26/0.55        = ( ( plus_plus_rat @ A @ B )
% 0.26/0.55          = zero_zero_rat ) ) ).
% 0.26/0.55  
% 0.26/0.55  % eq_neg_iff_add_eq_0
% 0.26/0.55  thf(fact_5042_add_Oinverse__unique,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( ( plus_plus_real @ A @ B )
% 0.26/0.55          = zero_zero_real )
% 0.26/0.55       => ( ( uminus_uminus_real @ A )
% 0.26/0.55          = B ) ) ).
% 0.26/0.55  
% 0.26/0.55  % add.inverse_unique
% 0.26/0.55  thf(fact_5043_add_Oinverse__unique,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( ( plus_plus_int @ A @ B )
% 0.26/0.55          = zero_zero_int )
% 0.26/0.55       => ( ( uminus_uminus_int @ A )
% 0.26/0.55          = B ) ) ).
% 0.26/0.55  
% 0.26/0.55  % add.inverse_unique
% 0.26/0.55  thf(fact_5044_add_Oinverse__unique,axiom,
% 0.26/0.55      ! [A: complex,B: complex] :
% 0.26/0.55        ( ( ( plus_plus_complex @ A @ B )
% 0.26/0.55          = zero_zero_complex )
% 0.26/0.55       => ( ( uminus1482373934393186551omplex @ A )
% 0.26/0.55          = B ) ) ).
% 0.26/0.55  
% 0.26/0.55  % add.inverse_unique
% 0.26/0.55  thf(fact_5045_add_Oinverse__unique,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.26/0.55          = zero_z3403309356797280102nteger )
% 0.26/0.55       => ( ( uminus1351360451143612070nteger @ A )
% 0.26/0.55          = B ) ) ).
% 0.26/0.55  
% 0.26/0.55  % add.inverse_unique
% 0.26/0.55  thf(fact_5046_add_Oinverse__unique,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( ( plus_plus_rat @ A @ B )
% 0.26/0.55          = zero_zero_rat )
% 0.26/0.55       => ( ( uminus_uminus_rat @ A )
% 0.26/0.55          = B ) ) ).
% 0.26/0.55  
% 0.26/0.55  % add.inverse_unique
% 0.26/0.55  thf(fact_5047_ab__group__add__class_Oab__left__minus,axiom,
% 0.26/0.55      ! [A: real] :
% 0.26/0.55        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 0.26/0.55        = zero_zero_real ) ).
% 0.26/0.55  
% 0.26/0.55  % ab_group_add_class.ab_left_minus
% 0.26/0.55  thf(fact_5048_ab__group__add__class_Oab__left__minus,axiom,
% 0.26/0.55      ! [A: int] :
% 0.26/0.55        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 0.26/0.55        = zero_zero_int ) ).
% 0.26/0.55  
% 0.26/0.55  % ab_group_add_class.ab_left_minus
% 0.26/0.55  thf(fact_5049_ab__group__add__class_Oab__left__minus,axiom,
% 0.26/0.55      ! [A: complex] :
% 0.26/0.55        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 0.26/0.55        = zero_zero_complex ) ).
% 0.26/0.55  
% 0.26/0.55  % ab_group_add_class.ab_left_minus
% 0.26/0.55  thf(fact_5050_ab__group__add__class_Oab__left__minus,axiom,
% 0.26/0.55      ! [A: code_integer] :
% 0.26/0.55        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.26/0.55        = zero_z3403309356797280102nteger ) ).
% 0.26/0.55  
% 0.26/0.55  % ab_group_add_class.ab_left_minus
% 0.26/0.55  thf(fact_5051_ab__group__add__class_Oab__left__minus,axiom,
% 0.26/0.55      ! [A: rat] :
% 0.26/0.55        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.26/0.55        = zero_zero_rat ) ).
% 0.26/0.55  
% 0.26/0.55  % ab_group_add_class.ab_left_minus
% 0.26/0.55  thf(fact_5052_add__eq__0__iff,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( ( plus_plus_real @ A @ B )
% 0.26/0.55          = zero_zero_real )
% 0.26/0.55        = ( B
% 0.26/0.55          = ( uminus_uminus_real @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % add_eq_0_iff
% 0.26/0.55  thf(fact_5053_add__eq__0__iff,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( ( plus_plus_int @ A @ B )
% 0.26/0.55          = zero_zero_int )
% 0.26/0.55        = ( B
% 0.26/0.55          = ( uminus_uminus_int @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % add_eq_0_iff
% 0.26/0.55  thf(fact_5054_add__eq__0__iff,axiom,
% 0.26/0.55      ! [A: complex,B: complex] :
% 0.26/0.55        ( ( ( plus_plus_complex @ A @ B )
% 0.26/0.55          = zero_zero_complex )
% 0.26/0.55        = ( B
% 0.26/0.55          = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % add_eq_0_iff
% 0.26/0.55  thf(fact_5055_add__eq__0__iff,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.26/0.55          = zero_z3403309356797280102nteger )
% 0.26/0.55        = ( B
% 0.26/0.55          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % add_eq_0_iff
% 0.26/0.55  thf(fact_5056_add__eq__0__iff,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( ( plus_plus_rat @ A @ B )
% 0.26/0.55          = zero_zero_rat )
% 0.26/0.55        = ( B
% 0.26/0.55          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % add_eq_0_iff
% 0.26/0.55  thf(fact_5057_less__minus__one__simps_I2_J,axiom,
% 0.26/0.55      ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 0.26/0.55  
% 0.26/0.55  % less_minus_one_simps(2)
% 0.26/0.55  thf(fact_5058_less__minus__one__simps_I2_J,axiom,
% 0.26/0.55      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 0.26/0.55  
% 0.26/0.55  % less_minus_one_simps(2)
% 0.26/0.55  thf(fact_5059_less__minus__one__simps_I2_J,axiom,
% 0.26/0.55      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 0.26/0.55  
% 0.26/0.55  % less_minus_one_simps(2)
% 0.26/0.55  thf(fact_5060_less__minus__one__simps_I2_J,axiom,
% 0.26/0.55      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 0.26/0.55  
% 0.26/0.55  % less_minus_one_simps(2)
% 0.26/0.55  thf(fact_5061_less__minus__one__simps_I4_J,axiom,
% 0.26/0.55      ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.26/0.55  
% 0.26/0.55  % less_minus_one_simps(4)
% 0.26/0.55  thf(fact_5062_less__minus__one__simps_I4_J,axiom,
% 0.26/0.55      ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.55  
% 0.26/0.55  % less_minus_one_simps(4)
% 0.26/0.55  thf(fact_5063_less__minus__one__simps_I4_J,axiom,
% 0.26/0.55      ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.55  
% 0.26/0.55  % less_minus_one_simps(4)
% 0.26/0.55  thf(fact_5064_less__minus__one__simps_I4_J,axiom,
% 0.26/0.55      ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.26/0.55  
% 0.26/0.55  % less_minus_one_simps(4)
% 0.26/0.55  thf(fact_5065_numeral__times__minus__swap,axiom,
% 0.26/0.55      ! [W: num,X3: real] :
% 0.26/0.55        ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X3 ) )
% 0.26/0.55        = ( times_times_real @ X3 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % numeral_times_minus_swap
% 0.26/0.55  thf(fact_5066_numeral__times__minus__swap,axiom,
% 0.26/0.55      ! [W: num,X3: int] :
% 0.26/0.55        ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X3 ) )
% 0.26/0.55        = ( times_times_int @ X3 @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % numeral_times_minus_swap
% 0.26/0.55  thf(fact_5067_numeral__times__minus__swap,axiom,
% 0.26/0.55      ! [W: num,X3: complex] :
% 0.26/0.55        ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X3 ) )
% 0.26/0.55        = ( times_times_complex @ X3 @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % numeral_times_minus_swap
% 0.26/0.55  thf(fact_5068_numeral__times__minus__swap,axiom,
% 0.26/0.55      ! [W: num,X3: code_integer] :
% 0.26/0.55        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X3 ) )
% 0.26/0.55        = ( times_3573771949741848930nteger @ X3 @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % numeral_times_minus_swap
% 0.26/0.55  thf(fact_5069_numeral__times__minus__swap,axiom,
% 0.26/0.55      ! [W: num,X3: rat] :
% 0.26/0.55        ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X3 ) )
% 0.26/0.55        = ( times_times_rat @ X3 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % numeral_times_minus_swap
% 0.26/0.55  thf(fact_5070_one__neq__neg__numeral,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ( one_one_real
% 0.26/0.55       != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % one_neq_neg_numeral
% 0.26/0.55  thf(fact_5071_one__neq__neg__numeral,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ( one_one_int
% 0.26/0.55       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % one_neq_neg_numeral
% 0.26/0.55  thf(fact_5072_one__neq__neg__numeral,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ( one_one_complex
% 0.26/0.55       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % one_neq_neg_numeral
% 0.26/0.55  thf(fact_5073_one__neq__neg__numeral,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ( one_one_Code_integer
% 0.26/0.55       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % one_neq_neg_numeral
% 0.26/0.55  thf(fact_5074_one__neq__neg__numeral,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ( one_one_rat
% 0.26/0.55       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % one_neq_neg_numeral
% 0.26/0.55  thf(fact_5075_numeral__neq__neg__one,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ( ( numeral_numeral_real @ N )
% 0.26/0.55       != ( uminus_uminus_real @ one_one_real ) ) ).
% 0.26/0.55  
% 0.26/0.55  % numeral_neq_neg_one
% 0.26/0.55  thf(fact_5076_numeral__neq__neg__one,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ( ( numeral_numeral_int @ N )
% 0.26/0.55       != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.55  
% 0.26/0.55  % numeral_neq_neg_one
% 0.26/0.55  thf(fact_5077_numeral__neq__neg__one,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ( ( numera6690914467698888265omplex @ N )
% 0.26/0.55       != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.26/0.55  
% 0.26/0.55  % numeral_neq_neg_one
% 0.26/0.55  thf(fact_5078_numeral__neq__neg__one,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ( ( numera6620942414471956472nteger @ N )
% 0.26/0.55       != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.55  
% 0.26/0.55  % numeral_neq_neg_one
% 0.26/0.55  thf(fact_5079_numeral__neq__neg__one,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ( ( numeral_numeral_rat @ N )
% 0.26/0.55       != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.26/0.55  
% 0.26/0.55  % numeral_neq_neg_one
% 0.26/0.55  thf(fact_5080_nonzero__minus__divide__divide,axiom,
% 0.26/0.55      ! [B: real,A: real] :
% 0.26/0.55        ( ( B != zero_zero_real )
% 0.26/0.55       => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 0.26/0.55          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % nonzero_minus_divide_divide
% 0.26/0.55  thf(fact_5081_nonzero__minus__divide__divide,axiom,
% 0.26/0.55      ! [B: complex,A: complex] :
% 0.26/0.55        ( ( B != zero_zero_complex )
% 0.26/0.55       => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 0.26/0.55          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % nonzero_minus_divide_divide
% 0.26/0.55  thf(fact_5082_nonzero__minus__divide__divide,axiom,
% 0.26/0.55      ! [B: rat,A: rat] :
% 0.26/0.55        ( ( B != zero_zero_rat )
% 0.26/0.55       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.26/0.55          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % nonzero_minus_divide_divide
% 0.26/0.55  thf(fact_5083_nonzero__minus__divide__right,axiom,
% 0.26/0.55      ! [B: real,A: real] :
% 0.26/0.55        ( ( B != zero_zero_real )
% 0.26/0.55       => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 0.26/0.55          = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % nonzero_minus_divide_right
% 0.26/0.55  thf(fact_5084_nonzero__minus__divide__right,axiom,
% 0.26/0.55      ! [B: complex,A: complex] :
% 0.26/0.55        ( ( B != zero_zero_complex )
% 0.26/0.55       => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.26/0.55          = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % nonzero_minus_divide_right
% 0.26/0.55  thf(fact_5085_nonzero__minus__divide__right,axiom,
% 0.26/0.55      ! [B: rat,A: rat] :
% 0.26/0.55        ( ( B != zero_zero_rat )
% 0.26/0.55       => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.26/0.55          = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % nonzero_minus_divide_right
% 0.26/0.55  thf(fact_5086_norm__power,axiom,
% 0.26/0.55      ! [X3: real,N: nat] :
% 0.26/0.55        ( ( real_V7735802525324610683m_real @ ( power_power_real @ X3 @ N ) )
% 0.26/0.55        = ( power_power_real @ ( real_V7735802525324610683m_real @ X3 ) @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % norm_power
% 0.26/0.55  thf(fact_5087_norm__power,axiom,
% 0.26/0.55      ! [X3: complex,N: nat] :
% 0.26/0.55        ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X3 @ N ) )
% 0.26/0.55        = ( power_power_real @ ( real_V1022390504157884413omplex @ X3 ) @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % norm_power
% 0.26/0.55  thf(fact_5088_group__cancel_Osub2,axiom,
% 0.26/0.55      ! [B5: real,K: real,B: real,A: real] :
% 0.26/0.55        ( ( B5
% 0.26/0.55          = ( plus_plus_real @ K @ B ) )
% 0.26/0.55       => ( ( minus_minus_real @ A @ B5 )
% 0.26/0.55          = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % group_cancel.sub2
% 0.26/0.55  thf(fact_5089_group__cancel_Osub2,axiom,
% 0.26/0.55      ! [B5: int,K: int,B: int,A: int] :
% 0.26/0.55        ( ( B5
% 0.26/0.55          = ( plus_plus_int @ K @ B ) )
% 0.26/0.55       => ( ( minus_minus_int @ A @ B5 )
% 0.26/0.55          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % group_cancel.sub2
% 0.26/0.55  thf(fact_5090_group__cancel_Osub2,axiom,
% 0.26/0.55      ! [B5: complex,K: complex,B: complex,A: complex] :
% 0.26/0.55        ( ( B5
% 0.26/0.55          = ( plus_plus_complex @ K @ B ) )
% 0.26/0.55       => ( ( minus_minus_complex @ A @ B5 )
% 0.26/0.55          = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % group_cancel.sub2
% 0.26/0.55  thf(fact_5091_group__cancel_Osub2,axiom,
% 0.26/0.55      ! [B5: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 0.26/0.55        ( ( B5
% 0.26/0.55          = ( plus_p5714425477246183910nteger @ K @ B ) )
% 0.26/0.55       => ( ( minus_8373710615458151222nteger @ A @ B5 )
% 0.26/0.55          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % group_cancel.sub2
% 0.26/0.55  thf(fact_5092_group__cancel_Osub2,axiom,
% 0.26/0.55      ! [B5: rat,K: rat,B: rat,A: rat] :
% 0.26/0.55        ( ( B5
% 0.26/0.55          = ( plus_plus_rat @ K @ B ) )
% 0.26/0.55       => ( ( minus_minus_rat @ A @ B5 )
% 0.26/0.55          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % group_cancel.sub2
% 0.26/0.55  thf(fact_5093_diff__conv__add__uminus,axiom,
% 0.26/0.55      ( minus_minus_real
% 0.26/0.55      = ( ^ [A4: real,B3: real] : ( plus_plus_real @ A4 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_conv_add_uminus
% 0.26/0.55  thf(fact_5094_diff__conv__add__uminus,axiom,
% 0.26/0.55      ( minus_minus_int
% 0.26/0.55      = ( ^ [A4: int,B3: int] : ( plus_plus_int @ A4 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_conv_add_uminus
% 0.26/0.55  thf(fact_5095_diff__conv__add__uminus,axiom,
% 0.26/0.55      ( minus_minus_complex
% 0.26/0.55      = ( ^ [A4: complex,B3: complex] : ( plus_plus_complex @ A4 @ ( uminus1482373934393186551omplex @ B3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_conv_add_uminus
% 0.26/0.55  thf(fact_5096_diff__conv__add__uminus,axiom,
% 0.26/0.55      ( minus_8373710615458151222nteger
% 0.26/0.55      = ( ^ [A4: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A4 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_conv_add_uminus
% 0.26/0.55  thf(fact_5097_diff__conv__add__uminus,axiom,
% 0.26/0.55      ( minus_minus_rat
% 0.26/0.55      = ( ^ [A4: rat,B3: rat] : ( plus_plus_rat @ A4 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % diff_conv_add_uminus
% 0.26/0.55  thf(fact_5098_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.26/0.55      ( minus_minus_real
% 0.26/0.55      = ( ^ [A4: real,B3: real] : ( plus_plus_real @ A4 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.26/0.55  thf(fact_5099_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.26/0.55      ( minus_minus_int
% 0.26/0.55      = ( ^ [A4: int,B3: int] : ( plus_plus_int @ A4 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.26/0.55  thf(fact_5100_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.26/0.55      ( minus_minus_complex
% 0.26/0.55      = ( ^ [A4: complex,B3: complex] : ( plus_plus_complex @ A4 @ ( uminus1482373934393186551omplex @ B3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.26/0.55  thf(fact_5101_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.26/0.55      ( minus_8373710615458151222nteger
% 0.26/0.55      = ( ^ [A4: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A4 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.26/0.55  thf(fact_5102_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.26/0.55      ( minus_minus_rat
% 0.26/0.55      = ( ^ [A4: rat,B3: rat] : ( plus_plus_rat @ A4 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.26/0.55  thf(fact_5103_minus__real__def,axiom,
% 0.26/0.55      ( minus_minus_real
% 0.26/0.55      = ( ^ [X: real,Y: real] : ( plus_plus_real @ X @ ( uminus_uminus_real @ Y ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % minus_real_def
% 0.26/0.55  thf(fact_5104_of__int__of__nat,axiom,
% 0.26/0.55      ( ring_18347121197199848620nteger
% 0.26/0.55      = ( ^ [K3: int] : ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri4939895301339042750nteger @ ( nat2 @ K3 ) ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_of_nat
% 0.26/0.55  thf(fact_5105_of__int__of__nat,axiom,
% 0.26/0.55      ( ring_17405671764205052669omplex
% 0.26/0.55      = ( ^ [K3: int] : ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri8010041392384452111omplex @ ( nat2 @ K3 ) ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_of_nat
% 0.26/0.55  thf(fact_5106_of__int__of__nat,axiom,
% 0.26/0.55      ( ring_1_of_int_real
% 0.26/0.55      = ( ^ [K3: int] : ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri5074537144036343181t_real @ ( nat2 @ K3 ) ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_of_nat
% 0.26/0.55  thf(fact_5107_of__int__of__nat,axiom,
% 0.26/0.55      ( ring_1_of_int_rat
% 0.26/0.55      = ( ^ [K3: int] : ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri681578069525770553at_rat @ ( nat2 @ K3 ) ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_of_nat
% 0.26/0.55  thf(fact_5108_of__int__of__nat,axiom,
% 0.26/0.55      ( ring_1_of_int_int
% 0.26/0.55      = ( ^ [K3: int] : ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri1314217659103216013at_int @ ( nat2 @ K3 ) ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % of_int_of_nat
% 0.26/0.55  thf(fact_5109_dense__eq0__I,axiom,
% 0.26/0.55      ! [X3: real] :
% 0.26/0.55        ( ! [E: real] :
% 0.26/0.55            ( ( ord_less_real @ zero_zero_real @ E )
% 0.26/0.55           => ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ E ) )
% 0.26/0.55       => ( X3 = zero_zero_real ) ) ).
% 0.26/0.55  
% 0.26/0.55  % dense_eq0_I
% 0.26/0.55  thf(fact_5110_dense__eq0__I,axiom,
% 0.26/0.55      ! [X3: rat] :
% 0.26/0.55        ( ! [E: rat] :
% 0.26/0.55            ( ( ord_less_rat @ zero_zero_rat @ E )
% 0.26/0.55           => ( ord_less_eq_rat @ ( abs_abs_rat @ X3 ) @ E ) )
% 0.26/0.55       => ( X3 = zero_zero_rat ) ) ).
% 0.26/0.55  
% 0.26/0.55  % dense_eq0_I
% 0.26/0.55  thf(fact_5111_abs__mult__pos,axiom,
% 0.26/0.55      ! [X3: code_integer,Y3: code_integer] :
% 0.26/0.55        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 0.26/0.55       => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y3 ) @ X3 )
% 0.26/0.55          = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y3 @ X3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_mult_pos
% 0.26/0.55  thf(fact_5112_abs__mult__pos,axiom,
% 0.26/0.55      ! [X3: real,Y3: real] :
% 0.26/0.55        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.55       => ( ( times_times_real @ ( abs_abs_real @ Y3 ) @ X3 )
% 0.26/0.55          = ( abs_abs_real @ ( times_times_real @ Y3 @ X3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_mult_pos
% 0.26/0.55  thf(fact_5113_abs__mult__pos,axiom,
% 0.26/0.55      ! [X3: rat,Y3: rat] :
% 0.26/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.26/0.55       => ( ( times_times_rat @ ( abs_abs_rat @ Y3 ) @ X3 )
% 0.26/0.55          = ( abs_abs_rat @ ( times_times_rat @ Y3 @ X3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_mult_pos
% 0.26/0.55  thf(fact_5114_abs__mult__pos,axiom,
% 0.26/0.55      ! [X3: int,Y3: int] :
% 0.26/0.55        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.26/0.55       => ( ( times_times_int @ ( abs_abs_int @ Y3 ) @ X3 )
% 0.26/0.55          = ( abs_abs_int @ ( times_times_int @ Y3 @ X3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_mult_pos
% 0.26/0.55  thf(fact_5115_abs__eq__mult,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer] :
% 0.26/0.55        ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.26/0.55            | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 0.26/0.55          & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.26/0.55            | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 0.26/0.55       => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.26/0.55          = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_eq_mult
% 0.26/0.55  thf(fact_5116_abs__eq__mult,axiom,
% 0.26/0.55      ! [A: real,B: real] :
% 0.26/0.55        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.26/0.55            | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 0.26/0.55          & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.26/0.55            | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 0.26/0.55       => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 0.26/0.55          = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_eq_mult
% 0.26/0.55  thf(fact_5117_abs__eq__mult,axiom,
% 0.26/0.55      ! [A: rat,B: rat] :
% 0.26/0.55        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.26/0.55            | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 0.26/0.55          & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.26/0.55            | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 0.26/0.55       => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 0.26/0.55          = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_eq_mult
% 0.26/0.55  thf(fact_5118_abs__eq__mult,axiom,
% 0.26/0.55      ! [A: int,B: int] :
% 0.26/0.55        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.55            | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 0.26/0.55          & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.26/0.55            | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 0.26/0.55       => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 0.26/0.55          = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_eq_mult
% 0.26/0.55  thf(fact_5119_abs__div__pos,axiom,
% 0.26/0.55      ! [Y3: real,X3: real] :
% 0.26/0.55        ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.55       => ( ( divide_divide_real @ ( abs_abs_real @ X3 ) @ Y3 )
% 0.26/0.55          = ( abs_abs_real @ ( divide_divide_real @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_div_pos
% 0.26/0.55  thf(fact_5120_abs__div__pos,axiom,
% 0.26/0.55      ! [Y3: rat,X3: rat] :
% 0.26/0.55        ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 0.26/0.55       => ( ( divide_divide_rat @ ( abs_abs_rat @ X3 ) @ Y3 )
% 0.26/0.55          = ( abs_abs_rat @ ( divide_divide_rat @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_div_pos
% 0.26/0.55  thf(fact_5121_zero__le__power__abs,axiom,
% 0.26/0.55      ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % zero_le_power_abs
% 0.26/0.55  thf(fact_5122_zero__le__power__abs,axiom,
% 0.26/0.55      ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % zero_le_power_abs
% 0.26/0.55  thf(fact_5123_zero__le__power__abs,axiom,
% 0.26/0.55      ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % zero_le_power_abs
% 0.26/0.55  thf(fact_5124_zero__le__power__abs,axiom,
% 0.26/0.55      ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 0.26/0.55  
% 0.26/0.55  % zero_le_power_abs
% 0.26/0.55  thf(fact_5125_abs__diff__le__iff,axiom,
% 0.26/0.55      ! [X3: code_integer,A: code_integer,R2: code_integer] :
% 0.26/0.55        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X3 @ A ) ) @ R2 )
% 0.26/0.55        = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X3 )
% 0.26/0.55          & ( ord_le3102999989581377725nteger @ X3 @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_diff_le_iff
% 0.26/0.55  thf(fact_5126_abs__diff__le__iff,axiom,
% 0.26/0.55      ! [X3: real,A: real,R2: real] :
% 0.26/0.55        ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ A ) ) @ R2 )
% 0.26/0.55        = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R2 ) @ X3 )
% 0.26/0.55          & ( ord_less_eq_real @ X3 @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_diff_le_iff
% 0.26/0.55  thf(fact_5127_abs__diff__le__iff,axiom,
% 0.26/0.55      ! [X3: rat,A: rat,R2: rat] :
% 0.26/0.55        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X3 @ A ) ) @ R2 )
% 0.26/0.55        = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R2 ) @ X3 )
% 0.26/0.55          & ( ord_less_eq_rat @ X3 @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_diff_le_iff
% 0.26/0.55  thf(fact_5128_abs__diff__le__iff,axiom,
% 0.26/0.55      ! [X3: int,A: int,R2: int] :
% 0.26/0.55        ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X3 @ A ) ) @ R2 )
% 0.26/0.55        = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R2 ) @ X3 )
% 0.26/0.55          & ( ord_less_eq_int @ X3 @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_diff_le_iff
% 0.26/0.55  thf(fact_5129_abs__diff__triangle__ineq,axiom,
% 0.26/0.55      ! [A: code_integer,B: code_integer,C: code_integer,D3: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D3 ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_diff_triangle_ineq
% 0.26/0.55  thf(fact_5130_abs__diff__triangle__ineq,axiom,
% 0.26/0.55      ! [A: real,B: real,C: real,D3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D3 ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_diff_triangle_ineq
% 0.26/0.55  thf(fact_5131_abs__diff__triangle__ineq,axiom,
% 0.26/0.55      ! [A: rat,B: rat,C: rat,D3: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D3 ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_diff_triangle_ineq
% 0.26/0.55  thf(fact_5132_abs__diff__triangle__ineq,axiom,
% 0.26/0.55      ! [A: int,B: int,C: int,D3: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D3 ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D3 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_diff_triangle_ineq
% 0.26/0.55  thf(fact_5133_abs__triangle__ineq4,axiom,
% 0.26/0.55      ! [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 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_triangle_ineq4
% 0.26/0.55  thf(fact_5134_abs__triangle__ineq4,axiom,
% 0.26/0.55      ! [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 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_triangle_ineq4
% 0.26/0.55  thf(fact_5135_abs__triangle__ineq4,axiom,
% 0.26/0.55      ! [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 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_triangle_ineq4
% 0.26/0.55  thf(fact_5136_abs__triangle__ineq4,axiom,
% 0.26/0.55      ! [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 ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_triangle_ineq4
% 0.26/0.55  thf(fact_5137_abs__diff__less__iff,axiom,
% 0.26/0.55      ! [X3: code_integer,A: code_integer,R2: code_integer] :
% 0.26/0.55        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X3 @ A ) ) @ R2 )
% 0.26/0.55        = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X3 )
% 0.26/0.55          & ( ord_le6747313008572928689nteger @ X3 @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_diff_less_iff
% 0.26/0.55  thf(fact_5138_abs__diff__less__iff,axiom,
% 0.26/0.55      ! [X3: real,A: real,R2: real] :
% 0.26/0.55        ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ A ) ) @ R2 )
% 0.26/0.55        = ( ( ord_less_real @ ( minus_minus_real @ A @ R2 ) @ X3 )
% 0.26/0.55          & ( ord_less_real @ X3 @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_diff_less_iff
% 0.26/0.55  thf(fact_5139_abs__diff__less__iff,axiom,
% 0.26/0.55      ! [X3: rat,A: rat,R2: rat] :
% 0.26/0.55        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X3 @ A ) ) @ R2 )
% 0.26/0.55        = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R2 ) @ X3 )
% 0.26/0.55          & ( ord_less_rat @ X3 @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_diff_less_iff
% 0.26/0.55  thf(fact_5140_abs__diff__less__iff,axiom,
% 0.26/0.55      ! [X3: int,A: int,R2: int] :
% 0.26/0.55        ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X3 @ A ) ) @ R2 )
% 0.26/0.55        = ( ( ord_less_int @ ( minus_minus_int @ A @ R2 ) @ X3 )
% 0.26/0.55          & ( ord_less_int @ X3 @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % abs_diff_less_iff
% 0.26/0.55  thf(fact_5141_nonzero__norm__divide,axiom,
% 0.26/0.55      ! [B: real,A: real] :
% 0.26/0.55        ( ( B != zero_zero_real )
% 0.26/0.55       => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 0.26/0.55          = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % nonzero_norm_divide
% 0.26/0.55  thf(fact_5142_nonzero__norm__divide,axiom,
% 0.26/0.55      ! [B: complex,A: complex] :
% 0.26/0.55        ( ( B != zero_zero_complex )
% 0.26/0.55       => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.26/0.55          = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % nonzero_norm_divide
% 0.26/0.55  thf(fact_5143_power__eq__imp__eq__norm,axiom,
% 0.26/0.55      ! [W: real,N: nat,Z: real] :
% 0.26/0.55        ( ( ( power_power_real @ W @ N )
% 0.26/0.55          = ( power_power_real @ Z @ N ) )
% 0.26/0.55       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.55         => ( ( real_V7735802525324610683m_real @ W )
% 0.26/0.55            = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power_eq_imp_eq_norm
% 0.26/0.55  thf(fact_5144_power__eq__imp__eq__norm,axiom,
% 0.26/0.55      ! [W: complex,N: nat,Z: complex] :
% 0.26/0.55        ( ( ( power_power_complex @ W @ N )
% 0.26/0.55          = ( power_power_complex @ Z @ N ) )
% 0.26/0.55       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.55         => ( ( real_V1022390504157884413omplex @ W )
% 0.26/0.55            = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % power_eq_imp_eq_norm
% 0.26/0.55  thf(fact_5145_not__zero__le__neg__numeral,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_zero_le_neg_numeral
% 0.26/0.55  thf(fact_5146_not__zero__le__neg__numeral,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_zero_le_neg_numeral
% 0.26/0.55  thf(fact_5147_not__zero__le__neg__numeral,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_zero_le_neg_numeral
% 0.26/0.55  thf(fact_5148_not__zero__le__neg__numeral,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_zero_le_neg_numeral
% 0.26/0.55  thf(fact_5149_neg__numeral__le__zero,axiom,
% 0.26/0.55      ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_le_zero
% 0.26/0.55  thf(fact_5150_neg__numeral__le__zero,axiom,
% 0.26/0.55      ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_le_zero
% 0.26/0.55  thf(fact_5151_neg__numeral__le__zero,axiom,
% 0.26/0.55      ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_le_zero
% 0.26/0.55  thf(fact_5152_neg__numeral__le__zero,axiom,
% 0.26/0.55      ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_le_zero
% 0.26/0.55  thf(fact_5153_neg__numeral__less__zero,axiom,
% 0.26/0.55      ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_less_zero
% 0.26/0.55  thf(fact_5154_neg__numeral__less__zero,axiom,
% 0.26/0.55      ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_less_zero
% 0.26/0.55  thf(fact_5155_neg__numeral__less__zero,axiom,
% 0.26/0.55      ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_less_zero
% 0.26/0.55  thf(fact_5156_neg__numeral__less__zero,axiom,
% 0.26/0.55      ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_less_zero
% 0.26/0.55  thf(fact_5157_not__zero__less__neg__numeral,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_zero_less_neg_numeral
% 0.26/0.55  thf(fact_5158_not__zero__less__neg__numeral,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_zero_less_neg_numeral
% 0.26/0.55  thf(fact_5159_not__zero__less__neg__numeral,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_zero_less_neg_numeral
% 0.26/0.55  thf(fact_5160_not__zero__less__neg__numeral,axiom,
% 0.26/0.55      ! [N: num] :
% 0.26/0.55        ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_zero_less_neg_numeral
% 0.26/0.55  thf(fact_5161_le__minus__one__simps_I3_J,axiom,
% 0.26/0.55      ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.26/0.55  
% 0.26/0.55  % le_minus_one_simps(3)
% 0.26/0.55  thf(fact_5162_le__minus__one__simps_I3_J,axiom,
% 0.26/0.55      ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.55  
% 0.26/0.55  % le_minus_one_simps(3)
% 0.26/0.55  thf(fact_5163_le__minus__one__simps_I3_J,axiom,
% 0.26/0.55      ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.26/0.55  
% 0.26/0.55  % le_minus_one_simps(3)
% 0.26/0.55  thf(fact_5164_le__minus__one__simps_I3_J,axiom,
% 0.26/0.55      ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.55  
% 0.26/0.55  % le_minus_one_simps(3)
% 0.26/0.55  thf(fact_5165_le__minus__one__simps_I1_J,axiom,
% 0.26/0.55      ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 0.26/0.55  
% 0.26/0.55  % le_minus_one_simps(1)
% 0.26/0.55  thf(fact_5166_le__minus__one__simps_I1_J,axiom,
% 0.26/0.55      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 0.26/0.55  
% 0.26/0.55  % le_minus_one_simps(1)
% 0.26/0.55  thf(fact_5167_le__minus__one__simps_I1_J,axiom,
% 0.26/0.55      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 0.26/0.55  
% 0.26/0.55  % le_minus_one_simps(1)
% 0.26/0.55  thf(fact_5168_le__minus__one__simps_I1_J,axiom,
% 0.26/0.55      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 0.26/0.55  
% 0.26/0.55  % le_minus_one_simps(1)
% 0.26/0.55  thf(fact_5169_less__minus__one__simps_I3_J,axiom,
% 0.26/0.55      ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.26/0.55  
% 0.26/0.55  % less_minus_one_simps(3)
% 0.26/0.55  thf(fact_5170_less__minus__one__simps_I3_J,axiom,
% 0.26/0.55      ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.55  
% 0.26/0.55  % less_minus_one_simps(3)
% 0.26/0.55  thf(fact_5171_less__minus__one__simps_I3_J,axiom,
% 0.26/0.55      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.55  
% 0.26/0.55  % less_minus_one_simps(3)
% 0.26/0.55  thf(fact_5172_less__minus__one__simps_I3_J,axiom,
% 0.26/0.55      ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.26/0.55  
% 0.26/0.55  % less_minus_one_simps(3)
% 0.26/0.55  thf(fact_5173_less__minus__one__simps_I1_J,axiom,
% 0.26/0.55      ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 0.26/0.55  
% 0.26/0.55  % less_minus_one_simps(1)
% 0.26/0.55  thf(fact_5174_less__minus__one__simps_I1_J,axiom,
% 0.26/0.55      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 0.26/0.55  
% 0.26/0.55  % less_minus_one_simps(1)
% 0.26/0.55  thf(fact_5175_less__minus__one__simps_I1_J,axiom,
% 0.26/0.55      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 0.26/0.55  
% 0.26/0.55  % less_minus_one_simps(1)
% 0.26/0.55  thf(fact_5176_less__minus__one__simps_I1_J,axiom,
% 0.26/0.55      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 0.26/0.55  
% 0.26/0.55  % less_minus_one_simps(1)
% 0.26/0.55  thf(fact_5177_not__one__le__neg__numeral,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_one_le_neg_numeral
% 0.26/0.55  thf(fact_5178_not__one__le__neg__numeral,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_one_le_neg_numeral
% 0.26/0.55  thf(fact_5179_not__one__le__neg__numeral,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_one_le_neg_numeral
% 0.26/0.55  thf(fact_5180_not__one__le__neg__numeral,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_one_le_neg_numeral
% 0.26/0.55  thf(fact_5181_not__numeral__le__neg__one,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_numeral_le_neg_one
% 0.26/0.55  thf(fact_5182_not__numeral__le__neg__one,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_numeral_le_neg_one
% 0.26/0.55  thf(fact_5183_not__numeral__le__neg__one,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_numeral_le_neg_one
% 0.26/0.55  thf(fact_5184_not__numeral__le__neg__one,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_numeral_le_neg_one
% 0.26/0.55  thf(fact_5185_neg__numeral__le__neg__one,axiom,
% 0.26/0.55      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_le_neg_one
% 0.26/0.55  thf(fact_5186_neg__numeral__le__neg__one,axiom,
% 0.26/0.55      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_le_neg_one
% 0.26/0.55  thf(fact_5187_neg__numeral__le__neg__one,axiom,
% 0.26/0.55      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_le_neg_one
% 0.26/0.55  thf(fact_5188_neg__numeral__le__neg__one,axiom,
% 0.26/0.55      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_le_neg_one
% 0.26/0.55  thf(fact_5189_neg__one__le__numeral,axiom,
% 0.26/0.55      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_one_le_numeral
% 0.26/0.55  thf(fact_5190_neg__one__le__numeral,axiom,
% 0.26/0.55      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_one_le_numeral
% 0.26/0.55  thf(fact_5191_neg__one__le__numeral,axiom,
% 0.26/0.55      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_one_le_numeral
% 0.26/0.55  thf(fact_5192_neg__one__le__numeral,axiom,
% 0.26/0.55      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_one_le_numeral
% 0.26/0.55  thf(fact_5193_neg__numeral__le__one,axiom,
% 0.26/0.55      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_le_one
% 0.26/0.55  thf(fact_5194_neg__numeral__le__one,axiom,
% 0.26/0.55      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_le_one
% 0.26/0.55  thf(fact_5195_neg__numeral__le__one,axiom,
% 0.26/0.55      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_le_one
% 0.26/0.55  thf(fact_5196_neg__numeral__le__one,axiom,
% 0.26/0.55      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_le_one
% 0.26/0.55  thf(fact_5197_neg__numeral__less__one,axiom,
% 0.26/0.55      ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_less_one
% 0.26/0.55  thf(fact_5198_neg__numeral__less__one,axiom,
% 0.26/0.55      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_less_one
% 0.26/0.55  thf(fact_5199_neg__numeral__less__one,axiom,
% 0.26/0.55      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_less_one
% 0.26/0.55  thf(fact_5200_neg__numeral__less__one,axiom,
% 0.26/0.55      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_numeral_less_one
% 0.26/0.55  thf(fact_5201_neg__one__less__numeral,axiom,
% 0.26/0.55      ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_one_less_numeral
% 0.26/0.55  thf(fact_5202_neg__one__less__numeral,axiom,
% 0.26/0.55      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_one_less_numeral
% 0.26/0.55  thf(fact_5203_neg__one__less__numeral,axiom,
% 0.26/0.55      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_one_less_numeral
% 0.26/0.55  thf(fact_5204_neg__one__less__numeral,axiom,
% 0.26/0.55      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 0.26/0.55  
% 0.26/0.55  % neg_one_less_numeral
% 0.26/0.55  thf(fact_5205_not__numeral__less__neg__one,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_numeral_less_neg_one
% 0.26/0.55  thf(fact_5206_not__numeral__less__neg__one,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_numeral_less_neg_one
% 0.26/0.55  thf(fact_5207_not__numeral__less__neg__one,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_numeral_less_neg_one
% 0.26/0.55  thf(fact_5208_not__numeral__less__neg__one,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_numeral_less_neg_one
% 0.26/0.55  thf(fact_5209_not__one__less__neg__numeral,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_one_less_neg_numeral
% 0.26/0.55  thf(fact_5210_not__one__less__neg__numeral,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_one_less_neg_numeral
% 0.26/0.55  thf(fact_5211_not__one__less__neg__numeral,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_one_less_neg_numeral
% 0.26/0.55  thf(fact_5212_not__one__less__neg__numeral,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_one_less_neg_numeral
% 0.26/0.55  thf(fact_5213_not__neg__one__less__neg__numeral,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_neg_one_less_neg_numeral
% 0.26/0.55  thf(fact_5214_not__neg__one__less__neg__numeral,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_neg_one_less_neg_numeral
% 0.26/0.55  thf(fact_5215_not__neg__one__less__neg__numeral,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_neg_one_less_neg_numeral
% 0.26/0.55  thf(fact_5216_not__neg__one__less__neg__numeral,axiom,
% 0.26/0.55      ! [M: num] :
% 0.26/0.55        ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % not_neg_one_less_neg_numeral
% 0.26/0.55  thf(fact_5217_nonzero__neg__divide__eq__eq2,axiom,
% 0.26/0.55      ! [B: real,C: real,A: real] :
% 0.26/0.55        ( ( B != zero_zero_real )
% 0.26/0.55       => ( ( C
% 0.26/0.55            = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 0.26/0.55          = ( ( times_times_real @ C @ B )
% 0.26/0.55            = ( uminus_uminus_real @ A ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % nonzero_neg_divide_eq_eq2
% 0.26/0.55  thf(fact_5218_nonzero__neg__divide__eq__eq2,axiom,
% 0.26/0.55      ! [B: complex,C: complex,A: complex] :
% 0.26/0.55        ( ( B != zero_zero_complex )
% 0.26/0.55       => ( ( C
% 0.26/0.55            = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.26/0.55          = ( ( times_times_complex @ C @ B )
% 0.26/0.55            = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % nonzero_neg_divide_eq_eq2
% 0.26/0.55  thf(fact_5219_nonzero__neg__divide__eq__eq2,axiom,
% 0.26/0.55      ! [B: rat,C: rat,A: rat] :
% 0.26/0.55        ( ( B != zero_zero_rat )
% 0.26/0.55       => ( ( C
% 0.26/0.55            = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 0.26/0.55          = ( ( times_times_rat @ C @ B )
% 0.26/0.55            = ( uminus_uminus_rat @ A ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % nonzero_neg_divide_eq_eq2
% 0.26/0.55  thf(fact_5220_nonzero__neg__divide__eq__eq,axiom,
% 0.26/0.55      ! [B: real,A: real,C: real] :
% 0.26/0.55        ( ( B != zero_zero_real )
% 0.26/0.55       => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 0.26/0.55            = C )
% 0.26/0.55          = ( ( uminus_uminus_real @ A )
% 0.26/0.55            = ( times_times_real @ C @ B ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % nonzero_neg_divide_eq_eq
% 0.26/0.55  thf(fact_5221_nonzero__neg__divide__eq__eq,axiom,
% 0.26/0.55      ! [B: complex,A: complex,C: complex] :
% 0.26/0.55        ( ( B != zero_zero_complex )
% 0.26/0.55       => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.26/0.55            = C )
% 0.26/0.55          = ( ( uminus1482373934393186551omplex @ A )
% 0.26/0.55            = ( times_times_complex @ C @ B ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % nonzero_neg_divide_eq_eq
% 0.26/0.55  thf(fact_5222_nonzero__neg__divide__eq__eq,axiom,
% 0.26/0.55      ! [B: rat,A: rat,C: rat] :
% 0.26/0.55        ( ( B != zero_zero_rat )
% 0.26/0.55       => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.26/0.55            = C )
% 0.26/0.55          = ( ( uminus_uminus_rat @ A )
% 0.26/0.55            = ( times_times_rat @ C @ B ) ) ) ) ).
% 0.26/0.55  
% 0.26/0.55  % nonzero_neg_divide_eq_eq
% 0.26/0.55  thf(fact_5223_minus__divide__eq__eq,axiom,
% 0.26/0.55      ! [B: real,C: real,A: real] :
% 0.26/0.55        ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 0.26/0.55          = A )
% 0.26/0.55        = ( ( ( C != zero_zero_real )
% 0.26/0.55           => ( ( uminus_uminus_real @ B )
% 0.26/0.55              = ( times_times_real @ A @ C ) ) )
% 0.26/0.56          & ( ( C = zero_zero_real )
% 0.26/0.56           => ( A = zero_zero_real ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_divide_eq_eq
% 0.26/0.56  thf(fact_5224_minus__divide__eq__eq,axiom,
% 0.26/0.56      ! [B: complex,C: complex,A: complex] :
% 0.26/0.56        ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 0.26/0.56          = A )
% 0.26/0.56        = ( ( ( C != zero_zero_complex )
% 0.26/0.56           => ( ( uminus1482373934393186551omplex @ B )
% 0.26/0.56              = ( times_times_complex @ A @ C ) ) )
% 0.26/0.56          & ( ( C = zero_zero_complex )
% 0.26/0.56           => ( A = zero_zero_complex ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_divide_eq_eq
% 0.26/0.56  thf(fact_5225_minus__divide__eq__eq,axiom,
% 0.26/0.56      ! [B: rat,C: rat,A: rat] :
% 0.26/0.56        ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 0.26/0.56          = A )
% 0.26/0.56        = ( ( ( C != zero_zero_rat )
% 0.26/0.56           => ( ( uminus_uminus_rat @ B )
% 0.26/0.56              = ( times_times_rat @ A @ C ) ) )
% 0.26/0.56          & ( ( C = zero_zero_rat )
% 0.26/0.56           => ( A = zero_zero_rat ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_divide_eq_eq
% 0.26/0.56  thf(fact_5226_eq__minus__divide__eq,axiom,
% 0.26/0.56      ! [A: real,B: real,C: real] :
% 0.26/0.56        ( ( A
% 0.26/0.56          = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.26/0.56        = ( ( ( C != zero_zero_real )
% 0.26/0.56           => ( ( times_times_real @ A @ C )
% 0.26/0.56              = ( uminus_uminus_real @ B ) ) )
% 0.26/0.56          & ( ( C = zero_zero_real )
% 0.26/0.56           => ( A = zero_zero_real ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % eq_minus_divide_eq
% 0.26/0.56  thf(fact_5227_eq__minus__divide__eq,axiom,
% 0.26/0.56      ! [A: complex,B: complex,C: complex] :
% 0.26/0.56        ( ( A
% 0.26/0.56          = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 0.26/0.56        = ( ( ( C != zero_zero_complex )
% 0.26/0.56           => ( ( times_times_complex @ A @ C )
% 0.26/0.56              = ( uminus1482373934393186551omplex @ B ) ) )
% 0.26/0.56          & ( ( C = zero_zero_complex )
% 0.26/0.56           => ( A = zero_zero_complex ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % eq_minus_divide_eq
% 0.26/0.56  thf(fact_5228_eq__minus__divide__eq,axiom,
% 0.26/0.56      ! [A: rat,B: rat,C: rat] :
% 0.26/0.56        ( ( A
% 0.26/0.56          = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.26/0.56        = ( ( ( C != zero_zero_rat )
% 0.26/0.56           => ( ( times_times_rat @ A @ C )
% 0.26/0.56              = ( uminus_uminus_rat @ B ) ) )
% 0.26/0.56          & ( ( C = zero_zero_rat )
% 0.26/0.56           => ( A = zero_zero_rat ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % eq_minus_divide_eq
% 0.26/0.56  thf(fact_5229_norm__triangle__lt,axiom,
% 0.26/0.56      ! [X3: real,Y3: real,E2: real] :
% 0.26/0.56        ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) @ E2 )
% 0.26/0.56       => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y3 ) ) @ E2 ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_triangle_lt
% 0.26/0.56  thf(fact_5230_norm__triangle__lt,axiom,
% 0.26/0.56      ! [X3: complex,Y3: complex,E2: real] :
% 0.26/0.56        ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) @ E2 )
% 0.26/0.56       => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y3 ) ) @ E2 ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_triangle_lt
% 0.26/0.56  thf(fact_5231_norm__add__less,axiom,
% 0.26/0.56      ! [X3: real,R2: real,Y3: real,S: real] :
% 0.26/0.56        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ R2 )
% 0.26/0.56       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y3 ) @ S )
% 0.26/0.56         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y3 ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_add_less
% 0.26/0.56  thf(fact_5232_norm__add__less,axiom,
% 0.26/0.56      ! [X3: complex,R2: real,Y3: complex,S: real] :
% 0.26/0.56        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ R2 )
% 0.26/0.56       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y3 ) @ S )
% 0.26/0.56         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y3 ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_add_less
% 0.26/0.56  thf(fact_5233_divide__eq__minus__1__iff,axiom,
% 0.26/0.56      ! [A: real,B: real] :
% 0.26/0.56        ( ( ( divide_divide_real @ A @ B )
% 0.26/0.56          = ( uminus_uminus_real @ one_one_real ) )
% 0.26/0.56        = ( ( B != zero_zero_real )
% 0.26/0.56          & ( A
% 0.26/0.56            = ( uminus_uminus_real @ B ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % divide_eq_minus_1_iff
% 0.26/0.56  thf(fact_5234_divide__eq__minus__1__iff,axiom,
% 0.26/0.56      ! [A: complex,B: complex] :
% 0.26/0.56        ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.26/0.56          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.26/0.56        = ( ( B != zero_zero_complex )
% 0.26/0.56          & ( A
% 0.26/0.56            = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % divide_eq_minus_1_iff
% 0.26/0.56  thf(fact_5235_divide__eq__minus__1__iff,axiom,
% 0.26/0.56      ! [A: rat,B: rat] :
% 0.26/0.56        ( ( ( divide_divide_rat @ A @ B )
% 0.26/0.56          = ( uminus_uminus_rat @ one_one_rat ) )
% 0.26/0.56        = ( ( B != zero_zero_rat )
% 0.26/0.56          & ( A
% 0.26/0.56            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % divide_eq_minus_1_iff
% 0.26/0.56  thf(fact_5236_mult__1s__ring__1_I2_J,axiom,
% 0.26/0.56      ! [B: real] :
% 0.26/0.56        ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 0.26/0.56        = ( uminus_uminus_real @ B ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mult_1s_ring_1(2)
% 0.26/0.56  thf(fact_5237_mult__1s__ring__1_I2_J,axiom,
% 0.26/0.56      ! [B: int] :
% 0.26/0.56        ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 0.26/0.56        = ( uminus_uminus_int @ B ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mult_1s_ring_1(2)
% 0.26/0.56  thf(fact_5238_mult__1s__ring__1_I2_J,axiom,
% 0.26/0.56      ! [B: complex] :
% 0.26/0.56        ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 0.26/0.56        = ( uminus1482373934393186551omplex @ B ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mult_1s_ring_1(2)
% 0.26/0.56  thf(fact_5239_mult__1s__ring__1_I2_J,axiom,
% 0.26/0.56      ! [B: code_integer] :
% 0.26/0.56        ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 0.26/0.56        = ( uminus1351360451143612070nteger @ B ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mult_1s_ring_1(2)
% 0.26/0.56  thf(fact_5240_mult__1s__ring__1_I2_J,axiom,
% 0.26/0.56      ! [B: rat] :
% 0.26/0.56        ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 0.26/0.56        = ( uminus_uminus_rat @ B ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mult_1s_ring_1(2)
% 0.26/0.56  thf(fact_5241_mult__1s__ring__1_I1_J,axiom,
% 0.26/0.56      ! [B: real] :
% 0.26/0.56        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 0.26/0.56        = ( uminus_uminus_real @ B ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mult_1s_ring_1(1)
% 0.26/0.56  thf(fact_5242_mult__1s__ring__1_I1_J,axiom,
% 0.26/0.56      ! [B: int] :
% 0.26/0.56        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 0.26/0.56        = ( uminus_uminus_int @ B ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mult_1s_ring_1(1)
% 0.26/0.56  thf(fact_5243_mult__1s__ring__1_I1_J,axiom,
% 0.26/0.56      ! [B: complex] :
% 0.26/0.56        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 0.26/0.56        = ( uminus1482373934393186551omplex @ B ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mult_1s_ring_1(1)
% 0.26/0.56  thf(fact_5244_mult__1s__ring__1_I1_J,axiom,
% 0.26/0.56      ! [B: code_integer] :
% 0.26/0.56        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 0.26/0.56        = ( uminus1351360451143612070nteger @ B ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mult_1s_ring_1(1)
% 0.26/0.56  thf(fact_5245_mult__1s__ring__1_I1_J,axiom,
% 0.26/0.56      ! [B: rat] :
% 0.26/0.56        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 0.26/0.56        = ( uminus_uminus_rat @ B ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mult_1s_ring_1(1)
% 0.26/0.56  thf(fact_5246_uminus__numeral__One,axiom,
% 0.26/0.56      ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 0.26/0.56      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.26/0.56  
% 0.26/0.56  % uminus_numeral_One
% 0.26/0.56  thf(fact_5247_uminus__numeral__One,axiom,
% 0.26/0.56      ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 0.26/0.56      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.56  
% 0.26/0.56  % uminus_numeral_One
% 0.26/0.56  thf(fact_5248_uminus__numeral__One,axiom,
% 0.26/0.56      ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 0.26/0.56      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.26/0.56  
% 0.26/0.56  % uminus_numeral_One
% 0.26/0.56  thf(fact_5249_uminus__numeral__One,axiom,
% 0.26/0.56      ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 0.26/0.56      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.56  
% 0.26/0.56  % uminus_numeral_One
% 0.26/0.56  thf(fact_5250_uminus__numeral__One,axiom,
% 0.26/0.56      ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 0.26/0.56      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.26/0.56  
% 0.26/0.56  % uminus_numeral_One
% 0.26/0.56  thf(fact_5251_norm__add__leD,axiom,
% 0.26/0.56      ! [A: real,B: real,C: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 0.26/0.56       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_add_leD
% 0.26/0.56  thf(fact_5252_norm__add__leD,axiom,
% 0.26/0.56      ! [A: complex,B: complex,C: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 0.26/0.56       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_add_leD
% 0.26/0.56  thf(fact_5253_norm__triangle__le,axiom,
% 0.26/0.56      ! [X3: real,Y3: real,E2: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) @ E2 )
% 0.26/0.56       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y3 ) ) @ E2 ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_triangle_le
% 0.26/0.56  thf(fact_5254_norm__triangle__le,axiom,
% 0.26/0.56      ! [X3: complex,Y3: complex,E2: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) @ E2 )
% 0.26/0.56       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y3 ) ) @ E2 ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_triangle_le
% 0.26/0.56  thf(fact_5255_norm__triangle__ineq,axiom,
% 0.26/0.56      ! [X3: real,Y3: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y3 ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_triangle_ineq
% 0.26/0.56  thf(fact_5256_norm__triangle__ineq,axiom,
% 0.26/0.56      ! [X3: complex,Y3: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y3 ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_triangle_ineq
% 0.26/0.56  thf(fact_5257_norm__triangle__mono,axiom,
% 0.26/0.56      ! [A: real,R2: real,B: real,S: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R2 )
% 0.26/0.56       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S )
% 0.26/0.56         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_triangle_mono
% 0.26/0.56  thf(fact_5258_norm__triangle__mono,axiom,
% 0.26/0.56      ! [A: complex,R2: real,B: complex,S: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R2 )
% 0.26/0.56       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S )
% 0.26/0.56         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_triangle_mono
% 0.26/0.56  thf(fact_5259_norm__power__ineq,axiom,
% 0.26/0.56      ! [X3: real,N: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X3 @ N ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X3 ) @ N ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_power_ineq
% 0.26/0.56  thf(fact_5260_norm__power__ineq,axiom,
% 0.26/0.56      ! [X3: complex,N: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X3 @ N ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X3 ) @ N ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_power_ineq
% 0.26/0.56  thf(fact_5261_norm__diff__triangle__less,axiom,
% 0.26/0.56      ! [X3: real,Y3: real,E1: real,Z: real,E22: real] :
% 0.26/0.56        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X3 @ Y3 ) ) @ E1 )
% 0.26/0.56       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y3 @ Z ) ) @ E22 )
% 0.26/0.56         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X3 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_diff_triangle_less
% 0.26/0.56  thf(fact_5262_norm__diff__triangle__less,axiom,
% 0.26/0.56      ! [X3: complex,Y3: complex,E1: real,Z: complex,E22: real] :
% 0.26/0.56        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Y3 ) ) @ E1 )
% 0.26/0.56       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y3 @ Z ) ) @ E22 )
% 0.26/0.56         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_diff_triangle_less
% 0.26/0.56  thf(fact_5263_norm__triangle__sub,axiom,
% 0.26/0.56      ! [X3: real,Y3: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ Y3 ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_triangle_sub
% 0.26/0.56  thf(fact_5264_norm__triangle__sub,axiom,
% 0.26/0.56      ! [X3: complex,Y3: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y3 ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_triangle_sub
% 0.26/0.56  thf(fact_5265_norm__triangle__ineq4,axiom,
% 0.26/0.56      ! [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 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_triangle_ineq4
% 0.26/0.56  thf(fact_5266_norm__triangle__ineq4,axiom,
% 0.26/0.56      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_triangle_ineq4
% 0.26/0.56  thf(fact_5267_norm__diff__triangle__le,axiom,
% 0.26/0.56      ! [X3: real,Y3: real,E1: real,Z: real,E22: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X3 @ Y3 ) ) @ E1 )
% 0.26/0.56       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y3 @ Z ) ) @ E22 )
% 0.26/0.56         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X3 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_diff_triangle_le
% 0.26/0.56  thf(fact_5268_norm__diff__triangle__le,axiom,
% 0.26/0.56      ! [X3: complex,Y3: complex,E1: real,Z: complex,E22: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Y3 ) ) @ E1 )
% 0.26/0.56       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y3 @ Z ) ) @ E22 )
% 0.26/0.56         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_diff_triangle_le
% 0.26/0.56  thf(fact_5269_norm__triangle__le__diff,axiom,
% 0.26/0.56      ! [X3: real,Y3: real,E2: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) @ E2 )
% 0.26/0.56       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X3 @ Y3 ) ) @ E2 ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_triangle_le_diff
% 0.26/0.56  thf(fact_5270_norm__triangle__le__diff,axiom,
% 0.26/0.56      ! [X3: complex,Y3: complex,E2: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) @ E2 )
% 0.26/0.56       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Y3 ) ) @ E2 ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_triangle_le_diff
% 0.26/0.56  thf(fact_5271_power__minus,axiom,
% 0.26/0.56      ! [A: real,N: nat] :
% 0.26/0.56        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 0.26/0.56        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ A @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_minus
% 0.26/0.56  thf(fact_5272_power__minus,axiom,
% 0.26/0.56      ! [A: int,N: nat] :
% 0.26/0.56        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 0.26/0.56        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_minus
% 0.26/0.56  thf(fact_5273_power__minus,axiom,
% 0.26/0.56      ! [A: complex,N: nat] :
% 0.26/0.56        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 0.26/0.56        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ A @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_minus
% 0.26/0.56  thf(fact_5274_power__minus,axiom,
% 0.26/0.56      ! [A: code_integer,N: nat] :
% 0.26/0.56        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 0.26/0.56        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_minus
% 0.26/0.56  thf(fact_5275_power__minus,axiom,
% 0.26/0.56      ! [A: rat,N: nat] :
% 0.26/0.56        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 0.26/0.56        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_minus
% 0.26/0.56  thf(fact_5276_norm__diff__ineq,axiom,
% 0.26/0.56      ! [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 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_diff_ineq
% 0.26/0.56  thf(fact_5277_norm__diff__ineq,axiom,
% 0.26/0.56      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_diff_ineq
% 0.26/0.56  thf(fact_5278_norm__triangle__ineq2,axiom,
% 0.26/0.56      ! [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 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_triangle_ineq2
% 0.26/0.56  thf(fact_5279_norm__triangle__ineq2,axiom,
% 0.26/0.56      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_triangle_ineq2
% 0.26/0.56  thf(fact_5280_power__minus__Bit0,axiom,
% 0.26/0.56      ! [X3: real,K: num] :
% 0.26/0.56        ( ( power_power_real @ ( uminus_uminus_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.26/0.56        = ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_minus_Bit0
% 0.26/0.56  thf(fact_5281_power__minus__Bit0,axiom,
% 0.26/0.56      ! [X3: int,K: num] :
% 0.26/0.56        ( ( power_power_int @ ( uminus_uminus_int @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.26/0.56        = ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_minus_Bit0
% 0.26/0.56  thf(fact_5282_power__minus__Bit0,axiom,
% 0.26/0.56      ! [X3: complex,K: num] :
% 0.26/0.56        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.26/0.56        = ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_minus_Bit0
% 0.26/0.56  thf(fact_5283_power__minus__Bit0,axiom,
% 0.26/0.56      ! [X3: code_integer,K: num] :
% 0.26/0.56        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.26/0.56        = ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_minus_Bit0
% 0.26/0.56  thf(fact_5284_power__minus__Bit0,axiom,
% 0.26/0.56      ! [X3: rat,K: num] :
% 0.26/0.56        ( ( power_power_rat @ ( uminus_uminus_rat @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.26/0.56        = ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_minus_Bit0
% 0.26/0.56  thf(fact_5285_lemma__interval__lt,axiom,
% 0.26/0.56      ! [A: real,X3: real,B: real] :
% 0.26/0.56        ( ( ord_less_real @ A @ X3 )
% 0.26/0.56       => ( ( ord_less_real @ X3 @ B )
% 0.26/0.56         => ? [D6: real] :
% 0.26/0.56              ( ( ord_less_real @ zero_zero_real @ D6 )
% 0.26/0.56              & ! [Y6: real] :
% 0.26/0.56                  ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y6 ) ) @ D6 )
% 0.26/0.56                 => ( ( ord_less_real @ A @ Y6 )
% 0.26/0.56                    & ( ord_less_real @ Y6 @ B ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % lemma_interval_lt
% 0.26/0.56  thf(fact_5286_sin__bound__lemma,axiom,
% 0.26/0.56      ! [X3: real,Y3: real,U: real,V: real] :
% 0.26/0.56        ( ( X3 = Y3 )
% 0.26/0.56       => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 0.26/0.56         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X3 @ U ) @ Y3 ) ) @ V ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % sin_bound_lemma
% 0.26/0.56  thf(fact_5287_real__0__less__add__iff,axiom,
% 0.26/0.56      ! [X3: real,Y3: real] :
% 0.26/0.56        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X3 @ Y3 ) )
% 0.26/0.56        = ( ord_less_real @ ( uminus_uminus_real @ X3 ) @ Y3 ) ) ).
% 0.26/0.56  
% 0.26/0.56  % real_0_less_add_iff
% 0.26/0.56  thf(fact_5288_real__add__less__0__iff,axiom,
% 0.26/0.56      ! [X3: real,Y3: real] :
% 0.26/0.56        ( ( ord_less_real @ ( plus_plus_real @ X3 @ Y3 ) @ zero_zero_real )
% 0.26/0.56        = ( ord_less_real @ Y3 @ ( uminus_uminus_real @ X3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % real_add_less_0_iff
% 0.26/0.56  thf(fact_5289_real__0__le__add__iff,axiom,
% 0.26/0.56      ! [X3: real,Y3: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X3 @ Y3 ) )
% 0.26/0.56        = ( ord_less_eq_real @ ( uminus_uminus_real @ X3 ) @ Y3 ) ) ).
% 0.26/0.56  
% 0.26/0.56  % real_0_le_add_iff
% 0.26/0.56  thf(fact_5290_real__add__le__0__iff,axiom,
% 0.26/0.56      ! [X3: real,Y3: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( plus_plus_real @ X3 @ Y3 ) @ zero_zero_real )
% 0.26/0.56        = ( ord_less_eq_real @ Y3 @ ( uminus_uminus_real @ X3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % real_add_le_0_iff
% 0.26/0.56  thf(fact_5291_tanh__real__gt__neg1,axiom,
% 0.26/0.56      ! [X3: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X3 ) ) ).
% 0.26/0.56  
% 0.26/0.56  % tanh_real_gt_neg1
% 0.26/0.56  thf(fact_5292_abs__add__one__gt__zero,axiom,
% 0.26/0.56      ! [X3: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_add_one_gt_zero
% 0.26/0.56  thf(fact_5293_abs__add__one__gt__zero,axiom,
% 0.26/0.56      ! [X3: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_add_one_gt_zero
% 0.26/0.56  thf(fact_5294_abs__add__one__gt__zero,axiom,
% 0.26/0.56      ! [X3: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_add_one_gt_zero
% 0.26/0.56  thf(fact_5295_abs__add__one__gt__zero,axiom,
% 0.26/0.56      ! [X3: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_add_one_gt_zero
% 0.26/0.56  thf(fact_5296_of__int__leD,axiom,
% 0.26/0.56      ! [N: int,X3: code_integer] :
% 0.26/0.56        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X3 )
% 0.26/0.56       => ( ( N = zero_zero_int )
% 0.26/0.56          | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % of_int_leD
% 0.26/0.56  thf(fact_5297_of__int__leD,axiom,
% 0.26/0.56      ! [N: int,X3: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X3 )
% 0.26/0.56       => ( ( N = zero_zero_int )
% 0.26/0.56          | ( ord_less_eq_real @ one_one_real @ X3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % of_int_leD
% 0.26/0.56  thf(fact_5298_of__int__leD,axiom,
% 0.26/0.56      ! [N: int,X3: rat] :
% 0.26/0.56        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X3 )
% 0.26/0.56       => ( ( N = zero_zero_int )
% 0.26/0.56          | ( ord_less_eq_rat @ one_one_rat @ X3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % of_int_leD
% 0.26/0.56  thf(fact_5299_of__int__leD,axiom,
% 0.26/0.56      ! [N: int,X3: int] :
% 0.26/0.56        ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X3 )
% 0.26/0.56       => ( ( N = zero_zero_int )
% 0.26/0.56          | ( ord_less_eq_int @ one_one_int @ X3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % of_int_leD
% 0.26/0.56  thf(fact_5300_of__int__lessD,axiom,
% 0.26/0.56      ! [N: int,X3: code_integer] :
% 0.26/0.56        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X3 )
% 0.26/0.56       => ( ( N = zero_zero_int )
% 0.26/0.56          | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % of_int_lessD
% 0.26/0.56  thf(fact_5301_of__int__lessD,axiom,
% 0.26/0.56      ! [N: int,X3: real] :
% 0.26/0.56        ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X3 )
% 0.26/0.56       => ( ( N = zero_zero_int )
% 0.26/0.56          | ( ord_less_real @ one_one_real @ X3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % of_int_lessD
% 0.26/0.56  thf(fact_5302_of__int__lessD,axiom,
% 0.26/0.56      ! [N: int,X3: rat] :
% 0.26/0.56        ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X3 )
% 0.26/0.56       => ( ( N = zero_zero_int )
% 0.26/0.56          | ( ord_less_rat @ one_one_rat @ X3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % of_int_lessD
% 0.26/0.56  thf(fact_5303_of__int__lessD,axiom,
% 0.26/0.56      ! [N: int,X3: int] :
% 0.26/0.56        ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X3 )
% 0.26/0.56       => ( ( N = zero_zero_int )
% 0.26/0.56          | ( ord_less_int @ one_one_int @ X3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % of_int_lessD
% 0.26/0.56  thf(fact_5304_power__eq__1__iff,axiom,
% 0.26/0.56      ! [W: real,N: nat] :
% 0.26/0.56        ( ( ( power_power_real @ W @ N )
% 0.26/0.56          = one_one_real )
% 0.26/0.56       => ( ( ( real_V7735802525324610683m_real @ W )
% 0.26/0.56            = one_one_real )
% 0.26/0.56          | ( N = zero_zero_nat ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_eq_1_iff
% 0.26/0.56  thf(fact_5305_power__eq__1__iff,axiom,
% 0.26/0.56      ! [W: complex,N: nat] :
% 0.26/0.56        ( ( ( power_power_complex @ W @ N )
% 0.26/0.56          = one_one_complex )
% 0.26/0.56       => ( ( ( real_V1022390504157884413omplex @ W )
% 0.26/0.56            = one_one_real )
% 0.26/0.56          | ( N = zero_zero_nat ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_eq_1_iff
% 0.26/0.56  thf(fact_5306_norm__diff__triangle__ineq,axiom,
% 0.26/0.56      ! [A: real,B: real,C: real,D3: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D3 ) ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ C ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ D3 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_diff_triangle_ineq
% 0.26/0.56  thf(fact_5307_norm__diff__triangle__ineq,axiom,
% 0.26/0.56      ! [A: complex,B: complex,C: complex,D3: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ ( plus_plus_complex @ C @ D3 ) ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ C ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ D3 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_diff_triangle_ineq
% 0.26/0.56  thf(fact_5308_norm__less__p1,axiom,
% 0.26/0.56      ! [X3: real] : ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ ( real_V7735802525324610683m_real @ X3 ) ) @ one_one_real ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_less_p1
% 0.26/0.56  thf(fact_5309_norm__less__p1,axiom,
% 0.26/0.56      ! [X3: complex] : ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( real_V1022390504157884413omplex @ X3 ) ) @ one_one_complex ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_less_p1
% 0.26/0.56  thf(fact_5310_less__minus__divide__eq,axiom,
% 0.26/0.56      ! [A: real,B: real,C: real] :
% 0.26/0.56        ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.26/0.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.56           => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 0.26/0.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.56               => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 0.26/0.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.56               => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % less_minus_divide_eq
% 0.26/0.56  thf(fact_5311_less__minus__divide__eq,axiom,
% 0.26/0.56      ! [A: rat,B: rat,C: rat] :
% 0.26/0.56        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.26/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.56           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.26/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.56               => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.26/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.56               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % less_minus_divide_eq
% 0.26/0.56  thf(fact_5312_minus__divide__less__eq,axiom,
% 0.26/0.56      ! [B: real,C: real,A: real] :
% 0.26/0.56        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.26/0.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.56           => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 0.26/0.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.56               => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 0.26/0.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.56               => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_divide_less_eq
% 0.26/0.56  thf(fact_5313_minus__divide__less__eq,axiom,
% 0.26/0.56      ! [B: rat,C: rat,A: rat] :
% 0.26/0.56        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.26/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.56           => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.26/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.56               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.26/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.56               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_divide_less_eq
% 0.26/0.56  thf(fact_5314_neg__less__minus__divide__eq,axiom,
% 0.26/0.56      ! [C: real,A: real,B: real] :
% 0.26/0.56        ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.56       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.26/0.56          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % neg_less_minus_divide_eq
% 0.26/0.56  thf(fact_5315_neg__less__minus__divide__eq,axiom,
% 0.26/0.56      ! [C: rat,A: rat,B: rat] :
% 0.26/0.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.56       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.26/0.56          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % neg_less_minus_divide_eq
% 0.26/0.56  thf(fact_5316_neg__minus__divide__less__eq,axiom,
% 0.26/0.56      ! [C: real,B: real,A: real] :
% 0.26/0.56        ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.56       => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.26/0.56          = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % neg_minus_divide_less_eq
% 0.26/0.56  thf(fact_5317_neg__minus__divide__less__eq,axiom,
% 0.26/0.56      ! [C: rat,B: rat,A: rat] :
% 0.26/0.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.56       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.26/0.56          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % neg_minus_divide_less_eq
% 0.26/0.56  thf(fact_5318_pos__less__minus__divide__eq,axiom,
% 0.26/0.56      ! [C: real,A: real,B: real] :
% 0.26/0.56        ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.56       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.26/0.56          = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pos_less_minus_divide_eq
% 0.26/0.56  thf(fact_5319_pos__less__minus__divide__eq,axiom,
% 0.26/0.56      ! [C: rat,A: rat,B: rat] :
% 0.26/0.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.56       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.26/0.56          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pos_less_minus_divide_eq
% 0.26/0.56  thf(fact_5320_pos__minus__divide__less__eq,axiom,
% 0.26/0.56      ! [C: real,B: real,A: real] :
% 0.26/0.56        ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.56       => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.26/0.56          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pos_minus_divide_less_eq
% 0.26/0.56  thf(fact_5321_pos__minus__divide__less__eq,axiom,
% 0.26/0.56      ! [C: rat,B: rat,A: rat] :
% 0.26/0.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.56       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.26/0.56          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pos_minus_divide_less_eq
% 0.26/0.56  thf(fact_5322_divide__eq__eq__numeral_I2_J,axiom,
% 0.26/0.56      ! [B: real,C: real,W: num] :
% 0.26/0.56        ( ( ( divide_divide_real @ B @ C )
% 0.26/0.56          = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.26/0.56        = ( ( ( C != zero_zero_real )
% 0.26/0.56           => ( B
% 0.26/0.56              = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 0.26/0.56          & ( ( C = zero_zero_real )
% 0.26/0.56           => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.26/0.56              = zero_zero_real ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % divide_eq_eq_numeral(2)
% 0.26/0.56  thf(fact_5323_divide__eq__eq__numeral_I2_J,axiom,
% 0.26/0.56      ! [B: complex,C: complex,W: num] :
% 0.26/0.56        ( ( ( divide1717551699836669952omplex @ B @ C )
% 0.26/0.56          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.26/0.56        = ( ( ( C != zero_zero_complex )
% 0.26/0.56           => ( B
% 0.26/0.56              = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 0.26/0.56          & ( ( C = zero_zero_complex )
% 0.26/0.56           => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.26/0.56              = zero_zero_complex ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % divide_eq_eq_numeral(2)
% 0.26/0.56  thf(fact_5324_divide__eq__eq__numeral_I2_J,axiom,
% 0.26/0.56      ! [B: rat,C: rat,W: num] :
% 0.26/0.56        ( ( ( divide_divide_rat @ B @ C )
% 0.26/0.56          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.26/0.56        = ( ( ( C != zero_zero_rat )
% 0.26/0.56           => ( B
% 0.26/0.56              = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.26/0.56          & ( ( C = zero_zero_rat )
% 0.26/0.56           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.26/0.56              = zero_zero_rat ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % divide_eq_eq_numeral(2)
% 0.26/0.56  thf(fact_5325_eq__divide__eq__numeral_I2_J,axiom,
% 0.26/0.56      ! [W: num,B: real,C: real] :
% 0.26/0.56        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.26/0.56          = ( divide_divide_real @ B @ C ) )
% 0.26/0.56        = ( ( ( C != zero_zero_real )
% 0.26/0.56           => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 0.26/0.56              = B ) )
% 0.26/0.56          & ( ( C = zero_zero_real )
% 0.26/0.56           => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.26/0.56              = zero_zero_real ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % eq_divide_eq_numeral(2)
% 0.26/0.56  thf(fact_5326_eq__divide__eq__numeral_I2_J,axiom,
% 0.26/0.56      ! [W: num,B: complex,C: complex] :
% 0.26/0.56        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.26/0.56          = ( divide1717551699836669952omplex @ B @ C ) )
% 0.26/0.56        = ( ( ( C != zero_zero_complex )
% 0.26/0.56           => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 0.26/0.56              = B ) )
% 0.26/0.56          & ( ( C = zero_zero_complex )
% 0.26/0.56           => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.26/0.56              = zero_zero_complex ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % eq_divide_eq_numeral(2)
% 0.26/0.56  thf(fact_5327_eq__divide__eq__numeral_I2_J,axiom,
% 0.26/0.56      ! [W: num,B: rat,C: rat] :
% 0.26/0.56        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.26/0.56          = ( divide_divide_rat @ B @ C ) )
% 0.26/0.56        = ( ( ( C != zero_zero_rat )
% 0.26/0.56           => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 0.26/0.56              = B ) )
% 0.26/0.56          & ( ( C = zero_zero_rat )
% 0.26/0.56           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.26/0.56              = zero_zero_rat ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % eq_divide_eq_numeral(2)
% 0.26/0.56  thf(fact_5328_minus__divide__add__eq__iff,axiom,
% 0.26/0.56      ! [Z: real,X3: real,Y3: real] :
% 0.26/0.56        ( ( Z != zero_zero_real )
% 0.26/0.56       => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X3 @ Z ) ) @ Y3 )
% 0.26/0.56          = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X3 ) @ ( times_times_real @ Y3 @ Z ) ) @ Z ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_divide_add_eq_iff
% 0.26/0.56  thf(fact_5329_minus__divide__add__eq__iff,axiom,
% 0.26/0.56      ! [Z: complex,X3: complex,Y3: complex] :
% 0.26/0.56        ( ( Z != zero_zero_complex )
% 0.26/0.56       => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X3 @ Z ) ) @ Y3 )
% 0.26/0.56          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X3 ) @ ( times_times_complex @ Y3 @ Z ) ) @ Z ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_divide_add_eq_iff
% 0.26/0.56  thf(fact_5330_minus__divide__add__eq__iff,axiom,
% 0.26/0.56      ! [Z: rat,X3: rat,Y3: rat] :
% 0.26/0.56        ( ( Z != zero_zero_rat )
% 0.26/0.56       => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X3 @ Z ) ) @ Y3 )
% 0.26/0.56          = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X3 ) @ ( times_times_rat @ Y3 @ Z ) ) @ Z ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_divide_add_eq_iff
% 0.26/0.56  thf(fact_5331_add__divide__eq__if__simps_I3_J,axiom,
% 0.26/0.56      ! [Z: real,A: real,B: real] :
% 0.26/0.56        ( ( ( Z = zero_zero_real )
% 0.26/0.56         => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 0.26/0.56            = B ) )
% 0.26/0.56        & ( ( Z != zero_zero_real )
% 0.26/0.56         => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 0.26/0.56            = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % add_divide_eq_if_simps(3)
% 0.26/0.56  thf(fact_5332_add__divide__eq__if__simps_I3_J,axiom,
% 0.26/0.56      ! [Z: complex,A: complex,B: complex] :
% 0.26/0.56        ( ( ( Z = zero_zero_complex )
% 0.26/0.56         => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 0.26/0.56            = B ) )
% 0.26/0.56        & ( ( Z != zero_zero_complex )
% 0.26/0.56         => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 0.26/0.56            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % add_divide_eq_if_simps(3)
% 0.26/0.56  thf(fact_5333_add__divide__eq__if__simps_I3_J,axiom,
% 0.26/0.56      ! [Z: rat,A: rat,B: rat] :
% 0.26/0.56        ( ( ( Z = zero_zero_rat )
% 0.26/0.56         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 0.26/0.56            = B ) )
% 0.26/0.56        & ( ( Z != zero_zero_rat )
% 0.26/0.56         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 0.26/0.56            = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % add_divide_eq_if_simps(3)
% 0.26/0.56  thf(fact_5334_minus__divide__diff__eq__iff,axiom,
% 0.26/0.56      ! [Z: real,X3: real,Y3: real] :
% 0.26/0.56        ( ( Z != zero_zero_real )
% 0.26/0.56       => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X3 @ Z ) ) @ Y3 )
% 0.26/0.56          = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X3 ) @ ( times_times_real @ Y3 @ Z ) ) @ Z ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_divide_diff_eq_iff
% 0.26/0.56  thf(fact_5335_minus__divide__diff__eq__iff,axiom,
% 0.26/0.56      ! [Z: complex,X3: complex,Y3: complex] :
% 0.26/0.56        ( ( Z != zero_zero_complex )
% 0.26/0.56       => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X3 @ Z ) ) @ Y3 )
% 0.26/0.56          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X3 ) @ ( times_times_complex @ Y3 @ Z ) ) @ Z ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_divide_diff_eq_iff
% 0.26/0.56  thf(fact_5336_minus__divide__diff__eq__iff,axiom,
% 0.26/0.56      ! [Z: rat,X3: rat,Y3: rat] :
% 0.26/0.56        ( ( Z != zero_zero_rat )
% 0.26/0.56       => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X3 @ Z ) ) @ Y3 )
% 0.26/0.56          = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X3 ) @ ( times_times_rat @ Y3 @ Z ) ) @ Z ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_divide_diff_eq_iff
% 0.26/0.56  thf(fact_5337_add__divide__eq__if__simps_I5_J,axiom,
% 0.26/0.56      ! [Z: real,A: real,B: real] :
% 0.26/0.56        ( ( ( Z = zero_zero_real )
% 0.26/0.56         => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 0.26/0.56            = ( uminus_uminus_real @ B ) ) )
% 0.26/0.56        & ( ( Z != zero_zero_real )
% 0.26/0.56         => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 0.26/0.56            = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % add_divide_eq_if_simps(5)
% 0.26/0.56  thf(fact_5338_add__divide__eq__if__simps_I5_J,axiom,
% 0.26/0.56      ! [Z: complex,A: complex,B: complex] :
% 0.26/0.56        ( ( ( Z = zero_zero_complex )
% 0.26/0.56         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 0.26/0.56            = ( uminus1482373934393186551omplex @ B ) ) )
% 0.26/0.56        & ( ( Z != zero_zero_complex )
% 0.26/0.56         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 0.26/0.56            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % add_divide_eq_if_simps(5)
% 0.26/0.56  thf(fact_5339_add__divide__eq__if__simps_I5_J,axiom,
% 0.26/0.56      ! [Z: rat,A: rat,B: rat] :
% 0.26/0.56        ( ( ( Z = zero_zero_rat )
% 0.26/0.56         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 0.26/0.56            = ( uminus_uminus_rat @ B ) ) )
% 0.26/0.56        & ( ( Z != zero_zero_rat )
% 0.26/0.56         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 0.26/0.56            = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % add_divide_eq_if_simps(5)
% 0.26/0.56  thf(fact_5340_add__divide__eq__if__simps_I6_J,axiom,
% 0.26/0.56      ! [Z: real,A: real,B: real] :
% 0.26/0.56        ( ( ( Z = zero_zero_real )
% 0.26/0.56         => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 0.26/0.56            = ( uminus_uminus_real @ B ) ) )
% 0.26/0.56        & ( ( Z != zero_zero_real )
% 0.26/0.56         => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 0.26/0.56            = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % add_divide_eq_if_simps(6)
% 0.26/0.56  thf(fact_5341_add__divide__eq__if__simps_I6_J,axiom,
% 0.26/0.56      ! [Z: complex,A: complex,B: complex] :
% 0.26/0.56        ( ( ( Z = zero_zero_complex )
% 0.26/0.56         => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 0.26/0.56            = ( uminus1482373934393186551omplex @ B ) ) )
% 0.26/0.56        & ( ( Z != zero_zero_complex )
% 0.26/0.56         => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 0.26/0.56            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % add_divide_eq_if_simps(6)
% 0.26/0.56  thf(fact_5342_add__divide__eq__if__simps_I6_J,axiom,
% 0.26/0.56      ! [Z: rat,A: rat,B: rat] :
% 0.26/0.56        ( ( ( Z = zero_zero_rat )
% 0.26/0.56         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 0.26/0.56            = ( uminus_uminus_rat @ B ) ) )
% 0.26/0.56        & ( ( Z != zero_zero_rat )
% 0.26/0.56         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 0.26/0.56            = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % add_divide_eq_if_simps(6)
% 0.26/0.56  thf(fact_5343_even__minus,axiom,
% 0.26/0.56      ! [A: int] :
% 0.26/0.56        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 0.26/0.56        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 0.26/0.56  
% 0.26/0.56  % even_minus
% 0.26/0.56  thf(fact_5344_even__minus,axiom,
% 0.26/0.56      ! [A: code_integer] :
% 0.26/0.56        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.26/0.56        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 0.26/0.56  
% 0.26/0.56  % even_minus
% 0.26/0.56  thf(fact_5345_power2__eq__iff,axiom,
% 0.26/0.56      ! [X3: real,Y3: real] :
% 0.26/0.56        ( ( ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56          = ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.56        = ( ( X3 = Y3 )
% 0.26/0.56          | ( X3
% 0.26/0.56            = ( uminus_uminus_real @ Y3 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power2_eq_iff
% 0.26/0.56  thf(fact_5346_power2__eq__iff,axiom,
% 0.26/0.56      ! [X3: int,Y3: int] :
% 0.26/0.56        ( ( ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56          = ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.56        = ( ( X3 = Y3 )
% 0.26/0.56          | ( X3
% 0.26/0.56            = ( uminus_uminus_int @ Y3 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power2_eq_iff
% 0.26/0.56  thf(fact_5347_power2__eq__iff,axiom,
% 0.26/0.56      ! [X3: complex,Y3: complex] :
% 0.26/0.56        ( ( ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56          = ( power_power_complex @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.56        = ( ( X3 = Y3 )
% 0.26/0.56          | ( X3
% 0.26/0.56            = ( uminus1482373934393186551omplex @ Y3 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power2_eq_iff
% 0.26/0.56  thf(fact_5348_power2__eq__iff,axiom,
% 0.26/0.56      ! [X3: code_integer,Y3: code_integer] :
% 0.26/0.56        ( ( ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56          = ( power_8256067586552552935nteger @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.56        = ( ( X3 = Y3 )
% 0.26/0.56          | ( X3
% 0.26/0.56            = ( uminus1351360451143612070nteger @ Y3 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power2_eq_iff
% 0.26/0.56  thf(fact_5349_power2__eq__iff,axiom,
% 0.26/0.56      ! [X3: rat,Y3: rat] :
% 0.26/0.56        ( ( ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56          = ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.56        = ( ( X3 = Y3 )
% 0.26/0.56          | ( X3
% 0.26/0.56            = ( uminus_uminus_rat @ Y3 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power2_eq_iff
% 0.26/0.56  thf(fact_5350_lemma__interval,axiom,
% 0.26/0.56      ! [A: real,X3: real,B: real] :
% 0.26/0.56        ( ( ord_less_real @ A @ X3 )
% 0.26/0.56       => ( ( ord_less_real @ X3 @ B )
% 0.26/0.56         => ? [D6: real] :
% 0.26/0.56              ( ( ord_less_real @ zero_zero_real @ D6 )
% 0.26/0.56              & ! [Y6: real] :
% 0.26/0.56                  ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y6 ) ) @ D6 )
% 0.26/0.56                 => ( ( ord_less_eq_real @ A @ Y6 )
% 0.26/0.56                    & ( ord_less_eq_real @ Y6 @ B ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % lemma_interval
% 0.26/0.56  thf(fact_5351_round__diff__minimal,axiom,
% 0.26/0.56      ! [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 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % round_diff_minimal
% 0.26/0.56  thf(fact_5352_round__diff__minimal,axiom,
% 0.26/0.56      ! [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 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % round_diff_minimal
% 0.26/0.56  thf(fact_5353_abs__le__square__iff,axiom,
% 0.26/0.56      ! [X3: code_integer,Y3: code_integer] :
% 0.26/0.56        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X3 ) @ ( abs_abs_Code_integer @ Y3 ) )
% 0.26/0.56        = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_le_square_iff
% 0.26/0.56  thf(fact_5354_abs__le__square__iff,axiom,
% 0.26/0.56      ! [X3: real,Y3: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ ( abs_abs_real @ Y3 ) )
% 0.26/0.56        = ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_le_square_iff
% 0.26/0.56  thf(fact_5355_abs__le__square__iff,axiom,
% 0.26/0.56      ! [X3: rat,Y3: rat] :
% 0.26/0.56        ( ( ord_less_eq_rat @ ( abs_abs_rat @ X3 ) @ ( abs_abs_rat @ Y3 ) )
% 0.26/0.56        = ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_le_square_iff
% 0.26/0.56  thf(fact_5356_abs__le__square__iff,axiom,
% 0.26/0.56      ! [X3: int,Y3: int] :
% 0.26/0.56        ( ( ord_less_eq_int @ ( abs_abs_int @ X3 ) @ ( abs_abs_int @ Y3 ) )
% 0.26/0.56        = ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_le_square_iff
% 0.26/0.56  thf(fact_5357_abs__square__eq__1,axiom,
% 0.26/0.56      ! [X3: code_integer] :
% 0.26/0.56        ( ( ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56          = one_one_Code_integer )
% 0.26/0.56        = ( ( abs_abs_Code_integer @ X3 )
% 0.26/0.56          = one_one_Code_integer ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_square_eq_1
% 0.26/0.56  thf(fact_5358_abs__square__eq__1,axiom,
% 0.26/0.56      ! [X3: rat] :
% 0.26/0.56        ( ( ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56          = one_one_rat )
% 0.26/0.56        = ( ( abs_abs_rat @ X3 )
% 0.26/0.56          = one_one_rat ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_square_eq_1
% 0.26/0.56  thf(fact_5359_abs__square__eq__1,axiom,
% 0.26/0.56      ! [X3: int] :
% 0.26/0.56        ( ( ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56          = one_one_int )
% 0.26/0.56        = ( ( abs_abs_int @ X3 )
% 0.26/0.56          = one_one_int ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_square_eq_1
% 0.26/0.56  thf(fact_5360_abs__square__eq__1,axiom,
% 0.26/0.56      ! [X3: real] :
% 0.26/0.56        ( ( ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56          = one_one_real )
% 0.26/0.56        = ( ( abs_abs_real @ X3 )
% 0.26/0.56          = one_one_real ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_square_eq_1
% 0.26/0.56  thf(fact_5361_power__even__abs,axiom,
% 0.26/0.56      ! [N: nat,A: code_integer] :
% 0.26/0.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56       => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N )
% 0.26/0.56          = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_even_abs
% 0.26/0.56  thf(fact_5362_power__even__abs,axiom,
% 0.26/0.56      ! [N: nat,A: rat] :
% 0.26/0.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56       => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ N )
% 0.26/0.56          = ( power_power_rat @ A @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_even_abs
% 0.26/0.56  thf(fact_5363_power__even__abs,axiom,
% 0.26/0.56      ! [N: nat,A: int] :
% 0.26/0.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56       => ( ( power_power_int @ ( abs_abs_int @ A ) @ N )
% 0.26/0.56          = ( power_power_int @ A @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_even_abs
% 0.26/0.56  thf(fact_5364_power__even__abs,axiom,
% 0.26/0.56      ! [N: nat,A: real] :
% 0.26/0.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56       => ( ( power_power_real @ ( abs_abs_real @ A ) @ N )
% 0.26/0.56          = ( power_power_real @ A @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_even_abs
% 0.26/0.56  thf(fact_5365_le__minus__divide__eq,axiom,
% 0.26/0.56      ! [A: real,B: real,C: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.26/0.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.56           => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 0.26/0.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.56               => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 0.26/0.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.56               => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % le_minus_divide_eq
% 0.26/0.56  thf(fact_5366_le__minus__divide__eq,axiom,
% 0.26/0.56      ! [A: rat,B: rat,C: rat] :
% 0.26/0.56        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.26/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.56           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.26/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.56               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.26/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.56               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % le_minus_divide_eq
% 0.26/0.56  thf(fact_5367_minus__divide__le__eq,axiom,
% 0.26/0.56      ! [B: real,C: real,A: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.26/0.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.56           => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 0.26/0.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.56               => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 0.26/0.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.56               => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_divide_le_eq
% 0.26/0.56  thf(fact_5368_minus__divide__le__eq,axiom,
% 0.26/0.56      ! [B: rat,C: rat,A: rat] :
% 0.26/0.56        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.26/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.56           => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.26/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.56               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.26/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.56               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_divide_le_eq
% 0.26/0.56  thf(fact_5369_neg__le__minus__divide__eq,axiom,
% 0.26/0.56      ! [C: real,A: real,B: real] :
% 0.26/0.56        ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.56       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.26/0.56          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % neg_le_minus_divide_eq
% 0.26/0.56  thf(fact_5370_neg__le__minus__divide__eq,axiom,
% 0.26/0.56      ! [C: rat,A: rat,B: rat] :
% 0.26/0.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.56       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.26/0.56          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % neg_le_minus_divide_eq
% 0.26/0.56  thf(fact_5371_neg__minus__divide__le__eq,axiom,
% 0.26/0.56      ! [C: real,B: real,A: real] :
% 0.26/0.56        ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.56       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.26/0.56          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % neg_minus_divide_le_eq
% 0.26/0.56  thf(fact_5372_neg__minus__divide__le__eq,axiom,
% 0.26/0.56      ! [C: rat,B: rat,A: rat] :
% 0.26/0.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.56       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.26/0.56          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % neg_minus_divide_le_eq
% 0.26/0.56  thf(fact_5373_pos__le__minus__divide__eq,axiom,
% 0.26/0.56      ! [C: real,A: real,B: real] :
% 0.26/0.56        ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.56       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.26/0.56          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pos_le_minus_divide_eq
% 0.26/0.56  thf(fact_5374_pos__le__minus__divide__eq,axiom,
% 0.26/0.56      ! [C: rat,A: rat,B: rat] :
% 0.26/0.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.56       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.26/0.56          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pos_le_minus_divide_eq
% 0.26/0.56  thf(fact_5375_pos__minus__divide__le__eq,axiom,
% 0.26/0.56      ! [C: real,B: real,A: real] :
% 0.26/0.56        ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.56       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.26/0.56          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pos_minus_divide_le_eq
% 0.26/0.56  thf(fact_5376_pos__minus__divide__le__eq,axiom,
% 0.26/0.56      ! [C: rat,B: rat,A: rat] :
% 0.26/0.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.56       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.26/0.56          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pos_minus_divide_le_eq
% 0.26/0.56  thf(fact_5377_divide__less__eq__numeral_I2_J,axiom,
% 0.26/0.56      ! [B: real,C: real,W: num] :
% 0.26/0.56        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.26/0.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.56           => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 0.26/0.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.56               => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 0.26/0.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.56               => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % divide_less_eq_numeral(2)
% 0.26/0.56  thf(fact_5378_divide__less__eq__numeral_I2_J,axiom,
% 0.26/0.56      ! [B: rat,C: rat,W: num] :
% 0.26/0.56        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.26/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.56           => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.26/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.56               => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 0.26/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.56               => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % divide_less_eq_numeral(2)
% 0.26/0.56  thf(fact_5379_less__divide__eq__numeral_I2_J,axiom,
% 0.26/0.56      ! [W: num,B: real,C: real] :
% 0.26/0.56        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 0.26/0.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.56           => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 0.26/0.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.56               => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 0.26/0.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.56               => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % less_divide_eq_numeral(2)
% 0.26/0.56  thf(fact_5380_less__divide__eq__numeral_I2_J,axiom,
% 0.26/0.56      ! [W: num,B: rat,C: rat] :
% 0.26/0.56        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 0.26/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.56           => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 0.26/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.56               => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.26/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.56               => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % less_divide_eq_numeral(2)
% 0.26/0.56  thf(fact_5381_norm__power__diff,axiom,
% 0.26/0.56      ! [Z: real,W: real,M: nat] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 0.26/0.56       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W ) @ one_one_real )
% 0.26/0.56         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( power_power_real @ Z @ M ) @ ( power_power_real @ W @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Z @ W ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_power_diff
% 0.26/0.56  thf(fact_5382_norm__power__diff,axiom,
% 0.26/0.56      ! [Z: complex,W: complex,M: nat] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 0.26/0.56       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 0.26/0.56         => ( 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 ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % norm_power_diff
% 0.26/0.56  thf(fact_5383_power2__eq__1__iff,axiom,
% 0.26/0.56      ! [A: real] :
% 0.26/0.56        ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56          = one_one_real )
% 0.26/0.56        = ( ( A = one_one_real )
% 0.26/0.56          | ( A
% 0.26/0.56            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power2_eq_1_iff
% 0.26/0.56  thf(fact_5384_power2__eq__1__iff,axiom,
% 0.26/0.56      ! [A: int] :
% 0.26/0.56        ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56          = one_one_int )
% 0.26/0.56        = ( ( A = one_one_int )
% 0.26/0.56          | ( A
% 0.26/0.56            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power2_eq_1_iff
% 0.26/0.56  thf(fact_5385_power2__eq__1__iff,axiom,
% 0.26/0.56      ! [A: complex] :
% 0.26/0.56        ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56          = one_one_complex )
% 0.26/0.56        = ( ( A = one_one_complex )
% 0.26/0.56          | ( A
% 0.26/0.56            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power2_eq_1_iff
% 0.26/0.56  thf(fact_5386_power2__eq__1__iff,axiom,
% 0.26/0.56      ! [A: code_integer] :
% 0.26/0.56        ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56          = one_one_Code_integer )
% 0.26/0.56        = ( ( A = one_one_Code_integer )
% 0.26/0.56          | ( A
% 0.26/0.56            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power2_eq_1_iff
% 0.26/0.56  thf(fact_5387_power2__eq__1__iff,axiom,
% 0.26/0.56      ! [A: rat] :
% 0.26/0.56        ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56          = one_one_rat )
% 0.26/0.56        = ( ( A = one_one_rat )
% 0.26/0.56          | ( A
% 0.26/0.56            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power2_eq_1_iff
% 0.26/0.56  thf(fact_5388_uminus__power__if,axiom,
% 0.26/0.56      ! [N: nat,A: real] :
% 0.26/0.56        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56         => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 0.26/0.56            = ( power_power_real @ A @ N ) ) )
% 0.26/0.56        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56         => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 0.26/0.56            = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % uminus_power_if
% 0.26/0.56  thf(fact_5389_uminus__power__if,axiom,
% 0.26/0.56      ! [N: nat,A: int] :
% 0.26/0.56        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56         => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 0.26/0.56            = ( power_power_int @ A @ N ) ) )
% 0.26/0.56        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56         => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 0.26/0.56            = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % uminus_power_if
% 0.26/0.56  thf(fact_5390_uminus__power__if,axiom,
% 0.26/0.56      ! [N: nat,A: complex] :
% 0.26/0.56        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 0.26/0.56            = ( power_power_complex @ A @ N ) ) )
% 0.26/0.56        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 0.26/0.56            = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % uminus_power_if
% 0.26/0.56  thf(fact_5391_uminus__power__if,axiom,
% 0.26/0.56      ! [N: nat,A: code_integer] :
% 0.26/0.56        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 0.26/0.56            = ( power_8256067586552552935nteger @ A @ N ) ) )
% 0.26/0.56        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 0.26/0.56            = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % uminus_power_if
% 0.26/0.56  thf(fact_5392_uminus__power__if,axiom,
% 0.26/0.56      ! [N: nat,A: rat] :
% 0.26/0.56        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56         => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 0.26/0.56            = ( power_power_rat @ A @ N ) ) )
% 0.26/0.56        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56         => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 0.26/0.56            = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % uminus_power_if
% 0.26/0.56  thf(fact_5393_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.26/0.56      ! [K: nat,N: nat] :
% 0.26/0.56        ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.56       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K ) )
% 0.26/0.56          = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % neg_one_power_add_eq_neg_one_power_diff
% 0.26/0.56  thf(fact_5394_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.26/0.56      ! [K: nat,N: nat] :
% 0.26/0.56        ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.56       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 0.26/0.56          = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % neg_one_power_add_eq_neg_one_power_diff
% 0.26/0.56  thf(fact_5395_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.26/0.56      ! [K: nat,N: nat] :
% 0.26/0.56        ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.56       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K ) )
% 0.26/0.56          = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % neg_one_power_add_eq_neg_one_power_diff
% 0.26/0.56  thf(fact_5396_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.26/0.56      ! [K: nat,N: nat] :
% 0.26/0.56        ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.56       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 0.26/0.56          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % neg_one_power_add_eq_neg_one_power_diff
% 0.26/0.56  thf(fact_5397_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.26/0.56      ! [K: nat,N: nat] :
% 0.26/0.56        ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.56       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 0.26/0.56          = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % neg_one_power_add_eq_neg_one_power_diff
% 0.26/0.56  thf(fact_5398_realpow__square__minus__le,axiom,
% 0.26/0.56      ! [U: real,X3: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % realpow_square_minus_le
% 0.26/0.56  thf(fact_5399_powr__neg__one,axiom,
% 0.26/0.56      ! [X3: real] :
% 0.26/0.56        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.56       => ( ( powr_real @ X3 @ ( uminus_uminus_real @ one_one_real ) )
% 0.26/0.56          = ( divide_divide_real @ one_one_real @ X3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % powr_neg_one
% 0.26/0.56  thf(fact_5400_Bernoulli__inequality,axiom,
% 0.26/0.56      ! [X3: real,N: nat] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.26/0.56       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X3 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X3 ) @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % Bernoulli_inequality
% 0.26/0.56  thf(fact_5401_ln__add__one__self__le__self2,axiom,
% 0.26/0.56      ! [X3: real] :
% 0.26/0.56        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.26/0.56       => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X3 ) ) @ X3 ) ) ).
% 0.26/0.56  
% 0.26/0.56  % ln_add_one_self_le_self2
% 0.26/0.56  thf(fact_5402_power2__le__iff__abs__le,axiom,
% 0.26/0.56      ! [Y3: code_integer,X3: code_integer] :
% 0.26/0.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y3 )
% 0.26/0.56       => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.56          = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X3 ) @ Y3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power2_le_iff_abs_le
% 0.26/0.56  thf(fact_5403_power2__le__iff__abs__le,axiom,
% 0.26/0.56      ! [Y3: real,X3: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.56       => ( ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.56          = ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ Y3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power2_le_iff_abs_le
% 0.26/0.56  thf(fact_5404_power2__le__iff__abs__le,axiom,
% 0.26/0.56      ! [Y3: rat,X3: rat] :
% 0.26/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 0.26/0.56       => ( ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.56          = ( ord_less_eq_rat @ ( abs_abs_rat @ X3 ) @ Y3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power2_le_iff_abs_le
% 0.26/0.56  thf(fact_5405_power2__le__iff__abs__le,axiom,
% 0.26/0.56      ! [Y3: int,X3: int] :
% 0.26/0.56        ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 0.26/0.56       => ( ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.56          = ( ord_less_eq_int @ ( abs_abs_int @ X3 ) @ Y3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power2_le_iff_abs_le
% 0.26/0.56  thf(fact_5406_abs__square__le__1,axiom,
% 0.26/0.56      ! [X3: code_integer] :
% 0.26/0.56        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 0.26/0.56        = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X3 ) @ one_one_Code_integer ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_square_le_1
% 0.26/0.56  thf(fact_5407_abs__square__le__1,axiom,
% 0.26/0.56      ! [X3: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 0.26/0.56        = ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_square_le_1
% 0.26/0.56  thf(fact_5408_abs__square__le__1,axiom,
% 0.26/0.56      ! [X3: rat] :
% 0.26/0.56        ( ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 0.26/0.56        = ( ord_less_eq_rat @ ( abs_abs_rat @ X3 ) @ one_one_rat ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_square_le_1
% 0.26/0.56  thf(fact_5409_abs__square__le__1,axiom,
% 0.26/0.56      ! [X3: int] :
% 0.26/0.56        ( ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 0.26/0.56        = ( ord_less_eq_int @ ( abs_abs_int @ X3 ) @ one_one_int ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_square_le_1
% 0.26/0.56  thf(fact_5410_abs__square__less__1,axiom,
% 0.26/0.56      ! [X3: code_integer] :
% 0.26/0.56        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 0.26/0.56        = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X3 ) @ one_one_Code_integer ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_square_less_1
% 0.26/0.56  thf(fact_5411_abs__square__less__1,axiom,
% 0.26/0.56      ! [X3: real] :
% 0.26/0.56        ( ( ord_less_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 0.26/0.56        = ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_square_less_1
% 0.26/0.56  thf(fact_5412_abs__square__less__1,axiom,
% 0.26/0.56      ! [X3: rat] :
% 0.26/0.56        ( ( ord_less_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 0.26/0.56        = ( ord_less_rat @ ( abs_abs_rat @ X3 ) @ one_one_rat ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_square_less_1
% 0.26/0.56  thf(fact_5413_abs__square__less__1,axiom,
% 0.26/0.56      ! [X3: int] :
% 0.26/0.56        ( ( ord_less_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 0.26/0.56        = ( ord_less_int @ ( abs_abs_int @ X3 ) @ one_one_int ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_square_less_1
% 0.26/0.56  thf(fact_5414_power__mono__even,axiom,
% 0.26/0.56      ! [N: nat,A: code_integer,B: code_integer] :
% 0.26/0.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56       => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 0.26/0.56         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_mono_even
% 0.26/0.56  thf(fact_5415_power__mono__even,axiom,
% 0.26/0.56      ! [N: nat,A: real,B: real] :
% 0.26/0.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56       => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 0.26/0.56         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_mono_even
% 0.26/0.56  thf(fact_5416_power__mono__even,axiom,
% 0.26/0.56      ! [N: nat,A: rat,B: rat] :
% 0.26/0.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56       => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 0.26/0.56         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_mono_even
% 0.26/0.56  thf(fact_5417_power__mono__even,axiom,
% 0.26/0.56      ! [N: nat,A: int,B: int] :
% 0.26/0.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56       => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 0.26/0.56         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_mono_even
% 0.26/0.56  thf(fact_5418_square__norm__one,axiom,
% 0.26/0.56      ! [X3: real] :
% 0.26/0.56        ( ( ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56          = one_one_real )
% 0.26/0.56       => ( ( real_V7735802525324610683m_real @ X3 )
% 0.26/0.56          = one_one_real ) ) ).
% 0.26/0.56  
% 0.26/0.56  % square_norm_one
% 0.26/0.56  thf(fact_5419_square__norm__one,axiom,
% 0.26/0.56      ! [X3: complex] :
% 0.26/0.56        ( ( ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56          = one_one_complex )
% 0.26/0.56       => ( ( real_V1022390504157884413omplex @ X3 )
% 0.26/0.56          = one_one_real ) ) ).
% 0.26/0.56  
% 0.26/0.56  % square_norm_one
% 0.26/0.56  thf(fact_5420_le__divide__eq__numeral_I2_J,axiom,
% 0.26/0.56      ! [W: num,B: real,C: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 0.26/0.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.56           => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 0.26/0.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.56               => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 0.26/0.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.56               => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % le_divide_eq_numeral(2)
% 0.26/0.56  thf(fact_5421_le__divide__eq__numeral_I2_J,axiom,
% 0.26/0.56      ! [W: num,B: rat,C: rat] :
% 0.26/0.56        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 0.26/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.56           => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 0.26/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.56               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.26/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.56               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % le_divide_eq_numeral(2)
% 0.26/0.56  thf(fact_5422_divide__le__eq__numeral_I2_J,axiom,
% 0.26/0.56      ! [B: real,C: real,W: num] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.26/0.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.56           => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 0.26/0.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.56               => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 0.26/0.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.26/0.56               => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % divide_le_eq_numeral(2)
% 0.26/0.56  thf(fact_5423_divide__le__eq__numeral_I2_J,axiom,
% 0.26/0.56      ! [B: rat,C: rat,W: num] :
% 0.26/0.56        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.26/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.56           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.26/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.26/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.56               => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 0.26/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.26/0.56               => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % divide_le_eq_numeral(2)
% 0.26/0.56  thf(fact_5424_sqrt__ge__absD,axiom,
% 0.26/0.56      ! [X3: real,Y3: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ ( sqrt @ Y3 ) )
% 0.26/0.56       => ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y3 ) ) ).
% 0.26/0.56  
% 0.26/0.56  % sqrt_ge_absD
% 0.26/0.56  thf(fact_5425_square__le__1,axiom,
% 0.26/0.56      ! [X3: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.26/0.56       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 0.26/0.56         => ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % square_le_1
% 0.26/0.56  thf(fact_5426_square__le__1,axiom,
% 0.26/0.56      ! [X3: code_integer] :
% 0.26/0.56        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X3 )
% 0.26/0.56       => ( ( ord_le3102999989581377725nteger @ X3 @ one_one_Code_integer )
% 0.26/0.56         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % square_le_1
% 0.26/0.56  thf(fact_5427_square__le__1,axiom,
% 0.26/0.56      ! [X3: rat] :
% 0.26/0.56        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X3 )
% 0.26/0.56       => ( ( ord_less_eq_rat @ X3 @ one_one_rat )
% 0.26/0.56         => ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % square_le_1
% 0.26/0.56  thf(fact_5428_square__le__1,axiom,
% 0.26/0.56      ! [X3: int] :
% 0.26/0.56        ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X3 )
% 0.26/0.56       => ( ( ord_less_eq_int @ X3 @ one_one_int )
% 0.26/0.56         => ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % square_le_1
% 0.26/0.56  thf(fact_5429_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 0.26/0.56      ! [X3: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.26/0.56       => ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 0.26/0.56         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X3 ) ) @ X3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_ln_one_plus_x_minus_x_bound_nonpos
% 0.26/0.56  thf(fact_5430_minus__power__mult__self,axiom,
% 0.26/0.56      ! [A: real,N: nat] :
% 0.26/0.56        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 0.26/0.56        = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_power_mult_self
% 0.26/0.56  thf(fact_5431_minus__power__mult__self,axiom,
% 0.26/0.56      ! [A: int,N: nat] :
% 0.26/0.56        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 0.26/0.56        = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_power_mult_self
% 0.26/0.56  thf(fact_5432_minus__power__mult__self,axiom,
% 0.26/0.56      ! [A: complex,N: nat] :
% 0.26/0.56        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) )
% 0.26/0.56        = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_power_mult_self
% 0.26/0.56  thf(fact_5433_minus__power__mult__self,axiom,
% 0.26/0.56      ! [A: code_integer,N: nat] :
% 0.26/0.56        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 0.26/0.56        = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_power_mult_self
% 0.26/0.56  thf(fact_5434_minus__power__mult__self,axiom,
% 0.26/0.56      ! [A: rat,N: nat] :
% 0.26/0.56        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 0.26/0.56        = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_power_mult_self
% 0.26/0.56  thf(fact_5435_minus__one__power__iff,axiom,
% 0.26/0.56      ! [N: nat] :
% 0.26/0.56        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56         => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 0.26/0.56            = one_one_real ) )
% 0.26/0.56        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56         => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 0.26/0.56            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_one_power_iff
% 0.26/0.56  thf(fact_5436_minus__one__power__iff,axiom,
% 0.26/0.56      ! [N: nat] :
% 0.26/0.56        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56         => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 0.26/0.56            = one_one_int ) )
% 0.26/0.56        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56         => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 0.26/0.56            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_one_power_iff
% 0.26/0.56  thf(fact_5437_minus__one__power__iff,axiom,
% 0.26/0.56      ! [N: nat] :
% 0.26/0.56        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 0.26/0.56            = one_one_complex ) )
% 0.26/0.56        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 0.26/0.56            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_one_power_iff
% 0.26/0.56  thf(fact_5438_minus__one__power__iff,axiom,
% 0.26/0.56      ! [N: nat] :
% 0.26/0.56        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 0.26/0.56            = one_one_Code_integer ) )
% 0.26/0.56        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 0.26/0.56            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_one_power_iff
% 0.26/0.56  thf(fact_5439_minus__one__power__iff,axiom,
% 0.26/0.56      ! [N: nat] :
% 0.26/0.56        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56         => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 0.26/0.56            = one_one_rat ) )
% 0.26/0.56        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56         => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 0.26/0.56            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_one_power_iff
% 0.26/0.56  thf(fact_5440_ln__one__minus__pos__upper__bound,axiom,
% 0.26/0.56      ! [X3: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.56       => ( ( ord_less_real @ X3 @ one_one_real )
% 0.26/0.56         => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X3 ) ) @ ( uminus_uminus_real @ X3 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % ln_one_minus_pos_upper_bound
% 0.26/0.56  thf(fact_5441_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 0.26/0.56      ! [X3: nat,N: nat,M: nat] :
% 0.26/0.56        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 0.26/0.56       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.56         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.56           => ( ord_less_nat @ ( vEBT_VEBT_low @ X3 @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % VEBT_internal.exp_split_high_low(2)
% 0.26/0.56  thf(fact_5442_log__minus__eq__powr,axiom,
% 0.26/0.56      ! [B: real,X3: real,Y3: real] :
% 0.26/0.56        ( ( ord_less_real @ zero_zero_real @ B )
% 0.26/0.56       => ( ( B != one_one_real )
% 0.26/0.56         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.56           => ( ( minus_minus_real @ ( log @ B @ X3 ) @ Y3 )
% 0.26/0.56              = ( log @ B @ ( times_times_real @ X3 @ ( powr_real @ B @ ( uminus_uminus_real @ Y3 ) ) ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % log_minus_eq_powr
% 0.26/0.56  thf(fact_5443_real__sqrt__ge__abs1,axiom,
% 0.26/0.56      ! [X3: real,Y3: real] : ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % real_sqrt_ge_abs1
% 0.26/0.56  thf(fact_5444_real__sqrt__ge__abs2,axiom,
% 0.26/0.56      ! [Y3: real,X3: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % real_sqrt_ge_abs2
% 0.26/0.56  thf(fact_5445_sqrt__sum__squares__le__sum__abs,axiom,
% 0.26/0.56      ! [X3: real,Y3: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X3 ) @ ( abs_abs_real @ Y3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % sqrt_sum_squares_le_sum_abs
% 0.26/0.56  thf(fact_5446_power__minus1__odd,axiom,
% 0.26/0.56      ! [N: nat] :
% 0.26/0.56        ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.26/0.56        = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_minus1_odd
% 0.26/0.56  thf(fact_5447_power__minus1__odd,axiom,
% 0.26/0.56      ! [N: nat] :
% 0.26/0.56        ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.26/0.56        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_minus1_odd
% 0.26/0.56  thf(fact_5448_power__minus1__odd,axiom,
% 0.26/0.56      ! [N: nat] :
% 0.26/0.56        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.26/0.56        = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_minus1_odd
% 0.26/0.56  thf(fact_5449_power__minus1__odd,axiom,
% 0.26/0.56      ! [N: nat] :
% 0.26/0.56        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.26/0.56        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_minus1_odd
% 0.26/0.56  thf(fact_5450_power__minus1__odd,axiom,
% 0.26/0.56      ! [N: nat] :
% 0.26/0.56        ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.26/0.56        = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_minus1_odd
% 0.26/0.56  thf(fact_5451_take__bit__Suc__minus__1__eq,axiom,
% 0.26/0.56      ! [N: nat] :
% 0.26/0.56        ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.26/0.56        = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_Code_integer ) ) ).
% 0.26/0.56  
% 0.26/0.56  % take_bit_Suc_minus_1_eq
% 0.26/0.56  thf(fact_5452_take__bit__Suc__minus__1__eq,axiom,
% 0.26/0.56      ! [N: nat] :
% 0.26/0.56        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.56        = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_int ) ) ).
% 0.26/0.56  
% 0.26/0.56  % take_bit_Suc_minus_1_eq
% 0.26/0.56  thf(fact_5453_take__bit__numeral__minus__1__eq,axiom,
% 0.26/0.56      ! [K: num] :
% 0.26/0.56        ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.26/0.56        = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 0.26/0.56  
% 0.26/0.56  % take_bit_numeral_minus_1_eq
% 0.26/0.56  thf(fact_5454_take__bit__numeral__minus__1__eq,axiom,
% 0.26/0.56      ! [K: num] :
% 0.26/0.56        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.56        = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 0.26/0.56  
% 0.26/0.56  % take_bit_numeral_minus_1_eq
% 0.26/0.56  thf(fact_5455_powr__neg__numeral,axiom,
% 0.26/0.56      ! [X3: real,N: num] :
% 0.26/0.56        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.56       => ( ( powr_real @ X3 @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.26/0.56          = ( divide_divide_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % powr_neg_numeral
% 0.26/0.56  thf(fact_5456_of__int__round__abs__le,axiom,
% 0.26/0.56      ! [X3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X3 ) ) @ X3 ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % of_int_round_abs_le
% 0.26/0.56  thf(fact_5457_of__int__round__abs__le,axiom,
% 0.26/0.56      ! [X3: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X3 ) ) @ X3 ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % of_int_round_abs_le
% 0.26/0.56  thf(fact_5458_round__unique_H,axiom,
% 0.26/0.56      ! [X3: real,N: int] :
% 0.26/0.56        ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ ( ring_1_of_int_real @ N ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.56       => ( ( archim8280529875227126926d_real @ X3 )
% 0.26/0.56          = N ) ) ).
% 0.26/0.56  
% 0.26/0.56  % round_unique'
% 0.26/0.56  thf(fact_5459_round__unique_H,axiom,
% 0.26/0.56      ! [X3: rat,N: int] :
% 0.26/0.56        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X3 @ ( ring_1_of_int_rat @ N ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.26/0.56       => ( ( archim7778729529865785530nd_rat @ X3 )
% 0.26/0.56          = N ) ) ).
% 0.26/0.56  
% 0.26/0.56  % round_unique'
% 0.26/0.56  thf(fact_5460_cos__x__y__le__one,axiom,
% 0.26/0.56      ! [X3: real,Y3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X3 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 0.26/0.56  
% 0.26/0.56  % cos_x_y_le_one
% 0.26/0.56  thf(fact_5461_real__sqrt__sum__squares__less,axiom,
% 0.26/0.56      ! [X3: real,U: real,Y3: real] :
% 0.26/0.56        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.26/0.56       => ( ( ord_less_real @ ( abs_abs_real @ Y3 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.26/0.56         => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % real_sqrt_sum_squares_less
% 0.26/0.56  thf(fact_5462_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 0.26/0.56      ! [X3: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.56       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 0.26/0.56         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X3 ) ) @ X3 ) ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_ln_one_plus_x_minus_x_bound_nonneg
% 0.26/0.56  thf(fact_5463_mult__less__iff1,axiom,
% 0.26/0.56      ! [Z: real,X3: real,Y3: real] :
% 0.26/0.56        ( ( ord_less_real @ zero_zero_real @ Z )
% 0.26/0.56       => ( ( ord_less_real @ ( times_times_real @ X3 @ Z ) @ ( times_times_real @ Y3 @ Z ) )
% 0.26/0.56          = ( ord_less_real @ X3 @ Y3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mult_less_iff1
% 0.26/0.56  thf(fact_5464_mult__less__iff1,axiom,
% 0.26/0.56      ! [Z: rat,X3: rat,Y3: rat] :
% 0.26/0.56        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 0.26/0.56       => ( ( ord_less_rat @ ( times_times_rat @ X3 @ Z ) @ ( times_times_rat @ Y3 @ Z ) )
% 0.26/0.56          = ( ord_less_rat @ X3 @ Y3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mult_less_iff1
% 0.26/0.56  thf(fact_5465_mult__less__iff1,axiom,
% 0.26/0.56      ! [Z: int,X3: int,Y3: int] :
% 0.26/0.56        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.26/0.56       => ( ( ord_less_int @ ( times_times_int @ X3 @ Z ) @ ( times_times_int @ Y3 @ Z ) )
% 0.26/0.56          = ( ord_less_int @ X3 @ Y3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mult_less_iff1
% 0.26/0.56  thf(fact_5466_abs__sqrt__wlog,axiom,
% 0.26/0.56      ! [P: code_integer > code_integer > $o,X3: code_integer] :
% 0.26/0.56        ( ! [X4: code_integer] :
% 0.26/0.56            ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X4 )
% 0.26/0.56           => ( P @ X4 @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.56       => ( P @ ( abs_abs_Code_integer @ X3 ) @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_sqrt_wlog
% 0.26/0.56  thf(fact_5467_abs__sqrt__wlog,axiom,
% 0.26/0.56      ! [P: real > real > $o,X3: real] :
% 0.26/0.56        ( ! [X4: real] :
% 0.26/0.56            ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.26/0.56           => ( P @ X4 @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.56       => ( P @ ( abs_abs_real @ X3 ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_sqrt_wlog
% 0.26/0.56  thf(fact_5468_abs__sqrt__wlog,axiom,
% 0.26/0.56      ! [P: rat > rat > $o,X3: rat] :
% 0.26/0.56        ( ! [X4: rat] :
% 0.26/0.56            ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 0.26/0.56           => ( P @ X4 @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.56       => ( P @ ( abs_abs_rat @ X3 ) @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_sqrt_wlog
% 0.26/0.56  thf(fact_5469_abs__sqrt__wlog,axiom,
% 0.26/0.56      ! [P: int > int > $o,X3: int] :
% 0.26/0.56        ( ! [X4: int] :
% 0.26/0.56            ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.26/0.56           => ( P @ X4 @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.56       => ( P @ ( abs_abs_int @ X3 ) @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_sqrt_wlog
% 0.26/0.56  thf(fact_5470__C5_Ohyps_C_I9_J,axiom,
% 0.26/0.56      ( ( mi != ma )
% 0.26/0.56     => ! [I2: nat] :
% 0.26/0.56          ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 0.26/0.56         => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 0.26/0.56                = I2 )
% 0.26/0.56             => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 0.26/0.56            & ! [X6: nat] :
% 0.26/0.56                ( ( ( ( vEBT_VEBT_high @ X6 @ na )
% 0.26/0.56                    = I2 )
% 0.26/0.56                  & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ ( vEBT_VEBT_low @ X6 @ na ) ) )
% 0.26/0.56               => ( ( ord_less_nat @ mi @ X6 )
% 0.26/0.56                  & ( ord_less_eq_nat @ X6 @ ma ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % "5.hyps"(9)
% 0.26/0.56  thf(fact_5471_compl__le__compl__iff,axiom,
% 0.26/0.56      ! [X3: set_nat,Y3: set_nat] :
% 0.26/0.56        ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X3 ) @ ( uminus5710092332889474511et_nat @ Y3 ) )
% 0.26/0.56        = ( ord_less_eq_set_nat @ Y3 @ X3 ) ) ).
% 0.26/0.56  
% 0.26/0.56  % compl_le_compl_iff
% 0.26/0.56  thf(fact_5472_low__def,axiom,
% 0.26/0.56      ( vEBT_VEBT_low
% 0.26/0.56      = ( ^ [X: nat,N3: nat] : ( modulo_modulo_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % low_def
% 0.26/0.56  thf(fact_5473_arctan__double,axiom,
% 0.26/0.56      ! [X3: real] :
% 0.26/0.56        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.26/0.56       => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X3 ) )
% 0.26/0.56          = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % arctan_double
% 0.26/0.56  thf(fact_5474_pochhammer__double,axiom,
% 0.26/0.56      ! [Z: complex,N: nat] :
% 0.26/0.56        ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.56        = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_double
% 0.26/0.56  thf(fact_5475_pochhammer__double,axiom,
% 0.26/0.56      ! [Z: real,N: nat] :
% 0.26/0.56        ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.56        = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_double
% 0.26/0.56  thf(fact_5476_pochhammer__double,axiom,
% 0.26/0.56      ! [Z: rat,N: nat] :
% 0.26/0.56        ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.56        = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_double
% 0.26/0.56  thf(fact_5477_mod__0,axiom,
% 0.26/0.56      ! [A: nat] :
% 0.26/0.56        ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 0.26/0.56        = zero_zero_nat ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_0
% 0.26/0.56  thf(fact_5478_mod__0,axiom,
% 0.26/0.56      ! [A: int] :
% 0.26/0.56        ( ( modulo_modulo_int @ zero_zero_int @ A )
% 0.26/0.56        = zero_zero_int ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_0
% 0.26/0.56  thf(fact_5479_mod__0,axiom,
% 0.26/0.56      ! [A: code_integer] :
% 0.26/0.56        ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 0.26/0.56        = zero_z3403309356797280102nteger ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_0
% 0.26/0.56  thf(fact_5480_mod__by__0,axiom,
% 0.26/0.56      ! [A: nat] :
% 0.26/0.56        ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 0.26/0.56        = A ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_by_0
% 0.26/0.56  thf(fact_5481_mod__by__0,axiom,
% 0.26/0.56      ! [A: int] :
% 0.26/0.56        ( ( modulo_modulo_int @ A @ zero_zero_int )
% 0.26/0.56        = A ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_by_0
% 0.26/0.56  thf(fact_5482_mod__by__0,axiom,
% 0.26/0.56      ! [A: code_integer] :
% 0.26/0.56        ( ( modulo364778990260209775nteger @ A @ zero_z3403309356797280102nteger )
% 0.26/0.56        = A ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_by_0
% 0.26/0.56  thf(fact_5483_mod__self,axiom,
% 0.26/0.56      ! [A: nat] :
% 0.26/0.56        ( ( modulo_modulo_nat @ A @ A )
% 0.26/0.56        = zero_zero_nat ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_self
% 0.26/0.56  thf(fact_5484_mod__self,axiom,
% 0.26/0.56      ! [A: int] :
% 0.26/0.56        ( ( modulo_modulo_int @ A @ A )
% 0.26/0.56        = zero_zero_int ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_self
% 0.26/0.56  thf(fact_5485_mod__self,axiom,
% 0.26/0.56      ! [A: code_integer] :
% 0.26/0.56        ( ( modulo364778990260209775nteger @ A @ A )
% 0.26/0.56        = zero_z3403309356797280102nteger ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_self
% 0.26/0.56  thf(fact_5486_bits__mod__0,axiom,
% 0.26/0.56      ! [A: nat] :
% 0.26/0.56        ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 0.26/0.56        = zero_zero_nat ) ).
% 0.26/0.56  
% 0.26/0.56  % bits_mod_0
% 0.26/0.56  thf(fact_5487_bits__mod__0,axiom,
% 0.26/0.56      ! [A: int] :
% 0.26/0.56        ( ( modulo_modulo_int @ zero_zero_int @ A )
% 0.26/0.56        = zero_zero_int ) ).
% 0.26/0.56  
% 0.26/0.56  % bits_mod_0
% 0.26/0.56  thf(fact_5488_bits__mod__0,axiom,
% 0.26/0.56      ! [A: code_integer] :
% 0.26/0.56        ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 0.26/0.56        = zero_z3403309356797280102nteger ) ).
% 0.26/0.56  
% 0.26/0.56  % bits_mod_0
% 0.26/0.56  thf(fact_5489_mod__less,axiom,
% 0.26/0.56      ! [M: nat,N: nat] :
% 0.26/0.56        ( ( ord_less_nat @ M @ N )
% 0.26/0.56       => ( ( modulo_modulo_nat @ M @ N )
% 0.26/0.56          = M ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_less
% 0.26/0.56  thf(fact_5490_arctan__eq__zero__iff,axiom,
% 0.26/0.56      ! [X3: real] :
% 0.26/0.56        ( ( ( arctan @ X3 )
% 0.26/0.56          = zero_zero_real )
% 0.26/0.56        = ( X3 = zero_zero_real ) ) ).
% 0.26/0.56  
% 0.26/0.56  % arctan_eq_zero_iff
% 0.26/0.56  thf(fact_5491_arctan__zero__zero,axiom,
% 0.26/0.56      ( ( arctan @ zero_zero_real )
% 0.26/0.56      = zero_zero_real ) ).
% 0.26/0.56  
% 0.26/0.56  % arctan_zero_zero
% 0.26/0.56  thf(fact_5492_mod__mult__self2__is__0,axiom,
% 0.26/0.56      ! [A: nat,B: nat] :
% 0.26/0.56        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 0.26/0.56        = zero_zero_nat ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_mult_self2_is_0
% 0.26/0.56  thf(fact_5493_mod__mult__self2__is__0,axiom,
% 0.26/0.56      ! [A: int,B: int] :
% 0.26/0.56        ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 0.26/0.56        = zero_zero_int ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_mult_self2_is_0
% 0.26/0.56  thf(fact_5494_mod__mult__self2__is__0,axiom,
% 0.26/0.56      ! [A: code_integer,B: code_integer] :
% 0.26/0.56        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 0.26/0.56        = zero_z3403309356797280102nteger ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_mult_self2_is_0
% 0.26/0.56  thf(fact_5495_mod__mult__self1__is__0,axiom,
% 0.26/0.56      ! [B: nat,A: nat] :
% 0.26/0.56        ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 0.26/0.56        = zero_zero_nat ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_mult_self1_is_0
% 0.26/0.56  thf(fact_5496_mod__mult__self1__is__0,axiom,
% 0.26/0.56      ! [B: int,A: int] :
% 0.26/0.56        ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 0.26/0.56        = zero_zero_int ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_mult_self1_is_0
% 0.26/0.56  thf(fact_5497_mod__mult__self1__is__0,axiom,
% 0.26/0.56      ! [B: code_integer,A: code_integer] :
% 0.26/0.56        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 0.26/0.56        = zero_z3403309356797280102nteger ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_mult_self1_is_0
% 0.26/0.56  thf(fact_5498_mod__by__1,axiom,
% 0.26/0.56      ! [A: nat] :
% 0.26/0.56        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 0.26/0.56        = zero_zero_nat ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_by_1
% 0.26/0.56  thf(fact_5499_mod__by__1,axiom,
% 0.26/0.56      ! [A: int] :
% 0.26/0.56        ( ( modulo_modulo_int @ A @ one_one_int )
% 0.26/0.56        = zero_zero_int ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_by_1
% 0.26/0.56  thf(fact_5500_mod__by__1,axiom,
% 0.26/0.56      ! [A: code_integer] :
% 0.26/0.56        ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 0.26/0.56        = zero_z3403309356797280102nteger ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_by_1
% 0.26/0.56  thf(fact_5501_bits__mod__by__1,axiom,
% 0.26/0.56      ! [A: nat] :
% 0.26/0.56        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 0.26/0.56        = zero_zero_nat ) ).
% 0.26/0.56  
% 0.26/0.56  % bits_mod_by_1
% 0.26/0.56  thf(fact_5502_bits__mod__by__1,axiom,
% 0.26/0.56      ! [A: int] :
% 0.26/0.56        ( ( modulo_modulo_int @ A @ one_one_int )
% 0.26/0.56        = zero_zero_int ) ).
% 0.26/0.56  
% 0.26/0.56  % bits_mod_by_1
% 0.26/0.56  thf(fact_5503_bits__mod__by__1,axiom,
% 0.26/0.56      ! [A: code_integer] :
% 0.26/0.56        ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 0.26/0.56        = zero_z3403309356797280102nteger ) ).
% 0.26/0.56  
% 0.26/0.56  % bits_mod_by_1
% 0.26/0.56  thf(fact_5504_mod__div__trivial,axiom,
% 0.26/0.56      ! [A: nat,B: nat] :
% 0.26/0.56        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 0.26/0.56        = zero_zero_nat ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_div_trivial
% 0.26/0.56  thf(fact_5505_mod__div__trivial,axiom,
% 0.26/0.56      ! [A: int,B: int] :
% 0.26/0.56        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 0.26/0.56        = zero_zero_int ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_div_trivial
% 0.26/0.56  thf(fact_5506_mod__div__trivial,axiom,
% 0.26/0.56      ! [A: code_integer,B: code_integer] :
% 0.26/0.56        ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 0.26/0.56        = zero_z3403309356797280102nteger ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_div_trivial
% 0.26/0.56  thf(fact_5507_bits__mod__div__trivial,axiom,
% 0.26/0.56      ! [A: nat,B: nat] :
% 0.26/0.56        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 0.26/0.56        = zero_zero_nat ) ).
% 0.26/0.56  
% 0.26/0.56  % bits_mod_div_trivial
% 0.26/0.56  thf(fact_5508_bits__mod__div__trivial,axiom,
% 0.26/0.56      ! [A: int,B: int] :
% 0.26/0.56        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 0.26/0.56        = zero_zero_int ) ).
% 0.26/0.56  
% 0.26/0.56  % bits_mod_div_trivial
% 0.26/0.56  thf(fact_5509_bits__mod__div__trivial,axiom,
% 0.26/0.56      ! [A: code_integer,B: code_integer] :
% 0.26/0.56        ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 0.26/0.56        = zero_z3403309356797280102nteger ) ).
% 0.26/0.56  
% 0.26/0.56  % bits_mod_div_trivial
% 0.26/0.56  thf(fact_5510_dvd__imp__mod__0,axiom,
% 0.26/0.56      ! [A: nat,B: nat] :
% 0.26/0.56        ( ( dvd_dvd_nat @ A @ B )
% 0.26/0.56       => ( ( modulo_modulo_nat @ B @ A )
% 0.26/0.56          = zero_zero_nat ) ) ).
% 0.26/0.56  
% 0.26/0.56  % dvd_imp_mod_0
% 0.26/0.56  thf(fact_5511_dvd__imp__mod__0,axiom,
% 0.26/0.56      ! [A: int,B: int] :
% 0.26/0.56        ( ( dvd_dvd_int @ A @ B )
% 0.26/0.56       => ( ( modulo_modulo_int @ B @ A )
% 0.26/0.56          = zero_zero_int ) ) ).
% 0.26/0.56  
% 0.26/0.56  % dvd_imp_mod_0
% 0.26/0.56  thf(fact_5512_dvd__imp__mod__0,axiom,
% 0.26/0.56      ! [A: code_integer,B: code_integer] :
% 0.26/0.56        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.26/0.56       => ( ( modulo364778990260209775nteger @ B @ A )
% 0.26/0.56          = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.56  
% 0.26/0.56  % dvd_imp_mod_0
% 0.26/0.56  thf(fact_5513_mod__by__Suc__0,axiom,
% 0.26/0.56      ! [M: nat] :
% 0.26/0.56        ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.26/0.56        = zero_zero_nat ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_by_Suc_0
% 0.26/0.56  thf(fact_5514_negative__eq__positive,axiom,
% 0.26/0.56      ! [N: nat,M: nat] :
% 0.26/0.56        ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.56          = ( semiri1314217659103216013at_int @ M ) )
% 0.26/0.56        = ( ( N = zero_zero_nat )
% 0.26/0.56          & ( M = zero_zero_nat ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % negative_eq_positive
% 0.26/0.56  thf(fact_5515_pochhammer__0,axiom,
% 0.26/0.56      ! [A: complex] :
% 0.26/0.56        ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 0.26/0.56        = one_one_complex ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_0
% 0.26/0.56  thf(fact_5516_pochhammer__0,axiom,
% 0.26/0.56      ! [A: real] :
% 0.26/0.56        ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 0.26/0.56        = one_one_real ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_0
% 0.26/0.56  thf(fact_5517_pochhammer__0,axiom,
% 0.26/0.56      ! [A: rat] :
% 0.26/0.56        ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 0.26/0.56        = one_one_rat ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_0
% 0.26/0.56  thf(fact_5518_pochhammer__0,axiom,
% 0.26/0.56      ! [A: nat] :
% 0.26/0.56        ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 0.26/0.56        = one_one_nat ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_0
% 0.26/0.56  thf(fact_5519_pochhammer__0,axiom,
% 0.26/0.56      ! [A: int] :
% 0.26/0.56        ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 0.26/0.56        = one_one_int ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_0
% 0.26/0.56  thf(fact_5520_negative__zle,axiom,
% 0.26/0.56      ! [N: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 0.26/0.56  
% 0.26/0.56  % negative_zle
% 0.26/0.56  thf(fact_5521_zero__less__arctan__iff,axiom,
% 0.26/0.56      ! [X3: real] :
% 0.26/0.56        ( ( ord_less_real @ zero_zero_real @ ( arctan @ X3 ) )
% 0.26/0.56        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 0.26/0.56  
% 0.26/0.56  % zero_less_arctan_iff
% 0.26/0.56  thf(fact_5522_arctan__less__zero__iff,axiom,
% 0.26/0.56      ! [X3: real] :
% 0.26/0.56        ( ( ord_less_real @ ( arctan @ X3 ) @ zero_zero_real )
% 0.26/0.56        = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 0.26/0.56  
% 0.26/0.56  % arctan_less_zero_iff
% 0.26/0.56  thf(fact_5523_zero__le__arctan__iff,axiom,
% 0.26/0.56      ! [X3: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X3 ) )
% 0.26/0.56        = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 0.26/0.56  
% 0.26/0.56  % zero_le_arctan_iff
% 0.26/0.56  thf(fact_5524_arctan__le__zero__iff,axiom,
% 0.26/0.56      ! [X3: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( arctan @ X3 ) @ zero_zero_real )
% 0.26/0.56        = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ).
% 0.26/0.56  
% 0.26/0.56  % arctan_le_zero_iff
% 0.26/0.56  thf(fact_5525_zdvd1__eq,axiom,
% 0.26/0.56      ! [X3: int] :
% 0.26/0.56        ( ( dvd_dvd_int @ X3 @ one_one_int )
% 0.26/0.56        = ( ( abs_abs_int @ X3 )
% 0.26/0.56          = one_one_int ) ) ).
% 0.26/0.56  
% 0.26/0.56  % zdvd1_eq
% 0.26/0.56  thf(fact_5526__C5_Ohyps_C_I5_J,axiom,
% 0.26/0.56      ! [I2: nat] :
% 0.26/0.56        ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 0.26/0.56       => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ X8 ) )
% 0.26/0.56          = ( vEBT_V8194947554948674370ptions @ summary @ I2 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % "5.hyps"(5)
% 0.26/0.56  thf(fact_5527_mod__minus1__right,axiom,
% 0.26/0.56      ! [A: int] :
% 0.26/0.56        ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.56        = zero_zero_int ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_minus1_right
% 0.26/0.56  thf(fact_5528_mod__minus1__right,axiom,
% 0.26/0.56      ! [A: code_integer] :
% 0.26/0.56        ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.26/0.56        = zero_z3403309356797280102nteger ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_minus1_right
% 0.26/0.56  thf(fact_5529_negative__zless,axiom,
% 0.26/0.56      ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 0.26/0.56  
% 0.26/0.56  % negative_zless
% 0.26/0.56  thf(fact_5530_nat__neg__numeral,axiom,
% 0.26/0.56      ! [K: num] :
% 0.26/0.56        ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.26/0.56        = zero_zero_nat ) ).
% 0.26/0.56  
% 0.26/0.56  % nat_neg_numeral
% 0.26/0.56  thf(fact_5531_nat__zminus__int,axiom,
% 0.26/0.56      ! [N: nat] :
% 0.26/0.56        ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.26/0.56        = zero_zero_nat ) ).
% 0.26/0.56  
% 0.26/0.56  % nat_zminus_int
% 0.26/0.56  thf(fact_5532_zabs__less__one__iff,axiom,
% 0.26/0.56      ! [Z: int] :
% 0.26/0.56        ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 0.26/0.56        = ( Z = zero_zero_int ) ) ).
% 0.26/0.56  
% 0.26/0.56  % zabs_less_one_iff
% 0.26/0.56  thf(fact_5533_one__mod__two__eq__one,axiom,
% 0.26/0.56      ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56      = one_one_nat ) ).
% 0.26/0.56  
% 0.26/0.56  % one_mod_two_eq_one
% 0.26/0.56  thf(fact_5534_one__mod__two__eq__one,axiom,
% 0.26/0.56      ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.56      = one_one_int ) ).
% 0.26/0.56  
% 0.26/0.56  % one_mod_two_eq_one
% 0.26/0.56  thf(fact_5535_one__mod__two__eq__one,axiom,
% 0.26/0.56      ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.26/0.56      = one_one_Code_integer ) ).
% 0.26/0.56  
% 0.26/0.56  % one_mod_two_eq_one
% 0.26/0.56  thf(fact_5536_bits__one__mod__two__eq__one,axiom,
% 0.26/0.56      ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56      = one_one_nat ) ).
% 0.26/0.56  
% 0.26/0.56  % bits_one_mod_two_eq_one
% 0.26/0.56  thf(fact_5537_bits__one__mod__two__eq__one,axiom,
% 0.26/0.56      ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.56      = one_one_int ) ).
% 0.26/0.56  
% 0.26/0.56  % bits_one_mod_two_eq_one
% 0.26/0.56  thf(fact_5538_bits__one__mod__two__eq__one,axiom,
% 0.26/0.56      ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.26/0.56      = one_one_Code_integer ) ).
% 0.26/0.56  
% 0.26/0.56  % bits_one_mod_two_eq_one
% 0.26/0.56  thf(fact_5539_even__mod__2__iff,axiom,
% 0.26/0.56      ! [A: nat] :
% 0.26/0.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.56        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 0.26/0.56  
% 0.26/0.56  % even_mod_2_iff
% 0.26/0.56  thf(fact_5540_even__mod__2__iff,axiom,
% 0.26/0.56      ! [A: int] :
% 0.26/0.56        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.26/0.56        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 0.26/0.56  
% 0.26/0.56  % even_mod_2_iff
% 0.26/0.56  thf(fact_5541_even__mod__2__iff,axiom,
% 0.26/0.56      ! [A: code_integer] :
% 0.26/0.56        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 0.26/0.56        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 0.26/0.56  
% 0.26/0.56  % even_mod_2_iff
% 0.26/0.56  thf(fact_5542_mod2__Suc__Suc,axiom,
% 0.26/0.56      ! [M: nat] :
% 0.26/0.56        ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56        = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod2_Suc_Suc
% 0.26/0.56  thf(fact_5543_Suc__times__numeral__mod__eq,axiom,
% 0.26/0.56      ! [K: num,N: nat] :
% 0.26/0.56        ( ( ( numeral_numeral_nat @ K )
% 0.26/0.56         != one_one_nat )
% 0.26/0.56       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 0.26/0.56          = one_one_nat ) ) ).
% 0.26/0.56  
% 0.26/0.56  % Suc_times_numeral_mod_eq
% 0.26/0.56  thf(fact_5544_dvd__nat__abs__iff,axiom,
% 0.26/0.56      ! [N: nat,K: int] :
% 0.26/0.56        ( ( dvd_dvd_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 0.26/0.56        = ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ).
% 0.26/0.56  
% 0.26/0.56  % dvd_nat_abs_iff
% 0.26/0.56  thf(fact_5545_nat__abs__dvd__iff,axiom,
% 0.26/0.56      ! [K: int,N: nat] :
% 0.26/0.56        ( ( dvd_dvd_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 0.26/0.56        = ( dvd_dvd_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % nat_abs_dvd_iff
% 0.26/0.56  thf(fact_5546_not__mod__2__eq__1__eq__0,axiom,
% 0.26/0.56      ! [A: nat] :
% 0.26/0.56        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56         != one_one_nat )
% 0.26/0.56        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56          = zero_zero_nat ) ) ).
% 0.26/0.56  
% 0.26/0.56  % not_mod_2_eq_1_eq_0
% 0.26/0.56  thf(fact_5547_not__mod__2__eq__1__eq__0,axiom,
% 0.26/0.56      ! [A: int] :
% 0.26/0.56        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.56         != one_one_int )
% 0.26/0.56        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.56          = zero_zero_int ) ) ).
% 0.26/0.56  
% 0.26/0.56  % not_mod_2_eq_1_eq_0
% 0.26/0.56  thf(fact_5548_not__mod__2__eq__1__eq__0,axiom,
% 0.26/0.56      ! [A: code_integer] :
% 0.26/0.56        ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.26/0.56         != one_one_Code_integer )
% 0.26/0.56        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.26/0.56          = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.56  
% 0.26/0.56  % not_mod_2_eq_1_eq_0
% 0.26/0.56  thf(fact_5549_not__mod__2__eq__0__eq__1,axiom,
% 0.26/0.56      ! [A: nat] :
% 0.26/0.56        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56         != zero_zero_nat )
% 0.26/0.56        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56          = one_one_nat ) ) ).
% 0.26/0.56  
% 0.26/0.56  % not_mod_2_eq_0_eq_1
% 0.26/0.56  thf(fact_5550_not__mod__2__eq__0__eq__1,axiom,
% 0.26/0.56      ! [A: int] :
% 0.26/0.56        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.56         != zero_zero_int )
% 0.26/0.56        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.56          = one_one_int ) ) ).
% 0.26/0.56  
% 0.26/0.56  % not_mod_2_eq_0_eq_1
% 0.26/0.56  thf(fact_5551_not__mod__2__eq__0__eq__1,axiom,
% 0.26/0.56      ! [A: code_integer] :
% 0.26/0.56        ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.26/0.56         != zero_z3403309356797280102nteger )
% 0.26/0.56        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.26/0.56          = one_one_Code_integer ) ) ).
% 0.26/0.56  
% 0.26/0.56  % not_mod_2_eq_0_eq_1
% 0.26/0.56  thf(fact_5552_bits__minus__1__mod__2__eq,axiom,
% 0.26/0.56      ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.56      = one_one_int ) ).
% 0.26/0.56  
% 0.26/0.56  % bits_minus_1_mod_2_eq
% 0.26/0.56  thf(fact_5553_bits__minus__1__mod__2__eq,axiom,
% 0.26/0.56      ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.26/0.56      = one_one_Code_integer ) ).
% 0.26/0.56  
% 0.26/0.56  % bits_minus_1_mod_2_eq
% 0.26/0.56  thf(fact_5554_minus__1__mod__2__eq,axiom,
% 0.26/0.56      ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.56      = one_one_int ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_1_mod_2_eq
% 0.26/0.56  thf(fact_5555_minus__1__mod__2__eq,axiom,
% 0.26/0.56      ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.26/0.56      = one_one_Code_integer ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_1_mod_2_eq
% 0.26/0.56  thf(fact_5556_not__mod2__eq__Suc__0__eq__0,axiom,
% 0.26/0.56      ! [N: nat] :
% 0.26/0.56        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56         != ( suc @ zero_zero_nat ) )
% 0.26/0.56        = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56          = zero_zero_nat ) ) ).
% 0.26/0.56  
% 0.26/0.56  % not_mod2_eq_Suc_0_eq_0
% 0.26/0.56  thf(fact_5557_add__self__mod__2,axiom,
% 0.26/0.56      ! [M: nat] :
% 0.26/0.56        ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56        = zero_zero_nat ) ).
% 0.26/0.56  
% 0.26/0.56  % add_self_mod_2
% 0.26/0.56  thf(fact_5558_ceiling__divide__eq__div__numeral,axiom,
% 0.26/0.56      ! [A: num,B: num] :
% 0.26/0.56        ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 0.26/0.56        = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % ceiling_divide_eq_div_numeral
% 0.26/0.56  thf(fact_5559_take__bit__Suc__0,axiom,
% 0.26/0.56      ! [A: code_integer] :
% 0.26/0.56        ( ( bit_se1745604003318907178nteger @ ( suc @ zero_zero_nat ) @ A )
% 0.26/0.56        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % take_bit_Suc_0
% 0.26/0.56  thf(fact_5560_take__bit__Suc__0,axiom,
% 0.26/0.56      ! [A: int] :
% 0.26/0.56        ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 0.26/0.56        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % take_bit_Suc_0
% 0.26/0.56  thf(fact_5561_take__bit__Suc__0,axiom,
% 0.26/0.56      ! [A: nat] :
% 0.26/0.56        ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 0.26/0.56        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % take_bit_Suc_0
% 0.26/0.56  thf(fact_5562_mod2__gr__0,axiom,
% 0.26/0.56      ! [M: nat] :
% 0.26/0.56        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.56        = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.56          = one_one_nat ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod2_gr_0
% 0.26/0.56  thf(fact_5563_floor__minus__divide__eq__div__numeral,axiom,
% 0.26/0.56      ! [A: num,B: num] :
% 0.26/0.56        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 0.26/0.56        = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % floor_minus_divide_eq_div_numeral
% 0.26/0.56  thf(fact_5564_ceiling__minus__divide__eq__div__numeral,axiom,
% 0.26/0.56      ! [A: num,B: num] :
% 0.26/0.56        ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 0.26/0.56        = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % ceiling_minus_divide_eq_div_numeral
% 0.26/0.56  thf(fact_5565__C5_Ohyps_C_I6_J,axiom,
% 0.26/0.56      ( ( mi = ma )
% 0.26/0.56     => ! [X6: vEBT_VEBT] :
% 0.26/0.56          ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ treeList ) )
% 0.26/0.56         => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_12 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % "5.hyps"(6)
% 0.26/0.56  thf(fact_5566_floor__minus__one__divide__eq__div__numeral,axiom,
% 0.26/0.56      ! [B: num] :
% 0.26/0.56        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 0.26/0.56        = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % floor_minus_one_divide_eq_div_numeral
% 0.26/0.56  thf(fact_5567_even__succ__mod__exp,axiom,
% 0.26/0.56      ! [A: nat,N: nat] :
% 0.26/0.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.56       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.56         => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.56            = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % even_succ_mod_exp
% 0.26/0.56  thf(fact_5568_even__succ__mod__exp,axiom,
% 0.26/0.56      ! [A: int,N: nat] :
% 0.26/0.56        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.56       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.56         => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.56            = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % even_succ_mod_exp
% 0.26/0.56  thf(fact_5569_even__succ__mod__exp,axiom,
% 0.26/0.56      ! [A: code_integer,N: nat] :
% 0.26/0.56        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.56       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.56         => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.56            = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % even_succ_mod_exp
% 0.26/0.56  thf(fact_5570_pochhammer__of__int,axiom,
% 0.26/0.56      ! [X3: int,N: nat] :
% 0.26/0.56        ( ( comm_s7457072308508201937r_real @ ( ring_1_of_int_real @ X3 ) @ N )
% 0.26/0.56        = ( ring_1_of_int_real @ ( comm_s4660882817536571857er_int @ X3 @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_of_int
% 0.26/0.56  thf(fact_5571_pochhammer__of__int,axiom,
% 0.26/0.56      ! [X3: int,N: nat] :
% 0.26/0.56        ( ( comm_s2602460028002588243omplex @ ( ring_17405671764205052669omplex @ X3 ) @ N )
% 0.26/0.56        = ( ring_17405671764205052669omplex @ ( comm_s4660882817536571857er_int @ X3 @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_of_int
% 0.26/0.56  thf(fact_5572_pochhammer__of__int,axiom,
% 0.26/0.56      ! [X3: int,N: nat] :
% 0.26/0.56        ( ( comm_s4028243227959126397er_rat @ ( ring_1_of_int_rat @ X3 ) @ N )
% 0.26/0.56        = ( ring_1_of_int_rat @ ( comm_s4660882817536571857er_int @ X3 @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_of_int
% 0.26/0.56  thf(fact_5573_pochhammer__of__nat,axiom,
% 0.26/0.56      ! [X3: nat,N: nat] :
% 0.26/0.56        ( ( comm_s2602460028002588243omplex @ ( semiri8010041392384452111omplex @ X3 ) @ N )
% 0.26/0.56        = ( semiri8010041392384452111omplex @ ( comm_s4663373288045622133er_nat @ X3 @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_of_nat
% 0.26/0.56  thf(fact_5574_pochhammer__of__nat,axiom,
% 0.26/0.56      ! [X3: nat,N: nat] :
% 0.26/0.56        ( ( comm_s7457072308508201937r_real @ ( semiri5074537144036343181t_real @ X3 ) @ N )
% 0.26/0.56        = ( semiri5074537144036343181t_real @ ( comm_s4663373288045622133er_nat @ X3 @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_of_nat
% 0.26/0.56  thf(fact_5575_pochhammer__of__nat,axiom,
% 0.26/0.56      ! [X3: nat,N: nat] :
% 0.26/0.56        ( ( comm_s4028243227959126397er_rat @ ( semiri681578069525770553at_rat @ X3 ) @ N )
% 0.26/0.56        = ( semiri681578069525770553at_rat @ ( comm_s4663373288045622133er_nat @ X3 @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_of_nat
% 0.26/0.56  thf(fact_5576_pochhammer__of__nat,axiom,
% 0.26/0.56      ! [X3: nat,N: nat] :
% 0.26/0.56        ( ( comm_s4663373288045622133er_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ N )
% 0.26/0.56        = ( semiri1316708129612266289at_nat @ ( comm_s4663373288045622133er_nat @ X3 @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_of_nat
% 0.26/0.56  thf(fact_5577_pochhammer__of__nat,axiom,
% 0.26/0.56      ! [X3: nat,N: nat] :
% 0.26/0.56        ( ( comm_s4660882817536571857er_int @ ( semiri1314217659103216013at_int @ X3 ) @ N )
% 0.26/0.56        = ( semiri1314217659103216013at_int @ ( comm_s4663373288045622133er_nat @ X3 @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_of_nat
% 0.26/0.56  thf(fact_5578_of__nat__mod,axiom,
% 0.26/0.56      ! [M: nat,N: nat] :
% 0.26/0.56        ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M @ N ) )
% 0.26/0.56        = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % of_nat_mod
% 0.26/0.56  thf(fact_5579_of__nat__mod,axiom,
% 0.26/0.56      ! [M: nat,N: nat] :
% 0.26/0.56        ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N ) )
% 0.26/0.56        = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % of_nat_mod
% 0.26/0.56  thf(fact_5580_of__nat__mod,axiom,
% 0.26/0.56      ! [M: nat,N: nat] :
% 0.26/0.56        ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) )
% 0.26/0.56        = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % of_nat_mod
% 0.26/0.56  thf(fact_5581_zabs__def,axiom,
% 0.26/0.56      ( abs_abs_int
% 0.26/0.56      = ( ^ [I4: int] : ( if_int @ ( ord_less_int @ I4 @ zero_zero_int ) @ ( uminus_uminus_int @ I4 ) @ I4 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % zabs_def
% 0.26/0.56  thf(fact_5582_power__mod,axiom,
% 0.26/0.56      ! [A: nat,B: nat,N: nat] :
% 0.26/0.56        ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N ) @ B )
% 0.26/0.56        = ( modulo_modulo_nat @ ( power_power_nat @ A @ N ) @ B ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_mod
% 0.26/0.56  thf(fact_5583_power__mod,axiom,
% 0.26/0.56      ! [A: int,B: int,N: nat] :
% 0.26/0.56        ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N ) @ B )
% 0.26/0.56        = ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ B ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_mod
% 0.26/0.56  thf(fact_5584_power__mod,axiom,
% 0.26/0.56      ! [A: code_integer,B: code_integer,N: nat] :
% 0.26/0.56        ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( modulo364778990260209775nteger @ A @ B ) @ N ) @ B )
% 0.26/0.56        = ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ A @ N ) @ B ) ) ).
% 0.26/0.56  
% 0.26/0.56  % power_mod
% 0.26/0.56  thf(fact_5585_mod__less__eq__dividend,axiom,
% 0.26/0.56      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_less_eq_dividend
% 0.26/0.56  thf(fact_5586_uminus__int__code_I1_J,axiom,
% 0.26/0.56      ( ( uminus_uminus_int @ zero_zero_int )
% 0.26/0.56      = zero_zero_int ) ).
% 0.26/0.56  
% 0.26/0.56  % uminus_int_code(1)
% 0.26/0.56  thf(fact_5587_zdvd__antisym__abs,axiom,
% 0.26/0.56      ! [A: int,B: int] :
% 0.26/0.56        ( ( dvd_dvd_int @ A @ B )
% 0.26/0.56       => ( ( dvd_dvd_int @ B @ A )
% 0.26/0.56         => ( ( abs_abs_int @ A )
% 0.26/0.56            = ( abs_abs_int @ B ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % zdvd_antisym_abs
% 0.26/0.56  thf(fact_5588_arctan__less__iff,axiom,
% 0.26/0.56      ! [X3: real,Y3: real] :
% 0.26/0.56        ( ( ord_less_real @ ( arctan @ X3 ) @ ( arctan @ Y3 ) )
% 0.26/0.56        = ( ord_less_real @ X3 @ Y3 ) ) ).
% 0.26/0.56  
% 0.26/0.56  % arctan_less_iff
% 0.26/0.56  thf(fact_5589_arctan__monotone,axiom,
% 0.26/0.56      ! [X3: real,Y3: real] :
% 0.26/0.56        ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.56       => ( ord_less_real @ ( arctan @ X3 ) @ ( arctan @ Y3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % arctan_monotone
% 0.26/0.56  thf(fact_5590_arctan__le__iff,axiom,
% 0.26/0.56      ! [X3: real,Y3: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ ( arctan @ X3 ) @ ( arctan @ Y3 ) )
% 0.26/0.56        = ( ord_less_eq_real @ X3 @ Y3 ) ) ).
% 0.26/0.56  
% 0.26/0.56  % arctan_le_iff
% 0.26/0.56  thf(fact_5591_arctan__monotone_H,axiom,
% 0.26/0.56      ! [X3: real,Y3: real] :
% 0.26/0.56        ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.26/0.56       => ( ord_less_eq_real @ ( arctan @ X3 ) @ ( arctan @ Y3 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % arctan_monotone'
% 0.26/0.56  thf(fact_5592_int__cases2,axiom,
% 0.26/0.56      ! [Z: int] :
% 0.26/0.56        ( ! [N2: nat] :
% 0.26/0.56            ( Z
% 0.26/0.56           != ( semiri1314217659103216013at_int @ N2 ) )
% 0.26/0.56       => ~ ! [N2: nat] :
% 0.26/0.56              ( Z
% 0.26/0.56             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % int_cases2
% 0.26/0.56  thf(fact_5593_uminus__dvd__conv_I2_J,axiom,
% 0.26/0.56      ( dvd_dvd_int
% 0.26/0.56      = ( ^ [D4: int,T2: int] : ( dvd_dvd_int @ D4 @ ( uminus_uminus_int @ T2 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % uminus_dvd_conv(2)
% 0.26/0.56  thf(fact_5594_uminus__dvd__conv_I1_J,axiom,
% 0.26/0.56      ( dvd_dvd_int
% 0.26/0.56      = ( ^ [D4: int] : ( dvd_dvd_int @ ( uminus_uminus_int @ D4 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % uminus_dvd_conv(1)
% 0.26/0.56  thf(fact_5595_take__bit__minus,axiom,
% 0.26/0.56      ! [N: nat,K: int] :
% 0.26/0.56        ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 0.26/0.56        = ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % take_bit_minus
% 0.26/0.56  thf(fact_5596_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 0.26/0.56      ! [A: code_integer,B: code_integer] :
% 0.26/0.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.26/0.56       => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B ) @ A ) ) ).
% 0.26/0.56  
% 0.26/0.56  % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 0.26/0.56  thf(fact_5597_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 0.26/0.56      ! [A: nat,B: nat] :
% 0.26/0.56        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.56       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 0.26/0.56  
% 0.26/0.56  % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 0.26/0.56  thf(fact_5598_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 0.26/0.56      ! [A: int,B: int] :
% 0.26/0.56        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.56       => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 0.26/0.56  
% 0.26/0.56  % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 0.26/0.56  thf(fact_5599_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 0.26/0.56      ! [B: nat,A: nat] :
% 0.26/0.56        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.26/0.56       => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 0.26/0.56  
% 0.26/0.56  % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 0.26/0.56  thf(fact_5600_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 0.26/0.56      ! [B: int,A: int] :
% 0.26/0.56        ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.56       => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 0.26/0.56  
% 0.26/0.56  % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 0.26/0.56  thf(fact_5601_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 0.26/0.56      ! [B: code_integer,A: code_integer] :
% 0.26/0.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.26/0.56       => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B ) ) ).
% 0.26/0.56  
% 0.26/0.56  % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 0.26/0.56  thf(fact_5602_cong__exp__iff__simps_I9_J,axiom,
% 0.26/0.56      ! [M: num,Q3: num,N: num] :
% 0.26/0.56        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 0.26/0.56          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 0.26/0.56        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 0.26/0.56          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q3 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % cong_exp_iff_simps(9)
% 0.26/0.56  thf(fact_5603_cong__exp__iff__simps_I9_J,axiom,
% 0.26/0.56      ! [M: num,Q3: num,N: num] :
% 0.26/0.56        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 0.26/0.56          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 0.26/0.56        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 0.26/0.56          = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q3 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % cong_exp_iff_simps(9)
% 0.26/0.56  thf(fact_5604_cong__exp__iff__simps_I9_J,axiom,
% 0.26/0.56      ! [M: num,Q3: num,N: num] :
% 0.26/0.56        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 0.26/0.56          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 0.26/0.56        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 0.26/0.56          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q3 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % cong_exp_iff_simps(9)
% 0.26/0.56  thf(fact_5605_mod__eq__self__iff__div__eq__0,axiom,
% 0.26/0.56      ! [A: nat,B: nat] :
% 0.26/0.56        ( ( ( modulo_modulo_nat @ A @ B )
% 0.26/0.56          = A )
% 0.26/0.56        = ( ( divide_divide_nat @ A @ B )
% 0.26/0.56          = zero_zero_nat ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_eq_self_iff_div_eq_0
% 0.26/0.56  thf(fact_5606_mod__eq__self__iff__div__eq__0,axiom,
% 0.26/0.56      ! [A: int,B: int] :
% 0.26/0.56        ( ( ( modulo_modulo_int @ A @ B )
% 0.26/0.56          = A )
% 0.26/0.56        = ( ( divide_divide_int @ A @ B )
% 0.26/0.56          = zero_zero_int ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_eq_self_iff_div_eq_0
% 0.26/0.56  thf(fact_5607_mod__eq__self__iff__div__eq__0,axiom,
% 0.26/0.56      ! [A: code_integer,B: code_integer] :
% 0.26/0.56        ( ( ( modulo364778990260209775nteger @ A @ B )
% 0.26/0.56          = A )
% 0.26/0.56        = ( ( divide6298287555418463151nteger @ A @ B )
% 0.26/0.56          = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_eq_self_iff_div_eq_0
% 0.26/0.56  thf(fact_5608_cong__exp__iff__simps_I4_J,axiom,
% 0.26/0.56      ! [M: num,N: num] :
% 0.26/0.56        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 0.26/0.56        = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % cong_exp_iff_simps(4)
% 0.26/0.56  thf(fact_5609_cong__exp__iff__simps_I4_J,axiom,
% 0.26/0.56      ! [M: num,N: num] :
% 0.26/0.56        ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 0.26/0.56        = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % cong_exp_iff_simps(4)
% 0.26/0.56  thf(fact_5610_cong__exp__iff__simps_I4_J,axiom,
% 0.26/0.56      ! [M: num,N: num] :
% 0.26/0.56        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ one ) )
% 0.26/0.56        = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % cong_exp_iff_simps(4)
% 0.26/0.56  thf(fact_5611_mod__0__imp__dvd,axiom,
% 0.26/0.56      ! [A: nat,B: nat] :
% 0.26/0.56        ( ( ( modulo_modulo_nat @ A @ B )
% 0.26/0.56          = zero_zero_nat )
% 0.26/0.56       => ( dvd_dvd_nat @ B @ A ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_0_imp_dvd
% 0.26/0.56  thf(fact_5612_mod__0__imp__dvd,axiom,
% 0.26/0.56      ! [A: int,B: int] :
% 0.26/0.56        ( ( ( modulo_modulo_int @ A @ B )
% 0.26/0.56          = zero_zero_int )
% 0.26/0.56       => ( dvd_dvd_int @ B @ A ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_0_imp_dvd
% 0.26/0.56  thf(fact_5613_mod__0__imp__dvd,axiom,
% 0.26/0.56      ! [A: code_integer,B: code_integer] :
% 0.26/0.56        ( ( ( modulo364778990260209775nteger @ A @ B )
% 0.26/0.56          = zero_z3403309356797280102nteger )
% 0.26/0.56       => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_0_imp_dvd
% 0.26/0.56  thf(fact_5614_dvd__eq__mod__eq__0,axiom,
% 0.26/0.56      ( dvd_dvd_nat
% 0.26/0.56      = ( ^ [A4: nat,B3: nat] :
% 0.26/0.56            ( ( modulo_modulo_nat @ B3 @ A4 )
% 0.26/0.56            = zero_zero_nat ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % dvd_eq_mod_eq_0
% 0.26/0.56  thf(fact_5615_dvd__eq__mod__eq__0,axiom,
% 0.26/0.56      ( dvd_dvd_int
% 0.26/0.56      = ( ^ [A4: int,B3: int] :
% 0.26/0.56            ( ( modulo_modulo_int @ B3 @ A4 )
% 0.26/0.56            = zero_zero_int ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % dvd_eq_mod_eq_0
% 0.26/0.56  thf(fact_5616_dvd__eq__mod__eq__0,axiom,
% 0.26/0.56      ( dvd_dvd_Code_integer
% 0.26/0.56      = ( ^ [A4: code_integer,B3: code_integer] :
% 0.26/0.56            ( ( modulo364778990260209775nteger @ B3 @ A4 )
% 0.26/0.56            = zero_z3403309356797280102nteger ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % dvd_eq_mod_eq_0
% 0.26/0.56  thf(fact_5617_mod__eq__0__iff__dvd,axiom,
% 0.26/0.56      ! [A: nat,B: nat] :
% 0.26/0.56        ( ( ( modulo_modulo_nat @ A @ B )
% 0.26/0.56          = zero_zero_nat )
% 0.26/0.56        = ( dvd_dvd_nat @ B @ A ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_eq_0_iff_dvd
% 0.26/0.56  thf(fact_5618_mod__eq__0__iff__dvd,axiom,
% 0.26/0.56      ! [A: int,B: int] :
% 0.26/0.56        ( ( ( modulo_modulo_int @ A @ B )
% 0.26/0.56          = zero_zero_int )
% 0.26/0.56        = ( dvd_dvd_int @ B @ A ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_eq_0_iff_dvd
% 0.26/0.56  thf(fact_5619_mod__eq__0__iff__dvd,axiom,
% 0.26/0.56      ! [A: code_integer,B: code_integer] :
% 0.26/0.56        ( ( ( modulo364778990260209775nteger @ A @ B )
% 0.26/0.56          = zero_z3403309356797280102nteger )
% 0.26/0.56        = ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_eq_0_iff_dvd
% 0.26/0.56  thf(fact_5620_mod__Suc,axiom,
% 0.26/0.56      ! [M: nat,N: nat] :
% 0.26/0.56        ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 0.26/0.56            = N )
% 0.26/0.56         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 0.26/0.56            = zero_zero_nat ) )
% 0.26/0.56        & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 0.26/0.56           != N )
% 0.26/0.56         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 0.26/0.56            = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_Suc
% 0.26/0.56  thf(fact_5621_mod__induct,axiom,
% 0.26/0.56      ! [P: nat > $o,N: nat,P6: nat,M: nat] :
% 0.26/0.56        ( ( P @ N )
% 0.26/0.56       => ( ( ord_less_nat @ N @ P6 )
% 0.26/0.56         => ( ( ord_less_nat @ M @ P6 )
% 0.26/0.56           => ( ! [N2: nat] :
% 0.26/0.56                  ( ( ord_less_nat @ N2 @ P6 )
% 0.26/0.56                 => ( ( P @ N2 )
% 0.26/0.56                   => ( P @ ( modulo_modulo_nat @ ( suc @ N2 ) @ P6 ) ) ) )
% 0.26/0.56             => ( P @ M ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_induct
% 0.26/0.56  thf(fact_5622_mod__less__divisor,axiom,
% 0.26/0.56      ! [N: nat,M: nat] :
% 0.26/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.56       => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_less_divisor
% 0.26/0.56  thf(fact_5623_gcd__nat__induct,axiom,
% 0.26/0.56      ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.26/0.56        ( ! [M4: nat] : ( P @ M4 @ zero_zero_nat )
% 0.26/0.56       => ( ! [M4: nat,N2: nat] :
% 0.26/0.56              ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.26/0.56             => ( ( P @ N2 @ ( modulo_modulo_nat @ M4 @ N2 ) )
% 0.26/0.56               => ( P @ M4 @ N2 ) ) )
% 0.26/0.56         => ( P @ M @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % gcd_nat_induct
% 0.26/0.56  thf(fact_5624_mod__Suc__le__divisor,axiom,
% 0.26/0.56      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_Suc_le_divisor
% 0.26/0.56  thf(fact_5625_mod__eq__0D,axiom,
% 0.26/0.56      ! [M: nat,D3: nat] :
% 0.26/0.56        ( ( ( modulo_modulo_nat @ M @ D3 )
% 0.26/0.56          = zero_zero_nat )
% 0.26/0.56       => ? [Q4: nat] :
% 0.26/0.56            ( M
% 0.26/0.56            = ( times_times_nat @ D3 @ Q4 ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_eq_0D
% 0.26/0.56  thf(fact_5626_mod__if,axiom,
% 0.26/0.56      ( modulo_modulo_nat
% 0.26/0.56      = ( ^ [M3: nat,N3: nat] : ( if_nat @ ( ord_less_nat @ M3 @ N3 ) @ M3 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M3 @ N3 ) @ N3 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_if
% 0.26/0.56  thf(fact_5627_mod__geq,axiom,
% 0.26/0.56      ! [M: nat,N: nat] :
% 0.26/0.56        ( ~ ( ord_less_nat @ M @ N )
% 0.26/0.56       => ( ( modulo_modulo_nat @ M @ N )
% 0.26/0.56          = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_geq
% 0.26/0.56  thf(fact_5628_le__mod__geq,axiom,
% 0.26/0.56      ! [N: nat,M: nat] :
% 0.26/0.56        ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.56       => ( ( modulo_modulo_nat @ M @ N )
% 0.26/0.56          = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % le_mod_geq
% 0.26/0.56  thf(fact_5629_pochhammer__pos,axiom,
% 0.26/0.56      ! [X3: real,N: nat] :
% 0.26/0.56        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.56       => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X3 @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_pos
% 0.26/0.56  thf(fact_5630_pochhammer__pos,axiom,
% 0.26/0.56      ! [X3: rat,N: nat] :
% 0.26/0.56        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 0.26/0.56       => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X3 @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_pos
% 0.26/0.56  thf(fact_5631_pochhammer__pos,axiom,
% 0.26/0.56      ! [X3: nat,N: nat] :
% 0.26/0.56        ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 0.26/0.56       => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X3 @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_pos
% 0.26/0.56  thf(fact_5632_pochhammer__pos,axiom,
% 0.26/0.56      ! [X3: int,N: nat] :
% 0.26/0.56        ( ( ord_less_int @ zero_zero_int @ X3 )
% 0.26/0.56       => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X3 @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_pos
% 0.26/0.56  thf(fact_5633_abs__zmult__eq__1,axiom,
% 0.26/0.56      ! [M: int,N: int] :
% 0.26/0.56        ( ( ( abs_abs_int @ ( times_times_int @ M @ N ) )
% 0.26/0.56          = one_one_int )
% 0.26/0.56       => ( ( abs_abs_int @ M )
% 0.26/0.56          = one_one_int ) ) ).
% 0.26/0.56  
% 0.26/0.56  % abs_zmult_eq_1
% 0.26/0.56  thf(fact_5634_pochhammer__neq__0__mono,axiom,
% 0.26/0.56      ! [A: real,M: nat,N: nat] :
% 0.26/0.56        ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 0.26/0.56         != zero_zero_real )
% 0.26/0.56       => ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.56         => ( ( comm_s7457072308508201937r_real @ A @ N )
% 0.26/0.56           != zero_zero_real ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_neq_0_mono
% 0.26/0.56  thf(fact_5635_pochhammer__neq__0__mono,axiom,
% 0.26/0.56      ! [A: rat,M: nat,N: nat] :
% 0.26/0.56        ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 0.26/0.56         != zero_zero_rat )
% 0.26/0.56       => ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.56         => ( ( comm_s4028243227959126397er_rat @ A @ N )
% 0.26/0.56           != zero_zero_rat ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_neq_0_mono
% 0.26/0.56  thf(fact_5636_pochhammer__eq__0__mono,axiom,
% 0.26/0.56      ! [A: real,N: nat,M: nat] :
% 0.26/0.56        ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 0.26/0.56          = zero_zero_real )
% 0.26/0.56       => ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.56         => ( ( comm_s7457072308508201937r_real @ A @ M )
% 0.26/0.56            = zero_zero_real ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_eq_0_mono
% 0.26/0.56  thf(fact_5637_pochhammer__eq__0__mono,axiom,
% 0.26/0.56      ! [A: rat,N: nat,M: nat] :
% 0.26/0.56        ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 0.26/0.56          = zero_zero_rat )
% 0.26/0.56       => ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.56         => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 0.26/0.56            = zero_zero_rat ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_eq_0_mono
% 0.26/0.56  thf(fact_5638_int__cases,axiom,
% 0.26/0.56      ! [Z: int] :
% 0.26/0.56        ( ! [N2: nat] :
% 0.26/0.56            ( Z
% 0.26/0.56           != ( semiri1314217659103216013at_int @ N2 ) )
% 0.26/0.56       => ~ ! [N2: nat] :
% 0.26/0.56              ( Z
% 0.26/0.56             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % int_cases
% 0.26/0.56  thf(fact_5639_int__of__nat__induct,axiom,
% 0.26/0.56      ! [P: int > $o,Z: int] :
% 0.26/0.56        ( ! [N2: nat] : ( P @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.26/0.56       => ( ! [N2: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) )
% 0.26/0.56         => ( P @ Z ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % int_of_nat_induct
% 0.26/0.56  thf(fact_5640_zmult__eq__1__iff,axiom,
% 0.26/0.56      ! [M: int,N: int] :
% 0.26/0.56        ( ( ( times_times_int @ M @ N )
% 0.26/0.56          = one_one_int )
% 0.26/0.56        = ( ( ( M = one_one_int )
% 0.26/0.56            & ( N = one_one_int ) )
% 0.26/0.56          | ( ( M
% 0.26/0.56              = ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.56            & ( N
% 0.26/0.56              = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % zmult_eq_1_iff
% 0.26/0.56  thf(fact_5641_pos__zmult__eq__1__iff__lemma,axiom,
% 0.26/0.56      ! [M: int,N: int] :
% 0.26/0.56        ( ( ( times_times_int @ M @ N )
% 0.26/0.56          = one_one_int )
% 0.26/0.56       => ( ( M = one_one_int )
% 0.26/0.56          | ( M
% 0.26/0.56            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pos_zmult_eq_1_iff_lemma
% 0.26/0.56  thf(fact_5642_minus__int__code_I2_J,axiom,
% 0.26/0.56      ! [L: int] :
% 0.26/0.56        ( ( minus_minus_int @ zero_zero_int @ L )
% 0.26/0.56        = ( uminus_uminus_int @ L ) ) ).
% 0.26/0.56  
% 0.26/0.56  % minus_int_code(2)
% 0.26/0.56  thf(fact_5643_not__int__zless__negative,axiom,
% 0.26/0.56      ! [N: nat,M: nat] :
% 0.26/0.56        ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % not_int_zless_negative
% 0.26/0.56  thf(fact_5644_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 0.26/0.56      ! [A: code_integer,B: code_integer] :
% 0.26/0.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.26/0.56       => ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.26/0.56         => ( ( modulo364778990260209775nteger @ A @ B )
% 0.26/0.56            = A ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % unique_euclidean_semiring_numeral_class.mod_less
% 0.26/0.56  thf(fact_5645_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 0.26/0.56      ! [A: nat,B: nat] :
% 0.26/0.56        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.56       => ( ( ord_less_nat @ A @ B )
% 0.26/0.56         => ( ( modulo_modulo_nat @ A @ B )
% 0.26/0.56            = A ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % unique_euclidean_semiring_numeral_class.mod_less
% 0.26/0.56  thf(fact_5646_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 0.26/0.56      ! [A: int,B: int] :
% 0.26/0.56        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.56       => ( ( ord_less_int @ A @ B )
% 0.26/0.56         => ( ( modulo_modulo_int @ A @ B )
% 0.26/0.56            = A ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % unique_euclidean_semiring_numeral_class.mod_less
% 0.26/0.56  thf(fact_5647_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 0.26/0.56      ! [B: code_integer,A: code_integer] :
% 0.26/0.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.26/0.56       => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 0.26/0.56  thf(fact_5648_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 0.26/0.56      ! [B: nat,A: nat] :
% 0.26/0.56        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.26/0.56       => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 0.26/0.56  thf(fact_5649_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 0.26/0.56      ! [B: int,A: int] :
% 0.26/0.56        ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.56       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 0.26/0.56  thf(fact_5650_cong__exp__iff__simps_I2_J,axiom,
% 0.26/0.56      ! [N: num,Q3: num] :
% 0.26/0.56        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 0.26/0.56          = zero_zero_nat )
% 0.26/0.56        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q3 ) )
% 0.26/0.56          = zero_zero_nat ) ) ).
% 0.26/0.56  
% 0.26/0.56  % cong_exp_iff_simps(2)
% 0.26/0.56  thf(fact_5651_cong__exp__iff__simps_I2_J,axiom,
% 0.26/0.56      ! [N: num,Q3: num] :
% 0.26/0.56        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 0.26/0.56          = zero_zero_int )
% 0.26/0.56        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q3 ) )
% 0.26/0.56          = zero_zero_int ) ) ).
% 0.26/0.56  
% 0.26/0.56  % cong_exp_iff_simps(2)
% 0.26/0.56  thf(fact_5652_cong__exp__iff__simps_I2_J,axiom,
% 0.26/0.56      ! [N: num,Q3: num] :
% 0.26/0.56        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 0.26/0.56          = zero_z3403309356797280102nteger )
% 0.26/0.56        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 0.26/0.56          = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.56  
% 0.26/0.56  % cong_exp_iff_simps(2)
% 0.26/0.56  thf(fact_5653_cong__exp__iff__simps_I1_J,axiom,
% 0.26/0.56      ! [N: num] :
% 0.26/0.56        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 0.26/0.56        = zero_zero_nat ) ).
% 0.26/0.56  
% 0.26/0.56  % cong_exp_iff_simps(1)
% 0.26/0.56  thf(fact_5654_cong__exp__iff__simps_I1_J,axiom,
% 0.26/0.56      ! [N: num] :
% 0.26/0.56        ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 0.26/0.56        = zero_zero_int ) ).
% 0.26/0.56  
% 0.26/0.56  % cong_exp_iff_simps(1)
% 0.26/0.56  thf(fact_5655_cong__exp__iff__simps_I1_J,axiom,
% 0.26/0.56      ! [N: num] :
% 0.26/0.56        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) )
% 0.26/0.56        = zero_z3403309356797280102nteger ) ).
% 0.26/0.56  
% 0.26/0.56  % cong_exp_iff_simps(1)
% 0.26/0.56  thf(fact_5656_cong__exp__iff__simps_I6_J,axiom,
% 0.26/0.56      ! [Q3: num,N: num] :
% 0.26/0.56        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 0.26/0.56       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % cong_exp_iff_simps(6)
% 0.26/0.56  thf(fact_5657_cong__exp__iff__simps_I6_J,axiom,
% 0.26/0.56      ! [Q3: num,N: num] :
% 0.26/0.56        ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 0.26/0.56       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % cong_exp_iff_simps(6)
% 0.26/0.56  thf(fact_5658_cong__exp__iff__simps_I6_J,axiom,
% 0.26/0.56      ! [Q3: num,N: num] :
% 0.26/0.56        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 0.26/0.56       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % cong_exp_iff_simps(6)
% 0.26/0.56  thf(fact_5659_cong__exp__iff__simps_I8_J,axiom,
% 0.26/0.56      ! [M: num,Q3: num] :
% 0.26/0.56        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 0.26/0.56       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % cong_exp_iff_simps(8)
% 0.26/0.56  thf(fact_5660_cong__exp__iff__simps_I8_J,axiom,
% 0.26/0.56      ! [M: num,Q3: num] :
% 0.26/0.56        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 0.26/0.56       != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % cong_exp_iff_simps(8)
% 0.26/0.56  thf(fact_5661_cong__exp__iff__simps_I8_J,axiom,
% 0.26/0.56      ! [M: num,Q3: num] :
% 0.26/0.56        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 0.26/0.56       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % cong_exp_iff_simps(8)
% 0.26/0.56  thf(fact_5662_unit__imp__mod__eq__0,axiom,
% 0.26/0.56      ! [B: nat,A: nat] :
% 0.26/0.56        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.26/0.56       => ( ( modulo_modulo_nat @ A @ B )
% 0.26/0.56          = zero_zero_nat ) ) ).
% 0.26/0.56  
% 0.26/0.56  % unit_imp_mod_eq_0
% 0.26/0.56  thf(fact_5663_unit__imp__mod__eq__0,axiom,
% 0.26/0.56      ! [B: int,A: int] :
% 0.26/0.56        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.26/0.56       => ( ( modulo_modulo_int @ A @ B )
% 0.26/0.56          = zero_zero_int ) ) ).
% 0.26/0.56  
% 0.26/0.56  % unit_imp_mod_eq_0
% 0.26/0.56  thf(fact_5664_unit__imp__mod__eq__0,axiom,
% 0.26/0.56      ! [B: code_integer,A: code_integer] :
% 0.26/0.56        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.26/0.56       => ( ( modulo364778990260209775nteger @ A @ B )
% 0.26/0.56          = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.56  
% 0.26/0.56  % unit_imp_mod_eq_0
% 0.26/0.56  thf(fact_5665_mod__le__divisor,axiom,
% 0.26/0.56      ! [N: nat,M: nat] :
% 0.26/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.56       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_le_divisor
% 0.26/0.56  thf(fact_5666_div__less__mono,axiom,
% 0.26/0.56      ! [A3: nat,B5: nat,N: nat] :
% 0.26/0.56        ( ( ord_less_nat @ A3 @ B5 )
% 0.26/0.56       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.56         => ( ( ( modulo_modulo_nat @ A3 @ N )
% 0.26/0.56              = zero_zero_nat )
% 0.26/0.56           => ( ( ( modulo_modulo_nat @ B5 @ N )
% 0.26/0.56                = zero_zero_nat )
% 0.26/0.56             => ( ord_less_nat @ ( divide_divide_nat @ A3 @ N ) @ ( divide_divide_nat @ B5 @ N ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % div_less_mono
% 0.26/0.56  thf(fact_5667_mod__greater__zero__iff__not__dvd,axiom,
% 0.26/0.56      ! [M: nat,N: nat] :
% 0.26/0.56        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 0.26/0.56        = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_greater_zero_iff_not_dvd
% 0.26/0.56  thf(fact_5668_mod__eq__nat1E,axiom,
% 0.26/0.56      ! [M: nat,Q3: nat,N: nat] :
% 0.26/0.56        ( ( ( modulo_modulo_nat @ M @ Q3 )
% 0.26/0.56          = ( modulo_modulo_nat @ N @ Q3 ) )
% 0.26/0.56       => ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.56         => ~ ! [S3: nat] :
% 0.26/0.56                ( M
% 0.26/0.56               != ( plus_plus_nat @ N @ ( times_times_nat @ Q3 @ S3 ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_eq_nat1E
% 0.26/0.56  thf(fact_5669_mod__eq__nat2E,axiom,
% 0.26/0.56      ! [M: nat,Q3: nat,N: nat] :
% 0.26/0.56        ( ( ( modulo_modulo_nat @ M @ Q3 )
% 0.26/0.56          = ( modulo_modulo_nat @ N @ Q3 ) )
% 0.26/0.56       => ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.56         => ~ ! [S3: nat] :
% 0.26/0.56                ( N
% 0.26/0.56               != ( plus_plus_nat @ M @ ( times_times_nat @ Q3 @ S3 ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_eq_nat2E
% 0.26/0.56  thf(fact_5670_nat__mod__eq__lemma,axiom,
% 0.26/0.56      ! [X3: nat,N: nat,Y3: nat] :
% 0.26/0.56        ( ( ( modulo_modulo_nat @ X3 @ N )
% 0.26/0.56          = ( modulo_modulo_nat @ Y3 @ N ) )
% 0.26/0.56       => ( ( ord_less_eq_nat @ Y3 @ X3 )
% 0.26/0.56         => ? [Q4: nat] :
% 0.26/0.56              ( X3
% 0.26/0.56              = ( plus_plus_nat @ Y3 @ ( times_times_nat @ N @ Q4 ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % nat_mod_eq_lemma
% 0.26/0.56  thf(fact_5671_div__mod__decomp,axiom,
% 0.26/0.56      ! [A3: nat,N: nat] :
% 0.26/0.56        ( A3
% 0.26/0.56        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A3 @ N ) @ N ) @ ( modulo_modulo_nat @ A3 @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % div_mod_decomp
% 0.26/0.56  thf(fact_5672_pochhammer__nonneg,axiom,
% 0.26/0.56      ! [X3: real,N: nat] :
% 0.26/0.56        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.56       => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X3 @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_nonneg
% 0.26/0.56  thf(fact_5673_pochhammer__nonneg,axiom,
% 0.26/0.56      ! [X3: rat,N: nat] :
% 0.26/0.56        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 0.26/0.56       => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X3 @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_nonneg
% 0.26/0.56  thf(fact_5674_pochhammer__nonneg,axiom,
% 0.26/0.56      ! [X3: nat,N: nat] :
% 0.26/0.56        ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 0.26/0.56       => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X3 @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_nonneg
% 0.26/0.56  thf(fact_5675_pochhammer__nonneg,axiom,
% 0.26/0.56      ! [X3: int,N: nat] :
% 0.26/0.56        ( ( ord_less_int @ zero_zero_int @ X3 )
% 0.26/0.56       => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X3 @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_nonneg
% 0.26/0.56  thf(fact_5676_mod__eq__dvd__iff__nat,axiom,
% 0.26/0.56      ! [N: nat,M: nat,Q3: nat] :
% 0.26/0.56        ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.56       => ( ( ( modulo_modulo_nat @ M @ Q3 )
% 0.26/0.56            = ( modulo_modulo_nat @ N @ Q3 ) )
% 0.26/0.56          = ( dvd_dvd_nat @ Q3 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_eq_dvd_iff_nat
% 0.26/0.56  thf(fact_5677_dvd__imp__le__int,axiom,
% 0.26/0.56      ! [I: int,D3: int] :
% 0.26/0.56        ( ( I != zero_zero_int )
% 0.26/0.56       => ( ( dvd_dvd_int @ D3 @ I )
% 0.26/0.56         => ( ord_less_eq_int @ ( abs_abs_int @ D3 ) @ ( abs_abs_int @ I ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % dvd_imp_le_int
% 0.26/0.56  thf(fact_5678_nat__abs__mult__distrib,axiom,
% 0.26/0.56      ! [W: int,Z: int] :
% 0.26/0.56        ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 0.26/0.56        = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % nat_abs_mult_distrib
% 0.26/0.56  thf(fact_5679_pochhammer__0__left,axiom,
% 0.26/0.56      ! [N: nat] :
% 0.26/0.56        ( ( ( N = zero_zero_nat )
% 0.26/0.56         => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 0.26/0.56            = one_one_complex ) )
% 0.26/0.56        & ( ( N != zero_zero_nat )
% 0.26/0.56         => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 0.26/0.56            = zero_zero_complex ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_0_left
% 0.26/0.56  thf(fact_5680_pochhammer__0__left,axiom,
% 0.26/0.56      ! [N: nat] :
% 0.26/0.56        ( ( ( N = zero_zero_nat )
% 0.26/0.56         => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 0.26/0.56            = one_one_real ) )
% 0.26/0.56        & ( ( N != zero_zero_nat )
% 0.26/0.56         => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 0.26/0.56            = zero_zero_real ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_0_left
% 0.26/0.56  thf(fact_5681_pochhammer__0__left,axiom,
% 0.26/0.56      ! [N: nat] :
% 0.26/0.56        ( ( ( N = zero_zero_nat )
% 0.26/0.56         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 0.26/0.56            = one_one_rat ) )
% 0.26/0.56        & ( ( N != zero_zero_nat )
% 0.26/0.56         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 0.26/0.56            = zero_zero_rat ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_0_left
% 0.26/0.56  thf(fact_5682_pochhammer__0__left,axiom,
% 0.26/0.56      ! [N: nat] :
% 0.26/0.56        ( ( ( N = zero_zero_nat )
% 0.26/0.56         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 0.26/0.56            = one_one_nat ) )
% 0.26/0.56        & ( ( N != zero_zero_nat )
% 0.26/0.56         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 0.26/0.56            = zero_zero_nat ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_0_left
% 0.26/0.56  thf(fact_5683_pochhammer__0__left,axiom,
% 0.26/0.56      ! [N: nat] :
% 0.26/0.56        ( ( ( N = zero_zero_nat )
% 0.26/0.56         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 0.26/0.56            = one_one_int ) )
% 0.26/0.56        & ( ( N != zero_zero_nat )
% 0.26/0.56         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 0.26/0.56            = zero_zero_int ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_0_left
% 0.26/0.56  thf(fact_5684_int__cases4,axiom,
% 0.26/0.56      ! [M: int] :
% 0.26/0.56        ( ! [N2: nat] :
% 0.26/0.56            ( M
% 0.26/0.56           != ( semiri1314217659103216013at_int @ N2 ) )
% 0.26/0.56       => ~ ! [N2: nat] :
% 0.26/0.56              ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.26/0.56             => ( M
% 0.26/0.56               != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % int_cases4
% 0.26/0.56  thf(fact_5685_int__zle__neg,axiom,
% 0.26/0.56      ! [N: nat,M: nat] :
% 0.26/0.56        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 0.26/0.56        = ( ( N = zero_zero_nat )
% 0.26/0.56          & ( M = zero_zero_nat ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % int_zle_neg
% 0.26/0.56  thf(fact_5686_negative__zle__0,axiom,
% 0.26/0.56      ! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% 0.26/0.56  
% 0.26/0.56  % negative_zle_0
% 0.26/0.56  thf(fact_5687_nonpos__int__cases,axiom,
% 0.26/0.56      ! [K: int] :
% 0.26/0.56        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 0.26/0.56       => ~ ! [N2: nat] :
% 0.26/0.56              ( K
% 0.26/0.56             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % nonpos_int_cases
% 0.26/0.56  thf(fact_5688_mod__mult2__eq_H,axiom,
% 0.26/0.56      ! [A: code_integer,M: nat,N: nat] :
% 0.26/0.56        ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 0.26/0.56        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_mult2_eq'
% 0.26/0.56  thf(fact_5689_mod__mult2__eq_H,axiom,
% 0.26/0.56      ! [A: nat,M: nat,N: nat] :
% 0.26/0.56        ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 0.26/0.56        = ( 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 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_mult2_eq'
% 0.26/0.56  thf(fact_5690_mod__mult2__eq_H,axiom,
% 0.26/0.56      ! [A: int,M: nat,N: nat] :
% 0.26/0.56        ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.26/0.56        = ( 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 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_mult2_eq'
% 0.26/0.56  thf(fact_5691_even__even__mod__4__iff,axiom,
% 0.26/0.56      ! [N: nat] :
% 0.26/0.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.56        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % even_even_mod_4_iff
% 0.26/0.56  thf(fact_5692_field__char__0__class_Oof__nat__div,axiom,
% 0.26/0.56      ! [M: nat,N: nat] :
% 0.26/0.56        ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N ) )
% 0.26/0.56        = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % field_char_0_class.of_nat_div
% 0.26/0.56  thf(fact_5693_field__char__0__class_Oof__nat__div,axiom,
% 0.26/0.56      ! [M: nat,N: nat] :
% 0.26/0.56        ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N ) )
% 0.26/0.56        = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % field_char_0_class.of_nat_div
% 0.26/0.56  thf(fact_5694_field__char__0__class_Oof__nat__div,axiom,
% 0.26/0.56      ! [M: nat,N: nat] :
% 0.26/0.56        ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N ) )
% 0.26/0.56        = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % field_char_0_class.of_nat_div
% 0.26/0.56  thf(fact_5695_split__mod,axiom,
% 0.26/0.56      ! [P: nat > $o,M: nat,N: nat] :
% 0.26/0.56        ( ( P @ ( modulo_modulo_nat @ M @ N ) )
% 0.26/0.56        = ( ( ( N = zero_zero_nat )
% 0.26/0.56           => ( P @ M ) )
% 0.26/0.56          & ( ( N != zero_zero_nat )
% 0.26/0.56           => ! [I4: nat,J3: nat] :
% 0.26/0.56                ( ( ord_less_nat @ J3 @ N )
% 0.26/0.56               => ( ( M
% 0.26/0.56                    = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J3 ) )
% 0.26/0.56                 => ( P @ J3 ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % split_mod
% 0.26/0.56  thf(fact_5696_mod__nat__eqI,axiom,
% 0.26/0.56      ! [R2: nat,N: nat,M: nat] :
% 0.26/0.56        ( ( ord_less_nat @ R2 @ N )
% 0.26/0.56       => ( ( ord_less_eq_nat @ R2 @ M )
% 0.26/0.56         => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R2 ) )
% 0.26/0.56           => ( ( modulo_modulo_nat @ M @ N )
% 0.26/0.56              = R2 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % mod_nat_eqI
% 0.26/0.56  thf(fact_5697_nat__abs__triangle__ineq,axiom,
% 0.26/0.56      ! [K: int,L: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % nat_abs_triangle_ineq
% 0.26/0.56  thf(fact_5698_zdvd__mult__cancel1,axiom,
% 0.26/0.56      ! [M: int,N: int] :
% 0.26/0.56        ( ( M != zero_zero_int )
% 0.26/0.56       => ( ( dvd_dvd_int @ ( times_times_int @ M @ N ) @ M )
% 0.26/0.56          = ( ( abs_abs_int @ N )
% 0.26/0.56            = one_one_int ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % zdvd_mult_cancel1
% 0.26/0.56  thf(fact_5699_real__of__nat__div__aux,axiom,
% 0.26/0.56      ! [X3: nat,D3: nat] :
% 0.26/0.56        ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( semiri5074537144036343181t_real @ D3 ) )
% 0.26/0.56        = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X3 @ D3 ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X3 @ D3 ) ) @ ( semiri5074537144036343181t_real @ D3 ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % real_of_nat_div_aux
% 0.26/0.56  thf(fact_5700_div__abs__eq__div__nat,axiom,
% 0.26/0.56      ! [K: int,L: int] :
% 0.26/0.56        ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 0.26/0.56        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % div_abs_eq_div_nat
% 0.26/0.56  thf(fact_5701_pochhammer__rec_H,axiom,
% 0.26/0.56      ! [Z: complex,N: nat] :
% 0.26/0.56        ( ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) )
% 0.26/0.56        = ( times_times_complex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_rec'
% 0.26/0.56  thf(fact_5702_pochhammer__rec_H,axiom,
% 0.26/0.56      ! [Z: real,N: nat] :
% 0.26/0.56        ( ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) )
% 0.26/0.56        = ( times_times_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_rec'
% 0.26/0.56  thf(fact_5703_pochhammer__rec_H,axiom,
% 0.26/0.56      ! [Z: rat,N: nat] :
% 0.26/0.56        ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) )
% 0.26/0.56        = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_rec'
% 0.26/0.56  thf(fact_5704_pochhammer__rec_H,axiom,
% 0.26/0.56      ! [Z: nat,N: nat] :
% 0.26/0.56        ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N ) )
% 0.26/0.56        = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_rec'
% 0.26/0.56  thf(fact_5705_pochhammer__rec_H,axiom,
% 0.26/0.56      ! [Z: int,N: nat] :
% 0.26/0.56        ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N ) )
% 0.26/0.56        = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z @ N ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_rec'
% 0.26/0.56  thf(fact_5706_pochhammer__Suc,axiom,
% 0.26/0.56      ! [A: complex,N: nat] :
% 0.26/0.56        ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 0.26/0.56        = ( times_times_complex @ ( comm_s2602460028002588243omplex @ A @ N ) @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_Suc
% 0.26/0.56  thf(fact_5707_pochhammer__Suc,axiom,
% 0.26/0.56      ! [A: real,N: nat] :
% 0.26/0.56        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 0.26/0.56        = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_Suc
% 0.26/0.56  thf(fact_5708_pochhammer__Suc,axiom,
% 0.26/0.56      ! [A: rat,N: nat] :
% 0.26/0.56        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 0.26/0.56        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_Suc
% 0.26/0.56  thf(fact_5709_pochhammer__Suc,axiom,
% 0.26/0.56      ! [A: nat,N: nat] :
% 0.26/0.56        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 0.26/0.56        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_Suc
% 0.26/0.56  thf(fact_5710_pochhammer__Suc,axiom,
% 0.26/0.56      ! [A: int,N: nat] :
% 0.26/0.56        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 0.26/0.56        = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_Suc
% 0.26/0.56  thf(fact_5711_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.26/0.56      ! [N: nat,K: nat] :
% 0.26/0.56        ( ( ord_less_nat @ N @ K )
% 0.26/0.56       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 0.26/0.56          = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_of_nat_eq_0_lemma
% 0.26/0.56  thf(fact_5712_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.26/0.56      ! [N: nat,K: nat] :
% 0.26/0.56        ( ( ord_less_nat @ N @ K )
% 0.26/0.56       => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 0.26/0.56          = zero_zero_complex ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_of_nat_eq_0_lemma
% 0.26/0.56  thf(fact_5713_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.26/0.56      ! [N: nat,K: nat] :
% 0.26/0.56        ( ( ord_less_nat @ N @ K )
% 0.26/0.56       => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 0.26/0.56          = zero_zero_real ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_of_nat_eq_0_lemma
% 0.26/0.56  thf(fact_5714_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.26/0.56      ! [N: nat,K: nat] :
% 0.26/0.56        ( ( ord_less_nat @ N @ K )
% 0.26/0.56       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 0.26/0.56          = zero_zero_rat ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_of_nat_eq_0_lemma
% 0.26/0.56  thf(fact_5715_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.26/0.56      ! [N: nat,K: nat] :
% 0.26/0.56        ( ( ord_less_nat @ N @ K )
% 0.26/0.56       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 0.26/0.56          = zero_zero_int ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_of_nat_eq_0_lemma
% 0.26/0.56  thf(fact_5716_pochhammer__of__nat__eq__0__iff,axiom,
% 0.26/0.56      ! [N: nat,K: nat] :
% 0.26/0.56        ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 0.26/0.56          = zero_z3403309356797280102nteger )
% 0.26/0.56        = ( ord_less_nat @ N @ K ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_of_nat_eq_0_iff
% 0.26/0.56  thf(fact_5717_pochhammer__of__nat__eq__0__iff,axiom,
% 0.26/0.56      ! [N: nat,K: nat] :
% 0.26/0.56        ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 0.26/0.56          = zero_zero_complex )
% 0.26/0.56        = ( ord_less_nat @ N @ K ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_of_nat_eq_0_iff
% 0.26/0.56  thf(fact_5718_pochhammer__of__nat__eq__0__iff,axiom,
% 0.26/0.56      ! [N: nat,K: nat] :
% 0.26/0.56        ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 0.26/0.56          = zero_zero_real )
% 0.26/0.56        = ( ord_less_nat @ N @ K ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_of_nat_eq_0_iff
% 0.26/0.56  thf(fact_5719_pochhammer__of__nat__eq__0__iff,axiom,
% 0.26/0.56      ! [N: nat,K: nat] :
% 0.26/0.56        ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 0.26/0.56          = zero_zero_rat )
% 0.26/0.56        = ( ord_less_nat @ N @ K ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_of_nat_eq_0_iff
% 0.26/0.56  thf(fact_5720_pochhammer__of__nat__eq__0__iff,axiom,
% 0.26/0.56      ! [N: nat,K: nat] :
% 0.26/0.56        ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 0.26/0.56          = zero_zero_int )
% 0.26/0.56        = ( ord_less_nat @ N @ K ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_of_nat_eq_0_iff
% 0.26/0.56  thf(fact_5721_pochhammer__eq__0__iff,axiom,
% 0.26/0.56      ! [A: complex,N: nat] :
% 0.26/0.56        ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 0.26/0.56          = zero_zero_complex )
% 0.26/0.56        = ( ? [K3: nat] :
% 0.26/0.56              ( ( ord_less_nat @ K3 @ N )
% 0.26/0.56              & ( A
% 0.26/0.56                = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K3 ) ) ) ) ) ) ).
% 0.26/0.56  
% 0.26/0.56  % pochhammer_eq_0_iff
% 0.26/0.56  thf(fact_5722_pochhammer__eq__0__iff,axiom,
% 0.26/0.56      ! [A: real,N: nat] :
% 0.26/0.56        ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 0.26/0.56          = zero_zero_real )
% 0.26/0.56        = ( ? [K3: nat] :
% 0.26/0.56              ( ( ord_less_nat @ K3 @ N )
% 0.26/0.56              & ( A
% 0.26/0.56                = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K3 ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_eq_0_iff
% 0.26/0.57  thf(fact_5723_pochhammer__eq__0__iff,axiom,
% 0.26/0.57      ! [A: rat,N: nat] :
% 0.26/0.57        ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 0.26/0.57          = zero_zero_rat )
% 0.26/0.57        = ( ? [K3: nat] :
% 0.26/0.57              ( ( ord_less_nat @ K3 @ N )
% 0.26/0.57              & ( A
% 0.26/0.57                = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_eq_0_iff
% 0.26/0.57  thf(fact_5724_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.26/0.57      ! [K: nat,N: nat] :
% 0.26/0.57        ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.57       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 0.26/0.57         != zero_z3403309356797280102nteger ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_of_nat_eq_0_lemma'
% 0.26/0.57  thf(fact_5725_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.26/0.57      ! [K: nat,N: nat] :
% 0.26/0.57        ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.57       => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 0.26/0.57         != zero_zero_complex ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_of_nat_eq_0_lemma'
% 0.26/0.57  thf(fact_5726_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.26/0.57      ! [K: nat,N: nat] :
% 0.26/0.57        ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.57       => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 0.26/0.57         != zero_zero_real ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_of_nat_eq_0_lemma'
% 0.26/0.57  thf(fact_5727_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.26/0.57      ! [K: nat,N: nat] :
% 0.26/0.57        ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.57       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 0.26/0.57         != zero_zero_rat ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_of_nat_eq_0_lemma'
% 0.26/0.57  thf(fact_5728_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.26/0.57      ! [K: nat,N: nat] :
% 0.26/0.57        ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.57       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 0.26/0.57         != zero_zero_int ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_of_nat_eq_0_lemma'
% 0.26/0.57  thf(fact_5729_pochhammer__product_H,axiom,
% 0.26/0.57      ! [Z: complex,N: nat,M: nat] :
% 0.26/0.57        ( ( comm_s2602460028002588243omplex @ Z @ ( plus_plus_nat @ N @ M ) )
% 0.26/0.57        = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ N ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N ) ) @ M ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_product'
% 0.26/0.57  thf(fact_5730_pochhammer__product_H,axiom,
% 0.26/0.57      ! [Z: real,N: nat,M: nat] :
% 0.26/0.57        ( ( comm_s7457072308508201937r_real @ Z @ ( plus_plus_nat @ N @ M ) )
% 0.26/0.57        = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ N ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ M ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_product'
% 0.26/0.57  thf(fact_5731_pochhammer__product_H,axiom,
% 0.26/0.57      ! [Z: rat,N: nat,M: nat] :
% 0.26/0.57        ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N @ M ) )
% 0.26/0.57        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ M ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_product'
% 0.26/0.57  thf(fact_5732_pochhammer__product_H,axiom,
% 0.26/0.57      ! [Z: nat,N: nat,M: nat] :
% 0.26/0.57        ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N @ M ) )
% 0.26/0.57        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ M ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_product'
% 0.26/0.57  thf(fact_5733_pochhammer__product_H,axiom,
% 0.26/0.57      ! [Z: int,N: nat,M: nat] :
% 0.26/0.57        ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N @ M ) )
% 0.26/0.57        = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ M ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_product'
% 0.26/0.57  thf(fact_5734_int__cases3,axiom,
% 0.26/0.57      ! [K: int] :
% 0.26/0.57        ( ( K != zero_zero_int )
% 0.26/0.57       => ( ! [N2: nat] :
% 0.26/0.57              ( ( K
% 0.26/0.57                = ( semiri1314217659103216013at_int @ N2 ) )
% 0.26/0.57             => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 0.26/0.57         => ~ ! [N2: nat] :
% 0.26/0.57                ( ( K
% 0.26/0.57                  = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.26/0.57               => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % int_cases3
% 0.26/0.57  thf(fact_5735_not__zle__0__negative,axiom,
% 0.26/0.57      ! [N: nat] :
% 0.26/0.57        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % not_zle_0_negative
% 0.26/0.57  thf(fact_5736_negD,axiom,
% 0.26/0.57      ! [X3: int] :
% 0.26/0.57        ( ( ord_less_int @ X3 @ zero_zero_int )
% 0.26/0.57       => ? [N2: nat] :
% 0.26/0.57            ( X3
% 0.26/0.57            = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % negD
% 0.26/0.57  thf(fact_5737_negative__zless__0,axiom,
% 0.26/0.57      ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 0.26/0.57  
% 0.26/0.57  % negative_zless_0
% 0.26/0.57  thf(fact_5738_verit__less__mono__div__int2,axiom,
% 0.26/0.57      ! [A3: int,B5: int,N: int] :
% 0.26/0.57        ( ( ord_less_eq_int @ A3 @ B5 )
% 0.26/0.57       => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 0.26/0.57         => ( ord_less_eq_int @ ( divide_divide_int @ B5 @ N ) @ ( divide_divide_int @ A3 @ N ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % verit_less_mono_div_int2
% 0.26/0.57  thf(fact_5739_div__eq__minus1,axiom,
% 0.26/0.57      ! [B: int] :
% 0.26/0.57        ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.57       => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 0.26/0.57          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % div_eq_minus1
% 0.26/0.57  thf(fact_5740_ceiling__divide__eq__div,axiom,
% 0.26/0.57      ! [A: int,B: int] :
% 0.26/0.57        ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) )
% 0.26/0.57        = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % ceiling_divide_eq_div
% 0.26/0.57  thf(fact_5741_ceiling__divide__eq__div,axiom,
% 0.26/0.57      ! [A: int,B: int] :
% 0.26/0.57        ( ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B ) ) )
% 0.26/0.57        = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % ceiling_divide_eq_div
% 0.26/0.57  thf(fact_5742_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.26/0.57      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.26/0.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.26/0.57       => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.26/0.57          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.26/0.57  thf(fact_5743_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.26/0.57      ! [C: nat,A: nat,B: nat] :
% 0.26/0.57        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.26/0.57       => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.26/0.57          = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.26/0.57  thf(fact_5744_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.26/0.57      ! [C: int,A: int,B: int] :
% 0.26/0.57        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.26/0.57       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 0.26/0.57          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.26/0.57  thf(fact_5745_even__iff__mod__2__eq__zero,axiom,
% 0.26/0.57      ! [A: nat] :
% 0.26/0.57        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.57        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.57          = zero_zero_nat ) ) ).
% 0.26/0.57  
% 0.26/0.57  % even_iff_mod_2_eq_zero
% 0.26/0.57  thf(fact_5746_even__iff__mod__2__eq__zero,axiom,
% 0.26/0.57      ! [A: int] :
% 0.26/0.57        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.57        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.57          = zero_zero_int ) ) ).
% 0.26/0.57  
% 0.26/0.57  % even_iff_mod_2_eq_zero
% 0.26/0.57  thf(fact_5747_even__iff__mod__2__eq__zero,axiom,
% 0.26/0.57      ! [A: code_integer] :
% 0.26/0.57        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.57        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.26/0.57          = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.57  
% 0.26/0.57  % even_iff_mod_2_eq_zero
% 0.26/0.57  thf(fact_5748_odd__iff__mod__2__eq__one,axiom,
% 0.26/0.57      ! [A: nat] :
% 0.26/0.57        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 0.26/0.57        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.57          = one_one_nat ) ) ).
% 0.26/0.57  
% 0.26/0.57  % odd_iff_mod_2_eq_one
% 0.26/0.57  thf(fact_5749_odd__iff__mod__2__eq__one,axiom,
% 0.26/0.57      ! [A: int] :
% 0.26/0.57        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.26/0.57        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.57          = one_one_int ) ) ).
% 0.26/0.57  
% 0.26/0.57  % odd_iff_mod_2_eq_one
% 0.26/0.57  thf(fact_5750_odd__iff__mod__2__eq__one,axiom,
% 0.26/0.57      ! [A: code_integer] :
% 0.26/0.57        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 0.26/0.57        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.26/0.57          = one_one_Code_integer ) ) ).
% 0.26/0.57  
% 0.26/0.57  % odd_iff_mod_2_eq_one
% 0.26/0.57  thf(fact_5751_take__bit__eq__mod,axiom,
% 0.26/0.57      ( bit_se1745604003318907178nteger
% 0.26/0.57      = ( ^ [N3: nat,A4: code_integer] : ( modulo364778990260209775nteger @ A4 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % take_bit_eq_mod
% 0.26/0.57  thf(fact_5752_take__bit__eq__mod,axiom,
% 0.26/0.57      ( bit_se2923211474154528505it_int
% 0.26/0.57      = ( ^ [N3: nat,A4: int] : ( modulo_modulo_int @ A4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % take_bit_eq_mod
% 0.26/0.57  thf(fact_5753_take__bit__eq__mod,axiom,
% 0.26/0.57      ( bit_se2925701944663578781it_nat
% 0.26/0.57      = ( ^ [N3: nat,A4: nat] : ( modulo_modulo_nat @ A4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % take_bit_eq_mod
% 0.26/0.57  thf(fact_5754_Suc__times__mod__eq,axiom,
% 0.26/0.57      ! [M: nat,N: nat] :
% 0.26/0.57        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.26/0.57       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 0.26/0.57          = one_one_nat ) ) ).
% 0.26/0.57  
% 0.26/0.57  % Suc_times_mod_eq
% 0.26/0.57  thf(fact_5755_even__abs__add__iff,axiom,
% 0.26/0.57      ! [K: int,L: int] :
% 0.26/0.57        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L ) )
% 0.26/0.57        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % even_abs_add_iff
% 0.26/0.57  thf(fact_5756_even__add__abs__iff,axiom,
% 0.26/0.57      ! [K: int,L: int] :
% 0.26/0.57        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L ) ) )
% 0.26/0.57        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % even_add_abs_iff
% 0.26/0.57  thf(fact_5757_nat__abs__int__diff,axiom,
% 0.26/0.57      ! [A: nat,B: nat] :
% 0.26/0.57        ( ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.57         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 0.26/0.57            = ( minus_minus_nat @ B @ A ) ) )
% 0.26/0.57        & ( ~ ( ord_less_eq_nat @ A @ B )
% 0.26/0.57         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 0.26/0.57            = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % nat_abs_int_diff
% 0.26/0.57  thf(fact_5758_take__bit__nat__def,axiom,
% 0.26/0.57      ( bit_se2925701944663578781it_nat
% 0.26/0.57      = ( ^ [N3: nat,M3: nat] : ( modulo_modulo_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % take_bit_nat_def
% 0.26/0.57  thf(fact_5759_neg__int__cases,axiom,
% 0.26/0.57      ! [K: int] :
% 0.26/0.57        ( ( ord_less_int @ K @ zero_zero_int )
% 0.26/0.57       => ~ ! [N2: nat] :
% 0.26/0.57              ( ( K
% 0.26/0.57                = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.26/0.57             => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % neg_int_cases
% 0.26/0.57  thf(fact_5760_pochhammer__product,axiom,
% 0.26/0.57      ! [M: nat,N: nat,Z: complex] :
% 0.26/0.57        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.57       => ( ( comm_s2602460028002588243omplex @ Z @ N )
% 0.26/0.57          = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ M ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_product
% 0.26/0.57  thf(fact_5761_pochhammer__product,axiom,
% 0.26/0.57      ! [M: nat,N: nat,Z: real] :
% 0.26/0.57        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.57       => ( ( comm_s7457072308508201937r_real @ Z @ N )
% 0.26/0.57          = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_product
% 0.26/0.57  thf(fact_5762_pochhammer__product,axiom,
% 0.26/0.57      ! [M: nat,N: nat,Z: rat] :
% 0.26/0.57        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.57       => ( ( comm_s4028243227959126397er_rat @ Z @ N )
% 0.26/0.57          = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_product
% 0.26/0.57  thf(fact_5763_pochhammer__product,axiom,
% 0.26/0.57      ! [M: nat,N: nat,Z: nat] :
% 0.26/0.57        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.57       => ( ( comm_s4663373288045622133er_nat @ Z @ N )
% 0.26/0.57          = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_product
% 0.26/0.57  thf(fact_5764_pochhammer__product,axiom,
% 0.26/0.57      ! [M: nat,N: nat,Z: int] :
% 0.26/0.57        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.57       => ( ( comm_s4660882817536571857er_int @ Z @ N )
% 0.26/0.57          = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_product
% 0.26/0.57  thf(fact_5765_nat__mult__distrib__neg,axiom,
% 0.26/0.57      ! [Z: int,Z5: int] :
% 0.26/0.57        ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 0.26/0.57       => ( ( nat2 @ ( times_times_int @ Z @ Z5 ) )
% 0.26/0.57          = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z5 ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % nat_mult_distrib_neg
% 0.26/0.57  thf(fact_5766_divmod__digit__0_I2_J,axiom,
% 0.26/0.57      ! [B: nat,A: nat] :
% 0.26/0.57        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.26/0.57       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.26/0.57         => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 0.26/0.57            = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % divmod_digit_0(2)
% 0.26/0.57  thf(fact_5767_divmod__digit__0_I2_J,axiom,
% 0.26/0.57      ! [B: int,A: int] :
% 0.26/0.57        ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.57       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.26/0.57         => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 0.26/0.57            = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % divmod_digit_0(2)
% 0.26/0.57  thf(fact_5768_divmod__digit__0_I2_J,axiom,
% 0.26/0.57      ! [B: code_integer,A: code_integer] :
% 0.26/0.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.26/0.57       => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.26/0.57         => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 0.26/0.57            = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % divmod_digit_0(2)
% 0.26/0.57  thf(fact_5769_bits__stable__imp__add__self,axiom,
% 0.26/0.57      ! [A: nat] :
% 0.26/0.57        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.57          = A )
% 0.26/0.57       => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.57          = zero_zero_nat ) ) ).
% 0.26/0.57  
% 0.26/0.57  % bits_stable_imp_add_self
% 0.26/0.57  thf(fact_5770_bits__stable__imp__add__self,axiom,
% 0.26/0.57      ! [A: int] :
% 0.26/0.57        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.57          = A )
% 0.26/0.57       => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.26/0.57          = zero_zero_int ) ) ).
% 0.26/0.57  
% 0.26/0.57  % bits_stable_imp_add_self
% 0.26/0.57  thf(fact_5771_bits__stable__imp__add__self,axiom,
% 0.26/0.57      ! [A: code_integer] :
% 0.26/0.57        ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.26/0.57          = A )
% 0.26/0.57       => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 0.26/0.57          = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.57  
% 0.26/0.57  % bits_stable_imp_add_self
% 0.26/0.57  thf(fact_5772_parity__cases,axiom,
% 0.26/0.57      ! [A: nat] :
% 0.26/0.57        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.57         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.57           != zero_zero_nat ) )
% 0.26/0.57       => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.57           => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.57             != one_one_nat ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % parity_cases
% 0.26/0.57  thf(fact_5773_parity__cases,axiom,
% 0.26/0.57      ! [A: int] :
% 0.26/0.57        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.57         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.57           != zero_zero_int ) )
% 0.26/0.57       => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.57           => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.57             != one_one_int ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % parity_cases
% 0.26/0.57  thf(fact_5774_parity__cases,axiom,
% 0.26/0.57      ! [A: code_integer] :
% 0.26/0.57        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.57         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.26/0.57           != zero_z3403309356797280102nteger ) )
% 0.26/0.57       => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.57           => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.26/0.57             != one_one_Code_integer ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % parity_cases
% 0.26/0.57  thf(fact_5775_mod2__eq__if,axiom,
% 0.26/0.57      ! [A: nat] :
% 0.26/0.57        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.57         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.57            = zero_zero_nat ) )
% 0.26/0.57        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.26/0.57         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.57            = one_one_nat ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % mod2_eq_if
% 0.26/0.57  thf(fact_5776_mod2__eq__if,axiom,
% 0.26/0.57      ! [A: int] :
% 0.26/0.57        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.57         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.57            = zero_zero_int ) )
% 0.26/0.57        & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.26/0.57         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.57            = one_one_int ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % mod2_eq_if
% 0.26/0.57  thf(fact_5777_mod2__eq__if,axiom,
% 0.26/0.57      ! [A: code_integer] :
% 0.26/0.57        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.57         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.26/0.57            = zero_z3403309356797280102nteger ) )
% 0.26/0.57        & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.26/0.57         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.26/0.57            = one_one_Code_integer ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % mod2_eq_if
% 0.26/0.57  thf(fact_5778_div__exp__mod__exp__eq,axiom,
% 0.26/0.57      ! [A: nat,N: nat,M: nat] :
% 0.26/0.57        ( ( 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 ) )
% 0.26/0.57        = ( 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 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % div_exp_mod_exp_eq
% 0.26/0.57  thf(fact_5779_div__exp__mod__exp__eq,axiom,
% 0.26/0.57      ! [A: int,N: nat,M: nat] :
% 0.26/0.57        ( ( 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 ) )
% 0.26/0.57        = ( 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 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % div_exp_mod_exp_eq
% 0.26/0.57  thf(fact_5780_div__exp__mod__exp__eq,axiom,
% 0.26/0.57      ! [A: code_integer,N: nat,M: nat] :
% 0.26/0.57        ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 0.26/0.57        = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % div_exp_mod_exp_eq
% 0.26/0.57  thf(fact_5781_verit__le__mono__div,axiom,
% 0.26/0.57      ! [A3: nat,B5: nat,N: nat] :
% 0.26/0.57        ( ( ord_less_nat @ A3 @ B5 )
% 0.26/0.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.57         => ( ord_less_eq_nat
% 0.26/0.57            @ ( plus_plus_nat @ ( divide_divide_nat @ A3 @ N )
% 0.26/0.57              @ ( if_nat
% 0.26/0.57                @ ( ( modulo_modulo_nat @ B5 @ N )
% 0.26/0.57                  = zero_zero_nat )
% 0.26/0.57                @ one_one_nat
% 0.26/0.57                @ zero_zero_nat ) )
% 0.26/0.57            @ ( divide_divide_nat @ B5 @ N ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % verit_le_mono_div
% 0.26/0.57  thf(fact_5782_nat__intermed__int__val,axiom,
% 0.26/0.57      ! [M: nat,N: nat,F: nat > int,K: int] :
% 0.26/0.57        ( ! [I3: nat] :
% 0.26/0.57            ( ( ( ord_less_eq_nat @ M @ I3 )
% 0.26/0.57              & ( ord_less_nat @ I3 @ N ) )
% 0.26/0.57           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 0.26/0.57       => ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.57         => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 0.26/0.57           => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 0.26/0.57             => ? [I3: nat] :
% 0.26/0.57                  ( ( ord_less_eq_nat @ M @ I3 )
% 0.26/0.57                  & ( ord_less_eq_nat @ I3 @ N )
% 0.26/0.57                  & ( ( F @ I3 )
% 0.26/0.57                    = K ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % nat_intermed_int_val
% 0.26/0.57  thf(fact_5783_decr__lemma,axiom,
% 0.26/0.57      ! [D3: int,X3: int,Z: int] :
% 0.26/0.57        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.26/0.57       => ( ord_less_int @ ( minus_minus_int @ X3 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X3 @ Z ) ) @ one_one_int ) @ D3 ) ) @ Z ) ) ).
% 0.26/0.57  
% 0.26/0.57  % decr_lemma
% 0.26/0.57  thf(fact_5784_incr__lemma,axiom,
% 0.26/0.57      ! [D3: int,Z: int,X3: int] :
% 0.26/0.57        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.26/0.57       => ( ord_less_int @ Z @ ( plus_plus_int @ X3 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X3 @ Z ) ) @ one_one_int ) @ D3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % incr_lemma
% 0.26/0.57  thf(fact_5785_pochhammer__absorb__comp,axiom,
% 0.26/0.57      ! [R2: code_integer,K: nat] :
% 0.26/0.57        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R2 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R2 ) @ K ) )
% 0.26/0.57        = ( times_3573771949741848930nteger @ R2 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_absorb_comp
% 0.26/0.57  thf(fact_5786_pochhammer__absorb__comp,axiom,
% 0.26/0.57      ! [R2: complex,K: nat] :
% 0.26/0.57        ( ( times_times_complex @ ( minus_minus_complex @ R2 @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R2 ) @ K ) )
% 0.26/0.57        = ( times_times_complex @ R2 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R2 ) @ one_one_complex ) @ K ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_absorb_comp
% 0.26/0.57  thf(fact_5787_pochhammer__absorb__comp,axiom,
% 0.26/0.57      ! [R2: real,K: nat] :
% 0.26/0.57        ( ( times_times_real @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R2 ) @ K ) )
% 0.26/0.57        = ( times_times_real @ R2 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R2 ) @ one_one_real ) @ K ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_absorb_comp
% 0.26/0.57  thf(fact_5788_pochhammer__absorb__comp,axiom,
% 0.26/0.57      ! [R2: rat,K: nat] :
% 0.26/0.57        ( ( times_times_rat @ ( minus_minus_rat @ R2 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R2 ) @ K ) )
% 0.26/0.57        = ( times_times_rat @ R2 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R2 ) @ one_one_rat ) @ K ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_absorb_comp
% 0.26/0.57  thf(fact_5789_pochhammer__absorb__comp,axiom,
% 0.26/0.57      ! [R2: int,K: nat] :
% 0.26/0.57        ( ( times_times_int @ ( minus_minus_int @ R2 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R2 ) @ K ) )
% 0.26/0.57        = ( times_times_int @ R2 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R2 ) @ one_one_int ) @ K ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_absorb_comp
% 0.26/0.57  thf(fact_5790_take__bit__Suc__minus__bit0,axiom,
% 0.26/0.57      ! [N: nat,K: num] :
% 0.26/0.57        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.26/0.57        = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % take_bit_Suc_minus_bit0
% 0.26/0.57  thf(fact_5791_minus__1__div__exp__eq__int,axiom,
% 0.26/0.57      ! [N: nat] :
% 0.26/0.57        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.57        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.57  
% 0.26/0.57  % minus_1_div_exp_eq_int
% 0.26/0.57  thf(fact_5792_div__pos__neg__trivial,axiom,
% 0.26/0.57      ! [K: int,L: int] :
% 0.26/0.57        ( ( ord_less_int @ zero_zero_int @ K )
% 0.26/0.57       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 0.26/0.57         => ( ( divide_divide_int @ K @ L )
% 0.26/0.57            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % div_pos_neg_trivial
% 0.26/0.57  thf(fact_5793_divmod__digit__0_I1_J,axiom,
% 0.26/0.57      ! [B: nat,A: nat] :
% 0.26/0.57        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.26/0.57       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.26/0.57         => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 0.26/0.57            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % divmod_digit_0(1)
% 0.26/0.57  thf(fact_5794_divmod__digit__0_I1_J,axiom,
% 0.26/0.57      ! [B: int,A: int] :
% 0.26/0.57        ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.57       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.26/0.57         => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 0.26/0.57            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % divmod_digit_0(1)
% 0.26/0.57  thf(fact_5795_divmod__digit__0_I1_J,axiom,
% 0.26/0.57      ! [B: code_integer,A: code_integer] :
% 0.26/0.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.26/0.57       => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.26/0.57         => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 0.26/0.57            = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % divmod_digit_0(1)
% 0.26/0.57  thf(fact_5796_mult__exp__mod__exp__eq,axiom,
% 0.26/0.57      ! [M: nat,N: nat,A: nat] :
% 0.26/0.57        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.57       => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.57          = ( 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 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % mult_exp_mod_exp_eq
% 0.26/0.57  thf(fact_5797_mult__exp__mod__exp__eq,axiom,
% 0.26/0.57      ! [M: nat,N: nat,A: int] :
% 0.26/0.57        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.57       => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.57          = ( 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 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % mult_exp_mod_exp_eq
% 0.26/0.57  thf(fact_5798_mult__exp__mod__exp__eq,axiom,
% 0.26/0.57      ! [M: nat,N: nat,A: code_integer] :
% 0.26/0.57        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.57       => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.57          = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % mult_exp_mod_exp_eq
% 0.26/0.57  thf(fact_5799_compl__le__swap2,axiom,
% 0.26/0.57      ! [Y3: set_nat,X3: set_nat] :
% 0.26/0.57        ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y3 ) @ X3 )
% 0.26/0.57       => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X3 ) @ Y3 ) ) ).
% 0.26/0.57  
% 0.26/0.57  % compl_le_swap2
% 0.26/0.57  thf(fact_5800_compl__le__swap1,axiom,
% 0.26/0.57      ! [Y3: set_nat,X3: set_nat] :
% 0.26/0.57        ( ( ord_less_eq_set_nat @ Y3 @ ( uminus5710092332889474511et_nat @ X3 ) )
% 0.26/0.57       => ( ord_less_eq_set_nat @ X3 @ ( uminus5710092332889474511et_nat @ Y3 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % compl_le_swap1
% 0.26/0.57  thf(fact_5801_compl__mono,axiom,
% 0.26/0.57      ! [X3: set_nat,Y3: set_nat] :
% 0.26/0.57        ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 0.26/0.57       => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y3 ) @ ( uminus5710092332889474511et_nat @ X3 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % compl_mono
% 0.26/0.57  thf(fact_5802_nat__ivt__aux,axiom,
% 0.26/0.57      ! [N: nat,F: nat > int,K: int] :
% 0.26/0.57        ( ! [I3: nat] :
% 0.26/0.57            ( ( ord_less_nat @ I3 @ N )
% 0.26/0.57           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 0.26/0.57       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 0.26/0.57         => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 0.26/0.57           => ? [I3: nat] :
% 0.26/0.57                ( ( ord_less_eq_nat @ I3 @ N )
% 0.26/0.57                & ( ( F @ I3 )
% 0.26/0.57                  = K ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % nat_ivt_aux
% 0.26/0.57  thf(fact_5803_complex__mod__minus__le__complex__mod,axiom,
% 0.26/0.57      ! [X3: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X3 ) ) @ ( real_V1022390504157884413omplex @ X3 ) ) ).
% 0.26/0.57  
% 0.26/0.57  % complex_mod_minus_le_complex_mod
% 0.26/0.57  thf(fact_5804_pochhammer__minus,axiom,
% 0.26/0.57      ! [B: code_integer,K: nat] :
% 0.26/0.57        ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 0.26/0.57        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_minus
% 0.26/0.57  thf(fact_5805_pochhammer__minus,axiom,
% 0.26/0.57      ! [B: complex,K: nat] :
% 0.26/0.57        ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 0.26/0.57        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_minus
% 0.26/0.57  thf(fact_5806_pochhammer__minus,axiom,
% 0.26/0.57      ! [B: real,K: nat] :
% 0.26/0.57        ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 0.26/0.57        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_minus
% 0.26/0.57  thf(fact_5807_pochhammer__minus,axiom,
% 0.26/0.57      ! [B: rat,K: nat] :
% 0.26/0.57        ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 0.26/0.57        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_minus
% 0.26/0.57  thf(fact_5808_pochhammer__minus,axiom,
% 0.26/0.57      ! [B: int,K: nat] :
% 0.26/0.57        ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 0.26/0.57        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_minus
% 0.26/0.57  thf(fact_5809_pochhammer__minus_H,axiom,
% 0.26/0.57      ! [B: code_integer,K: nat] :
% 0.26/0.57        ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 0.26/0.57        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_minus'
% 0.26/0.57  thf(fact_5810_pochhammer__minus_H,axiom,
% 0.26/0.57      ! [B: complex,K: nat] :
% 0.26/0.57        ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 0.26/0.57        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_minus'
% 0.26/0.57  thf(fact_5811_pochhammer__minus_H,axiom,
% 0.26/0.57      ! [B: real,K: nat] :
% 0.26/0.57        ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 0.26/0.57        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_minus'
% 0.26/0.57  thf(fact_5812_pochhammer__minus_H,axiom,
% 0.26/0.57      ! [B: rat,K: nat] :
% 0.26/0.57        ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 0.26/0.57        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_minus'
% 0.26/0.57  thf(fact_5813_pochhammer__minus_H,axiom,
% 0.26/0.57      ! [B: int,K: nat] :
% 0.26/0.57        ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 0.26/0.57        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pochhammer_minus'
% 0.26/0.57  thf(fact_5814_complex__mod__triangle__ineq2,axiom,
% 0.26/0.57      ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 0.26/0.57  
% 0.26/0.57  % complex_mod_triangle_ineq2
% 0.26/0.57  thf(fact_5815_int__bit__induct,axiom,
% 0.26/0.57      ! [P: int > $o,K: int] :
% 0.26/0.57        ( ( P @ zero_zero_int )
% 0.26/0.57       => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.57         => ( ! [K2: int] :
% 0.26/0.57                ( ( P @ K2 )
% 0.26/0.57               => ( ( K2 != zero_zero_int )
% 0.26/0.57                 => ( P @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.57           => ( ! [K2: int] :
% 0.26/0.57                  ( ( P @ K2 )
% 0.26/0.57                 => ( ( K2
% 0.26/0.57                     != ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.57                   => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 0.26/0.57             => ( P @ K ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % int_bit_induct
% 0.26/0.57  thf(fact_5816_mod__double__modulus,axiom,
% 0.26/0.57      ! [M: code_integer,X3: code_integer] :
% 0.26/0.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 0.26/0.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 0.26/0.57         => ( ( ( modulo364778990260209775nteger @ X3 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 0.26/0.57              = ( modulo364778990260209775nteger @ X3 @ M ) )
% 0.26/0.57            | ( ( modulo364778990260209775nteger @ X3 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 0.26/0.57              = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X3 @ M ) @ M ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % mod_double_modulus
% 0.26/0.57  thf(fact_5817_mod__double__modulus,axiom,
% 0.26/0.57      ! [M: nat,X3: nat] :
% 0.26/0.57        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ X3 )
% 0.26/0.57         => ( ( ( modulo_modulo_nat @ X3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.26/0.57              = ( modulo_modulo_nat @ X3 @ M ) )
% 0.26/0.57            | ( ( modulo_modulo_nat @ X3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.26/0.57              = ( plus_plus_nat @ ( modulo_modulo_nat @ X3 @ M ) @ M ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % mod_double_modulus
% 0.26/0.57  thf(fact_5818_mod__double__modulus,axiom,
% 0.26/0.57      ! [M: int,X3: int] :
% 0.26/0.57        ( ( ord_less_int @ zero_zero_int @ M )
% 0.26/0.57       => ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.26/0.57         => ( ( ( modulo_modulo_int @ X3 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 0.26/0.57              = ( modulo_modulo_int @ X3 @ M ) )
% 0.26/0.57            | ( ( modulo_modulo_int @ X3 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 0.26/0.57              = ( plus_plus_int @ ( modulo_modulo_int @ X3 @ M ) @ M ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % mod_double_modulus
% 0.26/0.57  thf(fact_5819_divmod__digit__1_I2_J,axiom,
% 0.26/0.57      ! [A: code_integer,B: code_integer] :
% 0.26/0.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.26/0.57       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.26/0.57         => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 0.26/0.57           => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.26/0.57              = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % divmod_digit_1(2)
% 0.26/0.57  thf(fact_5820_divmod__digit__1_I2_J,axiom,
% 0.26/0.57      ! [A: nat,B: nat] :
% 0.26/0.57        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.57       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.26/0.57         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 0.26/0.57           => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.26/0.57              = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % divmod_digit_1(2)
% 0.26/0.57  thf(fact_5821_divmod__digit__1_I2_J,axiom,
% 0.26/0.57      ! [A: int,B: int] :
% 0.26/0.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.57       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.57         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 0.26/0.57           => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.26/0.57              = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % divmod_digit_1(2)
% 0.26/0.57  thf(fact_5822_take__bit__Suc,axiom,
% 0.26/0.57      ! [N: nat,A: code_integer] :
% 0.26/0.57        ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A )
% 0.26/0.57        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % take_bit_Suc
% 0.26/0.57  thf(fact_5823_take__bit__Suc,axiom,
% 0.26/0.57      ! [N: nat,A: int] :
% 0.26/0.57        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 0.26/0.57        = ( 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 ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % take_bit_Suc
% 0.26/0.57  thf(fact_5824_take__bit__Suc,axiom,
% 0.26/0.57      ! [N: nat,A: nat] :
% 0.26/0.57        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ A )
% 0.26/0.57        = ( 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 ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % take_bit_Suc
% 0.26/0.57  thf(fact_5825_unset__bit__Suc,axiom,
% 0.26/0.57      ! [N: nat,A: code_integer] :
% 0.26/0.57        ( ( bit_se8260200283734997820nteger @ ( suc @ N ) @ A )
% 0.26/0.57        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % unset_bit_Suc
% 0.26/0.57  thf(fact_5826_unset__bit__Suc,axiom,
% 0.26/0.57      ! [N: nat,A: int] :
% 0.26/0.57        ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 0.26/0.57        = ( 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 ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % unset_bit_Suc
% 0.26/0.57  thf(fact_5827_unset__bit__Suc,axiom,
% 0.26/0.57      ! [N: nat,A: nat] :
% 0.26/0.57        ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 0.26/0.57        = ( 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 ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % unset_bit_Suc
% 0.26/0.57  thf(fact_5828_set__bit__Suc,axiom,
% 0.26/0.57      ! [N: nat,A: code_integer] :
% 0.26/0.57        ( ( bit_se2793503036327961859nteger @ ( suc @ N ) @ A )
% 0.26/0.57        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % set_bit_Suc
% 0.26/0.57  thf(fact_5829_set__bit__Suc,axiom,
% 0.26/0.57      ! [N: nat,A: int] :
% 0.26/0.57        ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 0.26/0.57        = ( 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 ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % set_bit_Suc
% 0.26/0.57  thf(fact_5830_set__bit__Suc,axiom,
% 0.26/0.57      ! [N: nat,A: nat] :
% 0.26/0.57        ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 0.26/0.57        = ( 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 ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % set_bit_Suc
% 0.26/0.57  thf(fact_5831_flip__bit__Suc,axiom,
% 0.26/0.57      ! [N: nat,A: code_integer] :
% 0.26/0.57        ( ( bit_se1345352211410354436nteger @ ( suc @ N ) @ A )
% 0.26/0.57        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % flip_bit_Suc
% 0.26/0.57  thf(fact_5832_flip__bit__Suc,axiom,
% 0.26/0.57      ! [N: nat,A: int] :
% 0.26/0.57        ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 0.26/0.57        = ( 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 ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % flip_bit_Suc
% 0.26/0.57  thf(fact_5833_flip__bit__Suc,axiom,
% 0.26/0.57      ! [N: nat,A: nat] :
% 0.26/0.57        ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 0.26/0.57        = ( 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 ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % flip_bit_Suc
% 0.26/0.57  thf(fact_5834_even__mod__4__div__2,axiom,
% 0.26/0.57      ! [N: nat] :
% 0.26/0.57        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.26/0.57          = ( suc @ zero_zero_nat ) )
% 0.26/0.57       => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % even_mod_4_div_2
% 0.26/0.57  thf(fact_5835_nat0__intermed__int__val,axiom,
% 0.26/0.57      ! [N: nat,F: nat > int,K: int] :
% 0.26/0.57        ( ! [I3: nat] :
% 0.26/0.57            ( ( ord_less_nat @ I3 @ N )
% 0.26/0.57           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 0.26/0.57       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 0.26/0.57         => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 0.26/0.57           => ? [I3: nat] :
% 0.26/0.57                ( ( ord_less_eq_nat @ I3 @ N )
% 0.26/0.57                & ( ( F @ I3 )
% 0.26/0.57                  = K ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % nat0_intermed_int_val
% 0.26/0.57  thf(fact_5836_xor__nat__unfold,axiom,
% 0.26/0.57      ( bit_se6528837805403552850or_nat
% 0.26/0.57      = ( ^ [M3: nat,N3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N3 @ ( if_nat @ ( N3 = 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 @ N3 @ ( 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 @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % xor_nat_unfold
% 0.26/0.57  thf(fact_5837_arctan__add,axiom,
% 0.26/0.57      ! [X3: real,Y3: real] :
% 0.26/0.57        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.26/0.57       => ( ( ord_less_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 0.26/0.57         => ( ( plus_plus_real @ ( arctan @ X3 ) @ ( arctan @ Y3 ) )
% 0.26/0.57            = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X3 @ Y3 ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X3 @ Y3 ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % arctan_add
% 0.26/0.57  thf(fact_5838_divmod__digit__1_I1_J,axiom,
% 0.26/0.57      ! [A: code_integer,B: code_integer] :
% 0.26/0.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.26/0.57       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.26/0.57         => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 0.26/0.57           => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 0.26/0.57              = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % divmod_digit_1(1)
% 0.26/0.57  thf(fact_5839_divmod__digit__1_I1_J,axiom,
% 0.26/0.57      ! [A: nat,B: nat] :
% 0.26/0.57        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.26/0.57       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.26/0.57         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 0.26/0.57           => ( ( 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 )
% 0.26/0.57              = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % divmod_digit_1(1)
% 0.26/0.57  thf(fact_5840_divmod__digit__1_I1_J,axiom,
% 0.26/0.57      ! [A: int,B: int] :
% 0.26/0.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.57       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.57         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 0.26/0.57           => ( ( 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 )
% 0.26/0.57              = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % divmod_digit_1(1)
% 0.26/0.57  thf(fact_5841_take__bit__minus__small__eq,axiom,
% 0.26/0.57      ! [K: int,N: nat] :
% 0.26/0.57        ( ( ord_less_int @ zero_zero_int @ K )
% 0.26/0.57       => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.57         => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 0.26/0.57            = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % take_bit_minus_small_eq
% 0.26/0.57  thf(fact_5842_take__bit__rec,axiom,
% 0.26/0.57      ( bit_se1745604003318907178nteger
% 0.26/0.57      = ( ^ [N3: nat,A4: code_integer] : ( if_Code_integer @ ( N3 = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % take_bit_rec
% 0.26/0.57  thf(fact_5843_take__bit__rec,axiom,
% 0.26/0.57      ( bit_se2923211474154528505it_int
% 0.26/0.57      = ( ^ [N3: nat,A4: int] : ( if_int @ ( N3 = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % take_bit_rec
% 0.26/0.57  thf(fact_5844_take__bit__rec,axiom,
% 0.26/0.57      ( bit_se2925701944663578781it_nat
% 0.26/0.57      = ( ^ [N3: nat,A4: nat] : ( if_nat @ ( N3 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % take_bit_rec
% 0.26/0.57  thf(fact_5845_powr__int,axiom,
% 0.26/0.57      ! [X3: real,I: int] :
% 0.26/0.57        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.57       => ( ( ( ord_less_eq_int @ zero_zero_int @ I )
% 0.26/0.57           => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ I ) )
% 0.26/0.57              = ( power_power_real @ X3 @ ( nat2 @ I ) ) ) )
% 0.26/0.57          & ( ~ ( ord_less_eq_int @ zero_zero_int @ I )
% 0.26/0.57           => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ I ) )
% 0.26/0.57              = ( divide_divide_real @ one_one_real @ ( power_power_real @ X3 @ ( nat2 @ ( uminus_uminus_int @ I ) ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % powr_int
% 0.26/0.57  thf(fact_5846_arctan__half,axiom,
% 0.26/0.57      ( arctan
% 0.26/0.57      = ( ^ [X: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % arctan_half
% 0.26/0.57  thf(fact_5847_in__children__def,axiom,
% 0.26/0.57      ( vEBT_V5917875025757280293ildren
% 0.26/0.57      = ( ^ [N3: nat,TreeList: list_VEBT_VEBT,X: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ N3 ) ) @ ( vEBT_VEBT_low @ X @ N3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % in_children_def
% 0.26/0.57  thf(fact_5848_signed__take__bit__rec,axiom,
% 0.26/0.57      ( bit_ri6519982836138164636nteger
% 0.26/0.57      = ( ^ [N3: nat,A4: code_integer] : ( if_Code_integer @ ( N3 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_rec
% 0.26/0.57  thf(fact_5849_signed__take__bit__rec,axiom,
% 0.26/0.57      ( bit_ri631733984087533419it_int
% 0.26/0.57      = ( ^ [N3: nat,A4: int] : ( if_int @ ( N3 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_rec
% 0.26/0.57  thf(fact_5850_central__binomial__lower__bound,axiom,
% 0.26/0.57      ! [N: nat] :
% 0.26/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.57       => ( 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 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % central_binomial_lower_bound
% 0.26/0.57  thf(fact_5851_nth__equalityI,axiom,
% 0.26/0.57      ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.26/0.57        ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.26/0.57          = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.26/0.57       => ( ! [I3: nat] :
% 0.26/0.57              ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.26/0.57             => ( ( nth_VEBT_VEBT @ Xs2 @ I3 )
% 0.26/0.57                = ( nth_VEBT_VEBT @ Ys @ I3 ) ) )
% 0.26/0.57         => ( Xs2 = Ys ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % nth_equalityI
% 0.26/0.57  thf(fact_5852_nth__equalityI,axiom,
% 0.26/0.57      ! [Xs2: list_o,Ys: list_o] :
% 0.26/0.57        ( ( ( size_size_list_o @ Xs2 )
% 0.26/0.57          = ( size_size_list_o @ Ys ) )
% 0.26/0.57       => ( ! [I3: nat] :
% 0.26/0.57              ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 0.26/0.57             => ( ( nth_o @ Xs2 @ I3 )
% 0.26/0.57                = ( nth_o @ Ys @ I3 ) ) )
% 0.26/0.57         => ( Xs2 = Ys ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % nth_equalityI
% 0.26/0.57  thf(fact_5853_nth__equalityI,axiom,
% 0.26/0.57      ! [Xs2: list_nat,Ys: list_nat] :
% 0.26/0.57        ( ( ( size_size_list_nat @ Xs2 )
% 0.26/0.57          = ( size_size_list_nat @ Ys ) )
% 0.26/0.57       => ( ! [I3: nat] :
% 0.26/0.57              ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 0.26/0.57             => ( ( nth_nat @ Xs2 @ I3 )
% 0.26/0.57                = ( nth_nat @ Ys @ I3 ) ) )
% 0.26/0.57         => ( Xs2 = Ys ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % nth_equalityI
% 0.26/0.57  thf(fact_5854_nth__equalityI,axiom,
% 0.26/0.57      ! [Xs2: list_int,Ys: list_int] :
% 0.26/0.57        ( ( ( size_size_list_int @ Xs2 )
% 0.26/0.57          = ( size_size_list_int @ Ys ) )
% 0.26/0.57       => ( ! [I3: nat] :
% 0.26/0.57              ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 0.26/0.57             => ( ( nth_int @ Xs2 @ I3 )
% 0.26/0.57                = ( nth_int @ Ys @ I3 ) ) )
% 0.26/0.57         => ( Xs2 = Ys ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % nth_equalityI
% 0.26/0.57  thf(fact_5855_inthall,axiom,
% 0.26/0.57      ! [Xs2: list_option_nat,P: option_nat > $o,N: nat] :
% 0.26/0.57        ( ! [X4: option_nat] :
% 0.26/0.57            ( ( member_option_nat @ X4 @ ( set_option_nat2 @ Xs2 ) )
% 0.26/0.57           => ( P @ X4 ) )
% 0.26/0.57       => ( ( ord_less_nat @ N @ ( size_s6086282163384603972on_nat @ Xs2 ) )
% 0.26/0.57         => ( P @ ( nth_option_nat @ Xs2 @ N ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % inthall
% 0.26/0.57  thf(fact_5856_inthall,axiom,
% 0.26/0.57      ! [Xs2: list_real,P: real > $o,N: nat] :
% 0.26/0.57        ( ! [X4: real] :
% 0.26/0.57            ( ( member_real @ X4 @ ( set_real2 @ Xs2 ) )
% 0.26/0.57           => ( P @ X4 ) )
% 0.26/0.57       => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 0.26/0.57         => ( P @ ( nth_real @ Xs2 @ N ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % inthall
% 0.26/0.57  thf(fact_5857_inthall,axiom,
% 0.26/0.57      ! [Xs2: list_set_nat,P: set_nat > $o,N: nat] :
% 0.26/0.57        ( ! [X4: set_nat] :
% 0.26/0.57            ( ( member_set_nat @ X4 @ ( set_set_nat2 @ Xs2 ) )
% 0.26/0.57           => ( P @ X4 ) )
% 0.26/0.57       => ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 0.26/0.57         => ( P @ ( nth_set_nat @ Xs2 @ N ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % inthall
% 0.26/0.57  thf(fact_5858_inthall,axiom,
% 0.26/0.57      ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,N: nat] :
% 0.26/0.57        ( ! [X4: vEBT_VEBT] :
% 0.26/0.57            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.26/0.57           => ( P @ X4 ) )
% 0.26/0.57       => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.26/0.57         => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % inthall
% 0.26/0.57  thf(fact_5859_inthall,axiom,
% 0.26/0.57      ! [Xs2: list_o,P: $o > $o,N: nat] :
% 0.26/0.57        ( ! [X4: $o] :
% 0.26/0.57            ( ( member_o @ X4 @ ( set_o2 @ Xs2 ) )
% 0.26/0.57           => ( P @ X4 ) )
% 0.26/0.57       => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 0.26/0.57         => ( P @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % inthall
% 0.26/0.57  thf(fact_5860_inthall,axiom,
% 0.26/0.57      ! [Xs2: list_nat,P: nat > $o,N: nat] :
% 0.26/0.57        ( ! [X4: nat] :
% 0.26/0.57            ( ( member_nat @ X4 @ ( set_nat2 @ Xs2 ) )
% 0.26/0.57           => ( P @ X4 ) )
% 0.26/0.57       => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 0.26/0.57         => ( P @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % inthall
% 0.26/0.57  thf(fact_5861_inthall,axiom,
% 0.26/0.57      ! [Xs2: list_int,P: int > $o,N: nat] :
% 0.26/0.57        ( ! [X4: int] :
% 0.26/0.57            ( ( member_int @ X4 @ ( set_int2 @ Xs2 ) )
% 0.26/0.57           => ( P @ X4 ) )
% 0.26/0.57       => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 0.26/0.57         => ( P @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % inthall
% 0.26/0.57  thf(fact_5862_signed__take__bit__of__0,axiom,
% 0.26/0.57      ! [N: nat] :
% 0.26/0.57        ( ( bit_ri631733984087533419it_int @ N @ zero_zero_int )
% 0.26/0.57        = zero_zero_int ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_of_0
% 0.26/0.57  thf(fact_5863_mod__pos__pos__trivial,axiom,
% 0.26/0.57      ! [K: int,L: int] :
% 0.26/0.57        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.26/0.57       => ( ( ord_less_int @ K @ L )
% 0.26/0.57         => ( ( modulo_modulo_int @ K @ L )
% 0.26/0.57            = K ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % mod_pos_pos_trivial
% 0.26/0.57  thf(fact_5864_mod__neg__neg__trivial,axiom,
% 0.26/0.57      ! [K: int,L: int] :
% 0.26/0.57        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 0.26/0.57       => ( ( ord_less_int @ L @ K )
% 0.26/0.57         => ( ( modulo_modulo_int @ K @ L )
% 0.26/0.57            = K ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % mod_neg_neg_trivial
% 0.26/0.57  thf(fact_5865_signed__take__bit__Suc__1,axiom,
% 0.26/0.57      ! [N: nat] :
% 0.26/0.57        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 0.26/0.57        = one_one_int ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_Suc_1
% 0.26/0.57  thf(fact_5866_signed__take__bit__of__minus__1,axiom,
% 0.26/0.57      ! [N: nat] :
% 0.26/0.57        ( ( bit_ri6519982836138164636nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.26/0.57        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_of_minus_1
% 0.26/0.57  thf(fact_5867_signed__take__bit__of__minus__1,axiom,
% 0.26/0.57      ! [N: nat] :
% 0.26/0.57        ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.57        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_of_minus_1
% 0.26/0.57  thf(fact_5868_signed__take__bit__numeral__of__1,axiom,
% 0.26/0.57      ! [K: num] :
% 0.26/0.57        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 0.26/0.57        = one_one_int ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_numeral_of_1
% 0.26/0.57  thf(fact_5869_zmod__numeral__Bit0,axiom,
% 0.26/0.57      ! [V: num,W: num] :
% 0.26/0.57        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 0.26/0.57        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % zmod_numeral_Bit0
% 0.26/0.57  thf(fact_5870_signed__take__bit__Suc__bit0,axiom,
% 0.26/0.57      ! [N: nat,K: num] :
% 0.26/0.57        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 0.26/0.57        = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_Suc_bit0
% 0.26/0.57  thf(fact_5871_signed__take__bit__Suc__minus__bit0,axiom,
% 0.26/0.57      ! [N: nat,K: num] :
% 0.26/0.57        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.26/0.57        = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_Suc_minus_bit0
% 0.26/0.57  thf(fact_5872_signed__take__bit__0,axiom,
% 0.26/0.57      ! [A: code_integer] :
% 0.26/0.57        ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 0.26/0.57        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_0
% 0.26/0.57  thf(fact_5873_signed__take__bit__0,axiom,
% 0.26/0.57      ! [A: int] :
% 0.26/0.57        ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 0.26/0.57        = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_0
% 0.26/0.57  thf(fact_5874__C5_Ohyps_C_I1_J,axiom,
% 0.26/0.57      vEBT_invar_vebt @ summary @ m ).
% 0.26/0.57  
% 0.26/0.57  % "5.hyps"(1)
% 0.26/0.57  thf(fact_5875_signed__take__bit__minus,axiom,
% 0.26/0.57      ! [N: nat,K: int] :
% 0.26/0.57        ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N @ K ) ) )
% 0.26/0.57        = ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_minus
% 0.26/0.57  thf(fact_5876_signed__take__bit__mult,axiom,
% 0.26/0.57      ! [N: nat,K: int,L: int] :
% 0.26/0.57        ( ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 0.26/0.57        = ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ K @ L ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_mult
% 0.26/0.57  thf(fact_5877_signed__take__bit__add,axiom,
% 0.26/0.57      ! [N: nat,K: int,L: int] :
% 0.26/0.57        ( ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 0.26/0.57        = ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ K @ L ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_add
% 0.26/0.57  thf(fact_5878_signed__take__bit__diff,axiom,
% 0.26/0.57      ! [N: nat,K: int,L: int] :
% 0.26/0.57        ( ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 0.26/0.57        = ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ K @ L ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_diff
% 0.26/0.57  thf(fact_5879_length__pos__if__in__set,axiom,
% 0.26/0.57      ! [X3: option_nat,Xs2: list_option_nat] :
% 0.26/0.57        ( ( member_option_nat @ X3 @ ( set_option_nat2 @ Xs2 ) )
% 0.26/0.57       => ( ord_less_nat @ zero_zero_nat @ ( size_s6086282163384603972on_nat @ Xs2 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % length_pos_if_in_set
% 0.26/0.57  thf(fact_5880_length__pos__if__in__set,axiom,
% 0.26/0.57      ! [X3: real,Xs2: list_real] :
% 0.26/0.57        ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 0.26/0.57       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs2 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % length_pos_if_in_set
% 0.26/0.57  thf(fact_5881_length__pos__if__in__set,axiom,
% 0.26/0.57      ! [X3: set_nat,Xs2: list_set_nat] :
% 0.26/0.57        ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs2 ) )
% 0.26/0.57       => ( ord_less_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ Xs2 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % length_pos_if_in_set
% 0.26/0.57  thf(fact_5882_length__pos__if__in__set,axiom,
% 0.26/0.57      ! [X3: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 0.26/0.57        ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.26/0.57       => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % length_pos_if_in_set
% 0.26/0.57  thf(fact_5883_length__pos__if__in__set,axiom,
% 0.26/0.57      ! [X3: $o,Xs2: list_o] :
% 0.26/0.57        ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 0.26/0.57       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs2 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % length_pos_if_in_set
% 0.26/0.57  thf(fact_5884_length__pos__if__in__set,axiom,
% 0.26/0.57      ! [X3: nat,Xs2: list_nat] :
% 0.26/0.57        ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 0.26/0.57       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs2 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % length_pos_if_in_set
% 0.26/0.57  thf(fact_5885_length__pos__if__in__set,axiom,
% 0.26/0.57      ! [X3: int,Xs2: list_int] :
% 0.26/0.57        ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 0.26/0.57       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs2 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % length_pos_if_in_set
% 0.26/0.57  thf(fact_5886_all__set__conv__all__nth,axiom,
% 0.26/0.57      ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.26/0.57        ( ( ! [X: vEBT_VEBT] :
% 0.26/0.57              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.26/0.57             => ( P @ X ) ) )
% 0.26/0.57        = ( ! [I4: nat] :
% 0.26/0.57              ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.26/0.57             => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I4 ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % all_set_conv_all_nth
% 0.26/0.57  thf(fact_5887_all__set__conv__all__nth,axiom,
% 0.26/0.57      ! [Xs2: list_o,P: $o > $o] :
% 0.26/0.57        ( ( ! [X: $o] :
% 0.26/0.57              ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 0.26/0.57             => ( P @ X ) ) )
% 0.26/0.57        = ( ! [I4: nat] :
% 0.26/0.57              ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs2 ) )
% 0.26/0.57             => ( P @ ( nth_o @ Xs2 @ I4 ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % all_set_conv_all_nth
% 0.26/0.57  thf(fact_5888_all__set__conv__all__nth,axiom,
% 0.26/0.57      ! [Xs2: list_nat,P: nat > $o] :
% 0.26/0.57        ( ( ! [X: nat] :
% 0.26/0.57              ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 0.26/0.57             => ( P @ X ) ) )
% 0.26/0.57        = ( ! [I4: nat] :
% 0.26/0.57              ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 0.26/0.57             => ( P @ ( nth_nat @ Xs2 @ I4 ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % all_set_conv_all_nth
% 0.26/0.57  thf(fact_5889_all__set__conv__all__nth,axiom,
% 0.26/0.57      ! [Xs2: list_int,P: int > $o] :
% 0.26/0.57        ( ( ! [X: int] :
% 0.26/0.57              ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 0.26/0.57             => ( P @ X ) ) )
% 0.26/0.57        = ( ! [I4: nat] :
% 0.26/0.57              ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs2 ) )
% 0.26/0.57             => ( P @ ( nth_int @ Xs2 @ I4 ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % all_set_conv_all_nth
% 0.26/0.57  thf(fact_5890_all__nth__imp__all__set,axiom,
% 0.26/0.57      ! [Xs2: list_option_nat,P: option_nat > $o,X3: option_nat] :
% 0.26/0.57        ( ! [I3: nat] :
% 0.26/0.57            ( ( ord_less_nat @ I3 @ ( size_s6086282163384603972on_nat @ Xs2 ) )
% 0.26/0.57           => ( P @ ( nth_option_nat @ Xs2 @ I3 ) ) )
% 0.26/0.57       => ( ( member_option_nat @ X3 @ ( set_option_nat2 @ Xs2 ) )
% 0.26/0.57         => ( P @ X3 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % all_nth_imp_all_set
% 0.26/0.57  thf(fact_5891_all__nth__imp__all__set,axiom,
% 0.26/0.57      ! [Xs2: list_real,P: real > $o,X3: real] :
% 0.26/0.57        ( ! [I3: nat] :
% 0.26/0.57            ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs2 ) )
% 0.26/0.57           => ( P @ ( nth_real @ Xs2 @ I3 ) ) )
% 0.26/0.57       => ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 0.26/0.57         => ( P @ X3 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % all_nth_imp_all_set
% 0.26/0.57  thf(fact_5892_all__nth__imp__all__set,axiom,
% 0.26/0.57      ! [Xs2: list_set_nat,P: set_nat > $o,X3: set_nat] :
% 0.26/0.57        ( ! [I3: nat] :
% 0.26/0.57            ( ( ord_less_nat @ I3 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 0.26/0.57           => ( P @ ( nth_set_nat @ Xs2 @ I3 ) ) )
% 0.26/0.57       => ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs2 ) )
% 0.26/0.57         => ( P @ X3 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % all_nth_imp_all_set
% 0.26/0.57  thf(fact_5893_all__nth__imp__all__set,axiom,
% 0.26/0.57      ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,X3: vEBT_VEBT] :
% 0.26/0.57        ( ! [I3: nat] :
% 0.26/0.57            ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.26/0.57           => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I3 ) ) )
% 0.26/0.57       => ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.26/0.57         => ( P @ X3 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % all_nth_imp_all_set
% 0.26/0.57  thf(fact_5894_all__nth__imp__all__set,axiom,
% 0.26/0.57      ! [Xs2: list_o,P: $o > $o,X3: $o] :
% 0.26/0.57        ( ! [I3: nat] :
% 0.26/0.57            ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 0.26/0.57           => ( P @ ( nth_o @ Xs2 @ I3 ) ) )
% 0.26/0.57       => ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 0.26/0.57         => ( P @ X3 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % all_nth_imp_all_set
% 0.26/0.57  thf(fact_5895_all__nth__imp__all__set,axiom,
% 0.26/0.57      ! [Xs2: list_nat,P: nat > $o,X3: nat] :
% 0.26/0.57        ( ! [I3: nat] :
% 0.26/0.57            ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 0.26/0.57           => ( P @ ( nth_nat @ Xs2 @ I3 ) ) )
% 0.26/0.57       => ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 0.26/0.57         => ( P @ X3 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % all_nth_imp_all_set
% 0.26/0.57  thf(fact_5896_all__nth__imp__all__set,axiom,
% 0.26/0.57      ! [Xs2: list_int,P: int > $o,X3: int] :
% 0.26/0.57        ( ! [I3: nat] :
% 0.26/0.57            ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 0.26/0.57           => ( P @ ( nth_int @ Xs2 @ I3 ) ) )
% 0.26/0.57       => ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 0.26/0.57         => ( P @ X3 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % all_nth_imp_all_set
% 0.26/0.57  thf(fact_5897_in__set__conv__nth,axiom,
% 0.26/0.57      ! [X3: option_nat,Xs2: list_option_nat] :
% 0.26/0.57        ( ( member_option_nat @ X3 @ ( set_option_nat2 @ Xs2 ) )
% 0.26/0.57        = ( ? [I4: nat] :
% 0.26/0.57              ( ( ord_less_nat @ I4 @ ( size_s6086282163384603972on_nat @ Xs2 ) )
% 0.26/0.57              & ( ( nth_option_nat @ Xs2 @ I4 )
% 0.26/0.57                = X3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % in_set_conv_nth
% 0.26/0.57  thf(fact_5898_in__set__conv__nth,axiom,
% 0.26/0.57      ! [X3: real,Xs2: list_real] :
% 0.26/0.57        ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 0.26/0.57        = ( ? [I4: nat] :
% 0.26/0.57              ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs2 ) )
% 0.26/0.57              & ( ( nth_real @ Xs2 @ I4 )
% 0.26/0.57                = X3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % in_set_conv_nth
% 0.26/0.57  thf(fact_5899_in__set__conv__nth,axiom,
% 0.26/0.57      ! [X3: set_nat,Xs2: list_set_nat] :
% 0.26/0.57        ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs2 ) )
% 0.26/0.57        = ( ? [I4: nat] :
% 0.26/0.57              ( ( ord_less_nat @ I4 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 0.26/0.57              & ( ( nth_set_nat @ Xs2 @ I4 )
% 0.26/0.57                = X3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % in_set_conv_nth
% 0.26/0.57  thf(fact_5900_in__set__conv__nth,axiom,
% 0.26/0.57      ! [X3: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 0.26/0.57        ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.26/0.57        = ( ? [I4: nat] :
% 0.26/0.57              ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.26/0.57              & ( ( nth_VEBT_VEBT @ Xs2 @ I4 )
% 0.26/0.57                = X3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % in_set_conv_nth
% 0.26/0.57  thf(fact_5901_in__set__conv__nth,axiom,
% 0.26/0.57      ! [X3: $o,Xs2: list_o] :
% 0.26/0.57        ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 0.26/0.57        = ( ? [I4: nat] :
% 0.26/0.57              ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs2 ) )
% 0.26/0.57              & ( ( nth_o @ Xs2 @ I4 )
% 0.26/0.57                = X3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % in_set_conv_nth
% 0.26/0.57  thf(fact_5902_in__set__conv__nth,axiom,
% 0.26/0.57      ! [X3: nat,Xs2: list_nat] :
% 0.26/0.57        ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 0.26/0.57        = ( ? [I4: nat] :
% 0.26/0.57              ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 0.26/0.57              & ( ( nth_nat @ Xs2 @ I4 )
% 0.26/0.57                = X3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % in_set_conv_nth
% 0.26/0.57  thf(fact_5903_in__set__conv__nth,axiom,
% 0.26/0.57      ! [X3: int,Xs2: list_int] :
% 0.26/0.57        ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 0.26/0.57        = ( ? [I4: nat] :
% 0.26/0.57              ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs2 ) )
% 0.26/0.57              & ( ( nth_int @ Xs2 @ I4 )
% 0.26/0.57                = X3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % in_set_conv_nth
% 0.26/0.57  thf(fact_5904_list__ball__nth,axiom,
% 0.26/0.57      ! [N: nat,Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.26/0.57        ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.26/0.57       => ( ! [X4: vEBT_VEBT] :
% 0.26/0.57              ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.26/0.57             => ( P @ X4 ) )
% 0.26/0.57         => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % list_ball_nth
% 0.26/0.57  thf(fact_5905_list__ball__nth,axiom,
% 0.26/0.57      ! [N: nat,Xs2: list_o,P: $o > $o] :
% 0.26/0.57        ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 0.26/0.57       => ( ! [X4: $o] :
% 0.26/0.57              ( ( member_o @ X4 @ ( set_o2 @ Xs2 ) )
% 0.26/0.57             => ( P @ X4 ) )
% 0.26/0.57         => ( P @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % list_ball_nth
% 0.26/0.57  thf(fact_5906_list__ball__nth,axiom,
% 0.26/0.57      ! [N: nat,Xs2: list_nat,P: nat > $o] :
% 0.26/0.57        ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 0.26/0.57       => ( ! [X4: nat] :
% 0.26/0.57              ( ( member_nat @ X4 @ ( set_nat2 @ Xs2 ) )
% 0.26/0.57             => ( P @ X4 ) )
% 0.26/0.57         => ( P @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % list_ball_nth
% 0.26/0.57  thf(fact_5907_list__ball__nth,axiom,
% 0.26/0.57      ! [N: nat,Xs2: list_int,P: int > $o] :
% 0.26/0.57        ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 0.26/0.57       => ( ! [X4: int] :
% 0.26/0.57              ( ( member_int @ X4 @ ( set_int2 @ Xs2 ) )
% 0.26/0.57             => ( P @ X4 ) )
% 0.26/0.57         => ( P @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % list_ball_nth
% 0.26/0.57  thf(fact_5908_nth__mem,axiom,
% 0.26/0.57      ! [N: nat,Xs2: list_option_nat] :
% 0.26/0.57        ( ( ord_less_nat @ N @ ( size_s6086282163384603972on_nat @ Xs2 ) )
% 0.26/0.57       => ( member_option_nat @ ( nth_option_nat @ Xs2 @ N ) @ ( set_option_nat2 @ Xs2 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % nth_mem
% 0.26/0.57  thf(fact_5909_nth__mem,axiom,
% 0.26/0.57      ! [N: nat,Xs2: list_real] :
% 0.26/0.57        ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 0.26/0.57       => ( member_real @ ( nth_real @ Xs2 @ N ) @ ( set_real2 @ Xs2 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % nth_mem
% 0.26/0.57  thf(fact_5910_nth__mem,axiom,
% 0.26/0.57      ! [N: nat,Xs2: list_set_nat] :
% 0.26/0.57        ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 0.26/0.57       => ( member_set_nat @ ( nth_set_nat @ Xs2 @ N ) @ ( set_set_nat2 @ Xs2 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % nth_mem
% 0.26/0.57  thf(fact_5911_nth__mem,axiom,
% 0.26/0.57      ! [N: nat,Xs2: list_VEBT_VEBT] :
% 0.26/0.57        ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.26/0.57       => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N ) @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % nth_mem
% 0.26/0.57  thf(fact_5912_nth__mem,axiom,
% 0.26/0.57      ! [N: nat,Xs2: list_o] :
% 0.26/0.57        ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 0.26/0.57       => ( member_o @ ( nth_o @ Xs2 @ N ) @ ( set_o2 @ Xs2 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % nth_mem
% 0.26/0.57  thf(fact_5913_nth__mem,axiom,
% 0.26/0.57      ! [N: nat,Xs2: list_nat] :
% 0.26/0.57        ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 0.26/0.57       => ( member_nat @ ( nth_nat @ Xs2 @ N ) @ ( set_nat2 @ Xs2 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % nth_mem
% 0.26/0.57  thf(fact_5914_nth__mem,axiom,
% 0.26/0.57      ! [N: nat,Xs2: list_int] :
% 0.26/0.57        ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 0.26/0.57       => ( member_int @ ( nth_int @ Xs2 @ N ) @ ( set_int2 @ Xs2 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % nth_mem
% 0.26/0.57  thf(fact_5915_zmod__le__nonneg__dividend,axiom,
% 0.26/0.57      ! [M: int,K: int] :
% 0.26/0.57        ( ( ord_less_eq_int @ zero_zero_int @ M )
% 0.26/0.57       => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 0.26/0.57  
% 0.26/0.57  % zmod_le_nonneg_dividend
% 0.26/0.57  thf(fact_5916_neg__mod__bound,axiom,
% 0.26/0.57      ! [L: int,K: int] :
% 0.26/0.57        ( ( ord_less_int @ L @ zero_zero_int )
% 0.26/0.57       => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % neg_mod_bound
% 0.26/0.57  thf(fact_5917_Euclidean__Division_Opos__mod__bound,axiom,
% 0.26/0.57      ! [L: int,K: int] :
% 0.26/0.57        ( ( ord_less_int @ zero_zero_int @ L )
% 0.26/0.57       => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).
% 0.26/0.57  
% 0.26/0.57  % Euclidean_Division.pos_mod_bound
% 0.26/0.57  thf(fact_5918_zmod__zminus2__not__zero,axiom,
% 0.26/0.57      ! [K: int,L: int] :
% 0.26/0.57        ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L ) )
% 0.26/0.57         != zero_zero_int )
% 0.26/0.57       => ( ( modulo_modulo_int @ K @ L )
% 0.26/0.57         != zero_zero_int ) ) ).
% 0.26/0.57  
% 0.26/0.57  % zmod_zminus2_not_zero
% 0.26/0.57  thf(fact_5919_zmod__zminus1__not__zero,axiom,
% 0.26/0.57      ! [K: int,L: int] :
% 0.26/0.57        ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 0.26/0.57         != zero_zero_int )
% 0.26/0.57       => ( ( modulo_modulo_int @ K @ L )
% 0.26/0.57         != zero_zero_int ) ) ).
% 0.26/0.57  
% 0.26/0.57  % zmod_zminus1_not_zero
% 0.26/0.57  thf(fact_5920_zmod__eq__0__iff,axiom,
% 0.26/0.57      ! [M: int,D3: int] :
% 0.26/0.57        ( ( ( modulo_modulo_int @ M @ D3 )
% 0.26/0.57          = zero_zero_int )
% 0.26/0.57        = ( ? [Q5: int] :
% 0.26/0.57              ( M
% 0.26/0.57              = ( times_times_int @ D3 @ Q5 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % zmod_eq_0_iff
% 0.26/0.57  thf(fact_5921_zmod__eq__0D,axiom,
% 0.26/0.57      ! [M: int,D3: int] :
% 0.26/0.57        ( ( ( modulo_modulo_int @ M @ D3 )
% 0.26/0.57          = zero_zero_int )
% 0.26/0.57       => ? [Q4: int] :
% 0.26/0.57            ( M
% 0.26/0.57            = ( times_times_int @ D3 @ Q4 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % zmod_eq_0D
% 0.26/0.57  thf(fact_5922_zmod__int,axiom,
% 0.26/0.57      ! [A: nat,B: nat] :
% 0.26/0.57        ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 0.26/0.57        = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % zmod_int
% 0.26/0.57  thf(fact_5923_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 0.26/0.57      ! [N: nat,A: int,B: int] :
% 0.26/0.57        ( ( ( bit_ri631733984087533419it_int @ N @ A )
% 0.26/0.57          = ( bit_ri631733984087533419it_int @ N @ B ) )
% 0.26/0.57        = ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 0.26/0.57          = ( bit_se2923211474154528505it_int @ ( suc @ N ) @ B ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_eq_iff_take_bit_eq
% 0.26/0.57  thf(fact_5924_signed__take__bit__take__bit,axiom,
% 0.26/0.57      ! [M: nat,N: nat,A: int] :
% 0.26/0.57        ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 0.26/0.57        = ( if_int_int @ ( ord_less_eq_nat @ N @ M ) @ ( bit_se2923211474154528505it_int @ N ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_take_bit
% 0.26/0.57  thf(fact_5925_zmod__trivial__iff,axiom,
% 0.26/0.57      ! [I: int,K: int] :
% 0.26/0.57        ( ( ( modulo_modulo_int @ I @ K )
% 0.26/0.57          = I )
% 0.26/0.57        = ( ( K = zero_zero_int )
% 0.26/0.57          | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 0.26/0.57            & ( ord_less_int @ I @ K ) )
% 0.26/0.57          | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 0.26/0.57            & ( ord_less_int @ K @ I ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % zmod_trivial_iff
% 0.26/0.57  thf(fact_5926_pos__mod__conj,axiom,
% 0.26/0.57      ! [B: int,A: int] :
% 0.26/0.57        ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.57       => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 0.26/0.57          & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pos_mod_conj
% 0.26/0.57  thf(fact_5927_neg__mod__conj,axiom,
% 0.26/0.57      ! [B: int,A: int] :
% 0.26/0.57        ( ( ord_less_int @ B @ zero_zero_int )
% 0.26/0.57       => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 0.26/0.57          & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % neg_mod_conj
% 0.26/0.57  thf(fact_5928_Euclidean__Division_Opos__mod__sign,axiom,
% 0.26/0.57      ! [L: int,K: int] :
% 0.26/0.57        ( ( ord_less_int @ zero_zero_int @ L )
% 0.26/0.57       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % Euclidean_Division.pos_mod_sign
% 0.26/0.57  thf(fact_5929_neg__mod__sign,axiom,
% 0.26/0.57      ! [L: int,K: int] :
% 0.26/0.57        ( ( ord_less_int @ L @ zero_zero_int )
% 0.26/0.57       => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 0.26/0.57  
% 0.26/0.57  % neg_mod_sign
% 0.26/0.57  thf(fact_5930_zdiv__mono__strict,axiom,
% 0.26/0.57      ! [A3: int,B5: int,N: int] :
% 0.26/0.57        ( ( ord_less_int @ A3 @ B5 )
% 0.26/0.57       => ( ( ord_less_int @ zero_zero_int @ N )
% 0.26/0.57         => ( ( ( modulo_modulo_int @ A3 @ N )
% 0.26/0.57              = zero_zero_int )
% 0.26/0.57           => ( ( ( modulo_modulo_int @ B5 @ N )
% 0.26/0.57                = zero_zero_int )
% 0.26/0.57             => ( ord_less_int @ ( divide_divide_int @ A3 @ N ) @ ( divide_divide_int @ B5 @ N ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % zdiv_mono_strict
% 0.26/0.57  thf(fact_5931_zmod__zminus2__eq__if,axiom,
% 0.26/0.57      ! [A: int,B: int] :
% 0.26/0.57        ( ( ( ( modulo_modulo_int @ A @ B )
% 0.26/0.57            = zero_zero_int )
% 0.26/0.57         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 0.26/0.57            = zero_zero_int ) )
% 0.26/0.57        & ( ( ( modulo_modulo_int @ A @ B )
% 0.26/0.57           != zero_zero_int )
% 0.26/0.57         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 0.26/0.57            = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % zmod_zminus2_eq_if
% 0.26/0.57  thf(fact_5932_zmod__zminus1__eq__if,axiom,
% 0.26/0.57      ! [A: int,B: int] :
% 0.26/0.57        ( ( ( ( modulo_modulo_int @ A @ B )
% 0.26/0.57            = zero_zero_int )
% 0.26/0.57         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 0.26/0.57            = zero_zero_int ) )
% 0.26/0.57        & ( ( ( modulo_modulo_int @ A @ B )
% 0.26/0.57           != zero_zero_int )
% 0.26/0.57         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 0.26/0.57            = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % zmod_zminus1_eq_if
% 0.26/0.57  thf(fact_5933_abs__mod__less,axiom,
% 0.26/0.57      ! [L: int,K: int] :
% 0.26/0.57        ( ( L != zero_zero_int )
% 0.26/0.57       => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % abs_mod_less
% 0.26/0.57  thf(fact_5934_div__mod__decomp__int,axiom,
% 0.26/0.57      ! [A3: int,N: int] :
% 0.26/0.57        ( A3
% 0.26/0.57        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A3 @ N ) @ N ) @ ( modulo_modulo_int @ A3 @ N ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % div_mod_decomp_int
% 0.26/0.57  thf(fact_5935_mod__pos__neg__trivial,axiom,
% 0.26/0.57      ! [K: int,L: int] :
% 0.26/0.57        ( ( ord_less_int @ zero_zero_int @ K )
% 0.26/0.57       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 0.26/0.57         => ( ( modulo_modulo_int @ K @ L )
% 0.26/0.57            = ( plus_plus_int @ K @ L ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % mod_pos_neg_trivial
% 0.26/0.57  thf(fact_5936_mod__pos__geq,axiom,
% 0.26/0.57      ! [L: int,K: int] :
% 0.26/0.57        ( ( ord_less_int @ zero_zero_int @ L )
% 0.26/0.57       => ( ( ord_less_eq_int @ L @ K )
% 0.26/0.57         => ( ( modulo_modulo_int @ K @ L )
% 0.26/0.57            = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % mod_pos_geq
% 0.26/0.57  thf(fact_5937_mod__int__pos__iff,axiom,
% 0.26/0.57      ! [K: int,L: int] :
% 0.26/0.57        ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 0.26/0.57        = ( ( dvd_dvd_int @ L @ K )
% 0.26/0.57          | ( ( L = zero_zero_int )
% 0.26/0.57            & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 0.26/0.57          | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % mod_int_pos_iff
% 0.26/0.57  thf(fact_5938_nat__mod__distrib,axiom,
% 0.26/0.57      ! [X3: int,Y3: int] :
% 0.26/0.57        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.26/0.57       => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 0.26/0.57         => ( ( nat2 @ ( modulo_modulo_int @ X3 @ Y3 ) )
% 0.26/0.57            = ( modulo_modulo_nat @ ( nat2 @ X3 ) @ ( nat2 @ Y3 ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % nat_mod_distrib
% 0.26/0.57  thf(fact_5939_take__bit__signed__take__bit,axiom,
% 0.26/0.57      ! [M: nat,N: nat,A: int] :
% 0.26/0.57        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.26/0.57       => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N @ A ) )
% 0.26/0.57          = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % take_bit_signed_take_bit
% 0.26/0.57  thf(fact_5940_mod__abs__eq__div__nat,axiom,
% 0.26/0.57      ! [K: int,L: int] :
% 0.26/0.57        ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 0.26/0.57        = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % mod_abs_eq_div_nat
% 0.26/0.57  thf(fact_5941_real__of__int__div__aux,axiom,
% 0.26/0.57      ! [X3: int,D3: int] :
% 0.26/0.57        ( ( divide_divide_real @ ( ring_1_of_int_real @ X3 ) @ ( ring_1_of_int_real @ D3 ) )
% 0.26/0.57        = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X3 @ D3 ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X3 @ D3 ) ) @ ( ring_1_of_int_real @ D3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % real_of_int_div_aux
% 0.26/0.57  thf(fact_5942_binomial__maximum,axiom,
% 0.26/0.57      ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % binomial_maximum
% 0.26/0.57  thf(fact_5943_binomial__antimono,axiom,
% 0.26/0.57      ! [K: nat,K6: nat,N: nat] :
% 0.26/0.57        ( ( ord_less_eq_nat @ K @ K6 )
% 0.26/0.57       => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 0.26/0.57         => ( ( ord_less_eq_nat @ K6 @ N )
% 0.26/0.57           => ( ord_less_eq_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % binomial_antimono
% 0.26/0.57  thf(fact_5944_binomial__mono,axiom,
% 0.26/0.57      ! [K: nat,K6: nat,N: nat] :
% 0.26/0.57        ( ( ord_less_eq_nat @ K @ K6 )
% 0.26/0.57       => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 0.26/0.57         => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % binomial_mono
% 0.26/0.57  thf(fact_5945_binomial__maximum_H,axiom,
% 0.26/0.57      ! [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 ) ) ).
% 0.26/0.57  
% 0.26/0.57  % binomial_maximum'
% 0.26/0.57  thf(fact_5946_split__zmod,axiom,
% 0.26/0.57      ! [P: int > $o,N: int,K: int] :
% 0.26/0.57        ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 0.26/0.57        = ( ( ( K = zero_zero_int )
% 0.26/0.57           => ( P @ N ) )
% 0.26/0.57          & ( ( ord_less_int @ zero_zero_int @ K )
% 0.26/0.57           => ! [I4: int,J3: int] :
% 0.26/0.57                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 0.26/0.57                  & ( ord_less_int @ J3 @ K )
% 0.26/0.57                  & ( N
% 0.26/0.57                    = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 0.26/0.57               => ( P @ J3 ) ) )
% 0.26/0.57          & ( ( ord_less_int @ K @ zero_zero_int )
% 0.26/0.57           => ! [I4: int,J3: int] :
% 0.26/0.57                ( ( ( ord_less_int @ K @ J3 )
% 0.26/0.57                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 0.26/0.57                  & ( N
% 0.26/0.57                    = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 0.26/0.57               => ( P @ J3 ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % split_zmod
% 0.26/0.57  thf(fact_5947_int__mod__neg__eq,axiom,
% 0.26/0.57      ! [A: int,B: int,Q3: int,R2: int] :
% 0.26/0.57        ( ( A
% 0.26/0.57          = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 0.26/0.57       => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 0.26/0.57         => ( ( ord_less_int @ B @ R2 )
% 0.26/0.57           => ( ( modulo_modulo_int @ A @ B )
% 0.26/0.57              = R2 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % int_mod_neg_eq
% 0.26/0.57  thf(fact_5948_int__mod__pos__eq,axiom,
% 0.26/0.57      ! [A: int,B: int,Q3: int,R2: int] :
% 0.26/0.57        ( ( A
% 0.26/0.57          = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 0.26/0.57       => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 0.26/0.57         => ( ( ord_less_int @ R2 @ B )
% 0.26/0.57           => ( ( modulo_modulo_int @ A @ B )
% 0.26/0.57              = R2 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % int_mod_pos_eq
% 0.26/0.57  thf(fact_5949_minus__mod__int__eq,axiom,
% 0.26/0.57      ! [L: int,K: int] :
% 0.26/0.57        ( ( ord_less_eq_int @ zero_zero_int @ L )
% 0.26/0.57       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 0.26/0.57          = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % minus_mod_int_eq
% 0.26/0.57  thf(fact_5950_zmod__minus1,axiom,
% 0.26/0.57      ! [B: int] :
% 0.26/0.57        ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.57       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 0.26/0.57          = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % zmod_minus1
% 0.26/0.57  thf(fact_5951_signed__take__bit__int__less__exp,axiom,
% 0.26/0.57      ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_int_less_exp
% 0.26/0.57  thf(fact_5952_take__bit__int__def,axiom,
% 0.26/0.57      ( bit_se2923211474154528505it_int
% 0.26/0.57      = ( ^ [N3: nat,K3: int] : ( modulo_modulo_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % take_bit_int_def
% 0.26/0.57  thf(fact_5953_zmod__zmult2__eq,axiom,
% 0.26/0.57      ! [C: int,A: int,B: int] :
% 0.26/0.57        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.26/0.57       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 0.26/0.57          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % zmod_zmult2_eq
% 0.26/0.57  thf(fact_5954_zdiv__zminus2__eq__if,axiom,
% 0.26/0.57      ! [B: int,A: int] :
% 0.26/0.57        ( ( B != zero_zero_int )
% 0.26/0.57       => ( ( ( ( modulo_modulo_int @ A @ B )
% 0.26/0.57              = zero_zero_int )
% 0.26/0.57           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.26/0.57              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 0.26/0.57          & ( ( ( modulo_modulo_int @ A @ B )
% 0.26/0.57             != zero_zero_int )
% 0.26/0.57           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.26/0.57              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % zdiv_zminus2_eq_if
% 0.26/0.57  thf(fact_5955_zdiv__zminus1__eq__if,axiom,
% 0.26/0.57      ! [B: int,A: int] :
% 0.26/0.57        ( ( B != zero_zero_int )
% 0.26/0.57       => ( ( ( ( modulo_modulo_int @ A @ B )
% 0.26/0.57              = zero_zero_int )
% 0.26/0.57           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 0.26/0.57              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 0.26/0.57          & ( ( ( modulo_modulo_int @ A @ B )
% 0.26/0.57             != zero_zero_int )
% 0.26/0.57           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 0.26/0.57              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % zdiv_zminus1_eq_if
% 0.26/0.57  thf(fact_5956_even__signed__take__bit__iff,axiom,
% 0.26/0.57      ! [M: nat,A: code_integer] :
% 0.26/0.57        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 0.26/0.57        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 0.26/0.57  
% 0.26/0.57  % even_signed_take_bit_iff
% 0.26/0.57  thf(fact_5957_even__signed__take__bit__iff,axiom,
% 0.26/0.57      ! [M: nat,A: int] :
% 0.26/0.57        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 0.26/0.57        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 0.26/0.57  
% 0.26/0.57  % even_signed_take_bit_iff
% 0.26/0.57  thf(fact_5958_binomial__less__binomial__Suc,axiom,
% 0.26/0.57      ! [K: nat,N: nat] :
% 0.26/0.57        ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.57       => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % binomial_less_binomial_Suc
% 0.26/0.57  thf(fact_5959_binomial__strict__mono,axiom,
% 0.26/0.57      ! [K: nat,K6: nat,N: nat] :
% 0.26/0.57        ( ( ord_less_nat @ K @ K6 )
% 0.26/0.57       => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 0.26/0.57         => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % binomial_strict_mono
% 0.26/0.57  thf(fact_5960_binomial__strict__antimono,axiom,
% 0.26/0.57      ! [K: nat,K6: nat,N: nat] :
% 0.26/0.57        ( ( ord_less_nat @ K @ K6 )
% 0.26/0.57       => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 0.26/0.57         => ( ( ord_less_eq_nat @ K6 @ N )
% 0.26/0.57           => ( ord_less_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % binomial_strict_antimono
% 0.26/0.57  thf(fact_5961_central__binomial__odd,axiom,
% 0.26/0.57      ! [N: nat] :
% 0.26/0.57        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.57       => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.57          = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % central_binomial_odd
% 0.26/0.57  thf(fact_5962_verit__le__mono__div__int,axiom,
% 0.26/0.57      ! [A3: int,B5: int,N: int] :
% 0.26/0.57        ( ( ord_less_int @ A3 @ B5 )
% 0.26/0.57       => ( ( ord_less_int @ zero_zero_int @ N )
% 0.26/0.57         => ( ord_less_eq_int
% 0.26/0.57            @ ( plus_plus_int @ ( divide_divide_int @ A3 @ N )
% 0.26/0.57              @ ( if_int
% 0.26/0.57                @ ( ( modulo_modulo_int @ B5 @ N )
% 0.26/0.57                  = zero_zero_int )
% 0.26/0.57                @ one_one_int
% 0.26/0.57                @ zero_zero_int ) )
% 0.26/0.57            @ ( divide_divide_int @ B5 @ N ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % verit_le_mono_div_int
% 0.26/0.57  thf(fact_5963_signed__take__bit__int__greater__eq__self__iff,axiom,
% 0.26/0.57      ! [K: int,N: nat] :
% 0.26/0.57        ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 0.26/0.57        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_int_greater_eq_self_iff
% 0.26/0.57  thf(fact_5964_signed__take__bit__int__less__self__iff,axiom,
% 0.26/0.57      ! [N: nat,K: int] :
% 0.26/0.57        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 0.26/0.57        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_int_less_self_iff
% 0.26/0.57  thf(fact_5965_split__pos__lemma,axiom,
% 0.26/0.57      ! [K: int,P: int > int > $o,N: int] :
% 0.26/0.57        ( ( ord_less_int @ zero_zero_int @ K )
% 0.26/0.57       => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 0.26/0.57          = ( ! [I4: int,J3: int] :
% 0.26/0.57                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 0.26/0.57                  & ( ord_less_int @ J3 @ K )
% 0.26/0.57                  & ( N
% 0.26/0.57                    = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 0.26/0.57               => ( P @ I4 @ J3 ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % split_pos_lemma
% 0.26/0.57  thf(fact_5966_split__neg__lemma,axiom,
% 0.26/0.57      ! [K: int,P: int > int > $o,N: int] :
% 0.26/0.57        ( ( ord_less_int @ K @ zero_zero_int )
% 0.26/0.57       => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 0.26/0.57          = ( ! [I4: int,J3: int] :
% 0.26/0.57                ( ( ( ord_less_int @ K @ J3 )
% 0.26/0.57                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 0.26/0.57                  & ( N
% 0.26/0.57                    = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 0.26/0.57               => ( P @ I4 @ J3 ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % split_neg_lemma
% 0.26/0.57  thf(fact_5967_signed__take__bit__int__less__eq__self__iff,axiom,
% 0.26/0.57      ! [N: nat,K: int] :
% 0.26/0.57        ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 0.26/0.57        = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_int_less_eq_self_iff
% 0.26/0.57  thf(fact_5968_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 0.26/0.57      ! [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 ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_int_greater_eq_minus_exp
% 0.26/0.57  thf(fact_5969_signed__take__bit__int__greater__self__iff,axiom,
% 0.26/0.57      ! [K: int,N: nat] :
% 0.26/0.57        ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 0.26/0.57        = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_int_greater_self_iff
% 0.26/0.57  thf(fact_5970_length__induct,axiom,
% 0.26/0.57      ! [P: list_VEBT_VEBT > $o,Xs2: list_VEBT_VEBT] :
% 0.26/0.57        ( ! [Xs3: list_VEBT_VEBT] :
% 0.26/0.57            ( ! [Ys2: list_VEBT_VEBT] :
% 0.26/0.57                ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 0.26/0.57               => ( P @ Ys2 ) )
% 0.26/0.57           => ( P @ Xs3 ) )
% 0.26/0.57       => ( P @ Xs2 ) ) ).
% 0.26/0.57  
% 0.26/0.57  % length_induct
% 0.26/0.57  thf(fact_5971_length__induct,axiom,
% 0.26/0.57      ! [P: list_o > $o,Xs2: list_o] :
% 0.26/0.57        ( ! [Xs3: list_o] :
% 0.26/0.57            ( ! [Ys2: list_o] :
% 0.26/0.57                ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs3 ) )
% 0.26/0.57               => ( P @ Ys2 ) )
% 0.26/0.57           => ( P @ Xs3 ) )
% 0.26/0.57       => ( P @ Xs2 ) ) ).
% 0.26/0.57  
% 0.26/0.57  % length_induct
% 0.26/0.57  thf(fact_5972_length__induct,axiom,
% 0.26/0.57      ! [P: list_nat > $o,Xs2: list_nat] :
% 0.26/0.57        ( ! [Xs3: list_nat] :
% 0.26/0.57            ( ! [Ys2: list_nat] :
% 0.26/0.57                ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs3 ) )
% 0.26/0.57               => ( P @ Ys2 ) )
% 0.26/0.57           => ( P @ Xs3 ) )
% 0.26/0.57       => ( P @ Xs2 ) ) ).
% 0.26/0.57  
% 0.26/0.57  % length_induct
% 0.26/0.57  thf(fact_5973_length__induct,axiom,
% 0.26/0.57      ! [P: list_int > $o,Xs2: list_int] :
% 0.26/0.57        ( ! [Xs3: list_int] :
% 0.26/0.57            ( ! [Ys2: list_int] :
% 0.26/0.57                ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs3 ) )
% 0.26/0.57               => ( P @ Ys2 ) )
% 0.26/0.57           => ( P @ Xs3 ) )
% 0.26/0.57       => ( P @ Xs2 ) ) ).
% 0.26/0.57  
% 0.26/0.57  % length_induct
% 0.26/0.57  thf(fact_5974_signed__take__bit__int__less__eq,axiom,
% 0.26/0.57      ! [N: nat,K: int] :
% 0.26/0.57        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 0.26/0.57       => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_int_less_eq
% 0.26/0.57  thf(fact_5975_signed__take__bit__int__eq__self,axiom,
% 0.26/0.57      ! [N: nat,K: int] :
% 0.26/0.57        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 0.26/0.57       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.57         => ( ( bit_ri631733984087533419it_int @ N @ K )
% 0.26/0.57            = K ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_int_eq_self
% 0.26/0.57  thf(fact_5976_signed__take__bit__int__eq__self__iff,axiom,
% 0.26/0.57      ! [N: nat,K: int] :
% 0.26/0.57        ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 0.26/0.57          = K )
% 0.26/0.57        = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 0.26/0.57          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_int_eq_self_iff
% 0.26/0.57  thf(fact_5977_pos__zmod__mult__2,axiom,
% 0.26/0.57      ! [A: int,B: int] :
% 0.26/0.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.26/0.57       => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.26/0.57          = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pos_zmod_mult_2
% 0.26/0.57  thf(fact_5978_signed__take__bit__eq__take__bit__shift,axiom,
% 0.26/0.57      ( bit_ri631733984087533419it_int
% 0.26/0.57      = ( ^ [N3: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N3 ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_eq_take_bit_shift
% 0.26/0.57  thf(fact_5979_neg__zmod__mult__2,axiom,
% 0.26/0.57      ! [A: int,B: int] :
% 0.26/0.57        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.26/0.57       => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.26/0.57          = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) @ one_one_int ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % neg_zmod_mult_2
% 0.26/0.57  thf(fact_5980_signed__take__bit__int__greater__eq,axiom,
% 0.26/0.57      ! [K: int,N: nat] :
% 0.26/0.57        ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 0.26/0.57       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_int_greater_eq
% 0.26/0.57  thf(fact_5981_signed__take__bit__Suc,axiom,
% 0.26/0.57      ! [N: nat,A: code_integer] :
% 0.26/0.57        ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ A )
% 0.26/0.57        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_Suc
% 0.26/0.57  thf(fact_5982_signed__take__bit__Suc,axiom,
% 0.26/0.57      ! [N: nat,A: int] :
% 0.26/0.57        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 0.26/0.57        = ( 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 ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % signed_take_bit_Suc
% 0.26/0.57  thf(fact_5983_list__eq__iff__nth__eq,axiom,
% 0.26/0.57      ( ( ^ [Y5: list_VEBT_VEBT,Z2: list_VEBT_VEBT] : ( Y5 = Z2 ) )
% 0.26/0.57      = ( ^ [Xs: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 0.26/0.57            ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.26/0.57              = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 0.26/0.57            & ! [I4: nat] :
% 0.26/0.57                ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.26/0.57               => ( ( nth_VEBT_VEBT @ Xs @ I4 )
% 0.26/0.57                  = ( nth_VEBT_VEBT @ Ys3 @ I4 ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % list_eq_iff_nth_eq
% 0.26/0.57  thf(fact_5984_list__eq__iff__nth__eq,axiom,
% 0.26/0.57      ( ( ^ [Y5: list_o,Z2: list_o] : ( Y5 = Z2 ) )
% 0.26/0.57      = ( ^ [Xs: list_o,Ys3: list_o] :
% 0.26/0.57            ( ( ( size_size_list_o @ Xs )
% 0.26/0.57              = ( size_size_list_o @ Ys3 ) )
% 0.26/0.57            & ! [I4: nat] :
% 0.26/0.57                ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 0.26/0.57               => ( ( nth_o @ Xs @ I4 )
% 0.26/0.57                  = ( nth_o @ Ys3 @ I4 ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % list_eq_iff_nth_eq
% 0.26/0.57  thf(fact_5985_list__eq__iff__nth__eq,axiom,
% 0.26/0.57      ( ( ^ [Y5: list_nat,Z2: list_nat] : ( Y5 = Z2 ) )
% 0.26/0.57      = ( ^ [Xs: list_nat,Ys3: list_nat] :
% 0.26/0.57            ( ( ( size_size_list_nat @ Xs )
% 0.26/0.57              = ( size_size_list_nat @ Ys3 ) )
% 0.26/0.57            & ! [I4: nat] :
% 0.26/0.57                ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 0.26/0.57               => ( ( nth_nat @ Xs @ I4 )
% 0.26/0.57                  = ( nth_nat @ Ys3 @ I4 ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % list_eq_iff_nth_eq
% 0.26/0.57  thf(fact_5986_list__eq__iff__nth__eq,axiom,
% 0.26/0.57      ( ( ^ [Y5: list_int,Z2: list_int] : ( Y5 = Z2 ) )
% 0.26/0.57      = ( ^ [Xs: list_int,Ys3: list_int] :
% 0.26/0.57            ( ( ( size_size_list_int @ Xs )
% 0.26/0.57              = ( size_size_list_int @ Ys3 ) )
% 0.26/0.57            & ! [I4: nat] :
% 0.26/0.57                ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 0.26/0.57               => ( ( nth_int @ Xs @ I4 )
% 0.26/0.57                  = ( nth_int @ Ys3 @ I4 ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % list_eq_iff_nth_eq
% 0.26/0.57  thf(fact_5987_Skolem__list__nth,axiom,
% 0.26/0.57      ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 0.26/0.57        ( ( ! [I4: nat] :
% 0.26/0.57              ( ( ord_less_nat @ I4 @ K )
% 0.26/0.57             => ? [X8: vEBT_VEBT] : ( P @ I4 @ X8 ) ) )
% 0.26/0.57        = ( ? [Xs: list_VEBT_VEBT] :
% 0.26/0.57              ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.26/0.57                = K )
% 0.26/0.57              & ! [I4: nat] :
% 0.26/0.57                  ( ( ord_less_nat @ I4 @ K )
% 0.26/0.57                 => ( P @ I4 @ ( nth_VEBT_VEBT @ Xs @ I4 ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % Skolem_list_nth
% 0.26/0.57  thf(fact_5988_Skolem__list__nth,axiom,
% 0.26/0.57      ! [K: nat,P: nat > $o > $o] :
% 0.26/0.57        ( ( ! [I4: nat] :
% 0.26/0.57              ( ( ord_less_nat @ I4 @ K )
% 0.26/0.57             => ? [X8: $o] : ( P @ I4 @ X8 ) ) )
% 0.26/0.57        = ( ? [Xs: list_o] :
% 0.26/0.57              ( ( ( size_size_list_o @ Xs )
% 0.26/0.57                = K )
% 0.26/0.57              & ! [I4: nat] :
% 0.26/0.57                  ( ( ord_less_nat @ I4 @ K )
% 0.26/0.57                 => ( P @ I4 @ ( nth_o @ Xs @ I4 ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % Skolem_list_nth
% 0.26/0.57  thf(fact_5989_Skolem__list__nth,axiom,
% 0.26/0.57      ! [K: nat,P: nat > nat > $o] :
% 0.26/0.57        ( ( ! [I4: nat] :
% 0.26/0.57              ( ( ord_less_nat @ I4 @ K )
% 0.26/0.57             => ? [X8: nat] : ( P @ I4 @ X8 ) ) )
% 0.26/0.57        = ( ? [Xs: list_nat] :
% 0.26/0.57              ( ( ( size_size_list_nat @ Xs )
% 0.26/0.57                = K )
% 0.26/0.57              & ! [I4: nat] :
% 0.26/0.57                  ( ( ord_less_nat @ I4 @ K )
% 0.26/0.57                 => ( P @ I4 @ ( nth_nat @ Xs @ I4 ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % Skolem_list_nth
% 0.26/0.57  thf(fact_5990_Skolem__list__nth,axiom,
% 0.26/0.57      ! [K: nat,P: nat > int > $o] :
% 0.26/0.57        ( ( ! [I4: nat] :
% 0.26/0.57              ( ( ord_less_nat @ I4 @ K )
% 0.26/0.57             => ? [X8: int] : ( P @ I4 @ X8 ) ) )
% 0.26/0.57        = ( ? [Xs: list_int] :
% 0.26/0.57              ( ( ( size_size_list_int @ Xs )
% 0.26/0.57                = K )
% 0.26/0.57              & ! [I4: nat] :
% 0.26/0.57                  ( ( ord_less_nat @ I4 @ K )
% 0.26/0.57                 => ( P @ I4 @ ( nth_int @ Xs @ I4 ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % Skolem_list_nth
% 0.26/0.57  thf(fact_5991_zero__less__binomial__iff,axiom,
% 0.26/0.57      ! [N: nat,K: nat] :
% 0.26/0.57        ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 0.26/0.57        = ( ord_less_eq_nat @ K @ N ) ) ).
% 0.26/0.57  
% 0.26/0.57  % zero_less_binomial_iff
% 0.26/0.57  thf(fact_5992_choose__two,axiom,
% 0.26/0.57      ! [N: nat] :
% 0.26/0.57        ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.57        = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % choose_two
% 0.26/0.57  thf(fact_5993_binomial__n__0,axiom,
% 0.26/0.57      ! [N: nat] :
% 0.26/0.57        ( ( binomial @ N @ zero_zero_nat )
% 0.26/0.57        = one_one_nat ) ).
% 0.26/0.57  
% 0.26/0.57  % binomial_n_0
% 0.26/0.57  thf(fact_5994_binomial__eq__0__iff,axiom,
% 0.26/0.57      ! [N: nat,K: nat] :
% 0.26/0.57        ( ( ( binomial @ N @ K )
% 0.26/0.57          = zero_zero_nat )
% 0.26/0.57        = ( ord_less_nat @ N @ K ) ) ).
% 0.26/0.57  
% 0.26/0.57  % binomial_eq_0_iff
% 0.26/0.57  thf(fact_5995_binomial__0__Suc,axiom,
% 0.26/0.57      ! [K: nat] :
% 0.26/0.57        ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 0.26/0.57        = zero_zero_nat ) ).
% 0.26/0.57  
% 0.26/0.57  % binomial_0_Suc
% 0.26/0.57  thf(fact_5996_binomial__1,axiom,
% 0.26/0.57      ! [N: nat] :
% 0.26/0.57        ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 0.26/0.57        = N ) ).
% 0.26/0.57  
% 0.26/0.57  % binomial_1
% 0.26/0.57  thf(fact_5997_valid__0__not,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT] :
% 0.26/0.57        ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 0.26/0.57  
% 0.26/0.57  % valid_0_not
% 0.26/0.57  thf(fact_5998_valid__tree__deg__neq__0,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT] :
% 0.26/0.57        ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 0.26/0.57  
% 0.26/0.57  % valid_tree_deg_neq_0
% 0.26/0.57  thf(fact_5999_deg__not__0,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.26/0.57  
% 0.26/0.57  % deg_not_0
% 0.26/0.57  thf(fact_6000_set__n__deg__not__0,axiom,
% 0.26/0.57      ! [TreeList2: list_VEBT_VEBT,N: nat,M: nat] :
% 0.26/0.57        ( ! [X4: vEBT_VEBT] :
% 0.26/0.57            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.26/0.57           => ( vEBT_invar_vebt @ X4 @ N ) )
% 0.26/0.57       => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.26/0.57            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.26/0.57         => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % set_n_deg_not_0
% 0.26/0.57  thf(fact_6001_binomial__eq__0,axiom,
% 0.26/0.57      ! [N: nat,K: nat] :
% 0.26/0.57        ( ( ord_less_nat @ N @ K )
% 0.26/0.57       => ( ( binomial @ N @ K )
% 0.26/0.57          = zero_zero_nat ) ) ).
% 0.26/0.57  
% 0.26/0.57  % binomial_eq_0
% 0.26/0.57  thf(fact_6002_binomial__symmetric,axiom,
% 0.26/0.57      ! [K: nat,N: nat] :
% 0.26/0.57        ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.57       => ( ( binomial @ N @ K )
% 0.26/0.57          = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % binomial_symmetric
% 0.26/0.57  thf(fact_6003_binomial__le__pow,axiom,
% 0.26/0.57      ! [R2: nat,N: nat] :
% 0.26/0.57        ( ( ord_less_eq_nat @ R2 @ N )
% 0.26/0.57       => ( ord_less_eq_nat @ ( binomial @ N @ R2 ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % binomial_le_pow
% 0.26/0.57  thf(fact_6004_zero__less__binomial,axiom,
% 0.26/0.57      ! [K: nat,N: nat] :
% 0.26/0.57        ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.57       => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % zero_less_binomial
% 0.26/0.57  thf(fact_6005_choose__mult,axiom,
% 0.26/0.57      ! [K: nat,M: nat,N: nat] :
% 0.26/0.57        ( ( ord_less_eq_nat @ K @ M )
% 0.26/0.57       => ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.57         => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 0.26/0.57            = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % choose_mult
% 0.26/0.57  thf(fact_6006_binomial__ge__n__over__k__pow__k,axiom,
% 0.26/0.57      ! [K: nat,N: nat] :
% 0.26/0.57        ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.57       => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % binomial_ge_n_over_k_pow_k
% 0.26/0.57  thf(fact_6007_binomial__ge__n__over__k__pow__k,axiom,
% 0.26/0.57      ! [K: nat,N: nat] :
% 0.26/0.57        ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.57       => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % binomial_ge_n_over_k_pow_k
% 0.26/0.57  thf(fact_6008_binomial__le__pow2,axiom,
% 0.26/0.57      ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.26/0.57  
% 0.26/0.57  % binomial_le_pow2
% 0.26/0.57  thf(fact_6009_choose__reduce__nat,axiom,
% 0.26/0.57      ! [N: nat,K: nat] :
% 0.26/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.57       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.26/0.57         => ( ( binomial @ N @ K )
% 0.26/0.57            = ( 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 ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % choose_reduce_nat
% 0.26/0.57  thf(fact_6010_times__binomial__minus1__eq,axiom,
% 0.26/0.57      ! [K: nat,N: nat] :
% 0.26/0.57        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.26/0.57       => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 0.26/0.57          = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % times_binomial_minus1_eq
% 0.26/0.57  thf(fact_6011_binomial__addition__formula,axiom,
% 0.26/0.57      ! [N: nat,K: nat] :
% 0.26/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.57       => ( ( binomial @ N @ ( suc @ K ) )
% 0.26/0.57          = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % binomial_addition_formula
% 0.26/0.57  thf(fact_6012_valid__insert__both__member__options__pres,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,X3: nat,Y3: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.57         => ( ( ord_less_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.57           => ( ( vEBT_V8194947554948674370ptions @ T @ X3 )
% 0.26/0.57             => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y3 ) @ X3 ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % valid_insert_both_member_options_pres
% 0.26/0.57  thf(fact_6013_valid__insert__both__member__options__add,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.57         => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X3 ) @ X3 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % valid_insert_both_member_options_add
% 0.26/0.57  thf(fact_6014_height__double__log__univ__size,axiom,
% 0.26/0.57      ! [U: real,Deg: nat,T: vEBT_VEBT] :
% 0.26/0.57        ( ( U
% 0.26/0.57          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Deg ) )
% 0.26/0.57       => ( ( vEBT_invar_vebt @ T @ Deg )
% 0.26/0.57         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_VEBT_height @ T ) ) @ ( plus_plus_real @ one_one_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % height_double_log_univ_size
% 0.26/0.57  thf(fact_6015_heigt__uplog__rel,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ T ) )
% 0.26/0.57          = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % heigt_uplog_rel
% 0.26/0.57  thf(fact_6016_helpypredd,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,X3: nat,Y3: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( ( vEBT_vebt_pred @ T @ X3 )
% 0.26/0.57            = ( some_nat @ Y3 ) )
% 0.26/0.57         => ( ord_less_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % helpypredd
% 0.26/0.57  thf(fact_6017_helpyd,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,X3: nat,Y3: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( ( vEBT_vebt_succ @ T @ X3 )
% 0.26/0.57            = ( some_nat @ Y3 ) )
% 0.26/0.57         => ( ord_less_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % helpyd
% 0.26/0.57  thf(fact_6018_two__powr__height__bound__deg,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_VEBT_height @ T ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % two_powr_height_bound_deg
% 0.26/0.57  thf(fact_6019_both__member__options__ding,axiom,
% 0.26/0.57      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 0.26/0.57       => ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.26/0.57         => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.57           => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ X3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % both_member_options_ding
% 0.26/0.57  thf(fact_6020_post__member__pre__member,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,X3: nat,Y3: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.57         => ( ( ord_less_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.57           => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X3 ) @ Y3 )
% 0.26/0.57             => ( ( vEBT_vebt_member @ T @ Y3 )
% 0.26/0.57                | ( X3 = Y3 ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % post_member_pre_member
% 0.26/0.57  thf(fact_6021_buildup__gives__valid,axiom,
% 0.26/0.57      ! [N: nat] :
% 0.26/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.57       => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 0.26/0.57  
% 0.26/0.57  % buildup_gives_valid
% 0.26/0.57  thf(fact_6022_member__bound,axiom,
% 0.26/0.57      ! [Tree: vEBT_VEBT,X3: nat,N: nat] :
% 0.26/0.57        ( ( vEBT_vebt_member @ Tree @ X3 )
% 0.26/0.57       => ( ( vEBT_invar_vebt @ Tree @ N )
% 0.26/0.57         => ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % member_bound
% 0.26/0.57  thf(fact_6023_misiz,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,M: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( ( some_nat @ M )
% 0.26/0.57            = ( vEBT_vebt_mint @ T ) )
% 0.26/0.57         => ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % misiz
% 0.26/0.57  thf(fact_6024_height__compose__child,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,Summary: vEBT_VEBT] :
% 0.26/0.57        ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.26/0.57       => ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % height_compose_child
% 0.26/0.57  thf(fact_6025_deg__deg__n,axiom,
% 0.26/0.57      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 0.26/0.57       => ( Deg = N ) ) ).
% 0.26/0.57  
% 0.26/0.57  % deg_deg_n
% 0.26/0.57  thf(fact_6026_deg__SUcn__Node,axiom,
% 0.26/0.57      ! [Tree: vEBT_VEBT,N: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 0.26/0.57       => ? [Info2: option4927543243414619207at_nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.26/0.57            ( Tree
% 0.26/0.57            = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N ) ) @ TreeList3 @ S3 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % deg_SUcn_Node
% 0.26/0.57  thf(fact_6027_valid__member__both__member__options,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( vEBT_V8194947554948674370ptions @ T @ X3 )
% 0.26/0.57         => ( vEBT_vebt_member @ T @ X3 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % valid_member_both_member_options
% 0.26/0.57  thf(fact_6028_both__member__options__equiv__member,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( vEBT_V8194947554948674370ptions @ T @ X3 )
% 0.26/0.57          = ( vEBT_vebt_member @ T @ X3 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % both_member_options_equiv_member
% 0.26/0.57  thf(fact_6029_mint__member,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( ( vEBT_vebt_mint @ T )
% 0.26/0.57            = ( some_nat @ Maxi ) )
% 0.26/0.57         => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % mint_member
% 0.26/0.57  thf(fact_6030_height__compose__summary,axiom,
% 0.26/0.57      ! [Summary: vEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ Summary ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % height_compose_summary
% 0.26/0.57  thf(fact_6031_mint__corr__help,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,Mini: nat,X3: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( ( vEBT_vebt_mint @ T )
% 0.26/0.57            = ( some_nat @ Mini ) )
% 0.26/0.57         => ( ( vEBT_vebt_member @ T @ X3 )
% 0.26/0.57           => ( ord_less_eq_nat @ Mini @ X3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % mint_corr_help
% 0.26/0.57  thf(fact_6032_member__correct,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( vEBT_vebt_member @ T @ X3 )
% 0.26/0.57          = ( member_nat @ X3 @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % member_correct
% 0.26/0.57  thf(fact_6033_mint__corr,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( ( vEBT_vebt_mint @ T )
% 0.26/0.57            = ( some_nat @ X3 ) )
% 0.26/0.57         => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X3 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % mint_corr
% 0.26/0.57  thf(fact_6034_mint__sound,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X3 )
% 0.26/0.57         => ( ( vEBT_vebt_mint @ T )
% 0.26/0.57            = ( some_nat @ X3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % mint_sound
% 0.26/0.57  thf(fact_6035_both__member__options__from__chilf__to__complete__tree,axiom,
% 0.26/0.57      ! [X3: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 0.26/0.57        ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.57       => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 0.26/0.57         => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.57           => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % both_member_options_from_chilf_to_complete_tree
% 0.26/0.57  thf(fact_6036_member__inv,axiom,
% 0.26/0.57      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 0.26/0.57        ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.57       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.57          & ( ( X3 = Mi )
% 0.26/0.57            | ( X3 = Ma )
% 0.26/0.57            | ( ( ord_less_nat @ X3 @ Ma )
% 0.26/0.57              & ( ord_less_nat @ Mi @ X3 )
% 0.26/0.57              & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.57              & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % member_inv
% 0.26/0.57  thf(fact_6037_mintlistlength,axiom,
% 0.26/0.57      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 0.26/0.57       => ( ( Mi != Ma )
% 0.26/0.57         => ( ( ord_less_nat @ Mi @ Ma )
% 0.26/0.57            & ? [M4: nat] :
% 0.26/0.57                ( ( ( some_nat @ M4 )
% 0.26/0.57                  = ( vEBT_vebt_mint @ Summary ) )
% 0.26/0.57                & ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % mintlistlength
% 0.26/0.57  thf(fact_6038_both__member__options__from__complete__tree__to__child,axiom,
% 0.26/0.57      ! [Deg: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 0.26/0.57        ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 0.26/0.57       => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.57         => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.57            | ( X3 = Mi )
% 0.26/0.57            | ( X3 = Ma ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % both_member_options_from_complete_tree_to_child
% 0.26/0.57  thf(fact_6039_set__vebt__set__vebt_H__valid,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( vEBT_set_vebt @ T )
% 0.26/0.57          = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % set_vebt_set_vebt'_valid
% 0.26/0.57  thf(fact_6040_mi__eq__ma__no__ch,axiom,
% 0.26/0.57      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 0.26/0.57       => ( ( Mi = Ma )
% 0.26/0.57         => ( ! [X6: vEBT_VEBT] :
% 0.26/0.57                ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.26/0.57               => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_12 ) )
% 0.26/0.57            & ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % mi_eq_ma_no_ch
% 0.26/0.57  thf(fact_6041_insert__simp__mima,axiom,
% 0.26/0.57      ! [X3: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.26/0.57        ( ( ( X3 = Mi )
% 0.26/0.57          | ( X3 = Ma ) )
% 0.26/0.57       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.57         => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.57            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % insert_simp_mima
% 0.26/0.57  thf(fact_6042_mi__ma__2__deg,axiom,
% 0.26/0.57      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 0.26/0.57       => ( ( ord_less_eq_nat @ Mi @ Ma )
% 0.26/0.57          & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % mi_ma_2_deg
% 0.26/0.57  thf(fact_6043_pred__max,axiom,
% 0.26/0.57      ! [Deg: nat,Ma: nat,X3: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.26/0.57        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.57       => ( ( ord_less_nat @ Ma @ X3 )
% 0.26/0.57         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.57            = ( some_nat @ Ma ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pred_max
% 0.26/0.57  thf(fact_6044_succ__min,axiom,
% 0.26/0.57      ! [Deg: nat,X3: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.26/0.57        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.57       => ( ( ord_less_nat @ X3 @ Mi )
% 0.26/0.57         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.57            = ( some_nat @ Mi ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % succ_min
% 0.26/0.57  thf(fact_6045_succ__member,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,X3: nat,Y3: nat] :
% 0.26/0.57        ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X3 @ Y3 )
% 0.26/0.57        = ( ( vEBT_vebt_member @ T @ Y3 )
% 0.26/0.57          & ( ord_less_nat @ X3 @ Y3 )
% 0.26/0.57          & ! [Z6: nat] :
% 0.26/0.57              ( ( ( vEBT_vebt_member @ T @ Z6 )
% 0.26/0.57                & ( ord_less_nat @ X3 @ Z6 ) )
% 0.26/0.57             => ( ord_less_eq_nat @ Y3 @ Z6 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % succ_member
% 0.26/0.57  thf(fact_6046_pred__member,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,X3: nat,Y3: nat] :
% 0.26/0.57        ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X3 @ Y3 )
% 0.26/0.57        = ( ( vEBT_vebt_member @ T @ Y3 )
% 0.26/0.57          & ( ord_less_nat @ Y3 @ X3 )
% 0.26/0.57          & ! [Z6: nat] :
% 0.26/0.57              ( ( ( vEBT_vebt_member @ T @ Z6 )
% 0.26/0.57                & ( ord_less_nat @ Z6 @ X3 ) )
% 0.26/0.57             => ( ord_less_eq_nat @ Z6 @ Y3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pred_member
% 0.26/0.57  thf(fact_6047_pred__corr,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,X3: nat,Px: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( ( vEBT_vebt_pred @ T @ X3 )
% 0.26/0.57            = ( some_nat @ Px ) )
% 0.26/0.57          = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X3 @ Px ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pred_corr
% 0.26/0.57  thf(fact_6048_succ__corr,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,X3: nat,Sx: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( ( vEBT_vebt_succ @ T @ X3 )
% 0.26/0.57            = ( some_nat @ Sx ) )
% 0.26/0.57          = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X3 @ Sx ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % succ_corr
% 0.26/0.57  thf(fact_6049_pred__correct,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,X3: nat,Sx: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( ( vEBT_vebt_pred @ T @ X3 )
% 0.26/0.57            = ( some_nat @ Sx ) )
% 0.26/0.57          = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X3 @ Sx ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pred_correct
% 0.26/0.57  thf(fact_6050_succ__correct,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,X3: nat,Sx: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( ( vEBT_vebt_succ @ T @ X3 )
% 0.26/0.57            = ( some_nat @ Sx ) )
% 0.26/0.57          = ( vEBT_is_succ_in_set @ ( vEBT_set_vebt @ T ) @ X3 @ Sx ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % succ_correct
% 0.26/0.57  thf(fact_6051_vebt__mint_Osimps_I3_J,axiom,
% 0.26/0.57      ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 0.26/0.57        ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 0.26/0.57        = ( some_nat @ Mi ) ) ).
% 0.26/0.57  
% 0.26/0.57  % vebt_mint.simps(3)
% 0.26/0.57  thf(fact_6052_invar__vebt_Ointros_I4_J,axiom,
% 0.26/0.57      ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 0.26/0.57        ( ! [X4: vEBT_VEBT] :
% 0.26/0.57            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.26/0.57           => ( vEBT_invar_vebt @ X4 @ N ) )
% 0.26/0.57       => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.26/0.57         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.26/0.57              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.26/0.57           => ( ( M = N )
% 0.26/0.57             => ( ( Deg
% 0.26/0.57                  = ( plus_plus_nat @ N @ M ) )
% 0.26/0.57               => ( ! [I3: nat] :
% 0.26/0.57                      ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.26/0.57                     => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X8 ) )
% 0.26/0.57                        = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 0.26/0.57                 => ( ( ( Mi = Ma )
% 0.26/0.57                     => ! [X4: vEBT_VEBT] :
% 0.26/0.57                          ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.26/0.57                         => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) ) )
% 0.26/0.57                   => ( ( ord_less_eq_nat @ Mi @ Ma )
% 0.26/0.57                     => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.26/0.57                       => ( ( ( Mi != Ma )
% 0.26/0.57                           => ! [I3: nat] :
% 0.26/0.57                                ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.26/0.57                               => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 0.26/0.57                                      = I3 )
% 0.26/0.57                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 0.26/0.57                                  & ! [X4: nat] :
% 0.26/0.57                                      ( ( ( ( vEBT_VEBT_high @ X4 @ N )
% 0.26/0.57                                          = I3 )
% 0.26/0.57                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N ) ) )
% 0.26/0.57                                     => ( ( ord_less_nat @ Mi @ X4 )
% 0.26/0.57                                        & ( ord_less_eq_nat @ X4 @ Ma ) ) ) ) ) )
% 0.26/0.57                         => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % invar_vebt.intros(4)
% 0.26/0.57  thf(fact_6053_invar__vebt_Ointros_I5_J,axiom,
% 0.26/0.57      ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 0.26/0.57        ( ! [X4: vEBT_VEBT] :
% 0.26/0.57            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.26/0.57           => ( vEBT_invar_vebt @ X4 @ N ) )
% 0.26/0.57       => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.26/0.57         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.26/0.57              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.26/0.57           => ( ( M
% 0.26/0.57                = ( suc @ N ) )
% 0.26/0.57             => ( ( Deg
% 0.26/0.57                  = ( plus_plus_nat @ N @ M ) )
% 0.26/0.57               => ( ! [I3: nat] :
% 0.26/0.57                      ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.26/0.57                     => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X8 ) )
% 0.26/0.57                        = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 0.26/0.57                 => ( ( ( Mi = Ma )
% 0.26/0.57                     => ! [X4: vEBT_VEBT] :
% 0.26/0.57                          ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.26/0.57                         => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) ) )
% 0.26/0.57                   => ( ( ord_less_eq_nat @ Mi @ Ma )
% 0.26/0.57                     => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.26/0.57                       => ( ( ( Mi != Ma )
% 0.26/0.57                           => ! [I3: nat] :
% 0.26/0.57                                ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.26/0.57                               => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 0.26/0.57                                      = I3 )
% 0.26/0.57                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 0.26/0.57                                  & ! [X4: nat] :
% 0.26/0.57                                      ( ( ( ( vEBT_VEBT_high @ X4 @ N )
% 0.26/0.57                                          = I3 )
% 0.26/0.57                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N ) ) )
% 0.26/0.57                                     => ( ( ord_less_nat @ Mi @ X4 )
% 0.26/0.57                                        & ( ord_less_eq_nat @ X4 @ Ma ) ) ) ) ) )
% 0.26/0.57                         => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % invar_vebt.intros(5)
% 0.26/0.57  thf(fact_6054_nested__mint,axiom,
% 0.26/0.57      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,Va2: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 0.26/0.57       => ( ( N
% 0.26/0.57            = ( suc @ ( suc @ Va2 ) ) )
% 0.26/0.57         => ( ~ ( ord_less_nat @ Ma @ Mi )
% 0.26/0.57           => ( ( Ma != Mi )
% 0.26/0.57             => ( 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 @ Va2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % nested_mint
% 0.26/0.57  thf(fact_6055_divmod__step__eq,axiom,
% 0.26/0.57      ! [L: num,R2: nat,Q3: nat] :
% 0.26/0.57        ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 0.26/0.57         => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 0.26/0.57            = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ one_one_nat ) @ ( minus_minus_nat @ R2 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 0.26/0.57        & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 0.26/0.57         => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 0.26/0.57            = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % divmod_step_eq
% 0.26/0.57  thf(fact_6056_divmod__step__eq,axiom,
% 0.26/0.57      ! [L: num,R2: int,Q3: int] :
% 0.26/0.57        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 0.26/0.57         => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 0.26/0.57            = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ one_one_int ) @ ( minus_minus_int @ R2 @ ( numeral_numeral_int @ L ) ) ) ) )
% 0.26/0.57        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 0.26/0.57         => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 0.26/0.57            = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % divmod_step_eq
% 0.26/0.57  thf(fact_6057_divmod__step__eq,axiom,
% 0.26/0.57      ! [L: num,R2: code_integer,Q3: code_integer] :
% 0.26/0.57        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 0.26/0.57         => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R2 ) )
% 0.26/0.57            = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R2 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 0.26/0.57        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 0.26/0.57         => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R2 ) )
% 0.26/0.57            = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % divmod_step_eq
% 0.26/0.57  thf(fact_6058_pred__list__to__short,axiom,
% 0.26/0.57      ! [Deg: nat,X3: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 0.26/0.57        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.57       => ( ( ord_less_eq_nat @ X3 @ Ma )
% 0.26/0.57         => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.57           => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.57              = none_nat ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % pred_list_to_short
% 0.26/0.57  thf(fact_6059_succ__list__to__short,axiom,
% 0.26/0.57      ! [Deg: nat,Mi: nat,X3: nat,TreeList2: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 0.26/0.57        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.57       => ( ( ord_less_eq_nat @ Mi @ X3 )
% 0.26/0.57         => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.57           => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.57              = none_nat ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % succ_list_to_short
% 0.26/0.57  thf(fact_6060_height__node,axiom,
% 0.26/0.57      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 0.26/0.57       => ( ord_less_eq_nat @ one_one_nat @ ( vEBT_VEBT_height @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % height_node
% 0.26/0.57  thf(fact_6061_inrange,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ord_less_eq_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % inrange
% 0.26/0.57  thf(fact_6062_geqmaxNone,axiom,
% 0.26/0.57      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 0.26/0.57       => ( ( ord_less_eq_nat @ Ma @ X3 )
% 0.26/0.57         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.57            = none_nat ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % geqmaxNone
% 0.26/0.57  thf(fact_6063_not__None__eq,axiom,
% 0.26/0.57      ! [X3: option_nat] :
% 0.26/0.57        ( ( X3 != none_nat )
% 0.26/0.57        = ( ? [Y: nat] :
% 0.26/0.57              ( X3
% 0.26/0.57              = ( some_nat @ Y ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % not_None_eq
% 0.26/0.57  thf(fact_6064_not__None__eq,axiom,
% 0.26/0.57      ! [X3: option4927543243414619207at_nat] :
% 0.26/0.57        ( ( X3 != none_P5556105721700978146at_nat )
% 0.26/0.57        = ( ? [Y: product_prod_nat_nat] :
% 0.26/0.57              ( X3
% 0.26/0.57              = ( some_P7363390416028606310at_nat @ Y ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % not_None_eq
% 0.26/0.57  thf(fact_6065_not__None__eq,axiom,
% 0.26/0.57      ! [X3: option_num] :
% 0.26/0.57        ( ( X3 != none_num )
% 0.26/0.57        = ( ? [Y: num] :
% 0.26/0.57              ( X3
% 0.26/0.57              = ( some_num @ Y ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % not_None_eq
% 0.26/0.57  thf(fact_6066_not__Some__eq,axiom,
% 0.26/0.57      ! [X3: option_nat] :
% 0.26/0.57        ( ( ! [Y: nat] :
% 0.26/0.57              ( X3
% 0.26/0.57             != ( some_nat @ Y ) ) )
% 0.26/0.57        = ( X3 = none_nat ) ) ).
% 0.26/0.57  
% 0.26/0.57  % not_Some_eq
% 0.26/0.57  thf(fact_6067_not__Some__eq,axiom,
% 0.26/0.57      ! [X3: option4927543243414619207at_nat] :
% 0.26/0.57        ( ( ! [Y: product_prod_nat_nat] :
% 0.26/0.57              ( X3
% 0.26/0.57             != ( some_P7363390416028606310at_nat @ Y ) ) )
% 0.26/0.57        = ( X3 = none_P5556105721700978146at_nat ) ) ).
% 0.26/0.57  
% 0.26/0.57  % not_Some_eq
% 0.26/0.57  thf(fact_6068_not__Some__eq,axiom,
% 0.26/0.57      ! [X3: option_num] :
% 0.26/0.57        ( ( ! [Y: num] :
% 0.26/0.57              ( X3
% 0.26/0.57             != ( some_num @ Y ) ) )
% 0.26/0.57        = ( X3 = none_num ) ) ).
% 0.26/0.57  
% 0.26/0.57  % not_Some_eq
% 0.26/0.57  thf(fact_6069_option_Ocollapse,axiom,
% 0.26/0.57      ! [Option: option_nat] :
% 0.26/0.57        ( ( Option != none_nat )
% 0.26/0.57       => ( ( some_nat @ ( the_nat @ Option ) )
% 0.26/0.57          = Option ) ) ).
% 0.26/0.57  
% 0.26/0.57  % option.collapse
% 0.26/0.57  thf(fact_6070_option_Ocollapse,axiom,
% 0.26/0.57      ! [Option: option4927543243414619207at_nat] :
% 0.26/0.57        ( ( Option != none_P5556105721700978146at_nat )
% 0.26/0.57       => ( ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) )
% 0.26/0.57          = Option ) ) ).
% 0.26/0.57  
% 0.26/0.57  % option.collapse
% 0.26/0.57  thf(fact_6071_option_Ocollapse,axiom,
% 0.26/0.57      ! [Option: option_num] :
% 0.26/0.57        ( ( Option != none_num )
% 0.26/0.57       => ( ( some_num @ ( the_num @ Option ) )
% 0.26/0.57          = Option ) ) ).
% 0.26/0.57  
% 0.26/0.57  % option.collapse
% 0.26/0.57  thf(fact_6072_option_Oexhaust__sel,axiom,
% 0.26/0.57      ! [Option: option_nat] :
% 0.26/0.57        ( ( Option != none_nat )
% 0.26/0.57       => ( Option
% 0.26/0.57          = ( some_nat @ ( the_nat @ Option ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % option.exhaust_sel
% 0.26/0.57  thf(fact_6073_option_Oexhaust__sel,axiom,
% 0.26/0.57      ! [Option: option4927543243414619207at_nat] :
% 0.26/0.57        ( ( Option != none_P5556105721700978146at_nat )
% 0.26/0.57       => ( Option
% 0.26/0.57          = ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % option.exhaust_sel
% 0.26/0.57  thf(fact_6074_option_Oexhaust__sel,axiom,
% 0.26/0.57      ! [Option: option_num] :
% 0.26/0.57        ( ( Option != none_num )
% 0.26/0.57       => ( Option
% 0.26/0.57          = ( some_num @ ( the_num @ Option ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % option.exhaust_sel
% 0.26/0.57  thf(fact_6075_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 0.26/0.57      ! [X3: produc2233624965454879586on_nat] :
% 0.26/0.57        ( ! [Uu: nat > nat > $o,Uv: option_nat] :
% 0.26/0.57            ( X3
% 0.26/0.57           != ( produc4035269172776083154on_nat @ Uu @ ( produc5098337634421038937on_nat @ none_nat @ Uv ) ) )
% 0.26/0.57       => ( ! [Uw: nat > nat > $o,V3: nat] :
% 0.26/0.57              ( X3
% 0.26/0.57             != ( produc4035269172776083154on_nat @ Uw @ ( produc5098337634421038937on_nat @ ( some_nat @ V3 ) @ none_nat ) ) )
% 0.26/0.57         => ~ ! [F2: nat > nat > $o,X4: nat,Y4: nat] :
% 0.26/0.57                ( X3
% 0.26/0.57               != ( produc4035269172776083154on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ X4 ) @ ( some_nat @ Y4 ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % VEBT_internal.option_comp_shift.cases
% 0.26/0.57  thf(fact_6076_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 0.26/0.57      ! [X3: produc5491161045314408544at_nat] :
% 0.26/0.57        ( ! [Uu: product_prod_nat_nat > product_prod_nat_nat > $o,Uv: option4927543243414619207at_nat] :
% 0.26/0.57            ( X3
% 0.26/0.57           != ( produc3994169339658061776at_nat @ Uu @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv ) ) )
% 0.26/0.57       => ( ! [Uw: product_prod_nat_nat > product_prod_nat_nat > $o,V3: product_prod_nat_nat] :
% 0.26/0.57              ( X3
% 0.26/0.57             != ( produc3994169339658061776at_nat @ Uw @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V3 ) @ none_P5556105721700978146at_nat ) ) )
% 0.26/0.57         => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > $o,X4: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 0.26/0.57                ( X3
% 0.26/0.57               != ( produc3994169339658061776at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ X4 ) @ ( some_P7363390416028606310at_nat @ Y4 ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % VEBT_internal.option_comp_shift.cases
% 0.26/0.57  thf(fact_6077_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 0.26/0.57      ! [X3: produc7036089656553540234on_num] :
% 0.26/0.57        ( ! [Uu: num > num > $o,Uv: option_num] :
% 0.26/0.57            ( X3
% 0.26/0.57           != ( produc3576312749637752826on_num @ Uu @ ( produc8585076106096196333on_num @ none_num @ Uv ) ) )
% 0.26/0.57       => ( ! [Uw: num > num > $o,V3: num] :
% 0.26/0.57              ( X3
% 0.26/0.57             != ( produc3576312749637752826on_num @ Uw @ ( produc8585076106096196333on_num @ ( some_num @ V3 ) @ none_num ) ) )
% 0.26/0.57         => ~ ! [F2: num > num > $o,X4: num,Y4: num] :
% 0.26/0.57                ( X3
% 0.26/0.57               != ( produc3576312749637752826on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ X4 ) @ ( some_num @ Y4 ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % VEBT_internal.option_comp_shift.cases
% 0.26/0.57  thf(fact_6078_VEBT__internal_Ooption__shift_Ocases,axiom,
% 0.26/0.57      ! [X3: produc8306885398267862888on_nat] :
% 0.26/0.57        ( ! [Uu: nat > nat > nat,Uv: option_nat] :
% 0.26/0.57            ( X3
% 0.26/0.57           != ( produc8929957630744042906on_nat @ Uu @ ( produc5098337634421038937on_nat @ none_nat @ Uv ) ) )
% 0.26/0.57       => ( ! [Uw: nat > nat > nat,V3: nat] :
% 0.26/0.57              ( X3
% 0.26/0.57             != ( produc8929957630744042906on_nat @ Uw @ ( produc5098337634421038937on_nat @ ( some_nat @ V3 ) @ none_nat ) ) )
% 0.26/0.57         => ~ ! [F2: nat > nat > nat,A5: nat,B4: nat] :
% 0.26/0.57                ( X3
% 0.26/0.57               != ( produc8929957630744042906on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ A5 ) @ ( some_nat @ B4 ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % VEBT_internal.option_shift.cases
% 0.26/0.57  thf(fact_6079_VEBT__internal_Ooption__shift_Ocases,axiom,
% 0.26/0.57      ! [X3: produc5542196010084753463at_nat] :
% 0.26/0.57        ( ! [Uu: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv: option4927543243414619207at_nat] :
% 0.26/0.57            ( X3
% 0.26/0.57           != ( produc2899441246263362727at_nat @ Uu @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv ) ) )
% 0.26/0.57       => ( ! [Uw: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V3: product_prod_nat_nat] :
% 0.26/0.57              ( X3
% 0.26/0.57             != ( produc2899441246263362727at_nat @ Uw @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V3 ) @ none_P5556105721700978146at_nat ) ) )
% 0.26/0.57         => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A5: product_prod_nat_nat,B4: product_prod_nat_nat] :
% 0.26/0.57                ( X3
% 0.26/0.57               != ( produc2899441246263362727at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A5 ) @ ( some_P7363390416028606310at_nat @ B4 ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % VEBT_internal.option_shift.cases
% 0.26/0.57  thf(fact_6080_VEBT__internal_Ooption__shift_Ocases,axiom,
% 0.26/0.57      ! [X3: produc1193250871479095198on_num] :
% 0.26/0.57        ( ! [Uu: num > num > num,Uv: option_num] :
% 0.26/0.57            ( X3
% 0.26/0.57           != ( produc5778274026573060048on_num @ Uu @ ( produc8585076106096196333on_num @ none_num @ Uv ) ) )
% 0.26/0.57       => ( ! [Uw: num > num > num,V3: num] :
% 0.26/0.57              ( X3
% 0.26/0.57             != ( produc5778274026573060048on_num @ Uw @ ( produc8585076106096196333on_num @ ( some_num @ V3 ) @ none_num ) ) )
% 0.26/0.57         => ~ ! [F2: num > num > num,A5: num,B4: num] :
% 0.26/0.57                ( X3
% 0.26/0.57               != ( produc5778274026573060048on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ A5 ) @ ( some_num @ B4 ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % VEBT_internal.option_shift.cases
% 0.26/0.57  thf(fact_6081_option_Oexpand,axiom,
% 0.26/0.57      ! [Option: option_nat,Option2: option_nat] :
% 0.26/0.57        ( ( ( Option = none_nat )
% 0.26/0.57          = ( Option2 = none_nat ) )
% 0.26/0.57       => ( ( ( Option != none_nat )
% 0.26/0.57           => ( ( Option2 != none_nat )
% 0.26/0.57             => ( ( the_nat @ Option )
% 0.26/0.57                = ( the_nat @ Option2 ) ) ) )
% 0.26/0.57         => ( Option = Option2 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % option.expand
% 0.26/0.57  thf(fact_6082_option_Oexpand,axiom,
% 0.26/0.57      ! [Option: option4927543243414619207at_nat,Option2: option4927543243414619207at_nat] :
% 0.26/0.57        ( ( ( Option = none_P5556105721700978146at_nat )
% 0.26/0.57          = ( Option2 = none_P5556105721700978146at_nat ) )
% 0.26/0.57       => ( ( ( Option != none_P5556105721700978146at_nat )
% 0.26/0.57           => ( ( Option2 != none_P5556105721700978146at_nat )
% 0.26/0.57             => ( ( the_Pr8591224930841456533at_nat @ Option )
% 0.26/0.57                = ( the_Pr8591224930841456533at_nat @ Option2 ) ) ) )
% 0.26/0.57         => ( Option = Option2 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % option.expand
% 0.26/0.57  thf(fact_6083_option_Oexpand,axiom,
% 0.26/0.57      ! [Option: option_num,Option2: option_num] :
% 0.26/0.57        ( ( ( Option = none_num )
% 0.26/0.57          = ( Option2 = none_num ) )
% 0.26/0.57       => ( ( ( Option != none_num )
% 0.26/0.57           => ( ( Option2 != none_num )
% 0.26/0.57             => ( ( the_num @ Option )
% 0.26/0.57                = ( the_num @ Option2 ) ) ) )
% 0.26/0.57         => ( Option = Option2 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % option.expand
% 0.26/0.57  thf(fact_6084_option_Odistinct_I1_J,axiom,
% 0.26/0.57      ! [X2: nat] :
% 0.26/0.57        ( none_nat
% 0.26/0.57       != ( some_nat @ X2 ) ) ).
% 0.26/0.57  
% 0.26/0.57  % option.distinct(1)
% 0.26/0.57  thf(fact_6085_option_Odistinct_I1_J,axiom,
% 0.26/0.57      ! [X2: product_prod_nat_nat] :
% 0.26/0.57        ( none_P5556105721700978146at_nat
% 0.26/0.57       != ( some_P7363390416028606310at_nat @ X2 ) ) ).
% 0.26/0.57  
% 0.26/0.57  % option.distinct(1)
% 0.26/0.57  thf(fact_6086_option_Odistinct_I1_J,axiom,
% 0.26/0.57      ! [X2: num] :
% 0.26/0.57        ( none_num
% 0.26/0.57       != ( some_num @ X2 ) ) ).
% 0.26/0.57  
% 0.26/0.57  % option.distinct(1)
% 0.26/0.57  thf(fact_6087_option_OdiscI,axiom,
% 0.26/0.57      ! [Option: option_nat,X2: nat] :
% 0.26/0.57        ( ( Option
% 0.26/0.57          = ( some_nat @ X2 ) )
% 0.26/0.57       => ( Option != none_nat ) ) ).
% 0.26/0.57  
% 0.26/0.57  % option.discI
% 0.26/0.57  thf(fact_6088_option_OdiscI,axiom,
% 0.26/0.57      ! [Option: option4927543243414619207at_nat,X2: product_prod_nat_nat] :
% 0.26/0.57        ( ( Option
% 0.26/0.57          = ( some_P7363390416028606310at_nat @ X2 ) )
% 0.26/0.57       => ( Option != none_P5556105721700978146at_nat ) ) ).
% 0.26/0.57  
% 0.26/0.57  % option.discI
% 0.26/0.57  thf(fact_6089_option_OdiscI,axiom,
% 0.26/0.57      ! [Option: option_num,X2: num] :
% 0.26/0.57        ( ( Option
% 0.26/0.57          = ( some_num @ X2 ) )
% 0.26/0.57       => ( Option != none_num ) ) ).
% 0.26/0.57  
% 0.26/0.57  % option.discI
% 0.26/0.57  thf(fact_6090_option_Oexhaust,axiom,
% 0.26/0.57      ! [Y3: option_nat] :
% 0.26/0.57        ( ( Y3 != none_nat )
% 0.26/0.57       => ~ ! [X22: nat] :
% 0.26/0.57              ( Y3
% 0.26/0.57             != ( some_nat @ X22 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % option.exhaust
% 0.26/0.57  thf(fact_6091_option_Oexhaust,axiom,
% 0.26/0.57      ! [Y3: option4927543243414619207at_nat] :
% 0.26/0.57        ( ( Y3 != none_P5556105721700978146at_nat )
% 0.26/0.57       => ~ ! [X22: product_prod_nat_nat] :
% 0.26/0.57              ( Y3
% 0.26/0.57             != ( some_P7363390416028606310at_nat @ X22 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % option.exhaust
% 0.26/0.57  thf(fact_6092_option_Oexhaust,axiom,
% 0.26/0.57      ! [Y3: option_num] :
% 0.26/0.57        ( ( Y3 != none_num )
% 0.26/0.57       => ~ ! [X22: num] :
% 0.26/0.57              ( Y3
% 0.26/0.57             != ( some_num @ X22 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % option.exhaust
% 0.26/0.57  thf(fact_6093_split__option__ex,axiom,
% 0.26/0.57      ( ( ^ [P2: option_nat > $o] :
% 0.26/0.57          ? [X5: option_nat] : ( P2 @ X5 ) )
% 0.26/0.57      = ( ^ [P3: option_nat > $o] :
% 0.26/0.57            ( ( P3 @ none_nat )
% 0.26/0.57            | ? [X: nat] : ( P3 @ ( some_nat @ X ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % split_option_ex
% 0.26/0.57  thf(fact_6094_split__option__ex,axiom,
% 0.26/0.57      ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 0.26/0.57          ? [X5: option4927543243414619207at_nat] : ( P2 @ X5 ) )
% 0.26/0.57      = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 0.26/0.57            ( ( P3 @ none_P5556105721700978146at_nat )
% 0.26/0.57            | ? [X: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % split_option_ex
% 0.26/0.57  thf(fact_6095_split__option__ex,axiom,
% 0.26/0.57      ( ( ^ [P2: option_num > $o] :
% 0.26/0.57          ? [X5: option_num] : ( P2 @ X5 ) )
% 0.26/0.57      = ( ^ [P3: option_num > $o] :
% 0.26/0.57            ( ( P3 @ none_num )
% 0.26/0.57            | ? [X: num] : ( P3 @ ( some_num @ X ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % split_option_ex
% 0.26/0.57  thf(fact_6096_split__option__all,axiom,
% 0.26/0.57      ( ( ^ [P2: option_nat > $o] :
% 0.26/0.57          ! [X5: option_nat] : ( P2 @ X5 ) )
% 0.26/0.57      = ( ^ [P3: option_nat > $o] :
% 0.26/0.57            ( ( P3 @ none_nat )
% 0.26/0.57            & ! [X: nat] : ( P3 @ ( some_nat @ X ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % split_option_all
% 0.26/0.57  thf(fact_6097_split__option__all,axiom,
% 0.26/0.57      ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 0.26/0.57          ! [X5: option4927543243414619207at_nat] : ( P2 @ X5 ) )
% 0.26/0.57      = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 0.26/0.57            ( ( P3 @ none_P5556105721700978146at_nat )
% 0.26/0.57            & ! [X: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % split_option_all
% 0.26/0.57  thf(fact_6098_split__option__all,axiom,
% 0.26/0.57      ( ( ^ [P2: option_num > $o] :
% 0.26/0.57          ! [X5: option_num] : ( P2 @ X5 ) )
% 0.26/0.57      = ( ^ [P3: option_num > $o] :
% 0.26/0.57            ( ( P3 @ none_num )
% 0.26/0.57            & ! [X: num] : ( P3 @ ( some_num @ X ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % split_option_all
% 0.26/0.57  thf(fact_6099_combine__options__cases,axiom,
% 0.26/0.57      ! [X3: option_nat,P: option_nat > option_nat > $o,Y3: option_nat] :
% 0.26/0.57        ( ( ( X3 = none_nat )
% 0.26/0.57         => ( P @ X3 @ Y3 ) )
% 0.26/0.57       => ( ( ( Y3 = none_nat )
% 0.26/0.57           => ( P @ X3 @ Y3 ) )
% 0.26/0.57         => ( ! [A5: nat,B4: nat] :
% 0.26/0.57                ( ( X3
% 0.26/0.57                  = ( some_nat @ A5 ) )
% 0.26/0.57               => ( ( Y3
% 0.26/0.57                    = ( some_nat @ B4 ) )
% 0.26/0.57                 => ( P @ X3 @ Y3 ) ) )
% 0.26/0.57           => ( P @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % combine_options_cases
% 0.26/0.57  thf(fact_6100_combine__options__cases,axiom,
% 0.26/0.57      ! [X3: option_nat,P: option_nat > option4927543243414619207at_nat > $o,Y3: option4927543243414619207at_nat] :
% 0.26/0.57        ( ( ( X3 = none_nat )
% 0.26/0.57         => ( P @ X3 @ Y3 ) )
% 0.26/0.57       => ( ( ( Y3 = none_P5556105721700978146at_nat )
% 0.26/0.57           => ( P @ X3 @ Y3 ) )
% 0.26/0.57         => ( ! [A5: nat,B4: product_prod_nat_nat] :
% 0.26/0.57                ( ( X3
% 0.26/0.57                  = ( some_nat @ A5 ) )
% 0.26/0.57               => ( ( Y3
% 0.26/0.57                    = ( some_P7363390416028606310at_nat @ B4 ) )
% 0.26/0.57                 => ( P @ X3 @ Y3 ) ) )
% 0.26/0.57           => ( P @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % combine_options_cases
% 0.26/0.57  thf(fact_6101_combine__options__cases,axiom,
% 0.26/0.57      ! [X3: option_nat,P: option_nat > option_num > $o,Y3: option_num] :
% 0.26/0.57        ( ( ( X3 = none_nat )
% 0.26/0.57         => ( P @ X3 @ Y3 ) )
% 0.26/0.57       => ( ( ( Y3 = none_num )
% 0.26/0.57           => ( P @ X3 @ Y3 ) )
% 0.26/0.57         => ( ! [A5: nat,B4: num] :
% 0.26/0.57                ( ( X3
% 0.26/0.57                  = ( some_nat @ A5 ) )
% 0.26/0.57               => ( ( Y3
% 0.26/0.57                    = ( some_num @ B4 ) )
% 0.26/0.57                 => ( P @ X3 @ Y3 ) ) )
% 0.26/0.57           => ( P @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % combine_options_cases
% 0.26/0.57  thf(fact_6102_combine__options__cases,axiom,
% 0.26/0.57      ! [X3: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_nat > $o,Y3: option_nat] :
% 0.26/0.57        ( ( ( X3 = none_P5556105721700978146at_nat )
% 0.26/0.57         => ( P @ X3 @ Y3 ) )
% 0.26/0.57       => ( ( ( Y3 = none_nat )
% 0.26/0.57           => ( P @ X3 @ Y3 ) )
% 0.26/0.57         => ( ! [A5: product_prod_nat_nat,B4: nat] :
% 0.26/0.57                ( ( X3
% 0.26/0.57                  = ( some_P7363390416028606310at_nat @ A5 ) )
% 0.26/0.57               => ( ( Y3
% 0.26/0.57                    = ( some_nat @ B4 ) )
% 0.26/0.57                 => ( P @ X3 @ Y3 ) ) )
% 0.26/0.57           => ( P @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % combine_options_cases
% 0.26/0.57  thf(fact_6103_combine__options__cases,axiom,
% 0.26/0.57      ! [X3: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y3: option4927543243414619207at_nat] :
% 0.26/0.57        ( ( ( X3 = none_P5556105721700978146at_nat )
% 0.26/0.57         => ( P @ X3 @ Y3 ) )
% 0.26/0.57       => ( ( ( Y3 = none_P5556105721700978146at_nat )
% 0.26/0.57           => ( P @ X3 @ Y3 ) )
% 0.26/0.57         => ( ! [A5: product_prod_nat_nat,B4: product_prod_nat_nat] :
% 0.26/0.57                ( ( X3
% 0.26/0.57                  = ( some_P7363390416028606310at_nat @ A5 ) )
% 0.26/0.57               => ( ( Y3
% 0.26/0.57                    = ( some_P7363390416028606310at_nat @ B4 ) )
% 0.26/0.57                 => ( P @ X3 @ Y3 ) ) )
% 0.26/0.57           => ( P @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % combine_options_cases
% 0.26/0.57  thf(fact_6104_combine__options__cases,axiom,
% 0.26/0.57      ! [X3: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y3: option_num] :
% 0.26/0.57        ( ( ( X3 = none_P5556105721700978146at_nat )
% 0.26/0.57         => ( P @ X3 @ Y3 ) )
% 0.26/0.57       => ( ( ( Y3 = none_num )
% 0.26/0.57           => ( P @ X3 @ Y3 ) )
% 0.26/0.57         => ( ! [A5: product_prod_nat_nat,B4: num] :
% 0.26/0.57                ( ( X3
% 0.26/0.57                  = ( some_P7363390416028606310at_nat @ A5 ) )
% 0.26/0.57               => ( ( Y3
% 0.26/0.57                    = ( some_num @ B4 ) )
% 0.26/0.57                 => ( P @ X3 @ Y3 ) ) )
% 0.26/0.57           => ( P @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % combine_options_cases
% 0.26/0.57  thf(fact_6105_combine__options__cases,axiom,
% 0.26/0.57      ! [X3: option_num,P: option_num > option_nat > $o,Y3: option_nat] :
% 0.26/0.57        ( ( ( X3 = none_num )
% 0.26/0.57         => ( P @ X3 @ Y3 ) )
% 0.26/0.57       => ( ( ( Y3 = none_nat )
% 0.26/0.57           => ( P @ X3 @ Y3 ) )
% 0.26/0.57         => ( ! [A5: num,B4: nat] :
% 0.26/0.57                ( ( X3
% 0.26/0.57                  = ( some_num @ A5 ) )
% 0.26/0.57               => ( ( Y3
% 0.26/0.57                    = ( some_nat @ B4 ) )
% 0.26/0.57                 => ( P @ X3 @ Y3 ) ) )
% 0.26/0.57           => ( P @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % combine_options_cases
% 0.26/0.57  thf(fact_6106_combine__options__cases,axiom,
% 0.26/0.57      ! [X3: option_num,P: option_num > option4927543243414619207at_nat > $o,Y3: option4927543243414619207at_nat] :
% 0.26/0.57        ( ( ( X3 = none_num )
% 0.26/0.57         => ( P @ X3 @ Y3 ) )
% 0.26/0.57       => ( ( ( Y3 = none_P5556105721700978146at_nat )
% 0.26/0.57           => ( P @ X3 @ Y3 ) )
% 0.26/0.57         => ( ! [A5: num,B4: product_prod_nat_nat] :
% 0.26/0.57                ( ( X3
% 0.26/0.57                  = ( some_num @ A5 ) )
% 0.26/0.57               => ( ( Y3
% 0.26/0.57                    = ( some_P7363390416028606310at_nat @ B4 ) )
% 0.26/0.57                 => ( P @ X3 @ Y3 ) ) )
% 0.26/0.57           => ( P @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % combine_options_cases
% 0.26/0.57  thf(fact_6107_combine__options__cases,axiom,
% 0.26/0.57      ! [X3: option_num,P: option_num > option_num > $o,Y3: option_num] :
% 0.26/0.57        ( ( ( X3 = none_num )
% 0.26/0.57         => ( P @ X3 @ Y3 ) )
% 0.26/0.57       => ( ( ( Y3 = none_num )
% 0.26/0.57           => ( P @ X3 @ Y3 ) )
% 0.26/0.57         => ( ! [A5: num,B4: num] :
% 0.26/0.57                ( ( X3
% 0.26/0.57                  = ( some_num @ A5 ) )
% 0.26/0.57               => ( ( Y3
% 0.26/0.57                    = ( some_num @ B4 ) )
% 0.26/0.57                 => ( P @ X3 @ Y3 ) ) )
% 0.26/0.57           => ( P @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % combine_options_cases
% 0.26/0.57  thf(fact_6108_option_Osel,axiom,
% 0.26/0.57      ! [X2: nat] :
% 0.26/0.57        ( ( the_nat @ ( some_nat @ X2 ) )
% 0.26/0.57        = X2 ) ).
% 0.26/0.57  
% 0.26/0.57  % option.sel
% 0.26/0.57  thf(fact_6109_option_Osel,axiom,
% 0.26/0.57      ! [X2: product_prod_nat_nat] :
% 0.26/0.57        ( ( the_Pr8591224930841456533at_nat @ ( some_P7363390416028606310at_nat @ X2 ) )
% 0.26/0.57        = X2 ) ).
% 0.26/0.57  
% 0.26/0.57  % option.sel
% 0.26/0.57  thf(fact_6110_option_Osel,axiom,
% 0.26/0.57      ! [X2: num] :
% 0.26/0.57        ( ( the_num @ ( some_num @ X2 ) )
% 0.26/0.57        = X2 ) ).
% 0.26/0.57  
% 0.26/0.57  % option.sel
% 0.26/0.57  thf(fact_6111_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 0.26/0.57      ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv2: option4927543243414619207at_nat] :
% 0.26/0.57        ( ( vEBT_V1502963449132264192at_nat @ Uu2 @ none_P5556105721700978146at_nat @ Uv2 )
% 0.26/0.57        = none_P5556105721700978146at_nat ) ).
% 0.26/0.57  
% 0.26/0.57  % VEBT_internal.option_shift.simps(1)
% 0.26/0.57  thf(fact_6112_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 0.26/0.57      ! [Uu2: num > num > num,Uv2: option_num] :
% 0.26/0.57        ( ( vEBT_V819420779217536731ft_num @ Uu2 @ none_num @ Uv2 )
% 0.26/0.57        = none_num ) ).
% 0.26/0.57  
% 0.26/0.57  % VEBT_internal.option_shift.simps(1)
% 0.26/0.57  thf(fact_6113_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 0.26/0.57      ! [Uu2: nat > nat > nat,Uv2: option_nat] :
% 0.26/0.57        ( ( vEBT_V4262088993061758097ft_nat @ Uu2 @ none_nat @ Uv2 )
% 0.26/0.57        = none_nat ) ).
% 0.26/0.57  
% 0.26/0.57  % VEBT_internal.option_shift.simps(1)
% 0.26/0.57  thf(fact_6114_all__nat__less,axiom,
% 0.26/0.57      ! [N: nat,P: nat > $o] :
% 0.26/0.57        ( ( ! [M3: nat] :
% 0.26/0.57              ( ( ord_less_eq_nat @ M3 @ N )
% 0.26/0.57             => ( P @ M3 ) ) )
% 0.26/0.57        = ( ! [X: nat] :
% 0.26/0.57              ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.26/0.57             => ( P @ X ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % all_nat_less
% 0.26/0.57  thf(fact_6115_ex__nat__less,axiom,
% 0.26/0.57      ! [N: nat,P: nat > $o] :
% 0.26/0.57        ( ( ? [M3: nat] :
% 0.26/0.57              ( ( ord_less_eq_nat @ M3 @ N )
% 0.26/0.57              & ( P @ M3 ) ) )
% 0.26/0.57        = ( ? [X: nat] :
% 0.26/0.57              ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.26/0.57              & ( P @ X ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % ex_nat_less
% 0.26/0.57  thf(fact_6116_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 0.26/0.57      ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V: product_prod_nat_nat] :
% 0.26/0.57        ( ( vEBT_V1502963449132264192at_nat @ Uw2 @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat )
% 0.26/0.57        = none_P5556105721700978146at_nat ) ).
% 0.26/0.57  
% 0.26/0.57  % VEBT_internal.option_shift.simps(2)
% 0.26/0.57  thf(fact_6117_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 0.26/0.57      ! [Uw2: num > num > num,V: num] :
% 0.26/0.57        ( ( vEBT_V819420779217536731ft_num @ Uw2 @ ( some_num @ V ) @ none_num )
% 0.26/0.57        = none_num ) ).
% 0.26/0.57  
% 0.26/0.57  % VEBT_internal.option_shift.simps(2)
% 0.26/0.57  thf(fact_6118_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 0.26/0.57      ! [Uw2: nat > nat > nat,V: nat] :
% 0.26/0.57        ( ( vEBT_V4262088993061758097ft_nat @ Uw2 @ ( some_nat @ V ) @ none_nat )
% 0.26/0.57        = none_nat ) ).
% 0.26/0.57  
% 0.26/0.57  % VEBT_internal.option_shift.simps(2)
% 0.26/0.57  thf(fact_6119_VEBT__internal_Ooption__shift_Oelims,axiom,
% 0.26/0.57      ! [X3: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa: option4927543243414619207at_nat,Xb: option4927543243414619207at_nat,Y3: option4927543243414619207at_nat] :
% 0.26/0.57        ( ( ( vEBT_V1502963449132264192at_nat @ X3 @ Xa @ Xb )
% 0.26/0.57          = Y3 )
% 0.26/0.57       => ( ( ( Xa = none_P5556105721700978146at_nat )
% 0.26/0.57           => ( Y3 != none_P5556105721700978146at_nat ) )
% 0.26/0.57         => ( ( ? [V3: product_prod_nat_nat] :
% 0.26/0.57                  ( Xa
% 0.26/0.57                  = ( some_P7363390416028606310at_nat @ V3 ) )
% 0.26/0.57             => ( ( Xb = none_P5556105721700978146at_nat )
% 0.26/0.57               => ( Y3 != none_P5556105721700978146at_nat ) ) )
% 0.26/0.57           => ~ ! [A5: product_prod_nat_nat] :
% 0.26/0.57                  ( ( Xa
% 0.26/0.57                    = ( some_P7363390416028606310at_nat @ A5 ) )
% 0.26/0.57                 => ! [B4: product_prod_nat_nat] :
% 0.26/0.57                      ( ( Xb
% 0.26/0.57                        = ( some_P7363390416028606310at_nat @ B4 ) )
% 0.26/0.57                     => ( Y3
% 0.26/0.57                       != ( some_P7363390416028606310at_nat @ ( X3 @ A5 @ B4 ) ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % VEBT_internal.option_shift.elims
% 0.26/0.57  thf(fact_6120_VEBT__internal_Ooption__shift_Oelims,axiom,
% 0.26/0.57      ! [X3: num > num > num,Xa: option_num,Xb: option_num,Y3: option_num] :
% 0.26/0.57        ( ( ( vEBT_V819420779217536731ft_num @ X3 @ Xa @ Xb )
% 0.26/0.57          = Y3 )
% 0.26/0.57       => ( ( ( Xa = none_num )
% 0.26/0.57           => ( Y3 != none_num ) )
% 0.26/0.57         => ( ( ? [V3: num] :
% 0.26/0.57                  ( Xa
% 0.26/0.57                  = ( some_num @ V3 ) )
% 0.26/0.57             => ( ( Xb = none_num )
% 0.26/0.57               => ( Y3 != none_num ) ) )
% 0.26/0.57           => ~ ! [A5: num] :
% 0.26/0.57                  ( ( Xa
% 0.26/0.57                    = ( some_num @ A5 ) )
% 0.26/0.57                 => ! [B4: num] :
% 0.26/0.57                      ( ( Xb
% 0.26/0.57                        = ( some_num @ B4 ) )
% 0.26/0.57                     => ( Y3
% 0.26/0.57                       != ( some_num @ ( X3 @ A5 @ B4 ) ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % VEBT_internal.option_shift.elims
% 0.26/0.57  thf(fact_6121_VEBT__internal_Ooption__shift_Oelims,axiom,
% 0.26/0.57      ! [X3: nat > nat > nat,Xa: option_nat,Xb: option_nat,Y3: option_nat] :
% 0.26/0.57        ( ( ( vEBT_V4262088993061758097ft_nat @ X3 @ Xa @ Xb )
% 0.26/0.57          = Y3 )
% 0.26/0.57       => ( ( ( Xa = none_nat )
% 0.26/0.57           => ( Y3 != none_nat ) )
% 0.26/0.57         => ( ( ? [V3: nat] :
% 0.26/0.57                  ( Xa
% 0.26/0.57                  = ( some_nat @ V3 ) )
% 0.26/0.57             => ( ( Xb = none_nat )
% 0.26/0.57               => ( Y3 != none_nat ) ) )
% 0.26/0.57           => ~ ! [A5: nat] :
% 0.26/0.57                  ( ( Xa
% 0.26/0.57                    = ( some_nat @ A5 ) )
% 0.26/0.57                 => ! [B4: nat] :
% 0.26/0.57                      ( ( Xb
% 0.26/0.57                        = ( some_nat @ B4 ) )
% 0.26/0.57                     => ( Y3
% 0.26/0.57                       != ( some_nat @ ( X3 @ A5 @ B4 ) ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % VEBT_internal.option_shift.elims
% 0.26/0.57  thf(fact_6122_option_Osize_I3_J,axiom,
% 0.26/0.57      ( ( size_size_option_nat @ none_nat )
% 0.26/0.57      = ( suc @ zero_zero_nat ) ) ).
% 0.26/0.57  
% 0.26/0.57  % option.size(3)
% 0.26/0.57  thf(fact_6123_option_Osize_I3_J,axiom,
% 0.26/0.57      ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 0.26/0.57      = ( suc @ zero_zero_nat ) ) ).
% 0.26/0.57  
% 0.26/0.57  % option.size(3)
% 0.26/0.57  thf(fact_6124_option_Osize_I3_J,axiom,
% 0.26/0.57      ( ( size_size_option_num @ none_num )
% 0.26/0.57      = ( suc @ zero_zero_nat ) ) ).
% 0.26/0.57  
% 0.26/0.57  % option.size(3)
% 0.26/0.57  thf(fact_6125_atLeastatMost__subset__iff,axiom,
% 0.26/0.57      ! [A: set_nat,B: set_nat,C: set_nat,D3: set_nat] :
% 0.26/0.57        ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D3 ) )
% 0.26/0.57        = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 0.26/0.57          | ( ( ord_less_eq_set_nat @ C @ A )
% 0.26/0.57            & ( ord_less_eq_set_nat @ B @ D3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % atLeastatMost_subset_iff
% 0.26/0.57  thf(fact_6126_atLeastatMost__subset__iff,axiom,
% 0.26/0.57      ! [A: rat,B: rat,C: rat,D3: rat] :
% 0.26/0.57        ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D3 ) )
% 0.26/0.57        = ( ~ ( ord_less_eq_rat @ A @ B )
% 0.26/0.57          | ( ( ord_less_eq_rat @ C @ A )
% 0.26/0.57            & ( ord_less_eq_rat @ B @ D3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % atLeastatMost_subset_iff
% 0.26/0.57  thf(fact_6127_atLeastatMost__subset__iff,axiom,
% 0.26/0.57      ! [A: num,B: num,C: num,D3: num] :
% 0.26/0.57        ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D3 ) )
% 0.26/0.57        = ( ~ ( ord_less_eq_num @ A @ B )
% 0.26/0.57          | ( ( ord_less_eq_num @ C @ A )
% 0.26/0.57            & ( ord_less_eq_num @ B @ D3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % atLeastatMost_subset_iff
% 0.26/0.57  thf(fact_6128_atLeastatMost__subset__iff,axiom,
% 0.26/0.57      ! [A: nat,B: nat,C: nat,D3: nat] :
% 0.26/0.57        ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D3 ) )
% 0.26/0.57        = ( ~ ( ord_less_eq_nat @ A @ B )
% 0.26/0.57          | ( ( ord_less_eq_nat @ C @ A )
% 0.26/0.57            & ( ord_less_eq_nat @ B @ D3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % atLeastatMost_subset_iff
% 0.26/0.57  thf(fact_6129_atLeastatMost__subset__iff,axiom,
% 0.26/0.57      ! [A: int,B: int,C: int,D3: int] :
% 0.26/0.57        ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D3 ) )
% 0.26/0.57        = ( ~ ( ord_less_eq_int @ A @ B )
% 0.26/0.57          | ( ( ord_less_eq_int @ C @ A )
% 0.26/0.57            & ( ord_less_eq_int @ B @ D3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % atLeastatMost_subset_iff
% 0.26/0.57  thf(fact_6130_atLeastatMost__subset__iff,axiom,
% 0.26/0.57      ! [A: real,B: real,C: real,D3: real] :
% 0.26/0.57        ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D3 ) )
% 0.26/0.57        = ( ~ ( ord_less_eq_real @ A @ B )
% 0.26/0.57          | ( ( ord_less_eq_real @ C @ A )
% 0.26/0.57            & ( ord_less_eq_real @ B @ D3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % atLeastatMost_subset_iff
% 0.26/0.57  thf(fact_6131_summaxma,axiom,
% 0.26/0.57      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 0.26/0.57       => ( ( Mi != Ma )
% 0.26/0.57         => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 0.26/0.57            = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % summaxma
% 0.26/0.57  thf(fact_6132_vebt__succ_Osimps_I5_J,axiom,
% 0.26/0.57      ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 0.26/0.57        ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi )
% 0.26/0.57        = none_nat ) ).
% 0.26/0.57  
% 0.26/0.57  % vebt_succ.simps(5)
% 0.26/0.57  thf(fact_6133_vebt__pred_Osimps_I6_J,axiom,
% 0.26/0.57      ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 0.26/0.57        ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj )
% 0.26/0.57        = none_nat ) ).
% 0.26/0.57  
% 0.26/0.57  % vebt_pred.simps(6)
% 0.26/0.57  thf(fact_6134__C5_Oprems_C,axiom,
% 0.26/0.57      vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ x ) ).
% 0.26/0.57  
% 0.26/0.57  % "5.prems"
% 0.26/0.57  thf(fact_6135_delt__out__of__range,axiom,
% 0.26/0.57      ! [X3: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.26/0.57        ( ( ( ord_less_nat @ X3 @ Mi )
% 0.26/0.57          | ( ord_less_nat @ Ma @ X3 ) )
% 0.26/0.57       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.57         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.57            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % delt_out_of_range
% 0.26/0.57  thf(fact_6136_delete__pres__valid,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( vEBT_invar_vebt @ ( vEBT_vebt_delete @ T @ X3 ) @ N ) ) ).
% 0.26/0.57  
% 0.26/0.57  % delete_pres_valid
% 0.26/0.57  thf(fact_6137_not__min__Null__member,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT] :
% 0.26/0.57        ( ~ ( vEBT_VEBT_minNull @ T )
% 0.26/0.57       => ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 ) ) ).
% 0.26/0.57  
% 0.26/0.57  % not_min_Null_member
% 0.26/0.57  thf(fact_6138_min__Null__member,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,X3: nat] :
% 0.26/0.57        ( ( vEBT_VEBT_minNull @ T )
% 0.26/0.57       => ~ ( vEBT_vebt_member @ T @ X3 ) ) ).
% 0.26/0.57  
% 0.26/0.57  % min_Null_member
% 0.26/0.57  thf(fact_6139_maxbmo,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,X3: nat] :
% 0.26/0.57        ( ( ( vEBT_vebt_maxt @ T )
% 0.26/0.57          = ( some_nat @ X3 ) )
% 0.26/0.57       => ( vEBT_V8194947554948674370ptions @ T @ X3 ) ) ).
% 0.26/0.57  
% 0.26/0.57  % maxbmo
% 0.26/0.57  thf(fact_6140_dele__bmo__cont__corr,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,X3: nat,Y3: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ T @ X3 ) @ Y3 )
% 0.26/0.57          = ( ( X3 != Y3 )
% 0.26/0.57            & ( vEBT_V8194947554948674370ptions @ T @ Y3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % dele_bmo_cont_corr
% 0.26/0.57  thf(fact_6141_minNullmin,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT] :
% 0.26/0.57        ( ( vEBT_VEBT_minNull @ T )
% 0.26/0.57       => ( ( vEBT_vebt_mint @ T )
% 0.26/0.57          = none_nat ) ) ).
% 0.26/0.57  
% 0.26/0.57  % minNullmin
% 0.26/0.57  thf(fact_6142_minminNull,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT] :
% 0.26/0.57        ( ( ( vEBT_vebt_mint @ T )
% 0.26/0.57          = none_nat )
% 0.26/0.57       => ( vEBT_VEBT_minNull @ T ) ) ).
% 0.26/0.57  
% 0.26/0.57  % minminNull
% 0.26/0.57  thf(fact_6143_dele__member__cont__corr,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,X3: nat,Y3: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( vEBT_vebt_member @ ( vEBT_vebt_delete @ T @ X3 ) @ Y3 )
% 0.26/0.57          = ( ( X3 != Y3 )
% 0.26/0.57            & ( vEBT_vebt_member @ T @ Y3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % dele_member_cont_corr
% 0.26/0.57  thf(fact_6144_maxt__member,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( ( vEBT_vebt_maxt @ T )
% 0.26/0.57            = ( some_nat @ Maxi ) )
% 0.26/0.57         => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % maxt_member
% 0.26/0.57  thf(fact_6145_maxt__corr__help,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,Maxi: nat,X3: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( ( vEBT_vebt_maxt @ T )
% 0.26/0.57            = ( some_nat @ Maxi ) )
% 0.26/0.57         => ( ( vEBT_vebt_member @ T @ X3 )
% 0.26/0.57           => ( ord_less_eq_nat @ X3 @ Maxi ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % maxt_corr_help
% 0.26/0.57  thf(fact_6146_maxt__sound,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X3 )
% 0.26/0.57         => ( ( vEBT_vebt_maxt @ T )
% 0.26/0.57            = ( some_nat @ X3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % maxt_sound
% 0.26/0.57  thf(fact_6147_maxt__corr,axiom,
% 0.26/0.57      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.57       => ( ( ( vEBT_vebt_maxt @ T )
% 0.26/0.57            = ( some_nat @ X3 ) )
% 0.26/0.57         => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X3 ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % maxt_corr
% 0.26/0.57  thf(fact_6148_del__single__cont,axiom,
% 0.26/0.57      ! [X3: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.26/0.57        ( ( ( X3 = Mi )
% 0.26/0.57          & ( X3 = Ma ) )
% 0.26/0.57       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.57         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.57            = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % del_single_cont
% 0.26/0.57  thf(fact_6149_Icc__eq__Icc,axiom,
% 0.26/0.57      ! [L: set_nat,H2: set_nat,L3: set_nat,H3: set_nat] :
% 0.26/0.57        ( ( ( set_or4548717258645045905et_nat @ L @ H2 )
% 0.26/0.57          = ( set_or4548717258645045905et_nat @ L3 @ H3 ) )
% 0.26/0.57        = ( ( ( L = L3 )
% 0.26/0.57            & ( H2 = H3 ) )
% 0.26/0.57          | ( ~ ( ord_less_eq_set_nat @ L @ H2 )
% 0.26/0.57            & ~ ( ord_less_eq_set_nat @ L3 @ H3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % Icc_eq_Icc
% 0.26/0.57  thf(fact_6150_Icc__eq__Icc,axiom,
% 0.26/0.57      ! [L: rat,H2: rat,L3: rat,H3: rat] :
% 0.26/0.57        ( ( ( set_or633870826150836451st_rat @ L @ H2 )
% 0.26/0.57          = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 0.26/0.57        = ( ( ( L = L3 )
% 0.26/0.57            & ( H2 = H3 ) )
% 0.26/0.57          | ( ~ ( ord_less_eq_rat @ L @ H2 )
% 0.26/0.57            & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % Icc_eq_Icc
% 0.26/0.57  thf(fact_6151_Icc__eq__Icc,axiom,
% 0.26/0.57      ! [L: num,H2: num,L3: num,H3: num] :
% 0.26/0.57        ( ( ( set_or7049704709247886629st_num @ L @ H2 )
% 0.26/0.57          = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 0.26/0.57        = ( ( ( L = L3 )
% 0.26/0.57            & ( H2 = H3 ) )
% 0.26/0.57          | ( ~ ( ord_less_eq_num @ L @ H2 )
% 0.26/0.57            & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % Icc_eq_Icc
% 0.26/0.57  thf(fact_6152_Icc__eq__Icc,axiom,
% 0.26/0.57      ! [L: nat,H2: nat,L3: nat,H3: nat] :
% 0.26/0.57        ( ( ( set_or1269000886237332187st_nat @ L @ H2 )
% 0.26/0.57          = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 0.26/0.57        = ( ( ( L = L3 )
% 0.26/0.57            & ( H2 = H3 ) )
% 0.26/0.57          | ( ~ ( ord_less_eq_nat @ L @ H2 )
% 0.26/0.57            & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % Icc_eq_Icc
% 0.26/0.57  thf(fact_6153_Icc__eq__Icc,axiom,
% 0.26/0.57      ! [L: int,H2: int,L3: int,H3: int] :
% 0.26/0.57        ( ( ( set_or1266510415728281911st_int @ L @ H2 )
% 0.26/0.57          = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 0.26/0.57        = ( ( ( L = L3 )
% 0.26/0.57            & ( H2 = H3 ) )
% 0.26/0.57          | ( ~ ( ord_less_eq_int @ L @ H2 )
% 0.26/0.57            & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % Icc_eq_Icc
% 0.26/0.57  thf(fact_6154_Icc__eq__Icc,axiom,
% 0.26/0.57      ! [L: real,H2: real,L3: real,H3: real] :
% 0.26/0.57        ( ( ( set_or1222579329274155063t_real @ L @ H2 )
% 0.26/0.57          = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 0.26/0.57        = ( ( ( L = L3 )
% 0.26/0.57            & ( H2 = H3 ) )
% 0.26/0.57          | ( ~ ( ord_less_eq_real @ L @ H2 )
% 0.26/0.57            & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % Icc_eq_Icc
% 0.26/0.57  thf(fact_6155_atLeastAtMost__iff,axiom,
% 0.26/0.57      ! [I: set_nat,L: set_nat,U: set_nat] :
% 0.26/0.57        ( ( member_set_nat @ I @ ( set_or4548717258645045905et_nat @ L @ U ) )
% 0.26/0.57        = ( ( ord_less_eq_set_nat @ L @ I )
% 0.26/0.57          & ( ord_less_eq_set_nat @ I @ U ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % atLeastAtMost_iff
% 0.26/0.57  thf(fact_6156_atLeastAtMost__iff,axiom,
% 0.26/0.57      ! [I: rat,L: rat,U: rat] :
% 0.26/0.57        ( ( member_rat @ I @ ( set_or633870826150836451st_rat @ L @ U ) )
% 0.26/0.57        = ( ( ord_less_eq_rat @ L @ I )
% 0.26/0.57          & ( ord_less_eq_rat @ I @ U ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % atLeastAtMost_iff
% 0.26/0.57  thf(fact_6157_atLeastAtMost__iff,axiom,
% 0.26/0.57      ! [I: num,L: num,U: num] :
% 0.26/0.57        ( ( member_num @ I @ ( set_or7049704709247886629st_num @ L @ U ) )
% 0.26/0.57        = ( ( ord_less_eq_num @ L @ I )
% 0.26/0.57          & ( ord_less_eq_num @ I @ U ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % atLeastAtMost_iff
% 0.26/0.57  thf(fact_6158_atLeastAtMost__iff,axiom,
% 0.26/0.57      ! [I: nat,L: nat,U: nat] :
% 0.26/0.57        ( ( member_nat @ I @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 0.26/0.57        = ( ( ord_less_eq_nat @ L @ I )
% 0.26/0.57          & ( ord_less_eq_nat @ I @ U ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % atLeastAtMost_iff
% 0.26/0.57  thf(fact_6159_atLeastAtMost__iff,axiom,
% 0.26/0.57      ! [I: int,L: int,U: int] :
% 0.26/0.57        ( ( member_int @ I @ ( set_or1266510415728281911st_int @ L @ U ) )
% 0.26/0.57        = ( ( ord_less_eq_int @ L @ I )
% 0.26/0.57          & ( ord_less_eq_int @ I @ U ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % atLeastAtMost_iff
% 0.26/0.57  thf(fact_6160_atLeastAtMost__iff,axiom,
% 0.26/0.57      ! [I: real,L: real,U: real] :
% 0.26/0.57        ( ( member_real @ I @ ( set_or1222579329274155063t_real @ L @ U ) )
% 0.26/0.57        = ( ( ord_less_eq_real @ L @ I )
% 0.26/0.57          & ( ord_less_eq_real @ I @ U ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % atLeastAtMost_iff
% 0.26/0.57  thf(fact_6161_vebt__maxt_Osimps_I2_J,axiom,
% 0.26/0.57      ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.26/0.57        ( ( vEBT_vebt_maxt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.26/0.57        = none_nat ) ).
% 0.26/0.57  
% 0.26/0.57  % vebt_maxt.simps(2)
% 0.26/0.57  thf(fact_6162_aset_I2_J,axiom,
% 0.26/0.57      ! [D5: int,A3: set_int,P: int > $o,Q: int > $o] :
% 0.26/0.57        ( ! [X4: int] :
% 0.26/0.57            ( ! [Xa2: int] :
% 0.26/0.57                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.57               => ! [Xb2: int] :
% 0.26/0.57                    ( ( member_int @ Xb2 @ A3 )
% 0.26/0.57                   => ( X4
% 0.26/0.57                     != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.26/0.57           => ( ( P @ X4 )
% 0.26/0.57             => ( P @ ( plus_plus_int @ X4 @ D5 ) ) ) )
% 0.26/0.57       => ( ! [X4: int] :
% 0.26/0.57              ( ! [Xa2: int] :
% 0.26/0.57                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.57                 => ! [Xb2: int] :
% 0.26/0.57                      ( ( member_int @ Xb2 @ A3 )
% 0.26/0.57                     => ( X4
% 0.26/0.57                       != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.26/0.57             => ( ( Q @ X4 )
% 0.26/0.57               => ( Q @ ( plus_plus_int @ X4 @ D5 ) ) ) )
% 0.26/0.57         => ! [X6: int] :
% 0.26/0.57              ( ! [Xa3: int] :
% 0.26/0.57                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.57                 => ! [Xb3: int] :
% 0.26/0.57                      ( ( member_int @ Xb3 @ A3 )
% 0.26/0.57                     => ( X6
% 0.26/0.57                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.26/0.57             => ( ( ( P @ X6 )
% 0.26/0.57                  | ( Q @ X6 ) )
% 0.26/0.57               => ( ( P @ ( plus_plus_int @ X6 @ D5 ) )
% 0.26/0.57                  | ( Q @ ( plus_plus_int @ X6 @ D5 ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % aset(2)
% 0.26/0.57  thf(fact_6163_aset_I1_J,axiom,
% 0.26/0.57      ! [D5: int,A3: set_int,P: int > $o,Q: int > $o] :
% 0.26/0.57        ( ! [X4: int] :
% 0.26/0.57            ( ! [Xa2: int] :
% 0.26/0.57                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.57               => ! [Xb2: int] :
% 0.26/0.57                    ( ( member_int @ Xb2 @ A3 )
% 0.26/0.57                   => ( X4
% 0.26/0.57                     != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.26/0.57           => ( ( P @ X4 )
% 0.26/0.57             => ( P @ ( plus_plus_int @ X4 @ D5 ) ) ) )
% 0.26/0.57       => ( ! [X4: int] :
% 0.26/0.57              ( ! [Xa2: int] :
% 0.26/0.57                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.57                 => ! [Xb2: int] :
% 0.26/0.57                      ( ( member_int @ Xb2 @ A3 )
% 0.26/0.57                     => ( X4
% 0.26/0.57                       != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.26/0.57             => ( ( Q @ X4 )
% 0.26/0.57               => ( Q @ ( plus_plus_int @ X4 @ D5 ) ) ) )
% 0.26/0.57         => ! [X6: int] :
% 0.26/0.57              ( ! [Xa3: int] :
% 0.26/0.57                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.57                 => ! [Xb3: int] :
% 0.26/0.57                      ( ( member_int @ Xb3 @ A3 )
% 0.26/0.57                     => ( X6
% 0.26/0.57                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.26/0.57             => ( ( ( P @ X6 )
% 0.26/0.57                  & ( Q @ X6 ) )
% 0.26/0.57               => ( ( P @ ( plus_plus_int @ X6 @ D5 ) )
% 0.26/0.57                  & ( Q @ ( plus_plus_int @ X6 @ D5 ) ) ) ) ) ) ) ).
% 0.26/0.57  
% 0.26/0.57  % aset(1)
% 0.26/0.57  thf(fact_6164_bset_I2_J,axiom,
% 0.26/0.57      ! [D5: int,B5: set_int,P: int > $o,Q: int > $o] :
% 0.26/0.57        ( ! [X4: int] :
% 0.26/0.57            ( ! [Xa2: int] :
% 0.26/0.57                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.57               => ! [Xb2: int] :
% 0.26/0.57                    ( ( member_int @ Xb2 @ B5 )
% 0.26/0.57                   => ( X4
% 0.26/0.57                     != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.26/0.57           => ( ( P @ X4 )
% 0.26/0.57             => ( P @ ( minus_minus_int @ X4 @ D5 ) ) ) )
% 0.26/0.58       => ( ! [X4: int] :
% 0.26/0.58              ( ! [Xa2: int] :
% 0.26/0.58                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58                 => ! [Xb2: int] :
% 0.26/0.58                      ( ( member_int @ Xb2 @ B5 )
% 0.26/0.58                     => ( X4
% 0.26/0.58                       != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.26/0.58             => ( ( Q @ X4 )
% 0.26/0.58               => ( Q @ ( minus_minus_int @ X4 @ D5 ) ) ) )
% 0.26/0.58         => ! [X6: int] :
% 0.26/0.58              ( ! [Xa3: int] :
% 0.26/0.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58                 => ! [Xb3: int] :
% 0.26/0.58                      ( ( member_int @ Xb3 @ B5 )
% 0.26/0.58                     => ( X6
% 0.26/0.58                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.26/0.58             => ( ( ( P @ X6 )
% 0.26/0.58                  | ( Q @ X6 ) )
% 0.26/0.58               => ( ( P @ ( minus_minus_int @ X6 @ D5 ) )
% 0.26/0.58                  | ( Q @ ( minus_minus_int @ X6 @ D5 ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % bset(2)
% 0.26/0.58  thf(fact_6165_bset_I1_J,axiom,
% 0.26/0.58      ! [D5: int,B5: set_int,P: int > $o,Q: int > $o] :
% 0.26/0.58        ( ! [X4: int] :
% 0.26/0.58            ( ! [Xa2: int] :
% 0.26/0.58                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58               => ! [Xb2: int] :
% 0.26/0.58                    ( ( member_int @ Xb2 @ B5 )
% 0.26/0.58                   => ( X4
% 0.26/0.58                     != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.26/0.58           => ( ( P @ X4 )
% 0.26/0.58             => ( P @ ( minus_minus_int @ X4 @ D5 ) ) ) )
% 0.26/0.58       => ( ! [X4: int] :
% 0.26/0.58              ( ! [Xa2: int] :
% 0.26/0.58                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58                 => ! [Xb2: int] :
% 0.26/0.58                      ( ( member_int @ Xb2 @ B5 )
% 0.26/0.58                     => ( X4
% 0.26/0.58                       != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.26/0.58             => ( ( Q @ X4 )
% 0.26/0.58               => ( Q @ ( minus_minus_int @ X4 @ D5 ) ) ) )
% 0.26/0.58         => ! [X6: int] :
% 0.26/0.58              ( ! [Xa3: int] :
% 0.26/0.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58                 => ! [Xb3: int] :
% 0.26/0.58                      ( ( member_int @ Xb3 @ B5 )
% 0.26/0.58                     => ( X6
% 0.26/0.58                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.26/0.58             => ( ( ( P @ X6 )
% 0.26/0.58                  & ( Q @ X6 ) )
% 0.26/0.58               => ( ( P @ ( minus_minus_int @ X6 @ D5 ) )
% 0.26/0.58                  & ( Q @ ( minus_minus_int @ X6 @ D5 ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % bset(1)
% 0.26/0.58  thf(fact_6166_bounded__Max__nat,axiom,
% 0.26/0.58      ! [P: nat > $o,X3: nat,M7: nat] :
% 0.26/0.58        ( ( P @ X3 )
% 0.26/0.58       => ( ! [X4: nat] :
% 0.26/0.58              ( ( P @ X4 )
% 0.26/0.58             => ( ord_less_eq_nat @ X4 @ M7 ) )
% 0.26/0.58         => ~ ! [M4: nat] :
% 0.26/0.58                ( ( P @ M4 )
% 0.26/0.58               => ~ ! [X6: nat] :
% 0.26/0.58                      ( ( P @ X6 )
% 0.26/0.58                     => ( ord_less_eq_nat @ X6 @ M4 ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % bounded_Max_nat
% 0.26/0.58  thf(fact_6167_vebt__mint_Osimps_I2_J,axiom,
% 0.26/0.58      ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.26/0.58        ( ( vEBT_vebt_mint @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.26/0.58        = none_nat ) ).
% 0.26/0.58  
% 0.26/0.58  % vebt_mint.simps(2)
% 0.26/0.58  thf(fact_6168_bset_I9_J,axiom,
% 0.26/0.58      ! [D3: int,D5: int,B5: set_int,T: int] :
% 0.26/0.58        ( ( dvd_dvd_int @ D3 @ D5 )
% 0.26/0.58       => ! [X6: int] :
% 0.26/0.58            ( ! [Xa3: int] :
% 0.26/0.58                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58               => ! [Xb3: int] :
% 0.26/0.58                    ( ( member_int @ Xb3 @ B5 )
% 0.26/0.58                   => ( X6
% 0.26/0.58                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.26/0.58           => ( ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ T ) )
% 0.26/0.58             => ( dvd_dvd_int @ D3 @ ( plus_plus_int @ ( minus_minus_int @ X6 @ D5 ) @ T ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % bset(9)
% 0.26/0.58  thf(fact_6169_bset_I10_J,axiom,
% 0.26/0.58      ! [D3: int,D5: int,B5: set_int,T: int] :
% 0.26/0.58        ( ( dvd_dvd_int @ D3 @ D5 )
% 0.26/0.58       => ! [X6: int] :
% 0.26/0.58            ( ! [Xa3: int] :
% 0.26/0.58                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58               => ! [Xb3: int] :
% 0.26/0.58                    ( ( member_int @ Xb3 @ B5 )
% 0.26/0.58                   => ( X6
% 0.26/0.58                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.26/0.58           => ( ~ ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ T ) )
% 0.26/0.58             => ~ ( dvd_dvd_int @ D3 @ ( plus_plus_int @ ( minus_minus_int @ X6 @ D5 ) @ T ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % bset(10)
% 0.26/0.58  thf(fact_6170_aset_I9_J,axiom,
% 0.26/0.58      ! [D3: int,D5: int,A3: set_int,T: int] :
% 0.26/0.58        ( ( dvd_dvd_int @ D3 @ D5 )
% 0.26/0.58       => ! [X6: int] :
% 0.26/0.58            ( ! [Xa3: int] :
% 0.26/0.58                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58               => ! [Xb3: int] :
% 0.26/0.58                    ( ( member_int @ Xb3 @ A3 )
% 0.26/0.58                   => ( X6
% 0.26/0.58                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.26/0.58           => ( ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ T ) )
% 0.26/0.58             => ( dvd_dvd_int @ D3 @ ( plus_plus_int @ ( plus_plus_int @ X6 @ D5 ) @ T ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % aset(9)
% 0.26/0.58  thf(fact_6171_aset_I10_J,axiom,
% 0.26/0.58      ! [D3: int,D5: int,A3: set_int,T: int] :
% 0.26/0.58        ( ( dvd_dvd_int @ D3 @ D5 )
% 0.26/0.58       => ! [X6: int] :
% 0.26/0.58            ( ! [Xa3: int] :
% 0.26/0.58                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58               => ! [Xb3: int] :
% 0.26/0.58                    ( ( member_int @ Xb3 @ A3 )
% 0.26/0.58                   => ( X6
% 0.26/0.58                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.26/0.58           => ( ~ ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ T ) )
% 0.26/0.58             => ~ ( dvd_dvd_int @ D3 @ ( plus_plus_int @ ( plus_plus_int @ X6 @ D5 ) @ T ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % aset(10)
% 0.26/0.58  thf(fact_6172_vebt__maxt_Osimps_I3_J,axiom,
% 0.26/0.58      ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 0.26/0.58        ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 0.26/0.58        = ( some_nat @ Ma ) ) ).
% 0.26/0.58  
% 0.26/0.58  % vebt_maxt.simps(3)
% 0.26/0.58  thf(fact_6173_periodic__finite__ex,axiom,
% 0.26/0.58      ! [D3: int,P: int > $o] :
% 0.26/0.58        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.26/0.58       => ( ! [X4: int,K2: int] :
% 0.26/0.58              ( ( P @ X4 )
% 0.26/0.58              = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 0.26/0.58         => ( ( ? [X8: int] : ( P @ X8 ) )
% 0.26/0.58            = ( ? [X: int] :
% 0.26/0.58                  ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.26/0.58                  & ( P @ X ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % periodic_finite_ex
% 0.26/0.58  thf(fact_6174_aset_I7_J,axiom,
% 0.26/0.58      ! [D5: int,A3: set_int,T: int] :
% 0.26/0.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 0.26/0.58       => ! [X6: int] :
% 0.26/0.58            ( ! [Xa3: int] :
% 0.26/0.58                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58               => ! [Xb3: int] :
% 0.26/0.58                    ( ( member_int @ Xb3 @ A3 )
% 0.26/0.58                   => ( X6
% 0.26/0.58                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.26/0.58           => ( ( ord_less_int @ T @ X6 )
% 0.26/0.58             => ( ord_less_int @ T @ ( plus_plus_int @ X6 @ D5 ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % aset(7)
% 0.26/0.58  thf(fact_6175_aset_I5_J,axiom,
% 0.26/0.58      ! [D5: int,T: int,A3: set_int] :
% 0.26/0.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 0.26/0.58       => ( ( member_int @ T @ A3 )
% 0.26/0.58         => ! [X6: int] :
% 0.26/0.58              ( ! [Xa3: int] :
% 0.26/0.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58                 => ! [Xb3: int] :
% 0.26/0.58                      ( ( member_int @ Xb3 @ A3 )
% 0.26/0.58                     => ( X6
% 0.26/0.58                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.26/0.58             => ( ( ord_less_int @ X6 @ T )
% 0.26/0.58               => ( ord_less_int @ ( plus_plus_int @ X6 @ D5 ) @ T ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % aset(5)
% 0.26/0.58  thf(fact_6176_aset_I4_J,axiom,
% 0.26/0.58      ! [D5: int,T: int,A3: set_int] :
% 0.26/0.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 0.26/0.58       => ( ( member_int @ T @ A3 )
% 0.26/0.58         => ! [X6: int] :
% 0.26/0.58              ( ! [Xa3: int] :
% 0.26/0.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58                 => ! [Xb3: int] :
% 0.26/0.58                      ( ( member_int @ Xb3 @ A3 )
% 0.26/0.58                     => ( X6
% 0.26/0.58                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.26/0.58             => ( ( X6 != T )
% 0.26/0.58               => ( ( plus_plus_int @ X6 @ D5 )
% 0.26/0.58                 != T ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % aset(4)
% 0.26/0.58  thf(fact_6177_aset_I3_J,axiom,
% 0.26/0.58      ! [D5: int,T: int,A3: set_int] :
% 0.26/0.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 0.26/0.58       => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A3 )
% 0.26/0.58         => ! [X6: int] :
% 0.26/0.58              ( ! [Xa3: int] :
% 0.26/0.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58                 => ! [Xb3: int] :
% 0.26/0.58                      ( ( member_int @ Xb3 @ A3 )
% 0.26/0.58                     => ( X6
% 0.26/0.58                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.26/0.58             => ( ( X6 = T )
% 0.26/0.58               => ( ( plus_plus_int @ X6 @ D5 )
% 0.26/0.58                  = T ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % aset(3)
% 0.26/0.58  thf(fact_6178_bset_I7_J,axiom,
% 0.26/0.58      ! [D5: int,T: int,B5: set_int] :
% 0.26/0.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 0.26/0.58       => ( ( member_int @ T @ B5 )
% 0.26/0.58         => ! [X6: int] :
% 0.26/0.58              ( ! [Xa3: int] :
% 0.26/0.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58                 => ! [Xb3: int] :
% 0.26/0.58                      ( ( member_int @ Xb3 @ B5 )
% 0.26/0.58                     => ( X6
% 0.26/0.58                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.26/0.58             => ( ( ord_less_int @ T @ X6 )
% 0.26/0.58               => ( ord_less_int @ T @ ( minus_minus_int @ X6 @ D5 ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % bset(7)
% 0.26/0.58  thf(fact_6179_bset_I5_J,axiom,
% 0.26/0.58      ! [D5: int,B5: set_int,T: int] :
% 0.26/0.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 0.26/0.58       => ! [X6: int] :
% 0.26/0.58            ( ! [Xa3: int] :
% 0.26/0.58                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58               => ! [Xb3: int] :
% 0.26/0.58                    ( ( member_int @ Xb3 @ B5 )
% 0.26/0.58                   => ( X6
% 0.26/0.58                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.26/0.58           => ( ( ord_less_int @ X6 @ T )
% 0.26/0.58             => ( ord_less_int @ ( minus_minus_int @ X6 @ D5 ) @ T ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % bset(5)
% 0.26/0.58  thf(fact_6180_bset_I4_J,axiom,
% 0.26/0.58      ! [D5: int,T: int,B5: set_int] :
% 0.26/0.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 0.26/0.58       => ( ( member_int @ T @ B5 )
% 0.26/0.58         => ! [X6: int] :
% 0.26/0.58              ( ! [Xa3: int] :
% 0.26/0.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58                 => ! [Xb3: int] :
% 0.26/0.58                      ( ( member_int @ Xb3 @ B5 )
% 0.26/0.58                     => ( X6
% 0.26/0.58                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.26/0.58             => ( ( X6 != T )
% 0.26/0.58               => ( ( minus_minus_int @ X6 @ D5 )
% 0.26/0.58                 != T ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % bset(4)
% 0.26/0.58  thf(fact_6181_bset_I3_J,axiom,
% 0.26/0.58      ! [D5: int,T: int,B5: set_int] :
% 0.26/0.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 0.26/0.58       => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B5 )
% 0.26/0.58         => ! [X6: int] :
% 0.26/0.58              ( ! [Xa3: int] :
% 0.26/0.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58                 => ! [Xb3: int] :
% 0.26/0.58                      ( ( member_int @ Xb3 @ B5 )
% 0.26/0.58                     => ( X6
% 0.26/0.58                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.26/0.58             => ( ( X6 = T )
% 0.26/0.58               => ( ( minus_minus_int @ X6 @ D5 )
% 0.26/0.58                  = T ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % bset(3)
% 0.26/0.58  thf(fact_6182_bset_I6_J,axiom,
% 0.26/0.58      ! [D5: int,B5: set_int,T: int] :
% 0.26/0.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 0.26/0.58       => ! [X6: int] :
% 0.26/0.58            ( ! [Xa3: int] :
% 0.26/0.58                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58               => ! [Xb3: int] :
% 0.26/0.58                    ( ( member_int @ Xb3 @ B5 )
% 0.26/0.58                   => ( X6
% 0.26/0.58                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.26/0.58           => ( ( ord_less_eq_int @ X6 @ T )
% 0.26/0.58             => ( ord_less_eq_int @ ( minus_minus_int @ X6 @ D5 ) @ T ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % bset(6)
% 0.26/0.58  thf(fact_6183_bset_I8_J,axiom,
% 0.26/0.58      ! [D5: int,T: int,B5: set_int] :
% 0.26/0.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 0.26/0.58       => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B5 )
% 0.26/0.58         => ! [X6: int] :
% 0.26/0.58              ( ! [Xa3: int] :
% 0.26/0.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58                 => ! [Xb3: int] :
% 0.26/0.58                      ( ( member_int @ Xb3 @ B5 )
% 0.26/0.58                     => ( X6
% 0.26/0.58                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.26/0.58             => ( ( ord_less_eq_int @ T @ X6 )
% 0.26/0.58               => ( ord_less_eq_int @ T @ ( minus_minus_int @ X6 @ D5 ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % bset(8)
% 0.26/0.58  thf(fact_6184_aset_I6_J,axiom,
% 0.26/0.58      ! [D5: int,T: int,A3: set_int] :
% 0.26/0.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 0.26/0.58       => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A3 )
% 0.26/0.58         => ! [X6: int] :
% 0.26/0.58              ( ! [Xa3: int] :
% 0.26/0.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58                 => ! [Xb3: int] :
% 0.26/0.58                      ( ( member_int @ Xb3 @ A3 )
% 0.26/0.58                     => ( X6
% 0.26/0.58                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.26/0.58             => ( ( ord_less_eq_int @ X6 @ T )
% 0.26/0.58               => ( ord_less_eq_int @ ( plus_plus_int @ X6 @ D5 ) @ T ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % aset(6)
% 0.26/0.58  thf(fact_6185_aset_I8_J,axiom,
% 0.26/0.58      ! [D5: int,A3: set_int,T: int] :
% 0.26/0.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 0.26/0.58       => ! [X6: int] :
% 0.26/0.58            ( ! [Xa3: int] :
% 0.26/0.58                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58               => ! [Xb3: int] :
% 0.26/0.58                    ( ( member_int @ Xb3 @ A3 )
% 0.26/0.58                   => ( X6
% 0.26/0.58                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.26/0.58           => ( ( ord_less_eq_int @ T @ X6 )
% 0.26/0.58             => ( ord_less_eq_int @ T @ ( plus_plus_int @ X6 @ D5 ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % aset(8)
% 0.26/0.58  thf(fact_6186_cppi,axiom,
% 0.26/0.58      ! [D5: int,P: int > $o,P4: int > $o,A3: set_int] :
% 0.26/0.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 0.26/0.58       => ( ? [Z4: int] :
% 0.26/0.58            ! [X4: int] :
% 0.26/0.58              ( ( ord_less_int @ Z4 @ X4 )
% 0.26/0.58             => ( ( P @ X4 )
% 0.26/0.58                = ( P4 @ X4 ) ) )
% 0.26/0.58         => ( ! [X4: int] :
% 0.26/0.58                ( ! [Xa2: int] :
% 0.26/0.58                    ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58                   => ! [Xb2: int] :
% 0.26/0.58                        ( ( member_int @ Xb2 @ A3 )
% 0.26/0.58                       => ( X4
% 0.26/0.58                         != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.26/0.58               => ( ( P @ X4 )
% 0.26/0.58                 => ( P @ ( plus_plus_int @ X4 @ D5 ) ) ) )
% 0.26/0.58           => ( ! [X4: int,K2: int] :
% 0.26/0.58                  ( ( P4 @ X4 )
% 0.26/0.58                  = ( P4 @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D5 ) ) ) )
% 0.26/0.58             => ( ( ? [X8: int] : ( P @ X8 ) )
% 0.26/0.58                = ( ? [X: int] :
% 0.26/0.58                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58                      & ( P4 @ X ) )
% 0.26/0.58                  | ? [X: int] :
% 0.26/0.58                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58                      & ? [Y: int] :
% 0.26/0.58                          ( ( member_int @ Y @ A3 )
% 0.26/0.58                          & ( P @ ( minus_minus_int @ Y @ X ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % cppi
% 0.26/0.58  thf(fact_6187_cpmi,axiom,
% 0.26/0.58      ! [D5: int,P: int > $o,P4: int > $o,B5: set_int] :
% 0.26/0.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 0.26/0.58       => ( ? [Z4: int] :
% 0.26/0.58            ! [X4: int] :
% 0.26/0.58              ( ( ord_less_int @ X4 @ Z4 )
% 0.26/0.58             => ( ( P @ X4 )
% 0.26/0.58                = ( P4 @ X4 ) ) )
% 0.26/0.58         => ( ! [X4: int] :
% 0.26/0.58                ( ! [Xa2: int] :
% 0.26/0.58                    ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58                   => ! [Xb2: int] :
% 0.26/0.58                        ( ( member_int @ Xb2 @ B5 )
% 0.26/0.58                       => ( X4
% 0.26/0.58                         != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.26/0.58               => ( ( P @ X4 )
% 0.26/0.58                 => ( P @ ( minus_minus_int @ X4 @ D5 ) ) ) )
% 0.26/0.58           => ( ! [X4: int,K2: int] :
% 0.26/0.58                  ( ( P4 @ X4 )
% 0.26/0.58                  = ( P4 @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D5 ) ) ) )
% 0.26/0.58             => ( ( ? [X8: int] : ( P @ X8 ) )
% 0.26/0.58                = ( ? [X: int] :
% 0.26/0.58                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58                      & ( P4 @ X ) )
% 0.26/0.58                  | ? [X: int] :
% 0.26/0.58                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 0.26/0.58                      & ? [Y: int] :
% 0.26/0.58                          ( ( member_int @ Y @ B5 )
% 0.26/0.58                          & ( P @ ( plus_plus_int @ Y @ X ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % cpmi
% 0.26/0.58  thf(fact_6188_atLeastatMost__psubset__iff,axiom,
% 0.26/0.58      ! [A: set_nat,B: set_nat,C: set_nat,D3: set_nat] :
% 0.26/0.58        ( ( ord_less_set_set_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D3 ) )
% 0.26/0.58        = ( ( ~ ( ord_less_eq_set_nat @ A @ B )
% 0.26/0.58            | ( ( ord_less_eq_set_nat @ C @ A )
% 0.26/0.58              & ( ord_less_eq_set_nat @ B @ D3 )
% 0.26/0.58              & ( ( ord_less_set_nat @ C @ A )
% 0.26/0.58                | ( ord_less_set_nat @ B @ D3 ) ) ) )
% 0.26/0.58          & ( ord_less_eq_set_nat @ C @ D3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % atLeastatMost_psubset_iff
% 0.26/0.58  thf(fact_6189_atLeastatMost__psubset__iff,axiom,
% 0.26/0.58      ! [A: rat,B: rat,C: rat,D3: rat] :
% 0.26/0.58        ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D3 ) )
% 0.26/0.58        = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 0.26/0.58            | ( ( ord_less_eq_rat @ C @ A )
% 0.26/0.58              & ( ord_less_eq_rat @ B @ D3 )
% 0.26/0.58              & ( ( ord_less_rat @ C @ A )
% 0.26/0.58                | ( ord_less_rat @ B @ D3 ) ) ) )
% 0.26/0.58          & ( ord_less_eq_rat @ C @ D3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % atLeastatMost_psubset_iff
% 0.26/0.58  thf(fact_6190_atLeastatMost__psubset__iff,axiom,
% 0.26/0.58      ! [A: num,B: num,C: num,D3: num] :
% 0.26/0.58        ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D3 ) )
% 0.26/0.58        = ( ( ~ ( ord_less_eq_num @ A @ B )
% 0.26/0.58            | ( ( ord_less_eq_num @ C @ A )
% 0.26/0.58              & ( ord_less_eq_num @ B @ D3 )
% 0.26/0.58              & ( ( ord_less_num @ C @ A )
% 0.26/0.58                | ( ord_less_num @ B @ D3 ) ) ) )
% 0.26/0.58          & ( ord_less_eq_num @ C @ D3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % atLeastatMost_psubset_iff
% 0.26/0.58  thf(fact_6191_atLeastatMost__psubset__iff,axiom,
% 0.26/0.58      ! [A: nat,B: nat,C: nat,D3: nat] :
% 0.26/0.58        ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D3 ) )
% 0.26/0.58        = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 0.26/0.58            | ( ( ord_less_eq_nat @ C @ A )
% 0.26/0.58              & ( ord_less_eq_nat @ B @ D3 )
% 0.26/0.58              & ( ( ord_less_nat @ C @ A )
% 0.26/0.58                | ( ord_less_nat @ B @ D3 ) ) ) )
% 0.26/0.58          & ( ord_less_eq_nat @ C @ D3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % atLeastatMost_psubset_iff
% 0.26/0.58  thf(fact_6192_atLeastatMost__psubset__iff,axiom,
% 0.26/0.58      ! [A: int,B: int,C: int,D3: int] :
% 0.26/0.58        ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D3 ) )
% 0.26/0.58        = ( ( ~ ( ord_less_eq_int @ A @ B )
% 0.26/0.58            | ( ( ord_less_eq_int @ C @ A )
% 0.26/0.58              & ( ord_less_eq_int @ B @ D3 )
% 0.26/0.58              & ( ( ord_less_int @ C @ A )
% 0.26/0.58                | ( ord_less_int @ B @ D3 ) ) ) )
% 0.26/0.58          & ( ord_less_eq_int @ C @ D3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % atLeastatMost_psubset_iff
% 0.26/0.58  thf(fact_6193_atLeastatMost__psubset__iff,axiom,
% 0.26/0.58      ! [A: real,B: real,C: real,D3: real] :
% 0.26/0.58        ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D3 ) )
% 0.26/0.58        = ( ( ~ ( ord_less_eq_real @ A @ B )
% 0.26/0.58            | ( ( ord_less_eq_real @ C @ A )
% 0.26/0.58              & ( ord_less_eq_real @ B @ D3 )
% 0.26/0.58              & ( ( ord_less_real @ C @ A )
% 0.26/0.58                | ( ord_less_real @ B @ D3 ) ) ) )
% 0.26/0.58          & ( ord_less_eq_real @ C @ D3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % atLeastatMost_psubset_iff
% 0.26/0.58  thf(fact_6194_invar__vebt_Ointros_I2_J,axiom,
% 0.26/0.58      ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 0.26/0.58        ( ! [X4: vEBT_VEBT] :
% 0.26/0.58            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.26/0.58           => ( vEBT_invar_vebt @ X4 @ N ) )
% 0.26/0.58       => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.26/0.58         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.26/0.58              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.26/0.58           => ( ( M = N )
% 0.26/0.58             => ( ( Deg
% 0.26/0.58                  = ( plus_plus_nat @ N @ M ) )
% 0.26/0.58               => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 0.26/0.58                 => ( ! [X4: vEBT_VEBT] :
% 0.26/0.58                        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.26/0.58                       => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) )
% 0.26/0.58                   => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % invar_vebt.intros(2)
% 0.26/0.58  thf(fact_6195_invar__vebt_Ointros_I3_J,axiom,
% 0.26/0.58      ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 0.26/0.58        ( ! [X4: vEBT_VEBT] :
% 0.26/0.58            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.26/0.58           => ( vEBT_invar_vebt @ X4 @ N ) )
% 0.26/0.58       => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.26/0.58         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.26/0.58              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.26/0.58           => ( ( M
% 0.26/0.58                = ( suc @ N ) )
% 0.26/0.58             => ( ( Deg
% 0.26/0.58                  = ( plus_plus_nat @ N @ M ) )
% 0.26/0.58               => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 0.26/0.58                 => ( ! [X4: vEBT_VEBT] :
% 0.26/0.58                        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.26/0.58                       => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) )
% 0.26/0.58                   => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % invar_vebt.intros(3)
% 0.26/0.58  thf(fact_6196_is__pred__in__set__def,axiom,
% 0.26/0.58      ( vEBT_is_pred_in_set
% 0.26/0.58      = ( ^ [Xs: set_nat,X: nat,Y: nat] :
% 0.26/0.58            ( ( member_nat @ Y @ Xs )
% 0.26/0.58            & ( ord_less_nat @ Y @ X )
% 0.26/0.58            & ! [Z6: nat] :
% 0.26/0.58                ( ( member_nat @ Z6 @ Xs )
% 0.26/0.58               => ( ( ord_less_nat @ Z6 @ X )
% 0.26/0.58                 => ( ord_less_eq_nat @ Z6 @ Y ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % is_pred_in_set_def
% 0.26/0.58  thf(fact_6197_is__succ__in__set__def,axiom,
% 0.26/0.58      ( vEBT_is_succ_in_set
% 0.26/0.58      = ( ^ [Xs: set_nat,X: nat,Y: nat] :
% 0.26/0.58            ( ( member_nat @ Y @ Xs )
% 0.26/0.58            & ( ord_less_nat @ X @ Y )
% 0.26/0.58            & ! [Z6: nat] :
% 0.26/0.58                ( ( member_nat @ Z6 @ Xs )
% 0.26/0.58               => ( ( ord_less_nat @ X @ Z6 )
% 0.26/0.58                 => ( ord_less_eq_nat @ Y @ Z6 ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % is_succ_in_set_def
% 0.26/0.58  thf(fact_6198_vebt__pred_Osimps_I5_J,axiom,
% 0.26/0.58      ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 0.26/0.58        ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf )
% 0.26/0.58        = none_nat ) ).
% 0.26/0.58  
% 0.26/0.58  % vebt_pred.simps(5)
% 0.26/0.58  thf(fact_6199_vebt__succ_Osimps_I4_J,axiom,
% 0.26/0.58      ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 0.26/0.58        ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve )
% 0.26/0.58        = none_nat ) ).
% 0.26/0.58  
% 0.26/0.58  % vebt_succ.simps(4)
% 0.26/0.58  thf(fact_6200_del__x__mi__lets__in__not__minNull,axiom,
% 0.26/0.58      ! [X3: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 0.26/0.58        ( ( ( X3 = Mi )
% 0.26/0.58          & ( ord_less_nat @ X3 @ Ma ) )
% 0.26/0.58       => ( ( Mi != Ma )
% 0.26/0.58         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.58           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.58                = H2 )
% 0.26/0.58             => ( ( Xn
% 0.26/0.58                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_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 ) ) ) ) ) ) )
% 0.26/0.58               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.58                    = L )
% 0.26/0.58                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.58                   => ( ( Newnode
% 0.26/0.58                        = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 0.26/0.58                     => ( ( Newlist
% 0.26/0.58                          = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 0.26/0.58                       => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 0.26/0.58                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.58                            = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % del_x_mi_lets_in_not_minNull
% 0.26/0.58  thf(fact_6201_del__x__not__mi__newnode__not__nil,axiom,
% 0.26/0.58      ! [Mi: nat,X3: nat,Ma: nat,Deg: nat,H2: nat,L: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.26/0.58        ( ( ( ord_less_nat @ Mi @ X3 )
% 0.26/0.58          & ( ord_less_eq_nat @ X3 @ Ma ) )
% 0.26/0.58       => ( ( Mi != Ma )
% 0.26/0.58         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.58           => ( ( ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.58                = H2 )
% 0.26/0.58             => ( ( ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.58                  = L )
% 0.26/0.58               => ( ( Newnode
% 0.26/0.58                    = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 0.26/0.58                 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 0.26/0.58                   => ( ( Newlist
% 0.26/0.58                        = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 0.26/0.58                     => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.58                       => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.58                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % del_x_not_mi_newnode_not_nil
% 0.26/0.58  thf(fact_6202__C5_OIH_C_I1_J,axiom,
% 0.26/0.58      ! [X6: vEBT_VEBT] :
% 0.26/0.58        ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ treeList ) )
% 0.26/0.58       => ( ( vEBT_invar_vebt @ X6 @ na )
% 0.26/0.58          & ( ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ X6 @ x ) )
% 0.26/0.58           => ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ X6 @ x ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % "5.IH"(1)
% 0.26/0.58  thf(fact_6203_vebt__delete_Osimps_I6_J,axiom,
% 0.26/0.58      ! [Mi: nat,Ma: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT,X3: nat] :
% 0.26/0.58        ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ X3 )
% 0.26/0.58        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) ) ).
% 0.26/0.58  
% 0.26/0.58  % vebt_delete.simps(6)
% 0.26/0.58  thf(fact_6204__C5_OIH_C_I2_J,axiom,
% 0.26/0.58      ( ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ summary @ x ) )
% 0.26/0.58     => ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ summary @ x ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % "5.IH"(2)
% 0.26/0.58  thf(fact_6205_Leaf__0__not,axiom,
% 0.26/0.58      ! [A: $o,B: $o] :
% 0.26/0.58        ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 0.26/0.58  
% 0.26/0.58  % Leaf_0_not
% 0.26/0.58  thf(fact_6206_deg1Leaf,axiom,
% 0.26/0.58      ! [T: vEBT_VEBT] :
% 0.26/0.58        ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 0.26/0.58        = ( ? [A4: $o,B3: $o] :
% 0.26/0.58              ( T
% 0.26/0.58              = ( vEBT_Leaf @ A4 @ B3 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % deg1Leaf
% 0.26/0.58  thf(fact_6207_deg__1__Leaf,axiom,
% 0.26/0.58      ! [T: vEBT_VEBT] :
% 0.26/0.58        ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 0.26/0.58       => ? [A5: $o,B4: $o] :
% 0.26/0.58            ( T
% 0.26/0.58            = ( vEBT_Leaf @ A5 @ B4 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % deg_1_Leaf
% 0.26/0.58  thf(fact_6208_deg__1__Leafy,axiom,
% 0.26/0.58      ! [T: vEBT_VEBT,N: nat] :
% 0.26/0.58        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.58       => ( ( N = one_one_nat )
% 0.26/0.58         => ? [A5: $o,B4: $o] :
% 0.26/0.58              ( T
% 0.26/0.58              = ( vEBT_Leaf @ A5 @ B4 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % deg_1_Leafy
% 0.26/0.58  thf(fact_6209_semiring__norm_I90_J,axiom,
% 0.26/0.58      ! [M: num,N: num] :
% 0.26/0.58        ( ( ( bit1 @ M )
% 0.26/0.58          = ( bit1 @ N ) )
% 0.26/0.58        = ( M = N ) ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(90)
% 0.26/0.58  thf(fact_6210_verit__eq__simplify_I9_J,axiom,
% 0.26/0.58      ! [X32: num,Y32: num] :
% 0.26/0.58        ( ( ( bit1 @ X32 )
% 0.26/0.58          = ( bit1 @ Y32 ) )
% 0.26/0.58        = ( X32 = Y32 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % verit_eq_simplify(9)
% 0.26/0.58  thf(fact_6211_semiring__norm_I88_J,axiom,
% 0.26/0.58      ! [M: num,N: num] :
% 0.26/0.58        ( ( bit0 @ M )
% 0.26/0.58       != ( bit1 @ N ) ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(88)
% 0.26/0.58  thf(fact_6212_semiring__norm_I89_J,axiom,
% 0.26/0.58      ! [M: num,N: num] :
% 0.26/0.58        ( ( bit1 @ M )
% 0.26/0.58       != ( bit0 @ N ) ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(89)
% 0.26/0.58  thf(fact_6213_semiring__norm_I84_J,axiom,
% 0.26/0.58      ! [N: num] :
% 0.26/0.58        ( one
% 0.26/0.58       != ( bit1 @ N ) ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(84)
% 0.26/0.58  thf(fact_6214_semiring__norm_I86_J,axiom,
% 0.26/0.58      ! [M: num] :
% 0.26/0.58        ( ( bit1 @ M )
% 0.26/0.58       != one ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(86)
% 0.26/0.58  thf(fact_6215_tdeletemimi,axiom,
% 0.26/0.58      ! [Deg: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 0.26/0.58        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.58       => ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Mi ) ) @ Deg @ TreeList2 @ Summary ) @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % tdeletemimi
% 0.26/0.58  thf(fact_6216_semiring__norm_I80_J,axiom,
% 0.26/0.58      ! [M: num,N: num] :
% 0.26/0.58        ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.26/0.58        = ( ord_less_num @ M @ N ) ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(80)
% 0.26/0.58  thf(fact_6217_semiring__norm_I73_J,axiom,
% 0.26/0.58      ! [M: num,N: num] :
% 0.26/0.58        ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.26/0.58        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(73)
% 0.26/0.58  thf(fact_6218_semiring__norm_I9_J,axiom,
% 0.26/0.58      ! [M: num,N: num] :
% 0.26/0.58        ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.26/0.58        = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(9)
% 0.26/0.58  thf(fact_6219_semiring__norm_I7_J,axiom,
% 0.26/0.58      ! [M: num,N: num] :
% 0.26/0.58        ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.26/0.58        = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(7)
% 0.26/0.58  thf(fact_6220_list__update__beyond,axiom,
% 0.26/0.58      ! [Xs2: list_VEBT_VEBT,I: nat,X3: vEBT_VEBT] :
% 0.26/0.58        ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ I )
% 0.26/0.58       => ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X3 )
% 0.26/0.58          = Xs2 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % list_update_beyond
% 0.26/0.58  thf(fact_6221_list__update__beyond,axiom,
% 0.26/0.58      ! [Xs2: list_o,I: nat,X3: $o] :
% 0.26/0.58        ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ I )
% 0.26/0.58       => ( ( list_update_o @ Xs2 @ I @ X3 )
% 0.26/0.58          = Xs2 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % list_update_beyond
% 0.26/0.58  thf(fact_6222_list__update__beyond,axiom,
% 0.26/0.58      ! [Xs2: list_nat,I: nat,X3: nat] :
% 0.26/0.58        ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ I )
% 0.26/0.58       => ( ( list_update_nat @ Xs2 @ I @ X3 )
% 0.26/0.58          = Xs2 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % list_update_beyond
% 0.26/0.58  thf(fact_6223_list__update__beyond,axiom,
% 0.26/0.58      ! [Xs2: list_int,I: nat,X3: int] :
% 0.26/0.58        ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ I )
% 0.26/0.58       => ( ( list_update_int @ Xs2 @ I @ X3 )
% 0.26/0.58          = Xs2 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % list_update_beyond
% 0.26/0.58  thf(fact_6224_semiring__norm_I15_J,axiom,
% 0.26/0.58      ! [M: num,N: num] :
% 0.26/0.58        ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.26/0.58        = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(15)
% 0.26/0.58  thf(fact_6225_semiring__norm_I14_J,axiom,
% 0.26/0.58      ! [M: num,N: num] :
% 0.26/0.58        ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.26/0.58        = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(14)
% 0.26/0.58  thf(fact_6226_semiring__norm_I81_J,axiom,
% 0.26/0.58      ! [M: num,N: num] :
% 0.26/0.58        ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.26/0.58        = ( ord_less_num @ M @ N ) ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(81)
% 0.26/0.58  thf(fact_6227_semiring__norm_I72_J,axiom,
% 0.26/0.58      ! [M: num,N: num] :
% 0.26/0.58        ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.26/0.58        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(72)
% 0.26/0.58  thf(fact_6228_semiring__norm_I77_J,axiom,
% 0.26/0.58      ! [N: num] : ( ord_less_num @ one @ ( bit1 @ N ) ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(77)
% 0.26/0.58  thf(fact_6229_semiring__norm_I70_J,axiom,
% 0.26/0.58      ! [M: num] :
% 0.26/0.58        ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(70)
% 0.26/0.58  thf(fact_6230_or__numerals_I8_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X3 ) ) @ one_one_int )
% 0.26/0.58        = ( numeral_numeral_int @ ( bit1 @ X3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % or_numerals(8)
% 0.26/0.58  thf(fact_6231_or__numerals_I8_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ one_one_nat )
% 0.26/0.58        = ( numeral_numeral_nat @ ( bit1 @ X3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % or_numerals(8)
% 0.26/0.58  thf(fact_6232_or__numerals_I2_J,axiom,
% 0.26/0.58      ! [Y3: num] :
% 0.26/0.58        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y3 ) ) )
% 0.26/0.58        = ( numeral_numeral_int @ ( bit1 @ Y3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % or_numerals(2)
% 0.26/0.58  thf(fact_6233_or__numerals_I2_J,axiom,
% 0.26/0.58      ! [Y3: num] :
% 0.26/0.58        ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 0.26/0.58        = ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % or_numerals(2)
% 0.26/0.58  thf(fact_6234_zdiv__numeral__Bit1,axiom,
% 0.26/0.58      ! [V: num,W: num] :
% 0.26/0.58        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 0.26/0.58        = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % zdiv_numeral_Bit1
% 0.26/0.58  thf(fact_6235_semiring__norm_I3_J,axiom,
% 0.26/0.58      ! [N: num] :
% 0.26/0.58        ( ( plus_plus_num @ one @ ( bit0 @ N ) )
% 0.26/0.58        = ( bit1 @ N ) ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(3)
% 0.26/0.58  thf(fact_6236_semiring__norm_I4_J,axiom,
% 0.26/0.58      ! [N: num] :
% 0.26/0.58        ( ( plus_plus_num @ one @ ( bit1 @ N ) )
% 0.26/0.58        = ( bit0 @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(4)
% 0.26/0.58  thf(fact_6237_semiring__norm_I5_J,axiom,
% 0.26/0.58      ! [M: num] :
% 0.26/0.58        ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 0.26/0.58        = ( bit1 @ M ) ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(5)
% 0.26/0.58  thf(fact_6238_semiring__norm_I8_J,axiom,
% 0.26/0.58      ! [M: num] :
% 0.26/0.58        ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 0.26/0.58        = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(8)
% 0.26/0.58  thf(fact_6239_semiring__norm_I10_J,axiom,
% 0.26/0.58      ! [M: num,N: num] :
% 0.26/0.58        ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.26/0.58        = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ one ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(10)
% 0.26/0.58  thf(fact_6240_nth__list__update__eq,axiom,
% 0.26/0.58      ! [I: nat,Xs2: list_VEBT_VEBT,X3: vEBT_VEBT] :
% 0.26/0.58        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.26/0.58       => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X3 ) @ I )
% 0.26/0.58          = X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % nth_list_update_eq
% 0.26/0.58  thf(fact_6241_nth__list__update__eq,axiom,
% 0.26/0.58      ! [I: nat,Xs2: list_o,X3: $o] :
% 0.26/0.58        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 0.26/0.58       => ( ( nth_o @ ( list_update_o @ Xs2 @ I @ X3 ) @ I )
% 0.26/0.58          = X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % nth_list_update_eq
% 0.26/0.58  thf(fact_6242_nth__list__update__eq,axiom,
% 0.26/0.58      ! [I: nat,Xs2: list_nat,X3: nat] :
% 0.26/0.58        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 0.26/0.58       => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X3 ) @ I )
% 0.26/0.58          = X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % nth_list_update_eq
% 0.26/0.58  thf(fact_6243_nth__list__update__eq,axiom,
% 0.26/0.58      ! [I: nat,Xs2: list_int,X3: int] :
% 0.26/0.58        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 0.26/0.58       => ( ( nth_int @ ( list_update_int @ Xs2 @ I @ X3 ) @ I )
% 0.26/0.58          = X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % nth_list_update_eq
% 0.26/0.58  thf(fact_6244_semiring__norm_I16_J,axiom,
% 0.26/0.58      ! [M: num,N: num] :
% 0.26/0.58        ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.26/0.58        = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(16)
% 0.26/0.58  thf(fact_6245_semiring__norm_I79_J,axiom,
% 0.26/0.58      ! [M: num,N: num] :
% 0.26/0.58        ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.26/0.58        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(79)
% 0.26/0.58  thf(fact_6246_semiring__norm_I74_J,axiom,
% 0.26/0.58      ! [M: num,N: num] :
% 0.26/0.58        ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.26/0.58        = ( ord_less_num @ M @ N ) ) ).
% 0.26/0.58  
% 0.26/0.58  % semiring_norm(74)
% 0.26/0.58  thf(fact_6247_or__numerals_I5_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X3 ) ) @ one_one_int )
% 0.26/0.58        = ( numeral_numeral_int @ ( bit1 @ X3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % or_numerals(5)
% 0.26/0.58  thf(fact_6248_or__numerals_I5_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ one_one_nat )
% 0.26/0.58        = ( numeral_numeral_nat @ ( bit1 @ X3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % or_numerals(5)
% 0.26/0.58  thf(fact_6249_or__numerals_I1_J,axiom,
% 0.26/0.58      ! [Y3: num] :
% 0.26/0.58        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y3 ) ) )
% 0.26/0.58        = ( numeral_numeral_int @ ( bit1 @ Y3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % or_numerals(1)
% 0.26/0.58  thf(fact_6250_or__numerals_I1_J,axiom,
% 0.26/0.58      ! [Y3: num] :
% 0.26/0.58        ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 0.26/0.58        = ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % or_numerals(1)
% 0.26/0.58  thf(fact_6251_xor__numerals_I1_J,axiom,
% 0.26/0.58      ! [Y3: num] :
% 0.26/0.58        ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y3 ) ) )
% 0.26/0.58        = ( numeral_numeral_int @ ( bit1 @ Y3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % xor_numerals(1)
% 0.26/0.58  thf(fact_6252_xor__numerals_I1_J,axiom,
% 0.26/0.58      ! [Y3: num] :
% 0.26/0.58        ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 0.26/0.58        = ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % xor_numerals(1)
% 0.26/0.58  thf(fact_6253_xor__numerals_I2_J,axiom,
% 0.26/0.58      ! [Y3: num] :
% 0.26/0.58        ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y3 ) ) )
% 0.26/0.58        = ( numeral_numeral_int @ ( bit0 @ Y3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % xor_numerals(2)
% 0.26/0.58  thf(fact_6254_xor__numerals_I2_J,axiom,
% 0.26/0.58      ! [Y3: num] :
% 0.26/0.58        ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 0.26/0.58        = ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % xor_numerals(2)
% 0.26/0.58  thf(fact_6255_xor__numerals_I5_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X3 ) ) @ one_one_int )
% 0.26/0.58        = ( numeral_numeral_int @ ( bit1 @ X3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % xor_numerals(5)
% 0.26/0.58  thf(fact_6256_xor__numerals_I5_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ one_one_nat )
% 0.26/0.58        = ( numeral_numeral_nat @ ( bit1 @ X3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % xor_numerals(5)
% 0.26/0.58  thf(fact_6257_xor__numerals_I8_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X3 ) ) @ one_one_int )
% 0.26/0.58        = ( numeral_numeral_int @ ( bit0 @ X3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % xor_numerals(8)
% 0.26/0.58  thf(fact_6258_xor__numerals_I8_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ one_one_nat )
% 0.26/0.58        = ( numeral_numeral_nat @ ( bit0 @ X3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % xor_numerals(8)
% 0.26/0.58  thf(fact_6259_set__swap,axiom,
% 0.26/0.58      ! [I: nat,Xs2: list_VEBT_VEBT,J: nat] :
% 0.26/0.58        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.26/0.58       => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.26/0.58         => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ ( nth_VEBT_VEBT @ Xs2 @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs2 @ I ) ) )
% 0.26/0.58            = ( set_VEBT_VEBT2 @ Xs2 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % set_swap
% 0.26/0.58  thf(fact_6260_set__swap,axiom,
% 0.26/0.58      ! [I: nat,Xs2: list_o,J: nat] :
% 0.26/0.58        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 0.26/0.58       => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs2 ) )
% 0.26/0.58         => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs2 @ I @ ( nth_o @ Xs2 @ J ) ) @ J @ ( nth_o @ Xs2 @ I ) ) )
% 0.26/0.58            = ( set_o2 @ Xs2 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % set_swap
% 0.26/0.58  thf(fact_6261_set__swap,axiom,
% 0.26/0.58      ! [I: nat,Xs2: list_nat,J: nat] :
% 0.26/0.58        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 0.26/0.58       => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.26/0.58         => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs2 @ I @ ( nth_nat @ Xs2 @ J ) ) @ J @ ( nth_nat @ Xs2 @ I ) ) )
% 0.26/0.58            = ( set_nat2 @ Xs2 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % set_swap
% 0.26/0.58  thf(fact_6262_set__swap,axiom,
% 0.26/0.58      ! [I: nat,Xs2: list_int,J: nat] :
% 0.26/0.58        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 0.26/0.58       => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs2 ) )
% 0.26/0.58         => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs2 @ I @ ( nth_int @ Xs2 @ J ) ) @ J @ ( nth_int @ Xs2 @ I ) ) )
% 0.26/0.58            = ( set_int2 @ Xs2 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % set_swap
% 0.26/0.58  thf(fact_6263_or__nat__numerals_I4_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 0.26/0.58        = ( numeral_numeral_nat @ ( bit1 @ X3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % or_nat_numerals(4)
% 0.26/0.58  thf(fact_6264_or__nat__numerals_I2_J,axiom,
% 0.26/0.58      ! [Y3: num] :
% 0.26/0.58        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 0.26/0.58        = ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % or_nat_numerals(2)
% 0.26/0.58  thf(fact_6265_or__minus__numerals_I6_J,axiom,
% 0.26/0.58      ! [N: num] :
% 0.26/0.58        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 0.26/0.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % or_minus_numerals(6)
% 0.26/0.58  thf(fact_6266_or__minus__numerals_I2_J,axiom,
% 0.26/0.58      ! [N: num] :
% 0.26/0.58        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.26/0.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % or_minus_numerals(2)
% 0.26/0.58  thf(fact_6267_div__Suc__eq__div__add3,axiom,
% 0.26/0.58      ! [M: nat,N: nat] :
% 0.26/0.58        ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 0.26/0.58        = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % div_Suc_eq_div_add3
% 0.26/0.58  thf(fact_6268_Suc__div__eq__add3__div__numeral,axiom,
% 0.26/0.58      ! [M: nat,V: num] :
% 0.26/0.58        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 0.26/0.58        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % Suc_div_eq_add3_div_numeral
% 0.26/0.58  thf(fact_6269_xor__numerals_I7_J,axiom,
% 0.26/0.58      ! [X3: num,Y3: num] :
% 0.26/0.58        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X3 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y3 ) ) )
% 0.26/0.58        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % xor_numerals(7)
% 0.26/0.58  thf(fact_6270_xor__numerals_I7_J,axiom,
% 0.26/0.58      ! [X3: num,Y3: num] :
% 0.26/0.58        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 0.26/0.58        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X3 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % xor_numerals(7)
% 0.26/0.58  thf(fact_6271_Suc__mod__eq__add3__mod__numeral,axiom,
% 0.26/0.58      ! [M: nat,V: num] :
% 0.26/0.58        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 0.26/0.58        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % Suc_mod_eq_add3_mod_numeral
% 0.26/0.58  thf(fact_6272_mod__Suc__eq__mod__add3,axiom,
% 0.26/0.58      ! [M: nat,N: nat] :
% 0.26/0.58        ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 0.26/0.58        = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % mod_Suc_eq_mod_add3
% 0.26/0.58  thf(fact_6273_or__nat__numerals_I3_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 0.26/0.58        = ( numeral_numeral_nat @ ( bit1 @ X3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % or_nat_numerals(3)
% 0.26/0.58  thf(fact_6274_or__nat__numerals_I1_J,axiom,
% 0.26/0.58      ! [Y3: num] :
% 0.26/0.58        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 0.26/0.58        = ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % or_nat_numerals(1)
% 0.26/0.58  thf(fact_6275_xor__nat__numerals_I4_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 0.26/0.58        = ( numeral_numeral_nat @ ( bit0 @ X3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % xor_nat_numerals(4)
% 0.26/0.58  thf(fact_6276_xor__nat__numerals_I3_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 0.26/0.58        = ( numeral_numeral_nat @ ( bit1 @ X3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % xor_nat_numerals(3)
% 0.26/0.58  thf(fact_6277_xor__nat__numerals_I2_J,axiom,
% 0.26/0.58      ! [Y3: num] :
% 0.26/0.58        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 0.26/0.58        = ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % xor_nat_numerals(2)
% 0.26/0.58  thf(fact_6278_xor__nat__numerals_I1_J,axiom,
% 0.26/0.58      ! [Y3: num] :
% 0.26/0.58        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 0.26/0.58        = ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % xor_nat_numerals(1)
% 0.26/0.58  thf(fact_6279_or__numerals_I4_J,axiom,
% 0.26/0.58      ! [X3: num,Y3: num] :
% 0.26/0.58        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X3 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y3 ) ) )
% 0.26/0.58        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % or_numerals(4)
% 0.26/0.58  thf(fact_6280_or__numerals_I4_J,axiom,
% 0.26/0.58      ! [X3: num,Y3: num] :
% 0.26/0.58        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 0.26/0.58        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X3 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % or_numerals(4)
% 0.26/0.58  thf(fact_6281_or__numerals_I6_J,axiom,
% 0.26/0.58      ! [X3: num,Y3: num] :
% 0.26/0.58        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X3 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y3 ) ) )
% 0.26/0.58        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % or_numerals(6)
% 0.26/0.58  thf(fact_6282_or__numerals_I6_J,axiom,
% 0.26/0.58      ! [X3: num,Y3: num] :
% 0.26/0.58        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 0.26/0.58        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X3 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % or_numerals(6)
% 0.26/0.58  thf(fact_6283_or__numerals_I7_J,axiom,
% 0.26/0.58      ! [X3: num,Y3: num] :
% 0.26/0.58        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X3 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y3 ) ) )
% 0.26/0.58        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % or_numerals(7)
% 0.26/0.58  thf(fact_6284_or__numerals_I7_J,axiom,
% 0.26/0.58      ! [X3: num,Y3: num] :
% 0.26/0.58        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 0.26/0.58        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X3 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % or_numerals(7)
% 0.26/0.58  thf(fact_6285_xor__numerals_I4_J,axiom,
% 0.26/0.58      ! [X3: num,Y3: num] :
% 0.26/0.58        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X3 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y3 ) ) )
% 0.26/0.58        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % xor_numerals(4)
% 0.26/0.58  thf(fact_6286_xor__numerals_I4_J,axiom,
% 0.26/0.58      ! [X3: num,Y3: num] :
% 0.26/0.58        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 0.26/0.58        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X3 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % xor_numerals(4)
% 0.26/0.58  thf(fact_6287_xor__numerals_I6_J,axiom,
% 0.26/0.58      ! [X3: num,Y3: num] :
% 0.26/0.58        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X3 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y3 ) ) )
% 0.26/0.58        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % xor_numerals(6)
% 0.26/0.58  thf(fact_6288_xor__numerals_I6_J,axiom,
% 0.26/0.58      ! [X3: num,Y3: num] :
% 0.26/0.58        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 0.26/0.58        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X3 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % xor_numerals(6)
% 0.26/0.58  thf(fact_6289_zmod__numeral__Bit1,axiom,
% 0.26/0.58      ! [V: num,W: num] :
% 0.26/0.58        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 0.26/0.58        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) @ one_one_int ) ) ).
% 0.26/0.58  
% 0.26/0.58  % zmod_numeral_Bit1
% 0.26/0.58  thf(fact_6290_signed__take__bit__Suc__bit1,axiom,
% 0.26/0.58      ! [N: nat,K: num] :
% 0.26/0.58        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.26/0.58        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.26/0.58  
% 0.26/0.58  % signed_take_bit_Suc_bit1
% 0.26/0.58  thf(fact_6291_signed__take__bit__Suc__minus__bit1,axiom,
% 0.26/0.58      ! [N: nat,K: num] :
% 0.26/0.58        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.26/0.58        = ( 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 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % signed_take_bit_Suc_minus_bit1
% 0.26/0.58  thf(fact_6292_VEBT_Osize_I4_J,axiom,
% 0.26/0.58      ! [X21: $o,X222: $o] :
% 0.26/0.58        ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 0.26/0.58        = zero_zero_nat ) ).
% 0.26/0.58  
% 0.26/0.58  % VEBT.size(4)
% 0.26/0.58  thf(fact_6293_verit__eq__simplify_I14_J,axiom,
% 0.26/0.58      ! [X2: num,X32: num] :
% 0.26/0.58        ( ( bit0 @ X2 )
% 0.26/0.58       != ( bit1 @ X32 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % verit_eq_simplify(14)
% 0.26/0.58  thf(fact_6294_verit__eq__simplify_I12_J,axiom,
% 0.26/0.58      ! [X32: num] :
% 0.26/0.58        ( one
% 0.26/0.58       != ( bit1 @ X32 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % verit_eq_simplify(12)
% 0.26/0.58  thf(fact_6295_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I3_J,axiom,
% 0.26/0.58      ! [A: $o,B: $o,N: nat] :
% 0.26/0.58        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N ) ) )
% 0.26/0.58        = one_one_nat ) ).
% 0.26/0.58  
% 0.26/0.58  % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(3)
% 0.26/0.58  thf(fact_6296_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I1_J,axiom,
% 0.26/0.58      ! [A: $o,B: $o] :
% 0.26/0.58        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 0.26/0.58        = one_one_nat ) ).
% 0.26/0.58  
% 0.26/0.58  % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(1)
% 0.26/0.58  thf(fact_6297_vebt__delete_Osimps_I1_J,axiom,
% 0.26/0.58      ! [A: $o,B: $o] :
% 0.26/0.58        ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 0.26/0.58        = ( vEBT_Leaf @ $false @ B ) ) ).
% 0.26/0.58  
% 0.26/0.58  % vebt_delete.simps(1)
% 0.26/0.58  thf(fact_6298_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I2_J,axiom,
% 0.26/0.58      ! [A: $o,B: $o] :
% 0.26/0.58        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 0.26/0.58        = one_one_nat ) ).
% 0.26/0.58  
% 0.26/0.58  % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(2)
% 0.26/0.58  thf(fact_6299_xor__num_Ocases,axiom,
% 0.26/0.58      ! [X3: product_prod_num_num] :
% 0.26/0.58        ( ( X3
% 0.26/0.58         != ( product_Pair_num_num @ one @ one ) )
% 0.26/0.58       => ( ! [N2: num] :
% 0.26/0.58              ( X3
% 0.26/0.58             != ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) )
% 0.26/0.58         => ( ! [N2: num] :
% 0.26/0.58                ( X3
% 0.26/0.58               != ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) )
% 0.26/0.58           => ( ! [M4: num] :
% 0.26/0.58                  ( X3
% 0.26/0.58                 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) )
% 0.26/0.58             => ( ! [M4: num,N2: num] :
% 0.26/0.58                    ( X3
% 0.26/0.58                   != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) ) )
% 0.26/0.58               => ( ! [M4: num,N2: num] :
% 0.26/0.58                      ( X3
% 0.26/0.58                     != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) ) )
% 0.26/0.58                 => ( ! [M4: num] :
% 0.26/0.58                        ( X3
% 0.26/0.58                       != ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) )
% 0.26/0.58                   => ( ! [M4: num,N2: num] :
% 0.26/0.58                          ( X3
% 0.26/0.58                         != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) ) )
% 0.26/0.58                     => ~ ! [M4: num,N2: num] :
% 0.26/0.58                            ( X3
% 0.26/0.58                           != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % xor_num.cases
% 0.26/0.58  thf(fact_6300_num_Oexhaust,axiom,
% 0.26/0.58      ! [Y3: num] :
% 0.26/0.58        ( ( Y3 != one )
% 0.26/0.58       => ( ! [X22: num] :
% 0.26/0.58              ( Y3
% 0.26/0.58             != ( bit0 @ X22 ) )
% 0.26/0.58         => ~ ! [X33: num] :
% 0.26/0.58                ( Y3
% 0.26/0.58               != ( bit1 @ X33 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % num.exhaust
% 0.26/0.58  thf(fact_6301_vebt__delete_Osimps_I2_J,axiom,
% 0.26/0.58      ! [A: $o,B: $o] :
% 0.26/0.58        ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 0.26/0.58        = ( vEBT_Leaf @ A @ $false ) ) ).
% 0.26/0.58  
% 0.26/0.58  % vebt_delete.simps(2)
% 0.26/0.58  thf(fact_6302_vebt__buildup_Osimps_I1_J,axiom,
% 0.26/0.58      ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 0.26/0.58      = ( vEBT_Leaf @ $false @ $false ) ) ).
% 0.26/0.58  
% 0.26/0.58  % vebt_buildup.simps(1)
% 0.26/0.58  thf(fact_6303_VEBT__internal_Onaive__member_Ocases,axiom,
% 0.26/0.58      ! [X3: produc9072475918466114483BT_nat] :
% 0.26/0.58        ( ! [A5: $o,B4: $o,X4: nat] :
% 0.26/0.58            ( X3
% 0.26/0.58           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ X4 ) )
% 0.26/0.58       => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux2: nat] :
% 0.26/0.58              ( X3
% 0.26/0.58             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux2 ) )
% 0.26/0.58         => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT,X4: nat] :
% 0.26/0.58                ( X3
% 0.26/0.58               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) @ X4 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % VEBT_internal.naive_member.cases
% 0.26/0.58  thf(fact_6304_numeral__Bit1,axiom,
% 0.26/0.58      ! [N: num] :
% 0.26/0.58        ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 0.26/0.58        = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 0.26/0.58  
% 0.26/0.58  % numeral_Bit1
% 0.26/0.58  thf(fact_6305_numeral__Bit1,axiom,
% 0.26/0.58      ! [N: num] :
% 0.26/0.58        ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 0.26/0.58        = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 0.26/0.58  
% 0.26/0.58  % numeral_Bit1
% 0.26/0.58  thf(fact_6306_numeral__Bit1,axiom,
% 0.26/0.58      ! [N: num] :
% 0.26/0.58        ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 0.26/0.58        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 0.26/0.58  
% 0.26/0.58  % numeral_Bit1
% 0.26/0.58  thf(fact_6307_numeral__Bit1,axiom,
% 0.26/0.58      ! [N: num] :
% 0.26/0.58        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 0.26/0.58        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 0.26/0.58  
% 0.26/0.58  % numeral_Bit1
% 0.26/0.58  thf(fact_6308_numeral__Bit1,axiom,
% 0.26/0.58      ! [N: num] :
% 0.26/0.58        ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 0.26/0.58        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 0.26/0.58  
% 0.26/0.58  % numeral_Bit1
% 0.26/0.58  thf(fact_6309_invar__vebt_Ointros_I1_J,axiom,
% 0.26/0.58      ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 0.26/0.58  
% 0.26/0.58  % invar_vebt.intros(1)
% 0.26/0.58  thf(fact_6310_eval__nat__numeral_I3_J,axiom,
% 0.26/0.58      ! [N: num] :
% 0.26/0.58        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 0.26/0.58        = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % eval_nat_numeral(3)
% 0.26/0.58  thf(fact_6311_cong__exp__iff__simps_I10_J,axiom,
% 0.26/0.58      ! [M: num,Q3: num,N: num] :
% 0.26/0.58        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 0.26/0.58       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % cong_exp_iff_simps(10)
% 0.26/0.58  thf(fact_6312_cong__exp__iff__simps_I10_J,axiom,
% 0.26/0.58      ! [M: num,Q3: num,N: num] :
% 0.26/0.58        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 0.26/0.58       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % cong_exp_iff_simps(10)
% 0.26/0.58  thf(fact_6313_cong__exp__iff__simps_I10_J,axiom,
% 0.26/0.58      ! [M: num,Q3: num,N: num] :
% 0.26/0.58        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 0.26/0.58       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % cong_exp_iff_simps(10)
% 0.26/0.58  thf(fact_6314_cong__exp__iff__simps_I12_J,axiom,
% 0.26/0.58      ! [M: num,Q3: num,N: num] :
% 0.26/0.58        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 0.26/0.58       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % cong_exp_iff_simps(12)
% 0.26/0.58  thf(fact_6315_cong__exp__iff__simps_I12_J,axiom,
% 0.26/0.58      ! [M: num,Q3: num,N: num] :
% 0.26/0.58        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 0.26/0.58       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % cong_exp_iff_simps(12)
% 0.26/0.58  thf(fact_6316_cong__exp__iff__simps_I12_J,axiom,
% 0.26/0.58      ! [M: num,Q3: num,N: num] :
% 0.26/0.58        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 0.26/0.58       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % cong_exp_iff_simps(12)
% 0.26/0.58  thf(fact_6317_cong__exp__iff__simps_I13_J,axiom,
% 0.26/0.58      ! [M: num,Q3: num,N: num] :
% 0.26/0.58        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 0.26/0.58          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 0.26/0.58        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 0.26/0.58          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q3 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % cong_exp_iff_simps(13)
% 0.26/0.58  thf(fact_6318_cong__exp__iff__simps_I13_J,axiom,
% 0.26/0.58      ! [M: num,Q3: num,N: num] :
% 0.26/0.58        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 0.26/0.58          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 0.26/0.58        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 0.26/0.58          = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q3 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % cong_exp_iff_simps(13)
% 0.26/0.58  thf(fact_6319_cong__exp__iff__simps_I13_J,axiom,
% 0.26/0.58      ! [M: num,Q3: num,N: num] :
% 0.26/0.58        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 0.26/0.58          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 0.26/0.58        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 0.26/0.58          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q3 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % cong_exp_iff_simps(13)
% 0.26/0.58  thf(fact_6320_power__minus__Bit1,axiom,
% 0.26/0.58      ! [X3: real,K: num] :
% 0.26/0.58        ( ( power_power_real @ ( uminus_uminus_real @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.26/0.58        = ( uminus_uminus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % power_minus_Bit1
% 0.26/0.58  thf(fact_6321_power__minus__Bit1,axiom,
% 0.26/0.58      ! [X3: int,K: num] :
% 0.26/0.58        ( ( power_power_int @ ( uminus_uminus_int @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.26/0.58        = ( uminus_uminus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % power_minus_Bit1
% 0.26/0.58  thf(fact_6322_power__minus__Bit1,axiom,
% 0.26/0.58      ! [X3: complex,K: num] :
% 0.26/0.58        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.26/0.58        = ( uminus1482373934393186551omplex @ ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % power_minus_Bit1
% 0.26/0.58  thf(fact_6323_power__minus__Bit1,axiom,
% 0.26/0.58      ! [X3: code_integer,K: num] :
% 0.26/0.58        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.26/0.58        = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % power_minus_Bit1
% 0.26/0.58  thf(fact_6324_power__minus__Bit1,axiom,
% 0.26/0.58      ! [X3: rat,K: num] :
% 0.26/0.58        ( ( power_power_rat @ ( uminus_uminus_rat @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.26/0.58        = ( uminus_uminus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % power_minus_Bit1
% 0.26/0.58  thf(fact_6325_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I4_J,axiom,
% 0.26/0.58      ! [Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu2: nat] :
% 0.26/0.58        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Uu2 )
% 0.26/0.58        = one_one_nat ) ).
% 0.26/0.58  
% 0.26/0.58  % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(4)
% 0.26/0.58  thf(fact_6326_set__update__memI,axiom,
% 0.26/0.58      ! [N: nat,Xs2: list_option_nat,X3: option_nat] :
% 0.26/0.58        ( ( ord_less_nat @ N @ ( size_s6086282163384603972on_nat @ Xs2 ) )
% 0.26/0.58       => ( member_option_nat @ X3 @ ( set_option_nat2 @ ( list_u3411377215356412978on_nat @ Xs2 @ N @ X3 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % set_update_memI
% 0.26/0.58  thf(fact_6327_set__update__memI,axiom,
% 0.26/0.58      ! [N: nat,Xs2: list_real,X3: real] :
% 0.26/0.58        ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 0.26/0.58       => ( member_real @ X3 @ ( set_real2 @ ( list_update_real @ Xs2 @ N @ X3 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % set_update_memI
% 0.26/0.58  thf(fact_6328_set__update__memI,axiom,
% 0.26/0.58      ! [N: nat,Xs2: list_set_nat,X3: set_nat] :
% 0.26/0.58        ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 0.26/0.58       => ( member_set_nat @ X3 @ ( set_set_nat2 @ ( list_update_set_nat @ Xs2 @ N @ X3 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % set_update_memI
% 0.26/0.58  thf(fact_6329_set__update__memI,axiom,
% 0.26/0.58      ! [N: nat,Xs2: list_VEBT_VEBT,X3: vEBT_VEBT] :
% 0.26/0.58        ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.26/0.58       => ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ N @ X3 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % set_update_memI
% 0.26/0.58  thf(fact_6330_set__update__memI,axiom,
% 0.26/0.58      ! [N: nat,Xs2: list_o,X3: $o] :
% 0.26/0.58        ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 0.26/0.58       => ( member_o @ X3 @ ( set_o2 @ ( list_update_o @ Xs2 @ N @ X3 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % set_update_memI
% 0.26/0.58  thf(fact_6331_set__update__memI,axiom,
% 0.26/0.58      ! [N: nat,Xs2: list_nat,X3: nat] :
% 0.26/0.58        ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 0.26/0.58       => ( member_nat @ X3 @ ( set_nat2 @ ( list_update_nat @ Xs2 @ N @ X3 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % set_update_memI
% 0.26/0.58  thf(fact_6332_set__update__memI,axiom,
% 0.26/0.58      ! [N: nat,Xs2: list_int,X3: int] :
% 0.26/0.58        ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 0.26/0.58       => ( member_int @ X3 @ ( set_int2 @ ( list_update_int @ Xs2 @ N @ X3 ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % set_update_memI
% 0.26/0.58  thf(fact_6333_nth__list__update,axiom,
% 0.26/0.58      ! [I: nat,Xs2: list_VEBT_VEBT,J: nat,X3: vEBT_VEBT] :
% 0.26/0.58        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.26/0.58       => ( ( ( I = J )
% 0.26/0.58           => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X3 ) @ J )
% 0.26/0.58              = X3 ) )
% 0.26/0.58          & ( ( I != J )
% 0.26/0.58           => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X3 ) @ J )
% 0.26/0.58              = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % nth_list_update
% 0.26/0.58  thf(fact_6334_nth__list__update,axiom,
% 0.26/0.58      ! [I: nat,Xs2: list_o,X3: $o,J: nat] :
% 0.26/0.58        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 0.26/0.58       => ( ( nth_o @ ( list_update_o @ Xs2 @ I @ X3 ) @ J )
% 0.26/0.58          = ( ( ( I = J )
% 0.26/0.58             => X3 )
% 0.26/0.58            & ( ( I != J )
% 0.26/0.58             => ( nth_o @ Xs2 @ J ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % nth_list_update
% 0.26/0.58  thf(fact_6335_nth__list__update,axiom,
% 0.26/0.58      ! [I: nat,Xs2: list_nat,J: nat,X3: nat] :
% 0.26/0.58        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 0.26/0.58       => ( ( ( I = J )
% 0.26/0.58           => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X3 ) @ J )
% 0.26/0.58              = X3 ) )
% 0.26/0.58          & ( ( I != J )
% 0.26/0.58           => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X3 ) @ J )
% 0.26/0.58              = ( nth_nat @ Xs2 @ J ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % nth_list_update
% 0.26/0.58  thf(fact_6336_nth__list__update,axiom,
% 0.26/0.58      ! [I: nat,Xs2: list_int,J: nat,X3: int] :
% 0.26/0.58        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 0.26/0.58       => ( ( ( I = J )
% 0.26/0.58           => ( ( nth_int @ ( list_update_int @ Xs2 @ I @ X3 ) @ J )
% 0.26/0.58              = X3 ) )
% 0.26/0.58          & ( ( I != J )
% 0.26/0.58           => ( ( nth_int @ ( list_update_int @ Xs2 @ I @ X3 ) @ J )
% 0.26/0.58              = ( nth_int @ Xs2 @ J ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % nth_list_update
% 0.26/0.58  thf(fact_6337_list__update__same__conv,axiom,
% 0.26/0.58      ! [I: nat,Xs2: list_VEBT_VEBT,X3: vEBT_VEBT] :
% 0.26/0.58        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.26/0.58       => ( ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X3 )
% 0.26/0.58            = Xs2 )
% 0.26/0.58          = ( ( nth_VEBT_VEBT @ Xs2 @ I )
% 0.26/0.58            = X3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % list_update_same_conv
% 0.26/0.58  thf(fact_6338_list__update__same__conv,axiom,
% 0.26/0.58      ! [I: nat,Xs2: list_o,X3: $o] :
% 0.26/0.58        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 0.26/0.58       => ( ( ( list_update_o @ Xs2 @ I @ X3 )
% 0.26/0.58            = Xs2 )
% 0.26/0.58          = ( ( nth_o @ Xs2 @ I )
% 0.26/0.58            = X3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % list_update_same_conv
% 0.26/0.58  thf(fact_6339_list__update__same__conv,axiom,
% 0.26/0.58      ! [I: nat,Xs2: list_nat,X3: nat] :
% 0.26/0.58        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 0.26/0.58       => ( ( ( list_update_nat @ Xs2 @ I @ X3 )
% 0.26/0.58            = Xs2 )
% 0.26/0.58          = ( ( nth_nat @ Xs2 @ I )
% 0.26/0.58            = X3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % list_update_same_conv
% 0.26/0.58  thf(fact_6340_list__update__same__conv,axiom,
% 0.26/0.58      ! [I: nat,Xs2: list_int,X3: int] :
% 0.26/0.58        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 0.26/0.58       => ( ( ( list_update_int @ Xs2 @ I @ X3 )
% 0.26/0.58            = Xs2 )
% 0.26/0.58          = ( ( nth_int @ Xs2 @ I )
% 0.26/0.58            = X3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % list_update_same_conv
% 0.26/0.58  thf(fact_6341_vebt__buildup_Osimps_I2_J,axiom,
% 0.26/0.58      ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 0.26/0.58      = ( vEBT_Leaf @ $false @ $false ) ) ).
% 0.26/0.58  
% 0.26/0.58  % vebt_buildup.simps(2)
% 0.26/0.58  thf(fact_6342_vebt__pred_Osimps_I1_J,axiom,
% 0.26/0.58      ! [Uu2: $o,Uv2: $o] :
% 0.26/0.58        ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat )
% 0.26/0.58        = none_nat ) ).
% 0.26/0.58  
% 0.26/0.58  % vebt_pred.simps(1)
% 0.26/0.58  thf(fact_6343_numeral__Bit1__div__2,axiom,
% 0.26/0.58      ! [N: num] :
% 0.26/0.58        ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.58        = ( numeral_numeral_nat @ N ) ) ).
% 0.26/0.58  
% 0.26/0.58  % numeral_Bit1_div_2
% 0.26/0.58  thf(fact_6344_numeral__Bit1__div__2,axiom,
% 0.26/0.58      ! [N: num] :
% 0.26/0.58        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.58        = ( numeral_numeral_int @ N ) ) ).
% 0.26/0.58  
% 0.26/0.58  % numeral_Bit1_div_2
% 0.26/0.58  thf(fact_6345_odd__numeral,axiom,
% 0.26/0.58      ! [N: num] :
% 0.26/0.58        ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % odd_numeral
% 0.26/0.58  thf(fact_6346_odd__numeral,axiom,
% 0.26/0.58      ! [N: num] :
% 0.26/0.58        ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % odd_numeral
% 0.26/0.58  thf(fact_6347_odd__numeral,axiom,
% 0.26/0.58      ! [N: num] :
% 0.26/0.58        ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % odd_numeral
% 0.26/0.58  thf(fact_6348_cong__exp__iff__simps_I3_J,axiom,
% 0.26/0.58      ! [N: num,Q3: num] :
% 0.26/0.58        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 0.26/0.58       != zero_zero_nat ) ).
% 0.26/0.58  
% 0.26/0.58  % cong_exp_iff_simps(3)
% 0.26/0.58  thf(fact_6349_cong__exp__iff__simps_I3_J,axiom,
% 0.26/0.58      ! [N: num,Q3: num] :
% 0.26/0.58        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 0.26/0.58       != zero_zero_int ) ).
% 0.26/0.58  
% 0.26/0.58  % cong_exp_iff_simps(3)
% 0.26/0.58  thf(fact_6350_cong__exp__iff__simps_I3_J,axiom,
% 0.26/0.58      ! [N: num,Q3: num] :
% 0.26/0.58        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 0.26/0.58       != zero_z3403309356797280102nteger ) ).
% 0.26/0.58  
% 0.26/0.58  % cong_exp_iff_simps(3)
% 0.26/0.58  thf(fact_6351_power3__eq__cube,axiom,
% 0.26/0.58      ! [A: complex] :
% 0.26/0.58        ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.26/0.58        = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 0.26/0.58  
% 0.26/0.58  % power3_eq_cube
% 0.26/0.58  thf(fact_6352_power3__eq__cube,axiom,
% 0.26/0.58      ! [A: real] :
% 0.26/0.58        ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.26/0.58        = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 0.26/0.58  
% 0.26/0.58  % power3_eq_cube
% 0.26/0.58  thf(fact_6353_power3__eq__cube,axiom,
% 0.26/0.58      ! [A: rat] :
% 0.26/0.58        ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.26/0.58        = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 0.26/0.58  
% 0.26/0.58  % power3_eq_cube
% 0.26/0.58  thf(fact_6354_power3__eq__cube,axiom,
% 0.26/0.58      ! [A: nat] :
% 0.26/0.58        ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.26/0.58        = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 0.26/0.58  
% 0.26/0.58  % power3_eq_cube
% 0.26/0.58  thf(fact_6355_power3__eq__cube,axiom,
% 0.26/0.58      ! [A: int] :
% 0.26/0.58        ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.26/0.58        = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 0.26/0.58  
% 0.26/0.58  % power3_eq_cube
% 0.26/0.58  thf(fact_6356_numeral__3__eq__3,axiom,
% 0.26/0.58      ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.26/0.58      = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % numeral_3_eq_3
% 0.26/0.58  thf(fact_6357_Suc3__eq__add__3,axiom,
% 0.26/0.58      ! [N: nat] :
% 0.26/0.58        ( ( suc @ ( suc @ ( suc @ N ) ) )
% 0.26/0.58        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 0.26/0.58  
% 0.26/0.58  % Suc3_eq_add_3
% 0.26/0.58  thf(fact_6358_num_Osize_I6_J,axiom,
% 0.26/0.58      ! [X32: num] :
% 0.26/0.58        ( ( size_size_num @ ( bit1 @ X32 ) )
% 0.26/0.58        = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % num.size(6)
% 0.26/0.58  thf(fact_6359_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Ocases,axiom,
% 0.26/0.58      ! [X3: produc9072475918466114483BT_nat] :
% 0.26/0.58        ( ! [Uu: $o,Uv: $o] :
% 0.26/0.58            ( X3
% 0.26/0.58           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat ) )
% 0.26/0.58       => ( ! [A5: $o,Uw: $o] :
% 0.26/0.58              ( X3
% 0.26/0.58             != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw ) @ ( suc @ zero_zero_nat ) ) )
% 0.26/0.58         => ( ! [A5: $o,B4: $o,Va: nat] :
% 0.26/0.58                ( X3
% 0.26/0.58               != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ ( suc @ ( suc @ Va ) ) ) )
% 0.26/0.58           => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT,Vb: nat] :
% 0.26/0.58                  ( X3
% 0.26/0.58                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Vb ) )
% 0.26/0.58             => ( ! [V3: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 0.26/0.58                    ( X3
% 0.26/0.58                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Vf2 ) )
% 0.26/0.58               => ( ! [V3: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 0.26/0.58                      ( X3
% 0.26/0.58                     != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 ) )
% 0.26/0.58                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 0.26/0.58                        ( X3
% 0.26/0.58                       != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ X4 ) ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.cases
% 0.26/0.58  thf(fact_6360_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Ocases,axiom,
% 0.26/0.58      ! [X3: produc9072475918466114483BT_nat] :
% 0.26/0.58        ( ! [Uu: $o,B4: $o] :
% 0.26/0.58            ( X3
% 0.26/0.58           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ B4 ) @ zero_zero_nat ) )
% 0.26/0.58       => ( ! [Uv: $o,Uw: $o,N2: nat] :
% 0.26/0.58              ( X3
% 0.26/0.58             != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N2 ) ) )
% 0.26/0.58         => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va3: nat] :
% 0.26/0.58                ( X3
% 0.26/0.58               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Va3 ) )
% 0.26/0.58           => ( ! [V3: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve2: nat] :
% 0.26/0.58                  ( X3
% 0.26/0.58                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Ve2 ) )
% 0.26/0.58             => ( ! [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 0.26/0.58                    ( X3
% 0.26/0.58                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 ) )
% 0.26/0.58               => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 0.26/0.58                      ( X3
% 0.26/0.58                     != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ X4 ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.cases
% 0.26/0.58  thf(fact_6361_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Ocases,axiom,
% 0.26/0.58      ! [X3: produc9072475918466114483BT_nat] :
% 0.26/0.58        ( ! [A5: $o,B4: $o,X4: nat] :
% 0.26/0.58            ( X3
% 0.26/0.58           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ X4 ) )
% 0.26/0.58       => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT,X4: nat] :
% 0.26/0.58              ( X3
% 0.26/0.58             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) @ X4 ) )
% 0.26/0.58         => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT,X4: nat] :
% 0.26/0.58                ( X3
% 0.26/0.58               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) @ X4 ) )
% 0.26/0.58           => ( ! [V3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 0.26/0.58                  ( X3
% 0.26/0.58                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) @ X4 ) )
% 0.26/0.58             => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 0.26/0.58                    ( X3
% 0.26/0.58                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ X4 ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.cases
% 0.26/0.58  thf(fact_6362_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Ocases,axiom,
% 0.26/0.58      ! [X3: produc9072475918466114483BT_nat] :
% 0.26/0.58        ( ! [A5: $o,B4: $o,X4: nat] :
% 0.26/0.58            ( X3
% 0.26/0.58           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ X4 ) )
% 0.26/0.58       => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X4: nat] :
% 0.26/0.58              ( X3
% 0.26/0.58             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X4 ) )
% 0.26/0.58         => ( ! [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X4: nat] :
% 0.26/0.58                ( X3
% 0.26/0.58               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X4 ) )
% 0.26/0.58           => ( ! [V3: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT,X4: nat] :
% 0.26/0.58                  ( X3
% 0.26/0.58                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) @ X4 ) )
% 0.26/0.58             => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 0.26/0.58                    ( X3
% 0.26/0.58                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ X4 ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.cases
% 0.26/0.58  thf(fact_6363_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Ocases,axiom,
% 0.26/0.58      ! [X3: produc9072475918466114483BT_nat] :
% 0.26/0.58        ( ! [A5: $o,B4: $o] :
% 0.26/0.58            ( X3
% 0.26/0.58           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ zero_zero_nat ) )
% 0.26/0.58       => ( ! [A5: $o,B4: $o] :
% 0.26/0.58              ( X3
% 0.26/0.58             != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ ( suc @ zero_zero_nat ) ) )
% 0.26/0.58         => ( ! [A5: $o,B4: $o,N2: nat] :
% 0.26/0.58                ( X3
% 0.26/0.58               != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ ( suc @ ( suc @ N2 ) ) ) )
% 0.26/0.58           => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,Uu: nat] :
% 0.26/0.58                  ( X3
% 0.26/0.58                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) @ Uu ) )
% 0.26/0.58             => ( ! [Mi2: nat,Ma2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 0.26/0.58                    ( X3
% 0.26/0.58                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList3 @ Summary2 ) @ X4 ) )
% 0.26/0.58               => ( ! [Mi2: nat,Ma2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 0.26/0.58                      ( X3
% 0.26/0.58                     != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList3 @ Summary2 ) @ X4 ) )
% 0.26/0.58                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 0.26/0.58                        ( X3
% 0.26/0.58                       != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ X4 ) ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.cases
% 0.26/0.58  thf(fact_6364_VEBT__internal_Omembermima_Ocases,axiom,
% 0.26/0.58      ! [X3: produc9072475918466114483BT_nat] :
% 0.26/0.58        ( ! [Uu: $o,Uv: $o,Uw: nat] :
% 0.26/0.58            ( X3
% 0.26/0.58           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) )
% 0.26/0.58       => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 0.26/0.58              ( X3
% 0.26/0.58             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 0.26/0.58         => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb: vEBT_VEBT,X4: nat] :
% 0.26/0.58                ( X3
% 0.26/0.58               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb ) @ X4 ) )
% 0.26/0.58           => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT,X4: nat] :
% 0.26/0.58                  ( X3
% 0.26/0.58                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) @ X4 ) )
% 0.26/0.58             => ~ ! [V3: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT,X4: nat] :
% 0.26/0.58                    ( X3
% 0.26/0.58                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) @ X4 ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % VEBT_internal.membermima.cases
% 0.26/0.58  thf(fact_6365_cong__exp__iff__simps_I7_J,axiom,
% 0.26/0.58      ! [Q3: num,N: num] :
% 0.26/0.58        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 0.26/0.58          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 0.26/0.58        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q3 ) )
% 0.26/0.58          = zero_zero_nat ) ) ).
% 0.26/0.58  
% 0.26/0.58  % cong_exp_iff_simps(7)
% 0.26/0.58  thf(fact_6366_cong__exp__iff__simps_I7_J,axiom,
% 0.26/0.58      ! [Q3: num,N: num] :
% 0.26/0.58        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 0.26/0.58          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 0.26/0.58        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q3 ) )
% 0.26/0.58          = zero_zero_int ) ) ).
% 0.26/0.58  
% 0.26/0.58  % cong_exp_iff_simps(7)
% 0.26/0.58  thf(fact_6367_cong__exp__iff__simps_I7_J,axiom,
% 0.26/0.58      ! [Q3: num,N: num] :
% 0.26/0.58        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 0.26/0.58          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 0.26/0.58        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 0.26/0.58          = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.58  
% 0.26/0.58  % cong_exp_iff_simps(7)
% 0.26/0.58  thf(fact_6368_cong__exp__iff__simps_I11_J,axiom,
% 0.26/0.58      ! [M: num,Q3: num] :
% 0.26/0.58        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 0.26/0.58          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 0.26/0.58        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 0.26/0.58          = zero_zero_nat ) ) ).
% 0.26/0.58  
% 0.26/0.58  % cong_exp_iff_simps(11)
% 0.26/0.58  thf(fact_6369_cong__exp__iff__simps_I11_J,axiom,
% 0.26/0.58      ! [M: num,Q3: num] :
% 0.26/0.58        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 0.26/0.58          = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 0.26/0.58        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 0.26/0.58          = zero_zero_int ) ) ).
% 0.26/0.58  
% 0.26/0.58  % cong_exp_iff_simps(11)
% 0.26/0.58  thf(fact_6370_cong__exp__iff__simps_I11_J,axiom,
% 0.26/0.58      ! [M: num,Q3: num] :
% 0.26/0.58        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 0.26/0.58          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 0.26/0.58        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 0.26/0.58          = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.58  
% 0.26/0.58  % cong_exp_iff_simps(11)
% 0.26/0.58  thf(fact_6371_Suc__div__eq__add3__div,axiom,
% 0.26/0.58      ! [M: nat,N: nat] :
% 0.26/0.58        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 0.26/0.58        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 0.26/0.58  
% 0.26/0.58  % Suc_div_eq_add3_div
% 0.26/0.58  thf(fact_6372_Suc__mod__eq__add3__mod,axiom,
% 0.26/0.58      ! [M: nat,N: nat] :
% 0.26/0.58        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 0.26/0.58        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 0.26/0.58  
% 0.26/0.58  % Suc_mod_eq_add3_mod
% 0.26/0.58  thf(fact_6373_vebt__mint_Osimps_I1_J,axiom,
% 0.26/0.58      ! [A: $o,B: $o] :
% 0.26/0.58        ( ( A
% 0.26/0.58         => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 0.26/0.58            = ( some_nat @ zero_zero_nat ) ) )
% 0.26/0.58        & ( ~ A
% 0.26/0.58         => ( ( B
% 0.26/0.58             => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 0.26/0.58                = ( some_nat @ one_one_nat ) ) )
% 0.26/0.58            & ( ~ B
% 0.26/0.58             => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 0.26/0.58                = none_nat ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % vebt_mint.simps(1)
% 0.26/0.58  thf(fact_6374_vebt__maxt_Osimps_I1_J,axiom,
% 0.26/0.58      ! [B: $o,A: $o] :
% 0.26/0.58        ( ( B
% 0.26/0.58         => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 0.26/0.58            = ( some_nat @ one_one_nat ) ) )
% 0.26/0.58        & ( ~ B
% 0.26/0.58         => ( ( A
% 0.26/0.58             => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 0.26/0.58                = ( some_nat @ zero_zero_nat ) ) )
% 0.26/0.58            & ( ~ A
% 0.26/0.58             => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 0.26/0.58                = none_nat ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % vebt_maxt.simps(1)
% 0.26/0.58  thf(fact_6375_vebt__pred_Osimps_I2_J,axiom,
% 0.26/0.58      ! [A: $o,Uw2: $o] :
% 0.26/0.58        ( ( A
% 0.26/0.58         => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 0.26/0.58            = ( some_nat @ zero_zero_nat ) ) )
% 0.26/0.58        & ( ~ A
% 0.26/0.58         => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 0.26/0.58            = none_nat ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % vebt_pred.simps(2)
% 0.26/0.58  thf(fact_6376_vebt__succ_Osimps_I1_J,axiom,
% 0.26/0.58      ! [B: $o,Uu2: $o] :
% 0.26/0.58        ( ( B
% 0.26/0.58         => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu2 @ B ) @ zero_zero_nat )
% 0.26/0.58            = ( some_nat @ one_one_nat ) ) )
% 0.26/0.58        & ( ~ B
% 0.26/0.58         => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu2 @ B ) @ zero_zero_nat )
% 0.26/0.58            = none_nat ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % vebt_succ.simps(1)
% 0.26/0.58  thf(fact_6377_mod__exhaust__less__4,axiom,
% 0.26/0.58      ! [M: nat] :
% 0.26/0.58        ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.26/0.58          = zero_zero_nat )
% 0.26/0.58        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.26/0.58          = one_one_nat )
% 0.26/0.58        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.26/0.58          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.58        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.26/0.58          = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % mod_exhaust_less_4
% 0.26/0.58  thf(fact_6378_vebt__pred_Osimps_I3_J,axiom,
% 0.26/0.58      ! [B: $o,A: $o,Va2: nat] :
% 0.26/0.58        ( ( B
% 0.26/0.58         => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.26/0.58            = ( some_nat @ one_one_nat ) ) )
% 0.26/0.58        & ( ~ B
% 0.26/0.58         => ( ( A
% 0.26/0.58             => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.26/0.58                = ( some_nat @ zero_zero_nat ) ) )
% 0.26/0.58            & ( ~ A
% 0.26/0.58             => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.26/0.58                = none_nat ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % vebt_pred.simps(3)
% 0.26/0.58  thf(fact_6379_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I5_J,axiom,
% 0.26/0.58      ! [Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 0.26/0.58        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.58        = one_one_nat ) ).
% 0.26/0.58  
% 0.26/0.58  % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(5)
% 0.26/0.58  thf(fact_6380_take__bit__Suc__bit1,axiom,
% 0.26/0.58      ! [N: nat,K: num] :
% 0.26/0.58        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.26/0.58        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.26/0.58  
% 0.26/0.58  % take_bit_Suc_bit1
% 0.26/0.58  thf(fact_6381_take__bit__Suc__bit1,axiom,
% 0.26/0.58      ! [N: nat,K: num] :
% 0.26/0.58        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.26/0.58        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 0.26/0.58  
% 0.26/0.58  % take_bit_Suc_bit1
% 0.26/0.58  thf(fact_6382_vebt__mint_Oelims,axiom,
% 0.26/0.58      ! [X3: vEBT_VEBT,Y3: option_nat] :
% 0.26/0.58        ( ( ( vEBT_vebt_mint @ X3 )
% 0.26/0.58          = Y3 )
% 0.26/0.58       => ( ! [A5: $o,B4: $o] :
% 0.26/0.58              ( ( X3
% 0.26/0.58                = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.58             => ~ ( ( A5
% 0.26/0.58                   => ( Y3
% 0.26/0.58                      = ( some_nat @ zero_zero_nat ) ) )
% 0.26/0.58                  & ( ~ A5
% 0.26/0.58                   => ( ( B4
% 0.26/0.58                       => ( Y3
% 0.26/0.58                          = ( some_nat @ one_one_nat ) ) )
% 0.26/0.58                      & ( ~ B4
% 0.26/0.58                       => ( Y3 = none_nat ) ) ) ) ) )
% 0.26/0.58         => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.26/0.58                  ( X3
% 0.26/0.58                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.26/0.58             => ( Y3 != none_nat ) )
% 0.26/0.58           => ~ ! [Mi2: nat] :
% 0.26/0.58                  ( ? [Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.26/0.58                      ( X3
% 0.26/0.58                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 0.26/0.58                 => ( Y3
% 0.26/0.58                   != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % vebt_mint.elims
% 0.26/0.58  thf(fact_6383_vebt__maxt_Oelims,axiom,
% 0.26/0.58      ! [X3: vEBT_VEBT,Y3: option_nat] :
% 0.26/0.58        ( ( ( vEBT_vebt_maxt @ X3 )
% 0.26/0.58          = Y3 )
% 0.26/0.58       => ( ! [A5: $o,B4: $o] :
% 0.26/0.58              ( ( X3
% 0.26/0.58                = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.58             => ~ ( ( B4
% 0.26/0.58                   => ( Y3
% 0.26/0.58                      = ( some_nat @ one_one_nat ) ) )
% 0.26/0.58                  & ( ~ B4
% 0.26/0.58                   => ( ( A5
% 0.26/0.58                       => ( Y3
% 0.26/0.58                          = ( some_nat @ zero_zero_nat ) ) )
% 0.26/0.58                      & ( ~ A5
% 0.26/0.58                       => ( Y3 = none_nat ) ) ) ) ) )
% 0.26/0.58         => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.26/0.58                  ( X3
% 0.26/0.58                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.26/0.58             => ( Y3 != none_nat ) )
% 0.26/0.58           => ~ ! [Mi2: nat,Ma2: nat] :
% 0.26/0.58                  ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.26/0.58                      ( X3
% 0.26/0.58                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 0.26/0.58                 => ( Y3
% 0.26/0.58                   != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % vebt_maxt.elims
% 0.26/0.58  thf(fact_6384_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I6_J,axiom,
% 0.26/0.58      ! [Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 0.26/0.58        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.58        = one_one_nat ) ).
% 0.26/0.58  
% 0.26/0.58  % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(6)
% 0.26/0.58  thf(fact_6385_odd__mod__4__div__2,axiom,
% 0.26/0.58      ! [N: nat] :
% 0.26/0.58        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.26/0.58          = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.26/0.58       => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % odd_mod_4_div_2
% 0.26/0.58  thf(fact_6386_vebt__delete_Osimps_I5_J,axiom,
% 0.26/0.58      ! [Mi: nat,Ma: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT,X3: nat] :
% 0.26/0.58        ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) @ X3 )
% 0.26/0.58        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) ) ).
% 0.26/0.58  
% 0.26/0.58  % vebt_delete.simps(5)
% 0.26/0.58  thf(fact_6387_invar__vebt_Ocases,axiom,
% 0.26/0.58      ! [A1: vEBT_VEBT,A22: nat] :
% 0.26/0.58        ( ( vEBT_invar_vebt @ A1 @ A22 )
% 0.26/0.58       => ( ( ? [A5: $o,B4: $o] :
% 0.26/0.58                ( A1
% 0.26/0.58                = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.58           => ( A22
% 0.26/0.58             != ( suc @ zero_zero_nat ) ) )
% 0.26/0.58         => ( ! [TreeList3: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 0.26/0.58                ( ( A1
% 0.26/0.58                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.26/0.58               => ( ( A22 = Deg2 )
% 0.26/0.58                 => ( ! [X6: vEBT_VEBT] :
% 0.26/0.58                        ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.58                       => ( vEBT_invar_vebt @ X6 @ N2 ) )
% 0.26/0.58                   => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 0.26/0.58                     => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.26/0.58                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.26/0.58                       => ( ( M4 = N2 )
% 0.26/0.58                         => ( ( Deg2
% 0.26/0.58                              = ( plus_plus_nat @ N2 @ M4 ) )
% 0.26/0.58                           => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 0.26/0.58                             => ~ ! [X6: vEBT_VEBT] :
% 0.26/0.58                                    ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.58                                   => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_12 ) ) ) ) ) ) ) ) ) )
% 0.26/0.58           => ( ! [TreeList3: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 0.26/0.58                  ( ( A1
% 0.26/0.58                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.26/0.58                 => ( ( A22 = Deg2 )
% 0.26/0.58                   => ( ! [X6: vEBT_VEBT] :
% 0.26/0.58                          ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.58                         => ( vEBT_invar_vebt @ X6 @ N2 ) )
% 0.26/0.58                     => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 0.26/0.58                       => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.26/0.58                            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.26/0.58                         => ( ( M4
% 0.26/0.58                              = ( suc @ N2 ) )
% 0.26/0.58                           => ( ( Deg2
% 0.26/0.58                                = ( plus_plus_nat @ N2 @ M4 ) )
% 0.26/0.58                             => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 0.26/0.58                               => ~ ! [X6: vEBT_VEBT] :
% 0.26/0.58                                      ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.58                                     => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_12 ) ) ) ) ) ) ) ) ) )
% 0.26/0.58             => ( ! [TreeList3: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 0.26/0.58                    ( ( A1
% 0.26/0.58                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.26/0.58                   => ( ( A22 = Deg2 )
% 0.26/0.58                     => ( ! [X6: vEBT_VEBT] :
% 0.26/0.58                            ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.58                           => ( vEBT_invar_vebt @ X6 @ N2 ) )
% 0.26/0.58                       => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 0.26/0.58                         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.26/0.58                              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.26/0.58                           => ( ( M4 = N2 )
% 0.26/0.58                             => ( ( Deg2
% 0.26/0.58                                  = ( plus_plus_nat @ N2 @ M4 ) )
% 0.26/0.58                               => ( ! [I2: nat] :
% 0.26/0.58                                      ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.26/0.58                                     => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X8 ) )
% 0.26/0.58                                        = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 0.26/0.58                                 => ( ( ( Mi2 = Ma2 )
% 0.26/0.58                                     => ! [X6: vEBT_VEBT] :
% 0.26/0.58                                          ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.58                                         => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_12 ) ) )
% 0.26/0.58                                   => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 0.26/0.58                                     => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.26/0.58                                       => ~ ( ( Mi2 != Ma2 )
% 0.26/0.58                                           => ! [I2: nat] :
% 0.26/0.58                                                ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.26/0.58                                               => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N2 )
% 0.26/0.58                                                      = I2 )
% 0.26/0.58                                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ Ma2 @ N2 ) ) )
% 0.26/0.58                                                  & ! [X6: nat] :
% 0.26/0.58                                                      ( ( ( ( vEBT_VEBT_high @ X6 @ N2 )
% 0.26/0.58                                                          = I2 )
% 0.26/0.58                                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ X6 @ N2 ) ) )
% 0.26/0.58                                                     => ( ( ord_less_nat @ Mi2 @ X6 )
% 0.26/0.58                                                        & ( ord_less_eq_nat @ X6 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.58               => ~ ! [TreeList3: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 0.26/0.58                      ( ( A1
% 0.26/0.58                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.26/0.58                     => ( ( A22 = Deg2 )
% 0.26/0.58                       => ( ! [X6: vEBT_VEBT] :
% 0.26/0.58                              ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.58                             => ( vEBT_invar_vebt @ X6 @ N2 ) )
% 0.26/0.58                         => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 0.26/0.58                           => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.26/0.58                                = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.26/0.58                             => ( ( M4
% 0.26/0.58                                  = ( suc @ N2 ) )
% 0.26/0.58                               => ( ( Deg2
% 0.26/0.58                                    = ( plus_plus_nat @ N2 @ M4 ) )
% 0.26/0.58                                 => ( ! [I2: nat] :
% 0.26/0.58                                        ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.26/0.58                                       => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X8 ) )
% 0.26/0.58                                          = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 0.26/0.58                                   => ( ( ( Mi2 = Ma2 )
% 0.26/0.58                                       => ! [X6: vEBT_VEBT] :
% 0.26/0.58                                            ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.58                                           => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_12 ) ) )
% 0.26/0.58                                     => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 0.26/0.58                                       => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.26/0.58                                         => ~ ( ( Mi2 != Ma2 )
% 0.26/0.58                                             => ! [I2: nat] :
% 0.26/0.58                                                  ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.26/0.58                                                 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N2 )
% 0.26/0.58                                                        = I2 )
% 0.26/0.58                                                     => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ Ma2 @ N2 ) ) )
% 0.26/0.58                                                    & ! [X6: nat] :
% 0.26/0.58                                                        ( ( ( ( vEBT_VEBT_high @ X6 @ N2 )
% 0.26/0.58                                                            = I2 )
% 0.26/0.58                                                          & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ X6 @ N2 ) ) )
% 0.26/0.58                                                       => ( ( ord_less_nat @ Mi2 @ X6 )
% 0.26/0.58                                                          & ( ord_less_eq_nat @ X6 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % invar_vebt.cases
% 0.26/0.58  thf(fact_6388_invar__vebt_Osimps,axiom,
% 0.26/0.58      ( vEBT_invar_vebt
% 0.26/0.58      = ( ^ [A12: vEBT_VEBT,A23: nat] :
% 0.26/0.58            ( ( ? [A4: $o,B3: $o] :
% 0.26/0.58                  ( A12
% 0.26/0.58                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.26/0.58              & ( A23
% 0.26/0.58                = ( suc @ zero_zero_nat ) ) )
% 0.26/0.58            | ? [TreeList: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT] :
% 0.26/0.58                ( ( A12
% 0.26/0.58                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList @ Summary3 ) )
% 0.26/0.58                & ! [X: vEBT_VEBT] :
% 0.26/0.58                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.26/0.58                   => ( vEBT_invar_vebt @ X @ N3 ) )
% 0.26/0.58                & ( vEBT_invar_vebt @ Summary3 @ N3 )
% 0.26/0.58                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.26/0.58                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 0.26/0.58                & ( A23
% 0.26/0.58                  = ( plus_plus_nat @ N3 @ N3 ) )
% 0.26/0.58                & ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X8 )
% 0.26/0.58                & ! [X: vEBT_VEBT] :
% 0.26/0.58                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.26/0.58                   => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 0.26/0.58            | ? [TreeList: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT] :
% 0.26/0.58                ( ( A12
% 0.26/0.58                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList @ Summary3 ) )
% 0.26/0.58                & ! [X: vEBT_VEBT] :
% 0.26/0.58                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.26/0.58                   => ( vEBT_invar_vebt @ X @ N3 ) )
% 0.26/0.58                & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N3 ) )
% 0.26/0.58                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.26/0.58                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 0.26/0.58                & ( A23
% 0.26/0.58                  = ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) )
% 0.26/0.58                & ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X8 )
% 0.26/0.58                & ! [X: vEBT_VEBT] :
% 0.26/0.58                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.26/0.58                   => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 0.26/0.58            | ? [TreeList: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 0.26/0.58                ( ( A12
% 0.26/0.58                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList @ Summary3 ) )
% 0.26/0.58                & ! [X: vEBT_VEBT] :
% 0.26/0.58                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.26/0.58                   => ( vEBT_invar_vebt @ X @ N3 ) )
% 0.26/0.58                & ( vEBT_invar_vebt @ Summary3 @ N3 )
% 0.26/0.58                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.26/0.58                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 0.26/0.58                & ( A23
% 0.26/0.58                  = ( plus_plus_nat @ N3 @ N3 ) )
% 0.26/0.58                & ! [I4: nat] :
% 0.26/0.58                    ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 0.26/0.58                   => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X8 ) )
% 0.26/0.58                      = ( vEBT_V8194947554948674370ptions @ Summary3 @ I4 ) ) )
% 0.26/0.58                & ( ( Mi3 = Ma3 )
% 0.26/0.58                 => ! [X: vEBT_VEBT] :
% 0.26/0.58                      ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.26/0.58                     => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 0.26/0.58                & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.26/0.58                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 0.26/0.58                & ( ( Mi3 != Ma3 )
% 0.26/0.58                 => ! [I4: nat] :
% 0.26/0.58                      ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 0.26/0.58                     => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N3 )
% 0.26/0.58                            = I4 )
% 0.26/0.58                         => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ Ma3 @ N3 ) ) )
% 0.26/0.58                        & ! [X: nat] :
% 0.26/0.58                            ( ( ( ( vEBT_VEBT_high @ X @ N3 )
% 0.26/0.58                                = I4 )
% 0.26/0.58                              & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ X @ N3 ) ) )
% 0.26/0.58                           => ( ( ord_less_nat @ Mi3 @ X )
% 0.26/0.58                              & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) )
% 0.26/0.58            | ? [TreeList: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 0.26/0.58                ( ( A12
% 0.26/0.58                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList @ Summary3 ) )
% 0.26/0.58                & ! [X: vEBT_VEBT] :
% 0.26/0.58                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.26/0.58                   => ( vEBT_invar_vebt @ X @ N3 ) )
% 0.26/0.58                & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N3 ) )
% 0.26/0.58                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.26/0.58                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 0.26/0.58                & ( A23
% 0.26/0.58                  = ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) )
% 0.26/0.58                & ! [I4: nat] :
% 0.26/0.58                    ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 0.26/0.58                   => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X8 ) )
% 0.26/0.58                      = ( vEBT_V8194947554948674370ptions @ Summary3 @ I4 ) ) )
% 0.26/0.58                & ( ( Mi3 = Ma3 )
% 0.26/0.58                 => ! [X: vEBT_VEBT] :
% 0.26/0.58                      ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.26/0.58                     => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 0.26/0.58                & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.26/0.58                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 0.26/0.58                & ( ( Mi3 != Ma3 )
% 0.26/0.58                 => ! [I4: nat] :
% 0.26/0.58                      ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 0.26/0.58                     => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N3 )
% 0.26/0.58                            = I4 )
% 0.26/0.58                         => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ Ma3 @ N3 ) ) )
% 0.26/0.58                        & ! [X: nat] :
% 0.26/0.58                            ( ( ( ( vEBT_VEBT_high @ X @ N3 )
% 0.26/0.58                                = I4 )
% 0.26/0.58                              & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ X @ N3 ) ) )
% 0.26/0.58                           => ( ( ord_less_nat @ Mi3 @ X )
% 0.26/0.58                              & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % invar_vebt.simps
% 0.26/0.58  thf(fact_6389_insert__simp__norm,axiom,
% 0.26/0.58      ! [X3: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 0.26/0.58        ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.58       => ( ( ord_less_nat @ Mi @ X3 )
% 0.26/0.58         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.58           => ( ( X3 != Ma )
% 0.26/0.58             => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.58                = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X3 @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % insert_simp_norm
% 0.26/0.58  thf(fact_6390_insert__simp__excp,axiom,
% 0.26/0.58      ! [Mi: nat,Deg: nat,TreeList2: list_VEBT_VEBT,X3: nat,Ma: nat,Summary: vEBT_VEBT] :
% 0.26/0.58        ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.58       => ( ( ord_less_nat @ X3 @ Mi )
% 0.26/0.58         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.58           => ( ( X3 != Ma )
% 0.26/0.58             => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.58                = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X3 @ ( 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 ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % insert_simp_excp
% 0.26/0.58  thf(fact_6391_member__bound__size__univ,axiom,
% 0.26/0.58      ! [T: vEBT_VEBT,N: nat,U: real,X3: nat] :
% 0.26/0.58        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.58       => ( ( U
% 0.26/0.58            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.58         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_m_e_m_b_e_r @ T @ X3 ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % member_bound_size_univ
% 0.26/0.58  thf(fact_6392_vebt__member_Osimps_I4_J,axiom,
% 0.26/0.58      ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc: vEBT_VEBT,X3: nat] :
% 0.26/0.58        ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc ) @ X3 ) ).
% 0.26/0.58  
% 0.26/0.58  % vebt_member.simps(4)
% 0.26/0.58  thf(fact_6393_succ__bound__size__univ,axiom,
% 0.26/0.58      ! [T: vEBT_VEBT,N: nat,U: real,X3: nat] :
% 0.26/0.58        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.58       => ( ( U
% 0.26/0.58            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.58         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_s_u_c_c @ T @ X3 ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % succ_bound_size_univ
% 0.26/0.58  thf(fact_6394_pred__bound__size__univ,axiom,
% 0.26/0.58      ! [T: vEBT_VEBT,N: nat,U: real,X3: nat] :
% 0.26/0.58        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.58       => ( ( U
% 0.26/0.58            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.58         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_p_r_e_d @ T @ X3 ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % pred_bound_size_univ
% 0.26/0.58  thf(fact_6395_max__Suc__Suc,axiom,
% 0.26/0.58      ! [M: nat,N: nat] :
% 0.26/0.58        ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.26/0.58        = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_Suc_Suc
% 0.26/0.58  thf(fact_6396_max__0R,axiom,
% 0.26/0.58      ! [N: nat] :
% 0.26/0.58        ( ( ord_max_nat @ N @ zero_zero_nat )
% 0.26/0.58        = N ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0R
% 0.26/0.58  thf(fact_6397_max__0L,axiom,
% 0.26/0.58      ! [N: nat] :
% 0.26/0.58        ( ( ord_max_nat @ zero_zero_nat @ N )
% 0.26/0.58        = N ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0L
% 0.26/0.58  thf(fact_6398_max__nat_Oright__neutral,axiom,
% 0.26/0.58      ! [A: nat] :
% 0.26/0.58        ( ( ord_max_nat @ A @ zero_zero_nat )
% 0.26/0.58        = A ) ).
% 0.26/0.58  
% 0.26/0.58  % max_nat.right_neutral
% 0.26/0.58  thf(fact_6399_max__nat_Oneutr__eq__iff,axiom,
% 0.26/0.58      ! [A: nat,B: nat] :
% 0.26/0.58        ( ( zero_zero_nat
% 0.26/0.58          = ( ord_max_nat @ A @ B ) )
% 0.26/0.58        = ( ( A = zero_zero_nat )
% 0.26/0.58          & ( B = zero_zero_nat ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_nat.neutr_eq_iff
% 0.26/0.58  thf(fact_6400_max__nat_Oleft__neutral,axiom,
% 0.26/0.58      ! [A: nat] :
% 0.26/0.58        ( ( ord_max_nat @ zero_zero_nat @ A )
% 0.26/0.58        = A ) ).
% 0.26/0.58  
% 0.26/0.58  % max_nat.left_neutral
% 0.26/0.58  thf(fact_6401_max__nat_Oeq__neutr__iff,axiom,
% 0.26/0.58      ! [A: nat,B: nat] :
% 0.26/0.58        ( ( ( ord_max_nat @ A @ B )
% 0.26/0.58          = zero_zero_nat )
% 0.26/0.58        = ( ( A = zero_zero_nat )
% 0.26/0.58          & ( B = zero_zero_nat ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_nat.eq_neutr_iff
% 0.26/0.58  thf(fact_6402_max__number__of_I1_J,axiom,
% 0.26/0.58      ! [U: num,V: num] :
% 0.26/0.58        ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 0.26/0.58         => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 0.26/0.58            = ( numera1916890842035813515d_enat @ V ) ) )
% 0.26/0.58        & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 0.26/0.58         => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 0.26/0.58            = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_number_of(1)
% 0.26/0.58  thf(fact_6403_max__number__of_I1_J,axiom,
% 0.26/0.58      ! [U: num,V: num] :
% 0.26/0.58        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 0.26/0.58         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 0.26/0.58            = ( numera6620942414471956472nteger @ V ) ) )
% 0.26/0.58        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 0.26/0.58         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 0.26/0.58            = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_number_of(1)
% 0.26/0.58  thf(fact_6404_max__number__of_I1_J,axiom,
% 0.26/0.58      ! [U: num,V: num] :
% 0.26/0.58        ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 0.26/0.58         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 0.26/0.58            = ( numeral_numeral_real @ V ) ) )
% 0.26/0.58        & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 0.26/0.58         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 0.26/0.58            = ( numeral_numeral_real @ U ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_number_of(1)
% 0.26/0.58  thf(fact_6405_max__number__of_I1_J,axiom,
% 0.26/0.58      ! [U: num,V: num] :
% 0.26/0.58        ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 0.26/0.58         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 0.26/0.58            = ( numeral_numeral_rat @ V ) ) )
% 0.26/0.58        & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 0.26/0.58         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 0.26/0.58            = ( numeral_numeral_rat @ U ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_number_of(1)
% 0.26/0.58  thf(fact_6406_max__number__of_I1_J,axiom,
% 0.26/0.58      ! [U: num,V: num] :
% 0.26/0.58        ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 0.26/0.58         => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 0.26/0.58            = ( numeral_numeral_nat @ V ) ) )
% 0.26/0.58        & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 0.26/0.58         => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 0.26/0.58            = ( numeral_numeral_nat @ U ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_number_of(1)
% 0.26/0.58  thf(fact_6407_max__number__of_I1_J,axiom,
% 0.26/0.58      ! [U: num,V: num] :
% 0.26/0.58        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 0.26/0.58         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 0.26/0.58            = ( numeral_numeral_int @ V ) ) )
% 0.26/0.58        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 0.26/0.58         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 0.26/0.58            = ( numeral_numeral_int @ U ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_number_of(1)
% 0.26/0.58  thf(fact_6408_max__0__1_I3_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X3 ) )
% 0.26/0.58        = ( numera1916890842035813515d_enat @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(3)
% 0.26/0.58  thf(fact_6409_max__0__1_I3_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ X3 ) )
% 0.26/0.58        = ( numera6620942414471956472nteger @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(3)
% 0.26/0.58  thf(fact_6410_max__0__1_I3_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X3 ) )
% 0.26/0.58        = ( numeral_numeral_real @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(3)
% 0.26/0.58  thf(fact_6411_max__0__1_I3_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X3 ) )
% 0.26/0.58        = ( numeral_numeral_rat @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(3)
% 0.26/0.58  thf(fact_6412_max__0__1_I3_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X3 ) )
% 0.26/0.58        = ( numeral_numeral_nat @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(3)
% 0.26/0.58  thf(fact_6413_max__0__1_I3_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X3 ) )
% 0.26/0.58        = ( numeral_numeral_int @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(3)
% 0.26/0.58  thf(fact_6414_max__0__1_I4_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X3 ) @ zero_z5237406670263579293d_enat )
% 0.26/0.58        = ( numera1916890842035813515d_enat @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(4)
% 0.26/0.58  thf(fact_6415_max__0__1_I4_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X3 ) @ zero_z3403309356797280102nteger )
% 0.26/0.58        = ( numera6620942414471956472nteger @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(4)
% 0.26/0.58  thf(fact_6416_max__0__1_I4_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_max_real @ ( numeral_numeral_real @ X3 ) @ zero_zero_real )
% 0.26/0.58        = ( numeral_numeral_real @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(4)
% 0.26/0.58  thf(fact_6417_max__0__1_I4_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_max_rat @ ( numeral_numeral_rat @ X3 ) @ zero_zero_rat )
% 0.26/0.58        = ( numeral_numeral_rat @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(4)
% 0.26/0.58  thf(fact_6418_max__0__1_I4_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_max_nat @ ( numeral_numeral_nat @ X3 ) @ zero_zero_nat )
% 0.26/0.58        = ( numeral_numeral_nat @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(4)
% 0.26/0.58  thf(fact_6419_max__0__1_I4_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_max_int @ ( numeral_numeral_int @ X3 ) @ zero_zero_int )
% 0.26/0.58        = ( numeral_numeral_int @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(4)
% 0.26/0.58  thf(fact_6420_max__0__1_I2_J,axiom,
% 0.26/0.58      ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 0.26/0.58      = one_one_real ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(2)
% 0.26/0.58  thf(fact_6421_max__0__1_I2_J,axiom,
% 0.26/0.58      ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 0.26/0.58      = one_one_rat ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(2)
% 0.26/0.58  thf(fact_6422_max__0__1_I2_J,axiom,
% 0.26/0.58      ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 0.26/0.58      = one_one_nat ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(2)
% 0.26/0.58  thf(fact_6423_max__0__1_I2_J,axiom,
% 0.26/0.58      ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat )
% 0.26/0.58      = one_on7984719198319812577d_enat ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(2)
% 0.26/0.58  thf(fact_6424_max__0__1_I2_J,axiom,
% 0.26/0.58      ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 0.26/0.58      = one_one_int ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(2)
% 0.26/0.58  thf(fact_6425_max__0__1_I2_J,axiom,
% 0.26/0.58      ( ( ord_max_Code_integer @ one_one_Code_integer @ zero_z3403309356797280102nteger )
% 0.26/0.58      = one_one_Code_integer ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(2)
% 0.26/0.58  thf(fact_6426_max__0__1_I1_J,axiom,
% 0.26/0.58      ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 0.26/0.58      = one_one_real ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(1)
% 0.26/0.58  thf(fact_6427_max__0__1_I1_J,axiom,
% 0.26/0.58      ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 0.26/0.58      = one_one_rat ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(1)
% 0.26/0.58  thf(fact_6428_max__0__1_I1_J,axiom,
% 0.26/0.58      ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 0.26/0.58      = one_one_nat ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(1)
% 0.26/0.58  thf(fact_6429_max__0__1_I1_J,axiom,
% 0.26/0.58      ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat )
% 0.26/0.58      = one_on7984719198319812577d_enat ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(1)
% 0.26/0.58  thf(fact_6430_max__0__1_I1_J,axiom,
% 0.26/0.58      ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 0.26/0.58      = one_one_int ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(1)
% 0.26/0.58  thf(fact_6431_max__0__1_I1_J,axiom,
% 0.26/0.58      ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer )
% 0.26/0.58      = one_one_Code_integer ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(1)
% 0.26/0.58  thf(fact_6432_max__0__1_I5_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X3 ) )
% 0.26/0.58        = ( numera1916890842035813515d_enat @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(5)
% 0.26/0.58  thf(fact_6433_max__0__1_I5_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_max_Code_integer @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X3 ) )
% 0.26/0.58        = ( numera6620942414471956472nteger @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(5)
% 0.26/0.58  thf(fact_6434_max__0__1_I5_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X3 ) )
% 0.26/0.58        = ( numeral_numeral_real @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(5)
% 0.26/0.58  thf(fact_6435_max__0__1_I5_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X3 ) )
% 0.26/0.58        = ( numeral_numeral_rat @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(5)
% 0.26/0.58  thf(fact_6436_max__0__1_I5_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X3 ) )
% 0.26/0.58        = ( numeral_numeral_nat @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(5)
% 0.26/0.58  thf(fact_6437_max__0__1_I5_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X3 ) )
% 0.26/0.58        = ( numeral_numeral_int @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(5)
% 0.26/0.58  thf(fact_6438_max__0__1_I6_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X3 ) @ one_on7984719198319812577d_enat )
% 0.26/0.58        = ( numera1916890842035813515d_enat @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(6)
% 0.26/0.58  thf(fact_6439_max__0__1_I6_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X3 ) @ one_one_Code_integer )
% 0.26/0.58        = ( numera6620942414471956472nteger @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(6)
% 0.26/0.58  thf(fact_6440_max__0__1_I6_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_max_real @ ( numeral_numeral_real @ X3 ) @ one_one_real )
% 0.26/0.58        = ( numeral_numeral_real @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(6)
% 0.26/0.58  thf(fact_6441_max__0__1_I6_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_max_rat @ ( numeral_numeral_rat @ X3 ) @ one_one_rat )
% 0.26/0.58        = ( numeral_numeral_rat @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(6)
% 0.26/0.58  thf(fact_6442_max__0__1_I6_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_max_nat @ ( numeral_numeral_nat @ X3 ) @ one_one_nat )
% 0.26/0.58        = ( numeral_numeral_nat @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(6)
% 0.26/0.58  thf(fact_6443_max__0__1_I6_J,axiom,
% 0.26/0.58      ! [X3: num] :
% 0.26/0.58        ( ( ord_max_int @ ( numeral_numeral_int @ X3 ) @ one_one_int )
% 0.26/0.58        = ( numeral_numeral_int @ X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_0_1(6)
% 0.26/0.58  thf(fact_6444_max__number__of_I2_J,axiom,
% 0.26/0.58      ! [U: num,V: num] :
% 0.26/0.58        ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.26/0.58         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.26/0.58            = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 0.26/0.58        & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.26/0.58         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.26/0.58            = ( numeral_numeral_real @ U ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_number_of(2)
% 0.26/0.58  thf(fact_6445_max__number__of_I2_J,axiom,
% 0.26/0.58      ! [U: num,V: num] :
% 0.26/0.58        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.26/0.58         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.26/0.58            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 0.26/0.58        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.26/0.58         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.26/0.58            = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_number_of(2)
% 0.26/0.58  thf(fact_6446_max__number__of_I2_J,axiom,
% 0.26/0.58      ! [U: num,V: num] :
% 0.26/0.58        ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.26/0.58         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.26/0.58            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 0.26/0.58        & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.26/0.58         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.26/0.58            = ( numeral_numeral_rat @ U ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_number_of(2)
% 0.26/0.58  thf(fact_6447_max__number__of_I2_J,axiom,
% 0.26/0.58      ! [U: num,V: num] :
% 0.26/0.58        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.26/0.58         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.26/0.58            = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 0.26/0.58        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.26/0.58         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.26/0.58            = ( numeral_numeral_int @ U ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_number_of(2)
% 0.26/0.58  thf(fact_6448_max__number__of_I3_J,axiom,
% 0.26/0.58      ! [U: num,V: num] :
% 0.26/0.58        ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 0.26/0.58         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 0.26/0.58            = ( numeral_numeral_real @ V ) ) )
% 0.26/0.58        & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 0.26/0.58         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 0.26/0.58            = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_number_of(3)
% 0.26/0.58  thf(fact_6449_max__number__of_I3_J,axiom,
% 0.26/0.58      ! [U: num,V: num] :
% 0.26/0.58        ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 0.26/0.58         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 0.26/0.58            = ( numera6620942414471956472nteger @ V ) ) )
% 0.26/0.58        & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 0.26/0.58         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 0.26/0.58            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_number_of(3)
% 0.26/0.58  thf(fact_6450_max__number__of_I3_J,axiom,
% 0.26/0.58      ! [U: num,V: num] :
% 0.26/0.58        ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 0.26/0.58         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 0.26/0.58            = ( numeral_numeral_rat @ V ) ) )
% 0.26/0.58        & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 0.26/0.58         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 0.26/0.58            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_number_of(3)
% 0.26/0.58  thf(fact_6451_max__number__of_I3_J,axiom,
% 0.26/0.58      ! [U: num,V: num] :
% 0.26/0.58        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 0.26/0.58         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 0.26/0.58            = ( numeral_numeral_int @ V ) ) )
% 0.26/0.58        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 0.26/0.58         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 0.26/0.58            = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_number_of(3)
% 0.26/0.58  thf(fact_6452_max__number__of_I4_J,axiom,
% 0.26/0.58      ! [U: num,V: num] :
% 0.26/0.58        ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.26/0.58         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.26/0.58            = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 0.26/0.58        & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.26/0.58         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.26/0.58            = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_number_of(4)
% 0.26/0.58  thf(fact_6453_max__number__of_I4_J,axiom,
% 0.26/0.58      ! [U: num,V: num] :
% 0.26/0.58        ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.26/0.58         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.26/0.58            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 0.26/0.58        & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.26/0.58         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.26/0.58            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_number_of(4)
% 0.26/0.58  thf(fact_6454_max__number__of_I4_J,axiom,
% 0.26/0.58      ! [U: num,V: num] :
% 0.26/0.58        ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.26/0.58         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.26/0.58            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 0.26/0.58        & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.26/0.58         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.26/0.58            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_number_of(4)
% 0.26/0.58  thf(fact_6455_max__number__of_I4_J,axiom,
% 0.26/0.58      ! [U: num,V: num] :
% 0.26/0.58        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.26/0.58         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.26/0.58            = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 0.26/0.58        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.26/0.58         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.26/0.58            = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_number_of(4)
% 0.26/0.58  thf(fact_6456_max__def,axiom,
% 0.26/0.58      ( ord_ma741700101516333627d_enat
% 0.26/0.58      = ( ^ [A4: extended_enat,B3: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_def
% 0.26/0.58  thf(fact_6457_max__def,axiom,
% 0.26/0.58      ( ord_max_Code_integer
% 0.26/0.58      = ( ^ [A4: code_integer,B3: code_integer] : ( if_Code_integer @ ( ord_le3102999989581377725nteger @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_def
% 0.26/0.58  thf(fact_6458_max__def,axiom,
% 0.26/0.58      ( ord_max_set_nat
% 0.26/0.58      = ( ^ [A4: set_nat,B3: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_def
% 0.26/0.58  thf(fact_6459_max__def,axiom,
% 0.26/0.58      ( ord_max_rat
% 0.26/0.58      = ( ^ [A4: rat,B3: rat] : ( if_rat @ ( ord_less_eq_rat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_def
% 0.26/0.58  thf(fact_6460_max__def,axiom,
% 0.26/0.58      ( ord_max_num
% 0.26/0.58      = ( ^ [A4: num,B3: num] : ( if_num @ ( ord_less_eq_num @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_def
% 0.26/0.58  thf(fact_6461_max__def,axiom,
% 0.26/0.58      ( ord_max_nat
% 0.26/0.58      = ( ^ [A4: nat,B3: nat] : ( if_nat @ ( ord_less_eq_nat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_def
% 0.26/0.58  thf(fact_6462_max__def,axiom,
% 0.26/0.58      ( ord_max_int
% 0.26/0.58      = ( ^ [A4: int,B3: int] : ( if_int @ ( ord_less_eq_int @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_def
% 0.26/0.58  thf(fact_6463_max__absorb1,axiom,
% 0.26/0.58      ! [Y3: extended_enat,X3: extended_enat] :
% 0.26/0.58        ( ( ord_le2932123472753598470d_enat @ Y3 @ X3 )
% 0.26/0.58       => ( ( ord_ma741700101516333627d_enat @ X3 @ Y3 )
% 0.26/0.58          = X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_absorb1
% 0.26/0.58  thf(fact_6464_max__absorb1,axiom,
% 0.26/0.58      ! [Y3: code_integer,X3: code_integer] :
% 0.26/0.58        ( ( ord_le3102999989581377725nteger @ Y3 @ X3 )
% 0.26/0.58       => ( ( ord_max_Code_integer @ X3 @ Y3 )
% 0.26/0.58          = X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_absorb1
% 0.26/0.58  thf(fact_6465_max__absorb1,axiom,
% 0.26/0.58      ! [Y3: set_nat,X3: set_nat] :
% 0.26/0.58        ( ( ord_less_eq_set_nat @ Y3 @ X3 )
% 0.26/0.58       => ( ( ord_max_set_nat @ X3 @ Y3 )
% 0.26/0.58          = X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_absorb1
% 0.26/0.58  thf(fact_6466_max__absorb1,axiom,
% 0.26/0.58      ! [Y3: rat,X3: rat] :
% 0.26/0.58        ( ( ord_less_eq_rat @ Y3 @ X3 )
% 0.26/0.58       => ( ( ord_max_rat @ X3 @ Y3 )
% 0.26/0.58          = X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_absorb1
% 0.26/0.58  thf(fact_6467_max__absorb1,axiom,
% 0.26/0.58      ! [Y3: num,X3: num] :
% 0.26/0.58        ( ( ord_less_eq_num @ Y3 @ X3 )
% 0.26/0.58       => ( ( ord_max_num @ X3 @ Y3 )
% 0.26/0.58          = X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_absorb1
% 0.26/0.58  thf(fact_6468_max__absorb1,axiom,
% 0.26/0.58      ! [Y3: nat,X3: nat] :
% 0.26/0.58        ( ( ord_less_eq_nat @ Y3 @ X3 )
% 0.26/0.58       => ( ( ord_max_nat @ X3 @ Y3 )
% 0.26/0.58          = X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_absorb1
% 0.26/0.58  thf(fact_6469_max__absorb1,axiom,
% 0.26/0.58      ! [Y3: int,X3: int] :
% 0.26/0.58        ( ( ord_less_eq_int @ Y3 @ X3 )
% 0.26/0.58       => ( ( ord_max_int @ X3 @ Y3 )
% 0.26/0.58          = X3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_absorb1
% 0.26/0.58  thf(fact_6470_max__absorb2,axiom,
% 0.26/0.58      ! [X3: extended_enat,Y3: extended_enat] :
% 0.26/0.58        ( ( ord_le2932123472753598470d_enat @ X3 @ Y3 )
% 0.26/0.58       => ( ( ord_ma741700101516333627d_enat @ X3 @ Y3 )
% 0.26/0.58          = Y3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_absorb2
% 0.26/0.58  thf(fact_6471_max__absorb2,axiom,
% 0.26/0.58      ! [X3: code_integer,Y3: code_integer] :
% 0.26/0.58        ( ( ord_le3102999989581377725nteger @ X3 @ Y3 )
% 0.26/0.58       => ( ( ord_max_Code_integer @ X3 @ Y3 )
% 0.26/0.58          = Y3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_absorb2
% 0.26/0.58  thf(fact_6472_max__absorb2,axiom,
% 0.26/0.58      ! [X3: set_nat,Y3: set_nat] :
% 0.26/0.58        ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 0.26/0.58       => ( ( ord_max_set_nat @ X3 @ Y3 )
% 0.26/0.58          = Y3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_absorb2
% 0.26/0.58  thf(fact_6473_max__absorb2,axiom,
% 0.26/0.58      ! [X3: rat,Y3: rat] :
% 0.26/0.58        ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.26/0.58       => ( ( ord_max_rat @ X3 @ Y3 )
% 0.26/0.58          = Y3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_absorb2
% 0.26/0.58  thf(fact_6474_max__absorb2,axiom,
% 0.26/0.58      ! [X3: num,Y3: num] :
% 0.26/0.58        ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.26/0.58       => ( ( ord_max_num @ X3 @ Y3 )
% 0.26/0.58          = Y3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_absorb2
% 0.26/0.58  thf(fact_6475_max__absorb2,axiom,
% 0.26/0.58      ! [X3: nat,Y3: nat] :
% 0.26/0.58        ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.26/0.58       => ( ( ord_max_nat @ X3 @ Y3 )
% 0.26/0.58          = Y3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_absorb2
% 0.26/0.58  thf(fact_6476_max__absorb2,axiom,
% 0.26/0.58      ! [X3: int,Y3: int] :
% 0.26/0.58        ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.26/0.58       => ( ( ord_max_int @ X3 @ Y3 )
% 0.26/0.58          = Y3 ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_absorb2
% 0.26/0.58  thf(fact_6477_of__int__max,axiom,
% 0.26/0.58      ! [X3: int,Y3: int] :
% 0.26/0.58        ( ( ring_1_of_int_real @ ( ord_max_int @ X3 @ Y3 ) )
% 0.26/0.58        = ( ord_max_real @ ( ring_1_of_int_real @ X3 ) @ ( ring_1_of_int_real @ Y3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % of_int_max
% 0.26/0.58  thf(fact_6478_of__int__max,axiom,
% 0.26/0.58      ! [X3: int,Y3: int] :
% 0.26/0.58        ( ( ring_1_of_int_rat @ ( ord_max_int @ X3 @ Y3 ) )
% 0.26/0.58        = ( ord_max_rat @ ( ring_1_of_int_rat @ X3 ) @ ( ring_1_of_int_rat @ Y3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % of_int_max
% 0.26/0.58  thf(fact_6479_of__int__max,axiom,
% 0.26/0.58      ! [X3: int,Y3: int] :
% 0.26/0.58        ( ( ring_1_of_int_int @ ( ord_max_int @ X3 @ Y3 ) )
% 0.26/0.58        = ( ord_max_int @ ( ring_1_of_int_int @ X3 ) @ ( ring_1_of_int_int @ Y3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % of_int_max
% 0.26/0.58  thf(fact_6480_of__int__max,axiom,
% 0.26/0.58      ! [X3: int,Y3: int] :
% 0.26/0.58        ( ( ring_18347121197199848620nteger @ ( ord_max_int @ X3 @ Y3 ) )
% 0.26/0.58        = ( ord_max_Code_integer @ ( ring_18347121197199848620nteger @ X3 ) @ ( ring_18347121197199848620nteger @ Y3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % of_int_max
% 0.26/0.58  thf(fact_6481_of__nat__max,axiom,
% 0.26/0.58      ! [X3: nat,Y3: nat] :
% 0.26/0.58        ( ( semiri4216267220026989637d_enat @ ( ord_max_nat @ X3 @ Y3 ) )
% 0.26/0.58        = ( ord_ma741700101516333627d_enat @ ( semiri4216267220026989637d_enat @ X3 ) @ ( semiri4216267220026989637d_enat @ Y3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % of_nat_max
% 0.26/0.58  thf(fact_6482_of__nat__max,axiom,
% 0.26/0.58      ! [X3: nat,Y3: nat] :
% 0.26/0.58        ( ( semiri4939895301339042750nteger @ ( ord_max_nat @ X3 @ Y3 ) )
% 0.26/0.58        = ( ord_max_Code_integer @ ( semiri4939895301339042750nteger @ X3 ) @ ( semiri4939895301339042750nteger @ Y3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % of_nat_max
% 0.26/0.58  thf(fact_6483_of__nat__max,axiom,
% 0.26/0.58      ! [X3: nat,Y3: nat] :
% 0.26/0.58        ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X3 @ Y3 ) )
% 0.26/0.58        = ( ord_max_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( semiri5074537144036343181t_real @ Y3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % of_nat_max
% 0.26/0.58  thf(fact_6484_of__nat__max,axiom,
% 0.26/0.58      ! [X3: nat,Y3: nat] :
% 0.26/0.58        ( ( semiri681578069525770553at_rat @ ( ord_max_nat @ X3 @ Y3 ) )
% 0.26/0.58        = ( ord_max_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( semiri681578069525770553at_rat @ Y3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % of_nat_max
% 0.26/0.58  thf(fact_6485_of__nat__max,axiom,
% 0.26/0.58      ! [X3: nat,Y3: nat] :
% 0.26/0.58        ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X3 @ Y3 ) )
% 0.26/0.58        = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( semiri1316708129612266289at_nat @ Y3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % of_nat_max
% 0.26/0.58  thf(fact_6486_of__nat__max,axiom,
% 0.26/0.58      ! [X3: nat,Y3: nat] :
% 0.26/0.58        ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X3 @ Y3 ) )
% 0.26/0.58        = ( ord_max_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( semiri1314217659103216013at_int @ Y3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % of_nat_max
% 0.26/0.58  thf(fact_6487_max__add__distrib__left,axiom,
% 0.26/0.58      ! [X3: real,Y3: real,Z: real] :
% 0.26/0.58        ( ( plus_plus_real @ ( ord_max_real @ X3 @ Y3 ) @ Z )
% 0.26/0.58        = ( ord_max_real @ ( plus_plus_real @ X3 @ Z ) @ ( plus_plus_real @ Y3 @ Z ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_add_distrib_left
% 0.26/0.58  thf(fact_6488_max__add__distrib__left,axiom,
% 0.26/0.58      ! [X3: rat,Y3: rat,Z: rat] :
% 0.26/0.58        ( ( plus_plus_rat @ ( ord_max_rat @ X3 @ Y3 ) @ Z )
% 0.26/0.58        = ( ord_max_rat @ ( plus_plus_rat @ X3 @ Z ) @ ( plus_plus_rat @ Y3 @ Z ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_add_distrib_left
% 0.26/0.58  thf(fact_6489_max__add__distrib__left,axiom,
% 0.26/0.58      ! [X3: nat,Y3: nat,Z: nat] :
% 0.26/0.58        ( ( plus_plus_nat @ ( ord_max_nat @ X3 @ Y3 ) @ Z )
% 0.26/0.58        = ( ord_max_nat @ ( plus_plus_nat @ X3 @ Z ) @ ( plus_plus_nat @ Y3 @ Z ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_add_distrib_left
% 0.26/0.58  thf(fact_6490_max__add__distrib__left,axiom,
% 0.26/0.58      ! [X3: int,Y3: int,Z: int] :
% 0.26/0.58        ( ( plus_plus_int @ ( ord_max_int @ X3 @ Y3 ) @ Z )
% 0.26/0.58        = ( ord_max_int @ ( plus_plus_int @ X3 @ Z ) @ ( plus_plus_int @ Y3 @ Z ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_add_distrib_left
% 0.26/0.58  thf(fact_6491_max__add__distrib__left,axiom,
% 0.26/0.58      ! [X3: code_integer,Y3: code_integer,Z: code_integer] :
% 0.26/0.58        ( ( plus_p5714425477246183910nteger @ ( ord_max_Code_integer @ X3 @ Y3 ) @ Z )
% 0.26/0.58        = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X3 @ Z ) @ ( plus_p5714425477246183910nteger @ Y3 @ Z ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_add_distrib_left
% 0.26/0.58  thf(fact_6492_max__add__distrib__right,axiom,
% 0.26/0.58      ! [X3: real,Y3: real,Z: real] :
% 0.26/0.58        ( ( plus_plus_real @ X3 @ ( ord_max_real @ Y3 @ Z ) )
% 0.26/0.58        = ( ord_max_real @ ( plus_plus_real @ X3 @ Y3 ) @ ( plus_plus_real @ X3 @ Z ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_add_distrib_right
% 0.26/0.58  thf(fact_6493_max__add__distrib__right,axiom,
% 0.26/0.58      ! [X3: rat,Y3: rat,Z: rat] :
% 0.26/0.58        ( ( plus_plus_rat @ X3 @ ( ord_max_rat @ Y3 @ Z ) )
% 0.26/0.58        = ( ord_max_rat @ ( plus_plus_rat @ X3 @ Y3 ) @ ( plus_plus_rat @ X3 @ Z ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_add_distrib_right
% 0.26/0.58  thf(fact_6494_max__add__distrib__right,axiom,
% 0.26/0.58      ! [X3: nat,Y3: nat,Z: nat] :
% 0.26/0.58        ( ( plus_plus_nat @ X3 @ ( ord_max_nat @ Y3 @ Z ) )
% 0.26/0.58        = ( ord_max_nat @ ( plus_plus_nat @ X3 @ Y3 ) @ ( plus_plus_nat @ X3 @ Z ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_add_distrib_right
% 0.26/0.58  thf(fact_6495_max__add__distrib__right,axiom,
% 0.26/0.58      ! [X3: int,Y3: int,Z: int] :
% 0.26/0.58        ( ( plus_plus_int @ X3 @ ( ord_max_int @ Y3 @ Z ) )
% 0.26/0.58        = ( ord_max_int @ ( plus_plus_int @ X3 @ Y3 ) @ ( plus_plus_int @ X3 @ Z ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_add_distrib_right
% 0.26/0.58  thf(fact_6496_max__add__distrib__right,axiom,
% 0.26/0.58      ! [X3: code_integer,Y3: code_integer,Z: code_integer] :
% 0.26/0.58        ( ( plus_p5714425477246183910nteger @ X3 @ ( ord_max_Code_integer @ Y3 @ Z ) )
% 0.26/0.58        = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X3 @ Y3 ) @ ( plus_p5714425477246183910nteger @ X3 @ Z ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_add_distrib_right
% 0.26/0.58  thf(fact_6497_max__diff__distrib__left,axiom,
% 0.26/0.58      ! [X3: code_integer,Y3: code_integer,Z: code_integer] :
% 0.26/0.58        ( ( minus_8373710615458151222nteger @ ( ord_max_Code_integer @ X3 @ Y3 ) @ Z )
% 0.26/0.58        = ( ord_max_Code_integer @ ( minus_8373710615458151222nteger @ X3 @ Z ) @ ( minus_8373710615458151222nteger @ Y3 @ Z ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_diff_distrib_left
% 0.26/0.58  thf(fact_6498_max__diff__distrib__left,axiom,
% 0.26/0.58      ! [X3: real,Y3: real,Z: real] :
% 0.26/0.58        ( ( minus_minus_real @ ( ord_max_real @ X3 @ Y3 ) @ Z )
% 0.26/0.58        = ( ord_max_real @ ( minus_minus_real @ X3 @ Z ) @ ( minus_minus_real @ Y3 @ Z ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_diff_distrib_left
% 0.26/0.58  thf(fact_6499_max__diff__distrib__left,axiom,
% 0.26/0.58      ! [X3: rat,Y3: rat,Z: rat] :
% 0.26/0.58        ( ( minus_minus_rat @ ( ord_max_rat @ X3 @ Y3 ) @ Z )
% 0.26/0.58        = ( ord_max_rat @ ( minus_minus_rat @ X3 @ Z ) @ ( minus_minus_rat @ Y3 @ Z ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_diff_distrib_left
% 0.26/0.58  thf(fact_6500_max__diff__distrib__left,axiom,
% 0.26/0.58      ! [X3: int,Y3: int,Z: int] :
% 0.26/0.58        ( ( minus_minus_int @ ( ord_max_int @ X3 @ Y3 ) @ Z )
% 0.26/0.58        = ( ord_max_int @ ( minus_minus_int @ X3 @ Z ) @ ( minus_minus_int @ Y3 @ Z ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_diff_distrib_left
% 0.26/0.58  thf(fact_6501_nat__add__max__right,axiom,
% 0.26/0.58      ! [M: nat,N: nat,Q3: nat] :
% 0.26/0.58        ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q3 ) )
% 0.26/0.58        = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % nat_add_max_right
% 0.26/0.58  thf(fact_6502_nat__add__max__left,axiom,
% 0.26/0.58      ! [M: nat,N: nat,Q3: nat] :
% 0.26/0.58        ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q3 )
% 0.26/0.58        = ( ord_max_nat @ ( plus_plus_nat @ M @ Q3 ) @ ( plus_plus_nat @ N @ Q3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % nat_add_max_left
% 0.26/0.58  thf(fact_6503_nat__mult__max__left,axiom,
% 0.26/0.58      ! [M: nat,N: nat,Q3: nat] :
% 0.26/0.58        ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q3 )
% 0.26/0.58        = ( ord_max_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N @ Q3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % nat_mult_max_left
% 0.26/0.58  thf(fact_6504_nat__mult__max__right,axiom,
% 0.26/0.58      ! [M: nat,N: nat,Q3: nat] :
% 0.26/0.58        ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q3 ) )
% 0.26/0.58        = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % nat_mult_max_right
% 0.26/0.58  thf(fact_6505_nat__minus__add__max,axiom,
% 0.26/0.58      ! [N: nat,M: nat] :
% 0.26/0.58        ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 0.26/0.58        = ( ord_max_nat @ N @ M ) ) ).
% 0.26/0.58  
% 0.26/0.58  % nat_minus_add_max
% 0.26/0.58  thf(fact_6506_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I1_J,axiom,
% 0.26/0.58      ! [Uu2: $o,Uv2: $o] :
% 0.26/0.58        ( ( vEBT_T_p_r_e_d @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat )
% 0.26/0.58        = one_one_nat ) ).
% 0.26/0.58  
% 0.26/0.58  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(1)
% 0.26/0.58  thf(fact_6507_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I5_J,axiom,
% 0.26/0.58      ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 0.26/0.58        ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf )
% 0.26/0.58        = one_one_nat ) ).
% 0.26/0.58  
% 0.26/0.58  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(5)
% 0.26/0.58  thf(fact_6508_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I1_J,axiom,
% 0.26/0.58      ! [Uu2: $o,B: $o] :
% 0.26/0.58        ( ( vEBT_T_s_u_c_c @ ( vEBT_Leaf @ Uu2 @ B ) @ zero_zero_nat )
% 0.26/0.58        = ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ).
% 0.26/0.58  
% 0.26/0.58  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(1)
% 0.26/0.58  thf(fact_6509_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I4_J,axiom,
% 0.26/0.58      ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 0.26/0.58        ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve )
% 0.26/0.58        = one_one_nat ) ).
% 0.26/0.58  
% 0.26/0.58  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(4)
% 0.26/0.58  thf(fact_6510_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I2_J,axiom,
% 0.26/0.58      ! [A: $o,Uw2: $o] :
% 0.26/0.58        ( ( vEBT_T_p_r_e_d @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 0.26/0.58        = ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ).
% 0.26/0.58  
% 0.26/0.58  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(2)
% 0.26/0.58  thf(fact_6511_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I6_J,axiom,
% 0.26/0.58      ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 0.26/0.58        ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj )
% 0.26/0.58        = one_one_nat ) ).
% 0.26/0.58  
% 0.26/0.58  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(6)
% 0.26/0.58  thf(fact_6512_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I5_J,axiom,
% 0.26/0.58      ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 0.26/0.58        ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi )
% 0.26/0.58        = one_one_nat ) ).
% 0.26/0.58  
% 0.26/0.58  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(5)
% 0.26/0.58  thf(fact_6513_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I2_J,axiom,
% 0.26/0.58      ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X3: nat] :
% 0.26/0.58        ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X3 )
% 0.26/0.58        = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(2)
% 0.26/0.58  thf(fact_6514_or__nat__unfold,axiom,
% 0.26/0.58      ( bit_se1412395901928357646or_nat
% 0.26/0.58      = ( ^ [M3: nat,N3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N3 @ ( if_nat @ ( N3 = zero_zero_nat ) @ M3 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N3 @ ( 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 @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % or_nat_unfold
% 0.26/0.58  thf(fact_6515_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I3_J,axiom,
% 0.26/0.58      ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X3: nat] :
% 0.26/0.58        ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X3 )
% 0.26/0.58        = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(3)
% 0.26/0.58  thf(fact_6516_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I4_J,axiom,
% 0.26/0.58      ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc: vEBT_VEBT,X3: nat] :
% 0.26/0.58        ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc ) @ X3 )
% 0.26/0.58        = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(4)
% 0.26/0.58  thf(fact_6517_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I1_J,axiom,
% 0.26/0.58      ! [A: $o,B: $o,X3: nat] :
% 0.26/0.58        ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 0.26/0.58        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X3 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(1)
% 0.26/0.58  thf(fact_6518_vebt__member_Osimps_I3_J,axiom,
% 0.26/0.58      ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X3: nat] :
% 0.26/0.58        ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X3 ) ).
% 0.26/0.58  
% 0.26/0.58  % vebt_member.simps(3)
% 0.26/0.58  thf(fact_6519_vebt__member_Osimps_I1_J,axiom,
% 0.26/0.58      ! [A: $o,B: $o,X3: nat] :
% 0.26/0.58        ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 0.26/0.58        = ( ( ( X3 = zero_zero_nat )
% 0.26/0.58           => A )
% 0.26/0.58          & ( ( X3 != zero_zero_nat )
% 0.26/0.58           => ( ( ( X3 = one_one_nat )
% 0.26/0.58               => B )
% 0.26/0.58              & ( X3 = one_one_nat ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % vebt_member.simps(1)
% 0.26/0.58  thf(fact_6520_pred__bound__height,axiom,
% 0.26/0.58      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.58        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.58       => ( ord_less_eq_nat @ ( vEBT_T_p_r_e_d @ T @ X3 ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % pred_bound_height
% 0.26/0.58  thf(fact_6521_succ__bound__height,axiom,
% 0.26/0.58      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.58        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.58       => ( ord_less_eq_nat @ ( vEBT_T_s_u_c_c @ T @ X3 ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % succ_bound_height
% 0.26/0.58  thf(fact_6522_member__bound__height,axiom,
% 0.26/0.58      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.58        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.58       => ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r @ T @ X3 ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % member_bound_height
% 0.26/0.58  thf(fact_6523_max_Oabsorb3,axiom,
% 0.26/0.58      ! [B: extended_enat,A: extended_enat] :
% 0.26/0.58        ( ( ord_le72135733267957522d_enat @ B @ A )
% 0.26/0.58       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 0.26/0.58          = A ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb3
% 0.26/0.58  thf(fact_6524_max_Oabsorb3,axiom,
% 0.26/0.58      ! [B: code_integer,A: code_integer] :
% 0.26/0.58        ( ( ord_le6747313008572928689nteger @ B @ A )
% 0.26/0.58       => ( ( ord_max_Code_integer @ A @ B )
% 0.26/0.58          = A ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb3
% 0.26/0.58  thf(fact_6525_max_Oabsorb3,axiom,
% 0.26/0.58      ! [B: real,A: real] :
% 0.26/0.58        ( ( ord_less_real @ B @ A )
% 0.26/0.58       => ( ( ord_max_real @ A @ B )
% 0.26/0.58          = A ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb3
% 0.26/0.58  thf(fact_6526_max_Oabsorb3,axiom,
% 0.26/0.58      ! [B: rat,A: rat] :
% 0.26/0.58        ( ( ord_less_rat @ B @ A )
% 0.26/0.58       => ( ( ord_max_rat @ A @ B )
% 0.26/0.58          = A ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb3
% 0.26/0.58  thf(fact_6527_max_Oabsorb3,axiom,
% 0.26/0.58      ! [B: num,A: num] :
% 0.26/0.58        ( ( ord_less_num @ B @ A )
% 0.26/0.58       => ( ( ord_max_num @ A @ B )
% 0.26/0.58          = A ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb3
% 0.26/0.58  thf(fact_6528_max_Oabsorb3,axiom,
% 0.26/0.58      ! [B: nat,A: nat] :
% 0.26/0.58        ( ( ord_less_nat @ B @ A )
% 0.26/0.58       => ( ( ord_max_nat @ A @ B )
% 0.26/0.58          = A ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb3
% 0.26/0.58  thf(fact_6529_max_Oabsorb3,axiom,
% 0.26/0.58      ! [B: int,A: int] :
% 0.26/0.58        ( ( ord_less_int @ B @ A )
% 0.26/0.58       => ( ( ord_max_int @ A @ B )
% 0.26/0.58          = A ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb3
% 0.26/0.58  thf(fact_6530_max_Oabsorb4,axiom,
% 0.26/0.58      ! [A: extended_enat,B: extended_enat] :
% 0.26/0.58        ( ( ord_le72135733267957522d_enat @ A @ B )
% 0.26/0.58       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 0.26/0.58          = B ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb4
% 0.26/0.58  thf(fact_6531_max_Oabsorb4,axiom,
% 0.26/0.58      ! [A: code_integer,B: code_integer] :
% 0.26/0.58        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.26/0.58       => ( ( ord_max_Code_integer @ A @ B )
% 0.26/0.58          = B ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb4
% 0.26/0.58  thf(fact_6532_max_Oabsorb4,axiom,
% 0.26/0.58      ! [A: real,B: real] :
% 0.26/0.58        ( ( ord_less_real @ A @ B )
% 0.26/0.58       => ( ( ord_max_real @ A @ B )
% 0.26/0.58          = B ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb4
% 0.26/0.58  thf(fact_6533_max_Oabsorb4,axiom,
% 0.26/0.58      ! [A: rat,B: rat] :
% 0.26/0.58        ( ( ord_less_rat @ A @ B )
% 0.26/0.58       => ( ( ord_max_rat @ A @ B )
% 0.26/0.58          = B ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb4
% 0.26/0.58  thf(fact_6534_max_Oabsorb4,axiom,
% 0.26/0.58      ! [A: num,B: num] :
% 0.26/0.58        ( ( ord_less_num @ A @ B )
% 0.26/0.58       => ( ( ord_max_num @ A @ B )
% 0.26/0.58          = B ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb4
% 0.26/0.58  thf(fact_6535_max_Oabsorb4,axiom,
% 0.26/0.58      ! [A: nat,B: nat] :
% 0.26/0.58        ( ( ord_less_nat @ A @ B )
% 0.26/0.58       => ( ( ord_max_nat @ A @ B )
% 0.26/0.58          = B ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb4
% 0.26/0.58  thf(fact_6536_max_Oabsorb4,axiom,
% 0.26/0.58      ! [A: int,B: int] :
% 0.26/0.58        ( ( ord_less_int @ A @ B )
% 0.26/0.58       => ( ( ord_max_int @ A @ B )
% 0.26/0.58          = B ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb4
% 0.26/0.58  thf(fact_6537_max__less__iff__conj,axiom,
% 0.26/0.58      ! [X3: extended_enat,Y3: extended_enat,Z: extended_enat] :
% 0.26/0.58        ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ X3 @ Y3 ) @ Z )
% 0.26/0.58        = ( ( ord_le72135733267957522d_enat @ X3 @ Z )
% 0.26/0.58          & ( ord_le72135733267957522d_enat @ Y3 @ Z ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_less_iff_conj
% 0.26/0.58  thf(fact_6538_max__less__iff__conj,axiom,
% 0.26/0.58      ! [X3: code_integer,Y3: code_integer,Z: code_integer] :
% 0.26/0.58        ( ( ord_le6747313008572928689nteger @ ( ord_max_Code_integer @ X3 @ Y3 ) @ Z )
% 0.26/0.58        = ( ( ord_le6747313008572928689nteger @ X3 @ Z )
% 0.26/0.58          & ( ord_le6747313008572928689nteger @ Y3 @ Z ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_less_iff_conj
% 0.26/0.58  thf(fact_6539_max__less__iff__conj,axiom,
% 0.26/0.58      ! [X3: real,Y3: real,Z: real] :
% 0.26/0.58        ( ( ord_less_real @ ( ord_max_real @ X3 @ Y3 ) @ Z )
% 0.26/0.58        = ( ( ord_less_real @ X3 @ Z )
% 0.26/0.58          & ( ord_less_real @ Y3 @ Z ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_less_iff_conj
% 0.26/0.58  thf(fact_6540_max__less__iff__conj,axiom,
% 0.26/0.58      ! [X3: rat,Y3: rat,Z: rat] :
% 0.26/0.58        ( ( ord_less_rat @ ( ord_max_rat @ X3 @ Y3 ) @ Z )
% 0.26/0.58        = ( ( ord_less_rat @ X3 @ Z )
% 0.26/0.58          & ( ord_less_rat @ Y3 @ Z ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_less_iff_conj
% 0.26/0.58  thf(fact_6541_max__less__iff__conj,axiom,
% 0.26/0.58      ! [X3: num,Y3: num,Z: num] :
% 0.26/0.58        ( ( ord_less_num @ ( ord_max_num @ X3 @ Y3 ) @ Z )
% 0.26/0.58        = ( ( ord_less_num @ X3 @ Z )
% 0.26/0.58          & ( ord_less_num @ Y3 @ Z ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_less_iff_conj
% 0.26/0.58  thf(fact_6542_max__less__iff__conj,axiom,
% 0.26/0.58      ! [X3: nat,Y3: nat,Z: nat] :
% 0.26/0.58        ( ( ord_less_nat @ ( ord_max_nat @ X3 @ Y3 ) @ Z )
% 0.26/0.58        = ( ( ord_less_nat @ X3 @ Z )
% 0.26/0.58          & ( ord_less_nat @ Y3 @ Z ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_less_iff_conj
% 0.26/0.58  thf(fact_6543_max__less__iff__conj,axiom,
% 0.26/0.58      ! [X3: int,Y3: int,Z: int] :
% 0.26/0.58        ( ( ord_less_int @ ( ord_max_int @ X3 @ Y3 ) @ Z )
% 0.26/0.58        = ( ( ord_less_int @ X3 @ Z )
% 0.26/0.58          & ( ord_less_int @ Y3 @ Z ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max_less_iff_conj
% 0.26/0.58  thf(fact_6544_max_Oabsorb1,axiom,
% 0.26/0.58      ! [B: extended_enat,A: extended_enat] :
% 0.26/0.58        ( ( ord_le2932123472753598470d_enat @ B @ A )
% 0.26/0.58       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 0.26/0.58          = A ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb1
% 0.26/0.58  thf(fact_6545_max_Oabsorb1,axiom,
% 0.26/0.58      ! [B: code_integer,A: code_integer] :
% 0.26/0.58        ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.26/0.58       => ( ( ord_max_Code_integer @ A @ B )
% 0.26/0.58          = A ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb1
% 0.26/0.58  thf(fact_6546_max_Oabsorb1,axiom,
% 0.26/0.58      ! [B: rat,A: rat] :
% 0.26/0.58        ( ( ord_less_eq_rat @ B @ A )
% 0.26/0.58       => ( ( ord_max_rat @ A @ B )
% 0.26/0.58          = A ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb1
% 0.26/0.58  thf(fact_6547_max_Oabsorb1,axiom,
% 0.26/0.58      ! [B: num,A: num] :
% 0.26/0.58        ( ( ord_less_eq_num @ B @ A )
% 0.26/0.58       => ( ( ord_max_num @ A @ B )
% 0.26/0.58          = A ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb1
% 0.26/0.58  thf(fact_6548_max_Oabsorb1,axiom,
% 0.26/0.58      ! [B: nat,A: nat] :
% 0.26/0.58        ( ( ord_less_eq_nat @ B @ A )
% 0.26/0.58       => ( ( ord_max_nat @ A @ B )
% 0.26/0.58          = A ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb1
% 0.26/0.58  thf(fact_6549_max_Oabsorb1,axiom,
% 0.26/0.58      ! [B: int,A: int] :
% 0.26/0.58        ( ( ord_less_eq_int @ B @ A )
% 0.26/0.58       => ( ( ord_max_int @ A @ B )
% 0.26/0.58          = A ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb1
% 0.26/0.58  thf(fact_6550_max_Oabsorb2,axiom,
% 0.26/0.58      ! [A: extended_enat,B: extended_enat] :
% 0.26/0.58        ( ( ord_le2932123472753598470d_enat @ A @ B )
% 0.26/0.58       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 0.26/0.58          = B ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb2
% 0.26/0.58  thf(fact_6551_max_Oabsorb2,axiom,
% 0.26/0.58      ! [A: code_integer,B: code_integer] :
% 0.26/0.58        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.26/0.58       => ( ( ord_max_Code_integer @ A @ B )
% 0.26/0.58          = B ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb2
% 0.26/0.58  thf(fact_6552_max_Oabsorb2,axiom,
% 0.26/0.58      ! [A: rat,B: rat] :
% 0.26/0.58        ( ( ord_less_eq_rat @ A @ B )
% 0.26/0.58       => ( ( ord_max_rat @ A @ B )
% 0.26/0.58          = B ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb2
% 0.26/0.58  thf(fact_6553_max_Oabsorb2,axiom,
% 0.26/0.58      ! [A: num,B: num] :
% 0.26/0.58        ( ( ord_less_eq_num @ A @ B )
% 0.26/0.58       => ( ( ord_max_num @ A @ B )
% 0.26/0.58          = B ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb2
% 0.26/0.58  thf(fact_6554_max_Oabsorb2,axiom,
% 0.26/0.58      ! [A: nat,B: nat] :
% 0.26/0.58        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.58       => ( ( ord_max_nat @ A @ B )
% 0.26/0.58          = B ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb2
% 0.26/0.58  thf(fact_6555_max_Oabsorb2,axiom,
% 0.26/0.58      ! [A: int,B: int] :
% 0.26/0.58        ( ( ord_less_eq_int @ A @ B )
% 0.26/0.58       => ( ( ord_max_int @ A @ B )
% 0.26/0.58          = B ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb2
% 0.26/0.58  thf(fact_6556_max_Obounded__iff,axiom,
% 0.26/0.58      ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 0.26/0.58        ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 0.26/0.58        = ( ( ord_le2932123472753598470d_enat @ B @ A )
% 0.26/0.58          & ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.bounded_iff
% 0.26/0.58  thf(fact_6557_max_Obounded__iff,axiom,
% 0.26/0.58      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.26/0.58        ( ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 0.26/0.58        = ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.26/0.58          & ( ord_le3102999989581377725nteger @ C @ A ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.bounded_iff
% 0.26/0.58  thf(fact_6558_max_Obounded__iff,axiom,
% 0.26/0.58      ! [B: rat,C: rat,A: rat] :
% 0.26/0.58        ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 0.26/0.58        = ( ( ord_less_eq_rat @ B @ A )
% 0.26/0.58          & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.bounded_iff
% 0.26/0.58  thf(fact_6559_max_Obounded__iff,axiom,
% 0.26/0.58      ! [B: num,C: num,A: num] :
% 0.26/0.58        ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 0.26/0.58        = ( ( ord_less_eq_num @ B @ A )
% 0.26/0.58          & ( ord_less_eq_num @ C @ A ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.bounded_iff
% 0.26/0.58  thf(fact_6560_max_Obounded__iff,axiom,
% 0.26/0.58      ! [B: nat,C: nat,A: nat] :
% 0.26/0.58        ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 0.26/0.58        = ( ( ord_less_eq_nat @ B @ A )
% 0.26/0.58          & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.bounded_iff
% 0.26/0.58  thf(fact_6561_max_Obounded__iff,axiom,
% 0.26/0.58      ! [B: int,C: int,A: int] :
% 0.26/0.58        ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 0.26/0.58        = ( ( ord_less_eq_int @ B @ A )
% 0.26/0.58          & ( ord_less_eq_int @ C @ A ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.bounded_iff
% 0.26/0.58  thf(fact_6562_max__enat__simps_I3_J,axiom,
% 0.26/0.58      ! [Q3: extended_enat] :
% 0.26/0.58        ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q3 )
% 0.26/0.58        = Q3 ) ).
% 0.26/0.58  
% 0.26/0.58  % max_enat_simps(3)
% 0.26/0.58  thf(fact_6563_max__enat__simps_I2_J,axiom,
% 0.26/0.58      ! [Q3: extended_enat] :
% 0.26/0.58        ( ( ord_ma741700101516333627d_enat @ Q3 @ zero_z5237406670263579293d_enat )
% 0.26/0.58        = Q3 ) ).
% 0.26/0.58  
% 0.26/0.58  % max_enat_simps(2)
% 0.26/0.58  thf(fact_6564_max_OcoboundedI2,axiom,
% 0.26/0.58      ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 0.26/0.58        ( ( ord_le2932123472753598470d_enat @ C @ B )
% 0.26/0.58       => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.coboundedI2
% 0.26/0.58  thf(fact_6565_max_OcoboundedI2,axiom,
% 0.26/0.58      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.26/0.58        ( ( ord_le3102999989581377725nteger @ C @ B )
% 0.26/0.58       => ( ord_le3102999989581377725nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.coboundedI2
% 0.26/0.58  thf(fact_6566_max_OcoboundedI2,axiom,
% 0.26/0.58      ! [C: rat,B: rat,A: rat] :
% 0.26/0.58        ( ( ord_less_eq_rat @ C @ B )
% 0.26/0.58       => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.coboundedI2
% 0.26/0.58  thf(fact_6567_max_OcoboundedI2,axiom,
% 0.26/0.58      ! [C: num,B: num,A: num] :
% 0.26/0.58        ( ( ord_less_eq_num @ C @ B )
% 0.26/0.58       => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.coboundedI2
% 0.26/0.58  thf(fact_6568_max_OcoboundedI2,axiom,
% 0.26/0.58      ! [C: nat,B: nat,A: nat] :
% 0.26/0.58        ( ( ord_less_eq_nat @ C @ B )
% 0.26/0.58       => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.coboundedI2
% 0.26/0.58  thf(fact_6569_max_OcoboundedI2,axiom,
% 0.26/0.58      ! [C: int,B: int,A: int] :
% 0.26/0.58        ( ( ord_less_eq_int @ C @ B )
% 0.26/0.58       => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.coboundedI2
% 0.26/0.58  thf(fact_6570_max_OcoboundedI1,axiom,
% 0.26/0.58      ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 0.26/0.58        ( ( ord_le2932123472753598470d_enat @ C @ A )
% 0.26/0.58       => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.coboundedI1
% 0.26/0.58  thf(fact_6571_max_OcoboundedI1,axiom,
% 0.26/0.58      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.26/0.58        ( ( ord_le3102999989581377725nteger @ C @ A )
% 0.26/0.58       => ( ord_le3102999989581377725nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.coboundedI1
% 0.26/0.58  thf(fact_6572_max_OcoboundedI1,axiom,
% 0.26/0.58      ! [C: rat,A: rat,B: rat] :
% 0.26/0.58        ( ( ord_less_eq_rat @ C @ A )
% 0.26/0.58       => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.coboundedI1
% 0.26/0.58  thf(fact_6573_max_OcoboundedI1,axiom,
% 0.26/0.58      ! [C: num,A: num,B: num] :
% 0.26/0.58        ( ( ord_less_eq_num @ C @ A )
% 0.26/0.58       => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.coboundedI1
% 0.26/0.58  thf(fact_6574_max_OcoboundedI1,axiom,
% 0.26/0.58      ! [C: nat,A: nat,B: nat] :
% 0.26/0.58        ( ( ord_less_eq_nat @ C @ A )
% 0.26/0.58       => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.coboundedI1
% 0.26/0.58  thf(fact_6575_max_OcoboundedI1,axiom,
% 0.26/0.58      ! [C: int,A: int,B: int] :
% 0.26/0.58        ( ( ord_less_eq_int @ C @ A )
% 0.26/0.58       => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.coboundedI1
% 0.26/0.58  thf(fact_6576_max_Oabsorb__iff2,axiom,
% 0.26/0.58      ( ord_le2932123472753598470d_enat
% 0.26/0.58      = ( ^ [A4: extended_enat,B3: extended_enat] :
% 0.26/0.58            ( ( ord_ma741700101516333627d_enat @ A4 @ B3 )
% 0.26/0.58            = B3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb_iff2
% 0.26/0.58  thf(fact_6577_max_Oabsorb__iff2,axiom,
% 0.26/0.58      ( ord_le3102999989581377725nteger
% 0.26/0.58      = ( ^ [A4: code_integer,B3: code_integer] :
% 0.26/0.58            ( ( ord_max_Code_integer @ A4 @ B3 )
% 0.26/0.58            = B3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb_iff2
% 0.26/0.58  thf(fact_6578_max_Oabsorb__iff2,axiom,
% 0.26/0.58      ( ord_less_eq_rat
% 0.26/0.58      = ( ^ [A4: rat,B3: rat] :
% 0.26/0.58            ( ( ord_max_rat @ A4 @ B3 )
% 0.26/0.58            = B3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb_iff2
% 0.26/0.58  thf(fact_6579_max_Oabsorb__iff2,axiom,
% 0.26/0.58      ( ord_less_eq_num
% 0.26/0.58      = ( ^ [A4: num,B3: num] :
% 0.26/0.58            ( ( ord_max_num @ A4 @ B3 )
% 0.26/0.58            = B3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb_iff2
% 0.26/0.58  thf(fact_6580_max_Oabsorb__iff2,axiom,
% 0.26/0.58      ( ord_less_eq_nat
% 0.26/0.58      = ( ^ [A4: nat,B3: nat] :
% 0.26/0.58            ( ( ord_max_nat @ A4 @ B3 )
% 0.26/0.58            = B3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb_iff2
% 0.26/0.58  thf(fact_6581_max_Oabsorb__iff2,axiom,
% 0.26/0.58      ( ord_less_eq_int
% 0.26/0.58      = ( ^ [A4: int,B3: int] :
% 0.26/0.58            ( ( ord_max_int @ A4 @ B3 )
% 0.26/0.58            = B3 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb_iff2
% 0.26/0.58  thf(fact_6582_max_Oabsorb__iff1,axiom,
% 0.26/0.58      ( ord_le2932123472753598470d_enat
% 0.26/0.58      = ( ^ [B3: extended_enat,A4: extended_enat] :
% 0.26/0.58            ( ( ord_ma741700101516333627d_enat @ A4 @ B3 )
% 0.26/0.58            = A4 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb_iff1
% 0.26/0.58  thf(fact_6583_max_Oabsorb__iff1,axiom,
% 0.26/0.58      ( ord_le3102999989581377725nteger
% 0.26/0.58      = ( ^ [B3: code_integer,A4: code_integer] :
% 0.26/0.58            ( ( ord_max_Code_integer @ A4 @ B3 )
% 0.26/0.58            = A4 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb_iff1
% 0.26/0.58  thf(fact_6584_max_Oabsorb__iff1,axiom,
% 0.26/0.58      ( ord_less_eq_rat
% 0.26/0.58      = ( ^ [B3: rat,A4: rat] :
% 0.26/0.58            ( ( ord_max_rat @ A4 @ B3 )
% 0.26/0.58            = A4 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb_iff1
% 0.26/0.58  thf(fact_6585_max_Oabsorb__iff1,axiom,
% 0.26/0.58      ( ord_less_eq_num
% 0.26/0.58      = ( ^ [B3: num,A4: num] :
% 0.26/0.58            ( ( ord_max_num @ A4 @ B3 )
% 0.26/0.58            = A4 ) ) ) ).
% 0.26/0.58  
% 0.26/0.58  % max.absorb_iff1
% 0.26/0.58  thf(fact_6586_max_Oabsorb__iff1,axiom,
% 0.26/0.58      ( ord_less_eq_nat
% 0.26/0.58      = ( ^ [B3: nat,A4: nat] :
% 0.26/0.58            ( ( ord_max_nat @ A4 @ B3 )
% 0.26/0.59            = A4 ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.absorb_iff1
% 0.26/0.59  thf(fact_6587_max_Oabsorb__iff1,axiom,
% 0.26/0.59      ( ord_less_eq_int
% 0.26/0.59      = ( ^ [B3: int,A4: int] :
% 0.26/0.59            ( ( ord_max_int @ A4 @ B3 )
% 0.26/0.59            = A4 ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.absorb_iff1
% 0.26/0.59  thf(fact_6588_le__max__iff__disj,axiom,
% 0.26/0.59      ! [Z: extended_enat,X3: extended_enat,Y3: extended_enat] :
% 0.26/0.59        ( ( ord_le2932123472753598470d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X3 @ Y3 ) )
% 0.26/0.59        = ( ( ord_le2932123472753598470d_enat @ Z @ X3 )
% 0.26/0.59          | ( ord_le2932123472753598470d_enat @ Z @ Y3 ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % le_max_iff_disj
% 0.26/0.59  thf(fact_6589_le__max__iff__disj,axiom,
% 0.26/0.59      ! [Z: code_integer,X3: code_integer,Y3: code_integer] :
% 0.26/0.59        ( ( ord_le3102999989581377725nteger @ Z @ ( ord_max_Code_integer @ X3 @ Y3 ) )
% 0.26/0.59        = ( ( ord_le3102999989581377725nteger @ Z @ X3 )
% 0.26/0.59          | ( ord_le3102999989581377725nteger @ Z @ Y3 ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % le_max_iff_disj
% 0.26/0.59  thf(fact_6590_le__max__iff__disj,axiom,
% 0.26/0.59      ! [Z: rat,X3: rat,Y3: rat] :
% 0.26/0.59        ( ( ord_less_eq_rat @ Z @ ( ord_max_rat @ X3 @ Y3 ) )
% 0.26/0.59        = ( ( ord_less_eq_rat @ Z @ X3 )
% 0.26/0.59          | ( ord_less_eq_rat @ Z @ Y3 ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % le_max_iff_disj
% 0.26/0.59  thf(fact_6591_le__max__iff__disj,axiom,
% 0.26/0.59      ! [Z: num,X3: num,Y3: num] :
% 0.26/0.59        ( ( ord_less_eq_num @ Z @ ( ord_max_num @ X3 @ Y3 ) )
% 0.26/0.59        = ( ( ord_less_eq_num @ Z @ X3 )
% 0.26/0.59          | ( ord_less_eq_num @ Z @ Y3 ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % le_max_iff_disj
% 0.26/0.59  thf(fact_6592_le__max__iff__disj,axiom,
% 0.26/0.59      ! [Z: nat,X3: nat,Y3: nat] :
% 0.26/0.59        ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X3 @ Y3 ) )
% 0.26/0.59        = ( ( ord_less_eq_nat @ Z @ X3 )
% 0.26/0.59          | ( ord_less_eq_nat @ Z @ Y3 ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % le_max_iff_disj
% 0.26/0.59  thf(fact_6593_le__max__iff__disj,axiom,
% 0.26/0.59      ! [Z: int,X3: int,Y3: int] :
% 0.26/0.59        ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X3 @ Y3 ) )
% 0.26/0.59        = ( ( ord_less_eq_int @ Z @ X3 )
% 0.26/0.59          | ( ord_less_eq_int @ Z @ Y3 ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % le_max_iff_disj
% 0.26/0.59  thf(fact_6594_max_Ocobounded2,axiom,
% 0.26/0.59      ! [B: extended_enat,A: extended_enat] : ( ord_le2932123472753598470d_enat @ B @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.cobounded2
% 0.26/0.59  thf(fact_6595_max_Ocobounded2,axiom,
% 0.26/0.59      ! [B: code_integer,A: code_integer] : ( ord_le3102999989581377725nteger @ B @ ( ord_max_Code_integer @ A @ B ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.cobounded2
% 0.26/0.59  thf(fact_6596_max_Ocobounded2,axiom,
% 0.26/0.59      ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.cobounded2
% 0.26/0.59  thf(fact_6597_max_Ocobounded2,axiom,
% 0.26/0.59      ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.cobounded2
% 0.26/0.59  thf(fact_6598_max_Ocobounded2,axiom,
% 0.26/0.59      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.cobounded2
% 0.26/0.59  thf(fact_6599_max_Ocobounded2,axiom,
% 0.26/0.59      ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.cobounded2
% 0.26/0.59  thf(fact_6600_max_Ocobounded1,axiom,
% 0.26/0.59      ! [A: extended_enat,B: extended_enat] : ( ord_le2932123472753598470d_enat @ A @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.cobounded1
% 0.26/0.59  thf(fact_6601_max_Ocobounded1,axiom,
% 0.26/0.59      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( ord_max_Code_integer @ A @ B ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.cobounded1
% 0.26/0.59  thf(fact_6602_max_Ocobounded1,axiom,
% 0.26/0.59      ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.cobounded1
% 0.26/0.59  thf(fact_6603_max_Ocobounded1,axiom,
% 0.26/0.59      ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.cobounded1
% 0.26/0.59  thf(fact_6604_max_Ocobounded1,axiom,
% 0.26/0.59      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.cobounded1
% 0.26/0.59  thf(fact_6605_max_Ocobounded1,axiom,
% 0.26/0.59      ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.cobounded1
% 0.26/0.59  thf(fact_6606_max_Oorder__iff,axiom,
% 0.26/0.59      ( ord_le2932123472753598470d_enat
% 0.26/0.59      = ( ^ [B3: extended_enat,A4: extended_enat] :
% 0.26/0.59            ( A4
% 0.26/0.59            = ( ord_ma741700101516333627d_enat @ A4 @ B3 ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.order_iff
% 0.26/0.59  thf(fact_6607_max_Oorder__iff,axiom,
% 0.26/0.59      ( ord_le3102999989581377725nteger
% 0.26/0.59      = ( ^ [B3: code_integer,A4: code_integer] :
% 0.26/0.59            ( A4
% 0.26/0.59            = ( ord_max_Code_integer @ A4 @ B3 ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.order_iff
% 0.26/0.59  thf(fact_6608_max_Oorder__iff,axiom,
% 0.26/0.59      ( ord_less_eq_rat
% 0.26/0.59      = ( ^ [B3: rat,A4: rat] :
% 0.26/0.59            ( A4
% 0.26/0.59            = ( ord_max_rat @ A4 @ B3 ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.order_iff
% 0.26/0.59  thf(fact_6609_max_Oorder__iff,axiom,
% 0.26/0.59      ( ord_less_eq_num
% 0.26/0.59      = ( ^ [B3: num,A4: num] :
% 0.26/0.59            ( A4
% 0.26/0.59            = ( ord_max_num @ A4 @ B3 ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.order_iff
% 0.26/0.59  thf(fact_6610_max_Oorder__iff,axiom,
% 0.26/0.59      ( ord_less_eq_nat
% 0.26/0.59      = ( ^ [B3: nat,A4: nat] :
% 0.26/0.59            ( A4
% 0.26/0.59            = ( ord_max_nat @ A4 @ B3 ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.order_iff
% 0.26/0.59  thf(fact_6611_max_Oorder__iff,axiom,
% 0.26/0.59      ( ord_less_eq_int
% 0.26/0.59      = ( ^ [B3: int,A4: int] :
% 0.26/0.59            ( A4
% 0.26/0.59            = ( ord_max_int @ A4 @ B3 ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.order_iff
% 0.26/0.59  thf(fact_6612_max_OboundedI,axiom,
% 0.26/0.59      ! [B: extended_enat,A: extended_enat,C: extended_enat] :
% 0.26/0.59        ( ( ord_le2932123472753598470d_enat @ B @ A )
% 0.26/0.59       => ( ( ord_le2932123472753598470d_enat @ C @ A )
% 0.26/0.59         => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.boundedI
% 0.26/0.59  thf(fact_6613_max_OboundedI,axiom,
% 0.26/0.59      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.26/0.59        ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.26/0.59       => ( ( ord_le3102999989581377725nteger @ C @ A )
% 0.26/0.59         => ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C ) @ A ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.boundedI
% 0.26/0.59  thf(fact_6614_max_OboundedI,axiom,
% 0.26/0.59      ! [B: rat,A: rat,C: rat] :
% 0.26/0.59        ( ( ord_less_eq_rat @ B @ A )
% 0.26/0.59       => ( ( ord_less_eq_rat @ C @ A )
% 0.26/0.59         => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.boundedI
% 0.26/0.59  thf(fact_6615_max_OboundedI,axiom,
% 0.26/0.59      ! [B: num,A: num,C: num] :
% 0.26/0.59        ( ( ord_less_eq_num @ B @ A )
% 0.26/0.59       => ( ( ord_less_eq_num @ C @ A )
% 0.26/0.59         => ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.boundedI
% 0.26/0.59  thf(fact_6616_max_OboundedI,axiom,
% 0.26/0.59      ! [B: nat,A: nat,C: nat] :
% 0.26/0.59        ( ( ord_less_eq_nat @ B @ A )
% 0.26/0.59       => ( ( ord_less_eq_nat @ C @ A )
% 0.26/0.59         => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.boundedI
% 0.26/0.59  thf(fact_6617_max_OboundedI,axiom,
% 0.26/0.59      ! [B: int,A: int,C: int] :
% 0.26/0.59        ( ( ord_less_eq_int @ B @ A )
% 0.26/0.59       => ( ( ord_less_eq_int @ C @ A )
% 0.26/0.59         => ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.boundedI
% 0.26/0.59  thf(fact_6618_max_OboundedE,axiom,
% 0.26/0.59      ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 0.26/0.59        ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 0.26/0.59       => ~ ( ( ord_le2932123472753598470d_enat @ B @ A )
% 0.26/0.59           => ~ ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.boundedE
% 0.26/0.59  thf(fact_6619_max_OboundedE,axiom,
% 0.26/0.59      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.26/0.59        ( ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 0.26/0.59       => ~ ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.26/0.59           => ~ ( ord_le3102999989581377725nteger @ C @ A ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.boundedE
% 0.26/0.59  thf(fact_6620_max_OboundedE,axiom,
% 0.26/0.59      ! [B: rat,C: rat,A: rat] :
% 0.26/0.59        ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 0.26/0.59       => ~ ( ( ord_less_eq_rat @ B @ A )
% 0.26/0.59           => ~ ( ord_less_eq_rat @ C @ A ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.boundedE
% 0.26/0.59  thf(fact_6621_max_OboundedE,axiom,
% 0.26/0.59      ! [B: num,C: num,A: num] :
% 0.26/0.59        ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 0.26/0.59       => ~ ( ( ord_less_eq_num @ B @ A )
% 0.26/0.59           => ~ ( ord_less_eq_num @ C @ A ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.boundedE
% 0.26/0.59  thf(fact_6622_max_OboundedE,axiom,
% 0.26/0.59      ! [B: nat,C: nat,A: nat] :
% 0.26/0.59        ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 0.26/0.59       => ~ ( ( ord_less_eq_nat @ B @ A )
% 0.26/0.59           => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.boundedE
% 0.26/0.59  thf(fact_6623_max_OboundedE,axiom,
% 0.26/0.59      ! [B: int,C: int,A: int] :
% 0.26/0.59        ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 0.26/0.59       => ~ ( ( ord_less_eq_int @ B @ A )
% 0.26/0.59           => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.boundedE
% 0.26/0.59  thf(fact_6624_max_OorderI,axiom,
% 0.26/0.59      ! [A: extended_enat,B: extended_enat] :
% 0.26/0.59        ( ( A
% 0.26/0.59          = ( ord_ma741700101516333627d_enat @ A @ B ) )
% 0.26/0.59       => ( ord_le2932123472753598470d_enat @ B @ A ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.orderI
% 0.26/0.59  thf(fact_6625_max_OorderI,axiom,
% 0.26/0.59      ! [A: code_integer,B: code_integer] :
% 0.26/0.59        ( ( A
% 0.26/0.59          = ( ord_max_Code_integer @ A @ B ) )
% 0.26/0.59       => ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.orderI
% 0.26/0.59  thf(fact_6626_max_OorderI,axiom,
% 0.26/0.59      ! [A: rat,B: rat] :
% 0.26/0.59        ( ( A
% 0.26/0.59          = ( ord_max_rat @ A @ B ) )
% 0.26/0.59       => ( ord_less_eq_rat @ B @ A ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.orderI
% 0.26/0.59  thf(fact_6627_max_OorderI,axiom,
% 0.26/0.59      ! [A: num,B: num] :
% 0.26/0.59        ( ( A
% 0.26/0.59          = ( ord_max_num @ A @ B ) )
% 0.26/0.59       => ( ord_less_eq_num @ B @ A ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.orderI
% 0.26/0.59  thf(fact_6628_max_OorderI,axiom,
% 0.26/0.59      ! [A: nat,B: nat] :
% 0.26/0.59        ( ( A
% 0.26/0.59          = ( ord_max_nat @ A @ B ) )
% 0.26/0.59       => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.orderI
% 0.26/0.59  thf(fact_6629_max_OorderI,axiom,
% 0.26/0.59      ! [A: int,B: int] :
% 0.26/0.59        ( ( A
% 0.26/0.59          = ( ord_max_int @ A @ B ) )
% 0.26/0.59       => ( ord_less_eq_int @ B @ A ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.orderI
% 0.26/0.59  thf(fact_6630_max_OorderE,axiom,
% 0.26/0.59      ! [B: extended_enat,A: extended_enat] :
% 0.26/0.59        ( ( ord_le2932123472753598470d_enat @ B @ A )
% 0.26/0.59       => ( A
% 0.26/0.59          = ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.orderE
% 0.26/0.59  thf(fact_6631_max_OorderE,axiom,
% 0.26/0.59      ! [B: code_integer,A: code_integer] :
% 0.26/0.59        ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.26/0.59       => ( A
% 0.26/0.59          = ( ord_max_Code_integer @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.orderE
% 0.26/0.59  thf(fact_6632_max_OorderE,axiom,
% 0.26/0.59      ! [B: rat,A: rat] :
% 0.26/0.59        ( ( ord_less_eq_rat @ B @ A )
% 0.26/0.59       => ( A
% 0.26/0.59          = ( ord_max_rat @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.orderE
% 0.26/0.59  thf(fact_6633_max_OorderE,axiom,
% 0.26/0.59      ! [B: num,A: num] :
% 0.26/0.59        ( ( ord_less_eq_num @ B @ A )
% 0.26/0.59       => ( A
% 0.26/0.59          = ( ord_max_num @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.orderE
% 0.26/0.59  thf(fact_6634_max_OorderE,axiom,
% 0.26/0.59      ! [B: nat,A: nat] :
% 0.26/0.59        ( ( ord_less_eq_nat @ B @ A )
% 0.26/0.59       => ( A
% 0.26/0.59          = ( ord_max_nat @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.orderE
% 0.26/0.59  thf(fact_6635_max_OorderE,axiom,
% 0.26/0.59      ! [B: int,A: int] :
% 0.26/0.59        ( ( ord_less_eq_int @ B @ A )
% 0.26/0.59       => ( A
% 0.26/0.59          = ( ord_max_int @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.orderE
% 0.26/0.59  thf(fact_6636_max_Omono,axiom,
% 0.26/0.59      ! [C: extended_enat,A: extended_enat,D3: extended_enat,B: extended_enat] :
% 0.26/0.59        ( ( ord_le2932123472753598470d_enat @ C @ A )
% 0.26/0.59       => ( ( ord_le2932123472753598470d_enat @ D3 @ B )
% 0.26/0.59         => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ C @ D3 ) @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.mono
% 0.26/0.59  thf(fact_6637_max_Omono,axiom,
% 0.26/0.59      ! [C: code_integer,A: code_integer,D3: code_integer,B: code_integer] :
% 0.26/0.59        ( ( ord_le3102999989581377725nteger @ C @ A )
% 0.26/0.59       => ( ( ord_le3102999989581377725nteger @ D3 @ B )
% 0.26/0.59         => ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ C @ D3 ) @ ( ord_max_Code_integer @ A @ B ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.mono
% 0.26/0.59  thf(fact_6638_max_Omono,axiom,
% 0.26/0.59      ! [C: rat,A: rat,D3: rat,B: rat] :
% 0.26/0.59        ( ( ord_less_eq_rat @ C @ A )
% 0.26/0.59       => ( ( ord_less_eq_rat @ D3 @ B )
% 0.26/0.59         => ( ord_less_eq_rat @ ( ord_max_rat @ C @ D3 ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.mono
% 0.26/0.59  thf(fact_6639_max_Omono,axiom,
% 0.26/0.59      ! [C: num,A: num,D3: num,B: num] :
% 0.26/0.59        ( ( ord_less_eq_num @ C @ A )
% 0.26/0.59       => ( ( ord_less_eq_num @ D3 @ B )
% 0.26/0.59         => ( ord_less_eq_num @ ( ord_max_num @ C @ D3 ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.mono
% 0.26/0.59  thf(fact_6640_max_Omono,axiom,
% 0.26/0.59      ! [C: nat,A: nat,D3: nat,B: nat] :
% 0.26/0.59        ( ( ord_less_eq_nat @ C @ A )
% 0.26/0.59       => ( ( ord_less_eq_nat @ D3 @ B )
% 0.26/0.59         => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D3 ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.mono
% 0.26/0.59  thf(fact_6641_max_Omono,axiom,
% 0.26/0.59      ! [C: int,A: int,D3: int,B: int] :
% 0.26/0.59        ( ( ord_less_eq_int @ C @ A )
% 0.26/0.59       => ( ( ord_less_eq_int @ D3 @ B )
% 0.26/0.59         => ( ord_less_eq_int @ ( ord_max_int @ C @ D3 ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.mono
% 0.26/0.59  thf(fact_6642_max_Ostrict__coboundedI2,axiom,
% 0.26/0.59      ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 0.26/0.59        ( ( ord_le72135733267957522d_enat @ C @ B )
% 0.26/0.59       => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_coboundedI2
% 0.26/0.59  thf(fact_6643_max_Ostrict__coboundedI2,axiom,
% 0.26/0.59      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.26/0.59        ( ( ord_le6747313008572928689nteger @ C @ B )
% 0.26/0.59       => ( ord_le6747313008572928689nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_coboundedI2
% 0.26/0.59  thf(fact_6644_max_Ostrict__coboundedI2,axiom,
% 0.26/0.59      ! [C: real,B: real,A: real] :
% 0.26/0.59        ( ( ord_less_real @ C @ B )
% 0.26/0.59       => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_coboundedI2
% 0.26/0.59  thf(fact_6645_max_Ostrict__coboundedI2,axiom,
% 0.26/0.59      ! [C: rat,B: rat,A: rat] :
% 0.26/0.59        ( ( ord_less_rat @ C @ B )
% 0.26/0.59       => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_coboundedI2
% 0.26/0.59  thf(fact_6646_max_Ostrict__coboundedI2,axiom,
% 0.26/0.59      ! [C: num,B: num,A: num] :
% 0.26/0.59        ( ( ord_less_num @ C @ B )
% 0.26/0.59       => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_coboundedI2
% 0.26/0.59  thf(fact_6647_max_Ostrict__coboundedI2,axiom,
% 0.26/0.59      ! [C: nat,B: nat,A: nat] :
% 0.26/0.59        ( ( ord_less_nat @ C @ B )
% 0.26/0.59       => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_coboundedI2
% 0.26/0.59  thf(fact_6648_max_Ostrict__coboundedI2,axiom,
% 0.26/0.59      ! [C: int,B: int,A: int] :
% 0.26/0.59        ( ( ord_less_int @ C @ B )
% 0.26/0.59       => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_coboundedI2
% 0.26/0.59  thf(fact_6649_max_Ostrict__coboundedI1,axiom,
% 0.26/0.59      ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 0.26/0.59        ( ( ord_le72135733267957522d_enat @ C @ A )
% 0.26/0.59       => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_coboundedI1
% 0.26/0.59  thf(fact_6650_max_Ostrict__coboundedI1,axiom,
% 0.26/0.59      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.26/0.59        ( ( ord_le6747313008572928689nteger @ C @ A )
% 0.26/0.59       => ( ord_le6747313008572928689nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_coboundedI1
% 0.26/0.59  thf(fact_6651_max_Ostrict__coboundedI1,axiom,
% 0.26/0.59      ! [C: real,A: real,B: real] :
% 0.26/0.59        ( ( ord_less_real @ C @ A )
% 0.26/0.59       => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_coboundedI1
% 0.26/0.59  thf(fact_6652_max_Ostrict__coboundedI1,axiom,
% 0.26/0.59      ! [C: rat,A: rat,B: rat] :
% 0.26/0.59        ( ( ord_less_rat @ C @ A )
% 0.26/0.59       => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_coboundedI1
% 0.26/0.59  thf(fact_6653_max_Ostrict__coboundedI1,axiom,
% 0.26/0.59      ! [C: num,A: num,B: num] :
% 0.26/0.59        ( ( ord_less_num @ C @ A )
% 0.26/0.59       => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_coboundedI1
% 0.26/0.59  thf(fact_6654_max_Ostrict__coboundedI1,axiom,
% 0.26/0.59      ! [C: nat,A: nat,B: nat] :
% 0.26/0.59        ( ( ord_less_nat @ C @ A )
% 0.26/0.59       => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_coboundedI1
% 0.26/0.59  thf(fact_6655_max_Ostrict__coboundedI1,axiom,
% 0.26/0.59      ! [C: int,A: int,B: int] :
% 0.26/0.59        ( ( ord_less_int @ C @ A )
% 0.26/0.59       => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_coboundedI1
% 0.26/0.59  thf(fact_6656_max_Ostrict__order__iff,axiom,
% 0.26/0.59      ( ord_le72135733267957522d_enat
% 0.26/0.59      = ( ^ [B3: extended_enat,A4: extended_enat] :
% 0.26/0.59            ( ( A4
% 0.26/0.59              = ( ord_ma741700101516333627d_enat @ A4 @ B3 ) )
% 0.26/0.59            & ( A4 != B3 ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_order_iff
% 0.26/0.59  thf(fact_6657_max_Ostrict__order__iff,axiom,
% 0.26/0.59      ( ord_le6747313008572928689nteger
% 0.26/0.59      = ( ^ [B3: code_integer,A4: code_integer] :
% 0.26/0.59            ( ( A4
% 0.26/0.59              = ( ord_max_Code_integer @ A4 @ B3 ) )
% 0.26/0.59            & ( A4 != B3 ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_order_iff
% 0.26/0.59  thf(fact_6658_max_Ostrict__order__iff,axiom,
% 0.26/0.59      ( ord_less_real
% 0.26/0.59      = ( ^ [B3: real,A4: real] :
% 0.26/0.59            ( ( A4
% 0.26/0.59              = ( ord_max_real @ A4 @ B3 ) )
% 0.26/0.59            & ( A4 != B3 ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_order_iff
% 0.26/0.59  thf(fact_6659_max_Ostrict__order__iff,axiom,
% 0.26/0.59      ( ord_less_rat
% 0.26/0.59      = ( ^ [B3: rat,A4: rat] :
% 0.26/0.59            ( ( A4
% 0.26/0.59              = ( ord_max_rat @ A4 @ B3 ) )
% 0.26/0.59            & ( A4 != B3 ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_order_iff
% 0.26/0.59  thf(fact_6660_max_Ostrict__order__iff,axiom,
% 0.26/0.59      ( ord_less_num
% 0.26/0.59      = ( ^ [B3: num,A4: num] :
% 0.26/0.59            ( ( A4
% 0.26/0.59              = ( ord_max_num @ A4 @ B3 ) )
% 0.26/0.59            & ( A4 != B3 ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_order_iff
% 0.26/0.59  thf(fact_6661_max_Ostrict__order__iff,axiom,
% 0.26/0.59      ( ord_less_nat
% 0.26/0.59      = ( ^ [B3: nat,A4: nat] :
% 0.26/0.59            ( ( A4
% 0.26/0.59              = ( ord_max_nat @ A4 @ B3 ) )
% 0.26/0.59            & ( A4 != B3 ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_order_iff
% 0.26/0.59  thf(fact_6662_max_Ostrict__order__iff,axiom,
% 0.26/0.59      ( ord_less_int
% 0.26/0.59      = ( ^ [B3: int,A4: int] :
% 0.26/0.59            ( ( A4
% 0.26/0.59              = ( ord_max_int @ A4 @ B3 ) )
% 0.26/0.59            & ( A4 != B3 ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_order_iff
% 0.26/0.59  thf(fact_6663_max_Ostrict__boundedE,axiom,
% 0.26/0.59      ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 0.26/0.59        ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 0.26/0.59       => ~ ( ( ord_le72135733267957522d_enat @ B @ A )
% 0.26/0.59           => ~ ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_boundedE
% 0.26/0.59  thf(fact_6664_max_Ostrict__boundedE,axiom,
% 0.26/0.59      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.26/0.59        ( ( ord_le6747313008572928689nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 0.26/0.59       => ~ ( ( ord_le6747313008572928689nteger @ B @ A )
% 0.26/0.59           => ~ ( ord_le6747313008572928689nteger @ C @ A ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_boundedE
% 0.26/0.59  thf(fact_6665_max_Ostrict__boundedE,axiom,
% 0.26/0.59      ! [B: real,C: real,A: real] :
% 0.26/0.59        ( ( ord_less_real @ ( ord_max_real @ B @ C ) @ A )
% 0.26/0.59       => ~ ( ( ord_less_real @ B @ A )
% 0.26/0.59           => ~ ( ord_less_real @ C @ A ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_boundedE
% 0.26/0.59  thf(fact_6666_max_Ostrict__boundedE,axiom,
% 0.26/0.59      ! [B: rat,C: rat,A: rat] :
% 0.26/0.59        ( ( ord_less_rat @ ( ord_max_rat @ B @ C ) @ A )
% 0.26/0.59       => ~ ( ( ord_less_rat @ B @ A )
% 0.26/0.59           => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_boundedE
% 0.26/0.59  thf(fact_6667_max_Ostrict__boundedE,axiom,
% 0.26/0.59      ! [B: num,C: num,A: num] :
% 0.26/0.59        ( ( ord_less_num @ ( ord_max_num @ B @ C ) @ A )
% 0.26/0.59       => ~ ( ( ord_less_num @ B @ A )
% 0.26/0.59           => ~ ( ord_less_num @ C @ A ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_boundedE
% 0.26/0.59  thf(fact_6668_max_Ostrict__boundedE,axiom,
% 0.26/0.59      ! [B: nat,C: nat,A: nat] :
% 0.26/0.59        ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
% 0.26/0.59       => ~ ( ( ord_less_nat @ B @ A )
% 0.26/0.59           => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_boundedE
% 0.26/0.59  thf(fact_6669_max_Ostrict__boundedE,axiom,
% 0.26/0.59      ! [B: int,C: int,A: int] :
% 0.26/0.59        ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
% 0.26/0.59       => ~ ( ( ord_less_int @ B @ A )
% 0.26/0.59           => ~ ( ord_less_int @ C @ A ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max.strict_boundedE
% 0.26/0.59  thf(fact_6670_less__max__iff__disj,axiom,
% 0.26/0.59      ! [Z: extended_enat,X3: extended_enat,Y3: extended_enat] :
% 0.26/0.59        ( ( ord_le72135733267957522d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X3 @ Y3 ) )
% 0.26/0.59        = ( ( ord_le72135733267957522d_enat @ Z @ X3 )
% 0.26/0.59          | ( ord_le72135733267957522d_enat @ Z @ Y3 ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % less_max_iff_disj
% 0.26/0.59  thf(fact_6671_less__max__iff__disj,axiom,
% 0.26/0.59      ! [Z: code_integer,X3: code_integer,Y3: code_integer] :
% 0.26/0.59        ( ( ord_le6747313008572928689nteger @ Z @ ( ord_max_Code_integer @ X3 @ Y3 ) )
% 0.26/0.59        = ( ( ord_le6747313008572928689nteger @ Z @ X3 )
% 0.26/0.59          | ( ord_le6747313008572928689nteger @ Z @ Y3 ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % less_max_iff_disj
% 0.26/0.59  thf(fact_6672_less__max__iff__disj,axiom,
% 0.26/0.59      ! [Z: real,X3: real,Y3: real] :
% 0.26/0.59        ( ( ord_less_real @ Z @ ( ord_max_real @ X3 @ Y3 ) )
% 0.26/0.59        = ( ( ord_less_real @ Z @ X3 )
% 0.26/0.59          | ( ord_less_real @ Z @ Y3 ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % less_max_iff_disj
% 0.26/0.59  thf(fact_6673_less__max__iff__disj,axiom,
% 0.26/0.59      ! [Z: rat,X3: rat,Y3: rat] :
% 0.26/0.59        ( ( ord_less_rat @ Z @ ( ord_max_rat @ X3 @ Y3 ) )
% 0.26/0.59        = ( ( ord_less_rat @ Z @ X3 )
% 0.26/0.59          | ( ord_less_rat @ Z @ Y3 ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % less_max_iff_disj
% 0.26/0.59  thf(fact_6674_less__max__iff__disj,axiom,
% 0.26/0.59      ! [Z: num,X3: num,Y3: num] :
% 0.26/0.59        ( ( ord_less_num @ Z @ ( ord_max_num @ X3 @ Y3 ) )
% 0.26/0.59        = ( ( ord_less_num @ Z @ X3 )
% 0.26/0.59          | ( ord_less_num @ Z @ Y3 ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % less_max_iff_disj
% 0.26/0.59  thf(fact_6675_less__max__iff__disj,axiom,
% 0.26/0.59      ! [Z: nat,X3: nat,Y3: nat] :
% 0.26/0.59        ( ( ord_less_nat @ Z @ ( ord_max_nat @ X3 @ Y3 ) )
% 0.26/0.59        = ( ( ord_less_nat @ Z @ X3 )
% 0.26/0.59          | ( ord_less_nat @ Z @ Y3 ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % less_max_iff_disj
% 0.26/0.59  thf(fact_6676_less__max__iff__disj,axiom,
% 0.26/0.59      ! [Z: int,X3: int,Y3: int] :
% 0.26/0.59        ( ( ord_less_int @ Z @ ( ord_max_int @ X3 @ Y3 ) )
% 0.26/0.59        = ( ( ord_less_int @ Z @ X3 )
% 0.26/0.59          | ( ord_less_int @ Z @ Y3 ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % less_max_iff_disj
% 0.26/0.59  thf(fact_6677_or__int__unfold,axiom,
% 0.26/0.59      ( bit_se1409905431419307370or_int
% 0.26/0.59      = ( ^ [K3: int,L2: int] :
% 0.26/0.59            ( if_int
% 0.26/0.59            @ ( ( K3
% 0.26/0.59                = ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.59              | ( L2
% 0.26/0.59                = ( uminus_uminus_int @ one_one_int ) ) )
% 0.26/0.59            @ ( uminus_uminus_int @ one_one_int )
% 0.26/0.59            @ ( if_int @ ( K3 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % or_int_unfold
% 0.26/0.59  thf(fact_6678_insert__bound__size__univ,axiom,
% 0.26/0.59      ! [T: vEBT_VEBT,N: nat,U: real,X3: nat] :
% 0.26/0.59        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.59       => ( ( U
% 0.26/0.59            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.59         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_i_n_s_e_r_t @ T @ X3 ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % insert_bound_size_univ
% 0.26/0.59  thf(fact_6679_pred__less__length__list,axiom,
% 0.26/0.59      ! [Deg: nat,X3: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 0.26/0.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.59       => ( ( ord_less_eq_nat @ X3 @ Ma )
% 0.26/0.59         => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59           => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59              = ( if_option_nat
% 0.26/0.59                @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                   != none_nat )
% 0.26/0.59                  & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.59                @ ( 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 @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                @ ( if_option_nat
% 0.26/0.59                  @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.59                    = none_nat )
% 0.26/0.59                  @ ( if_option_nat @ ( ord_less_nat @ Mi @ X3 ) @ ( some_nat @ Mi ) @ none_nat )
% 0.26/0.59                  @ ( 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 @ X3 @ ( 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 @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % pred_less_length_list
% 0.26/0.59  thf(fact_6680_pred__lesseq__max,axiom,
% 0.26/0.59      ! [Deg: nat,X3: nat,Ma: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.26/0.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.59       => ( ( ord_less_eq_nat @ X3 @ Ma )
% 0.26/0.59         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59              @ ( if_option_nat
% 0.26/0.59                @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                   != none_nat )
% 0.26/0.59                  & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.59                @ ( 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 @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                @ ( if_option_nat
% 0.26/0.59                  @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.59                    = none_nat )
% 0.26/0.59                  @ ( if_option_nat @ ( ord_less_nat @ Mi @ X3 ) @ ( some_nat @ Mi ) @ none_nat )
% 0.26/0.59                  @ ( 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 @ X3 @ ( 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 @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.59              @ none_nat ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % pred_lesseq_max
% 0.26/0.59  thf(fact_6681_succ__greatereq__min,axiom,
% 0.26/0.59      ! [Deg: nat,Mi: nat,X3: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.26/0.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.59       => ( ( ord_less_eq_nat @ Mi @ X3 )
% 0.26/0.59         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59              @ ( if_option_nat
% 0.26/0.59                @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                   != none_nat )
% 0.26/0.59                  & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.59                @ ( 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 @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                @ ( if_option_nat
% 0.26/0.59                  @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.59                    = none_nat )
% 0.26/0.59                  @ none_nat
% 0.26/0.59                  @ ( 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 @ X3 @ ( 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 @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.59              @ none_nat ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % succ_greatereq_min
% 0.26/0.59  thf(fact_6682_succ__less__length__list,axiom,
% 0.26/0.59      ! [Deg: nat,Mi: nat,X3: nat,TreeList2: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 0.26/0.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.59       => ( ( ord_less_eq_nat @ Mi @ X3 )
% 0.26/0.59         => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59           => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59              = ( if_option_nat
% 0.26/0.59                @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                   != none_nat )
% 0.26/0.59                  & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.59                @ ( 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 @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                @ ( if_option_nat
% 0.26/0.59                  @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.59                    = none_nat )
% 0.26/0.59                  @ none_nat
% 0.26/0.59                  @ ( 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 @ X3 @ ( 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 @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % succ_less_length_list
% 0.26/0.59  thf(fact_6683_set__vebt_H__def,axiom,
% 0.26/0.59      ( vEBT_VEBT_set_vebt
% 0.26/0.59      = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % set_vebt'_def
% 0.26/0.59  thf(fact_6684_del__x__not__mia,axiom,
% 0.26/0.59      ! [Mi: nat,X3: nat,Ma: nat,Deg: nat,H2: nat,L: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.26/0.59        ( ( ( ord_less_nat @ Mi @ X3 )
% 0.26/0.59          & ( ord_less_eq_nat @ X3 @ Ma ) )
% 0.26/0.59       => ( ( Mi != Ma )
% 0.26/0.59         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.59           => ( ( ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.59                = H2 )
% 0.26/0.59             => ( ( ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.59                  = L )
% 0.26/0.59               => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59                 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59                    = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 0.26/0.59                      @ ( vEBT_Node
% 0.26/0.59                        @ ( some_P7363390416028606310at_nat
% 0.26/0.59                          @ ( product_Pair_nat_nat @ Mi
% 0.26/0.59                            @ ( if_nat @ ( X3 = Ma )
% 0.26/0.59                              @ ( if_nat
% 0.26/0.59                                @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.26/0.59                                  = none_nat )
% 0.26/0.59                                @ Mi
% 0.26/0.59                                @ ( 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 ) @ L ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 0.26/0.59                              @ Ma ) ) )
% 0.26/0.59                        @ Deg
% 0.26/0.59                        @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 0.26/0.59                        @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.26/0.59                      @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X3 = 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 ) @ L ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) ) @ Summary ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % del_x_not_mia
% 0.26/0.59  thf(fact_6685_del__x__not__mi__new__node__nil,axiom,
% 0.26/0.59      ! [Mi: nat,X3: nat,Ma: nat,Deg: nat,H2: nat,L: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Sn: vEBT_VEBT,Summary: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 0.26/0.59        ( ( ( ord_less_nat @ Mi @ X3 )
% 0.26/0.59          & ( ord_less_eq_nat @ X3 @ Ma ) )
% 0.26/0.59       => ( ( Mi != Ma )
% 0.26/0.59         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.59           => ( ( ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.59                = H2 )
% 0.26/0.59             => ( ( ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.59                  = L )
% 0.26/0.59               => ( ( Newnode
% 0.26/0.59                    = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 0.26/0.59                 => ( ( vEBT_VEBT_minNull @ Newnode )
% 0.26/0.59                   => ( ( Sn
% 0.26/0.59                        = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.26/0.59                     => ( ( Newlist
% 0.26/0.59                          = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 0.26/0.59                       => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59                            = ( vEBT_Node
% 0.26/0.59                              @ ( some_P7363390416028606310at_nat
% 0.26/0.59                                @ ( product_Pair_nat_nat @ Mi
% 0.26/0.59                                  @ ( if_nat @ ( X3 = Ma )
% 0.26/0.59                                    @ ( if_nat
% 0.26/0.59                                      @ ( ( vEBT_vebt_maxt @ Sn )
% 0.26/0.59                                        = none_nat )
% 0.26/0.59                                      @ Mi
% 0.26/0.59                                      @ ( 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 ) ) ) ) ) ) )
% 0.26/0.59                                    @ Ma ) ) )
% 0.26/0.59                              @ Deg
% 0.26/0.59                              @ Newlist
% 0.26/0.59                              @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % del_x_not_mi_new_node_nil
% 0.26/0.59  thf(fact_6686_del__x__not__mi,axiom,
% 0.26/0.59      ! [Mi: nat,X3: nat,Ma: nat,Deg: nat,H2: nat,L: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.26/0.59        ( ( ( ord_less_nat @ Mi @ X3 )
% 0.26/0.59          & ( ord_less_eq_nat @ X3 @ Ma ) )
% 0.26/0.59       => ( ( Mi != Ma )
% 0.26/0.59         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.59           => ( ( ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.59                = H2 )
% 0.26/0.59             => ( ( ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.59                  = L )
% 0.26/0.59               => ( ( Newnode
% 0.26/0.59                    = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 0.26/0.59                 => ( ( Newlist
% 0.26/0.59                      = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 0.26/0.59                   => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59                     => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 0.26/0.59                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59                            = ( vEBT_Node
% 0.26/0.59                              @ ( some_P7363390416028606310at_nat
% 0.26/0.59                                @ ( product_Pair_nat_nat @ Mi
% 0.26/0.59                                  @ ( if_nat @ ( X3 = Ma )
% 0.26/0.59                                    @ ( if_nat
% 0.26/0.59                                      @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.26/0.59                                        = none_nat )
% 0.26/0.59                                      @ Mi
% 0.26/0.59                                      @ ( 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 ) ) ) ) ) ) ) )
% 0.26/0.59                                    @ Ma ) ) )
% 0.26/0.59                              @ Deg
% 0.26/0.59                              @ Newlist
% 0.26/0.59                              @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 0.26/0.59                        & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 0.26/0.59                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % del_x_not_mi
% 0.26/0.59  thf(fact_6687_del__x__mia,axiom,
% 0.26/0.59      ! [X3: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.26/0.59        ( ( ( X3 = Mi )
% 0.26/0.59          & ( ord_less_nat @ X3 @ Ma ) )
% 0.26/0.59       => ( ( Mi != Ma )
% 0.26/0.59         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.59           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59              = ( 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 ) )
% 0.26/0.59                @ ( 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 ) ) ) ) ) )
% 0.26/0.59                  @ ( vEBT_Node
% 0.26/0.59                    @ ( some_P7363390416028606310at_nat
% 0.26/0.59                      @ ( 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 ) ) ) ) ) )
% 0.26/0.59                        @ ( if_nat
% 0.26/0.59                          @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_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 ) ) ) ) ) )
% 0.26/0.59                            = Ma )
% 0.26/0.59                          @ ( if_nat
% 0.26/0.59                            @ ( ( 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 ) ) ) ) ) )
% 0.26/0.59                              = none_nat )
% 0.26/0.59                            @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_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 ) ) ) ) ) )
% 0.26/0.59                            @ ( 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 ) ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.59                          @ Ma ) ) )
% 0.26/0.59                    @ Deg
% 0.26/0.59                    @ ( 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 ) ) ) ) ) )
% 0.26/0.59                    @ ( 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 ) ) ) ) ) )
% 0.26/0.59                  @ ( vEBT_Node
% 0.26/0.59                    @ ( some_P7363390416028606310at_nat
% 0.26/0.59                      @ ( 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 ) ) ) ) ) )
% 0.26/0.59                        @ ( if_nat
% 0.26/0.59                          @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_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 ) ) ) ) ) )
% 0.26/0.59                            = Ma )
% 0.26/0.59                          @ ( 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 ) ) ) ) ) ) ) )
% 0.26/0.59                          @ Ma ) ) )
% 0.26/0.59                    @ Deg
% 0.26/0.59                    @ ( 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 ) ) ) ) ) )
% 0.26/0.59                    @ Summary ) )
% 0.26/0.59                @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % del_x_mia
% 0.26/0.59  thf(fact_6688_del__x__mi__lets__in__minNull,axiom,
% 0.26/0.59      ! [X3: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT,Sn: vEBT_VEBT] :
% 0.26/0.59        ( ( ( X3 = Mi )
% 0.26/0.59          & ( ord_less_nat @ X3 @ Ma ) )
% 0.26/0.59       => ( ( Mi != Ma )
% 0.26/0.59         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.59           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.59                = H2 )
% 0.26/0.59             => ( ( Xn
% 0.26/0.59                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_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 ) ) ) ) ) ) )
% 0.26/0.59               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.59                    = L )
% 0.26/0.59                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59                   => ( ( Newnode
% 0.26/0.59                        = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 0.26/0.59                     => ( ( Newlist
% 0.26/0.59                          = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 0.26/0.59                       => ( ( vEBT_VEBT_minNull @ Newnode )
% 0.26/0.59                         => ( ( Sn
% 0.26/0.59                              = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.26/0.59                           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59                              = ( vEBT_Node
% 0.26/0.59                                @ ( some_P7363390416028606310at_nat
% 0.26/0.59                                  @ ( product_Pair_nat_nat @ Xn
% 0.26/0.59                                    @ ( if_nat @ ( Xn = Ma )
% 0.26/0.59                                      @ ( if_nat
% 0.26/0.59                                        @ ( ( vEBT_vebt_maxt @ Sn )
% 0.26/0.59                                          = none_nat )
% 0.26/0.59                                        @ Xn
% 0.26/0.59                                        @ ( 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 ) ) ) ) ) ) )
% 0.26/0.59                                      @ Ma ) ) )
% 0.26/0.59                                @ Deg
% 0.26/0.59                                @ Newlist
% 0.26/0.59                                @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % del_x_mi_lets_in_minNull
% 0.26/0.59  thf(fact_6689_del__x__mi__lets__in,axiom,
% 0.26/0.59      ! [X3: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 0.26/0.59        ( ( ( X3 = Mi )
% 0.26/0.59          & ( ord_less_nat @ X3 @ Ma ) )
% 0.26/0.59       => ( ( Mi != Ma )
% 0.26/0.59         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.59           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.59                = H2 )
% 0.26/0.59             => ( ( Xn
% 0.26/0.59                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_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 ) ) ) ) ) ) )
% 0.26/0.59               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.59                    = L )
% 0.26/0.59                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59                   => ( ( Newnode
% 0.26/0.59                        = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 0.26/0.59                     => ( ( Newlist
% 0.26/0.59                          = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 0.26/0.59                       => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 0.26/0.59                           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59                              = ( vEBT_Node
% 0.26/0.59                                @ ( some_P7363390416028606310at_nat
% 0.26/0.59                                  @ ( product_Pair_nat_nat @ Xn
% 0.26/0.59                                    @ ( if_nat @ ( Xn = Ma )
% 0.26/0.59                                      @ ( if_nat
% 0.26/0.59                                        @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.26/0.59                                          = none_nat )
% 0.26/0.59                                        @ Xn
% 0.26/0.59                                        @ ( 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 ) ) ) ) ) ) ) )
% 0.26/0.59                                      @ Ma ) ) )
% 0.26/0.59                                @ Deg
% 0.26/0.59                                @ Newlist
% 0.26/0.59                                @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 0.26/0.59                          & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 0.26/0.59                           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59                              = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % del_x_mi_lets_in
% 0.26/0.59  thf(fact_6690_del__x__mi,axiom,
% 0.26/0.59      ! [X3: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat] :
% 0.26/0.59        ( ( ( X3 = Mi )
% 0.26/0.59          & ( ord_less_nat @ X3 @ Ma ) )
% 0.26/0.59       => ( ( Mi != Ma )
% 0.26/0.59         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.59           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.59                = H2 )
% 0.26/0.59             => ( ( Xn
% 0.26/0.59                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_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 ) ) ) ) ) ) )
% 0.26/0.59               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.59                    = L )
% 0.26/0.59                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59                   => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59                      = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 0.26/0.59                        @ ( vEBT_Node
% 0.26/0.59                          @ ( some_P7363390416028606310at_nat
% 0.26/0.59                            @ ( product_Pair_nat_nat @ Xn
% 0.26/0.59                              @ ( if_nat @ ( Xn = Ma )
% 0.26/0.59                                @ ( if_nat
% 0.26/0.59                                  @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.26/0.59                                    = none_nat )
% 0.26/0.59                                  @ Xn
% 0.26/0.59                                  @ ( 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 ) @ L ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 0.26/0.59                                @ Ma ) ) )
% 0.26/0.59                          @ Deg
% 0.26/0.59                          @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 0.26/0.59                          @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.26/0.59                        @ ( 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 ) @ L ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) ) @ Summary ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % del_x_mi
% 0.26/0.59  thf(fact_6691_del__in__range,axiom,
% 0.26/0.59      ! [Mi: nat,X3: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.26/0.59        ( ( ( ord_less_eq_nat @ Mi @ X3 )
% 0.26/0.59          & ( ord_less_eq_nat @ X3 @ Ma ) )
% 0.26/0.59       => ( ( Mi != Ma )
% 0.26/0.59         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.26/0.59           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59              = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59                @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                  @ ( vEBT_Node
% 0.26/0.59                    @ ( some_P7363390416028606310at_nat
% 0.26/0.59                      @ ( product_Pair_nat_nat @ ( if_nat @ ( X3 = Mi ) @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ Mi )
% 0.26/0.59                        @ ( if_nat
% 0.26/0.59                          @ ( ( ( X3 = Mi )
% 0.26/0.59                             => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_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 ) ) ) ) ) )
% 0.26/0.59                                = Ma ) )
% 0.26/0.59                            & ( ( X3 != Mi )
% 0.26/0.59                             => ( X3 = Ma ) ) )
% 0.26/0.59                          @ ( if_nat
% 0.26/0.59                            @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                              = none_nat )
% 0.26/0.59                            @ ( if_nat @ ( X3 = Mi ) @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ Mi )
% 0.26/0.59                            @ ( 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 @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( 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 @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.59                          @ Ma ) ) )
% 0.26/0.59                    @ Deg
% 0.26/0.59                    @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                    @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                  @ ( vEBT_Node
% 0.26/0.59                    @ ( some_P7363390416028606310at_nat
% 0.26/0.59                      @ ( product_Pair_nat_nat @ ( if_nat @ ( X3 = Mi ) @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ Mi )
% 0.26/0.59                        @ ( if_nat
% 0.26/0.59                          @ ( ( ( X3 = Mi )
% 0.26/0.59                             => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_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 ) ) ) ) ) )
% 0.26/0.59                                = Ma ) )
% 0.26/0.59                            & ( ( X3 != Mi )
% 0.26/0.59                             => ( X3 = Ma ) ) )
% 0.26/0.59                          @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( 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 @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.59                          @ Ma ) ) )
% 0.26/0.59                    @ Deg
% 0.26/0.59                    @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                    @ Summary ) )
% 0.26/0.59                @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % del_in_range
% 0.26/0.59  thf(fact_6692_max__def__raw,axiom,
% 0.26/0.59      ( ord_ma741700101516333627d_enat
% 0.26/0.59      = ( ^ [A4: extended_enat,B3: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max_def_raw
% 0.26/0.59  thf(fact_6693_max__def__raw,axiom,
% 0.26/0.59      ( ord_max_Code_integer
% 0.26/0.59      = ( ^ [A4: code_integer,B3: code_integer] : ( if_Code_integer @ ( ord_le3102999989581377725nteger @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max_def_raw
% 0.26/0.59  thf(fact_6694_max__def__raw,axiom,
% 0.26/0.59      ( ord_max_set_nat
% 0.26/0.59      = ( ^ [A4: set_nat,B3: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max_def_raw
% 0.26/0.59  thf(fact_6695_max__def__raw,axiom,
% 0.26/0.59      ( ord_max_rat
% 0.26/0.59      = ( ^ [A4: rat,B3: rat] : ( if_rat @ ( ord_less_eq_rat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max_def_raw
% 0.26/0.59  thf(fact_6696_max__def__raw,axiom,
% 0.26/0.59      ( ord_max_num
% 0.26/0.59      = ( ^ [A4: num,B3: num] : ( if_num @ ( ord_less_eq_num @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max_def_raw
% 0.26/0.59  thf(fact_6697_max__def__raw,axiom,
% 0.26/0.59      ( ord_max_nat
% 0.26/0.59      = ( ^ [A4: nat,B3: nat] : ( if_nat @ ( ord_less_eq_nat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max_def_raw
% 0.26/0.59  thf(fact_6698_max__def__raw,axiom,
% 0.26/0.59      ( ord_max_int
% 0.26/0.59      = ( ^ [A4: int,B3: int] : ( if_int @ ( ord_less_eq_int @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % max_def_raw
% 0.26/0.59  thf(fact_6699_lambda__zero,axiom,
% 0.26/0.59      ( ( ^ [H: real] : zero_zero_real )
% 0.26/0.59      = ( times_times_real @ zero_zero_real ) ) ).
% 0.26/0.59  
% 0.26/0.59  % lambda_zero
% 0.26/0.59  thf(fact_6700_lambda__zero,axiom,
% 0.26/0.59      ( ( ^ [H: rat] : zero_zero_rat )
% 0.26/0.59      = ( times_times_rat @ zero_zero_rat ) ) ).
% 0.26/0.59  
% 0.26/0.59  % lambda_zero
% 0.26/0.59  thf(fact_6701_lambda__zero,axiom,
% 0.26/0.59      ( ( ^ [H: nat] : zero_zero_nat )
% 0.26/0.59      = ( times_times_nat @ zero_zero_nat ) ) ).
% 0.26/0.59  
% 0.26/0.59  % lambda_zero
% 0.26/0.59  thf(fact_6702_lambda__zero,axiom,
% 0.26/0.59      ( ( ^ [H: int] : zero_zero_int )
% 0.26/0.59      = ( times_times_int @ zero_zero_int ) ) ).
% 0.26/0.59  
% 0.26/0.59  % lambda_zero
% 0.26/0.59  thf(fact_6703_numeral__code_I2_J,axiom,
% 0.26/0.59      ! [N: num] :
% 0.26/0.59        ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 0.26/0.59        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % numeral_code(2)
% 0.26/0.59  thf(fact_6704_numeral__code_I2_J,axiom,
% 0.26/0.59      ! [N: num] :
% 0.26/0.59        ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 0.26/0.59        = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % numeral_code(2)
% 0.26/0.59  thf(fact_6705_numeral__code_I2_J,axiom,
% 0.26/0.59      ! [N: num] :
% 0.26/0.59        ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 0.26/0.59        = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % numeral_code(2)
% 0.26/0.59  thf(fact_6706_numeral__code_I2_J,axiom,
% 0.26/0.59      ! [N: num] :
% 0.26/0.59        ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 0.26/0.59        = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % numeral_code(2)
% 0.26/0.59  thf(fact_6707_numeral__code_I2_J,axiom,
% 0.26/0.59      ! [N: num] :
% 0.26/0.59        ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 0.26/0.59        = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % numeral_code(2)
% 0.26/0.59  thf(fact_6708_nat__less__as__int,axiom,
% 0.26/0.59      ( ord_less_nat
% 0.26/0.59      = ( ^ [A4: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % nat_less_as_int
% 0.26/0.59  thf(fact_6709_nat__leq__as__int,axiom,
% 0.26/0.59      ( ord_less_eq_nat
% 0.26/0.59      = ( ^ [A4: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % nat_leq_as_int
% 0.26/0.59  thf(fact_6710_numeral__code_I3_J,axiom,
% 0.26/0.59      ! [N: num] :
% 0.26/0.59        ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 0.26/0.59        = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 0.26/0.59  
% 0.26/0.59  % numeral_code(3)
% 0.26/0.59  thf(fact_6711_numeral__code_I3_J,axiom,
% 0.26/0.59      ! [N: num] :
% 0.26/0.59        ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 0.26/0.59        = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 0.26/0.59  
% 0.26/0.59  % numeral_code(3)
% 0.26/0.59  thf(fact_6712_numeral__code_I3_J,axiom,
% 0.26/0.59      ! [N: num] :
% 0.26/0.59        ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 0.26/0.59        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 0.26/0.59  
% 0.26/0.59  % numeral_code(3)
% 0.26/0.59  thf(fact_6713_numeral__code_I3_J,axiom,
% 0.26/0.59      ! [N: num] :
% 0.26/0.59        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 0.26/0.59        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 0.26/0.59  
% 0.26/0.59  % numeral_code(3)
% 0.26/0.59  thf(fact_6714_numeral__code_I3_J,axiom,
% 0.26/0.59      ! [N: num] :
% 0.26/0.59        ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 0.26/0.59        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 0.26/0.59  
% 0.26/0.59  % numeral_code(3)
% 0.26/0.59  thf(fact_6715_power__numeral__even,axiom,
% 0.26/0.59      ! [Z: complex,W: num] :
% 0.26/0.59        ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.26/0.59        = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % power_numeral_even
% 0.26/0.59  thf(fact_6716_power__numeral__even,axiom,
% 0.26/0.59      ! [Z: real,W: num] :
% 0.26/0.59        ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.26/0.59        = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % power_numeral_even
% 0.26/0.59  thf(fact_6717_power__numeral__even,axiom,
% 0.26/0.59      ! [Z: rat,W: num] :
% 0.26/0.59        ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.26/0.59        = ( times_times_rat @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % power_numeral_even
% 0.26/0.59  thf(fact_6718_power__numeral__even,axiom,
% 0.26/0.59      ! [Z: nat,W: num] :
% 0.26/0.59        ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.26/0.59        = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % power_numeral_even
% 0.26/0.59  thf(fact_6719_power__numeral__even,axiom,
% 0.26/0.59      ! [Z: int,W: num] :
% 0.26/0.59        ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.26/0.59        = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % power_numeral_even
% 0.26/0.59  thf(fact_6720_power__numeral__odd,axiom,
% 0.26/0.59      ! [Z: complex,W: num] :
% 0.26/0.59        ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.26/0.59        = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % power_numeral_odd
% 0.26/0.59  thf(fact_6721_power__numeral__odd,axiom,
% 0.26/0.59      ! [Z: real,W: num] :
% 0.26/0.59        ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.26/0.59        = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % power_numeral_odd
% 0.26/0.59  thf(fact_6722_power__numeral__odd,axiom,
% 0.26/0.59      ! [Z: rat,W: num] :
% 0.26/0.59        ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.26/0.59        = ( times_times_rat @ ( times_times_rat @ Z @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % power_numeral_odd
% 0.26/0.59  thf(fact_6723_power__numeral__odd,axiom,
% 0.26/0.59      ! [Z: nat,W: num] :
% 0.26/0.59        ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.26/0.59        = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % power_numeral_odd
% 0.26/0.59  thf(fact_6724_power__numeral__odd,axiom,
% 0.26/0.59      ! [Z: int,W: num] :
% 0.26/0.59        ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.26/0.59        = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % power_numeral_odd
% 0.26/0.59  thf(fact_6725_nat__plus__as__int,axiom,
% 0.26/0.59      ( plus_plus_nat
% 0.26/0.59      = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % nat_plus_as_int
% 0.26/0.59  thf(fact_6726_nat__times__as__int,axiom,
% 0.26/0.59      ( times_times_nat
% 0.26/0.59      = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % nat_times_as_int
% 0.26/0.59  thf(fact_6727_nat__minus__as__int,axiom,
% 0.26/0.59      ( minus_minus_nat
% 0.26/0.59      = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % nat_minus_as_int
% 0.26/0.59  thf(fact_6728_nat__div__as__int,axiom,
% 0.26/0.59      ( divide_divide_nat
% 0.26/0.59      = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % nat_div_as_int
% 0.26/0.59  thf(fact_6729_nat__mod__as__int,axiom,
% 0.26/0.59      ( modulo_modulo_nat
% 0.26/0.59      = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % nat_mod_as_int
% 0.26/0.59  thf(fact_6730_diff__nat__eq__if,axiom,
% 0.26/0.59      ! [Z5: int,Z: int] :
% 0.26/0.59        ( ( ( ord_less_int @ Z5 @ zero_zero_int )
% 0.26/0.59         => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z5 ) )
% 0.26/0.59            = ( nat2 @ Z ) ) )
% 0.26/0.59        & ( ~ ( ord_less_int @ Z5 @ zero_zero_int )
% 0.26/0.59         => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z5 ) )
% 0.26/0.59            = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z5 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z5 ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % diff_nat_eq_if
% 0.26/0.59  thf(fact_6731_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I2_J,axiom,
% 0.26/0.59      ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 0.26/0.59        ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S ) @ X3 )
% 0.26/0.59        = one_one_nat ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(2)
% 0.26/0.59  thf(fact_6732_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I3_J,axiom,
% 0.26/0.59      ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 0.26/0.59        ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ X3 )
% 0.26/0.59        = one_one_nat ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(3)
% 0.26/0.59  thf(fact_6733_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I1_J,axiom,
% 0.26/0.59      ! [A: $o,B: $o,X3: nat] :
% 0.26/0.59        ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 0.26/0.59        = ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( X3 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(1)
% 0.26/0.59  thf(fact_6734_vebt__member_Osimps_I5_J,axiom,
% 0.26/0.59      ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 0.26/0.59        ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59        = ( ( X3 != Mi )
% 0.26/0.59         => ( ( X3 != Ma )
% 0.26/0.59           => ( ~ ( ord_less_nat @ X3 @ Mi )
% 0.26/0.59              & ( ~ ( ord_less_nat @ X3 @ Mi )
% 0.26/0.59               => ( ~ ( ord_less_nat @ Ma @ X3 )
% 0.26/0.59                  & ( ~ ( ord_less_nat @ Ma @ X3 )
% 0.26/0.59                   => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59                       => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                      & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % vebt_member.simps(5)
% 0.26/0.59  thf(fact_6735_vebt__member_Oelims_I2_J,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat] :
% 0.26/0.59        ( ( vEBT_vebt_member @ X3 @ Xa )
% 0.26/0.59       => ( ! [A5: $o,B4: $o] :
% 0.26/0.59              ( ( X3
% 0.26/0.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59             => ~ ( ( ( Xa = zero_zero_nat )
% 0.26/0.59                   => A5 )
% 0.26/0.59                  & ( ( Xa != zero_zero_nat )
% 0.26/0.59                   => ( ( ( Xa = one_one_nat )
% 0.26/0.59                       => B4 )
% 0.26/0.59                      & ( Xa = one_one_nat ) ) ) ) )
% 0.26/0.59         => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT] :
% 0.26/0.59                ( ? [Summary2: vEBT_VEBT] :
% 0.26/0.59                    ( X3
% 0.26/0.59                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59               => ~ ( ( Xa != Mi2 )
% 0.26/0.59                   => ( ( Xa != Ma2 )
% 0.26/0.59                     => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.59                        & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.59                         => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 0.26/0.59                            & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 0.26/0.59                             => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                                 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % vebt_member.elims(2)
% 0.26/0.59  thf(fact_6736_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I5_J,axiom,
% 0.26/0.59      ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 0.26/0.59        ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X3 = Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( X3 = Ma ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma @ X3 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(5)
% 0.26/0.59  thf(fact_6737_vebt__member_Oelims_I1_J,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: $o] :
% 0.26/0.59        ( ( ( vEBT_vebt_member @ X3 @ Xa )
% 0.26/0.59          = Y3 )
% 0.26/0.59       => ( ! [A5: $o,B4: $o] :
% 0.26/0.59              ( ( X3
% 0.26/0.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59             => ( Y3
% 0.26/0.59                = ( ~ ( ( ( Xa = zero_zero_nat )
% 0.26/0.59                       => A5 )
% 0.26/0.59                      & ( ( Xa != zero_zero_nat )
% 0.26/0.59                       => ( ( ( Xa = one_one_nat )
% 0.26/0.59                           => B4 )
% 0.26/0.59                          & ( Xa = one_one_nat ) ) ) ) ) ) )
% 0.26/0.59         => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.26/0.59                  ( X3
% 0.26/0.59                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.26/0.59             => Y3 )
% 0.26/0.59           => ( ( ? [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.26/0.59                    ( X3
% 0.26/0.59                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.26/0.59               => Y3 )
% 0.26/0.59             => ( ( ? [V3: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.26/0.59                      ( X3
% 0.26/0.59                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) )
% 0.26/0.59                 => Y3 )
% 0.26/0.59               => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT] :
% 0.26/0.59                      ( ? [Summary2: vEBT_VEBT] :
% 0.26/0.59                          ( X3
% 0.26/0.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                     => ( Y3
% 0.26/0.59                        = ( ~ ( ( Xa != Mi2 )
% 0.26/0.59                             => ( ( Xa != Ma2 )
% 0.26/0.59                               => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.59                                  & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.59                                   => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 0.26/0.59                                      & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 0.26/0.59                                       => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                                           => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % vebt_member.elims(1)
% 0.26/0.59  thf(fact_6738_vebt__member_Oelims_I3_J,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat] :
% 0.26/0.59        ( ~ ( vEBT_vebt_member @ X3 @ Xa )
% 0.26/0.59       => ( ! [A5: $o,B4: $o] :
% 0.26/0.59              ( ( X3
% 0.26/0.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59             => ( ( ( Xa = zero_zero_nat )
% 0.26/0.59                 => A5 )
% 0.26/0.59                & ( ( Xa != zero_zero_nat )
% 0.26/0.59                 => ( ( ( Xa = one_one_nat )
% 0.26/0.59                     => B4 )
% 0.26/0.59                    & ( Xa = one_one_nat ) ) ) ) )
% 0.26/0.59         => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.26/0.59                ( X3
% 0.26/0.59               != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.26/0.59           => ( ! [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.26/0.59                  ( X3
% 0.26/0.59                 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.26/0.59             => ( ! [V3: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.26/0.59                    ( X3
% 0.26/0.59                   != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) )
% 0.26/0.59               => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT] :
% 0.26/0.59                      ( ? [Summary2: vEBT_VEBT] :
% 0.26/0.59                          ( X3
% 0.26/0.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                     => ( ( Xa != Mi2 )
% 0.26/0.59                       => ( ( Xa != Ma2 )
% 0.26/0.59                         => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.59                            & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.59                             => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 0.26/0.59                                & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 0.26/0.59                                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                                     => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % vebt_member.elims(3)
% 0.26/0.59  thf(fact_6739_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I4_J,axiom,
% 0.26/0.59      ! [V: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 0.26/0.59        ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59        = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(4)
% 0.26/0.59  thf(fact_6740_insersimp,axiom,
% 0.26/0.59      ! [T: vEBT_VEBT,N: nat,Y3: nat] :
% 0.26/0.59        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.59       => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 )
% 0.26/0.59         => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ Y3 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % insersimp
% 0.26/0.59  thf(fact_6741_insertsimp,axiom,
% 0.26/0.59      ! [T: vEBT_VEBT,N: nat,L: nat] :
% 0.26/0.59        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.59       => ( ( vEBT_VEBT_minNull @ T )
% 0.26/0.59         => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ L ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % insertsimp
% 0.26/0.59  thf(fact_6742_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Oelims,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 0.26/0.59        ( ( ( vEBT_T_m_e_m_b_e_r @ X3 @ Xa )
% 0.26/0.59          = Y3 )
% 0.26/0.59       => ( ( ? [A5: $o,B4: $o] :
% 0.26/0.59                ( X3
% 0.26/0.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59           => ( Y3
% 0.26/0.59             != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 0.26/0.59         => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.26/0.59                  ( X3
% 0.26/0.59                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.26/0.59             => ( Y3
% 0.26/0.59               != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.59           => ( ( ? [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.26/0.59                    ( X3
% 0.26/0.59                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.26/0.59               => ( Y3
% 0.26/0.59                 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.59             => ( ( ? [V3: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.26/0.59                      ( X3
% 0.26/0.59                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) )
% 0.26/0.59                 => ( Y3
% 0.26/0.59                   != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.59               => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT] :
% 0.26/0.59                      ( ? [Summary2: vEBT_VEBT] :
% 0.26/0.59                          ( X3
% 0.26/0.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                     => ( Y3
% 0.26/0.59                       != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa = Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.elims
% 0.26/0.59  thf(fact_6743_vebt__succ_Osimps_I6_J,axiom,
% 0.26/0.59      ! [X3: nat,Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.26/0.59        ( ( ( ord_less_nat @ X3 @ Mi )
% 0.26/0.59         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59            = ( some_nat @ Mi ) ) )
% 0.26/0.59        & ( ~ ( ord_less_nat @ X3 @ Mi )
% 0.26/0.59         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59              @ ( if_option_nat
% 0.26/0.59                @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                   != none_nat )
% 0.26/0.59                  & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.59                @ ( 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 @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                @ ( if_option_nat
% 0.26/0.59                  @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.59                    = none_nat )
% 0.26/0.59                  @ none_nat
% 0.26/0.59                  @ ( 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 @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.59              @ none_nat ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % vebt_succ.simps(6)
% 0.26/0.59  thf(fact_6744_vebt__pred_Osimps_I7_J,axiom,
% 0.26/0.59      ! [Ma: nat,X3: nat,Mi: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.26/0.59        ( ( ( ord_less_nat @ Ma @ X3 )
% 0.26/0.59         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59            = ( some_nat @ Ma ) ) )
% 0.26/0.59        & ( ~ ( ord_less_nat @ Ma @ X3 )
% 0.26/0.59         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59              @ ( if_option_nat
% 0.26/0.59                @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                   != none_nat )
% 0.26/0.59                  & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.59                @ ( 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 @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                @ ( if_option_nat
% 0.26/0.59                  @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.59                    = none_nat )
% 0.26/0.59                  @ ( if_option_nat @ ( ord_less_nat @ Mi @ X3 ) @ ( some_nat @ Mi ) @ none_nat )
% 0.26/0.59                  @ ( 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 @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.59              @ none_nat ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % vebt_pred.simps(7)
% 0.26/0.59  thf(fact_6745_vebt__delete_Osimps_I7_J,axiom,
% 0.26/0.59      ! [X3: nat,Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.26/0.59        ( ( ( ( ord_less_nat @ X3 @ Mi )
% 0.26/0.59            | ( ord_less_nat @ Ma @ X3 ) )
% 0.26/0.59         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) ) )
% 0.26/0.59        & ( ~ ( ( ord_less_nat @ X3 @ Mi )
% 0.26/0.59              | ( ord_less_nat @ Ma @ X3 ) )
% 0.26/0.59         => ( ( ( ( X3 = Mi )
% 0.26/0.59                & ( X3 = Ma ) )
% 0.26/0.59             => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59                = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) ) )
% 0.26/0.59            & ( ~ ( ( X3 = Mi )
% 0.26/0.59                  & ( X3 = Ma ) )
% 0.26/0.59             => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59                = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59                  @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                    @ ( vEBT_Node
% 0.26/0.59                      @ ( some_P7363390416028606310at_nat
% 0.26/0.59                        @ ( product_Pair_nat_nat @ ( if_nat @ ( X3 = Mi ) @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ Mi )
% 0.26/0.59                          @ ( if_nat
% 0.26/0.59                            @ ( ( ( X3 = Mi )
% 0.26/0.59                               => ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.26/0.59                                  = Ma ) )
% 0.26/0.59                              & ( ( X3 != Mi )
% 0.26/0.59                               => ( X3 = Ma ) ) )
% 0.26/0.59                            @ ( if_nat
% 0.26/0.59                              @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                = none_nat )
% 0.26/0.59                              @ ( if_nat @ ( X3 = Mi ) @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ Mi )
% 0.26/0.59                              @ ( 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 @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.59                            @ Ma ) ) )
% 0.26/0.59                      @ ( suc @ ( suc @ Va2 ) )
% 0.26/0.59                      @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                      @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                    @ ( vEBT_Node
% 0.26/0.59                      @ ( some_P7363390416028606310at_nat
% 0.26/0.59                        @ ( product_Pair_nat_nat @ ( if_nat @ ( X3 = Mi ) @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ Mi )
% 0.26/0.59                          @ ( if_nat
% 0.26/0.59                            @ ( ( ( X3 = Mi )
% 0.26/0.59                               => ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.26/0.59                                  = Ma ) )
% 0.26/0.59                              & ( ( X3 != Mi )
% 0.26/0.59                               => ( X3 = Ma ) ) )
% 0.26/0.59                            @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.59                            @ Ma ) ) )
% 0.26/0.59                      @ ( suc @ ( suc @ Va2 ) )
% 0.26/0.59                      @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                      @ Summary ) )
% 0.26/0.59                  @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % vebt_delete.simps(7)
% 0.26/0.59  thf(fact_6746_vebt__delete_Oelims,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: vEBT_VEBT] :
% 0.26/0.59        ( ( ( vEBT_vebt_delete @ X3 @ Xa )
% 0.26/0.59          = Y3 )
% 0.26/0.59       => ( ! [A5: $o,B4: $o] :
% 0.26/0.59              ( ( X3
% 0.26/0.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59             => ( ( Xa = zero_zero_nat )
% 0.26/0.59               => ( Y3
% 0.26/0.59                 != ( vEBT_Leaf @ $false @ B4 ) ) ) )
% 0.26/0.59         => ( ! [A5: $o] :
% 0.26/0.59                ( ? [B4: $o] :
% 0.26/0.59                    ( X3
% 0.26/0.59                    = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59               => ( ( Xa
% 0.26/0.59                    = ( suc @ zero_zero_nat ) )
% 0.26/0.59                 => ( Y3
% 0.26/0.59                   != ( vEBT_Leaf @ A5 @ $false ) ) ) )
% 0.26/0.59           => ( ! [A5: $o,B4: $o] :
% 0.26/0.59                  ( ( X3
% 0.26/0.59                    = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59                 => ( ? [N2: nat] :
% 0.26/0.59                        ( Xa
% 0.26/0.59                        = ( suc @ ( suc @ N2 ) ) )
% 0.26/0.59                   => ( Y3
% 0.26/0.59                     != ( vEBT_Leaf @ A5 @ B4 ) ) ) )
% 0.26/0.59             => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                    ( ( X3
% 0.26/0.59                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.26/0.59                   => ( Y3
% 0.26/0.59                     != ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) ) )
% 0.26/0.59               => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 0.26/0.59                      ( ( X3
% 0.26/0.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 0.26/0.59                     => ( Y3
% 0.26/0.59                       != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) ) )
% 0.26/0.59                 => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 0.26/0.59                        ( ( X3
% 0.26/0.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 0.26/0.59                       => ( Y3
% 0.26/0.59                         != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) ) )
% 0.26/0.59                   => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                          ( ( X3
% 0.26/0.59                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                         => ~ ( ( ( ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.59                                  | ( ord_less_nat @ Ma2 @ Xa ) )
% 0.26/0.59                               => ( Y3
% 0.26/0.59                                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) )
% 0.26/0.59                              & ( ~ ( ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.59                                    | ( ord_less_nat @ Ma2 @ Xa ) )
% 0.26/0.59                               => ( ( ( ( Xa = Mi2 )
% 0.26/0.59                                      & ( Xa = Ma2 ) )
% 0.26/0.59                                   => ( Y3
% 0.26/0.59                                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) )
% 0.26/0.59                                  & ( ~ ( ( Xa = Mi2 )
% 0.26/0.59                                        & ( Xa = Ma2 ) )
% 0.26/0.59                                   => ( Y3
% 0.26/0.59                                      = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                                        @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                          @ ( vEBT_Node
% 0.26/0.59                                            @ ( some_P7363390416028606310at_nat
% 0.26/0.59                                              @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa = Mi2 ) @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ Mi2 )
% 0.26/0.59                                                @ ( if_nat
% 0.26/0.59                                                  @ ( ( ( Xa = Mi2 )
% 0.26/0.59                                                     => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.26/0.59                                                        = Ma2 ) )
% 0.26/0.59                                                    & ( ( Xa != Mi2 )
% 0.26/0.59                                                     => ( Xa = Ma2 ) ) )
% 0.26/0.59                                                  @ ( if_nat
% 0.26/0.59                                                    @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                                      = none_nat )
% 0.26/0.59                                                    @ ( if_nat @ ( Xa = Mi2 ) @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ Mi2 )
% 0.26/0.59                                                    @ ( 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 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.59                                                  @ Ma2 ) ) )
% 0.26/0.59                                            @ ( suc @ ( suc @ Va ) )
% 0.26/0.59                                            @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                            @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                          @ ( vEBT_Node
% 0.26/0.59                                            @ ( some_P7363390416028606310at_nat
% 0.26/0.59                                              @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa = Mi2 ) @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ Mi2 )
% 0.26/0.59                                                @ ( if_nat
% 0.26/0.59                                                  @ ( ( ( Xa = Mi2 )
% 0.26/0.59                                                     => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.26/0.59                                                        = Ma2 ) )
% 0.26/0.59                                                    & ( ( Xa != Mi2 )
% 0.26/0.59                                                     => ( Xa = Ma2 ) ) )
% 0.26/0.59                                                  @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( 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 @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.59                                                  @ Ma2 ) ) )
% 0.26/0.59                                            @ ( suc @ ( suc @ Va ) )
% 0.26/0.59                                            @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                            @ Summary2 ) )
% 0.26/0.59                                        @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % vebt_delete.elims
% 0.26/0.59  thf(fact_6747_vebt__succ_Oelims,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: option_nat] :
% 0.26/0.59        ( ( ( vEBT_vebt_succ @ X3 @ Xa )
% 0.26/0.59          = Y3 )
% 0.26/0.59       => ( ! [Uu: $o,B4: $o] :
% 0.26/0.59              ( ( X3
% 0.26/0.59                = ( vEBT_Leaf @ Uu @ B4 ) )
% 0.26/0.59             => ( ( Xa = zero_zero_nat )
% 0.26/0.59               => ~ ( ( B4
% 0.26/0.59                     => ( Y3
% 0.26/0.59                        = ( some_nat @ one_one_nat ) ) )
% 0.26/0.59                    & ( ~ B4
% 0.26/0.59                     => ( Y3 = none_nat ) ) ) ) )
% 0.26/0.59         => ( ( ? [Uv: $o,Uw: $o] :
% 0.26/0.59                  ( X3
% 0.26/0.59                  = ( vEBT_Leaf @ Uv @ Uw ) )
% 0.26/0.59             => ( ? [N2: nat] :
% 0.26/0.59                    ( Xa
% 0.26/0.59                    = ( suc @ N2 ) )
% 0.26/0.59               => ( Y3 != none_nat ) ) )
% 0.26/0.59           => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.26/0.59                    ( X3
% 0.26/0.59                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 0.26/0.59               => ( Y3 != none_nat ) )
% 0.26/0.59             => ( ( ? [V3: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.26/0.59                      ( X3
% 0.26/0.59                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 0.26/0.59                 => ( Y3 != none_nat ) )
% 0.26/0.59               => ( ( ? [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 0.26/0.59                        ( X3
% 0.26/0.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 0.26/0.59                   => ( Y3 != none_nat ) )
% 0.26/0.59                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                        ( ( X3
% 0.26/0.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                       => ~ ( ( ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.59                             => ( Y3
% 0.26/0.59                                = ( some_nat @ Mi2 ) ) )
% 0.26/0.59                            & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.59                             => ( Y3
% 0.26/0.59                                = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                                  @ ( if_option_nat
% 0.26/0.59                                    @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                       != none_nat )
% 0.26/0.59                                      & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.59                                    @ ( 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 @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                    @ ( if_option_nat
% 0.26/0.59                                      @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.59                                        = none_nat )
% 0.26/0.59                                      @ none_nat
% 0.26/0.59                                      @ ( 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 @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.59                                  @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % vebt_succ.elims
% 0.26/0.59  thf(fact_6748_vebt__pred_Oelims,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: option_nat] :
% 0.26/0.59        ( ( ( vEBT_vebt_pred @ X3 @ Xa )
% 0.26/0.59          = Y3 )
% 0.26/0.59       => ( ( ? [Uu: $o,Uv: $o] :
% 0.26/0.59                ( X3
% 0.26/0.59                = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.26/0.59           => ( ( Xa = zero_zero_nat )
% 0.26/0.59             => ( Y3 != none_nat ) ) )
% 0.26/0.59         => ( ! [A5: $o] :
% 0.26/0.59                ( ? [Uw: $o] :
% 0.26/0.59                    ( X3
% 0.26/0.59                    = ( vEBT_Leaf @ A5 @ Uw ) )
% 0.26/0.59               => ( ( Xa
% 0.26/0.59                    = ( suc @ zero_zero_nat ) )
% 0.26/0.59                 => ~ ( ( A5
% 0.26/0.59                       => ( Y3
% 0.26/0.59                          = ( some_nat @ zero_zero_nat ) ) )
% 0.26/0.59                      & ( ~ A5
% 0.26/0.59                       => ( Y3 = none_nat ) ) ) ) )
% 0.26/0.59           => ( ! [A5: $o,B4: $o] :
% 0.26/0.59                  ( ( X3
% 0.26/0.59                    = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59                 => ( ? [Va: nat] :
% 0.26/0.59                        ( Xa
% 0.26/0.59                        = ( suc @ ( suc @ Va ) ) )
% 0.26/0.59                   => ~ ( ( B4
% 0.26/0.59                         => ( Y3
% 0.26/0.59                            = ( some_nat @ one_one_nat ) ) )
% 0.26/0.59                        & ( ~ B4
% 0.26/0.59                         => ( ( A5
% 0.26/0.59                             => ( Y3
% 0.26/0.59                                = ( some_nat @ zero_zero_nat ) ) )
% 0.26/0.59                            & ( ~ A5
% 0.26/0.59                             => ( Y3 = none_nat ) ) ) ) ) ) )
% 0.26/0.59             => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 0.26/0.59                      ( X3
% 0.26/0.59                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 0.26/0.59                 => ( Y3 != none_nat ) )
% 0.26/0.59               => ( ( ? [V3: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 0.26/0.59                        ( X3
% 0.26/0.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 0.26/0.59                   => ( Y3 != none_nat ) )
% 0.26/0.59                 => ( ( ? [V3: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 0.26/0.59                          ( X3
% 0.26/0.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 0.26/0.59                     => ( Y3 != none_nat ) )
% 0.26/0.59                   => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                          ( ( X3
% 0.26/0.59                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                         => ~ ( ( ( ord_less_nat @ Ma2 @ Xa )
% 0.26/0.59                               => ( Y3
% 0.26/0.59                                  = ( some_nat @ Ma2 ) ) )
% 0.26/0.59                              & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 0.26/0.59                               => ( Y3
% 0.26/0.59                                  = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                                    @ ( if_option_nat
% 0.26/0.59                                      @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                         != none_nat )
% 0.26/0.59                                        & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.59                                      @ ( 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 @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                      @ ( if_option_nat
% 0.26/0.59                                        @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.59                                          = none_nat )
% 0.26/0.59                                        @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa ) @ ( some_nat @ Mi2 ) @ none_nat )
% 0.26/0.59                                        @ ( 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 @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.59                                    @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % vebt_pred.elims
% 0.26/0.59  thf(fact_6749_insert__bound__height,axiom,
% 0.26/0.59      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.59        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.59       => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ X3 ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % insert_bound_height
% 0.26/0.59  thf(fact_6750_vebt__insert_Oelims,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: vEBT_VEBT] :
% 0.26/0.59        ( ( ( vEBT_vebt_insert @ X3 @ Xa )
% 0.26/0.59          = Y3 )
% 0.26/0.59       => ( ! [A5: $o,B4: $o] :
% 0.26/0.59              ( ( X3
% 0.26/0.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59             => ~ ( ( ( Xa = zero_zero_nat )
% 0.26/0.59                   => ( Y3
% 0.26/0.59                      = ( vEBT_Leaf @ $true @ B4 ) ) )
% 0.26/0.59                  & ( ( Xa != zero_zero_nat )
% 0.26/0.59                   => ( ( ( Xa = one_one_nat )
% 0.26/0.59                       => ( Y3
% 0.26/0.59                          = ( vEBT_Leaf @ A5 @ $true ) ) )
% 0.26/0.59                      & ( ( Xa != one_one_nat )
% 0.26/0.59                       => ( Y3
% 0.26/0.59                          = ( vEBT_Leaf @ A5 @ B4 ) ) ) ) ) ) )
% 0.26/0.59         => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.26/0.59                ( ( X3
% 0.26/0.59                  = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 0.26/0.59               => ( Y3
% 0.26/0.59                 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) ) )
% 0.26/0.59           => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.26/0.59                  ( ( X3
% 0.26/0.59                    = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 0.26/0.59                 => ( Y3
% 0.26/0.59                   != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) ) )
% 0.26/0.59             => ( ! [V3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                    ( ( X3
% 0.26/0.59                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                   => ( Y3
% 0.26/0.59                     != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa @ Xa ) ) @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) ) )
% 0.26/0.59               => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                      ( ( X3
% 0.26/0.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                     => ( Y3
% 0.26/0.59                       != ( if_VEBT_VEBT
% 0.26/0.59                          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                            & ~ ( ( Xa = Mi2 )
% 0.26/0.59                                | ( Xa = Ma2 ) ) )
% 0.26/0.59                          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Xa @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 0.26/0.59                          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % vebt_insert.elims
% 0.26/0.59  thf(fact_6751_vebt__insert_Osimps_I5_J,axiom,
% 0.26/0.59      ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 0.26/0.59        ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59        = ( if_VEBT_VEBT
% 0.26/0.59          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59            & ~ ( ( X3 = Mi )
% 0.26/0.59                | ( X3 = Ma ) ) )
% 0.26/0.59          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ X3 @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ Ma ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 0.26/0.59          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % vebt_insert.simps(5)
% 0.26/0.59  thf(fact_6752_of__int__code__if,axiom,
% 0.26/0.59      ( ring_1_of_int_real
% 0.26/0.59      = ( ^ [K3: int] :
% 0.26/0.59            ( if_real @ ( K3 = zero_zero_int ) @ zero_zero_real
% 0.26/0.59            @ ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K3 ) ) )
% 0.26/0.59              @ ( if_real
% 0.26/0.59                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.59                  = zero_zero_int )
% 0.26/0.59                @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.26/0.59                @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % of_int_code_if
% 0.26/0.59  thf(fact_6753_of__int__code__if,axiom,
% 0.26/0.59      ( ring_1_of_int_int
% 0.26/0.59      = ( ^ [K3: int] :
% 0.26/0.59            ( if_int @ ( K3 = zero_zero_int ) @ zero_zero_int
% 0.26/0.59            @ ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K3 ) ) )
% 0.26/0.59              @ ( if_int
% 0.26/0.59                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.59                  = zero_zero_int )
% 0.26/0.59                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.26/0.59                @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_int ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % of_int_code_if
% 0.26/0.59  thf(fact_6754_of__int__code__if,axiom,
% 0.26/0.59      ( ring_17405671764205052669omplex
% 0.26/0.59      = ( ^ [K3: int] :
% 0.26/0.59            ( if_complex @ ( K3 = zero_zero_int ) @ zero_zero_complex
% 0.26/0.59            @ ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K3 ) ) )
% 0.26/0.59              @ ( if_complex
% 0.26/0.59                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.59                  = zero_zero_int )
% 0.26/0.59                @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.26/0.59                @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % of_int_code_if
% 0.26/0.59  thf(fact_6755_of__int__code__if,axiom,
% 0.26/0.59      ( ring_18347121197199848620nteger
% 0.26/0.59      = ( ^ [K3: int] :
% 0.26/0.59            ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 0.26/0.59            @ ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K3 ) ) )
% 0.26/0.59              @ ( if_Code_integer
% 0.26/0.59                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.59                  = zero_zero_int )
% 0.26/0.59                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.26/0.59                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % of_int_code_if
% 0.26/0.59  thf(fact_6756_of__int__code__if,axiom,
% 0.26/0.59      ( ring_1_of_int_rat
% 0.26/0.59      = ( ^ [K3: int] :
% 0.26/0.59            ( if_rat @ ( K3 = zero_zero_int ) @ zero_zero_rat
% 0.26/0.59            @ ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K3 ) ) )
% 0.26/0.59              @ ( if_rat
% 0.26/0.59                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.59                  = zero_zero_int )
% 0.26/0.59                @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.26/0.59                @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_rat ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % of_int_code_if
% 0.26/0.59  thf(fact_6757_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Oelims,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 0.26/0.59        ( ( ( vEBT_T_s_u_c_c2 @ X3 @ Xa )
% 0.26/0.59          = Y3 )
% 0.26/0.59       => ( ( ? [Uu: $o,B4: $o] :
% 0.26/0.59                ( X3
% 0.26/0.59                = ( vEBT_Leaf @ Uu @ B4 ) )
% 0.26/0.59           => ( ( Xa = zero_zero_nat )
% 0.26/0.59             => ( Y3 != one_one_nat ) ) )
% 0.26/0.59         => ( ( ? [Uv: $o,Uw: $o] :
% 0.26/0.59                  ( X3
% 0.26/0.59                  = ( vEBT_Leaf @ Uv @ Uw ) )
% 0.26/0.59             => ( ? [N2: nat] :
% 0.26/0.59                    ( Xa
% 0.26/0.59                    = ( suc @ N2 ) )
% 0.26/0.59               => ( Y3 != one_one_nat ) ) )
% 0.26/0.59           => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.26/0.59                    ( X3
% 0.26/0.59                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 0.26/0.59               => ( Y3 != one_one_nat ) )
% 0.26/0.59             => ( ( ? [V3: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.26/0.59                      ( X3
% 0.26/0.59                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 0.26/0.59                 => ( Y3 != one_one_nat ) )
% 0.26/0.59               => ( ( ? [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 0.26/0.59                        ( X3
% 0.26/0.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 0.26/0.59                   => ( Y3 != one_one_nat ) )
% 0.26/0.59                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                        ( ( X3
% 0.26/0.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                       => ~ ( ( ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.59                             => ( Y3 = one_one_nat ) )
% 0.26/0.59                            & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.59                             => ( Y3
% 0.26/0.59                                = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                                  @ ( if_nat
% 0.26/0.59                                    @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                       != none_nat )
% 0.26/0.59                                      & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.59                                    @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                    @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.26/0.59                                  @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.elims
% 0.26/0.59  thf(fact_6758_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Oelims,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 0.26/0.59        ( ( ( vEBT_T_p_r_e_d2 @ X3 @ Xa )
% 0.26/0.59          = Y3 )
% 0.26/0.59       => ( ( ? [Uu: $o,Uv: $o] :
% 0.26/0.59                ( X3
% 0.26/0.59                = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.26/0.59           => ( ( Xa = zero_zero_nat )
% 0.26/0.59             => ( Y3 != one_one_nat ) ) )
% 0.26/0.59         => ( ( ? [A5: $o,Uw: $o] :
% 0.26/0.59                  ( X3
% 0.26/0.59                  = ( vEBT_Leaf @ A5 @ Uw ) )
% 0.26/0.59             => ( ( Xa
% 0.26/0.59                  = ( suc @ zero_zero_nat ) )
% 0.26/0.59               => ( Y3 != one_one_nat ) ) )
% 0.26/0.59           => ( ( ? [A5: $o,B4: $o] :
% 0.26/0.59                    ( X3
% 0.26/0.59                    = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59               => ( ? [Va: nat] :
% 0.26/0.59                      ( Xa
% 0.26/0.59                      = ( suc @ ( suc @ Va ) ) )
% 0.26/0.59                 => ( Y3 != one_one_nat ) ) )
% 0.26/0.59             => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 0.26/0.59                      ( X3
% 0.26/0.59                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 0.26/0.59                 => ( Y3 != one_one_nat ) )
% 0.26/0.59               => ( ( ? [V3: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 0.26/0.59                        ( X3
% 0.26/0.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 0.26/0.59                   => ( Y3 != one_one_nat ) )
% 0.26/0.59                 => ( ( ? [V3: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 0.26/0.59                          ( X3
% 0.26/0.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 0.26/0.59                     => ( Y3 != one_one_nat ) )
% 0.26/0.59                   => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                          ( ( X3
% 0.26/0.59                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                         => ~ ( ( ( ord_less_nat @ Ma2 @ Xa )
% 0.26/0.59                               => ( Y3 = one_one_nat ) )
% 0.26/0.59                              & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 0.26/0.59                               => ( Y3
% 0.26/0.59                                  = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                                    @ ( if_nat
% 0.26/0.59                                      @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                         != none_nat )
% 0.26/0.59                                        & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.59                                      @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                      @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.26/0.59                                    @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.elims
% 0.26/0.59  thf(fact_6759_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I1_J,axiom,
% 0.26/0.59      ! [Uu2: $o,Uv2: $o] :
% 0.26/0.59        ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat )
% 0.26/0.59        = one_one_nat ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(1)
% 0.26/0.59  thf(fact_6760_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I1_J,axiom,
% 0.26/0.59      ! [Uu2: $o,B: $o] :
% 0.26/0.59        ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Leaf @ Uu2 @ B ) @ zero_zero_nat )
% 0.26/0.59        = one_one_nat ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(1)
% 0.26/0.59  thf(fact_6761_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I2_J,axiom,
% 0.26/0.59      ! [A: $o,Uw2: $o] :
% 0.26/0.59        ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 0.26/0.59        = one_one_nat ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(2)
% 0.26/0.59  thf(fact_6762_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I5_J,axiom,
% 0.26/0.59      ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 0.26/0.59        ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf )
% 0.26/0.59        = one_one_nat ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(5)
% 0.26/0.59  thf(fact_6763_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I4_J,axiom,
% 0.26/0.59      ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 0.26/0.59        ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve )
% 0.26/0.59        = one_one_nat ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(4)
% 0.26/0.59  thf(fact_6764_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I6_J,axiom,
% 0.26/0.59      ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 0.26/0.59        ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj )
% 0.26/0.59        = one_one_nat ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(6)
% 0.26/0.59  thf(fact_6765_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I5_J,axiom,
% 0.26/0.59      ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 0.26/0.59        ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi )
% 0.26/0.59        = one_one_nat ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(5)
% 0.26/0.59  thf(fact_6766_pred__bound__height_H,axiom,
% 0.26/0.59      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.59        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.59       => ( ord_less_eq_nat @ ( vEBT_T_p_r_e_d2 @ T @ X3 ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % pred_bound_height'
% 0.26/0.59  thf(fact_6767_succ_H__bound__height,axiom,
% 0.26/0.59      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.59        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.59       => ( ord_less_eq_nat @ ( vEBT_T_s_u_c_c2 @ T @ X3 ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % succ'_bound_height
% 0.26/0.59  thf(fact_6768_vebt__insert_Osimps_I2_J,axiom,
% 0.26/0.59      ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 0.26/0.59        ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S ) @ X3 )
% 0.26/0.59        = ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S ) ) ).
% 0.26/0.59  
% 0.26/0.59  % vebt_insert.simps(2)
% 0.26/0.59  thf(fact_6769_pred__bound__size__univ_H,axiom,
% 0.26/0.59      ! [T: vEBT_VEBT,N: nat,U: real,X3: nat] :
% 0.26/0.59        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.59       => ( ( U
% 0.26/0.59            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.59         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_p_r_e_d2 @ T @ X3 ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % pred_bound_size_univ'
% 0.26/0.59  thf(fact_6770_succ__bound__size__univ_H,axiom,
% 0.26/0.59      ! [T: vEBT_VEBT,N: nat,U: real,X3: nat] :
% 0.26/0.59        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.59       => ( ( U
% 0.26/0.59            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.26/0.59         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_s_u_c_c2 @ T @ X3 ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % succ_bound_size_univ'
% 0.26/0.59  thf(fact_6771_vebt__insert_Osimps_I3_J,axiom,
% 0.26/0.59      ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 0.26/0.59        ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ X3 )
% 0.26/0.59        = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) ) ).
% 0.26/0.59  
% 0.26/0.59  % vebt_insert.simps(3)
% 0.26/0.59  thf(fact_6772_vebt__insert_Osimps_I1_J,axiom,
% 0.26/0.59      ! [X3: nat,A: $o,B: $o] :
% 0.26/0.59        ( ( ( X3 = zero_zero_nat )
% 0.26/0.59         => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 0.26/0.59            = ( vEBT_Leaf @ $true @ B ) ) )
% 0.26/0.59        & ( ( X3 != zero_zero_nat )
% 0.26/0.59         => ( ( ( X3 = one_one_nat )
% 0.26/0.59             => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 0.26/0.59                = ( vEBT_Leaf @ A @ $true ) ) )
% 0.26/0.59            & ( ( X3 != one_one_nat )
% 0.26/0.59             => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 0.26/0.59                = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % vebt_insert.simps(1)
% 0.26/0.59  thf(fact_6773_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I7_J,axiom,
% 0.26/0.59      ! [Ma: nat,X3: nat,Mi: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.26/0.59        ( ( ( ord_less_nat @ Ma @ X3 )
% 0.26/0.59         => ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59            = one_one_nat ) )
% 0.26/0.59        & ( ~ ( ord_less_nat @ Ma @ X3 )
% 0.26/0.59         => ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59            = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59              @ ( if_nat
% 0.26/0.59                @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                   != none_nat )
% 0.26/0.59                  & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.59                @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.26/0.59              @ one_one_nat ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(7)
% 0.26/0.59  thf(fact_6774_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I6_J,axiom,
% 0.26/0.59      ! [X3: nat,Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.26/0.59        ( ( ( ord_less_nat @ X3 @ Mi )
% 0.26/0.59         => ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59            = one_one_nat ) )
% 0.26/0.59        & ( ~ ( ord_less_nat @ X3 @ Mi )
% 0.26/0.59         => ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59            = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59              @ ( if_nat
% 0.26/0.59                @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                   != none_nat )
% 0.26/0.59                  & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.59                @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.26/0.59              @ one_one_nat ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(6)
% 0.26/0.59  thf(fact_6775_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Oelims,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 0.26/0.59        ( ( ( vEBT_T_i_n_s_e_r_t @ X3 @ Xa )
% 0.26/0.59          = Y3 )
% 0.26/0.59       => ( ( ? [A5: $o,B4: $o] :
% 0.26/0.59                ( X3
% 0.26/0.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59           => ( Y3
% 0.26/0.59             != ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 0.26/0.59         => ( ( ? [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.26/0.59                  ( X3
% 0.26/0.59                  = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 0.26/0.59             => ( Y3 != one_one_nat ) )
% 0.26/0.59           => ( ( ? [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.26/0.59                    ( X3
% 0.26/0.59                    = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 0.26/0.59               => ( Y3 != one_one_nat ) )
% 0.26/0.59             => ( ( ? [V3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                      ( X3
% 0.26/0.59                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                 => ( Y3
% 0.26/0.59                   != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.59               => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                      ( ( X3
% 0.26/0.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                     => ( Y3
% 0.26/0.59                       != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.26/0.59                          @ ( if_nat
% 0.26/0.59                            @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                              & ~ ( ( Xa = Mi2 )
% 0.26/0.59                                  | ( Xa = Ma2 ) ) )
% 0.26/0.59                            @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.26/0.59                            @ one_one_nat ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.elims
% 0.26/0.59  thf(fact_6776_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Oelims,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 0.26/0.59        ( ( ( vEBT_T_m_e_m_b_e_r2 @ X3 @ Xa )
% 0.26/0.59          = Y3 )
% 0.26/0.59       => ( ( ? [A5: $o,B4: $o] :
% 0.26/0.59                ( X3
% 0.26/0.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59           => ( Y3 != one_one_nat ) )
% 0.26/0.59         => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.26/0.59                  ( X3
% 0.26/0.59                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.26/0.59             => ( Y3 != one_one_nat ) )
% 0.26/0.59           => ( ( ? [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.26/0.59                    ( X3
% 0.26/0.59                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.26/0.59               => ( Y3 != one_one_nat ) )
% 0.26/0.59             => ( ( ? [V3: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.26/0.59                      ( X3
% 0.26/0.59                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) )
% 0.26/0.59                 => ( Y3 != one_one_nat ) )
% 0.26/0.59               => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT] :
% 0.26/0.59                      ( ? [Summary2: vEBT_VEBT] :
% 0.26/0.59                          ( X3
% 0.26/0.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                     => ( Y3
% 0.26/0.59                       != ( plus_plus_nat @ one_one_nat
% 0.26/0.59                          @ ( if_nat @ ( Xa = Mi2 ) @ zero_zero_nat
% 0.26/0.59                            @ ( if_nat @ ( Xa = Ma2 ) @ zero_zero_nat
% 0.26/0.59                              @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ zero_zero_nat
% 0.26/0.59                                @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa ) @ zero_zero_nat
% 0.26/0.59                                  @ ( if_nat
% 0.26/0.59                                    @ ( ( ord_less_nat @ Mi2 @ Xa )
% 0.26/0.59                                      & ( ord_less_nat @ Xa @ Ma2 ) )
% 0.26/0.59                                    @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 0.26/0.59                                    @ zero_zero_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.elims
% 0.26/0.59  thf(fact_6777_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I5_J,axiom,
% 0.26/0.59      ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 0.26/0.59        ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.26/0.59          @ ( if_nat
% 0.26/0.59            @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59              & ~ ( ( X3 = Mi )
% 0.26/0.59                  | ( X3 = Ma ) ) )
% 0.26/0.59            @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.26/0.59            @ one_one_nat ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(5)
% 0.26/0.59  thf(fact_6778_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Oelims,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 0.26/0.59        ( ( ( vEBT_T_i_n_s_e_r_t2 @ X3 @ Xa )
% 0.26/0.59          = Y3 )
% 0.26/0.59       => ( ( ? [A5: $o,B4: $o] :
% 0.26/0.59                ( X3
% 0.26/0.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59           => ( Y3 != one_one_nat ) )
% 0.26/0.59         => ( ( ? [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.26/0.59                  ( X3
% 0.26/0.59                  = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 0.26/0.59             => ( Y3 != one_one_nat ) )
% 0.26/0.59           => ( ( ? [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.26/0.59                    ( X3
% 0.26/0.59                    = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 0.26/0.59               => ( Y3 != one_one_nat ) )
% 0.26/0.59             => ( ( ? [V3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                      ( X3
% 0.26/0.59                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                 => ( Y3 != one_one_nat ) )
% 0.26/0.59               => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                      ( ( X3
% 0.26/0.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                     => ( Y3
% 0.26/0.59                       != ( if_nat
% 0.26/0.59                          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                            & ~ ( ( Xa = Mi2 )
% 0.26/0.59                                | ( Xa = Ma2 ) ) )
% 0.26/0.59                          @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.26/0.59                          @ one_one_nat ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.elims
% 0.26/0.59  thf(fact_6779_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I5_J,axiom,
% 0.26/0.59      ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 0.26/0.59        ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59        = ( plus_plus_nat @ one_one_nat
% 0.26/0.59          @ ( if_nat @ ( X3 = Mi ) @ zero_zero_nat
% 0.26/0.59            @ ( if_nat @ ( X3 = Ma ) @ zero_zero_nat
% 0.26/0.59              @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ zero_zero_nat
% 0.26/0.59                @ ( if_nat @ ( ord_less_nat @ Ma @ X3 ) @ zero_zero_nat
% 0.26/0.59                  @ ( if_nat
% 0.26/0.59                    @ ( ( ord_less_nat @ Mi @ X3 )
% 0.26/0.59                      & ( ord_less_nat @ X3 @ Ma ) )
% 0.26/0.59                    @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 0.26/0.59                    @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(5)
% 0.26/0.59  thf(fact_6780_minNull__bound,axiom,
% 0.26/0.59      ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_i_n_N_u_l_l @ T ) @ one_one_nat ) ).
% 0.26/0.59  
% 0.26/0.59  % minNull_bound
% 0.26/0.59  thf(fact_6781_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I2_J,axiom,
% 0.26/0.59      ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 0.26/0.59        ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S ) @ X3 )
% 0.26/0.59        = one_one_nat ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(2)
% 0.26/0.59  thf(fact_6782_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I3_J,axiom,
% 0.26/0.59      ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 0.26/0.59        ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ X3 )
% 0.26/0.59        = one_one_nat ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(3)
% 0.26/0.59  thf(fact_6783_insersimp_H,axiom,
% 0.26/0.59      ! [T: vEBT_VEBT,N: nat,Y3: nat] :
% 0.26/0.59        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.59       => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 )
% 0.26/0.59         => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ Y3 ) @ one_one_nat ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % insersimp'
% 0.26/0.59  thf(fact_6784_insertsimp_H,axiom,
% 0.26/0.59      ! [T: vEBT_VEBT,N: nat,L: nat] :
% 0.26/0.59        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.59       => ( ( vEBT_VEBT_minNull @ T )
% 0.26/0.59         => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ L ) @ one_one_nat ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % insertsimp'
% 0.26/0.59  thf(fact_6785_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I3_J,axiom,
% 0.26/0.59      ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X3: nat] :
% 0.26/0.59        ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X3 )
% 0.26/0.59        = one_one_nat ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(3)
% 0.26/0.59  thf(fact_6786_insert_H__bound__height,axiom,
% 0.26/0.59      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.59        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.59       => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ X3 ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % insert'_bound_height
% 0.26/0.59  thf(fact_6787_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I4_J,axiom,
% 0.26/0.59      ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc: vEBT_VEBT,X3: nat] :
% 0.26/0.59        ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc ) @ X3 )
% 0.26/0.59        = one_one_nat ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(4)
% 0.26/0.59  thf(fact_6788_member__bound__height_H,axiom,
% 0.26/0.59      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.59        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.59       => ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r2 @ T @ X3 ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % member_bound_height'
% 0.26/0.59  thf(fact_6789_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I5_J,axiom,
% 0.26/0.59      ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 0.26/0.59        ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59        = ( if_nat
% 0.26/0.59          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59            & ~ ( ( X3 = Mi )
% 0.26/0.59                | ( X3 = Ma ) ) )
% 0.26/0.59          @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.26/0.59          @ one_one_nat ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(5)
% 0.26/0.59  thf(fact_6790_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Oelims,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 0.26/0.59        ( ( ( vEBT_T_d_e_l_e_t_e @ X3 @ Xa )
% 0.26/0.59          = Y3 )
% 0.26/0.59       => ( ( ? [A5: $o,B4: $o] :
% 0.26/0.59                ( X3
% 0.26/0.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59           => ( ( Xa = zero_zero_nat )
% 0.26/0.59             => ( Y3 != one_one_nat ) ) )
% 0.26/0.59         => ( ( ? [A5: $o,B4: $o] :
% 0.26/0.59                  ( X3
% 0.26/0.59                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59             => ( ( Xa
% 0.26/0.59                  = ( suc @ zero_zero_nat ) )
% 0.26/0.59               => ( Y3 != one_one_nat ) ) )
% 0.26/0.59           => ( ( ? [A5: $o,B4: $o] :
% 0.26/0.59                    ( X3
% 0.26/0.59                    = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59               => ( ? [N2: nat] :
% 0.26/0.59                      ( Xa
% 0.26/0.59                      = ( suc @ ( suc @ N2 ) ) )
% 0.26/0.59                 => ( Y3 != one_one_nat ) ) )
% 0.26/0.59             => ( ( ? [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                      ( X3
% 0.26/0.59                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.26/0.59                 => ( Y3 != one_one_nat ) )
% 0.26/0.59               => ( ( ? [Mi2: nat,Ma2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                        ( X3
% 0.26/0.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList3 @ Summary2 ) )
% 0.26/0.59                   => ( Y3 != one_one_nat ) )
% 0.26/0.59                 => ( ( ? [Mi2: nat,Ma2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                          ( X3
% 0.26/0.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                     => ( Y3 != one_one_nat ) )
% 0.26/0.59                   => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                          ( ( X3
% 0.26/0.59                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                         => ( Y3
% 0.26/0.59                           != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.26/0.59                              @ ( if_nat
% 0.26/0.59                                @ ( ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.59                                  | ( ord_less_nat @ Ma2 @ Xa ) )
% 0.26/0.59                                @ one_one_nat
% 0.26/0.59                                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.26/0.59                                  @ ( if_nat
% 0.26/0.59                                    @ ( ( Xa = Mi2 )
% 0.26/0.59                                      & ( Xa = Ma2 ) )
% 0.26/0.59                                    @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.26/0.59                                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ Summary2 ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 0.26/0.59                                      @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                                        @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                          @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.26/0.59                                            @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                              @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.26/0.59                                                  @ ( if_nat
% 0.26/0.59                                                    @ ( ( ( Xa = Mi2 )
% 0.26/0.59                                                       => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.26/0.59                                                          = Ma2 ) )
% 0.26/0.59                                                      & ( ( Xa != Mi2 )
% 0.26/0.59                                                       => ( Xa = Ma2 ) ) )
% 0.26/0.59                                                    @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.26/0.59                                                      @ ( plus_plus_nat @ one_one_nat
% 0.26/0.59                                                        @ ( if_nat
% 0.26/0.59                                                          @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                                            = none_nat )
% 0.26/0.59                                                          @ one_one_nat
% 0.26/0.59                                                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.59                                                    @ one_one_nat ) ) )
% 0.26/0.59                                              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.26/0.59                                                @ ( if_nat
% 0.26/0.59                                                  @ ( ( ( Xa = Mi2 )
% 0.26/0.59                                                     => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.26/0.59                                                        = Ma2 ) )
% 0.26/0.59                                                    & ( ( Xa != Mi2 )
% 0.26/0.59                                                     => ( Xa = Ma2 ) ) )
% 0.26/0.59                                                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.26/0.59                                                  @ one_one_nat ) ) ) ) )
% 0.26/0.59                                        @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.elims
% 0.26/0.59  thf(fact_6791_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: $o] :
% 0.26/0.59        ( ( ( vEBT_VEBT_membermima @ X3 @ Xa )
% 0.26/0.59          = Y3 )
% 0.26/0.59       => ( ( ? [Uu: $o,Uv: $o] :
% 0.26/0.59                ( X3
% 0.26/0.59                = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.26/0.59           => Y3 )
% 0.26/0.59         => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.26/0.59                  ( X3
% 0.26/0.59                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 0.26/0.59             => Y3 )
% 0.26/0.59           => ( ! [Mi2: nat,Ma2: nat] :
% 0.26/0.59                  ( ? [Va3: list_VEBT_VEBT,Vb: vEBT_VEBT] :
% 0.26/0.59                      ( X3
% 0.26/0.59                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb ) )
% 0.26/0.59                 => ( Y3
% 0.26/0.59                    = ( ~ ( ( Xa = Mi2 )
% 0.26/0.59                          | ( Xa = Ma2 ) ) ) ) )
% 0.26/0.59             => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList3: list_VEBT_VEBT] :
% 0.26/0.59                    ( ? [Vc2: vEBT_VEBT] :
% 0.26/0.59                        ( X3
% 0.26/0.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) )
% 0.26/0.59                   => ( Y3
% 0.26/0.59                      = ( ~ ( ( Xa = Mi2 )
% 0.26/0.59                            | ( Xa = Ma2 )
% 0.26/0.59                            | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) )
% 0.26/0.59               => ~ ! [V3: nat,TreeList3: list_VEBT_VEBT] :
% 0.26/0.59                      ( ? [Vd2: vEBT_VEBT] :
% 0.26/0.59                          ( X3
% 0.26/0.59                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) )
% 0.26/0.59                     => ( Y3
% 0.26/0.59                        = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % VEBT_internal.membermima.elims(1)
% 0.26/0.59  thf(fact_6792_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat] :
% 0.26/0.59        ( ~ ( vEBT_VEBT_membermima @ X3 @ Xa )
% 0.26/0.59       => ( ! [Uu: $o,Uv: $o] :
% 0.26/0.59              ( X3
% 0.26/0.59             != ( vEBT_Leaf @ Uu @ Uv ) )
% 0.26/0.59         => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.26/0.59                ( X3
% 0.26/0.59               != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 0.26/0.59           => ( ! [Mi2: nat,Ma2: nat] :
% 0.26/0.59                  ( ? [Va3: list_VEBT_VEBT,Vb: vEBT_VEBT] :
% 0.26/0.59                      ( X3
% 0.26/0.59                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb ) )
% 0.26/0.59                 => ( ( Xa = Mi2 )
% 0.26/0.59                    | ( Xa = Ma2 ) ) )
% 0.26/0.59             => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList3: list_VEBT_VEBT] :
% 0.26/0.59                    ( ? [Vc2: vEBT_VEBT] :
% 0.26/0.59                        ( X3
% 0.26/0.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) )
% 0.26/0.59                   => ( ( Xa = Mi2 )
% 0.26/0.59                      | ( Xa = Ma2 )
% 0.26/0.59                      | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                         => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 0.26/0.59               => ~ ! [V3: nat,TreeList3: list_VEBT_VEBT] :
% 0.26/0.59                      ( ? [Vd2: vEBT_VEBT] :
% 0.26/0.59                          ( X3
% 0.26/0.59                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) )
% 0.26/0.59                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                         => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % VEBT_internal.membermima.elims(3)
% 0.26/0.59  thf(fact_6793_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: $o] :
% 0.26/0.59        ( ( ( vEBT_V5719532721284313246member @ X3 @ Xa )
% 0.26/0.59          = Y3 )
% 0.26/0.59       => ( ! [A5: $o,B4: $o] :
% 0.26/0.59              ( ( X3
% 0.26/0.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59             => ( Y3
% 0.26/0.59                = ( ~ ( ( ( Xa = zero_zero_nat )
% 0.26/0.59                       => A5 )
% 0.26/0.59                      & ( ( Xa != zero_zero_nat )
% 0.26/0.59                       => ( ( ( Xa = one_one_nat )
% 0.26/0.59                           => B4 )
% 0.26/0.59                          & ( Xa = one_one_nat ) ) ) ) ) ) )
% 0.26/0.59         => ( ( ? [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.26/0.59                  ( X3
% 0.26/0.59                  = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 0.26/0.59             => Y3 )
% 0.26/0.59           => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList3: list_VEBT_VEBT] :
% 0.26/0.59                  ( ? [S3: vEBT_VEBT] :
% 0.26/0.59                      ( X3
% 0.26/0.59                      = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) )
% 0.26/0.59                 => ( Y3
% 0.26/0.59                    = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % VEBT_internal.naive_member.elims(1)
% 0.26/0.59  thf(fact_6794_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat] :
% 0.26/0.59        ( ( vEBT_V5719532721284313246member @ X3 @ Xa )
% 0.26/0.59       => ( ! [A5: $o,B4: $o] :
% 0.26/0.59              ( ( X3
% 0.26/0.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59             => ~ ( ( ( Xa = zero_zero_nat )
% 0.26/0.59                   => A5 )
% 0.26/0.59                  & ( ( Xa != zero_zero_nat )
% 0.26/0.59                   => ( ( ( Xa = one_one_nat )
% 0.26/0.59                       => B4 )
% 0.26/0.59                      & ( Xa = one_one_nat ) ) ) ) )
% 0.26/0.59         => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList3: list_VEBT_VEBT] :
% 0.26/0.59                ( ? [S3: vEBT_VEBT] :
% 0.26/0.59                    ( X3
% 0.26/0.59                    = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) )
% 0.26/0.59               => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                     => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % VEBT_internal.naive_member.elims(2)
% 0.26/0.59  thf(fact_6795_buildup__nothing__in__min__max,axiom,
% 0.26/0.59      ! [N: nat,X3: nat] :
% 0.26/0.59        ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X3 ) ).
% 0.26/0.59  
% 0.26/0.59  % buildup_nothing_in_min_max
% 0.26/0.59  thf(fact_6796_buildup__nothing__in__leaf,axiom,
% 0.26/0.59      ! [N: nat,X3: nat] :
% 0.26/0.59        ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X3 ) ).
% 0.26/0.59  
% 0.26/0.59  % buildup_nothing_in_leaf
% 0.26/0.59  thf(fact_6797_both__member__options__def,axiom,
% 0.26/0.59      ( vEBT_V8194947554948674370ptions
% 0.26/0.59      = ( ^ [T2: vEBT_VEBT,X: nat] :
% 0.26/0.59            ( ( vEBT_V5719532721284313246member @ T2 @ X )
% 0.26/0.59            | ( vEBT_VEBT_membermima @ T2 @ X ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % both_member_options_def
% 0.26/0.59  thf(fact_6798_member__valid__both__member__options,axiom,
% 0.26/0.59      ! [Tree: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.59        ( ( vEBT_invar_vebt @ Tree @ N )
% 0.26/0.59       => ( ( vEBT_vebt_member @ Tree @ X3 )
% 0.26/0.59         => ( ( vEBT_V5719532721284313246member @ Tree @ X3 )
% 0.26/0.59            | ( vEBT_VEBT_membermima @ Tree @ X3 ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % member_valid_both_member_options
% 0.26/0.59  thf(fact_6799_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 0.26/0.59      ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux: nat] :
% 0.26/0.59        ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux ) ).
% 0.26/0.59  
% 0.26/0.59  % VEBT_internal.naive_member.simps(2)
% 0.26/0.59  thf(fact_6800_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 0.26/0.59      ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 0.26/0.59        ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 0.26/0.59  
% 0.26/0.59  % VEBT_internal.membermima.simps(2)
% 0.26/0.59  thf(fact_6801_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 0.26/0.59      ! [A: $o,B: $o,X3: nat] :
% 0.26/0.59        ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 0.26/0.59        = ( ( ( X3 = zero_zero_nat )
% 0.26/0.59           => A )
% 0.26/0.59          & ( ( X3 != zero_zero_nat )
% 0.26/0.59           => ( ( ( X3 = one_one_nat )
% 0.26/0.59               => B )
% 0.26/0.59              & ( X3 = one_one_nat ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % VEBT_internal.naive_member.simps(1)
% 0.26/0.59  thf(fact_6802_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 0.26/0.59      ! [Mi: nat,Ma: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT,X3: nat] :
% 0.26/0.59        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ X3 )
% 0.26/0.59        = ( ( X3 = Mi )
% 0.26/0.59          | ( X3 = Ma ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % VEBT_internal.membermima.simps(3)
% 0.26/0.59  thf(fact_6803_maxt__bound,axiom,
% 0.26/0.59      ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_a_x_t @ T ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % maxt_bound
% 0.26/0.59  thf(fact_6804_mint__bound,axiom,
% 0.26/0.59      ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_i_n_t @ T ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % mint_bound
% 0.26/0.59  thf(fact_6805_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I1_J,axiom,
% 0.26/0.59      ! [A: $o,B: $o] :
% 0.26/0.59        ( ( vEBT_T_m_i_n_t @ ( vEBT_Leaf @ A @ B ) )
% 0.26/0.59        = ( plus_plus_nat @ one_one_nat @ ( if_nat @ A @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.simps(1)
% 0.26/0.59  thf(fact_6806_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Oelims,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Y3: nat] :
% 0.26/0.59        ( ( ( vEBT_T_m_i_n_t @ X3 )
% 0.26/0.59          = Y3 )
% 0.26/0.59       => ( ! [A5: $o] :
% 0.26/0.59              ( ? [B4: $o] :
% 0.26/0.59                  ( X3
% 0.26/0.59                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59             => ( Y3
% 0.26/0.59               != ( plus_plus_nat @ one_one_nat @ ( if_nat @ A5 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 0.26/0.59         => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.26/0.59                  ( X3
% 0.26/0.59                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.26/0.59             => ( Y3 != one_one_nat ) )
% 0.26/0.59           => ~ ( ? [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.26/0.59                    ( X3
% 0.26/0.59                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 0.26/0.59               => ( Y3 != one_one_nat ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.elims
% 0.26/0.59  thf(fact_6807_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 0.26/0.59      ! [V: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT,X3: nat] :
% 0.26/0.59        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) @ X3 )
% 0.26/0.59        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59          & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % VEBT_internal.membermima.simps(5)
% 0.26/0.59  thf(fact_6808_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 0.26/0.59      ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 0.26/0.59        ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S ) @ X3 )
% 0.26/0.59        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59          & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % VEBT_internal.naive_member.simps(3)
% 0.26/0.59  thf(fact_6809_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 0.26/0.59      ! [Mi: nat,Ma: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT,X3: nat] :
% 0.26/0.59        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList2 @ Vc ) @ X3 )
% 0.26/0.59        = ( ( X3 = Mi )
% 0.26/0.59          | ( X3 = Ma )
% 0.26/0.59          | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59            & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % VEBT_internal.membermima.simps(4)
% 0.26/0.59  thf(fact_6810_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I7_J,axiom,
% 0.26/0.59      ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 0.26/0.59        ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59        = ( plus_plus_nat @ one_one_nat
% 0.26/0.59          @ ( if_nat @ ( ord_less_nat @ Ma @ X3 ) @ one_one_nat
% 0.26/0.59            @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 0.26/0.59              @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59                @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.26/0.59                  @ ( if_nat
% 0.26/0.59                    @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                       != none_nat )
% 0.26/0.59                      & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.59                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 0.26/0.59                      @ ( if_nat
% 0.26/0.59                        @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.59                          = none_nat )
% 0.26/0.59                        @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.26/0.59                        @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.59                @ one_one_nat ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(7)
% 0.26/0.59  thf(fact_6811_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I6_J,axiom,
% 0.26/0.59      ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 0.26/0.59        ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59        = ( plus_plus_nat @ one_one_nat
% 0.26/0.59          @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ one_one_nat
% 0.26/0.59            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 0.26/0.59              @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59                @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.26/0.59                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.26/0.59                    @ ( if_nat
% 0.26/0.59                      @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                         != none_nat )
% 0.26/0.59                        & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.59                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                      @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 0.26/0.59                        @ ( if_nat
% 0.26/0.59                          @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.59                            = none_nat )
% 0.26/0.59                          @ one_one_nat
% 0.26/0.59                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.59                @ one_one_nat ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(6)
% 0.26/0.59  thf(fact_6812_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Oelims,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 0.26/0.59        ( ( ( vEBT_T_p_r_e_d @ X3 @ Xa )
% 0.26/0.59          = Y3 )
% 0.26/0.59       => ( ( ? [Uu: $o,Uv: $o] :
% 0.26/0.59                ( X3
% 0.26/0.59                = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.26/0.59           => ( ( Xa = zero_zero_nat )
% 0.26/0.59             => ( Y3 != one_one_nat ) ) )
% 0.26/0.59         => ( ( ? [A5: $o,Uw: $o] :
% 0.26/0.59                  ( X3
% 0.26/0.59                  = ( vEBT_Leaf @ A5 @ Uw ) )
% 0.26/0.59             => ( ( Xa
% 0.26/0.59                  = ( suc @ zero_zero_nat ) )
% 0.26/0.59               => ( Y3
% 0.26/0.59                 != ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 0.26/0.59           => ( ! [A5: $o,B4: $o] :
% 0.26/0.59                  ( ( X3
% 0.26/0.59                    = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59                 => ( ? [Va: nat] :
% 0.26/0.59                        ( Xa
% 0.26/0.59                        = ( suc @ ( suc @ Va ) ) )
% 0.26/0.59                   => ( Y3
% 0.26/0.59                     != ( plus_plus_nat @ one_one_nat @ ( if_nat @ B4 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ) )
% 0.26/0.59             => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 0.26/0.59                      ( X3
% 0.26/0.59                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 0.26/0.59                 => ( Y3 != one_one_nat ) )
% 0.26/0.59               => ( ( ? [V3: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 0.26/0.59                        ( X3
% 0.26/0.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 0.26/0.59                   => ( Y3 != one_one_nat ) )
% 0.26/0.59                 => ( ( ? [V3: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 0.26/0.59                          ( X3
% 0.26/0.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 0.26/0.59                     => ( Y3 != one_one_nat ) )
% 0.26/0.59                   => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                          ( ( X3
% 0.26/0.59                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                         => ( Y3
% 0.26/0.59                           != ( plus_plus_nat @ one_one_nat
% 0.26/0.59                              @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa ) @ one_one_nat
% 0.26/0.59                                @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 0.26/0.59                                  @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.26/0.59                                      @ ( if_nat
% 0.26/0.59                                        @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                           != none_nat )
% 0.26/0.59                                          & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.59                                        @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                        @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 0.26/0.59                                          @ ( if_nat
% 0.26/0.59                                            @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.59                                              = none_nat )
% 0.26/0.59                                            @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.26/0.59                                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.59                                    @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.elims
% 0.26/0.59  thf(fact_6813_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Oelims,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 0.26/0.59        ( ( ( vEBT_T_s_u_c_c @ X3 @ Xa )
% 0.26/0.59          = Y3 )
% 0.26/0.59       => ( ( ? [Uu: $o,B4: $o] :
% 0.26/0.59                ( X3
% 0.26/0.59                = ( vEBT_Leaf @ Uu @ B4 ) )
% 0.26/0.59           => ( ( Xa = zero_zero_nat )
% 0.26/0.59             => ( Y3
% 0.26/0.59               != ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 0.26/0.59         => ( ( ? [Uv: $o,Uw: $o] :
% 0.26/0.59                  ( X3
% 0.26/0.59                  = ( vEBT_Leaf @ Uv @ Uw ) )
% 0.26/0.59             => ( ? [N2: nat] :
% 0.26/0.59                    ( Xa
% 0.26/0.59                    = ( suc @ N2 ) )
% 0.26/0.59               => ( Y3 != one_one_nat ) ) )
% 0.26/0.59           => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.26/0.59                    ( X3
% 0.26/0.59                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 0.26/0.59               => ( Y3 != one_one_nat ) )
% 0.26/0.59             => ( ( ? [V3: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.26/0.59                      ( X3
% 0.26/0.59                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 0.26/0.59                 => ( Y3 != one_one_nat ) )
% 0.26/0.59               => ( ( ? [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 0.26/0.59                        ( X3
% 0.26/0.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 0.26/0.59                   => ( Y3 != one_one_nat ) )
% 0.26/0.59                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                        ( ( X3
% 0.26/0.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                       => ( Y3
% 0.26/0.59                         != ( plus_plus_nat @ one_one_nat
% 0.26/0.59                            @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ one_one_nat
% 0.26/0.59                              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 0.26/0.59                                @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                                  @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.26/0.59                                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.26/0.59                                      @ ( if_nat
% 0.26/0.59                                        @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                           != none_nat )
% 0.26/0.59                                          & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.59                                        @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                        @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 0.26/0.59                                          @ ( if_nat
% 0.26/0.59                                            @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.59                                              = none_nat )
% 0.26/0.59                                            @ one_one_nat
% 0.26/0.59                                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.59                                  @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.elims
% 0.26/0.59  thf(fact_6814_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat] :
% 0.26/0.59        ( ( vEBT_VEBT_membermima @ X3 @ Xa )
% 0.26/0.59       => ( ! [Mi2: nat,Ma2: nat] :
% 0.26/0.59              ( ? [Va3: list_VEBT_VEBT,Vb: vEBT_VEBT] :
% 0.26/0.59                  ( X3
% 0.26/0.59                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb ) )
% 0.26/0.59             => ~ ( ( Xa = Mi2 )
% 0.26/0.59                  | ( Xa = Ma2 ) ) )
% 0.26/0.59         => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList3: list_VEBT_VEBT] :
% 0.26/0.59                ( ? [Vc2: vEBT_VEBT] :
% 0.26/0.59                    ( X3
% 0.26/0.59                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) )
% 0.26/0.59               => ~ ( ( Xa = Mi2 )
% 0.26/0.59                    | ( Xa = Ma2 )
% 0.26/0.59                    | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                       => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                      & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 0.26/0.59           => ~ ! [V3: nat,TreeList3: list_VEBT_VEBT] :
% 0.26/0.59                  ( ? [Vd2: vEBT_VEBT] :
% 0.26/0.59                      ( X3
% 0.26/0.59                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) )
% 0.26/0.59                 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                       => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                      & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % VEBT_internal.membermima.elims(2)
% 0.26/0.59  thf(fact_6815_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I7_J,axiom,
% 0.26/0.59      ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 0.26/0.59        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.26/0.59        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.26/0.59          @ ( if_nat
% 0.26/0.59            @ ( ( ord_less_nat @ X3 @ Mi )
% 0.26/0.59              | ( ord_less_nat @ Ma @ X3 ) )
% 0.26/0.59            @ one_one_nat
% 0.26/0.59            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.26/0.59              @ ( if_nat
% 0.26/0.59                @ ( ( X3 = Mi )
% 0.26/0.59                  & ( X3 = Ma ) )
% 0.26/0.59                @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.26/0.59                @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( X3 = Mi ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ Summary ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 0.26/0.59                  @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.26/0.59                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                      @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.26/0.59                        @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                          @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.26/0.59                              @ ( if_nat
% 0.26/0.59                                @ ( ( ( X3 = Mi )
% 0.26/0.59                                   => ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.26/0.59                                      = Ma ) )
% 0.26/0.59                                  & ( ( X3 != Mi )
% 0.26/0.59                                   => ( X3 = Ma ) ) )
% 0.26/0.59                                @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.26/0.59                                  @ ( plus_plus_nat @ one_one_nat
% 0.26/0.59                                    @ ( if_nat
% 0.26/0.59                                      @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                        = none_nat )
% 0.26/0.59                                      @ one_one_nat
% 0.26/0.59                                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.59                                @ one_one_nat ) ) )
% 0.26/0.59                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.26/0.59                            @ ( if_nat
% 0.26/0.59                              @ ( ( ( X3 = Mi )
% 0.26/0.59                                 => ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.26/0.59                                    = Ma ) )
% 0.26/0.59                                & ( ( X3 != Mi )
% 0.26/0.59                                 => ( X3 = Ma ) ) )
% 0.26/0.59                              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.26/0.59                              @ one_one_nat ) ) ) ) )
% 0.26/0.59                    @ one_one_nat ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(7)
% 0.26/0.59  thf(fact_6816_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat] :
% 0.26/0.59        ( ~ ( vEBT_V5719532721284313246member @ X3 @ Xa )
% 0.26/0.59       => ( ! [A5: $o,B4: $o] :
% 0.26/0.59              ( ( X3
% 0.26/0.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59             => ( ( ( Xa = zero_zero_nat )
% 0.26/0.59                 => A5 )
% 0.26/0.59                & ( ( Xa != zero_zero_nat )
% 0.26/0.59                 => ( ( ( Xa = one_one_nat )
% 0.26/0.59                     => B4 )
% 0.26/0.59                    & ( Xa = one_one_nat ) ) ) ) )
% 0.26/0.59         => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.26/0.59                ( X3
% 0.26/0.59               != ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 0.26/0.59           => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList3: list_VEBT_VEBT] :
% 0.26/0.59                  ( ? [S3: vEBT_VEBT] :
% 0.26/0.59                      ( X3
% 0.26/0.59                      = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) )
% 0.26/0.59                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                     => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % VEBT_internal.naive_member.elims(3)
% 0.26/0.59  thf(fact_6817_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Opelims,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 0.26/0.59        ( ( ( vEBT_T_d_e_l_e_t_e @ X3 @ Xa )
% 0.26/0.59          = Y3 )
% 0.26/0.59       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.59         => ( ! [A5: $o,B4: $o] :
% 0.26/0.59                ( ( X3
% 0.26/0.59                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59               => ( ( Xa = zero_zero_nat )
% 0.26/0.59                 => ( ( Y3 = one_one_nat )
% 0.26/0.59                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ zero_zero_nat ) ) ) ) )
% 0.26/0.59           => ( ! [A5: $o,B4: $o] :
% 0.26/0.59                  ( ( X3
% 0.26/0.59                    = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59                 => ( ( Xa
% 0.26/0.59                      = ( suc @ zero_zero_nat ) )
% 0.26/0.59                   => ( ( Y3 = one_one_nat )
% 0.26/0.59                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 0.26/0.59             => ( ! [A5: $o,B4: $o] :
% 0.26/0.59                    ( ( X3
% 0.26/0.59                      = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59                   => ! [N2: nat] :
% 0.26/0.59                        ( ( Xa
% 0.26/0.59                          = ( suc @ ( suc @ N2 ) ) )
% 0.26/0.59                       => ( ( Y3 = one_one_nat )
% 0.26/0.59                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ ( suc @ ( suc @ N2 ) ) ) ) ) ) )
% 0.26/0.59               => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                      ( ( X3
% 0.26/0.59                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.26/0.59                     => ( ( Y3 = one_one_nat )
% 0.26/0.59                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) @ Xa ) ) ) )
% 0.26/0.59                 => ( ! [Mi2: nat,Ma2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                        ( ( X3
% 0.26/0.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList3 @ Summary2 ) )
% 0.26/0.59                       => ( ( Y3 = one_one_nat )
% 0.26/0.59                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList3 @ Summary2 ) @ Xa ) ) ) )
% 0.26/0.59                   => ( ! [Mi2: nat,Ma2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                          ( ( X3
% 0.26/0.59                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                         => ( ( Y3 = one_one_nat )
% 0.26/0.59                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) )
% 0.26/0.59                     => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                            ( ( X3
% 0.26/0.59                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                           => ( ( Y3
% 0.26/0.59                                = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.26/0.59                                  @ ( if_nat
% 0.26/0.59                                    @ ( ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.59                                      | ( ord_less_nat @ Ma2 @ Xa ) )
% 0.26/0.59                                    @ one_one_nat
% 0.26/0.59                                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.26/0.59                                      @ ( if_nat
% 0.26/0.59                                        @ ( ( Xa = Mi2 )
% 0.26/0.59                                          & ( Xa = Ma2 ) )
% 0.26/0.59                                        @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.26/0.59                                        @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ Summary2 ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 0.26/0.59                                          @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                                            @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                              @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.26/0.59                                                @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                                  @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.26/0.59                                                      @ ( if_nat
% 0.26/0.59                                                        @ ( ( ( Xa = Mi2 )
% 0.26/0.59                                                           => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.26/0.59                                                              = Ma2 ) )
% 0.26/0.59                                                          & ( ( Xa != Mi2 )
% 0.26/0.59                                                           => ( Xa = Ma2 ) ) )
% 0.26/0.59                                                        @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.26/0.59                                                          @ ( plus_plus_nat @ one_one_nat
% 0.26/0.59                                                            @ ( if_nat
% 0.26/0.59                                                              @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                                                = none_nat )
% 0.26/0.59                                                              @ one_one_nat
% 0.26/0.59                                                              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.59                                                        @ one_one_nat ) ) )
% 0.26/0.59                                                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.26/0.59                                                    @ ( if_nat
% 0.26/0.59                                                      @ ( ( ( Xa = Mi2 )
% 0.26/0.59                                                         => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.26/0.59                                                            = Ma2 ) )
% 0.26/0.59                                                        & ( ( Xa != Mi2 )
% 0.26/0.59                                                         => ( Xa = Ma2 ) ) )
% 0.26/0.59                                                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.26/0.59                                                      @ one_one_nat ) ) ) ) )
% 0.26/0.59                                            @ one_one_nat ) ) ) ) ) ) )
% 0.26/0.59                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.pelims
% 0.26/0.59  thf(fact_6818_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Opelims,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 0.26/0.59        ( ( ( vEBT_T_s_u_c_c @ X3 @ Xa )
% 0.26/0.59          = Y3 )
% 0.26/0.59       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.59         => ( ! [Uu: $o,B4: $o] :
% 0.26/0.59                ( ( X3
% 0.26/0.59                  = ( vEBT_Leaf @ Uu @ B4 ) )
% 0.26/0.59               => ( ( Xa = zero_zero_nat )
% 0.26/0.59                 => ( ( Y3
% 0.26/0.59                      = ( plus_plus_nat @ one_one_nat @ one_one_nat ) )
% 0.26/0.59                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ B4 ) @ zero_zero_nat ) ) ) ) )
% 0.26/0.59           => ( ! [Uv: $o,Uw: $o] :
% 0.26/0.59                  ( ( X3
% 0.26/0.59                    = ( vEBT_Leaf @ Uv @ Uw ) )
% 0.26/0.59                 => ! [N2: nat] :
% 0.26/0.59                      ( ( Xa
% 0.26/0.59                        = ( suc @ N2 ) )
% 0.26/0.59                     => ( ( Y3 = one_one_nat )
% 0.26/0.59                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N2 ) ) ) ) ) )
% 0.26/0.59             => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.26/0.59                    ( ( X3
% 0.26/0.59                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 0.26/0.59                   => ( ( Y3 = one_one_nat )
% 0.26/0.59                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa ) ) ) )
% 0.26/0.59               => ( ! [V3: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.26/0.59                      ( ( X3
% 0.26/0.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 0.26/0.59                     => ( ( Y3 = one_one_nat )
% 0.26/0.59                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa ) ) ) )
% 0.26/0.59                 => ( ! [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 0.26/0.59                        ( ( X3
% 0.26/0.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 0.26/0.59                       => ( ( Y3 = one_one_nat )
% 0.26/0.59                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Xa ) ) ) )
% 0.26/0.59                   => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                          ( ( X3
% 0.26/0.59                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                         => ( ( Y3
% 0.26/0.59                              = ( plus_plus_nat @ one_one_nat
% 0.26/0.59                                @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ one_one_nat
% 0.26/0.59                                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 0.26/0.59                                    @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                                      @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.26/0.59                                        @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.26/0.59                                          @ ( if_nat
% 0.26/0.59                                            @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                               != none_nat )
% 0.26/0.59                                              & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.59                                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                            @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 0.26/0.59                                              @ ( if_nat
% 0.26/0.59                                                @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.59                                                  = none_nat )
% 0.26/0.59                                                @ one_one_nat
% 0.26/0.59                                                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.59                                      @ one_one_nat ) ) ) ) )
% 0.26/0.59                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.pelims
% 0.26/0.59  thf(fact_6819_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Opelims,axiom,
% 0.26/0.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 0.26/0.59        ( ( ( vEBT_T_p_r_e_d @ X3 @ Xa )
% 0.26/0.59          = Y3 )
% 0.26/0.59       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.59         => ( ! [Uu: $o,Uv: $o] :
% 0.26/0.59                ( ( X3
% 0.26/0.59                  = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.26/0.59               => ( ( Xa = zero_zero_nat )
% 0.26/0.59                 => ( ( Y3 = one_one_nat )
% 0.26/0.59                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat ) ) ) ) )
% 0.26/0.59           => ( ! [A5: $o,Uw: $o] :
% 0.26/0.59                  ( ( X3
% 0.26/0.59                    = ( vEBT_Leaf @ A5 @ Uw ) )
% 0.26/0.59                 => ( ( Xa
% 0.26/0.59                      = ( suc @ zero_zero_nat ) )
% 0.26/0.59                   => ( ( Y3
% 0.26/0.59                        = ( plus_plus_nat @ one_one_nat @ one_one_nat ) )
% 0.26/0.59                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 0.26/0.59             => ( ! [A5: $o,B4: $o] :
% 0.26/0.59                    ( ( X3
% 0.26/0.59                      = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.59                   => ! [Va: nat] :
% 0.26/0.59                        ( ( Xa
% 0.26/0.59                          = ( suc @ ( suc @ Va ) ) )
% 0.26/0.59                       => ( ( Y3
% 0.26/0.59                            = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B4 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 0.26/0.59                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ ( suc @ ( suc @ Va ) ) ) ) ) ) )
% 0.26/0.59               => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 0.26/0.59                      ( ( X3
% 0.26/0.59                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 0.26/0.59                     => ( ( Y3 = one_one_nat )
% 0.26/0.59                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa ) ) ) )
% 0.26/0.59                 => ( ! [V3: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 0.26/0.59                        ( ( X3
% 0.26/0.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 0.26/0.59                       => ( ( Y3 = one_one_nat )
% 0.26/0.59                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa ) ) ) )
% 0.26/0.59                   => ( ! [V3: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 0.26/0.59                          ( ( X3
% 0.26/0.59                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 0.26/0.59                         => ( ( Y3 = one_one_nat )
% 0.26/0.59                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Xa ) ) ) )
% 0.26/0.59                     => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.59                            ( ( X3
% 0.26/0.59                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.59                           => ( ( Y3
% 0.26/0.59                                = ( plus_plus_nat @ one_one_nat
% 0.26/0.59                                  @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa ) @ one_one_nat
% 0.26/0.59                                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 0.26/0.59                                      @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.59                                        @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.26/0.59                                          @ ( if_nat
% 0.26/0.59                                            @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                               != none_nat )
% 0.26/0.59                                              & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.59                                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.59                                            @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 0.26/0.59                                              @ ( if_nat
% 0.26/0.59                                                @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.59                                                  = none_nat )
% 0.26/0.59                                                @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.26/0.59                                                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.59                                        @ one_one_nat ) ) ) ) )
% 0.26/0.59                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.pelims
% 0.26/0.59  thf(fact_6820_pred__empty,axiom,
% 0.26/0.59      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.59        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.59       => ( ( ( vEBT_vebt_pred @ T @ X3 )
% 0.26/0.59            = none_nat )
% 0.26/0.59          = ( ( collect_nat
% 0.26/0.59              @ ^ [Y: nat] :
% 0.26/0.59                  ( ( vEBT_vebt_member @ T @ Y )
% 0.26/0.59                  & ( ord_less_nat @ Y @ X3 ) ) )
% 0.26/0.59            = bot_bot_set_nat ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % pred_empty
% 0.26/0.59  thf(fact_6821_succ__empty,axiom,
% 0.26/0.59      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.59        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.59       => ( ( ( vEBT_vebt_succ @ T @ X3 )
% 0.26/0.59            = none_nat )
% 0.26/0.59          = ( ( collect_nat
% 0.26/0.59              @ ^ [Y: nat] :
% 0.26/0.59                  ( ( vEBT_vebt_member @ T @ Y )
% 0.26/0.59                  & ( ord_less_nat @ X3 @ Y ) ) )
% 0.26/0.59            = bot_bot_set_nat ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % succ_empty
% 0.26/0.59  thf(fact_6822_buildup__gives__empty,axiom,
% 0.26/0.59      ! [N: nat] :
% 0.26/0.59        ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 0.26/0.59        = bot_bot_set_nat ) ).
% 0.26/0.59  
% 0.26/0.59  % buildup_gives_empty
% 0.26/0.59  thf(fact_6823_mint__corr__help__empty,axiom,
% 0.26/0.59      ! [T: vEBT_VEBT,N: nat] :
% 0.26/0.59        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.59       => ( ( ( vEBT_vebt_mint @ T )
% 0.26/0.59            = none_nat )
% 0.26/0.59         => ( ( vEBT_VEBT_set_vebt @ T )
% 0.26/0.59            = bot_bot_set_nat ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % mint_corr_help_empty
% 0.26/0.59  thf(fact_6824_maxt__corr__help__empty,axiom,
% 0.26/0.59      ! [T: vEBT_VEBT,N: nat] :
% 0.26/0.59        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.59       => ( ( ( vEBT_vebt_maxt @ T )
% 0.26/0.59            = none_nat )
% 0.26/0.59         => ( ( vEBT_VEBT_set_vebt @ T )
% 0.26/0.59            = bot_bot_set_nat ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % maxt_corr_help_empty
% 0.26/0.59  thf(fact_6825_max__bot,axiom,
% 0.26/0.59      ! [X3: set_Extended_enat] :
% 0.26/0.59        ( ( ord_ma4205026669011143323d_enat @ bot_bo7653980558646680370d_enat @ X3 )
% 0.26/0.59        = X3 ) ).
% 0.26/0.59  
% 0.26/0.59  % max_bot
% 0.26/0.59  thf(fact_6826_max__bot,axiom,
% 0.26/0.59      ! [X3: set_real] :
% 0.26/0.59        ( ( ord_max_set_real @ bot_bot_set_real @ X3 )
% 0.26/0.59        = X3 ) ).
% 0.26/0.59  
% 0.26/0.59  % max_bot
% 0.26/0.59  thf(fact_6827_max__bot,axiom,
% 0.26/0.59      ! [X3: set_nat] :
% 0.26/0.59        ( ( ord_max_set_nat @ bot_bot_set_nat @ X3 )
% 0.26/0.59        = X3 ) ).
% 0.26/0.59  
% 0.26/0.59  % max_bot
% 0.26/0.59  thf(fact_6828_max__bot,axiom,
% 0.26/0.59      ! [X3: set_int] :
% 0.26/0.59        ( ( ord_max_set_int @ bot_bot_set_int @ X3 )
% 0.26/0.59        = X3 ) ).
% 0.26/0.59  
% 0.26/0.59  % max_bot
% 0.26/0.59  thf(fact_6829_max__bot,axiom,
% 0.26/0.59      ! [X3: nat] :
% 0.26/0.59        ( ( ord_max_nat @ bot_bot_nat @ X3 )
% 0.26/0.59        = X3 ) ).
% 0.26/0.59  
% 0.26/0.59  % max_bot
% 0.26/0.59  thf(fact_6830_max__bot,axiom,
% 0.26/0.59      ! [X3: extended_enat] :
% 0.26/0.59        ( ( ord_ma741700101516333627d_enat @ bot_bo4199563552545308370d_enat @ X3 )
% 0.26/0.59        = X3 ) ).
% 0.26/0.59  
% 0.26/0.59  % max_bot
% 0.26/0.59  thf(fact_6831_max__bot2,axiom,
% 0.26/0.59      ! [X3: set_Extended_enat] :
% 0.26/0.59        ( ( ord_ma4205026669011143323d_enat @ X3 @ bot_bo7653980558646680370d_enat )
% 0.26/0.59        = X3 ) ).
% 0.26/0.59  
% 0.26/0.59  % max_bot2
% 0.26/0.59  thf(fact_6832_max__bot2,axiom,
% 0.26/0.59      ! [X3: set_real] :
% 0.26/0.59        ( ( ord_max_set_real @ X3 @ bot_bot_set_real )
% 0.26/0.59        = X3 ) ).
% 0.26/0.59  
% 0.26/0.59  % max_bot2
% 0.26/0.59  thf(fact_6833_max__bot2,axiom,
% 0.26/0.59      ! [X3: set_nat] :
% 0.26/0.59        ( ( ord_max_set_nat @ X3 @ bot_bot_set_nat )
% 0.26/0.59        = X3 ) ).
% 0.26/0.59  
% 0.26/0.59  % max_bot2
% 0.26/0.59  thf(fact_6834_max__bot2,axiom,
% 0.26/0.59      ! [X3: set_int] :
% 0.26/0.59        ( ( ord_max_set_int @ X3 @ bot_bot_set_int )
% 0.26/0.59        = X3 ) ).
% 0.26/0.59  
% 0.26/0.59  % max_bot2
% 0.26/0.59  thf(fact_6835_max__bot2,axiom,
% 0.26/0.59      ! [X3: nat] :
% 0.26/0.59        ( ( ord_max_nat @ X3 @ bot_bot_nat )
% 0.26/0.59        = X3 ) ).
% 0.26/0.59  
% 0.26/0.59  % max_bot2
% 0.26/0.59  thf(fact_6836_max__bot2,axiom,
% 0.26/0.59      ! [X3: extended_enat] :
% 0.26/0.59        ( ( ord_ma741700101516333627d_enat @ X3 @ bot_bo4199563552545308370d_enat )
% 0.26/0.59        = X3 ) ).
% 0.26/0.59  
% 0.26/0.59  % max_bot2
% 0.26/0.59  thf(fact_6837_atLeastatMost__empty__iff,axiom,
% 0.26/0.59      ! [A: extended_enat,B: extended_enat] :
% 0.26/0.59        ( ( ( set_or5403411693681687835d_enat @ A @ B )
% 0.26/0.59          = bot_bo7653980558646680370d_enat )
% 0.26/0.59        = ( ~ ( ord_le2932123472753598470d_enat @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % atLeastatMost_empty_iff
% 0.26/0.59  thf(fact_6838_atLeastatMost__empty__iff,axiom,
% 0.26/0.59      ! [A: set_nat,B: set_nat] :
% 0.26/0.59        ( ( ( set_or4548717258645045905et_nat @ A @ B )
% 0.26/0.59          = bot_bot_set_set_nat )
% 0.26/0.59        = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % atLeastatMost_empty_iff
% 0.26/0.59  thf(fact_6839_atLeastatMost__empty__iff,axiom,
% 0.26/0.59      ! [A: rat,B: rat] :
% 0.26/0.59        ( ( ( set_or633870826150836451st_rat @ A @ B )
% 0.26/0.59          = bot_bot_set_rat )
% 0.26/0.59        = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.26/0.59  
% 0.26/0.59  % atLeastatMost_empty_iff
% 0.26/0.59  thf(fact_6840_atLeastatMost__empty__iff,axiom,
% 0.26/0.60      ! [A: num,B: num] :
% 0.26/0.60        ( ( ( set_or7049704709247886629st_num @ A @ B )
% 0.26/0.60          = bot_bot_set_num )
% 0.26/0.60        = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % atLeastatMost_empty_iff
% 0.26/0.60  thf(fact_6841_atLeastatMost__empty__iff,axiom,
% 0.26/0.60      ! [A: nat,B: nat] :
% 0.26/0.60        ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.26/0.60          = bot_bot_set_nat )
% 0.26/0.60        = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % atLeastatMost_empty_iff
% 0.26/0.60  thf(fact_6842_atLeastatMost__empty__iff,axiom,
% 0.26/0.60      ! [A: int,B: int] :
% 0.26/0.60        ( ( ( set_or1266510415728281911st_int @ A @ B )
% 0.26/0.60          = bot_bot_set_int )
% 0.26/0.60        = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % atLeastatMost_empty_iff
% 0.26/0.60  thf(fact_6843_atLeastatMost__empty__iff,axiom,
% 0.26/0.60      ! [A: real,B: real] :
% 0.26/0.60        ( ( ( set_or1222579329274155063t_real @ A @ B )
% 0.26/0.60          = bot_bot_set_real )
% 0.26/0.60        = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % atLeastatMost_empty_iff
% 0.26/0.60  thf(fact_6844_atLeastatMost__empty__iff2,axiom,
% 0.26/0.60      ! [A: extended_enat,B: extended_enat] :
% 0.26/0.60        ( ( bot_bo7653980558646680370d_enat
% 0.26/0.60          = ( set_or5403411693681687835d_enat @ A @ B ) )
% 0.26/0.60        = ( ~ ( ord_le2932123472753598470d_enat @ A @ B ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % atLeastatMost_empty_iff2
% 0.26/0.60  thf(fact_6845_atLeastatMost__empty__iff2,axiom,
% 0.26/0.60      ! [A: set_nat,B: set_nat] :
% 0.26/0.60        ( ( bot_bot_set_set_nat
% 0.26/0.60          = ( set_or4548717258645045905et_nat @ A @ B ) )
% 0.26/0.60        = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % atLeastatMost_empty_iff2
% 0.26/0.60  thf(fact_6846_atLeastatMost__empty__iff2,axiom,
% 0.26/0.60      ! [A: rat,B: rat] :
% 0.26/0.60        ( ( bot_bot_set_rat
% 0.26/0.60          = ( set_or633870826150836451st_rat @ A @ B ) )
% 0.26/0.60        = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % atLeastatMost_empty_iff2
% 0.26/0.60  thf(fact_6847_atLeastatMost__empty__iff2,axiom,
% 0.26/0.60      ! [A: num,B: num] :
% 0.26/0.60        ( ( bot_bot_set_num
% 0.26/0.60          = ( set_or7049704709247886629st_num @ A @ B ) )
% 0.26/0.60        = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % atLeastatMost_empty_iff2
% 0.26/0.60  thf(fact_6848_atLeastatMost__empty__iff2,axiom,
% 0.26/0.60      ! [A: nat,B: nat] :
% 0.26/0.60        ( ( bot_bot_set_nat
% 0.26/0.60          = ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.26/0.60        = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % atLeastatMost_empty_iff2
% 0.26/0.60  thf(fact_6849_atLeastatMost__empty__iff2,axiom,
% 0.26/0.60      ! [A: int,B: int] :
% 0.26/0.60        ( ( bot_bot_set_int
% 0.26/0.60          = ( set_or1266510415728281911st_int @ A @ B ) )
% 0.26/0.60        = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % atLeastatMost_empty_iff2
% 0.26/0.60  thf(fact_6850_atLeastatMost__empty__iff2,axiom,
% 0.26/0.60      ! [A: real,B: real] :
% 0.26/0.60        ( ( bot_bot_set_real
% 0.26/0.60          = ( set_or1222579329274155063t_real @ A @ B ) )
% 0.26/0.60        = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % atLeastatMost_empty_iff2
% 0.26/0.60  thf(fact_6851_atLeastatMost__empty,axiom,
% 0.26/0.60      ! [B: extended_enat,A: extended_enat] :
% 0.26/0.60        ( ( ord_le72135733267957522d_enat @ B @ A )
% 0.26/0.60       => ( ( set_or5403411693681687835d_enat @ A @ B )
% 0.26/0.60          = bot_bo7653980558646680370d_enat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % atLeastatMost_empty
% 0.26/0.60  thf(fact_6852_atLeastatMost__empty,axiom,
% 0.26/0.60      ! [B: rat,A: rat] :
% 0.26/0.60        ( ( ord_less_rat @ B @ A )
% 0.26/0.60       => ( ( set_or633870826150836451st_rat @ A @ B )
% 0.26/0.60          = bot_bot_set_rat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % atLeastatMost_empty
% 0.26/0.60  thf(fact_6853_atLeastatMost__empty,axiom,
% 0.26/0.60      ! [B: num,A: num] :
% 0.26/0.60        ( ( ord_less_num @ B @ A )
% 0.26/0.60       => ( ( set_or7049704709247886629st_num @ A @ B )
% 0.26/0.60          = bot_bot_set_num ) ) ).
% 0.26/0.60  
% 0.26/0.60  % atLeastatMost_empty
% 0.26/0.60  thf(fact_6854_atLeastatMost__empty,axiom,
% 0.26/0.60      ! [B: nat,A: nat] :
% 0.26/0.60        ( ( ord_less_nat @ B @ A )
% 0.26/0.60       => ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.26/0.60          = bot_bot_set_nat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % atLeastatMost_empty
% 0.26/0.60  thf(fact_6855_atLeastatMost__empty,axiom,
% 0.26/0.60      ! [B: int,A: int] :
% 0.26/0.60        ( ( ord_less_int @ B @ A )
% 0.26/0.60       => ( ( set_or1266510415728281911st_int @ A @ B )
% 0.26/0.60          = bot_bot_set_int ) ) ).
% 0.26/0.60  
% 0.26/0.60  % atLeastatMost_empty
% 0.26/0.60  thf(fact_6856_atLeastatMost__empty,axiom,
% 0.26/0.60      ! [B: real,A: real] :
% 0.26/0.60        ( ( ord_less_real @ B @ A )
% 0.26/0.60       => ( ( set_or1222579329274155063t_real @ A @ B )
% 0.26/0.60          = bot_bot_set_real ) ) ).
% 0.26/0.60  
% 0.26/0.60  % atLeastatMost_empty
% 0.26/0.60  thf(fact_6857_bot_Oextremum,axiom,
% 0.26/0.60      ! [A: set_Extended_enat] : ( ord_le7203529160286727270d_enat @ bot_bo7653980558646680370d_enat @ A ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.extremum
% 0.26/0.60  thf(fact_6858_bot_Oextremum,axiom,
% 0.26/0.60      ! [A: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.extremum
% 0.26/0.60  thf(fact_6859_bot_Oextremum,axiom,
% 0.26/0.60      ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.extremum
% 0.26/0.60  thf(fact_6860_bot_Oextremum,axiom,
% 0.26/0.60      ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.extremum
% 0.26/0.60  thf(fact_6861_bot_Oextremum,axiom,
% 0.26/0.60      ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.extremum
% 0.26/0.60  thf(fact_6862_bot_Oextremum__unique,axiom,
% 0.26/0.60      ! [A: set_Extended_enat] :
% 0.26/0.60        ( ( ord_le7203529160286727270d_enat @ A @ bot_bo7653980558646680370d_enat )
% 0.26/0.60        = ( A = bot_bo7653980558646680370d_enat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.extremum_unique
% 0.26/0.60  thf(fact_6863_bot_Oextremum__unique,axiom,
% 0.26/0.60      ! [A: set_real] :
% 0.26/0.60        ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 0.26/0.60        = ( A = bot_bot_set_real ) ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.extremum_unique
% 0.26/0.60  thf(fact_6864_bot_Oextremum__unique,axiom,
% 0.26/0.60      ! [A: set_int] :
% 0.26/0.60        ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 0.26/0.60        = ( A = bot_bot_set_int ) ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.extremum_unique
% 0.26/0.60  thf(fact_6865_bot_Oextremum__unique,axiom,
% 0.26/0.60      ! [A: set_nat] :
% 0.26/0.60        ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 0.26/0.60        = ( A = bot_bot_set_nat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.extremum_unique
% 0.26/0.60  thf(fact_6866_bot_Oextremum__unique,axiom,
% 0.26/0.60      ! [A: nat] :
% 0.26/0.60        ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 0.26/0.60        = ( A = bot_bot_nat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.extremum_unique
% 0.26/0.60  thf(fact_6867_bot_Oextremum__uniqueI,axiom,
% 0.26/0.60      ! [A: set_Extended_enat] :
% 0.26/0.60        ( ( ord_le7203529160286727270d_enat @ A @ bot_bo7653980558646680370d_enat )
% 0.26/0.60       => ( A = bot_bo7653980558646680370d_enat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.extremum_uniqueI
% 0.26/0.60  thf(fact_6868_bot_Oextremum__uniqueI,axiom,
% 0.26/0.60      ! [A: set_real] :
% 0.26/0.60        ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 0.26/0.60       => ( A = bot_bot_set_real ) ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.extremum_uniqueI
% 0.26/0.60  thf(fact_6869_bot_Oextremum__uniqueI,axiom,
% 0.26/0.60      ! [A: set_int] :
% 0.26/0.60        ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 0.26/0.60       => ( A = bot_bot_set_int ) ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.extremum_uniqueI
% 0.26/0.60  thf(fact_6870_bot_Oextremum__uniqueI,axiom,
% 0.26/0.60      ! [A: set_nat] :
% 0.26/0.60        ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 0.26/0.60       => ( A = bot_bot_set_nat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.extremum_uniqueI
% 0.26/0.60  thf(fact_6871_bot_Oextremum__uniqueI,axiom,
% 0.26/0.60      ! [A: nat] :
% 0.26/0.60        ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 0.26/0.60       => ( A = bot_bot_nat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.extremum_uniqueI
% 0.26/0.60  thf(fact_6872_bot_Onot__eq__extremum,axiom,
% 0.26/0.60      ! [A: set_Extended_enat] :
% 0.26/0.60        ( ( A != bot_bo7653980558646680370d_enat )
% 0.26/0.60        = ( ord_le2529575680413868914d_enat @ bot_bo7653980558646680370d_enat @ A ) ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.not_eq_extremum
% 0.26/0.60  thf(fact_6873_bot_Onot__eq__extremum,axiom,
% 0.26/0.60      ! [A: set_real] :
% 0.26/0.60        ( ( A != bot_bot_set_real )
% 0.26/0.60        = ( ord_less_set_real @ bot_bot_set_real @ A ) ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.not_eq_extremum
% 0.26/0.60  thf(fact_6874_bot_Onot__eq__extremum,axiom,
% 0.26/0.60      ! [A: set_nat] :
% 0.26/0.60        ( ( A != bot_bot_set_nat )
% 0.26/0.60        = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.not_eq_extremum
% 0.26/0.60  thf(fact_6875_bot_Onot__eq__extremum,axiom,
% 0.26/0.60      ! [A: set_int] :
% 0.26/0.60        ( ( A != bot_bot_set_int )
% 0.26/0.60        = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.not_eq_extremum
% 0.26/0.60  thf(fact_6876_bot_Onot__eq__extremum,axiom,
% 0.26/0.60      ! [A: nat] :
% 0.26/0.60        ( ( A != bot_bot_nat )
% 0.26/0.60        = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.not_eq_extremum
% 0.26/0.60  thf(fact_6877_bot_Oextremum__strict,axiom,
% 0.26/0.60      ! [A: set_Extended_enat] :
% 0.26/0.60        ~ ( ord_le2529575680413868914d_enat @ A @ bot_bo7653980558646680370d_enat ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.extremum_strict
% 0.26/0.60  thf(fact_6878_bot_Oextremum__strict,axiom,
% 0.26/0.60      ! [A: set_real] :
% 0.26/0.60        ~ ( ord_less_set_real @ A @ bot_bot_set_real ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.extremum_strict
% 0.26/0.60  thf(fact_6879_bot_Oextremum__strict,axiom,
% 0.26/0.60      ! [A: set_nat] :
% 0.26/0.60        ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.extremum_strict
% 0.26/0.60  thf(fact_6880_bot_Oextremum__strict,axiom,
% 0.26/0.60      ! [A: set_int] :
% 0.26/0.60        ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.extremum_strict
% 0.26/0.60  thf(fact_6881_bot_Oextremum__strict,axiom,
% 0.26/0.60      ! [A: nat] :
% 0.26/0.60        ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 0.26/0.60  
% 0.26/0.60  % bot.extremum_strict
% 0.26/0.60  thf(fact_6882_diff__shunt__var,axiom,
% 0.26/0.60      ! [X3: set_Extended_enat,Y3: set_Extended_enat] :
% 0.26/0.60        ( ( ( minus_925952699566721837d_enat @ X3 @ Y3 )
% 0.26/0.60          = bot_bo7653980558646680370d_enat )
% 0.26/0.60        = ( ord_le7203529160286727270d_enat @ X3 @ Y3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % diff_shunt_var
% 0.26/0.60  thf(fact_6883_diff__shunt__var,axiom,
% 0.26/0.60      ! [X3: set_real,Y3: set_real] :
% 0.26/0.60        ( ( ( minus_minus_set_real @ X3 @ Y3 )
% 0.26/0.60          = bot_bot_set_real )
% 0.26/0.60        = ( ord_less_eq_set_real @ X3 @ Y3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % diff_shunt_var
% 0.26/0.60  thf(fact_6884_diff__shunt__var,axiom,
% 0.26/0.60      ! [X3: set_int,Y3: set_int] :
% 0.26/0.60        ( ( ( minus_minus_set_int @ X3 @ Y3 )
% 0.26/0.60          = bot_bot_set_int )
% 0.26/0.60        = ( ord_less_eq_set_int @ X3 @ Y3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % diff_shunt_var
% 0.26/0.60  thf(fact_6885_diff__shunt__var,axiom,
% 0.26/0.60      ! [X3: set_nat,Y3: set_nat] :
% 0.26/0.60        ( ( ( minus_minus_set_nat @ X3 @ Y3 )
% 0.26/0.60          = bot_bot_set_nat )
% 0.26/0.60        = ( ord_less_eq_set_nat @ X3 @ Y3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % diff_shunt_var
% 0.26/0.60  thf(fact_6886_vebt__succ_Opelims,axiom,
% 0.26/0.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: option_nat] :
% 0.26/0.60        ( ( ( vEBT_vebt_succ @ X3 @ Xa )
% 0.26/0.60          = Y3 )
% 0.26/0.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.60         => ( ! [Uu: $o,B4: $o] :
% 0.26/0.60                ( ( X3
% 0.26/0.60                  = ( vEBT_Leaf @ Uu @ B4 ) )
% 0.26/0.60               => ( ( Xa = zero_zero_nat )
% 0.26/0.60                 => ( ( ( B4
% 0.26/0.60                       => ( Y3
% 0.26/0.60                          = ( some_nat @ one_one_nat ) ) )
% 0.26/0.60                      & ( ~ B4
% 0.26/0.60                       => ( Y3 = none_nat ) ) )
% 0.26/0.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ B4 ) @ zero_zero_nat ) ) ) ) )
% 0.26/0.60           => ( ! [Uv: $o,Uw: $o] :
% 0.26/0.60                  ( ( X3
% 0.26/0.60                    = ( vEBT_Leaf @ Uv @ Uw ) )
% 0.26/0.60                 => ! [N2: nat] :
% 0.26/0.60                      ( ( Xa
% 0.26/0.60                        = ( suc @ N2 ) )
% 0.26/0.60                     => ( ( Y3 = none_nat )
% 0.26/0.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N2 ) ) ) ) ) )
% 0.26/0.60             => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.26/0.60                    ( ( X3
% 0.26/0.60                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 0.26/0.60                   => ( ( Y3 = none_nat )
% 0.26/0.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa ) ) ) )
% 0.26/0.60               => ( ! [V3: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.26/0.60                      ( ( X3
% 0.26/0.60                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 0.26/0.60                     => ( ( Y3 = none_nat )
% 0.26/0.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa ) ) ) )
% 0.26/0.60                 => ( ! [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 0.26/0.60                        ( ( X3
% 0.26/0.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 0.26/0.60                       => ( ( Y3 = none_nat )
% 0.26/0.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Xa ) ) ) )
% 0.26/0.60                   => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.60                          ( ( X3
% 0.26/0.60                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.60                         => ( ( ( ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.60                               => ( Y3
% 0.26/0.60                                  = ( some_nat @ Mi2 ) ) )
% 0.26/0.60                              & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.60                               => ( Y3
% 0.26/0.60                                  = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.60                                    @ ( if_option_nat
% 0.26/0.60                                      @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                                         != none_nat )
% 0.26/0.60                                        & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.60                                      @ ( 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 @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                                      @ ( if_option_nat
% 0.26/0.60                                        @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.60                                          = none_nat )
% 0.26/0.60                                        @ none_nat
% 0.26/0.60                                        @ ( 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 @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.60                                    @ none_nat ) ) ) )
% 0.26/0.60                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % vebt_succ.pelims
% 0.26/0.60  thf(fact_6887_vebt__pred_Opelims,axiom,
% 0.26/0.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: option_nat] :
% 0.26/0.60        ( ( ( vEBT_vebt_pred @ X3 @ Xa )
% 0.26/0.60          = Y3 )
% 0.26/0.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.60         => ( ! [Uu: $o,Uv: $o] :
% 0.26/0.60                ( ( X3
% 0.26/0.60                  = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.26/0.60               => ( ( Xa = zero_zero_nat )
% 0.26/0.60                 => ( ( Y3 = none_nat )
% 0.26/0.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat ) ) ) ) )
% 0.26/0.60           => ( ! [A5: $o,Uw: $o] :
% 0.26/0.60                  ( ( X3
% 0.26/0.60                    = ( vEBT_Leaf @ A5 @ Uw ) )
% 0.26/0.60                 => ( ( Xa
% 0.26/0.60                      = ( suc @ zero_zero_nat ) )
% 0.26/0.60                   => ( ( ( A5
% 0.26/0.60                         => ( Y3
% 0.26/0.60                            = ( some_nat @ zero_zero_nat ) ) )
% 0.26/0.60                        & ( ~ A5
% 0.26/0.60                         => ( Y3 = none_nat ) ) )
% 0.26/0.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 0.26/0.60             => ( ! [A5: $o,B4: $o] :
% 0.26/0.60                    ( ( X3
% 0.26/0.60                      = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.60                   => ! [Va: nat] :
% 0.26/0.60                        ( ( Xa
% 0.26/0.60                          = ( suc @ ( suc @ Va ) ) )
% 0.26/0.60                       => ( ( ( B4
% 0.26/0.60                             => ( Y3
% 0.26/0.60                                = ( some_nat @ one_one_nat ) ) )
% 0.26/0.60                            & ( ~ B4
% 0.26/0.60                             => ( ( A5
% 0.26/0.60                                 => ( Y3
% 0.26/0.60                                    = ( some_nat @ zero_zero_nat ) ) )
% 0.26/0.60                                & ( ~ A5
% 0.26/0.60                                 => ( Y3 = none_nat ) ) ) ) )
% 0.26/0.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ ( suc @ ( suc @ Va ) ) ) ) ) ) )
% 0.26/0.60               => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 0.26/0.60                      ( ( X3
% 0.26/0.60                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 0.26/0.60                     => ( ( Y3 = none_nat )
% 0.26/0.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa ) ) ) )
% 0.26/0.60                 => ( ! [V3: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 0.26/0.60                        ( ( X3
% 0.26/0.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 0.26/0.60                       => ( ( Y3 = none_nat )
% 0.26/0.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa ) ) ) )
% 0.26/0.60                   => ( ! [V3: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 0.26/0.60                          ( ( X3
% 0.26/0.60                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 0.26/0.60                         => ( ( Y3 = none_nat )
% 0.26/0.60                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Xa ) ) ) )
% 0.26/0.60                     => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.60                            ( ( X3
% 0.26/0.60                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.60                           => ( ( ( ( ord_less_nat @ Ma2 @ Xa )
% 0.26/0.60                                 => ( Y3
% 0.26/0.60                                    = ( some_nat @ Ma2 ) ) )
% 0.26/0.60                                & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 0.26/0.60                                 => ( Y3
% 0.26/0.60                                    = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.60                                      @ ( if_option_nat
% 0.26/0.60                                        @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                                           != none_nat )
% 0.26/0.60                                          & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.60                                        @ ( 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 @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                                        @ ( if_option_nat
% 0.26/0.60                                          @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.60                                            = none_nat )
% 0.26/0.60                                          @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa ) @ ( some_nat @ Mi2 ) @ none_nat )
% 0.26/0.60                                          @ ( 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 @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.60                                      @ none_nat ) ) ) )
% 0.26/0.60                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % vebt_pred.pelims
% 0.26/0.60  thf(fact_6888_vebt__delete_Opelims,axiom,
% 0.26/0.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: vEBT_VEBT] :
% 0.26/0.60        ( ( ( vEBT_vebt_delete @ X3 @ Xa )
% 0.26/0.60          = Y3 )
% 0.26/0.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.60         => ( ! [A5: $o,B4: $o] :
% 0.26/0.60                ( ( X3
% 0.26/0.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.60               => ( ( Xa = zero_zero_nat )
% 0.26/0.60                 => ( ( Y3
% 0.26/0.60                      = ( vEBT_Leaf @ $false @ B4 ) )
% 0.26/0.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ zero_zero_nat ) ) ) ) )
% 0.26/0.60           => ( ! [A5: $o,B4: $o] :
% 0.26/0.60                  ( ( X3
% 0.26/0.60                    = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.60                 => ( ( Xa
% 0.26/0.60                      = ( suc @ zero_zero_nat ) )
% 0.26/0.60                   => ( ( Y3
% 0.26/0.60                        = ( vEBT_Leaf @ A5 @ $false ) )
% 0.26/0.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 0.26/0.60             => ( ! [A5: $o,B4: $o] :
% 0.26/0.60                    ( ( X3
% 0.26/0.60                      = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.60                   => ! [N2: nat] :
% 0.26/0.60                        ( ( Xa
% 0.26/0.60                          = ( suc @ ( suc @ N2 ) ) )
% 0.26/0.60                       => ( ( Y3
% 0.26/0.60                            = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ ( suc @ ( suc @ N2 ) ) ) ) ) ) )
% 0.26/0.60               => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.60                      ( ( X3
% 0.26/0.60                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.26/0.60                     => ( ( Y3
% 0.26/0.60                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.26/0.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) @ Xa ) ) ) )
% 0.26/0.60                 => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 0.26/0.60                        ( ( X3
% 0.26/0.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 0.26/0.60                       => ( ( Y3
% 0.26/0.60                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 0.26/0.60                         => ~ ( 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 ) @ Xa ) ) ) )
% 0.26/0.60                   => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 0.26/0.60                          ( ( X3
% 0.26/0.60                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 0.26/0.60                         => ( ( Y3
% 0.26/0.60                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 0.26/0.60                           => ~ ( 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 ) @ Xa ) ) ) )
% 0.26/0.60                     => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.60                            ( ( X3
% 0.26/0.60                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.60                           => ( ( ( ( ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.60                                    | ( ord_less_nat @ Ma2 @ Xa ) )
% 0.26/0.60                                 => ( Y3
% 0.26/0.60                                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) )
% 0.26/0.60                                & ( ~ ( ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.60                                      | ( ord_less_nat @ Ma2 @ Xa ) )
% 0.26/0.60                                 => ( ( ( ( Xa = Mi2 )
% 0.26/0.60                                        & ( Xa = Ma2 ) )
% 0.26/0.60                                     => ( Y3
% 0.26/0.60                                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) )
% 0.26/0.60                                    & ( ~ ( ( Xa = Mi2 )
% 0.26/0.60                                          & ( Xa = Ma2 ) )
% 0.26/0.60                                     => ( Y3
% 0.26/0.60                                        = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.60                                          @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                                            @ ( vEBT_Node
% 0.26/0.60                                              @ ( some_P7363390416028606310at_nat
% 0.26/0.60                                                @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa = Mi2 ) @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ Mi2 )
% 0.26/0.60                                                  @ ( if_nat
% 0.26/0.60                                                    @ ( ( ( Xa = Mi2 )
% 0.26/0.60                                                       => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.26/0.60                                                          = Ma2 ) )
% 0.26/0.60                                                      & ( ( Xa != Mi2 )
% 0.26/0.60                                                       => ( Xa = Ma2 ) ) )
% 0.26/0.60                                                    @ ( if_nat
% 0.26/0.60                                                      @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                                                        = none_nat )
% 0.26/0.60                                                      @ ( if_nat @ ( Xa = Mi2 ) @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ Mi2 )
% 0.26/0.60                                                      @ ( 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 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.60                                                    @ Ma2 ) ) )
% 0.26/0.60                                              @ ( suc @ ( suc @ Va ) )
% 0.26/0.60                                              @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                                              @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                                            @ ( vEBT_Node
% 0.26/0.60                                              @ ( some_P7363390416028606310at_nat
% 0.26/0.60                                                @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa = Mi2 ) @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ Mi2 )
% 0.26/0.60                                                  @ ( if_nat
% 0.26/0.60                                                    @ ( ( ( Xa = Mi2 )
% 0.26/0.60                                                       => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.26/0.60                                                          = Ma2 ) )
% 0.26/0.60                                                      & ( ( Xa != Mi2 )
% 0.26/0.60                                                       => ( Xa = Ma2 ) ) )
% 0.26/0.60                                                    @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( 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 @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.60                                                    @ Ma2 ) ) )
% 0.26/0.60                                              @ ( suc @ ( suc @ Va ) )
% 0.26/0.60                                              @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                                              @ Summary2 ) )
% 0.26/0.60                                          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) )
% 0.26/0.60                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % vebt_delete.pelims
% 0.26/0.60  thf(fact_6889_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Opelims,axiom,
% 0.26/0.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 0.26/0.60        ( ( ( vEBT_T_s_u_c_c2 @ X3 @ Xa )
% 0.26/0.60          = Y3 )
% 0.26/0.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.60         => ( ! [Uu: $o,B4: $o] :
% 0.26/0.60                ( ( X3
% 0.26/0.60                  = ( vEBT_Leaf @ Uu @ B4 ) )
% 0.26/0.60               => ( ( Xa = zero_zero_nat )
% 0.26/0.60                 => ( ( Y3 = one_one_nat )
% 0.26/0.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ B4 ) @ zero_zero_nat ) ) ) ) )
% 0.26/0.60           => ( ! [Uv: $o,Uw: $o] :
% 0.26/0.60                  ( ( X3
% 0.26/0.60                    = ( vEBT_Leaf @ Uv @ Uw ) )
% 0.26/0.60                 => ! [N2: nat] :
% 0.26/0.60                      ( ( Xa
% 0.26/0.60                        = ( suc @ N2 ) )
% 0.26/0.60                     => ( ( Y3 = one_one_nat )
% 0.26/0.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N2 ) ) ) ) ) )
% 0.26/0.60             => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.26/0.60                    ( ( X3
% 0.26/0.60                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 0.26/0.60                   => ( ( Y3 = one_one_nat )
% 0.26/0.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa ) ) ) )
% 0.26/0.60               => ( ! [V3: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.26/0.60                      ( ( X3
% 0.26/0.60                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 0.26/0.60                     => ( ( Y3 = one_one_nat )
% 0.26/0.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa ) ) ) )
% 0.26/0.60                 => ( ! [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 0.26/0.60                        ( ( X3
% 0.26/0.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 0.26/0.60                       => ( ( Y3 = one_one_nat )
% 0.26/0.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Xa ) ) ) )
% 0.26/0.60                   => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.60                          ( ( X3
% 0.26/0.60                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.60                         => ( ( ( ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.60                               => ( Y3 = one_one_nat ) )
% 0.26/0.60                              & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.60                               => ( Y3
% 0.26/0.60                                  = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.60                                    @ ( if_nat
% 0.26/0.60                                      @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                                         != none_nat )
% 0.26/0.60                                        & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.60                                      @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                                      @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.26/0.60                                    @ one_one_nat ) ) ) )
% 0.26/0.60                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.pelims
% 0.26/0.60  thf(fact_6890_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Opelims,axiom,
% 0.26/0.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 0.26/0.60        ( ( ( vEBT_T_i_n_s_e_r_t @ X3 @ Xa )
% 0.26/0.60          = Y3 )
% 0.26/0.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.60         => ( ! [A5: $o,B4: $o] :
% 0.26/0.60                ( ( X3
% 0.26/0.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.60               => ( ( Y3
% 0.26/0.60                    = ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 0.26/0.60                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) ) ) )
% 0.26/0.60           => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.26/0.60                  ( ( X3
% 0.26/0.60                    = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 0.26/0.60                 => ( ( Y3 = one_one_nat )
% 0.26/0.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) @ Xa ) ) ) )
% 0.26/0.60             => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.26/0.60                    ( ( X3
% 0.26/0.60                      = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 0.26/0.60                   => ( ( Y3 = one_one_nat )
% 0.26/0.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) @ Xa ) ) ) )
% 0.26/0.60               => ( ! [V3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.60                      ( ( X3
% 0.26/0.60                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.60                     => ( ( Y3
% 0.26/0.60                          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) )
% 0.26/0.60                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.60                        ( ( X3
% 0.26/0.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.60                       => ( ( Y3
% 0.26/0.60                            = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.26/0.60                              @ ( if_nat
% 0.26/0.60                                @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.60                                  & ~ ( ( Xa = Mi2 )
% 0.26/0.60                                      | ( Xa = Ma2 ) ) )
% 0.26/0.60                                @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.26/0.60                                @ one_one_nat ) ) )
% 0.26/0.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.pelims
% 0.26/0.60  thf(fact_6891_bot__nat__def,axiom,
% 0.26/0.60      bot_bot_nat = zero_zero_nat ).
% 0.26/0.60  
% 0.26/0.60  % bot_nat_def
% 0.26/0.60  thf(fact_6892_bot__enat__def,axiom,
% 0.26/0.60      bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 0.26/0.60  
% 0.26/0.60  % bot_enat_def
% 0.26/0.60  thf(fact_6893_vebt__insert_Opelims,axiom,
% 0.26/0.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: vEBT_VEBT] :
% 0.26/0.60        ( ( ( vEBT_vebt_insert @ X3 @ Xa )
% 0.26/0.60          = Y3 )
% 0.26/0.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.60         => ( ! [A5: $o,B4: $o] :
% 0.26/0.60                ( ( X3
% 0.26/0.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.60               => ( ( ( ( Xa = zero_zero_nat )
% 0.26/0.60                     => ( Y3
% 0.26/0.60                        = ( vEBT_Leaf @ $true @ B4 ) ) )
% 0.26/0.60                    & ( ( Xa != zero_zero_nat )
% 0.26/0.60                     => ( ( ( Xa = one_one_nat )
% 0.26/0.60                         => ( Y3
% 0.26/0.60                            = ( vEBT_Leaf @ A5 @ $true ) ) )
% 0.26/0.60                        & ( ( Xa != one_one_nat )
% 0.26/0.60                         => ( Y3
% 0.26/0.60                            = ( vEBT_Leaf @ A5 @ B4 ) ) ) ) ) )
% 0.26/0.60                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) ) ) )
% 0.26/0.60           => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.26/0.60                  ( ( X3
% 0.26/0.60                    = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 0.26/0.60                 => ( ( Y3
% 0.26/0.60                      = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 0.26/0.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) @ Xa ) ) ) )
% 0.26/0.60             => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.26/0.60                    ( ( X3
% 0.26/0.60                      = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 0.26/0.60                   => ( ( Y3
% 0.26/0.60                        = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 0.26/0.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) @ Xa ) ) ) )
% 0.26/0.60               => ( ! [V3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.60                      ( ( X3
% 0.26/0.60                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.60                     => ( ( Y3
% 0.26/0.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa @ Xa ) ) @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) )
% 0.26/0.60                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.60                        ( ( X3
% 0.26/0.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.60                       => ( ( Y3
% 0.26/0.60                            = ( if_VEBT_VEBT
% 0.26/0.60                              @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.60                                & ~ ( ( Xa = Mi2 )
% 0.26/0.60                                    | ( Xa = Ma2 ) ) )
% 0.26/0.60                              @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Xa @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 0.26/0.60                              @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) )
% 0.26/0.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % vebt_insert.pelims
% 0.26/0.60  thf(fact_6894_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Opelims,axiom,
% 0.26/0.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 0.26/0.60        ( ( ( vEBT_T_p_r_e_d2 @ X3 @ Xa )
% 0.26/0.60          = Y3 )
% 0.26/0.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.60         => ( ! [Uu: $o,Uv: $o] :
% 0.26/0.60                ( ( X3
% 0.26/0.60                  = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.26/0.60               => ( ( Xa = zero_zero_nat )
% 0.26/0.60                 => ( ( Y3 = one_one_nat )
% 0.26/0.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat ) ) ) ) )
% 0.26/0.60           => ( ! [A5: $o,Uw: $o] :
% 0.26/0.60                  ( ( X3
% 0.26/0.60                    = ( vEBT_Leaf @ A5 @ Uw ) )
% 0.26/0.60                 => ( ( Xa
% 0.26/0.60                      = ( suc @ zero_zero_nat ) )
% 0.26/0.60                   => ( ( Y3 = one_one_nat )
% 0.26/0.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 0.26/0.60             => ( ! [A5: $o,B4: $o] :
% 0.26/0.60                    ( ( X3
% 0.26/0.60                      = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.60                   => ! [Va: nat] :
% 0.26/0.60                        ( ( Xa
% 0.26/0.60                          = ( suc @ ( suc @ Va ) ) )
% 0.26/0.60                       => ( ( Y3 = one_one_nat )
% 0.26/0.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ ( suc @ ( suc @ Va ) ) ) ) ) ) )
% 0.26/0.60               => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 0.26/0.60                      ( ( X3
% 0.26/0.60                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 0.26/0.60                     => ( ( Y3 = one_one_nat )
% 0.26/0.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa ) ) ) )
% 0.26/0.60                 => ( ! [V3: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 0.26/0.60                        ( ( X3
% 0.26/0.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 0.26/0.60                       => ( ( Y3 = one_one_nat )
% 0.26/0.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa ) ) ) )
% 0.26/0.60                   => ( ! [V3: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 0.26/0.60                          ( ( X3
% 0.26/0.60                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 0.26/0.60                         => ( ( Y3 = one_one_nat )
% 0.26/0.60                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Xa ) ) ) )
% 0.26/0.60                     => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.60                            ( ( X3
% 0.26/0.60                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.60                           => ( ( ( ( ord_less_nat @ Ma2 @ Xa )
% 0.26/0.60                                 => ( Y3 = one_one_nat ) )
% 0.26/0.60                                & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 0.26/0.60                                 => ( Y3
% 0.26/0.60                                    = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.60                                      @ ( if_nat
% 0.26/0.60                                        @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                                           != none_nat )
% 0.26/0.60                                          & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.26/0.60                                        @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                                        @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.26/0.60                                      @ one_one_nat ) ) ) )
% 0.26/0.60                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.pelims
% 0.26/0.60  thf(fact_6895_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Opelims,axiom,
% 0.26/0.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 0.26/0.60        ( ( ( vEBT_T_i_n_s_e_r_t2 @ X3 @ Xa )
% 0.26/0.60          = Y3 )
% 0.26/0.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.60         => ( ! [A5: $o,B4: $o] :
% 0.26/0.60                ( ( X3
% 0.26/0.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.60               => ( ( Y3 = one_one_nat )
% 0.26/0.60                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) ) ) )
% 0.26/0.60           => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.26/0.60                  ( ( X3
% 0.26/0.60                    = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 0.26/0.60                 => ( ( Y3 = one_one_nat )
% 0.26/0.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) @ Xa ) ) ) )
% 0.26/0.60             => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.26/0.60                    ( ( X3
% 0.26/0.60                      = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 0.26/0.60                   => ( ( Y3 = one_one_nat )
% 0.26/0.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) @ Xa ) ) ) )
% 0.26/0.60               => ( ! [V3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.60                      ( ( X3
% 0.26/0.60                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.60                     => ( ( Y3 = one_one_nat )
% 0.26/0.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) )
% 0.26/0.60                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.60                        ( ( X3
% 0.26/0.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.60                       => ( ( Y3
% 0.26/0.60                            = ( if_nat
% 0.26/0.60                              @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.60                                & ~ ( ( Xa = Mi2 )
% 0.26/0.60                                    | ( Xa = Ma2 ) ) )
% 0.26/0.60                              @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.26/0.60                              @ one_one_nat ) )
% 0.26/0.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.pelims
% 0.26/0.60  thf(fact_6896_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Opelims,axiom,
% 0.26/0.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 0.26/0.60        ( ( ( vEBT_T_m_e_m_b_e_r @ X3 @ Xa )
% 0.26/0.60          = Y3 )
% 0.26/0.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.60         => ( ! [A5: $o,B4: $o] :
% 0.26/0.60                ( ( X3
% 0.26/0.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.60               => ( ( Y3
% 0.26/0.60                    = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 0.26/0.60                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) ) ) )
% 0.26/0.60           => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.26/0.60                  ( ( X3
% 0.26/0.60                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.26/0.60                 => ( ( Y3
% 0.26/0.60                      = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa ) ) ) )
% 0.26/0.60             => ( ! [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.26/0.60                    ( ( X3
% 0.26/0.60                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.26/0.60                   => ( ( Y3
% 0.26/0.60                        = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa ) ) ) )
% 0.26/0.60               => ( ! [V3: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.26/0.60                      ( ( X3
% 0.26/0.60                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) )
% 0.26/0.60                     => ( ( Y3
% 0.26/0.60                          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) @ Xa ) ) ) )
% 0.26/0.60                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.60                        ( ( X3
% 0.26/0.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.60                       => ( ( Y3
% 0.26/0.60                            = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa = Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.pelims
% 0.26/0.60  thf(fact_6897_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Opelims,axiom,
% 0.26/0.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 0.26/0.60        ( ( ( vEBT_T_m_e_m_b_e_r2 @ X3 @ Xa )
% 0.26/0.60          = Y3 )
% 0.26/0.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.60         => ( ! [A5: $o,B4: $o] :
% 0.26/0.60                ( ( X3
% 0.26/0.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.60               => ( ( Y3 = one_one_nat )
% 0.26/0.60                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) ) ) )
% 0.26/0.60           => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.26/0.60                  ( ( X3
% 0.26/0.60                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.26/0.60                 => ( ( Y3 = one_one_nat )
% 0.26/0.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa ) ) ) )
% 0.26/0.60             => ( ! [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.26/0.60                    ( ( X3
% 0.26/0.60                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.26/0.60                   => ( ( Y3 = one_one_nat )
% 0.26/0.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa ) ) ) )
% 0.26/0.60               => ( ! [V3: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.26/0.60                      ( ( X3
% 0.26/0.60                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) )
% 0.26/0.60                     => ( ( Y3 = one_one_nat )
% 0.26/0.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) @ Xa ) ) ) )
% 0.26/0.60                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.60                        ( ( X3
% 0.26/0.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.60                       => ( ( Y3
% 0.26/0.60                            = ( plus_plus_nat @ one_one_nat
% 0.26/0.60                              @ ( if_nat @ ( Xa = Mi2 ) @ zero_zero_nat
% 0.26/0.60                                @ ( if_nat @ ( Xa = Ma2 ) @ zero_zero_nat
% 0.26/0.60                                  @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ zero_zero_nat
% 0.26/0.60                                    @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa ) @ zero_zero_nat
% 0.26/0.60                                      @ ( if_nat
% 0.26/0.60                                        @ ( ( ord_less_nat @ Mi2 @ Xa )
% 0.26/0.60                                          & ( ord_less_nat @ Xa @ Ma2 ) )
% 0.26/0.60                                        @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 0.26/0.60                                        @ zero_zero_nat ) ) ) ) ) ) )
% 0.26/0.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.pelims
% 0.26/0.60  thf(fact_6898_vebt__member_Opelims_I1_J,axiom,
% 0.26/0.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: $o] :
% 0.26/0.60        ( ( ( vEBT_vebt_member @ X3 @ Xa )
% 0.26/0.60          = Y3 )
% 0.26/0.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.60         => ( ! [A5: $o,B4: $o] :
% 0.26/0.60                ( ( X3
% 0.26/0.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.60               => ( ( Y3
% 0.26/0.60                    = ( ( ( Xa = zero_zero_nat )
% 0.26/0.60                       => A5 )
% 0.26/0.60                      & ( ( Xa != zero_zero_nat )
% 0.26/0.60                       => ( ( ( Xa = one_one_nat )
% 0.26/0.60                           => B4 )
% 0.26/0.60                          & ( Xa = one_one_nat ) ) ) ) )
% 0.26/0.60                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) ) ) )
% 0.26/0.60           => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.26/0.60                  ( ( X3
% 0.26/0.60                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.26/0.60                 => ( ~ Y3
% 0.26/0.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa ) ) ) )
% 0.26/0.60             => ( ! [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.26/0.60                    ( ( X3
% 0.26/0.60                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.26/0.60                   => ( ~ Y3
% 0.26/0.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa ) ) ) )
% 0.26/0.60               => ( ! [V3: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.26/0.60                      ( ( X3
% 0.26/0.60                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) )
% 0.26/0.60                     => ( ~ Y3
% 0.26/0.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) @ Xa ) ) ) )
% 0.26/0.60                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.60                        ( ( X3
% 0.26/0.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.60                       => ( ( Y3
% 0.26/0.60                            = ( ( Xa != Mi2 )
% 0.26/0.60                             => ( ( Xa != Ma2 )
% 0.26/0.60                               => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.60                                  & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.60                                   => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 0.26/0.60                                      & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 0.26/0.60                                       => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.60                                           => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) )
% 0.26/0.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % vebt_member.pelims(1)
% 0.26/0.60  thf(fact_6899_vebt__member_Opelims_I3_J,axiom,
% 0.26/0.60      ! [X3: vEBT_VEBT,Xa: nat] :
% 0.26/0.60        ( ~ ( vEBT_vebt_member @ X3 @ Xa )
% 0.26/0.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.60         => ( ! [A5: $o,B4: $o] :
% 0.26/0.60                ( ( X3
% 0.26/0.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.60               => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) )
% 0.26/0.60                 => ( ( ( Xa = zero_zero_nat )
% 0.26/0.60                     => A5 )
% 0.26/0.60                    & ( ( Xa != zero_zero_nat )
% 0.26/0.60                     => ( ( ( Xa = one_one_nat )
% 0.26/0.60                         => B4 )
% 0.26/0.60                        & ( Xa = one_one_nat ) ) ) ) ) )
% 0.26/0.60           => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.26/0.60                  ( ( X3
% 0.26/0.60                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.26/0.60                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa ) ) )
% 0.26/0.60             => ( ! [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.26/0.60                    ( ( X3
% 0.26/0.60                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.26/0.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa ) ) )
% 0.26/0.60               => ( ! [V3: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.26/0.60                      ( ( X3
% 0.26/0.60                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) )
% 0.26/0.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) @ Xa ) ) )
% 0.26/0.60                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.60                        ( ( X3
% 0.26/0.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.60                       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) )
% 0.26/0.60                         => ( ( Xa != Mi2 )
% 0.26/0.60                           => ( ( Xa != Ma2 )
% 0.26/0.60                             => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.60                                & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.60                                 => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 0.26/0.60                                    & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 0.26/0.60                                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.60                                         => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % vebt_member.pelims(3)
% 0.26/0.60  thf(fact_6900_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 0.26/0.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: $o] :
% 0.26/0.60        ( ( ( vEBT_V5719532721284313246member @ X3 @ Xa )
% 0.26/0.60          = Y3 )
% 0.26/0.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.60         => ( ! [A5: $o,B4: $o] :
% 0.26/0.60                ( ( X3
% 0.26/0.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.60               => ( ( Y3
% 0.26/0.60                    = ( ( ( Xa = zero_zero_nat )
% 0.26/0.60                       => A5 )
% 0.26/0.60                      & ( ( Xa != zero_zero_nat )
% 0.26/0.60                       => ( ( ( Xa = one_one_nat )
% 0.26/0.60                           => B4 )
% 0.26/0.60                          & ( Xa = one_one_nat ) ) ) ) )
% 0.26/0.60                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) ) ) )
% 0.26/0.60           => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.26/0.60                  ( ( X3
% 0.26/0.60                    = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 0.26/0.60                 => ( ~ Y3
% 0.26/0.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Xa ) ) ) )
% 0.26/0.60             => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.26/0.60                    ( ( X3
% 0.26/0.60                      = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) )
% 0.26/0.60                   => ( ( Y3
% 0.26/0.60                        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.60                           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 0.26/0.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) @ Xa ) ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % VEBT_internal.naive_member.pelims(1)
% 0.26/0.60  thf(fact_6901_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 0.26/0.60      ! [X3: vEBT_VEBT,Xa: nat] :
% 0.26/0.60        ( ( vEBT_V5719532721284313246member @ X3 @ Xa )
% 0.26/0.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.60         => ( ! [A5: $o,B4: $o] :
% 0.26/0.60                ( ( X3
% 0.26/0.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.60               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) )
% 0.26/0.60                 => ~ ( ( ( Xa = zero_zero_nat )
% 0.26/0.60                       => A5 )
% 0.26/0.60                      & ( ( Xa != zero_zero_nat )
% 0.26/0.60                       => ( ( ( Xa = one_one_nat )
% 0.26/0.60                           => B4 )
% 0.26/0.60                          & ( Xa = one_one_nat ) ) ) ) ) )
% 0.26/0.60           => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.26/0.60                  ( ( X3
% 0.26/0.60                    = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) )
% 0.26/0.60                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) @ Xa ) )
% 0.26/0.60                   => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.60                         => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % VEBT_internal.naive_member.pelims(2)
% 0.26/0.60  thf(fact_6902_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 0.26/0.60      ! [X3: vEBT_VEBT,Xa: nat] :
% 0.26/0.60        ( ~ ( vEBT_V5719532721284313246member @ X3 @ Xa )
% 0.26/0.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.60         => ( ! [A5: $o,B4: $o] :
% 0.26/0.60                ( ( X3
% 0.26/0.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.60               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) )
% 0.26/0.60                 => ( ( ( Xa = zero_zero_nat )
% 0.26/0.60                     => A5 )
% 0.26/0.60                    & ( ( Xa != zero_zero_nat )
% 0.26/0.60                     => ( ( ( Xa = one_one_nat )
% 0.26/0.60                         => B4 )
% 0.26/0.60                        & ( Xa = one_one_nat ) ) ) ) ) )
% 0.26/0.60           => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.26/0.60                  ( ( X3
% 0.26/0.60                    = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 0.26/0.60                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Xa ) ) )
% 0.26/0.60             => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.26/0.60                    ( ( X3
% 0.26/0.60                      = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) )
% 0.26/0.60                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) @ Xa ) )
% 0.26/0.60                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.60                         => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % VEBT_internal.naive_member.pelims(3)
% 0.26/0.60  thf(fact_6903_vebt__member_Opelims_I2_J,axiom,
% 0.26/0.60      ! [X3: vEBT_VEBT,Xa: nat] :
% 0.26/0.60        ( ( vEBT_vebt_member @ X3 @ Xa )
% 0.26/0.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.60         => ( ! [A5: $o,B4: $o] :
% 0.26/0.60                ( ( X3
% 0.26/0.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.60               => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) )
% 0.26/0.60                 => ~ ( ( ( Xa = zero_zero_nat )
% 0.26/0.60                       => A5 )
% 0.26/0.60                      & ( ( Xa != zero_zero_nat )
% 0.26/0.60                       => ( ( ( Xa = one_one_nat )
% 0.26/0.60                           => B4 )
% 0.26/0.60                          & ( Xa = one_one_nat ) ) ) ) ) )
% 0.26/0.60           => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.60                  ( ( X3
% 0.26/0.60                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 0.26/0.60                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) )
% 0.26/0.60                   => ~ ( ( Xa != Mi2 )
% 0.26/0.60                       => ( ( Xa != Ma2 )
% 0.26/0.60                         => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.60                            & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 0.26/0.60                             => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 0.26/0.60                                & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 0.26/0.60                                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.60                                     => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % vebt_member.pelims(2)
% 0.26/0.60  thf(fact_6904_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 0.26/0.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: $o] :
% 0.26/0.60        ( ( ( vEBT_VEBT_membermima @ X3 @ Xa )
% 0.26/0.60          = Y3 )
% 0.26/0.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.60         => ( ! [Uu: $o,Uv: $o] :
% 0.26/0.60                ( ( X3
% 0.26/0.60                  = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.26/0.60               => ( ~ Y3
% 0.26/0.60                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa ) ) ) )
% 0.26/0.60           => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.26/0.60                  ( ( X3
% 0.26/0.60                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 0.26/0.60                 => ( ~ Y3
% 0.26/0.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa ) ) ) )
% 0.26/0.60             => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb: vEBT_VEBT] :
% 0.26/0.60                    ( ( X3
% 0.26/0.60                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb ) )
% 0.26/0.60                   => ( ( Y3
% 0.26/0.60                        = ( ( Xa = Mi2 )
% 0.26/0.60                          | ( Xa = Ma2 ) ) )
% 0.26/0.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb ) @ Xa ) ) ) )
% 0.26/0.60               => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.26/0.60                      ( ( X3
% 0.26/0.60                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) )
% 0.26/0.60                     => ( ( Y3
% 0.26/0.60                          = ( ( Xa = Mi2 )
% 0.26/0.60                            | ( Xa = Ma2 )
% 0.26/0.60                            | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.60                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 0.26/0.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) @ Xa ) ) ) )
% 0.26/0.60                 => ~ ! [V3: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.26/0.60                        ( ( X3
% 0.26/0.60                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) )
% 0.26/0.60                       => ( ( Y3
% 0.26/0.60                            = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.60                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 0.26/0.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % VEBT_internal.membermima.pelims(1)
% 0.26/0.60  thf(fact_6905_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 0.26/0.60      ! [X3: vEBT_VEBT,Xa: nat] :
% 0.26/0.60        ( ~ ( vEBT_VEBT_membermima @ X3 @ Xa )
% 0.26/0.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.60         => ( ! [Uu: $o,Uv: $o] :
% 0.26/0.60                ( ( X3
% 0.26/0.60                  = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.26/0.60               => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa ) ) )
% 0.26/0.60           => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.26/0.60                  ( ( X3
% 0.26/0.60                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 0.26/0.60                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa ) ) )
% 0.26/0.60             => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb: vEBT_VEBT] :
% 0.26/0.60                    ( ( X3
% 0.26/0.60                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb ) )
% 0.26/0.60                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb ) @ Xa ) )
% 0.26/0.60                     => ( ( Xa = Mi2 )
% 0.26/0.60                        | ( Xa = Ma2 ) ) ) )
% 0.26/0.60               => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.26/0.60                      ( ( X3
% 0.26/0.60                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) )
% 0.26/0.60                     => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) @ Xa ) )
% 0.26/0.60                       => ( ( Xa = Mi2 )
% 0.26/0.60                          | ( Xa = Ma2 )
% 0.26/0.60                          | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.60                             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                            & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 0.26/0.60                 => ~ ! [V3: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.26/0.60                        ( ( X3
% 0.26/0.60                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) )
% 0.26/0.60                       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) @ Xa ) )
% 0.26/0.60                         => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.60                             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                            & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % VEBT_internal.membermima.pelims(3)
% 0.26/0.60  thf(fact_6906_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 0.26/0.60      ! [X3: vEBT_VEBT,Xa: nat] :
% 0.26/0.60        ( ( vEBT_VEBT_membermima @ X3 @ Xa )
% 0.26/0.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.60         => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb: vEBT_VEBT] :
% 0.26/0.60                ( ( X3
% 0.26/0.60                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb ) )
% 0.26/0.60               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb ) @ Xa ) )
% 0.26/0.60                 => ~ ( ( Xa = Mi2 )
% 0.26/0.60                      | ( Xa = Ma2 ) ) ) )
% 0.26/0.60           => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.26/0.60                  ( ( X3
% 0.26/0.60                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) )
% 0.26/0.60                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) @ Xa ) )
% 0.26/0.60                   => ~ ( ( Xa = Mi2 )
% 0.26/0.60                        | ( Xa = Ma2 )
% 0.26/0.60                        | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.60                           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 0.26/0.60             => ~ ! [V3: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.26/0.60                    ( ( X3
% 0.26/0.60                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) )
% 0.26/0.60                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) @ Xa ) )
% 0.26/0.60                     => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.26/0.60                           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.60                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % VEBT_internal.membermima.pelims(2)
% 0.26/0.60  thf(fact_6907_monoseq__arctan__series,axiom,
% 0.26/0.60      ! [X3: real] :
% 0.26/0.60        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.26/0.60       => ( topolo6980174941875973593q_real
% 0.26/0.60          @ ^ [N3: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % monoseq_arctan_series
% 0.26/0.60  thf(fact_6908_delete__correct,axiom,
% 0.26/0.60      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.60        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.60       => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X3 ) )
% 0.26/0.60          = ( minus_minus_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % delete_correct
% 0.26/0.60  thf(fact_6909_delete__correct_H,axiom,
% 0.26/0.60      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 0.26/0.60        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.60       => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X3 ) )
% 0.26/0.60          = ( minus_minus_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % delete_correct'
% 0.26/0.60  thf(fact_6910_atLeast0__atMost__Suc,axiom,
% 0.26/0.60      ! [N: nat] :
% 0.26/0.60        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.26/0.60        = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % atLeast0_atMost_Suc
% 0.26/0.60  thf(fact_6911_atLeastAtMost__insertL,axiom,
% 0.26/0.60      ! [M: nat,N: nat] :
% 0.26/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.60       => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 0.26/0.60          = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % atLeastAtMost_insertL
% 0.26/0.60  thf(fact_6912_atLeastAtMostSuc__conv,axiom,
% 0.26/0.60      ! [M: nat,N: nat] :
% 0.26/0.60        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.26/0.60       => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 0.26/0.60          = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % atLeastAtMostSuc_conv
% 0.26/0.60  thf(fact_6913_Icc__eq__insert__lb__nat,axiom,
% 0.26/0.60      ! [M: nat,N: nat] :
% 0.26/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.60       => ( ( set_or1269000886237332187st_nat @ M @ N )
% 0.26/0.60          = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % Icc_eq_insert_lb_nat
% 0.26/0.60  thf(fact_6914_monoseq__realpow,axiom,
% 0.26/0.60      ! [X3: real] :
% 0.26/0.60        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.60       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 0.26/0.60         => ( topolo6980174941875973593q_real @ ( power_power_real @ X3 ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % monoseq_realpow
% 0.26/0.60  thf(fact_6915_pochhammer__times__pochhammer__half,axiom,
% 0.26/0.60      ! [Z: complex,N: nat] :
% 0.26/0.60        ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 0.26/0.60        = ( groups6464643781859351333omplex
% 0.26/0.60          @ ^ [K3: nat] : ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 0.26/0.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pochhammer_times_pochhammer_half
% 0.26/0.60  thf(fact_6916_pochhammer__times__pochhammer__half,axiom,
% 0.26/0.60      ! [Z: real,N: nat] :
% 0.26/0.60        ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 0.26/0.60        = ( groups129246275422532515t_real
% 0.26/0.60          @ ^ [K3: nat] : ( plus_plus_real @ Z @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pochhammer_times_pochhammer_half
% 0.26/0.60  thf(fact_6917_pochhammer__times__pochhammer__half,axiom,
% 0.26/0.60      ! [Z: rat,N: nat] :
% 0.26/0.60        ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 0.26/0.60        = ( groups73079841787564623at_rat
% 0.26/0.60          @ ^ [K3: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.26/0.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pochhammer_times_pochhammer_half
% 0.26/0.60  thf(fact_6918_signed__take__bit__numeral__minus__bit1,axiom,
% 0.26/0.60      ! [L: num,K: num] :
% 0.26/0.60        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.26/0.60        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.26/0.60  
% 0.26/0.60  % signed_take_bit_numeral_minus_bit1
% 0.26/0.60  thf(fact_6919_ln__series,axiom,
% 0.26/0.60      ! [X3: real] :
% 0.26/0.60        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.60       => ( ( ord_less_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.26/0.60         => ( ( ln_ln_real @ X3 )
% 0.26/0.60            = ( suminf_real
% 0.26/0.60              @ ^ [N3: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X3 @ one_one_real ) @ ( suc @ N3 ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % ln_series
% 0.26/0.60  thf(fact_6920_dbl__dec__simps_I4_J,axiom,
% 0.26/0.60      ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.26/0.60      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % dbl_dec_simps(4)
% 0.26/0.60  thf(fact_6921_dbl__dec__simps_I4_J,axiom,
% 0.26/0.60      ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.60      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % dbl_dec_simps(4)
% 0.26/0.60  thf(fact_6922_dbl__dec__simps_I4_J,axiom,
% 0.26/0.60      ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.26/0.60      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % dbl_dec_simps(4)
% 0.26/0.60  thf(fact_6923_dbl__dec__simps_I4_J,axiom,
% 0.26/0.60      ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.26/0.60      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % dbl_dec_simps(4)
% 0.26/0.60  thf(fact_6924_dbl__dec__simps_I4_J,axiom,
% 0.26/0.60      ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.26/0.60      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % dbl_dec_simps(4)
% 0.26/0.60  thf(fact_6925_arctan__series,axiom,
% 0.26/0.60      ! [X3: real] :
% 0.26/0.60        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.26/0.60       => ( ( arctan @ X3 )
% 0.26/0.60          = ( suminf_real
% 0.26/0.60            @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % arctan_series
% 0.26/0.60  thf(fact_6926_of__nat__prod,axiom,
% 0.26/0.60      ! [F: int > nat,A3: set_int] :
% 0.26/0.60        ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F @ A3 ) )
% 0.26/0.60        = ( groups1705073143266064639nt_int
% 0.26/0.60          @ ^ [X: int] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 0.26/0.60          @ A3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % of_nat_prod
% 0.26/0.60  thf(fact_6927_of__nat__prod,axiom,
% 0.26/0.60      ! [F: nat > nat,A3: set_nat] :
% 0.26/0.60        ( ( semiri8010041392384452111omplex @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 0.26/0.60        = ( groups6464643781859351333omplex
% 0.26/0.60          @ ^ [X: nat] : ( semiri8010041392384452111omplex @ ( F @ X ) )
% 0.26/0.60          @ A3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % of_nat_prod
% 0.26/0.60  thf(fact_6928_of__nat__prod,axiom,
% 0.26/0.60      ! [F: nat > nat,A3: set_nat] :
% 0.26/0.60        ( ( semiri5074537144036343181t_real @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 0.26/0.60        = ( groups129246275422532515t_real
% 0.26/0.60          @ ^ [X: nat] : ( semiri5074537144036343181t_real @ ( F @ X ) )
% 0.26/0.60          @ A3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % of_nat_prod
% 0.26/0.60  thf(fact_6929_of__nat__prod,axiom,
% 0.26/0.60      ! [F: nat > nat,A3: set_nat] :
% 0.26/0.60        ( ( semiri681578069525770553at_rat @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 0.26/0.60        = ( groups73079841787564623at_rat
% 0.26/0.60          @ ^ [X: nat] : ( semiri681578069525770553at_rat @ ( F @ X ) )
% 0.26/0.60          @ A3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % of_nat_prod
% 0.26/0.60  thf(fact_6930_of__nat__prod,axiom,
% 0.26/0.60      ! [F: nat > nat,A3: set_nat] :
% 0.26/0.60        ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 0.26/0.60        = ( groups705719431365010083at_int
% 0.26/0.60          @ ^ [X: nat] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 0.26/0.60          @ A3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % of_nat_prod
% 0.26/0.60  thf(fact_6931_of__nat__prod,axiom,
% 0.26/0.60      ! [F: nat > nat,A3: set_nat] :
% 0.26/0.60        ( ( semiri1316708129612266289at_nat @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 0.26/0.60        = ( groups708209901874060359at_nat
% 0.26/0.60          @ ^ [X: nat] : ( semiri1316708129612266289at_nat @ ( F @ X ) )
% 0.26/0.60          @ A3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % of_nat_prod
% 0.26/0.60  thf(fact_6932_dbl__dec__simps_I3_J,axiom,
% 0.26/0.60      ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 0.26/0.60      = one_one_complex ) ).
% 0.26/0.60  
% 0.26/0.60  % dbl_dec_simps(3)
% 0.26/0.60  thf(fact_6933_dbl__dec__simps_I3_J,axiom,
% 0.26/0.60      ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 0.26/0.60      = one_one_real ) ).
% 0.26/0.60  
% 0.26/0.60  % dbl_dec_simps(3)
% 0.26/0.60  thf(fact_6934_dbl__dec__simps_I3_J,axiom,
% 0.26/0.60      ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 0.26/0.60      = one_one_rat ) ).
% 0.26/0.60  
% 0.26/0.60  % dbl_dec_simps(3)
% 0.26/0.60  thf(fact_6935_dbl__dec__simps_I3_J,axiom,
% 0.26/0.60      ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 0.26/0.60      = one_one_int ) ).
% 0.26/0.60  
% 0.26/0.60  % dbl_dec_simps(3)
% 0.26/0.60  thf(fact_6936_of__int__prod,axiom,
% 0.26/0.60      ! [F: nat > int,A3: set_nat] :
% 0.26/0.60        ( ( ring_1_of_int_real @ ( groups705719431365010083at_int @ F @ A3 ) )
% 0.26/0.60        = ( groups129246275422532515t_real
% 0.26/0.60          @ ^ [X: nat] : ( ring_1_of_int_real @ ( F @ X ) )
% 0.26/0.60          @ A3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % of_int_prod
% 0.26/0.60  thf(fact_6937_of__int__prod,axiom,
% 0.26/0.60      ! [F: nat > int,A3: set_nat] :
% 0.26/0.60        ( ( ring_17405671764205052669omplex @ ( groups705719431365010083at_int @ F @ A3 ) )
% 0.26/0.60        = ( groups6464643781859351333omplex
% 0.26/0.60          @ ^ [X: nat] : ( ring_17405671764205052669omplex @ ( F @ X ) )
% 0.26/0.60          @ A3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % of_int_prod
% 0.26/0.60  thf(fact_6938_of__int__prod,axiom,
% 0.26/0.60      ! [F: nat > int,A3: set_nat] :
% 0.26/0.60        ( ( ring_1_of_int_rat @ ( groups705719431365010083at_int @ F @ A3 ) )
% 0.26/0.60        = ( groups73079841787564623at_rat
% 0.26/0.60          @ ^ [X: nat] : ( ring_1_of_int_rat @ ( F @ X ) )
% 0.26/0.60          @ A3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % of_int_prod
% 0.26/0.60  thf(fact_6939_of__int__prod,axiom,
% 0.26/0.60      ! [F: nat > int,A3: set_nat] :
% 0.26/0.60        ( ( ring_1_of_int_int @ ( groups705719431365010083at_int @ F @ A3 ) )
% 0.26/0.60        = ( groups705719431365010083at_int
% 0.26/0.60          @ ^ [X: nat] : ( ring_1_of_int_int @ ( F @ X ) )
% 0.26/0.60          @ A3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % of_int_prod
% 0.26/0.60  thf(fact_6940_of__int__prod,axiom,
% 0.26/0.60      ! [F: int > int,A3: set_int] :
% 0.26/0.60        ( ( ring_1_of_int_real @ ( groups1705073143266064639nt_int @ F @ A3 ) )
% 0.26/0.60        = ( groups2316167850115554303t_real
% 0.26/0.60          @ ^ [X: int] : ( ring_1_of_int_real @ ( F @ X ) )
% 0.26/0.60          @ A3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % of_int_prod
% 0.26/0.60  thf(fact_6941_of__int__prod,axiom,
% 0.26/0.60      ! [F: int > int,A3: set_int] :
% 0.26/0.60        ( ( ring_17405671764205052669omplex @ ( groups1705073143266064639nt_int @ F @ A3 ) )
% 0.26/0.60        = ( groups7440179247065528705omplex
% 0.26/0.60          @ ^ [X: int] : ( ring_17405671764205052669omplex @ ( F @ X ) )
% 0.26/0.60          @ A3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % of_int_prod
% 0.26/0.60  thf(fact_6942_of__int__prod,axiom,
% 0.26/0.60      ! [F: int > int,A3: set_int] :
% 0.26/0.60        ( ( ring_1_of_int_rat @ ( groups1705073143266064639nt_int @ F @ A3 ) )
% 0.26/0.60        = ( groups1072433553688619179nt_rat
% 0.26/0.60          @ ^ [X: int] : ( ring_1_of_int_rat @ ( F @ X ) )
% 0.26/0.60          @ A3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % of_int_prod
% 0.26/0.60  thf(fact_6943_of__int__prod,axiom,
% 0.26/0.60      ! [F: int > int,A3: set_int] :
% 0.26/0.60        ( ( ring_1_of_int_int @ ( groups1705073143266064639nt_int @ F @ A3 ) )
% 0.26/0.60        = ( groups1705073143266064639nt_int
% 0.26/0.60          @ ^ [X: int] : ( ring_1_of_int_int @ ( F @ X ) )
% 0.26/0.60          @ A3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % of_int_prod
% 0.26/0.60  thf(fact_6944_pred__numeral__simps_I1_J,axiom,
% 0.26/0.60      ( ( pred_numeral @ one )
% 0.26/0.60      = zero_zero_nat ) ).
% 0.26/0.60  
% 0.26/0.60  % pred_numeral_simps(1)
% 0.26/0.60  thf(fact_6945_eq__numeral__Suc,axiom,
% 0.26/0.60      ! [K: num,N: nat] :
% 0.26/0.60        ( ( ( numeral_numeral_nat @ K )
% 0.26/0.60          = ( suc @ N ) )
% 0.26/0.60        = ( ( pred_numeral @ K )
% 0.26/0.60          = N ) ) ).
% 0.26/0.60  
% 0.26/0.60  % eq_numeral_Suc
% 0.26/0.60  thf(fact_6946_Suc__eq__numeral,axiom,
% 0.26/0.60      ! [N: nat,K: num] :
% 0.26/0.60        ( ( ( suc @ N )
% 0.26/0.60          = ( numeral_numeral_nat @ K ) )
% 0.26/0.60        = ( N
% 0.26/0.60          = ( pred_numeral @ K ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % Suc_eq_numeral
% 0.26/0.60  thf(fact_6947_less__numeral__Suc,axiom,
% 0.26/0.60      ! [K: num,N: nat] :
% 0.26/0.60        ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 0.26/0.60        = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 0.26/0.60  
% 0.26/0.60  % less_numeral_Suc
% 0.26/0.60  thf(fact_6948_less__Suc__numeral,axiom,
% 0.26/0.60      ! [N: nat,K: num] :
% 0.26/0.60        ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 0.26/0.60        = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % less_Suc_numeral
% 0.26/0.60  thf(fact_6949_pred__numeral__simps_I3_J,axiom,
% 0.26/0.60      ! [K: num] :
% 0.26/0.60        ( ( pred_numeral @ ( bit1 @ K ) )
% 0.26/0.60        = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pred_numeral_simps(3)
% 0.26/0.60  thf(fact_6950_le__Suc__numeral,axiom,
% 0.26/0.60      ! [N: nat,K: num] :
% 0.26/0.60        ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 0.26/0.60        = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % le_Suc_numeral
% 0.26/0.60  thf(fact_6951_le__numeral__Suc,axiom,
% 0.26/0.60      ! [K: num,N: nat] :
% 0.26/0.60        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 0.26/0.60        = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 0.26/0.60  
% 0.26/0.60  % le_numeral_Suc
% 0.26/0.60  thf(fact_6952_diff__numeral__Suc,axiom,
% 0.26/0.60      ! [K: num,N: nat] :
% 0.26/0.60        ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 0.26/0.60        = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 0.26/0.60  
% 0.26/0.60  % diff_numeral_Suc
% 0.26/0.60  thf(fact_6953_diff__Suc__numeral,axiom,
% 0.26/0.60      ! [N: nat,K: num] :
% 0.26/0.60        ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 0.26/0.60        = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % diff_Suc_numeral
% 0.26/0.60  thf(fact_6954_max__numeral__Suc,axiom,
% 0.26/0.60      ! [K: num,N: nat] :
% 0.26/0.60        ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 0.26/0.60        = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % max_numeral_Suc
% 0.26/0.60  thf(fact_6955_max__Suc__numeral,axiom,
% 0.26/0.60      ! [N: nat,K: num] :
% 0.26/0.60        ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 0.26/0.60        = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % max_Suc_numeral
% 0.26/0.60  thf(fact_6956_dbl__dec__simps_I2_J,axiom,
% 0.26/0.60      ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 0.26/0.60      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.26/0.60  
% 0.26/0.60  % dbl_dec_simps(2)
% 0.26/0.60  thf(fact_6957_dbl__dec__simps_I2_J,axiom,
% 0.26/0.60      ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 0.26/0.60      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.60  
% 0.26/0.60  % dbl_dec_simps(2)
% 0.26/0.60  thf(fact_6958_dbl__dec__simps_I2_J,axiom,
% 0.26/0.60      ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 0.26/0.60      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.26/0.60  
% 0.26/0.60  % dbl_dec_simps(2)
% 0.26/0.60  thf(fact_6959_dbl__dec__simps_I2_J,axiom,
% 0.26/0.60      ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 0.26/0.60      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.60  
% 0.26/0.60  % dbl_dec_simps(2)
% 0.26/0.60  thf(fact_6960_dbl__dec__simps_I2_J,axiom,
% 0.26/0.60      ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 0.26/0.60      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % dbl_dec_simps(2)
% 0.26/0.60  thf(fact_6961_powser__zero,axiom,
% 0.26/0.60      ! [F: nat > complex] :
% 0.26/0.60        ( ( suminf_complex
% 0.26/0.60          @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ zero_zero_complex @ N3 ) ) )
% 0.26/0.60        = ( F @ zero_zero_nat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % powser_zero
% 0.26/0.60  thf(fact_6962_powser__zero,axiom,
% 0.26/0.60      ! [F: nat > real] :
% 0.26/0.60        ( ( suminf_real
% 0.26/0.60          @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ zero_zero_real @ N3 ) ) )
% 0.26/0.60        = ( F @ zero_zero_nat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % powser_zero
% 0.26/0.60  thf(fact_6963_prod_Ocl__ivl__Suc,axiom,
% 0.26/0.60      ! [N: nat,M: nat,G: nat > complex] :
% 0.26/0.60        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.26/0.60         => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.60            = one_one_complex ) )
% 0.26/0.60        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.26/0.60         => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.60            = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.cl_ivl_Suc
% 0.26/0.60  thf(fact_6964_prod_Ocl__ivl__Suc,axiom,
% 0.26/0.60      ! [N: nat,M: nat,G: nat > real] :
% 0.26/0.60        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.26/0.60         => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.60            = one_one_real ) )
% 0.26/0.60        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.26/0.60         => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.60            = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.cl_ivl_Suc
% 0.26/0.60  thf(fact_6965_prod_Ocl__ivl__Suc,axiom,
% 0.26/0.60      ! [N: nat,M: nat,G: nat > rat] :
% 0.26/0.60        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.26/0.60         => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.60            = one_one_rat ) )
% 0.26/0.60        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.26/0.60         => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.60            = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.cl_ivl_Suc
% 0.26/0.60  thf(fact_6966_prod_Ocl__ivl__Suc,axiom,
% 0.26/0.60      ! [N: nat,M: nat,G: nat > int] :
% 0.26/0.60        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.26/0.60         => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.60            = one_one_int ) )
% 0.26/0.60        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.26/0.60         => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.60            = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.cl_ivl_Suc
% 0.26/0.60  thf(fact_6967_prod_Ocl__ivl__Suc,axiom,
% 0.26/0.60      ! [N: nat,M: nat,G: nat > nat] :
% 0.26/0.60        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.26/0.60         => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.60            = one_one_nat ) )
% 0.26/0.60        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.26/0.60         => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.60            = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.cl_ivl_Suc
% 0.26/0.60  thf(fact_6968_signed__take__bit__numeral__bit0,axiom,
% 0.26/0.60      ! [L: num,K: num] :
% 0.26/0.60        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 0.26/0.60        = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % signed_take_bit_numeral_bit0
% 0.26/0.60  thf(fact_6969_signed__take__bit__numeral__minus__bit0,axiom,
% 0.26/0.60      ! [L: num,K: num] :
% 0.26/0.60        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.26/0.60        = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % signed_take_bit_numeral_minus_bit0
% 0.26/0.60  thf(fact_6970_signed__take__bit__numeral__bit1,axiom,
% 0.26/0.60      ! [L: num,K: num] :
% 0.26/0.60        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.26/0.60        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.26/0.60  
% 0.26/0.60  % signed_take_bit_numeral_bit1
% 0.26/0.60  thf(fact_6971_numeral__eq__Suc,axiom,
% 0.26/0.60      ( numeral_numeral_nat
% 0.26/0.60      = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % numeral_eq_Suc
% 0.26/0.60  thf(fact_6972_pred__numeral__def,axiom,
% 0.26/0.60      ( pred_numeral
% 0.26/0.60      = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pred_numeral_def
% 0.26/0.60  thf(fact_6973_prod_OatLeast0__atMost__Suc,axiom,
% 0.26/0.60      ! [G: nat > real,N: nat] :
% 0.26/0.60        ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.26/0.60        = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.atLeast0_atMost_Suc
% 0.26/0.60  thf(fact_6974_prod_OatLeast0__atMost__Suc,axiom,
% 0.26/0.60      ! [G: nat > rat,N: nat] :
% 0.26/0.60        ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.26/0.60        = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.atLeast0_atMost_Suc
% 0.26/0.60  thf(fact_6975_prod_OatLeast0__atMost__Suc,axiom,
% 0.26/0.60      ! [G: nat > int,N: nat] :
% 0.26/0.60        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.26/0.60        = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.atLeast0_atMost_Suc
% 0.26/0.60  thf(fact_6976_prod_OatLeast0__atMost__Suc,axiom,
% 0.26/0.60      ! [G: nat > nat,N: nat] :
% 0.26/0.60        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.26/0.60        = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.atLeast0_atMost_Suc
% 0.26/0.60  thf(fact_6977_prod_Onat__ivl__Suc_H,axiom,
% 0.26/0.60      ! [M: nat,N: nat,G: nat > real] :
% 0.26/0.60        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.26/0.60       => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.60          = ( times_times_real @ ( G @ ( suc @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.nat_ivl_Suc'
% 0.26/0.60  thf(fact_6978_prod_Onat__ivl__Suc_H,axiom,
% 0.26/0.60      ! [M: nat,N: nat,G: nat > rat] :
% 0.26/0.60        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.26/0.60       => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.60          = ( times_times_rat @ ( G @ ( suc @ N ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.nat_ivl_Suc'
% 0.26/0.60  thf(fact_6979_prod_Onat__ivl__Suc_H,axiom,
% 0.26/0.60      ! [M: nat,N: nat,G: nat > int] :
% 0.26/0.60        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.26/0.60       => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.60          = ( times_times_int @ ( G @ ( suc @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.nat_ivl_Suc'
% 0.26/0.60  thf(fact_6980_prod_Onat__ivl__Suc_H,axiom,
% 0.26/0.60      ! [M: nat,N: nat,G: nat > nat] :
% 0.26/0.60        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.26/0.60       => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.60          = ( times_times_nat @ ( G @ ( suc @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.nat_ivl_Suc'
% 0.26/0.60  thf(fact_6981_prod_OatLeast__Suc__atMost,axiom,
% 0.26/0.60      ! [M: nat,N: nat,G: nat > real] :
% 0.26/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.60       => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.60          = ( times_times_real @ ( G @ M ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.atLeast_Suc_atMost
% 0.26/0.60  thf(fact_6982_prod_OatLeast__Suc__atMost,axiom,
% 0.26/0.60      ! [M: nat,N: nat,G: nat > rat] :
% 0.26/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.60       => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.60          = ( times_times_rat @ ( G @ M ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.atLeast_Suc_atMost
% 0.26/0.60  thf(fact_6983_prod_OatLeast__Suc__atMost,axiom,
% 0.26/0.60      ! [M: nat,N: nat,G: nat > int] :
% 0.26/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.60       => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.60          = ( times_times_int @ ( G @ M ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.atLeast_Suc_atMost
% 0.26/0.60  thf(fact_6984_prod_OatLeast__Suc__atMost,axiom,
% 0.26/0.60      ! [M: nat,N: nat,G: nat > nat] :
% 0.26/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.60       => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.60          = ( times_times_nat @ ( G @ M ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.atLeast_Suc_atMost
% 0.26/0.60  thf(fact_6985_prod_OSuc__reindex__ivl,axiom,
% 0.26/0.60      ! [M: nat,N: nat,G: nat > real] :
% 0.26/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.60       => ( ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 0.26/0.60          = ( times_times_real @ ( G @ M )
% 0.26/0.60            @ ( groups129246275422532515t_real
% 0.26/0.60              @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.60              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.Suc_reindex_ivl
% 0.26/0.60  thf(fact_6986_prod_OSuc__reindex__ivl,axiom,
% 0.26/0.60      ! [M: nat,N: nat,G: nat > rat] :
% 0.26/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.60       => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 0.26/0.60          = ( times_times_rat @ ( G @ M )
% 0.26/0.60            @ ( groups73079841787564623at_rat
% 0.26/0.60              @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.60              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.Suc_reindex_ivl
% 0.26/0.60  thf(fact_6987_prod_OSuc__reindex__ivl,axiom,
% 0.26/0.60      ! [M: nat,N: nat,G: nat > int] :
% 0.26/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.60       => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 0.26/0.60          = ( times_times_int @ ( G @ M )
% 0.26/0.60            @ ( groups705719431365010083at_int
% 0.26/0.60              @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.60              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.Suc_reindex_ivl
% 0.26/0.60  thf(fact_6988_prod_OSuc__reindex__ivl,axiom,
% 0.26/0.60      ! [M: nat,N: nat,G: nat > nat] :
% 0.26/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.60       => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 0.26/0.60          = ( times_times_nat @ ( G @ M )
% 0.26/0.60            @ ( groups708209901874060359at_nat
% 0.26/0.60              @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.60              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.Suc_reindex_ivl
% 0.26/0.60  thf(fact_6989_prod_Oub__add__nat,axiom,
% 0.26/0.60      ! [M: nat,N: nat,G: nat > real,P6: nat] :
% 0.26/0.60        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.26/0.60       => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 0.26/0.60          = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.ub_add_nat
% 0.26/0.60  thf(fact_6990_prod_Oub__add__nat,axiom,
% 0.26/0.60      ! [M: nat,N: nat,G: nat > rat,P6: nat] :
% 0.26/0.60        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.26/0.60       => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 0.26/0.60          = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.ub_add_nat
% 0.26/0.60  thf(fact_6991_prod_Oub__add__nat,axiom,
% 0.26/0.60      ! [M: nat,N: nat,G: nat > int,P6: nat] :
% 0.26/0.60        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.26/0.60       => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 0.26/0.60          = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.ub_add_nat
% 0.26/0.60  thf(fact_6992_prod_Oub__add__nat,axiom,
% 0.26/0.60      ! [M: nat,N: nat,G: nat > nat,P6: nat] :
% 0.26/0.60        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.26/0.60       => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 0.26/0.60          = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.ub_add_nat
% 0.26/0.60  thf(fact_6993_dbl__dec__def,axiom,
% 0.26/0.60      ( neg_nu6511756317524482435omplex
% 0.26/0.60      = ( ^ [X: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X @ X ) @ one_one_complex ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % dbl_dec_def
% 0.26/0.60  thf(fact_6994_dbl__dec__def,axiom,
% 0.26/0.60      ( neg_nu6075765906172075777c_real
% 0.26/0.60      = ( ^ [X: real] : ( minus_minus_real @ ( plus_plus_real @ X @ X ) @ one_one_real ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % dbl_dec_def
% 0.26/0.60  thf(fact_6995_dbl__dec__def,axiom,
% 0.26/0.60      ( neg_nu3179335615603231917ec_rat
% 0.26/0.60      = ( ^ [X: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % dbl_dec_def
% 0.26/0.60  thf(fact_6996_dbl__dec__def,axiom,
% 0.26/0.60      ( neg_nu3811975205180677377ec_int
% 0.26/0.60      = ( ^ [X: int] : ( minus_minus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % dbl_dec_def
% 0.26/0.60  thf(fact_6997_pochhammer__Suc__prod,axiom,
% 0.26/0.60      ! [A: complex,N: nat] :
% 0.26/0.60        ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 0.26/0.60        = ( groups6464643781859351333omplex
% 0.26/0.60          @ ^ [I4: nat] : ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ I4 ) )
% 0.26/0.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pochhammer_Suc_prod
% 0.26/0.60  thf(fact_6998_pochhammer__Suc__prod,axiom,
% 0.26/0.60      ! [A: real,N: nat] :
% 0.26/0.60        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 0.26/0.60        = ( groups129246275422532515t_real
% 0.26/0.60          @ ^ [I4: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ I4 ) )
% 0.26/0.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pochhammer_Suc_prod
% 0.26/0.60  thf(fact_6999_pochhammer__Suc__prod,axiom,
% 0.26/0.60      ! [A: rat,N: nat] :
% 0.26/0.60        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 0.26/0.60        = ( groups73079841787564623at_rat
% 0.26/0.60          @ ^ [I4: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I4 ) )
% 0.26/0.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pochhammer_Suc_prod
% 0.26/0.60  thf(fact_7000_pochhammer__Suc__prod,axiom,
% 0.26/0.60      ! [A: int,N: nat] :
% 0.26/0.60        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 0.26/0.60        = ( groups705719431365010083at_int
% 0.26/0.60          @ ^ [I4: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I4 ) )
% 0.26/0.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pochhammer_Suc_prod
% 0.26/0.60  thf(fact_7001_pochhammer__Suc__prod,axiom,
% 0.26/0.60      ! [A: nat,N: nat] :
% 0.26/0.60        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 0.26/0.60        = ( groups708209901874060359at_nat
% 0.26/0.60          @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I4 ) )
% 0.26/0.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pochhammer_Suc_prod
% 0.26/0.60  thf(fact_7002_pochhammer__prod__rev,axiom,
% 0.26/0.60      ( comm_s2602460028002588243omplex
% 0.26/0.60      = ( ^ [A4: complex,N3: nat] :
% 0.26/0.60            ( groups6464643781859351333omplex
% 0.26/0.60            @ ^ [I4: nat] : ( plus_plus_complex @ A4 @ ( semiri8010041392384452111omplex @ ( minus_minus_nat @ N3 @ I4 ) ) )
% 0.26/0.60            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pochhammer_prod_rev
% 0.26/0.60  thf(fact_7003_pochhammer__prod__rev,axiom,
% 0.26/0.60      ( comm_s7457072308508201937r_real
% 0.26/0.60      = ( ^ [A4: real,N3: nat] :
% 0.26/0.60            ( groups129246275422532515t_real
% 0.26/0.60            @ ^ [I4: nat] : ( plus_plus_real @ A4 @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N3 @ I4 ) ) )
% 0.26/0.60            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pochhammer_prod_rev
% 0.26/0.60  thf(fact_7004_pochhammer__prod__rev,axiom,
% 0.26/0.60      ( comm_s4028243227959126397er_rat
% 0.26/0.60      = ( ^ [A4: rat,N3: nat] :
% 0.26/0.60            ( groups73079841787564623at_rat
% 0.26/0.60            @ ^ [I4: nat] : ( plus_plus_rat @ A4 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N3 @ I4 ) ) )
% 0.26/0.60            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pochhammer_prod_rev
% 0.26/0.60  thf(fact_7005_pochhammer__prod__rev,axiom,
% 0.26/0.60      ( comm_s4660882817536571857er_int
% 0.26/0.60      = ( ^ [A4: int,N3: nat] :
% 0.26/0.60            ( groups705719431365010083at_int
% 0.26/0.60            @ ^ [I4: nat] : ( plus_plus_int @ A4 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N3 @ I4 ) ) )
% 0.26/0.60            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pochhammer_prod_rev
% 0.26/0.60  thf(fact_7006_pochhammer__prod__rev,axiom,
% 0.26/0.60      ( comm_s4663373288045622133er_nat
% 0.26/0.60      = ( ^ [A4: nat,N3: nat] :
% 0.26/0.60            ( groups708209901874060359at_nat
% 0.26/0.60            @ ^ [I4: nat] : ( plus_plus_nat @ A4 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N3 @ I4 ) ) )
% 0.26/0.60            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pochhammer_prod_rev
% 0.26/0.60  thf(fact_7007_take__bit__numeral__bit0,axiom,
% 0.26/0.60      ! [L: num,K: num] :
% 0.26/0.60        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 0.26/0.60        = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % take_bit_numeral_bit0
% 0.26/0.60  thf(fact_7008_take__bit__numeral__bit0,axiom,
% 0.26/0.60      ! [L: num,K: num] :
% 0.26/0.60        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.26/0.60        = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % take_bit_numeral_bit0
% 0.26/0.60  thf(fact_7009_prod_Oin__pairs,axiom,
% 0.26/0.60      ! [G: nat > real,M: nat,N: nat] :
% 0.26/0.60        ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.26/0.60        = ( groups129246275422532515t_real
% 0.26/0.60          @ ^ [I4: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 0.26/0.60          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.in_pairs
% 0.26/0.60  thf(fact_7010_prod_Oin__pairs,axiom,
% 0.26/0.60      ! [G: nat > rat,M: nat,N: nat] :
% 0.26/0.60        ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.26/0.60        = ( groups73079841787564623at_rat
% 0.26/0.60          @ ^ [I4: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 0.26/0.60          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.in_pairs
% 0.26/0.60  thf(fact_7011_prod_Oin__pairs,axiom,
% 0.26/0.60      ! [G: nat > int,M: nat,N: nat] :
% 0.26/0.60        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.26/0.60        = ( groups705719431365010083at_int
% 0.26/0.60          @ ^ [I4: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 0.26/0.60          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.in_pairs
% 0.26/0.60  thf(fact_7012_prod_Oin__pairs,axiom,
% 0.26/0.60      ! [G: nat > nat,M: nat,N: nat] :
% 0.26/0.60        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.26/0.60        = ( groups708209901874060359at_nat
% 0.26/0.60          @ ^ [I4: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 0.26/0.60          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod.in_pairs
% 0.26/0.60  thf(fact_7013_pochhammer__Suc__prod__rev,axiom,
% 0.26/0.60      ! [A: complex,N: nat] :
% 0.26/0.60        ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 0.26/0.60        = ( groups6464643781859351333omplex
% 0.26/0.60          @ ^ [I4: nat] : ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ ( minus_minus_nat @ N @ I4 ) ) )
% 0.26/0.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pochhammer_Suc_prod_rev
% 0.26/0.60  thf(fact_7014_pochhammer__Suc__prod__rev,axiom,
% 0.26/0.60      ! [A: real,N: nat] :
% 0.26/0.60        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 0.26/0.60        = ( groups129246275422532515t_real
% 0.26/0.60          @ ^ [I4: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ I4 ) ) )
% 0.26/0.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pochhammer_Suc_prod_rev
% 0.26/0.60  thf(fact_7015_pochhammer__Suc__prod__rev,axiom,
% 0.26/0.60      ! [A: rat,N: nat] :
% 0.26/0.60        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 0.26/0.60        = ( groups73079841787564623at_rat
% 0.26/0.60          @ ^ [I4: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I4 ) ) )
% 0.26/0.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pochhammer_Suc_prod_rev
% 0.26/0.60  thf(fact_7016_pochhammer__Suc__prod__rev,axiom,
% 0.26/0.60      ! [A: int,N: nat] :
% 0.26/0.60        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 0.26/0.60        = ( groups705719431365010083at_int
% 0.26/0.60          @ ^ [I4: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I4 ) ) )
% 0.26/0.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pochhammer_Suc_prod_rev
% 0.26/0.60  thf(fact_7017_pochhammer__Suc__prod__rev,axiom,
% 0.26/0.60      ! [A: nat,N: nat] :
% 0.26/0.60        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 0.26/0.60        = ( groups708209901874060359at_nat
% 0.26/0.60          @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I4 ) ) )
% 0.26/0.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pochhammer_Suc_prod_rev
% 0.26/0.60  thf(fact_7018_take__bit__numeral__minus__bit0,axiom,
% 0.26/0.60      ! [L: num,K: num] :
% 0.26/0.60        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.26/0.60        = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % take_bit_numeral_minus_bit0
% 0.26/0.60  thf(fact_7019_take__bit__numeral__bit1,axiom,
% 0.26/0.60      ! [L: num,K: num] :
% 0.26/0.60        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.26/0.60        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.26/0.60  
% 0.26/0.60  % take_bit_numeral_bit1
% 0.26/0.60  thf(fact_7020_take__bit__numeral__bit1,axiom,
% 0.26/0.60      ! [L: num,K: num] :
% 0.26/0.60        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.26/0.60        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % take_bit_numeral_bit1
% 0.26/0.60  thf(fact_7021_suminf__geometric,axiom,
% 0.26/0.60      ! [C: real] :
% 0.26/0.60        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 0.26/0.60       => ( ( suminf_real @ ( power_power_real @ C ) )
% 0.26/0.60          = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_geometric
% 0.26/0.60  thf(fact_7022_suminf__geometric,axiom,
% 0.26/0.60      ! [C: complex] :
% 0.26/0.60        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 0.26/0.60       => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 0.26/0.60          = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_geometric
% 0.26/0.60  thf(fact_7023_suminf__zero,axiom,
% 0.26/0.60      ( ( suminf_real
% 0.26/0.60        @ ^ [N3: nat] : zero_zero_real )
% 0.26/0.60      = zero_zero_real ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_zero
% 0.26/0.60  thf(fact_7024_suminf__zero,axiom,
% 0.26/0.60      ( ( suminf_nat
% 0.26/0.60        @ ^ [N3: nat] : zero_zero_nat )
% 0.26/0.60      = zero_zero_nat ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_zero
% 0.26/0.60  thf(fact_7025_suminf__zero,axiom,
% 0.26/0.60      ( ( suminf_int
% 0.26/0.60        @ ^ [N3: nat] : zero_zero_int )
% 0.26/0.60      = zero_zero_int ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_zero
% 0.26/0.60  thf(fact_7026_pi__series,axiom,
% 0.26/0.60      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.26/0.60      = ( suminf_real
% 0.26/0.60        @ ^ [K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pi_series
% 0.26/0.60  thf(fact_7027_take__bit__numeral__minus__bit1,axiom,
% 0.26/0.60      ! [L: num,K: num] :
% 0.26/0.60        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.26/0.60        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.26/0.60  
% 0.26/0.60  % take_bit_numeral_minus_bit1
% 0.26/0.60  thf(fact_7028_prod__le__1,axiom,
% 0.26/0.60      ! [A3: set_real,F: real > real] :
% 0.26/0.60        ( ! [X4: real] :
% 0.26/0.60            ( ( member_real @ X4 @ A3 )
% 0.26/0.60           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 0.26/0.60              & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 0.26/0.60       => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A3 ) @ one_one_real ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_le_1
% 0.26/0.60  thf(fact_7029_prod__le__1,axiom,
% 0.26/0.60      ! [A3: set_nat,F: nat > real] :
% 0.26/0.60        ( ! [X4: nat] :
% 0.26/0.60            ( ( member_nat @ X4 @ A3 )
% 0.26/0.60           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 0.26/0.60              & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 0.26/0.60       => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A3 ) @ one_one_real ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_le_1
% 0.26/0.60  thf(fact_7030_prod__le__1,axiom,
% 0.26/0.60      ! [A3: set_int,F: int > real] :
% 0.26/0.60        ( ! [X4: int] :
% 0.26/0.60            ( ( member_int @ X4 @ A3 )
% 0.26/0.60           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 0.26/0.60              & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 0.26/0.60       => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A3 ) @ one_one_real ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_le_1
% 0.26/0.60  thf(fact_7031_prod__le__1,axiom,
% 0.26/0.60      ! [A3: set_real,F: real > rat] :
% 0.26/0.60        ( ! [X4: real] :
% 0.26/0.60            ( ( member_real @ X4 @ A3 )
% 0.26/0.60           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 0.26/0.60              & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 0.26/0.60       => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A3 ) @ one_one_rat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_le_1
% 0.26/0.60  thf(fact_7032_prod__le__1,axiom,
% 0.26/0.60      ! [A3: set_nat,F: nat > rat] :
% 0.26/0.60        ( ! [X4: nat] :
% 0.26/0.60            ( ( member_nat @ X4 @ A3 )
% 0.26/0.60           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 0.26/0.60              & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 0.26/0.60       => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A3 ) @ one_one_rat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_le_1
% 0.26/0.60  thf(fact_7033_prod__le__1,axiom,
% 0.26/0.60      ! [A3: set_int,F: int > rat] :
% 0.26/0.60        ( ! [X4: int] :
% 0.26/0.60            ( ( member_int @ X4 @ A3 )
% 0.26/0.60           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 0.26/0.60              & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 0.26/0.60       => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A3 ) @ one_one_rat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_le_1
% 0.26/0.60  thf(fact_7034_prod__le__1,axiom,
% 0.26/0.60      ! [A3: set_real,F: real > nat] :
% 0.26/0.60        ( ! [X4: real] :
% 0.26/0.60            ( ( member_real @ X4 @ A3 )
% 0.26/0.60           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 0.26/0.60              & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 0.26/0.60       => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A3 ) @ one_one_nat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_le_1
% 0.26/0.60  thf(fact_7035_prod__le__1,axiom,
% 0.26/0.60      ! [A3: set_int,F: int > nat] :
% 0.26/0.60        ( ! [X4: int] :
% 0.26/0.60            ( ( member_int @ X4 @ A3 )
% 0.26/0.60           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 0.26/0.60              & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 0.26/0.60       => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A3 ) @ one_one_nat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_le_1
% 0.26/0.60  thf(fact_7036_prod__le__1,axiom,
% 0.26/0.60      ! [A3: set_real,F: real > int] :
% 0.26/0.60        ( ! [X4: real] :
% 0.26/0.60            ( ( member_real @ X4 @ A3 )
% 0.26/0.60           => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) )
% 0.26/0.60              & ( ord_less_eq_int @ ( F @ X4 ) @ one_one_int ) ) )
% 0.26/0.60       => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F @ A3 ) @ one_one_int ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_le_1
% 0.26/0.60  thf(fact_7037_prod__le__1,axiom,
% 0.26/0.60      ! [A3: set_nat,F: nat > int] :
% 0.26/0.60        ( ! [X4: nat] :
% 0.26/0.60            ( ( member_nat @ X4 @ A3 )
% 0.26/0.60           => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) )
% 0.26/0.60              & ( ord_less_eq_int @ ( F @ X4 ) @ one_one_int ) ) )
% 0.26/0.60       => ( ord_less_eq_int @ ( groups705719431365010083at_int @ F @ A3 ) @ one_one_int ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_le_1
% 0.26/0.60  thf(fact_7038_pred__numeral__inc,axiom,
% 0.26/0.60      ! [K: num] :
% 0.26/0.60        ( ( pred_numeral @ ( inc @ K ) )
% 0.26/0.60        = ( numeral_numeral_nat @ K ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pred_numeral_inc
% 0.26/0.60  thf(fact_7039_add__neg__numeral__special_I6_J,axiom,
% 0.26/0.60      ! [M: num] :
% 0.26/0.60        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.26/0.60        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % add_neg_numeral_special(6)
% 0.26/0.60  thf(fact_7040_add__neg__numeral__special_I6_J,axiom,
% 0.26/0.60      ! [M: num] :
% 0.26/0.60        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.60        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % add_neg_numeral_special(6)
% 0.26/0.60  thf(fact_7041_add__neg__numeral__special_I6_J,axiom,
% 0.26/0.60      ! [M: num] :
% 0.26/0.60        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.26/0.60        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % add_neg_numeral_special(6)
% 0.26/0.60  thf(fact_7042_add__neg__numeral__special_I6_J,axiom,
% 0.26/0.60      ! [M: num] :
% 0.26/0.60        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.26/0.60        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % add_neg_numeral_special(6)
% 0.26/0.60  thf(fact_7043_add__neg__numeral__special_I6_J,axiom,
% 0.26/0.60      ! [M: num] :
% 0.26/0.60        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.26/0.60        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % add_neg_numeral_special(6)
% 0.26/0.60  thf(fact_7044_add__neg__numeral__special_I5_J,axiom,
% 0.26/0.60      ! [N: num] :
% 0.26/0.60        ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.26/0.60        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % add_neg_numeral_special(5)
% 0.26/0.60  thf(fact_7045_add__neg__numeral__special_I5_J,axiom,
% 0.26/0.60      ! [N: num] :
% 0.26/0.60        ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.60        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % add_neg_numeral_special(5)
% 0.26/0.60  thf(fact_7046_add__neg__numeral__special_I5_J,axiom,
% 0.26/0.60      ! [N: num] :
% 0.26/0.60        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.26/0.60        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % add_neg_numeral_special(5)
% 0.26/0.60  thf(fact_7047_add__neg__numeral__special_I5_J,axiom,
% 0.26/0.60      ! [N: num] :
% 0.26/0.60        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.26/0.60        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % add_neg_numeral_special(5)
% 0.26/0.60  thf(fact_7048_add__neg__numeral__special_I5_J,axiom,
% 0.26/0.60      ! [N: num] :
% 0.26/0.60        ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.26/0.60        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % add_neg_numeral_special(5)
% 0.26/0.60  thf(fact_7049_diff__numeral__special_I6_J,axiom,
% 0.26/0.60      ! [M: num] :
% 0.26/0.60        ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.26/0.60        = ( numeral_numeral_real @ ( inc @ M ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % diff_numeral_special(6)
% 0.26/0.60  thf(fact_7050_diff__numeral__special_I6_J,axiom,
% 0.26/0.60      ! [M: num] :
% 0.26/0.60        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.60        = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % diff_numeral_special(6)
% 0.26/0.60  thf(fact_7051_diff__numeral__special_I6_J,axiom,
% 0.26/0.60      ! [M: num] :
% 0.26/0.60        ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.26/0.60        = ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % diff_numeral_special(6)
% 0.26/0.60  thf(fact_7052_diff__numeral__special_I6_J,axiom,
% 0.26/0.60      ! [M: num] :
% 0.26/0.60        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.26/0.60        = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % diff_numeral_special(6)
% 0.26/0.60  thf(fact_7053_diff__numeral__special_I6_J,axiom,
% 0.26/0.60      ! [M: num] :
% 0.26/0.60        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.26/0.60        = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % diff_numeral_special(6)
% 0.26/0.60  thf(fact_7054_diff__numeral__special_I5_J,axiom,
% 0.26/0.60      ! [N: num] :
% 0.26/0.60        ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ N ) )
% 0.26/0.60        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % diff_numeral_special(5)
% 0.26/0.60  thf(fact_7055_diff__numeral__special_I5_J,axiom,
% 0.26/0.60      ! [N: num] :
% 0.26/0.60        ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.60        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % diff_numeral_special(5)
% 0.26/0.60  thf(fact_7056_diff__numeral__special_I5_J,axiom,
% 0.26/0.60      ! [N: num] :
% 0.26/0.60        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( numera6690914467698888265omplex @ N ) )
% 0.26/0.60        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % diff_numeral_special(5)
% 0.26/0.60  thf(fact_7057_diff__numeral__special_I5_J,axiom,
% 0.26/0.60      ! [N: num] :
% 0.26/0.60        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 0.26/0.60        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % diff_numeral_special(5)
% 0.26/0.60  thf(fact_7058_diff__numeral__special_I5_J,axiom,
% 0.26/0.60      ! [N: num] :
% 0.26/0.60        ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 0.26/0.60        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % diff_numeral_special(5)
% 0.26/0.60  thf(fact_7059_int__prod,axiom,
% 0.26/0.60      ! [F: int > nat,A3: set_int] :
% 0.26/0.60        ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F @ A3 ) )
% 0.26/0.60        = ( groups1705073143266064639nt_int
% 0.26/0.60          @ ^ [X: int] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 0.26/0.60          @ A3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % int_prod
% 0.26/0.60  thf(fact_7060_int__prod,axiom,
% 0.26/0.60      ! [F: nat > nat,A3: set_nat] :
% 0.26/0.60        ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 0.26/0.60        = ( groups705719431365010083at_int
% 0.26/0.60          @ ^ [X: nat] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 0.26/0.60          @ A3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % int_prod
% 0.26/0.60  thf(fact_7061_pi__neq__zero,axiom,
% 0.26/0.60      pi != zero_zero_real ).
% 0.26/0.60  
% 0.26/0.60  % pi_neq_zero
% 0.26/0.60  thf(fact_7062_num__induct,axiom,
% 0.26/0.60      ! [P: num > $o,X3: num] :
% 0.26/0.60        ( ( P @ one )
% 0.26/0.60       => ( ! [X4: num] :
% 0.26/0.60              ( ( P @ X4 )
% 0.26/0.60             => ( P @ ( inc @ X4 ) ) )
% 0.26/0.60         => ( P @ X3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % num_induct
% 0.26/0.60  thf(fact_7063_add__inc,axiom,
% 0.26/0.60      ! [X3: num,Y3: num] :
% 0.26/0.60        ( ( plus_plus_num @ X3 @ ( inc @ Y3 ) )
% 0.26/0.60        = ( inc @ ( plus_plus_num @ X3 @ Y3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % add_inc
% 0.26/0.60  thf(fact_7064_pi__gt__zero,axiom,
% 0.26/0.60      ord_less_real @ zero_zero_real @ pi ).
% 0.26/0.60  
% 0.26/0.60  % pi_gt_zero
% 0.26/0.60  thf(fact_7065_pi__not__less__zero,axiom,
% 0.26/0.60      ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 0.26/0.60  
% 0.26/0.60  % pi_not_less_zero
% 0.26/0.60  thf(fact_7066_pi__ge__zero,axiom,
% 0.26/0.60      ord_less_eq_real @ zero_zero_real @ pi ).
% 0.26/0.60  
% 0.26/0.60  % pi_ge_zero
% 0.26/0.60  thf(fact_7067_inc_Osimps_I1_J,axiom,
% 0.26/0.60      ( ( inc @ one )
% 0.26/0.60      = ( bit0 @ one ) ) ).
% 0.26/0.60  
% 0.26/0.60  % inc.simps(1)
% 0.26/0.60  thf(fact_7068_inc_Osimps_I3_J,axiom,
% 0.26/0.60      ! [X3: num] :
% 0.26/0.60        ( ( inc @ ( bit1 @ X3 ) )
% 0.26/0.60        = ( bit0 @ ( inc @ X3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % inc.simps(3)
% 0.26/0.60  thf(fact_7069_inc_Osimps_I2_J,axiom,
% 0.26/0.60      ! [X3: num] :
% 0.26/0.60        ( ( inc @ ( bit0 @ X3 ) )
% 0.26/0.60        = ( bit1 @ X3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % inc.simps(2)
% 0.26/0.60  thf(fact_7070_add__One,axiom,
% 0.26/0.60      ! [X3: num] :
% 0.26/0.60        ( ( plus_plus_num @ X3 @ one )
% 0.26/0.60        = ( inc @ X3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % add_One
% 0.26/0.60  thf(fact_7071_mult__inc,axiom,
% 0.26/0.60      ! [X3: num,Y3: num] :
% 0.26/0.60        ( ( times_times_num @ X3 @ ( inc @ Y3 ) )
% 0.26/0.60        = ( plus_plus_num @ ( times_times_num @ X3 @ Y3 ) @ X3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % mult_inc
% 0.26/0.60  thf(fact_7072_prod__int__eq,axiom,
% 0.26/0.60      ! [I: nat,J: nat] :
% 0.26/0.60        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 0.26/0.60        = ( groups1705073143266064639nt_int
% 0.26/0.60          @ ^ [X: int] : X
% 0.26/0.60          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_int_eq
% 0.26/0.60  thf(fact_7073_numeral__inc,axiom,
% 0.26/0.60      ! [X3: num] :
% 0.26/0.60        ( ( numera6690914467698888265omplex @ ( inc @ X3 ) )
% 0.26/0.60        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X3 ) @ one_one_complex ) ) ).
% 0.26/0.60  
% 0.26/0.60  % numeral_inc
% 0.26/0.60  thf(fact_7074_numeral__inc,axiom,
% 0.26/0.60      ! [X3: num] :
% 0.26/0.60        ( ( numeral_numeral_real @ ( inc @ X3 ) )
% 0.26/0.60        = ( plus_plus_real @ ( numeral_numeral_real @ X3 ) @ one_one_real ) ) ).
% 0.26/0.60  
% 0.26/0.60  % numeral_inc
% 0.26/0.60  thf(fact_7075_numeral__inc,axiom,
% 0.26/0.60      ! [X3: num] :
% 0.26/0.60        ( ( numeral_numeral_rat @ ( inc @ X3 ) )
% 0.26/0.60        = ( plus_plus_rat @ ( numeral_numeral_rat @ X3 ) @ one_one_rat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % numeral_inc
% 0.26/0.60  thf(fact_7076_numeral__inc,axiom,
% 0.26/0.60      ! [X3: num] :
% 0.26/0.60        ( ( numeral_numeral_nat @ ( inc @ X3 ) )
% 0.26/0.60        = ( plus_plus_nat @ ( numeral_numeral_nat @ X3 ) @ one_one_nat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % numeral_inc
% 0.26/0.60  thf(fact_7077_numeral__inc,axiom,
% 0.26/0.60      ! [X3: num] :
% 0.26/0.60        ( ( numeral_numeral_int @ ( inc @ X3 ) )
% 0.26/0.60        = ( plus_plus_int @ ( numeral_numeral_int @ X3 ) @ one_one_int ) ) ).
% 0.26/0.60  
% 0.26/0.60  % numeral_inc
% 0.26/0.60  thf(fact_7078_pi__less__4,axiom,
% 0.26/0.60      ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pi_less_4
% 0.26/0.60  thf(fact_7079_pi__ge__two,axiom,
% 0.26/0.60      ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 0.26/0.60  
% 0.26/0.60  % pi_ge_two
% 0.26/0.60  thf(fact_7080_pi__half__neq__two,axiom,
% 0.26/0.60      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.26/0.60     != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pi_half_neq_two
% 0.26/0.60  thf(fact_7081_prod__int__plus__eq,axiom,
% 0.26/0.60      ! [I: nat,J: nat] :
% 0.26/0.60        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 0.26/0.60        = ( groups1705073143266064639nt_int
% 0.26/0.60          @ ^ [X: int] : X
% 0.26/0.60          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_int_plus_eq
% 0.26/0.60  thf(fact_7082_pi__half__neq__zero,axiom,
% 0.26/0.60      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.26/0.60     != zero_zero_real ) ).
% 0.26/0.60  
% 0.26/0.60  % pi_half_neq_zero
% 0.26/0.60  thf(fact_7083_pi__half__less__two,axiom,
% 0.26/0.60      ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pi_half_less_two
% 0.26/0.60  thf(fact_7084_pi__half__le__two,axiom,
% 0.26/0.60      ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pi_half_le_two
% 0.26/0.60  thf(fact_7085_pi__half__gt__zero,axiom,
% 0.26/0.60      ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pi_half_gt_zero
% 0.26/0.60  thf(fact_7086_pi__half__ge__zero,axiom,
% 0.26/0.60      ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % pi_half_ge_zero
% 0.26/0.60  thf(fact_7087_m2pi__less__pi,axiom,
% 0.26/0.60      ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 0.26/0.60  
% 0.26/0.60  % m2pi_less_pi
% 0.26/0.60  thf(fact_7088_arctan__ubound,axiom,
% 0.26/0.60      ! [Y3: real] : ( ord_less_real @ ( arctan @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % arctan_ubound
% 0.26/0.60  thf(fact_7089_arctan__one,axiom,
% 0.26/0.60      ( ( arctan @ one_one_real )
% 0.26/0.60      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % arctan_one
% 0.26/0.60  thf(fact_7090_minus__pi__half__less__zero,axiom,
% 0.26/0.60      ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 0.26/0.60  
% 0.26/0.60  % minus_pi_half_less_zero
% 0.26/0.60  thf(fact_7091_arctan__bounded,axiom,
% 0.26/0.60      ! [Y3: real] :
% 0.26/0.60        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y3 ) )
% 0.26/0.60        & ( ord_less_real @ ( arctan @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % arctan_bounded
% 0.26/0.60  thf(fact_7092_arctan__lbound,axiom,
% 0.26/0.60      ! [Y3: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % arctan_lbound
% 0.26/0.60  thf(fact_7093_prod__power__distrib,axiom,
% 0.26/0.60      ! [F: nat > int,A3: set_nat,N: nat] :
% 0.26/0.60        ( ( power_power_int @ ( groups705719431365010083at_int @ F @ A3 ) @ N )
% 0.26/0.60        = ( groups705719431365010083at_int
% 0.26/0.60          @ ^ [X: nat] : ( power_power_int @ ( F @ X ) @ N )
% 0.26/0.60          @ A3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_power_distrib
% 0.26/0.60  thf(fact_7094_prod__power__distrib,axiom,
% 0.26/0.60      ! [F: int > int,A3: set_int,N: nat] :
% 0.26/0.60        ( ( power_power_int @ ( groups1705073143266064639nt_int @ F @ A3 ) @ N )
% 0.26/0.60        = ( groups1705073143266064639nt_int
% 0.26/0.60          @ ^ [X: int] : ( power_power_int @ ( F @ X ) @ N )
% 0.26/0.60          @ A3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_power_distrib
% 0.26/0.60  thf(fact_7095_prod__power__distrib,axiom,
% 0.26/0.60      ! [F: nat > nat,A3: set_nat,N: nat] :
% 0.26/0.60        ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A3 ) @ N )
% 0.26/0.60        = ( groups708209901874060359at_nat
% 0.26/0.60          @ ^ [X: nat] : ( power_power_nat @ ( F @ X ) @ N )
% 0.26/0.60          @ A3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_power_distrib
% 0.26/0.60  thf(fact_7096_machin__Euler,axiom,
% 0.26/0.60      ( ( 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 ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.60      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % machin_Euler
% 0.26/0.60  thf(fact_7097_machin,axiom,
% 0.26/0.60      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.26/0.60      = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % machin
% 0.26/0.60  thf(fact_7098_prod__mono,axiom,
% 0.26/0.60      ! [A3: set_real,F: real > real,G: real > real] :
% 0.26/0.60        ( ! [I3: real] :
% 0.26/0.60            ( ( member_real @ I3 @ A3 )
% 0.26/0.60           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 0.26/0.60              & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.26/0.60       => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A3 ) @ ( groups1681761925125756287l_real @ G @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_mono
% 0.26/0.60  thf(fact_7099_prod__mono,axiom,
% 0.26/0.60      ! [A3: set_nat,F: nat > real,G: nat > real] :
% 0.26/0.60        ( ! [I3: nat] :
% 0.26/0.60            ( ( member_nat @ I3 @ A3 )
% 0.26/0.60           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 0.26/0.60              & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.26/0.60       => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A3 ) @ ( groups129246275422532515t_real @ G @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_mono
% 0.26/0.60  thf(fact_7100_prod__mono,axiom,
% 0.26/0.60      ! [A3: set_int,F: int > real,G: int > real] :
% 0.26/0.60        ( ! [I3: int] :
% 0.26/0.60            ( ( member_int @ I3 @ A3 )
% 0.26/0.60           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 0.26/0.60              & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.26/0.60       => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A3 ) @ ( groups2316167850115554303t_real @ G @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_mono
% 0.26/0.60  thf(fact_7101_prod__mono,axiom,
% 0.26/0.60      ! [A3: set_real,F: real > rat,G: real > rat] :
% 0.26/0.60        ( ! [I3: real] :
% 0.26/0.60            ( ( member_real @ I3 @ A3 )
% 0.26/0.60           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 0.26/0.60              & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.26/0.60       => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A3 ) @ ( groups4061424788464935467al_rat @ G @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_mono
% 0.26/0.60  thf(fact_7102_prod__mono,axiom,
% 0.26/0.60      ! [A3: set_nat,F: nat > rat,G: nat > rat] :
% 0.26/0.60        ( ! [I3: nat] :
% 0.26/0.60            ( ( member_nat @ I3 @ A3 )
% 0.26/0.60           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 0.26/0.60              & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.26/0.60       => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A3 ) @ ( groups73079841787564623at_rat @ G @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_mono
% 0.26/0.60  thf(fact_7103_prod__mono,axiom,
% 0.26/0.60      ! [A3: set_int,F: int > rat,G: int > rat] :
% 0.26/0.60        ( ! [I3: int] :
% 0.26/0.60            ( ( member_int @ I3 @ A3 )
% 0.26/0.60           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 0.26/0.60              & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.26/0.60       => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A3 ) @ ( groups1072433553688619179nt_rat @ G @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_mono
% 0.26/0.60  thf(fact_7104_prod__mono,axiom,
% 0.26/0.60      ! [A3: set_real,F: real > nat,G: real > nat] :
% 0.26/0.60        ( ! [I3: real] :
% 0.26/0.60            ( ( member_real @ I3 @ A3 )
% 0.26/0.60           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 0.26/0.60              & ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.26/0.60       => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A3 ) @ ( groups4696554848551431203al_nat @ G @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_mono
% 0.26/0.60  thf(fact_7105_prod__mono,axiom,
% 0.26/0.60      ! [A3: set_int,F: int > nat,G: int > nat] :
% 0.26/0.60        ( ! [I3: int] :
% 0.26/0.60            ( ( member_int @ I3 @ A3 )
% 0.26/0.60           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 0.26/0.60              & ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.26/0.60       => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A3 ) @ ( groups1707563613775114915nt_nat @ G @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_mono
% 0.26/0.60  thf(fact_7106_prod__mono,axiom,
% 0.26/0.60      ! [A3: set_real,F: real > int,G: real > int] :
% 0.26/0.60        ( ! [I3: real] :
% 0.26/0.60            ( ( member_real @ I3 @ A3 )
% 0.26/0.60           => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I3 ) )
% 0.26/0.60              & ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.26/0.60       => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F @ A3 ) @ ( groups4694064378042380927al_int @ G @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_mono
% 0.26/0.60  thf(fact_7107_prod__mono,axiom,
% 0.26/0.60      ! [A3: set_nat,F: nat > int,G: nat > int] :
% 0.26/0.60        ( ! [I3: nat] :
% 0.26/0.60            ( ( member_nat @ I3 @ A3 )
% 0.26/0.60           => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I3 ) )
% 0.26/0.60              & ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.26/0.60       => ( ord_less_eq_int @ ( groups705719431365010083at_int @ F @ A3 ) @ ( groups705719431365010083at_int @ G @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_mono
% 0.26/0.60  thf(fact_7108_prod__nonneg,axiom,
% 0.26/0.60      ! [A3: set_nat,F: nat > int] :
% 0.26/0.60        ( ! [X4: nat] :
% 0.26/0.60            ( ( member_nat @ X4 @ A3 )
% 0.26/0.60           => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 0.26/0.60       => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_nonneg
% 0.26/0.60  thf(fact_7109_prod__nonneg,axiom,
% 0.26/0.60      ! [A3: set_int,F: int > int] :
% 0.26/0.60        ( ! [X4: int] :
% 0.26/0.60            ( ( member_int @ X4 @ A3 )
% 0.26/0.60           => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 0.26/0.60       => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_nonneg
% 0.26/0.60  thf(fact_7110_prod__nonneg,axiom,
% 0.26/0.60      ! [A3: set_nat,F: nat > nat] :
% 0.26/0.60        ( ! [X4: nat] :
% 0.26/0.60            ( ( member_nat @ X4 @ A3 )
% 0.26/0.60           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 0.26/0.60       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_nonneg
% 0.26/0.60  thf(fact_7111_prod__pos,axiom,
% 0.26/0.60      ! [A3: set_nat,F: nat > int] :
% 0.26/0.60        ( ! [X4: nat] :
% 0.26/0.60            ( ( member_nat @ X4 @ A3 )
% 0.26/0.60           => ( ord_less_int @ zero_zero_int @ ( F @ X4 ) ) )
% 0.26/0.60       => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_pos
% 0.26/0.60  thf(fact_7112_prod__pos,axiom,
% 0.26/0.60      ! [A3: set_int,F: int > int] :
% 0.26/0.60        ( ! [X4: int] :
% 0.26/0.60            ( ( member_int @ X4 @ A3 )
% 0.26/0.60           => ( ord_less_int @ zero_zero_int @ ( F @ X4 ) ) )
% 0.26/0.60       => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_pos
% 0.26/0.60  thf(fact_7113_prod__pos,axiom,
% 0.26/0.60      ! [A3: set_nat,F: nat > nat] :
% 0.26/0.60        ( ! [X4: nat] :
% 0.26/0.60            ( ( member_nat @ X4 @ A3 )
% 0.26/0.60           => ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 0.26/0.60       => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_pos
% 0.26/0.60  thf(fact_7114_prod__ge__1,axiom,
% 0.26/0.60      ! [A3: set_real,F: real > real] :
% 0.26/0.60        ( ! [X4: real] :
% 0.26/0.60            ( ( member_real @ X4 @ A3 )
% 0.26/0.60           => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 0.26/0.60       => ( ord_less_eq_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_ge_1
% 0.26/0.60  thf(fact_7115_prod__ge__1,axiom,
% 0.26/0.60      ! [A3: set_nat,F: nat > real] :
% 0.26/0.60        ( ! [X4: nat] :
% 0.26/0.60            ( ( member_nat @ X4 @ A3 )
% 0.26/0.60           => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 0.26/0.60       => ( ord_less_eq_real @ one_one_real @ ( groups129246275422532515t_real @ F @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_ge_1
% 0.26/0.60  thf(fact_7116_prod__ge__1,axiom,
% 0.26/0.60      ! [A3: set_int,F: int > real] :
% 0.26/0.60        ( ! [X4: int] :
% 0.26/0.60            ( ( member_int @ X4 @ A3 )
% 0.26/0.60           => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 0.26/0.60       => ( ord_less_eq_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_ge_1
% 0.26/0.60  thf(fact_7117_prod__ge__1,axiom,
% 0.26/0.60      ! [A3: set_real,F: real > rat] :
% 0.26/0.60        ( ! [X4: real] :
% 0.26/0.60            ( ( member_real @ X4 @ A3 )
% 0.26/0.60           => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 0.26/0.60       => ( ord_less_eq_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_ge_1
% 0.26/0.60  thf(fact_7118_prod__ge__1,axiom,
% 0.26/0.60      ! [A3: set_nat,F: nat > rat] :
% 0.26/0.60        ( ! [X4: nat] :
% 0.26/0.60            ( ( member_nat @ X4 @ A3 )
% 0.26/0.60           => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 0.26/0.60       => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_ge_1
% 0.26/0.60  thf(fact_7119_prod__ge__1,axiom,
% 0.26/0.60      ! [A3: set_int,F: int > rat] :
% 0.26/0.60        ( ! [X4: int] :
% 0.26/0.60            ( ( member_int @ X4 @ A3 )
% 0.26/0.60           => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 0.26/0.60       => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_ge_1
% 0.26/0.60  thf(fact_7120_prod__ge__1,axiom,
% 0.26/0.60      ! [A3: set_real,F: real > nat] :
% 0.26/0.60        ( ! [X4: real] :
% 0.26/0.60            ( ( member_real @ X4 @ A3 )
% 0.26/0.60           => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 0.26/0.60       => ( ord_less_eq_nat @ one_one_nat @ ( groups4696554848551431203al_nat @ F @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_ge_1
% 0.26/0.60  thf(fact_7121_prod__ge__1,axiom,
% 0.26/0.60      ! [A3: set_int,F: int > nat] :
% 0.26/0.60        ( ! [X4: int] :
% 0.26/0.60            ( ( member_int @ X4 @ A3 )
% 0.26/0.60           => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 0.26/0.60       => ( ord_less_eq_nat @ one_one_nat @ ( groups1707563613775114915nt_nat @ F @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_ge_1
% 0.26/0.60  thf(fact_7122_prod__ge__1,axiom,
% 0.26/0.60      ! [A3: set_real,F: real > int] :
% 0.26/0.60        ( ! [X4: real] :
% 0.26/0.60            ( ( member_real @ X4 @ A3 )
% 0.26/0.60           => ( ord_less_eq_int @ one_one_int @ ( F @ X4 ) ) )
% 0.26/0.60       => ( ord_less_eq_int @ one_one_int @ ( groups4694064378042380927al_int @ F @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_ge_1
% 0.26/0.60  thf(fact_7123_prod__ge__1,axiom,
% 0.26/0.60      ! [A3: set_nat,F: nat > int] :
% 0.26/0.60        ( ! [X4: nat] :
% 0.26/0.60            ( ( member_nat @ X4 @ A3 )
% 0.26/0.60           => ( ord_less_eq_int @ one_one_int @ ( F @ X4 ) ) )
% 0.26/0.60       => ( ord_less_eq_int @ one_one_int @ ( groups705719431365010083at_int @ F @ A3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % prod_ge_1
% 0.26/0.60  thf(fact_7124_take__bit__Suc__minus__bit1,axiom,
% 0.26/0.60      ! [N: nat,K: num] :
% 0.26/0.60        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.26/0.60        = ( 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 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % take_bit_Suc_minus_bit1
% 0.26/0.60  thf(fact_7125_sin__cos__npi,axiom,
% 0.26/0.60      ! [N: nat] :
% 0.26/0.60        ( ( 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 ) ) ) )
% 0.26/0.60        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_cos_npi
% 0.26/0.60  thf(fact_7126_divmod__algorithm__code_I7_J,axiom,
% 0.26/0.60      ! [M: num,N: num] :
% 0.26/0.60        ( ( ( ord_less_eq_num @ M @ N )
% 0.26/0.60         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.26/0.60            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 0.26/0.60        & ( ~ ( ord_less_eq_num @ M @ N )
% 0.26/0.60         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.26/0.60            = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % divmod_algorithm_code(7)
% 0.26/0.60  thf(fact_7127_divmod__algorithm__code_I7_J,axiom,
% 0.26/0.60      ! [M: num,N: num] :
% 0.26/0.60        ( ( ( ord_less_eq_num @ M @ N )
% 0.26/0.60         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.26/0.60            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 0.26/0.60        & ( ~ ( ord_less_eq_num @ M @ N )
% 0.26/0.60         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.26/0.60            = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % divmod_algorithm_code(7)
% 0.26/0.60  thf(fact_7128_divmod__algorithm__code_I7_J,axiom,
% 0.26/0.60      ! [M: num,N: num] :
% 0.26/0.60        ( ( ( ord_less_eq_num @ M @ N )
% 0.26/0.60         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.26/0.60            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 0.26/0.60        & ( ~ ( ord_less_eq_num @ M @ N )
% 0.26/0.60         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.26/0.60            = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % divmod_algorithm_code(7)
% 0.26/0.60  thf(fact_7129_divmod__algorithm__code_I8_J,axiom,
% 0.26/0.60      ! [M: num,N: num] :
% 0.26/0.60        ( ( ( ord_less_num @ M @ N )
% 0.26/0.60         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.26/0.60            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 0.26/0.60        & ( ~ ( ord_less_num @ M @ N )
% 0.26/0.60         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.26/0.60            = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % divmod_algorithm_code(8)
% 0.26/0.60  thf(fact_7130_divmod__algorithm__code_I8_J,axiom,
% 0.26/0.60      ! [M: num,N: num] :
% 0.26/0.60        ( ( ( ord_less_num @ M @ N )
% 0.26/0.60         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.26/0.60            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 0.26/0.60        & ( ~ ( ord_less_num @ M @ N )
% 0.26/0.60         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.26/0.60            = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % divmod_algorithm_code(8)
% 0.26/0.60  thf(fact_7131_divmod__algorithm__code_I8_J,axiom,
% 0.26/0.60      ! [M: num,N: num] :
% 0.26/0.60        ( ( ( ord_less_num @ M @ N )
% 0.26/0.60         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.26/0.60            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 0.26/0.60        & ( ~ ( ord_less_num @ M @ N )
% 0.26/0.60         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.26/0.60            = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % divmod_algorithm_code(8)
% 0.26/0.60  thf(fact_7132_divides__aux__eq,axiom,
% 0.26/0.60      ! [Q3: nat,R2: nat] :
% 0.26/0.60        ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 0.26/0.60        = ( R2 = zero_zero_nat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % divides_aux_eq
% 0.26/0.60  thf(fact_7133_divides__aux__eq,axiom,
% 0.26/0.60      ! [Q3: int,R2: int] :
% 0.26/0.60        ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 0.26/0.60        = ( R2 = zero_zero_int ) ) ).
% 0.26/0.60  
% 0.26/0.60  % divides_aux_eq
% 0.26/0.60  thf(fact_7134_summable__arctan__series,axiom,
% 0.26/0.60      ! [X3: real] :
% 0.26/0.60        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.26/0.60       => ( summable_real
% 0.26/0.60          @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_arctan_series
% 0.26/0.60  thf(fact_7135_sin__zero,axiom,
% 0.26/0.60      ( ( sin_real @ zero_zero_real )
% 0.26/0.60      = zero_zero_real ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_zero
% 0.26/0.60  thf(fact_7136_summable__single,axiom,
% 0.26/0.60      ! [I: nat,F: nat > real] :
% 0.26/0.60        ( summable_real
% 0.26/0.60        @ ^ [R5: nat] : ( if_real @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_real ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_single
% 0.26/0.60  thf(fact_7137_summable__single,axiom,
% 0.26/0.60      ! [I: nat,F: nat > nat] :
% 0.26/0.60        ( summable_nat
% 0.26/0.60        @ ^ [R5: nat] : ( if_nat @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_nat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_single
% 0.26/0.60  thf(fact_7138_summable__single,axiom,
% 0.26/0.60      ! [I: nat,F: nat > int] :
% 0.26/0.60        ( summable_int
% 0.26/0.60        @ ^ [R5: nat] : ( if_int @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_int ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_single
% 0.26/0.60  thf(fact_7139_summable__zero,axiom,
% 0.26/0.60      ( summable_real
% 0.26/0.60      @ ^ [N3: nat] : zero_zero_real ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_zero
% 0.26/0.60  thf(fact_7140_summable__zero,axiom,
% 0.26/0.60      ( summable_nat
% 0.26/0.60      @ ^ [N3: nat] : zero_zero_nat ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_zero
% 0.26/0.60  thf(fact_7141_summable__zero,axiom,
% 0.26/0.60      ( summable_int
% 0.26/0.60      @ ^ [N3: nat] : zero_zero_int ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_zero
% 0.26/0.60  thf(fact_7142_sin__pi,axiom,
% 0.26/0.60      ( ( sin_real @ pi )
% 0.26/0.60      = zero_zero_real ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_pi
% 0.26/0.60  thf(fact_7143_summable__cmult__iff,axiom,
% 0.26/0.60      ! [C: real,F: nat > real] :
% 0.26/0.60        ( ( summable_real
% 0.26/0.60          @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) ) )
% 0.26/0.60        = ( ( C = zero_zero_real )
% 0.26/0.60          | ( summable_real @ F ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_cmult_iff
% 0.26/0.60  thf(fact_7144_summable__divide__iff,axiom,
% 0.26/0.60      ! [F: nat > complex,C: complex] :
% 0.26/0.60        ( ( summable_complex
% 0.26/0.60          @ ^ [N3: nat] : ( divide1717551699836669952omplex @ ( F @ N3 ) @ C ) )
% 0.26/0.60        = ( ( C = zero_zero_complex )
% 0.26/0.60          | ( summable_complex @ F ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_divide_iff
% 0.26/0.60  thf(fact_7145_summable__divide__iff,axiom,
% 0.26/0.60      ! [F: nat > real,C: real] :
% 0.26/0.60        ( ( summable_real
% 0.26/0.60          @ ^ [N3: nat] : ( divide_divide_real @ ( F @ N3 ) @ C ) )
% 0.26/0.60        = ( ( C = zero_zero_real )
% 0.26/0.60          | ( summable_real @ F ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_divide_iff
% 0.26/0.60  thf(fact_7146_sin__of__real__pi,axiom,
% 0.26/0.60      ( ( sin_real @ ( real_V1803761363581548252l_real @ pi ) )
% 0.26/0.60      = zero_zero_real ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_of_real_pi
% 0.26/0.60  thf(fact_7147_sin__of__real__pi,axiom,
% 0.26/0.60      ( ( sin_complex @ ( real_V4546457046886955230omplex @ pi ) )
% 0.26/0.60      = zero_zero_complex ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_of_real_pi
% 0.26/0.60  thf(fact_7148_dvd__numeral__simp,axiom,
% 0.26/0.60      ! [M: num,N: num] :
% 0.26/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 0.26/0.60        = ( unique5706413561485394159nteger @ ( unique3479559517661332726nteger @ N @ M ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % dvd_numeral_simp
% 0.26/0.60  thf(fact_7149_dvd__numeral__simp,axiom,
% 0.26/0.60      ! [M: num,N: num] :
% 0.26/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.60        = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N @ M ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % dvd_numeral_simp
% 0.26/0.60  thf(fact_7150_dvd__numeral__simp,axiom,
% 0.26/0.60      ! [M: num,N: num] :
% 0.26/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.26/0.60        = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N @ M ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % dvd_numeral_simp
% 0.26/0.60  thf(fact_7151_divmod__algorithm__code_I2_J,axiom,
% 0.26/0.60      ! [M: num] :
% 0.26/0.60        ( ( unique5052692396658037445od_int @ M @ one )
% 0.26/0.60        = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 0.26/0.60  
% 0.26/0.60  % divmod_algorithm_code(2)
% 0.26/0.60  thf(fact_7152_divmod__algorithm__code_I2_J,axiom,
% 0.26/0.60      ! [M: num] :
% 0.26/0.60        ( ( unique5055182867167087721od_nat @ M @ one )
% 0.26/0.60        = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 0.26/0.60  
% 0.26/0.60  % divmod_algorithm_code(2)
% 0.26/0.60  thf(fact_7153_sin__npi,axiom,
% 0.26/0.60      ! [N: nat] :
% 0.26/0.60        ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 0.26/0.60        = zero_zero_real ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_npi
% 0.26/0.60  thf(fact_7154_sin__npi2,axiom,
% 0.26/0.60      ! [N: nat] :
% 0.26/0.60        ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.26/0.60        = zero_zero_real ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_npi2
% 0.26/0.60  thf(fact_7155_sin__npi__int,axiom,
% 0.26/0.60      ! [N: int] :
% 0.26/0.60        ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 0.26/0.60        = zero_zero_real ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_npi_int
% 0.26/0.60  thf(fact_7156_summable__geometric__iff,axiom,
% 0.26/0.60      ! [C: real] :
% 0.26/0.60        ( ( summable_real @ ( power_power_real @ C ) )
% 0.26/0.60        = ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_geometric_iff
% 0.26/0.60  thf(fact_7157_summable__geometric__iff,axiom,
% 0.26/0.60      ! [C: complex] :
% 0.26/0.60        ( ( summable_complex @ ( power_power_complex @ C ) )
% 0.26/0.60        = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_geometric_iff
% 0.26/0.60  thf(fact_7158_divmod__algorithm__code_I3_J,axiom,
% 0.26/0.60      ! [N: num] :
% 0.26/0.60        ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 0.26/0.60        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % divmod_algorithm_code(3)
% 0.26/0.60  thf(fact_7159_divmod__algorithm__code_I3_J,axiom,
% 0.26/0.60      ! [N: num] :
% 0.26/0.60        ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 0.26/0.60        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % divmod_algorithm_code(3)
% 0.26/0.60  thf(fact_7160_divmod__algorithm__code_I4_J,axiom,
% 0.26/0.60      ! [N: num] :
% 0.26/0.60        ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 0.26/0.60        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % divmod_algorithm_code(4)
% 0.26/0.60  thf(fact_7161_divmod__algorithm__code_I4_J,axiom,
% 0.26/0.60      ! [N: num] :
% 0.26/0.60        ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 0.26/0.60        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % divmod_algorithm_code(4)
% 0.26/0.60  thf(fact_7162_sin__two__pi,axiom,
% 0.26/0.60      ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.26/0.60      = zero_zero_real ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_two_pi
% 0.26/0.60  thf(fact_7163_sin__pi__half,axiom,
% 0.26/0.60      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.60      = one_one_real ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_pi_half
% 0.26/0.60  thf(fact_7164_sin__periodic,axiom,
% 0.26/0.60      ! [X3: real] :
% 0.26/0.60        ( ( sin_real @ ( plus_plus_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.26/0.60        = ( sin_real @ X3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_periodic
% 0.26/0.60  thf(fact_7165_sin__of__real__pi__half,axiom,
% 0.26/0.60      ( ( sin_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.60      = one_one_real ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_of_real_pi_half
% 0.26/0.60  thf(fact_7166_sin__of__real__pi__half,axiom,
% 0.26/0.60      ( ( sin_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 0.26/0.60      = one_one_complex ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_of_real_pi_half
% 0.26/0.60  thf(fact_7167_sin__2npi,axiom,
% 0.26/0.60      ! [N: nat] :
% 0.26/0.60        ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 0.26/0.60        = zero_zero_real ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_2npi
% 0.26/0.60  thf(fact_7168_sin__2pi__minus,axiom,
% 0.26/0.60      ! [X3: real] :
% 0.26/0.60        ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X3 ) )
% 0.26/0.60        = ( uminus_uminus_real @ ( sin_real @ X3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_2pi_minus
% 0.26/0.60  thf(fact_7169_sin__int__2pin,axiom,
% 0.26/0.60      ! [N: int] :
% 0.26/0.60        ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 0.26/0.60        = zero_zero_real ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_int_2pin
% 0.26/0.60  thf(fact_7170_sin__3over2__pi,axiom,
% 0.26/0.60      ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 0.26/0.60      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_3over2_pi
% 0.26/0.60  thf(fact_7171_summable__comparison__test,axiom,
% 0.26/0.60      ! [F: nat > real,G: nat > real] :
% 0.26/0.60        ( ? [N6: nat] :
% 0.26/0.60          ! [N2: nat] :
% 0.26/0.60            ( ( ord_less_eq_nat @ N6 @ N2 )
% 0.26/0.60           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N2 ) ) @ ( G @ N2 ) ) )
% 0.26/0.60       => ( ( summable_real @ G )
% 0.26/0.60         => ( summable_real @ F ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_comparison_test
% 0.26/0.60  thf(fact_7172_summable__comparison__test,axiom,
% 0.26/0.60      ! [F: nat > complex,G: nat > real] :
% 0.26/0.60        ( ? [N6: nat] :
% 0.26/0.60          ! [N2: nat] :
% 0.26/0.60            ( ( ord_less_eq_nat @ N6 @ N2 )
% 0.26/0.60           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N2 ) ) @ ( G @ N2 ) ) )
% 0.26/0.60       => ( ( summable_real @ G )
% 0.26/0.60         => ( summable_complex @ F ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_comparison_test
% 0.26/0.60  thf(fact_7173_summable__comparison__test_H,axiom,
% 0.26/0.60      ! [G: nat > real,N4: nat,F: nat > real] :
% 0.26/0.60        ( ( summable_real @ G )
% 0.26/0.60       => ( ! [N2: nat] :
% 0.26/0.60              ( ( ord_less_eq_nat @ N4 @ N2 )
% 0.26/0.60             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N2 ) ) @ ( G @ N2 ) ) )
% 0.26/0.60         => ( summable_real @ F ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_comparison_test'
% 0.26/0.60  thf(fact_7174_summable__comparison__test_H,axiom,
% 0.26/0.60      ! [G: nat > real,N4: nat,F: nat > complex] :
% 0.26/0.60        ( ( summable_real @ G )
% 0.26/0.60       => ( ! [N2: nat] :
% 0.26/0.60              ( ( ord_less_eq_nat @ N4 @ N2 )
% 0.26/0.60             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N2 ) ) @ ( G @ N2 ) ) )
% 0.26/0.60         => ( summable_complex @ F ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_comparison_test'
% 0.26/0.60  thf(fact_7175_summable__const__iff,axiom,
% 0.26/0.60      ! [C: real] :
% 0.26/0.60        ( ( summable_real
% 0.26/0.60          @ ^ [Uu3: nat] : C )
% 0.26/0.60        = ( C = zero_zero_real ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_const_iff
% 0.26/0.60  thf(fact_7176_powser__insidea,axiom,
% 0.26/0.60      ! [F: nat > real,X3: real,Z: real] :
% 0.26/0.60        ( ( summable_real
% 0.26/0.60          @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ X3 @ N3 ) ) )
% 0.26/0.60       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X3 ) )
% 0.26/0.60         => ( summable_real
% 0.26/0.60            @ ^ [N3: nat] : ( real_V7735802525324610683m_real @ ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % powser_insidea
% 0.26/0.60  thf(fact_7177_powser__insidea,axiom,
% 0.26/0.60      ! [F: nat > complex,X3: complex,Z: complex] :
% 0.26/0.60        ( ( summable_complex
% 0.26/0.60          @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ X3 @ N3 ) ) )
% 0.26/0.60       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X3 ) )
% 0.26/0.60         => ( summable_real
% 0.26/0.60            @ ^ [N3: nat] : ( real_V1022390504157884413omplex @ ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % powser_insidea
% 0.26/0.60  thf(fact_7178_suminf__le,axiom,
% 0.26/0.60      ! [F: nat > real,G: nat > real] :
% 0.26/0.60        ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 0.26/0.60       => ( ( summable_real @ F )
% 0.26/0.60         => ( ( summable_real @ G )
% 0.26/0.60           => ( ord_less_eq_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_le
% 0.26/0.60  thf(fact_7179_suminf__le,axiom,
% 0.26/0.60      ! [F: nat > nat,G: nat > nat] :
% 0.26/0.60        ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( G @ N2 ) )
% 0.26/0.60       => ( ( summable_nat @ F )
% 0.26/0.60         => ( ( summable_nat @ G )
% 0.26/0.60           => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_le
% 0.26/0.60  thf(fact_7180_suminf__le,axiom,
% 0.26/0.60      ! [F: nat > int,G: nat > int] :
% 0.26/0.60        ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ N2 ) @ ( G @ N2 ) )
% 0.26/0.60       => ( ( summable_int @ F )
% 0.26/0.60         => ( ( summable_int @ G )
% 0.26/0.60           => ( ord_less_eq_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_le
% 0.26/0.60  thf(fact_7181_sin__x__le__x,axiom,
% 0.26/0.60      ! [X3: real] :
% 0.26/0.60        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.60       => ( ord_less_eq_real @ ( sin_real @ X3 ) @ X3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_x_le_x
% 0.26/0.60  thf(fact_7182_sin__le__one,axiom,
% 0.26/0.60      ! [X3: real] : ( ord_less_eq_real @ ( sin_real @ X3 ) @ one_one_real ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_le_one
% 0.26/0.60  thf(fact_7183_abs__sin__x__le__abs__x,axiom,
% 0.26/0.60      ! [X3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X3 ) ) @ ( abs_abs_real @ X3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % abs_sin_x_le_abs_x
% 0.26/0.60  thf(fact_7184_summable__mult__D,axiom,
% 0.26/0.60      ! [C: real,F: nat > real] :
% 0.26/0.60        ( ( summable_real
% 0.26/0.60          @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) ) )
% 0.26/0.60       => ( ( C != zero_zero_real )
% 0.26/0.60         => ( summable_real @ F ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_mult_D
% 0.26/0.60  thf(fact_7185_summable__zero__power,axiom,
% 0.26/0.60      summable_int @ ( power_power_int @ zero_zero_int ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_zero_power
% 0.26/0.60  thf(fact_7186_summable__zero__power,axiom,
% 0.26/0.60      summable_real @ ( power_power_real @ zero_zero_real ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_zero_power
% 0.26/0.60  thf(fact_7187_summable__zero__power,axiom,
% 0.26/0.60      summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_zero_power
% 0.26/0.60  thf(fact_7188_sin__int__times__real,axiom,
% 0.26/0.60      ! [M: int,X3: real] :
% 0.26/0.60        ( ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X3 ) ) )
% 0.26/0.60        = ( real_V1803761363581548252l_real @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X3 ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_int_times_real
% 0.26/0.60  thf(fact_7189_sin__int__times__real,axiom,
% 0.26/0.60      ! [M: int,X3: real] :
% 0.26/0.60        ( ( sin_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X3 ) ) )
% 0.26/0.60        = ( real_V4546457046886955230omplex @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X3 ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_int_times_real
% 0.26/0.60  thf(fact_7190_suminf__nonneg,axiom,
% 0.26/0.60      ! [F: nat > real] :
% 0.26/0.60        ( ( summable_real @ F )
% 0.26/0.60       => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 0.26/0.60         => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_nonneg
% 0.26/0.60  thf(fact_7191_suminf__nonneg,axiom,
% 0.26/0.60      ! [F: nat > nat] :
% 0.26/0.60        ( ( summable_nat @ F )
% 0.26/0.60       => ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 0.26/0.60         => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_nonneg
% 0.26/0.60  thf(fact_7192_suminf__nonneg,axiom,
% 0.26/0.60      ! [F: nat > int] :
% 0.26/0.60        ( ( summable_int @ F )
% 0.26/0.60       => ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 0.26/0.60         => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_nonneg
% 0.26/0.60  thf(fact_7193_suminf__eq__zero__iff,axiom,
% 0.26/0.60      ! [F: nat > real] :
% 0.26/0.60        ( ( summable_real @ F )
% 0.26/0.60       => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 0.26/0.60         => ( ( ( suminf_real @ F )
% 0.26/0.60              = zero_zero_real )
% 0.26/0.60            = ( ! [N3: nat] :
% 0.26/0.60                  ( ( F @ N3 )
% 0.26/0.60                  = zero_zero_real ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_eq_zero_iff
% 0.26/0.60  thf(fact_7194_suminf__eq__zero__iff,axiom,
% 0.26/0.60      ! [F: nat > nat] :
% 0.26/0.60        ( ( summable_nat @ F )
% 0.26/0.60       => ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 0.26/0.60         => ( ( ( suminf_nat @ F )
% 0.26/0.60              = zero_zero_nat )
% 0.26/0.60            = ( ! [N3: nat] :
% 0.26/0.60                  ( ( F @ N3 )
% 0.26/0.60                  = zero_zero_nat ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_eq_zero_iff
% 0.26/0.60  thf(fact_7195_suminf__eq__zero__iff,axiom,
% 0.26/0.60      ! [F: nat > int] :
% 0.26/0.60        ( ( summable_int @ F )
% 0.26/0.60       => ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 0.26/0.60         => ( ( ( suminf_int @ F )
% 0.26/0.60              = zero_zero_int )
% 0.26/0.60            = ( ! [N3: nat] :
% 0.26/0.60                  ( ( F @ N3 )
% 0.26/0.60                  = zero_zero_int ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_eq_zero_iff
% 0.26/0.60  thf(fact_7196_suminf__pos,axiom,
% 0.26/0.60      ! [F: nat > real] :
% 0.26/0.60        ( ( summable_real @ F )
% 0.26/0.60       => ( ! [N2: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N2 ) )
% 0.26/0.60         => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_pos
% 0.26/0.60  thf(fact_7197_suminf__pos,axiom,
% 0.26/0.60      ! [F: nat > nat] :
% 0.26/0.60        ( ( summable_nat @ F )
% 0.26/0.60       => ( ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N2 ) )
% 0.26/0.60         => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_pos
% 0.26/0.60  thf(fact_7198_suminf__pos,axiom,
% 0.26/0.60      ! [F: nat > int] :
% 0.26/0.60        ( ( summable_int @ F )
% 0.26/0.60       => ( ! [N2: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N2 ) )
% 0.26/0.60         => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_pos
% 0.26/0.60  thf(fact_7199_sin__gt__zero,axiom,
% 0.26/0.60      ! [X3: real] :
% 0.26/0.60        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.60       => ( ( ord_less_real @ X3 @ pi )
% 0.26/0.60         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X3 ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_gt_zero
% 0.26/0.60  thf(fact_7200_sin__x__ge__neg__x,axiom,
% 0.26/0.60      ! [X3: real] :
% 0.26/0.60        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.60       => ( ord_less_eq_real @ ( uminus_uminus_real @ X3 ) @ ( sin_real @ X3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_x_ge_neg_x
% 0.26/0.60  thf(fact_7201_sin__ge__zero,axiom,
% 0.26/0.60      ! [X3: real] :
% 0.26/0.60        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.60       => ( ( ord_less_eq_real @ X3 @ pi )
% 0.26/0.60         => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X3 ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_ge_zero
% 0.26/0.60  thf(fact_7202_summable__0__powser,axiom,
% 0.26/0.60      ! [F: nat > complex] :
% 0.26/0.60        ( summable_complex
% 0.26/0.60        @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ zero_zero_complex @ N3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_0_powser
% 0.26/0.60  thf(fact_7203_summable__0__powser,axiom,
% 0.26/0.60      ! [F: nat > real] :
% 0.26/0.60        ( summable_real
% 0.26/0.60        @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ zero_zero_real @ N3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_0_powser
% 0.26/0.60  thf(fact_7204_summable__zero__power_H,axiom,
% 0.26/0.60      ! [F: nat > complex] :
% 0.26/0.60        ( summable_complex
% 0.26/0.60        @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ zero_zero_complex @ N3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_zero_power'
% 0.26/0.60  thf(fact_7205_summable__zero__power_H,axiom,
% 0.26/0.60      ! [F: nat > real] :
% 0.26/0.60        ( summable_real
% 0.26/0.60        @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ zero_zero_real @ N3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_zero_power'
% 0.26/0.60  thf(fact_7206_summable__zero__power_H,axiom,
% 0.26/0.60      ! [F: nat > int] :
% 0.26/0.60        ( summable_int
% 0.26/0.60        @ ^ [N3: nat] : ( times_times_int @ ( F @ N3 ) @ ( power_power_int @ zero_zero_int @ N3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_zero_power'
% 0.26/0.60  thf(fact_7207_sin__ge__minus__one,axiom,
% 0.26/0.60      ! [X3: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X3 ) ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_ge_minus_one
% 0.26/0.60  thf(fact_7208_summable__powser__split__head,axiom,
% 0.26/0.60      ! [F: nat > complex,Z: complex] :
% 0.26/0.60        ( ( summable_complex
% 0.26/0.60          @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) ) )
% 0.26/0.60        = ( summable_complex
% 0.26/0.60          @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_powser_split_head
% 0.26/0.60  thf(fact_7209_summable__powser__split__head,axiom,
% 0.26/0.60      ! [F: nat > real,Z: real] :
% 0.26/0.60        ( ( summable_real
% 0.26/0.60          @ ^ [N3: nat] : ( times_times_real @ ( F @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) ) )
% 0.26/0.60        = ( summable_real
% 0.26/0.60          @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_powser_split_head
% 0.26/0.60  thf(fact_7210_powser__split__head_I3_J,axiom,
% 0.26/0.60      ! [F: nat > complex,Z: complex] :
% 0.26/0.60        ( ( summable_complex
% 0.26/0.60          @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 0.26/0.60       => ( summable_complex
% 0.26/0.60          @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % powser_split_head(3)
% 0.26/0.60  thf(fact_7211_powser__split__head_I3_J,axiom,
% 0.26/0.60      ! [F: nat > real,Z: real] :
% 0.26/0.60        ( ( summable_real
% 0.26/0.60          @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 0.26/0.60       => ( summable_real
% 0.26/0.60          @ ^ [N3: nat] : ( times_times_real @ ( F @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % powser_split_head(3)
% 0.26/0.60  thf(fact_7212_abs__sin__le__one,axiom,
% 0.26/0.60      ! [X3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X3 ) ) @ one_one_real ) ).
% 0.26/0.60  
% 0.26/0.60  % abs_sin_le_one
% 0.26/0.60  thf(fact_7213_summable__powser__ignore__initial__segment,axiom,
% 0.26/0.60      ! [F: nat > complex,M: nat,Z: complex] :
% 0.26/0.60        ( ( summable_complex
% 0.26/0.60          @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( plus_plus_nat @ N3 @ M ) ) @ ( power_power_complex @ Z @ N3 ) ) )
% 0.26/0.60        = ( summable_complex
% 0.26/0.60          @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_powser_ignore_initial_segment
% 0.26/0.60  thf(fact_7214_summable__powser__ignore__initial__segment,axiom,
% 0.26/0.60      ! [F: nat > real,M: nat,Z: real] :
% 0.26/0.60        ( ( summable_real
% 0.26/0.60          @ ^ [N3: nat] : ( times_times_real @ ( F @ ( plus_plus_nat @ N3 @ M ) ) @ ( power_power_real @ Z @ N3 ) ) )
% 0.26/0.60        = ( summable_real
% 0.26/0.60          @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_powser_ignore_initial_segment
% 0.26/0.60  thf(fact_7215_summable__norm__comparison__test,axiom,
% 0.26/0.60      ! [F: nat > complex,G: nat > real] :
% 0.26/0.60        ( ? [N6: nat] :
% 0.26/0.60          ! [N2: nat] :
% 0.26/0.60            ( ( ord_less_eq_nat @ N6 @ N2 )
% 0.26/0.60           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N2 ) ) @ ( G @ N2 ) ) )
% 0.26/0.60       => ( ( summable_real @ G )
% 0.26/0.60         => ( summable_real
% 0.26/0.60            @ ^ [N3: nat] : ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_norm_comparison_test
% 0.26/0.60  thf(fact_7216_summable__rabs__comparison__test,axiom,
% 0.26/0.60      ! [F: nat > real,G: nat > real] :
% 0.26/0.60        ( ? [N6: nat] :
% 0.26/0.60          ! [N2: nat] :
% 0.26/0.60            ( ( ord_less_eq_nat @ N6 @ N2 )
% 0.26/0.60           => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N2 ) ) @ ( G @ N2 ) ) )
% 0.26/0.60       => ( ( summable_real @ G )
% 0.26/0.60         => ( summable_real
% 0.26/0.60            @ ^ [N3: nat] : ( abs_abs_real @ ( F @ N3 ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_rabs_comparison_test
% 0.26/0.60  thf(fact_7217_summable__rabs,axiom,
% 0.26/0.60      ! [F: nat > real] :
% 0.26/0.60        ( ( summable_real
% 0.26/0.60          @ ^ [N3: nat] : ( abs_abs_real @ ( F @ N3 ) ) )
% 0.26/0.60       => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 0.26/0.60          @ ( suminf_real
% 0.26/0.60            @ ^ [N3: nat] : ( abs_abs_real @ ( F @ N3 ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_rabs
% 0.26/0.60  thf(fact_7218_suminf__pos__iff,axiom,
% 0.26/0.60      ! [F: nat > real] :
% 0.26/0.60        ( ( summable_real @ F )
% 0.26/0.60       => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 0.26/0.60         => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 0.26/0.60            = ( ? [I4: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_pos_iff
% 0.26/0.60  thf(fact_7219_suminf__pos__iff,axiom,
% 0.26/0.60      ! [F: nat > nat] :
% 0.26/0.60        ( ( summable_nat @ F )
% 0.26/0.60       => ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 0.26/0.60         => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 0.26/0.60            = ( ? [I4: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_pos_iff
% 0.26/0.60  thf(fact_7220_suminf__pos__iff,axiom,
% 0.26/0.60      ! [F: nat > int] :
% 0.26/0.60        ( ( summable_int @ F )
% 0.26/0.60       => ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 0.26/0.60         => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 0.26/0.60            = ( ? [I4: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I4 ) ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_pos_iff
% 0.26/0.60  thf(fact_7221_suminf__pos2,axiom,
% 0.26/0.60      ! [F: nat > real,I: nat] :
% 0.26/0.60        ( ( summable_real @ F )
% 0.26/0.60       => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 0.26/0.60         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 0.26/0.60           => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_pos2
% 0.26/0.60  thf(fact_7222_suminf__pos2,axiom,
% 0.26/0.60      ! [F: nat > nat,I: nat] :
% 0.26/0.60        ( ( summable_nat @ F )
% 0.26/0.60       => ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 0.26/0.60         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 0.26/0.60           => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_pos2
% 0.26/0.60  thf(fact_7223_suminf__pos2,axiom,
% 0.26/0.60      ! [F: nat > int,I: nat] :
% 0.26/0.60        ( ( summable_int @ F )
% 0.26/0.60       => ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 0.26/0.60         => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 0.26/0.60           => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_pos2
% 0.26/0.60  thf(fact_7224_powser__inside,axiom,
% 0.26/0.60      ! [F: nat > real,X3: real,Z: real] :
% 0.26/0.60        ( ( summable_real
% 0.26/0.60          @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ X3 @ N3 ) ) )
% 0.26/0.60       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X3 ) )
% 0.26/0.60         => ( summable_real
% 0.26/0.60            @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % powser_inside
% 0.26/0.60  thf(fact_7225_powser__inside,axiom,
% 0.26/0.60      ! [F: nat > complex,X3: complex,Z: complex] :
% 0.26/0.60        ( ( summable_complex
% 0.26/0.60          @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ X3 @ N3 ) ) )
% 0.26/0.60       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X3 ) )
% 0.26/0.60         => ( summable_complex
% 0.26/0.60            @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % powser_inside
% 0.26/0.60  thf(fact_7226_sin__eq__0__pi,axiom,
% 0.26/0.60      ! [X3: real] :
% 0.26/0.60        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X3 )
% 0.26/0.60       => ( ( ord_less_real @ X3 @ pi )
% 0.26/0.60         => ( ( ( sin_real @ X3 )
% 0.26/0.60              = zero_zero_real )
% 0.26/0.60           => ( X3 = zero_zero_real ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_eq_0_pi
% 0.26/0.60  thf(fact_7227_complete__algebra__summable__geometric,axiom,
% 0.26/0.60      ! [X3: real] :
% 0.26/0.60        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ one_one_real )
% 0.26/0.60       => ( summable_real @ ( power_power_real @ X3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % complete_algebra_summable_geometric
% 0.26/0.60  thf(fact_7228_complete__algebra__summable__geometric,axiom,
% 0.26/0.60      ! [X3: complex] :
% 0.26/0.60        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ one_one_real )
% 0.26/0.60       => ( summable_complex @ ( power_power_complex @ X3 ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % complete_algebra_summable_geometric
% 0.26/0.60  thf(fact_7229_summable__geometric,axiom,
% 0.26/0.60      ! [C: real] :
% 0.26/0.60        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 0.26/0.60       => ( summable_real @ ( power_power_real @ C ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_geometric
% 0.26/0.60  thf(fact_7230_summable__geometric,axiom,
% 0.26/0.60      ! [C: complex] :
% 0.26/0.60        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 0.26/0.60       => ( summable_complex @ ( power_power_complex @ C ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % summable_geometric
% 0.26/0.60  thf(fact_7231_suminf__split__head,axiom,
% 0.26/0.60      ! [F: nat > real] :
% 0.26/0.60        ( ( summable_real @ F )
% 0.26/0.60       => ( ( suminf_real
% 0.26/0.60            @ ^ [N3: nat] : ( F @ ( suc @ N3 ) ) )
% 0.26/0.60          = ( minus_minus_real @ ( suminf_real @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % suminf_split_head
% 0.26/0.60  thf(fact_7232_sin__zero__pi__iff,axiom,
% 0.26/0.60      ! [X3: real] :
% 0.26/0.60        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ pi )
% 0.26/0.60       => ( ( ( sin_real @ X3 )
% 0.26/0.60            = zero_zero_real )
% 0.26/0.60          = ( X3 = zero_zero_real ) ) ) ).
% 0.26/0.60  
% 0.26/0.60  % sin_zero_pi_iff
% 0.26/0.60  thf(fact_7233_sin__zero__iff__int2,axiom,
% 0.26/0.60      ! [X3: real] :
% 0.26/0.60        ( ( ( sin_real @ X3 )
% 0.26/0.60          = zero_zero_real )
% 0.26/0.61        = ( ? [I4: int] :
% 0.26/0.61              ( X3
% 0.26/0.61              = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ pi ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_zero_iff_int2
% 0.26/0.61  thf(fact_7234_divmod__int__def,axiom,
% 0.26/0.61      ( unique5052692396658037445od_int
% 0.26/0.61      = ( ^ [M3: num,N3: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N3 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N3 ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % divmod_int_def
% 0.26/0.61  thf(fact_7235_summable__norm,axiom,
% 0.26/0.61      ! [F: nat > real] :
% 0.26/0.61        ( ( summable_real
% 0.26/0.61          @ ^ [N3: nat] : ( real_V7735802525324610683m_real @ ( F @ N3 ) ) )
% 0.26/0.61       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( suminf_real @ F ) )
% 0.26/0.61          @ ( suminf_real
% 0.26/0.61            @ ^ [N3: nat] : ( real_V7735802525324610683m_real @ ( F @ N3 ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % summable_norm
% 0.26/0.61  thf(fact_7236_summable__norm,axiom,
% 0.26/0.61      ! [F: nat > complex] :
% 0.26/0.61        ( ( summable_real
% 0.26/0.61          @ ^ [N3: nat] : ( real_V1022390504157884413omplex @ ( F @ N3 ) ) )
% 0.26/0.61       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( suminf_complex @ F ) )
% 0.26/0.61          @ ( suminf_real
% 0.26/0.61            @ ^ [N3: nat] : ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % summable_norm
% 0.26/0.61  thf(fact_7237_sin__gt__zero__02,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.61       => ( ( ord_less_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.26/0.61         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X3 ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_gt_zero_02
% 0.26/0.61  thf(fact_7238_divmod__def,axiom,
% 0.26/0.61      ( unique3479559517661332726nteger
% 0.26/0.61      = ( ^ [M3: num,N3: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N3 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N3 ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % divmod_def
% 0.26/0.61  thf(fact_7239_divmod__def,axiom,
% 0.26/0.61      ( unique5052692396658037445od_int
% 0.26/0.61      = ( ^ [M3: num,N3: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N3 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N3 ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % divmod_def
% 0.26/0.61  thf(fact_7240_divmod__def,axiom,
% 0.26/0.61      ( unique5055182867167087721od_nat
% 0.26/0.61      = ( ^ [M3: num,N3: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N3 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N3 ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % divmod_def
% 0.26/0.61  thf(fact_7241_divmod_H__nat__def,axiom,
% 0.26/0.61      ( unique5055182867167087721od_nat
% 0.26/0.61      = ( ^ [M3: num,N3: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N3 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N3 ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % divmod'_nat_def
% 0.26/0.61  thf(fact_7242_powser__split__head_I1_J,axiom,
% 0.26/0.61      ! [F: nat > complex,Z: complex] :
% 0.26/0.61        ( ( summable_complex
% 0.26/0.61          @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 0.26/0.61       => ( ( suminf_complex
% 0.26/0.61            @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 0.26/0.61          = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 0.26/0.61            @ ( times_times_complex
% 0.26/0.61              @ ( suminf_complex
% 0.26/0.61                @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) ) )
% 0.26/0.61              @ Z ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % powser_split_head(1)
% 0.26/0.61  thf(fact_7243_powser__split__head_I1_J,axiom,
% 0.26/0.61      ! [F: nat > real,Z: real] :
% 0.26/0.61        ( ( summable_real
% 0.26/0.61          @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 0.26/0.61       => ( ( suminf_real
% 0.26/0.61            @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 0.26/0.61          = ( plus_plus_real @ ( F @ zero_zero_nat )
% 0.26/0.61            @ ( times_times_real
% 0.26/0.61              @ ( suminf_real
% 0.26/0.61                @ ^ [N3: nat] : ( times_times_real @ ( F @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) ) )
% 0.26/0.61              @ Z ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % powser_split_head(1)
% 0.26/0.61  thf(fact_7244_powser__split__head_I2_J,axiom,
% 0.26/0.61      ! [F: nat > complex,Z: complex] :
% 0.26/0.61        ( ( summable_complex
% 0.26/0.61          @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 0.26/0.61       => ( ( times_times_complex
% 0.26/0.61            @ ( suminf_complex
% 0.26/0.61              @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) ) )
% 0.26/0.61            @ Z )
% 0.26/0.61          = ( minus_minus_complex
% 0.26/0.61            @ ( suminf_complex
% 0.26/0.61              @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 0.26/0.61            @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % powser_split_head(2)
% 0.26/0.61  thf(fact_7245_powser__split__head_I2_J,axiom,
% 0.26/0.61      ! [F: nat > real,Z: real] :
% 0.26/0.61        ( ( summable_real
% 0.26/0.61          @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 0.26/0.61       => ( ( times_times_real
% 0.26/0.61            @ ( suminf_real
% 0.26/0.61              @ ^ [N3: nat] : ( times_times_real @ ( F @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) ) )
% 0.26/0.61            @ Z )
% 0.26/0.61          = ( minus_minus_real
% 0.26/0.61            @ ( suminf_real
% 0.26/0.61              @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 0.26/0.61            @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % powser_split_head(2)
% 0.26/0.61  thf(fact_7246_suminf__exist__split,axiom,
% 0.26/0.61      ! [R2: real,F: nat > real] :
% 0.26/0.61        ( ( ord_less_real @ zero_zero_real @ R2 )
% 0.26/0.61       => ( ( summable_real @ F )
% 0.26/0.61         => ? [N7: nat] :
% 0.26/0.61            ! [N8: nat] :
% 0.26/0.61              ( ( ord_less_eq_nat @ N7 @ N8 )
% 0.26/0.61             => ( ord_less_real
% 0.26/0.61                @ ( real_V7735802525324610683m_real
% 0.26/0.61                  @ ( suminf_real
% 0.26/0.61                    @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N8 ) ) ) )
% 0.26/0.61                @ R2 ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % suminf_exist_split
% 0.26/0.61  thf(fact_7247_suminf__exist__split,axiom,
% 0.26/0.61      ! [R2: real,F: nat > complex] :
% 0.26/0.61        ( ( ord_less_real @ zero_zero_real @ R2 )
% 0.26/0.61       => ( ( summable_complex @ F )
% 0.26/0.61         => ? [N7: nat] :
% 0.26/0.61            ! [N8: nat] :
% 0.26/0.61              ( ( ord_less_eq_nat @ N7 @ N8 )
% 0.26/0.61             => ( ord_less_real
% 0.26/0.61                @ ( real_V1022390504157884413omplex
% 0.26/0.61                  @ ( suminf_complex
% 0.26/0.61                    @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N8 ) ) ) )
% 0.26/0.61                @ R2 ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % suminf_exist_split
% 0.26/0.61  thf(fact_7248_sin__pi__divide__n__ge__0,axiom,
% 0.26/0.61      ! [N: nat] :
% 0.26/0.61        ( ( N != zero_zero_nat )
% 0.26/0.61       => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_pi_divide_n_ge_0
% 0.26/0.61  thf(fact_7249_summable__power__series,axiom,
% 0.26/0.61      ! [F: nat > real,Z: real] :
% 0.26/0.61        ( ! [I3: nat] : ( ord_less_eq_real @ ( F @ I3 ) @ one_one_real )
% 0.26/0.61       => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 0.26/0.61         => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 0.26/0.61           => ( ( ord_less_real @ Z @ one_one_real )
% 0.26/0.61             => ( summable_real
% 0.26/0.61                @ ^ [I4: nat] : ( times_times_real @ ( F @ I4 ) @ ( power_power_real @ Z @ I4 ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % summable_power_series
% 0.26/0.61  thf(fact_7250_sin__45,axiom,
% 0.26/0.61      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.26/0.61      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_45
% 0.26/0.61  thf(fact_7251_Abel__lemma,axiom,
% 0.26/0.61      ! [R2: real,R0: real,A: nat > complex,M7: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 0.26/0.61       => ( ( ord_less_real @ R2 @ R0 )
% 0.26/0.61         => ( ! [N2: nat] : ( ord_less_eq_real @ ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N2 ) ) @ ( power_power_real @ R0 @ N2 ) ) @ M7 )
% 0.26/0.61           => ( summable_real
% 0.26/0.61              @ ^ [N3: nat] : ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N3 ) ) @ ( power_power_real @ R2 @ N3 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % Abel_lemma
% 0.26/0.61  thf(fact_7252_summable__ratio__test,axiom,
% 0.26/0.61      ! [C: real,N4: nat,F: nat > real] :
% 0.26/0.61        ( ( ord_less_real @ C @ one_one_real )
% 0.26/0.61       => ( ! [N2: nat] :
% 0.26/0.61              ( ( ord_less_eq_nat @ N4 @ N2 )
% 0.26/0.61             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N2 ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N2 ) ) ) ) )
% 0.26/0.61         => ( summable_real @ F ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % summable_ratio_test
% 0.26/0.61  thf(fact_7253_summable__ratio__test,axiom,
% 0.26/0.61      ! [C: real,N4: nat,F: nat > complex] :
% 0.26/0.61        ( ( ord_less_real @ C @ one_one_real )
% 0.26/0.61       => ( ! [N2: nat] :
% 0.26/0.61              ( ( ord_less_eq_nat @ N4 @ N2 )
% 0.26/0.61             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N2 ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N2 ) ) ) ) )
% 0.26/0.61         => ( summable_complex @ F ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % summable_ratio_test
% 0.26/0.61  thf(fact_7254_sin__gt__zero2,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X3 ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_gt_zero2
% 0.26/0.61  thf(fact_7255_sin__lt__zero,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ord_less_real @ pi @ X3 )
% 0.26/0.61       => ( ( ord_less_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.26/0.61         => ( ord_less_real @ ( sin_real @ X3 ) @ zero_zero_real ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_lt_zero
% 0.26/0.61  thf(fact_7256_sin__30,axiom,
% 0.26/0.61      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 0.26/0.61      = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_30
% 0.26/0.61  thf(fact_7257_sin__inj__pi,axiom,
% 0.26/0.61      ! [X3: real,Y3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.26/0.61       => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 0.26/0.61           => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61             => ( ( ( sin_real @ X3 )
% 0.26/0.61                  = ( sin_real @ Y3 ) )
% 0.26/0.61               => ( X3 = Y3 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_inj_pi
% 0.26/0.61  thf(fact_7258_sin__mono__le__eq,axiom,
% 0.26/0.61      ! [X3: real,Y3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.26/0.61       => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 0.26/0.61           => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61             => ( ( ord_less_eq_real @ ( sin_real @ X3 ) @ ( sin_real @ Y3 ) )
% 0.26/0.61                = ( ord_less_eq_real @ X3 @ Y3 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_mono_le_eq
% 0.26/0.61  thf(fact_7259_sin__monotone__2pi__le,axiom,
% 0.26/0.61      ! [Y3: real,X3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 0.26/0.61       => ( ( ord_less_eq_real @ Y3 @ X3 )
% 0.26/0.61         => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61           => ( ord_less_eq_real @ ( sin_real @ Y3 ) @ ( sin_real @ X3 ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_monotone_2pi_le
% 0.26/0.61  thf(fact_7260_sin__60,axiom,
% 0.26/0.61      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 0.26/0.61      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_60
% 0.26/0.61  thf(fact_7261_sin__le__zero,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ pi @ X3 )
% 0.26/0.61       => ( ( ord_less_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.26/0.61         => ( ord_less_eq_real @ ( sin_real @ X3 ) @ zero_zero_real ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_le_zero
% 0.26/0.61  thf(fact_7262_sin__less__zero,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 )
% 0.26/0.61       => ( ( ord_less_real @ X3 @ zero_zero_real )
% 0.26/0.61         => ( ord_less_real @ ( sin_real @ X3 ) @ zero_zero_real ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_less_zero
% 0.26/0.61  thf(fact_7263_sin__mono__less__eq,axiom,
% 0.26/0.61      ! [X3: real,Y3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.26/0.61       => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 0.26/0.61           => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61             => ( ( ord_less_real @ ( sin_real @ X3 ) @ ( sin_real @ Y3 ) )
% 0.26/0.61                = ( ord_less_real @ X3 @ Y3 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_mono_less_eq
% 0.26/0.61  thf(fact_7264_sin__monotone__2pi,axiom,
% 0.26/0.61      ! [Y3: real,X3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 0.26/0.61       => ( ( ord_less_real @ Y3 @ X3 )
% 0.26/0.61         => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61           => ( ord_less_real @ ( sin_real @ Y3 ) @ ( sin_real @ X3 ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_monotone_2pi
% 0.26/0.61  thf(fact_7265_sin__total,axiom,
% 0.26/0.61      ! [Y3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 0.26/0.61       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 0.26/0.61         => ? [X4: real] :
% 0.26/0.61              ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 0.26/0.61              & ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61              & ( ( sin_real @ X4 )
% 0.26/0.61                = Y3 )
% 0.26/0.61              & ! [Y6: real] :
% 0.26/0.61                  ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y6 )
% 0.26/0.61                    & ( ord_less_eq_real @ Y6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61                    & ( ( sin_real @ Y6 )
% 0.26/0.61                      = Y3 ) )
% 0.26/0.61                 => ( Y6 = X4 ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_total
% 0.26/0.61  thf(fact_7266_sin__pi__divide__n__gt__0,axiom,
% 0.26/0.61      ! [N: nat] :
% 0.26/0.61        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.61       => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_pi_divide_n_gt_0
% 0.26/0.61  thf(fact_7267_sin__arctan,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( sin_real @ ( arctan @ X3 ) )
% 0.26/0.61        = ( divide_divide_real @ X3 @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_arctan
% 0.26/0.61  thf(fact_7268_divmod__divmod__step,axiom,
% 0.26/0.61      ( unique5055182867167087721od_nat
% 0.26/0.61      = ( ^ [M3: num,N3: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M3 @ N3 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M3 ) ) @ ( unique5026877609467782581ep_nat @ N3 @ ( unique5055182867167087721od_nat @ M3 @ ( bit0 @ N3 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % divmod_divmod_step
% 0.26/0.61  thf(fact_7269_divmod__divmod__step,axiom,
% 0.26/0.61      ( unique5052692396658037445od_int
% 0.26/0.61      = ( ^ [M3: num,N3: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M3 @ N3 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M3 ) ) @ ( unique5024387138958732305ep_int @ N3 @ ( unique5052692396658037445od_int @ M3 @ ( bit0 @ N3 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % divmod_divmod_step
% 0.26/0.61  thf(fact_7270_divmod__divmod__step,axiom,
% 0.26/0.61      ( unique3479559517661332726nteger
% 0.26/0.61      = ( ^ [M3: num,N3: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M3 @ N3 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M3 ) ) @ ( unique4921790084139445826nteger @ N3 @ ( unique3479559517661332726nteger @ M3 @ ( bit0 @ N3 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % divmod_divmod_step
% 0.26/0.61  thf(fact_7271_sin__zero__iff__int,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ( sin_real @ X3 )
% 0.26/0.61          = zero_zero_real )
% 0.26/0.61        = ( ? [I4: int] :
% 0.26/0.61              ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I4 )
% 0.26/0.61              & ( X3
% 0.26/0.61                = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_zero_iff_int
% 0.26/0.61  thf(fact_7272_sin__zero__lemma,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.61       => ( ( ( sin_real @ X3 )
% 0.26/0.61            = zero_zero_real )
% 0.26/0.61         => ? [N2: nat] :
% 0.26/0.61              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.26/0.61              & ( X3
% 0.26/0.61                = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_zero_lemma
% 0.26/0.61  thf(fact_7273_sin__zero__iff,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ( sin_real @ X3 )
% 0.26/0.61          = zero_zero_real )
% 0.26/0.61        = ( ? [N3: nat] :
% 0.26/0.61              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 0.26/0.61              & ( X3
% 0.26/0.61                = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.61          | ? [N3: nat] :
% 0.26/0.61              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 0.26/0.61              & ( X3
% 0.26/0.61                = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_zero_iff
% 0.26/0.61  thf(fact_7274_minus__one__div__numeral,axiom,
% 0.26/0.61      ! [N: num] :
% 0.26/0.61        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.61        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % minus_one_div_numeral
% 0.26/0.61  thf(fact_7275_one__div__minus__numeral,axiom,
% 0.26/0.61      ! [N: num] :
% 0.26/0.61        ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.61        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % one_div_minus_numeral
% 0.26/0.61  thf(fact_7276_pochhammer__code,axiom,
% 0.26/0.61      ( comm_s2602460028002588243omplex
% 0.26/0.61      = ( ^ [A4: complex,N3: nat] :
% 0.26/0.61            ( if_complex @ ( N3 = zero_zero_nat ) @ one_one_complex
% 0.26/0.61            @ ( set_fo1517530859248394432omplex
% 0.26/0.61              @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A4 @ ( semiri8010041392384452111omplex @ O ) ) )
% 0.26/0.61              @ zero_zero_nat
% 0.26/0.61              @ ( minus_minus_nat @ N3 @ one_one_nat )
% 0.26/0.61              @ one_one_complex ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % pochhammer_code
% 0.26/0.61  thf(fact_7277_pochhammer__code,axiom,
% 0.26/0.61      ( comm_s7457072308508201937r_real
% 0.26/0.61      = ( ^ [A4: real,N3: nat] :
% 0.26/0.61            ( if_real @ ( N3 = zero_zero_nat ) @ one_one_real
% 0.26/0.61            @ ( set_fo3111899725591712190t_real
% 0.26/0.61              @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A4 @ ( semiri5074537144036343181t_real @ O ) ) )
% 0.26/0.61              @ zero_zero_nat
% 0.26/0.61              @ ( minus_minus_nat @ N3 @ one_one_nat )
% 0.26/0.61              @ one_one_real ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % pochhammer_code
% 0.26/0.61  thf(fact_7278_pochhammer__code,axiom,
% 0.26/0.61      ( comm_s4028243227959126397er_rat
% 0.26/0.61      = ( ^ [A4: rat,N3: nat] :
% 0.26/0.61            ( if_rat @ ( N3 = zero_zero_nat ) @ one_one_rat
% 0.26/0.61            @ ( set_fo1949268297981939178at_rat
% 0.26/0.61              @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A4 @ ( semiri681578069525770553at_rat @ O ) ) )
% 0.26/0.61              @ zero_zero_nat
% 0.26/0.61              @ ( minus_minus_nat @ N3 @ one_one_nat )
% 0.26/0.61              @ one_one_rat ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % pochhammer_code
% 0.26/0.61  thf(fact_7279_pochhammer__code,axiom,
% 0.26/0.61      ( comm_s4660882817536571857er_int
% 0.26/0.61      = ( ^ [A4: int,N3: nat] :
% 0.26/0.61            ( if_int @ ( N3 = zero_zero_nat ) @ one_one_int
% 0.26/0.61            @ ( set_fo2581907887559384638at_int
% 0.26/0.61              @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A4 @ ( semiri1314217659103216013at_int @ O ) ) )
% 0.26/0.61              @ zero_zero_nat
% 0.26/0.61              @ ( minus_minus_nat @ N3 @ one_one_nat )
% 0.26/0.61              @ one_one_int ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % pochhammer_code
% 0.26/0.61  thf(fact_7280_pochhammer__code,axiom,
% 0.26/0.61      ( comm_s4663373288045622133er_nat
% 0.26/0.61      = ( ^ [A4: nat,N3: nat] :
% 0.26/0.61            ( if_nat @ ( N3 = zero_zero_nat ) @ one_one_nat
% 0.26/0.61            @ ( set_fo2584398358068434914at_nat
% 0.26/0.61              @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A4 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 0.26/0.61              @ zero_zero_nat
% 0.26/0.61              @ ( minus_minus_nat @ N3 @ one_one_nat )
% 0.26/0.61              @ one_one_nat ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % pochhammer_code
% 0.26/0.61  thf(fact_7281_neg__eucl__rel__int__mult__2,axiom,
% 0.26/0.61      ! [B: int,A: int,Q3: int,R2: int] :
% 0.26/0.61        ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.26/0.61       => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 0.26/0.61         => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q3 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) @ one_one_int ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % neg_eucl_rel_int_mult_2
% 0.26/0.61  thf(fact_7282_product__nth,axiom,
% 0.26/0.61      ! [N: nat,Xs2: list_num,Ys: list_num] :
% 0.26/0.61        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_num @ Xs2 ) @ ( size_size_list_num @ Ys ) ) )
% 0.26/0.61       => ( ( nth_Pr6456567536196504476um_num @ ( product_num_num @ Xs2 @ Ys ) @ N )
% 0.26/0.61          = ( product_Pair_num_num @ ( nth_num @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_num @ Ys ) ) ) @ ( nth_num @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_num @ Ys ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % product_nth
% 0.26/0.61  thf(fact_7283_product__nth,axiom,
% 0.26/0.61      ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.26/0.61        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 0.26/0.61       => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) @ N )
% 0.26/0.61          = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % product_nth
% 0.26/0.61  thf(fact_7284_product__nth,axiom,
% 0.26/0.61      ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_o] :
% 0.26/0.61        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 0.26/0.61       => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) @ N )
% 0.26/0.61          = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % product_nth
% 0.26/0.61  thf(fact_7285_product__nth,axiom,
% 0.26/0.61      ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 0.26/0.61        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 0.26/0.61       => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) @ N )
% 0.26/0.61          = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % product_nth
% 0.26/0.61  thf(fact_7286_product__nth,axiom,
% 0.26/0.61      ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_int] :
% 0.26/0.61        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 0.26/0.61       => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) @ N )
% 0.26/0.61          = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % product_nth
% 0.26/0.61  thf(fact_7287_product__nth,axiom,
% 0.26/0.61      ! [N: nat,Xs2: list_o,Ys: list_VEBT_VEBT] :
% 0.26/0.61        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 0.26/0.61       => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) @ N )
% 0.26/0.61          = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % product_nth
% 0.26/0.61  thf(fact_7288_product__nth,axiom,
% 0.26/0.61      ! [N: nat,Xs2: list_o,Ys: list_o] :
% 0.26/0.61        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 0.26/0.61       => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs2 @ Ys ) @ N )
% 0.26/0.61          = ( product_Pair_o_o @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % product_nth
% 0.26/0.61  thf(fact_7289_product__nth,axiom,
% 0.26/0.61      ! [N: nat,Xs2: list_o,Ys: list_nat] :
% 0.26/0.61        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 0.26/0.61       => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs2 @ Ys ) @ N )
% 0.26/0.61          = ( product_Pair_o_nat @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % product_nth
% 0.26/0.61  thf(fact_7290_product__nth,axiom,
% 0.26/0.61      ! [N: nat,Xs2: list_o,Ys: list_int] :
% 0.26/0.61        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 0.26/0.61       => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs2 @ Ys ) @ N )
% 0.26/0.61          = ( product_Pair_o_int @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % product_nth
% 0.26/0.61  thf(fact_7291_product__nth,axiom,
% 0.26/0.61      ! [N: nat,Xs2: list_nat,Ys: list_num] :
% 0.26/0.61        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_num @ Ys ) ) )
% 0.26/0.61       => ( ( nth_Pr8326237132889035090at_num @ ( product_nat_num @ Xs2 @ Ys ) @ N )
% 0.26/0.61          = ( product_Pair_nat_num @ ( nth_nat @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_num @ Ys ) ) ) @ ( nth_num @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_num @ Ys ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % product_nth
% 0.26/0.61  thf(fact_7292_minus__numeral__div__numeral,axiom,
% 0.26/0.61      ! [M: num,N: num] :
% 0.26/0.61        ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.61        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % minus_numeral_div_numeral
% 0.26/0.61  thf(fact_7293_numeral__div__minus__numeral,axiom,
% 0.26/0.61      ! [M: num,N: num] :
% 0.26/0.61        ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.61        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % numeral_div_minus_numeral
% 0.26/0.61  thf(fact_7294_eucl__rel__int__by0,axiom,
% 0.26/0.61      ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 0.26/0.61  
% 0.26/0.61  % eucl_rel_int_by0
% 0.26/0.61  thf(fact_7295_eucl__rel__int__dividesI,axiom,
% 0.26/0.61      ! [L: int,K: int,Q3: int] :
% 0.26/0.61        ( ( L != zero_zero_int )
% 0.26/0.61       => ( ( K
% 0.26/0.61            = ( times_times_int @ Q3 @ L ) )
% 0.26/0.61         => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ zero_zero_int ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % eucl_rel_int_dividesI
% 0.26/0.61  thf(fact_7296_fold__atLeastAtMost__nat_Oelims,axiom,
% 0.26/0.61      ! [X3: nat > nat > nat,Xa: nat,Xb: nat,Xc: nat,Y3: nat] :
% 0.26/0.61        ( ( ( set_fo2584398358068434914at_nat @ X3 @ Xa @ Xb @ Xc )
% 0.26/0.61          = Y3 )
% 0.26/0.61       => ( ( ( ord_less_nat @ Xb @ Xa )
% 0.26/0.61           => ( Y3 = Xc ) )
% 0.26/0.61          & ( ~ ( ord_less_nat @ Xb @ Xa )
% 0.26/0.61           => ( Y3
% 0.26/0.61              = ( set_fo2584398358068434914at_nat @ X3 @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb @ ( X3 @ Xa @ Xc ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % fold_atLeastAtMost_nat.elims
% 0.26/0.61  thf(fact_7297_fold__atLeastAtMost__nat_Osimps,axiom,
% 0.26/0.61      ( set_fo2584398358068434914at_nat
% 0.26/0.61      = ( ^ [F3: nat > nat > nat,A4: nat,B3: nat,Acc: nat] : ( if_nat @ ( ord_less_nat @ B3 @ A4 ) @ Acc @ ( set_fo2584398358068434914at_nat @ F3 @ ( plus_plus_nat @ A4 @ one_one_nat ) @ B3 @ ( F3 @ A4 @ Acc ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % fold_atLeastAtMost_nat.simps
% 0.26/0.61  thf(fact_7298_zminus1__lemma,axiom,
% 0.26/0.61      ! [A: int,B: int,Q3: int,R2: int] :
% 0.26/0.61        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 0.26/0.61       => ( ( B != zero_zero_int )
% 0.26/0.61         => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R2 = zero_zero_int ) @ ( uminus_uminus_int @ Q3 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q3 ) @ one_one_int ) ) @ ( if_int @ ( R2 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R2 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % zminus1_lemma
% 0.26/0.61  thf(fact_7299_eucl__rel__int__iff,axiom,
% 0.26/0.61      ! [K: int,L: int,Q3: int,R2: int] :
% 0.26/0.61        ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 0.26/0.61        = ( ( K
% 0.26/0.61            = ( plus_plus_int @ ( times_times_int @ L @ Q3 ) @ R2 ) )
% 0.26/0.61          & ( ( ord_less_int @ zero_zero_int @ L )
% 0.26/0.61           => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 0.26/0.61              & ( ord_less_int @ R2 @ L ) ) )
% 0.26/0.61          & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 0.26/0.61           => ( ( ( ord_less_int @ L @ zero_zero_int )
% 0.26/0.61               => ( ( ord_less_int @ L @ R2 )
% 0.26/0.61                  & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 0.26/0.61              & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 0.26/0.61               => ( Q3 = zero_zero_int ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % eucl_rel_int_iff
% 0.26/0.61  thf(fact_7300_pos__eucl__rel__int__mult__2,axiom,
% 0.26/0.61      ! [B: int,A: int,Q3: int,R2: int] :
% 0.26/0.61        ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.26/0.61       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 0.26/0.61         => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q3 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % pos_eucl_rel_int_mult_2
% 0.26/0.61  thf(fact_7301_xor__int__unfold,axiom,
% 0.26/0.61      ( bit_se6526347334894502574or_int
% 0.26/0.61      = ( ^ [K3: int,L2: int] :
% 0.26/0.61            ( if_int
% 0.26/0.61            @ ( K3
% 0.26/0.61              = ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.61            @ ( bit_ri7919022796975470100ot_int @ L2 )
% 0.26/0.61            @ ( if_int
% 0.26/0.61              @ ( L2
% 0.26/0.61                = ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.61              @ ( bit_ri7919022796975470100ot_int @ K3 )
% 0.26/0.61              @ ( if_int @ ( K3 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % xor_int_unfold
% 0.26/0.61  thf(fact_7302_cos__pi__eq__zero,axiom,
% 0.26/0.61      ! [M: nat] :
% 0.26/0.61        ( ( cos_real @ ( divide_divide_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61        = zero_zero_real ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_pi_eq_zero
% 0.26/0.61  thf(fact_7303_sincos__total__2pi,axiom,
% 0.26/0.61      ! [X3: real,Y3: real] :
% 0.26/0.61        ( ( ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.61          = one_one_real )
% 0.26/0.61       => ~ ! [T3: real] :
% 0.26/0.61              ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 0.26/0.61             => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.26/0.61               => ( ( X3
% 0.26/0.61                    = ( cos_real @ T3 ) )
% 0.26/0.61                 => ( Y3
% 0.26/0.61                   != ( sin_real @ T3 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sincos_total_2pi
% 0.26/0.61  thf(fact_7304_sin__tan,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61       => ( ( sin_real @ X3 )
% 0.26/0.61          = ( divide_divide_real @ ( tan_real @ X3 ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_tan
% 0.26/0.61  thf(fact_7305_vebt__buildup_Oelims,axiom,
% 0.26/0.61      ! [X3: nat,Y3: vEBT_VEBT] :
% 0.26/0.61        ( ( ( vEBT_vebt_buildup @ X3 )
% 0.26/0.61          = Y3 )
% 0.26/0.61       => ( ( ( X3 = zero_zero_nat )
% 0.26/0.61           => ( Y3
% 0.26/0.61             != ( vEBT_Leaf @ $false @ $false ) ) )
% 0.26/0.61         => ( ( ( X3
% 0.26/0.61                = ( suc @ zero_zero_nat ) )
% 0.26/0.61             => ( Y3
% 0.26/0.61               != ( vEBT_Leaf @ $false @ $false ) ) )
% 0.26/0.61           => ~ ! [Va: nat] :
% 0.26/0.61                  ( ( X3
% 0.26/0.61                    = ( suc @ ( suc @ Va ) ) )
% 0.26/0.61                 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.26/0.61                       => ( Y3
% 0.26/0.61                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.26/0.61                      & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.26/0.61                       => ( Y3
% 0.26/0.61                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % vebt_buildup.elims
% 0.26/0.61  thf(fact_7306_intind,axiom,
% 0.26/0.61      ! [I: nat,N: nat,P: nat > $o,X3: nat] :
% 0.26/0.61        ( ( ord_less_nat @ I @ N )
% 0.26/0.61       => ( ( P @ X3 )
% 0.26/0.61         => ( P @ ( nth_nat @ ( replicate_nat @ N @ X3 ) @ I ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % intind
% 0.26/0.61  thf(fact_7307_intind,axiom,
% 0.26/0.61      ! [I: nat,N: nat,P: int > $o,X3: int] :
% 0.26/0.61        ( ( ord_less_nat @ I @ N )
% 0.26/0.61       => ( ( P @ X3 )
% 0.26/0.61         => ( P @ ( nth_int @ ( replicate_int @ N @ X3 ) @ I ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % intind
% 0.26/0.61  thf(fact_7308_intind,axiom,
% 0.26/0.61      ! [I: nat,N: nat,P: vEBT_VEBT > $o,X3: vEBT_VEBT] :
% 0.26/0.61        ( ( ord_less_nat @ I @ N )
% 0.26/0.61       => ( ( P @ X3 )
% 0.26/0.61         => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X3 ) @ I ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % intind
% 0.26/0.61  thf(fact_7309_bit_Ocompl__eq__compl__iff,axiom,
% 0.26/0.61      ! [X3: int,Y3: int] :
% 0.26/0.61        ( ( ( bit_ri7919022796975470100ot_int @ X3 )
% 0.26/0.61          = ( bit_ri7919022796975470100ot_int @ Y3 ) )
% 0.26/0.61        = ( X3 = Y3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % bit.compl_eq_compl_iff
% 0.26/0.61  thf(fact_7310_bit_Odouble__compl,axiom,
% 0.26/0.61      ! [X3: int] :
% 0.26/0.61        ( ( bit_ri7919022796975470100ot_int @ ( bit_ri7919022796975470100ot_int @ X3 ) )
% 0.26/0.61        = X3 ) ).
% 0.26/0.61  
% 0.26/0.61  % bit.double_compl
% 0.26/0.61  thf(fact_7311_tan__zero,axiom,
% 0.26/0.61      ( ( tan_real @ zero_zero_real )
% 0.26/0.61      = zero_zero_real ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_zero
% 0.26/0.61  thf(fact_7312_replicate__eq__replicate,axiom,
% 0.26/0.61      ! [M: nat,X3: vEBT_VEBT,N: nat,Y3: vEBT_VEBT] :
% 0.26/0.61        ( ( ( replicate_VEBT_VEBT @ M @ X3 )
% 0.26/0.61          = ( replicate_VEBT_VEBT @ N @ Y3 ) )
% 0.26/0.61        = ( ( M = N )
% 0.26/0.61          & ( ( M != zero_zero_nat )
% 0.26/0.61           => ( X3 = Y3 ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % replicate_eq_replicate
% 0.26/0.61  thf(fact_7313_bit_Oxor__compl__right,axiom,
% 0.26/0.61      ! [X3: int,Y3: int] :
% 0.26/0.61        ( ( bit_se6526347334894502574or_int @ X3 @ ( bit_ri7919022796975470100ot_int @ Y3 ) )
% 0.26/0.61        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ X3 @ Y3 ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % bit.xor_compl_right
% 0.26/0.61  thf(fact_7314_bit_Oxor__compl__left,axiom,
% 0.26/0.61      ! [X3: int,Y3: int] :
% 0.26/0.61        ( ( bit_se6526347334894502574or_int @ ( bit_ri7919022796975470100ot_int @ X3 ) @ Y3 )
% 0.26/0.61        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ X3 @ Y3 ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % bit.xor_compl_left
% 0.26/0.61  thf(fact_7315_cos__zero,axiom,
% 0.26/0.61      ( ( cos_complex @ zero_zero_complex )
% 0.26/0.61      = one_one_complex ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_zero
% 0.26/0.61  thf(fact_7316_cos__zero,axiom,
% 0.26/0.61      ( ( cos_real @ zero_zero_real )
% 0.26/0.61      = one_one_real ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_zero
% 0.26/0.61  thf(fact_7317_in__set__replicate,axiom,
% 0.26/0.61      ! [X3: option_nat,N: nat,Y3: option_nat] :
% 0.26/0.61        ( ( member_option_nat @ X3 @ ( set_option_nat2 @ ( replicate_option_nat @ N @ Y3 ) ) )
% 0.26/0.61        = ( ( X3 = Y3 )
% 0.26/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % in_set_replicate
% 0.26/0.61  thf(fact_7318_in__set__replicate,axiom,
% 0.26/0.61      ! [X3: real,N: nat,Y3: real] :
% 0.26/0.61        ( ( member_real @ X3 @ ( set_real2 @ ( replicate_real @ N @ Y3 ) ) )
% 0.26/0.61        = ( ( X3 = Y3 )
% 0.26/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % in_set_replicate
% 0.26/0.61  thf(fact_7319_in__set__replicate,axiom,
% 0.26/0.61      ! [X3: set_nat,N: nat,Y3: set_nat] :
% 0.26/0.61        ( ( member_set_nat @ X3 @ ( set_set_nat2 @ ( replicate_set_nat @ N @ Y3 ) ) )
% 0.26/0.61        = ( ( X3 = Y3 )
% 0.26/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % in_set_replicate
% 0.26/0.61  thf(fact_7320_in__set__replicate,axiom,
% 0.26/0.61      ! [X3: nat,N: nat,Y3: nat] :
% 0.26/0.61        ( ( member_nat @ X3 @ ( set_nat2 @ ( replicate_nat @ N @ Y3 ) ) )
% 0.26/0.61        = ( ( X3 = Y3 )
% 0.26/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % in_set_replicate
% 0.26/0.61  thf(fact_7321_in__set__replicate,axiom,
% 0.26/0.61      ! [X3: int,N: nat,Y3: int] :
% 0.26/0.61        ( ( member_int @ X3 @ ( set_int2 @ ( replicate_int @ N @ Y3 ) ) )
% 0.26/0.61        = ( ( X3 = Y3 )
% 0.26/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % in_set_replicate
% 0.26/0.61  thf(fact_7322_in__set__replicate,axiom,
% 0.26/0.61      ! [X3: vEBT_VEBT,N: nat,Y3: vEBT_VEBT] :
% 0.26/0.61        ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ Y3 ) ) )
% 0.26/0.61        = ( ( X3 = Y3 )
% 0.26/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % in_set_replicate
% 0.26/0.61  thf(fact_7323_Bex__set__replicate,axiom,
% 0.26/0.61      ! [N: nat,A: nat,P: nat > $o] :
% 0.26/0.61        ( ( ? [X: nat] :
% 0.26/0.61              ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 0.26/0.61              & ( P @ X ) ) )
% 0.26/0.61        = ( ( P @ A )
% 0.26/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % Bex_set_replicate
% 0.26/0.61  thf(fact_7324_Bex__set__replicate,axiom,
% 0.26/0.61      ! [N: nat,A: int,P: int > $o] :
% 0.26/0.61        ( ( ? [X: int] :
% 0.26/0.61              ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 0.26/0.61              & ( P @ X ) ) )
% 0.26/0.61        = ( ( P @ A )
% 0.26/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % Bex_set_replicate
% 0.26/0.61  thf(fact_7325_Bex__set__replicate,axiom,
% 0.26/0.61      ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.26/0.61        ( ( ? [X: vEBT_VEBT] :
% 0.26/0.61              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 0.26/0.61              & ( P @ X ) ) )
% 0.26/0.61        = ( ( P @ A )
% 0.26/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % Bex_set_replicate
% 0.26/0.61  thf(fact_7326_Ball__set__replicate,axiom,
% 0.26/0.61      ! [N: nat,A: nat,P: nat > $o] :
% 0.26/0.61        ( ( ! [X: nat] :
% 0.26/0.61              ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 0.26/0.61             => ( P @ X ) ) )
% 0.26/0.61        = ( ( P @ A )
% 0.26/0.61          | ( N = zero_zero_nat ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % Ball_set_replicate
% 0.26/0.61  thf(fact_7327_Ball__set__replicate,axiom,
% 0.26/0.61      ! [N: nat,A: int,P: int > $o] :
% 0.26/0.61        ( ( ! [X: int] :
% 0.26/0.61              ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 0.26/0.61             => ( P @ X ) ) )
% 0.26/0.61        = ( ( P @ A )
% 0.26/0.61          | ( N = zero_zero_nat ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % Ball_set_replicate
% 0.26/0.61  thf(fact_7328_Ball__set__replicate,axiom,
% 0.26/0.61      ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.26/0.61        ( ( ! [X: vEBT_VEBT] :
% 0.26/0.61              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 0.26/0.61             => ( P @ X ) ) )
% 0.26/0.61        = ( ( P @ A )
% 0.26/0.61          | ( N = zero_zero_nat ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % Ball_set_replicate
% 0.26/0.61  thf(fact_7329_nth__replicate,axiom,
% 0.26/0.61      ! [I: nat,N: nat,X3: nat] :
% 0.26/0.61        ( ( ord_less_nat @ I @ N )
% 0.26/0.61       => ( ( nth_nat @ ( replicate_nat @ N @ X3 ) @ I )
% 0.26/0.61          = X3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % nth_replicate
% 0.26/0.61  thf(fact_7330_nth__replicate,axiom,
% 0.26/0.61      ! [I: nat,N: nat,X3: int] :
% 0.26/0.61        ( ( ord_less_nat @ I @ N )
% 0.26/0.61       => ( ( nth_int @ ( replicate_int @ N @ X3 ) @ I )
% 0.26/0.61          = X3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % nth_replicate
% 0.26/0.61  thf(fact_7331_nth__replicate,axiom,
% 0.26/0.61      ! [I: nat,N: nat,X3: vEBT_VEBT] :
% 0.26/0.61        ( ( ord_less_nat @ I @ N )
% 0.26/0.61       => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X3 ) @ I )
% 0.26/0.61          = X3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % nth_replicate
% 0.26/0.61  thf(fact_7332_tan__pi,axiom,
% 0.26/0.61      ( ( tan_real @ pi )
% 0.26/0.61      = zero_zero_real ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_pi
% 0.26/0.61  thf(fact_7333_bit_Ocompl__one,axiom,
% 0.26/0.61      ( ( bit_ri7632146776885996613nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.26/0.61      = zero_z3403309356797280102nteger ) ).
% 0.26/0.61  
% 0.26/0.61  % bit.compl_one
% 0.26/0.61  thf(fact_7334_bit_Ocompl__one,axiom,
% 0.26/0.61      ( ( bit_ri7919022796975470100ot_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.61      = zero_zero_int ) ).
% 0.26/0.61  
% 0.26/0.61  % bit.compl_one
% 0.26/0.61  thf(fact_7335_bit_Ocompl__zero,axiom,
% 0.26/0.61      ( ( bit_ri7632146776885996613nteger @ zero_z3403309356797280102nteger )
% 0.26/0.61      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.61  
% 0.26/0.61  % bit.compl_zero
% 0.26/0.61  thf(fact_7336_bit_Ocompl__zero,axiom,
% 0.26/0.61      ( ( bit_ri7919022796975470100ot_int @ zero_zero_int )
% 0.26/0.61      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.61  
% 0.26/0.61  % bit.compl_zero
% 0.26/0.61  thf(fact_7337_bit_Odisj__cancel__right,axiom,
% 0.26/0.61      ! [X3: code_integer] :
% 0.26/0.61        ( ( bit_se1080825931792720795nteger @ X3 @ ( bit_ri7632146776885996613nteger @ X3 ) )
% 0.26/0.61        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.61  
% 0.26/0.61  % bit.disj_cancel_right
% 0.26/0.61  thf(fact_7338_bit_Odisj__cancel__right,axiom,
% 0.26/0.61      ! [X3: int] :
% 0.26/0.61        ( ( bit_se1409905431419307370or_int @ X3 @ ( bit_ri7919022796975470100ot_int @ X3 ) )
% 0.26/0.61        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.61  
% 0.26/0.61  % bit.disj_cancel_right
% 0.26/0.61  thf(fact_7339_bit_Odisj__cancel__left,axiom,
% 0.26/0.61      ! [X3: code_integer] :
% 0.26/0.61        ( ( bit_se1080825931792720795nteger @ ( bit_ri7632146776885996613nteger @ X3 ) @ X3 )
% 0.26/0.61        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.61  
% 0.26/0.61  % bit.disj_cancel_left
% 0.26/0.61  thf(fact_7340_bit_Odisj__cancel__left,axiom,
% 0.26/0.61      ! [X3: int] :
% 0.26/0.61        ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ X3 ) @ X3 )
% 0.26/0.61        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.61  
% 0.26/0.61  % bit.disj_cancel_left
% 0.26/0.61  thf(fact_7341_bit_Oxor__cancel__right,axiom,
% 0.26/0.61      ! [X3: code_integer] :
% 0.26/0.61        ( ( bit_se3222712562003087583nteger @ X3 @ ( bit_ri7632146776885996613nteger @ X3 ) )
% 0.26/0.61        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.61  
% 0.26/0.61  % bit.xor_cancel_right
% 0.26/0.61  thf(fact_7342_bit_Oxor__cancel__right,axiom,
% 0.26/0.61      ! [X3: int] :
% 0.26/0.61        ( ( bit_se6526347334894502574or_int @ X3 @ ( bit_ri7919022796975470100ot_int @ X3 ) )
% 0.26/0.61        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.61  
% 0.26/0.61  % bit.xor_cancel_right
% 0.26/0.61  thf(fact_7343_bit_Oxor__cancel__left,axiom,
% 0.26/0.61      ! [X3: code_integer] :
% 0.26/0.61        ( ( bit_se3222712562003087583nteger @ ( bit_ri7632146776885996613nteger @ X3 ) @ X3 )
% 0.26/0.61        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.61  
% 0.26/0.61  % bit.xor_cancel_left
% 0.26/0.61  thf(fact_7344_bit_Oxor__cancel__left,axiom,
% 0.26/0.61      ! [X3: int] :
% 0.26/0.61        ( ( bit_se6526347334894502574or_int @ ( bit_ri7919022796975470100ot_int @ X3 ) @ X3 )
% 0.26/0.61        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.61  
% 0.26/0.61  % bit.xor_cancel_left
% 0.26/0.61  thf(fact_7345_bit_Oxor__one__right,axiom,
% 0.26/0.61      ! [X3: code_integer] :
% 0.26/0.61        ( ( bit_se3222712562003087583nteger @ X3 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.26/0.61        = ( bit_ri7632146776885996613nteger @ X3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % bit.xor_one_right
% 0.26/0.61  thf(fact_7346_bit_Oxor__one__right,axiom,
% 0.26/0.61      ! [X3: int] :
% 0.26/0.61        ( ( bit_se6526347334894502574or_int @ X3 @ ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.61        = ( bit_ri7919022796975470100ot_int @ X3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % bit.xor_one_right
% 0.26/0.61  thf(fact_7347_bit_Oxor__one__left,axiom,
% 0.26/0.61      ! [X3: code_integer] :
% 0.26/0.61        ( ( bit_se3222712562003087583nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X3 )
% 0.26/0.61        = ( bit_ri7632146776885996613nteger @ X3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % bit.xor_one_left
% 0.26/0.61  thf(fact_7348_bit_Oxor__one__left,axiom,
% 0.26/0.61      ! [X3: int] :
% 0.26/0.61        ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ one_one_int ) @ X3 )
% 0.26/0.61        = ( bit_ri7919022796975470100ot_int @ X3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % bit.xor_one_left
% 0.26/0.61  thf(fact_7349_not__negative__int__iff,axiom,
% 0.26/0.61      ! [K: int] :
% 0.26/0.61        ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 0.26/0.61        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.26/0.61  
% 0.26/0.61  % not_negative_int_iff
% 0.26/0.61  thf(fact_7350_not__nonnegative__int__iff,axiom,
% 0.26/0.61      ! [K: int] :
% 0.26/0.61        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 0.26/0.61        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.26/0.61  
% 0.26/0.61  % not_nonnegative_int_iff
% 0.26/0.61  thf(fact_7351_minus__not__numeral__eq,axiom,
% 0.26/0.61      ! [N: num] :
% 0.26/0.61        ( ( uminus1351360451143612070nteger @ ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.26/0.61        = ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % minus_not_numeral_eq
% 0.26/0.61  thf(fact_7352_minus__not__numeral__eq,axiom,
% 0.26/0.61      ! [N: num] :
% 0.26/0.61        ( ( uminus_uminus_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.61        = ( numeral_numeral_int @ ( inc @ N ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % minus_not_numeral_eq
% 0.26/0.61  thf(fact_7353_even__not__iff,axiom,
% 0.26/0.61      ! [A: code_integer] :
% 0.26/0.61        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri7632146776885996613nteger @ A ) )
% 0.26/0.61        = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % even_not_iff
% 0.26/0.61  thf(fact_7354_even__not__iff,axiom,
% 0.26/0.61      ! [A: int] :
% 0.26/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ A ) )
% 0.26/0.61        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % even_not_iff
% 0.26/0.61  thf(fact_7355_set__replicate,axiom,
% 0.26/0.61      ! [N: nat,X3: produc3843707927480180839at_nat] :
% 0.26/0.61        ( ( N != zero_zero_nat )
% 0.26/0.61       => ( ( set_Pr3765526544606949372at_nat @ ( replic2264142908078655527at_nat @ N @ X3 ) )
% 0.26/0.61          = ( insert9069300056098147895at_nat @ X3 @ bot_bo228742789529271731at_nat ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % set_replicate
% 0.26/0.61  thf(fact_7356_set__replicate,axiom,
% 0.26/0.61      ! [N: nat,X3: product_prod_nat_nat] :
% 0.26/0.61        ( ( N != zero_zero_nat )
% 0.26/0.61       => ( ( set_Pr5648618587558075414at_nat @ ( replic4235873036481779905at_nat @ N @ X3 ) )
% 0.26/0.61          = ( insert8211810215607154385at_nat @ X3 @ bot_bo2099793752762293965at_nat ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % set_replicate
% 0.26/0.61  thf(fact_7357_set__replicate,axiom,
% 0.26/0.61      ! [N: nat,X3: vEBT_VEBT] :
% 0.26/0.61        ( ( N != zero_zero_nat )
% 0.26/0.61       => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X3 ) )
% 0.26/0.61          = ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % set_replicate
% 0.26/0.61  thf(fact_7358_set__replicate,axiom,
% 0.26/0.61      ! [N: nat,X3: extended_enat] :
% 0.26/0.61        ( ( N != zero_zero_nat )
% 0.26/0.61       => ( ( set_Extended_enat2 @ ( replic7216382294607269926d_enat @ N @ X3 ) )
% 0.26/0.61          = ( insert_Extended_enat @ X3 @ bot_bo7653980558646680370d_enat ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % set_replicate
% 0.26/0.61  thf(fact_7359_set__replicate,axiom,
% 0.26/0.61      ! [N: nat,X3: real] :
% 0.26/0.61        ( ( N != zero_zero_nat )
% 0.26/0.61       => ( ( set_real2 @ ( replicate_real @ N @ X3 ) )
% 0.26/0.61          = ( insert_real @ X3 @ bot_bot_set_real ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % set_replicate
% 0.26/0.61  thf(fact_7360_set__replicate,axiom,
% 0.26/0.61      ! [N: nat,X3: nat] :
% 0.26/0.61        ( ( N != zero_zero_nat )
% 0.26/0.61       => ( ( set_nat2 @ ( replicate_nat @ N @ X3 ) )
% 0.26/0.61          = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % set_replicate
% 0.26/0.61  thf(fact_7361_set__replicate,axiom,
% 0.26/0.61      ! [N: nat,X3: int] :
% 0.26/0.61        ( ( N != zero_zero_nat )
% 0.26/0.61       => ( ( set_int2 @ ( replicate_int @ N @ X3 ) )
% 0.26/0.61          = ( insert_int @ X3 @ bot_bot_set_int ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % set_replicate
% 0.26/0.61  thf(fact_7362_tan__npi,axiom,
% 0.26/0.61      ! [N: nat] :
% 0.26/0.61        ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 0.26/0.61        = zero_zero_real ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_npi
% 0.26/0.61  thf(fact_7363_tan__periodic__n,axiom,
% 0.26/0.61      ! [X3: real,N: num] :
% 0.26/0.61        ( ( tan_real @ ( plus_plus_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ N ) @ pi ) ) )
% 0.26/0.61        = ( tan_real @ X3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_periodic_n
% 0.26/0.61  thf(fact_7364_tan__periodic__nat,axiom,
% 0.26/0.61      ! [X3: real,N: nat] :
% 0.26/0.61        ( ( tan_real @ ( plus_plus_real @ X3 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) ) )
% 0.26/0.61        = ( tan_real @ X3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_periodic_nat
% 0.26/0.61  thf(fact_7365_not__one__eq,axiom,
% 0.26/0.61      ( ( bit_ri7632146776885996613nteger @ one_one_Code_integer )
% 0.26/0.61      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % not_one_eq
% 0.26/0.61  thf(fact_7366_not__one__eq,axiom,
% 0.26/0.61      ( ( bit_ri7919022796975470100ot_int @ one_one_int )
% 0.26/0.61      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % not_one_eq
% 0.26/0.61  thf(fact_7367_cos__pi__half,axiom,
% 0.26/0.61      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61      = zero_zero_real ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_pi_half
% 0.26/0.61  thf(fact_7368_cos__two__pi,axiom,
% 0.26/0.61      ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.26/0.61      = one_one_real ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_two_pi
% 0.26/0.61  thf(fact_7369_cos__periodic,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( cos_real @ ( plus_plus_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.26/0.61        = ( cos_real @ X3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_periodic
% 0.26/0.61  thf(fact_7370_cos__2pi__minus,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X3 ) )
% 0.26/0.61        = ( cos_real @ X3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_2pi_minus
% 0.26/0.61  thf(fact_7371_tan__periodic,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( tan_real @ ( plus_plus_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.26/0.61        = ( tan_real @ X3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_periodic
% 0.26/0.61  thf(fact_7372_cos__npi2,axiom,
% 0.26/0.61      ! [N: nat] :
% 0.26/0.61        ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.26/0.61        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_npi2
% 0.26/0.61  thf(fact_7373_cos__npi,axiom,
% 0.26/0.61      ! [N: nat] :
% 0.26/0.61        ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 0.26/0.61        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_npi
% 0.26/0.61  thf(fact_7374_sin__cos__squared__add2,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( plus_plus_real @ ( power_power_real @ ( cos_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.61        = one_one_real ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_cos_squared_add2
% 0.26/0.61  thf(fact_7375_sin__cos__squared__add2,axiom,
% 0.26/0.61      ! [X3: complex] :
% 0.26/0.61        ( ( plus_plus_complex @ ( power_power_complex @ ( cos_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.61        = one_one_complex ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_cos_squared_add2
% 0.26/0.61  thf(fact_7376_sin__cos__squared__add,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( plus_plus_real @ ( power_power_real @ ( sin_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.61        = one_one_real ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_cos_squared_add
% 0.26/0.61  thf(fact_7377_sin__cos__squared__add,axiom,
% 0.26/0.61      ! [X3: complex] :
% 0.26/0.61        ( ( plus_plus_complex @ ( power_power_complex @ ( sin_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.61        = one_one_complex ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_cos_squared_add
% 0.26/0.61  thf(fact_7378_cos__of__real__pi__half,axiom,
% 0.26/0.61      ( ( cos_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61      = zero_zero_real ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_of_real_pi_half
% 0.26/0.61  thf(fact_7379_cos__of__real__pi__half,axiom,
% 0.26/0.61      ( ( cos_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 0.26/0.61      = zero_zero_complex ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_of_real_pi_half
% 0.26/0.61  thf(fact_7380_cos__2npi,axiom,
% 0.26/0.61      ! [N: nat] :
% 0.26/0.61        ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 0.26/0.61        = one_one_real ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_2npi
% 0.26/0.61  thf(fact_7381_cos__int__2pin,axiom,
% 0.26/0.61      ! [N: int] :
% 0.26/0.61        ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 0.26/0.61        = one_one_real ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_int_2pin
% 0.26/0.61  thf(fact_7382_cos__3over2__pi,axiom,
% 0.26/0.61      ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 0.26/0.61      = zero_zero_real ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_3over2_pi
% 0.26/0.61  thf(fact_7383_cos__npi__int,axiom,
% 0.26/0.61      ! [N: int] :
% 0.26/0.61        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.26/0.61         => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 0.26/0.61            = one_one_real ) )
% 0.26/0.61        & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.26/0.61         => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 0.26/0.61            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_npi_int
% 0.26/0.61  thf(fact_7384_of__int__not__eq,axiom,
% 0.26/0.61      ! [K: int] :
% 0.26/0.61        ( ( ring_1_of_int_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 0.26/0.61        = ( bit_ri7919022796975470100ot_int @ ( ring_1_of_int_int @ K ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % of_int_not_eq
% 0.26/0.61  thf(fact_7385_take__bit__not__take__bit,axiom,
% 0.26/0.61      ! [N: nat,A: int] :
% 0.26/0.61        ( ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 0.26/0.61        = ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ A ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % take_bit_not_take_bit
% 0.26/0.61  thf(fact_7386_take__bit__not__iff,axiom,
% 0.26/0.61      ! [N: nat,A: int,B: int] :
% 0.26/0.61        ( ( ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ A ) )
% 0.26/0.61          = ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ B ) ) )
% 0.26/0.61        = ( ( bit_se2923211474154528505it_int @ N @ A )
% 0.26/0.61          = ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % take_bit_not_iff
% 0.26/0.61  thf(fact_7387_of__int__not__numeral,axiom,
% 0.26/0.61      ! [K: num] :
% 0.26/0.61        ( ( ring_1_of_int_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ K ) ) )
% 0.26/0.61        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ K ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % of_int_not_numeral
% 0.26/0.61  thf(fact_7388_not__diff__distrib,axiom,
% 0.26/0.61      ! [A: int,B: int] :
% 0.26/0.61        ( ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A @ B ) )
% 0.26/0.61        = ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B ) ) ).
% 0.26/0.61  
% 0.26/0.61  % not_diff_distrib
% 0.26/0.61  thf(fact_7389_not__add__distrib,axiom,
% 0.26/0.61      ! [A: int,B: int] :
% 0.26/0.61        ( ( bit_ri7919022796975470100ot_int @ ( plus_plus_int @ A @ B ) )
% 0.26/0.61        = ( minus_minus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B ) ) ).
% 0.26/0.61  
% 0.26/0.61  % not_add_distrib
% 0.26/0.61  thf(fact_7390_cos__le__one,axiom,
% 0.26/0.61      ! [X3: real] : ( ord_less_eq_real @ ( cos_real @ X3 ) @ one_one_real ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_le_one
% 0.26/0.61  thf(fact_7391_cos__arctan__not__zero,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( cos_real @ ( arctan @ X3 ) )
% 0.26/0.61       != zero_zero_real ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_arctan_not_zero
% 0.26/0.61  thf(fact_7392_cos__int__times__real,axiom,
% 0.26/0.61      ! [M: int,X3: real] :
% 0.26/0.61        ( ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X3 ) ) )
% 0.26/0.61        = ( real_V1803761363581548252l_real @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X3 ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_int_times_real
% 0.26/0.61  thf(fact_7393_cos__int__times__real,axiom,
% 0.26/0.61      ! [M: int,X3: real] :
% 0.26/0.61        ( ( cos_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X3 ) ) )
% 0.26/0.61        = ( real_V4546457046886955230omplex @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X3 ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_int_times_real
% 0.26/0.61  thf(fact_7394_add__tan__eq,axiom,
% 0.26/0.61      ! [X3: complex,Y3: complex] :
% 0.26/0.61        ( ( ( cos_complex @ X3 )
% 0.26/0.61         != zero_zero_complex )
% 0.26/0.61       => ( ( ( cos_complex @ Y3 )
% 0.26/0.61           != zero_zero_complex )
% 0.26/0.61         => ( ( plus_plus_complex @ ( tan_complex @ X3 ) @ ( tan_complex @ Y3 ) )
% 0.26/0.61            = ( divide1717551699836669952omplex @ ( sin_complex @ ( plus_plus_complex @ X3 @ Y3 ) ) @ ( times_times_complex @ ( cos_complex @ X3 ) @ ( cos_complex @ Y3 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % add_tan_eq
% 0.26/0.61  thf(fact_7395_add__tan__eq,axiom,
% 0.26/0.61      ! [X3: real,Y3: real] :
% 0.26/0.61        ( ( ( cos_real @ X3 )
% 0.26/0.61         != zero_zero_real )
% 0.26/0.61       => ( ( ( cos_real @ Y3 )
% 0.26/0.61           != zero_zero_real )
% 0.26/0.61         => ( ( plus_plus_real @ ( tan_real @ X3 ) @ ( tan_real @ Y3 ) )
% 0.26/0.61            = ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ X3 @ Y3 ) ) @ ( times_times_real @ ( cos_real @ X3 ) @ ( cos_real @ Y3 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % add_tan_eq
% 0.26/0.61  thf(fact_7396_cos__one__sin__zero,axiom,
% 0.26/0.61      ! [X3: complex] :
% 0.26/0.61        ( ( ( cos_complex @ X3 )
% 0.26/0.61          = one_one_complex )
% 0.26/0.61       => ( ( sin_complex @ X3 )
% 0.26/0.61          = zero_zero_complex ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_one_sin_zero
% 0.26/0.61  thf(fact_7397_cos__one__sin__zero,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ( cos_real @ X3 )
% 0.26/0.61          = one_one_real )
% 0.26/0.61       => ( ( sin_real @ X3 )
% 0.26/0.61          = zero_zero_real ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_one_sin_zero
% 0.26/0.61  thf(fact_7398_tan__add,axiom,
% 0.26/0.61      ! [X3: complex,Y3: complex] :
% 0.26/0.61        ( ( ( cos_complex @ X3 )
% 0.26/0.61         != zero_zero_complex )
% 0.26/0.61       => ( ( ( cos_complex @ Y3 )
% 0.26/0.61           != zero_zero_complex )
% 0.26/0.61         => ( ( ( cos_complex @ ( plus_plus_complex @ X3 @ Y3 ) )
% 0.26/0.61             != zero_zero_complex )
% 0.26/0.61           => ( ( tan_complex @ ( plus_plus_complex @ X3 @ Y3 ) )
% 0.26/0.61              = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tan_complex @ X3 ) @ ( tan_complex @ Y3 ) ) @ ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X3 ) @ ( tan_complex @ Y3 ) ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_add
% 0.26/0.61  thf(fact_7399_tan__add,axiom,
% 0.26/0.61      ! [X3: real,Y3: real] :
% 0.26/0.61        ( ( ( cos_real @ X3 )
% 0.26/0.61         != zero_zero_real )
% 0.26/0.61       => ( ( ( cos_real @ Y3 )
% 0.26/0.61           != zero_zero_real )
% 0.26/0.61         => ( ( ( cos_real @ ( plus_plus_real @ X3 @ Y3 ) )
% 0.26/0.61             != zero_zero_real )
% 0.26/0.61           => ( ( tan_real @ ( plus_plus_real @ X3 @ Y3 ) )
% 0.26/0.61              = ( divide_divide_real @ ( plus_plus_real @ ( tan_real @ X3 ) @ ( tan_real @ Y3 ) ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X3 ) @ ( tan_real @ Y3 ) ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_add
% 0.26/0.61  thf(fact_7400_tan__diff,axiom,
% 0.26/0.61      ! [X3: complex,Y3: complex] :
% 0.26/0.61        ( ( ( cos_complex @ X3 )
% 0.26/0.61         != zero_zero_complex )
% 0.26/0.61       => ( ( ( cos_complex @ Y3 )
% 0.26/0.61           != zero_zero_complex )
% 0.26/0.61         => ( ( ( cos_complex @ ( minus_minus_complex @ X3 @ Y3 ) )
% 0.26/0.61             != zero_zero_complex )
% 0.26/0.61           => ( ( tan_complex @ ( minus_minus_complex @ X3 @ Y3 ) )
% 0.26/0.61              = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( tan_complex @ X3 ) @ ( tan_complex @ Y3 ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X3 ) @ ( tan_complex @ Y3 ) ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_diff
% 0.26/0.61  thf(fact_7401_tan__diff,axiom,
% 0.26/0.61      ! [X3: real,Y3: real] :
% 0.26/0.61        ( ( ( cos_real @ X3 )
% 0.26/0.61         != zero_zero_real )
% 0.26/0.61       => ( ( ( cos_real @ Y3 )
% 0.26/0.61           != zero_zero_real )
% 0.26/0.61         => ( ( ( cos_real @ ( minus_minus_real @ X3 @ Y3 ) )
% 0.26/0.61             != zero_zero_real )
% 0.26/0.61           => ( ( tan_real @ ( minus_minus_real @ X3 @ Y3 ) )
% 0.26/0.61              = ( divide_divide_real @ ( minus_minus_real @ ( tan_real @ X3 ) @ ( tan_real @ Y3 ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X3 ) @ ( tan_real @ Y3 ) ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_diff
% 0.26/0.61  thf(fact_7402_lemma__tan__add1,axiom,
% 0.26/0.61      ! [X3: complex,Y3: complex] :
% 0.26/0.61        ( ( ( cos_complex @ X3 )
% 0.26/0.61         != zero_zero_complex )
% 0.26/0.61       => ( ( ( cos_complex @ Y3 )
% 0.26/0.61           != zero_zero_complex )
% 0.26/0.61         => ( ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X3 ) @ ( tan_complex @ Y3 ) ) )
% 0.26/0.61            = ( divide1717551699836669952omplex @ ( cos_complex @ ( plus_plus_complex @ X3 @ Y3 ) ) @ ( times_times_complex @ ( cos_complex @ X3 ) @ ( cos_complex @ Y3 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % lemma_tan_add1
% 0.26/0.61  thf(fact_7403_lemma__tan__add1,axiom,
% 0.26/0.61      ! [X3: real,Y3: real] :
% 0.26/0.61        ( ( ( cos_real @ X3 )
% 0.26/0.61         != zero_zero_real )
% 0.26/0.61       => ( ( ( cos_real @ Y3 )
% 0.26/0.61           != zero_zero_real )
% 0.26/0.61         => ( ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X3 ) @ ( tan_real @ Y3 ) ) )
% 0.26/0.61            = ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ X3 @ Y3 ) ) @ ( times_times_real @ ( cos_real @ X3 ) @ ( cos_real @ Y3 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % lemma_tan_add1
% 0.26/0.61  thf(fact_7404_minus__eq__not__plus__1,axiom,
% 0.26/0.61      ( uminus1351360451143612070nteger
% 0.26/0.61      = ( ^ [A4: code_integer] : ( plus_p5714425477246183910nteger @ ( bit_ri7632146776885996613nteger @ A4 ) @ one_one_Code_integer ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % minus_eq_not_plus_1
% 0.26/0.61  thf(fact_7405_minus__eq__not__plus__1,axiom,
% 0.26/0.61      ( uminus_uminus_int
% 0.26/0.61      = ( ^ [A4: int] : ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A4 ) @ one_one_int ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % minus_eq_not_plus_1
% 0.26/0.61  thf(fact_7406_minus__eq__not__minus__1,axiom,
% 0.26/0.61      ( uminus1351360451143612070nteger
% 0.26/0.61      = ( ^ [A4: code_integer] : ( bit_ri7632146776885996613nteger @ ( minus_8373710615458151222nteger @ A4 @ one_one_Code_integer ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % minus_eq_not_minus_1
% 0.26/0.61  thf(fact_7407_minus__eq__not__minus__1,axiom,
% 0.26/0.61      ( uminus_uminus_int
% 0.26/0.61      = ( ^ [A4: int] : ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A4 @ one_one_int ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % minus_eq_not_minus_1
% 0.26/0.61  thf(fact_7408_not__eq__complement,axiom,
% 0.26/0.61      ( bit_ri7632146776885996613nteger
% 0.26/0.61      = ( ^ [A4: code_integer] : ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A4 ) @ one_one_Code_integer ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % not_eq_complement
% 0.26/0.61  thf(fact_7409_not__eq__complement,axiom,
% 0.26/0.61      ( bit_ri7919022796975470100ot_int
% 0.26/0.61      = ( ^ [A4: int] : ( minus_minus_int @ ( uminus_uminus_int @ A4 ) @ one_one_int ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % not_eq_complement
% 0.26/0.61  thf(fact_7410_cos__monotone__0__pi__le,axiom,
% 0.26/0.61      ! [Y3: real,X3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.61       => ( ( ord_less_eq_real @ Y3 @ X3 )
% 0.26/0.61         => ( ( ord_less_eq_real @ X3 @ pi )
% 0.26/0.61           => ( ord_less_eq_real @ ( cos_real @ X3 ) @ ( cos_real @ Y3 ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_monotone_0_pi_le
% 0.26/0.61  thf(fact_7411_cos__mono__le__eq,axiom,
% 0.26/0.61      ! [X3: real,Y3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.61       => ( ( ord_less_eq_real @ X3 @ pi )
% 0.26/0.61         => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.61           => ( ( ord_less_eq_real @ Y3 @ pi )
% 0.26/0.61             => ( ( ord_less_eq_real @ ( cos_real @ X3 ) @ ( cos_real @ Y3 ) )
% 0.26/0.61                = ( ord_less_eq_real @ Y3 @ X3 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_mono_le_eq
% 0.26/0.61  thf(fact_7412_cos__inj__pi,axiom,
% 0.26/0.61      ! [X3: real,Y3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.61       => ( ( ord_less_eq_real @ X3 @ pi )
% 0.26/0.61         => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.61           => ( ( ord_less_eq_real @ Y3 @ pi )
% 0.26/0.61             => ( ( ( cos_real @ X3 )
% 0.26/0.61                  = ( cos_real @ Y3 ) )
% 0.26/0.61               => ( X3 = Y3 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_inj_pi
% 0.26/0.61  thf(fact_7413_cos__ge__minus__one,axiom,
% 0.26/0.61      ! [X3: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_ge_minus_one
% 0.26/0.61  thf(fact_7414_not__int__def,axiom,
% 0.26/0.61      ( bit_ri7919022796975470100ot_int
% 0.26/0.61      = ( ^ [K3: int] : ( minus_minus_int @ ( uminus_uminus_int @ K3 ) @ one_one_int ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % not_int_def
% 0.26/0.61  thf(fact_7415_abs__cos__le__one,axiom,
% 0.26/0.61      ! [X3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X3 ) ) @ one_one_real ) ).
% 0.26/0.61  
% 0.26/0.61  % abs_cos_le_one
% 0.26/0.61  thf(fact_7416_or__not__numerals_I1_J,axiom,
% 0.26/0.61      ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.26/0.61      = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 0.26/0.61  
% 0.26/0.61  % or_not_numerals(1)
% 0.26/0.61  thf(fact_7417_minus__numeral__inc__eq,axiom,
% 0.26/0.61      ! [N: num] :
% 0.26/0.61        ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) )
% 0.26/0.61        = ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % minus_numeral_inc_eq
% 0.26/0.61  thf(fact_7418_minus__numeral__inc__eq,axiom,
% 0.26/0.61      ! [N: num] :
% 0.26/0.61        ( ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) )
% 0.26/0.61        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % minus_numeral_inc_eq
% 0.26/0.61  thf(fact_7419_sin__zero__norm__cos__one,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ( sin_real @ X3 )
% 0.26/0.61          = zero_zero_real )
% 0.26/0.61       => ( ( real_V7735802525324610683m_real @ ( cos_real @ X3 ) )
% 0.26/0.61          = one_one_real ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_zero_norm_cos_one
% 0.26/0.61  thf(fact_7420_sin__zero__norm__cos__one,axiom,
% 0.26/0.61      ! [X3: complex] :
% 0.26/0.61        ( ( ( sin_complex @ X3 )
% 0.26/0.61          = zero_zero_complex )
% 0.26/0.61       => ( ( real_V1022390504157884413omplex @ ( cos_complex @ X3 ) )
% 0.26/0.61          = one_one_real ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_zero_norm_cos_one
% 0.26/0.61  thf(fact_7421_not__int__div__2,axiom,
% 0.26/0.61      ! [K: int] :
% 0.26/0.61        ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.61        = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % not_int_div_2
% 0.26/0.61  thf(fact_7422_even__not__iff__int,axiom,
% 0.26/0.61      ! [K: int] :
% 0.26/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 0.26/0.61        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % even_not_iff_int
% 0.26/0.61  thf(fact_7423_cos__two__neq__zero,axiom,
% 0.26/0.61      ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.26/0.61     != zero_zero_real ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_two_neq_zero
% 0.26/0.61  thf(fact_7424_cos__mono__less__eq,axiom,
% 0.26/0.61      ! [X3: real,Y3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.61       => ( ( ord_less_eq_real @ X3 @ pi )
% 0.26/0.61         => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.61           => ( ( ord_less_eq_real @ Y3 @ pi )
% 0.26/0.61             => ( ( ord_less_real @ ( cos_real @ X3 ) @ ( cos_real @ Y3 ) )
% 0.26/0.61                = ( ord_less_real @ Y3 @ X3 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_mono_less_eq
% 0.26/0.61  thf(fact_7425_cos__monotone__0__pi,axiom,
% 0.26/0.61      ! [Y3: real,X3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.61       => ( ( ord_less_real @ Y3 @ X3 )
% 0.26/0.61         => ( ( ord_less_eq_real @ X3 @ pi )
% 0.26/0.61           => ( ord_less_real @ ( cos_real @ X3 ) @ ( cos_real @ Y3 ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_monotone_0_pi
% 0.26/0.61  thf(fact_7426_tan__half,axiom,
% 0.26/0.61      ( tan_complex
% 0.26/0.61      = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) ) @ ( plus_plus_complex @ ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) ) @ one_one_complex ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_half
% 0.26/0.61  thf(fact_7427_tan__half,axiom,
% 0.26/0.61      ( tan_real
% 0.26/0.61      = ( ^ [X: real] : ( divide_divide_real @ ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ ( plus_plus_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_half
% 0.26/0.61  thf(fact_7428_not__numeral__Bit0__eq,axiom,
% 0.26/0.61      ! [N: num] :
% 0.26/0.61        ( ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) )
% 0.26/0.61        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % not_numeral_Bit0_eq
% 0.26/0.61  thf(fact_7429_not__numeral__Bit0__eq,axiom,
% 0.26/0.61      ! [N: num] :
% 0.26/0.61        ( ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) )
% 0.26/0.61        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % not_numeral_Bit0_eq
% 0.26/0.61  thf(fact_7430_or__not__numerals_I2_J,axiom,
% 0.26/0.61      ! [N: num] :
% 0.26/0.61        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.26/0.61        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % or_not_numerals(2)
% 0.26/0.61  thf(fact_7431_or__not__numerals_I4_J,axiom,
% 0.26/0.61      ! [M: num] :
% 0.26/0.61        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.26/0.61        = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 0.26/0.61  
% 0.26/0.61  % or_not_numerals(4)
% 0.26/0.61  thf(fact_7432_cos__monotone__minus__pi__0_H,axiom,
% 0.26/0.61      ! [Y3: real,X3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 0.26/0.61       => ( ( ord_less_eq_real @ Y3 @ X3 )
% 0.26/0.61         => ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 0.26/0.61           => ( ord_less_eq_real @ ( cos_real @ Y3 ) @ ( cos_real @ X3 ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_monotone_minus_pi_0'
% 0.26/0.61  thf(fact_7433_set__replicate__conv__if,axiom,
% 0.26/0.61      ! [N: nat,X3: produc3843707927480180839at_nat] :
% 0.26/0.61        ( ( ( N = zero_zero_nat )
% 0.26/0.61         => ( ( set_Pr3765526544606949372at_nat @ ( replic2264142908078655527at_nat @ N @ X3 ) )
% 0.26/0.61            = bot_bo228742789529271731at_nat ) )
% 0.26/0.61        & ( ( N != zero_zero_nat )
% 0.26/0.61         => ( ( set_Pr3765526544606949372at_nat @ ( replic2264142908078655527at_nat @ N @ X3 ) )
% 0.26/0.61            = ( insert9069300056098147895at_nat @ X3 @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % set_replicate_conv_if
% 0.26/0.61  thf(fact_7434_set__replicate__conv__if,axiom,
% 0.26/0.61      ! [N: nat,X3: product_prod_nat_nat] :
% 0.26/0.61        ( ( ( N = zero_zero_nat )
% 0.26/0.61         => ( ( set_Pr5648618587558075414at_nat @ ( replic4235873036481779905at_nat @ N @ X3 ) )
% 0.26/0.61            = bot_bo2099793752762293965at_nat ) )
% 0.26/0.61        & ( ( N != zero_zero_nat )
% 0.26/0.61         => ( ( set_Pr5648618587558075414at_nat @ ( replic4235873036481779905at_nat @ N @ X3 ) )
% 0.26/0.61            = ( insert8211810215607154385at_nat @ X3 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % set_replicate_conv_if
% 0.26/0.61  thf(fact_7435_set__replicate__conv__if,axiom,
% 0.26/0.61      ! [N: nat,X3: vEBT_VEBT] :
% 0.26/0.61        ( ( ( N = zero_zero_nat )
% 0.26/0.61         => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X3 ) )
% 0.26/0.61            = bot_bo8194388402131092736T_VEBT ) )
% 0.26/0.61        & ( ( N != zero_zero_nat )
% 0.26/0.61         => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X3 ) )
% 0.26/0.61            = ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % set_replicate_conv_if
% 0.26/0.61  thf(fact_7436_set__replicate__conv__if,axiom,
% 0.26/0.61      ! [N: nat,X3: extended_enat] :
% 0.26/0.61        ( ( ( N = zero_zero_nat )
% 0.26/0.61         => ( ( set_Extended_enat2 @ ( replic7216382294607269926d_enat @ N @ X3 ) )
% 0.26/0.61            = bot_bo7653980558646680370d_enat ) )
% 0.26/0.61        & ( ( N != zero_zero_nat )
% 0.26/0.61         => ( ( set_Extended_enat2 @ ( replic7216382294607269926d_enat @ N @ X3 ) )
% 0.26/0.61            = ( insert_Extended_enat @ X3 @ bot_bo7653980558646680370d_enat ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % set_replicate_conv_if
% 0.26/0.61  thf(fact_7437_set__replicate__conv__if,axiom,
% 0.26/0.61      ! [N: nat,X3: real] :
% 0.26/0.61        ( ( ( N = zero_zero_nat )
% 0.26/0.61         => ( ( set_real2 @ ( replicate_real @ N @ X3 ) )
% 0.26/0.61            = bot_bot_set_real ) )
% 0.26/0.61        & ( ( N != zero_zero_nat )
% 0.26/0.61         => ( ( set_real2 @ ( replicate_real @ N @ X3 ) )
% 0.26/0.61            = ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % set_replicate_conv_if
% 0.26/0.61  thf(fact_7438_set__replicate__conv__if,axiom,
% 0.26/0.61      ! [N: nat,X3: nat] :
% 0.26/0.61        ( ( ( N = zero_zero_nat )
% 0.26/0.61         => ( ( set_nat2 @ ( replicate_nat @ N @ X3 ) )
% 0.26/0.61            = bot_bot_set_nat ) )
% 0.26/0.61        & ( ( N != zero_zero_nat )
% 0.26/0.61         => ( ( set_nat2 @ ( replicate_nat @ N @ X3 ) )
% 0.26/0.61            = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % set_replicate_conv_if
% 0.26/0.61  thf(fact_7439_set__replicate__conv__if,axiom,
% 0.26/0.61      ! [N: nat,X3: int] :
% 0.26/0.61        ( ( ( N = zero_zero_nat )
% 0.26/0.61         => ( ( set_int2 @ ( replicate_int @ N @ X3 ) )
% 0.26/0.61            = bot_bot_set_int ) )
% 0.26/0.61        & ( ( N != zero_zero_nat )
% 0.26/0.61         => ( ( set_int2 @ ( replicate_int @ N @ X3 ) )
% 0.26/0.61            = ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % set_replicate_conv_if
% 0.26/0.61  thf(fact_7440_sin__zero__abs__cos__one,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ( sin_real @ X3 )
% 0.26/0.61          = zero_zero_real )
% 0.26/0.61       => ( ( abs_abs_real @ ( cos_real @ X3 ) )
% 0.26/0.61          = one_one_real ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_zero_abs_cos_one
% 0.26/0.61  thf(fact_7441_sin__double,axiom,
% 0.26/0.61      ! [X3: complex] :
% 0.26/0.61        ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) )
% 0.26/0.61        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X3 ) ) @ ( cos_complex @ X3 ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_double
% 0.26/0.61  thf(fact_7442_sin__double,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) )
% 0.26/0.61        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X3 ) ) @ ( cos_real @ X3 ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_double
% 0.26/0.61  thf(fact_7443_cos__two__less__zero,axiom,
% 0.26/0.61      ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 0.26/0.61  
% 0.26/0.61  % cos_two_less_zero
% 0.26/0.61  thf(fact_7444_cos__is__zero,axiom,
% 0.26/0.61      ? [X4: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.26/0.61        & ( ord_less_eq_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.26/0.61        & ( ( cos_real @ X4 )
% 0.26/0.61          = zero_zero_real )
% 0.26/0.61        & ! [Y6: real] :
% 0.26/0.61            ( ( ( ord_less_eq_real @ zero_zero_real @ Y6 )
% 0.26/0.61              & ( ord_less_eq_real @ Y6 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.26/0.61              & ( ( cos_real @ Y6 )
% 0.26/0.61                = zero_zero_real ) )
% 0.26/0.61           => ( Y6 = X4 ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_is_zero
% 0.26/0.61  thf(fact_7445_cos__two__le__zero,axiom,
% 0.26/0.61      ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 0.26/0.61  
% 0.26/0.61  % cos_two_le_zero
% 0.26/0.61  thf(fact_7446_tan__double,axiom,
% 0.26/0.61      ! [X3: complex] :
% 0.26/0.61        ( ( ( cos_complex @ X3 )
% 0.26/0.61         != zero_zero_complex )
% 0.26/0.61       => ( ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) )
% 0.26/0.61           != zero_zero_complex )
% 0.26/0.61         => ( ( tan_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) )
% 0.26/0.61            = ( divide1717551699836669952omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( tan_complex @ X3 ) ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_double
% 0.26/0.61  thf(fact_7447_tan__double,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ( cos_real @ X3 )
% 0.26/0.61         != zero_zero_real )
% 0.26/0.61       => ( ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) )
% 0.26/0.61           != zero_zero_real )
% 0.26/0.61         => ( ( tan_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) )
% 0.26/0.61            = ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( tan_real @ X3 ) ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_double
% 0.26/0.61  thf(fact_7448_or__not__numerals_I3_J,axiom,
% 0.26/0.61      ! [N: num] :
% 0.26/0.61        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.26/0.61        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % or_not_numerals(3)
% 0.26/0.61  thf(fact_7449_cos__monotone__minus__pi__0,axiom,
% 0.26/0.61      ! [Y3: real,X3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 0.26/0.61       => ( ( ord_less_real @ Y3 @ X3 )
% 0.26/0.61         => ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 0.26/0.61           => ( ord_less_real @ ( cos_real @ Y3 ) @ ( cos_real @ X3 ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_monotone_minus_pi_0
% 0.26/0.61  thf(fact_7450_or__not__numerals_I7_J,axiom,
% 0.26/0.61      ! [M: num] :
% 0.26/0.61        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.26/0.61        = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 0.26/0.61  
% 0.26/0.61  % or_not_numerals(7)
% 0.26/0.61  thf(fact_7451_cos__total,axiom,
% 0.26/0.61      ! [Y3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 0.26/0.61       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 0.26/0.61         => ? [X4: real] :
% 0.26/0.61              ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.26/0.61              & ( ord_less_eq_real @ X4 @ pi )
% 0.26/0.61              & ( ( cos_real @ X4 )
% 0.26/0.61                = Y3 )
% 0.26/0.61              & ! [Y6: real] :
% 0.26/0.61                  ( ( ( ord_less_eq_real @ zero_zero_real @ Y6 )
% 0.26/0.61                    & ( ord_less_eq_real @ Y6 @ pi )
% 0.26/0.61                    & ( ( cos_real @ Y6 )
% 0.26/0.61                      = Y3 ) )
% 0.26/0.61                 => ( Y6 = X4 ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_total
% 0.26/0.61  thf(fact_7452_sincos__principal__value,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61      ? [Y4: real] :
% 0.26/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y4 )
% 0.26/0.61        & ( ord_less_eq_real @ Y4 @ pi )
% 0.26/0.61        & ( ( sin_real @ Y4 )
% 0.26/0.61          = ( sin_real @ X3 ) )
% 0.26/0.61        & ( ( cos_real @ Y4 )
% 0.26/0.61          = ( cos_real @ X3 ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sincos_principal_value
% 0.26/0.61  thf(fact_7453_cos__tan,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61       => ( ( cos_real @ X3 )
% 0.26/0.61          = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_tan
% 0.26/0.61  thf(fact_7454_tan__45,axiom,
% 0.26/0.61      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.26/0.61      = one_one_real ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_45
% 0.26/0.61  thf(fact_7455_or__not__numerals_I6_J,axiom,
% 0.26/0.61      ! [M: num,N: num] :
% 0.26/0.61        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.26/0.61        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % or_not_numerals(6)
% 0.26/0.61  thf(fact_7456_tan__60,axiom,
% 0.26/0.61      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 0.26/0.61      = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_60
% 0.26/0.61  thf(fact_7457_cos__45,axiom,
% 0.26/0.61      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.26/0.61      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_45
% 0.26/0.61  thf(fact_7458_sin__cos__le1,axiom,
% 0.26/0.61      ! [X3: real,Y3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X3 ) @ ( sin_real @ Y3 ) ) @ ( times_times_real @ ( cos_real @ X3 ) @ ( cos_real @ Y3 ) ) ) ) @ one_one_real ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_cos_le1
% 0.26/0.61  thf(fact_7459_cos__plus__cos,axiom,
% 0.26/0.61      ! [W: complex,Z: complex] :
% 0.26/0.61        ( ( plus_plus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 0.26/0.61        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_plus_cos
% 0.26/0.61  thf(fact_7460_cos__plus__cos,axiom,
% 0.26/0.61      ! [W: real,Z: real] :
% 0.26/0.61        ( ( plus_plus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 0.26/0.61        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_plus_cos
% 0.26/0.61  thf(fact_7461_cos__times__cos,axiom,
% 0.26/0.61      ! [W: complex,Z: complex] :
% 0.26/0.61        ( ( times_times_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 0.26/0.61        = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_times_cos
% 0.26/0.61  thf(fact_7462_cos__times__cos,axiom,
% 0.26/0.61      ! [W: real,Z: real] :
% 0.26/0.61        ( ( times_times_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 0.26/0.61        = ( divide_divide_real @ ( plus_plus_real @ ( cos_real @ ( minus_minus_real @ W @ Z ) ) @ ( cos_real @ ( plus_plus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_times_cos
% 0.26/0.61  thf(fact_7463_sin__squared__eq,axiom,
% 0.26/0.61      ! [X3: complex] :
% 0.26/0.61        ( ( power_power_complex @ ( sin_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.61        = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( cos_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_squared_eq
% 0.26/0.61  thf(fact_7464_sin__squared__eq,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( power_power_real @ ( sin_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.61        = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_squared_eq
% 0.26/0.61  thf(fact_7465_cos__squared__eq,axiom,
% 0.26/0.61      ! [X3: complex] :
% 0.26/0.61        ( ( power_power_complex @ ( cos_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.61        = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( sin_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_squared_eq
% 0.26/0.61  thf(fact_7466_cos__squared__eq,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( power_power_real @ ( cos_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.61        = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( sin_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_squared_eq
% 0.26/0.61  thf(fact_7467_tan__gt__zero,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61         => ( ord_less_real @ zero_zero_real @ ( tan_real @ X3 ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_gt_zero
% 0.26/0.61  thf(fact_7468_lemma__tan__total,axiom,
% 0.26/0.61      ! [Y3: real] :
% 0.26/0.61        ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.61       => ? [X4: real] :
% 0.26/0.61            ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.26/0.61            & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61            & ( ord_less_real @ Y3 @ ( tan_real @ X4 ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % lemma_tan_total
% 0.26/0.61  thf(fact_7469_tan__total,axiom,
% 0.26/0.61      ! [Y3: real] :
% 0.26/0.61      ? [X4: real] :
% 0.26/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 0.26/0.61        & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61        & ( ( tan_real @ X4 )
% 0.26/0.61          = Y3 )
% 0.26/0.61        & ! [Y6: real] :
% 0.26/0.61            ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y6 )
% 0.26/0.61              & ( ord_less_real @ Y6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61              & ( ( tan_real @ Y6 )
% 0.26/0.61                = Y3 ) )
% 0.26/0.61           => ( Y6 = X4 ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_total
% 0.26/0.61  thf(fact_7470_tan__monotone,axiom,
% 0.26/0.61      ! [Y3: real,X3: real] :
% 0.26/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 0.26/0.61       => ( ( ord_less_real @ Y3 @ X3 )
% 0.26/0.61         => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61           => ( ord_less_real @ ( tan_real @ Y3 ) @ ( tan_real @ X3 ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_monotone
% 0.26/0.61  thf(fact_7471_tan__monotone_H,axiom,
% 0.26/0.61      ! [Y3: real,X3: real] :
% 0.26/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 0.26/0.61       => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.26/0.61           => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61             => ( ( ord_less_real @ Y3 @ X3 )
% 0.26/0.61                = ( ord_less_real @ ( tan_real @ Y3 ) @ ( tan_real @ X3 ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_monotone'
% 0.26/0.61  thf(fact_7472_tan__mono__lt__eq,axiom,
% 0.26/0.61      ! [X3: real,Y3: real] :
% 0.26/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.26/0.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 0.26/0.61           => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61             => ( ( ord_less_real @ ( tan_real @ X3 ) @ ( tan_real @ Y3 ) )
% 0.26/0.61                = ( ord_less_real @ X3 @ Y3 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_mono_lt_eq
% 0.26/0.61  thf(fact_7473_lemma__tan__total1,axiom,
% 0.26/0.61      ! [Y3: real] :
% 0.26/0.61      ? [X4: real] :
% 0.26/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 0.26/0.61        & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61        & ( ( tan_real @ X4 )
% 0.26/0.61          = Y3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % lemma_tan_total1
% 0.26/0.61  thf(fact_7474_tan__minus__45,axiom,
% 0.26/0.61      ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.61      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_minus_45
% 0.26/0.61  thf(fact_7475_cos__double__less__one,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.61       => ( ( ord_less_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.26/0.61         => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) ) @ one_one_real ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_double_less_one
% 0.26/0.61  thf(fact_7476_tan__inverse,axiom,
% 0.26/0.61      ! [Y3: real] :
% 0.26/0.61        ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y3 ) )
% 0.26/0.61        = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y3 ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_inverse
% 0.26/0.61  thf(fact_7477_cos__gt__zero,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61         => ( ord_less_real @ zero_zero_real @ ( cos_real @ X3 ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_gt_zero
% 0.26/0.61  thf(fact_7478_cos__60,axiom,
% 0.26/0.61      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 0.26/0.61      = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_60
% 0.26/0.61  thf(fact_7479_or__not__numerals_I5_J,axiom,
% 0.26/0.61      ! [M: num,N: num] :
% 0.26/0.61        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.26/0.61        = ( 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 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % or_not_numerals(5)
% 0.26/0.61  thf(fact_7480_cos__30,axiom,
% 0.26/0.61      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 0.26/0.61      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_30
% 0.26/0.61  thf(fact_7481_cos__one__2pi__int,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ( cos_real @ X3 )
% 0.26/0.61          = one_one_real )
% 0.26/0.61        = ( ? [X: int] :
% 0.26/0.61              ( X3
% 0.26/0.61              = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_one_2pi_int
% 0.26/0.61  thf(fact_7482_cos__double__cos,axiom,
% 0.26/0.61      ! [W: complex] :
% 0.26/0.61        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 0.26/0.61        = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_double_cos
% 0.26/0.61  thf(fact_7483_cos__double__cos,axiom,
% 0.26/0.61      ! [W: real] :
% 0.26/0.61        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 0.26/0.61        = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( cos_real @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_real ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_double_cos
% 0.26/0.61  thf(fact_7484_cos__treble__cos,axiom,
% 0.26/0.61      ! [X3: complex] :
% 0.26/0.61        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X3 ) )
% 0.26/0.61        = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ ( cos_complex @ X3 ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_treble_cos
% 0.26/0.61  thf(fact_7485_cos__treble__cos,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X3 ) )
% 0.26/0.61        = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( cos_real @ X3 ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_treble_cos
% 0.26/0.61  thf(fact_7486_cos__diff__cos,axiom,
% 0.26/0.61      ! [W: complex,Z: complex] :
% 0.26/0.61        ( ( minus_minus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 0.26/0.61        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ Z @ W ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_diff_cos
% 0.26/0.61  thf(fact_7487_cos__diff__cos,axiom,
% 0.26/0.61      ! [W: real,Z: real] :
% 0.26/0.61        ( ( minus_minus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 0.26/0.61        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ Z @ W ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_diff_cos
% 0.26/0.61  thf(fact_7488_sin__diff__sin,axiom,
% 0.26/0.61      ! [W: complex,Z: complex] :
% 0.26/0.61        ( ( minus_minus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 0.26/0.61        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_diff_sin
% 0.26/0.61  thf(fact_7489_sin__diff__sin,axiom,
% 0.26/0.61      ! [W: real,Z: real] :
% 0.26/0.61        ( ( minus_minus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 0.26/0.61        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_diff_sin
% 0.26/0.61  thf(fact_7490_sin__plus__sin,axiom,
% 0.26/0.61      ! [W: complex,Z: complex] :
% 0.26/0.61        ( ( plus_plus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 0.26/0.61        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_plus_sin
% 0.26/0.61  thf(fact_7491_sin__plus__sin,axiom,
% 0.26/0.61      ! [W: real,Z: real] :
% 0.26/0.61        ( ( plus_plus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 0.26/0.61        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_plus_sin
% 0.26/0.61  thf(fact_7492_cos__times__sin,axiom,
% 0.26/0.61      ! [W: complex,Z: complex] :
% 0.26/0.61        ( ( times_times_complex @ ( cos_complex @ W ) @ ( sin_complex @ Z ) )
% 0.26/0.61        = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_times_sin
% 0.26/0.61  thf(fact_7493_cos__times__sin,axiom,
% 0.26/0.61      ! [W: real,Z: real] :
% 0.26/0.61        ( ( times_times_real @ ( cos_real @ W ) @ ( sin_real @ Z ) )
% 0.26/0.61        = ( divide_divide_real @ ( minus_minus_real @ ( sin_real @ ( plus_plus_real @ W @ Z ) ) @ ( sin_real @ ( minus_minus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_times_sin
% 0.26/0.61  thf(fact_7494_sin__times__cos,axiom,
% 0.26/0.61      ! [W: complex,Z: complex] :
% 0.26/0.61        ( ( times_times_complex @ ( sin_complex @ W ) @ ( cos_complex @ Z ) )
% 0.26/0.61        = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_times_cos
% 0.26/0.61  thf(fact_7495_sin__times__cos,axiom,
% 0.26/0.61      ! [W: real,Z: real] :
% 0.26/0.61        ( ( times_times_real @ ( sin_real @ W ) @ ( cos_real @ Z ) )
% 0.26/0.61        = ( divide_divide_real @ ( plus_plus_real @ ( sin_real @ ( plus_plus_real @ W @ Z ) ) @ ( sin_real @ ( minus_minus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_times_cos
% 0.26/0.61  thf(fact_7496_sin__times__sin,axiom,
% 0.26/0.61      ! [W: complex,Z: complex] :
% 0.26/0.61        ( ( times_times_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 0.26/0.61        = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_times_sin
% 0.26/0.61  thf(fact_7497_sin__times__sin,axiom,
% 0.26/0.61      ! [W: real,Z: real] :
% 0.26/0.61        ( ( times_times_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 0.26/0.61        = ( divide_divide_real @ ( minus_minus_real @ ( cos_real @ ( minus_minus_real @ W @ Z ) ) @ ( cos_real @ ( plus_plus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_times_sin
% 0.26/0.61  thf(fact_7498_cos__double,axiom,
% 0.26/0.61      ! [X3: complex] :
% 0.26/0.61        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) )
% 0.26/0.61        = ( minus_minus_complex @ ( power_power_complex @ ( cos_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_double
% 0.26/0.61  thf(fact_7499_cos__double,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) )
% 0.26/0.61        = ( minus_minus_real @ ( power_power_real @ ( cos_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_double
% 0.26/0.61  thf(fact_7500_cos__sin__eq,axiom,
% 0.26/0.61      ( cos_real
% 0.26/0.61      = ( ^ [X: real] : ( sin_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_sin_eq
% 0.26/0.61  thf(fact_7501_cos__sin__eq,axiom,
% 0.26/0.61      ( cos_complex
% 0.26/0.61      = ( ^ [X: complex] : ( sin_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_sin_eq
% 0.26/0.61  thf(fact_7502_sin__cos__eq,axiom,
% 0.26/0.61      ( sin_real
% 0.26/0.61      = ( ^ [X: real] : ( cos_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_cos_eq
% 0.26/0.61  thf(fact_7503_sin__cos__eq,axiom,
% 0.26/0.61      ( sin_complex
% 0.26/0.61      = ( ^ [X: complex] : ( cos_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_cos_eq
% 0.26/0.61  thf(fact_7504_tan__total__pos,axiom,
% 0.26/0.61      ! [Y3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.61       => ? [X4: real] :
% 0.26/0.61            ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.26/0.61            & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61            & ( ( tan_real @ X4 )
% 0.26/0.61              = Y3 ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_total_pos
% 0.26/0.61  thf(fact_7505_tan__pos__pi2__le,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61         => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X3 ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_pos_pi2_le
% 0.26/0.61  thf(fact_7506_tan__less__zero,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 )
% 0.26/0.61       => ( ( ord_less_real @ X3 @ zero_zero_real )
% 0.26/0.61         => ( ord_less_real @ ( tan_real @ X3 ) @ zero_zero_real ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_less_zero
% 0.26/0.61  thf(fact_7507_tan__mono__le,axiom,
% 0.26/0.61      ! [X3: real,Y3: real] :
% 0.26/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.26/0.61       => ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.26/0.61         => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61           => ( ord_less_eq_real @ ( tan_real @ X3 ) @ ( tan_real @ Y3 ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_mono_le
% 0.26/0.61  thf(fact_7508_tan__mono__le__eq,axiom,
% 0.26/0.61      ! [X3: real,Y3: real] :
% 0.26/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.26/0.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 0.26/0.61           => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61             => ( ( ord_less_eq_real @ ( tan_real @ X3 ) @ ( tan_real @ Y3 ) )
% 0.26/0.61                = ( ord_less_eq_real @ X3 @ Y3 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_mono_le_eq
% 0.26/0.61  thf(fact_7509_tan__bound__pi2,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.26/0.61       => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X3 ) ) @ one_one_real ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_bound_pi2
% 0.26/0.61  thf(fact_7510_tan__30,axiom,
% 0.26/0.61      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 0.26/0.61      = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_30
% 0.26/0.61  thf(fact_7511_or__not__numerals_I9_J,axiom,
% 0.26/0.61      ! [M: num,N: num] :
% 0.26/0.61        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.26/0.61        = ( 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 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % or_not_numerals(9)
% 0.26/0.61  thf(fact_7512_or__not__numerals_I8_J,axiom,
% 0.26/0.61      ! [M: num,N: num] :
% 0.26/0.61        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.26/0.61        = ( 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 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % or_not_numerals(8)
% 0.26/0.61  thf(fact_7513_cos__gt__zero__pi,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.26/0.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61         => ( ord_less_real @ zero_zero_real @ ( cos_real @ X3 ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_gt_zero_pi
% 0.26/0.61  thf(fact_7514_cos__ge__zero,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.26/0.61       => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61         => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X3 ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_ge_zero
% 0.26/0.61  thf(fact_7515_arctan,axiom,
% 0.26/0.61      ! [Y3: real] :
% 0.26/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y3 ) )
% 0.26/0.61        & ( ord_less_real @ ( arctan @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61        & ( ( tan_real @ ( arctan @ Y3 ) )
% 0.26/0.61          = Y3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % arctan
% 0.26/0.61  thf(fact_7516_arctan__tan,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.26/0.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61         => ( ( arctan @ ( tan_real @ X3 ) )
% 0.26/0.61            = X3 ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % arctan_tan
% 0.26/0.61  thf(fact_7517_arctan__unique,axiom,
% 0.26/0.61      ! [X3: real,Y3: real] :
% 0.26/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.26/0.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61         => ( ( ( tan_real @ X3 )
% 0.26/0.61              = Y3 )
% 0.26/0.61           => ( ( arctan @ Y3 )
% 0.26/0.61              = X3 ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % arctan_unique
% 0.26/0.61  thf(fact_7518_cos__one__2pi,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ( cos_real @ X3 )
% 0.26/0.61          = one_one_real )
% 0.26/0.61        = ( ? [X: nat] :
% 0.26/0.61              ( X3
% 0.26/0.61              = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 0.26/0.61          | ? [X: nat] :
% 0.26/0.61              ( X3
% 0.26/0.61              = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_one_2pi
% 0.26/0.61  thf(fact_7519_cos__double__sin,axiom,
% 0.26/0.61      ! [W: complex] :
% 0.26/0.61        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 0.26/0.61        = ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( sin_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_double_sin
% 0.26/0.61  thf(fact_7520_cos__double__sin,axiom,
% 0.26/0.61      ! [W: real] :
% 0.26/0.61        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 0.26/0.61        = ( minus_minus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( sin_real @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_double_sin
% 0.26/0.61  thf(fact_7521_minus__sin__cos__eq,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( uminus_uminus_real @ ( sin_real @ X3 ) )
% 0.26/0.61        = ( cos_real @ ( plus_plus_real @ X3 @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % minus_sin_cos_eq
% 0.26/0.61  thf(fact_7522_minus__sin__cos__eq,axiom,
% 0.26/0.61      ! [X3: complex] :
% 0.26/0.61        ( ( uminus1482373934393186551omplex @ ( sin_complex @ X3 ) )
% 0.26/0.61        = ( cos_complex @ ( plus_plus_complex @ X3 @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % minus_sin_cos_eq
% 0.26/0.61  thf(fact_7523_tan__total__pi4,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.26/0.61       => ? [Z3: real] :
% 0.26/0.61            ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z3 )
% 0.26/0.61            & ( ord_less_real @ Z3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.26/0.61            & ( ( tan_real @ Z3 )
% 0.26/0.61              = X3 ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % tan_total_pi4
% 0.26/0.61  thf(fact_7524_cos__arctan,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( cos_real @ ( arctan @ X3 ) )
% 0.26/0.61        = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_arctan
% 0.26/0.61  thf(fact_7525_sincos__total__pi,axiom,
% 0.26/0.61      ! [Y3: real,X3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.61       => ( ( ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.61            = one_one_real )
% 0.26/0.61         => ? [T3: real] :
% 0.26/0.61              ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 0.26/0.61              & ( ord_less_eq_real @ T3 @ pi )
% 0.26/0.61              & ( X3
% 0.26/0.61                = ( cos_real @ T3 ) )
% 0.26/0.61              & ( Y3
% 0.26/0.61                = ( sin_real @ T3 ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sincos_total_pi
% 0.26/0.61  thf(fact_7526_sin__cos__sqrt,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X3 ) )
% 0.26/0.61       => ( ( sin_real @ X3 )
% 0.26/0.61          = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_cos_sqrt
% 0.26/0.61  thf(fact_7527_sin__expansion__lemma,axiom,
% 0.26/0.61      ! [X3: real,M: nat] :
% 0.26/0.61        ( ( sin_real @ ( plus_plus_real @ X3 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.26/0.61        = ( cos_real @ ( plus_plus_real @ X3 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_expansion_lemma
% 0.26/0.61  thf(fact_7528_cos__zero__iff__int,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ( cos_real @ X3 )
% 0.26/0.61          = zero_zero_real )
% 0.26/0.61        = ( ? [I4: int] :
% 0.26/0.61              ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I4 )
% 0.26/0.61              & ( X3
% 0.26/0.61                = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_zero_iff_int
% 0.26/0.61  thf(fact_7529_vebt__buildup_Osimps_I3_J,axiom,
% 0.26/0.61      ! [Va2: nat] :
% 0.26/0.61        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.26/0.61         => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 0.26/0.61            = ( 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 ) ) ) ) ) ) )
% 0.26/0.61        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.26/0.61         => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 0.26/0.61            = ( 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 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % vebt_buildup.simps(3)
% 0.26/0.61  thf(fact_7530_cos__zero__lemma,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.61       => ( ( ( cos_real @ X3 )
% 0.26/0.61            = zero_zero_real )
% 0.26/0.61         => ? [N2: nat] :
% 0.26/0.61              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.26/0.61              & ( X3
% 0.26/0.61                = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_zero_lemma
% 0.26/0.61  thf(fact_7531_cos__zero__iff,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ( cos_real @ X3 )
% 0.26/0.61          = zero_zero_real )
% 0.26/0.61        = ( ? [N3: nat] :
% 0.26/0.61              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 0.26/0.61              & ( X3
% 0.26/0.61                = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.61          | ? [N3: nat] :
% 0.26/0.61              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 0.26/0.61              & ( X3
% 0.26/0.61                = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_zero_iff
% 0.26/0.61  thf(fact_7532_cos__expansion__lemma,axiom,
% 0.26/0.61      ! [X3: real,M: nat] :
% 0.26/0.61        ( ( cos_real @ ( plus_plus_real @ X3 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.26/0.61        = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X3 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_expansion_lemma
% 0.26/0.61  thf(fact_7533_sincos__total__pi__half,axiom,
% 0.26/0.61      ! [X3: real,Y3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.61       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.61         => ( ( ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.61              = one_one_real )
% 0.26/0.61           => ? [T3: real] :
% 0.26/0.61                ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 0.26/0.61                & ( ord_less_eq_real @ T3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.61                & ( X3
% 0.26/0.61                  = ( cos_real @ T3 ) )
% 0.26/0.61                & ( Y3
% 0.26/0.61                  = ( sin_real @ T3 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sincos_total_pi_half
% 0.26/0.61  thf(fact_7534_sincos__total__2pi__le,axiom,
% 0.26/0.61      ! [X3: real,Y3: real] :
% 0.26/0.61        ( ( ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.61          = one_one_real )
% 0.26/0.61       => ? [T3: real] :
% 0.26/0.61            ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 0.26/0.61            & ( ord_less_eq_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.26/0.61            & ( X3
% 0.26/0.61              = ( cos_real @ T3 ) )
% 0.26/0.61            & ( Y3
% 0.26/0.61              = ( sin_real @ T3 ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sincos_total_2pi_le
% 0.26/0.61  thf(fact_7535_complex__unimodular__polar,axiom,
% 0.26/0.61      ! [Z: complex] :
% 0.26/0.61        ( ( ( real_V1022390504157884413omplex @ Z )
% 0.26/0.61          = one_one_real )
% 0.26/0.61       => ~ ! [T3: real] :
% 0.26/0.61              ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 0.26/0.61             => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.26/0.61               => ( Z
% 0.26/0.61                 != ( complex2 @ ( cos_real @ T3 ) @ ( sin_real @ T3 ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % complex_unimodular_polar
% 0.26/0.61  thf(fact_7536_obtain__set__succ,axiom,
% 0.26/0.61      ! [X3: nat,Z: nat,A3: set_nat,B5: set_nat] :
% 0.26/0.61        ( ( ord_less_nat @ X3 @ Z )
% 0.26/0.61       => ( ( vEBT_VEBT_max_in_set @ A3 @ Z )
% 0.26/0.61         => ( ( finite_finite_nat @ B5 )
% 0.26/0.61           => ( ( A3 = B5 )
% 0.26/0.61             => ? [X_1: nat] : ( vEBT_is_succ_in_set @ A3 @ X3 @ X_1 ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % obtain_set_succ
% 0.26/0.61  thf(fact_7537_obtain__set__pred,axiom,
% 0.26/0.61      ! [Z: nat,X3: nat,A3: set_nat] :
% 0.26/0.61        ( ( ord_less_nat @ Z @ X3 )
% 0.26/0.61       => ( ( vEBT_VEBT_min_in_set @ A3 @ Z )
% 0.26/0.61         => ( ( finite_finite_nat @ A3 )
% 0.26/0.61           => ? [X_1: nat] : ( vEBT_is_pred_in_set @ A3 @ X3 @ X_1 ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % obtain_set_pred
% 0.26/0.61  thf(fact_7538_cos__arcsin,axiom,
% 0.26/0.61      ! [X3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.26/0.61       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 0.26/0.61         => ( ( cos_real @ ( arcsin @ X3 ) )
% 0.26/0.61            = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % cos_arcsin
% 0.26/0.61  thf(fact_7539_sum__gp,axiom,
% 0.26/0.61      ! [N: nat,M: nat,X3: complex] :
% 0.26/0.61        ( ( ( ord_less_nat @ N @ M )
% 0.26/0.61         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.61            = zero_zero_complex ) )
% 0.26/0.61        & ( ~ ( ord_less_nat @ N @ M )
% 0.26/0.61         => ( ( ( X3 = one_one_complex )
% 0.26/0.61             => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.61                = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 0.26/0.61            & ( ( X3 != one_one_complex )
% 0.26/0.61             => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.61                = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X3 @ M ) @ ( power_power_complex @ X3 @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X3 ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_gp
% 0.26/0.61  thf(fact_7540_sum__gp,axiom,
% 0.26/0.61      ! [N: nat,M: nat,X3: rat] :
% 0.26/0.61        ( ( ( ord_less_nat @ N @ M )
% 0.26/0.61         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.61            = zero_zero_rat ) )
% 0.26/0.61        & ( ~ ( ord_less_nat @ N @ M )
% 0.26/0.61         => ( ( ( X3 = one_one_rat )
% 0.26/0.61             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.61                = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 0.26/0.61            & ( ( X3 != one_one_rat )
% 0.26/0.61             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.61                = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X3 @ M ) @ ( power_power_rat @ X3 @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X3 ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_gp
% 0.26/0.61  thf(fact_7541_sum__gp,axiom,
% 0.26/0.61      ! [N: nat,M: nat,X3: real] :
% 0.26/0.61        ( ( ( ord_less_nat @ N @ M )
% 0.26/0.61         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.61            = zero_zero_real ) )
% 0.26/0.61        & ( ~ ( ord_less_nat @ N @ M )
% 0.26/0.61         => ( ( ( X3 = one_one_real )
% 0.26/0.61             => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.61                = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 0.26/0.61            & ( ( X3 != one_one_real )
% 0.26/0.61             => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.61                = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X3 @ M ) @ ( power_power_real @ X3 @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_gp
% 0.26/0.61  thf(fact_7542_set__vebt__finite,axiom,
% 0.26/0.61      ! [T: vEBT_VEBT,N: nat] :
% 0.26/0.61        ( ( vEBT_invar_vebt @ T @ N )
% 0.26/0.61       => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % set_vebt_finite
% 0.26/0.61  thf(fact_7543_pred__none__empty,axiom,
% 0.26/0.61      ! [Xs2: set_nat,A: nat] :
% 0.26/0.61        ( ~ ? [X_1: nat] : ( vEBT_is_pred_in_set @ Xs2 @ A @ X_1 )
% 0.26/0.61       => ( ( finite_finite_nat @ Xs2 )
% 0.26/0.61         => ~ ? [X6: nat] :
% 0.26/0.61                ( ( member_nat @ X6 @ Xs2 )
% 0.26/0.61                & ( ord_less_nat @ X6 @ A ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % pred_none_empty
% 0.26/0.61  thf(fact_7544_succ__none__empty,axiom,
% 0.26/0.61      ! [Xs2: set_nat,A: nat] :
% 0.26/0.61        ( ~ ? [X_1: nat] : ( vEBT_is_succ_in_set @ Xs2 @ A @ X_1 )
% 0.26/0.61       => ( ( finite_finite_nat @ Xs2 )
% 0.26/0.61         => ~ ? [X6: nat] :
% 0.26/0.61                ( ( member_nat @ X6 @ Xs2 )
% 0.26/0.61                & ( ord_less_nat @ A @ X6 ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % succ_none_empty
% 0.26/0.61  thf(fact_7545_arcsin__0,axiom,
% 0.26/0.61      ( ( arcsin @ zero_zero_real )
% 0.26/0.61      = zero_zero_real ) ).
% 0.26/0.61  
% 0.26/0.61  % arcsin_0
% 0.26/0.61  thf(fact_7546_sum_Oneutral__const,axiom,
% 0.26/0.61      ! [A3: set_nat] :
% 0.26/0.61        ( ( groups3542108847815614940at_nat
% 0.26/0.61          @ ^ [Uu3: nat] : zero_zero_nat
% 0.26/0.61          @ A3 )
% 0.26/0.61        = zero_zero_nat ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.neutral_const
% 0.26/0.61  thf(fact_7547_sum_Oneutral__const,axiom,
% 0.26/0.61      ! [A3: set_complex] :
% 0.26/0.61        ( ( groups7754918857620584856omplex
% 0.26/0.61          @ ^ [Uu3: complex] : zero_zero_complex
% 0.26/0.61          @ A3 )
% 0.26/0.61        = zero_zero_complex ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.neutral_const
% 0.26/0.61  thf(fact_7548_sum_Oneutral__const,axiom,
% 0.26/0.61      ! [A3: set_nat] :
% 0.26/0.61        ( ( groups6591440286371151544t_real
% 0.26/0.61          @ ^ [Uu3: nat] : zero_zero_real
% 0.26/0.61          @ A3 )
% 0.26/0.61        = zero_zero_real ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.neutral_const
% 0.26/0.61  thf(fact_7549_sum_Oneutral__const,axiom,
% 0.26/0.61      ! [A3: set_int] :
% 0.26/0.61        ( ( groups4538972089207619220nt_int
% 0.26/0.61          @ ^ [Uu3: int] : zero_zero_int
% 0.26/0.61          @ A3 )
% 0.26/0.61        = zero_zero_int ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.neutral_const
% 0.26/0.61  thf(fact_7550_of__nat__sum,axiom,
% 0.26/0.61      ! [F: complex > nat,A3: set_complex] :
% 0.26/0.61        ( ( semiri8010041392384452111omplex @ ( groups5693394587270226106ex_nat @ F @ A3 ) )
% 0.26/0.61        = ( groups7754918857620584856omplex
% 0.26/0.61          @ ^ [X: complex] : ( semiri8010041392384452111omplex @ ( F @ X ) )
% 0.26/0.61          @ A3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % of_nat_sum
% 0.26/0.61  thf(fact_7551_of__nat__sum,axiom,
% 0.26/0.61      ! [F: int > nat,A3: set_int] :
% 0.26/0.61        ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A3 ) )
% 0.26/0.61        = ( groups4538972089207619220nt_int
% 0.26/0.61          @ ^ [X: int] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 0.26/0.61          @ A3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % of_nat_sum
% 0.26/0.61  thf(fact_7552_of__nat__sum,axiom,
% 0.26/0.61      ! [F: nat > nat,A3: set_nat] :
% 0.26/0.61        ( ( semiri8010041392384452111omplex @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 0.26/0.61        = ( groups2073611262835488442omplex
% 0.26/0.61          @ ^ [X: nat] : ( semiri8010041392384452111omplex @ ( F @ X ) )
% 0.26/0.61          @ A3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % of_nat_sum
% 0.26/0.61  thf(fact_7553_of__nat__sum,axiom,
% 0.26/0.61      ! [F: nat > nat,A3: set_nat] :
% 0.26/0.61        ( ( semiri681578069525770553at_rat @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 0.26/0.61        = ( groups2906978787729119204at_rat
% 0.26/0.61          @ ^ [X: nat] : ( semiri681578069525770553at_rat @ ( F @ X ) )
% 0.26/0.61          @ A3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % of_nat_sum
% 0.26/0.61  thf(fact_7554_of__nat__sum,axiom,
% 0.26/0.61      ! [F: nat > nat,A3: set_nat] :
% 0.26/0.61        ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 0.26/0.61        = ( groups3539618377306564664at_int
% 0.26/0.61          @ ^ [X: nat] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 0.26/0.61          @ A3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % of_nat_sum
% 0.26/0.61  thf(fact_7555_of__nat__sum,axiom,
% 0.26/0.61      ! [F: nat > nat,A3: set_nat] :
% 0.26/0.61        ( ( semiri1316708129612266289at_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 0.26/0.61        = ( groups3542108847815614940at_nat
% 0.26/0.61          @ ^ [X: nat] : ( semiri1316708129612266289at_nat @ ( F @ X ) )
% 0.26/0.61          @ A3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % of_nat_sum
% 0.26/0.61  thf(fact_7556_of__nat__sum,axiom,
% 0.26/0.61      ! [F: nat > nat,A3: set_nat] :
% 0.26/0.61        ( ( semiri5074537144036343181t_real @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 0.26/0.61        = ( groups6591440286371151544t_real
% 0.26/0.61          @ ^ [X: nat] : ( semiri5074537144036343181t_real @ ( F @ X ) )
% 0.26/0.61          @ A3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % of_nat_sum
% 0.26/0.61  thf(fact_7557_of__int__sum,axiom,
% 0.26/0.61      ! [F: complex > int,A3: set_complex] :
% 0.26/0.61        ( ( ring_17405671764205052669omplex @ ( groups5690904116761175830ex_int @ F @ A3 ) )
% 0.26/0.61        = ( groups7754918857620584856omplex
% 0.26/0.61          @ ^ [X: complex] : ( ring_17405671764205052669omplex @ ( F @ X ) )
% 0.26/0.61          @ A3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % of_int_sum
% 0.26/0.61  thf(fact_7558_of__int__sum,axiom,
% 0.26/0.61      ! [F: nat > int,A3: set_nat] :
% 0.26/0.61        ( ( ring_1_of_int_real @ ( groups3539618377306564664at_int @ F @ A3 ) )
% 0.26/0.61        = ( groups6591440286371151544t_real
% 0.26/0.61          @ ^ [X: nat] : ( ring_1_of_int_real @ ( F @ X ) )
% 0.26/0.61          @ A3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % of_int_sum
% 0.26/0.61  thf(fact_7559_of__int__sum,axiom,
% 0.26/0.61      ! [F: int > int,A3: set_int] :
% 0.26/0.61        ( ( ring_1_of_int_real @ ( groups4538972089207619220nt_int @ F @ A3 ) )
% 0.26/0.61        = ( groups8778361861064173332t_real
% 0.26/0.61          @ ^ [X: int] : ( ring_1_of_int_real @ ( F @ X ) )
% 0.26/0.61          @ A3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % of_int_sum
% 0.26/0.61  thf(fact_7560_of__int__sum,axiom,
% 0.26/0.61      ! [F: int > int,A3: set_int] :
% 0.26/0.61        ( ( ring_17405671764205052669omplex @ ( groups4538972089207619220nt_int @ F @ A3 ) )
% 0.26/0.61        = ( groups3049146728041665814omplex
% 0.26/0.61          @ ^ [X: int] : ( ring_17405671764205052669omplex @ ( F @ X ) )
% 0.26/0.61          @ A3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % of_int_sum
% 0.26/0.61  thf(fact_7561_of__int__sum,axiom,
% 0.26/0.61      ! [F: int > int,A3: set_int] :
% 0.26/0.61        ( ( ring_1_of_int_rat @ ( groups4538972089207619220nt_int @ F @ A3 ) )
% 0.26/0.61        = ( groups3906332499630173760nt_rat
% 0.26/0.61          @ ^ [X: int] : ( ring_1_of_int_rat @ ( F @ X ) )
% 0.26/0.61          @ A3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % of_int_sum
% 0.26/0.61  thf(fact_7562_of__int__sum,axiom,
% 0.26/0.61      ! [F: int > int,A3: set_int] :
% 0.26/0.61        ( ( ring_1_of_int_int @ ( groups4538972089207619220nt_int @ F @ A3 ) )
% 0.26/0.61        = ( groups4538972089207619220nt_int
% 0.26/0.61          @ ^ [X: int] : ( ring_1_of_int_int @ ( F @ X ) )
% 0.26/0.61          @ A3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % of_int_sum
% 0.26/0.61  thf(fact_7563_sum_Oempty,axiom,
% 0.26/0.61      ! [G: extended_enat > real] :
% 0.26/0.61        ( ( groups4148127829035722712t_real @ G @ bot_bo7653980558646680370d_enat )
% 0.26/0.61        = zero_zero_real ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.empty
% 0.26/0.61  thf(fact_7564_sum_Oempty,axiom,
% 0.26/0.61      ! [G: extended_enat > rat] :
% 0.26/0.61        ( ( groups1392844769737527556at_rat @ G @ bot_bo7653980558646680370d_enat )
% 0.26/0.61        = zero_zero_rat ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.empty
% 0.26/0.61  thf(fact_7565_sum_Oempty,axiom,
% 0.26/0.61      ! [G: extended_enat > nat] :
% 0.26/0.61        ( ( groups2027974829824023292at_nat @ G @ bot_bo7653980558646680370d_enat )
% 0.26/0.61        = zero_zero_nat ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.empty
% 0.26/0.61  thf(fact_7566_sum_Oempty,axiom,
% 0.26/0.61      ! [G: extended_enat > int] :
% 0.26/0.61        ( ( groups2025484359314973016at_int @ G @ bot_bo7653980558646680370d_enat )
% 0.26/0.61        = zero_zero_int ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.empty
% 0.26/0.61  thf(fact_7567_sum_Oempty,axiom,
% 0.26/0.61      ! [G: real > real] :
% 0.26/0.61        ( ( groups8097168146408367636l_real @ G @ bot_bot_set_real )
% 0.26/0.61        = zero_zero_real ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.empty
% 0.26/0.61  thf(fact_7568_sum_Oempty,axiom,
% 0.26/0.61      ! [G: real > rat] :
% 0.26/0.61        ( ( groups1300246762558778688al_rat @ G @ bot_bot_set_real )
% 0.26/0.61        = zero_zero_rat ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.empty
% 0.26/0.61  thf(fact_7569_sum_Oempty,axiom,
% 0.26/0.61      ! [G: real > nat] :
% 0.26/0.61        ( ( groups1935376822645274424al_nat @ G @ bot_bot_set_real )
% 0.26/0.61        = zero_zero_nat ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.empty
% 0.26/0.61  thf(fact_7570_sum_Oempty,axiom,
% 0.26/0.61      ! [G: real > int] :
% 0.26/0.61        ( ( groups1932886352136224148al_int @ G @ bot_bot_set_real )
% 0.26/0.61        = zero_zero_int ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.empty
% 0.26/0.61  thf(fact_7571_sum_Oempty,axiom,
% 0.26/0.61      ! [G: nat > rat] :
% 0.26/0.61        ( ( groups2906978787729119204at_rat @ G @ bot_bot_set_nat )
% 0.26/0.61        = zero_zero_rat ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.empty
% 0.26/0.61  thf(fact_7572_sum_Oempty,axiom,
% 0.26/0.61      ! [G: nat > int] :
% 0.26/0.61        ( ( groups3539618377306564664at_int @ G @ bot_bot_set_nat )
% 0.26/0.61        = zero_zero_int ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.empty
% 0.26/0.61  thf(fact_7573_sum_Oinfinite,axiom,
% 0.26/0.61      ! [A3: set_int,G: int > real] :
% 0.26/0.61        ( ~ ( finite_finite_int @ A3 )
% 0.26/0.61       => ( ( groups8778361861064173332t_real @ G @ A3 )
% 0.26/0.61          = zero_zero_real ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.infinite
% 0.26/0.61  thf(fact_7574_sum_Oinfinite,axiom,
% 0.26/0.61      ! [A3: set_complex,G: complex > real] :
% 0.26/0.61        ( ~ ( finite3207457112153483333omplex @ A3 )
% 0.26/0.61       => ( ( groups5808333547571424918x_real @ G @ A3 )
% 0.26/0.61          = zero_zero_real ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.infinite
% 0.26/0.61  thf(fact_7575_sum_Oinfinite,axiom,
% 0.26/0.61      ! [A3: set_Extended_enat,G: extended_enat > real] :
% 0.26/0.61        ( ~ ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.61       => ( ( groups4148127829035722712t_real @ G @ A3 )
% 0.26/0.61          = zero_zero_real ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.infinite
% 0.26/0.61  thf(fact_7576_sum_Oinfinite,axiom,
% 0.26/0.61      ! [A3: set_nat,G: nat > rat] :
% 0.26/0.61        ( ~ ( finite_finite_nat @ A3 )
% 0.26/0.61       => ( ( groups2906978787729119204at_rat @ G @ A3 )
% 0.26/0.61          = zero_zero_rat ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.infinite
% 0.26/0.61  thf(fact_7577_sum_Oinfinite,axiom,
% 0.26/0.61      ! [A3: set_int,G: int > rat] :
% 0.26/0.61        ( ~ ( finite_finite_int @ A3 )
% 0.26/0.61       => ( ( groups3906332499630173760nt_rat @ G @ A3 )
% 0.26/0.61          = zero_zero_rat ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.infinite
% 0.26/0.61  thf(fact_7578_sum_Oinfinite,axiom,
% 0.26/0.61      ! [A3: set_complex,G: complex > rat] :
% 0.26/0.61        ( ~ ( finite3207457112153483333omplex @ A3 )
% 0.26/0.61       => ( ( groups5058264527183730370ex_rat @ G @ A3 )
% 0.26/0.61          = zero_zero_rat ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.infinite
% 0.26/0.61  thf(fact_7579_sum_Oinfinite,axiom,
% 0.26/0.61      ! [A3: set_Extended_enat,G: extended_enat > rat] :
% 0.26/0.61        ( ~ ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.61       => ( ( groups1392844769737527556at_rat @ G @ A3 )
% 0.26/0.61          = zero_zero_rat ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.infinite
% 0.26/0.61  thf(fact_7580_sum_Oinfinite,axiom,
% 0.26/0.61      ! [A3: set_int,G: int > nat] :
% 0.26/0.61        ( ~ ( finite_finite_int @ A3 )
% 0.26/0.61       => ( ( groups4541462559716669496nt_nat @ G @ A3 )
% 0.26/0.61          = zero_zero_nat ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.infinite
% 0.26/0.61  thf(fact_7581_sum_Oinfinite,axiom,
% 0.26/0.61      ! [A3: set_complex,G: complex > nat] :
% 0.26/0.61        ( ~ ( finite3207457112153483333omplex @ A3 )
% 0.26/0.61       => ( ( groups5693394587270226106ex_nat @ G @ A3 )
% 0.26/0.61          = zero_zero_nat ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.infinite
% 0.26/0.61  thf(fact_7582_sum_Oinfinite,axiom,
% 0.26/0.61      ! [A3: set_Extended_enat,G: extended_enat > nat] :
% 0.26/0.61        ( ~ ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.61       => ( ( groups2027974829824023292at_nat @ G @ A3 )
% 0.26/0.61          = zero_zero_nat ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.infinite
% 0.26/0.61  thf(fact_7583_sum__eq__0__iff,axiom,
% 0.26/0.61      ! [F4: set_int,F: int > nat] :
% 0.26/0.61        ( ( finite_finite_int @ F4 )
% 0.26/0.61       => ( ( ( groups4541462559716669496nt_nat @ F @ F4 )
% 0.26/0.61            = zero_zero_nat )
% 0.26/0.61          = ( ! [X: int] :
% 0.26/0.61                ( ( member_int @ X @ F4 )
% 0.26/0.61               => ( ( F @ X )
% 0.26/0.61                  = zero_zero_nat ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_eq_0_iff
% 0.26/0.61  thf(fact_7584_sum__eq__0__iff,axiom,
% 0.26/0.61      ! [F4: set_complex,F: complex > nat] :
% 0.26/0.61        ( ( finite3207457112153483333omplex @ F4 )
% 0.26/0.61       => ( ( ( groups5693394587270226106ex_nat @ F @ F4 )
% 0.26/0.61            = zero_zero_nat )
% 0.26/0.61          = ( ! [X: complex] :
% 0.26/0.61                ( ( member_complex @ X @ F4 )
% 0.26/0.61               => ( ( F @ X )
% 0.26/0.61                  = zero_zero_nat ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_eq_0_iff
% 0.26/0.61  thf(fact_7585_sum__eq__0__iff,axiom,
% 0.26/0.61      ! [F4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 0.26/0.61        ( ( finite6177210948735845034at_nat @ F4 )
% 0.26/0.61       => ( ( ( groups977919841031483927at_nat @ F @ F4 )
% 0.26/0.61            = zero_zero_nat )
% 0.26/0.61          = ( ! [X: product_prod_nat_nat] :
% 0.26/0.61                ( ( member8440522571783428010at_nat @ X @ F4 )
% 0.26/0.61               => ( ( F @ X )
% 0.26/0.61                  = zero_zero_nat ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_eq_0_iff
% 0.26/0.61  thf(fact_7586_sum__eq__0__iff,axiom,
% 0.26/0.61      ! [F4: set_Extended_enat,F: extended_enat > nat] :
% 0.26/0.61        ( ( finite4001608067531595151d_enat @ F4 )
% 0.26/0.61       => ( ( ( groups2027974829824023292at_nat @ F @ F4 )
% 0.26/0.61            = zero_zero_nat )
% 0.26/0.61          = ( ! [X: extended_enat] :
% 0.26/0.61                ( ( member_Extended_enat @ X @ F4 )
% 0.26/0.61               => ( ( F @ X )
% 0.26/0.61                  = zero_zero_nat ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_eq_0_iff
% 0.26/0.61  thf(fact_7587_sum__eq__0__iff,axiom,
% 0.26/0.61      ! [F4: set_nat,F: nat > nat] :
% 0.26/0.61        ( ( finite_finite_nat @ F4 )
% 0.26/0.61       => ( ( ( groups3542108847815614940at_nat @ F @ F4 )
% 0.26/0.61            = zero_zero_nat )
% 0.26/0.61          = ( ! [X: nat] :
% 0.26/0.61                ( ( member_nat @ X @ F4 )
% 0.26/0.61               => ( ( F @ X )
% 0.26/0.61                  = zero_zero_nat ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_eq_0_iff
% 0.26/0.61  thf(fact_7588_prod__zero__iff,axiom,
% 0.26/0.61      ! [A3: set_nat,F: nat > real] :
% 0.26/0.61        ( ( finite_finite_nat @ A3 )
% 0.26/0.61       => ( ( ( groups129246275422532515t_real @ F @ A3 )
% 0.26/0.61            = zero_zero_real )
% 0.26/0.61          = ( ? [X: nat] :
% 0.26/0.61                ( ( member_nat @ X @ A3 )
% 0.26/0.61                & ( ( F @ X )
% 0.26/0.61                  = zero_zero_real ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % prod_zero_iff
% 0.26/0.61  thf(fact_7589_prod__zero__iff,axiom,
% 0.26/0.61      ! [A3: set_int,F: int > real] :
% 0.26/0.61        ( ( finite_finite_int @ A3 )
% 0.26/0.61       => ( ( ( groups2316167850115554303t_real @ F @ A3 )
% 0.26/0.61            = zero_zero_real )
% 0.26/0.61          = ( ? [X: int] :
% 0.26/0.61                ( ( member_int @ X @ A3 )
% 0.26/0.61                & ( ( F @ X )
% 0.26/0.61                  = zero_zero_real ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % prod_zero_iff
% 0.26/0.61  thf(fact_7590_prod__zero__iff,axiom,
% 0.26/0.61      ! [A3: set_complex,F: complex > real] :
% 0.26/0.61        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.61       => ( ( ( groups766887009212190081x_real @ F @ A3 )
% 0.26/0.61            = zero_zero_real )
% 0.26/0.61          = ( ? [X: complex] :
% 0.26/0.61                ( ( member_complex @ X @ A3 )
% 0.26/0.61                & ( ( F @ X )
% 0.26/0.61                  = zero_zero_real ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % prod_zero_iff
% 0.26/0.61  thf(fact_7591_prod__zero__iff,axiom,
% 0.26/0.61      ! [A3: set_Extended_enat,F: extended_enat > real] :
% 0.26/0.61        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.61       => ( ( ( groups97031904164794029t_real @ F @ A3 )
% 0.26/0.61            = zero_zero_real )
% 0.26/0.61          = ( ? [X: extended_enat] :
% 0.26/0.61                ( ( member_Extended_enat @ X @ A3 )
% 0.26/0.61                & ( ( F @ X )
% 0.26/0.61                  = zero_zero_real ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % prod_zero_iff
% 0.26/0.61  thf(fact_7592_prod__zero__iff,axiom,
% 0.26/0.61      ! [A3: set_nat,F: nat > rat] :
% 0.26/0.61        ( ( finite_finite_nat @ A3 )
% 0.26/0.61       => ( ( ( groups73079841787564623at_rat @ F @ A3 )
% 0.26/0.61            = zero_zero_rat )
% 0.26/0.61          = ( ? [X: nat] :
% 0.26/0.61                ( ( member_nat @ X @ A3 )
% 0.26/0.61                & ( ( F @ X )
% 0.26/0.61                  = zero_zero_rat ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % prod_zero_iff
% 0.26/0.61  thf(fact_7593_prod__zero__iff,axiom,
% 0.26/0.61      ! [A3: set_int,F: int > rat] :
% 0.26/0.61        ( ( finite_finite_int @ A3 )
% 0.26/0.61       => ( ( ( groups1072433553688619179nt_rat @ F @ A3 )
% 0.26/0.61            = zero_zero_rat )
% 0.26/0.61          = ( ? [X: int] :
% 0.26/0.61                ( ( member_int @ X @ A3 )
% 0.26/0.61                & ( ( F @ X )
% 0.26/0.61                  = zero_zero_rat ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % prod_zero_iff
% 0.26/0.61  thf(fact_7594_prod__zero__iff,axiom,
% 0.26/0.61      ! [A3: set_complex,F: complex > rat] :
% 0.26/0.61        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.61       => ( ( ( groups225925009352817453ex_rat @ F @ A3 )
% 0.26/0.61            = zero_zero_rat )
% 0.26/0.61          = ( ? [X: complex] :
% 0.26/0.61                ( ( member_complex @ X @ A3 )
% 0.26/0.61                & ( ( F @ X )
% 0.26/0.61                  = zero_zero_rat ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % prod_zero_iff
% 0.26/0.61  thf(fact_7595_prod__zero__iff,axiom,
% 0.26/0.61      ! [A3: set_Extended_enat,F: extended_enat > rat] :
% 0.26/0.61        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.61       => ( ( ( groups2245840878043517529at_rat @ F @ A3 )
% 0.26/0.61            = zero_zero_rat )
% 0.26/0.61          = ( ? [X: extended_enat] :
% 0.26/0.61                ( ( member_Extended_enat @ X @ A3 )
% 0.26/0.61                & ( ( F @ X )
% 0.26/0.61                  = zero_zero_rat ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % prod_zero_iff
% 0.26/0.61  thf(fact_7596_prod__zero__iff,axiom,
% 0.26/0.61      ! [A3: set_int,F: int > nat] :
% 0.26/0.61        ( ( finite_finite_int @ A3 )
% 0.26/0.61       => ( ( ( groups1707563613775114915nt_nat @ F @ A3 )
% 0.26/0.61            = zero_zero_nat )
% 0.26/0.61          = ( ? [X: int] :
% 0.26/0.61                ( ( member_int @ X @ A3 )
% 0.26/0.61                & ( ( F @ X )
% 0.26/0.61                  = zero_zero_nat ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % prod_zero_iff
% 0.26/0.61  thf(fact_7597_prod__zero__iff,axiom,
% 0.26/0.61      ! [A3: set_complex,F: complex > nat] :
% 0.26/0.61        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.61       => ( ( ( groups861055069439313189ex_nat @ F @ A3 )
% 0.26/0.61            = zero_zero_nat )
% 0.26/0.61          = ( ? [X: complex] :
% 0.26/0.61                ( ( member_complex @ X @ A3 )
% 0.26/0.61                & ( ( F @ X )
% 0.26/0.61                  = zero_zero_nat ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % prod_zero_iff
% 0.26/0.61  thf(fact_7598_infinite__Icc__iff,axiom,
% 0.26/0.61      ! [A: rat,B: rat] :
% 0.26/0.61        ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 0.26/0.61        = ( ord_less_rat @ A @ B ) ) ).
% 0.26/0.61  
% 0.26/0.61  % infinite_Icc_iff
% 0.26/0.61  thf(fact_7599_infinite__Icc__iff,axiom,
% 0.26/0.61      ! [A: real,B: real] :
% 0.26/0.61        ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) )
% 0.26/0.61        = ( ord_less_real @ A @ B ) ) ).
% 0.26/0.61  
% 0.26/0.61  % infinite_Icc_iff
% 0.26/0.61  thf(fact_7600_sum_Odelta_H,axiom,
% 0.26/0.61      ! [S2: set_real,A: real,B: real > real] :
% 0.26/0.61        ( ( finite_finite_real @ S2 )
% 0.26/0.61       => ( ( ( member_real @ A @ S2 )
% 0.26/0.61           => ( ( groups8097168146408367636l_real
% 0.26/0.61                @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = ( B @ A ) ) )
% 0.26/0.61          & ( ~ ( member_real @ A @ S2 )
% 0.26/0.61           => ( ( groups8097168146408367636l_real
% 0.26/0.61                @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = zero_zero_real ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.delta'
% 0.26/0.61  thf(fact_7601_sum_Odelta_H,axiom,
% 0.26/0.61      ! [S2: set_int,A: int,B: int > real] :
% 0.26/0.61        ( ( finite_finite_int @ S2 )
% 0.26/0.61       => ( ( ( member_int @ A @ S2 )
% 0.26/0.61           => ( ( groups8778361861064173332t_real
% 0.26/0.61                @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = ( B @ A ) ) )
% 0.26/0.61          & ( ~ ( member_int @ A @ S2 )
% 0.26/0.61           => ( ( groups8778361861064173332t_real
% 0.26/0.61                @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = zero_zero_real ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.delta'
% 0.26/0.61  thf(fact_7602_sum_Odelta_H,axiom,
% 0.26/0.61      ! [S2: set_complex,A: complex,B: complex > real] :
% 0.26/0.61        ( ( finite3207457112153483333omplex @ S2 )
% 0.26/0.61       => ( ( ( member_complex @ A @ S2 )
% 0.26/0.61           => ( ( groups5808333547571424918x_real
% 0.26/0.61                @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = ( B @ A ) ) )
% 0.26/0.61          & ( ~ ( member_complex @ A @ S2 )
% 0.26/0.61           => ( ( groups5808333547571424918x_real
% 0.26/0.61                @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = zero_zero_real ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.delta'
% 0.26/0.61  thf(fact_7603_sum_Odelta_H,axiom,
% 0.26/0.61      ! [S2: set_Extended_enat,A: extended_enat,B: extended_enat > real] :
% 0.26/0.61        ( ( finite4001608067531595151d_enat @ S2 )
% 0.26/0.61       => ( ( ( member_Extended_enat @ A @ S2 )
% 0.26/0.61           => ( ( groups4148127829035722712t_real
% 0.26/0.61                @ ^ [K3: extended_enat] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = ( B @ A ) ) )
% 0.26/0.61          & ( ~ ( member_Extended_enat @ A @ S2 )
% 0.26/0.61           => ( ( groups4148127829035722712t_real
% 0.26/0.61                @ ^ [K3: extended_enat] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = zero_zero_real ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.delta'
% 0.26/0.61  thf(fact_7604_sum_Odelta_H,axiom,
% 0.26/0.61      ! [S2: set_real,A: real,B: real > rat] :
% 0.26/0.61        ( ( finite_finite_real @ S2 )
% 0.26/0.61       => ( ( ( member_real @ A @ S2 )
% 0.26/0.61           => ( ( groups1300246762558778688al_rat
% 0.26/0.61                @ ^ [K3: real] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = ( B @ A ) ) )
% 0.26/0.61          & ( ~ ( member_real @ A @ S2 )
% 0.26/0.61           => ( ( groups1300246762558778688al_rat
% 0.26/0.61                @ ^ [K3: real] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = zero_zero_rat ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.delta'
% 0.26/0.61  thf(fact_7605_sum_Odelta_H,axiom,
% 0.26/0.61      ! [S2: set_nat,A: nat,B: nat > rat] :
% 0.26/0.61        ( ( finite_finite_nat @ S2 )
% 0.26/0.61       => ( ( ( member_nat @ A @ S2 )
% 0.26/0.61           => ( ( groups2906978787729119204at_rat
% 0.26/0.61                @ ^ [K3: nat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = ( B @ A ) ) )
% 0.26/0.61          & ( ~ ( member_nat @ A @ S2 )
% 0.26/0.61           => ( ( groups2906978787729119204at_rat
% 0.26/0.61                @ ^ [K3: nat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = zero_zero_rat ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.delta'
% 0.26/0.61  thf(fact_7606_sum_Odelta_H,axiom,
% 0.26/0.61      ! [S2: set_int,A: int,B: int > rat] :
% 0.26/0.61        ( ( finite_finite_int @ S2 )
% 0.26/0.61       => ( ( ( member_int @ A @ S2 )
% 0.26/0.61           => ( ( groups3906332499630173760nt_rat
% 0.26/0.61                @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = ( B @ A ) ) )
% 0.26/0.61          & ( ~ ( member_int @ A @ S2 )
% 0.26/0.61           => ( ( groups3906332499630173760nt_rat
% 0.26/0.61                @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = zero_zero_rat ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.delta'
% 0.26/0.61  thf(fact_7607_sum_Odelta_H,axiom,
% 0.26/0.61      ! [S2: set_complex,A: complex,B: complex > rat] :
% 0.26/0.61        ( ( finite3207457112153483333omplex @ S2 )
% 0.26/0.61       => ( ( ( member_complex @ A @ S2 )
% 0.26/0.61           => ( ( groups5058264527183730370ex_rat
% 0.26/0.61                @ ^ [K3: complex] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = ( B @ A ) ) )
% 0.26/0.61          & ( ~ ( member_complex @ A @ S2 )
% 0.26/0.61           => ( ( groups5058264527183730370ex_rat
% 0.26/0.61                @ ^ [K3: complex] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = zero_zero_rat ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.delta'
% 0.26/0.61  thf(fact_7608_sum_Odelta_H,axiom,
% 0.26/0.61      ! [S2: set_Extended_enat,A: extended_enat,B: extended_enat > rat] :
% 0.26/0.61        ( ( finite4001608067531595151d_enat @ S2 )
% 0.26/0.61       => ( ( ( member_Extended_enat @ A @ S2 )
% 0.26/0.61           => ( ( groups1392844769737527556at_rat
% 0.26/0.61                @ ^ [K3: extended_enat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = ( B @ A ) ) )
% 0.26/0.61          & ( ~ ( member_Extended_enat @ A @ S2 )
% 0.26/0.61           => ( ( groups1392844769737527556at_rat
% 0.26/0.61                @ ^ [K3: extended_enat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = zero_zero_rat ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.delta'
% 0.26/0.61  thf(fact_7609_sum_Odelta_H,axiom,
% 0.26/0.61      ! [S2: set_real,A: real,B: real > nat] :
% 0.26/0.61        ( ( finite_finite_real @ S2 )
% 0.26/0.61       => ( ( ( member_real @ A @ S2 )
% 0.26/0.61           => ( ( groups1935376822645274424al_nat
% 0.26/0.61                @ ^ [K3: real] : ( if_nat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_nat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = ( B @ A ) ) )
% 0.26/0.61          & ( ~ ( member_real @ A @ S2 )
% 0.26/0.61           => ( ( groups1935376822645274424al_nat
% 0.26/0.61                @ ^ [K3: real] : ( if_nat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_nat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = zero_zero_nat ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.delta'
% 0.26/0.61  thf(fact_7610_sum_Odelta,axiom,
% 0.26/0.61      ! [S2: set_real,A: real,B: real > real] :
% 0.26/0.61        ( ( finite_finite_real @ S2 )
% 0.26/0.61       => ( ( ( member_real @ A @ S2 )
% 0.26/0.61           => ( ( groups8097168146408367636l_real
% 0.26/0.61                @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = ( B @ A ) ) )
% 0.26/0.61          & ( ~ ( member_real @ A @ S2 )
% 0.26/0.61           => ( ( groups8097168146408367636l_real
% 0.26/0.61                @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = zero_zero_real ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.delta
% 0.26/0.61  thf(fact_7611_sum_Odelta,axiom,
% 0.26/0.61      ! [S2: set_int,A: int,B: int > real] :
% 0.26/0.61        ( ( finite_finite_int @ S2 )
% 0.26/0.61       => ( ( ( member_int @ A @ S2 )
% 0.26/0.61           => ( ( groups8778361861064173332t_real
% 0.26/0.61                @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = ( B @ A ) ) )
% 0.26/0.61          & ( ~ ( member_int @ A @ S2 )
% 0.26/0.61           => ( ( groups8778361861064173332t_real
% 0.26/0.61                @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = zero_zero_real ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.delta
% 0.26/0.61  thf(fact_7612_sum_Odelta,axiom,
% 0.26/0.61      ! [S2: set_complex,A: complex,B: complex > real] :
% 0.26/0.61        ( ( finite3207457112153483333omplex @ S2 )
% 0.26/0.61       => ( ( ( member_complex @ A @ S2 )
% 0.26/0.61           => ( ( groups5808333547571424918x_real
% 0.26/0.61                @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = ( B @ A ) ) )
% 0.26/0.61          & ( ~ ( member_complex @ A @ S2 )
% 0.26/0.61           => ( ( groups5808333547571424918x_real
% 0.26/0.61                @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = zero_zero_real ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.delta
% 0.26/0.61  thf(fact_7613_sum_Odelta,axiom,
% 0.26/0.61      ! [S2: set_Extended_enat,A: extended_enat,B: extended_enat > real] :
% 0.26/0.61        ( ( finite4001608067531595151d_enat @ S2 )
% 0.26/0.61       => ( ( ( member_Extended_enat @ A @ S2 )
% 0.26/0.61           => ( ( groups4148127829035722712t_real
% 0.26/0.61                @ ^ [K3: extended_enat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = ( B @ A ) ) )
% 0.26/0.61          & ( ~ ( member_Extended_enat @ A @ S2 )
% 0.26/0.61           => ( ( groups4148127829035722712t_real
% 0.26/0.61                @ ^ [K3: extended_enat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = zero_zero_real ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.delta
% 0.26/0.61  thf(fact_7614_sum_Odelta,axiom,
% 0.26/0.61      ! [S2: set_real,A: real,B: real > rat] :
% 0.26/0.61        ( ( finite_finite_real @ S2 )
% 0.26/0.61       => ( ( ( member_real @ A @ S2 )
% 0.26/0.61           => ( ( groups1300246762558778688al_rat
% 0.26/0.61                @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = ( B @ A ) ) )
% 0.26/0.61          & ( ~ ( member_real @ A @ S2 )
% 0.26/0.61           => ( ( groups1300246762558778688al_rat
% 0.26/0.61                @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = zero_zero_rat ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.delta
% 0.26/0.61  thf(fact_7615_sum_Odelta,axiom,
% 0.26/0.61      ! [S2: set_nat,A: nat,B: nat > rat] :
% 0.26/0.61        ( ( finite_finite_nat @ S2 )
% 0.26/0.61       => ( ( ( member_nat @ A @ S2 )
% 0.26/0.61           => ( ( groups2906978787729119204at_rat
% 0.26/0.61                @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = ( B @ A ) ) )
% 0.26/0.61          & ( ~ ( member_nat @ A @ S2 )
% 0.26/0.61           => ( ( groups2906978787729119204at_rat
% 0.26/0.61                @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = zero_zero_rat ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.delta
% 0.26/0.61  thf(fact_7616_sum_Odelta,axiom,
% 0.26/0.61      ! [S2: set_int,A: int,B: int > rat] :
% 0.26/0.61        ( ( finite_finite_int @ S2 )
% 0.26/0.61       => ( ( ( member_int @ A @ S2 )
% 0.26/0.61           => ( ( groups3906332499630173760nt_rat
% 0.26/0.61                @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = ( B @ A ) ) )
% 0.26/0.61          & ( ~ ( member_int @ A @ S2 )
% 0.26/0.61           => ( ( groups3906332499630173760nt_rat
% 0.26/0.61                @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = zero_zero_rat ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.delta
% 0.26/0.61  thf(fact_7617_sum_Odelta,axiom,
% 0.26/0.61      ! [S2: set_complex,A: complex,B: complex > rat] :
% 0.26/0.61        ( ( finite3207457112153483333omplex @ S2 )
% 0.26/0.61       => ( ( ( member_complex @ A @ S2 )
% 0.26/0.61           => ( ( groups5058264527183730370ex_rat
% 0.26/0.61                @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = ( B @ A ) ) )
% 0.26/0.61          & ( ~ ( member_complex @ A @ S2 )
% 0.26/0.61           => ( ( groups5058264527183730370ex_rat
% 0.26/0.61                @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = zero_zero_rat ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.delta
% 0.26/0.61  thf(fact_7618_sum_Odelta,axiom,
% 0.26/0.61      ! [S2: set_Extended_enat,A: extended_enat,B: extended_enat > rat] :
% 0.26/0.61        ( ( finite4001608067531595151d_enat @ S2 )
% 0.26/0.61       => ( ( ( member_Extended_enat @ A @ S2 )
% 0.26/0.61           => ( ( groups1392844769737527556at_rat
% 0.26/0.61                @ ^ [K3: extended_enat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = ( B @ A ) ) )
% 0.26/0.61          & ( ~ ( member_Extended_enat @ A @ S2 )
% 0.26/0.61           => ( ( groups1392844769737527556at_rat
% 0.26/0.61                @ ^ [K3: extended_enat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = zero_zero_rat ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.delta
% 0.26/0.61  thf(fact_7619_sum_Odelta,axiom,
% 0.26/0.61      ! [S2: set_real,A: real,B: real > nat] :
% 0.26/0.61        ( ( finite_finite_real @ S2 )
% 0.26/0.61       => ( ( ( member_real @ A @ S2 )
% 0.26/0.61           => ( ( groups1935376822645274424al_nat
% 0.26/0.61                @ ^ [K3: real] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_nat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = ( B @ A ) ) )
% 0.26/0.61          & ( ~ ( member_real @ A @ S2 )
% 0.26/0.61           => ( ( groups1935376822645274424al_nat
% 0.26/0.61                @ ^ [K3: real] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_nat )
% 0.26/0.61                @ S2 )
% 0.26/0.61              = zero_zero_nat ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.delta
% 0.26/0.61  thf(fact_7620_sum__abs,axiom,
% 0.26/0.61      ! [F: nat > real,A3: set_nat] :
% 0.26/0.61        ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A3 ) )
% 0.26/0.61        @ ( groups6591440286371151544t_real
% 0.26/0.61          @ ^ [I4: nat] : ( abs_abs_real @ ( F @ I4 ) )
% 0.26/0.61          @ A3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_abs
% 0.26/0.61  thf(fact_7621_sum__abs,axiom,
% 0.26/0.61      ! [F: int > int,A3: set_int] :
% 0.26/0.61        ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A3 ) )
% 0.26/0.61        @ ( groups4538972089207619220nt_int
% 0.26/0.61          @ ^ [I4: int] : ( abs_abs_int @ ( F @ I4 ) )
% 0.26/0.61          @ A3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_abs
% 0.26/0.61  thf(fact_7622_summable__If__finite__set,axiom,
% 0.26/0.61      ! [A3: set_nat,F: nat > real] :
% 0.26/0.61        ( ( finite_finite_nat @ A3 )
% 0.26/0.61       => ( summable_real
% 0.26/0.61          @ ^ [R5: nat] : ( if_real @ ( member_nat @ R5 @ A3 ) @ ( F @ R5 ) @ zero_zero_real ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % summable_If_finite_set
% 0.26/0.61  thf(fact_7623_summable__If__finite__set,axiom,
% 0.26/0.61      ! [A3: set_nat,F: nat > nat] :
% 0.26/0.61        ( ( finite_finite_nat @ A3 )
% 0.26/0.61       => ( summable_nat
% 0.26/0.61          @ ^ [R5: nat] : ( if_nat @ ( member_nat @ R5 @ A3 ) @ ( F @ R5 ) @ zero_zero_nat ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % summable_If_finite_set
% 0.26/0.61  thf(fact_7624_summable__If__finite__set,axiom,
% 0.26/0.61      ! [A3: set_nat,F: nat > int] :
% 0.26/0.61        ( ( finite_finite_nat @ A3 )
% 0.26/0.61       => ( summable_int
% 0.26/0.61          @ ^ [R5: nat] : ( if_int @ ( member_nat @ R5 @ A3 ) @ ( F @ R5 ) @ zero_zero_int ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % summable_If_finite_set
% 0.26/0.61  thf(fact_7625_summable__If__finite,axiom,
% 0.26/0.61      ! [P: nat > $o,F: nat > real] :
% 0.26/0.61        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 0.26/0.61       => ( summable_real
% 0.26/0.61          @ ^ [R5: nat] : ( if_real @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_real ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % summable_If_finite
% 0.26/0.61  thf(fact_7626_summable__If__finite,axiom,
% 0.26/0.61      ! [P: nat > $o,F: nat > nat] :
% 0.26/0.61        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 0.26/0.61       => ( summable_nat
% 0.26/0.61          @ ^ [R5: nat] : ( if_nat @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_nat ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % summable_If_finite
% 0.26/0.61  thf(fact_7627_summable__If__finite,axiom,
% 0.26/0.61      ! [P: nat > $o,F: nat > int] :
% 0.26/0.61        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 0.26/0.61       => ( summable_int
% 0.26/0.61          @ ^ [R5: nat] : ( if_int @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_int ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % summable_If_finite
% 0.26/0.61  thf(fact_7628_prod__pos__nat__iff,axiom,
% 0.26/0.61      ! [A3: set_int,F: int > nat] :
% 0.26/0.61        ( ( finite_finite_int @ A3 )
% 0.26/0.61       => ( ( ord_less_nat @ zero_zero_nat @ ( groups1707563613775114915nt_nat @ F @ A3 ) )
% 0.26/0.61          = ( ! [X: int] :
% 0.26/0.61                ( ( member_int @ X @ A3 )
% 0.26/0.61               => ( ord_less_nat @ zero_zero_nat @ ( F @ X ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % prod_pos_nat_iff
% 0.26/0.61  thf(fact_7629_prod__pos__nat__iff,axiom,
% 0.26/0.61      ! [A3: set_complex,F: complex > nat] :
% 0.26/0.61        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.61       => ( ( ord_less_nat @ zero_zero_nat @ ( groups861055069439313189ex_nat @ F @ A3 ) )
% 0.26/0.61          = ( ! [X: complex] :
% 0.26/0.61                ( ( member_complex @ X @ A3 )
% 0.26/0.61               => ( ord_less_nat @ zero_zero_nat @ ( F @ X ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % prod_pos_nat_iff
% 0.26/0.61  thf(fact_7630_prod__pos__nat__iff,axiom,
% 0.26/0.61      ! [A3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 0.26/0.61        ( ( finite6177210948735845034at_nat @ A3 )
% 0.26/0.61       => ( ( ord_less_nat @ zero_zero_nat @ ( groups4077766827762148844at_nat @ F @ A3 ) )
% 0.26/0.61          = ( ! [X: product_prod_nat_nat] :
% 0.26/0.61                ( ( member8440522571783428010at_nat @ X @ A3 )
% 0.26/0.61               => ( ord_less_nat @ zero_zero_nat @ ( F @ X ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % prod_pos_nat_iff
% 0.26/0.61  thf(fact_7631_prod__pos__nat__iff,axiom,
% 0.26/0.61      ! [A3: set_Extended_enat,F: extended_enat > nat] :
% 0.26/0.61        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.61       => ( ( ord_less_nat @ zero_zero_nat @ ( groups2880970938130013265at_nat @ F @ A3 ) )
% 0.26/0.61          = ( ! [X: extended_enat] :
% 0.26/0.61                ( ( member_Extended_enat @ X @ A3 )
% 0.26/0.61               => ( ord_less_nat @ zero_zero_nat @ ( F @ X ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % prod_pos_nat_iff
% 0.26/0.61  thf(fact_7632_prod__pos__nat__iff,axiom,
% 0.26/0.61      ! [A3: set_nat,F: nat > nat] :
% 0.26/0.61        ( ( finite_finite_nat @ A3 )
% 0.26/0.61       => ( ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 0.26/0.61          = ( ! [X: nat] :
% 0.26/0.61                ( ( member_nat @ X @ A3 )
% 0.26/0.61               => ( ord_less_nat @ zero_zero_nat @ ( F @ X ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % prod_pos_nat_iff
% 0.26/0.61  thf(fact_7633_sum__abs__ge__zero,axiom,
% 0.26/0.61      ! [F: nat > real,A3: set_nat] :
% 0.26/0.61        ( ord_less_eq_real @ zero_zero_real
% 0.26/0.61        @ ( groups6591440286371151544t_real
% 0.26/0.61          @ ^ [I4: nat] : ( abs_abs_real @ ( F @ I4 ) )
% 0.26/0.61          @ A3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_abs_ge_zero
% 0.26/0.61  thf(fact_7634_sum__abs__ge__zero,axiom,
% 0.26/0.61      ! [F: int > int,A3: set_int] :
% 0.26/0.61        ( ord_less_eq_int @ zero_zero_int
% 0.26/0.61        @ ( groups4538972089207619220nt_int
% 0.26/0.61          @ ^ [I4: int] : ( abs_abs_int @ ( F @ I4 ) )
% 0.26/0.61          @ A3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_abs_ge_zero
% 0.26/0.61  thf(fact_7635_sin__arcsin,axiom,
% 0.26/0.61      ! [Y3: real] :
% 0.26/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 0.26/0.61       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 0.26/0.61         => ( ( sin_real @ ( arcsin @ Y3 ) )
% 0.26/0.61            = Y3 ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sin_arcsin
% 0.26/0.61  thf(fact_7636_sum_Ocl__ivl__Suc,axiom,
% 0.26/0.61      ! [N: nat,M: nat,G: nat > rat] :
% 0.26/0.61        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.26/0.61         => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.61            = zero_zero_rat ) )
% 0.26/0.61        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.26/0.61         => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.61            = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.cl_ivl_Suc
% 0.26/0.61  thf(fact_7637_sum_Ocl__ivl__Suc,axiom,
% 0.26/0.61      ! [N: nat,M: nat,G: nat > int] :
% 0.26/0.61        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.26/0.61         => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.61            = zero_zero_int ) )
% 0.26/0.61        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.26/0.61         => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.61            = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.cl_ivl_Suc
% 0.26/0.61  thf(fact_7638_sum_Ocl__ivl__Suc,axiom,
% 0.26/0.61      ! [N: nat,M: nat,G: nat > nat] :
% 0.26/0.61        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.26/0.61         => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.61            = zero_zero_nat ) )
% 0.26/0.61        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.26/0.61         => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.61            = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.cl_ivl_Suc
% 0.26/0.61  thf(fact_7639_sum_Ocl__ivl__Suc,axiom,
% 0.26/0.61      ! [N: nat,M: nat,G: nat > real] :
% 0.26/0.61        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.26/0.61         => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.61            = zero_zero_real ) )
% 0.26/0.61        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.26/0.61         => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.61            = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.cl_ivl_Suc
% 0.26/0.61  thf(fact_7640_sum__zero__power,axiom,
% 0.26/0.61      ! [A3: set_nat,C: nat > complex] :
% 0.26/0.61        ( ( ( ( finite_finite_nat @ A3 )
% 0.26/0.61            & ( member_nat @ zero_zero_nat @ A3 ) )
% 0.26/0.61         => ( ( groups2073611262835488442omplex
% 0.26/0.61              @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) )
% 0.26/0.61              @ A3 )
% 0.26/0.61            = ( C @ zero_zero_nat ) ) )
% 0.26/0.61        & ( ~ ( ( finite_finite_nat @ A3 )
% 0.26/0.61              & ( member_nat @ zero_zero_nat @ A3 ) )
% 0.26/0.61         => ( ( groups2073611262835488442omplex
% 0.26/0.61              @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) )
% 0.26/0.61              @ A3 )
% 0.26/0.61            = zero_zero_complex ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_zero_power
% 0.26/0.61  thf(fact_7641_sum__zero__power,axiom,
% 0.26/0.61      ! [A3: set_nat,C: nat > rat] :
% 0.26/0.61        ( ( ( ( finite_finite_nat @ A3 )
% 0.26/0.61            & ( member_nat @ zero_zero_nat @ A3 ) )
% 0.26/0.61         => ( ( groups2906978787729119204at_rat
% 0.26/0.61              @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) )
% 0.26/0.61              @ A3 )
% 0.26/0.61            = ( C @ zero_zero_nat ) ) )
% 0.26/0.61        & ( ~ ( ( finite_finite_nat @ A3 )
% 0.26/0.61              & ( member_nat @ zero_zero_nat @ A3 ) )
% 0.26/0.61         => ( ( groups2906978787729119204at_rat
% 0.26/0.61              @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) )
% 0.26/0.61              @ A3 )
% 0.26/0.61            = zero_zero_rat ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_zero_power
% 0.26/0.61  thf(fact_7642_sum__zero__power,axiom,
% 0.26/0.61      ! [A3: set_nat,C: nat > real] :
% 0.26/0.61        ( ( ( ( finite_finite_nat @ A3 )
% 0.26/0.61            & ( member_nat @ zero_zero_nat @ A3 ) )
% 0.26/0.61         => ( ( groups6591440286371151544t_real
% 0.26/0.61              @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) )
% 0.26/0.61              @ A3 )
% 0.26/0.61            = ( C @ zero_zero_nat ) ) )
% 0.26/0.61        & ( ~ ( ( finite_finite_nat @ A3 )
% 0.26/0.61              & ( member_nat @ zero_zero_nat @ A3 ) )
% 0.26/0.61         => ( ( groups6591440286371151544t_real
% 0.26/0.61              @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) )
% 0.26/0.61              @ A3 )
% 0.26/0.61            = zero_zero_real ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_zero_power
% 0.26/0.61  thf(fact_7643_arcsin__1,axiom,
% 0.26/0.61      ( ( arcsin @ one_one_real )
% 0.26/0.61      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % arcsin_1
% 0.26/0.61  thf(fact_7644_sum__zero__power_H,axiom,
% 0.26/0.61      ! [A3: set_nat,C: nat > complex,D3: nat > complex] :
% 0.26/0.61        ( ( ( ( finite_finite_nat @ A3 )
% 0.26/0.61            & ( member_nat @ zero_zero_nat @ A3 ) )
% 0.26/0.61         => ( ( groups2073611262835488442omplex
% 0.26/0.61              @ ^ [I4: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) ) @ ( D3 @ I4 ) )
% 0.26/0.61              @ A3 )
% 0.26/0.61            = ( divide1717551699836669952omplex @ ( C @ zero_zero_nat ) @ ( D3 @ zero_zero_nat ) ) ) )
% 0.26/0.61        & ( ~ ( ( finite_finite_nat @ A3 )
% 0.26/0.61              & ( member_nat @ zero_zero_nat @ A3 ) )
% 0.26/0.61         => ( ( groups2073611262835488442omplex
% 0.26/0.61              @ ^ [I4: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) ) @ ( D3 @ I4 ) )
% 0.26/0.61              @ A3 )
% 0.26/0.61            = zero_zero_complex ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_zero_power'
% 0.26/0.61  thf(fact_7645_sum__zero__power_H,axiom,
% 0.26/0.61      ! [A3: set_nat,C: nat > rat,D3: nat > rat] :
% 0.26/0.61        ( ( ( ( finite_finite_nat @ A3 )
% 0.26/0.61            & ( member_nat @ zero_zero_nat @ A3 ) )
% 0.26/0.61         => ( ( groups2906978787729119204at_rat
% 0.26/0.61              @ ^ [I4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) ) @ ( D3 @ I4 ) )
% 0.26/0.61              @ A3 )
% 0.26/0.61            = ( divide_divide_rat @ ( C @ zero_zero_nat ) @ ( D3 @ zero_zero_nat ) ) ) )
% 0.26/0.61        & ( ~ ( ( finite_finite_nat @ A3 )
% 0.26/0.61              & ( member_nat @ zero_zero_nat @ A3 ) )
% 0.26/0.61         => ( ( groups2906978787729119204at_rat
% 0.26/0.61              @ ^ [I4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) ) @ ( D3 @ I4 ) )
% 0.26/0.61              @ A3 )
% 0.26/0.61            = zero_zero_rat ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_zero_power'
% 0.26/0.61  thf(fact_7646_sum__zero__power_H,axiom,
% 0.26/0.61      ! [A3: set_nat,C: nat > real,D3: nat > real] :
% 0.26/0.61        ( ( ( ( finite_finite_nat @ A3 )
% 0.26/0.61            & ( member_nat @ zero_zero_nat @ A3 ) )
% 0.26/0.61         => ( ( groups6591440286371151544t_real
% 0.26/0.61              @ ^ [I4: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) ) @ ( D3 @ I4 ) )
% 0.26/0.61              @ A3 )
% 0.26/0.61            = ( divide_divide_real @ ( C @ zero_zero_nat ) @ ( D3 @ zero_zero_nat ) ) ) )
% 0.26/0.61        & ( ~ ( ( finite_finite_nat @ A3 )
% 0.26/0.61              & ( member_nat @ zero_zero_nat @ A3 ) )
% 0.26/0.61         => ( ( groups6591440286371151544t_real
% 0.26/0.61              @ ^ [I4: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) ) @ ( D3 @ I4 ) )
% 0.26/0.61              @ A3 )
% 0.26/0.61            = zero_zero_real ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_zero_power'
% 0.26/0.61  thf(fact_7647_arcsin__minus__1,axiom,
% 0.26/0.61      ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 0.26/0.61      = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % arcsin_minus_1
% 0.26/0.61  thf(fact_7648_suminf__finite,axiom,
% 0.26/0.61      ! [N4: set_nat,F: nat > int] :
% 0.26/0.61        ( ( finite_finite_nat @ N4 )
% 0.26/0.61       => ( ! [N2: nat] :
% 0.26/0.61              ( ~ ( member_nat @ N2 @ N4 )
% 0.26/0.61             => ( ( F @ N2 )
% 0.26/0.61                = zero_zero_int ) )
% 0.26/0.61         => ( ( suminf_int @ F )
% 0.26/0.61            = ( groups3539618377306564664at_int @ F @ N4 ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % suminf_finite
% 0.26/0.61  thf(fact_7649_suminf__finite,axiom,
% 0.26/0.61      ! [N4: set_nat,F: nat > nat] :
% 0.26/0.61        ( ( finite_finite_nat @ N4 )
% 0.26/0.61       => ( ! [N2: nat] :
% 0.26/0.61              ( ~ ( member_nat @ N2 @ N4 )
% 0.26/0.61             => ( ( F @ N2 )
% 0.26/0.61                = zero_zero_nat ) )
% 0.26/0.61         => ( ( suminf_nat @ F )
% 0.26/0.61            = ( groups3542108847815614940at_nat @ F @ N4 ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % suminf_finite
% 0.26/0.61  thf(fact_7650_suminf__finite,axiom,
% 0.26/0.61      ! [N4: set_nat,F: nat > real] :
% 0.26/0.61        ( ( finite_finite_nat @ N4 )
% 0.26/0.61       => ( ! [N2: nat] :
% 0.26/0.61              ( ~ ( member_nat @ N2 @ N4 )
% 0.26/0.61             => ( ( F @ N2 )
% 0.26/0.61                = zero_zero_real ) )
% 0.26/0.61         => ( ( suminf_real @ F )
% 0.26/0.61            = ( groups6591440286371151544t_real @ F @ N4 ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % suminf_finite
% 0.26/0.61  thf(fact_7651_sum__norm__le,axiom,
% 0.26/0.61      ! [S2: set_option_nat,F: option_nat > complex,G: option_nat > real] :
% 0.26/0.61        ( ! [X4: option_nat] :
% 0.26/0.61            ( ( member_option_nat @ X4 @ S2 )
% 0.26/0.61           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G @ X4 ) ) )
% 0.26/0.61       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3209896439523537802omplex @ F @ S2 ) ) @ ( groups4518532050878116744t_real @ G @ S2 ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_norm_le
% 0.26/0.61  thf(fact_7652_sum__norm__le,axiom,
% 0.26/0.61      ! [S2: set_real,F: real > complex,G: real > real] :
% 0.26/0.61        ( ! [X4: real] :
% 0.26/0.61            ( ( member_real @ X4 @ S2 )
% 0.26/0.61           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G @ X4 ) ) )
% 0.26/0.61       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5754745047067104278omplex @ F @ S2 ) ) @ ( groups8097168146408367636l_real @ G @ S2 ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_norm_le
% 0.26/0.61  thf(fact_7653_sum__norm__le,axiom,
% 0.26/0.61      ! [S2: set_set_nat,F: set_nat > complex,G: set_nat > real] :
% 0.26/0.61        ( ! [X4: set_nat] :
% 0.26/0.61            ( ( member_set_nat @ X4 @ S2 )
% 0.26/0.61           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G @ X4 ) ) )
% 0.26/0.61       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups8255218700646806128omplex @ F @ S2 ) ) @ ( groups5107569545109728110t_real @ G @ S2 ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_norm_le
% 0.26/0.61  thf(fact_7654_sum__norm__le,axiom,
% 0.26/0.61      ! [S2: set_int,F: int > complex,G: int > real] :
% 0.26/0.61        ( ! [X4: int] :
% 0.26/0.61            ( ( member_int @ X4 @ S2 )
% 0.26/0.61           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G @ X4 ) ) )
% 0.26/0.61       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F @ S2 ) ) @ ( groups8778361861064173332t_real @ G @ S2 ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_norm_le
% 0.26/0.61  thf(fact_7655_sum__norm__le,axiom,
% 0.26/0.61      ! [S2: set_nat,F: nat > complex,G: nat > real] :
% 0.26/0.61        ( ! [X4: nat] :
% 0.26/0.61            ( ( member_nat @ X4 @ S2 )
% 0.26/0.61           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G @ X4 ) ) )
% 0.26/0.61       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G @ S2 ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_norm_le
% 0.26/0.61  thf(fact_7656_sum__norm__le,axiom,
% 0.26/0.61      ! [S2: set_complex,F: complex > complex,G: complex > real] :
% 0.26/0.61        ( ! [X4: complex] :
% 0.26/0.61            ( ( member_complex @ X4 @ S2 )
% 0.26/0.61           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G @ X4 ) ) )
% 0.26/0.61       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ S2 ) ) @ ( groups5808333547571424918x_real @ G @ S2 ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_norm_le
% 0.26/0.61  thf(fact_7657_sum__norm__le,axiom,
% 0.26/0.61      ! [S2: set_nat,F: nat > real,G: nat > real] :
% 0.26/0.61        ( ! [X4: nat] :
% 0.26/0.61            ( ( member_nat @ X4 @ S2 )
% 0.26/0.61           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ X4 ) ) @ ( G @ X4 ) ) )
% 0.26/0.61       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G @ S2 ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum_norm_le
% 0.26/0.61  thf(fact_7658_norm__sum,axiom,
% 0.26/0.61      ! [F: nat > complex,A3: set_nat] :
% 0.26/0.61        ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ A3 ) )
% 0.26/0.61        @ ( groups6591440286371151544t_real
% 0.26/0.61          @ ^ [I4: nat] : ( real_V1022390504157884413omplex @ ( F @ I4 ) )
% 0.26/0.61          @ A3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % norm_sum
% 0.26/0.61  thf(fact_7659_norm__sum,axiom,
% 0.26/0.61      ! [F: complex > complex,A3: set_complex] :
% 0.26/0.61        ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ A3 ) )
% 0.26/0.61        @ ( groups5808333547571424918x_real
% 0.26/0.61          @ ^ [I4: complex] : ( real_V1022390504157884413omplex @ ( F @ I4 ) )
% 0.26/0.61          @ A3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % norm_sum
% 0.26/0.61  thf(fact_7660_norm__sum,axiom,
% 0.26/0.61      ! [F: nat > real,A3: set_nat] :
% 0.26/0.61        ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ A3 ) )
% 0.26/0.61        @ ( groups6591440286371151544t_real
% 0.26/0.61          @ ^ [I4: nat] : ( real_V7735802525324610683m_real @ ( F @ I4 ) )
% 0.26/0.61          @ A3 ) ) ).
% 0.26/0.61  
% 0.26/0.61  % norm_sum
% 0.26/0.61  thf(fact_7661_complex__eq__cancel__iff2,axiom,
% 0.26/0.61      ! [X3: real,Y3: real,Xa: real] :
% 0.26/0.61        ( ( ( complex2 @ X3 @ Y3 )
% 0.26/0.61          = ( real_V4546457046886955230omplex @ Xa ) )
% 0.26/0.61        = ( ( X3 = Xa )
% 0.26/0.61          & ( Y3 = zero_zero_real ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % complex_eq_cancel_iff2
% 0.26/0.61  thf(fact_7662_complex__of__real__code,axiom,
% 0.26/0.61      ( real_V4546457046886955230omplex
% 0.26/0.61      = ( ^ [X: real] : ( complex2 @ X @ zero_zero_real ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % complex_of_real_code
% 0.26/0.61  thf(fact_7663_complex__of__real__def,axiom,
% 0.26/0.61      ( real_V4546457046886955230omplex
% 0.26/0.61      = ( ^ [R5: real] : ( complex2 @ R5 @ zero_zero_real ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % complex_of_real_def
% 0.26/0.61  thf(fact_7664_zero__complex_Ocode,axiom,
% 0.26/0.61      ( zero_zero_complex
% 0.26/0.61      = ( complex2 @ zero_zero_real @ zero_zero_real ) ) ).
% 0.26/0.61  
% 0.26/0.61  % zero_complex.code
% 0.26/0.61  thf(fact_7665_Complex__eq__0,axiom,
% 0.26/0.61      ! [A: real,B: real] :
% 0.26/0.61        ( ( ( complex2 @ A @ B )
% 0.26/0.61          = zero_zero_complex )
% 0.26/0.61        = ( ( A = zero_zero_real )
% 0.26/0.61          & ( B = zero_zero_real ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % Complex_eq_0
% 0.26/0.61  thf(fact_7666_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.26/0.61      ! [S4: set_real,T4: set_real,S2: set_real,I: real > real,J: real > real,T5: set_real,G: real > real,H2: real > real] :
% 0.26/0.61        ( ( finite_finite_real @ S4 )
% 0.26/0.61       => ( ( finite_finite_real @ T4 )
% 0.26/0.61         => ( ! [A5: real] :
% 0.26/0.61                ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.26/0.61               => ( ( I @ ( J @ A5 ) )
% 0.26/0.61                  = A5 ) )
% 0.26/0.61           => ( ! [A5: real] :
% 0.26/0.61                  ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.26/0.61                 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 0.26/0.61             => ( ! [B4: real] :
% 0.26/0.61                    ( ( member_real @ B4 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 0.26/0.61                   => ( ( J @ ( I @ B4 ) )
% 0.26/0.61                      = B4 ) )
% 0.26/0.61               => ( ! [B4: real] :
% 0.26/0.61                      ( ( member_real @ B4 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 0.26/0.61                     => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 0.26/0.61                 => ( ! [A5: real] :
% 0.26/0.61                        ( ( member_real @ A5 @ S4 )
% 0.26/0.61                       => ( ( G @ A5 )
% 0.26/0.61                          = zero_zero_real ) )
% 0.26/0.61                   => ( ! [B4: real] :
% 0.26/0.61                          ( ( member_real @ B4 @ T4 )
% 0.26/0.61                         => ( ( H2 @ B4 )
% 0.26/0.61                            = zero_zero_real ) )
% 0.26/0.61                     => ( ! [A5: real] :
% 0.26/0.61                            ( ( member_real @ A5 @ S2 )
% 0.26/0.61                           => ( ( H2 @ ( J @ A5 ) )
% 0.26/0.61                              = ( G @ A5 ) ) )
% 0.26/0.61                       => ( ( groups8097168146408367636l_real @ G @ S2 )
% 0.26/0.61                          = ( groups8097168146408367636l_real @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.61  
% 0.26/0.61  % sum.reindex_bij_witness_not_neutral
% 0.26/0.62  thf(fact_7667_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.26/0.62      ! [S4: set_real,T4: set_int,S2: set_real,I: int > real,J: real > int,T5: set_int,G: real > real,H2: int > real] :
% 0.26/0.62        ( ( finite_finite_real @ S4 )
% 0.26/0.62       => ( ( finite_finite_int @ T4 )
% 0.26/0.62         => ( ! [A5: real] :
% 0.26/0.62                ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.26/0.62               => ( ( I @ ( J @ A5 ) )
% 0.26/0.62                  = A5 ) )
% 0.26/0.62           => ( ! [A5: real] :
% 0.26/0.62                  ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.26/0.62                 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 0.26/0.62             => ( ! [B4: int] :
% 0.26/0.62                    ( ( member_int @ B4 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 0.26/0.62                   => ( ( J @ ( I @ B4 ) )
% 0.26/0.62                      = B4 ) )
% 0.26/0.62               => ( ! [B4: int] :
% 0.26/0.62                      ( ( member_int @ B4 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 0.26/0.62                     => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 0.26/0.62                 => ( ! [A5: real] :
% 0.26/0.62                        ( ( member_real @ A5 @ S4 )
% 0.26/0.62                       => ( ( G @ A5 )
% 0.26/0.62                          = zero_zero_real ) )
% 0.26/0.62                   => ( ! [B4: int] :
% 0.26/0.62                          ( ( member_int @ B4 @ T4 )
% 0.26/0.62                         => ( ( H2 @ B4 )
% 0.26/0.62                            = zero_zero_real ) )
% 0.26/0.62                     => ( ! [A5: real] :
% 0.26/0.62                            ( ( member_real @ A5 @ S2 )
% 0.26/0.62                           => ( ( H2 @ ( J @ A5 ) )
% 0.26/0.62                              = ( G @ A5 ) ) )
% 0.26/0.62                       => ( ( groups8097168146408367636l_real @ G @ S2 )
% 0.26/0.62                          = ( groups8778361861064173332t_real @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.reindex_bij_witness_not_neutral
% 0.26/0.62  thf(fact_7668_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.26/0.62      ! [S4: set_real,T4: set_complex,S2: set_real,I: complex > real,J: real > complex,T5: set_complex,G: real > real,H2: complex > real] :
% 0.26/0.62        ( ( finite_finite_real @ S4 )
% 0.26/0.62       => ( ( finite3207457112153483333omplex @ T4 )
% 0.26/0.62         => ( ! [A5: real] :
% 0.26/0.62                ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.26/0.62               => ( ( I @ ( J @ A5 ) )
% 0.26/0.62                  = A5 ) )
% 0.26/0.62           => ( ! [A5: real] :
% 0.26/0.62                  ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.26/0.62                 => ( member_complex @ ( J @ A5 ) @ ( minus_811609699411566653omplex @ T5 @ T4 ) ) )
% 0.26/0.62             => ( ! [B4: complex] :
% 0.26/0.62                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 0.26/0.62                   => ( ( J @ ( I @ B4 ) )
% 0.26/0.62                      = B4 ) )
% 0.26/0.62               => ( ! [B4: complex] :
% 0.26/0.62                      ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 0.26/0.62                     => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 0.26/0.62                 => ( ! [A5: real] :
% 0.26/0.62                        ( ( member_real @ A5 @ S4 )
% 0.26/0.62                       => ( ( G @ A5 )
% 0.26/0.62                          = zero_zero_real ) )
% 0.26/0.62                   => ( ! [B4: complex] :
% 0.26/0.62                          ( ( member_complex @ B4 @ T4 )
% 0.26/0.62                         => ( ( H2 @ B4 )
% 0.26/0.62                            = zero_zero_real ) )
% 0.26/0.62                     => ( ! [A5: real] :
% 0.26/0.62                            ( ( member_real @ A5 @ S2 )
% 0.26/0.62                           => ( ( H2 @ ( J @ A5 ) )
% 0.26/0.62                              = ( G @ A5 ) ) )
% 0.26/0.62                       => ( ( groups8097168146408367636l_real @ G @ S2 )
% 0.26/0.62                          = ( groups5808333547571424918x_real @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.reindex_bij_witness_not_neutral
% 0.26/0.62  thf(fact_7669_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.26/0.62      ! [S4: set_real,T4: set_Extended_enat,S2: set_real,I: extended_enat > real,J: real > extended_enat,T5: set_Extended_enat,G: real > real,H2: extended_enat > real] :
% 0.26/0.62        ( ( finite_finite_real @ S4 )
% 0.26/0.62       => ( ( finite4001608067531595151d_enat @ T4 )
% 0.26/0.62         => ( ! [A5: real] :
% 0.26/0.62                ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.26/0.62               => ( ( I @ ( J @ A5 ) )
% 0.26/0.62                  = A5 ) )
% 0.26/0.62           => ( ! [A5: real] :
% 0.26/0.62                  ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.26/0.62                 => ( member_Extended_enat @ ( J @ A5 ) @ ( minus_925952699566721837d_enat @ T5 @ T4 ) ) )
% 0.26/0.62             => ( ! [B4: extended_enat] :
% 0.26/0.62                    ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ T5 @ T4 ) )
% 0.26/0.62                   => ( ( J @ ( I @ B4 ) )
% 0.26/0.62                      = B4 ) )
% 0.26/0.62               => ( ! [B4: extended_enat] :
% 0.26/0.62                      ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ T5 @ T4 ) )
% 0.26/0.62                     => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 0.26/0.62                 => ( ! [A5: real] :
% 0.26/0.62                        ( ( member_real @ A5 @ S4 )
% 0.26/0.62                       => ( ( G @ A5 )
% 0.26/0.62                          = zero_zero_real ) )
% 0.26/0.62                   => ( ! [B4: extended_enat] :
% 0.26/0.62                          ( ( member_Extended_enat @ B4 @ T4 )
% 0.26/0.62                         => ( ( H2 @ B4 )
% 0.26/0.62                            = zero_zero_real ) )
% 0.26/0.62                     => ( ! [A5: real] :
% 0.26/0.62                            ( ( member_real @ A5 @ S2 )
% 0.26/0.62                           => ( ( H2 @ ( J @ A5 ) )
% 0.26/0.62                              = ( G @ A5 ) ) )
% 0.26/0.62                       => ( ( groups8097168146408367636l_real @ G @ S2 )
% 0.26/0.62                          = ( groups4148127829035722712t_real @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.reindex_bij_witness_not_neutral
% 0.26/0.62  thf(fact_7670_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.26/0.62      ! [S4: set_int,T4: set_real,S2: set_int,I: real > int,J: int > real,T5: set_real,G: int > real,H2: real > real] :
% 0.26/0.62        ( ( finite_finite_int @ S4 )
% 0.26/0.62       => ( ( finite_finite_real @ T4 )
% 0.26/0.62         => ( ! [A5: int] :
% 0.26/0.62                ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.26/0.62               => ( ( I @ ( J @ A5 ) )
% 0.26/0.62                  = A5 ) )
% 0.26/0.62           => ( ! [A5: int] :
% 0.26/0.62                  ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.26/0.62                 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 0.26/0.62             => ( ! [B4: real] :
% 0.26/0.62                    ( ( member_real @ B4 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 0.26/0.62                   => ( ( J @ ( I @ B4 ) )
% 0.26/0.62                      = B4 ) )
% 0.26/0.62               => ( ! [B4: real] :
% 0.26/0.62                      ( ( member_real @ B4 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 0.26/0.62                     => ( member_int @ ( I @ B4 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 0.26/0.62                 => ( ! [A5: int] :
% 0.26/0.62                        ( ( member_int @ A5 @ S4 )
% 0.26/0.62                       => ( ( G @ A5 )
% 0.26/0.62                          = zero_zero_real ) )
% 0.26/0.62                   => ( ! [B4: real] :
% 0.26/0.62                          ( ( member_real @ B4 @ T4 )
% 0.26/0.62                         => ( ( H2 @ B4 )
% 0.26/0.62                            = zero_zero_real ) )
% 0.26/0.62                     => ( ! [A5: int] :
% 0.26/0.62                            ( ( member_int @ A5 @ S2 )
% 0.26/0.62                           => ( ( H2 @ ( J @ A5 ) )
% 0.26/0.62                              = ( G @ A5 ) ) )
% 0.26/0.62                       => ( ( groups8778361861064173332t_real @ G @ S2 )
% 0.26/0.62                          = ( groups8097168146408367636l_real @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.reindex_bij_witness_not_neutral
% 0.26/0.62  thf(fact_7671_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.26/0.62      ! [S4: set_int,T4: set_int,S2: set_int,I: int > int,J: int > int,T5: set_int,G: int > real,H2: int > real] :
% 0.26/0.62        ( ( finite_finite_int @ S4 )
% 0.26/0.62       => ( ( finite_finite_int @ T4 )
% 0.26/0.62         => ( ! [A5: int] :
% 0.26/0.62                ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.26/0.62               => ( ( I @ ( J @ A5 ) )
% 0.26/0.62                  = A5 ) )
% 0.26/0.62           => ( ! [A5: int] :
% 0.26/0.62                  ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.26/0.62                 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 0.26/0.62             => ( ! [B4: int] :
% 0.26/0.62                    ( ( member_int @ B4 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 0.26/0.62                   => ( ( J @ ( I @ B4 ) )
% 0.26/0.62                      = B4 ) )
% 0.26/0.62               => ( ! [B4: int] :
% 0.26/0.62                      ( ( member_int @ B4 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 0.26/0.62                     => ( member_int @ ( I @ B4 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 0.26/0.62                 => ( ! [A5: int] :
% 0.26/0.62                        ( ( member_int @ A5 @ S4 )
% 0.26/0.62                       => ( ( G @ A5 )
% 0.26/0.62                          = zero_zero_real ) )
% 0.26/0.62                   => ( ! [B4: int] :
% 0.26/0.62                          ( ( member_int @ B4 @ T4 )
% 0.26/0.62                         => ( ( H2 @ B4 )
% 0.26/0.62                            = zero_zero_real ) )
% 0.26/0.62                     => ( ! [A5: int] :
% 0.26/0.62                            ( ( member_int @ A5 @ S2 )
% 0.26/0.62                           => ( ( H2 @ ( J @ A5 ) )
% 0.26/0.62                              = ( G @ A5 ) ) )
% 0.26/0.62                       => ( ( groups8778361861064173332t_real @ G @ S2 )
% 0.26/0.62                          = ( groups8778361861064173332t_real @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.reindex_bij_witness_not_neutral
% 0.26/0.62  thf(fact_7672_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.26/0.62      ! [S4: set_int,T4: set_complex,S2: set_int,I: complex > int,J: int > complex,T5: set_complex,G: int > real,H2: complex > real] :
% 0.26/0.62        ( ( finite_finite_int @ S4 )
% 0.26/0.62       => ( ( finite3207457112153483333omplex @ T4 )
% 0.26/0.62         => ( ! [A5: int] :
% 0.26/0.62                ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.26/0.62               => ( ( I @ ( J @ A5 ) )
% 0.26/0.62                  = A5 ) )
% 0.26/0.62           => ( ! [A5: int] :
% 0.26/0.62                  ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.26/0.62                 => ( member_complex @ ( J @ A5 ) @ ( minus_811609699411566653omplex @ T5 @ T4 ) ) )
% 0.26/0.62             => ( ! [B4: complex] :
% 0.26/0.62                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 0.26/0.62                   => ( ( J @ ( I @ B4 ) )
% 0.26/0.62                      = B4 ) )
% 0.26/0.62               => ( ! [B4: complex] :
% 0.26/0.62                      ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 0.26/0.62                     => ( member_int @ ( I @ B4 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 0.26/0.62                 => ( ! [A5: int] :
% 0.26/0.62                        ( ( member_int @ A5 @ S4 )
% 0.26/0.62                       => ( ( G @ A5 )
% 0.26/0.62                          = zero_zero_real ) )
% 0.26/0.62                   => ( ! [B4: complex] :
% 0.26/0.62                          ( ( member_complex @ B4 @ T4 )
% 0.26/0.62                         => ( ( H2 @ B4 )
% 0.26/0.62                            = zero_zero_real ) )
% 0.26/0.62                     => ( ! [A5: int] :
% 0.26/0.62                            ( ( member_int @ A5 @ S2 )
% 0.26/0.62                           => ( ( H2 @ ( J @ A5 ) )
% 0.26/0.62                              = ( G @ A5 ) ) )
% 0.26/0.62                       => ( ( groups8778361861064173332t_real @ G @ S2 )
% 0.26/0.62                          = ( groups5808333547571424918x_real @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.reindex_bij_witness_not_neutral
% 0.26/0.62  thf(fact_7673_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.26/0.62      ! [S4: set_int,T4: set_Extended_enat,S2: set_int,I: extended_enat > int,J: int > extended_enat,T5: set_Extended_enat,G: int > real,H2: extended_enat > real] :
% 0.26/0.62        ( ( finite_finite_int @ S4 )
% 0.26/0.62       => ( ( finite4001608067531595151d_enat @ T4 )
% 0.26/0.62         => ( ! [A5: int] :
% 0.26/0.62                ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.26/0.62               => ( ( I @ ( J @ A5 ) )
% 0.26/0.62                  = A5 ) )
% 0.26/0.62           => ( ! [A5: int] :
% 0.26/0.62                  ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.26/0.62                 => ( member_Extended_enat @ ( J @ A5 ) @ ( minus_925952699566721837d_enat @ T5 @ T4 ) ) )
% 0.26/0.62             => ( ! [B4: extended_enat] :
% 0.26/0.62                    ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ T5 @ T4 ) )
% 0.26/0.62                   => ( ( J @ ( I @ B4 ) )
% 0.26/0.62                      = B4 ) )
% 0.26/0.62               => ( ! [B4: extended_enat] :
% 0.26/0.62                      ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ T5 @ T4 ) )
% 0.26/0.62                     => ( member_int @ ( I @ B4 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 0.26/0.62                 => ( ! [A5: int] :
% 0.26/0.62                        ( ( member_int @ A5 @ S4 )
% 0.26/0.62                       => ( ( G @ A5 )
% 0.26/0.62                          = zero_zero_real ) )
% 0.26/0.62                   => ( ! [B4: extended_enat] :
% 0.26/0.62                          ( ( member_Extended_enat @ B4 @ T4 )
% 0.26/0.62                         => ( ( H2 @ B4 )
% 0.26/0.62                            = zero_zero_real ) )
% 0.26/0.62                     => ( ! [A5: int] :
% 0.26/0.62                            ( ( member_int @ A5 @ S2 )
% 0.26/0.62                           => ( ( H2 @ ( J @ A5 ) )
% 0.26/0.62                              = ( G @ A5 ) ) )
% 0.26/0.62                       => ( ( groups8778361861064173332t_real @ G @ S2 )
% 0.26/0.62                          = ( groups4148127829035722712t_real @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.reindex_bij_witness_not_neutral
% 0.26/0.62  thf(fact_7674_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.26/0.62      ! [S4: set_complex,T4: set_real,S2: set_complex,I: real > complex,J: complex > real,T5: set_real,G: complex > real,H2: real > real] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ S4 )
% 0.26/0.62       => ( ( finite_finite_real @ T4 )
% 0.26/0.62         => ( ! [A5: complex] :
% 0.26/0.62                ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ S2 @ S4 ) )
% 0.26/0.62               => ( ( I @ ( J @ A5 ) )
% 0.26/0.62                  = A5 ) )
% 0.26/0.62           => ( ! [A5: complex] :
% 0.26/0.62                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ S2 @ S4 ) )
% 0.26/0.62                 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 0.26/0.62             => ( ! [B4: real] :
% 0.26/0.62                    ( ( member_real @ B4 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 0.26/0.62                   => ( ( J @ ( I @ B4 ) )
% 0.26/0.62                      = B4 ) )
% 0.26/0.62               => ( ! [B4: real] :
% 0.26/0.62                      ( ( member_real @ B4 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 0.26/0.62                     => ( member_complex @ ( I @ B4 ) @ ( minus_811609699411566653omplex @ S2 @ S4 ) ) )
% 0.26/0.62                 => ( ! [A5: complex] :
% 0.26/0.62                        ( ( member_complex @ A5 @ S4 )
% 0.26/0.62                       => ( ( G @ A5 )
% 0.26/0.62                          = zero_zero_real ) )
% 0.26/0.62                   => ( ! [B4: real] :
% 0.26/0.62                          ( ( member_real @ B4 @ T4 )
% 0.26/0.62                         => ( ( H2 @ B4 )
% 0.26/0.62                            = zero_zero_real ) )
% 0.26/0.62                     => ( ! [A5: complex] :
% 0.26/0.62                            ( ( member_complex @ A5 @ S2 )
% 0.26/0.62                           => ( ( H2 @ ( J @ A5 ) )
% 0.26/0.62                              = ( G @ A5 ) ) )
% 0.26/0.62                       => ( ( groups5808333547571424918x_real @ G @ S2 )
% 0.26/0.62                          = ( groups8097168146408367636l_real @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.reindex_bij_witness_not_neutral
% 0.26/0.62  thf(fact_7675_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.26/0.62      ! [S4: set_complex,T4: set_int,S2: set_complex,I: int > complex,J: complex > int,T5: set_int,G: complex > real,H2: int > real] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ S4 )
% 0.26/0.62       => ( ( finite_finite_int @ T4 )
% 0.26/0.62         => ( ! [A5: complex] :
% 0.26/0.62                ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ S2 @ S4 ) )
% 0.26/0.62               => ( ( I @ ( J @ A5 ) )
% 0.26/0.62                  = A5 ) )
% 0.26/0.62           => ( ! [A5: complex] :
% 0.26/0.62                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ S2 @ S4 ) )
% 0.26/0.62                 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 0.26/0.62             => ( ! [B4: int] :
% 0.26/0.62                    ( ( member_int @ B4 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 0.26/0.62                   => ( ( J @ ( I @ B4 ) )
% 0.26/0.62                      = B4 ) )
% 0.26/0.62               => ( ! [B4: int] :
% 0.26/0.62                      ( ( member_int @ B4 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 0.26/0.62                     => ( member_complex @ ( I @ B4 ) @ ( minus_811609699411566653omplex @ S2 @ S4 ) ) )
% 0.26/0.62                 => ( ! [A5: complex] :
% 0.26/0.62                        ( ( member_complex @ A5 @ S4 )
% 0.26/0.62                       => ( ( G @ A5 )
% 0.26/0.62                          = zero_zero_real ) )
% 0.26/0.62                   => ( ! [B4: int] :
% 0.26/0.62                          ( ( member_int @ B4 @ T4 )
% 0.26/0.62                         => ( ( H2 @ B4 )
% 0.26/0.62                            = zero_zero_real ) )
% 0.26/0.62                     => ( ! [A5: complex] :
% 0.26/0.62                            ( ( member_complex @ A5 @ S2 )
% 0.26/0.62                           => ( ( H2 @ ( J @ A5 ) )
% 0.26/0.62                              = ( G @ A5 ) ) )
% 0.26/0.62                       => ( ( groups5808333547571424918x_real @ G @ S2 )
% 0.26/0.62                          = ( groups8778361861064173332t_real @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.reindex_bij_witness_not_neutral
% 0.26/0.62  thf(fact_7676_sum_Osetdiff__irrelevant,axiom,
% 0.26/0.62      ! [A3: set_real,G: real > real] :
% 0.26/0.62        ( ( finite_finite_real @ A3 )
% 0.26/0.62       => ( ( groups8097168146408367636l_real @ G
% 0.26/0.62            @ ( minus_minus_set_real @ A3
% 0.26/0.62              @ ( collect_real
% 0.26/0.62                @ ^ [X: real] :
% 0.26/0.62                    ( ( G @ X )
% 0.26/0.62                    = zero_zero_real ) ) ) )
% 0.26/0.62          = ( groups8097168146408367636l_real @ G @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.setdiff_irrelevant
% 0.26/0.62  thf(fact_7677_sum_Osetdiff__irrelevant,axiom,
% 0.26/0.62      ! [A3: set_int,G: int > real] :
% 0.26/0.62        ( ( finite_finite_int @ A3 )
% 0.26/0.62       => ( ( groups8778361861064173332t_real @ G
% 0.26/0.62            @ ( minus_minus_set_int @ A3
% 0.26/0.62              @ ( collect_int
% 0.26/0.62                @ ^ [X: int] :
% 0.26/0.62                    ( ( G @ X )
% 0.26/0.62                    = zero_zero_real ) ) ) )
% 0.26/0.62          = ( groups8778361861064173332t_real @ G @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.setdiff_irrelevant
% 0.26/0.62  thf(fact_7678_sum_Osetdiff__irrelevant,axiom,
% 0.26/0.62      ! [A3: set_complex,G: complex > real] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.62       => ( ( groups5808333547571424918x_real @ G
% 0.26/0.62            @ ( minus_811609699411566653omplex @ A3
% 0.26/0.62              @ ( collect_complex
% 0.26/0.62                @ ^ [X: complex] :
% 0.26/0.62                    ( ( G @ X )
% 0.26/0.62                    = zero_zero_real ) ) ) )
% 0.26/0.62          = ( groups5808333547571424918x_real @ G @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.setdiff_irrelevant
% 0.26/0.62  thf(fact_7679_sum_Osetdiff__irrelevant,axiom,
% 0.26/0.62      ! [A3: set_Extended_enat,G: extended_enat > real] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.62       => ( ( groups4148127829035722712t_real @ G
% 0.26/0.62            @ ( minus_925952699566721837d_enat @ A3
% 0.26/0.62              @ ( collec4429806609662206161d_enat
% 0.26/0.62                @ ^ [X: extended_enat] :
% 0.26/0.62                    ( ( G @ X )
% 0.26/0.62                    = zero_zero_real ) ) ) )
% 0.26/0.62          = ( groups4148127829035722712t_real @ G @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.setdiff_irrelevant
% 0.26/0.62  thf(fact_7680_sum_Osetdiff__irrelevant,axiom,
% 0.26/0.62      ! [A3: set_real,G: real > rat] :
% 0.26/0.62        ( ( finite_finite_real @ A3 )
% 0.26/0.62       => ( ( groups1300246762558778688al_rat @ G
% 0.26/0.62            @ ( minus_minus_set_real @ A3
% 0.26/0.62              @ ( collect_real
% 0.26/0.62                @ ^ [X: real] :
% 0.26/0.62                    ( ( G @ X )
% 0.26/0.62                    = zero_zero_rat ) ) ) )
% 0.26/0.62          = ( groups1300246762558778688al_rat @ G @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.setdiff_irrelevant
% 0.26/0.62  thf(fact_7681_sum_Osetdiff__irrelevant,axiom,
% 0.26/0.62      ! [A3: set_int,G: int > rat] :
% 0.26/0.62        ( ( finite_finite_int @ A3 )
% 0.26/0.62       => ( ( groups3906332499630173760nt_rat @ G
% 0.26/0.62            @ ( minus_minus_set_int @ A3
% 0.26/0.62              @ ( collect_int
% 0.26/0.62                @ ^ [X: int] :
% 0.26/0.62                    ( ( G @ X )
% 0.26/0.62                    = zero_zero_rat ) ) ) )
% 0.26/0.62          = ( groups3906332499630173760nt_rat @ G @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.setdiff_irrelevant
% 0.26/0.62  thf(fact_7682_sum_Osetdiff__irrelevant,axiom,
% 0.26/0.62      ! [A3: set_complex,G: complex > rat] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.62       => ( ( groups5058264527183730370ex_rat @ G
% 0.26/0.62            @ ( minus_811609699411566653omplex @ A3
% 0.26/0.62              @ ( collect_complex
% 0.26/0.62                @ ^ [X: complex] :
% 0.26/0.62                    ( ( G @ X )
% 0.26/0.62                    = zero_zero_rat ) ) ) )
% 0.26/0.62          = ( groups5058264527183730370ex_rat @ G @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.setdiff_irrelevant
% 0.26/0.62  thf(fact_7683_sum_Osetdiff__irrelevant,axiom,
% 0.26/0.62      ! [A3: set_Extended_enat,G: extended_enat > rat] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.62       => ( ( groups1392844769737527556at_rat @ G
% 0.26/0.62            @ ( minus_925952699566721837d_enat @ A3
% 0.26/0.62              @ ( collec4429806609662206161d_enat
% 0.26/0.62                @ ^ [X: extended_enat] :
% 0.26/0.62                    ( ( G @ X )
% 0.26/0.62                    = zero_zero_rat ) ) ) )
% 0.26/0.62          = ( groups1392844769737527556at_rat @ G @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.setdiff_irrelevant
% 0.26/0.62  thf(fact_7684_sum_Osetdiff__irrelevant,axiom,
% 0.26/0.62      ! [A3: set_real,G: real > nat] :
% 0.26/0.62        ( ( finite_finite_real @ A3 )
% 0.26/0.62       => ( ( groups1935376822645274424al_nat @ G
% 0.26/0.62            @ ( minus_minus_set_real @ A3
% 0.26/0.62              @ ( collect_real
% 0.26/0.62                @ ^ [X: real] :
% 0.26/0.62                    ( ( G @ X )
% 0.26/0.62                    = zero_zero_nat ) ) ) )
% 0.26/0.62          = ( groups1935376822645274424al_nat @ G @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.setdiff_irrelevant
% 0.26/0.62  thf(fact_7685_sum_Osetdiff__irrelevant,axiom,
% 0.26/0.62      ! [A3: set_int,G: int > nat] :
% 0.26/0.62        ( ( finite_finite_int @ A3 )
% 0.26/0.62       => ( ( groups4541462559716669496nt_nat @ G
% 0.26/0.62            @ ( minus_minus_set_int @ A3
% 0.26/0.62              @ ( collect_int
% 0.26/0.62                @ ^ [X: int] :
% 0.26/0.62                    ( ( G @ X )
% 0.26/0.62                    = zero_zero_nat ) ) ) )
% 0.26/0.62          = ( groups4541462559716669496nt_nat @ G @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.setdiff_irrelevant
% 0.26/0.62  thf(fact_7686_sum__strict__mono,axiom,
% 0.26/0.62      ! [A3: set_complex,F: complex > real,G: complex > real] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.62       => ( ( A3 != bot_bot_set_complex )
% 0.26/0.62         => ( ! [X4: complex] :
% 0.26/0.62                ( ( member_complex @ X4 @ A3 )
% 0.26/0.62               => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62           => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A3 ) @ ( groups5808333547571424918x_real @ G @ A3 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_strict_mono
% 0.26/0.62  thf(fact_7687_sum__strict__mono,axiom,
% 0.26/0.62      ! [A3: set_Extended_enat,F: extended_enat > real,G: extended_enat > real] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.62       => ( ( A3 != bot_bo7653980558646680370d_enat )
% 0.26/0.62         => ( ! [X4: extended_enat] :
% 0.26/0.62                ( ( member_Extended_enat @ X4 @ A3 )
% 0.26/0.62               => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62           => ( ord_less_real @ ( groups4148127829035722712t_real @ F @ A3 ) @ ( groups4148127829035722712t_real @ G @ A3 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_strict_mono
% 0.26/0.62  thf(fact_7688_sum__strict__mono,axiom,
% 0.26/0.62      ! [A3: set_real,F: real > real,G: real > real] :
% 0.26/0.62        ( ( finite_finite_real @ A3 )
% 0.26/0.62       => ( ( A3 != bot_bot_set_real )
% 0.26/0.62         => ( ! [X4: real] :
% 0.26/0.62                ( ( member_real @ X4 @ A3 )
% 0.26/0.62               => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62           => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A3 ) @ ( groups8097168146408367636l_real @ G @ A3 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_strict_mono
% 0.26/0.62  thf(fact_7689_sum__strict__mono,axiom,
% 0.26/0.62      ! [A3: set_int,F: int > real,G: int > real] :
% 0.26/0.62        ( ( finite_finite_int @ A3 )
% 0.26/0.62       => ( ( A3 != bot_bot_set_int )
% 0.26/0.62         => ( ! [X4: int] :
% 0.26/0.62                ( ( member_int @ X4 @ A3 )
% 0.26/0.62               => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62           => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A3 ) @ ( groups8778361861064173332t_real @ G @ A3 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_strict_mono
% 0.26/0.62  thf(fact_7690_sum__strict__mono,axiom,
% 0.26/0.62      ! [A3: set_complex,F: complex > rat,G: complex > rat] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.62       => ( ( A3 != bot_bot_set_complex )
% 0.26/0.62         => ( ! [X4: complex] :
% 0.26/0.62                ( ( member_complex @ X4 @ A3 )
% 0.26/0.62               => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62           => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A3 ) @ ( groups5058264527183730370ex_rat @ G @ A3 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_strict_mono
% 0.26/0.62  thf(fact_7691_sum__strict__mono,axiom,
% 0.26/0.62      ! [A3: set_Extended_enat,F: extended_enat > rat,G: extended_enat > rat] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.62       => ( ( A3 != bot_bo7653980558646680370d_enat )
% 0.26/0.62         => ( ! [X4: extended_enat] :
% 0.26/0.62                ( ( member_Extended_enat @ X4 @ A3 )
% 0.26/0.62               => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62           => ( ord_less_rat @ ( groups1392844769737527556at_rat @ F @ A3 ) @ ( groups1392844769737527556at_rat @ G @ A3 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_strict_mono
% 0.26/0.62  thf(fact_7692_sum__strict__mono,axiom,
% 0.26/0.62      ! [A3: set_real,F: real > rat,G: real > rat] :
% 0.26/0.62        ( ( finite_finite_real @ A3 )
% 0.26/0.62       => ( ( A3 != bot_bot_set_real )
% 0.26/0.62         => ( ! [X4: real] :
% 0.26/0.62                ( ( member_real @ X4 @ A3 )
% 0.26/0.62               => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62           => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A3 ) @ ( groups1300246762558778688al_rat @ G @ A3 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_strict_mono
% 0.26/0.62  thf(fact_7693_sum__strict__mono,axiom,
% 0.26/0.62      ! [A3: set_nat,F: nat > rat,G: nat > rat] :
% 0.26/0.62        ( ( finite_finite_nat @ A3 )
% 0.26/0.62       => ( ( A3 != bot_bot_set_nat )
% 0.26/0.62         => ( ! [X4: nat] :
% 0.26/0.62                ( ( member_nat @ X4 @ A3 )
% 0.26/0.62               => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62           => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ ( groups2906978787729119204at_rat @ G @ A3 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_strict_mono
% 0.26/0.62  thf(fact_7694_sum__strict__mono,axiom,
% 0.26/0.62      ! [A3: set_int,F: int > rat,G: int > rat] :
% 0.26/0.62        ( ( finite_finite_int @ A3 )
% 0.26/0.62       => ( ( A3 != bot_bot_set_int )
% 0.26/0.62         => ( ! [X4: int] :
% 0.26/0.62                ( ( member_int @ X4 @ A3 )
% 0.26/0.62               => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62           => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ ( groups3906332499630173760nt_rat @ G @ A3 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_strict_mono
% 0.26/0.62  thf(fact_7695_sum__strict__mono,axiom,
% 0.26/0.62      ! [A3: set_complex,F: complex > nat,G: complex > nat] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.62       => ( ( A3 != bot_bot_set_complex )
% 0.26/0.62         => ( ! [X4: complex] :
% 0.26/0.62                ( ( member_complex @ X4 @ A3 )
% 0.26/0.62               => ( ord_less_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62           => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A3 ) @ ( groups5693394587270226106ex_nat @ G @ A3 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_strict_mono
% 0.26/0.62  thf(fact_7696_sum_Ointer__filter,axiom,
% 0.26/0.62      ! [A3: set_real,G: real > real,P: real > $o] :
% 0.26/0.62        ( ( finite_finite_real @ A3 )
% 0.26/0.62       => ( ( groups8097168146408367636l_real @ G
% 0.26/0.62            @ ( collect_real
% 0.26/0.62              @ ^ [X: real] :
% 0.26/0.62                  ( ( member_real @ X @ A3 )
% 0.26/0.62                  & ( P @ X ) ) ) )
% 0.26/0.62          = ( groups8097168146408367636l_real
% 0.26/0.62            @ ^ [X: real] : ( if_real @ ( P @ X ) @ ( G @ X ) @ zero_zero_real )
% 0.26/0.62            @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.inter_filter
% 0.26/0.62  thf(fact_7697_sum_Ointer__filter,axiom,
% 0.26/0.62      ! [A3: set_int,G: int > real,P: int > $o] :
% 0.26/0.62        ( ( finite_finite_int @ A3 )
% 0.26/0.62       => ( ( groups8778361861064173332t_real @ G
% 0.26/0.62            @ ( collect_int
% 0.26/0.62              @ ^ [X: int] :
% 0.26/0.62                  ( ( member_int @ X @ A3 )
% 0.26/0.62                  & ( P @ X ) ) ) )
% 0.26/0.62          = ( groups8778361861064173332t_real
% 0.26/0.62            @ ^ [X: int] : ( if_real @ ( P @ X ) @ ( G @ X ) @ zero_zero_real )
% 0.26/0.62            @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.inter_filter
% 0.26/0.62  thf(fact_7698_sum_Ointer__filter,axiom,
% 0.26/0.62      ! [A3: set_complex,G: complex > real,P: complex > $o] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.62       => ( ( groups5808333547571424918x_real @ G
% 0.26/0.62            @ ( collect_complex
% 0.26/0.62              @ ^ [X: complex] :
% 0.26/0.62                  ( ( member_complex @ X @ A3 )
% 0.26/0.62                  & ( P @ X ) ) ) )
% 0.26/0.62          = ( groups5808333547571424918x_real
% 0.26/0.62            @ ^ [X: complex] : ( if_real @ ( P @ X ) @ ( G @ X ) @ zero_zero_real )
% 0.26/0.62            @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.inter_filter
% 0.26/0.62  thf(fact_7699_sum_Ointer__filter,axiom,
% 0.26/0.62      ! [A3: set_Extended_enat,G: extended_enat > real,P: extended_enat > $o] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.62       => ( ( groups4148127829035722712t_real @ G
% 0.26/0.62            @ ( collec4429806609662206161d_enat
% 0.26/0.62              @ ^ [X: extended_enat] :
% 0.26/0.62                  ( ( member_Extended_enat @ X @ A3 )
% 0.26/0.62                  & ( P @ X ) ) ) )
% 0.26/0.62          = ( groups4148127829035722712t_real
% 0.26/0.62            @ ^ [X: extended_enat] : ( if_real @ ( P @ X ) @ ( G @ X ) @ zero_zero_real )
% 0.26/0.62            @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.inter_filter
% 0.26/0.62  thf(fact_7700_sum_Ointer__filter,axiom,
% 0.26/0.62      ! [A3: set_real,G: real > rat,P: real > $o] :
% 0.26/0.62        ( ( finite_finite_real @ A3 )
% 0.26/0.62       => ( ( groups1300246762558778688al_rat @ G
% 0.26/0.62            @ ( collect_real
% 0.26/0.62              @ ^ [X: real] :
% 0.26/0.62                  ( ( member_real @ X @ A3 )
% 0.26/0.62                  & ( P @ X ) ) ) )
% 0.26/0.62          = ( groups1300246762558778688al_rat
% 0.26/0.62            @ ^ [X: real] : ( if_rat @ ( P @ X ) @ ( G @ X ) @ zero_zero_rat )
% 0.26/0.62            @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.inter_filter
% 0.26/0.62  thf(fact_7701_sum_Ointer__filter,axiom,
% 0.26/0.62      ! [A3: set_nat,G: nat > rat,P: nat > $o] :
% 0.26/0.62        ( ( finite_finite_nat @ A3 )
% 0.26/0.62       => ( ( groups2906978787729119204at_rat @ G
% 0.26/0.62            @ ( collect_nat
% 0.26/0.62              @ ^ [X: nat] :
% 0.26/0.62                  ( ( member_nat @ X @ A3 )
% 0.26/0.62                  & ( P @ X ) ) ) )
% 0.26/0.62          = ( groups2906978787729119204at_rat
% 0.26/0.62            @ ^ [X: nat] : ( if_rat @ ( P @ X ) @ ( G @ X ) @ zero_zero_rat )
% 0.26/0.62            @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.inter_filter
% 0.26/0.62  thf(fact_7702_sum_Ointer__filter,axiom,
% 0.26/0.62      ! [A3: set_int,G: int > rat,P: int > $o] :
% 0.26/0.62        ( ( finite_finite_int @ A3 )
% 0.26/0.62       => ( ( groups3906332499630173760nt_rat @ G
% 0.26/0.62            @ ( collect_int
% 0.26/0.62              @ ^ [X: int] :
% 0.26/0.62                  ( ( member_int @ X @ A3 )
% 0.26/0.62                  & ( P @ X ) ) ) )
% 0.26/0.62          = ( groups3906332499630173760nt_rat
% 0.26/0.62            @ ^ [X: int] : ( if_rat @ ( P @ X ) @ ( G @ X ) @ zero_zero_rat )
% 0.26/0.62            @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.inter_filter
% 0.26/0.62  thf(fact_7703_sum_Ointer__filter,axiom,
% 0.26/0.62      ! [A3: set_complex,G: complex > rat,P: complex > $o] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.62       => ( ( groups5058264527183730370ex_rat @ G
% 0.26/0.62            @ ( collect_complex
% 0.26/0.62              @ ^ [X: complex] :
% 0.26/0.62                  ( ( member_complex @ X @ A3 )
% 0.26/0.62                  & ( P @ X ) ) ) )
% 0.26/0.62          = ( groups5058264527183730370ex_rat
% 0.26/0.62            @ ^ [X: complex] : ( if_rat @ ( P @ X ) @ ( G @ X ) @ zero_zero_rat )
% 0.26/0.62            @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.inter_filter
% 0.26/0.62  thf(fact_7704_sum_Ointer__filter,axiom,
% 0.26/0.62      ! [A3: set_Extended_enat,G: extended_enat > rat,P: extended_enat > $o] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.62       => ( ( groups1392844769737527556at_rat @ G
% 0.26/0.62            @ ( collec4429806609662206161d_enat
% 0.26/0.62              @ ^ [X: extended_enat] :
% 0.26/0.62                  ( ( member_Extended_enat @ X @ A3 )
% 0.26/0.62                  & ( P @ X ) ) ) )
% 0.26/0.62          = ( groups1392844769737527556at_rat
% 0.26/0.62            @ ^ [X: extended_enat] : ( if_rat @ ( P @ X ) @ ( G @ X ) @ zero_zero_rat )
% 0.26/0.62            @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.inter_filter
% 0.26/0.62  thf(fact_7705_sum_Ointer__filter,axiom,
% 0.26/0.62      ! [A3: set_real,G: real > nat,P: real > $o] :
% 0.26/0.62        ( ( finite_finite_real @ A3 )
% 0.26/0.62       => ( ( groups1935376822645274424al_nat @ G
% 0.26/0.62            @ ( collect_real
% 0.26/0.62              @ ^ [X: real] :
% 0.26/0.62                  ( ( member_real @ X @ A3 )
% 0.26/0.62                  & ( P @ X ) ) ) )
% 0.26/0.62          = ( groups1935376822645274424al_nat
% 0.26/0.62            @ ^ [X: real] : ( if_nat @ ( P @ X ) @ ( G @ X ) @ zero_zero_nat )
% 0.26/0.62            @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.inter_filter
% 0.26/0.62  thf(fact_7706_sum__nonneg__0,axiom,
% 0.26/0.62      ! [S: set_real,F: real > real,I: real] :
% 0.26/0.62        ( ( finite_finite_real @ S )
% 0.26/0.62       => ( ! [I3: real] :
% 0.26/0.62              ( ( member_real @ I3 @ S )
% 0.26/0.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.62         => ( ( ( groups8097168146408367636l_real @ F @ S )
% 0.26/0.62              = zero_zero_real )
% 0.26/0.62           => ( ( member_real @ I @ S )
% 0.26/0.62             => ( ( F @ I )
% 0.26/0.62                = zero_zero_real ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_0
% 0.26/0.62  thf(fact_7707_sum__nonneg__0,axiom,
% 0.26/0.62      ! [S: set_int,F: int > real,I: int] :
% 0.26/0.62        ( ( finite_finite_int @ S )
% 0.26/0.62       => ( ! [I3: int] :
% 0.26/0.62              ( ( member_int @ I3 @ S )
% 0.26/0.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.62         => ( ( ( groups8778361861064173332t_real @ F @ S )
% 0.26/0.62              = zero_zero_real )
% 0.26/0.62           => ( ( member_int @ I @ S )
% 0.26/0.62             => ( ( F @ I )
% 0.26/0.62                = zero_zero_real ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_0
% 0.26/0.62  thf(fact_7708_sum__nonneg__0,axiom,
% 0.26/0.62      ! [S: set_complex,F: complex > real,I: complex] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ S )
% 0.26/0.62       => ( ! [I3: complex] :
% 0.26/0.62              ( ( member_complex @ I3 @ S )
% 0.26/0.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.62         => ( ( ( groups5808333547571424918x_real @ F @ S )
% 0.26/0.62              = zero_zero_real )
% 0.26/0.62           => ( ( member_complex @ I @ S )
% 0.26/0.62             => ( ( F @ I )
% 0.26/0.62                = zero_zero_real ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_0
% 0.26/0.62  thf(fact_7709_sum__nonneg__0,axiom,
% 0.26/0.62      ! [S: set_Extended_enat,F: extended_enat > real,I: extended_enat] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ S )
% 0.26/0.62       => ( ! [I3: extended_enat] :
% 0.26/0.62              ( ( member_Extended_enat @ I3 @ S )
% 0.26/0.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.62         => ( ( ( groups4148127829035722712t_real @ F @ S )
% 0.26/0.62              = zero_zero_real )
% 0.26/0.62           => ( ( member_Extended_enat @ I @ S )
% 0.26/0.62             => ( ( F @ I )
% 0.26/0.62                = zero_zero_real ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_0
% 0.26/0.62  thf(fact_7710_sum__nonneg__0,axiom,
% 0.26/0.62      ! [S: set_real,F: real > rat,I: real] :
% 0.26/0.62        ( ( finite_finite_real @ S )
% 0.26/0.62       => ( ! [I3: real] :
% 0.26/0.62              ( ( member_real @ I3 @ S )
% 0.26/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.26/0.62         => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 0.26/0.62              = zero_zero_rat )
% 0.26/0.62           => ( ( member_real @ I @ S )
% 0.26/0.62             => ( ( F @ I )
% 0.26/0.62                = zero_zero_rat ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_0
% 0.26/0.62  thf(fact_7711_sum__nonneg__0,axiom,
% 0.26/0.62      ! [S: set_nat,F: nat > rat,I: nat] :
% 0.26/0.62        ( ( finite_finite_nat @ S )
% 0.26/0.62       => ( ! [I3: nat] :
% 0.26/0.62              ( ( member_nat @ I3 @ S )
% 0.26/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.26/0.62         => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 0.26/0.62              = zero_zero_rat )
% 0.26/0.62           => ( ( member_nat @ I @ S )
% 0.26/0.62             => ( ( F @ I )
% 0.26/0.62                = zero_zero_rat ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_0
% 0.26/0.62  thf(fact_7712_sum__nonneg__0,axiom,
% 0.26/0.62      ! [S: set_int,F: int > rat,I: int] :
% 0.26/0.62        ( ( finite_finite_int @ S )
% 0.26/0.62       => ( ! [I3: int] :
% 0.26/0.62              ( ( member_int @ I3 @ S )
% 0.26/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.26/0.62         => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 0.26/0.62              = zero_zero_rat )
% 0.26/0.62           => ( ( member_int @ I @ S )
% 0.26/0.62             => ( ( F @ I )
% 0.26/0.62                = zero_zero_rat ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_0
% 0.26/0.62  thf(fact_7713_sum__nonneg__0,axiom,
% 0.26/0.62      ! [S: set_complex,F: complex > rat,I: complex] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ S )
% 0.26/0.62       => ( ! [I3: complex] :
% 0.26/0.62              ( ( member_complex @ I3 @ S )
% 0.26/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.26/0.62         => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 0.26/0.62              = zero_zero_rat )
% 0.26/0.62           => ( ( member_complex @ I @ S )
% 0.26/0.62             => ( ( F @ I )
% 0.26/0.62                = zero_zero_rat ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_0
% 0.26/0.62  thf(fact_7714_sum__nonneg__0,axiom,
% 0.26/0.62      ! [S: set_Extended_enat,F: extended_enat > rat,I: extended_enat] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ S )
% 0.26/0.62       => ( ! [I3: extended_enat] :
% 0.26/0.62              ( ( member_Extended_enat @ I3 @ S )
% 0.26/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.26/0.62         => ( ( ( groups1392844769737527556at_rat @ F @ S )
% 0.26/0.62              = zero_zero_rat )
% 0.26/0.62           => ( ( member_Extended_enat @ I @ S )
% 0.26/0.62             => ( ( F @ I )
% 0.26/0.62                = zero_zero_rat ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_0
% 0.26/0.62  thf(fact_7715_sum__nonneg__0,axiom,
% 0.26/0.62      ! [S: set_real,F: real > nat,I: real] :
% 0.26/0.62        ( ( finite_finite_real @ S )
% 0.26/0.62       => ( ! [I3: real] :
% 0.26/0.62              ( ( member_real @ I3 @ S )
% 0.26/0.62             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 0.26/0.62         => ( ( ( groups1935376822645274424al_nat @ F @ S )
% 0.26/0.62              = zero_zero_nat )
% 0.26/0.62           => ( ( member_real @ I @ S )
% 0.26/0.62             => ( ( F @ I )
% 0.26/0.62                = zero_zero_nat ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_0
% 0.26/0.62  thf(fact_7716_sum__nonneg__leq__bound,axiom,
% 0.26/0.62      ! [S: set_real,F: real > real,B5: real,I: real] :
% 0.26/0.62        ( ( finite_finite_real @ S )
% 0.26/0.62       => ( ! [I3: real] :
% 0.26/0.62              ( ( member_real @ I3 @ S )
% 0.26/0.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.62         => ( ( ( groups8097168146408367636l_real @ F @ S )
% 0.26/0.62              = B5 )
% 0.26/0.62           => ( ( member_real @ I @ S )
% 0.26/0.62             => ( ord_less_eq_real @ ( F @ I ) @ B5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_leq_bound
% 0.26/0.62  thf(fact_7717_sum__nonneg__leq__bound,axiom,
% 0.26/0.62      ! [S: set_int,F: int > real,B5: real,I: int] :
% 0.26/0.62        ( ( finite_finite_int @ S )
% 0.26/0.62       => ( ! [I3: int] :
% 0.26/0.62              ( ( member_int @ I3 @ S )
% 0.26/0.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.62         => ( ( ( groups8778361861064173332t_real @ F @ S )
% 0.26/0.62              = B5 )
% 0.26/0.62           => ( ( member_int @ I @ S )
% 0.26/0.62             => ( ord_less_eq_real @ ( F @ I ) @ B5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_leq_bound
% 0.26/0.62  thf(fact_7718_sum__nonneg__leq__bound,axiom,
% 0.26/0.62      ! [S: set_complex,F: complex > real,B5: real,I: complex] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ S )
% 0.26/0.62       => ( ! [I3: complex] :
% 0.26/0.62              ( ( member_complex @ I3 @ S )
% 0.26/0.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.62         => ( ( ( groups5808333547571424918x_real @ F @ S )
% 0.26/0.62              = B5 )
% 0.26/0.62           => ( ( member_complex @ I @ S )
% 0.26/0.62             => ( ord_less_eq_real @ ( F @ I ) @ B5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_leq_bound
% 0.26/0.62  thf(fact_7719_sum__nonneg__leq__bound,axiom,
% 0.26/0.62      ! [S: set_Extended_enat,F: extended_enat > real,B5: real,I: extended_enat] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ S )
% 0.26/0.62       => ( ! [I3: extended_enat] :
% 0.26/0.62              ( ( member_Extended_enat @ I3 @ S )
% 0.26/0.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.62         => ( ( ( groups4148127829035722712t_real @ F @ S )
% 0.26/0.62              = B5 )
% 0.26/0.62           => ( ( member_Extended_enat @ I @ S )
% 0.26/0.62             => ( ord_less_eq_real @ ( F @ I ) @ B5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_leq_bound
% 0.26/0.62  thf(fact_7720_sum__nonneg__leq__bound,axiom,
% 0.26/0.62      ! [S: set_real,F: real > rat,B5: rat,I: real] :
% 0.26/0.62        ( ( finite_finite_real @ S )
% 0.26/0.62       => ( ! [I3: real] :
% 0.26/0.62              ( ( member_real @ I3 @ S )
% 0.26/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.26/0.62         => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 0.26/0.62              = B5 )
% 0.26/0.62           => ( ( member_real @ I @ S )
% 0.26/0.62             => ( ord_less_eq_rat @ ( F @ I ) @ B5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_leq_bound
% 0.26/0.62  thf(fact_7721_sum__nonneg__leq__bound,axiom,
% 0.26/0.62      ! [S: set_nat,F: nat > rat,B5: rat,I: nat] :
% 0.26/0.62        ( ( finite_finite_nat @ S )
% 0.26/0.62       => ( ! [I3: nat] :
% 0.26/0.62              ( ( member_nat @ I3 @ S )
% 0.26/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.26/0.62         => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 0.26/0.62              = B5 )
% 0.26/0.62           => ( ( member_nat @ I @ S )
% 0.26/0.62             => ( ord_less_eq_rat @ ( F @ I ) @ B5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_leq_bound
% 0.26/0.62  thf(fact_7722_sum__nonneg__leq__bound,axiom,
% 0.26/0.62      ! [S: set_int,F: int > rat,B5: rat,I: int] :
% 0.26/0.62        ( ( finite_finite_int @ S )
% 0.26/0.62       => ( ! [I3: int] :
% 0.26/0.62              ( ( member_int @ I3 @ S )
% 0.26/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.26/0.62         => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 0.26/0.62              = B5 )
% 0.26/0.62           => ( ( member_int @ I @ S )
% 0.26/0.62             => ( ord_less_eq_rat @ ( F @ I ) @ B5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_leq_bound
% 0.26/0.62  thf(fact_7723_sum__nonneg__leq__bound,axiom,
% 0.26/0.62      ! [S: set_complex,F: complex > rat,B5: rat,I: complex] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ S )
% 0.26/0.62       => ( ! [I3: complex] :
% 0.26/0.62              ( ( member_complex @ I3 @ S )
% 0.26/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.26/0.62         => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 0.26/0.62              = B5 )
% 0.26/0.62           => ( ( member_complex @ I @ S )
% 0.26/0.62             => ( ord_less_eq_rat @ ( F @ I ) @ B5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_leq_bound
% 0.26/0.62  thf(fact_7724_sum__nonneg__leq__bound,axiom,
% 0.26/0.62      ! [S: set_Extended_enat,F: extended_enat > rat,B5: rat,I: extended_enat] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ S )
% 0.26/0.62       => ( ! [I3: extended_enat] :
% 0.26/0.62              ( ( member_Extended_enat @ I3 @ S )
% 0.26/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.26/0.62         => ( ( ( groups1392844769737527556at_rat @ F @ S )
% 0.26/0.62              = B5 )
% 0.26/0.62           => ( ( member_Extended_enat @ I @ S )
% 0.26/0.62             => ( ord_less_eq_rat @ ( F @ I ) @ B5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_leq_bound
% 0.26/0.62  thf(fact_7725_sum__nonneg__leq__bound,axiom,
% 0.26/0.62      ! [S: set_real,F: real > nat,B5: nat,I: real] :
% 0.26/0.62        ( ( finite_finite_real @ S )
% 0.26/0.62       => ( ! [I3: real] :
% 0.26/0.62              ( ( member_real @ I3 @ S )
% 0.26/0.62             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 0.26/0.62         => ( ( ( groups1935376822645274424al_nat @ F @ S )
% 0.26/0.62              = B5 )
% 0.26/0.62           => ( ( member_real @ I @ S )
% 0.26/0.62             => ( ord_less_eq_nat @ ( F @ I ) @ B5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_leq_bound
% 0.26/0.62  thf(fact_7726_sum__le__included,axiom,
% 0.26/0.62      ! [S: set_int,T: set_int,G: int > real,I: int > int,F: int > real] :
% 0.26/0.62        ( ( finite_finite_int @ S )
% 0.26/0.62       => ( ( finite_finite_int @ T )
% 0.26/0.62         => ( ! [X4: int] :
% 0.26/0.62                ( ( member_int @ X4 @ T )
% 0.26/0.62               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 0.26/0.62           => ( ! [X4: int] :
% 0.26/0.62                  ( ( member_int @ X4 @ S )
% 0.26/0.62                 => ? [Xa2: int] :
% 0.26/0.62                      ( ( member_int @ Xa2 @ T )
% 0.26/0.62                      & ( ( I @ Xa2 )
% 0.26/0.62                        = X4 )
% 0.26/0.62                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 0.26/0.62             => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_le_included
% 0.26/0.62  thf(fact_7727_sum__le__included,axiom,
% 0.26/0.62      ! [S: set_int,T: set_complex,G: complex > real,I: complex > int,F: int > real] :
% 0.26/0.62        ( ( finite_finite_int @ S )
% 0.26/0.62       => ( ( finite3207457112153483333omplex @ T )
% 0.26/0.62         => ( ! [X4: complex] :
% 0.26/0.62                ( ( member_complex @ X4 @ T )
% 0.26/0.62               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 0.26/0.62           => ( ! [X4: int] :
% 0.26/0.62                  ( ( member_int @ X4 @ S )
% 0.26/0.62                 => ? [Xa2: complex] :
% 0.26/0.62                      ( ( member_complex @ Xa2 @ T )
% 0.26/0.62                      & ( ( I @ Xa2 )
% 0.26/0.62                        = X4 )
% 0.26/0.62                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 0.26/0.62             => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_le_included
% 0.26/0.62  thf(fact_7728_sum__le__included,axiom,
% 0.26/0.62      ! [S: set_int,T: set_Extended_enat,G: extended_enat > real,I: extended_enat > int,F: int > real] :
% 0.26/0.62        ( ( finite_finite_int @ S )
% 0.26/0.62       => ( ( finite4001608067531595151d_enat @ T )
% 0.26/0.62         => ( ! [X4: extended_enat] :
% 0.26/0.62                ( ( member_Extended_enat @ X4 @ T )
% 0.26/0.62               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 0.26/0.62           => ( ! [X4: int] :
% 0.26/0.62                  ( ( member_int @ X4 @ S )
% 0.26/0.62                 => ? [Xa2: extended_enat] :
% 0.26/0.62                      ( ( member_Extended_enat @ Xa2 @ T )
% 0.26/0.62                      & ( ( I @ Xa2 )
% 0.26/0.62                        = X4 )
% 0.26/0.62                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 0.26/0.62             => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups4148127829035722712t_real @ G @ T ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_le_included
% 0.26/0.62  thf(fact_7729_sum__le__included,axiom,
% 0.26/0.62      ! [S: set_complex,T: set_int,G: int > real,I: int > complex,F: complex > real] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ S )
% 0.26/0.62       => ( ( finite_finite_int @ T )
% 0.26/0.62         => ( ! [X4: int] :
% 0.26/0.62                ( ( member_int @ X4 @ T )
% 0.26/0.62               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 0.26/0.62           => ( ! [X4: complex] :
% 0.26/0.62                  ( ( member_complex @ X4 @ S )
% 0.26/0.62                 => ? [Xa2: int] :
% 0.26/0.62                      ( ( member_int @ Xa2 @ T )
% 0.26/0.62                      & ( ( I @ Xa2 )
% 0.26/0.62                        = X4 )
% 0.26/0.62                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 0.26/0.62             => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_le_included
% 0.26/0.62  thf(fact_7730_sum__le__included,axiom,
% 0.26/0.62      ! [S: set_complex,T: set_complex,G: complex > real,I: complex > complex,F: complex > real] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ S )
% 0.26/0.62       => ( ( finite3207457112153483333omplex @ T )
% 0.26/0.62         => ( ! [X4: complex] :
% 0.26/0.62                ( ( member_complex @ X4 @ T )
% 0.26/0.62               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 0.26/0.62           => ( ! [X4: complex] :
% 0.26/0.62                  ( ( member_complex @ X4 @ S )
% 0.26/0.62                 => ? [Xa2: complex] :
% 0.26/0.62                      ( ( member_complex @ Xa2 @ T )
% 0.26/0.62                      & ( ( I @ Xa2 )
% 0.26/0.62                        = X4 )
% 0.26/0.62                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 0.26/0.62             => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_le_included
% 0.26/0.62  thf(fact_7731_sum__le__included,axiom,
% 0.26/0.62      ! [S: set_complex,T: set_Extended_enat,G: extended_enat > real,I: extended_enat > complex,F: complex > real] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ S )
% 0.26/0.62       => ( ( finite4001608067531595151d_enat @ T )
% 0.26/0.62         => ( ! [X4: extended_enat] :
% 0.26/0.62                ( ( member_Extended_enat @ X4 @ T )
% 0.26/0.62               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 0.26/0.62           => ( ! [X4: complex] :
% 0.26/0.62                  ( ( member_complex @ X4 @ S )
% 0.26/0.62                 => ? [Xa2: extended_enat] :
% 0.26/0.62                      ( ( member_Extended_enat @ Xa2 @ T )
% 0.26/0.62                      & ( ( I @ Xa2 )
% 0.26/0.62                        = X4 )
% 0.26/0.62                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 0.26/0.62             => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups4148127829035722712t_real @ G @ T ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_le_included
% 0.26/0.62  thf(fact_7732_sum__le__included,axiom,
% 0.26/0.62      ! [S: set_Extended_enat,T: set_int,G: int > real,I: int > extended_enat,F: extended_enat > real] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ S )
% 0.26/0.62       => ( ( finite_finite_int @ T )
% 0.26/0.62         => ( ! [X4: int] :
% 0.26/0.62                ( ( member_int @ X4 @ T )
% 0.26/0.62               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 0.26/0.62           => ( ! [X4: extended_enat] :
% 0.26/0.62                  ( ( member_Extended_enat @ X4 @ S )
% 0.26/0.62                 => ? [Xa2: int] :
% 0.26/0.62                      ( ( member_int @ Xa2 @ T )
% 0.26/0.62                      & ( ( I @ Xa2 )
% 0.26/0.62                        = X4 )
% 0.26/0.62                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 0.26/0.62             => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_le_included
% 0.26/0.62  thf(fact_7733_sum__le__included,axiom,
% 0.26/0.62      ! [S: set_Extended_enat,T: set_complex,G: complex > real,I: complex > extended_enat,F: extended_enat > real] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ S )
% 0.26/0.62       => ( ( finite3207457112153483333omplex @ T )
% 0.26/0.62         => ( ! [X4: complex] :
% 0.26/0.62                ( ( member_complex @ X4 @ T )
% 0.26/0.62               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 0.26/0.62           => ( ! [X4: extended_enat] :
% 0.26/0.62                  ( ( member_Extended_enat @ X4 @ S )
% 0.26/0.62                 => ? [Xa2: complex] :
% 0.26/0.62                      ( ( member_complex @ Xa2 @ T )
% 0.26/0.62                      & ( ( I @ Xa2 )
% 0.26/0.62                        = X4 )
% 0.26/0.62                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 0.26/0.62             => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_le_included
% 0.26/0.62  thf(fact_7734_sum__le__included,axiom,
% 0.26/0.62      ! [S: set_Extended_enat,T: set_Extended_enat,G: extended_enat > real,I: extended_enat > extended_enat,F: extended_enat > real] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ S )
% 0.26/0.62       => ( ( finite4001608067531595151d_enat @ T )
% 0.26/0.62         => ( ! [X4: extended_enat] :
% 0.26/0.62                ( ( member_Extended_enat @ X4 @ T )
% 0.26/0.62               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 0.26/0.62           => ( ! [X4: extended_enat] :
% 0.26/0.62                  ( ( member_Extended_enat @ X4 @ S )
% 0.26/0.62                 => ? [Xa2: extended_enat] :
% 0.26/0.62                      ( ( member_Extended_enat @ Xa2 @ T )
% 0.26/0.62                      & ( ( I @ Xa2 )
% 0.26/0.62                        = X4 )
% 0.26/0.62                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 0.26/0.62             => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ S ) @ ( groups4148127829035722712t_real @ G @ T ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_le_included
% 0.26/0.62  thf(fact_7735_sum__le__included,axiom,
% 0.26/0.62      ! [S: set_nat,T: set_nat,G: nat > rat,I: nat > nat,F: nat > rat] :
% 0.26/0.62        ( ( finite_finite_nat @ S )
% 0.26/0.62       => ( ( finite_finite_nat @ T )
% 0.26/0.62         => ( ! [X4: nat] :
% 0.26/0.62                ( ( member_nat @ X4 @ T )
% 0.26/0.62               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 0.26/0.62           => ( ! [X4: nat] :
% 0.26/0.62                  ( ( member_nat @ X4 @ S )
% 0.26/0.62                 => ? [Xa2: nat] :
% 0.26/0.62                      ( ( member_nat @ Xa2 @ T )
% 0.26/0.62                      & ( ( I @ Xa2 )
% 0.26/0.62                        = X4 )
% 0.26/0.62                      & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 0.26/0.62             => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_le_included
% 0.26/0.62  thf(fact_7736_sum__nonneg__eq__0__iff,axiom,
% 0.26/0.62      ! [A3: set_real,F: real > real] :
% 0.26/0.62        ( ( finite_finite_real @ A3 )
% 0.26/0.62       => ( ! [X4: real] :
% 0.26/0.62              ( ( member_real @ X4 @ A3 )
% 0.26/0.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.26/0.62         => ( ( ( groups8097168146408367636l_real @ F @ A3 )
% 0.26/0.62              = zero_zero_real )
% 0.26/0.62            = ( ! [X: real] :
% 0.26/0.62                  ( ( member_real @ X @ A3 )
% 0.26/0.62                 => ( ( F @ X )
% 0.26/0.62                    = zero_zero_real ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_eq_0_iff
% 0.26/0.62  thf(fact_7737_sum__nonneg__eq__0__iff,axiom,
% 0.26/0.62      ! [A3: set_int,F: int > real] :
% 0.26/0.62        ( ( finite_finite_int @ A3 )
% 0.26/0.62       => ( ! [X4: int] :
% 0.26/0.62              ( ( member_int @ X4 @ A3 )
% 0.26/0.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.26/0.62         => ( ( ( groups8778361861064173332t_real @ F @ A3 )
% 0.26/0.62              = zero_zero_real )
% 0.26/0.62            = ( ! [X: int] :
% 0.26/0.62                  ( ( member_int @ X @ A3 )
% 0.26/0.62                 => ( ( F @ X )
% 0.26/0.62                    = zero_zero_real ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_eq_0_iff
% 0.26/0.62  thf(fact_7738_sum__nonneg__eq__0__iff,axiom,
% 0.26/0.62      ! [A3: set_complex,F: complex > real] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.62       => ( ! [X4: complex] :
% 0.26/0.62              ( ( member_complex @ X4 @ A3 )
% 0.26/0.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.26/0.62         => ( ( ( groups5808333547571424918x_real @ F @ A3 )
% 0.26/0.62              = zero_zero_real )
% 0.26/0.62            = ( ! [X: complex] :
% 0.26/0.62                  ( ( member_complex @ X @ A3 )
% 0.26/0.62                 => ( ( F @ X )
% 0.26/0.62                    = zero_zero_real ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_eq_0_iff
% 0.26/0.62  thf(fact_7739_sum__nonneg__eq__0__iff,axiom,
% 0.26/0.62      ! [A3: set_Extended_enat,F: extended_enat > real] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.62       => ( ! [X4: extended_enat] :
% 0.26/0.62              ( ( member_Extended_enat @ X4 @ A3 )
% 0.26/0.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.26/0.62         => ( ( ( groups4148127829035722712t_real @ F @ A3 )
% 0.26/0.62              = zero_zero_real )
% 0.26/0.62            = ( ! [X: extended_enat] :
% 0.26/0.62                  ( ( member_Extended_enat @ X @ A3 )
% 0.26/0.62                 => ( ( F @ X )
% 0.26/0.62                    = zero_zero_real ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_eq_0_iff
% 0.26/0.62  thf(fact_7740_sum__nonneg__eq__0__iff,axiom,
% 0.26/0.62      ! [A3: set_real,F: real > rat] :
% 0.26/0.62        ( ( finite_finite_real @ A3 )
% 0.26/0.62       => ( ! [X4: real] :
% 0.26/0.62              ( ( member_real @ X4 @ A3 )
% 0.26/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.26/0.62         => ( ( ( groups1300246762558778688al_rat @ F @ A3 )
% 0.26/0.62              = zero_zero_rat )
% 0.26/0.62            = ( ! [X: real] :
% 0.26/0.62                  ( ( member_real @ X @ A3 )
% 0.26/0.62                 => ( ( F @ X )
% 0.26/0.62                    = zero_zero_rat ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_eq_0_iff
% 0.26/0.62  thf(fact_7741_sum__nonneg__eq__0__iff,axiom,
% 0.26/0.62      ! [A3: set_nat,F: nat > rat] :
% 0.26/0.62        ( ( finite_finite_nat @ A3 )
% 0.26/0.62       => ( ! [X4: nat] :
% 0.26/0.62              ( ( member_nat @ X4 @ A3 )
% 0.26/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.26/0.62         => ( ( ( groups2906978787729119204at_rat @ F @ A3 )
% 0.26/0.62              = zero_zero_rat )
% 0.26/0.62            = ( ! [X: nat] :
% 0.26/0.62                  ( ( member_nat @ X @ A3 )
% 0.26/0.62                 => ( ( F @ X )
% 0.26/0.62                    = zero_zero_rat ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_eq_0_iff
% 0.26/0.62  thf(fact_7742_sum__nonneg__eq__0__iff,axiom,
% 0.26/0.62      ! [A3: set_int,F: int > rat] :
% 0.26/0.62        ( ( finite_finite_int @ A3 )
% 0.26/0.62       => ( ! [X4: int] :
% 0.26/0.62              ( ( member_int @ X4 @ A3 )
% 0.26/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.26/0.62         => ( ( ( groups3906332499630173760nt_rat @ F @ A3 )
% 0.26/0.62              = zero_zero_rat )
% 0.26/0.62            = ( ! [X: int] :
% 0.26/0.62                  ( ( member_int @ X @ A3 )
% 0.26/0.62                 => ( ( F @ X )
% 0.26/0.62                    = zero_zero_rat ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_eq_0_iff
% 0.26/0.62  thf(fact_7743_sum__nonneg__eq__0__iff,axiom,
% 0.26/0.62      ! [A3: set_complex,F: complex > rat] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.62       => ( ! [X4: complex] :
% 0.26/0.62              ( ( member_complex @ X4 @ A3 )
% 0.26/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.26/0.62         => ( ( ( groups5058264527183730370ex_rat @ F @ A3 )
% 0.26/0.62              = zero_zero_rat )
% 0.26/0.62            = ( ! [X: complex] :
% 0.26/0.62                  ( ( member_complex @ X @ A3 )
% 0.26/0.62                 => ( ( F @ X )
% 0.26/0.62                    = zero_zero_rat ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_eq_0_iff
% 0.26/0.62  thf(fact_7744_sum__nonneg__eq__0__iff,axiom,
% 0.26/0.62      ! [A3: set_Extended_enat,F: extended_enat > rat] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.62       => ( ! [X4: extended_enat] :
% 0.26/0.62              ( ( member_Extended_enat @ X4 @ A3 )
% 0.26/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.26/0.62         => ( ( ( groups1392844769737527556at_rat @ F @ A3 )
% 0.26/0.62              = zero_zero_rat )
% 0.26/0.62            = ( ! [X: extended_enat] :
% 0.26/0.62                  ( ( member_Extended_enat @ X @ A3 )
% 0.26/0.62                 => ( ( F @ X )
% 0.26/0.62                    = zero_zero_rat ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_eq_0_iff
% 0.26/0.62  thf(fact_7745_sum__nonneg__eq__0__iff,axiom,
% 0.26/0.62      ! [A3: set_real,F: real > nat] :
% 0.26/0.62        ( ( finite_finite_real @ A3 )
% 0.26/0.62       => ( ! [X4: real] :
% 0.26/0.62              ( ( member_real @ X4 @ A3 )
% 0.26/0.62             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 0.26/0.62         => ( ( ( groups1935376822645274424al_nat @ F @ A3 )
% 0.26/0.62              = zero_zero_nat )
% 0.26/0.62            = ( ! [X: real] :
% 0.26/0.62                  ( ( member_real @ X @ A3 )
% 0.26/0.62                 => ( ( F @ X )
% 0.26/0.62                    = zero_zero_nat ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg_eq_0_iff
% 0.26/0.62  thf(fact_7746_sum__mono__inv,axiom,
% 0.26/0.62      ! [F: real > rat,I5: set_real,G: real > rat,I: real] :
% 0.26/0.62        ( ( ( groups1300246762558778688al_rat @ F @ I5 )
% 0.26/0.62          = ( groups1300246762558778688al_rat @ G @ I5 ) )
% 0.26/0.62       => ( ! [I3: real] :
% 0.26/0.62              ( ( member_real @ I3 @ I5 )
% 0.26/0.62             => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.26/0.62         => ( ( member_real @ I @ I5 )
% 0.26/0.62           => ( ( finite_finite_real @ I5 )
% 0.26/0.62             => ( ( F @ I )
% 0.26/0.62                = ( G @ I ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono_inv
% 0.26/0.62  thf(fact_7747_sum__mono__inv,axiom,
% 0.26/0.62      ! [F: nat > rat,I5: set_nat,G: nat > rat,I: nat] :
% 0.26/0.62        ( ( ( groups2906978787729119204at_rat @ F @ I5 )
% 0.26/0.62          = ( groups2906978787729119204at_rat @ G @ I5 ) )
% 0.26/0.62       => ( ! [I3: nat] :
% 0.26/0.62              ( ( member_nat @ I3 @ I5 )
% 0.26/0.62             => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.26/0.62         => ( ( member_nat @ I @ I5 )
% 0.26/0.62           => ( ( finite_finite_nat @ I5 )
% 0.26/0.62             => ( ( F @ I )
% 0.26/0.62                = ( G @ I ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono_inv
% 0.26/0.62  thf(fact_7748_sum__mono__inv,axiom,
% 0.26/0.62      ! [F: int > rat,I5: set_int,G: int > rat,I: int] :
% 0.26/0.62        ( ( ( groups3906332499630173760nt_rat @ F @ I5 )
% 0.26/0.62          = ( groups3906332499630173760nt_rat @ G @ I5 ) )
% 0.26/0.62       => ( ! [I3: int] :
% 0.26/0.62              ( ( member_int @ I3 @ I5 )
% 0.26/0.62             => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.26/0.62         => ( ( member_int @ I @ I5 )
% 0.26/0.62           => ( ( finite_finite_int @ I5 )
% 0.26/0.62             => ( ( F @ I )
% 0.26/0.62                = ( G @ I ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono_inv
% 0.26/0.62  thf(fact_7749_sum__mono__inv,axiom,
% 0.26/0.62      ! [F: complex > rat,I5: set_complex,G: complex > rat,I: complex] :
% 0.26/0.62        ( ( ( groups5058264527183730370ex_rat @ F @ I5 )
% 0.26/0.62          = ( groups5058264527183730370ex_rat @ G @ I5 ) )
% 0.26/0.62       => ( ! [I3: complex] :
% 0.26/0.62              ( ( member_complex @ I3 @ I5 )
% 0.26/0.62             => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.26/0.62         => ( ( member_complex @ I @ I5 )
% 0.26/0.62           => ( ( finite3207457112153483333omplex @ I5 )
% 0.26/0.62             => ( ( F @ I )
% 0.26/0.62                = ( G @ I ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono_inv
% 0.26/0.62  thf(fact_7750_sum__mono__inv,axiom,
% 0.26/0.62      ! [F: extended_enat > rat,I5: set_Extended_enat,G: extended_enat > rat,I: extended_enat] :
% 0.26/0.62        ( ( ( groups1392844769737527556at_rat @ F @ I5 )
% 0.26/0.62          = ( groups1392844769737527556at_rat @ G @ I5 ) )
% 0.26/0.62       => ( ! [I3: extended_enat] :
% 0.26/0.62              ( ( member_Extended_enat @ I3 @ I5 )
% 0.26/0.62             => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.26/0.62         => ( ( member_Extended_enat @ I @ I5 )
% 0.26/0.62           => ( ( finite4001608067531595151d_enat @ I5 )
% 0.26/0.62             => ( ( F @ I )
% 0.26/0.62                = ( G @ I ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono_inv
% 0.26/0.62  thf(fact_7751_sum__mono__inv,axiom,
% 0.26/0.62      ! [F: real > nat,I5: set_real,G: real > nat,I: real] :
% 0.26/0.62        ( ( ( groups1935376822645274424al_nat @ F @ I5 )
% 0.26/0.62          = ( groups1935376822645274424al_nat @ G @ I5 ) )
% 0.26/0.62       => ( ! [I3: real] :
% 0.26/0.62              ( ( member_real @ I3 @ I5 )
% 0.26/0.62             => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.26/0.62         => ( ( member_real @ I @ I5 )
% 0.26/0.62           => ( ( finite_finite_real @ I5 )
% 0.26/0.62             => ( ( F @ I )
% 0.26/0.62                = ( G @ I ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono_inv
% 0.26/0.62  thf(fact_7752_sum__mono__inv,axiom,
% 0.26/0.62      ! [F: int > nat,I5: set_int,G: int > nat,I: int] :
% 0.26/0.62        ( ( ( groups4541462559716669496nt_nat @ F @ I5 )
% 0.26/0.62          = ( groups4541462559716669496nt_nat @ G @ I5 ) )
% 0.26/0.62       => ( ! [I3: int] :
% 0.26/0.62              ( ( member_int @ I3 @ I5 )
% 0.26/0.62             => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.26/0.62         => ( ( member_int @ I @ I5 )
% 0.26/0.62           => ( ( finite_finite_int @ I5 )
% 0.26/0.62             => ( ( F @ I )
% 0.26/0.62                = ( G @ I ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono_inv
% 0.26/0.62  thf(fact_7753_sum__mono__inv,axiom,
% 0.26/0.62      ! [F: complex > nat,I5: set_complex,G: complex > nat,I: complex] :
% 0.26/0.62        ( ( ( groups5693394587270226106ex_nat @ F @ I5 )
% 0.26/0.62          = ( groups5693394587270226106ex_nat @ G @ I5 ) )
% 0.26/0.62       => ( ! [I3: complex] :
% 0.26/0.62              ( ( member_complex @ I3 @ I5 )
% 0.26/0.62             => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.26/0.62         => ( ( member_complex @ I @ I5 )
% 0.26/0.62           => ( ( finite3207457112153483333omplex @ I5 )
% 0.26/0.62             => ( ( F @ I )
% 0.26/0.62                = ( G @ I ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono_inv
% 0.26/0.62  thf(fact_7754_sum__mono__inv,axiom,
% 0.26/0.62      ! [F: extended_enat > nat,I5: set_Extended_enat,G: extended_enat > nat,I: extended_enat] :
% 0.26/0.62        ( ( ( groups2027974829824023292at_nat @ F @ I5 )
% 0.26/0.62          = ( groups2027974829824023292at_nat @ G @ I5 ) )
% 0.26/0.62       => ( ! [I3: extended_enat] :
% 0.26/0.62              ( ( member_Extended_enat @ I3 @ I5 )
% 0.26/0.62             => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.26/0.62         => ( ( member_Extended_enat @ I @ I5 )
% 0.26/0.62           => ( ( finite4001608067531595151d_enat @ I5 )
% 0.26/0.62             => ( ( F @ I )
% 0.26/0.62                = ( G @ I ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono_inv
% 0.26/0.62  thf(fact_7755_sum__mono__inv,axiom,
% 0.26/0.62      ! [F: real > int,I5: set_real,G: real > int,I: real] :
% 0.26/0.62        ( ( ( groups1932886352136224148al_int @ F @ I5 )
% 0.26/0.62          = ( groups1932886352136224148al_int @ G @ I5 ) )
% 0.26/0.62       => ( ! [I3: real] :
% 0.26/0.62              ( ( member_real @ I3 @ I5 )
% 0.26/0.62             => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.26/0.62         => ( ( member_real @ I @ I5 )
% 0.26/0.62           => ( ( finite_finite_real @ I5 )
% 0.26/0.62             => ( ( F @ I )
% 0.26/0.62                = ( G @ I ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono_inv
% 0.26/0.62  thf(fact_7756_sum_Orelated,axiom,
% 0.26/0.62      ! [R3: real > real > $o,S2: set_int,H2: int > real,G: int > real] :
% 0.26/0.62        ( ( R3 @ zero_zero_real @ zero_zero_real )
% 0.26/0.62       => ( ! [X1: real,Y1: real,X22: real,Y22: real] :
% 0.26/0.62              ( ( ( R3 @ X1 @ X22 )
% 0.26/0.62                & ( R3 @ Y1 @ Y22 ) )
% 0.26/0.62             => ( R3 @ ( plus_plus_real @ X1 @ Y1 ) @ ( plus_plus_real @ X22 @ Y22 ) ) )
% 0.26/0.62         => ( ( finite_finite_int @ S2 )
% 0.26/0.62           => ( ! [X4: int] :
% 0.26/0.62                  ( ( member_int @ X4 @ S2 )
% 0.26/0.62                 => ( R3 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62             => ( R3 @ ( groups8778361861064173332t_real @ H2 @ S2 ) @ ( groups8778361861064173332t_real @ G @ S2 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.related
% 0.26/0.62  thf(fact_7757_sum_Orelated,axiom,
% 0.26/0.62      ! [R3: real > real > $o,S2: set_complex,H2: complex > real,G: complex > real] :
% 0.26/0.62        ( ( R3 @ zero_zero_real @ zero_zero_real )
% 0.26/0.62       => ( ! [X1: real,Y1: real,X22: real,Y22: real] :
% 0.26/0.62              ( ( ( R3 @ X1 @ X22 )
% 0.26/0.62                & ( R3 @ Y1 @ Y22 ) )
% 0.26/0.62             => ( R3 @ ( plus_plus_real @ X1 @ Y1 ) @ ( plus_plus_real @ X22 @ Y22 ) ) )
% 0.26/0.62         => ( ( finite3207457112153483333omplex @ S2 )
% 0.26/0.62           => ( ! [X4: complex] :
% 0.26/0.62                  ( ( member_complex @ X4 @ S2 )
% 0.26/0.62                 => ( R3 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62             => ( R3 @ ( groups5808333547571424918x_real @ H2 @ S2 ) @ ( groups5808333547571424918x_real @ G @ S2 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.related
% 0.26/0.62  thf(fact_7758_sum_Orelated,axiom,
% 0.26/0.62      ! [R3: real > real > $o,S2: set_Extended_enat,H2: extended_enat > real,G: extended_enat > real] :
% 0.26/0.62        ( ( R3 @ zero_zero_real @ zero_zero_real )
% 0.26/0.62       => ( ! [X1: real,Y1: real,X22: real,Y22: real] :
% 0.26/0.62              ( ( ( R3 @ X1 @ X22 )
% 0.26/0.62                & ( R3 @ Y1 @ Y22 ) )
% 0.26/0.62             => ( R3 @ ( plus_plus_real @ X1 @ Y1 ) @ ( plus_plus_real @ X22 @ Y22 ) ) )
% 0.26/0.62         => ( ( finite4001608067531595151d_enat @ S2 )
% 0.26/0.62           => ( ! [X4: extended_enat] :
% 0.26/0.62                  ( ( member_Extended_enat @ X4 @ S2 )
% 0.26/0.62                 => ( R3 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62             => ( R3 @ ( groups4148127829035722712t_real @ H2 @ S2 ) @ ( groups4148127829035722712t_real @ G @ S2 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.related
% 0.26/0.62  thf(fact_7759_sum_Orelated,axiom,
% 0.26/0.62      ! [R3: rat > rat > $o,S2: set_nat,H2: nat > rat,G: nat > rat] :
% 0.26/0.62        ( ( R3 @ zero_zero_rat @ zero_zero_rat )
% 0.26/0.62       => ( ! [X1: rat,Y1: rat,X22: rat,Y22: rat] :
% 0.26/0.62              ( ( ( R3 @ X1 @ X22 )
% 0.26/0.62                & ( R3 @ Y1 @ Y22 ) )
% 0.26/0.62             => ( R3 @ ( plus_plus_rat @ X1 @ Y1 ) @ ( plus_plus_rat @ X22 @ Y22 ) ) )
% 0.26/0.62         => ( ( finite_finite_nat @ S2 )
% 0.26/0.62           => ( ! [X4: nat] :
% 0.26/0.62                  ( ( member_nat @ X4 @ S2 )
% 0.26/0.62                 => ( R3 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62             => ( R3 @ ( groups2906978787729119204at_rat @ H2 @ S2 ) @ ( groups2906978787729119204at_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.related
% 0.26/0.62  thf(fact_7760_sum_Orelated,axiom,
% 0.26/0.62      ! [R3: rat > rat > $o,S2: set_int,H2: int > rat,G: int > rat] :
% 0.26/0.62        ( ( R3 @ zero_zero_rat @ zero_zero_rat )
% 0.26/0.62       => ( ! [X1: rat,Y1: rat,X22: rat,Y22: rat] :
% 0.26/0.62              ( ( ( R3 @ X1 @ X22 )
% 0.26/0.62                & ( R3 @ Y1 @ Y22 ) )
% 0.26/0.62             => ( R3 @ ( plus_plus_rat @ X1 @ Y1 ) @ ( plus_plus_rat @ X22 @ Y22 ) ) )
% 0.26/0.62         => ( ( finite_finite_int @ S2 )
% 0.26/0.62           => ( ! [X4: int] :
% 0.26/0.62                  ( ( member_int @ X4 @ S2 )
% 0.26/0.62                 => ( R3 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62             => ( R3 @ ( groups3906332499630173760nt_rat @ H2 @ S2 ) @ ( groups3906332499630173760nt_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.related
% 0.26/0.62  thf(fact_7761_sum_Orelated,axiom,
% 0.26/0.62      ! [R3: rat > rat > $o,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 0.26/0.62        ( ( R3 @ zero_zero_rat @ zero_zero_rat )
% 0.26/0.62       => ( ! [X1: rat,Y1: rat,X22: rat,Y22: rat] :
% 0.26/0.62              ( ( ( R3 @ X1 @ X22 )
% 0.26/0.62                & ( R3 @ Y1 @ Y22 ) )
% 0.26/0.62             => ( R3 @ ( plus_plus_rat @ X1 @ Y1 ) @ ( plus_plus_rat @ X22 @ Y22 ) ) )
% 0.26/0.62         => ( ( finite3207457112153483333omplex @ S2 )
% 0.26/0.62           => ( ! [X4: complex] :
% 0.26/0.62                  ( ( member_complex @ X4 @ S2 )
% 0.26/0.62                 => ( R3 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62             => ( R3 @ ( groups5058264527183730370ex_rat @ H2 @ S2 ) @ ( groups5058264527183730370ex_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.related
% 0.26/0.62  thf(fact_7762_sum_Orelated,axiom,
% 0.26/0.62      ! [R3: rat > rat > $o,S2: set_Extended_enat,H2: extended_enat > rat,G: extended_enat > rat] :
% 0.26/0.62        ( ( R3 @ zero_zero_rat @ zero_zero_rat )
% 0.26/0.62       => ( ! [X1: rat,Y1: rat,X22: rat,Y22: rat] :
% 0.26/0.62              ( ( ( R3 @ X1 @ X22 )
% 0.26/0.62                & ( R3 @ Y1 @ Y22 ) )
% 0.26/0.62             => ( R3 @ ( plus_plus_rat @ X1 @ Y1 ) @ ( plus_plus_rat @ X22 @ Y22 ) ) )
% 0.26/0.62         => ( ( finite4001608067531595151d_enat @ S2 )
% 0.26/0.62           => ( ! [X4: extended_enat] :
% 0.26/0.62                  ( ( member_Extended_enat @ X4 @ S2 )
% 0.26/0.62                 => ( R3 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62             => ( R3 @ ( groups1392844769737527556at_rat @ H2 @ S2 ) @ ( groups1392844769737527556at_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.related
% 0.26/0.62  thf(fact_7763_sum_Orelated,axiom,
% 0.26/0.62      ! [R3: nat > nat > $o,S2: set_int,H2: int > nat,G: int > nat] :
% 0.26/0.62        ( ( R3 @ zero_zero_nat @ zero_zero_nat )
% 0.26/0.62       => ( ! [X1: nat,Y1: nat,X22: nat,Y22: nat] :
% 0.26/0.62              ( ( ( R3 @ X1 @ X22 )
% 0.26/0.62                & ( R3 @ Y1 @ Y22 ) )
% 0.26/0.62             => ( R3 @ ( plus_plus_nat @ X1 @ Y1 ) @ ( plus_plus_nat @ X22 @ Y22 ) ) )
% 0.26/0.62         => ( ( finite_finite_int @ S2 )
% 0.26/0.62           => ( ! [X4: int] :
% 0.26/0.62                  ( ( member_int @ X4 @ S2 )
% 0.26/0.62                 => ( R3 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62             => ( R3 @ ( groups4541462559716669496nt_nat @ H2 @ S2 ) @ ( groups4541462559716669496nt_nat @ G @ S2 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.related
% 0.26/0.62  thf(fact_7764_sum_Orelated,axiom,
% 0.26/0.62      ! [R3: nat > nat > $o,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 0.26/0.62        ( ( R3 @ zero_zero_nat @ zero_zero_nat )
% 0.26/0.62       => ( ! [X1: nat,Y1: nat,X22: nat,Y22: nat] :
% 0.26/0.62              ( ( ( R3 @ X1 @ X22 )
% 0.26/0.62                & ( R3 @ Y1 @ Y22 ) )
% 0.26/0.62             => ( R3 @ ( plus_plus_nat @ X1 @ Y1 ) @ ( plus_plus_nat @ X22 @ Y22 ) ) )
% 0.26/0.62         => ( ( finite3207457112153483333omplex @ S2 )
% 0.26/0.62           => ( ! [X4: complex] :
% 0.26/0.62                  ( ( member_complex @ X4 @ S2 )
% 0.26/0.62                 => ( R3 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62             => ( R3 @ ( groups5693394587270226106ex_nat @ H2 @ S2 ) @ ( groups5693394587270226106ex_nat @ G @ S2 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.related
% 0.26/0.62  thf(fact_7765_sum_Orelated,axiom,
% 0.26/0.62      ! [R3: nat > nat > $o,S2: set_Extended_enat,H2: extended_enat > nat,G: extended_enat > nat] :
% 0.26/0.62        ( ( R3 @ zero_zero_nat @ zero_zero_nat )
% 0.26/0.62       => ( ! [X1: nat,Y1: nat,X22: nat,Y22: nat] :
% 0.26/0.62              ( ( ( R3 @ X1 @ X22 )
% 0.26/0.62                & ( R3 @ Y1 @ Y22 ) )
% 0.26/0.62             => ( R3 @ ( plus_plus_nat @ X1 @ Y1 ) @ ( plus_plus_nat @ X22 @ Y22 ) ) )
% 0.26/0.62         => ( ( finite4001608067531595151d_enat @ S2 )
% 0.26/0.62           => ( ! [X4: extended_enat] :
% 0.26/0.62                  ( ( member_Extended_enat @ X4 @ S2 )
% 0.26/0.62                 => ( R3 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62             => ( R3 @ ( groups2027974829824023292at_nat @ H2 @ S2 ) @ ( groups2027974829824023292at_nat @ G @ S2 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.related
% 0.26/0.62  thf(fact_7766_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.26/0.62      ! [G: real > real,A3: set_real] :
% 0.26/0.62        ( ( ( groups8097168146408367636l_real @ G @ A3 )
% 0.26/0.62         != zero_zero_real )
% 0.26/0.62       => ~ ! [A5: real] :
% 0.26/0.62              ( ( member_real @ A5 @ A3 )
% 0.26/0.62             => ( ( G @ A5 )
% 0.26/0.62                = zero_zero_real ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.not_neutral_contains_not_neutral
% 0.26/0.62  thf(fact_7767_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.26/0.62      ! [G: int > real,A3: set_int] :
% 0.26/0.62        ( ( ( groups8778361861064173332t_real @ G @ A3 )
% 0.26/0.62         != zero_zero_real )
% 0.26/0.62       => ~ ! [A5: int] :
% 0.26/0.62              ( ( member_int @ A5 @ A3 )
% 0.26/0.62             => ( ( G @ A5 )
% 0.26/0.62                = zero_zero_real ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.not_neutral_contains_not_neutral
% 0.26/0.62  thf(fact_7768_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.26/0.62      ! [G: real > rat,A3: set_real] :
% 0.26/0.62        ( ( ( groups1300246762558778688al_rat @ G @ A3 )
% 0.26/0.62         != zero_zero_rat )
% 0.26/0.62       => ~ ! [A5: real] :
% 0.26/0.62              ( ( member_real @ A5 @ A3 )
% 0.26/0.62             => ( ( G @ A5 )
% 0.26/0.62                = zero_zero_rat ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.not_neutral_contains_not_neutral
% 0.26/0.62  thf(fact_7769_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.26/0.62      ! [G: nat > rat,A3: set_nat] :
% 0.26/0.62        ( ( ( groups2906978787729119204at_rat @ G @ A3 )
% 0.26/0.62         != zero_zero_rat )
% 0.26/0.62       => ~ ! [A5: nat] :
% 0.26/0.62              ( ( member_nat @ A5 @ A3 )
% 0.26/0.62             => ( ( G @ A5 )
% 0.26/0.62                = zero_zero_rat ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.not_neutral_contains_not_neutral
% 0.26/0.62  thf(fact_7770_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.26/0.62      ! [G: int > rat,A3: set_int] :
% 0.26/0.62        ( ( ( groups3906332499630173760nt_rat @ G @ A3 )
% 0.26/0.62         != zero_zero_rat )
% 0.26/0.62       => ~ ! [A5: int] :
% 0.26/0.62              ( ( member_int @ A5 @ A3 )
% 0.26/0.62             => ( ( G @ A5 )
% 0.26/0.62                = zero_zero_rat ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.not_neutral_contains_not_neutral
% 0.26/0.62  thf(fact_7771_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.26/0.62      ! [G: real > nat,A3: set_real] :
% 0.26/0.62        ( ( ( groups1935376822645274424al_nat @ G @ A3 )
% 0.26/0.62         != zero_zero_nat )
% 0.26/0.62       => ~ ! [A5: real] :
% 0.26/0.62              ( ( member_real @ A5 @ A3 )
% 0.26/0.62             => ( ( G @ A5 )
% 0.26/0.62                = zero_zero_nat ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.not_neutral_contains_not_neutral
% 0.26/0.62  thf(fact_7772_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.26/0.62      ! [G: int > nat,A3: set_int] :
% 0.26/0.62        ( ( ( groups4541462559716669496nt_nat @ G @ A3 )
% 0.26/0.62         != zero_zero_nat )
% 0.26/0.62       => ~ ! [A5: int] :
% 0.26/0.62              ( ( member_int @ A5 @ A3 )
% 0.26/0.62             => ( ( G @ A5 )
% 0.26/0.62                = zero_zero_nat ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.not_neutral_contains_not_neutral
% 0.26/0.62  thf(fact_7773_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.26/0.62      ! [G: real > int,A3: set_real] :
% 0.26/0.62        ( ( ( groups1932886352136224148al_int @ G @ A3 )
% 0.26/0.62         != zero_zero_int )
% 0.26/0.62       => ~ ! [A5: real] :
% 0.26/0.62              ( ( member_real @ A5 @ A3 )
% 0.26/0.62             => ( ( G @ A5 )
% 0.26/0.62                = zero_zero_int ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.not_neutral_contains_not_neutral
% 0.26/0.62  thf(fact_7774_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.26/0.62      ! [G: nat > int,A3: set_nat] :
% 0.26/0.62        ( ( ( groups3539618377306564664at_int @ G @ A3 )
% 0.26/0.62         != zero_zero_int )
% 0.26/0.62       => ~ ! [A5: nat] :
% 0.26/0.62              ( ( member_nat @ A5 @ A3 )
% 0.26/0.62             => ( ( G @ A5 )
% 0.26/0.62                = zero_zero_int ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.not_neutral_contains_not_neutral
% 0.26/0.62  thf(fact_7775_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.26/0.62      ! [G: nat > nat,A3: set_nat] :
% 0.26/0.62        ( ( ( groups3542108847815614940at_nat @ G @ A3 )
% 0.26/0.62         != zero_zero_nat )
% 0.26/0.62       => ~ ! [A5: nat] :
% 0.26/0.62              ( ( member_nat @ A5 @ A3 )
% 0.26/0.62             => ( ( G @ A5 )
% 0.26/0.62                = zero_zero_nat ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.not_neutral_contains_not_neutral
% 0.26/0.62  thf(fact_7776_sum_Oneutral,axiom,
% 0.26/0.62      ! [A3: set_nat,G: nat > nat] :
% 0.26/0.62        ( ! [X4: nat] :
% 0.26/0.62            ( ( member_nat @ X4 @ A3 )
% 0.26/0.62           => ( ( G @ X4 )
% 0.26/0.62              = zero_zero_nat ) )
% 0.26/0.62       => ( ( groups3542108847815614940at_nat @ G @ A3 )
% 0.26/0.62          = zero_zero_nat ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.neutral
% 0.26/0.62  thf(fact_7777_sum_Oneutral,axiom,
% 0.26/0.62      ! [A3: set_complex,G: complex > complex] :
% 0.26/0.62        ( ! [X4: complex] :
% 0.26/0.62            ( ( member_complex @ X4 @ A3 )
% 0.26/0.62           => ( ( G @ X4 )
% 0.26/0.62              = zero_zero_complex ) )
% 0.26/0.62       => ( ( groups7754918857620584856omplex @ G @ A3 )
% 0.26/0.62          = zero_zero_complex ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.neutral
% 0.26/0.62  thf(fact_7778_sum_Oneutral,axiom,
% 0.26/0.62      ! [A3: set_nat,G: nat > real] :
% 0.26/0.62        ( ! [X4: nat] :
% 0.26/0.62            ( ( member_nat @ X4 @ A3 )
% 0.26/0.62           => ( ( G @ X4 )
% 0.26/0.62              = zero_zero_real ) )
% 0.26/0.62       => ( ( groups6591440286371151544t_real @ G @ A3 )
% 0.26/0.62          = zero_zero_real ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.neutral
% 0.26/0.62  thf(fact_7779_sum_Oneutral,axiom,
% 0.26/0.62      ! [A3: set_int,G: int > int] :
% 0.26/0.62        ( ! [X4: int] :
% 0.26/0.62            ( ( member_int @ X4 @ A3 )
% 0.26/0.62           => ( ( G @ X4 )
% 0.26/0.62              = zero_zero_int ) )
% 0.26/0.62       => ( ( groups4538972089207619220nt_int @ G @ A3 )
% 0.26/0.62          = zero_zero_int ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.neutral
% 0.26/0.62  thf(fact_7780_sum__strict__mono__ex1,axiom,
% 0.26/0.62      ! [A3: set_int,F: int > real,G: int > real] :
% 0.26/0.62        ( ( finite_finite_int @ A3 )
% 0.26/0.62       => ( ! [X4: int] :
% 0.26/0.62              ( ( member_int @ X4 @ A3 )
% 0.26/0.62             => ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62         => ( ? [X6: int] :
% 0.26/0.62                ( ( member_int @ X6 @ A3 )
% 0.26/0.62                & ( ord_less_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.26/0.62           => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A3 ) @ ( groups8778361861064173332t_real @ G @ A3 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_strict_mono_ex1
% 0.26/0.62  thf(fact_7781_sum__strict__mono__ex1,axiom,
% 0.26/0.62      ! [A3: set_complex,F: complex > real,G: complex > real] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.62       => ( ! [X4: complex] :
% 0.26/0.62              ( ( member_complex @ X4 @ A3 )
% 0.26/0.62             => ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62         => ( ? [X6: complex] :
% 0.26/0.62                ( ( member_complex @ X6 @ A3 )
% 0.26/0.62                & ( ord_less_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.26/0.62           => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A3 ) @ ( groups5808333547571424918x_real @ G @ A3 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_strict_mono_ex1
% 0.26/0.62  thf(fact_7782_sum__strict__mono__ex1,axiom,
% 0.26/0.62      ! [A3: set_Extended_enat,F: extended_enat > real,G: extended_enat > real] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.62       => ( ! [X4: extended_enat] :
% 0.26/0.62              ( ( member_Extended_enat @ X4 @ A3 )
% 0.26/0.62             => ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62         => ( ? [X6: extended_enat] :
% 0.26/0.62                ( ( member_Extended_enat @ X6 @ A3 )
% 0.26/0.62                & ( ord_less_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.26/0.62           => ( ord_less_real @ ( groups4148127829035722712t_real @ F @ A3 ) @ ( groups4148127829035722712t_real @ G @ A3 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_strict_mono_ex1
% 0.26/0.62  thf(fact_7783_sum__strict__mono__ex1,axiom,
% 0.26/0.62      ! [A3: set_nat,F: nat > rat,G: nat > rat] :
% 0.26/0.62        ( ( finite_finite_nat @ A3 )
% 0.26/0.62       => ( ! [X4: nat] :
% 0.26/0.62              ( ( member_nat @ X4 @ A3 )
% 0.26/0.62             => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62         => ( ? [X6: nat] :
% 0.26/0.62                ( ( member_nat @ X6 @ A3 )
% 0.26/0.62                & ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.26/0.62           => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ ( groups2906978787729119204at_rat @ G @ A3 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_strict_mono_ex1
% 0.26/0.62  thf(fact_7784_sum__strict__mono__ex1,axiom,
% 0.26/0.62      ! [A3: set_int,F: int > rat,G: int > rat] :
% 0.26/0.62        ( ( finite_finite_int @ A3 )
% 0.26/0.62       => ( ! [X4: int] :
% 0.26/0.62              ( ( member_int @ X4 @ A3 )
% 0.26/0.62             => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62         => ( ? [X6: int] :
% 0.26/0.62                ( ( member_int @ X6 @ A3 )
% 0.26/0.62                & ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.26/0.62           => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ ( groups3906332499630173760nt_rat @ G @ A3 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_strict_mono_ex1
% 0.26/0.62  thf(fact_7785_sum__strict__mono__ex1,axiom,
% 0.26/0.62      ! [A3: set_complex,F: complex > rat,G: complex > rat] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.62       => ( ! [X4: complex] :
% 0.26/0.62              ( ( member_complex @ X4 @ A3 )
% 0.26/0.62             => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62         => ( ? [X6: complex] :
% 0.26/0.62                ( ( member_complex @ X6 @ A3 )
% 0.26/0.62                & ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.26/0.62           => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A3 ) @ ( groups5058264527183730370ex_rat @ G @ A3 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_strict_mono_ex1
% 0.26/0.62  thf(fact_7786_sum__strict__mono__ex1,axiom,
% 0.26/0.62      ! [A3: set_Extended_enat,F: extended_enat > rat,G: extended_enat > rat] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.62       => ( ! [X4: extended_enat] :
% 0.26/0.62              ( ( member_Extended_enat @ X4 @ A3 )
% 0.26/0.62             => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62         => ( ? [X6: extended_enat] :
% 0.26/0.62                ( ( member_Extended_enat @ X6 @ A3 )
% 0.26/0.62                & ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.26/0.62           => ( ord_less_rat @ ( groups1392844769737527556at_rat @ F @ A3 ) @ ( groups1392844769737527556at_rat @ G @ A3 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_strict_mono_ex1
% 0.26/0.62  thf(fact_7787_sum__strict__mono__ex1,axiom,
% 0.26/0.62      ! [A3: set_int,F: int > nat,G: int > nat] :
% 0.26/0.62        ( ( finite_finite_int @ A3 )
% 0.26/0.62       => ( ! [X4: int] :
% 0.26/0.62              ( ( member_int @ X4 @ A3 )
% 0.26/0.62             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62         => ( ? [X6: int] :
% 0.26/0.62                ( ( member_int @ X6 @ A3 )
% 0.26/0.62                & ( ord_less_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.26/0.62           => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ ( groups4541462559716669496nt_nat @ G @ A3 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_strict_mono_ex1
% 0.26/0.62  thf(fact_7788_sum__strict__mono__ex1,axiom,
% 0.26/0.62      ! [A3: set_complex,F: complex > nat,G: complex > nat] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.62       => ( ! [X4: complex] :
% 0.26/0.62              ( ( member_complex @ X4 @ A3 )
% 0.26/0.62             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62         => ( ? [X6: complex] :
% 0.26/0.62                ( ( member_complex @ X6 @ A3 )
% 0.26/0.62                & ( ord_less_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.26/0.62           => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A3 ) @ ( groups5693394587270226106ex_nat @ G @ A3 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_strict_mono_ex1
% 0.26/0.62  thf(fact_7789_sum__strict__mono__ex1,axiom,
% 0.26/0.62      ! [A3: set_Extended_enat,F: extended_enat > nat,G: extended_enat > nat] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.62       => ( ! [X4: extended_enat] :
% 0.26/0.62              ( ( member_Extended_enat @ X4 @ A3 )
% 0.26/0.62             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.26/0.62         => ( ? [X6: extended_enat] :
% 0.26/0.62                ( ( member_Extended_enat @ X6 @ A3 )
% 0.26/0.62                & ( ord_less_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.26/0.62           => ( ord_less_nat @ ( groups2027974829824023292at_nat @ F @ A3 ) @ ( groups2027974829824023292at_nat @ G @ A3 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_strict_mono_ex1
% 0.26/0.62  thf(fact_7790_finite__nat__set__iff__bounded__le,axiom,
% 0.26/0.62      ( finite_finite_nat
% 0.26/0.62      = ( ^ [N9: set_nat] :
% 0.26/0.62          ? [M3: nat] :
% 0.26/0.62          ! [X: nat] :
% 0.26/0.62            ( ( member_nat @ X @ N9 )
% 0.26/0.62           => ( ord_less_eq_nat @ X @ M3 ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % finite_nat_set_iff_bounded_le
% 0.26/0.62  thf(fact_7791_bounded__nat__set__is__finite,axiom,
% 0.26/0.62      ! [N4: set_nat,N: nat] :
% 0.26/0.62        ( ! [X4: nat] :
% 0.26/0.62            ( ( member_nat @ X4 @ N4 )
% 0.26/0.62           => ( ord_less_nat @ X4 @ N ) )
% 0.26/0.62       => ( finite_finite_nat @ N4 ) ) ).
% 0.26/0.62  
% 0.26/0.62  % bounded_nat_set_is_finite
% 0.26/0.62  thf(fact_7792_finite__nat__set__iff__bounded,axiom,
% 0.26/0.62      ( finite_finite_nat
% 0.26/0.62      = ( ^ [N9: set_nat] :
% 0.26/0.62          ? [M3: nat] :
% 0.26/0.62          ! [X: nat] :
% 0.26/0.62            ( ( member_nat @ X @ N9 )
% 0.26/0.62           => ( ord_less_nat @ X @ M3 ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % finite_nat_set_iff_bounded
% 0.26/0.62  thf(fact_7793_sum__pos2,axiom,
% 0.26/0.62      ! [I5: set_real,I: real,F: real > real] :
% 0.26/0.62        ( ( finite_finite_real @ I5 )
% 0.26/0.62       => ( ( member_real @ I @ I5 )
% 0.26/0.62         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 0.26/0.62           => ( ! [I3: real] :
% 0.26/0.62                  ( ( member_real @ I3 @ I5 )
% 0.26/0.62                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.62             => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I5 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_pos2
% 0.26/0.62  thf(fact_7794_sum__pos2,axiom,
% 0.26/0.62      ! [I5: set_int,I: int,F: int > real] :
% 0.26/0.62        ( ( finite_finite_int @ I5 )
% 0.26/0.62       => ( ( member_int @ I @ I5 )
% 0.26/0.62         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 0.26/0.62           => ( ! [I3: int] :
% 0.26/0.62                  ( ( member_int @ I3 @ I5 )
% 0.26/0.62                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.62             => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_pos2
% 0.26/0.62  thf(fact_7795_sum__pos2,axiom,
% 0.26/0.62      ! [I5: set_complex,I: complex,F: complex > real] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ I5 )
% 0.26/0.62       => ( ( member_complex @ I @ I5 )
% 0.26/0.62         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 0.26/0.62           => ( ! [I3: complex] :
% 0.26/0.62                  ( ( member_complex @ I3 @ I5 )
% 0.26/0.62                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.62             => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_pos2
% 0.26/0.62  thf(fact_7796_sum__pos2,axiom,
% 0.26/0.62      ! [I5: set_Extended_enat,I: extended_enat,F: extended_enat > real] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ I5 )
% 0.26/0.62       => ( ( member_Extended_enat @ I @ I5 )
% 0.26/0.62         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 0.26/0.62           => ( ! [I3: extended_enat] :
% 0.26/0.62                  ( ( member_Extended_enat @ I3 @ I5 )
% 0.26/0.62                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.62             => ( ord_less_real @ zero_zero_real @ ( groups4148127829035722712t_real @ F @ I5 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_pos2
% 0.26/0.62  thf(fact_7797_sum__pos2,axiom,
% 0.26/0.62      ! [I5: set_real,I: real,F: real > rat] :
% 0.26/0.62        ( ( finite_finite_real @ I5 )
% 0.26/0.62       => ( ( member_real @ I @ I5 )
% 0.26/0.62         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 0.26/0.62           => ( ! [I3: real] :
% 0.26/0.62                  ( ( member_real @ I3 @ I5 )
% 0.26/0.62                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.26/0.62             => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_pos2
% 0.26/0.62  thf(fact_7798_sum__pos2,axiom,
% 0.26/0.62      ! [I5: set_nat,I: nat,F: nat > rat] :
% 0.26/0.62        ( ( finite_finite_nat @ I5 )
% 0.26/0.62       => ( ( member_nat @ I @ I5 )
% 0.26/0.62         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 0.26/0.62           => ( ! [I3: nat] :
% 0.26/0.62                  ( ( member_nat @ I3 @ I5 )
% 0.26/0.62                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.26/0.62             => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_pos2
% 0.26/0.62  thf(fact_7799_sum__pos2,axiom,
% 0.26/0.62      ! [I5: set_int,I: int,F: int > rat] :
% 0.26/0.62        ( ( finite_finite_int @ I5 )
% 0.26/0.62       => ( ( member_int @ I @ I5 )
% 0.26/0.62         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 0.26/0.62           => ( ! [I3: int] :
% 0.26/0.62                  ( ( member_int @ I3 @ I5 )
% 0.26/0.62                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.26/0.62             => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_pos2
% 0.26/0.62  thf(fact_7800_sum__pos2,axiom,
% 0.26/0.62      ! [I5: set_complex,I: complex,F: complex > rat] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ I5 )
% 0.26/0.62       => ( ( member_complex @ I @ I5 )
% 0.26/0.62         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 0.26/0.62           => ( ! [I3: complex] :
% 0.26/0.62                  ( ( member_complex @ I3 @ I5 )
% 0.26/0.62                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.26/0.62             => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_pos2
% 0.26/0.62  thf(fact_7801_sum__pos2,axiom,
% 0.26/0.62      ! [I5: set_Extended_enat,I: extended_enat,F: extended_enat > rat] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ I5 )
% 0.26/0.62       => ( ( member_Extended_enat @ I @ I5 )
% 0.26/0.62         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 0.26/0.62           => ( ! [I3: extended_enat] :
% 0.26/0.62                  ( ( member_Extended_enat @ I3 @ I5 )
% 0.26/0.62                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.26/0.62             => ( ord_less_rat @ zero_zero_rat @ ( groups1392844769737527556at_rat @ F @ I5 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_pos2
% 0.26/0.62  thf(fact_7802_sum__pos2,axiom,
% 0.26/0.62      ! [I5: set_real,I: real,F: real > nat] :
% 0.26/0.62        ( ( finite_finite_real @ I5 )
% 0.26/0.62       => ( ( member_real @ I @ I5 )
% 0.26/0.62         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 0.26/0.62           => ( ! [I3: real] :
% 0.26/0.62                  ( ( member_real @ I3 @ I5 )
% 0.26/0.62                 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 0.26/0.62             => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I5 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_pos2
% 0.26/0.62  thf(fact_7803_sum__pos,axiom,
% 0.26/0.62      ! [I5: set_complex,F: complex > real] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ I5 )
% 0.26/0.62       => ( ( I5 != bot_bot_set_complex )
% 0.26/0.62         => ( ! [I3: complex] :
% 0.26/0.62                ( ( member_complex @ I3 @ I5 )
% 0.26/0.62               => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.62           => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_pos
% 0.26/0.62  thf(fact_7804_sum__pos,axiom,
% 0.26/0.62      ! [I5: set_Extended_enat,F: extended_enat > real] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ I5 )
% 0.26/0.62       => ( ( I5 != bot_bo7653980558646680370d_enat )
% 0.26/0.62         => ( ! [I3: extended_enat] :
% 0.26/0.62                ( ( member_Extended_enat @ I3 @ I5 )
% 0.26/0.62               => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.62           => ( ord_less_real @ zero_zero_real @ ( groups4148127829035722712t_real @ F @ I5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_pos
% 0.26/0.62  thf(fact_7805_sum__pos,axiom,
% 0.26/0.62      ! [I5: set_real,F: real > real] :
% 0.26/0.62        ( ( finite_finite_real @ I5 )
% 0.26/0.62       => ( ( I5 != bot_bot_set_real )
% 0.26/0.62         => ( ! [I3: real] :
% 0.26/0.62                ( ( member_real @ I3 @ I5 )
% 0.26/0.62               => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.62           => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_pos
% 0.26/0.62  thf(fact_7806_sum__pos,axiom,
% 0.26/0.62      ! [I5: set_int,F: int > real] :
% 0.26/0.62        ( ( finite_finite_int @ I5 )
% 0.26/0.62       => ( ( I5 != bot_bot_set_int )
% 0.26/0.62         => ( ! [I3: int] :
% 0.26/0.62                ( ( member_int @ I3 @ I5 )
% 0.26/0.62               => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.62           => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_pos
% 0.26/0.62  thf(fact_7807_sum__pos,axiom,
% 0.26/0.62      ! [I5: set_complex,F: complex > rat] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ I5 )
% 0.26/0.62       => ( ( I5 != bot_bot_set_complex )
% 0.26/0.62         => ( ! [I3: complex] :
% 0.26/0.62                ( ( member_complex @ I3 @ I5 )
% 0.26/0.62               => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.26/0.62           => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_pos
% 0.26/0.62  thf(fact_7808_sum__pos,axiom,
% 0.26/0.62      ! [I5: set_Extended_enat,F: extended_enat > rat] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ I5 )
% 0.26/0.62       => ( ( I5 != bot_bo7653980558646680370d_enat )
% 0.26/0.62         => ( ! [I3: extended_enat] :
% 0.26/0.62                ( ( member_Extended_enat @ I3 @ I5 )
% 0.26/0.62               => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.26/0.62           => ( ord_less_rat @ zero_zero_rat @ ( groups1392844769737527556at_rat @ F @ I5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_pos
% 0.26/0.62  thf(fact_7809_sum__pos,axiom,
% 0.26/0.62      ! [I5: set_real,F: real > rat] :
% 0.26/0.62        ( ( finite_finite_real @ I5 )
% 0.26/0.62       => ( ( I5 != bot_bot_set_real )
% 0.26/0.62         => ( ! [I3: real] :
% 0.26/0.62                ( ( member_real @ I3 @ I5 )
% 0.26/0.62               => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.26/0.62           => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_pos
% 0.26/0.62  thf(fact_7810_sum__pos,axiom,
% 0.26/0.62      ! [I5: set_nat,F: nat > rat] :
% 0.26/0.62        ( ( finite_finite_nat @ I5 )
% 0.26/0.62       => ( ( I5 != bot_bot_set_nat )
% 0.26/0.62         => ( ! [I3: nat] :
% 0.26/0.62                ( ( member_nat @ I3 @ I5 )
% 0.26/0.62               => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.26/0.62           => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_pos
% 0.26/0.62  thf(fact_7811_sum__pos,axiom,
% 0.26/0.62      ! [I5: set_int,F: int > rat] :
% 0.26/0.62        ( ( finite_finite_int @ I5 )
% 0.26/0.62       => ( ( I5 != bot_bot_set_int )
% 0.26/0.62         => ( ! [I3: int] :
% 0.26/0.62                ( ( member_int @ I3 @ I5 )
% 0.26/0.62               => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.26/0.62           => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_pos
% 0.26/0.62  thf(fact_7812_sum__pos,axiom,
% 0.26/0.62      ! [I5: set_complex,F: complex > nat] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ I5 )
% 0.26/0.62       => ( ( I5 != bot_bot_set_complex )
% 0.26/0.62         => ( ! [I3: complex] :
% 0.26/0.62                ( ( member_complex @ I3 @ I5 )
% 0.26/0.62               => ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 0.26/0.62           => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_pos
% 0.26/0.62  thf(fact_7813_sum__mono,axiom,
% 0.26/0.62      ! [K5: set_real,F: real > rat,G: real > rat] :
% 0.26/0.62        ( ! [I3: real] :
% 0.26/0.62            ( ( member_real @ I3 @ K5 )
% 0.26/0.62           => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.26/0.62       => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K5 ) @ ( groups1300246762558778688al_rat @ G @ K5 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono
% 0.26/0.62  thf(fact_7814_sum__mono,axiom,
% 0.26/0.62      ! [K5: set_nat,F: nat > rat,G: nat > rat] :
% 0.26/0.62        ( ! [I3: nat] :
% 0.26/0.62            ( ( member_nat @ I3 @ K5 )
% 0.26/0.62           => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.26/0.62       => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K5 ) @ ( groups2906978787729119204at_rat @ G @ K5 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono
% 0.26/0.62  thf(fact_7815_sum__mono,axiom,
% 0.26/0.62      ! [K5: set_int,F: int > rat,G: int > rat] :
% 0.26/0.62        ( ! [I3: int] :
% 0.26/0.62            ( ( member_int @ I3 @ K5 )
% 0.26/0.62           => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.26/0.62       => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K5 ) @ ( groups3906332499630173760nt_rat @ G @ K5 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono
% 0.26/0.62  thf(fact_7816_sum__mono,axiom,
% 0.26/0.62      ! [K5: set_real,F: real > nat,G: real > nat] :
% 0.26/0.62        ( ! [I3: real] :
% 0.26/0.62            ( ( member_real @ I3 @ K5 )
% 0.26/0.62           => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.26/0.62       => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono
% 0.26/0.62  thf(fact_7817_sum__mono,axiom,
% 0.26/0.62      ! [K5: set_int,F: int > nat,G: int > nat] :
% 0.26/0.62        ( ! [I3: int] :
% 0.26/0.62            ( ( member_int @ I3 @ K5 )
% 0.26/0.62           => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.26/0.62       => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono
% 0.26/0.62  thf(fact_7818_sum__mono,axiom,
% 0.26/0.62      ! [K5: set_real,F: real > int,G: real > int] :
% 0.26/0.62        ( ! [I3: real] :
% 0.26/0.62            ( ( member_real @ I3 @ K5 )
% 0.26/0.62           => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.26/0.62       => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono
% 0.26/0.62  thf(fact_7819_sum__mono,axiom,
% 0.26/0.62      ! [K5: set_nat,F: nat > int,G: nat > int] :
% 0.26/0.62        ( ! [I3: nat] :
% 0.26/0.62            ( ( member_nat @ I3 @ K5 )
% 0.26/0.62           => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.26/0.62       => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono
% 0.26/0.62  thf(fact_7820_sum__mono,axiom,
% 0.26/0.62      ! [K5: set_nat,F: nat > nat,G: nat > nat] :
% 0.26/0.62        ( ! [I3: nat] :
% 0.26/0.62            ( ( member_nat @ I3 @ K5 )
% 0.26/0.62           => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.26/0.62       => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ K5 ) @ ( groups3542108847815614940at_nat @ G @ K5 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono
% 0.26/0.62  thf(fact_7821_sum__mono,axiom,
% 0.26/0.62      ! [K5: set_nat,F: nat > real,G: nat > real] :
% 0.26/0.62        ( ! [I3: nat] :
% 0.26/0.62            ( ( member_nat @ I3 @ K5 )
% 0.26/0.62           => ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.26/0.62       => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ K5 ) @ ( groups6591440286371151544t_real @ G @ K5 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono
% 0.26/0.62  thf(fact_7822_sum__mono,axiom,
% 0.26/0.62      ! [K5: set_int,F: int > int,G: int > int] :
% 0.26/0.62        ( ! [I3: int] :
% 0.26/0.62            ( ( member_int @ I3 @ K5 )
% 0.26/0.62           => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.26/0.62       => ( ord_less_eq_int @ ( groups4538972089207619220nt_int @ F @ K5 ) @ ( groups4538972089207619220nt_int @ G @ K5 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono
% 0.26/0.62  thf(fact_7823_sum_Omono__neutral__cong__right,axiom,
% 0.26/0.62      ! [T5: set_real,S2: set_real,G: real > real,H2: real > real] :
% 0.26/0.62        ( ( finite_finite_real @ T5 )
% 0.26/0.62       => ( ( ord_less_eq_set_real @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: real] :
% 0.26/0.62                ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_real ) )
% 0.26/0.62           => ( ! [X4: real] :
% 0.26/0.62                  ( ( member_real @ X4 @ S2 )
% 0.26/0.62                 => ( ( G @ X4 )
% 0.26/0.62                    = ( H2 @ X4 ) ) )
% 0.26/0.62             => ( ( groups8097168146408367636l_real @ G @ T5 )
% 0.26/0.62                = ( groups8097168146408367636l_real @ H2 @ S2 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_cong_right
% 0.26/0.62  thf(fact_7824_sum_Omono__neutral__cong__right,axiom,
% 0.26/0.62      ! [T5: set_int,S2: set_int,G: int > real,H2: int > real] :
% 0.26/0.62        ( ( finite_finite_int @ T5 )
% 0.26/0.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: int] :
% 0.26/0.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_real ) )
% 0.26/0.62           => ( ! [X4: int] :
% 0.26/0.62                  ( ( member_int @ X4 @ S2 )
% 0.26/0.62                 => ( ( G @ X4 )
% 0.26/0.62                    = ( H2 @ X4 ) ) )
% 0.26/0.62             => ( ( groups8778361861064173332t_real @ G @ T5 )
% 0.26/0.62                = ( groups8778361861064173332t_real @ H2 @ S2 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_cong_right
% 0.26/0.62  thf(fact_7825_sum_Omono__neutral__cong__right,axiom,
% 0.26/0.62      ! [T5: set_complex,S2: set_complex,G: complex > real,H2: complex > real] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ T5 )
% 0.26/0.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: complex] :
% 0.26/0.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_real ) )
% 0.26/0.62           => ( ! [X4: complex] :
% 0.26/0.62                  ( ( member_complex @ X4 @ S2 )
% 0.26/0.62                 => ( ( G @ X4 )
% 0.26/0.62                    = ( H2 @ X4 ) ) )
% 0.26/0.62             => ( ( groups5808333547571424918x_real @ G @ T5 )
% 0.26/0.62                = ( groups5808333547571424918x_real @ H2 @ S2 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_cong_right
% 0.26/0.62  thf(fact_7826_sum_Omono__neutral__cong__right,axiom,
% 0.26/0.62      ! [T5: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > real,H2: extended_enat > real] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ T5 )
% 0.26/0.62       => ( ( ord_le7203529160286727270d_enat @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: extended_enat] :
% 0.26/0.62                ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_real ) )
% 0.26/0.62           => ( ! [X4: extended_enat] :
% 0.26/0.62                  ( ( member_Extended_enat @ X4 @ S2 )
% 0.26/0.62                 => ( ( G @ X4 )
% 0.26/0.62                    = ( H2 @ X4 ) ) )
% 0.26/0.62             => ( ( groups4148127829035722712t_real @ G @ T5 )
% 0.26/0.62                = ( groups4148127829035722712t_real @ H2 @ S2 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_cong_right
% 0.26/0.62  thf(fact_7827_sum_Omono__neutral__cong__right,axiom,
% 0.26/0.62      ! [T5: set_real,S2: set_real,G: real > rat,H2: real > rat] :
% 0.26/0.62        ( ( finite_finite_real @ T5 )
% 0.26/0.62       => ( ( ord_less_eq_set_real @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: real] :
% 0.26/0.62                ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_rat ) )
% 0.26/0.62           => ( ! [X4: real] :
% 0.26/0.62                  ( ( member_real @ X4 @ S2 )
% 0.26/0.62                 => ( ( G @ X4 )
% 0.26/0.62                    = ( H2 @ X4 ) ) )
% 0.26/0.62             => ( ( groups1300246762558778688al_rat @ G @ T5 )
% 0.26/0.62                = ( groups1300246762558778688al_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_cong_right
% 0.26/0.62  thf(fact_7828_sum_Omono__neutral__cong__right,axiom,
% 0.26/0.62      ! [T5: set_int,S2: set_int,G: int > rat,H2: int > rat] :
% 0.26/0.62        ( ( finite_finite_int @ T5 )
% 0.26/0.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: int] :
% 0.26/0.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_rat ) )
% 0.26/0.62           => ( ! [X4: int] :
% 0.26/0.62                  ( ( member_int @ X4 @ S2 )
% 0.26/0.62                 => ( ( G @ X4 )
% 0.26/0.62                    = ( H2 @ X4 ) ) )
% 0.26/0.62             => ( ( groups3906332499630173760nt_rat @ G @ T5 )
% 0.26/0.62                = ( groups3906332499630173760nt_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_cong_right
% 0.26/0.62  thf(fact_7829_sum_Omono__neutral__cong__right,axiom,
% 0.26/0.62      ! [T5: set_complex,S2: set_complex,G: complex > rat,H2: complex > rat] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ T5 )
% 0.26/0.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: complex] :
% 0.26/0.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_rat ) )
% 0.26/0.62           => ( ! [X4: complex] :
% 0.26/0.62                  ( ( member_complex @ X4 @ S2 )
% 0.26/0.62                 => ( ( G @ X4 )
% 0.26/0.62                    = ( H2 @ X4 ) ) )
% 0.26/0.62             => ( ( groups5058264527183730370ex_rat @ G @ T5 )
% 0.26/0.62                = ( groups5058264527183730370ex_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_cong_right
% 0.26/0.62  thf(fact_7830_sum_Omono__neutral__cong__right,axiom,
% 0.26/0.62      ! [T5: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > rat,H2: extended_enat > rat] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ T5 )
% 0.26/0.62       => ( ( ord_le7203529160286727270d_enat @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: extended_enat] :
% 0.26/0.62                ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_rat ) )
% 0.26/0.62           => ( ! [X4: extended_enat] :
% 0.26/0.62                  ( ( member_Extended_enat @ X4 @ S2 )
% 0.26/0.62                 => ( ( G @ X4 )
% 0.26/0.62                    = ( H2 @ X4 ) ) )
% 0.26/0.62             => ( ( groups1392844769737527556at_rat @ G @ T5 )
% 0.26/0.62                = ( groups1392844769737527556at_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_cong_right
% 0.26/0.62  thf(fact_7831_sum_Omono__neutral__cong__right,axiom,
% 0.26/0.62      ! [T5: set_real,S2: set_real,G: real > nat,H2: real > nat] :
% 0.26/0.62        ( ( finite_finite_real @ T5 )
% 0.26/0.62       => ( ( ord_less_eq_set_real @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: real] :
% 0.26/0.62                ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_nat ) )
% 0.26/0.62           => ( ! [X4: real] :
% 0.26/0.62                  ( ( member_real @ X4 @ S2 )
% 0.26/0.62                 => ( ( G @ X4 )
% 0.26/0.62                    = ( H2 @ X4 ) ) )
% 0.26/0.62             => ( ( groups1935376822645274424al_nat @ G @ T5 )
% 0.26/0.62                = ( groups1935376822645274424al_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_cong_right
% 0.26/0.62  thf(fact_7832_sum_Omono__neutral__cong__right,axiom,
% 0.26/0.62      ! [T5: set_int,S2: set_int,G: int > nat,H2: int > nat] :
% 0.26/0.62        ( ( finite_finite_int @ T5 )
% 0.26/0.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: int] :
% 0.26/0.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_nat ) )
% 0.26/0.62           => ( ! [X4: int] :
% 0.26/0.62                  ( ( member_int @ X4 @ S2 )
% 0.26/0.62                 => ( ( G @ X4 )
% 0.26/0.62                    = ( H2 @ X4 ) ) )
% 0.26/0.62             => ( ( groups4541462559716669496nt_nat @ G @ T5 )
% 0.26/0.62                = ( groups4541462559716669496nt_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_cong_right
% 0.26/0.62  thf(fact_7833_sum_Omono__neutral__cong__left,axiom,
% 0.26/0.62      ! [T5: set_real,S2: set_real,H2: real > real,G: real > real] :
% 0.26/0.62        ( ( finite_finite_real @ T5 )
% 0.26/0.62       => ( ( ord_less_eq_set_real @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: real] :
% 0.26/0.62                ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S2 ) )
% 0.26/0.62               => ( ( H2 @ X4 )
% 0.26/0.62                  = zero_zero_real ) )
% 0.26/0.62           => ( ! [X4: real] :
% 0.26/0.62                  ( ( member_real @ X4 @ S2 )
% 0.26/0.62                 => ( ( G @ X4 )
% 0.26/0.62                    = ( H2 @ X4 ) ) )
% 0.26/0.62             => ( ( groups8097168146408367636l_real @ G @ S2 )
% 0.26/0.62                = ( groups8097168146408367636l_real @ H2 @ T5 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_cong_left
% 0.26/0.62  thf(fact_7834_sum_Omono__neutral__cong__left,axiom,
% 0.26/0.62      ! [T5: set_int,S2: set_int,H2: int > real,G: int > real] :
% 0.26/0.62        ( ( finite_finite_int @ T5 )
% 0.26/0.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: int] :
% 0.26/0.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.26/0.62               => ( ( H2 @ X4 )
% 0.26/0.62                  = zero_zero_real ) )
% 0.26/0.62           => ( ! [X4: int] :
% 0.26/0.62                  ( ( member_int @ X4 @ S2 )
% 0.26/0.62                 => ( ( G @ X4 )
% 0.26/0.62                    = ( H2 @ X4 ) ) )
% 0.26/0.62             => ( ( groups8778361861064173332t_real @ G @ S2 )
% 0.26/0.62                = ( groups8778361861064173332t_real @ H2 @ T5 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_cong_left
% 0.26/0.62  thf(fact_7835_sum_Omono__neutral__cong__left,axiom,
% 0.26/0.62      ! [T5: set_complex,S2: set_complex,H2: complex > real,G: complex > real] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ T5 )
% 0.26/0.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: complex] :
% 0.26/0.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 0.26/0.62               => ( ( H2 @ X4 )
% 0.26/0.62                  = zero_zero_real ) )
% 0.26/0.62           => ( ! [X4: complex] :
% 0.26/0.62                  ( ( member_complex @ X4 @ S2 )
% 0.26/0.62                 => ( ( G @ X4 )
% 0.26/0.62                    = ( H2 @ X4 ) ) )
% 0.26/0.62             => ( ( groups5808333547571424918x_real @ G @ S2 )
% 0.26/0.62                = ( groups5808333547571424918x_real @ H2 @ T5 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_cong_left
% 0.26/0.62  thf(fact_7836_sum_Omono__neutral__cong__left,axiom,
% 0.26/0.62      ! [T5: set_Extended_enat,S2: set_Extended_enat,H2: extended_enat > real,G: extended_enat > real] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ T5 )
% 0.26/0.62       => ( ( ord_le7203529160286727270d_enat @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: extended_enat] :
% 0.26/0.62                ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T5 @ S2 ) )
% 0.26/0.62               => ( ( H2 @ X4 )
% 0.26/0.62                  = zero_zero_real ) )
% 0.26/0.62           => ( ! [X4: extended_enat] :
% 0.26/0.62                  ( ( member_Extended_enat @ X4 @ S2 )
% 0.26/0.62                 => ( ( G @ X4 )
% 0.26/0.62                    = ( H2 @ X4 ) ) )
% 0.26/0.62             => ( ( groups4148127829035722712t_real @ G @ S2 )
% 0.26/0.62                = ( groups4148127829035722712t_real @ H2 @ T5 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_cong_left
% 0.26/0.62  thf(fact_7837_sum_Omono__neutral__cong__left,axiom,
% 0.26/0.62      ! [T5: set_real,S2: set_real,H2: real > rat,G: real > rat] :
% 0.26/0.62        ( ( finite_finite_real @ T5 )
% 0.26/0.62       => ( ( ord_less_eq_set_real @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: real] :
% 0.26/0.62                ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S2 ) )
% 0.26/0.62               => ( ( H2 @ X4 )
% 0.26/0.62                  = zero_zero_rat ) )
% 0.26/0.62           => ( ! [X4: real] :
% 0.26/0.62                  ( ( member_real @ X4 @ S2 )
% 0.26/0.62                 => ( ( G @ X4 )
% 0.26/0.62                    = ( H2 @ X4 ) ) )
% 0.26/0.62             => ( ( groups1300246762558778688al_rat @ G @ S2 )
% 0.26/0.62                = ( groups1300246762558778688al_rat @ H2 @ T5 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_cong_left
% 0.26/0.62  thf(fact_7838_sum_Omono__neutral__cong__left,axiom,
% 0.26/0.62      ! [T5: set_int,S2: set_int,H2: int > rat,G: int > rat] :
% 0.26/0.62        ( ( finite_finite_int @ T5 )
% 0.26/0.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: int] :
% 0.26/0.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.26/0.62               => ( ( H2 @ X4 )
% 0.26/0.62                  = zero_zero_rat ) )
% 0.26/0.62           => ( ! [X4: int] :
% 0.26/0.62                  ( ( member_int @ X4 @ S2 )
% 0.26/0.62                 => ( ( G @ X4 )
% 0.26/0.62                    = ( H2 @ X4 ) ) )
% 0.26/0.62             => ( ( groups3906332499630173760nt_rat @ G @ S2 )
% 0.26/0.62                = ( groups3906332499630173760nt_rat @ H2 @ T5 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_cong_left
% 0.26/0.62  thf(fact_7839_sum_Omono__neutral__cong__left,axiom,
% 0.26/0.62      ! [T5: set_complex,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ T5 )
% 0.26/0.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: complex] :
% 0.26/0.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 0.26/0.62               => ( ( H2 @ X4 )
% 0.26/0.62                  = zero_zero_rat ) )
% 0.26/0.62           => ( ! [X4: complex] :
% 0.26/0.62                  ( ( member_complex @ X4 @ S2 )
% 0.26/0.62                 => ( ( G @ X4 )
% 0.26/0.62                    = ( H2 @ X4 ) ) )
% 0.26/0.62             => ( ( groups5058264527183730370ex_rat @ G @ S2 )
% 0.26/0.62                = ( groups5058264527183730370ex_rat @ H2 @ T5 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_cong_left
% 0.26/0.62  thf(fact_7840_sum_Omono__neutral__cong__left,axiom,
% 0.26/0.62      ! [T5: set_Extended_enat,S2: set_Extended_enat,H2: extended_enat > rat,G: extended_enat > rat] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ T5 )
% 0.26/0.62       => ( ( ord_le7203529160286727270d_enat @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: extended_enat] :
% 0.26/0.62                ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T5 @ S2 ) )
% 0.26/0.62               => ( ( H2 @ X4 )
% 0.26/0.62                  = zero_zero_rat ) )
% 0.26/0.62           => ( ! [X4: extended_enat] :
% 0.26/0.62                  ( ( member_Extended_enat @ X4 @ S2 )
% 0.26/0.62                 => ( ( G @ X4 )
% 0.26/0.62                    = ( H2 @ X4 ) ) )
% 0.26/0.62             => ( ( groups1392844769737527556at_rat @ G @ S2 )
% 0.26/0.62                = ( groups1392844769737527556at_rat @ H2 @ T5 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_cong_left
% 0.26/0.62  thf(fact_7841_sum_Omono__neutral__cong__left,axiom,
% 0.26/0.62      ! [T5: set_real,S2: set_real,H2: real > nat,G: real > nat] :
% 0.26/0.62        ( ( finite_finite_real @ T5 )
% 0.26/0.62       => ( ( ord_less_eq_set_real @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: real] :
% 0.26/0.62                ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S2 ) )
% 0.26/0.62               => ( ( H2 @ X4 )
% 0.26/0.62                  = zero_zero_nat ) )
% 0.26/0.62           => ( ! [X4: real] :
% 0.26/0.62                  ( ( member_real @ X4 @ S2 )
% 0.26/0.62                 => ( ( G @ X4 )
% 0.26/0.62                    = ( H2 @ X4 ) ) )
% 0.26/0.62             => ( ( groups1935376822645274424al_nat @ G @ S2 )
% 0.26/0.62                = ( groups1935376822645274424al_nat @ H2 @ T5 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_cong_left
% 0.26/0.62  thf(fact_7842_sum_Omono__neutral__cong__left,axiom,
% 0.26/0.62      ! [T5: set_int,S2: set_int,H2: int > nat,G: int > nat] :
% 0.26/0.62        ( ( finite_finite_int @ T5 )
% 0.26/0.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: int] :
% 0.26/0.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.26/0.62               => ( ( H2 @ X4 )
% 0.26/0.62                  = zero_zero_nat ) )
% 0.26/0.62           => ( ! [X4: int] :
% 0.26/0.62                  ( ( member_int @ X4 @ S2 )
% 0.26/0.62                 => ( ( G @ X4 )
% 0.26/0.62                    = ( H2 @ X4 ) ) )
% 0.26/0.62             => ( ( groups4541462559716669496nt_nat @ G @ S2 )
% 0.26/0.62                = ( groups4541462559716669496nt_nat @ H2 @ T5 ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_cong_left
% 0.26/0.62  thf(fact_7843_sum_Omono__neutral__right,axiom,
% 0.26/0.62      ! [T5: set_int,S2: set_int,G: int > real] :
% 0.26/0.62        ( ( finite_finite_int @ T5 )
% 0.26/0.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: int] :
% 0.26/0.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_real ) )
% 0.26/0.62           => ( ( groups8778361861064173332t_real @ G @ T5 )
% 0.26/0.62              = ( groups8778361861064173332t_real @ G @ S2 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_right
% 0.26/0.62  thf(fact_7844_sum_Omono__neutral__right,axiom,
% 0.26/0.62      ! [T5: set_complex,S2: set_complex,G: complex > real] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ T5 )
% 0.26/0.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: complex] :
% 0.26/0.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_real ) )
% 0.26/0.62           => ( ( groups5808333547571424918x_real @ G @ T5 )
% 0.26/0.62              = ( groups5808333547571424918x_real @ G @ S2 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_right
% 0.26/0.62  thf(fact_7845_sum_Omono__neutral__right,axiom,
% 0.26/0.62      ! [T5: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > real] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ T5 )
% 0.26/0.62       => ( ( ord_le7203529160286727270d_enat @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: extended_enat] :
% 0.26/0.62                ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_real ) )
% 0.26/0.62           => ( ( groups4148127829035722712t_real @ G @ T5 )
% 0.26/0.62              = ( groups4148127829035722712t_real @ G @ S2 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_right
% 0.26/0.62  thf(fact_7846_sum_Omono__neutral__right,axiom,
% 0.26/0.62      ! [T5: set_int,S2: set_int,G: int > rat] :
% 0.26/0.62        ( ( finite_finite_int @ T5 )
% 0.26/0.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: int] :
% 0.26/0.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_rat ) )
% 0.26/0.62           => ( ( groups3906332499630173760nt_rat @ G @ T5 )
% 0.26/0.62              = ( groups3906332499630173760nt_rat @ G @ S2 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_right
% 0.26/0.62  thf(fact_7847_sum_Omono__neutral__right,axiom,
% 0.26/0.62      ! [T5: set_complex,S2: set_complex,G: complex > rat] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ T5 )
% 0.26/0.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: complex] :
% 0.26/0.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_rat ) )
% 0.26/0.62           => ( ( groups5058264527183730370ex_rat @ G @ T5 )
% 0.26/0.62              = ( groups5058264527183730370ex_rat @ G @ S2 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_right
% 0.26/0.62  thf(fact_7848_sum_Omono__neutral__right,axiom,
% 0.26/0.62      ! [T5: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > rat] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ T5 )
% 0.26/0.62       => ( ( ord_le7203529160286727270d_enat @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: extended_enat] :
% 0.26/0.62                ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_rat ) )
% 0.26/0.62           => ( ( groups1392844769737527556at_rat @ G @ T5 )
% 0.26/0.62              = ( groups1392844769737527556at_rat @ G @ S2 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_right
% 0.26/0.62  thf(fact_7849_sum_Omono__neutral__right,axiom,
% 0.26/0.62      ! [T5: set_int,S2: set_int,G: int > nat] :
% 0.26/0.62        ( ( finite_finite_int @ T5 )
% 0.26/0.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: int] :
% 0.26/0.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_nat ) )
% 0.26/0.62           => ( ( groups4541462559716669496nt_nat @ G @ T5 )
% 0.26/0.62              = ( groups4541462559716669496nt_nat @ G @ S2 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_right
% 0.26/0.62  thf(fact_7850_sum_Omono__neutral__right,axiom,
% 0.26/0.62      ! [T5: set_complex,S2: set_complex,G: complex > nat] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ T5 )
% 0.26/0.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: complex] :
% 0.26/0.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_nat ) )
% 0.26/0.62           => ( ( groups5693394587270226106ex_nat @ G @ T5 )
% 0.26/0.62              = ( groups5693394587270226106ex_nat @ G @ S2 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_right
% 0.26/0.62  thf(fact_7851_sum_Omono__neutral__right,axiom,
% 0.26/0.62      ! [T5: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > nat] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ T5 )
% 0.26/0.62       => ( ( ord_le7203529160286727270d_enat @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: extended_enat] :
% 0.26/0.62                ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_nat ) )
% 0.26/0.62           => ( ( groups2027974829824023292at_nat @ G @ T5 )
% 0.26/0.62              = ( groups2027974829824023292at_nat @ G @ S2 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_right
% 0.26/0.62  thf(fact_7852_sum_Omono__neutral__right,axiom,
% 0.26/0.62      ! [T5: set_complex,S2: set_complex,G: complex > int] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ T5 )
% 0.26/0.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: complex] :
% 0.26/0.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_int ) )
% 0.26/0.62           => ( ( groups5690904116761175830ex_int @ G @ T5 )
% 0.26/0.62              = ( groups5690904116761175830ex_int @ G @ S2 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_right
% 0.26/0.62  thf(fact_7853_sum_Omono__neutral__left,axiom,
% 0.26/0.62      ! [T5: set_int,S2: set_int,G: int > real] :
% 0.26/0.62        ( ( finite_finite_int @ T5 )
% 0.26/0.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: int] :
% 0.26/0.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_real ) )
% 0.26/0.62           => ( ( groups8778361861064173332t_real @ G @ S2 )
% 0.26/0.62              = ( groups8778361861064173332t_real @ G @ T5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_left
% 0.26/0.62  thf(fact_7854_sum_Omono__neutral__left,axiom,
% 0.26/0.62      ! [T5: set_complex,S2: set_complex,G: complex > real] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ T5 )
% 0.26/0.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: complex] :
% 0.26/0.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_real ) )
% 0.26/0.62           => ( ( groups5808333547571424918x_real @ G @ S2 )
% 0.26/0.62              = ( groups5808333547571424918x_real @ G @ T5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_left
% 0.26/0.62  thf(fact_7855_sum_Omono__neutral__left,axiom,
% 0.26/0.62      ! [T5: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > real] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ T5 )
% 0.26/0.62       => ( ( ord_le7203529160286727270d_enat @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: extended_enat] :
% 0.26/0.62                ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_real ) )
% 0.26/0.62           => ( ( groups4148127829035722712t_real @ G @ S2 )
% 0.26/0.62              = ( groups4148127829035722712t_real @ G @ T5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_left
% 0.26/0.62  thf(fact_7856_sum_Omono__neutral__left,axiom,
% 0.26/0.62      ! [T5: set_int,S2: set_int,G: int > rat] :
% 0.26/0.62        ( ( finite_finite_int @ T5 )
% 0.26/0.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: int] :
% 0.26/0.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_rat ) )
% 0.26/0.62           => ( ( groups3906332499630173760nt_rat @ G @ S2 )
% 0.26/0.62              = ( groups3906332499630173760nt_rat @ G @ T5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_left
% 0.26/0.62  thf(fact_7857_sum_Omono__neutral__left,axiom,
% 0.26/0.62      ! [T5: set_complex,S2: set_complex,G: complex > rat] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ T5 )
% 0.26/0.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: complex] :
% 0.26/0.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_rat ) )
% 0.26/0.62           => ( ( groups5058264527183730370ex_rat @ G @ S2 )
% 0.26/0.62              = ( groups5058264527183730370ex_rat @ G @ T5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_left
% 0.26/0.62  thf(fact_7858_sum_Omono__neutral__left,axiom,
% 0.26/0.62      ! [T5: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > rat] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ T5 )
% 0.26/0.62       => ( ( ord_le7203529160286727270d_enat @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: extended_enat] :
% 0.26/0.62                ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_rat ) )
% 0.26/0.62           => ( ( groups1392844769737527556at_rat @ G @ S2 )
% 0.26/0.62              = ( groups1392844769737527556at_rat @ G @ T5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_left
% 0.26/0.62  thf(fact_7859_sum_Omono__neutral__left,axiom,
% 0.26/0.62      ! [T5: set_int,S2: set_int,G: int > nat] :
% 0.26/0.62        ( ( finite_finite_int @ T5 )
% 0.26/0.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: int] :
% 0.26/0.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_nat ) )
% 0.26/0.62           => ( ( groups4541462559716669496nt_nat @ G @ S2 )
% 0.26/0.62              = ( groups4541462559716669496nt_nat @ G @ T5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_left
% 0.26/0.62  thf(fact_7860_sum_Omono__neutral__left,axiom,
% 0.26/0.62      ! [T5: set_complex,S2: set_complex,G: complex > nat] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ T5 )
% 0.26/0.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: complex] :
% 0.26/0.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_nat ) )
% 0.26/0.62           => ( ( groups5693394587270226106ex_nat @ G @ S2 )
% 0.26/0.62              = ( groups5693394587270226106ex_nat @ G @ T5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_left
% 0.26/0.62  thf(fact_7861_sum_Omono__neutral__left,axiom,
% 0.26/0.62      ! [T5: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > nat] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ T5 )
% 0.26/0.62       => ( ( ord_le7203529160286727270d_enat @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: extended_enat] :
% 0.26/0.62                ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_nat ) )
% 0.26/0.62           => ( ( groups2027974829824023292at_nat @ G @ S2 )
% 0.26/0.62              = ( groups2027974829824023292at_nat @ G @ T5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_left
% 0.26/0.62  thf(fact_7862_sum_Omono__neutral__left,axiom,
% 0.26/0.62      ! [T5: set_complex,S2: set_complex,G: complex > int] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ T5 )
% 0.26/0.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 0.26/0.62         => ( ! [X4: complex] :
% 0.26/0.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 0.26/0.62               => ( ( G @ X4 )
% 0.26/0.62                  = zero_zero_int ) )
% 0.26/0.62           => ( ( groups5690904116761175830ex_int @ G @ S2 )
% 0.26/0.62              = ( groups5690904116761175830ex_int @ G @ T5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.mono_neutral_left
% 0.26/0.62  thf(fact_7863_sum_Osame__carrierI,axiom,
% 0.26/0.62      ! [C4: set_real,A3: set_real,B5: set_real,G: real > real,H2: real > real] :
% 0.26/0.62        ( ( finite_finite_real @ C4 )
% 0.26/0.62       => ( ( ord_less_eq_set_real @ A3 @ C4 )
% 0.26/0.62         => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 0.26/0.62           => ( ! [A5: real] :
% 0.26/0.62                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A3 ) )
% 0.26/0.62                 => ( ( G @ A5 )
% 0.26/0.62                    = zero_zero_real ) )
% 0.26/0.62             => ( ! [B4: real] :
% 0.26/0.62                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 0.26/0.62                   => ( ( H2 @ B4 )
% 0.26/0.62                      = zero_zero_real ) )
% 0.26/0.62               => ( ( ( groups8097168146408367636l_real @ G @ C4 )
% 0.26/0.62                    = ( groups8097168146408367636l_real @ H2 @ C4 ) )
% 0.26/0.62                 => ( ( groups8097168146408367636l_real @ G @ A3 )
% 0.26/0.62                    = ( groups8097168146408367636l_real @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.same_carrierI
% 0.26/0.62  thf(fact_7864_sum_Osame__carrierI,axiom,
% 0.26/0.62      ! [C4: set_int,A3: set_int,B5: set_int,G: int > real,H2: int > real] :
% 0.26/0.62        ( ( finite_finite_int @ C4 )
% 0.26/0.62       => ( ( ord_less_eq_set_int @ A3 @ C4 )
% 0.26/0.62         => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 0.26/0.62           => ( ! [A5: int] :
% 0.26/0.62                  ( ( member_int @ A5 @ ( minus_minus_set_int @ C4 @ A3 ) )
% 0.26/0.62                 => ( ( G @ A5 )
% 0.26/0.62                    = zero_zero_real ) )
% 0.26/0.62             => ( ! [B4: int] :
% 0.26/0.62                    ( ( member_int @ B4 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 0.26/0.62                   => ( ( H2 @ B4 )
% 0.26/0.62                      = zero_zero_real ) )
% 0.26/0.62               => ( ( ( groups8778361861064173332t_real @ G @ C4 )
% 0.26/0.62                    = ( groups8778361861064173332t_real @ H2 @ C4 ) )
% 0.26/0.62                 => ( ( groups8778361861064173332t_real @ G @ A3 )
% 0.26/0.62                    = ( groups8778361861064173332t_real @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.same_carrierI
% 0.26/0.62  thf(fact_7865_sum_Osame__carrierI,axiom,
% 0.26/0.62      ! [C4: set_complex,A3: set_complex,B5: set_complex,G: complex > real,H2: complex > real] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ C4 )
% 0.26/0.62       => ( ( ord_le211207098394363844omplex @ A3 @ C4 )
% 0.26/0.62         => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 0.26/0.62           => ( ! [A5: complex] :
% 0.26/0.62                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A3 ) )
% 0.26/0.62                 => ( ( G @ A5 )
% 0.26/0.62                    = zero_zero_real ) )
% 0.26/0.62             => ( ! [B4: complex] :
% 0.26/0.62                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 0.26/0.62                   => ( ( H2 @ B4 )
% 0.26/0.62                      = zero_zero_real ) )
% 0.26/0.62               => ( ( ( groups5808333547571424918x_real @ G @ C4 )
% 0.26/0.62                    = ( groups5808333547571424918x_real @ H2 @ C4 ) )
% 0.26/0.62                 => ( ( groups5808333547571424918x_real @ G @ A3 )
% 0.26/0.62                    = ( groups5808333547571424918x_real @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.same_carrierI
% 0.26/0.62  thf(fact_7866_sum_Osame__carrierI,axiom,
% 0.26/0.62      ! [C4: set_Extended_enat,A3: set_Extended_enat,B5: set_Extended_enat,G: extended_enat > real,H2: extended_enat > real] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ C4 )
% 0.26/0.62       => ( ( ord_le7203529160286727270d_enat @ A3 @ C4 )
% 0.26/0.62         => ( ( ord_le7203529160286727270d_enat @ B5 @ C4 )
% 0.26/0.62           => ( ! [A5: extended_enat] :
% 0.26/0.62                  ( ( member_Extended_enat @ A5 @ ( minus_925952699566721837d_enat @ C4 @ A3 ) )
% 0.26/0.62                 => ( ( G @ A5 )
% 0.26/0.62                    = zero_zero_real ) )
% 0.26/0.62             => ( ! [B4: extended_enat] :
% 0.26/0.62                    ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ C4 @ B5 ) )
% 0.26/0.62                   => ( ( H2 @ B4 )
% 0.26/0.62                      = zero_zero_real ) )
% 0.26/0.62               => ( ( ( groups4148127829035722712t_real @ G @ C4 )
% 0.26/0.62                    = ( groups4148127829035722712t_real @ H2 @ C4 ) )
% 0.26/0.62                 => ( ( groups4148127829035722712t_real @ G @ A3 )
% 0.26/0.62                    = ( groups4148127829035722712t_real @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.same_carrierI
% 0.26/0.62  thf(fact_7867_sum_Osame__carrierI,axiom,
% 0.26/0.62      ! [C4: set_real,A3: set_real,B5: set_real,G: real > rat,H2: real > rat] :
% 0.26/0.62        ( ( finite_finite_real @ C4 )
% 0.26/0.62       => ( ( ord_less_eq_set_real @ A3 @ C4 )
% 0.26/0.62         => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 0.26/0.62           => ( ! [A5: real] :
% 0.26/0.62                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A3 ) )
% 0.26/0.62                 => ( ( G @ A5 )
% 0.26/0.62                    = zero_zero_rat ) )
% 0.26/0.62             => ( ! [B4: real] :
% 0.26/0.62                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 0.26/0.62                   => ( ( H2 @ B4 )
% 0.26/0.62                      = zero_zero_rat ) )
% 0.26/0.62               => ( ( ( groups1300246762558778688al_rat @ G @ C4 )
% 0.26/0.62                    = ( groups1300246762558778688al_rat @ H2 @ C4 ) )
% 0.26/0.62                 => ( ( groups1300246762558778688al_rat @ G @ A3 )
% 0.26/0.62                    = ( groups1300246762558778688al_rat @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.same_carrierI
% 0.26/0.62  thf(fact_7868_sum_Osame__carrierI,axiom,
% 0.26/0.62      ! [C4: set_int,A3: set_int,B5: set_int,G: int > rat,H2: int > rat] :
% 0.26/0.62        ( ( finite_finite_int @ C4 )
% 0.26/0.62       => ( ( ord_less_eq_set_int @ A3 @ C4 )
% 0.26/0.62         => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 0.26/0.62           => ( ! [A5: int] :
% 0.26/0.62                  ( ( member_int @ A5 @ ( minus_minus_set_int @ C4 @ A3 ) )
% 0.26/0.62                 => ( ( G @ A5 )
% 0.26/0.62                    = zero_zero_rat ) )
% 0.26/0.62             => ( ! [B4: int] :
% 0.26/0.62                    ( ( member_int @ B4 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 0.26/0.62                   => ( ( H2 @ B4 )
% 0.26/0.62                      = zero_zero_rat ) )
% 0.26/0.62               => ( ( ( groups3906332499630173760nt_rat @ G @ C4 )
% 0.26/0.62                    = ( groups3906332499630173760nt_rat @ H2 @ C4 ) )
% 0.26/0.62                 => ( ( groups3906332499630173760nt_rat @ G @ A3 )
% 0.26/0.62                    = ( groups3906332499630173760nt_rat @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.same_carrierI
% 0.26/0.62  thf(fact_7869_sum_Osame__carrierI,axiom,
% 0.26/0.62      ! [C4: set_complex,A3: set_complex,B5: set_complex,G: complex > rat,H2: complex > rat] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ C4 )
% 0.26/0.62       => ( ( ord_le211207098394363844omplex @ A3 @ C4 )
% 0.26/0.62         => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 0.26/0.62           => ( ! [A5: complex] :
% 0.26/0.62                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A3 ) )
% 0.26/0.62                 => ( ( G @ A5 )
% 0.26/0.62                    = zero_zero_rat ) )
% 0.26/0.62             => ( ! [B4: complex] :
% 0.26/0.62                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 0.26/0.62                   => ( ( H2 @ B4 )
% 0.26/0.62                      = zero_zero_rat ) )
% 0.26/0.62               => ( ( ( groups5058264527183730370ex_rat @ G @ C4 )
% 0.26/0.62                    = ( groups5058264527183730370ex_rat @ H2 @ C4 ) )
% 0.26/0.62                 => ( ( groups5058264527183730370ex_rat @ G @ A3 )
% 0.26/0.62                    = ( groups5058264527183730370ex_rat @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.same_carrierI
% 0.26/0.62  thf(fact_7870_sum_Osame__carrierI,axiom,
% 0.26/0.62      ! [C4: set_Extended_enat,A3: set_Extended_enat,B5: set_Extended_enat,G: extended_enat > rat,H2: extended_enat > rat] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ C4 )
% 0.26/0.62       => ( ( ord_le7203529160286727270d_enat @ A3 @ C4 )
% 0.26/0.62         => ( ( ord_le7203529160286727270d_enat @ B5 @ C4 )
% 0.26/0.62           => ( ! [A5: extended_enat] :
% 0.26/0.62                  ( ( member_Extended_enat @ A5 @ ( minus_925952699566721837d_enat @ C4 @ A3 ) )
% 0.26/0.62                 => ( ( G @ A5 )
% 0.26/0.62                    = zero_zero_rat ) )
% 0.26/0.62             => ( ! [B4: extended_enat] :
% 0.26/0.62                    ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ C4 @ B5 ) )
% 0.26/0.62                   => ( ( H2 @ B4 )
% 0.26/0.62                      = zero_zero_rat ) )
% 0.26/0.62               => ( ( ( groups1392844769737527556at_rat @ G @ C4 )
% 0.26/0.62                    = ( groups1392844769737527556at_rat @ H2 @ C4 ) )
% 0.26/0.62                 => ( ( groups1392844769737527556at_rat @ G @ A3 )
% 0.26/0.62                    = ( groups1392844769737527556at_rat @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.same_carrierI
% 0.26/0.62  thf(fact_7871_sum_Osame__carrierI,axiom,
% 0.26/0.62      ! [C4: set_real,A3: set_real,B5: set_real,G: real > nat,H2: real > nat] :
% 0.26/0.62        ( ( finite_finite_real @ C4 )
% 0.26/0.62       => ( ( ord_less_eq_set_real @ A3 @ C4 )
% 0.26/0.62         => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 0.26/0.62           => ( ! [A5: real] :
% 0.26/0.62                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A3 ) )
% 0.26/0.62                 => ( ( G @ A5 )
% 0.26/0.62                    = zero_zero_nat ) )
% 0.26/0.62             => ( ! [B4: real] :
% 0.26/0.62                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 0.26/0.62                   => ( ( H2 @ B4 )
% 0.26/0.62                      = zero_zero_nat ) )
% 0.26/0.62               => ( ( ( groups1935376822645274424al_nat @ G @ C4 )
% 0.26/0.62                    = ( groups1935376822645274424al_nat @ H2 @ C4 ) )
% 0.26/0.62                 => ( ( groups1935376822645274424al_nat @ G @ A3 )
% 0.26/0.62                    = ( groups1935376822645274424al_nat @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.same_carrierI
% 0.26/0.62  thf(fact_7872_sum_Osame__carrierI,axiom,
% 0.26/0.62      ! [C4: set_int,A3: set_int,B5: set_int,G: int > nat,H2: int > nat] :
% 0.26/0.62        ( ( finite_finite_int @ C4 )
% 0.26/0.62       => ( ( ord_less_eq_set_int @ A3 @ C4 )
% 0.26/0.62         => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 0.26/0.62           => ( ! [A5: int] :
% 0.26/0.62                  ( ( member_int @ A5 @ ( minus_minus_set_int @ C4 @ A3 ) )
% 0.26/0.62                 => ( ( G @ A5 )
% 0.26/0.62                    = zero_zero_nat ) )
% 0.26/0.62             => ( ! [B4: int] :
% 0.26/0.62                    ( ( member_int @ B4 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 0.26/0.62                   => ( ( H2 @ B4 )
% 0.26/0.62                      = zero_zero_nat ) )
% 0.26/0.62               => ( ( ( groups4541462559716669496nt_nat @ G @ C4 )
% 0.26/0.62                    = ( groups4541462559716669496nt_nat @ H2 @ C4 ) )
% 0.26/0.62                 => ( ( groups4541462559716669496nt_nat @ G @ A3 )
% 0.26/0.62                    = ( groups4541462559716669496nt_nat @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.same_carrierI
% 0.26/0.62  thf(fact_7873_sum_Osame__carrier,axiom,
% 0.26/0.62      ! [C4: set_real,A3: set_real,B5: set_real,G: real > real,H2: real > real] :
% 0.26/0.62        ( ( finite_finite_real @ C4 )
% 0.26/0.62       => ( ( ord_less_eq_set_real @ A3 @ C4 )
% 0.26/0.62         => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 0.26/0.62           => ( ! [A5: real] :
% 0.26/0.62                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A3 ) )
% 0.26/0.62                 => ( ( G @ A5 )
% 0.26/0.62                    = zero_zero_real ) )
% 0.26/0.62             => ( ! [B4: real] :
% 0.26/0.62                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 0.26/0.62                   => ( ( H2 @ B4 )
% 0.26/0.62                      = zero_zero_real ) )
% 0.26/0.62               => ( ( ( groups8097168146408367636l_real @ G @ A3 )
% 0.26/0.62                    = ( groups8097168146408367636l_real @ H2 @ B5 ) )
% 0.26/0.62                  = ( ( groups8097168146408367636l_real @ G @ C4 )
% 0.26/0.62                    = ( groups8097168146408367636l_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.same_carrier
% 0.26/0.62  thf(fact_7874_sum_Osame__carrier,axiom,
% 0.26/0.62      ! [C4: set_int,A3: set_int,B5: set_int,G: int > real,H2: int > real] :
% 0.26/0.62        ( ( finite_finite_int @ C4 )
% 0.26/0.62       => ( ( ord_less_eq_set_int @ A3 @ C4 )
% 0.26/0.62         => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 0.26/0.62           => ( ! [A5: int] :
% 0.26/0.62                  ( ( member_int @ A5 @ ( minus_minus_set_int @ C4 @ A3 ) )
% 0.26/0.62                 => ( ( G @ A5 )
% 0.26/0.62                    = zero_zero_real ) )
% 0.26/0.62             => ( ! [B4: int] :
% 0.26/0.62                    ( ( member_int @ B4 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 0.26/0.62                   => ( ( H2 @ B4 )
% 0.26/0.62                      = zero_zero_real ) )
% 0.26/0.62               => ( ( ( groups8778361861064173332t_real @ G @ A3 )
% 0.26/0.62                    = ( groups8778361861064173332t_real @ H2 @ B5 ) )
% 0.26/0.62                  = ( ( groups8778361861064173332t_real @ G @ C4 )
% 0.26/0.62                    = ( groups8778361861064173332t_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.same_carrier
% 0.26/0.62  thf(fact_7875_sum_Osame__carrier,axiom,
% 0.26/0.62      ! [C4: set_complex,A3: set_complex,B5: set_complex,G: complex > real,H2: complex > real] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ C4 )
% 0.26/0.62       => ( ( ord_le211207098394363844omplex @ A3 @ C4 )
% 0.26/0.62         => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 0.26/0.62           => ( ! [A5: complex] :
% 0.26/0.62                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A3 ) )
% 0.26/0.62                 => ( ( G @ A5 )
% 0.26/0.62                    = zero_zero_real ) )
% 0.26/0.62             => ( ! [B4: complex] :
% 0.26/0.62                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 0.26/0.62                   => ( ( H2 @ B4 )
% 0.26/0.62                      = zero_zero_real ) )
% 0.26/0.62               => ( ( ( groups5808333547571424918x_real @ G @ A3 )
% 0.26/0.62                    = ( groups5808333547571424918x_real @ H2 @ B5 ) )
% 0.26/0.62                  = ( ( groups5808333547571424918x_real @ G @ C4 )
% 0.26/0.62                    = ( groups5808333547571424918x_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.same_carrier
% 0.26/0.62  thf(fact_7876_sum_Osame__carrier,axiom,
% 0.26/0.62      ! [C4: set_Extended_enat,A3: set_Extended_enat,B5: set_Extended_enat,G: extended_enat > real,H2: extended_enat > real] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ C4 )
% 0.26/0.62       => ( ( ord_le7203529160286727270d_enat @ A3 @ C4 )
% 0.26/0.62         => ( ( ord_le7203529160286727270d_enat @ B5 @ C4 )
% 0.26/0.62           => ( ! [A5: extended_enat] :
% 0.26/0.62                  ( ( member_Extended_enat @ A5 @ ( minus_925952699566721837d_enat @ C4 @ A3 ) )
% 0.26/0.62                 => ( ( G @ A5 )
% 0.26/0.62                    = zero_zero_real ) )
% 0.26/0.62             => ( ! [B4: extended_enat] :
% 0.26/0.62                    ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ C4 @ B5 ) )
% 0.26/0.62                   => ( ( H2 @ B4 )
% 0.26/0.62                      = zero_zero_real ) )
% 0.26/0.62               => ( ( ( groups4148127829035722712t_real @ G @ A3 )
% 0.26/0.62                    = ( groups4148127829035722712t_real @ H2 @ B5 ) )
% 0.26/0.62                  = ( ( groups4148127829035722712t_real @ G @ C4 )
% 0.26/0.62                    = ( groups4148127829035722712t_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.same_carrier
% 0.26/0.62  thf(fact_7877_sum_Osame__carrier,axiom,
% 0.26/0.62      ! [C4: set_real,A3: set_real,B5: set_real,G: real > rat,H2: real > rat] :
% 0.26/0.62        ( ( finite_finite_real @ C4 )
% 0.26/0.62       => ( ( ord_less_eq_set_real @ A3 @ C4 )
% 0.26/0.62         => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 0.26/0.62           => ( ! [A5: real] :
% 0.26/0.62                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A3 ) )
% 0.26/0.62                 => ( ( G @ A5 )
% 0.26/0.62                    = zero_zero_rat ) )
% 0.26/0.62             => ( ! [B4: real] :
% 0.26/0.62                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 0.26/0.62                   => ( ( H2 @ B4 )
% 0.26/0.62                      = zero_zero_rat ) )
% 0.26/0.62               => ( ( ( groups1300246762558778688al_rat @ G @ A3 )
% 0.26/0.62                    = ( groups1300246762558778688al_rat @ H2 @ B5 ) )
% 0.26/0.62                  = ( ( groups1300246762558778688al_rat @ G @ C4 )
% 0.26/0.62                    = ( groups1300246762558778688al_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.same_carrier
% 0.26/0.62  thf(fact_7878_sum_Osame__carrier,axiom,
% 0.26/0.62      ! [C4: set_int,A3: set_int,B5: set_int,G: int > rat,H2: int > rat] :
% 0.26/0.62        ( ( finite_finite_int @ C4 )
% 0.26/0.62       => ( ( ord_less_eq_set_int @ A3 @ C4 )
% 0.26/0.62         => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 0.26/0.62           => ( ! [A5: int] :
% 0.26/0.62                  ( ( member_int @ A5 @ ( minus_minus_set_int @ C4 @ A3 ) )
% 0.26/0.62                 => ( ( G @ A5 )
% 0.26/0.62                    = zero_zero_rat ) )
% 0.26/0.62             => ( ! [B4: int] :
% 0.26/0.62                    ( ( member_int @ B4 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 0.26/0.62                   => ( ( H2 @ B4 )
% 0.26/0.62                      = zero_zero_rat ) )
% 0.26/0.62               => ( ( ( groups3906332499630173760nt_rat @ G @ A3 )
% 0.26/0.62                    = ( groups3906332499630173760nt_rat @ H2 @ B5 ) )
% 0.26/0.62                  = ( ( groups3906332499630173760nt_rat @ G @ C4 )
% 0.26/0.62                    = ( groups3906332499630173760nt_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.same_carrier
% 0.26/0.62  thf(fact_7879_sum_Osame__carrier,axiom,
% 0.26/0.62      ! [C4: set_complex,A3: set_complex,B5: set_complex,G: complex > rat,H2: complex > rat] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ C4 )
% 0.26/0.62       => ( ( ord_le211207098394363844omplex @ A3 @ C4 )
% 0.26/0.62         => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 0.26/0.62           => ( ! [A5: complex] :
% 0.26/0.62                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A3 ) )
% 0.26/0.62                 => ( ( G @ A5 )
% 0.26/0.62                    = zero_zero_rat ) )
% 0.26/0.62             => ( ! [B4: complex] :
% 0.26/0.62                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 0.26/0.62                   => ( ( H2 @ B4 )
% 0.26/0.62                      = zero_zero_rat ) )
% 0.26/0.62               => ( ( ( groups5058264527183730370ex_rat @ G @ A3 )
% 0.26/0.62                    = ( groups5058264527183730370ex_rat @ H2 @ B5 ) )
% 0.26/0.62                  = ( ( groups5058264527183730370ex_rat @ G @ C4 )
% 0.26/0.62                    = ( groups5058264527183730370ex_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.same_carrier
% 0.26/0.62  thf(fact_7880_sum_Osame__carrier,axiom,
% 0.26/0.62      ! [C4: set_Extended_enat,A3: set_Extended_enat,B5: set_Extended_enat,G: extended_enat > rat,H2: extended_enat > rat] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ C4 )
% 0.26/0.62       => ( ( ord_le7203529160286727270d_enat @ A3 @ C4 )
% 0.26/0.62         => ( ( ord_le7203529160286727270d_enat @ B5 @ C4 )
% 0.26/0.62           => ( ! [A5: extended_enat] :
% 0.26/0.62                  ( ( member_Extended_enat @ A5 @ ( minus_925952699566721837d_enat @ C4 @ A3 ) )
% 0.26/0.62                 => ( ( G @ A5 )
% 0.26/0.62                    = zero_zero_rat ) )
% 0.26/0.62             => ( ! [B4: extended_enat] :
% 0.26/0.62                    ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ C4 @ B5 ) )
% 0.26/0.62                   => ( ( H2 @ B4 )
% 0.26/0.62                      = zero_zero_rat ) )
% 0.26/0.62               => ( ( ( groups1392844769737527556at_rat @ G @ A3 )
% 0.26/0.62                    = ( groups1392844769737527556at_rat @ H2 @ B5 ) )
% 0.26/0.62                  = ( ( groups1392844769737527556at_rat @ G @ C4 )
% 0.26/0.62                    = ( groups1392844769737527556at_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.same_carrier
% 0.26/0.62  thf(fact_7881_sum_Osame__carrier,axiom,
% 0.26/0.62      ! [C4: set_real,A3: set_real,B5: set_real,G: real > nat,H2: real > nat] :
% 0.26/0.62        ( ( finite_finite_real @ C4 )
% 0.26/0.62       => ( ( ord_less_eq_set_real @ A3 @ C4 )
% 0.26/0.62         => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 0.26/0.62           => ( ! [A5: real] :
% 0.26/0.62                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A3 ) )
% 0.26/0.62                 => ( ( G @ A5 )
% 0.26/0.62                    = zero_zero_nat ) )
% 0.26/0.62             => ( ! [B4: real] :
% 0.26/0.62                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 0.26/0.62                   => ( ( H2 @ B4 )
% 0.26/0.62                      = zero_zero_nat ) )
% 0.26/0.62               => ( ( ( groups1935376822645274424al_nat @ G @ A3 )
% 0.26/0.62                    = ( groups1935376822645274424al_nat @ H2 @ B5 ) )
% 0.26/0.62                  = ( ( groups1935376822645274424al_nat @ G @ C4 )
% 0.26/0.62                    = ( groups1935376822645274424al_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.same_carrier
% 0.26/0.62  thf(fact_7882_sum_Osame__carrier,axiom,
% 0.26/0.62      ! [C4: set_int,A3: set_int,B5: set_int,G: int > nat,H2: int > nat] :
% 0.26/0.62        ( ( finite_finite_int @ C4 )
% 0.26/0.62       => ( ( ord_less_eq_set_int @ A3 @ C4 )
% 0.26/0.62         => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 0.26/0.62           => ( ! [A5: int] :
% 0.26/0.62                  ( ( member_int @ A5 @ ( minus_minus_set_int @ C4 @ A3 ) )
% 0.26/0.62                 => ( ( G @ A5 )
% 0.26/0.62                    = zero_zero_nat ) )
% 0.26/0.62             => ( ! [B4: int] :
% 0.26/0.62                    ( ( member_int @ B4 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 0.26/0.62                   => ( ( H2 @ B4 )
% 0.26/0.62                      = zero_zero_nat ) )
% 0.26/0.62               => ( ( ( groups4541462559716669496nt_nat @ G @ A3 )
% 0.26/0.62                    = ( groups4541462559716669496nt_nat @ H2 @ B5 ) )
% 0.26/0.62                  = ( ( groups4541462559716669496nt_nat @ G @ C4 )
% 0.26/0.62                    = ( groups4541462559716669496nt_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum.same_carrier
% 0.26/0.62  thf(fact_7883_finite__M__bounded__by__nat,axiom,
% 0.26/0.62      ! [P: nat > $o,I: nat] :
% 0.26/0.62        ( finite_finite_nat
% 0.26/0.62        @ ( collect_nat
% 0.26/0.62          @ ^ [K3: nat] :
% 0.26/0.62              ( ( P @ K3 )
% 0.26/0.62              & ( ord_less_nat @ K3 @ I ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % finite_M_bounded_by_nat
% 0.26/0.62  thf(fact_7884_finite__less__ub,axiom,
% 0.26/0.62      ! [F: nat > nat,U: nat] :
% 0.26/0.62        ( ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( F @ N2 ) )
% 0.26/0.62       => ( finite_finite_nat
% 0.26/0.62          @ ( collect_nat
% 0.26/0.62            @ ^ [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ U ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % finite_less_ub
% 0.26/0.62  thf(fact_7885_sum__mono2,axiom,
% 0.26/0.62      ! [B5: set_real,A3: set_real,F: real > real] :
% 0.26/0.62        ( ( finite_finite_real @ B5 )
% 0.26/0.62       => ( ( ord_less_eq_set_real @ A3 @ B5 )
% 0.26/0.62         => ( ! [B4: real] :
% 0.26/0.62                ( ( member_real @ B4 @ ( minus_minus_set_real @ B5 @ A3 ) )
% 0.26/0.62               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B4 ) ) )
% 0.26/0.62           => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A3 ) @ ( groups8097168146408367636l_real @ F @ B5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono2
% 0.26/0.62  thf(fact_7886_sum__mono2,axiom,
% 0.26/0.62      ! [B5: set_int,A3: set_int,F: int > real] :
% 0.26/0.62        ( ( finite_finite_int @ B5 )
% 0.26/0.62       => ( ( ord_less_eq_set_int @ A3 @ B5 )
% 0.26/0.62         => ( ! [B4: int] :
% 0.26/0.62                ( ( member_int @ B4 @ ( minus_minus_set_int @ B5 @ A3 ) )
% 0.26/0.62               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B4 ) ) )
% 0.26/0.62           => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A3 ) @ ( groups8778361861064173332t_real @ F @ B5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono2
% 0.26/0.62  thf(fact_7887_sum__mono2,axiom,
% 0.26/0.62      ! [B5: set_complex,A3: set_complex,F: complex > real] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ B5 )
% 0.26/0.62       => ( ( ord_le211207098394363844omplex @ A3 @ B5 )
% 0.26/0.62         => ( ! [B4: complex] :
% 0.26/0.62                ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B5 @ A3 ) )
% 0.26/0.62               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B4 ) ) )
% 0.26/0.62           => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A3 ) @ ( groups5808333547571424918x_real @ F @ B5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono2
% 0.26/0.62  thf(fact_7888_sum__mono2,axiom,
% 0.26/0.62      ! [B5: set_Extended_enat,A3: set_Extended_enat,F: extended_enat > real] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ B5 )
% 0.26/0.62       => ( ( ord_le7203529160286727270d_enat @ A3 @ B5 )
% 0.26/0.62         => ( ! [B4: extended_enat] :
% 0.26/0.62                ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ B5 @ A3 ) )
% 0.26/0.62               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B4 ) ) )
% 0.26/0.62           => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ A3 ) @ ( groups4148127829035722712t_real @ F @ B5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono2
% 0.26/0.62  thf(fact_7889_sum__mono2,axiom,
% 0.26/0.62      ! [B5: set_real,A3: set_real,F: real > rat] :
% 0.26/0.62        ( ( finite_finite_real @ B5 )
% 0.26/0.62       => ( ( ord_less_eq_set_real @ A3 @ B5 )
% 0.26/0.62         => ( ! [B4: real] :
% 0.26/0.62                ( ( member_real @ B4 @ ( minus_minus_set_real @ B5 @ A3 ) )
% 0.26/0.62               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B4 ) ) )
% 0.26/0.62           => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A3 ) @ ( groups1300246762558778688al_rat @ F @ B5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono2
% 0.26/0.62  thf(fact_7890_sum__mono2,axiom,
% 0.26/0.62      ! [B5: set_int,A3: set_int,F: int > rat] :
% 0.26/0.62        ( ( finite_finite_int @ B5 )
% 0.26/0.62       => ( ( ord_less_eq_set_int @ A3 @ B5 )
% 0.26/0.62         => ( ! [B4: int] :
% 0.26/0.62                ( ( member_int @ B4 @ ( minus_minus_set_int @ B5 @ A3 ) )
% 0.26/0.62               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B4 ) ) )
% 0.26/0.62           => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ ( groups3906332499630173760nt_rat @ F @ B5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono2
% 0.26/0.62  thf(fact_7891_sum__mono2,axiom,
% 0.26/0.62      ! [B5: set_complex,A3: set_complex,F: complex > rat] :
% 0.26/0.62        ( ( finite3207457112153483333omplex @ B5 )
% 0.26/0.62       => ( ( ord_le211207098394363844omplex @ A3 @ B5 )
% 0.26/0.62         => ( ! [B4: complex] :
% 0.26/0.62                ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B5 @ A3 ) )
% 0.26/0.62               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B4 ) ) )
% 0.26/0.62           => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A3 ) @ ( groups5058264527183730370ex_rat @ F @ B5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono2
% 0.26/0.62  thf(fact_7892_sum__mono2,axiom,
% 0.26/0.62      ! [B5: set_Extended_enat,A3: set_Extended_enat,F: extended_enat > rat] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ B5 )
% 0.26/0.62       => ( ( ord_le7203529160286727270d_enat @ A3 @ B5 )
% 0.26/0.62         => ( ! [B4: extended_enat] :
% 0.26/0.62                ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ B5 @ A3 ) )
% 0.26/0.62               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B4 ) ) )
% 0.26/0.62           => ( ord_less_eq_rat @ ( groups1392844769737527556at_rat @ F @ A3 ) @ ( groups1392844769737527556at_rat @ F @ B5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono2
% 0.26/0.62  thf(fact_7893_sum__mono2,axiom,
% 0.26/0.62      ! [B5: set_real,A3: set_real,F: real > nat] :
% 0.26/0.62        ( ( finite_finite_real @ B5 )
% 0.26/0.62       => ( ( ord_less_eq_set_real @ A3 @ B5 )
% 0.26/0.62         => ( ! [B4: real] :
% 0.26/0.62                ( ( member_real @ B4 @ ( minus_minus_set_real @ B5 @ A3 ) )
% 0.26/0.62               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B4 ) ) )
% 0.26/0.62           => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A3 ) @ ( groups1935376822645274424al_nat @ F @ B5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono2
% 0.26/0.62  thf(fact_7894_sum__mono2,axiom,
% 0.26/0.62      ! [B5: set_int,A3: set_int,F: int > nat] :
% 0.26/0.62        ( ( finite_finite_int @ B5 )
% 0.26/0.62       => ( ( ord_less_eq_set_int @ A3 @ B5 )
% 0.26/0.62         => ( ! [B4: int] :
% 0.26/0.62                ( ( member_int @ B4 @ ( minus_minus_set_int @ B5 @ A3 ) )
% 0.26/0.62               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B4 ) ) )
% 0.26/0.62           => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ ( groups4541462559716669496nt_nat @ F @ B5 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_mono2
% 0.26/0.62  thf(fact_7895_sum__nonneg,axiom,
% 0.26/0.62      ! [A3: set_real,F: real > real] :
% 0.26/0.62        ( ! [X4: real] :
% 0.26/0.62            ( ( member_real @ X4 @ A3 )
% 0.26/0.62           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.26/0.62       => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg
% 0.26/0.62  thf(fact_7896_sum__nonneg,axiom,
% 0.26/0.62      ! [A3: set_int,F: int > real] :
% 0.26/0.62        ( ! [X4: int] :
% 0.26/0.62            ( ( member_int @ X4 @ A3 )
% 0.26/0.62           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.26/0.62       => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg
% 0.26/0.62  thf(fact_7897_sum__nonneg,axiom,
% 0.26/0.62      ! [A3: set_real,F: real > rat] :
% 0.26/0.62        ( ! [X4: real] :
% 0.26/0.62            ( ( member_real @ X4 @ A3 )
% 0.26/0.62           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.26/0.62       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg
% 0.26/0.62  thf(fact_7898_sum__nonneg,axiom,
% 0.26/0.62      ! [A3: set_nat,F: nat > rat] :
% 0.26/0.62        ( ! [X4: nat] :
% 0.26/0.62            ( ( member_nat @ X4 @ A3 )
% 0.26/0.62           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.26/0.62       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg
% 0.26/0.62  thf(fact_7899_sum__nonneg,axiom,
% 0.26/0.62      ! [A3: set_int,F: int > rat] :
% 0.26/0.62        ( ! [X4: int] :
% 0.26/0.62            ( ( member_int @ X4 @ A3 )
% 0.26/0.62           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.26/0.62       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg
% 0.26/0.62  thf(fact_7900_sum__nonneg,axiom,
% 0.26/0.62      ! [A3: set_real,F: real > nat] :
% 0.26/0.62        ( ! [X4: real] :
% 0.26/0.62            ( ( member_real @ X4 @ A3 )
% 0.26/0.62           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 0.26/0.62       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg
% 0.26/0.62  thf(fact_7901_sum__nonneg,axiom,
% 0.26/0.62      ! [A3: set_int,F: int > nat] :
% 0.26/0.62        ( ! [X4: int] :
% 0.26/0.62            ( ( member_int @ X4 @ A3 )
% 0.26/0.62           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 0.26/0.62       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg
% 0.26/0.62  thf(fact_7902_sum__nonneg,axiom,
% 0.26/0.62      ! [A3: set_real,F: real > int] :
% 0.26/0.62        ( ! [X4: real] :
% 0.26/0.62            ( ( member_real @ X4 @ A3 )
% 0.26/0.62           => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 0.26/0.62       => ( ord_less_eq_int @ zero_zero_int @ ( groups1932886352136224148al_int @ F @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg
% 0.26/0.62  thf(fact_7903_sum__nonneg,axiom,
% 0.26/0.62      ! [A3: set_nat,F: nat > int] :
% 0.26/0.62        ( ! [X4: nat] :
% 0.26/0.62            ( ( member_nat @ X4 @ A3 )
% 0.26/0.62           => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 0.26/0.62       => ( ord_less_eq_int @ zero_zero_int @ ( groups3539618377306564664at_int @ F @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg
% 0.26/0.62  thf(fact_7904_sum__nonneg,axiom,
% 0.26/0.62      ! [A3: set_nat,F: nat > nat] :
% 0.26/0.62        ( ! [X4: nat] :
% 0.26/0.62            ( ( member_nat @ X4 @ A3 )
% 0.26/0.62           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 0.26/0.62       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonneg
% 0.26/0.62  thf(fact_7905_sum__nonpos,axiom,
% 0.26/0.62      ! [A3: set_real,F: real > real] :
% 0.26/0.62        ( ! [X4: real] :
% 0.26/0.62            ( ( member_real @ X4 @ A3 )
% 0.26/0.62           => ( ord_less_eq_real @ ( F @ X4 ) @ zero_zero_real ) )
% 0.26/0.62       => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A3 ) @ zero_zero_real ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonpos
% 0.26/0.62  thf(fact_7906_sum__nonpos,axiom,
% 0.26/0.62      ! [A3: set_int,F: int > real] :
% 0.26/0.62        ( ! [X4: int] :
% 0.26/0.62            ( ( member_int @ X4 @ A3 )
% 0.26/0.62           => ( ord_less_eq_real @ ( F @ X4 ) @ zero_zero_real ) )
% 0.26/0.62       => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A3 ) @ zero_zero_real ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonpos
% 0.26/0.62  thf(fact_7907_sum__nonpos,axiom,
% 0.26/0.62      ! [A3: set_real,F: real > rat] :
% 0.26/0.62        ( ! [X4: real] :
% 0.26/0.62            ( ( member_real @ X4 @ A3 )
% 0.26/0.62           => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 0.26/0.62       => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A3 ) @ zero_zero_rat ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonpos
% 0.26/0.62  thf(fact_7908_sum__nonpos,axiom,
% 0.26/0.62      ! [A3: set_nat,F: nat > rat] :
% 0.26/0.62        ( ! [X4: nat] :
% 0.26/0.62            ( ( member_nat @ X4 @ A3 )
% 0.26/0.62           => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 0.26/0.62       => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ zero_zero_rat ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonpos
% 0.26/0.62  thf(fact_7909_sum__nonpos,axiom,
% 0.26/0.62      ! [A3: set_int,F: int > rat] :
% 0.26/0.62        ( ! [X4: int] :
% 0.26/0.62            ( ( member_int @ X4 @ A3 )
% 0.26/0.62           => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 0.26/0.62       => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ zero_zero_rat ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonpos
% 0.26/0.62  thf(fact_7910_sum__nonpos,axiom,
% 0.26/0.62      ! [A3: set_real,F: real > nat] :
% 0.26/0.62        ( ! [X4: real] :
% 0.26/0.62            ( ( member_real @ X4 @ A3 )
% 0.26/0.62           => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 0.26/0.62       => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A3 ) @ zero_zero_nat ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonpos
% 0.26/0.62  thf(fact_7911_sum__nonpos,axiom,
% 0.26/0.62      ! [A3: set_int,F: int > nat] :
% 0.26/0.62        ( ! [X4: int] :
% 0.26/0.62            ( ( member_int @ X4 @ A3 )
% 0.26/0.62           => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 0.26/0.62       => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ zero_zero_nat ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonpos
% 0.26/0.62  thf(fact_7912_sum__nonpos,axiom,
% 0.26/0.62      ! [A3: set_real,F: real > int] :
% 0.26/0.62        ( ! [X4: real] :
% 0.26/0.62            ( ( member_real @ X4 @ A3 )
% 0.26/0.62           => ( ord_less_eq_int @ ( F @ X4 ) @ zero_zero_int ) )
% 0.26/0.62       => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ A3 ) @ zero_zero_int ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonpos
% 0.26/0.62  thf(fact_7913_sum__nonpos,axiom,
% 0.26/0.62      ! [A3: set_nat,F: nat > int] :
% 0.26/0.62        ( ! [X4: nat] :
% 0.26/0.62            ( ( member_nat @ X4 @ A3 )
% 0.26/0.62           => ( ord_less_eq_int @ ( F @ X4 ) @ zero_zero_int ) )
% 0.26/0.62       => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ A3 ) @ zero_zero_int ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonpos
% 0.26/0.62  thf(fact_7914_sum__nonpos,axiom,
% 0.26/0.62      ! [A3: set_nat,F: nat > nat] :
% 0.26/0.62        ( ! [X4: nat] :
% 0.26/0.62            ( ( member_nat @ X4 @ A3 )
% 0.26/0.62           => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 0.26/0.62       => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) @ zero_zero_nat ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_nonpos
% 0.26/0.62  thf(fact_7915_sum__le__suminf,axiom,
% 0.26/0.62      ! [F: nat > int,I5: set_nat] :
% 0.26/0.62        ( ( summable_int @ F )
% 0.26/0.62       => ( ( finite_finite_nat @ I5 )
% 0.26/0.62         => ( ! [N2: nat] :
% 0.26/0.62                ( ( member_nat @ N2 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 0.26/0.62               => ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) ) )
% 0.26/0.62           => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ I5 ) @ ( suminf_int @ F ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_le_suminf
% 0.26/0.62  thf(fact_7916_sum__le__suminf,axiom,
% 0.26/0.62      ! [F: nat > nat,I5: set_nat] :
% 0.26/0.62        ( ( summable_nat @ F )
% 0.26/0.62       => ( ( finite_finite_nat @ I5 )
% 0.26/0.62         => ( ! [N2: nat] :
% 0.26/0.62                ( ( member_nat @ N2 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 0.26/0.62               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) ) )
% 0.26/0.62           => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ I5 ) @ ( suminf_nat @ F ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_le_suminf
% 0.26/0.62  thf(fact_7917_sum__le__suminf,axiom,
% 0.26/0.62      ! [F: nat > real,I5: set_nat] :
% 0.26/0.62        ( ( summable_real @ F )
% 0.26/0.62       => ( ( finite_finite_nat @ I5 )
% 0.26/0.62         => ( ! [N2: nat] :
% 0.26/0.62                ( ( member_nat @ N2 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 0.26/0.62               => ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) ) )
% 0.26/0.62           => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ I5 ) @ ( suminf_real @ F ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_le_suminf
% 0.26/0.62  thf(fact_7918_sum__cong__Suc,axiom,
% 0.26/0.62      ! [A3: set_nat,F: nat > nat,G: nat > nat] :
% 0.26/0.62        ( ~ ( member_nat @ zero_zero_nat @ A3 )
% 0.26/0.62       => ( ! [X4: nat] :
% 0.26/0.62              ( ( member_nat @ ( suc @ X4 ) @ A3 )
% 0.26/0.62             => ( ( F @ ( suc @ X4 ) )
% 0.26/0.62                = ( G @ ( suc @ X4 ) ) ) )
% 0.26/0.62         => ( ( groups3542108847815614940at_nat @ F @ A3 )
% 0.26/0.62            = ( groups3542108847815614940at_nat @ G @ A3 ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_cong_Suc
% 0.26/0.62  thf(fact_7919_sum__cong__Suc,axiom,
% 0.26/0.62      ! [A3: set_nat,F: nat > real,G: nat > real] :
% 0.26/0.62        ( ~ ( member_nat @ zero_zero_nat @ A3 )
% 0.26/0.62       => ( ! [X4: nat] :
% 0.26/0.62              ( ( member_nat @ ( suc @ X4 ) @ A3 )
% 0.26/0.62             => ( ( F @ ( suc @ X4 ) )
% 0.26/0.62                = ( G @ ( suc @ X4 ) ) ) )
% 0.26/0.62         => ( ( groups6591440286371151544t_real @ F @ A3 )
% 0.26/0.62            = ( groups6591440286371151544t_real @ G @ A3 ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % sum_cong_Suc
% 0.26/0.62  thf(fact_7920_Complex__eq__1,axiom,
% 0.26/0.62      ! [A: real,B: real] :
% 0.26/0.62        ( ( ( complex2 @ A @ B )
% 0.26/0.62          = one_one_complex )
% 0.26/0.62        = ( ( A = one_one_real )
% 0.26/0.62          & ( B = zero_zero_real ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % Complex_eq_1
% 0.26/0.62  thf(fact_7921_one__complex_Ocode,axiom,
% 0.26/0.62      ( one_one_complex
% 0.26/0.62      = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 0.26/0.62  
% 0.26/0.62  % one_complex.code
% 0.26/0.62  thf(fact_7922_Complex__eq__numeral,axiom,
% 0.26/0.62      ! [A: real,B: real,W: num] :
% 0.26/0.62        ( ( ( complex2 @ A @ B )
% 0.26/0.62          = ( numera6690914467698888265omplex @ W ) )
% 0.26/0.62        = ( ( A
% 0.26/0.62            = ( numeral_numeral_real @ W ) )
% 0.26/0.62          & ( B = zero_zero_real ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % Complex_eq_numeral
% 0.26/0.62  thf(fact_7923_infinite__growing,axiom,
% 0.26/0.62      ! [X9: set_Extended_enat] :
% 0.26/0.62        ( ( X9 != bot_bo7653980558646680370d_enat )
% 0.26/0.62       => ( ! [X4: extended_enat] :
% 0.26/0.62              ( ( member_Extended_enat @ X4 @ X9 )
% 0.26/0.62             => ? [Xa2: extended_enat] :
% 0.26/0.62                  ( ( member_Extended_enat @ Xa2 @ X9 )
% 0.26/0.62                  & ( ord_le72135733267957522d_enat @ X4 @ Xa2 ) ) )
% 0.26/0.62         => ~ ( finite4001608067531595151d_enat @ X9 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % infinite_growing
% 0.26/0.62  thf(fact_7924_infinite__growing,axiom,
% 0.26/0.62      ! [X9: set_real] :
% 0.26/0.62        ( ( X9 != bot_bot_set_real )
% 0.26/0.62       => ( ! [X4: real] :
% 0.26/0.62              ( ( member_real @ X4 @ X9 )
% 0.26/0.62             => ? [Xa2: real] :
% 0.26/0.62                  ( ( member_real @ Xa2 @ X9 )
% 0.26/0.62                  & ( ord_less_real @ X4 @ Xa2 ) ) )
% 0.26/0.62         => ~ ( finite_finite_real @ X9 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % infinite_growing
% 0.26/0.62  thf(fact_7925_infinite__growing,axiom,
% 0.26/0.62      ! [X9: set_rat] :
% 0.26/0.62        ( ( X9 != bot_bot_set_rat )
% 0.26/0.62       => ( ! [X4: rat] :
% 0.26/0.62              ( ( member_rat @ X4 @ X9 )
% 0.26/0.62             => ? [Xa2: rat] :
% 0.26/0.62                  ( ( member_rat @ Xa2 @ X9 )
% 0.26/0.62                  & ( ord_less_rat @ X4 @ Xa2 ) ) )
% 0.26/0.62         => ~ ( finite_finite_rat @ X9 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % infinite_growing
% 0.26/0.62  thf(fact_7926_infinite__growing,axiom,
% 0.26/0.62      ! [X9: set_num] :
% 0.26/0.62        ( ( X9 != bot_bot_set_num )
% 0.26/0.62       => ( ! [X4: num] :
% 0.26/0.62              ( ( member_num @ X4 @ X9 )
% 0.26/0.62             => ? [Xa2: num] :
% 0.26/0.62                  ( ( member_num @ Xa2 @ X9 )
% 0.26/0.62                  & ( ord_less_num @ X4 @ Xa2 ) ) )
% 0.26/0.62         => ~ ( finite_finite_num @ X9 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % infinite_growing
% 0.26/0.62  thf(fact_7927_infinite__growing,axiom,
% 0.26/0.62      ! [X9: set_nat] :
% 0.26/0.62        ( ( X9 != bot_bot_set_nat )
% 0.26/0.62       => ( ! [X4: nat] :
% 0.26/0.62              ( ( member_nat @ X4 @ X9 )
% 0.26/0.62             => ? [Xa2: nat] :
% 0.26/0.62                  ( ( member_nat @ Xa2 @ X9 )
% 0.26/0.62                  & ( ord_less_nat @ X4 @ Xa2 ) ) )
% 0.26/0.62         => ~ ( finite_finite_nat @ X9 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % infinite_growing
% 0.26/0.62  thf(fact_7928_infinite__growing,axiom,
% 0.26/0.62      ! [X9: set_int] :
% 0.26/0.62        ( ( X9 != bot_bot_set_int )
% 0.26/0.62       => ( ! [X4: int] :
% 0.26/0.62              ( ( member_int @ X4 @ X9 )
% 0.26/0.62             => ? [Xa2: int] :
% 0.26/0.62                  ( ( member_int @ Xa2 @ X9 )
% 0.26/0.62                  & ( ord_less_int @ X4 @ Xa2 ) ) )
% 0.26/0.62         => ~ ( finite_finite_int @ X9 ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % infinite_growing
% 0.26/0.62  thf(fact_7929_ex__min__if__finite,axiom,
% 0.26/0.62      ! [S2: set_Extended_enat] :
% 0.26/0.62        ( ( finite4001608067531595151d_enat @ S2 )
% 0.26/0.62       => ( ( S2 != bot_bo7653980558646680370d_enat )
% 0.26/0.62         => ? [X4: extended_enat] :
% 0.26/0.62              ( ( member_Extended_enat @ X4 @ S2 )
% 0.26/0.62              & ~ ? [Xa2: extended_enat] :
% 0.26/0.62                    ( ( member_Extended_enat @ Xa2 @ S2 )
% 0.26/0.62                    & ( ord_le72135733267957522d_enat @ Xa2 @ X4 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % ex_min_if_finite
% 0.26/0.62  thf(fact_7930_ex__min__if__finite,axiom,
% 0.26/0.62      ! [S2: set_real] :
% 0.26/0.62        ( ( finite_finite_real @ S2 )
% 0.26/0.62       => ( ( S2 != bot_bot_set_real )
% 0.26/0.62         => ? [X4: real] :
% 0.26/0.62              ( ( member_real @ X4 @ S2 )
% 0.26/0.62              & ~ ? [Xa2: real] :
% 0.26/0.62                    ( ( member_real @ Xa2 @ S2 )
% 0.26/0.62                    & ( ord_less_real @ Xa2 @ X4 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % ex_min_if_finite
% 0.26/0.62  thf(fact_7931_ex__min__if__finite,axiom,
% 0.26/0.62      ! [S2: set_rat] :
% 0.26/0.62        ( ( finite_finite_rat @ S2 )
% 0.26/0.62       => ( ( S2 != bot_bot_set_rat )
% 0.26/0.62         => ? [X4: rat] :
% 0.26/0.62              ( ( member_rat @ X4 @ S2 )
% 0.26/0.62              & ~ ? [Xa2: rat] :
% 0.26/0.62                    ( ( member_rat @ Xa2 @ S2 )
% 0.26/0.62                    & ( ord_less_rat @ Xa2 @ X4 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % ex_min_if_finite
% 0.26/0.62  thf(fact_7932_ex__min__if__finite,axiom,
% 0.26/0.62      ! [S2: set_num] :
% 0.26/0.62        ( ( finite_finite_num @ S2 )
% 0.26/0.62       => ( ( S2 != bot_bot_set_num )
% 0.26/0.62         => ? [X4: num] :
% 0.26/0.62              ( ( member_num @ X4 @ S2 )
% 0.26/0.62              & ~ ? [Xa2: num] :
% 0.26/0.62                    ( ( member_num @ Xa2 @ S2 )
% 0.26/0.62                    & ( ord_less_num @ Xa2 @ X4 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % ex_min_if_finite
% 0.26/0.62  thf(fact_7933_ex__min__if__finite,axiom,
% 0.26/0.62      ! [S2: set_nat] :
% 0.26/0.62        ( ( finite_finite_nat @ S2 )
% 0.26/0.62       => ( ( S2 != bot_bot_set_nat )
% 0.26/0.62         => ? [X4: nat] :
% 0.26/0.62              ( ( member_nat @ X4 @ S2 )
% 0.26/0.62              & ~ ? [Xa2: nat] :
% 0.26/0.62                    ( ( member_nat @ Xa2 @ S2 )
% 0.26/0.62                    & ( ord_less_nat @ Xa2 @ X4 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % ex_min_if_finite
% 0.26/0.62  thf(fact_7934_ex__min__if__finite,axiom,
% 0.26/0.62      ! [S2: set_int] :
% 0.26/0.62        ( ( finite_finite_int @ S2 )
% 0.26/0.62       => ( ( S2 != bot_bot_set_int )
% 0.26/0.62         => ? [X4: int] :
% 0.26/0.62              ( ( member_int @ X4 @ S2 )
% 0.26/0.62              & ~ ? [Xa2: int] :
% 0.26/0.62                    ( ( member_int @ Xa2 @ S2 )
% 0.26/0.62                    & ( ord_less_int @ Xa2 @ X4 ) ) ) ) ) ).
% 0.26/0.62  
% 0.26/0.62  % ex_min_if_finite
% 0.26/0.62  thf(fact_7935_prod__zero,axiom,
% 0.26/0.62      ! [A3: set_nat,F: nat > real] :
% 0.26/0.62        ( ( finite_finite_nat @ A3 )
% 0.26/0.62       => ( ? [X6: nat] :
% 0.26/0.62              ( ( member_nat @ X6 @ A3 )
% 0.26/0.63              & ( ( F @ X6 )
% 0.26/0.63                = zero_zero_real ) )
% 0.26/0.63         => ( ( groups129246275422532515t_real @ F @ A3 )
% 0.26/0.63            = zero_zero_real ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_zero
% 0.26/0.63  thf(fact_7936_prod__zero,axiom,
% 0.26/0.63      ! [A3: set_int,F: int > real] :
% 0.26/0.63        ( ( finite_finite_int @ A3 )
% 0.26/0.63       => ( ? [X6: int] :
% 0.26/0.63              ( ( member_int @ X6 @ A3 )
% 0.26/0.63              & ( ( F @ X6 )
% 0.26/0.63                = zero_zero_real ) )
% 0.26/0.63         => ( ( groups2316167850115554303t_real @ F @ A3 )
% 0.26/0.63            = zero_zero_real ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_zero
% 0.26/0.63  thf(fact_7937_prod__zero,axiom,
% 0.26/0.63      ! [A3: set_complex,F: complex > real] :
% 0.26/0.63        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.63       => ( ? [X6: complex] :
% 0.26/0.63              ( ( member_complex @ X6 @ A3 )
% 0.26/0.63              & ( ( F @ X6 )
% 0.26/0.63                = zero_zero_real ) )
% 0.26/0.63         => ( ( groups766887009212190081x_real @ F @ A3 )
% 0.26/0.63            = zero_zero_real ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_zero
% 0.26/0.63  thf(fact_7938_prod__zero,axiom,
% 0.26/0.63      ! [A3: set_Extended_enat,F: extended_enat > real] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.63       => ( ? [X6: extended_enat] :
% 0.26/0.63              ( ( member_Extended_enat @ X6 @ A3 )
% 0.26/0.63              & ( ( F @ X6 )
% 0.26/0.63                = zero_zero_real ) )
% 0.26/0.63         => ( ( groups97031904164794029t_real @ F @ A3 )
% 0.26/0.63            = zero_zero_real ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_zero
% 0.26/0.63  thf(fact_7939_prod__zero,axiom,
% 0.26/0.63      ! [A3: set_nat,F: nat > rat] :
% 0.26/0.63        ( ( finite_finite_nat @ A3 )
% 0.26/0.63       => ( ? [X6: nat] :
% 0.26/0.63              ( ( member_nat @ X6 @ A3 )
% 0.26/0.63              & ( ( F @ X6 )
% 0.26/0.63                = zero_zero_rat ) )
% 0.26/0.63         => ( ( groups73079841787564623at_rat @ F @ A3 )
% 0.26/0.63            = zero_zero_rat ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_zero
% 0.26/0.63  thf(fact_7940_prod__zero,axiom,
% 0.26/0.63      ! [A3: set_int,F: int > rat] :
% 0.26/0.63        ( ( finite_finite_int @ A3 )
% 0.26/0.63       => ( ? [X6: int] :
% 0.26/0.63              ( ( member_int @ X6 @ A3 )
% 0.26/0.63              & ( ( F @ X6 )
% 0.26/0.63                = zero_zero_rat ) )
% 0.26/0.63         => ( ( groups1072433553688619179nt_rat @ F @ A3 )
% 0.26/0.63            = zero_zero_rat ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_zero
% 0.26/0.63  thf(fact_7941_prod__zero,axiom,
% 0.26/0.63      ! [A3: set_complex,F: complex > rat] :
% 0.26/0.63        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.63       => ( ? [X6: complex] :
% 0.26/0.63              ( ( member_complex @ X6 @ A3 )
% 0.26/0.63              & ( ( F @ X6 )
% 0.26/0.63                = zero_zero_rat ) )
% 0.26/0.63         => ( ( groups225925009352817453ex_rat @ F @ A3 )
% 0.26/0.63            = zero_zero_rat ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_zero
% 0.26/0.63  thf(fact_7942_prod__zero,axiom,
% 0.26/0.63      ! [A3: set_Extended_enat,F: extended_enat > rat] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.63       => ( ? [X6: extended_enat] :
% 0.26/0.63              ( ( member_Extended_enat @ X6 @ A3 )
% 0.26/0.63              & ( ( F @ X6 )
% 0.26/0.63                = zero_zero_rat ) )
% 0.26/0.63         => ( ( groups2245840878043517529at_rat @ F @ A3 )
% 0.26/0.63            = zero_zero_rat ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_zero
% 0.26/0.63  thf(fact_7943_prod__zero,axiom,
% 0.26/0.63      ! [A3: set_int,F: int > nat] :
% 0.26/0.63        ( ( finite_finite_int @ A3 )
% 0.26/0.63       => ( ? [X6: int] :
% 0.26/0.63              ( ( member_int @ X6 @ A3 )
% 0.26/0.63              & ( ( F @ X6 )
% 0.26/0.63                = zero_zero_nat ) )
% 0.26/0.63         => ( ( groups1707563613775114915nt_nat @ F @ A3 )
% 0.26/0.63            = zero_zero_nat ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_zero
% 0.26/0.63  thf(fact_7944_prod__zero,axiom,
% 0.26/0.63      ! [A3: set_complex,F: complex > nat] :
% 0.26/0.63        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.63       => ( ? [X6: complex] :
% 0.26/0.63              ( ( member_complex @ X6 @ A3 )
% 0.26/0.63              & ( ( F @ X6 )
% 0.26/0.63                = zero_zero_nat ) )
% 0.26/0.63         => ( ( groups861055069439313189ex_nat @ F @ A3 )
% 0.26/0.63            = zero_zero_nat ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_zero
% 0.26/0.63  thf(fact_7945_infinite__Icc,axiom,
% 0.26/0.63      ! [A: rat,B: rat] :
% 0.26/0.63        ( ( ord_less_rat @ A @ B )
% 0.26/0.63       => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % infinite_Icc
% 0.26/0.63  thf(fact_7946_infinite__Icc,axiom,
% 0.26/0.63      ! [A: real,B: real] :
% 0.26/0.63        ( ( ord_less_real @ A @ B )
% 0.26/0.63       => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % infinite_Icc
% 0.26/0.63  thf(fact_7947_finite__lists__length__le,axiom,
% 0.26/0.63      ! [A3: set_complex,N: nat] :
% 0.26/0.63        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.63       => ( finite8712137658972009173omplex
% 0.26/0.63          @ ( collect_list_complex
% 0.26/0.63            @ ^ [Xs: list_complex] :
% 0.26/0.63                ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A3 )
% 0.26/0.63                & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs ) @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_lists_length_le
% 0.26/0.63  thf(fact_7948_finite__lists__length__le,axiom,
% 0.26/0.63      ! [A3: set_Pr1261947904930325089at_nat,N: nat] :
% 0.26/0.63        ( ( finite6177210948735845034at_nat @ A3 )
% 0.26/0.63       => ( finite500796754983035824at_nat
% 0.26/0.63          @ ( collec3343600615725829874at_nat
% 0.26/0.63            @ ^ [Xs: list_P6011104703257516679at_nat] :
% 0.26/0.63                ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs ) @ A3 )
% 0.26/0.63                & ( ord_less_eq_nat @ ( size_s5460976970255530739at_nat @ Xs ) @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_lists_length_le
% 0.26/0.63  thf(fact_7949_finite__lists__length__le,axiom,
% 0.26/0.63      ! [A3: set_Extended_enat,N: nat] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.63       => ( finite1862508098717546133d_enat
% 0.26/0.63          @ ( collec8433460942617342167d_enat
% 0.26/0.63            @ ^ [Xs: list_Extended_enat] :
% 0.26/0.63                ( ( ord_le7203529160286727270d_enat @ ( set_Extended_enat2 @ Xs ) @ A3 )
% 0.26/0.63                & ( ord_less_eq_nat @ ( size_s3941691890525107288d_enat @ Xs ) @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_lists_length_le
% 0.26/0.63  thf(fact_7950_finite__lists__length__le,axiom,
% 0.26/0.63      ! [A3: set_VEBT_VEBT,N: nat] :
% 0.26/0.63        ( ( finite5795047828879050333T_VEBT @ A3 )
% 0.26/0.63       => ( finite3004134309566078307T_VEBT
% 0.26/0.63          @ ( collec5608196760682091941T_VEBT
% 0.26/0.63            @ ^ [Xs: list_VEBT_VEBT] :
% 0.26/0.63                ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A3 )
% 0.26/0.63                & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_lists_length_le
% 0.26/0.63  thf(fact_7951_finite__lists__length__le,axiom,
% 0.26/0.63      ! [A3: set_o,N: nat] :
% 0.26/0.63        ( ( finite_finite_o @ A3 )
% 0.26/0.63       => ( finite_finite_list_o
% 0.26/0.63          @ ( collect_list_o
% 0.26/0.63            @ ^ [Xs: list_o] :
% 0.26/0.63                ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A3 )
% 0.26/0.63                & ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_lists_length_le
% 0.26/0.63  thf(fact_7952_finite__lists__length__le,axiom,
% 0.26/0.63      ! [A3: set_int,N: nat] :
% 0.26/0.63        ( ( finite_finite_int @ A3 )
% 0.26/0.63       => ( finite3922522038869484883st_int
% 0.26/0.63          @ ( collect_list_int
% 0.26/0.63            @ ^ [Xs: list_int] :
% 0.26/0.63                ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A3 )
% 0.26/0.63                & ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_lists_length_le
% 0.26/0.63  thf(fact_7953_finite__lists__length__le,axiom,
% 0.26/0.63      ! [A3: set_nat,N: nat] :
% 0.26/0.63        ( ( finite_finite_nat @ A3 )
% 0.26/0.63       => ( finite8100373058378681591st_nat
% 0.26/0.63          @ ( collect_list_nat
% 0.26/0.63            @ ^ [Xs: list_nat] :
% 0.26/0.63                ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A3 )
% 0.26/0.63                & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_lists_length_le
% 0.26/0.63  thf(fact_7954_summable__finite,axiom,
% 0.26/0.63      ! [N4: set_nat,F: nat > real] :
% 0.26/0.63        ( ( finite_finite_nat @ N4 )
% 0.26/0.63       => ( ! [N2: nat] :
% 0.26/0.63              ( ~ ( member_nat @ N2 @ N4 )
% 0.26/0.63             => ( ( F @ N2 )
% 0.26/0.63                = zero_zero_real ) )
% 0.26/0.63         => ( summable_real @ F ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % summable_finite
% 0.26/0.63  thf(fact_7955_summable__finite,axiom,
% 0.26/0.63      ! [N4: set_nat,F: nat > nat] :
% 0.26/0.63        ( ( finite_finite_nat @ N4 )
% 0.26/0.63       => ( ! [N2: nat] :
% 0.26/0.63              ( ~ ( member_nat @ N2 @ N4 )
% 0.26/0.63             => ( ( F @ N2 )
% 0.26/0.63                = zero_zero_nat ) )
% 0.26/0.63         => ( summable_nat @ F ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % summable_finite
% 0.26/0.63  thf(fact_7956_summable__finite,axiom,
% 0.26/0.63      ! [N4: set_nat,F: nat > int] :
% 0.26/0.63        ( ( finite_finite_nat @ N4 )
% 0.26/0.63       => ( ! [N2: nat] :
% 0.26/0.63              ( ~ ( member_nat @ N2 @ N4 )
% 0.26/0.63             => ( ( F @ N2 )
% 0.26/0.63                = zero_zero_int ) )
% 0.26/0.63         => ( summable_int @ F ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % summable_finite
% 0.26/0.63  thf(fact_7957_sum__strict__mono2,axiom,
% 0.26/0.63      ! [B5: set_real,A3: set_real,B: real,F: real > real] :
% 0.26/0.63        ( ( finite_finite_real @ B5 )
% 0.26/0.63       => ( ( ord_less_eq_set_real @ A3 @ B5 )
% 0.26/0.63         => ( ( member_real @ B @ ( minus_minus_set_real @ B5 @ A3 ) )
% 0.26/0.63           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 0.26/0.63             => ( ! [X4: real] :
% 0.26/0.63                    ( ( member_real @ X4 @ B5 )
% 0.26/0.63                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.26/0.63               => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A3 ) @ ( groups8097168146408367636l_real @ F @ B5 ) ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_strict_mono2
% 0.26/0.63  thf(fact_7958_sum__strict__mono2,axiom,
% 0.26/0.63      ! [B5: set_int,A3: set_int,B: int,F: int > real] :
% 0.26/0.63        ( ( finite_finite_int @ B5 )
% 0.26/0.63       => ( ( ord_less_eq_set_int @ A3 @ B5 )
% 0.26/0.63         => ( ( member_int @ B @ ( minus_minus_set_int @ B5 @ A3 ) )
% 0.26/0.63           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 0.26/0.63             => ( ! [X4: int] :
% 0.26/0.63                    ( ( member_int @ X4 @ B5 )
% 0.26/0.63                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.26/0.63               => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A3 ) @ ( groups8778361861064173332t_real @ F @ B5 ) ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_strict_mono2
% 0.26/0.63  thf(fact_7959_sum__strict__mono2,axiom,
% 0.26/0.63      ! [B5: set_complex,A3: set_complex,B: complex,F: complex > real] :
% 0.26/0.63        ( ( finite3207457112153483333omplex @ B5 )
% 0.26/0.63       => ( ( ord_le211207098394363844omplex @ A3 @ B5 )
% 0.26/0.63         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B5 @ A3 ) )
% 0.26/0.63           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 0.26/0.63             => ( ! [X4: complex] :
% 0.26/0.63                    ( ( member_complex @ X4 @ B5 )
% 0.26/0.63                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.26/0.63               => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A3 ) @ ( groups5808333547571424918x_real @ F @ B5 ) ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_strict_mono2
% 0.26/0.63  thf(fact_7960_sum__strict__mono2,axiom,
% 0.26/0.63      ! [B5: set_Extended_enat,A3: set_Extended_enat,B: extended_enat,F: extended_enat > real] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat @ B5 )
% 0.26/0.63       => ( ( ord_le7203529160286727270d_enat @ A3 @ B5 )
% 0.26/0.63         => ( ( member_Extended_enat @ B @ ( minus_925952699566721837d_enat @ B5 @ A3 ) )
% 0.26/0.63           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 0.26/0.63             => ( ! [X4: extended_enat] :
% 0.26/0.63                    ( ( member_Extended_enat @ X4 @ B5 )
% 0.26/0.63                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.26/0.63               => ( ord_less_real @ ( groups4148127829035722712t_real @ F @ A3 ) @ ( groups4148127829035722712t_real @ F @ B5 ) ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_strict_mono2
% 0.26/0.63  thf(fact_7961_sum__strict__mono2,axiom,
% 0.26/0.63      ! [B5: set_real,A3: set_real,B: real,F: real > rat] :
% 0.26/0.63        ( ( finite_finite_real @ B5 )
% 0.26/0.63       => ( ( ord_less_eq_set_real @ A3 @ B5 )
% 0.26/0.63         => ( ( member_real @ B @ ( minus_minus_set_real @ B5 @ A3 ) )
% 0.26/0.63           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 0.26/0.63             => ( ! [X4: real] :
% 0.26/0.63                    ( ( member_real @ X4 @ B5 )
% 0.26/0.63                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.26/0.63               => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A3 ) @ ( groups1300246762558778688al_rat @ F @ B5 ) ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_strict_mono2
% 0.26/0.63  thf(fact_7962_sum__strict__mono2,axiom,
% 0.26/0.63      ! [B5: set_int,A3: set_int,B: int,F: int > rat] :
% 0.26/0.63        ( ( finite_finite_int @ B5 )
% 0.26/0.63       => ( ( ord_less_eq_set_int @ A3 @ B5 )
% 0.26/0.63         => ( ( member_int @ B @ ( minus_minus_set_int @ B5 @ A3 ) )
% 0.26/0.63           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 0.26/0.63             => ( ! [X4: int] :
% 0.26/0.63                    ( ( member_int @ X4 @ B5 )
% 0.26/0.63                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.26/0.63               => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ ( groups3906332499630173760nt_rat @ F @ B5 ) ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_strict_mono2
% 0.26/0.63  thf(fact_7963_sum__strict__mono2,axiom,
% 0.26/0.63      ! [B5: set_complex,A3: set_complex,B: complex,F: complex > rat] :
% 0.26/0.63        ( ( finite3207457112153483333omplex @ B5 )
% 0.26/0.63       => ( ( ord_le211207098394363844omplex @ A3 @ B5 )
% 0.26/0.63         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B5 @ A3 ) )
% 0.26/0.63           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 0.26/0.63             => ( ! [X4: complex] :
% 0.26/0.63                    ( ( member_complex @ X4 @ B5 )
% 0.26/0.63                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.26/0.63               => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A3 ) @ ( groups5058264527183730370ex_rat @ F @ B5 ) ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_strict_mono2
% 0.26/0.63  thf(fact_7964_sum__strict__mono2,axiom,
% 0.26/0.63      ! [B5: set_Extended_enat,A3: set_Extended_enat,B: extended_enat,F: extended_enat > rat] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat @ B5 )
% 0.26/0.63       => ( ( ord_le7203529160286727270d_enat @ A3 @ B5 )
% 0.26/0.63         => ( ( member_Extended_enat @ B @ ( minus_925952699566721837d_enat @ B5 @ A3 ) )
% 0.26/0.63           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 0.26/0.63             => ( ! [X4: extended_enat] :
% 0.26/0.63                    ( ( member_Extended_enat @ X4 @ B5 )
% 0.26/0.63                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.26/0.63               => ( ord_less_rat @ ( groups1392844769737527556at_rat @ F @ A3 ) @ ( groups1392844769737527556at_rat @ F @ B5 ) ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_strict_mono2
% 0.26/0.63  thf(fact_7965_sum__strict__mono2,axiom,
% 0.26/0.63      ! [B5: set_real,A3: set_real,B: real,F: real > nat] :
% 0.26/0.63        ( ( finite_finite_real @ B5 )
% 0.26/0.63       => ( ( ord_less_eq_set_real @ A3 @ B5 )
% 0.26/0.63         => ( ( member_real @ B @ ( minus_minus_set_real @ B5 @ A3 ) )
% 0.26/0.63           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 0.26/0.63             => ( ! [X4: real] :
% 0.26/0.63                    ( ( member_real @ X4 @ B5 )
% 0.26/0.63                   => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 0.26/0.63               => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A3 ) @ ( groups1935376822645274424al_nat @ F @ B5 ) ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_strict_mono2
% 0.26/0.63  thf(fact_7966_sum__strict__mono2,axiom,
% 0.26/0.63      ! [B5: set_int,A3: set_int,B: int,F: int > nat] :
% 0.26/0.63        ( ( finite_finite_int @ B5 )
% 0.26/0.63       => ( ( ord_less_eq_set_int @ A3 @ B5 )
% 0.26/0.63         => ( ( member_int @ B @ ( minus_minus_set_int @ B5 @ A3 ) )
% 0.26/0.63           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 0.26/0.63             => ( ! [X4: int] :
% 0.26/0.63                    ( ( member_int @ X4 @ B5 )
% 0.26/0.63                   => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 0.26/0.63               => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ ( groups4541462559716669496nt_nat @ F @ B5 ) ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_strict_mono2
% 0.26/0.63  thf(fact_7967_member__le__sum,axiom,
% 0.26/0.63      ! [I: complex,A3: set_complex,F: complex > real] :
% 0.26/0.63        ( ( member_complex @ I @ A3 )
% 0.26/0.63       => ( ! [X4: complex] :
% 0.26/0.63              ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 0.26/0.63             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.26/0.63         => ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.63           => ( ord_less_eq_real @ ( F @ I ) @ ( groups5808333547571424918x_real @ F @ A3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % member_le_sum
% 0.26/0.63  thf(fact_7968_member__le__sum,axiom,
% 0.26/0.63      ! [I: extended_enat,A3: set_Extended_enat,F: extended_enat > real] :
% 0.26/0.63        ( ( member_Extended_enat @ I @ A3 )
% 0.26/0.63       => ( ! [X4: extended_enat] :
% 0.26/0.63              ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ I @ bot_bo7653980558646680370d_enat ) ) )
% 0.26/0.63             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.26/0.63         => ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.63           => ( ord_less_eq_real @ ( F @ I ) @ ( groups4148127829035722712t_real @ F @ A3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % member_le_sum
% 0.26/0.63  thf(fact_7969_member__le__sum,axiom,
% 0.26/0.63      ! [I: real,A3: set_real,F: real > real] :
% 0.26/0.63        ( ( member_real @ I @ A3 )
% 0.26/0.63       => ( ! [X4: real] :
% 0.26/0.63              ( ( member_real @ X4 @ ( minus_minus_set_real @ A3 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 0.26/0.63             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.26/0.63         => ( ( finite_finite_real @ A3 )
% 0.26/0.63           => ( ord_less_eq_real @ ( F @ I ) @ ( groups8097168146408367636l_real @ F @ A3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % member_le_sum
% 0.26/0.63  thf(fact_7970_member__le__sum,axiom,
% 0.26/0.63      ! [I: int,A3: set_int,F: int > real] :
% 0.26/0.63        ( ( member_int @ I @ A3 )
% 0.26/0.63       => ( ! [X4: int] :
% 0.26/0.63              ( ( member_int @ X4 @ ( minus_minus_set_int @ A3 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 0.26/0.63             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.26/0.63         => ( ( finite_finite_int @ A3 )
% 0.26/0.63           => ( ord_less_eq_real @ ( F @ I ) @ ( groups8778361861064173332t_real @ F @ A3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % member_le_sum
% 0.26/0.63  thf(fact_7971_member__le__sum,axiom,
% 0.26/0.63      ! [I: complex,A3: set_complex,F: complex > rat] :
% 0.26/0.63        ( ( member_complex @ I @ A3 )
% 0.26/0.63       => ( ! [X4: complex] :
% 0.26/0.63              ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 0.26/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.26/0.63         => ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.63           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups5058264527183730370ex_rat @ F @ A3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % member_le_sum
% 0.26/0.63  thf(fact_7972_member__le__sum,axiom,
% 0.26/0.63      ! [I: extended_enat,A3: set_Extended_enat,F: extended_enat > rat] :
% 0.26/0.63        ( ( member_Extended_enat @ I @ A3 )
% 0.26/0.63       => ( ! [X4: extended_enat] :
% 0.26/0.63              ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ I @ bot_bo7653980558646680370d_enat ) ) )
% 0.26/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.26/0.63         => ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.63           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups1392844769737527556at_rat @ F @ A3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % member_le_sum
% 0.26/0.63  thf(fact_7973_member__le__sum,axiom,
% 0.26/0.63      ! [I: real,A3: set_real,F: real > rat] :
% 0.26/0.63        ( ( member_real @ I @ A3 )
% 0.26/0.63       => ( ! [X4: real] :
% 0.26/0.63              ( ( member_real @ X4 @ ( minus_minus_set_real @ A3 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 0.26/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.26/0.63         => ( ( finite_finite_real @ A3 )
% 0.26/0.63           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups1300246762558778688al_rat @ F @ A3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % member_le_sum
% 0.26/0.63  thf(fact_7974_member__le__sum,axiom,
% 0.26/0.63      ! [I: int,A3: set_int,F: int > rat] :
% 0.26/0.63        ( ( member_int @ I @ A3 )
% 0.26/0.63       => ( ! [X4: int] :
% 0.26/0.63              ( ( member_int @ X4 @ ( minus_minus_set_int @ A3 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 0.26/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.26/0.63         => ( ( finite_finite_int @ A3 )
% 0.26/0.63           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups3906332499630173760nt_rat @ F @ A3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % member_le_sum
% 0.26/0.63  thf(fact_7975_member__le__sum,axiom,
% 0.26/0.63      ! [I: nat,A3: set_nat,F: nat > rat] :
% 0.26/0.63        ( ( member_nat @ I @ A3 )
% 0.26/0.63       => ( ! [X4: nat] :
% 0.26/0.63              ( ( member_nat @ X4 @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 0.26/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.26/0.63         => ( ( finite_finite_nat @ A3 )
% 0.26/0.63           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups2906978787729119204at_rat @ F @ A3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % member_le_sum
% 0.26/0.63  thf(fact_7976_member__le__sum,axiom,
% 0.26/0.63      ! [I: complex,A3: set_complex,F: complex > nat] :
% 0.26/0.63        ( ( member_complex @ I @ A3 )
% 0.26/0.63       => ( ! [X4: complex] :
% 0.26/0.63              ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 0.26/0.63             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 0.26/0.63         => ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.63           => ( ord_less_eq_nat @ ( F @ I ) @ ( groups5693394587270226106ex_nat @ F @ A3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % member_le_sum
% 0.26/0.63  thf(fact_7977_sum_Ofinite__Collect__op,axiom,
% 0.26/0.63      ! [I5: set_real,X3: real > real,Y3: real > real] :
% 0.26/0.63        ( ( finite_finite_real
% 0.26/0.63          @ ( collect_real
% 0.26/0.63            @ ^ [I4: real] :
% 0.26/0.63                ( ( member_real @ I4 @ I5 )
% 0.26/0.63                & ( ( X3 @ I4 )
% 0.26/0.63                 != zero_zero_real ) ) ) )
% 0.26/0.63       => ( ( finite_finite_real
% 0.26/0.63            @ ( collect_real
% 0.26/0.63              @ ^ [I4: real] :
% 0.26/0.63                  ( ( member_real @ I4 @ I5 )
% 0.26/0.63                  & ( ( Y3 @ I4 )
% 0.26/0.63                   != zero_zero_real ) ) ) )
% 0.26/0.63         => ( finite_finite_real
% 0.26/0.63            @ ( collect_real
% 0.26/0.63              @ ^ [I4: real] :
% 0.26/0.63                  ( ( member_real @ I4 @ I5 )
% 0.26/0.63                  & ( ( plus_plus_real @ ( X3 @ I4 ) @ ( Y3 @ I4 ) )
% 0.26/0.63                   != zero_zero_real ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.finite_Collect_op
% 0.26/0.63  thf(fact_7978_sum_Ofinite__Collect__op,axiom,
% 0.26/0.63      ! [I5: set_nat,X3: nat > real,Y3: nat > real] :
% 0.26/0.63        ( ( finite_finite_nat
% 0.26/0.63          @ ( collect_nat
% 0.26/0.63            @ ^ [I4: nat] :
% 0.26/0.63                ( ( member_nat @ I4 @ I5 )
% 0.26/0.63                & ( ( X3 @ I4 )
% 0.26/0.63                 != zero_zero_real ) ) ) )
% 0.26/0.63       => ( ( finite_finite_nat
% 0.26/0.63            @ ( collect_nat
% 0.26/0.63              @ ^ [I4: nat] :
% 0.26/0.63                  ( ( member_nat @ I4 @ I5 )
% 0.26/0.63                  & ( ( Y3 @ I4 )
% 0.26/0.63                   != zero_zero_real ) ) ) )
% 0.26/0.63         => ( finite_finite_nat
% 0.26/0.63            @ ( collect_nat
% 0.26/0.63              @ ^ [I4: nat] :
% 0.26/0.63                  ( ( member_nat @ I4 @ I5 )
% 0.26/0.63                  & ( ( plus_plus_real @ ( X3 @ I4 ) @ ( Y3 @ I4 ) )
% 0.26/0.63                   != zero_zero_real ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.finite_Collect_op
% 0.26/0.63  thf(fact_7979_sum_Ofinite__Collect__op,axiom,
% 0.26/0.63      ! [I5: set_int,X3: int > real,Y3: int > real] :
% 0.26/0.63        ( ( finite_finite_int
% 0.26/0.63          @ ( collect_int
% 0.26/0.63            @ ^ [I4: int] :
% 0.26/0.63                ( ( member_int @ I4 @ I5 )
% 0.26/0.63                & ( ( X3 @ I4 )
% 0.26/0.63                 != zero_zero_real ) ) ) )
% 0.26/0.63       => ( ( finite_finite_int
% 0.26/0.63            @ ( collect_int
% 0.26/0.63              @ ^ [I4: int] :
% 0.26/0.63                  ( ( member_int @ I4 @ I5 )
% 0.26/0.63                  & ( ( Y3 @ I4 )
% 0.26/0.63                   != zero_zero_real ) ) ) )
% 0.26/0.63         => ( finite_finite_int
% 0.26/0.63            @ ( collect_int
% 0.26/0.63              @ ^ [I4: int] :
% 0.26/0.63                  ( ( member_int @ I4 @ I5 )
% 0.26/0.63                  & ( ( plus_plus_real @ ( X3 @ I4 ) @ ( Y3 @ I4 ) )
% 0.26/0.63                   != zero_zero_real ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.finite_Collect_op
% 0.26/0.63  thf(fact_7980_sum_Ofinite__Collect__op,axiom,
% 0.26/0.63      ! [I5: set_complex,X3: complex > real,Y3: complex > real] :
% 0.26/0.63        ( ( finite3207457112153483333omplex
% 0.26/0.63          @ ( collect_complex
% 0.26/0.63            @ ^ [I4: complex] :
% 0.26/0.63                ( ( member_complex @ I4 @ I5 )
% 0.26/0.63                & ( ( X3 @ I4 )
% 0.26/0.63                 != zero_zero_real ) ) ) )
% 0.26/0.63       => ( ( finite3207457112153483333omplex
% 0.26/0.63            @ ( collect_complex
% 0.26/0.63              @ ^ [I4: complex] :
% 0.26/0.63                  ( ( member_complex @ I4 @ I5 )
% 0.26/0.63                  & ( ( Y3 @ I4 )
% 0.26/0.63                   != zero_zero_real ) ) ) )
% 0.26/0.63         => ( finite3207457112153483333omplex
% 0.26/0.63            @ ( collect_complex
% 0.26/0.63              @ ^ [I4: complex] :
% 0.26/0.63                  ( ( member_complex @ I4 @ I5 )
% 0.26/0.63                  & ( ( plus_plus_real @ ( X3 @ I4 ) @ ( Y3 @ I4 ) )
% 0.26/0.63                   != zero_zero_real ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.finite_Collect_op
% 0.26/0.63  thf(fact_7981_sum_Ofinite__Collect__op,axiom,
% 0.26/0.63      ! [I5: set_Extended_enat,X3: extended_enat > real,Y3: extended_enat > real] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat
% 0.26/0.63          @ ( collec4429806609662206161d_enat
% 0.26/0.63            @ ^ [I4: extended_enat] :
% 0.26/0.63                ( ( member_Extended_enat @ I4 @ I5 )
% 0.26/0.63                & ( ( X3 @ I4 )
% 0.26/0.63                 != zero_zero_real ) ) ) )
% 0.26/0.63       => ( ( finite4001608067531595151d_enat
% 0.26/0.63            @ ( collec4429806609662206161d_enat
% 0.26/0.63              @ ^ [I4: extended_enat] :
% 0.26/0.63                  ( ( member_Extended_enat @ I4 @ I5 )
% 0.26/0.63                  & ( ( Y3 @ I4 )
% 0.26/0.63                   != zero_zero_real ) ) ) )
% 0.26/0.63         => ( finite4001608067531595151d_enat
% 0.26/0.63            @ ( collec4429806609662206161d_enat
% 0.26/0.63              @ ^ [I4: extended_enat] :
% 0.26/0.63                  ( ( member_Extended_enat @ I4 @ I5 )
% 0.26/0.63                  & ( ( plus_plus_real @ ( X3 @ I4 ) @ ( Y3 @ I4 ) )
% 0.26/0.63                   != zero_zero_real ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.finite_Collect_op
% 0.26/0.63  thf(fact_7982_sum_Ofinite__Collect__op,axiom,
% 0.26/0.63      ! [I5: set_real,X3: real > rat,Y3: real > rat] :
% 0.26/0.63        ( ( finite_finite_real
% 0.26/0.63          @ ( collect_real
% 0.26/0.63            @ ^ [I4: real] :
% 0.26/0.63                ( ( member_real @ I4 @ I5 )
% 0.26/0.63                & ( ( X3 @ I4 )
% 0.26/0.63                 != zero_zero_rat ) ) ) )
% 0.26/0.63       => ( ( finite_finite_real
% 0.26/0.63            @ ( collect_real
% 0.26/0.63              @ ^ [I4: real] :
% 0.26/0.63                  ( ( member_real @ I4 @ I5 )
% 0.26/0.63                  & ( ( Y3 @ I4 )
% 0.26/0.63                   != zero_zero_rat ) ) ) )
% 0.26/0.63         => ( finite_finite_real
% 0.26/0.63            @ ( collect_real
% 0.26/0.63              @ ^ [I4: real] :
% 0.26/0.63                  ( ( member_real @ I4 @ I5 )
% 0.26/0.63                  & ( ( plus_plus_rat @ ( X3 @ I4 ) @ ( Y3 @ I4 ) )
% 0.26/0.63                   != zero_zero_rat ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.finite_Collect_op
% 0.26/0.63  thf(fact_7983_sum_Ofinite__Collect__op,axiom,
% 0.26/0.63      ! [I5: set_nat,X3: nat > rat,Y3: nat > rat] :
% 0.26/0.63        ( ( finite_finite_nat
% 0.26/0.63          @ ( collect_nat
% 0.26/0.63            @ ^ [I4: nat] :
% 0.26/0.63                ( ( member_nat @ I4 @ I5 )
% 0.26/0.63                & ( ( X3 @ I4 )
% 0.26/0.63                 != zero_zero_rat ) ) ) )
% 0.26/0.63       => ( ( finite_finite_nat
% 0.26/0.63            @ ( collect_nat
% 0.26/0.63              @ ^ [I4: nat] :
% 0.26/0.63                  ( ( member_nat @ I4 @ I5 )
% 0.26/0.63                  & ( ( Y3 @ I4 )
% 0.26/0.63                   != zero_zero_rat ) ) ) )
% 0.26/0.63         => ( finite_finite_nat
% 0.26/0.63            @ ( collect_nat
% 0.26/0.63              @ ^ [I4: nat] :
% 0.26/0.63                  ( ( member_nat @ I4 @ I5 )
% 0.26/0.63                  & ( ( plus_plus_rat @ ( X3 @ I4 ) @ ( Y3 @ I4 ) )
% 0.26/0.63                   != zero_zero_rat ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.finite_Collect_op
% 0.26/0.63  thf(fact_7984_sum_Ofinite__Collect__op,axiom,
% 0.26/0.63      ! [I5: set_int,X3: int > rat,Y3: int > rat] :
% 0.26/0.63        ( ( finite_finite_int
% 0.26/0.63          @ ( collect_int
% 0.26/0.63            @ ^ [I4: int] :
% 0.26/0.63                ( ( member_int @ I4 @ I5 )
% 0.26/0.63                & ( ( X3 @ I4 )
% 0.26/0.63                 != zero_zero_rat ) ) ) )
% 0.26/0.63       => ( ( finite_finite_int
% 0.26/0.63            @ ( collect_int
% 0.26/0.63              @ ^ [I4: int] :
% 0.26/0.63                  ( ( member_int @ I4 @ I5 )
% 0.26/0.63                  & ( ( Y3 @ I4 )
% 0.26/0.63                   != zero_zero_rat ) ) ) )
% 0.26/0.63         => ( finite_finite_int
% 0.26/0.63            @ ( collect_int
% 0.26/0.63              @ ^ [I4: int] :
% 0.26/0.63                  ( ( member_int @ I4 @ I5 )
% 0.26/0.63                  & ( ( plus_plus_rat @ ( X3 @ I4 ) @ ( Y3 @ I4 ) )
% 0.26/0.63                   != zero_zero_rat ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.finite_Collect_op
% 0.26/0.63  thf(fact_7985_sum_Ofinite__Collect__op,axiom,
% 0.26/0.63      ! [I5: set_complex,X3: complex > rat,Y3: complex > rat] :
% 0.26/0.63        ( ( finite3207457112153483333omplex
% 0.26/0.63          @ ( collect_complex
% 0.26/0.63            @ ^ [I4: complex] :
% 0.26/0.63                ( ( member_complex @ I4 @ I5 )
% 0.26/0.63                & ( ( X3 @ I4 )
% 0.26/0.63                 != zero_zero_rat ) ) ) )
% 0.26/0.63       => ( ( finite3207457112153483333omplex
% 0.26/0.63            @ ( collect_complex
% 0.26/0.63              @ ^ [I4: complex] :
% 0.26/0.63                  ( ( member_complex @ I4 @ I5 )
% 0.26/0.63                  & ( ( Y3 @ I4 )
% 0.26/0.63                   != zero_zero_rat ) ) ) )
% 0.26/0.63         => ( finite3207457112153483333omplex
% 0.26/0.63            @ ( collect_complex
% 0.26/0.63              @ ^ [I4: complex] :
% 0.26/0.63                  ( ( member_complex @ I4 @ I5 )
% 0.26/0.63                  & ( ( plus_plus_rat @ ( X3 @ I4 ) @ ( Y3 @ I4 ) )
% 0.26/0.63                   != zero_zero_rat ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.finite_Collect_op
% 0.26/0.63  thf(fact_7986_sum_Ofinite__Collect__op,axiom,
% 0.26/0.63      ! [I5: set_Extended_enat,X3: extended_enat > rat,Y3: extended_enat > rat] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat
% 0.26/0.63          @ ( collec4429806609662206161d_enat
% 0.26/0.63            @ ^ [I4: extended_enat] :
% 0.26/0.63                ( ( member_Extended_enat @ I4 @ I5 )
% 0.26/0.63                & ( ( X3 @ I4 )
% 0.26/0.63                 != zero_zero_rat ) ) ) )
% 0.26/0.63       => ( ( finite4001608067531595151d_enat
% 0.26/0.63            @ ( collec4429806609662206161d_enat
% 0.26/0.63              @ ^ [I4: extended_enat] :
% 0.26/0.63                  ( ( member_Extended_enat @ I4 @ I5 )
% 0.26/0.63                  & ( ( Y3 @ I4 )
% 0.26/0.63                   != zero_zero_rat ) ) ) )
% 0.26/0.63         => ( finite4001608067531595151d_enat
% 0.26/0.63            @ ( collec4429806609662206161d_enat
% 0.26/0.63              @ ^ [I4: extended_enat] :
% 0.26/0.63                  ( ( member_Extended_enat @ I4 @ I5 )
% 0.26/0.63                  & ( ( plus_plus_rat @ ( X3 @ I4 ) @ ( Y3 @ I4 ) )
% 0.26/0.63                   != zero_zero_rat ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.finite_Collect_op
% 0.26/0.63  thf(fact_7987_Complex__eq__neg__1,axiom,
% 0.26/0.63      ! [A: real,B: real] :
% 0.26/0.63        ( ( ( complex2 @ A @ B )
% 0.26/0.63          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.26/0.63        = ( ( A
% 0.26/0.63            = ( uminus_uminus_real @ one_one_real ) )
% 0.26/0.63          & ( B = zero_zero_real ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % Complex_eq_neg_1
% 0.26/0.63  thf(fact_7988_Complex__eq__neg__numeral,axiom,
% 0.26/0.63      ! [A: real,B: real,W: num] :
% 0.26/0.63        ( ( ( complex2 @ A @ B )
% 0.26/0.63          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.26/0.63        = ( ( A
% 0.26/0.63            = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.26/0.63          & ( B = zero_zero_real ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % Complex_eq_neg_numeral
% 0.26/0.63  thf(fact_7989_finite__ranking__induct,axiom,
% 0.26/0.63      ! [S2: set_complex,P: set_complex > $o,F: complex > rat] :
% 0.26/0.63        ( ( finite3207457112153483333omplex @ S2 )
% 0.26/0.63       => ( ( P @ bot_bot_set_complex )
% 0.26/0.63         => ( ! [X4: complex,S5: set_complex] :
% 0.26/0.63                ( ( finite3207457112153483333omplex @ S5 )
% 0.26/0.63               => ( ! [Y6: complex] :
% 0.26/0.63                      ( ( member_complex @ Y6 @ S5 )
% 0.26/0.63                     => ( ord_less_eq_rat @ ( F @ Y6 ) @ ( F @ X4 ) ) )
% 0.26/0.63                 => ( ( P @ S5 )
% 0.26/0.63                   => ( P @ ( insert_complex @ X4 @ S5 ) ) ) ) )
% 0.26/0.63           => ( P @ S2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_ranking_induct
% 0.26/0.63  thf(fact_7990_finite__ranking__induct,axiom,
% 0.26/0.63      ! [S2: set_Extended_enat,P: set_Extended_enat > $o,F: extended_enat > rat] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat @ S2 )
% 0.26/0.63       => ( ( P @ bot_bo7653980558646680370d_enat )
% 0.26/0.63         => ( ! [X4: extended_enat,S5: set_Extended_enat] :
% 0.26/0.63                ( ( finite4001608067531595151d_enat @ S5 )
% 0.26/0.63               => ( ! [Y6: extended_enat] :
% 0.26/0.63                      ( ( member_Extended_enat @ Y6 @ S5 )
% 0.26/0.63                     => ( ord_less_eq_rat @ ( F @ Y6 ) @ ( F @ X4 ) ) )
% 0.26/0.63                 => ( ( P @ S5 )
% 0.26/0.63                   => ( P @ ( insert_Extended_enat @ X4 @ S5 ) ) ) ) )
% 0.26/0.63           => ( P @ S2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_ranking_induct
% 0.26/0.63  thf(fact_7991_finite__ranking__induct,axiom,
% 0.26/0.63      ! [S2: set_real,P: set_real > $o,F: real > rat] :
% 0.26/0.63        ( ( finite_finite_real @ S2 )
% 0.26/0.63       => ( ( P @ bot_bot_set_real )
% 0.26/0.63         => ( ! [X4: real,S5: set_real] :
% 0.26/0.63                ( ( finite_finite_real @ S5 )
% 0.26/0.63               => ( ! [Y6: real] :
% 0.26/0.63                      ( ( member_real @ Y6 @ S5 )
% 0.26/0.63                     => ( ord_less_eq_rat @ ( F @ Y6 ) @ ( F @ X4 ) ) )
% 0.26/0.63                 => ( ( P @ S5 )
% 0.26/0.63                   => ( P @ ( insert_real @ X4 @ S5 ) ) ) ) )
% 0.26/0.63           => ( P @ S2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_ranking_induct
% 0.26/0.63  thf(fact_7992_finite__ranking__induct,axiom,
% 0.26/0.63      ! [S2: set_nat,P: set_nat > $o,F: nat > rat] :
% 0.26/0.63        ( ( finite_finite_nat @ S2 )
% 0.26/0.63       => ( ( P @ bot_bot_set_nat )
% 0.26/0.63         => ( ! [X4: nat,S5: set_nat] :
% 0.26/0.63                ( ( finite_finite_nat @ S5 )
% 0.26/0.63               => ( ! [Y6: nat] :
% 0.26/0.63                      ( ( member_nat @ Y6 @ S5 )
% 0.26/0.63                     => ( ord_less_eq_rat @ ( F @ Y6 ) @ ( F @ X4 ) ) )
% 0.26/0.63                 => ( ( P @ S5 )
% 0.26/0.63                   => ( P @ ( insert_nat @ X4 @ S5 ) ) ) ) )
% 0.26/0.63           => ( P @ S2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_ranking_induct
% 0.26/0.63  thf(fact_7993_finite__ranking__induct,axiom,
% 0.26/0.63      ! [S2: set_int,P: set_int > $o,F: int > rat] :
% 0.26/0.63        ( ( finite_finite_int @ S2 )
% 0.26/0.63       => ( ( P @ bot_bot_set_int )
% 0.26/0.63         => ( ! [X4: int,S5: set_int] :
% 0.26/0.63                ( ( finite_finite_int @ S5 )
% 0.26/0.63               => ( ! [Y6: int] :
% 0.26/0.63                      ( ( member_int @ Y6 @ S5 )
% 0.26/0.63                     => ( ord_less_eq_rat @ ( F @ Y6 ) @ ( F @ X4 ) ) )
% 0.26/0.63                 => ( ( P @ S5 )
% 0.26/0.63                   => ( P @ ( insert_int @ X4 @ S5 ) ) ) ) )
% 0.26/0.63           => ( P @ S2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_ranking_induct
% 0.26/0.63  thf(fact_7994_finite__ranking__induct,axiom,
% 0.26/0.63      ! [S2: set_complex,P: set_complex > $o,F: complex > num] :
% 0.26/0.63        ( ( finite3207457112153483333omplex @ S2 )
% 0.26/0.63       => ( ( P @ bot_bot_set_complex )
% 0.26/0.63         => ( ! [X4: complex,S5: set_complex] :
% 0.26/0.63                ( ( finite3207457112153483333omplex @ S5 )
% 0.26/0.63               => ( ! [Y6: complex] :
% 0.26/0.63                      ( ( member_complex @ Y6 @ S5 )
% 0.26/0.63                     => ( ord_less_eq_num @ ( F @ Y6 ) @ ( F @ X4 ) ) )
% 0.26/0.63                 => ( ( P @ S5 )
% 0.26/0.63                   => ( P @ ( insert_complex @ X4 @ S5 ) ) ) ) )
% 0.26/0.63           => ( P @ S2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_ranking_induct
% 0.26/0.63  thf(fact_7995_finite__ranking__induct,axiom,
% 0.26/0.63      ! [S2: set_Extended_enat,P: set_Extended_enat > $o,F: extended_enat > num] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat @ S2 )
% 0.26/0.63       => ( ( P @ bot_bo7653980558646680370d_enat )
% 0.26/0.63         => ( ! [X4: extended_enat,S5: set_Extended_enat] :
% 0.26/0.63                ( ( finite4001608067531595151d_enat @ S5 )
% 0.26/0.63               => ( ! [Y6: extended_enat] :
% 0.26/0.63                      ( ( member_Extended_enat @ Y6 @ S5 )
% 0.26/0.63                     => ( ord_less_eq_num @ ( F @ Y6 ) @ ( F @ X4 ) ) )
% 0.26/0.63                 => ( ( P @ S5 )
% 0.26/0.63                   => ( P @ ( insert_Extended_enat @ X4 @ S5 ) ) ) ) )
% 0.26/0.63           => ( P @ S2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_ranking_induct
% 0.26/0.63  thf(fact_7996_finite__ranking__induct,axiom,
% 0.26/0.63      ! [S2: set_real,P: set_real > $o,F: real > num] :
% 0.26/0.63        ( ( finite_finite_real @ S2 )
% 0.26/0.63       => ( ( P @ bot_bot_set_real )
% 0.26/0.63         => ( ! [X4: real,S5: set_real] :
% 0.26/0.63                ( ( finite_finite_real @ S5 )
% 0.26/0.63               => ( ! [Y6: real] :
% 0.26/0.63                      ( ( member_real @ Y6 @ S5 )
% 0.26/0.63                     => ( ord_less_eq_num @ ( F @ Y6 ) @ ( F @ X4 ) ) )
% 0.26/0.63                 => ( ( P @ S5 )
% 0.26/0.63                   => ( P @ ( insert_real @ X4 @ S5 ) ) ) ) )
% 0.26/0.63           => ( P @ S2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_ranking_induct
% 0.26/0.63  thf(fact_7997_finite__ranking__induct,axiom,
% 0.26/0.63      ! [S2: set_nat,P: set_nat > $o,F: nat > num] :
% 0.26/0.63        ( ( finite_finite_nat @ S2 )
% 0.26/0.63       => ( ( P @ bot_bot_set_nat )
% 0.26/0.63         => ( ! [X4: nat,S5: set_nat] :
% 0.26/0.63                ( ( finite_finite_nat @ S5 )
% 0.26/0.63               => ( ! [Y6: nat] :
% 0.26/0.63                      ( ( member_nat @ Y6 @ S5 )
% 0.26/0.63                     => ( ord_less_eq_num @ ( F @ Y6 ) @ ( F @ X4 ) ) )
% 0.26/0.63                 => ( ( P @ S5 )
% 0.26/0.63                   => ( P @ ( insert_nat @ X4 @ S5 ) ) ) ) )
% 0.26/0.63           => ( P @ S2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_ranking_induct
% 0.26/0.63  thf(fact_7998_finite__ranking__induct,axiom,
% 0.26/0.63      ! [S2: set_int,P: set_int > $o,F: int > num] :
% 0.26/0.63        ( ( finite_finite_int @ S2 )
% 0.26/0.63       => ( ( P @ bot_bot_set_int )
% 0.26/0.63         => ( ! [X4: int,S5: set_int] :
% 0.26/0.63                ( ( finite_finite_int @ S5 )
% 0.26/0.63               => ( ! [Y6: int] :
% 0.26/0.63                      ( ( member_int @ Y6 @ S5 )
% 0.26/0.63                     => ( ord_less_eq_num @ ( F @ Y6 ) @ ( F @ X4 ) ) )
% 0.26/0.63                 => ( ( P @ S5 )
% 0.26/0.63                   => ( P @ ( insert_int @ X4 @ S5 ) ) ) ) )
% 0.26/0.63           => ( P @ S2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_ranking_induct
% 0.26/0.63  thf(fact_7999_finite__linorder__min__induct,axiom,
% 0.26/0.63      ! [A3: set_Extended_enat,P: set_Extended_enat > $o] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.63       => ( ( P @ bot_bo7653980558646680370d_enat )
% 0.26/0.63         => ( ! [B4: extended_enat,A6: set_Extended_enat] :
% 0.26/0.63                ( ( finite4001608067531595151d_enat @ A6 )
% 0.26/0.63               => ( ! [X6: extended_enat] :
% 0.26/0.63                      ( ( member_Extended_enat @ X6 @ A6 )
% 0.26/0.63                     => ( ord_le72135733267957522d_enat @ B4 @ X6 ) )
% 0.26/0.63                 => ( ( P @ A6 )
% 0.26/0.63                   => ( P @ ( insert_Extended_enat @ B4 @ A6 ) ) ) ) )
% 0.26/0.63           => ( P @ A3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_linorder_min_induct
% 0.26/0.63  thf(fact_8000_finite__linorder__min__induct,axiom,
% 0.26/0.63      ! [A3: set_real,P: set_real > $o] :
% 0.26/0.63        ( ( finite_finite_real @ A3 )
% 0.26/0.63       => ( ( P @ bot_bot_set_real )
% 0.26/0.63         => ( ! [B4: real,A6: set_real] :
% 0.26/0.63                ( ( finite_finite_real @ A6 )
% 0.26/0.63               => ( ! [X6: real] :
% 0.26/0.63                      ( ( member_real @ X6 @ A6 )
% 0.26/0.63                     => ( ord_less_real @ B4 @ X6 ) )
% 0.26/0.63                 => ( ( P @ A6 )
% 0.26/0.63                   => ( P @ ( insert_real @ B4 @ A6 ) ) ) ) )
% 0.26/0.63           => ( P @ A3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_linorder_min_induct
% 0.26/0.63  thf(fact_8001_finite__linorder__min__induct,axiom,
% 0.26/0.63      ! [A3: set_rat,P: set_rat > $o] :
% 0.26/0.63        ( ( finite_finite_rat @ A3 )
% 0.26/0.63       => ( ( P @ bot_bot_set_rat )
% 0.26/0.63         => ( ! [B4: rat,A6: set_rat] :
% 0.26/0.63                ( ( finite_finite_rat @ A6 )
% 0.26/0.63               => ( ! [X6: rat] :
% 0.26/0.63                      ( ( member_rat @ X6 @ A6 )
% 0.26/0.63                     => ( ord_less_rat @ B4 @ X6 ) )
% 0.26/0.63                 => ( ( P @ A6 )
% 0.26/0.63                   => ( P @ ( insert_rat @ B4 @ A6 ) ) ) ) )
% 0.26/0.63           => ( P @ A3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_linorder_min_induct
% 0.26/0.63  thf(fact_8002_finite__linorder__min__induct,axiom,
% 0.26/0.63      ! [A3: set_num,P: set_num > $o] :
% 0.26/0.63        ( ( finite_finite_num @ A3 )
% 0.26/0.63       => ( ( P @ bot_bot_set_num )
% 0.26/0.63         => ( ! [B4: num,A6: set_num] :
% 0.26/0.63                ( ( finite_finite_num @ A6 )
% 0.26/0.63               => ( ! [X6: num] :
% 0.26/0.63                      ( ( member_num @ X6 @ A6 )
% 0.26/0.63                     => ( ord_less_num @ B4 @ X6 ) )
% 0.26/0.63                 => ( ( P @ A6 )
% 0.26/0.63                   => ( P @ ( insert_num @ B4 @ A6 ) ) ) ) )
% 0.26/0.63           => ( P @ A3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_linorder_min_induct
% 0.26/0.63  thf(fact_8003_finite__linorder__min__induct,axiom,
% 0.26/0.63      ! [A3: set_nat,P: set_nat > $o] :
% 0.26/0.63        ( ( finite_finite_nat @ A3 )
% 0.26/0.63       => ( ( P @ bot_bot_set_nat )
% 0.26/0.63         => ( ! [B4: nat,A6: set_nat] :
% 0.26/0.63                ( ( finite_finite_nat @ A6 )
% 0.26/0.63               => ( ! [X6: nat] :
% 0.26/0.63                      ( ( member_nat @ X6 @ A6 )
% 0.26/0.63                     => ( ord_less_nat @ B4 @ X6 ) )
% 0.26/0.63                 => ( ( P @ A6 )
% 0.26/0.63                   => ( P @ ( insert_nat @ B4 @ A6 ) ) ) ) )
% 0.26/0.63           => ( P @ A3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_linorder_min_induct
% 0.26/0.63  thf(fact_8004_finite__linorder__min__induct,axiom,
% 0.26/0.63      ! [A3: set_int,P: set_int > $o] :
% 0.26/0.63        ( ( finite_finite_int @ A3 )
% 0.26/0.63       => ( ( P @ bot_bot_set_int )
% 0.26/0.63         => ( ! [B4: int,A6: set_int] :
% 0.26/0.63                ( ( finite_finite_int @ A6 )
% 0.26/0.63               => ( ! [X6: int] :
% 0.26/0.63                      ( ( member_int @ X6 @ A6 )
% 0.26/0.63                     => ( ord_less_int @ B4 @ X6 ) )
% 0.26/0.63                 => ( ( P @ A6 )
% 0.26/0.63                   => ( P @ ( insert_int @ B4 @ A6 ) ) ) ) )
% 0.26/0.63           => ( P @ A3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_linorder_min_induct
% 0.26/0.63  thf(fact_8005_finite__linorder__max__induct,axiom,
% 0.26/0.63      ! [A3: set_Extended_enat,P: set_Extended_enat > $o] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.63       => ( ( P @ bot_bo7653980558646680370d_enat )
% 0.26/0.63         => ( ! [B4: extended_enat,A6: set_Extended_enat] :
% 0.26/0.63                ( ( finite4001608067531595151d_enat @ A6 )
% 0.26/0.63               => ( ! [X6: extended_enat] :
% 0.26/0.63                      ( ( member_Extended_enat @ X6 @ A6 )
% 0.26/0.63                     => ( ord_le72135733267957522d_enat @ X6 @ B4 ) )
% 0.26/0.63                 => ( ( P @ A6 )
% 0.26/0.63                   => ( P @ ( insert_Extended_enat @ B4 @ A6 ) ) ) ) )
% 0.26/0.63           => ( P @ A3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_linorder_max_induct
% 0.26/0.63  thf(fact_8006_finite__linorder__max__induct,axiom,
% 0.26/0.63      ! [A3: set_real,P: set_real > $o] :
% 0.26/0.63        ( ( finite_finite_real @ A3 )
% 0.26/0.63       => ( ( P @ bot_bot_set_real )
% 0.26/0.63         => ( ! [B4: real,A6: set_real] :
% 0.26/0.63                ( ( finite_finite_real @ A6 )
% 0.26/0.63               => ( ! [X6: real] :
% 0.26/0.63                      ( ( member_real @ X6 @ A6 )
% 0.26/0.63                     => ( ord_less_real @ X6 @ B4 ) )
% 0.26/0.63                 => ( ( P @ A6 )
% 0.26/0.63                   => ( P @ ( insert_real @ B4 @ A6 ) ) ) ) )
% 0.26/0.63           => ( P @ A3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_linorder_max_induct
% 0.26/0.63  thf(fact_8007_finite__linorder__max__induct,axiom,
% 0.26/0.63      ! [A3: set_rat,P: set_rat > $o] :
% 0.26/0.63        ( ( finite_finite_rat @ A3 )
% 0.26/0.63       => ( ( P @ bot_bot_set_rat )
% 0.26/0.63         => ( ! [B4: rat,A6: set_rat] :
% 0.26/0.63                ( ( finite_finite_rat @ A6 )
% 0.26/0.63               => ( ! [X6: rat] :
% 0.26/0.63                      ( ( member_rat @ X6 @ A6 )
% 0.26/0.63                     => ( ord_less_rat @ X6 @ B4 ) )
% 0.26/0.63                 => ( ( P @ A6 )
% 0.26/0.63                   => ( P @ ( insert_rat @ B4 @ A6 ) ) ) ) )
% 0.26/0.63           => ( P @ A3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_linorder_max_induct
% 0.26/0.63  thf(fact_8008_finite__linorder__max__induct,axiom,
% 0.26/0.63      ! [A3: set_num,P: set_num > $o] :
% 0.26/0.63        ( ( finite_finite_num @ A3 )
% 0.26/0.63       => ( ( P @ bot_bot_set_num )
% 0.26/0.63         => ( ! [B4: num,A6: set_num] :
% 0.26/0.63                ( ( finite_finite_num @ A6 )
% 0.26/0.63               => ( ! [X6: num] :
% 0.26/0.63                      ( ( member_num @ X6 @ A6 )
% 0.26/0.63                     => ( ord_less_num @ X6 @ B4 ) )
% 0.26/0.63                 => ( ( P @ A6 )
% 0.26/0.63                   => ( P @ ( insert_num @ B4 @ A6 ) ) ) ) )
% 0.26/0.63           => ( P @ A3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_linorder_max_induct
% 0.26/0.63  thf(fact_8009_finite__linorder__max__induct,axiom,
% 0.26/0.63      ! [A3: set_nat,P: set_nat > $o] :
% 0.26/0.63        ( ( finite_finite_nat @ A3 )
% 0.26/0.63       => ( ( P @ bot_bot_set_nat )
% 0.26/0.63         => ( ! [B4: nat,A6: set_nat] :
% 0.26/0.63                ( ( finite_finite_nat @ A6 )
% 0.26/0.63               => ( ! [X6: nat] :
% 0.26/0.63                      ( ( member_nat @ X6 @ A6 )
% 0.26/0.63                     => ( ord_less_nat @ X6 @ B4 ) )
% 0.26/0.63                 => ( ( P @ A6 )
% 0.26/0.63                   => ( P @ ( insert_nat @ B4 @ A6 ) ) ) ) )
% 0.26/0.63           => ( P @ A3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_linorder_max_induct
% 0.26/0.63  thf(fact_8010_finite__linorder__max__induct,axiom,
% 0.26/0.63      ! [A3: set_int,P: set_int > $o] :
% 0.26/0.63        ( ( finite_finite_int @ A3 )
% 0.26/0.63       => ( ( P @ bot_bot_set_int )
% 0.26/0.63         => ( ! [B4: int,A6: set_int] :
% 0.26/0.63                ( ( finite_finite_int @ A6 )
% 0.26/0.63               => ( ! [X6: int] :
% 0.26/0.63                      ( ( member_int @ X6 @ A6 )
% 0.26/0.63                     => ( ord_less_int @ X6 @ B4 ) )
% 0.26/0.63                 => ( ( P @ A6 )
% 0.26/0.63                   => ( P @ ( insert_int @ B4 @ A6 ) ) ) ) )
% 0.26/0.63           => ( P @ A3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_linorder_max_induct
% 0.26/0.63  thf(fact_8011_sum__power__add,axiom,
% 0.26/0.63      ! [X3: complex,M: nat,I5: set_nat] :
% 0.26/0.63        ( ( groups2073611262835488442omplex
% 0.26/0.63          @ ^ [I4: nat] : ( power_power_complex @ X3 @ ( plus_plus_nat @ M @ I4 ) )
% 0.26/0.63          @ I5 )
% 0.26/0.63        = ( times_times_complex @ ( power_power_complex @ X3 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ I5 ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_power_add
% 0.26/0.63  thf(fact_8012_sum__power__add,axiom,
% 0.26/0.63      ! [X3: rat,M: nat,I5: set_nat] :
% 0.26/0.63        ( ( groups2906978787729119204at_rat
% 0.26/0.63          @ ^ [I4: nat] : ( power_power_rat @ X3 @ ( plus_plus_nat @ M @ I4 ) )
% 0.26/0.63          @ I5 )
% 0.26/0.63        = ( times_times_rat @ ( power_power_rat @ X3 @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ I5 ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_power_add
% 0.26/0.63  thf(fact_8013_sum__power__add,axiom,
% 0.26/0.63      ! [X3: int,M: nat,I5: set_nat] :
% 0.26/0.63        ( ( groups3539618377306564664at_int
% 0.26/0.63          @ ^ [I4: nat] : ( power_power_int @ X3 @ ( plus_plus_nat @ M @ I4 ) )
% 0.26/0.63          @ I5 )
% 0.26/0.63        = ( times_times_int @ ( power_power_int @ X3 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ I5 ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_power_add
% 0.26/0.63  thf(fact_8014_sum__power__add,axiom,
% 0.26/0.63      ! [X3: real,M: nat,I5: set_nat] :
% 0.26/0.63        ( ( groups6591440286371151544t_real
% 0.26/0.63          @ ^ [I4: nat] : ( power_power_real @ X3 @ ( plus_plus_nat @ M @ I4 ) )
% 0.26/0.63          @ I5 )
% 0.26/0.63        = ( times_times_real @ ( power_power_real @ X3 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ I5 ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_power_add
% 0.26/0.63  thf(fact_8015_finite__divisors__nat,axiom,
% 0.26/0.63      ! [M: nat] :
% 0.26/0.63        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.63       => ( finite_finite_nat
% 0.26/0.63          @ ( collect_nat
% 0.26/0.63            @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_divisors_nat
% 0.26/0.63  thf(fact_8016_arcsin__minus,axiom,
% 0.26/0.63      ! [X3: real] :
% 0.26/0.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.26/0.63       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 0.26/0.63         => ( ( arcsin @ ( uminus_uminus_real @ X3 ) )
% 0.26/0.63            = ( uminus_uminus_real @ ( arcsin @ X3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % arcsin_minus
% 0.26/0.63  thf(fact_8017_arcsin__le__arcsin,axiom,
% 0.26/0.63      ! [X3: real,Y3: real] :
% 0.26/0.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.26/0.63       => ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.26/0.63         => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 0.26/0.63           => ( ord_less_eq_real @ ( arcsin @ X3 ) @ ( arcsin @ Y3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % arcsin_le_arcsin
% 0.26/0.63  thf(fact_8018_subset__eq__atLeast0__atMost__finite,axiom,
% 0.26/0.63      ! [N4: set_nat,N: nat] :
% 0.26/0.63        ( ( ord_less_eq_set_nat @ N4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.26/0.63       => ( finite_finite_nat @ N4 ) ) ).
% 0.26/0.63  
% 0.26/0.63  % subset_eq_atLeast0_atMost_finite
% 0.26/0.63  thf(fact_8019_arcsin__eq__iff,axiom,
% 0.26/0.63      ! [X3: real,Y3: real] :
% 0.26/0.63        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.26/0.63       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 0.26/0.63         => ( ( ( arcsin @ X3 )
% 0.26/0.63              = ( arcsin @ Y3 ) )
% 0.26/0.63            = ( X3 = Y3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % arcsin_eq_iff
% 0.26/0.63  thf(fact_8020_arcsin__le__mono,axiom,
% 0.26/0.63      ! [X3: real,Y3: real] :
% 0.26/0.63        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.26/0.63       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 0.26/0.63         => ( ( ord_less_eq_real @ ( arcsin @ X3 ) @ ( arcsin @ Y3 ) )
% 0.26/0.63            = ( ord_less_eq_real @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % arcsin_le_mono
% 0.26/0.63  thf(fact_8021_sum__shift__lb__Suc0__0,axiom,
% 0.26/0.63      ! [F: nat > rat,K: nat] :
% 0.26/0.63        ( ( ( F @ zero_zero_nat )
% 0.26/0.63          = zero_zero_rat )
% 0.26/0.63       => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.26/0.63          = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_shift_lb_Suc0_0
% 0.26/0.63  thf(fact_8022_sum__shift__lb__Suc0__0,axiom,
% 0.26/0.63      ! [F: nat > int,K: nat] :
% 0.26/0.63        ( ( ( F @ zero_zero_nat )
% 0.26/0.63          = zero_zero_int )
% 0.26/0.63       => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.26/0.63          = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_shift_lb_Suc0_0
% 0.26/0.63  thf(fact_8023_sum__shift__lb__Suc0__0,axiom,
% 0.26/0.63      ! [F: nat > nat,K: nat] :
% 0.26/0.63        ( ( ( F @ zero_zero_nat )
% 0.26/0.63          = zero_zero_nat )
% 0.26/0.63       => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.26/0.63          = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_shift_lb_Suc0_0
% 0.26/0.63  thf(fact_8024_sum__shift__lb__Suc0__0,axiom,
% 0.26/0.63      ! [F: nat > real,K: nat] :
% 0.26/0.63        ( ( ( F @ zero_zero_nat )
% 0.26/0.63          = zero_zero_real )
% 0.26/0.63       => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.26/0.63          = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_shift_lb_Suc0_0
% 0.26/0.63  thf(fact_8025_sum_OatLeast0__atMost__Suc,axiom,
% 0.26/0.63      ! [G: nat > rat,N: nat] :
% 0.26/0.63        ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.26/0.63        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.atLeast0_atMost_Suc
% 0.26/0.63  thf(fact_8026_sum_OatLeast0__atMost__Suc,axiom,
% 0.26/0.63      ! [G: nat > int,N: nat] :
% 0.26/0.63        ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.26/0.63        = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.atLeast0_atMost_Suc
% 0.26/0.63  thf(fact_8027_sum_OatLeast0__atMost__Suc,axiom,
% 0.26/0.63      ! [G: nat > nat,N: nat] :
% 0.26/0.63        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.26/0.63        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.atLeast0_atMost_Suc
% 0.26/0.63  thf(fact_8028_sum_OatLeast0__atMost__Suc,axiom,
% 0.26/0.63      ! [G: nat > real,N: nat] :
% 0.26/0.63        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.26/0.63        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.atLeast0_atMost_Suc
% 0.26/0.63  thf(fact_8029_sum_OatLeast__Suc__atMost,axiom,
% 0.26/0.63      ! [M: nat,N: nat,G: nat > rat] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.63       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.63          = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.atLeast_Suc_atMost
% 0.26/0.63  thf(fact_8030_sum_OatLeast__Suc__atMost,axiom,
% 0.26/0.63      ! [M: nat,N: nat,G: nat > int] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.63       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.63          = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.atLeast_Suc_atMost
% 0.26/0.63  thf(fact_8031_sum_OatLeast__Suc__atMost,axiom,
% 0.26/0.63      ! [M: nat,N: nat,G: nat > nat] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.63       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.63          = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.atLeast_Suc_atMost
% 0.26/0.63  thf(fact_8032_sum_OatLeast__Suc__atMost,axiom,
% 0.26/0.63      ! [M: nat,N: nat,G: nat > real] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.63       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.63          = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.atLeast_Suc_atMost
% 0.26/0.63  thf(fact_8033_sum_Onat__ivl__Suc_H,axiom,
% 0.26/0.63      ! [M: nat,N: nat,G: nat > rat] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.26/0.63       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.63          = ( plus_plus_rat @ ( G @ ( suc @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.nat_ivl_Suc'
% 0.26/0.63  thf(fact_8034_sum_Onat__ivl__Suc_H,axiom,
% 0.26/0.63      ! [M: nat,N: nat,G: nat > int] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.26/0.63       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.63          = ( plus_plus_int @ ( G @ ( suc @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.nat_ivl_Suc'
% 0.26/0.63  thf(fact_8035_sum_Onat__ivl__Suc_H,axiom,
% 0.26/0.63      ! [M: nat,N: nat,G: nat > nat] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.26/0.63       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.63          = ( plus_plus_nat @ ( G @ ( suc @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.nat_ivl_Suc'
% 0.26/0.63  thf(fact_8036_sum_Onat__ivl__Suc_H,axiom,
% 0.26/0.63      ! [M: nat,N: nat,G: nat > real] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.26/0.63       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.26/0.63          = ( plus_plus_real @ ( G @ ( suc @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.nat_ivl_Suc'
% 0.26/0.63  thf(fact_8037_less__1__prod2,axiom,
% 0.26/0.63      ! [I5: set_real,I: real,F: real > real] :
% 0.26/0.63        ( ( finite_finite_real @ I5 )
% 0.26/0.63       => ( ( member_real @ I @ I5 )
% 0.26/0.63         => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 0.26/0.63           => ( ! [I3: real] :
% 0.26/0.63                  ( ( member_real @ I3 @ I5 )
% 0.26/0.63                 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 0.26/0.63             => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I5 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % less_1_prod2
% 0.26/0.63  thf(fact_8038_less__1__prod2,axiom,
% 0.26/0.63      ! [I5: set_nat,I: nat,F: nat > real] :
% 0.26/0.63        ( ( finite_finite_nat @ I5 )
% 0.26/0.63       => ( ( member_nat @ I @ I5 )
% 0.26/0.63         => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 0.26/0.63           => ( ! [I3: nat] :
% 0.26/0.63                  ( ( member_nat @ I3 @ I5 )
% 0.26/0.63                 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 0.26/0.63             => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I5 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % less_1_prod2
% 0.26/0.63  thf(fact_8039_less__1__prod2,axiom,
% 0.26/0.63      ! [I5: set_int,I: int,F: int > real] :
% 0.26/0.63        ( ( finite_finite_int @ I5 )
% 0.26/0.63       => ( ( member_int @ I @ I5 )
% 0.26/0.63         => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 0.26/0.63           => ( ! [I3: int] :
% 0.26/0.63                  ( ( member_int @ I3 @ I5 )
% 0.26/0.63                 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 0.26/0.63             => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I5 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % less_1_prod2
% 0.26/0.63  thf(fact_8040_less__1__prod2,axiom,
% 0.26/0.63      ! [I5: set_complex,I: complex,F: complex > real] :
% 0.26/0.63        ( ( finite3207457112153483333omplex @ I5 )
% 0.26/0.63       => ( ( member_complex @ I @ I5 )
% 0.26/0.63         => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 0.26/0.63           => ( ! [I3: complex] :
% 0.26/0.63                  ( ( member_complex @ I3 @ I5 )
% 0.26/0.63                 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 0.26/0.63             => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I5 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % less_1_prod2
% 0.26/0.63  thf(fact_8041_less__1__prod2,axiom,
% 0.26/0.63      ! [I5: set_Extended_enat,I: extended_enat,F: extended_enat > real] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat @ I5 )
% 0.26/0.63       => ( ( member_Extended_enat @ I @ I5 )
% 0.26/0.63         => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 0.26/0.63           => ( ! [I3: extended_enat] :
% 0.26/0.63                  ( ( member_Extended_enat @ I3 @ I5 )
% 0.26/0.63                 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 0.26/0.63             => ( ord_less_real @ one_one_real @ ( groups97031904164794029t_real @ F @ I5 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % less_1_prod2
% 0.26/0.63  thf(fact_8042_less__1__prod2,axiom,
% 0.26/0.63      ! [I5: set_real,I: real,F: real > rat] :
% 0.26/0.63        ( ( finite_finite_real @ I5 )
% 0.26/0.63       => ( ( member_real @ I @ I5 )
% 0.26/0.63         => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 0.26/0.63           => ( ! [I3: real] :
% 0.26/0.63                  ( ( member_real @ I3 @ I5 )
% 0.26/0.63                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 0.26/0.63             => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I5 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % less_1_prod2
% 0.26/0.63  thf(fact_8043_less__1__prod2,axiom,
% 0.26/0.63      ! [I5: set_nat,I: nat,F: nat > rat] :
% 0.26/0.63        ( ( finite_finite_nat @ I5 )
% 0.26/0.63       => ( ( member_nat @ I @ I5 )
% 0.26/0.63         => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 0.26/0.63           => ( ! [I3: nat] :
% 0.26/0.63                  ( ( member_nat @ I3 @ I5 )
% 0.26/0.63                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 0.26/0.63             => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I5 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % less_1_prod2
% 0.26/0.63  thf(fact_8044_less__1__prod2,axiom,
% 0.26/0.63      ! [I5: set_int,I: int,F: int > rat] :
% 0.26/0.63        ( ( finite_finite_int @ I5 )
% 0.26/0.63       => ( ( member_int @ I @ I5 )
% 0.26/0.63         => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 0.26/0.63           => ( ! [I3: int] :
% 0.26/0.63                  ( ( member_int @ I3 @ I5 )
% 0.26/0.63                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 0.26/0.63             => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % less_1_prod2
% 0.26/0.63  thf(fact_8045_less__1__prod2,axiom,
% 0.26/0.63      ! [I5: set_complex,I: complex,F: complex > rat] :
% 0.26/0.63        ( ( finite3207457112153483333omplex @ I5 )
% 0.26/0.63       => ( ( member_complex @ I @ I5 )
% 0.26/0.63         => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 0.26/0.63           => ( ! [I3: complex] :
% 0.26/0.63                  ( ( member_complex @ I3 @ I5 )
% 0.26/0.63                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 0.26/0.63             => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I5 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % less_1_prod2
% 0.26/0.63  thf(fact_8046_less__1__prod2,axiom,
% 0.26/0.63      ! [I5: set_Extended_enat,I: extended_enat,F: extended_enat > rat] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat @ I5 )
% 0.26/0.63       => ( ( member_Extended_enat @ I @ I5 )
% 0.26/0.63         => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 0.26/0.63           => ( ! [I3: extended_enat] :
% 0.26/0.63                  ( ( member_Extended_enat @ I3 @ I5 )
% 0.26/0.63                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 0.26/0.63             => ( ord_less_rat @ one_one_rat @ ( groups2245840878043517529at_rat @ F @ I5 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % less_1_prod2
% 0.26/0.63  thf(fact_8047_less__1__prod,axiom,
% 0.26/0.63      ! [I5: set_complex,F: complex > real] :
% 0.26/0.63        ( ( finite3207457112153483333omplex @ I5 )
% 0.26/0.63       => ( ( I5 != bot_bot_set_complex )
% 0.26/0.63         => ( ! [I3: complex] :
% 0.26/0.63                ( ( member_complex @ I3 @ I5 )
% 0.26/0.63               => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 0.26/0.63           => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I5 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % less_1_prod
% 0.26/0.63  thf(fact_8048_less__1__prod,axiom,
% 0.26/0.63      ! [I5: set_Extended_enat,F: extended_enat > real] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat @ I5 )
% 0.26/0.63       => ( ( I5 != bot_bo7653980558646680370d_enat )
% 0.26/0.63         => ( ! [I3: extended_enat] :
% 0.26/0.63                ( ( member_Extended_enat @ I3 @ I5 )
% 0.26/0.63               => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 0.26/0.63           => ( ord_less_real @ one_one_real @ ( groups97031904164794029t_real @ F @ I5 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % less_1_prod
% 0.26/0.63  thf(fact_8049_less__1__prod,axiom,
% 0.26/0.63      ! [I5: set_real,F: real > real] :
% 0.26/0.63        ( ( finite_finite_real @ I5 )
% 0.26/0.63       => ( ( I5 != bot_bot_set_real )
% 0.26/0.63         => ( ! [I3: real] :
% 0.26/0.63                ( ( member_real @ I3 @ I5 )
% 0.26/0.63               => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 0.26/0.63           => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I5 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % less_1_prod
% 0.26/0.63  thf(fact_8050_less__1__prod,axiom,
% 0.26/0.63      ! [I5: set_nat,F: nat > real] :
% 0.26/0.63        ( ( finite_finite_nat @ I5 )
% 0.26/0.63       => ( ( I5 != bot_bot_set_nat )
% 0.26/0.63         => ( ! [I3: nat] :
% 0.26/0.63                ( ( member_nat @ I3 @ I5 )
% 0.26/0.63               => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 0.26/0.63           => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I5 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % less_1_prod
% 0.26/0.63  thf(fact_8051_less__1__prod,axiom,
% 0.26/0.63      ! [I5: set_int,F: int > real] :
% 0.26/0.63        ( ( finite_finite_int @ I5 )
% 0.26/0.63       => ( ( I5 != bot_bot_set_int )
% 0.26/0.63         => ( ! [I3: int] :
% 0.26/0.63                ( ( member_int @ I3 @ I5 )
% 0.26/0.63               => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 0.26/0.63           => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I5 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % less_1_prod
% 0.26/0.63  thf(fact_8052_less__1__prod,axiom,
% 0.26/0.63      ! [I5: set_complex,F: complex > rat] :
% 0.26/0.63        ( ( finite3207457112153483333omplex @ I5 )
% 0.26/0.63       => ( ( I5 != bot_bot_set_complex )
% 0.26/0.63         => ( ! [I3: complex] :
% 0.26/0.63                ( ( member_complex @ I3 @ I5 )
% 0.26/0.63               => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 0.26/0.63           => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I5 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % less_1_prod
% 0.26/0.63  thf(fact_8053_less__1__prod,axiom,
% 0.26/0.63      ! [I5: set_Extended_enat,F: extended_enat > rat] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat @ I5 )
% 0.26/0.63       => ( ( I5 != bot_bo7653980558646680370d_enat )
% 0.26/0.63         => ( ! [I3: extended_enat] :
% 0.26/0.63                ( ( member_Extended_enat @ I3 @ I5 )
% 0.26/0.63               => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 0.26/0.63           => ( ord_less_rat @ one_one_rat @ ( groups2245840878043517529at_rat @ F @ I5 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % less_1_prod
% 0.26/0.63  thf(fact_8054_less__1__prod,axiom,
% 0.26/0.63      ! [I5: set_real,F: real > rat] :
% 0.26/0.63        ( ( finite_finite_real @ I5 )
% 0.26/0.63       => ( ( I5 != bot_bot_set_real )
% 0.26/0.63         => ( ! [I3: real] :
% 0.26/0.63                ( ( member_real @ I3 @ I5 )
% 0.26/0.63               => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 0.26/0.63           => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I5 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % less_1_prod
% 0.26/0.63  thf(fact_8055_less__1__prod,axiom,
% 0.26/0.63      ! [I5: set_nat,F: nat > rat] :
% 0.26/0.63        ( ( finite_finite_nat @ I5 )
% 0.26/0.63       => ( ( I5 != bot_bot_set_nat )
% 0.26/0.63         => ( ! [I3: nat] :
% 0.26/0.63                ( ( member_nat @ I3 @ I5 )
% 0.26/0.63               => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 0.26/0.63           => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I5 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % less_1_prod
% 0.26/0.63  thf(fact_8056_less__1__prod,axiom,
% 0.26/0.63      ! [I5: set_int,F: int > rat] :
% 0.26/0.63        ( ( finite_finite_int @ I5 )
% 0.26/0.63       => ( ( I5 != bot_bot_set_int )
% 0.26/0.63         => ( ! [I3: int] :
% 0.26/0.63                ( ( member_int @ I3 @ I5 )
% 0.26/0.63               => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 0.26/0.63           => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I5 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % less_1_prod
% 0.26/0.63  thf(fact_8057_sum_OSuc__reindex__ivl,axiom,
% 0.26/0.63      ! [M: nat,N: nat,G: nat > rat] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.63       => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 0.26/0.63          = ( plus_plus_rat @ ( G @ M )
% 0.26/0.63            @ ( groups2906978787729119204at_rat
% 0.26/0.63              @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.63              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.Suc_reindex_ivl
% 0.26/0.63  thf(fact_8058_sum_OSuc__reindex__ivl,axiom,
% 0.26/0.63      ! [M: nat,N: nat,G: nat > int] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.63       => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 0.26/0.63          = ( plus_plus_int @ ( G @ M )
% 0.26/0.63            @ ( groups3539618377306564664at_int
% 0.26/0.63              @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.63              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.Suc_reindex_ivl
% 0.26/0.63  thf(fact_8059_sum_OSuc__reindex__ivl,axiom,
% 0.26/0.63      ! [M: nat,N: nat,G: nat > nat] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.63       => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 0.26/0.63          = ( plus_plus_nat @ ( G @ M )
% 0.26/0.63            @ ( groups3542108847815614940at_nat
% 0.26/0.63              @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.63              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.Suc_reindex_ivl
% 0.26/0.63  thf(fact_8060_sum_OSuc__reindex__ivl,axiom,
% 0.26/0.63      ! [M: nat,N: nat,G: nat > real] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.63       => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 0.26/0.63          = ( plus_plus_real @ ( G @ M )
% 0.26/0.63            @ ( groups6591440286371151544t_real
% 0.26/0.63              @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.63              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.Suc_reindex_ivl
% 0.26/0.63  thf(fact_8061_sum__Suc__diff,axiom,
% 0.26/0.63      ! [M: nat,N: nat,F: nat > rat] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.26/0.63       => ( ( groups2906978787729119204at_rat
% 0.26/0.63            @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 0.26/0.63            @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.63          = ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_Suc_diff
% 0.26/0.63  thf(fact_8062_sum__Suc__diff,axiom,
% 0.26/0.63      ! [M: nat,N: nat,F: nat > int] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.26/0.63       => ( ( groups3539618377306564664at_int
% 0.26/0.63            @ ^ [I4: nat] : ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 0.26/0.63            @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.63          = ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_Suc_diff
% 0.26/0.63  thf(fact_8063_sum__Suc__diff,axiom,
% 0.26/0.63      ! [M: nat,N: nat,F: nat > real] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.26/0.63       => ( ( groups6591440286371151544t_real
% 0.26/0.63            @ ^ [I4: nat] : ( minus_minus_real @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 0.26/0.63            @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.63          = ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_Suc_diff
% 0.26/0.63  thf(fact_8064_atLeastAtMostPlus1__int__conv,axiom,
% 0.26/0.63      ! [M: int,N: int] :
% 0.26/0.63        ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 0.26/0.63       => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 0.26/0.63          = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M @ N ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % atLeastAtMostPlus1_int_conv
% 0.26/0.63  thf(fact_8065_simp__from__to,axiom,
% 0.26/0.63      ( set_or1266510415728281911st_int
% 0.26/0.63      = ( ^ [I4: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I4 ) @ bot_bot_set_int @ ( insert_int @ I4 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % simp_from_to
% 0.26/0.63  thf(fact_8066_finite__roots__unity,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.26/0.63       => ( finite_finite_real
% 0.26/0.63          @ ( collect_real
% 0.26/0.63            @ ^ [Z6: real] :
% 0.26/0.63                ( ( power_power_real @ Z6 @ N )
% 0.26/0.63                = one_one_real ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_roots_unity
% 0.26/0.63  thf(fact_8067_finite__roots__unity,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.26/0.63       => ( finite3207457112153483333omplex
% 0.26/0.63          @ ( collect_complex
% 0.26/0.63            @ ^ [Z6: complex] :
% 0.26/0.63                ( ( power_power_complex @ Z6 @ N )
% 0.26/0.63                = one_one_complex ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_roots_unity
% 0.26/0.63  thf(fact_8068_sum__atLeastAtMost__code,axiom,
% 0.26/0.63      ! [F: nat > rat,A: nat,B: nat] :
% 0.26/0.63        ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.26/0.63        = ( set_fo1949268297981939178at_rat
% 0.26/0.63          @ ^ [A4: nat] : ( plus_plus_rat @ ( F @ A4 ) )
% 0.26/0.63          @ A
% 0.26/0.63          @ B
% 0.26/0.63          @ zero_zero_rat ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_atLeastAtMost_code
% 0.26/0.63  thf(fact_8069_sum__atLeastAtMost__code,axiom,
% 0.26/0.63      ! [F: nat > int,A: nat,B: nat] :
% 0.26/0.63        ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.26/0.63        = ( set_fo2581907887559384638at_int
% 0.26/0.63          @ ^ [A4: nat] : ( plus_plus_int @ ( F @ A4 ) )
% 0.26/0.63          @ A
% 0.26/0.63          @ B
% 0.26/0.63          @ zero_zero_int ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_atLeastAtMost_code
% 0.26/0.63  thf(fact_8070_sum__atLeastAtMost__code,axiom,
% 0.26/0.63      ! [F: nat > nat,A: nat,B: nat] :
% 0.26/0.63        ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.26/0.63        = ( set_fo2584398358068434914at_nat
% 0.26/0.63          @ ^ [A4: nat] : ( plus_plus_nat @ ( F @ A4 ) )
% 0.26/0.63          @ A
% 0.26/0.63          @ B
% 0.26/0.63          @ zero_zero_nat ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_atLeastAtMost_code
% 0.26/0.63  thf(fact_8071_sum__atLeastAtMost__code,axiom,
% 0.26/0.63      ! [F: nat > real,A: nat,B: nat] :
% 0.26/0.63        ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.26/0.63        = ( set_fo3111899725591712190t_real
% 0.26/0.63          @ ^ [A4: nat] : ( plus_plus_real @ ( F @ A4 ) )
% 0.26/0.63          @ A
% 0.26/0.63          @ B
% 0.26/0.63          @ zero_zero_real ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_atLeastAtMost_code
% 0.26/0.63  thf(fact_8072_arcsin__less__arcsin,axiom,
% 0.26/0.63      ! [X3: real,Y3: real] :
% 0.26/0.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.26/0.63       => ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.63         => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 0.26/0.63           => ( ord_less_real @ ( arcsin @ X3 ) @ ( arcsin @ Y3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % arcsin_less_arcsin
% 0.26/0.63  thf(fact_8073_arcsin__less__mono,axiom,
% 0.26/0.63      ! [X3: real,Y3: real] :
% 0.26/0.63        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.26/0.63       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 0.26/0.63         => ( ( ord_less_real @ ( arcsin @ X3 ) @ ( arcsin @ Y3 ) )
% 0.26/0.63            = ( ord_less_real @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % arcsin_less_mono
% 0.26/0.63  thf(fact_8074_sum_Oub__add__nat,axiom,
% 0.26/0.63      ! [M: nat,N: nat,G: nat > rat,P6: nat] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.26/0.63       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 0.26/0.63          = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.ub_add_nat
% 0.26/0.63  thf(fact_8075_sum_Oub__add__nat,axiom,
% 0.26/0.63      ! [M: nat,N: nat,G: nat > int,P6: nat] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.26/0.63       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 0.26/0.63          = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.ub_add_nat
% 0.26/0.63  thf(fact_8076_sum_Oub__add__nat,axiom,
% 0.26/0.63      ! [M: nat,N: nat,G: nat > nat,P6: nat] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.26/0.63       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 0.26/0.63          = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.ub_add_nat
% 0.26/0.63  thf(fact_8077_sum_Oub__add__nat,axiom,
% 0.26/0.63      ! [M: nat,N: nat,G: nat > real,P6: nat] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.26/0.63       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 0.26/0.63          = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.ub_add_nat
% 0.26/0.63  thf(fact_8078_prod__mono__strict,axiom,
% 0.26/0.63      ! [A3: set_complex,F: complex > real,G: complex > real] :
% 0.26/0.63        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.63       => ( ! [I3: complex] :
% 0.26/0.63              ( ( member_complex @ I3 @ A3 )
% 0.26/0.63             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 0.26/0.63                & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.26/0.63         => ( ( A3 != bot_bot_set_complex )
% 0.26/0.63           => ( ord_less_real @ ( groups766887009212190081x_real @ F @ A3 ) @ ( groups766887009212190081x_real @ G @ A3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_mono_strict
% 0.26/0.63  thf(fact_8079_prod__mono__strict,axiom,
% 0.26/0.63      ! [A3: set_Extended_enat,F: extended_enat > real,G: extended_enat > real] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.63       => ( ! [I3: extended_enat] :
% 0.26/0.63              ( ( member_Extended_enat @ I3 @ A3 )
% 0.26/0.63             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 0.26/0.63                & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.26/0.63         => ( ( A3 != bot_bo7653980558646680370d_enat )
% 0.26/0.63           => ( ord_less_real @ ( groups97031904164794029t_real @ F @ A3 ) @ ( groups97031904164794029t_real @ G @ A3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_mono_strict
% 0.26/0.63  thf(fact_8080_prod__mono__strict,axiom,
% 0.26/0.63      ! [A3: set_real,F: real > real,G: real > real] :
% 0.26/0.63        ( ( finite_finite_real @ A3 )
% 0.26/0.63       => ( ! [I3: real] :
% 0.26/0.63              ( ( member_real @ I3 @ A3 )
% 0.26/0.63             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 0.26/0.63                & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.26/0.63         => ( ( A3 != bot_bot_set_real )
% 0.26/0.63           => ( ord_less_real @ ( groups1681761925125756287l_real @ F @ A3 ) @ ( groups1681761925125756287l_real @ G @ A3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_mono_strict
% 0.26/0.63  thf(fact_8081_prod__mono__strict,axiom,
% 0.26/0.63      ! [A3: set_nat,F: nat > real,G: nat > real] :
% 0.26/0.63        ( ( finite_finite_nat @ A3 )
% 0.26/0.63       => ( ! [I3: nat] :
% 0.26/0.63              ( ( member_nat @ I3 @ A3 )
% 0.26/0.63             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 0.26/0.63                & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.26/0.63         => ( ( A3 != bot_bot_set_nat )
% 0.26/0.63           => ( ord_less_real @ ( groups129246275422532515t_real @ F @ A3 ) @ ( groups129246275422532515t_real @ G @ A3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_mono_strict
% 0.26/0.63  thf(fact_8082_prod__mono__strict,axiom,
% 0.26/0.63      ! [A3: set_int,F: int > real,G: int > real] :
% 0.26/0.63        ( ( finite_finite_int @ A3 )
% 0.26/0.63       => ( ! [I3: int] :
% 0.26/0.63              ( ( member_int @ I3 @ A3 )
% 0.26/0.63             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 0.26/0.63                & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.26/0.63         => ( ( A3 != bot_bot_set_int )
% 0.26/0.63           => ( ord_less_real @ ( groups2316167850115554303t_real @ F @ A3 ) @ ( groups2316167850115554303t_real @ G @ A3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_mono_strict
% 0.26/0.63  thf(fact_8083_prod__mono__strict,axiom,
% 0.26/0.63      ! [A3: set_complex,F: complex > rat,G: complex > rat] :
% 0.26/0.63        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.63       => ( ! [I3: complex] :
% 0.26/0.63              ( ( member_complex @ I3 @ A3 )
% 0.26/0.63             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 0.26/0.63                & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.26/0.63         => ( ( A3 != bot_bot_set_complex )
% 0.26/0.63           => ( ord_less_rat @ ( groups225925009352817453ex_rat @ F @ A3 ) @ ( groups225925009352817453ex_rat @ G @ A3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_mono_strict
% 0.26/0.63  thf(fact_8084_prod__mono__strict,axiom,
% 0.26/0.63      ! [A3: set_Extended_enat,F: extended_enat > rat,G: extended_enat > rat] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.63       => ( ! [I3: extended_enat] :
% 0.26/0.63              ( ( member_Extended_enat @ I3 @ A3 )
% 0.26/0.63             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 0.26/0.63                & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.26/0.63         => ( ( A3 != bot_bo7653980558646680370d_enat )
% 0.26/0.63           => ( ord_less_rat @ ( groups2245840878043517529at_rat @ F @ A3 ) @ ( groups2245840878043517529at_rat @ G @ A3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_mono_strict
% 0.26/0.63  thf(fact_8085_prod__mono__strict,axiom,
% 0.26/0.63      ! [A3: set_real,F: real > rat,G: real > rat] :
% 0.26/0.63        ( ( finite_finite_real @ A3 )
% 0.26/0.63       => ( ! [I3: real] :
% 0.26/0.63              ( ( member_real @ I3 @ A3 )
% 0.26/0.63             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 0.26/0.63                & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.26/0.63         => ( ( A3 != bot_bot_set_real )
% 0.26/0.63           => ( ord_less_rat @ ( groups4061424788464935467al_rat @ F @ A3 ) @ ( groups4061424788464935467al_rat @ G @ A3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_mono_strict
% 0.26/0.63  thf(fact_8086_prod__mono__strict,axiom,
% 0.26/0.63      ! [A3: set_nat,F: nat > rat,G: nat > rat] :
% 0.26/0.63        ( ( finite_finite_nat @ A3 )
% 0.26/0.63       => ( ! [I3: nat] :
% 0.26/0.63              ( ( member_nat @ I3 @ A3 )
% 0.26/0.63             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 0.26/0.63                & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.26/0.63         => ( ( A3 != bot_bot_set_nat )
% 0.26/0.63           => ( ord_less_rat @ ( groups73079841787564623at_rat @ F @ A3 ) @ ( groups73079841787564623at_rat @ G @ A3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_mono_strict
% 0.26/0.63  thf(fact_8087_prod__mono__strict,axiom,
% 0.26/0.63      ! [A3: set_int,F: int > rat,G: int > rat] :
% 0.26/0.63        ( ( finite_finite_int @ A3 )
% 0.26/0.63       => ( ! [I3: int] :
% 0.26/0.63              ( ( member_int @ I3 @ A3 )
% 0.26/0.63             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 0.26/0.63                & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.26/0.63         => ( ( A3 != bot_bot_set_int )
% 0.26/0.63           => ( ord_less_rat @ ( groups1072433553688619179nt_rat @ F @ A3 ) @ ( groups1072433553688619179nt_rat @ G @ A3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_mono_strict
% 0.26/0.63  thf(fact_8088_even__prod__iff,axiom,
% 0.26/0.63      ! [A3: set_nat,F: nat > code_integer] :
% 0.26/0.63        ( ( finite_finite_nat @ A3 )
% 0.26/0.63       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups3455450783089532116nteger @ F @ A3 ) )
% 0.26/0.63          = ( ? [X: nat] :
% 0.26/0.63                ( ( member_nat @ X @ A3 )
% 0.26/0.63                & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % even_prod_iff
% 0.26/0.63  thf(fact_8089_even__prod__iff,axiom,
% 0.26/0.63      ! [A3: set_int,F: int > code_integer] :
% 0.26/0.63        ( ( finite_finite_int @ A3 )
% 0.26/0.63       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups3827104343326376752nteger @ F @ A3 ) )
% 0.26/0.63          = ( ? [X: int] :
% 0.26/0.63                ( ( member_int @ X @ A3 )
% 0.26/0.63                & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % even_prod_iff
% 0.26/0.63  thf(fact_8090_even__prod__iff,axiom,
% 0.26/0.63      ! [A3: set_complex,F: complex > code_integer] :
% 0.26/0.63        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.63       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups8682486955453173170nteger @ F @ A3 ) )
% 0.26/0.63          = ( ? [X: complex] :
% 0.26/0.63                ( ( member_complex @ X @ A3 )
% 0.26/0.63                & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % even_prod_iff
% 0.26/0.63  thf(fact_8091_even__prod__iff,axiom,
% 0.26/0.63      ! [A3: set_Extended_enat,F: extended_enat > code_integer] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.63       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups845124408420398302nteger @ F @ A3 ) )
% 0.26/0.63          = ( ? [X: extended_enat] :
% 0.26/0.63                ( ( member_Extended_enat @ X @ A3 )
% 0.26/0.63                & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % even_prod_iff
% 0.26/0.63  thf(fact_8092_even__prod__iff,axiom,
% 0.26/0.63      ! [A3: set_int,F: int > nat] :
% 0.26/0.63        ( ( finite_finite_int @ A3 )
% 0.26/0.63       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups1707563613775114915nt_nat @ F @ A3 ) )
% 0.26/0.63          = ( ? [X: int] :
% 0.26/0.63                ( ( member_int @ X @ A3 )
% 0.26/0.63                & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % even_prod_iff
% 0.26/0.63  thf(fact_8093_even__prod__iff,axiom,
% 0.26/0.63      ! [A3: set_complex,F: complex > nat] :
% 0.26/0.63        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.63       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups861055069439313189ex_nat @ F @ A3 ) )
% 0.26/0.63          = ( ? [X: complex] :
% 0.26/0.63                ( ( member_complex @ X @ A3 )
% 0.26/0.63                & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % even_prod_iff
% 0.26/0.63  thf(fact_8094_even__prod__iff,axiom,
% 0.26/0.63      ! [A3: set_Extended_enat,F: extended_enat > nat] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.63       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups2880970938130013265at_nat @ F @ A3 ) )
% 0.26/0.63          = ( ? [X: extended_enat] :
% 0.26/0.63                ( ( member_Extended_enat @ X @ A3 )
% 0.26/0.63                & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % even_prod_iff
% 0.26/0.63  thf(fact_8095_even__prod__iff,axiom,
% 0.26/0.63      ! [A3: set_complex,F: complex > int] :
% 0.26/0.63        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.63       => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups858564598930262913ex_int @ F @ A3 ) )
% 0.26/0.63          = ( ? [X: complex] :
% 0.26/0.63                ( ( member_complex @ X @ A3 )
% 0.26/0.63                & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % even_prod_iff
% 0.26/0.63  thf(fact_8096_even__prod__iff,axiom,
% 0.26/0.63      ! [A3: set_Extended_enat,F: extended_enat > int] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.63       => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups2878480467620962989at_int @ F @ A3 ) )
% 0.26/0.63          = ( ? [X: extended_enat] :
% 0.26/0.63                ( ( member_Extended_enat @ X @ A3 )
% 0.26/0.63                & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % even_prod_iff
% 0.26/0.63  thf(fact_8097_even__prod__iff,axiom,
% 0.26/0.63      ! [A3: set_nat,F: nat > int] :
% 0.26/0.63        ( ( finite_finite_nat @ A3 )
% 0.26/0.63       => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups705719431365010083at_int @ F @ A3 ) )
% 0.26/0.63          = ( ? [X: nat] :
% 0.26/0.63                ( ( member_nat @ X @ A3 )
% 0.26/0.63                & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % even_prod_iff
% 0.26/0.63  thf(fact_8098_convex__sum__bound__le,axiom,
% 0.26/0.63      ! [I5: set_real,X3: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 0.26/0.63        ( ! [I3: real] :
% 0.26/0.63            ( ( member_real @ I3 @ I5 )
% 0.26/0.63           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X3 @ I3 ) ) )
% 0.26/0.63       => ( ( ( groups7713935264441627589nteger @ X3 @ I5 )
% 0.26/0.63            = one_one_Code_integer )
% 0.26/0.63         => ( ! [I3: real] :
% 0.26/0.63                ( ( member_real @ I3 @ I5 )
% 0.26/0.63               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.26/0.63           => ( ord_le3102999989581377725nteger
% 0.26/0.63              @ ( abs_abs_Code_integer
% 0.26/0.63                @ ( minus_8373710615458151222nteger
% 0.26/0.63                  @ ( groups7713935264441627589nteger
% 0.26/0.63                    @ ^ [I4: real] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X3 @ I4 ) )
% 0.26/0.63                    @ I5 )
% 0.26/0.63                  @ B ) )
% 0.26/0.63              @ Delta ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % convex_sum_bound_le
% 0.26/0.63  thf(fact_8099_convex__sum__bound__le,axiom,
% 0.26/0.63      ! [I5: set_nat,X3: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 0.26/0.63        ( ! [I3: nat] :
% 0.26/0.63            ( ( member_nat @ I3 @ I5 )
% 0.26/0.63           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X3 @ I3 ) ) )
% 0.26/0.63       => ( ( ( groups7501900531339628137nteger @ X3 @ I5 )
% 0.26/0.63            = one_one_Code_integer )
% 0.26/0.63         => ( ! [I3: nat] :
% 0.26/0.63                ( ( member_nat @ I3 @ I5 )
% 0.26/0.63               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.26/0.63           => ( ord_le3102999989581377725nteger
% 0.26/0.63              @ ( abs_abs_Code_integer
% 0.26/0.63                @ ( minus_8373710615458151222nteger
% 0.26/0.63                  @ ( groups7501900531339628137nteger
% 0.26/0.63                    @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X3 @ I4 ) )
% 0.26/0.63                    @ I5 )
% 0.26/0.63                  @ B ) )
% 0.26/0.63              @ Delta ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % convex_sum_bound_le
% 0.26/0.63  thf(fact_8100_convex__sum__bound__le,axiom,
% 0.26/0.63      ! [I5: set_int,X3: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 0.26/0.63        ( ! [I3: int] :
% 0.26/0.63            ( ( member_int @ I3 @ I5 )
% 0.26/0.63           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X3 @ I3 ) ) )
% 0.26/0.63       => ( ( ( groups7873554091576472773nteger @ X3 @ I5 )
% 0.26/0.63            = one_one_Code_integer )
% 0.26/0.63         => ( ! [I3: int] :
% 0.26/0.63                ( ( member_int @ I3 @ I5 )
% 0.26/0.63               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.26/0.63           => ( ord_le3102999989581377725nteger
% 0.26/0.63              @ ( abs_abs_Code_integer
% 0.26/0.63                @ ( minus_8373710615458151222nteger
% 0.26/0.63                  @ ( groups7873554091576472773nteger
% 0.26/0.63                    @ ^ [I4: int] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X3 @ I4 ) )
% 0.26/0.63                    @ I5 )
% 0.26/0.63                  @ B ) )
% 0.26/0.63              @ Delta ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % convex_sum_bound_le
% 0.26/0.63  thf(fact_8101_convex__sum__bound__le,axiom,
% 0.26/0.63      ! [I5: set_real,X3: real > real,A: real > real,B: real,Delta: real] :
% 0.26/0.63        ( ! [I3: real] :
% 0.26/0.63            ( ( member_real @ I3 @ I5 )
% 0.26/0.63           => ( ord_less_eq_real @ zero_zero_real @ ( X3 @ I3 ) ) )
% 0.26/0.63       => ( ( ( groups8097168146408367636l_real @ X3 @ I5 )
% 0.26/0.63            = one_one_real )
% 0.26/0.63         => ( ! [I3: real] :
% 0.26/0.63                ( ( member_real @ I3 @ I5 )
% 0.26/0.63               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.26/0.63           => ( ord_less_eq_real
% 0.26/0.63              @ ( abs_abs_real
% 0.26/0.63                @ ( minus_minus_real
% 0.26/0.63                  @ ( groups8097168146408367636l_real
% 0.26/0.63                    @ ^ [I4: real] : ( times_times_real @ ( A @ I4 ) @ ( X3 @ I4 ) )
% 0.26/0.63                    @ I5 )
% 0.26/0.63                  @ B ) )
% 0.26/0.63              @ Delta ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % convex_sum_bound_le
% 0.26/0.63  thf(fact_8102_convex__sum__bound__le,axiom,
% 0.26/0.63      ! [I5: set_int,X3: int > real,A: int > real,B: real,Delta: real] :
% 0.26/0.63        ( ! [I3: int] :
% 0.26/0.63            ( ( member_int @ I3 @ I5 )
% 0.26/0.63           => ( ord_less_eq_real @ zero_zero_real @ ( X3 @ I3 ) ) )
% 0.26/0.63       => ( ( ( groups8778361861064173332t_real @ X3 @ I5 )
% 0.26/0.63            = one_one_real )
% 0.26/0.63         => ( ! [I3: int] :
% 0.26/0.63                ( ( member_int @ I3 @ I5 )
% 0.26/0.63               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.26/0.63           => ( ord_less_eq_real
% 0.26/0.63              @ ( abs_abs_real
% 0.26/0.63                @ ( minus_minus_real
% 0.26/0.63                  @ ( groups8778361861064173332t_real
% 0.26/0.63                    @ ^ [I4: int] : ( times_times_real @ ( A @ I4 ) @ ( X3 @ I4 ) )
% 0.26/0.63                    @ I5 )
% 0.26/0.63                  @ B ) )
% 0.26/0.63              @ Delta ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % convex_sum_bound_le
% 0.26/0.63  thf(fact_8103_convex__sum__bound__le,axiom,
% 0.26/0.63      ! [I5: set_real,X3: real > rat,A: real > rat,B: rat,Delta: rat] :
% 0.26/0.63        ( ! [I3: real] :
% 0.26/0.63            ( ( member_real @ I3 @ I5 )
% 0.26/0.63           => ( ord_less_eq_rat @ zero_zero_rat @ ( X3 @ I3 ) ) )
% 0.26/0.63       => ( ( ( groups1300246762558778688al_rat @ X3 @ I5 )
% 0.26/0.63            = one_one_rat )
% 0.26/0.63         => ( ! [I3: real] :
% 0.26/0.63                ( ( member_real @ I3 @ I5 )
% 0.26/0.63               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.26/0.63           => ( ord_less_eq_rat
% 0.26/0.63              @ ( abs_abs_rat
% 0.26/0.63                @ ( minus_minus_rat
% 0.26/0.63                  @ ( groups1300246762558778688al_rat
% 0.26/0.63                    @ ^ [I4: real] : ( times_times_rat @ ( A @ I4 ) @ ( X3 @ I4 ) )
% 0.26/0.63                    @ I5 )
% 0.26/0.63                  @ B ) )
% 0.26/0.63              @ Delta ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % convex_sum_bound_le
% 0.26/0.63  thf(fact_8104_convex__sum__bound__le,axiom,
% 0.26/0.63      ! [I5: set_nat,X3: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 0.26/0.63        ( ! [I3: nat] :
% 0.26/0.63            ( ( member_nat @ I3 @ I5 )
% 0.26/0.63           => ( ord_less_eq_rat @ zero_zero_rat @ ( X3 @ I3 ) ) )
% 0.26/0.63       => ( ( ( groups2906978787729119204at_rat @ X3 @ I5 )
% 0.26/0.63            = one_one_rat )
% 0.26/0.63         => ( ! [I3: nat] :
% 0.26/0.63                ( ( member_nat @ I3 @ I5 )
% 0.26/0.63               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.26/0.63           => ( ord_less_eq_rat
% 0.26/0.63              @ ( abs_abs_rat
% 0.26/0.63                @ ( minus_minus_rat
% 0.26/0.63                  @ ( groups2906978787729119204at_rat
% 0.26/0.63                    @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( X3 @ I4 ) )
% 0.26/0.63                    @ I5 )
% 0.26/0.63                  @ B ) )
% 0.26/0.63              @ Delta ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % convex_sum_bound_le
% 0.26/0.63  thf(fact_8105_convex__sum__bound__le,axiom,
% 0.26/0.63      ! [I5: set_int,X3: int > rat,A: int > rat,B: rat,Delta: rat] :
% 0.26/0.63        ( ! [I3: int] :
% 0.26/0.63            ( ( member_int @ I3 @ I5 )
% 0.26/0.63           => ( ord_less_eq_rat @ zero_zero_rat @ ( X3 @ I3 ) ) )
% 0.26/0.63       => ( ( ( groups3906332499630173760nt_rat @ X3 @ I5 )
% 0.26/0.63            = one_one_rat )
% 0.26/0.63         => ( ! [I3: int] :
% 0.26/0.63                ( ( member_int @ I3 @ I5 )
% 0.26/0.63               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.26/0.63           => ( ord_less_eq_rat
% 0.26/0.63              @ ( abs_abs_rat
% 0.26/0.63                @ ( minus_minus_rat
% 0.26/0.63                  @ ( groups3906332499630173760nt_rat
% 0.26/0.63                    @ ^ [I4: int] : ( times_times_rat @ ( A @ I4 ) @ ( X3 @ I4 ) )
% 0.26/0.63                    @ I5 )
% 0.26/0.63                  @ B ) )
% 0.26/0.63              @ Delta ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % convex_sum_bound_le
% 0.26/0.63  thf(fact_8106_convex__sum__bound__le,axiom,
% 0.26/0.63      ! [I5: set_real,X3: real > int,A: real > int,B: int,Delta: int] :
% 0.26/0.63        ( ! [I3: real] :
% 0.26/0.63            ( ( member_real @ I3 @ I5 )
% 0.26/0.63           => ( ord_less_eq_int @ zero_zero_int @ ( X3 @ I3 ) ) )
% 0.26/0.63       => ( ( ( groups1932886352136224148al_int @ X3 @ I5 )
% 0.26/0.63            = one_one_int )
% 0.26/0.63         => ( ! [I3: real] :
% 0.26/0.63                ( ( member_real @ I3 @ I5 )
% 0.26/0.63               => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.26/0.63           => ( ord_less_eq_int
% 0.26/0.63              @ ( abs_abs_int
% 0.26/0.63                @ ( minus_minus_int
% 0.26/0.63                  @ ( groups1932886352136224148al_int
% 0.26/0.63                    @ ^ [I4: real] : ( times_times_int @ ( A @ I4 ) @ ( X3 @ I4 ) )
% 0.26/0.63                    @ I5 )
% 0.26/0.63                  @ B ) )
% 0.26/0.63              @ Delta ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % convex_sum_bound_le
% 0.26/0.63  thf(fact_8107_convex__sum__bound__le,axiom,
% 0.26/0.63      ! [I5: set_nat,X3: nat > int,A: nat > int,B: int,Delta: int] :
% 0.26/0.63        ( ! [I3: nat] :
% 0.26/0.63            ( ( member_nat @ I3 @ I5 )
% 0.26/0.63           => ( ord_less_eq_int @ zero_zero_int @ ( X3 @ I3 ) ) )
% 0.26/0.63       => ( ( ( groups3539618377306564664at_int @ X3 @ I5 )
% 0.26/0.63            = one_one_int )
% 0.26/0.63         => ( ! [I3: nat] :
% 0.26/0.63                ( ( member_nat @ I3 @ I5 )
% 0.26/0.63               => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.26/0.63           => ( ord_less_eq_int
% 0.26/0.63              @ ( abs_abs_int
% 0.26/0.63                @ ( minus_minus_int
% 0.26/0.63                  @ ( groups3539618377306564664at_int
% 0.26/0.63                    @ ^ [I4: nat] : ( times_times_int @ ( A @ I4 ) @ ( X3 @ I4 ) )
% 0.26/0.63                    @ I5 )
% 0.26/0.63                  @ B ) )
% 0.26/0.63              @ Delta ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % convex_sum_bound_le
% 0.26/0.63  thf(fact_8108_cos__arcsin__nonzero,axiom,
% 0.26/0.63      ! [X3: real] :
% 0.26/0.63        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.26/0.63       => ( ( ord_less_real @ X3 @ one_one_real )
% 0.26/0.63         => ( ( cos_real @ ( arcsin @ X3 ) )
% 0.26/0.63           != zero_zero_real ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % cos_arcsin_nonzero
% 0.26/0.63  thf(fact_8109_prod__mono2,axiom,
% 0.26/0.63      ! [B5: set_real,A3: set_real,F: real > real] :
% 0.26/0.63        ( ( finite_finite_real @ B5 )
% 0.26/0.63       => ( ( ord_less_eq_set_real @ A3 @ B5 )
% 0.26/0.63         => ( ! [B4: real] :
% 0.26/0.63                ( ( member_real @ B4 @ ( minus_minus_set_real @ B5 @ A3 ) )
% 0.26/0.63               => ( ord_less_eq_real @ one_one_real @ ( F @ B4 ) ) )
% 0.26/0.63           => ( ! [A5: real] :
% 0.26/0.63                  ( ( member_real @ A5 @ A3 )
% 0.26/0.63                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A5 ) ) )
% 0.26/0.63             => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A3 ) @ ( groups1681761925125756287l_real @ F @ B5 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_mono2
% 0.26/0.63  thf(fact_8110_prod__mono2,axiom,
% 0.26/0.63      ! [B5: set_int,A3: set_int,F: int > real] :
% 0.26/0.63        ( ( finite_finite_int @ B5 )
% 0.26/0.63       => ( ( ord_less_eq_set_int @ A3 @ B5 )
% 0.26/0.63         => ( ! [B4: int] :
% 0.26/0.63                ( ( member_int @ B4 @ ( minus_minus_set_int @ B5 @ A3 ) )
% 0.26/0.63               => ( ord_less_eq_real @ one_one_real @ ( F @ B4 ) ) )
% 0.26/0.63           => ( ! [A5: int] :
% 0.26/0.63                  ( ( member_int @ A5 @ A3 )
% 0.26/0.63                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A5 ) ) )
% 0.26/0.63             => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A3 ) @ ( groups2316167850115554303t_real @ F @ B5 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_mono2
% 0.26/0.63  thf(fact_8111_prod__mono2,axiom,
% 0.26/0.63      ! [B5: set_complex,A3: set_complex,F: complex > real] :
% 0.26/0.63        ( ( finite3207457112153483333omplex @ B5 )
% 0.26/0.63       => ( ( ord_le211207098394363844omplex @ A3 @ B5 )
% 0.26/0.63         => ( ! [B4: complex] :
% 0.26/0.63                ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B5 @ A3 ) )
% 0.26/0.63               => ( ord_less_eq_real @ one_one_real @ ( F @ B4 ) ) )
% 0.26/0.63           => ( ! [A5: complex] :
% 0.26/0.63                  ( ( member_complex @ A5 @ A3 )
% 0.26/0.63                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A5 ) ) )
% 0.26/0.63             => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A3 ) @ ( groups766887009212190081x_real @ F @ B5 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_mono2
% 0.26/0.63  thf(fact_8112_prod__mono2,axiom,
% 0.26/0.63      ! [B5: set_Extended_enat,A3: set_Extended_enat,F: extended_enat > real] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat @ B5 )
% 0.26/0.63       => ( ( ord_le7203529160286727270d_enat @ A3 @ B5 )
% 0.26/0.63         => ( ! [B4: extended_enat] :
% 0.26/0.63                ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ B5 @ A3 ) )
% 0.26/0.63               => ( ord_less_eq_real @ one_one_real @ ( F @ B4 ) ) )
% 0.26/0.63           => ( ! [A5: extended_enat] :
% 0.26/0.63                  ( ( member_Extended_enat @ A5 @ A3 )
% 0.26/0.63                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A5 ) ) )
% 0.26/0.63             => ( ord_less_eq_real @ ( groups97031904164794029t_real @ F @ A3 ) @ ( groups97031904164794029t_real @ F @ B5 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_mono2
% 0.26/0.63  thf(fact_8113_prod__mono2,axiom,
% 0.26/0.63      ! [B5: set_real,A3: set_real,F: real > rat] :
% 0.26/0.63        ( ( finite_finite_real @ B5 )
% 0.26/0.63       => ( ( ord_less_eq_set_real @ A3 @ B5 )
% 0.26/0.63         => ( ! [B4: real] :
% 0.26/0.63                ( ( member_real @ B4 @ ( minus_minus_set_real @ B5 @ A3 ) )
% 0.26/0.63               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B4 ) ) )
% 0.26/0.63           => ( ! [A5: real] :
% 0.26/0.63                  ( ( member_real @ A5 @ A3 )
% 0.26/0.63                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A5 ) ) )
% 0.26/0.63             => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A3 ) @ ( groups4061424788464935467al_rat @ F @ B5 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_mono2
% 0.26/0.63  thf(fact_8114_prod__mono2,axiom,
% 0.26/0.63      ! [B5: set_int,A3: set_int,F: int > rat] :
% 0.26/0.63        ( ( finite_finite_int @ B5 )
% 0.26/0.63       => ( ( ord_less_eq_set_int @ A3 @ B5 )
% 0.26/0.63         => ( ! [B4: int] :
% 0.26/0.63                ( ( member_int @ B4 @ ( minus_minus_set_int @ B5 @ A3 ) )
% 0.26/0.63               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B4 ) ) )
% 0.26/0.63           => ( ! [A5: int] :
% 0.26/0.63                  ( ( member_int @ A5 @ A3 )
% 0.26/0.63                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A5 ) ) )
% 0.26/0.63             => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A3 ) @ ( groups1072433553688619179nt_rat @ F @ B5 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_mono2
% 0.26/0.63  thf(fact_8115_prod__mono2,axiom,
% 0.26/0.63      ! [B5: set_complex,A3: set_complex,F: complex > rat] :
% 0.26/0.63        ( ( finite3207457112153483333omplex @ B5 )
% 0.26/0.63       => ( ( ord_le211207098394363844omplex @ A3 @ B5 )
% 0.26/0.63         => ( ! [B4: complex] :
% 0.26/0.63                ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B5 @ A3 ) )
% 0.26/0.63               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B4 ) ) )
% 0.26/0.63           => ( ! [A5: complex] :
% 0.26/0.63                  ( ( member_complex @ A5 @ A3 )
% 0.26/0.63                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A5 ) ) )
% 0.26/0.63             => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A3 ) @ ( groups225925009352817453ex_rat @ F @ B5 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_mono2
% 0.26/0.63  thf(fact_8116_prod__mono2,axiom,
% 0.26/0.63      ! [B5: set_Extended_enat,A3: set_Extended_enat,F: extended_enat > rat] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat @ B5 )
% 0.26/0.63       => ( ( ord_le7203529160286727270d_enat @ A3 @ B5 )
% 0.26/0.63         => ( ! [B4: extended_enat] :
% 0.26/0.63                ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ B5 @ A3 ) )
% 0.26/0.63               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B4 ) ) )
% 0.26/0.63           => ( ! [A5: extended_enat] :
% 0.26/0.63                  ( ( member_Extended_enat @ A5 @ A3 )
% 0.26/0.63                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A5 ) ) )
% 0.26/0.63             => ( ord_less_eq_rat @ ( groups2245840878043517529at_rat @ F @ A3 ) @ ( groups2245840878043517529at_rat @ F @ B5 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_mono2
% 0.26/0.63  thf(fact_8117_prod__mono2,axiom,
% 0.26/0.63      ! [B5: set_real,A3: set_real,F: real > int] :
% 0.26/0.63        ( ( finite_finite_real @ B5 )
% 0.26/0.63       => ( ( ord_less_eq_set_real @ A3 @ B5 )
% 0.26/0.63         => ( ! [B4: real] :
% 0.26/0.63                ( ( member_real @ B4 @ ( minus_minus_set_real @ B5 @ A3 ) )
% 0.26/0.63               => ( ord_less_eq_int @ one_one_int @ ( F @ B4 ) ) )
% 0.26/0.63           => ( ! [A5: real] :
% 0.26/0.63                  ( ( member_real @ A5 @ A3 )
% 0.26/0.63                 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A5 ) ) )
% 0.26/0.63             => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F @ A3 ) @ ( groups4694064378042380927al_int @ F @ B5 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_mono2
% 0.26/0.63  thf(fact_8118_prod__mono2,axiom,
% 0.26/0.63      ! [B5: set_complex,A3: set_complex,F: complex > int] :
% 0.26/0.63        ( ( finite3207457112153483333omplex @ B5 )
% 0.26/0.63       => ( ( ord_le211207098394363844omplex @ A3 @ B5 )
% 0.26/0.63         => ( ! [B4: complex] :
% 0.26/0.63                ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B5 @ A3 ) )
% 0.26/0.63               => ( ord_less_eq_int @ one_one_int @ ( F @ B4 ) ) )
% 0.26/0.63           => ( ! [A5: complex] :
% 0.26/0.63                  ( ( member_complex @ A5 @ A3 )
% 0.26/0.63                 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A5 ) ) )
% 0.26/0.63             => ( ord_less_eq_int @ ( groups858564598930262913ex_int @ F @ A3 ) @ ( groups858564598930262913ex_int @ F @ B5 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_mono2
% 0.26/0.63  thf(fact_8119_sum__natinterval__diff,axiom,
% 0.26/0.63      ! [M: nat,N: nat,F: nat > rat] :
% 0.26/0.63        ( ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.63         => ( ( groups2906978787729119204at_rat
% 0.26/0.63              @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.26/0.63              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.63            = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 0.26/0.63        & ( ~ ( ord_less_eq_nat @ M @ N )
% 0.26/0.63         => ( ( groups2906978787729119204at_rat
% 0.26/0.63              @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.26/0.63              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.63            = zero_zero_rat ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_natinterval_diff
% 0.26/0.63  thf(fact_8120_sum__natinterval__diff,axiom,
% 0.26/0.63      ! [M: nat,N: nat,F: nat > int] :
% 0.26/0.63        ( ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.63         => ( ( groups3539618377306564664at_int
% 0.26/0.63              @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.26/0.63              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.63            = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 0.26/0.63        & ( ~ ( ord_less_eq_nat @ M @ N )
% 0.26/0.63         => ( ( groups3539618377306564664at_int
% 0.26/0.63              @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.26/0.63              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.63            = zero_zero_int ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_natinterval_diff
% 0.26/0.63  thf(fact_8121_sum__natinterval__diff,axiom,
% 0.26/0.63      ! [M: nat,N: nat,F: nat > real] :
% 0.26/0.63        ( ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.63         => ( ( groups6591440286371151544t_real
% 0.26/0.63              @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.26/0.63              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.63            = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 0.26/0.63        & ( ~ ( ord_less_eq_nat @ M @ N )
% 0.26/0.63         => ( ( groups6591440286371151544t_real
% 0.26/0.63              @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.26/0.63              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.63            = zero_zero_real ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_natinterval_diff
% 0.26/0.63  thf(fact_8122_sum__telescope_H_H,axiom,
% 0.26/0.63      ! [M: nat,N: nat,F: nat > rat] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.63       => ( ( groups2906978787729119204at_rat
% 0.26/0.63            @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 0.26/0.63            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 0.26/0.63          = ( minus_minus_rat @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_telescope''
% 0.26/0.63  thf(fact_8123_sum__telescope_H_H,axiom,
% 0.26/0.63      ! [M: nat,N: nat,F: nat > int] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.63       => ( ( groups3539618377306564664at_int
% 0.26/0.63            @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 0.26/0.63            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 0.26/0.63          = ( minus_minus_int @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_telescope''
% 0.26/0.63  thf(fact_8124_sum__telescope_H_H,axiom,
% 0.26/0.63      ! [M: nat,N: nat,F: nat > real] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.63       => ( ( groups6591440286371151544t_real
% 0.26/0.63            @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 0.26/0.63            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 0.26/0.63          = ( minus_minus_real @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_telescope''
% 0.26/0.63  thf(fact_8125_prod__diff1,axiom,
% 0.26/0.63      ! [A3: set_complex,F: complex > complex,A: complex] :
% 0.26/0.63        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.63       => ( ( ( F @ A )
% 0.26/0.63           != zero_zero_complex )
% 0.26/0.63         => ( ( ( member_complex @ A @ A3 )
% 0.26/0.63             => ( ( groups3708469109370488835omplex @ F @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.26/0.63                = ( divide1717551699836669952omplex @ ( groups3708469109370488835omplex @ F @ A3 ) @ ( F @ A ) ) ) )
% 0.26/0.63            & ( ~ ( member_complex @ A @ A3 )
% 0.26/0.63             => ( ( groups3708469109370488835omplex @ F @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.26/0.63                = ( groups3708469109370488835omplex @ F @ A3 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_diff1
% 0.26/0.63  thf(fact_8126_prod__diff1,axiom,
% 0.26/0.63      ! [A3: set_Extended_enat,F: extended_enat > complex,A: extended_enat] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.63       => ( ( ( F @ A )
% 0.26/0.63           != zero_zero_complex )
% 0.26/0.63         => ( ( ( member_Extended_enat @ A @ A3 )
% 0.26/0.63             => ( ( groups4622424608036095791omplex @ F @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 0.26/0.63                = ( divide1717551699836669952omplex @ ( groups4622424608036095791omplex @ F @ A3 ) @ ( F @ A ) ) ) )
% 0.26/0.63            & ( ~ ( member_Extended_enat @ A @ A3 )
% 0.26/0.63             => ( ( groups4622424608036095791omplex @ F @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 0.26/0.63                = ( groups4622424608036095791omplex @ F @ A3 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_diff1
% 0.26/0.63  thf(fact_8127_prod__diff1,axiom,
% 0.26/0.63      ! [A3: set_real,F: real > complex,A: real] :
% 0.26/0.63        ( ( finite_finite_real @ A3 )
% 0.26/0.63       => ( ( ( F @ A )
% 0.26/0.63           != zero_zero_complex )
% 0.26/0.63         => ( ( ( member_real @ A @ A3 )
% 0.26/0.63             => ( ( groups713298508707869441omplex @ F @ ( minus_minus_set_real @ A3 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.26/0.63                = ( divide1717551699836669952omplex @ ( groups713298508707869441omplex @ F @ A3 ) @ ( F @ A ) ) ) )
% 0.26/0.63            & ( ~ ( member_real @ A @ A3 )
% 0.26/0.63             => ( ( groups713298508707869441omplex @ F @ ( minus_minus_set_real @ A3 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.26/0.63                = ( groups713298508707869441omplex @ F @ A3 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_diff1
% 0.26/0.63  thf(fact_8128_prod__diff1,axiom,
% 0.26/0.63      ! [A3: set_int,F: int > complex,A: int] :
% 0.26/0.63        ( ( finite_finite_int @ A3 )
% 0.26/0.63       => ( ( ( F @ A )
% 0.26/0.63           != zero_zero_complex )
% 0.26/0.63         => ( ( ( member_int @ A @ A3 )
% 0.26/0.63             => ( ( groups7440179247065528705omplex @ F @ ( minus_minus_set_int @ A3 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.26/0.63                = ( divide1717551699836669952omplex @ ( groups7440179247065528705omplex @ F @ A3 ) @ ( F @ A ) ) ) )
% 0.26/0.63            & ( ~ ( member_int @ A @ A3 )
% 0.26/0.63             => ( ( groups7440179247065528705omplex @ F @ ( minus_minus_set_int @ A3 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.26/0.63                = ( groups7440179247065528705omplex @ F @ A3 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_diff1
% 0.26/0.63  thf(fact_8129_prod__diff1,axiom,
% 0.26/0.63      ! [A3: set_nat,F: nat > complex,A: nat] :
% 0.26/0.63        ( ( finite_finite_nat @ A3 )
% 0.26/0.63       => ( ( ( F @ A )
% 0.26/0.63           != zero_zero_complex )
% 0.26/0.63         => ( ( ( member_nat @ A @ A3 )
% 0.26/0.63             => ( ( groups6464643781859351333omplex @ F @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.26/0.63                = ( divide1717551699836669952omplex @ ( groups6464643781859351333omplex @ F @ A3 ) @ ( F @ A ) ) ) )
% 0.26/0.63            & ( ~ ( member_nat @ A @ A3 )
% 0.26/0.63             => ( ( groups6464643781859351333omplex @ F @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.26/0.63                = ( groups6464643781859351333omplex @ F @ A3 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_diff1
% 0.26/0.63  thf(fact_8130_prod__diff1,axiom,
% 0.26/0.63      ! [A3: set_complex,F: complex > real,A: complex] :
% 0.26/0.63        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.63       => ( ( ( F @ A )
% 0.26/0.63           != zero_zero_real )
% 0.26/0.63         => ( ( ( member_complex @ A @ A3 )
% 0.26/0.63             => ( ( groups766887009212190081x_real @ F @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.26/0.63                = ( divide_divide_real @ ( groups766887009212190081x_real @ F @ A3 ) @ ( F @ A ) ) ) )
% 0.26/0.63            & ( ~ ( member_complex @ A @ A3 )
% 0.26/0.63             => ( ( groups766887009212190081x_real @ F @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.26/0.63                = ( groups766887009212190081x_real @ F @ A3 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_diff1
% 0.26/0.63  thf(fact_8131_prod__diff1,axiom,
% 0.26/0.63      ! [A3: set_Extended_enat,F: extended_enat > real,A: extended_enat] :
% 0.26/0.63        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.63       => ( ( ( F @ A )
% 0.26/0.63           != zero_zero_real )
% 0.26/0.63         => ( ( ( member_Extended_enat @ A @ A3 )
% 0.26/0.63             => ( ( groups97031904164794029t_real @ F @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 0.26/0.63                = ( divide_divide_real @ ( groups97031904164794029t_real @ F @ A3 ) @ ( F @ A ) ) ) )
% 0.26/0.63            & ( ~ ( member_Extended_enat @ A @ A3 )
% 0.26/0.63             => ( ( groups97031904164794029t_real @ F @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 0.26/0.63                = ( groups97031904164794029t_real @ F @ A3 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_diff1
% 0.26/0.63  thf(fact_8132_prod__diff1,axiom,
% 0.26/0.63      ! [A3: set_real,F: real > real,A: real] :
% 0.26/0.63        ( ( finite_finite_real @ A3 )
% 0.26/0.63       => ( ( ( F @ A )
% 0.26/0.63           != zero_zero_real )
% 0.26/0.63         => ( ( ( member_real @ A @ A3 )
% 0.26/0.63             => ( ( groups1681761925125756287l_real @ F @ ( minus_minus_set_real @ A3 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.26/0.63                = ( divide_divide_real @ ( groups1681761925125756287l_real @ F @ A3 ) @ ( F @ A ) ) ) )
% 0.26/0.63            & ( ~ ( member_real @ A @ A3 )
% 0.26/0.63             => ( ( groups1681761925125756287l_real @ F @ ( minus_minus_set_real @ A3 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.26/0.63                = ( groups1681761925125756287l_real @ F @ A3 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_diff1
% 0.26/0.63  thf(fact_8133_prod__diff1,axiom,
% 0.26/0.63      ! [A3: set_int,F: int > real,A: int] :
% 0.26/0.63        ( ( finite_finite_int @ A3 )
% 0.26/0.63       => ( ( ( F @ A )
% 0.26/0.63           != zero_zero_real )
% 0.26/0.63         => ( ( ( member_int @ A @ A3 )
% 0.26/0.63             => ( ( groups2316167850115554303t_real @ F @ ( minus_minus_set_int @ A3 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.26/0.63                = ( divide_divide_real @ ( groups2316167850115554303t_real @ F @ A3 ) @ ( F @ A ) ) ) )
% 0.26/0.63            & ( ~ ( member_int @ A @ A3 )
% 0.26/0.63             => ( ( groups2316167850115554303t_real @ F @ ( minus_minus_set_int @ A3 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.26/0.63                = ( groups2316167850115554303t_real @ F @ A3 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_diff1
% 0.26/0.63  thf(fact_8134_prod__diff1,axiom,
% 0.26/0.63      ! [A3: set_nat,F: nat > real,A: nat] :
% 0.26/0.63        ( ( finite_finite_nat @ A3 )
% 0.26/0.63       => ( ( ( F @ A )
% 0.26/0.63           != zero_zero_real )
% 0.26/0.63         => ( ( ( member_nat @ A @ A3 )
% 0.26/0.63             => ( ( groups129246275422532515t_real @ F @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.26/0.63                = ( divide_divide_real @ ( groups129246275422532515t_real @ F @ A3 ) @ ( F @ A ) ) ) )
% 0.26/0.63            & ( ~ ( member_nat @ A @ A3 )
% 0.26/0.63             => ( ( groups129246275422532515t_real @ F @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.26/0.63                = ( groups129246275422532515t_real @ F @ A3 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod_diff1
% 0.26/0.63  thf(fact_8135_summable__partial__sum__bound,axiom,
% 0.26/0.63      ! [F: nat > complex,E2: real] :
% 0.26/0.63        ( ( summable_complex @ F )
% 0.26/0.63       => ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.26/0.63         => ~ ! [N7: nat] :
% 0.26/0.63                ~ ! [M2: nat] :
% 0.26/0.63                    ( ( ord_less_eq_nat @ N7 @ M2 )
% 0.26/0.63                   => ! [N8: nat] : ( ord_less_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ M2 @ N8 ) ) ) @ E2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % summable_partial_sum_bound
% 0.26/0.63  thf(fact_8136_summable__partial__sum__bound,axiom,
% 0.26/0.63      ! [F: nat > real,E2: real] :
% 0.26/0.63        ( ( summable_real @ F )
% 0.26/0.63       => ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.26/0.63         => ~ ! [N7: nat] :
% 0.26/0.63                ~ ! [M2: nat] :
% 0.26/0.63                    ( ( ord_less_eq_nat @ N7 @ M2 )
% 0.26/0.63                   => ! [N8: nat] : ( ord_less_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ M2 @ N8 ) ) ) @ E2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % summable_partial_sum_bound
% 0.26/0.63  thf(fact_8137_mask__eq__sum__exp,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int )
% 0.26/0.63        = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.63          @ ( collect_nat
% 0.26/0.63            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % mask_eq_sum_exp
% 0.26/0.63  thf(fact_8138_mask__eq__sum__exp,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat )
% 0.26/0.63        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.63          @ ( collect_nat
% 0.26/0.63            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % mask_eq_sum_exp
% 0.26/0.63  thf(fact_8139_sum__gp__multiplied,axiom,
% 0.26/0.63      ! [M: nat,N: nat,X3: complex] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.63       => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X3 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 0.26/0.63          = ( minus_minus_complex @ ( power_power_complex @ X3 @ M ) @ ( power_power_complex @ X3 @ ( suc @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_gp_multiplied
% 0.26/0.63  thf(fact_8140_sum__gp__multiplied,axiom,
% 0.26/0.63      ! [M: nat,N: nat,X3: rat] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.63       => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X3 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 0.26/0.63          = ( minus_minus_rat @ ( power_power_rat @ X3 @ M ) @ ( power_power_rat @ X3 @ ( suc @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_gp_multiplied
% 0.26/0.63  thf(fact_8141_sum__gp__multiplied,axiom,
% 0.26/0.63      ! [M: nat,N: nat,X3: int] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.63       => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X3 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 0.26/0.63          = ( minus_minus_int @ ( power_power_int @ X3 @ M ) @ ( power_power_int @ X3 @ ( suc @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_gp_multiplied
% 0.26/0.63  thf(fact_8142_sum__gp__multiplied,axiom,
% 0.26/0.63      ! [M: nat,N: nat,X3: real] :
% 0.26/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.63       => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X3 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 0.26/0.63          = ( minus_minus_real @ ( power_power_real @ X3 @ M ) @ ( power_power_real @ X3 @ ( suc @ N ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_gp_multiplied
% 0.26/0.63  thf(fact_8143_sum_Oin__pairs,axiom,
% 0.26/0.63      ! [G: nat > rat,M: nat,N: nat] :
% 0.26/0.63        ( ( 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 ) ) ) )
% 0.26/0.63        = ( groups2906978787729119204at_rat
% 0.26/0.63          @ ^ [I4: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 0.26/0.63          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.in_pairs
% 0.26/0.63  thf(fact_8144_sum_Oin__pairs,axiom,
% 0.26/0.63      ! [G: nat > int,M: nat,N: nat] :
% 0.26/0.63        ( ( 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 ) ) ) )
% 0.26/0.63        = ( groups3539618377306564664at_int
% 0.26/0.63          @ ^ [I4: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 0.26/0.63          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.in_pairs
% 0.26/0.63  thf(fact_8145_sum_Oin__pairs,axiom,
% 0.26/0.63      ! [G: nat > nat,M: nat,N: nat] :
% 0.26/0.63        ( ( 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 ) ) ) )
% 0.26/0.63        = ( groups3542108847815614940at_nat
% 0.26/0.63          @ ^ [I4: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 0.26/0.63          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.in_pairs
% 0.26/0.63  thf(fact_8146_sum_Oin__pairs,axiom,
% 0.26/0.63      ! [G: nat > real,M: nat,N: nat] :
% 0.26/0.63        ( ( 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 ) ) ) )
% 0.26/0.63        = ( groups6591440286371151544t_real
% 0.26/0.63          @ ^ [I4: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 0.26/0.63          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.in_pairs
% 0.26/0.63  thf(fact_8147_complex__norm,axiom,
% 0.26/0.63      ! [X3: real,Y3: real] :
% 0.26/0.63        ( ( real_V1022390504157884413omplex @ ( complex2 @ X3 @ Y3 ) )
% 0.26/0.63        = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % complex_norm
% 0.26/0.63  thf(fact_8148_mask__eq__sum__exp__nat,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 0.26/0.63        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.63          @ ( collect_nat
% 0.26/0.63            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % mask_eq_sum_exp_nat
% 0.26/0.63  thf(fact_8149_gauss__sum__nat,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( groups3542108847815614940at_nat
% 0.26/0.63          @ ^ [X: nat] : X
% 0.26/0.63          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.26/0.63        = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % gauss_sum_nat
% 0.26/0.63  thf(fact_8150_double__arith__series,axiom,
% 0.26/0.63      ! [A: complex,D3: complex,N: nat] :
% 0.26/0.63        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 0.26/0.63          @ ( groups2073611262835488442omplex
% 0.26/0.63            @ ^ [I4: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I4 ) @ D3 ) )
% 0.26/0.63            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.26/0.63        = ( 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 ) @ D3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % double_arith_series
% 0.26/0.63  thf(fact_8151_double__arith__series,axiom,
% 0.26/0.63      ! [A: rat,D3: rat,N: nat] :
% 0.26/0.63        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 0.26/0.63          @ ( groups2906978787729119204at_rat
% 0.26/0.63            @ ^ [I4: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I4 ) @ D3 ) )
% 0.26/0.63            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.26/0.63        = ( 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 ) @ D3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % double_arith_series
% 0.26/0.63  thf(fact_8152_double__arith__series,axiom,
% 0.26/0.63      ! [A: int,D3: int,N: nat] :
% 0.26/0.63        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 0.26/0.63          @ ( groups3539618377306564664at_int
% 0.26/0.63            @ ^ [I4: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I4 ) @ D3 ) )
% 0.26/0.63            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.26/0.63        = ( 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 ) @ D3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % double_arith_series
% 0.26/0.63  thf(fact_8153_double__arith__series,axiom,
% 0.26/0.63      ! [A: nat,D3: nat,N: nat] :
% 0.26/0.63        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.26/0.63          @ ( groups3542108847815614940at_nat
% 0.26/0.63            @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I4 ) @ D3 ) )
% 0.26/0.63            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.26/0.63        = ( 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 ) @ D3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % double_arith_series
% 0.26/0.63  thf(fact_8154_double__arith__series,axiom,
% 0.26/0.63      ! [A: real,D3: real,N: nat] :
% 0.26/0.63        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 0.26/0.63          @ ( groups6591440286371151544t_real
% 0.26/0.63            @ ^ [I4: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I4 ) @ D3 ) )
% 0.26/0.63            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.26/0.63        = ( 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 ) @ D3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % double_arith_series
% 0.26/0.63  thf(fact_8155_double__gauss__sum,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.26/0.63        = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % double_gauss_sum
% 0.26/0.63  thf(fact_8156_double__gauss__sum,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.26/0.63        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % double_gauss_sum
% 0.26/0.63  thf(fact_8157_double__gauss__sum,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.26/0.63        = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % double_gauss_sum
% 0.26/0.63  thf(fact_8158_double__gauss__sum,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.26/0.63        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % double_gauss_sum
% 0.26/0.63  thf(fact_8159_double__gauss__sum,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.26/0.63        = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % double_gauss_sum
% 0.26/0.63  thf(fact_8160_arith__series__nat,axiom,
% 0.26/0.63      ! [A: nat,D3: nat,N: nat] :
% 0.26/0.63        ( ( groups3542108847815614940at_nat
% 0.26/0.63          @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I4 @ D3 ) )
% 0.26/0.63          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.26/0.63        = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N @ D3 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % arith_series_nat
% 0.26/0.63  thf(fact_8161_Sum__Icc__nat,axiom,
% 0.26/0.63      ! [M: nat,N: nat] :
% 0.26/0.63        ( ( groups3542108847815614940at_nat
% 0.26/0.63          @ ^ [X: nat] : X
% 0.26/0.63          @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.63        = ( 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 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % Sum_Icc_nat
% 0.26/0.63  thf(fact_8162_arcsin__lt__bounded,axiom,
% 0.26/0.63      ! [Y3: real] :
% 0.26/0.63        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 0.26/0.63       => ( ( ord_less_real @ Y3 @ one_one_real )
% 0.26/0.63         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) )
% 0.26/0.63            & ( ord_less_real @ ( arcsin @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % arcsin_lt_bounded
% 0.26/0.63  thf(fact_8163_arcsin__bounded,axiom,
% 0.26/0.63      ! [Y3: real] :
% 0.26/0.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 0.26/0.63       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 0.26/0.63         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) )
% 0.26/0.63            & ( ord_less_eq_real @ ( arcsin @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % arcsin_bounded
% 0.26/0.63  thf(fact_8164_arcsin__ubound,axiom,
% 0.26/0.63      ! [Y3: real] :
% 0.26/0.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 0.26/0.63       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 0.26/0.63         => ( ord_less_eq_real @ ( arcsin @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % arcsin_ubound
% 0.26/0.63  thf(fact_8165_arcsin__lbound,axiom,
% 0.26/0.63      ! [Y3: real] :
% 0.26/0.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 0.26/0.63       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 0.26/0.63         => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % arcsin_lbound
% 0.26/0.63  thf(fact_8166_arcsin__sin,axiom,
% 0.26/0.63      ! [X3: real] :
% 0.26/0.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.26/0.63       => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.63         => ( ( arcsin @ ( sin_real @ X3 ) )
% 0.26/0.63            = X3 ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % arcsin_sin
% 0.26/0.63  thf(fact_8167_double__gauss__sum__from__Suc__0,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.26/0.63        = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % double_gauss_sum_from_Suc_0
% 0.26/0.63  thf(fact_8168_double__gauss__sum__from__Suc__0,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.26/0.63        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % double_gauss_sum_from_Suc_0
% 0.26/0.63  thf(fact_8169_double__gauss__sum__from__Suc__0,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.26/0.63        = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % double_gauss_sum_from_Suc_0
% 0.26/0.63  thf(fact_8170_double__gauss__sum__from__Suc__0,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.26/0.63        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % double_gauss_sum_from_Suc_0
% 0.26/0.63  thf(fact_8171_double__gauss__sum__from__Suc__0,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.26/0.63        = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % double_gauss_sum_from_Suc_0
% 0.26/0.63  thf(fact_8172_gauss__sum,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.26/0.63        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % gauss_sum
% 0.26/0.63  thf(fact_8173_gauss__sum,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.26/0.63        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % gauss_sum
% 0.26/0.63  thf(fact_8174_arith__series,axiom,
% 0.26/0.63      ! [A: int,D3: int,N: nat] :
% 0.26/0.63        ( ( groups3539618377306564664at_int
% 0.26/0.63          @ ^ [I4: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I4 ) @ D3 ) )
% 0.26/0.63          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.26/0.63        = ( 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 ) @ D3 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % arith_series
% 0.26/0.63  thf(fact_8175_arith__series,axiom,
% 0.26/0.63      ! [A: nat,D3: nat,N: nat] :
% 0.26/0.63        ( ( groups3542108847815614940at_nat
% 0.26/0.63          @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I4 ) @ D3 ) )
% 0.26/0.63          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.26/0.63        = ( 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 ) @ D3 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % arith_series
% 0.26/0.63  thf(fact_8176_sum__gp__offset,axiom,
% 0.26/0.63      ! [X3: complex,M: nat,N: nat] :
% 0.26/0.63        ( ( ( X3 = one_one_complex )
% 0.26/0.63         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 0.26/0.63            = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) )
% 0.26/0.63        & ( ( X3 != one_one_complex )
% 0.26/0.63         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 0.26/0.63            = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X3 @ M ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ ( suc @ N ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_gp_offset
% 0.26/0.63  thf(fact_8177_sum__gp__offset,axiom,
% 0.26/0.63      ! [X3: rat,M: nat,N: nat] :
% 0.26/0.63        ( ( ( X3 = one_one_rat )
% 0.26/0.63         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 0.26/0.63            = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) )
% 0.26/0.63        & ( ( X3 != one_one_rat )
% 0.26/0.63         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 0.26/0.63            = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X3 @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ ( suc @ N ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_gp_offset
% 0.26/0.63  thf(fact_8178_sum__gp__offset,axiom,
% 0.26/0.63      ! [X3: real,M: nat,N: nat] :
% 0.26/0.63        ( ( ( X3 = one_one_real )
% 0.26/0.63         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 0.26/0.63            = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) )
% 0.26/0.63        & ( ( X3 != one_one_real )
% 0.26/0.63         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 0.26/0.63            = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X3 @ M ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( suc @ N ) ) ) ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_gp_offset
% 0.26/0.63  thf(fact_8179_arcsin,axiom,
% 0.26/0.63      ! [Y3: real] :
% 0.26/0.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 0.26/0.63       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 0.26/0.63         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) )
% 0.26/0.63            & ( ord_less_eq_real @ ( arcsin @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.63            & ( ( sin_real @ ( arcsin @ Y3 ) )
% 0.26/0.63              = Y3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % arcsin
% 0.26/0.63  thf(fact_8180_arcsin__pi,axiom,
% 0.26/0.63      ! [Y3: real] :
% 0.26/0.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 0.26/0.63       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 0.26/0.63         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) )
% 0.26/0.63            & ( ord_less_eq_real @ ( arcsin @ Y3 ) @ pi )
% 0.26/0.63            & ( ( sin_real @ ( arcsin @ Y3 ) )
% 0.26/0.63              = Y3 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % arcsin_pi
% 0.26/0.63  thf(fact_8181_arcsin__le__iff,axiom,
% 0.26/0.63      ! [X3: real,Y3: real] :
% 0.26/0.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.26/0.63       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 0.26/0.63         => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y3 )
% 0.26/0.63           => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.63             => ( ( ord_less_eq_real @ ( arcsin @ X3 ) @ Y3 )
% 0.26/0.63                = ( ord_less_eq_real @ X3 @ ( sin_real @ Y3 ) ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % arcsin_le_iff
% 0.26/0.63  thf(fact_8182_le__arcsin__iff,axiom,
% 0.26/0.63      ! [X3: real,Y3: real] :
% 0.26/0.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.26/0.63       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 0.26/0.63         => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y3 )
% 0.26/0.63           => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.63             => ( ( ord_less_eq_real @ Y3 @ ( arcsin @ X3 ) )
% 0.26/0.63                = ( ord_less_eq_real @ ( sin_real @ Y3 ) @ X3 ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % le_arcsin_iff
% 0.26/0.63  thf(fact_8183_gauss__sum__from__Suc__0,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.26/0.63        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % gauss_sum_from_Suc_0
% 0.26/0.63  thf(fact_8184_gauss__sum__from__Suc__0,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.26/0.63        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % gauss_sum_from_Suc_0
% 0.26/0.63  thf(fact_8185_finite__Collect__le__nat,axiom,
% 0.26/0.63      ! [K: nat] :
% 0.26/0.63        ( finite_finite_nat
% 0.26/0.63        @ ( collect_nat
% 0.26/0.63          @ ^ [N3: nat] : ( ord_less_eq_nat @ N3 @ K ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_Collect_le_nat
% 0.26/0.63  thf(fact_8186_finite__Collect__less__nat,axiom,
% 0.26/0.63      ! [K: nat] :
% 0.26/0.63        ( finite_finite_nat
% 0.26/0.63        @ ( collect_nat
% 0.26/0.63          @ ^ [N3: nat] : ( ord_less_nat @ N3 @ K ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_Collect_less_nat
% 0.26/0.63  thf(fact_8187_set__encode__insert,axiom,
% 0.26/0.63      ! [A3: set_nat,N: nat] :
% 0.26/0.63        ( ( finite_finite_nat @ A3 )
% 0.26/0.63       => ( ~ ( member_nat @ N @ A3 )
% 0.26/0.63         => ( ( nat_set_encode @ ( insert_nat @ N @ A3 ) )
% 0.26/0.63            = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A3 ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % set_encode_insert
% 0.26/0.63  thf(fact_8188_lemma__termdiff2,axiom,
% 0.26/0.63      ! [H2: complex,Z: complex,N: nat] :
% 0.26/0.63        ( ( H2 != zero_zero_complex )
% 0.26/0.63       => ( ( 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 ) ) ) ) )
% 0.26/0.63          = ( times_times_complex @ H2
% 0.26/0.63            @ ( groups2073611262835488442omplex
% 0.26/0.63              @ ^ [P5: nat] :
% 0.26/0.63                  ( groups2073611262835488442omplex
% 0.26/0.63                  @ ^ [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 ) ) )
% 0.26/0.63                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 0.26/0.63              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lemma_termdiff2
% 0.26/0.63  thf(fact_8189_lemma__termdiff2,axiom,
% 0.26/0.63      ! [H2: rat,Z: rat,N: nat] :
% 0.26/0.63        ( ( H2 != zero_zero_rat )
% 0.26/0.63       => ( ( 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 ) ) ) ) )
% 0.26/0.63          = ( times_times_rat @ H2
% 0.26/0.63            @ ( groups2906978787729119204at_rat
% 0.26/0.63              @ ^ [P5: nat] :
% 0.26/0.63                  ( groups2906978787729119204at_rat
% 0.26/0.63                  @ ^ [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 ) ) )
% 0.26/0.63                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 0.26/0.63              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lemma_termdiff2
% 0.26/0.63  thf(fact_8190_lemma__termdiff2,axiom,
% 0.26/0.63      ! [H2: real,Z: real,N: nat] :
% 0.26/0.63        ( ( H2 != zero_zero_real )
% 0.26/0.63       => ( ( 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 ) ) ) ) )
% 0.26/0.63          = ( times_times_real @ H2
% 0.26/0.63            @ ( groups6591440286371151544t_real
% 0.26/0.63              @ ^ [P5: nat] :
% 0.26/0.63                  ( groups6591440286371151544t_real
% 0.26/0.63                  @ ^ [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 ) ) )
% 0.26/0.63                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 0.26/0.63              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lemma_termdiff2
% 0.26/0.63  thf(fact_8191_choose__odd__sum,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.63       => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 0.26/0.63            @ ( groups2073611262835488442omplex
% 0.26/0.63              @ ^ [I4: nat] :
% 0.26/0.63                  ( if_complex
% 0.26/0.63                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 0.26/0.63                  @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I4 ) )
% 0.26/0.63                  @ zero_zero_complex )
% 0.26/0.63              @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.63          = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % choose_odd_sum
% 0.26/0.63  thf(fact_8192_choose__odd__sum,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.63       => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 0.26/0.63            @ ( groups2906978787729119204at_rat
% 0.26/0.63              @ ^ [I4: nat] :
% 0.26/0.63                  ( if_rat
% 0.26/0.63                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 0.26/0.63                  @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I4 ) )
% 0.26/0.63                  @ zero_zero_rat )
% 0.26/0.63              @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.63          = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % choose_odd_sum
% 0.26/0.63  thf(fact_8193_choose__odd__sum,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.63       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 0.26/0.63            @ ( groups3539618377306564664at_int
% 0.26/0.63              @ ^ [I4: nat] :
% 0.26/0.63                  ( if_int
% 0.26/0.63                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 0.26/0.63                  @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I4 ) )
% 0.26/0.63                  @ zero_zero_int )
% 0.26/0.63              @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.63          = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % choose_odd_sum
% 0.26/0.63  thf(fact_8194_choose__odd__sum,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.63       => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 0.26/0.63            @ ( groups6591440286371151544t_real
% 0.26/0.63              @ ^ [I4: nat] :
% 0.26/0.63                  ( if_real
% 0.26/0.63                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 0.26/0.63                  @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I4 ) )
% 0.26/0.63                  @ zero_zero_real )
% 0.26/0.63              @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.63          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % choose_odd_sum
% 0.26/0.63  thf(fact_8195_finite__interval__int1,axiom,
% 0.26/0.63      ! [A: int,B: int] :
% 0.26/0.63        ( finite_finite_int
% 0.26/0.63        @ ( collect_int
% 0.26/0.63          @ ^ [I4: int] :
% 0.26/0.63              ( ( ord_less_eq_int @ A @ I4 )
% 0.26/0.63              & ( ord_less_eq_int @ I4 @ B ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_interval_int1
% 0.26/0.63  thf(fact_8196_finite__interval__int4,axiom,
% 0.26/0.63      ! [A: int,B: int] :
% 0.26/0.63        ( finite_finite_int
% 0.26/0.63        @ ( collect_int
% 0.26/0.63          @ ^ [I4: int] :
% 0.26/0.63              ( ( ord_less_int @ A @ I4 )
% 0.26/0.63              & ( ord_less_int @ I4 @ B ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_interval_int4
% 0.26/0.63  thf(fact_8197_lessThan__iff,axiom,
% 0.26/0.63      ! [I: set_nat,K: set_nat] :
% 0.26/0.63        ( ( member_set_nat @ I @ ( set_or890127255671739683et_nat @ K ) )
% 0.26/0.63        = ( ord_less_set_nat @ I @ K ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_iff
% 0.26/0.63  thf(fact_8198_lessThan__iff,axiom,
% 0.26/0.63      ! [I: rat,K: rat] :
% 0.26/0.63        ( ( member_rat @ I @ ( set_ord_lessThan_rat @ K ) )
% 0.26/0.63        = ( ord_less_rat @ I @ K ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_iff
% 0.26/0.63  thf(fact_8199_lessThan__iff,axiom,
% 0.26/0.63      ! [I: num,K: num] :
% 0.26/0.63        ( ( member_num @ I @ ( set_ord_lessThan_num @ K ) )
% 0.26/0.63        = ( ord_less_num @ I @ K ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_iff
% 0.26/0.63  thf(fact_8200_lessThan__iff,axiom,
% 0.26/0.63      ! [I: int,K: int] :
% 0.26/0.63        ( ( member_int @ I @ ( set_ord_lessThan_int @ K ) )
% 0.26/0.63        = ( ord_less_int @ I @ K ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_iff
% 0.26/0.63  thf(fact_8201_lessThan__iff,axiom,
% 0.26/0.63      ! [I: nat,K: nat] :
% 0.26/0.63        ( ( member_nat @ I @ ( set_ord_lessThan_nat @ K ) )
% 0.26/0.63        = ( ord_less_nat @ I @ K ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_iff
% 0.26/0.63  thf(fact_8202_lessThan__iff,axiom,
% 0.26/0.63      ! [I: real,K: real] :
% 0.26/0.63        ( ( member_real @ I @ ( set_or5984915006950818249n_real @ K ) )
% 0.26/0.63        = ( ord_less_real @ I @ K ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_iff
% 0.26/0.63  thf(fact_8203_atMost__iff,axiom,
% 0.26/0.63      ! [I: real,K: real] :
% 0.26/0.63        ( ( member_real @ I @ ( set_ord_atMost_real @ K ) )
% 0.26/0.63        = ( ord_less_eq_real @ I @ K ) ) ).
% 0.26/0.63  
% 0.26/0.63  % atMost_iff
% 0.26/0.63  thf(fact_8204_atMost__iff,axiom,
% 0.26/0.63      ! [I: set_nat,K: set_nat] :
% 0.26/0.63        ( ( member_set_nat @ I @ ( set_or4236626031148496127et_nat @ K ) )
% 0.26/0.63        = ( ord_less_eq_set_nat @ I @ K ) ) ).
% 0.26/0.63  
% 0.26/0.63  % atMost_iff
% 0.26/0.63  thf(fact_8205_atMost__iff,axiom,
% 0.26/0.63      ! [I: rat,K: rat] :
% 0.26/0.63        ( ( member_rat @ I @ ( set_ord_atMost_rat @ K ) )
% 0.26/0.63        = ( ord_less_eq_rat @ I @ K ) ) ).
% 0.26/0.63  
% 0.26/0.63  % atMost_iff
% 0.26/0.63  thf(fact_8206_atMost__iff,axiom,
% 0.26/0.63      ! [I: num,K: num] :
% 0.26/0.63        ( ( member_num @ I @ ( set_ord_atMost_num @ K ) )
% 0.26/0.63        = ( ord_less_eq_num @ I @ K ) ) ).
% 0.26/0.63  
% 0.26/0.63  % atMost_iff
% 0.26/0.63  thf(fact_8207_atMost__iff,axiom,
% 0.26/0.63      ! [I: int,K: int] :
% 0.26/0.63        ( ( member_int @ I @ ( set_ord_atMost_int @ K ) )
% 0.26/0.63        = ( ord_less_eq_int @ I @ K ) ) ).
% 0.26/0.63  
% 0.26/0.63  % atMost_iff
% 0.26/0.63  thf(fact_8208_atMost__iff,axiom,
% 0.26/0.63      ! [I: nat,K: nat] :
% 0.26/0.63        ( ( member_nat @ I @ ( set_ord_atMost_nat @ K ) )
% 0.26/0.63        = ( ord_less_eq_nat @ I @ K ) ) ).
% 0.26/0.63  
% 0.26/0.63  % atMost_iff
% 0.26/0.63  thf(fact_8209_finite__nth__roots,axiom,
% 0.26/0.63      ! [N: nat,C: complex] :
% 0.26/0.63        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.63       => ( finite3207457112153483333omplex
% 0.26/0.63          @ ( collect_complex
% 0.26/0.63            @ ^ [Z6: complex] :
% 0.26/0.63                ( ( power_power_complex @ Z6 @ N )
% 0.26/0.63                = C ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_nth_roots
% 0.26/0.63  thf(fact_8210_finite__interval__int2,axiom,
% 0.26/0.63      ! [A: int,B: int] :
% 0.26/0.63        ( finite_finite_int
% 0.26/0.63        @ ( collect_int
% 0.26/0.63          @ ^ [I4: int] :
% 0.26/0.63              ( ( ord_less_eq_int @ A @ I4 )
% 0.26/0.63              & ( ord_less_int @ I4 @ B ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_interval_int2
% 0.26/0.63  thf(fact_8211_finite__interval__int3,axiom,
% 0.26/0.63      ! [A: int,B: int] :
% 0.26/0.63        ( finite_finite_int
% 0.26/0.63        @ ( collect_int
% 0.26/0.63          @ ^ [I4: int] :
% 0.26/0.63              ( ( ord_less_int @ A @ I4 )
% 0.26/0.63              & ( ord_less_eq_int @ I4 @ B ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_interval_int3
% 0.26/0.63  thf(fact_8212_lessThan__subset__iff,axiom,
% 0.26/0.63      ! [X3: rat,Y3: rat] :
% 0.26/0.63        ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X3 ) @ ( set_ord_lessThan_rat @ Y3 ) )
% 0.26/0.63        = ( ord_less_eq_rat @ X3 @ Y3 ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_subset_iff
% 0.26/0.63  thf(fact_8213_lessThan__subset__iff,axiom,
% 0.26/0.63      ! [X3: num,Y3: num] :
% 0.26/0.63        ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X3 ) @ ( set_ord_lessThan_num @ Y3 ) )
% 0.26/0.63        = ( ord_less_eq_num @ X3 @ Y3 ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_subset_iff
% 0.26/0.63  thf(fact_8214_lessThan__subset__iff,axiom,
% 0.26/0.63      ! [X3: int,Y3: int] :
% 0.26/0.63        ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X3 ) @ ( set_ord_lessThan_int @ Y3 ) )
% 0.26/0.63        = ( ord_less_eq_int @ X3 @ Y3 ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_subset_iff
% 0.26/0.63  thf(fact_8215_lessThan__subset__iff,axiom,
% 0.26/0.63      ! [X3: nat,Y3: nat] :
% 0.26/0.63        ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X3 ) @ ( set_ord_lessThan_nat @ Y3 ) )
% 0.26/0.63        = ( ord_less_eq_nat @ X3 @ Y3 ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_subset_iff
% 0.26/0.63  thf(fact_8216_lessThan__subset__iff,axiom,
% 0.26/0.63      ! [X3: real,Y3: real] :
% 0.26/0.63        ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X3 ) @ ( set_or5984915006950818249n_real @ Y3 ) )
% 0.26/0.63        = ( ord_less_eq_real @ X3 @ Y3 ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_subset_iff
% 0.26/0.63  thf(fact_8217_atMost__subset__iff,axiom,
% 0.26/0.63      ! [X3: set_nat,Y3: set_nat] :
% 0.26/0.63        ( ( ord_le6893508408891458716et_nat @ ( set_or4236626031148496127et_nat @ X3 ) @ ( set_or4236626031148496127et_nat @ Y3 ) )
% 0.26/0.63        = ( ord_less_eq_set_nat @ X3 @ Y3 ) ) ).
% 0.26/0.63  
% 0.26/0.63  % atMost_subset_iff
% 0.26/0.63  thf(fact_8218_atMost__subset__iff,axiom,
% 0.26/0.63      ! [X3: rat,Y3: rat] :
% 0.26/0.63        ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X3 ) @ ( set_ord_atMost_rat @ Y3 ) )
% 0.26/0.63        = ( ord_less_eq_rat @ X3 @ Y3 ) ) ).
% 0.26/0.63  
% 0.26/0.63  % atMost_subset_iff
% 0.26/0.63  thf(fact_8219_atMost__subset__iff,axiom,
% 0.26/0.63      ! [X3: num,Y3: num] :
% 0.26/0.63        ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X3 ) @ ( set_ord_atMost_num @ Y3 ) )
% 0.26/0.63        = ( ord_less_eq_num @ X3 @ Y3 ) ) ).
% 0.26/0.63  
% 0.26/0.63  % atMost_subset_iff
% 0.26/0.63  thf(fact_8220_atMost__subset__iff,axiom,
% 0.26/0.63      ! [X3: int,Y3: int] :
% 0.26/0.63        ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X3 ) @ ( set_ord_atMost_int @ Y3 ) )
% 0.26/0.63        = ( ord_less_eq_int @ X3 @ Y3 ) ) ).
% 0.26/0.63  
% 0.26/0.63  % atMost_subset_iff
% 0.26/0.63  thf(fact_8221_atMost__subset__iff,axiom,
% 0.26/0.63      ! [X3: nat,Y3: nat] :
% 0.26/0.63        ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X3 ) @ ( set_ord_atMost_nat @ Y3 ) )
% 0.26/0.63        = ( ord_less_eq_nat @ X3 @ Y3 ) ) ).
% 0.26/0.63  
% 0.26/0.63  % atMost_subset_iff
% 0.26/0.63  thf(fact_8222_lessThan__0,axiom,
% 0.26/0.63      ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 0.26/0.63      = bot_bot_set_nat ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_0
% 0.26/0.63  thf(fact_8223_set__encode__empty,axiom,
% 0.26/0.63      ( ( nat_set_encode @ bot_bot_set_nat )
% 0.26/0.63      = zero_zero_nat ) ).
% 0.26/0.63  
% 0.26/0.63  % set_encode_empty
% 0.26/0.63  thf(fact_8224_Icc__subset__Iic__iff,axiom,
% 0.26/0.63      ! [L: set_nat,H2: set_nat,H3: set_nat] :
% 0.26/0.63        ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ L @ H2 ) @ ( set_or4236626031148496127et_nat @ H3 ) )
% 0.26/0.63        = ( ~ ( ord_less_eq_set_nat @ L @ H2 )
% 0.26/0.63          | ( ord_less_eq_set_nat @ H2 @ H3 ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % Icc_subset_Iic_iff
% 0.26/0.63  thf(fact_8225_Icc__subset__Iic__iff,axiom,
% 0.26/0.63      ! [L: rat,H2: rat,H3: rat] :
% 0.26/0.63        ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L @ H2 ) @ ( set_ord_atMost_rat @ H3 ) )
% 0.26/0.63        = ( ~ ( ord_less_eq_rat @ L @ H2 )
% 0.26/0.63          | ( ord_less_eq_rat @ H2 @ H3 ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % Icc_subset_Iic_iff
% 0.26/0.63  thf(fact_8226_Icc__subset__Iic__iff,axiom,
% 0.26/0.63      ! [L: num,H2: num,H3: num] :
% 0.26/0.63        ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L @ H2 ) @ ( set_ord_atMost_num @ H3 ) )
% 0.26/0.63        = ( ~ ( ord_less_eq_num @ L @ H2 )
% 0.26/0.63          | ( ord_less_eq_num @ H2 @ H3 ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % Icc_subset_Iic_iff
% 0.26/0.63  thf(fact_8227_Icc__subset__Iic__iff,axiom,
% 0.26/0.63      ! [L: nat,H2: nat,H3: nat] :
% 0.26/0.63        ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L @ H2 ) @ ( set_ord_atMost_nat @ H3 ) )
% 0.26/0.63        = ( ~ ( ord_less_eq_nat @ L @ H2 )
% 0.26/0.63          | ( ord_less_eq_nat @ H2 @ H3 ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % Icc_subset_Iic_iff
% 0.26/0.63  thf(fact_8228_Icc__subset__Iic__iff,axiom,
% 0.26/0.63      ! [L: int,H2: int,H3: int] :
% 0.26/0.63        ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L @ H2 ) @ ( set_ord_atMost_int @ H3 ) )
% 0.26/0.63        = ( ~ ( ord_less_eq_int @ L @ H2 )
% 0.26/0.63          | ( ord_less_eq_int @ H2 @ H3 ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % Icc_subset_Iic_iff
% 0.26/0.63  thf(fact_8229_Icc__subset__Iic__iff,axiom,
% 0.26/0.63      ! [L: real,H2: real,H3: real] :
% 0.26/0.63        ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ L @ H2 ) @ ( set_ord_atMost_real @ H3 ) )
% 0.26/0.63        = ( ~ ( ord_less_eq_real @ L @ H2 )
% 0.26/0.63          | ( ord_less_eq_real @ H2 @ H3 ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % Icc_subset_Iic_iff
% 0.26/0.63  thf(fact_8230_atMost__0,axiom,
% 0.26/0.63      ( ( set_ord_atMost_nat @ zero_zero_nat )
% 0.26/0.63      = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 0.26/0.63  
% 0.26/0.63  % atMost_0
% 0.26/0.63  thf(fact_8231_int__sum,axiom,
% 0.26/0.63      ! [F: int > nat,A3: set_int] :
% 0.26/0.63        ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A3 ) )
% 0.26/0.63        = ( groups4538972089207619220nt_int
% 0.26/0.63          @ ^ [X: int] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 0.26/0.63          @ A3 ) ) ).
% 0.26/0.63  
% 0.26/0.63  % int_sum
% 0.26/0.63  thf(fact_8232_int__sum,axiom,
% 0.26/0.63      ! [F: nat > nat,A3: set_nat] :
% 0.26/0.63        ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 0.26/0.63        = ( groups3539618377306564664at_int
% 0.26/0.63          @ ^ [X: nat] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 0.26/0.63          @ A3 ) ) ).
% 0.26/0.63  
% 0.26/0.63  % int_sum
% 0.26/0.63  thf(fact_8233_Complex__sum_H,axiom,
% 0.26/0.63      ! [F: nat > real,S: set_nat] :
% 0.26/0.63        ( ( groups2073611262835488442omplex
% 0.26/0.63          @ ^ [X: nat] : ( complex2 @ ( F @ X ) @ zero_zero_real )
% 0.26/0.63          @ S )
% 0.26/0.63        = ( complex2 @ ( groups6591440286371151544t_real @ F @ S ) @ zero_zero_real ) ) ).
% 0.26/0.63  
% 0.26/0.63  % Complex_sum'
% 0.26/0.63  thf(fact_8234_Complex__sum_H,axiom,
% 0.26/0.63      ! [F: complex > real,S: set_complex] :
% 0.26/0.63        ( ( groups7754918857620584856omplex
% 0.26/0.63          @ ^ [X: complex] : ( complex2 @ ( F @ X ) @ zero_zero_real )
% 0.26/0.63          @ S )
% 0.26/0.63        = ( complex2 @ ( groups5808333547571424918x_real @ F @ S ) @ zero_zero_real ) ) ).
% 0.26/0.63  
% 0.26/0.63  % Complex_sum'
% 0.26/0.63  thf(fact_8235_sum__diff__distrib,axiom,
% 0.26/0.63      ! [Q: real > nat,P: real > nat,N: real] :
% 0.26/0.63        ( ! [X4: real] : ( ord_less_eq_nat @ ( Q @ X4 ) @ ( P @ X4 ) )
% 0.26/0.63       => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N ) ) )
% 0.26/0.63          = ( groups1935376822645274424al_nat
% 0.26/0.63            @ ^ [X: real] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 0.26/0.63            @ ( set_or5984915006950818249n_real @ N ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_diff_distrib
% 0.26/0.63  thf(fact_8236_sum__diff__distrib,axiom,
% 0.26/0.63      ! [Q: nat > nat,P: nat > nat,N: nat] :
% 0.26/0.63        ( ! [X4: nat] : ( ord_less_eq_nat @ ( Q @ X4 ) @ ( P @ X4 ) )
% 0.26/0.63       => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N ) ) )
% 0.26/0.63          = ( groups3542108847815614940at_nat
% 0.26/0.63            @ ^ [X: nat] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 0.26/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_diff_distrib
% 0.26/0.63  thf(fact_8237_Iic__subset__Iio__iff,axiom,
% 0.26/0.63      ! [A: rat,B: rat] :
% 0.26/0.63        ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ A ) @ ( set_ord_lessThan_rat @ B ) )
% 0.26/0.63        = ( ord_less_rat @ A @ B ) ) ).
% 0.26/0.63  
% 0.26/0.63  % Iic_subset_Iio_iff
% 0.26/0.63  thf(fact_8238_Iic__subset__Iio__iff,axiom,
% 0.26/0.63      ! [A: num,B: num] :
% 0.26/0.63        ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A ) @ ( set_ord_lessThan_num @ B ) )
% 0.26/0.63        = ( ord_less_num @ A @ B ) ) ).
% 0.26/0.63  
% 0.26/0.63  % Iic_subset_Iio_iff
% 0.26/0.63  thf(fact_8239_Iic__subset__Iio__iff,axiom,
% 0.26/0.63      ! [A: int,B: int] :
% 0.26/0.63        ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B ) )
% 0.26/0.63        = ( ord_less_int @ A @ B ) ) ).
% 0.26/0.63  
% 0.26/0.63  % Iic_subset_Iio_iff
% 0.26/0.63  thf(fact_8240_Iic__subset__Iio__iff,axiom,
% 0.26/0.63      ! [A: nat,B: nat] :
% 0.26/0.63        ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B ) )
% 0.26/0.63        = ( ord_less_nat @ A @ B ) ) ).
% 0.26/0.63  
% 0.26/0.63  % Iic_subset_Iio_iff
% 0.26/0.63  thf(fact_8241_Iic__subset__Iio__iff,axiom,
% 0.26/0.63      ! [A: real,B: real] :
% 0.26/0.63        ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ A ) @ ( set_or5984915006950818249n_real @ B ) )
% 0.26/0.63        = ( ord_less_real @ A @ B ) ) ).
% 0.26/0.63  
% 0.26/0.63  % Iic_subset_Iio_iff
% 0.26/0.63  thf(fact_8242_lessThan__def,axiom,
% 0.26/0.63      ( set_or890127255671739683et_nat
% 0.26/0.63      = ( ^ [U2: set_nat] :
% 0.26/0.63            ( collect_set_nat
% 0.26/0.63            @ ^ [X: set_nat] : ( ord_less_set_nat @ X @ U2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_def
% 0.26/0.63  thf(fact_8243_lessThan__def,axiom,
% 0.26/0.63      ( set_ord_lessThan_rat
% 0.26/0.63      = ( ^ [U2: rat] :
% 0.26/0.63            ( collect_rat
% 0.26/0.63            @ ^ [X: rat] : ( ord_less_rat @ X @ U2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_def
% 0.26/0.63  thf(fact_8244_lessThan__def,axiom,
% 0.26/0.63      ( set_ord_lessThan_num
% 0.26/0.63      = ( ^ [U2: num] :
% 0.26/0.63            ( collect_num
% 0.26/0.63            @ ^ [X: num] : ( ord_less_num @ X @ U2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_def
% 0.26/0.63  thf(fact_8245_lessThan__def,axiom,
% 0.26/0.63      ( set_ord_lessThan_int
% 0.26/0.63      = ( ^ [U2: int] :
% 0.26/0.63            ( collect_int
% 0.26/0.63            @ ^ [X: int] : ( ord_less_int @ X @ U2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_def
% 0.26/0.63  thf(fact_8246_lessThan__def,axiom,
% 0.26/0.63      ( set_ord_lessThan_nat
% 0.26/0.63      = ( ^ [U2: nat] :
% 0.26/0.63            ( collect_nat
% 0.26/0.63            @ ^ [X: nat] : ( ord_less_nat @ X @ U2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_def
% 0.26/0.63  thf(fact_8247_lessThan__def,axiom,
% 0.26/0.63      ( set_or5984915006950818249n_real
% 0.26/0.63      = ( ^ [U2: real] :
% 0.26/0.63            ( collect_real
% 0.26/0.63            @ ^ [X: real] : ( ord_less_real @ X @ U2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_def
% 0.26/0.63  thf(fact_8248_atMost__def,axiom,
% 0.26/0.63      ( set_ord_atMost_real
% 0.26/0.63      = ( ^ [U2: real] :
% 0.26/0.63            ( collect_real
% 0.26/0.63            @ ^ [X: real] : ( ord_less_eq_real @ X @ U2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % atMost_def
% 0.26/0.63  thf(fact_8249_atMost__def,axiom,
% 0.26/0.63      ( set_or4236626031148496127et_nat
% 0.26/0.63      = ( ^ [U2: set_nat] :
% 0.26/0.63            ( collect_set_nat
% 0.26/0.63            @ ^ [X: set_nat] : ( ord_less_eq_set_nat @ X @ U2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % atMost_def
% 0.26/0.63  thf(fact_8250_atMost__def,axiom,
% 0.26/0.63      ( set_ord_atMost_rat
% 0.26/0.63      = ( ^ [U2: rat] :
% 0.26/0.63            ( collect_rat
% 0.26/0.63            @ ^ [X: rat] : ( ord_less_eq_rat @ X @ U2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % atMost_def
% 0.26/0.63  thf(fact_8251_atMost__def,axiom,
% 0.26/0.63      ( set_ord_atMost_num
% 0.26/0.63      = ( ^ [U2: num] :
% 0.26/0.63            ( collect_num
% 0.26/0.63            @ ^ [X: num] : ( ord_less_eq_num @ X @ U2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % atMost_def
% 0.26/0.63  thf(fact_8252_atMost__def,axiom,
% 0.26/0.63      ( set_ord_atMost_int
% 0.26/0.63      = ( ^ [U2: int] :
% 0.26/0.63            ( collect_int
% 0.26/0.63            @ ^ [X: int] : ( ord_less_eq_int @ X @ U2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % atMost_def
% 0.26/0.63  thf(fact_8253_atMost__def,axiom,
% 0.26/0.63      ( set_ord_atMost_nat
% 0.26/0.63      = ( ^ [U2: nat] :
% 0.26/0.63            ( collect_nat
% 0.26/0.63            @ ^ [X: nat] : ( ord_less_eq_nat @ X @ U2 ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % atMost_def
% 0.26/0.63  thf(fact_8254_sum_OatMost__shift,axiom,
% 0.26/0.63      ! [G: nat > rat,N: nat] :
% 0.26/0.63        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.63        = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 0.26/0.63          @ ( groups2906978787729119204at_rat
% 0.26/0.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.atMost_shift
% 0.26/0.63  thf(fact_8255_sum_OatMost__shift,axiom,
% 0.26/0.63      ! [G: nat > int,N: nat] :
% 0.26/0.63        ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.63        = ( plus_plus_int @ ( G @ zero_zero_nat )
% 0.26/0.63          @ ( groups3539618377306564664at_int
% 0.26/0.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.atMost_shift
% 0.26/0.63  thf(fact_8256_sum_OatMost__shift,axiom,
% 0.26/0.63      ! [G: nat > nat,N: nat] :
% 0.26/0.63        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.63        = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 0.26/0.63          @ ( groups3542108847815614940at_nat
% 0.26/0.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.atMost_shift
% 0.26/0.63  thf(fact_8257_sum_OatMost__shift,axiom,
% 0.26/0.63      ! [G: nat > real,N: nat] :
% 0.26/0.63        ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.63        = ( plus_plus_real @ ( G @ zero_zero_nat )
% 0.26/0.63          @ ( groups6591440286371151544t_real
% 0.26/0.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum.atMost_shift
% 0.26/0.63  thf(fact_8258_prod_OatMost__shift,axiom,
% 0.26/0.63      ! [G: nat > real,N: nat] :
% 0.26/0.63        ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.63        = ( times_times_real @ ( G @ zero_zero_nat )
% 0.26/0.63          @ ( groups129246275422532515t_real
% 0.26/0.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod.atMost_shift
% 0.26/0.63  thf(fact_8259_prod_OatMost__shift,axiom,
% 0.26/0.63      ! [G: nat > rat,N: nat] :
% 0.26/0.63        ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.63        = ( times_times_rat @ ( G @ zero_zero_nat )
% 0.26/0.63          @ ( groups73079841787564623at_rat
% 0.26/0.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod.atMost_shift
% 0.26/0.63  thf(fact_8260_prod_OatMost__shift,axiom,
% 0.26/0.63      ! [G: nat > int,N: nat] :
% 0.26/0.63        ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.63        = ( times_times_int @ ( G @ zero_zero_nat )
% 0.26/0.63          @ ( groups705719431365010083at_int
% 0.26/0.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod.atMost_shift
% 0.26/0.63  thf(fact_8261_prod_OatMost__shift,axiom,
% 0.26/0.63      ! [G: nat > nat,N: nat] :
% 0.26/0.63        ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.63        = ( times_times_nat @ ( G @ zero_zero_nat )
% 0.26/0.63          @ ( groups708209901874060359at_nat
% 0.26/0.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % prod.atMost_shift
% 0.26/0.63  thf(fact_8262_atMost__atLeast0,axiom,
% 0.26/0.63      ( set_ord_atMost_nat
% 0.26/0.63      = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 0.26/0.63  
% 0.26/0.63  % atMost_atLeast0
% 0.26/0.63  thf(fact_8263_lessThan__strict__subset__iff,axiom,
% 0.26/0.63      ! [M: rat,N: rat] :
% 0.26/0.63        ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N ) )
% 0.26/0.63        = ( ord_less_rat @ M @ N ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_strict_subset_iff
% 0.26/0.63  thf(fact_8264_lessThan__strict__subset__iff,axiom,
% 0.26/0.63      ! [M: num,N: num] :
% 0.26/0.63        ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N ) )
% 0.26/0.63        = ( ord_less_num @ M @ N ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_strict_subset_iff
% 0.26/0.63  thf(fact_8265_lessThan__strict__subset__iff,axiom,
% 0.26/0.63      ! [M: int,N: int] :
% 0.26/0.63        ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N ) )
% 0.26/0.63        = ( ord_less_int @ M @ N ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_strict_subset_iff
% 0.26/0.63  thf(fact_8266_lessThan__strict__subset__iff,axiom,
% 0.26/0.63      ! [M: nat,N: nat] :
% 0.26/0.63        ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.63        = ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_strict_subset_iff
% 0.26/0.63  thf(fact_8267_lessThan__strict__subset__iff,axiom,
% 0.26/0.63      ! [M: real,N: real] :
% 0.26/0.63        ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N ) )
% 0.26/0.63        = ( ord_less_real @ M @ N ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_strict_subset_iff
% 0.26/0.63  thf(fact_8268_finite__maxlen,axiom,
% 0.26/0.63      ! [M7: set_list_VEBT_VEBT] :
% 0.26/0.63        ( ( finite3004134309566078307T_VEBT @ M7 )
% 0.26/0.63       => ? [N2: nat] :
% 0.26/0.63          ! [X6: list_VEBT_VEBT] :
% 0.26/0.63            ( ( member2936631157270082147T_VEBT @ X6 @ M7 )
% 0.26/0.63           => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X6 ) @ N2 ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_maxlen
% 0.26/0.63  thf(fact_8269_finite__maxlen,axiom,
% 0.26/0.63      ! [M7: set_list_o] :
% 0.26/0.63        ( ( finite_finite_list_o @ M7 )
% 0.26/0.63       => ? [N2: nat] :
% 0.26/0.63          ! [X6: list_o] :
% 0.26/0.63            ( ( member_list_o @ X6 @ M7 )
% 0.26/0.63           => ( ord_less_nat @ ( size_size_list_o @ X6 ) @ N2 ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_maxlen
% 0.26/0.63  thf(fact_8270_finite__maxlen,axiom,
% 0.26/0.63      ! [M7: set_list_nat] :
% 0.26/0.63        ( ( finite8100373058378681591st_nat @ M7 )
% 0.26/0.63       => ? [N2: nat] :
% 0.26/0.63          ! [X6: list_nat] :
% 0.26/0.63            ( ( member_list_nat @ X6 @ M7 )
% 0.26/0.63           => ( ord_less_nat @ ( size_size_list_nat @ X6 ) @ N2 ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_maxlen
% 0.26/0.63  thf(fact_8271_finite__maxlen,axiom,
% 0.26/0.63      ! [M7: set_list_int] :
% 0.26/0.63        ( ( finite3922522038869484883st_int @ M7 )
% 0.26/0.63       => ? [N2: nat] :
% 0.26/0.63          ! [X6: list_int] :
% 0.26/0.63            ( ( member_list_int @ X6 @ M7 )
% 0.26/0.63           => ( ord_less_nat @ ( size_size_list_int @ X6 ) @ N2 ) ) ) ).
% 0.26/0.63  
% 0.26/0.63  % finite_maxlen
% 0.26/0.63  thf(fact_8272_lessThan__empty__iff,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( ( set_ord_lessThan_nat @ N )
% 0.26/0.63          = bot_bot_set_nat )
% 0.26/0.63        = ( N = zero_zero_nat ) ) ).
% 0.26/0.63  
% 0.26/0.63  % lessThan_empty_iff
% 0.26/0.63  thf(fact_8273_sum__roots__unity,axiom,
% 0.26/0.63      ! [N: nat] :
% 0.26/0.63        ( ( ord_less_nat @ one_one_nat @ N )
% 0.26/0.63       => ( ( groups7754918857620584856omplex
% 0.26/0.63            @ ^ [X: complex] : X
% 0.26/0.63            @ ( collect_complex
% 0.26/0.63              @ ^ [Z6: complex] :
% 0.26/0.63                  ( ( power_power_complex @ Z6 @ N )
% 0.26/0.63                  = one_one_complex ) ) )
% 0.26/0.63          = zero_zero_complex ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_roots_unity
% 0.26/0.63  thf(fact_8274_sum__nth__roots,axiom,
% 0.26/0.63      ! [N: nat,C: complex] :
% 0.26/0.63        ( ( ord_less_nat @ one_one_nat @ N )
% 0.26/0.63       => ( ( groups7754918857620584856omplex
% 0.26/0.63            @ ^ [X: complex] : X
% 0.26/0.63            @ ( collect_complex
% 0.26/0.63              @ ^ [Z6: complex] :
% 0.26/0.63                  ( ( power_power_complex @ Z6 @ N )
% 0.26/0.63                  = C ) ) )
% 0.26/0.63          = zero_zero_complex ) ) ).
% 0.26/0.63  
% 0.26/0.63  % sum_nth_roots
% 0.26/0.63  thf(fact_8275_power__sum,axiom,
% 0.26/0.63      ! [C: real,F: nat > nat,A3: set_nat] :
% 0.26/0.63        ( ( power_power_real @ C @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 0.26/0.63        = ( groups129246275422532515t_real
% 0.26/0.63          @ ^ [A4: nat] : ( power_power_real @ C @ ( F @ A4 ) )
% 0.26/0.63          @ A3 ) ) ).
% 0.26/0.63  
% 0.26/0.63  % power_sum
% 0.26/0.63  thf(fact_8276_power__sum,axiom,
% 0.26/0.63      ! [C: complex,F: nat > nat,A3: set_nat] :
% 0.26/0.63        ( ( power_power_complex @ C @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 0.26/0.63        = ( groups6464643781859351333omplex
% 0.26/0.63          @ ^ [A4: nat] : ( power_power_complex @ C @ ( F @ A4 ) )
% 0.26/0.63          @ A3 ) ) ).
% 0.26/0.63  
% 0.26/0.63  % power_sum
% 0.26/0.63  thf(fact_8277_power__sum,axiom,
% 0.26/0.63      ! [C: int,F: nat > nat,A3: set_nat] :
% 0.26/0.63        ( ( power_power_int @ C @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 0.26/0.63        = ( groups705719431365010083at_int
% 0.26/0.63          @ ^ [A4: nat] : ( power_power_int @ C @ ( F @ A4 ) )
% 0.26/0.63          @ A3 ) ) ).
% 0.26/0.63  
% 0.26/0.63  % power_sum
% 0.26/0.63  thf(fact_8278_power__sum,axiom,
% 0.26/0.63      ! [C: int,F: int > nat,A3: set_int] :
% 0.26/0.63        ( ( power_power_int @ C @ ( groups4541462559716669496nt_nat @ F @ A3 ) )
% 0.26/0.63        = ( groups1705073143266064639nt_int
% 0.26/0.63          @ ^ [A4: int] : ( power_power_int @ C @ ( F @ A4 ) )
% 0.26/0.63          @ A3 ) ) ).
% 0.26/0.64  
% 0.26/0.64  % power_sum
% 0.26/0.64  thf(fact_8279_power__sum,axiom,
% 0.26/0.64      ! [C: nat,F: nat > nat,A3: set_nat] :
% 0.26/0.64        ( ( power_power_nat @ C @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 0.26/0.64        = ( groups708209901874060359at_nat
% 0.26/0.64          @ ^ [A4: nat] : ( power_power_nat @ C @ ( F @ A4 ) )
% 0.26/0.64          @ A3 ) ) ).
% 0.26/0.64  
% 0.26/0.64  % power_sum
% 0.26/0.64  thf(fact_8280_sum__subtractf__nat,axiom,
% 0.26/0.64      ! [A3: set_option_nat,G: option_nat > nat,F: option_nat > nat] :
% 0.26/0.64        ( ! [X4: option_nat] :
% 0.26/0.64            ( ( member_option_nat @ X4 @ A3 )
% 0.26/0.64           => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 0.26/0.64       => ( ( groups1921984841883549356at_nat
% 0.26/0.64            @ ^ [X: option_nat] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 0.26/0.64            @ A3 )
% 0.26/0.64          = ( minus_minus_nat @ ( groups1921984841883549356at_nat @ F @ A3 ) @ ( groups1921984841883549356at_nat @ G @ A3 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_subtractf_nat
% 0.26/0.64  thf(fact_8281_sum__subtractf__nat,axiom,
% 0.26/0.64      ! [A3: set_real,G: real > nat,F: real > nat] :
% 0.26/0.64        ( ! [X4: real] :
% 0.26/0.64            ( ( member_real @ X4 @ A3 )
% 0.26/0.64           => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 0.26/0.64       => ( ( groups1935376822645274424al_nat
% 0.26/0.64            @ ^ [X: real] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 0.26/0.64            @ A3 )
% 0.26/0.64          = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A3 ) @ ( groups1935376822645274424al_nat @ G @ A3 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_subtractf_nat
% 0.26/0.64  thf(fact_8282_sum__subtractf__nat,axiom,
% 0.26/0.64      ! [A3: set_set_nat,G: set_nat > nat,F: set_nat > nat] :
% 0.26/0.64        ( ! [X4: set_nat] :
% 0.26/0.64            ( ( member_set_nat @ X4 @ A3 )
% 0.26/0.64           => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 0.26/0.64       => ( ( groups8294997508430121362at_nat
% 0.26/0.64            @ ^ [X: set_nat] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 0.26/0.64            @ A3 )
% 0.26/0.64          = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A3 ) @ ( groups8294997508430121362at_nat @ G @ A3 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_subtractf_nat
% 0.26/0.64  thf(fact_8283_sum__subtractf__nat,axiom,
% 0.26/0.64      ! [A3: set_int,G: int > nat,F: int > nat] :
% 0.26/0.64        ( ! [X4: int] :
% 0.26/0.64            ( ( member_int @ X4 @ A3 )
% 0.26/0.64           => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 0.26/0.64       => ( ( groups4541462559716669496nt_nat
% 0.26/0.64            @ ^ [X: int] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 0.26/0.64            @ A3 )
% 0.26/0.64          = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ ( groups4541462559716669496nt_nat @ G @ A3 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_subtractf_nat
% 0.26/0.64  thf(fact_8284_sum__subtractf__nat,axiom,
% 0.26/0.64      ! [A3: set_nat,G: nat > nat,F: nat > nat] :
% 0.26/0.64        ( ! [X4: nat] :
% 0.26/0.64            ( ( member_nat @ X4 @ A3 )
% 0.26/0.64           => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 0.26/0.64       => ( ( groups3542108847815614940at_nat
% 0.26/0.64            @ ^ [X: nat] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 0.26/0.64            @ A3 )
% 0.26/0.64          = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) @ ( groups3542108847815614940at_nat @ G @ A3 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_subtractf_nat
% 0.26/0.64  thf(fact_8285_polyfun__linear__factor__root,axiom,
% 0.26/0.64      ! [C: nat > complex,A: complex,N: nat] :
% 0.26/0.64        ( ( ( groups2073611262835488442omplex
% 0.26/0.64            @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ A @ I4 ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64          = zero_zero_complex )
% 0.26/0.64       => ~ ! [B4: nat > complex] :
% 0.26/0.64              ~ ! [Z4: complex] :
% 0.26/0.64                  ( ( groups2073611262835488442omplex
% 0.26/0.64                    @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ Z4 @ I4 ) )
% 0.26/0.64                    @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64                  = ( times_times_complex @ ( minus_minus_complex @ Z4 @ A )
% 0.26/0.64                    @ ( groups2073611262835488442omplex
% 0.26/0.64                      @ ^ [I4: nat] : ( times_times_complex @ ( B4 @ I4 ) @ ( power_power_complex @ Z4 @ I4 ) )
% 0.26/0.64                      @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_linear_factor_root
% 0.26/0.64  thf(fact_8286_polyfun__linear__factor__root,axiom,
% 0.26/0.64      ! [C: nat > rat,A: rat,N: nat] :
% 0.26/0.64        ( ( ( groups2906978787729119204at_rat
% 0.26/0.64            @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ A @ I4 ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64          = zero_zero_rat )
% 0.26/0.64       => ~ ! [B4: nat > rat] :
% 0.26/0.64              ~ ! [Z4: rat] :
% 0.26/0.64                  ( ( groups2906978787729119204at_rat
% 0.26/0.64                    @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ Z4 @ I4 ) )
% 0.26/0.64                    @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64                  = ( times_times_rat @ ( minus_minus_rat @ Z4 @ A )
% 0.26/0.64                    @ ( groups2906978787729119204at_rat
% 0.26/0.64                      @ ^ [I4: nat] : ( times_times_rat @ ( B4 @ I4 ) @ ( power_power_rat @ Z4 @ I4 ) )
% 0.26/0.64                      @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_linear_factor_root
% 0.26/0.64  thf(fact_8287_polyfun__linear__factor__root,axiom,
% 0.26/0.64      ! [C: nat > int,A: int,N: nat] :
% 0.26/0.64        ( ( ( groups3539618377306564664at_int
% 0.26/0.64            @ ^ [I4: nat] : ( times_times_int @ ( C @ I4 ) @ ( power_power_int @ A @ I4 ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64          = zero_zero_int )
% 0.26/0.64       => ~ ! [B4: nat > int] :
% 0.26/0.64              ~ ! [Z4: int] :
% 0.26/0.64                  ( ( groups3539618377306564664at_int
% 0.26/0.64                    @ ^ [I4: nat] : ( times_times_int @ ( C @ I4 ) @ ( power_power_int @ Z4 @ I4 ) )
% 0.26/0.64                    @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64                  = ( times_times_int @ ( minus_minus_int @ Z4 @ A )
% 0.26/0.64                    @ ( groups3539618377306564664at_int
% 0.26/0.64                      @ ^ [I4: nat] : ( times_times_int @ ( B4 @ I4 ) @ ( power_power_int @ Z4 @ I4 ) )
% 0.26/0.64                      @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_linear_factor_root
% 0.26/0.64  thf(fact_8288_polyfun__linear__factor__root,axiom,
% 0.26/0.64      ! [C: nat > real,A: real,N: nat] :
% 0.26/0.64        ( ( ( groups6591440286371151544t_real
% 0.26/0.64            @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ A @ I4 ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64          = zero_zero_real )
% 0.26/0.64       => ~ ! [B4: nat > real] :
% 0.26/0.64              ~ ! [Z4: real] :
% 0.26/0.64                  ( ( groups6591440286371151544t_real
% 0.26/0.64                    @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ Z4 @ I4 ) )
% 0.26/0.64                    @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64                  = ( times_times_real @ ( minus_minus_real @ Z4 @ A )
% 0.26/0.64                    @ ( groups6591440286371151544t_real
% 0.26/0.64                      @ ^ [I4: nat] : ( times_times_real @ ( B4 @ I4 ) @ ( power_power_real @ Z4 @ I4 ) )
% 0.26/0.64                      @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_linear_factor_root
% 0.26/0.64  thf(fact_8289_polyfun__linear__factor,axiom,
% 0.26/0.64      ! [C: nat > complex,N: nat,A: complex] :
% 0.26/0.64      ? [B4: nat > complex] :
% 0.26/0.64      ! [Z4: complex] :
% 0.26/0.64        ( ( groups2073611262835488442omplex
% 0.26/0.64          @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ Z4 @ I4 ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64        = ( plus_plus_complex
% 0.26/0.64          @ ( times_times_complex @ ( minus_minus_complex @ Z4 @ A )
% 0.26/0.64            @ ( groups2073611262835488442omplex
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_complex @ ( B4 @ I4 ) @ ( power_power_complex @ Z4 @ I4 ) )
% 0.26/0.64              @ ( set_ord_lessThan_nat @ N ) ) )
% 0.26/0.64          @ ( groups2073611262835488442omplex
% 0.26/0.64            @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ A @ I4 ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_linear_factor
% 0.26/0.64  thf(fact_8290_polyfun__linear__factor,axiom,
% 0.26/0.64      ! [C: nat > rat,N: nat,A: rat] :
% 0.26/0.64      ? [B4: nat > rat] :
% 0.26/0.64      ! [Z4: rat] :
% 0.26/0.64        ( ( groups2906978787729119204at_rat
% 0.26/0.64          @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ Z4 @ I4 ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64        = ( plus_plus_rat
% 0.26/0.64          @ ( times_times_rat @ ( minus_minus_rat @ Z4 @ A )
% 0.26/0.64            @ ( groups2906978787729119204at_rat
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_rat @ ( B4 @ I4 ) @ ( power_power_rat @ Z4 @ I4 ) )
% 0.26/0.64              @ ( set_ord_lessThan_nat @ N ) ) )
% 0.26/0.64          @ ( groups2906978787729119204at_rat
% 0.26/0.64            @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ A @ I4 ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_linear_factor
% 0.26/0.64  thf(fact_8291_polyfun__linear__factor,axiom,
% 0.26/0.64      ! [C: nat > int,N: nat,A: int] :
% 0.26/0.64      ? [B4: nat > int] :
% 0.26/0.64      ! [Z4: int] :
% 0.26/0.64        ( ( groups3539618377306564664at_int
% 0.26/0.64          @ ^ [I4: nat] : ( times_times_int @ ( C @ I4 ) @ ( power_power_int @ Z4 @ I4 ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64        = ( plus_plus_int
% 0.26/0.64          @ ( times_times_int @ ( minus_minus_int @ Z4 @ A )
% 0.26/0.64            @ ( groups3539618377306564664at_int
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_int @ ( B4 @ I4 ) @ ( power_power_int @ Z4 @ I4 ) )
% 0.26/0.64              @ ( set_ord_lessThan_nat @ N ) ) )
% 0.26/0.64          @ ( groups3539618377306564664at_int
% 0.26/0.64            @ ^ [I4: nat] : ( times_times_int @ ( C @ I4 ) @ ( power_power_int @ A @ I4 ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_linear_factor
% 0.26/0.64  thf(fact_8292_polyfun__linear__factor,axiom,
% 0.26/0.64      ! [C: nat > real,N: nat,A: real] :
% 0.26/0.64      ? [B4: nat > real] :
% 0.26/0.64      ! [Z4: real] :
% 0.26/0.64        ( ( groups6591440286371151544t_real
% 0.26/0.64          @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ Z4 @ I4 ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64        = ( plus_plus_real
% 0.26/0.64          @ ( times_times_real @ ( minus_minus_real @ Z4 @ A )
% 0.26/0.64            @ ( groups6591440286371151544t_real
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_real @ ( B4 @ I4 ) @ ( power_power_real @ Z4 @ I4 ) )
% 0.26/0.64              @ ( set_ord_lessThan_nat @ N ) ) )
% 0.26/0.64          @ ( groups6591440286371151544t_real
% 0.26/0.64            @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ A @ I4 ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_linear_factor
% 0.26/0.64  thf(fact_8293_finite__divisors__int,axiom,
% 0.26/0.64      ! [I: int] :
% 0.26/0.64        ( ( I != zero_zero_int )
% 0.26/0.64       => ( finite_finite_int
% 0.26/0.64          @ ( collect_int
% 0.26/0.64            @ ^ [D4: int] : ( dvd_dvd_int @ D4 @ I ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_divisors_int
% 0.26/0.64  thf(fact_8294_sum__eq__Suc0__iff,axiom,
% 0.26/0.64      ! [A3: set_int,F: int > nat] :
% 0.26/0.64        ( ( finite_finite_int @ A3 )
% 0.26/0.64       => ( ( ( groups4541462559716669496nt_nat @ F @ A3 )
% 0.26/0.64            = ( suc @ zero_zero_nat ) )
% 0.26/0.64          = ( ? [X: int] :
% 0.26/0.64                ( ( member_int @ X @ A3 )
% 0.26/0.64                & ( ( F @ X )
% 0.26/0.64                  = ( suc @ zero_zero_nat ) )
% 0.26/0.64                & ! [Y: int] :
% 0.26/0.64                    ( ( member_int @ Y @ A3 )
% 0.26/0.64                   => ( ( X != Y )
% 0.26/0.64                     => ( ( F @ Y )
% 0.26/0.64                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_eq_Suc0_iff
% 0.26/0.64  thf(fact_8295_sum__eq__Suc0__iff,axiom,
% 0.26/0.64      ! [A3: set_complex,F: complex > nat] :
% 0.26/0.64        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.64       => ( ( ( groups5693394587270226106ex_nat @ F @ A3 )
% 0.26/0.64            = ( suc @ zero_zero_nat ) )
% 0.26/0.64          = ( ? [X: complex] :
% 0.26/0.64                ( ( member_complex @ X @ A3 )
% 0.26/0.64                & ( ( F @ X )
% 0.26/0.64                  = ( suc @ zero_zero_nat ) )
% 0.26/0.64                & ! [Y: complex] :
% 0.26/0.64                    ( ( member_complex @ Y @ A3 )
% 0.26/0.64                   => ( ( X != Y )
% 0.26/0.64                     => ( ( F @ Y )
% 0.26/0.64                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_eq_Suc0_iff
% 0.26/0.64  thf(fact_8296_sum__eq__Suc0__iff,axiom,
% 0.26/0.64      ! [A3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 0.26/0.64        ( ( finite6177210948735845034at_nat @ A3 )
% 0.26/0.64       => ( ( ( groups977919841031483927at_nat @ F @ A3 )
% 0.26/0.64            = ( suc @ zero_zero_nat ) )
% 0.26/0.64          = ( ? [X: product_prod_nat_nat] :
% 0.26/0.64                ( ( member8440522571783428010at_nat @ X @ A3 )
% 0.26/0.64                & ( ( F @ X )
% 0.26/0.64                  = ( suc @ zero_zero_nat ) )
% 0.26/0.64                & ! [Y: product_prod_nat_nat] :
% 0.26/0.64                    ( ( member8440522571783428010at_nat @ Y @ A3 )
% 0.26/0.64                   => ( ( X != Y )
% 0.26/0.64                     => ( ( F @ Y )
% 0.26/0.64                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_eq_Suc0_iff
% 0.26/0.64  thf(fact_8297_sum__eq__Suc0__iff,axiom,
% 0.26/0.64      ! [A3: set_Extended_enat,F: extended_enat > nat] :
% 0.26/0.64        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.64       => ( ( ( groups2027974829824023292at_nat @ F @ A3 )
% 0.26/0.64            = ( suc @ zero_zero_nat ) )
% 0.26/0.64          = ( ? [X: extended_enat] :
% 0.26/0.64                ( ( member_Extended_enat @ X @ A3 )
% 0.26/0.64                & ( ( F @ X )
% 0.26/0.64                  = ( suc @ zero_zero_nat ) )
% 0.26/0.64                & ! [Y: extended_enat] :
% 0.26/0.64                    ( ( member_Extended_enat @ Y @ A3 )
% 0.26/0.64                   => ( ( X != Y )
% 0.26/0.64                     => ( ( F @ Y )
% 0.26/0.64                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_eq_Suc0_iff
% 0.26/0.64  thf(fact_8298_sum__eq__Suc0__iff,axiom,
% 0.26/0.64      ! [A3: set_nat,F: nat > nat] :
% 0.26/0.64        ( ( finite_finite_nat @ A3 )
% 0.26/0.64       => ( ( ( groups3542108847815614940at_nat @ F @ A3 )
% 0.26/0.64            = ( suc @ zero_zero_nat ) )
% 0.26/0.64          = ( ? [X: nat] :
% 0.26/0.64                ( ( member_nat @ X @ A3 )
% 0.26/0.64                & ( ( F @ X )
% 0.26/0.64                  = ( suc @ zero_zero_nat ) )
% 0.26/0.64                & ! [Y: nat] :
% 0.26/0.64                    ( ( member_nat @ Y @ A3 )
% 0.26/0.64                   => ( ( X != Y )
% 0.26/0.64                     => ( ( F @ Y )
% 0.26/0.64                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_eq_Suc0_iff
% 0.26/0.64  thf(fact_8299_sum__SucD,axiom,
% 0.26/0.64      ! [F: nat > nat,A3: set_nat,N: nat] :
% 0.26/0.64        ( ( ( groups3542108847815614940at_nat @ F @ A3 )
% 0.26/0.64          = ( suc @ N ) )
% 0.26/0.64       => ? [X4: nat] :
% 0.26/0.64            ( ( member_nat @ X4 @ A3 )
% 0.26/0.64            & ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_SucD
% 0.26/0.64  thf(fact_8300_sum__eq__1__iff,axiom,
% 0.26/0.64      ! [A3: set_int,F: int > nat] :
% 0.26/0.64        ( ( finite_finite_int @ A3 )
% 0.26/0.64       => ( ( ( groups4541462559716669496nt_nat @ F @ A3 )
% 0.26/0.64            = one_one_nat )
% 0.26/0.64          = ( ? [X: int] :
% 0.26/0.64                ( ( member_int @ X @ A3 )
% 0.26/0.64                & ( ( F @ X )
% 0.26/0.64                  = one_one_nat )
% 0.26/0.64                & ! [Y: int] :
% 0.26/0.64                    ( ( member_int @ Y @ A3 )
% 0.26/0.64                   => ( ( X != Y )
% 0.26/0.64                     => ( ( F @ Y )
% 0.26/0.64                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_eq_1_iff
% 0.26/0.64  thf(fact_8301_sum__eq__1__iff,axiom,
% 0.26/0.64      ! [A3: set_complex,F: complex > nat] :
% 0.26/0.64        ( ( finite3207457112153483333omplex @ A3 )
% 0.26/0.64       => ( ( ( groups5693394587270226106ex_nat @ F @ A3 )
% 0.26/0.64            = one_one_nat )
% 0.26/0.64          = ( ? [X: complex] :
% 0.26/0.64                ( ( member_complex @ X @ A3 )
% 0.26/0.64                & ( ( F @ X )
% 0.26/0.64                  = one_one_nat )
% 0.26/0.64                & ! [Y: complex] :
% 0.26/0.64                    ( ( member_complex @ Y @ A3 )
% 0.26/0.64                   => ( ( X != Y )
% 0.26/0.64                     => ( ( F @ Y )
% 0.26/0.64                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_eq_1_iff
% 0.26/0.64  thf(fact_8302_sum__eq__1__iff,axiom,
% 0.26/0.64      ! [A3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 0.26/0.64        ( ( finite6177210948735845034at_nat @ A3 )
% 0.26/0.64       => ( ( ( groups977919841031483927at_nat @ F @ A3 )
% 0.26/0.64            = one_one_nat )
% 0.26/0.64          = ( ? [X: product_prod_nat_nat] :
% 0.26/0.64                ( ( member8440522571783428010at_nat @ X @ A3 )
% 0.26/0.64                & ( ( F @ X )
% 0.26/0.64                  = one_one_nat )
% 0.26/0.64                & ! [Y: product_prod_nat_nat] :
% 0.26/0.64                    ( ( member8440522571783428010at_nat @ Y @ A3 )
% 0.26/0.64                   => ( ( X != Y )
% 0.26/0.64                     => ( ( F @ Y )
% 0.26/0.64                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_eq_1_iff
% 0.26/0.64  thf(fact_8303_sum__eq__1__iff,axiom,
% 0.26/0.64      ! [A3: set_Extended_enat,F: extended_enat > nat] :
% 0.26/0.64        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.64       => ( ( ( groups2027974829824023292at_nat @ F @ A3 )
% 0.26/0.64            = one_one_nat )
% 0.26/0.64          = ( ? [X: extended_enat] :
% 0.26/0.64                ( ( member_Extended_enat @ X @ A3 )
% 0.26/0.64                & ( ( F @ X )
% 0.26/0.64                  = one_one_nat )
% 0.26/0.64                & ! [Y: extended_enat] :
% 0.26/0.64                    ( ( member_Extended_enat @ Y @ A3 )
% 0.26/0.64                   => ( ( X != Y )
% 0.26/0.64                     => ( ( F @ Y )
% 0.26/0.64                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_eq_1_iff
% 0.26/0.64  thf(fact_8304_sum__eq__1__iff,axiom,
% 0.26/0.64      ! [A3: set_nat,F: nat > nat] :
% 0.26/0.64        ( ( finite_finite_nat @ A3 )
% 0.26/0.64       => ( ( ( groups3542108847815614940at_nat @ F @ A3 )
% 0.26/0.64            = one_one_nat )
% 0.26/0.64          = ( ? [X: nat] :
% 0.26/0.64                ( ( member_nat @ X @ A3 )
% 0.26/0.64                & ( ( F @ X )
% 0.26/0.64                  = one_one_nat )
% 0.26/0.64                & ! [Y: nat] :
% 0.26/0.64                    ( ( member_nat @ Y @ A3 )
% 0.26/0.64                   => ( ( X != Y )
% 0.26/0.64                     => ( ( F @ Y )
% 0.26/0.64                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_eq_1_iff
% 0.26/0.64  thf(fact_8305_atMost__nat__numeral,axiom,
% 0.26/0.64      ! [K: num] :
% 0.26/0.64        ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 0.26/0.64        = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % atMost_nat_numeral
% 0.26/0.64  thf(fact_8306_lessThan__nat__numeral,axiom,
% 0.26/0.64      ! [K: num] :
% 0.26/0.64        ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 0.26/0.64        = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % lessThan_nat_numeral
% 0.26/0.64  thf(fact_8307_set__encode__inf,axiom,
% 0.26/0.64      ! [A3: set_nat] :
% 0.26/0.64        ( ~ ( finite_finite_nat @ A3 )
% 0.26/0.64       => ( ( nat_set_encode @ A3 )
% 0.26/0.64          = zero_zero_nat ) ) ).
% 0.26/0.64  
% 0.26/0.64  % set_encode_inf
% 0.26/0.64  thf(fact_8308_polyfun__diff__alt,axiom,
% 0.26/0.64      ! [N: nat,A: nat > complex,X3: complex,Y3: complex] :
% 0.26/0.64        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.26/0.64       => ( ( minus_minus_complex
% 0.26/0.64            @ ( groups2073611262835488442omplex
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( power_power_complex @ X3 @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64            @ ( groups2073611262835488442omplex
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( power_power_complex @ Y3 @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64          = ( times_times_complex @ ( minus_minus_complex @ X3 @ Y3 )
% 0.26/0.64            @ ( groups2073611262835488442omplex
% 0.26/0.64              @ ^ [J3: nat] :
% 0.26/0.64                  ( groups2073611262835488442omplex
% 0.26/0.64                  @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_complex @ Y3 @ K3 ) ) @ ( power_power_complex @ X3 @ J3 ) )
% 0.26/0.64                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 0.26/0.64              @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_diff_alt
% 0.26/0.64  thf(fact_8309_polyfun__diff__alt,axiom,
% 0.26/0.64      ! [N: nat,A: nat > rat,X3: rat,Y3: rat] :
% 0.26/0.64        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.26/0.64       => ( ( minus_minus_rat
% 0.26/0.64            @ ( groups2906978787729119204at_rat
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( power_power_rat @ X3 @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64            @ ( groups2906978787729119204at_rat
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( power_power_rat @ Y3 @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64          = ( times_times_rat @ ( minus_minus_rat @ X3 @ Y3 )
% 0.26/0.64            @ ( groups2906978787729119204at_rat
% 0.26/0.64              @ ^ [J3: nat] :
% 0.26/0.64                  ( groups2906978787729119204at_rat
% 0.26/0.64                  @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_rat @ Y3 @ K3 ) ) @ ( power_power_rat @ X3 @ J3 ) )
% 0.26/0.64                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 0.26/0.64              @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_diff_alt
% 0.26/0.64  thf(fact_8310_polyfun__diff__alt,axiom,
% 0.26/0.64      ! [N: nat,A: nat > int,X3: int,Y3: int] :
% 0.26/0.64        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.26/0.64       => ( ( minus_minus_int
% 0.26/0.64            @ ( groups3539618377306564664at_int
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_int @ ( A @ I4 ) @ ( power_power_int @ X3 @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64            @ ( groups3539618377306564664at_int
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_int @ ( A @ I4 ) @ ( power_power_int @ Y3 @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64          = ( times_times_int @ ( minus_minus_int @ X3 @ Y3 )
% 0.26/0.64            @ ( groups3539618377306564664at_int
% 0.26/0.64              @ ^ [J3: nat] :
% 0.26/0.64                  ( groups3539618377306564664at_int
% 0.26/0.64                  @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_int @ Y3 @ K3 ) ) @ ( power_power_int @ X3 @ J3 ) )
% 0.26/0.64                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 0.26/0.64              @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_diff_alt
% 0.26/0.64  thf(fact_8311_polyfun__diff__alt,axiom,
% 0.26/0.64      ! [N: nat,A: nat > real,X3: real,Y3: real] :
% 0.26/0.64        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.26/0.64       => ( ( minus_minus_real
% 0.26/0.64            @ ( groups6591440286371151544t_real
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( power_power_real @ X3 @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64            @ ( groups6591440286371151544t_real
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( power_power_real @ Y3 @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64          = ( times_times_real @ ( minus_minus_real @ X3 @ Y3 )
% 0.26/0.64            @ ( groups6591440286371151544t_real
% 0.26/0.64              @ ^ [J3: nat] :
% 0.26/0.64                  ( groups6591440286371151544t_real
% 0.26/0.64                  @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_real @ Y3 @ K3 ) ) @ ( power_power_real @ X3 @ J3 ) )
% 0.26/0.64                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 0.26/0.64              @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_diff_alt
% 0.26/0.64  thf(fact_8312_suminf__le__const,axiom,
% 0.26/0.64      ! [F: nat > int,X3: int] :
% 0.26/0.64        ( ( summable_int @ F )
% 0.26/0.64       => ( ! [N2: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ X3 )
% 0.26/0.64         => ( ord_less_eq_int @ ( suminf_int @ F ) @ X3 ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % suminf_le_const
% 0.26/0.64  thf(fact_8313_suminf__le__const,axiom,
% 0.26/0.64      ! [F: nat > nat,X3: nat] :
% 0.26/0.64        ( ( summable_nat @ F )
% 0.26/0.64       => ( ! [N2: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ X3 )
% 0.26/0.64         => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ X3 ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % suminf_le_const
% 0.26/0.64  thf(fact_8314_suminf__le__const,axiom,
% 0.26/0.64      ! [F: nat > real,X3: real] :
% 0.26/0.64        ( ( summable_real @ F )
% 0.26/0.64       => ( ! [N2: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ X3 )
% 0.26/0.64         => ( ord_less_eq_real @ ( suminf_real @ F ) @ X3 ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % suminf_le_const
% 0.26/0.64  thf(fact_8315_sum_OatMost__Suc__shift,axiom,
% 0.26/0.64      ! [G: nat > rat,N: nat] :
% 0.26/0.64        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.26/0.64        = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 0.26/0.64          @ ( groups2906978787729119204at_rat
% 0.26/0.64            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum.atMost_Suc_shift
% 0.26/0.64  thf(fact_8316_sum_OatMost__Suc__shift,axiom,
% 0.26/0.64      ! [G: nat > int,N: nat] :
% 0.26/0.64        ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.26/0.64        = ( plus_plus_int @ ( G @ zero_zero_nat )
% 0.26/0.64          @ ( groups3539618377306564664at_int
% 0.26/0.64            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum.atMost_Suc_shift
% 0.26/0.64  thf(fact_8317_sum_OatMost__Suc__shift,axiom,
% 0.26/0.64      ! [G: nat > nat,N: nat] :
% 0.26/0.64        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.26/0.64        = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 0.26/0.64          @ ( groups3542108847815614940at_nat
% 0.26/0.64            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum.atMost_Suc_shift
% 0.26/0.64  thf(fact_8318_sum_OatMost__Suc__shift,axiom,
% 0.26/0.64      ! [G: nat > real,N: nat] :
% 0.26/0.64        ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.26/0.64        = ( plus_plus_real @ ( G @ zero_zero_nat )
% 0.26/0.64          @ ( groups6591440286371151544t_real
% 0.26/0.64            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum.atMost_Suc_shift
% 0.26/0.64  thf(fact_8319_sum__telescope,axiom,
% 0.26/0.64      ! [F: nat > rat,I: nat] :
% 0.26/0.64        ( ( groups2906978787729119204at_rat
% 0.26/0.64          @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ I4 ) @ ( F @ ( suc @ I4 ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ I ) )
% 0.26/0.64        = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_telescope
% 0.26/0.64  thf(fact_8320_sum__telescope,axiom,
% 0.26/0.64      ! [F: nat > int,I: nat] :
% 0.26/0.64        ( ( groups3539618377306564664at_int
% 0.26/0.64          @ ^ [I4: nat] : ( minus_minus_int @ ( F @ I4 ) @ ( F @ ( suc @ I4 ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ I ) )
% 0.26/0.64        = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_telescope
% 0.26/0.64  thf(fact_8321_sum__telescope,axiom,
% 0.26/0.64      ! [F: nat > real,I: nat] :
% 0.26/0.64        ( ( groups6591440286371151544t_real
% 0.26/0.64          @ ^ [I4: nat] : ( minus_minus_real @ ( F @ I4 ) @ ( F @ ( suc @ I4 ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ I ) )
% 0.26/0.64        = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_telescope
% 0.26/0.64  thf(fact_8322_polyfun__eq__coeffs,axiom,
% 0.26/0.64      ! [C: nat > complex,N: nat,D3: nat > complex] :
% 0.26/0.64        ( ( ! [X: complex] :
% 0.26/0.64              ( ( groups2073611262835488442omplex
% 0.26/0.64                @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ X @ I4 ) )
% 0.26/0.64                @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64              = ( groups2073611262835488442omplex
% 0.26/0.64                @ ^ [I4: nat] : ( times_times_complex @ ( D3 @ I4 ) @ ( power_power_complex @ X @ I4 ) )
% 0.26/0.64                @ ( set_ord_atMost_nat @ N ) ) ) )
% 0.26/0.64        = ( ! [I4: nat] :
% 0.26/0.64              ( ( ord_less_eq_nat @ I4 @ N )
% 0.26/0.64             => ( ( C @ I4 )
% 0.26/0.64                = ( D3 @ I4 ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_eq_coeffs
% 0.26/0.64  thf(fact_8323_polyfun__eq__coeffs,axiom,
% 0.26/0.64      ! [C: nat > real,N: nat,D3: nat > real] :
% 0.26/0.64        ( ( ! [X: real] :
% 0.26/0.64              ( ( groups6591440286371151544t_real
% 0.26/0.64                @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ X @ I4 ) )
% 0.26/0.64                @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64              = ( groups6591440286371151544t_real
% 0.26/0.64                @ ^ [I4: nat] : ( times_times_real @ ( D3 @ I4 ) @ ( power_power_real @ X @ I4 ) )
% 0.26/0.64                @ ( set_ord_atMost_nat @ N ) ) ) )
% 0.26/0.64        = ( ! [I4: nat] :
% 0.26/0.64              ( ( ord_less_eq_nat @ I4 @ N )
% 0.26/0.64             => ( ( C @ I4 )
% 0.26/0.64                = ( D3 @ I4 ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_eq_coeffs
% 0.26/0.64  thf(fact_8324_bounded__imp__summable,axiom,
% 0.26/0.64      ! [A: nat > int,B5: int] :
% 0.26/0.64        ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( A @ N2 ) )
% 0.26/0.64       => ( ! [N2: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ A @ ( set_ord_atMost_nat @ N2 ) ) @ B5 )
% 0.26/0.64         => ( summable_int @ A ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % bounded_imp_summable
% 0.26/0.64  thf(fact_8325_bounded__imp__summable,axiom,
% 0.26/0.64      ! [A: nat > nat,B5: nat] :
% 0.26/0.64        ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( A @ N2 ) )
% 0.26/0.64       => ( ! [N2: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ A @ ( set_ord_atMost_nat @ N2 ) ) @ B5 )
% 0.26/0.64         => ( summable_nat @ A ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % bounded_imp_summable
% 0.26/0.64  thf(fact_8326_bounded__imp__summable,axiom,
% 0.26/0.64      ! [A: nat > real,B5: real] :
% 0.26/0.64        ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 0.26/0.64       => ( ! [N2: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ A @ ( set_ord_atMost_nat @ N2 ) ) @ B5 )
% 0.26/0.64         => ( summable_real @ A ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % bounded_imp_summable
% 0.26/0.64  thf(fact_8327_prod_OatMost__Suc__shift,axiom,
% 0.26/0.64      ! [G: nat > real,N: nat] :
% 0.26/0.64        ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.26/0.64        = ( times_times_real @ ( G @ zero_zero_nat )
% 0.26/0.64          @ ( groups129246275422532515t_real
% 0.26/0.64            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % prod.atMost_Suc_shift
% 0.26/0.64  thf(fact_8328_prod_OatMost__Suc__shift,axiom,
% 0.26/0.64      ! [G: nat > rat,N: nat] :
% 0.26/0.64        ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.26/0.64        = ( times_times_rat @ ( G @ zero_zero_nat )
% 0.26/0.64          @ ( groups73079841787564623at_rat
% 0.26/0.64            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % prod.atMost_Suc_shift
% 0.26/0.64  thf(fact_8329_prod_OatMost__Suc__shift,axiom,
% 0.26/0.64      ! [G: nat > int,N: nat] :
% 0.26/0.64        ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.26/0.64        = ( times_times_int @ ( G @ zero_zero_nat )
% 0.26/0.64          @ ( groups705719431365010083at_int
% 0.26/0.64            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % prod.atMost_Suc_shift
% 0.26/0.64  thf(fact_8330_prod_OatMost__Suc__shift,axiom,
% 0.26/0.64      ! [G: nat > nat,N: nat] :
% 0.26/0.64        ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.26/0.64        = ( times_times_nat @ ( G @ zero_zero_nat )
% 0.26/0.64          @ ( groups708209901874060359at_nat
% 0.26/0.64            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % prod.atMost_Suc_shift
% 0.26/0.64  thf(fact_8331_sum_OlessThan__Suc__shift,axiom,
% 0.26/0.64      ! [G: nat > rat,N: nat] :
% 0.26/0.64        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.26/0.64        = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 0.26/0.64          @ ( groups2906978787729119204at_rat
% 0.26/0.64            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.64            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum.lessThan_Suc_shift
% 0.26/0.64  thf(fact_8332_sum_OlessThan__Suc__shift,axiom,
% 0.26/0.64      ! [G: nat > int,N: nat] :
% 0.26/0.64        ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.26/0.64        = ( plus_plus_int @ ( G @ zero_zero_nat )
% 0.26/0.64          @ ( groups3539618377306564664at_int
% 0.26/0.64            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.64            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum.lessThan_Suc_shift
% 0.26/0.64  thf(fact_8333_sum_OlessThan__Suc__shift,axiom,
% 0.26/0.64      ! [G: nat > nat,N: nat] :
% 0.26/0.64        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.26/0.64        = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 0.26/0.64          @ ( groups3542108847815614940at_nat
% 0.26/0.64            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.64            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum.lessThan_Suc_shift
% 0.26/0.64  thf(fact_8334_sum_OlessThan__Suc__shift,axiom,
% 0.26/0.64      ! [G: nat > real,N: nat] :
% 0.26/0.64        ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.26/0.64        = ( plus_plus_real @ ( G @ zero_zero_nat )
% 0.26/0.64          @ ( groups6591440286371151544t_real
% 0.26/0.64            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.64            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum.lessThan_Suc_shift
% 0.26/0.64  thf(fact_8335_sum__lessThan__telescope,axiom,
% 0.26/0.64      ! [F: nat > rat,M: nat] :
% 0.26/0.64        ( ( groups2906978787729119204at_rat
% 0.26/0.64          @ ^ [N3: nat] : ( minus_minus_rat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ M ) )
% 0.26/0.64        = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_lessThan_telescope
% 0.26/0.64  thf(fact_8336_sum__lessThan__telescope,axiom,
% 0.26/0.64      ! [F: nat > int,M: nat] :
% 0.26/0.64        ( ( groups3539618377306564664at_int
% 0.26/0.64          @ ^ [N3: nat] : ( minus_minus_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ M ) )
% 0.26/0.64        = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_lessThan_telescope
% 0.26/0.64  thf(fact_8337_sum__lessThan__telescope,axiom,
% 0.26/0.64      ! [F: nat > real,M: nat] :
% 0.26/0.64        ( ( groups6591440286371151544t_real
% 0.26/0.64          @ ^ [N3: nat] : ( minus_minus_real @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ M ) )
% 0.26/0.64        = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_lessThan_telescope
% 0.26/0.64  thf(fact_8338_sum__lessThan__telescope_H,axiom,
% 0.26/0.64      ! [F: nat > rat,M: nat] :
% 0.26/0.64        ( ( groups2906978787729119204at_rat
% 0.26/0.64          @ ^ [N3: nat] : ( minus_minus_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ M ) )
% 0.26/0.64        = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_lessThan_telescope'
% 0.26/0.64  thf(fact_8339_sum__lessThan__telescope_H,axiom,
% 0.26/0.64      ! [F: nat > int,M: nat] :
% 0.26/0.64        ( ( groups3539618377306564664at_int
% 0.26/0.64          @ ^ [N3: nat] : ( minus_minus_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ M ) )
% 0.26/0.64        = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_lessThan_telescope'
% 0.26/0.64  thf(fact_8340_sum__lessThan__telescope_H,axiom,
% 0.26/0.64      ! [F: nat > real,M: nat] :
% 0.26/0.64        ( ( groups6591440286371151544t_real
% 0.26/0.64          @ ^ [N3: nat] : ( minus_minus_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ M ) )
% 0.26/0.64        = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_lessThan_telescope'
% 0.26/0.64  thf(fact_8341_sumr__diff__mult__const2,axiom,
% 0.26/0.64      ! [F: nat > complex,N: nat,R2: complex] :
% 0.26/0.64        ( ( minus_minus_complex @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ R2 ) )
% 0.26/0.64        = ( groups2073611262835488442omplex
% 0.26/0.64          @ ^ [I4: nat] : ( minus_minus_complex @ ( F @ I4 ) @ R2 )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sumr_diff_mult_const2
% 0.26/0.64  thf(fact_8342_sumr__diff__mult__const2,axiom,
% 0.26/0.64      ! [F: nat > rat,N: nat,R2: rat] :
% 0.26/0.64        ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ R2 ) )
% 0.26/0.64        = ( groups2906978787729119204at_rat
% 0.26/0.64          @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ I4 ) @ R2 )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sumr_diff_mult_const2
% 0.26/0.64  thf(fact_8343_sumr__diff__mult__const2,axiom,
% 0.26/0.64      ! [F: nat > int,N: nat,R2: int] :
% 0.26/0.64        ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ R2 ) )
% 0.26/0.64        = ( groups3539618377306564664at_int
% 0.26/0.64          @ ^ [I4: nat] : ( minus_minus_int @ ( F @ I4 ) @ R2 )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sumr_diff_mult_const2
% 0.26/0.64  thf(fact_8344_sumr__diff__mult__const2,axiom,
% 0.26/0.64      ! [F: nat > real,N: nat,R2: real] :
% 0.26/0.64        ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ R2 ) )
% 0.26/0.64        = ( groups6591440286371151544t_real
% 0.26/0.64          @ ^ [I4: nat] : ( minus_minus_real @ ( F @ I4 ) @ R2 )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sumr_diff_mult_const2
% 0.26/0.64  thf(fact_8345_summableI__nonneg__bounded,axiom,
% 0.26/0.64      ! [F: nat > int,X3: int] :
% 0.26/0.64        ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 0.26/0.64       => ( ! [N2: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ X3 )
% 0.26/0.64         => ( summable_int @ F ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % summableI_nonneg_bounded
% 0.26/0.64  thf(fact_8346_summableI__nonneg__bounded,axiom,
% 0.26/0.64      ! [F: nat > nat,X3: nat] :
% 0.26/0.64        ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 0.26/0.64       => ( ! [N2: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ X3 )
% 0.26/0.64         => ( summable_nat @ F ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % summableI_nonneg_bounded
% 0.26/0.64  thf(fact_8347_summableI__nonneg__bounded,axiom,
% 0.26/0.64      ! [F: nat > real,X3: real] :
% 0.26/0.64        ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 0.26/0.64       => ( ! [N2: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ X3 )
% 0.26/0.64         => ( summable_real @ F ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % summableI_nonneg_bounded
% 0.26/0.64  thf(fact_8348_prod_OlessThan__Suc__shift,axiom,
% 0.26/0.64      ! [G: nat > real,N: nat] :
% 0.26/0.64        ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.26/0.64        = ( times_times_real @ ( G @ zero_zero_nat )
% 0.26/0.64          @ ( groups129246275422532515t_real
% 0.26/0.64            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.64            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % prod.lessThan_Suc_shift
% 0.26/0.64  thf(fact_8349_prod_OlessThan__Suc__shift,axiom,
% 0.26/0.64      ! [G: nat > rat,N: nat] :
% 0.26/0.64        ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.26/0.64        = ( times_times_rat @ ( G @ zero_zero_nat )
% 0.26/0.64          @ ( groups73079841787564623at_rat
% 0.26/0.64            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.64            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % prod.lessThan_Suc_shift
% 0.26/0.64  thf(fact_8350_prod_OlessThan__Suc__shift,axiom,
% 0.26/0.64      ! [G: nat > int,N: nat] :
% 0.26/0.64        ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.26/0.64        = ( times_times_int @ ( G @ zero_zero_nat )
% 0.26/0.64          @ ( groups705719431365010083at_int
% 0.26/0.64            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.64            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % prod.lessThan_Suc_shift
% 0.26/0.64  thf(fact_8351_prod_OlessThan__Suc__shift,axiom,
% 0.26/0.64      ! [G: nat > nat,N: nat] :
% 0.26/0.64        ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.26/0.64        = ( times_times_nat @ ( G @ zero_zero_nat )
% 0.26/0.64          @ ( groups708209901874060359at_nat
% 0.26/0.64            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 0.26/0.64            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % prod.lessThan_Suc_shift
% 0.26/0.64  thf(fact_8352_sum__choose__diagonal,axiom,
% 0.26/0.64      ! [M: nat,N: nat] :
% 0.26/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.64       => ( ( groups3542108847815614940at_nat
% 0.26/0.64            @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ M ) )
% 0.26/0.64          = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_choose_diagonal
% 0.26/0.64  thf(fact_8353_sum_OatLeast1__atMost__eq,axiom,
% 0.26/0.64      ! [G: nat > nat,N: nat] :
% 0.26/0.64        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.26/0.64        = ( groups3542108847815614940at_nat
% 0.26/0.64          @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum.atLeast1_atMost_eq
% 0.26/0.64  thf(fact_8354_sum_OatLeast1__atMost__eq,axiom,
% 0.26/0.64      ! [G: nat > real,N: nat] :
% 0.26/0.64        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.26/0.64        = ( groups6591440286371151544t_real
% 0.26/0.64          @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum.atLeast1_atMost_eq
% 0.26/0.64  thf(fact_8355_polyfun__diff,axiom,
% 0.26/0.64      ! [N: nat,A: nat > complex,X3: complex,Y3: complex] :
% 0.26/0.64        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.26/0.64       => ( ( minus_minus_complex
% 0.26/0.64            @ ( groups2073611262835488442omplex
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( power_power_complex @ X3 @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64            @ ( groups2073611262835488442omplex
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( power_power_complex @ Y3 @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64          = ( times_times_complex @ ( minus_minus_complex @ X3 @ Y3 )
% 0.26/0.64            @ ( groups2073611262835488442omplex
% 0.26/0.64              @ ^ [J3: nat] :
% 0.26/0.64                  ( times_times_complex
% 0.26/0.64                  @ ( groups2073611262835488442omplex
% 0.26/0.64                    @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( power_power_complex @ Y3 @ ( minus_minus_nat @ ( minus_minus_nat @ I4 @ J3 ) @ one_one_nat ) ) )
% 0.26/0.64                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 0.26/0.64                  @ ( power_power_complex @ X3 @ J3 ) )
% 0.26/0.64              @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_diff
% 0.26/0.64  thf(fact_8356_polyfun__diff,axiom,
% 0.26/0.64      ! [N: nat,A: nat > rat,X3: rat,Y3: rat] :
% 0.26/0.64        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.26/0.64       => ( ( minus_minus_rat
% 0.26/0.64            @ ( groups2906978787729119204at_rat
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( power_power_rat @ X3 @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64            @ ( groups2906978787729119204at_rat
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( power_power_rat @ Y3 @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64          = ( times_times_rat @ ( minus_minus_rat @ X3 @ Y3 )
% 0.26/0.64            @ ( groups2906978787729119204at_rat
% 0.26/0.64              @ ^ [J3: nat] :
% 0.26/0.64                  ( times_times_rat
% 0.26/0.64                  @ ( groups2906978787729119204at_rat
% 0.26/0.64                    @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( power_power_rat @ Y3 @ ( minus_minus_nat @ ( minus_minus_nat @ I4 @ J3 ) @ one_one_nat ) ) )
% 0.26/0.64                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 0.26/0.64                  @ ( power_power_rat @ X3 @ J3 ) )
% 0.26/0.64              @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_diff
% 0.26/0.64  thf(fact_8357_polyfun__diff,axiom,
% 0.26/0.64      ! [N: nat,A: nat > int,X3: int,Y3: int] :
% 0.26/0.64        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.26/0.64       => ( ( minus_minus_int
% 0.26/0.64            @ ( groups3539618377306564664at_int
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_int @ ( A @ I4 ) @ ( power_power_int @ X3 @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64            @ ( groups3539618377306564664at_int
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_int @ ( A @ I4 ) @ ( power_power_int @ Y3 @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64          = ( times_times_int @ ( minus_minus_int @ X3 @ Y3 )
% 0.26/0.64            @ ( groups3539618377306564664at_int
% 0.26/0.64              @ ^ [J3: nat] :
% 0.26/0.64                  ( times_times_int
% 0.26/0.64                  @ ( groups3539618377306564664at_int
% 0.26/0.64                    @ ^ [I4: nat] : ( times_times_int @ ( A @ I4 ) @ ( power_power_int @ Y3 @ ( minus_minus_nat @ ( minus_minus_nat @ I4 @ J3 ) @ one_one_nat ) ) )
% 0.26/0.64                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 0.26/0.64                  @ ( power_power_int @ X3 @ J3 ) )
% 0.26/0.64              @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_diff
% 0.26/0.64  thf(fact_8358_polyfun__diff,axiom,
% 0.26/0.64      ! [N: nat,A: nat > real,X3: real,Y3: real] :
% 0.26/0.64        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.26/0.64       => ( ( minus_minus_real
% 0.26/0.64            @ ( groups6591440286371151544t_real
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( power_power_real @ X3 @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64            @ ( groups6591440286371151544t_real
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( power_power_real @ Y3 @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64          = ( times_times_real @ ( minus_minus_real @ X3 @ Y3 )
% 0.26/0.64            @ ( groups6591440286371151544t_real
% 0.26/0.64              @ ^ [J3: nat] :
% 0.26/0.64                  ( times_times_real
% 0.26/0.64                  @ ( groups6591440286371151544t_real
% 0.26/0.64                    @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( power_power_real @ Y3 @ ( minus_minus_nat @ ( minus_minus_nat @ I4 @ J3 ) @ one_one_nat ) ) )
% 0.26/0.64                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 0.26/0.64                  @ ( power_power_real @ X3 @ J3 ) )
% 0.26/0.64              @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_diff
% 0.26/0.64  thf(fact_8359_prod_OatLeast1__atMost__eq,axiom,
% 0.26/0.64      ! [G: nat > int,N: nat] :
% 0.26/0.64        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.26/0.64        = ( groups705719431365010083at_int
% 0.26/0.64          @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % prod.atLeast1_atMost_eq
% 0.26/0.64  thf(fact_8360_prod_OatLeast1__atMost__eq,axiom,
% 0.26/0.64      ! [G: nat > nat,N: nat] :
% 0.26/0.64        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.26/0.64        = ( groups708209901874060359at_nat
% 0.26/0.64          @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % prod.atLeast1_atMost_eq
% 0.26/0.64  thf(fact_8361_norm__prod__diff,axiom,
% 0.26/0.64      ! [I5: set_option_nat,Z: option_nat > real,W: option_nat > real] :
% 0.26/0.64        ( ! [I3: option_nat] :
% 0.26/0.64            ( ( member_option_nat @ I3 @ I5 )
% 0.26/0.64           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I3 ) ) @ one_one_real ) )
% 0.26/0.64       => ( ! [I3: option_nat] :
% 0.26/0.64              ( ( member_option_nat @ I3 @ I5 )
% 0.26/0.64             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I3 ) ) @ one_one_real ) )
% 0.26/0.64         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups6579596140936342515t_real @ Z @ I5 ) @ ( groups6579596140936342515t_real @ W @ I5 ) ) )
% 0.26/0.64            @ ( groups4518532050878116744t_real
% 0.26/0.64              @ ^ [I4: option_nat] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 0.26/0.64              @ I5 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % norm_prod_diff
% 0.26/0.64  thf(fact_8362_norm__prod__diff,axiom,
% 0.26/0.64      ! [I5: set_real,Z: real > real,W: real > real] :
% 0.26/0.64        ( ! [I3: real] :
% 0.26/0.64            ( ( member_real @ I3 @ I5 )
% 0.26/0.64           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I3 ) ) @ one_one_real ) )
% 0.26/0.64       => ( ! [I3: real] :
% 0.26/0.64              ( ( member_real @ I3 @ I5 )
% 0.26/0.64             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I3 ) ) @ one_one_real ) )
% 0.26/0.64         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups1681761925125756287l_real @ Z @ I5 ) @ ( groups1681761925125756287l_real @ W @ I5 ) ) )
% 0.26/0.64            @ ( groups8097168146408367636l_real
% 0.26/0.64              @ ^ [I4: real] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 0.26/0.64              @ I5 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % norm_prod_diff
% 0.26/0.64  thf(fact_8363_norm__prod__diff,axiom,
% 0.26/0.64      ! [I5: set_set_nat,Z: set_nat > real,W: set_nat > real] :
% 0.26/0.64        ( ! [I3: set_nat] :
% 0.26/0.64            ( ( member_set_nat @ I3 @ I5 )
% 0.26/0.64           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I3 ) ) @ one_one_real ) )
% 0.26/0.64       => ( ! [I3: set_nat] :
% 0.26/0.64              ( ( member_set_nat @ I3 @ I5 )
% 0.26/0.64             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I3 ) ) @ one_one_real ) )
% 0.26/0.64         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups3619160379726066777t_real @ Z @ I5 ) @ ( groups3619160379726066777t_real @ W @ I5 ) ) )
% 0.26/0.64            @ ( groups5107569545109728110t_real
% 0.26/0.64              @ ^ [I4: set_nat] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 0.26/0.64              @ I5 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % norm_prod_diff
% 0.26/0.64  thf(fact_8364_norm__prod__diff,axiom,
% 0.26/0.64      ! [I5: set_int,Z: int > real,W: int > real] :
% 0.26/0.64        ( ! [I3: int] :
% 0.26/0.64            ( ( member_int @ I3 @ I5 )
% 0.26/0.64           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I3 ) ) @ one_one_real ) )
% 0.26/0.64       => ( ! [I3: int] :
% 0.26/0.64              ( ( member_int @ I3 @ I5 )
% 0.26/0.64             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I3 ) ) @ one_one_real ) )
% 0.26/0.64         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups2316167850115554303t_real @ Z @ I5 ) @ ( groups2316167850115554303t_real @ W @ I5 ) ) )
% 0.26/0.64            @ ( groups8778361861064173332t_real
% 0.26/0.64              @ ^ [I4: int] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 0.26/0.64              @ I5 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % norm_prod_diff
% 0.26/0.64  thf(fact_8365_norm__prod__diff,axiom,
% 0.26/0.64      ! [I5: set_option_nat,Z: option_nat > complex,W: option_nat > complex] :
% 0.26/0.64        ( ! [I3: option_nat] :
% 0.26/0.64            ( ( member_option_nat @ I3 @ I5 )
% 0.26/0.64           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I3 ) ) @ one_one_real ) )
% 0.26/0.64       => ( ! [I3: option_nat] :
% 0.26/0.64              ( ( member_option_nat @ I3 @ I5 )
% 0.26/0.64             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I3 ) ) @ one_one_real ) )
% 0.26/0.64         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups1917955009447795573omplex @ Z @ I5 ) @ ( groups1917955009447795573omplex @ W @ I5 ) ) )
% 0.26/0.64            @ ( groups4518532050878116744t_real
% 0.26/0.64              @ ^ [I4: option_nat] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 0.26/0.64              @ I5 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % norm_prod_diff
% 0.26/0.64  thf(fact_8366_norm__prod__diff,axiom,
% 0.26/0.64      ! [I5: set_real,Z: real > complex,W: real > complex] :
% 0.26/0.64        ( ! [I3: real] :
% 0.26/0.64            ( ( member_real @ I3 @ I5 )
% 0.26/0.64           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I3 ) ) @ one_one_real ) )
% 0.26/0.64       => ( ! [I3: real] :
% 0.26/0.64              ( ( member_real @ I3 @ I5 )
% 0.26/0.64             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I3 ) ) @ one_one_real ) )
% 0.26/0.64         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups713298508707869441omplex @ Z @ I5 ) @ ( groups713298508707869441omplex @ W @ I5 ) ) )
% 0.26/0.64            @ ( groups8097168146408367636l_real
% 0.26/0.64              @ ^ [I4: real] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 0.26/0.64              @ I5 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % norm_prod_diff
% 0.26/0.64  thf(fact_8367_norm__prod__diff,axiom,
% 0.26/0.64      ! [I5: set_set_nat,Z: set_nat > complex,W: set_nat > complex] :
% 0.26/0.64        ( ! [I3: set_nat] :
% 0.26/0.64            ( ( member_set_nat @ I3 @ I5 )
% 0.26/0.64           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I3 ) ) @ one_one_real ) )
% 0.26/0.64       => ( ! [I3: set_nat] :
% 0.26/0.64              ( ( member_set_nat @ I3 @ I5 )
% 0.26/0.64             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I3 ) ) @ one_one_real ) )
% 0.26/0.64         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups1092910753850256091omplex @ Z @ I5 ) @ ( groups1092910753850256091omplex @ W @ I5 ) ) )
% 0.26/0.64            @ ( groups5107569545109728110t_real
% 0.26/0.64              @ ^ [I4: set_nat] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 0.26/0.64              @ I5 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % norm_prod_diff
% 0.26/0.64  thf(fact_8368_norm__prod__diff,axiom,
% 0.26/0.64      ! [I5: set_int,Z: int > complex,W: int > complex] :
% 0.26/0.64        ( ! [I3: int] :
% 0.26/0.64            ( ( member_int @ I3 @ I5 )
% 0.26/0.64           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I3 ) ) @ one_one_real ) )
% 0.26/0.64       => ( ! [I3: int] :
% 0.26/0.64              ( ( member_int @ I3 @ I5 )
% 0.26/0.64             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I3 ) ) @ one_one_real ) )
% 0.26/0.64         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups7440179247065528705omplex @ Z @ I5 ) @ ( groups7440179247065528705omplex @ W @ I5 ) ) )
% 0.26/0.64            @ ( groups8778361861064173332t_real
% 0.26/0.64              @ ^ [I4: int] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 0.26/0.64              @ I5 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % norm_prod_diff
% 0.26/0.64  thf(fact_8369_norm__prod__diff,axiom,
% 0.26/0.64      ! [I5: set_nat,Z: nat > real,W: nat > real] :
% 0.26/0.64        ( ! [I3: nat] :
% 0.26/0.64            ( ( member_nat @ I3 @ I5 )
% 0.26/0.64           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I3 ) ) @ one_one_real ) )
% 0.26/0.64       => ( ! [I3: nat] :
% 0.26/0.64              ( ( member_nat @ I3 @ I5 )
% 0.26/0.64             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I3 ) ) @ one_one_real ) )
% 0.26/0.64         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups129246275422532515t_real @ Z @ I5 ) @ ( groups129246275422532515t_real @ W @ I5 ) ) )
% 0.26/0.64            @ ( groups6591440286371151544t_real
% 0.26/0.64              @ ^ [I4: nat] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 0.26/0.64              @ I5 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % norm_prod_diff
% 0.26/0.64  thf(fact_8370_norm__prod__diff,axiom,
% 0.26/0.64      ! [I5: set_nat,Z: nat > complex,W: nat > complex] :
% 0.26/0.64        ( ! [I3: nat] :
% 0.26/0.64            ( ( member_nat @ I3 @ I5 )
% 0.26/0.64           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I3 ) ) @ one_one_real ) )
% 0.26/0.64       => ( ! [I3: nat] :
% 0.26/0.64              ( ( member_nat @ I3 @ I5 )
% 0.26/0.64             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I3 ) ) @ one_one_real ) )
% 0.26/0.64         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups6464643781859351333omplex @ Z @ I5 ) @ ( groups6464643781859351333omplex @ W @ I5 ) ) )
% 0.26/0.64            @ ( groups6591440286371151544t_real
% 0.26/0.64              @ ^ [I4: nat] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 0.26/0.64              @ I5 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % norm_prod_diff
% 0.26/0.64  thf(fact_8371_zero__polynom__imp__zero__coeffs,axiom,
% 0.26/0.64      ! [C: nat > complex,N: nat,K: nat] :
% 0.26/0.64        ( ! [W2: complex] :
% 0.26/0.64            ( ( groups2073611262835488442omplex
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ W2 @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64            = zero_zero_complex )
% 0.26/0.64       => ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.64         => ( ( C @ K )
% 0.26/0.64            = zero_zero_complex ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % zero_polynom_imp_zero_coeffs
% 0.26/0.64  thf(fact_8372_zero__polynom__imp__zero__coeffs,axiom,
% 0.26/0.64      ! [C: nat > real,N: nat,K: nat] :
% 0.26/0.64        ( ! [W2: real] :
% 0.26/0.64            ( ( groups6591440286371151544t_real
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ W2 @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64            = zero_zero_real )
% 0.26/0.64       => ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.64         => ( ( C @ K )
% 0.26/0.64            = zero_zero_real ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % zero_polynom_imp_zero_coeffs
% 0.26/0.64  thf(fact_8373_polyfun__eq__0,axiom,
% 0.26/0.64      ! [C: nat > complex,N: nat] :
% 0.26/0.64        ( ( ! [X: complex] :
% 0.26/0.64              ( ( groups2073611262835488442omplex
% 0.26/0.64                @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ X @ I4 ) )
% 0.26/0.64                @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64              = zero_zero_complex ) )
% 0.26/0.64        = ( ! [I4: nat] :
% 0.26/0.64              ( ( ord_less_eq_nat @ I4 @ N )
% 0.26/0.64             => ( ( C @ I4 )
% 0.26/0.64                = zero_zero_complex ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_eq_0
% 0.26/0.64  thf(fact_8374_polyfun__eq__0,axiom,
% 0.26/0.64      ! [C: nat > real,N: nat] :
% 0.26/0.64        ( ( ! [X: real] :
% 0.26/0.64              ( ( groups6591440286371151544t_real
% 0.26/0.64                @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ X @ I4 ) )
% 0.26/0.64                @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64              = zero_zero_real ) )
% 0.26/0.64        = ( ! [I4: nat] :
% 0.26/0.64              ( ( ord_less_eq_nat @ I4 @ N )
% 0.26/0.64             => ( ( C @ I4 )
% 0.26/0.64                = zero_zero_real ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_eq_0
% 0.26/0.64  thf(fact_8375_one__diff__power__eq,axiom,
% 0.26/0.64      ! [X3: complex,N: nat] :
% 0.26/0.64        ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ N ) )
% 0.26/0.64        = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X3 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % one_diff_power_eq
% 0.26/0.64  thf(fact_8376_one__diff__power__eq,axiom,
% 0.26/0.64      ! [X3: rat,N: nat] :
% 0.26/0.64        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ N ) )
% 0.26/0.64        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X3 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % one_diff_power_eq
% 0.26/0.64  thf(fact_8377_one__diff__power__eq,axiom,
% 0.26/0.64      ! [X3: int,N: nat] :
% 0.26/0.64        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X3 @ N ) )
% 0.26/0.64        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X3 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % one_diff_power_eq
% 0.26/0.64  thf(fact_8378_one__diff__power__eq,axiom,
% 0.26/0.64      ! [X3: real,N: nat] :
% 0.26/0.64        ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ N ) )
% 0.26/0.64        = ( times_times_real @ ( minus_minus_real @ one_one_real @ X3 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % one_diff_power_eq
% 0.26/0.64  thf(fact_8379_power__diff__1__eq,axiom,
% 0.26/0.64      ! [X3: complex,N: nat] :
% 0.26/0.64        ( ( minus_minus_complex @ ( power_power_complex @ X3 @ N ) @ one_one_complex )
% 0.26/0.64        = ( times_times_complex @ ( minus_minus_complex @ X3 @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % power_diff_1_eq
% 0.26/0.64  thf(fact_8380_power__diff__1__eq,axiom,
% 0.26/0.64      ! [X3: rat,N: nat] :
% 0.26/0.64        ( ( minus_minus_rat @ ( power_power_rat @ X3 @ N ) @ one_one_rat )
% 0.26/0.64        = ( times_times_rat @ ( minus_minus_rat @ X3 @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % power_diff_1_eq
% 0.26/0.64  thf(fact_8381_power__diff__1__eq,axiom,
% 0.26/0.64      ! [X3: int,N: nat] :
% 0.26/0.64        ( ( minus_minus_int @ ( power_power_int @ X3 @ N ) @ one_one_int )
% 0.26/0.64        = ( times_times_int @ ( minus_minus_int @ X3 @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % power_diff_1_eq
% 0.26/0.64  thf(fact_8382_power__diff__1__eq,axiom,
% 0.26/0.64      ! [X3: real,N: nat] :
% 0.26/0.64        ( ( minus_minus_real @ ( power_power_real @ X3 @ N ) @ one_one_real )
% 0.26/0.64        = ( times_times_real @ ( minus_minus_real @ X3 @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % power_diff_1_eq
% 0.26/0.64  thf(fact_8383_geometric__sum,axiom,
% 0.26/0.64      ! [X3: complex,N: nat] :
% 0.26/0.64        ( ( X3 != one_one_complex )
% 0.26/0.64       => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.64          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X3 @ N ) @ one_one_complex ) @ ( minus_minus_complex @ X3 @ one_one_complex ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % geometric_sum
% 0.26/0.64  thf(fact_8384_geometric__sum,axiom,
% 0.26/0.64      ! [X3: rat,N: nat] :
% 0.26/0.64        ( ( X3 != one_one_rat )
% 0.26/0.64       => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.64          = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X3 @ N ) @ one_one_rat ) @ ( minus_minus_rat @ X3 @ one_one_rat ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % geometric_sum
% 0.26/0.64  thf(fact_8385_geometric__sum,axiom,
% 0.26/0.64      ! [X3: real,N: nat] :
% 0.26/0.64        ( ( X3 != one_one_real )
% 0.26/0.64       => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.64          = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X3 @ N ) @ one_one_real ) @ ( minus_minus_real @ X3 @ one_one_real ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % geometric_sum
% 0.26/0.64  thf(fact_8386_choose__row__sum,axiom,
% 0.26/0.64      ! [N: nat] :
% 0.26/0.64        ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.26/0.64  
% 0.26/0.64  % choose_row_sum
% 0.26/0.64  thf(fact_8387_binomial,axiom,
% 0.26/0.64      ! [A: nat,B: nat,N: nat] :
% 0.26/0.64        ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 0.26/0.64        = ( groups3542108847815614940at_nat
% 0.26/0.64          @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % binomial
% 0.26/0.64  thf(fact_8388_ln__prod,axiom,
% 0.26/0.64      ! [I5: set_option_nat,F: option_nat > real] :
% 0.26/0.64        ( ( finite5523153139673422903on_nat @ I5 )
% 0.26/0.64       => ( ! [I3: option_nat] :
% 0.26/0.64              ( ( member_option_nat @ I3 @ I5 )
% 0.26/0.64             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.64         => ( ( ln_ln_real @ ( groups6579596140936342515t_real @ F @ I5 ) )
% 0.26/0.64            = ( groups4518532050878116744t_real
% 0.26/0.64              @ ^ [X: option_nat] : ( ln_ln_real @ ( F @ X ) )
% 0.26/0.64              @ I5 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % ln_prod
% 0.26/0.64  thf(fact_8389_ln__prod,axiom,
% 0.26/0.64      ! [I5: set_real,F: real > real] :
% 0.26/0.64        ( ( finite_finite_real @ I5 )
% 0.26/0.64       => ( ! [I3: real] :
% 0.26/0.64              ( ( member_real @ I3 @ I5 )
% 0.26/0.64             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.64         => ( ( ln_ln_real @ ( groups1681761925125756287l_real @ F @ I5 ) )
% 0.26/0.64            = ( groups8097168146408367636l_real
% 0.26/0.64              @ ^ [X: real] : ( ln_ln_real @ ( F @ X ) )
% 0.26/0.64              @ I5 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % ln_prod
% 0.26/0.64  thf(fact_8390_ln__prod,axiom,
% 0.26/0.64      ! [I5: set_set_nat,F: set_nat > real] :
% 0.26/0.64        ( ( finite1152437895449049373et_nat @ I5 )
% 0.26/0.64       => ( ! [I3: set_nat] :
% 0.26/0.64              ( ( member_set_nat @ I3 @ I5 )
% 0.26/0.64             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.64         => ( ( ln_ln_real @ ( groups3619160379726066777t_real @ F @ I5 ) )
% 0.26/0.64            = ( groups5107569545109728110t_real
% 0.26/0.64              @ ^ [X: set_nat] : ( ln_ln_real @ ( F @ X ) )
% 0.26/0.64              @ I5 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % ln_prod
% 0.26/0.64  thf(fact_8391_ln__prod,axiom,
% 0.26/0.64      ! [I5: set_int,F: int > real] :
% 0.26/0.64        ( ( finite_finite_int @ I5 )
% 0.26/0.64       => ( ! [I3: int] :
% 0.26/0.64              ( ( member_int @ I3 @ I5 )
% 0.26/0.64             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.64         => ( ( ln_ln_real @ ( groups2316167850115554303t_real @ F @ I5 ) )
% 0.26/0.64            = ( groups8778361861064173332t_real
% 0.26/0.64              @ ^ [X: int] : ( ln_ln_real @ ( F @ X ) )
% 0.26/0.64              @ I5 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % ln_prod
% 0.26/0.64  thf(fact_8392_ln__prod,axiom,
% 0.26/0.64      ! [I5: set_complex,F: complex > real] :
% 0.26/0.64        ( ( finite3207457112153483333omplex @ I5 )
% 0.26/0.64       => ( ! [I3: complex] :
% 0.26/0.64              ( ( member_complex @ I3 @ I5 )
% 0.26/0.64             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.64         => ( ( ln_ln_real @ ( groups766887009212190081x_real @ F @ I5 ) )
% 0.26/0.64            = ( groups5808333547571424918x_real
% 0.26/0.64              @ ^ [X: complex] : ( ln_ln_real @ ( F @ X ) )
% 0.26/0.64              @ I5 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % ln_prod
% 0.26/0.64  thf(fact_8393_ln__prod,axiom,
% 0.26/0.64      ! [I5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > real] :
% 0.26/0.64        ( ( finite6177210948735845034at_nat @ I5 )
% 0.26/0.64       => ( ! [I3: product_prod_nat_nat] :
% 0.26/0.64              ( ( member8440522571783428010at_nat @ I3 @ I5 )
% 0.26/0.64             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.64         => ( ( ln_ln_real @ ( groups6036352826371341000t_real @ F @ I5 ) )
% 0.26/0.64            = ( groups4567486121110086003t_real
% 0.26/0.64              @ ^ [X: product_prod_nat_nat] : ( ln_ln_real @ ( F @ X ) )
% 0.26/0.64              @ I5 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % ln_prod
% 0.26/0.64  thf(fact_8394_ln__prod,axiom,
% 0.26/0.64      ! [I5: set_Extended_enat,F: extended_enat > real] :
% 0.26/0.64        ( ( finite4001608067531595151d_enat @ I5 )
% 0.26/0.64       => ( ! [I3: extended_enat] :
% 0.26/0.64              ( ( member_Extended_enat @ I3 @ I5 )
% 0.26/0.64             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.64         => ( ( ln_ln_real @ ( groups97031904164794029t_real @ F @ I5 ) )
% 0.26/0.64            = ( groups4148127829035722712t_real
% 0.26/0.64              @ ^ [X: extended_enat] : ( ln_ln_real @ ( F @ X ) )
% 0.26/0.64              @ I5 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % ln_prod
% 0.26/0.64  thf(fact_8395_ln__prod,axiom,
% 0.26/0.64      ! [I5: set_nat,F: nat > real] :
% 0.26/0.64        ( ( finite_finite_nat @ I5 )
% 0.26/0.64       => ( ! [I3: nat] :
% 0.26/0.64              ( ( member_nat @ I3 @ I5 )
% 0.26/0.64             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.26/0.64         => ( ( ln_ln_real @ ( groups129246275422532515t_real @ F @ I5 ) )
% 0.26/0.64            = ( groups6591440286371151544t_real
% 0.26/0.64              @ ^ [X: nat] : ( ln_ln_real @ ( F @ X ) )
% 0.26/0.64              @ I5 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % ln_prod
% 0.26/0.64  thf(fact_8396_sum__less__suminf,axiom,
% 0.26/0.64      ! [F: nat > int,N: nat] :
% 0.26/0.64        ( ( summable_int @ F )
% 0.26/0.64       => ( ! [M4: nat] :
% 0.26/0.64              ( ( ord_less_eq_nat @ N @ M4 )
% 0.26/0.64             => ( ord_less_int @ zero_zero_int @ ( F @ M4 ) ) )
% 0.26/0.64         => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_int @ F ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_less_suminf
% 0.26/0.64  thf(fact_8397_sum__less__suminf,axiom,
% 0.26/0.64      ! [F: nat > nat,N: nat] :
% 0.26/0.64        ( ( summable_nat @ F )
% 0.26/0.64       => ( ! [M4: nat] :
% 0.26/0.64              ( ( ord_less_eq_nat @ N @ M4 )
% 0.26/0.64             => ( ord_less_nat @ zero_zero_nat @ ( F @ M4 ) ) )
% 0.26/0.64         => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_nat @ F ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_less_suminf
% 0.26/0.64  thf(fact_8398_sum__less__suminf,axiom,
% 0.26/0.64      ! [F: nat > real,N: nat] :
% 0.26/0.64        ( ( summable_real @ F )
% 0.26/0.64       => ( ! [M4: nat] :
% 0.26/0.64              ( ( ord_less_eq_nat @ N @ M4 )
% 0.26/0.64             => ( ord_less_real @ zero_zero_real @ ( F @ M4 ) ) )
% 0.26/0.64         => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_real @ F ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_less_suminf
% 0.26/0.64  thf(fact_8399_sum__gp__basic,axiom,
% 0.26/0.64      ! [X3: complex,N: nat] :
% 0.26/0.64        ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X3 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64        = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ ( suc @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_gp_basic
% 0.26/0.64  thf(fact_8400_sum__gp__basic,axiom,
% 0.26/0.64      ! [X3: rat,N: nat] :
% 0.26/0.64        ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X3 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64        = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ ( suc @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_gp_basic
% 0.26/0.64  thf(fact_8401_sum__gp__basic,axiom,
% 0.26/0.64      ! [X3: int,N: nat] :
% 0.26/0.64        ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X3 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64        = ( minus_minus_int @ one_one_int @ ( power_power_int @ X3 @ ( suc @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_gp_basic
% 0.26/0.64  thf(fact_8402_sum__gp__basic,axiom,
% 0.26/0.64      ! [X3: real,N: nat] :
% 0.26/0.64        ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X3 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64        = ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( suc @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_gp_basic
% 0.26/0.64  thf(fact_8403_polyfun__roots__finite,axiom,
% 0.26/0.64      ! [C: nat > complex,K: nat,N: nat] :
% 0.26/0.64        ( ( ( C @ K )
% 0.26/0.64         != zero_zero_complex )
% 0.26/0.64       => ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.64         => ( finite3207457112153483333omplex
% 0.26/0.64            @ ( collect_complex
% 0.26/0.64              @ ^ [Z6: complex] :
% 0.26/0.64                  ( ( groups2073611262835488442omplex
% 0.26/0.64                    @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ Z6 @ I4 ) )
% 0.26/0.64                    @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64                  = zero_zero_complex ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_roots_finite
% 0.26/0.64  thf(fact_8404_polyfun__roots__finite,axiom,
% 0.26/0.64      ! [C: nat > real,K: nat,N: nat] :
% 0.26/0.64        ( ( ( C @ K )
% 0.26/0.64         != zero_zero_real )
% 0.26/0.64       => ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.64         => ( finite_finite_real
% 0.26/0.64            @ ( collect_real
% 0.26/0.64              @ ^ [Z6: real] :
% 0.26/0.64                  ( ( groups6591440286371151544t_real
% 0.26/0.64                    @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ Z6 @ I4 ) )
% 0.26/0.64                    @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64                  = zero_zero_real ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_roots_finite
% 0.26/0.64  thf(fact_8405_polyfun__finite__roots,axiom,
% 0.26/0.64      ! [C: nat > complex,N: nat] :
% 0.26/0.64        ( ( finite3207457112153483333omplex
% 0.26/0.64          @ ( collect_complex
% 0.26/0.64            @ ^ [X: complex] :
% 0.26/0.64                ( ( groups2073611262835488442omplex
% 0.26/0.64                  @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ X @ I4 ) )
% 0.26/0.64                  @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64                = zero_zero_complex ) ) )
% 0.26/0.64        = ( ? [I4: nat] :
% 0.26/0.64              ( ( ord_less_eq_nat @ I4 @ N )
% 0.26/0.64              & ( ( C @ I4 )
% 0.26/0.64               != zero_zero_complex ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_finite_roots
% 0.26/0.64  thf(fact_8406_polyfun__finite__roots,axiom,
% 0.26/0.64      ! [C: nat > real,N: nat] :
% 0.26/0.64        ( ( finite_finite_real
% 0.26/0.64          @ ( collect_real
% 0.26/0.64            @ ^ [X: real] :
% 0.26/0.64                ( ( groups6591440286371151544t_real
% 0.26/0.64                  @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ X @ I4 ) )
% 0.26/0.64                  @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64                = zero_zero_real ) ) )
% 0.26/0.64        = ( ? [I4: nat] :
% 0.26/0.64              ( ( ord_less_eq_nat @ I4 @ N )
% 0.26/0.64              & ( ( C @ I4 )
% 0.26/0.64               != zero_zero_real ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_finite_roots
% 0.26/0.64  thf(fact_8407_sum__gp__strict,axiom,
% 0.26/0.64      ! [X3: complex,N: nat] :
% 0.26/0.64        ( ( ( X3 = one_one_complex )
% 0.26/0.64         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.64            = ( semiri8010041392384452111omplex @ N ) ) )
% 0.26/0.64        & ( ( X3 != one_one_complex )
% 0.26/0.64         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.64            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ N ) ) @ ( minus_minus_complex @ one_one_complex @ X3 ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_gp_strict
% 0.26/0.64  thf(fact_8408_sum__gp__strict,axiom,
% 0.26/0.64      ! [X3: rat,N: nat] :
% 0.26/0.64        ( ( ( X3 = one_one_rat )
% 0.26/0.64         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.64            = ( semiri681578069525770553at_rat @ N ) ) )
% 0.26/0.64        & ( ( X3 != one_one_rat )
% 0.26/0.64         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.64            = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ N ) ) @ ( minus_minus_rat @ one_one_rat @ X3 ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_gp_strict
% 0.26/0.64  thf(fact_8409_sum__gp__strict,axiom,
% 0.26/0.64      ! [X3: real,N: nat] :
% 0.26/0.64        ( ( ( X3 = one_one_real )
% 0.26/0.64         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.64            = ( semiri5074537144036343181t_real @ N ) ) )
% 0.26/0.64        & ( ( X3 != one_one_real )
% 0.26/0.64         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.64            = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ N ) ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_gp_strict
% 0.26/0.64  thf(fact_8410_lemma__termdiff1,axiom,
% 0.26/0.64      ! [Z: complex,H2: complex,M: nat] :
% 0.26/0.64        ( ( groups2073611262835488442omplex
% 0.26/0.64          @ ^ [P5: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_complex @ Z @ P5 ) ) @ ( power_power_complex @ Z @ M ) )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ M ) )
% 0.26/0.64        = ( groups2073611262835488442omplex
% 0.26/0.64          @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ Z @ P5 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % lemma_termdiff1
% 0.26/0.64  thf(fact_8411_lemma__termdiff1,axiom,
% 0.26/0.64      ! [Z: rat,H2: rat,M: nat] :
% 0.26/0.64        ( ( groups2906978787729119204at_rat
% 0.26/0.64          @ ^ [P5: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_rat @ Z @ P5 ) ) @ ( power_power_rat @ Z @ M ) )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ M ) )
% 0.26/0.64        = ( groups2906978787729119204at_rat
% 0.26/0.64          @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ Z @ P5 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % lemma_termdiff1
% 0.26/0.64  thf(fact_8412_lemma__termdiff1,axiom,
% 0.26/0.64      ! [Z: int,H2: int,M: nat] :
% 0.26/0.64        ( ( groups3539618377306564664at_int
% 0.26/0.64          @ ^ [P5: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_int @ Z @ P5 ) ) @ ( power_power_int @ Z @ M ) )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ M ) )
% 0.26/0.64        = ( groups3539618377306564664at_int
% 0.26/0.64          @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ Z @ P5 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_int @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % lemma_termdiff1
% 0.26/0.64  thf(fact_8413_lemma__termdiff1,axiom,
% 0.26/0.64      ! [Z: real,H2: real,M: nat] :
% 0.26/0.64        ( ( groups6591440286371151544t_real
% 0.26/0.64          @ ^ [P5: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_real @ Z @ P5 ) ) @ ( power_power_real @ Z @ M ) )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ M ) )
% 0.26/0.64        = ( groups6591440286371151544t_real
% 0.26/0.64          @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ Z @ P5 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_real @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % lemma_termdiff1
% 0.26/0.64  thf(fact_8414_power__diff__sumr2,axiom,
% 0.26/0.64      ! [X3: complex,N: nat,Y3: complex] :
% 0.26/0.64        ( ( minus_minus_complex @ ( power_power_complex @ X3 @ N ) @ ( power_power_complex @ Y3 @ N ) )
% 0.26/0.64        = ( times_times_complex @ ( minus_minus_complex @ X3 @ Y3 )
% 0.26/0.64          @ ( groups2073611262835488442omplex
% 0.26/0.64            @ ^ [I4: nat] : ( times_times_complex @ ( power_power_complex @ Y3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_complex @ X3 @ I4 ) )
% 0.26/0.64            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % power_diff_sumr2
% 0.26/0.64  thf(fact_8415_power__diff__sumr2,axiom,
% 0.26/0.64      ! [X3: rat,N: nat,Y3: rat] :
% 0.26/0.64        ( ( minus_minus_rat @ ( power_power_rat @ X3 @ N ) @ ( power_power_rat @ Y3 @ N ) )
% 0.26/0.64        = ( times_times_rat @ ( minus_minus_rat @ X3 @ Y3 )
% 0.26/0.64          @ ( groups2906978787729119204at_rat
% 0.26/0.64            @ ^ [I4: nat] : ( times_times_rat @ ( power_power_rat @ Y3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_rat @ X3 @ I4 ) )
% 0.26/0.64            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % power_diff_sumr2
% 0.26/0.64  thf(fact_8416_power__diff__sumr2,axiom,
% 0.26/0.64      ! [X3: int,N: nat,Y3: int] :
% 0.26/0.64        ( ( minus_minus_int @ ( power_power_int @ X3 @ N ) @ ( power_power_int @ Y3 @ N ) )
% 0.26/0.64        = ( times_times_int @ ( minus_minus_int @ X3 @ Y3 )
% 0.26/0.64          @ ( groups3539618377306564664at_int
% 0.26/0.64            @ ^ [I4: nat] : ( times_times_int @ ( power_power_int @ Y3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_int @ X3 @ I4 ) )
% 0.26/0.64            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % power_diff_sumr2
% 0.26/0.64  thf(fact_8417_power__diff__sumr2,axiom,
% 0.26/0.64      ! [X3: real,N: nat,Y3: real] :
% 0.26/0.64        ( ( minus_minus_real @ ( power_power_real @ X3 @ N ) @ ( power_power_real @ Y3 @ N ) )
% 0.26/0.64        = ( times_times_real @ ( minus_minus_real @ X3 @ Y3 )
% 0.26/0.64          @ ( groups6591440286371151544t_real
% 0.26/0.64            @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ Y3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_real @ X3 @ I4 ) )
% 0.26/0.64            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % power_diff_sumr2
% 0.26/0.64  thf(fact_8418_diff__power__eq__sum,axiom,
% 0.26/0.64      ! [X3: complex,N: nat,Y3: complex] :
% 0.26/0.64        ( ( minus_minus_complex @ ( power_power_complex @ X3 @ ( suc @ N ) ) @ ( power_power_complex @ Y3 @ ( suc @ N ) ) )
% 0.26/0.64        = ( times_times_complex @ ( minus_minus_complex @ X3 @ Y3 )
% 0.26/0.64          @ ( groups2073611262835488442omplex
% 0.26/0.64            @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ X3 @ P5 ) @ ( power_power_complex @ Y3 @ ( minus_minus_nat @ N @ P5 ) ) )
% 0.26/0.64            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % diff_power_eq_sum
% 0.26/0.64  thf(fact_8419_diff__power__eq__sum,axiom,
% 0.26/0.64      ! [X3: rat,N: nat,Y3: rat] :
% 0.26/0.64        ( ( minus_minus_rat @ ( power_power_rat @ X3 @ ( suc @ N ) ) @ ( power_power_rat @ Y3 @ ( suc @ N ) ) )
% 0.26/0.64        = ( times_times_rat @ ( minus_minus_rat @ X3 @ Y3 )
% 0.26/0.64          @ ( groups2906978787729119204at_rat
% 0.26/0.64            @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ X3 @ P5 ) @ ( power_power_rat @ Y3 @ ( minus_minus_nat @ N @ P5 ) ) )
% 0.26/0.64            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % diff_power_eq_sum
% 0.26/0.64  thf(fact_8420_diff__power__eq__sum,axiom,
% 0.26/0.64      ! [X3: int,N: nat,Y3: int] :
% 0.26/0.64        ( ( minus_minus_int @ ( power_power_int @ X3 @ ( suc @ N ) ) @ ( power_power_int @ Y3 @ ( suc @ N ) ) )
% 0.26/0.64        = ( times_times_int @ ( minus_minus_int @ X3 @ Y3 )
% 0.26/0.64          @ ( groups3539618377306564664at_int
% 0.26/0.64            @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ X3 @ P5 ) @ ( power_power_int @ Y3 @ ( minus_minus_nat @ N @ P5 ) ) )
% 0.26/0.64            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % diff_power_eq_sum
% 0.26/0.64  thf(fact_8421_diff__power__eq__sum,axiom,
% 0.26/0.64      ! [X3: real,N: nat,Y3: real] :
% 0.26/0.64        ( ( minus_minus_real @ ( power_power_real @ X3 @ ( suc @ N ) ) @ ( power_power_real @ Y3 @ ( suc @ N ) ) )
% 0.26/0.64        = ( times_times_real @ ( minus_minus_real @ X3 @ Y3 )
% 0.26/0.64          @ ( groups6591440286371151544t_real
% 0.26/0.64            @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ X3 @ P5 ) @ ( power_power_real @ Y3 @ ( minus_minus_nat @ N @ P5 ) ) )
% 0.26/0.64            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % diff_power_eq_sum
% 0.26/0.64  thf(fact_8422_polynomial__product__nat,axiom,
% 0.26/0.64      ! [M: nat,A: nat > nat,N: nat,B: nat > nat,X3: nat] :
% 0.26/0.64        ( ! [I3: nat] :
% 0.26/0.64            ( ( ord_less_nat @ M @ I3 )
% 0.26/0.64           => ( ( A @ I3 )
% 0.26/0.64              = zero_zero_nat ) )
% 0.26/0.64       => ( ! [J2: nat] :
% 0.26/0.64              ( ( ord_less_nat @ N @ J2 )
% 0.26/0.64             => ( ( B @ J2 )
% 0.26/0.64                = zero_zero_nat ) )
% 0.26/0.64         => ( ( times_times_nat
% 0.26/0.64              @ ( groups3542108847815614940at_nat
% 0.26/0.64                @ ^ [I4: nat] : ( times_times_nat @ ( A @ I4 ) @ ( power_power_nat @ X3 @ I4 ) )
% 0.26/0.64                @ ( set_ord_atMost_nat @ M ) )
% 0.26/0.64              @ ( groups3542108847815614940at_nat
% 0.26/0.64                @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X3 @ J3 ) )
% 0.26/0.64                @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64            = ( groups3542108847815614940at_nat
% 0.26/0.64              @ ^ [R5: nat] :
% 0.26/0.64                  ( times_times_nat
% 0.26/0.64                  @ ( groups3542108847815614940at_nat
% 0.26/0.64                    @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 0.26/0.64                    @ ( set_ord_atMost_nat @ R5 ) )
% 0.26/0.64                  @ ( power_power_nat @ X3 @ R5 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polynomial_product_nat
% 0.26/0.64  thf(fact_8423_sum__power__shift,axiom,
% 0.26/0.64      ! [M: nat,N: nat,X3: complex] :
% 0.26/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.64       => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.64          = ( times_times_complex @ ( power_power_complex @ X3 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_power_shift
% 0.26/0.64  thf(fact_8424_sum__power__shift,axiom,
% 0.26/0.64      ! [M: nat,N: nat,X3: rat] :
% 0.26/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.64       => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.64          = ( times_times_rat @ ( power_power_rat @ X3 @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_power_shift
% 0.26/0.64  thf(fact_8425_sum__power__shift,axiom,
% 0.26/0.64      ! [M: nat,N: nat,X3: int] :
% 0.26/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.64       => ( ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.64          = ( times_times_int @ ( power_power_int @ X3 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_power_shift
% 0.26/0.64  thf(fact_8426_sum__power__shift,axiom,
% 0.26/0.64      ! [M: nat,N: nat,X3: real] :
% 0.26/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.64       => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.26/0.64          = ( times_times_real @ ( power_power_real @ X3 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_power_shift
% 0.26/0.64  thf(fact_8427_choose__square__sum,axiom,
% 0.26/0.64      ! [N: nat] :
% 0.26/0.64        ( ( groups3542108847815614940at_nat
% 0.26/0.64          @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64        = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 0.26/0.64  
% 0.26/0.64  % choose_square_sum
% 0.26/0.64  thf(fact_8428_set__encode__def,axiom,
% 0.26/0.64      ( nat_set_encode
% 0.26/0.64      = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % set_encode_def
% 0.26/0.64  thf(fact_8429_atLeast1__atMost__eq__remove0,axiom,
% 0.26/0.64      ! [N: nat] :
% 0.26/0.64        ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.26/0.64        = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % atLeast1_atMost_eq_remove0
% 0.26/0.64  thf(fact_8430_real__sum__nat__ivl__bounded2,axiom,
% 0.26/0.64      ! [N: nat,F: nat > rat,K5: rat,K: nat] :
% 0.26/0.64        ( ! [P7: nat] :
% 0.26/0.64            ( ( ord_less_nat @ P7 @ N )
% 0.26/0.64           => ( ord_less_eq_rat @ ( F @ P7 ) @ K5 ) )
% 0.26/0.64       => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 0.26/0.64         => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ K5 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % real_sum_nat_ivl_bounded2
% 0.26/0.64  thf(fact_8431_real__sum__nat__ivl__bounded2,axiom,
% 0.26/0.64      ! [N: nat,F: nat > int,K5: int,K: nat] :
% 0.26/0.64        ( ! [P7: nat] :
% 0.26/0.64            ( ( ord_less_nat @ P7 @ N )
% 0.26/0.64           => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 0.26/0.64       => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 0.26/0.64         => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ K5 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % real_sum_nat_ivl_bounded2
% 0.26/0.64  thf(fact_8432_real__sum__nat__ivl__bounded2,axiom,
% 0.26/0.64      ! [N: nat,F: nat > nat,K5: nat,K: nat] :
% 0.26/0.64        ( ! [P7: nat] :
% 0.26/0.64            ( ( ord_less_nat @ P7 @ N )
% 0.26/0.64           => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 0.26/0.64       => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 0.26/0.64         => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ K5 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % real_sum_nat_ivl_bounded2
% 0.26/0.64  thf(fact_8433_real__sum__nat__ivl__bounded2,axiom,
% 0.26/0.64      ! [N: nat,F: nat > real,K5: real,K: nat] :
% 0.26/0.64        ( ! [P7: nat] :
% 0.26/0.64            ( ( ord_less_nat @ P7 @ N )
% 0.26/0.64           => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 0.26/0.64       => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 0.26/0.64         => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ K5 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % real_sum_nat_ivl_bounded2
% 0.26/0.64  thf(fact_8434_finite__has__minimal2,axiom,
% 0.26/0.64      ! [A3: set_real,A: real] :
% 0.26/0.64        ( ( finite_finite_real @ A3 )
% 0.26/0.64       => ( ( member_real @ A @ A3 )
% 0.26/0.64         => ? [X4: real] :
% 0.26/0.64              ( ( member_real @ X4 @ A3 )
% 0.26/0.64              & ( ord_less_eq_real @ X4 @ A )
% 0.26/0.64              & ! [Xa2: real] :
% 0.26/0.64                  ( ( member_real @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_real @ Xa2 @ X4 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_minimal2
% 0.26/0.64  thf(fact_8435_finite__has__minimal2,axiom,
% 0.26/0.64      ! [A3: set_Extended_enat,A: extended_enat] :
% 0.26/0.64        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.64       => ( ( member_Extended_enat @ A @ A3 )
% 0.26/0.64         => ? [X4: extended_enat] :
% 0.26/0.64              ( ( member_Extended_enat @ X4 @ A3 )
% 0.26/0.64              & ( ord_le2932123472753598470d_enat @ X4 @ A )
% 0.26/0.64              & ! [Xa2: extended_enat] :
% 0.26/0.64                  ( ( member_Extended_enat @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_le2932123472753598470d_enat @ Xa2 @ X4 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_minimal2
% 0.26/0.64  thf(fact_8436_finite__has__minimal2,axiom,
% 0.26/0.64      ! [A3: set_set_nat,A: set_nat] :
% 0.26/0.64        ( ( finite1152437895449049373et_nat @ A3 )
% 0.26/0.64       => ( ( member_set_nat @ A @ A3 )
% 0.26/0.64         => ? [X4: set_nat] :
% 0.26/0.64              ( ( member_set_nat @ X4 @ A3 )
% 0.26/0.64              & ( ord_less_eq_set_nat @ X4 @ A )
% 0.26/0.64              & ! [Xa2: set_nat] :
% 0.26/0.64                  ( ( member_set_nat @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_set_nat @ Xa2 @ X4 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_minimal2
% 0.26/0.64  thf(fact_8437_finite__has__minimal2,axiom,
% 0.26/0.64      ! [A3: set_rat,A: rat] :
% 0.26/0.64        ( ( finite_finite_rat @ A3 )
% 0.26/0.64       => ( ( member_rat @ A @ A3 )
% 0.26/0.64         => ? [X4: rat] :
% 0.26/0.64              ( ( member_rat @ X4 @ A3 )
% 0.26/0.64              & ( ord_less_eq_rat @ X4 @ A )
% 0.26/0.64              & ! [Xa2: rat] :
% 0.26/0.64                  ( ( member_rat @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_rat @ Xa2 @ X4 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_minimal2
% 0.26/0.64  thf(fact_8438_finite__has__minimal2,axiom,
% 0.26/0.64      ! [A3: set_num,A: num] :
% 0.26/0.64        ( ( finite_finite_num @ A3 )
% 0.26/0.64       => ( ( member_num @ A @ A3 )
% 0.26/0.64         => ? [X4: num] :
% 0.26/0.64              ( ( member_num @ X4 @ A3 )
% 0.26/0.64              & ( ord_less_eq_num @ X4 @ A )
% 0.26/0.64              & ! [Xa2: num] :
% 0.26/0.64                  ( ( member_num @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_num @ Xa2 @ X4 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_minimal2
% 0.26/0.64  thf(fact_8439_finite__has__minimal2,axiom,
% 0.26/0.64      ! [A3: set_nat,A: nat] :
% 0.26/0.64        ( ( finite_finite_nat @ A3 )
% 0.26/0.64       => ( ( member_nat @ A @ A3 )
% 0.26/0.64         => ? [X4: nat] :
% 0.26/0.64              ( ( member_nat @ X4 @ A3 )
% 0.26/0.64              & ( ord_less_eq_nat @ X4 @ A )
% 0.26/0.64              & ! [Xa2: nat] :
% 0.26/0.64                  ( ( member_nat @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_nat @ Xa2 @ X4 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_minimal2
% 0.26/0.64  thf(fact_8440_finite__has__minimal2,axiom,
% 0.26/0.64      ! [A3: set_int,A: int] :
% 0.26/0.64        ( ( finite_finite_int @ A3 )
% 0.26/0.64       => ( ( member_int @ A @ A3 )
% 0.26/0.64         => ? [X4: int] :
% 0.26/0.64              ( ( member_int @ X4 @ A3 )
% 0.26/0.64              & ( ord_less_eq_int @ X4 @ A )
% 0.26/0.64              & ! [Xa2: int] :
% 0.26/0.64                  ( ( member_int @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_int @ Xa2 @ X4 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_minimal2
% 0.26/0.64  thf(fact_8441_finite__has__maximal2,axiom,
% 0.26/0.64      ! [A3: set_real,A: real] :
% 0.26/0.64        ( ( finite_finite_real @ A3 )
% 0.26/0.64       => ( ( member_real @ A @ A3 )
% 0.26/0.64         => ? [X4: real] :
% 0.26/0.64              ( ( member_real @ X4 @ A3 )
% 0.26/0.64              & ( ord_less_eq_real @ A @ X4 )
% 0.26/0.64              & ! [Xa2: real] :
% 0.26/0.64                  ( ( member_real @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_real @ X4 @ Xa2 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_maximal2
% 0.26/0.64  thf(fact_8442_finite__has__maximal2,axiom,
% 0.26/0.64      ! [A3: set_Extended_enat,A: extended_enat] :
% 0.26/0.64        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.64       => ( ( member_Extended_enat @ A @ A3 )
% 0.26/0.64         => ? [X4: extended_enat] :
% 0.26/0.64              ( ( member_Extended_enat @ X4 @ A3 )
% 0.26/0.64              & ( ord_le2932123472753598470d_enat @ A @ X4 )
% 0.26/0.64              & ! [Xa2: extended_enat] :
% 0.26/0.64                  ( ( member_Extended_enat @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_le2932123472753598470d_enat @ X4 @ Xa2 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_maximal2
% 0.26/0.64  thf(fact_8443_finite__has__maximal2,axiom,
% 0.26/0.64      ! [A3: set_set_nat,A: set_nat] :
% 0.26/0.64        ( ( finite1152437895449049373et_nat @ A3 )
% 0.26/0.64       => ( ( member_set_nat @ A @ A3 )
% 0.26/0.64         => ? [X4: set_nat] :
% 0.26/0.64              ( ( member_set_nat @ X4 @ A3 )
% 0.26/0.64              & ( ord_less_eq_set_nat @ A @ X4 )
% 0.26/0.64              & ! [Xa2: set_nat] :
% 0.26/0.64                  ( ( member_set_nat @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_set_nat @ X4 @ Xa2 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_maximal2
% 0.26/0.64  thf(fact_8444_finite__has__maximal2,axiom,
% 0.26/0.64      ! [A3: set_rat,A: rat] :
% 0.26/0.64        ( ( finite_finite_rat @ A3 )
% 0.26/0.64       => ( ( member_rat @ A @ A3 )
% 0.26/0.64         => ? [X4: rat] :
% 0.26/0.64              ( ( member_rat @ X4 @ A3 )
% 0.26/0.64              & ( ord_less_eq_rat @ A @ X4 )
% 0.26/0.64              & ! [Xa2: rat] :
% 0.26/0.64                  ( ( member_rat @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_rat @ X4 @ Xa2 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_maximal2
% 0.26/0.64  thf(fact_8445_finite__has__maximal2,axiom,
% 0.26/0.64      ! [A3: set_num,A: num] :
% 0.26/0.64        ( ( finite_finite_num @ A3 )
% 0.26/0.64       => ( ( member_num @ A @ A3 )
% 0.26/0.64         => ? [X4: num] :
% 0.26/0.64              ( ( member_num @ X4 @ A3 )
% 0.26/0.64              & ( ord_less_eq_num @ A @ X4 )
% 0.26/0.64              & ! [Xa2: num] :
% 0.26/0.64                  ( ( member_num @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_num @ X4 @ Xa2 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_maximal2
% 0.26/0.64  thf(fact_8446_finite__has__maximal2,axiom,
% 0.26/0.64      ! [A3: set_nat,A: nat] :
% 0.26/0.64        ( ( finite_finite_nat @ A3 )
% 0.26/0.64       => ( ( member_nat @ A @ A3 )
% 0.26/0.64         => ? [X4: nat] :
% 0.26/0.64              ( ( member_nat @ X4 @ A3 )
% 0.26/0.64              & ( ord_less_eq_nat @ A @ X4 )
% 0.26/0.64              & ! [Xa2: nat] :
% 0.26/0.64                  ( ( member_nat @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_nat @ X4 @ Xa2 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_maximal2
% 0.26/0.64  thf(fact_8447_finite__has__maximal2,axiom,
% 0.26/0.64      ! [A3: set_int,A: int] :
% 0.26/0.64        ( ( finite_finite_int @ A3 )
% 0.26/0.64       => ( ( member_int @ A @ A3 )
% 0.26/0.64         => ? [X4: int] :
% 0.26/0.64              ( ( member_int @ X4 @ A3 )
% 0.26/0.64              & ( ord_less_eq_int @ A @ X4 )
% 0.26/0.64              & ! [Xa2: int] :
% 0.26/0.64                  ( ( member_int @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_int @ X4 @ Xa2 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_maximal2
% 0.26/0.64  thf(fact_8448_sum__less__suminf2,axiom,
% 0.26/0.64      ! [F: nat > int,N: nat,I: nat] :
% 0.26/0.64        ( ( summable_int @ F )
% 0.26/0.64       => ( ! [M4: nat] :
% 0.26/0.64              ( ( ord_less_eq_nat @ N @ M4 )
% 0.26/0.64             => ( ord_less_eq_int @ zero_zero_int @ ( F @ M4 ) ) )
% 0.26/0.64         => ( ( ord_less_eq_nat @ N @ I )
% 0.26/0.64           => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 0.26/0.64             => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_int @ F ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_less_suminf2
% 0.26/0.64  thf(fact_8449_sum__less__suminf2,axiom,
% 0.26/0.64      ! [F: nat > nat,N: nat,I: nat] :
% 0.26/0.64        ( ( summable_nat @ F )
% 0.26/0.64       => ( ! [M4: nat] :
% 0.26/0.64              ( ( ord_less_eq_nat @ N @ M4 )
% 0.26/0.64             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ M4 ) ) )
% 0.26/0.64         => ( ( ord_less_eq_nat @ N @ I )
% 0.26/0.64           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 0.26/0.64             => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_nat @ F ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_less_suminf2
% 0.26/0.64  thf(fact_8450_sum__less__suminf2,axiom,
% 0.26/0.64      ! [F: nat > real,N: nat,I: nat] :
% 0.26/0.64        ( ( summable_real @ F )
% 0.26/0.64       => ( ! [M4: nat] :
% 0.26/0.64              ( ( ord_less_eq_nat @ N @ M4 )
% 0.26/0.64             => ( ord_less_eq_real @ zero_zero_real @ ( F @ M4 ) ) )
% 0.26/0.64         => ( ( ord_less_eq_nat @ N @ I )
% 0.26/0.64           => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 0.26/0.64             => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_real @ F ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_less_suminf2
% 0.26/0.64  thf(fact_8451_sum_Oin__pairs__0,axiom,
% 0.26/0.64      ! [G: nat > rat,N: nat] :
% 0.26/0.64        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.26/0.64        = ( groups2906978787729119204at_rat
% 0.26/0.64          @ ^ [I4: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum.in_pairs_0
% 0.26/0.64  thf(fact_8452_sum_Oin__pairs__0,axiom,
% 0.26/0.64      ! [G: nat > int,N: nat] :
% 0.26/0.64        ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.26/0.64        = ( groups3539618377306564664at_int
% 0.26/0.64          @ ^ [I4: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum.in_pairs_0
% 0.26/0.64  thf(fact_8453_sum_Oin__pairs__0,axiom,
% 0.26/0.64      ! [G: nat > nat,N: nat] :
% 0.26/0.64        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.26/0.64        = ( groups3542108847815614940at_nat
% 0.26/0.64          @ ^ [I4: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum.in_pairs_0
% 0.26/0.64  thf(fact_8454_sum_Oin__pairs__0,axiom,
% 0.26/0.64      ! [G: nat > real,N: nat] :
% 0.26/0.64        ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.26/0.64        = ( groups6591440286371151544t_real
% 0.26/0.64          @ ^ [I4: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum.in_pairs_0
% 0.26/0.64  thf(fact_8455_polynomial__product,axiom,
% 0.26/0.64      ! [M: nat,A: nat > complex,N: nat,B: nat > complex,X3: complex] :
% 0.26/0.64        ( ! [I3: nat] :
% 0.26/0.64            ( ( ord_less_nat @ M @ I3 )
% 0.26/0.64           => ( ( A @ I3 )
% 0.26/0.64              = zero_zero_complex ) )
% 0.26/0.64       => ( ! [J2: nat] :
% 0.26/0.64              ( ( ord_less_nat @ N @ J2 )
% 0.26/0.64             => ( ( B @ J2 )
% 0.26/0.64                = zero_zero_complex ) )
% 0.26/0.64         => ( ( times_times_complex
% 0.26/0.64              @ ( groups2073611262835488442omplex
% 0.26/0.64                @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( power_power_complex @ X3 @ I4 ) )
% 0.26/0.64                @ ( set_ord_atMost_nat @ M ) )
% 0.26/0.64              @ ( groups2073611262835488442omplex
% 0.26/0.64                @ ^ [J3: nat] : ( times_times_complex @ ( B @ J3 ) @ ( power_power_complex @ X3 @ J3 ) )
% 0.26/0.64                @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64            = ( groups2073611262835488442omplex
% 0.26/0.64              @ ^ [R5: nat] :
% 0.26/0.64                  ( times_times_complex
% 0.26/0.64                  @ ( groups2073611262835488442omplex
% 0.26/0.64                    @ ^ [K3: nat] : ( times_times_complex @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 0.26/0.64                    @ ( set_ord_atMost_nat @ R5 ) )
% 0.26/0.64                  @ ( power_power_complex @ X3 @ R5 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polynomial_product
% 0.26/0.64  thf(fact_8456_polynomial__product,axiom,
% 0.26/0.64      ! [M: nat,A: nat > rat,N: nat,B: nat > rat,X3: rat] :
% 0.26/0.64        ( ! [I3: nat] :
% 0.26/0.64            ( ( ord_less_nat @ M @ I3 )
% 0.26/0.64           => ( ( A @ I3 )
% 0.26/0.64              = zero_zero_rat ) )
% 0.26/0.64       => ( ! [J2: nat] :
% 0.26/0.64              ( ( ord_less_nat @ N @ J2 )
% 0.26/0.64             => ( ( B @ J2 )
% 0.26/0.64                = zero_zero_rat ) )
% 0.26/0.64         => ( ( times_times_rat
% 0.26/0.64              @ ( groups2906978787729119204at_rat
% 0.26/0.64                @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( power_power_rat @ X3 @ I4 ) )
% 0.26/0.64                @ ( set_ord_atMost_nat @ M ) )
% 0.26/0.64              @ ( groups2906978787729119204at_rat
% 0.26/0.64                @ ^ [J3: nat] : ( times_times_rat @ ( B @ J3 ) @ ( power_power_rat @ X3 @ J3 ) )
% 0.26/0.64                @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64            = ( groups2906978787729119204at_rat
% 0.26/0.64              @ ^ [R5: nat] :
% 0.26/0.64                  ( times_times_rat
% 0.26/0.64                  @ ( groups2906978787729119204at_rat
% 0.26/0.64                    @ ^ [K3: nat] : ( times_times_rat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 0.26/0.64                    @ ( set_ord_atMost_nat @ R5 ) )
% 0.26/0.64                  @ ( power_power_rat @ X3 @ R5 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polynomial_product
% 0.26/0.64  thf(fact_8457_polynomial__product,axiom,
% 0.26/0.64      ! [M: nat,A: nat > int,N: nat,B: nat > int,X3: int] :
% 0.26/0.64        ( ! [I3: nat] :
% 0.26/0.64            ( ( ord_less_nat @ M @ I3 )
% 0.26/0.64           => ( ( A @ I3 )
% 0.26/0.64              = zero_zero_int ) )
% 0.26/0.64       => ( ! [J2: nat] :
% 0.26/0.64              ( ( ord_less_nat @ N @ J2 )
% 0.26/0.64             => ( ( B @ J2 )
% 0.26/0.64                = zero_zero_int ) )
% 0.26/0.64         => ( ( times_times_int
% 0.26/0.64              @ ( groups3539618377306564664at_int
% 0.26/0.64                @ ^ [I4: nat] : ( times_times_int @ ( A @ I4 ) @ ( power_power_int @ X3 @ I4 ) )
% 0.26/0.64                @ ( set_ord_atMost_nat @ M ) )
% 0.26/0.64              @ ( groups3539618377306564664at_int
% 0.26/0.64                @ ^ [J3: nat] : ( times_times_int @ ( B @ J3 ) @ ( power_power_int @ X3 @ J3 ) )
% 0.26/0.64                @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64            = ( groups3539618377306564664at_int
% 0.26/0.64              @ ^ [R5: nat] :
% 0.26/0.64                  ( times_times_int
% 0.26/0.64                  @ ( groups3539618377306564664at_int
% 0.26/0.64                    @ ^ [K3: nat] : ( times_times_int @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 0.26/0.64                    @ ( set_ord_atMost_nat @ R5 ) )
% 0.26/0.64                  @ ( power_power_int @ X3 @ R5 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polynomial_product
% 0.26/0.64  thf(fact_8458_polynomial__product,axiom,
% 0.26/0.64      ! [M: nat,A: nat > real,N: nat,B: nat > real,X3: real] :
% 0.26/0.64        ( ! [I3: nat] :
% 0.26/0.64            ( ( ord_less_nat @ M @ I3 )
% 0.26/0.64           => ( ( A @ I3 )
% 0.26/0.64              = zero_zero_real ) )
% 0.26/0.64       => ( ! [J2: nat] :
% 0.26/0.64              ( ( ord_less_nat @ N @ J2 )
% 0.26/0.64             => ( ( B @ J2 )
% 0.26/0.64                = zero_zero_real ) )
% 0.26/0.64         => ( ( times_times_real
% 0.26/0.64              @ ( groups6591440286371151544t_real
% 0.26/0.64                @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( power_power_real @ X3 @ I4 ) )
% 0.26/0.64                @ ( set_ord_atMost_nat @ M ) )
% 0.26/0.64              @ ( groups6591440286371151544t_real
% 0.26/0.64                @ ^ [J3: nat] : ( times_times_real @ ( B @ J3 ) @ ( power_power_real @ X3 @ J3 ) )
% 0.26/0.64                @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64            = ( groups6591440286371151544t_real
% 0.26/0.64              @ ^ [R5: nat] :
% 0.26/0.64                  ( times_times_real
% 0.26/0.64                  @ ( groups6591440286371151544t_real
% 0.26/0.64                    @ ^ [K3: nat] : ( times_times_real @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 0.26/0.64                    @ ( set_ord_atMost_nat @ R5 ) )
% 0.26/0.64                  @ ( power_power_real @ X3 @ R5 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polynomial_product
% 0.26/0.64  thf(fact_8459_prod_Oin__pairs__0,axiom,
% 0.26/0.64      ! [G: nat > real,N: nat] :
% 0.26/0.64        ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.26/0.64        = ( groups129246275422532515t_real
% 0.26/0.64          @ ^ [I4: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % prod.in_pairs_0
% 0.26/0.64  thf(fact_8460_prod_Oin__pairs__0,axiom,
% 0.26/0.64      ! [G: nat > rat,N: nat] :
% 0.26/0.64        ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.26/0.64        = ( groups73079841787564623at_rat
% 0.26/0.64          @ ^ [I4: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % prod.in_pairs_0
% 0.26/0.64  thf(fact_8461_prod_Oin__pairs__0,axiom,
% 0.26/0.64      ! [G: nat > int,N: nat] :
% 0.26/0.64        ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.26/0.64        = ( groups705719431365010083at_int
% 0.26/0.64          @ ^ [I4: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % prod.in_pairs_0
% 0.26/0.64  thf(fact_8462_prod_Oin__pairs__0,axiom,
% 0.26/0.64      ! [G: nat > nat,N: nat] :
% 0.26/0.64        ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.26/0.64        = ( groups708209901874060359at_nat
% 0.26/0.64          @ ^ [I4: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % prod.in_pairs_0
% 0.26/0.64  thf(fact_8463_polyfun__eq__const,axiom,
% 0.26/0.64      ! [C: nat > complex,N: nat,K: complex] :
% 0.26/0.64        ( ( ! [X: complex] :
% 0.26/0.64              ( ( groups2073611262835488442omplex
% 0.26/0.64                @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ X @ I4 ) )
% 0.26/0.64                @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64              = K ) )
% 0.26/0.64        = ( ( ( C @ zero_zero_nat )
% 0.26/0.64            = K )
% 0.26/0.64          & ! [X: nat] :
% 0.26/0.64              ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) )
% 0.26/0.64             => ( ( C @ X )
% 0.26/0.64                = zero_zero_complex ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_eq_const
% 0.26/0.64  thf(fact_8464_polyfun__eq__const,axiom,
% 0.26/0.64      ! [C: nat > real,N: nat,K: real] :
% 0.26/0.64        ( ( ! [X: real] :
% 0.26/0.64              ( ( groups6591440286371151544t_real
% 0.26/0.64                @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ X @ I4 ) )
% 0.26/0.64                @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64              = K ) )
% 0.26/0.64        = ( ( ( C @ zero_zero_nat )
% 0.26/0.64            = K )
% 0.26/0.64          & ! [X: nat] :
% 0.26/0.64              ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) )
% 0.26/0.64             => ( ( C @ X )
% 0.26/0.64                = zero_zero_real ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_eq_const
% 0.26/0.64  thf(fact_8465_one__diff__power__eq_H,axiom,
% 0.26/0.64      ! [X3: complex,N: nat] :
% 0.26/0.64        ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ N ) )
% 0.26/0.64        = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X3 )
% 0.26/0.64          @ ( groups2073611262835488442omplex
% 0.26/0.64            @ ^ [I4: nat] : ( power_power_complex @ X3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 0.26/0.64            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % one_diff_power_eq'
% 0.26/0.64  thf(fact_8466_one__diff__power__eq_H,axiom,
% 0.26/0.64      ! [X3: rat,N: nat] :
% 0.26/0.64        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ N ) )
% 0.26/0.64        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X3 )
% 0.26/0.64          @ ( groups2906978787729119204at_rat
% 0.26/0.64            @ ^ [I4: nat] : ( power_power_rat @ X3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 0.26/0.64            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % one_diff_power_eq'
% 0.26/0.64  thf(fact_8467_one__diff__power__eq_H,axiom,
% 0.26/0.64      ! [X3: int,N: nat] :
% 0.26/0.64        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X3 @ N ) )
% 0.26/0.64        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X3 )
% 0.26/0.64          @ ( groups3539618377306564664at_int
% 0.26/0.64            @ ^ [I4: nat] : ( power_power_int @ X3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 0.26/0.64            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % one_diff_power_eq'
% 0.26/0.64  thf(fact_8468_one__diff__power__eq_H,axiom,
% 0.26/0.64      ! [X3: real,N: nat] :
% 0.26/0.64        ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ N ) )
% 0.26/0.64        = ( times_times_real @ ( minus_minus_real @ one_one_real @ X3 )
% 0.26/0.64          @ ( groups6591440286371151544t_real
% 0.26/0.64            @ ^ [I4: nat] : ( power_power_real @ X3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 0.26/0.64            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % one_diff_power_eq'
% 0.26/0.64  thf(fact_8469_binomial__ring,axiom,
% 0.26/0.64      ! [A: complex,B: complex,N: nat] :
% 0.26/0.64        ( ( power_power_complex @ ( plus_plus_complex @ A @ B ) @ N )
% 0.26/0.64        = ( groups2073611262835488442omplex
% 0.26/0.64          @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K3 ) ) @ ( power_power_complex @ A @ K3 ) ) @ ( power_power_complex @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % binomial_ring
% 0.26/0.64  thf(fact_8470_binomial__ring,axiom,
% 0.26/0.64      ! [A: rat,B: rat,N: nat] :
% 0.26/0.64        ( ( power_power_rat @ ( plus_plus_rat @ A @ B ) @ N )
% 0.26/0.64        = ( groups2906978787729119204at_rat
% 0.26/0.64          @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K3 ) ) @ ( power_power_rat @ A @ K3 ) ) @ ( power_power_rat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % binomial_ring
% 0.26/0.64  thf(fact_8471_binomial__ring,axiom,
% 0.26/0.64      ! [A: int,B: int,N: nat] :
% 0.26/0.64        ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N )
% 0.26/0.64        = ( groups3539618377306564664at_int
% 0.26/0.64          @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N @ K3 ) ) @ ( power_power_int @ A @ K3 ) ) @ ( power_power_int @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % binomial_ring
% 0.26/0.64  thf(fact_8472_binomial__ring,axiom,
% 0.26/0.64      ! [A: nat,B: nat,N: nat] :
% 0.26/0.64        ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 0.26/0.64        = ( groups3542108847815614940at_nat
% 0.26/0.64          @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % binomial_ring
% 0.26/0.64  thf(fact_8473_binomial__ring,axiom,
% 0.26/0.64      ! [A: real,B: real,N: nat] :
% 0.26/0.64        ( ( power_power_real @ ( plus_plus_real @ A @ B ) @ N )
% 0.26/0.64        = ( groups6591440286371151544t_real
% 0.26/0.64          @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K3 ) ) @ ( power_power_real @ A @ K3 ) ) @ ( power_power_real @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % binomial_ring
% 0.26/0.64  thf(fact_8474_pochhammer__binomial__sum,axiom,
% 0.26/0.64      ! [A: complex,B: complex,N: nat] :
% 0.26/0.64        ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ B ) @ N )
% 0.26/0.64        = ( groups2073611262835488442omplex
% 0.26/0.64          @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K3 ) ) @ ( comm_s2602460028002588243omplex @ A @ K3 ) ) @ ( comm_s2602460028002588243omplex @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % pochhammer_binomial_sum
% 0.26/0.64  thf(fact_8475_pochhammer__binomial__sum,axiom,
% 0.26/0.64      ! [A: rat,B: rat,N: nat] :
% 0.26/0.64        ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ B ) @ N )
% 0.26/0.64        = ( groups2906978787729119204at_rat
% 0.26/0.64          @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ A @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % pochhammer_binomial_sum
% 0.26/0.64  thf(fact_8476_pochhammer__binomial__sum,axiom,
% 0.26/0.64      ! [A: int,B: int,N: nat] :
% 0.26/0.64        ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B ) @ N )
% 0.26/0.64        = ( groups3539618377306564664at_int
% 0.26/0.64          @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N @ K3 ) ) @ ( comm_s4660882817536571857er_int @ A @ K3 ) ) @ ( comm_s4660882817536571857er_int @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % pochhammer_binomial_sum
% 0.26/0.64  thf(fact_8477_pochhammer__binomial__sum,axiom,
% 0.26/0.64      ! [A: real,B: real,N: nat] :
% 0.26/0.64        ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ B ) @ N )
% 0.26/0.64        = ( groups6591440286371151544t_real
% 0.26/0.64          @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K3 ) ) @ ( comm_s7457072308508201937r_real @ A @ K3 ) ) @ ( comm_s7457072308508201937r_real @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % pochhammer_binomial_sum
% 0.26/0.64  thf(fact_8478_sum_Ozero__middle,axiom,
% 0.26/0.64      ! [P6: nat,K: nat,G: nat > rat,H2: nat > rat] :
% 0.26/0.64        ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 0.26/0.64       => ( ( ord_less_eq_nat @ K @ P6 )
% 0.26/0.64         => ( ( groups2906978787729119204at_rat
% 0.26/0.64              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_rat @ ( J3 = K ) @ zero_zero_rat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ P6 ) )
% 0.26/0.64            = ( groups2906978787729119204at_rat
% 0.26/0.64              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum.zero_middle
% 0.26/0.64  thf(fact_8479_sum_Ozero__middle,axiom,
% 0.26/0.64      ! [P6: nat,K: nat,G: nat > int,H2: nat > int] :
% 0.26/0.64        ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 0.26/0.64       => ( ( ord_less_eq_nat @ K @ P6 )
% 0.26/0.64         => ( ( groups3539618377306564664at_int
% 0.26/0.64              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_int @ ( J3 = K ) @ zero_zero_int @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ P6 ) )
% 0.26/0.64            = ( groups3539618377306564664at_int
% 0.26/0.64              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum.zero_middle
% 0.26/0.64  thf(fact_8480_sum_Ozero__middle,axiom,
% 0.26/0.64      ! [P6: nat,K: nat,G: nat > nat,H2: nat > nat] :
% 0.26/0.64        ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 0.26/0.64       => ( ( ord_less_eq_nat @ K @ P6 )
% 0.26/0.64         => ( ( groups3542108847815614940at_nat
% 0.26/0.64              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_nat @ ( J3 = K ) @ zero_zero_nat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ P6 ) )
% 0.26/0.64            = ( groups3542108847815614940at_nat
% 0.26/0.64              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum.zero_middle
% 0.26/0.64  thf(fact_8481_sum_Ozero__middle,axiom,
% 0.26/0.64      ! [P6: nat,K: nat,G: nat > real,H2: nat > real] :
% 0.26/0.64        ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 0.26/0.64       => ( ( ord_less_eq_nat @ K @ P6 )
% 0.26/0.64         => ( ( groups6591440286371151544t_real
% 0.26/0.64              @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_real @ ( J3 = K ) @ zero_zero_real @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ P6 ) )
% 0.26/0.64            = ( groups6591440286371151544t_real
% 0.26/0.64              @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum.zero_middle
% 0.26/0.64  thf(fact_8482_prod_Ozero__middle,axiom,
% 0.26/0.64      ! [P6: nat,K: nat,G: nat > complex,H2: nat > complex] :
% 0.26/0.64        ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 0.26/0.64       => ( ( ord_less_eq_nat @ K @ P6 )
% 0.26/0.64         => ( ( groups6464643781859351333omplex
% 0.26/0.64              @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_complex @ ( J3 = K ) @ one_one_complex @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ P6 ) )
% 0.26/0.64            = ( groups6464643781859351333omplex
% 0.26/0.64              @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % prod.zero_middle
% 0.26/0.64  thf(fact_8483_prod_Ozero__middle,axiom,
% 0.26/0.64      ! [P6: nat,K: nat,G: nat > real,H2: nat > real] :
% 0.26/0.64        ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 0.26/0.64       => ( ( ord_less_eq_nat @ K @ P6 )
% 0.26/0.64         => ( ( groups129246275422532515t_real
% 0.26/0.64              @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_real @ ( J3 = K ) @ one_one_real @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ P6 ) )
% 0.26/0.64            = ( groups129246275422532515t_real
% 0.26/0.64              @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % prod.zero_middle
% 0.26/0.64  thf(fact_8484_prod_Ozero__middle,axiom,
% 0.26/0.64      ! [P6: nat,K: nat,G: nat > rat,H2: nat > rat] :
% 0.26/0.64        ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 0.26/0.64       => ( ( ord_less_eq_nat @ K @ P6 )
% 0.26/0.64         => ( ( groups73079841787564623at_rat
% 0.26/0.64              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_rat @ ( J3 = K ) @ one_one_rat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ P6 ) )
% 0.26/0.64            = ( groups73079841787564623at_rat
% 0.26/0.64              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % prod.zero_middle
% 0.26/0.64  thf(fact_8485_prod_Ozero__middle,axiom,
% 0.26/0.64      ! [P6: nat,K: nat,G: nat > int,H2: nat > int] :
% 0.26/0.64        ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 0.26/0.64       => ( ( ord_less_eq_nat @ K @ P6 )
% 0.26/0.64         => ( ( groups705719431365010083at_int
% 0.26/0.64              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_int @ ( J3 = K ) @ one_one_int @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ P6 ) )
% 0.26/0.64            = ( groups705719431365010083at_int
% 0.26/0.64              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % prod.zero_middle
% 0.26/0.64  thf(fact_8486_prod_Ozero__middle,axiom,
% 0.26/0.64      ! [P6: nat,K: nat,G: nat > nat,H2: nat > nat] :
% 0.26/0.64        ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 0.26/0.64       => ( ( ord_less_eq_nat @ K @ P6 )
% 0.26/0.64         => ( ( groups708209901874060359at_nat
% 0.26/0.64              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_nat @ ( J3 = K ) @ one_one_nat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ P6 ) )
% 0.26/0.64            = ( groups708209901874060359at_nat
% 0.26/0.64              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % prod.zero_middle
% 0.26/0.64  thf(fact_8487_binomial__r__part__sum,axiom,
% 0.26/0.64      ! [M: nat] :
% 0.26/0.64        ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 0.26/0.64        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % binomial_r_part_sum
% 0.26/0.64  thf(fact_8488_choose__linear__sum,axiom,
% 0.26/0.64      ! [N: nat] :
% 0.26/0.64        ( ( groups3542108847815614940at_nat
% 0.26/0.64          @ ^ [I4: nat] : ( times_times_nat @ I4 @ ( binomial @ N @ I4 ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64        = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % choose_linear_sum
% 0.26/0.64  thf(fact_8489_sum__split__even__odd,axiom,
% 0.26/0.64      ! [F: nat > real,G: nat > real,N: nat] :
% 0.26/0.64        ( ( groups6591440286371151544t_real
% 0.26/0.64          @ ^ [I4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( F @ I4 ) @ ( G @ I4 ) )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.26/0.64        = ( plus_plus_real
% 0.26/0.64          @ ( groups6591440286371151544t_real
% 0.26/0.64            @ ^ [I4: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) )
% 0.26/0.64            @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.64          @ ( groups6591440286371151544t_real
% 0.26/0.64            @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ one_one_nat ) )
% 0.26/0.64            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_split_even_odd
% 0.26/0.64  thf(fact_8490_root__polyfun,axiom,
% 0.26/0.64      ! [N: nat,Z: int,A: int] :
% 0.26/0.64        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.26/0.64       => ( ( ( power_power_int @ Z @ N )
% 0.26/0.64            = A )
% 0.26/0.64          = ( ( groups3539618377306564664at_int
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_int @ ( if_int @ ( I4 = zero_zero_nat ) @ ( uminus_uminus_int @ A ) @ ( if_int @ ( I4 = N ) @ one_one_int @ zero_zero_int ) ) @ ( power_power_int @ Z @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64            = zero_zero_int ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % root_polyfun
% 0.26/0.64  thf(fact_8491_root__polyfun,axiom,
% 0.26/0.64      ! [N: nat,Z: complex,A: complex] :
% 0.26/0.64        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.26/0.64       => ( ( ( power_power_complex @ Z @ N )
% 0.26/0.64            = A )
% 0.26/0.64          = ( ( groups2073611262835488442omplex
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_complex @ ( if_complex @ ( I4 = zero_zero_nat ) @ ( uminus1482373934393186551omplex @ A ) @ ( if_complex @ ( I4 = N ) @ one_one_complex @ zero_zero_complex ) ) @ ( power_power_complex @ Z @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64            = zero_zero_complex ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % root_polyfun
% 0.26/0.64  thf(fact_8492_root__polyfun,axiom,
% 0.26/0.64      ! [N: nat,Z: code_integer,A: code_integer] :
% 0.26/0.64        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.26/0.64       => ( ( ( power_8256067586552552935nteger @ Z @ N )
% 0.26/0.64            = A )
% 0.26/0.64          = ( ( groups7501900531339628137nteger
% 0.26/0.64              @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( if_Code_integer @ ( I4 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ A ) @ ( if_Code_integer @ ( I4 = N ) @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) @ ( power_8256067586552552935nteger @ Z @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64            = zero_z3403309356797280102nteger ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % root_polyfun
% 0.26/0.64  thf(fact_8493_root__polyfun,axiom,
% 0.26/0.64      ! [N: nat,Z: rat,A: rat] :
% 0.26/0.64        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.26/0.64       => ( ( ( power_power_rat @ Z @ N )
% 0.26/0.64            = A )
% 0.26/0.64          = ( ( groups2906978787729119204at_rat
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_rat @ ( if_rat @ ( I4 = zero_zero_nat ) @ ( uminus_uminus_rat @ A ) @ ( if_rat @ ( I4 = N ) @ one_one_rat @ zero_zero_rat ) ) @ ( power_power_rat @ Z @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64            = zero_zero_rat ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % root_polyfun
% 0.26/0.64  thf(fact_8494_root__polyfun,axiom,
% 0.26/0.64      ! [N: nat,Z: real,A: real] :
% 0.26/0.64        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.26/0.64       => ( ( ( power_power_real @ Z @ N )
% 0.26/0.64            = A )
% 0.26/0.64          = ( ( groups6591440286371151544t_real
% 0.26/0.64              @ ^ [I4: nat] : ( times_times_real @ ( if_real @ ( I4 = zero_zero_nat ) @ ( uminus_uminus_real @ A ) @ ( if_real @ ( I4 = N ) @ one_one_real @ zero_zero_real ) ) @ ( power_power_real @ Z @ I4 ) )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64            = zero_zero_real ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % root_polyfun
% 0.26/0.64  thf(fact_8495_sum__gp0,axiom,
% 0.26/0.64      ! [X3: complex,N: nat] :
% 0.26/0.64        ( ( ( X3 = one_one_complex )
% 0.26/0.64         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64            = ( semiri8010041392384452111omplex @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 0.26/0.64        & ( ( X3 != one_one_complex )
% 0.26/0.64         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X3 ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_gp0
% 0.26/0.64  thf(fact_8496_sum__gp0,axiom,
% 0.26/0.64      ! [X3: rat,N: nat] :
% 0.26/0.64        ( ( ( X3 = one_one_rat )
% 0.26/0.64         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64            = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 0.26/0.64        & ( ( X3 != one_one_rat )
% 0.26/0.64         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64            = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X3 ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_gp0
% 0.26/0.64  thf(fact_8497_sum__gp0,axiom,
% 0.26/0.64      ! [X3: real,N: nat] :
% 0.26/0.64        ( ( ( X3 = one_one_real )
% 0.26/0.64         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64            = ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 0.26/0.64        & ( ( X3 != one_one_real )
% 0.26/0.64         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64            = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_gp0
% 0.26/0.64  thf(fact_8498_choose__alternating__linear__sum,axiom,
% 0.26/0.64      ! [N: nat] :
% 0.26/0.64        ( ( N != one_one_nat )
% 0.26/0.64       => ( ( groups7501900531339628137nteger
% 0.26/0.64            @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I4 ) @ ( semiri4939895301339042750nteger @ I4 ) ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I4 ) ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64          = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.64  
% 0.26/0.64  % choose_alternating_linear_sum
% 0.26/0.64  thf(fact_8499_choose__alternating__linear__sum,axiom,
% 0.26/0.64      ! [N: nat] :
% 0.26/0.64        ( ( N != one_one_nat )
% 0.26/0.64       => ( ( groups2073611262835488442omplex
% 0.26/0.64            @ ^ [I4: nat] : ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I4 ) @ ( semiri8010041392384452111omplex @ I4 ) ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I4 ) ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64          = zero_zero_complex ) ) ).
% 0.26/0.64  
% 0.26/0.64  % choose_alternating_linear_sum
% 0.26/0.64  thf(fact_8500_choose__alternating__linear__sum,axiom,
% 0.26/0.64      ! [N: nat] :
% 0.26/0.64        ( ( N != one_one_nat )
% 0.26/0.64       => ( ( groups2906978787729119204at_rat
% 0.26/0.64            @ ^ [I4: nat] : ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I4 ) @ ( semiri681578069525770553at_rat @ I4 ) ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I4 ) ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64          = zero_zero_rat ) ) ).
% 0.26/0.64  
% 0.26/0.64  % choose_alternating_linear_sum
% 0.26/0.64  thf(fact_8501_choose__alternating__linear__sum,axiom,
% 0.26/0.64      ! [N: nat] :
% 0.26/0.64        ( ( N != one_one_nat )
% 0.26/0.64       => ( ( groups3539618377306564664at_int
% 0.26/0.64            @ ^ [I4: nat] : ( times_times_int @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I4 ) @ ( semiri1314217659103216013at_int @ I4 ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I4 ) ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64          = zero_zero_int ) ) ).
% 0.26/0.64  
% 0.26/0.64  % choose_alternating_linear_sum
% 0.26/0.64  thf(fact_8502_choose__alternating__linear__sum,axiom,
% 0.26/0.64      ! [N: nat] :
% 0.26/0.64        ( ( N != one_one_nat )
% 0.26/0.64       => ( ( groups6591440286371151544t_real
% 0.26/0.64            @ ^ [I4: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( semiri5074537144036343181t_real @ I4 ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I4 ) ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64          = zero_zero_real ) ) ).
% 0.26/0.64  
% 0.26/0.64  % choose_alternating_linear_sum
% 0.26/0.64  thf(fact_8503_choose__alternating__sum,axiom,
% 0.26/0.64      ! [N: nat] :
% 0.26/0.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.64       => ( ( groups7501900531339628137nteger
% 0.26/0.64            @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I4 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I4 ) ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64          = zero_z3403309356797280102nteger ) ) ).
% 0.26/0.64  
% 0.26/0.64  % choose_alternating_sum
% 0.26/0.64  thf(fact_8504_choose__alternating__sum,axiom,
% 0.26/0.64      ! [N: nat] :
% 0.26/0.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.64       => ( ( groups2073611262835488442omplex
% 0.26/0.64            @ ^ [I4: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I4 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I4 ) ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64          = zero_zero_complex ) ) ).
% 0.26/0.64  
% 0.26/0.64  % choose_alternating_sum
% 0.26/0.64  thf(fact_8505_choose__alternating__sum,axiom,
% 0.26/0.64      ! [N: nat] :
% 0.26/0.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.64       => ( ( groups2906978787729119204at_rat
% 0.26/0.64            @ ^ [I4: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I4 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I4 ) ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64          = zero_zero_rat ) ) ).
% 0.26/0.64  
% 0.26/0.64  % choose_alternating_sum
% 0.26/0.64  thf(fact_8506_choose__alternating__sum,axiom,
% 0.26/0.64      ! [N: nat] :
% 0.26/0.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.64       => ( ( groups3539618377306564664at_int
% 0.26/0.64            @ ^ [I4: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I4 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I4 ) ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64          = zero_zero_int ) ) ).
% 0.26/0.64  
% 0.26/0.64  % choose_alternating_sum
% 0.26/0.64  thf(fact_8507_choose__alternating__sum,axiom,
% 0.26/0.64      ! [N: nat] :
% 0.26/0.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.64       => ( ( groups6591440286371151544t_real
% 0.26/0.64            @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I4 ) ) )
% 0.26/0.64            @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64          = zero_zero_real ) ) ).
% 0.26/0.64  
% 0.26/0.64  % choose_alternating_sum
% 0.26/0.64  thf(fact_8508_polyfun__extremal__lemma,axiom,
% 0.26/0.64      ! [E2: real,C: nat > complex,N: nat] :
% 0.26/0.64        ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.26/0.64       => ? [M8: real] :
% 0.26/0.64          ! [Z4: complex] :
% 0.26/0.64            ( ( ord_less_eq_real @ M8 @ ( real_V1022390504157884413omplex @ Z4 ) )
% 0.26/0.64           => ( ord_less_eq_real
% 0.26/0.64              @ ( real_V1022390504157884413omplex
% 0.26/0.64                @ ( groups2073611262835488442omplex
% 0.26/0.64                  @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ Z4 @ I4 ) )
% 0.26/0.64                  @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64              @ ( times_times_real @ E2 @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( suc @ N ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_extremal_lemma
% 0.26/0.64  thf(fact_8509_polyfun__extremal__lemma,axiom,
% 0.26/0.64      ! [E2: real,C: nat > real,N: nat] :
% 0.26/0.64        ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.26/0.64       => ? [M8: real] :
% 0.26/0.64          ! [Z4: real] :
% 0.26/0.64            ( ( ord_less_eq_real @ M8 @ ( real_V7735802525324610683m_real @ Z4 ) )
% 0.26/0.64           => ( ord_less_eq_real
% 0.26/0.64              @ ( real_V7735802525324610683m_real
% 0.26/0.64                @ ( groups6591440286371151544t_real
% 0.26/0.64                  @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ Z4 @ I4 ) )
% 0.26/0.64                  @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64              @ ( times_times_real @ E2 @ ( power_power_real @ ( real_V7735802525324610683m_real @ Z4 ) @ ( suc @ N ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % polyfun_extremal_lemma
% 0.26/0.64  thf(fact_8510_even__set__encode__iff,axiom,
% 0.26/0.64      ! [A3: set_nat] :
% 0.26/0.64        ( ( finite_finite_nat @ A3 )
% 0.26/0.64       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A3 ) )
% 0.26/0.64          = ( ~ ( member_nat @ zero_zero_nat @ A3 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % even_set_encode_iff
% 0.26/0.64  thf(fact_8511_sum__pos__lt__pair,axiom,
% 0.26/0.64      ! [F: nat > real,K: nat] :
% 0.26/0.64        ( ( summable_real @ F )
% 0.26/0.64       => ( ! [D6: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F @ ( plus_plus_nat @ K @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D6 ) ) ) @ ( F @ ( plus_plus_nat @ K @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D6 ) @ one_one_nat ) ) ) ) )
% 0.26/0.64         => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sum_pos_lt_pair
% 0.26/0.64  thf(fact_8512_Sum__Icc__int,axiom,
% 0.26/0.64      ! [M: int,N: int] :
% 0.26/0.64        ( ( ord_less_eq_int @ M @ N )
% 0.26/0.64       => ( ( groups4538972089207619220nt_int
% 0.26/0.64            @ ^ [X: int] : X
% 0.26/0.64            @ ( set_or1266510415728281911st_int @ M @ N ) )
% 0.26/0.64          = ( 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 ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % Sum_Icc_int
% 0.26/0.64  thf(fact_8513_finite__has__minimal,axiom,
% 0.26/0.64      ! [A3: set_Extended_enat] :
% 0.26/0.64        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.64       => ( ( A3 != bot_bo7653980558646680370d_enat )
% 0.26/0.64         => ? [X4: extended_enat] :
% 0.26/0.64              ( ( member_Extended_enat @ X4 @ A3 )
% 0.26/0.64              & ! [Xa2: extended_enat] :
% 0.26/0.64                  ( ( member_Extended_enat @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_le2932123472753598470d_enat @ Xa2 @ X4 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_minimal
% 0.26/0.64  thf(fact_8514_finite__has__minimal,axiom,
% 0.26/0.64      ! [A3: set_real] :
% 0.26/0.64        ( ( finite_finite_real @ A3 )
% 0.26/0.64       => ( ( A3 != bot_bot_set_real )
% 0.26/0.64         => ? [X4: real] :
% 0.26/0.64              ( ( member_real @ X4 @ A3 )
% 0.26/0.64              & ! [Xa2: real] :
% 0.26/0.64                  ( ( member_real @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_real @ Xa2 @ X4 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_minimal
% 0.26/0.64  thf(fact_8515_finite__has__minimal,axiom,
% 0.26/0.64      ! [A3: set_set_nat] :
% 0.26/0.64        ( ( finite1152437895449049373et_nat @ A3 )
% 0.26/0.64       => ( ( A3 != bot_bot_set_set_nat )
% 0.26/0.64         => ? [X4: set_nat] :
% 0.26/0.64              ( ( member_set_nat @ X4 @ A3 )
% 0.26/0.64              & ! [Xa2: set_nat] :
% 0.26/0.64                  ( ( member_set_nat @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_set_nat @ Xa2 @ X4 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_minimal
% 0.26/0.64  thf(fact_8516_finite__has__minimal,axiom,
% 0.26/0.64      ! [A3: set_rat] :
% 0.26/0.64        ( ( finite_finite_rat @ A3 )
% 0.26/0.64       => ( ( A3 != bot_bot_set_rat )
% 0.26/0.64         => ? [X4: rat] :
% 0.26/0.64              ( ( member_rat @ X4 @ A3 )
% 0.26/0.64              & ! [Xa2: rat] :
% 0.26/0.64                  ( ( member_rat @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_rat @ Xa2 @ X4 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_minimal
% 0.26/0.64  thf(fact_8517_finite__has__minimal,axiom,
% 0.26/0.64      ! [A3: set_num] :
% 0.26/0.64        ( ( finite_finite_num @ A3 )
% 0.26/0.64       => ( ( A3 != bot_bot_set_num )
% 0.26/0.64         => ? [X4: num] :
% 0.26/0.64              ( ( member_num @ X4 @ A3 )
% 0.26/0.64              & ! [Xa2: num] :
% 0.26/0.64                  ( ( member_num @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_num @ Xa2 @ X4 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_minimal
% 0.26/0.64  thf(fact_8518_finite__has__minimal,axiom,
% 0.26/0.64      ! [A3: set_nat] :
% 0.26/0.64        ( ( finite_finite_nat @ A3 )
% 0.26/0.64       => ( ( A3 != bot_bot_set_nat )
% 0.26/0.64         => ? [X4: nat] :
% 0.26/0.64              ( ( member_nat @ X4 @ A3 )
% 0.26/0.64              & ! [Xa2: nat] :
% 0.26/0.64                  ( ( member_nat @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_nat @ Xa2 @ X4 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_minimal
% 0.26/0.64  thf(fact_8519_finite__has__minimal,axiom,
% 0.26/0.64      ! [A3: set_int] :
% 0.26/0.64        ( ( finite_finite_int @ A3 )
% 0.26/0.64       => ( ( A3 != bot_bot_set_int )
% 0.26/0.64         => ? [X4: int] :
% 0.26/0.64              ( ( member_int @ X4 @ A3 )
% 0.26/0.64              & ! [Xa2: int] :
% 0.26/0.64                  ( ( member_int @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_int @ Xa2 @ X4 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_minimal
% 0.26/0.64  thf(fact_8520_finite__has__maximal,axiom,
% 0.26/0.64      ! [A3: set_Extended_enat] :
% 0.26/0.64        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.64       => ( ( A3 != bot_bo7653980558646680370d_enat )
% 0.26/0.64         => ? [X4: extended_enat] :
% 0.26/0.64              ( ( member_Extended_enat @ X4 @ A3 )
% 0.26/0.64              & ! [Xa2: extended_enat] :
% 0.26/0.64                  ( ( member_Extended_enat @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_le2932123472753598470d_enat @ X4 @ Xa2 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_maximal
% 0.26/0.64  thf(fact_8521_finite__has__maximal,axiom,
% 0.26/0.64      ! [A3: set_real] :
% 0.26/0.64        ( ( finite_finite_real @ A3 )
% 0.26/0.64       => ( ( A3 != bot_bot_set_real )
% 0.26/0.64         => ? [X4: real] :
% 0.26/0.64              ( ( member_real @ X4 @ A3 )
% 0.26/0.64              & ! [Xa2: real] :
% 0.26/0.64                  ( ( member_real @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_real @ X4 @ Xa2 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_maximal
% 0.26/0.64  thf(fact_8522_finite__has__maximal,axiom,
% 0.26/0.64      ! [A3: set_set_nat] :
% 0.26/0.64        ( ( finite1152437895449049373et_nat @ A3 )
% 0.26/0.64       => ( ( A3 != bot_bot_set_set_nat )
% 0.26/0.64         => ? [X4: set_nat] :
% 0.26/0.64              ( ( member_set_nat @ X4 @ A3 )
% 0.26/0.64              & ! [Xa2: set_nat] :
% 0.26/0.64                  ( ( member_set_nat @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_set_nat @ X4 @ Xa2 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_maximal
% 0.26/0.64  thf(fact_8523_finite__has__maximal,axiom,
% 0.26/0.64      ! [A3: set_rat] :
% 0.26/0.64        ( ( finite_finite_rat @ A3 )
% 0.26/0.64       => ( ( A3 != bot_bot_set_rat )
% 0.26/0.64         => ? [X4: rat] :
% 0.26/0.64              ( ( member_rat @ X4 @ A3 )
% 0.26/0.64              & ! [Xa2: rat] :
% 0.26/0.64                  ( ( member_rat @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_rat @ X4 @ Xa2 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_maximal
% 0.26/0.64  thf(fact_8524_finite__has__maximal,axiom,
% 0.26/0.64      ! [A3: set_num] :
% 0.26/0.64        ( ( finite_finite_num @ A3 )
% 0.26/0.64       => ( ( A3 != bot_bot_set_num )
% 0.26/0.64         => ? [X4: num] :
% 0.26/0.64              ( ( member_num @ X4 @ A3 )
% 0.26/0.64              & ! [Xa2: num] :
% 0.26/0.64                  ( ( member_num @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_num @ X4 @ Xa2 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_maximal
% 0.26/0.64  thf(fact_8525_finite__has__maximal,axiom,
% 0.26/0.64      ! [A3: set_nat] :
% 0.26/0.64        ( ( finite_finite_nat @ A3 )
% 0.26/0.64       => ( ( A3 != bot_bot_set_nat )
% 0.26/0.64         => ? [X4: nat] :
% 0.26/0.64              ( ( member_nat @ X4 @ A3 )
% 0.26/0.64              & ! [Xa2: nat] :
% 0.26/0.64                  ( ( member_nat @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_nat @ X4 @ Xa2 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_maximal
% 0.26/0.64  thf(fact_8526_finite__has__maximal,axiom,
% 0.26/0.64      ! [A3: set_int] :
% 0.26/0.64        ( ( finite_finite_int @ A3 )
% 0.26/0.64       => ( ( A3 != bot_bot_set_int )
% 0.26/0.64         => ? [X4: int] :
% 0.26/0.64              ( ( member_int @ X4 @ A3 )
% 0.26/0.64              & ! [Xa2: int] :
% 0.26/0.64                  ( ( member_int @ Xa2 @ A3 )
% 0.26/0.64                 => ( ( ord_less_eq_int @ X4 @ Xa2 )
% 0.26/0.64                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % finite_has_maximal
% 0.26/0.64  thf(fact_8527_choose__even__sum,axiom,
% 0.26/0.64      ! [N: nat] :
% 0.26/0.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.64       => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 0.26/0.64            @ ( groups2073611262835488442omplex
% 0.26/0.64              @ ^ [I4: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I4 ) ) @ zero_zero_complex )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64          = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % choose_even_sum
% 0.26/0.64  thf(fact_8528_choose__even__sum,axiom,
% 0.26/0.64      ! [N: nat] :
% 0.26/0.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.64       => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 0.26/0.64            @ ( groups2906978787729119204at_rat
% 0.26/0.64              @ ^ [I4: nat] : ( if_rat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I4 ) ) @ zero_zero_rat )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64          = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % choose_even_sum
% 0.26/0.64  thf(fact_8529_choose__even__sum,axiom,
% 0.26/0.64      ! [N: nat] :
% 0.26/0.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.64       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 0.26/0.64            @ ( groups3539618377306564664at_int
% 0.26/0.64              @ ^ [I4: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I4 ) ) @ zero_zero_int )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64          = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % choose_even_sum
% 0.26/0.64  thf(fact_8530_choose__even__sum,axiom,
% 0.26/0.64      ! [N: nat] :
% 0.26/0.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.64       => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 0.26/0.64            @ ( groups6591440286371151544t_real
% 0.26/0.64              @ ^ [I4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I4 ) ) @ zero_zero_real )
% 0.26/0.64              @ ( set_ord_atMost_nat @ N ) ) )
% 0.26/0.64          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % choose_even_sum
% 0.26/0.64  thf(fact_8531_sumr__cos__zero__one,axiom,
% 0.26/0.64      ! [N: nat] :
% 0.26/0.64        ( ( groups6591440286371151544t_real
% 0.26/0.64          @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ zero_zero_real @ M3 ) )
% 0.26/0.64          @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.26/0.64        = one_one_real ) ).
% 0.26/0.64  
% 0.26/0.64  % sumr_cos_zero_one
% 0.26/0.64  thf(fact_8532_gbinomial__partial__row__sum,axiom,
% 0.26/0.64      ! [A: complex,M: nat] :
% 0.26/0.64        ( ( groups2073611262835488442omplex
% 0.26/0.64          @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ M ) )
% 0.26/0.64        = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ one_one_complex ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_partial_row_sum
% 0.26/0.64  thf(fact_8533_gbinomial__partial__row__sum,axiom,
% 0.26/0.64      ! [A: rat,M: nat] :
% 0.26/0.64        ( ( groups2906978787729119204at_rat
% 0.26/0.64          @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ M ) )
% 0.26/0.64        = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ one_one_rat ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_partial_row_sum
% 0.26/0.64  thf(fact_8534_gbinomial__partial__row__sum,axiom,
% 0.26/0.64      ! [A: real,M: nat] :
% 0.26/0.64        ( ( groups6591440286371151544t_real
% 0.26/0.64          @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 0.26/0.64          @ ( set_ord_atMost_nat @ M ) )
% 0.26/0.64        = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ one_one_real ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_partial_row_sum
% 0.26/0.64  thf(fact_8535_gbinomial__r__part__sum,axiom,
% 0.26/0.64      ! [M: nat] :
% 0.26/0.64        ( ( groups2073611262835488442omplex @ ( gbinomial_complex @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M ) ) @ one_one_complex ) ) @ ( set_ord_atMost_nat @ M ) )
% 0.26/0.64        = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_r_part_sum
% 0.26/0.64  thf(fact_8536_gbinomial__r__part__sum,axiom,
% 0.26/0.64      ! [M: nat] :
% 0.26/0.64        ( ( groups2906978787729119204at_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M ) ) @ one_one_rat ) ) @ ( set_ord_atMost_nat @ M ) )
% 0.26/0.64        = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_r_part_sum
% 0.26/0.64  thf(fact_8537_gbinomial__r__part__sum,axiom,
% 0.26/0.64      ! [M: nat] :
% 0.26/0.64        ( ( groups6591440286371151544t_real @ ( gbinomial_real @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ one_one_real ) ) @ ( set_ord_atMost_nat @ M ) )
% 0.26/0.64        = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_r_part_sum
% 0.26/0.64  thf(fact_8538_dbl__inc__simps_I3_J,axiom,
% 0.26/0.64      ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 0.26/0.64      = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_simps(3)
% 0.26/0.64  thf(fact_8539_dbl__inc__simps_I3_J,axiom,
% 0.26/0.64      ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 0.26/0.64      = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_simps(3)
% 0.26/0.64  thf(fact_8540_dbl__inc__simps_I3_J,axiom,
% 0.26/0.64      ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 0.26/0.64      = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_simps(3)
% 0.26/0.64  thf(fact_8541_dbl__inc__simps_I3_J,axiom,
% 0.26/0.64      ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 0.26/0.64      = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_simps(3)
% 0.26/0.64  thf(fact_8542_sin__arccos__abs,axiom,
% 0.26/0.64      ! [Y3: real] :
% 0.26/0.64        ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 0.26/0.64       => ( ( sin_real @ ( arccos @ Y3 ) )
% 0.26/0.64          = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sin_arccos_abs
% 0.26/0.64  thf(fact_8543_gbinomial__0_I2_J,axiom,
% 0.26/0.64      ! [K: nat] :
% 0.26/0.64        ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 0.26/0.64        = zero_zero_real ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_0(2)
% 0.26/0.64  thf(fact_8544_gbinomial__0_I2_J,axiom,
% 0.26/0.64      ! [K: nat] :
% 0.26/0.64        ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 0.26/0.64        = zero_zero_rat ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_0(2)
% 0.26/0.64  thf(fact_8545_gbinomial__0_I2_J,axiom,
% 0.26/0.64      ! [K: nat] :
% 0.26/0.64        ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 0.26/0.64        = zero_zero_nat ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_0(2)
% 0.26/0.64  thf(fact_8546_gbinomial__0_I2_J,axiom,
% 0.26/0.64      ! [K: nat] :
% 0.26/0.64        ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 0.26/0.64        = zero_zero_int ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_0(2)
% 0.26/0.64  thf(fact_8547_gbinomial__0_I1_J,axiom,
% 0.26/0.64      ! [A: complex] :
% 0.26/0.64        ( ( gbinomial_complex @ A @ zero_zero_nat )
% 0.26/0.64        = one_one_complex ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_0(1)
% 0.26/0.64  thf(fact_8548_gbinomial__0_I1_J,axiom,
% 0.26/0.64      ! [A: real] :
% 0.26/0.64        ( ( gbinomial_real @ A @ zero_zero_nat )
% 0.26/0.64        = one_one_real ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_0(1)
% 0.26/0.64  thf(fact_8549_gbinomial__0_I1_J,axiom,
% 0.26/0.64      ! [A: rat] :
% 0.26/0.64        ( ( gbinomial_rat @ A @ zero_zero_nat )
% 0.26/0.64        = one_one_rat ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_0(1)
% 0.26/0.64  thf(fact_8550_gbinomial__0_I1_J,axiom,
% 0.26/0.64      ! [A: nat] :
% 0.26/0.64        ( ( gbinomial_nat @ A @ zero_zero_nat )
% 0.26/0.64        = one_one_nat ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_0(1)
% 0.26/0.64  thf(fact_8551_gbinomial__0_I1_J,axiom,
% 0.26/0.64      ! [A: int] :
% 0.26/0.64        ( ( gbinomial_int @ A @ zero_zero_nat )
% 0.26/0.64        = one_one_int ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_0(1)
% 0.26/0.64  thf(fact_8552_arccos__1,axiom,
% 0.26/0.64      ( ( arccos @ one_one_real )
% 0.26/0.64      = zero_zero_real ) ).
% 0.26/0.64  
% 0.26/0.64  % arccos_1
% 0.26/0.64  thf(fact_8553_cos__coeff__0,axiom,
% 0.26/0.64      ( ( cos_coeff @ zero_zero_nat )
% 0.26/0.64      = one_one_real ) ).
% 0.26/0.64  
% 0.26/0.64  % cos_coeff_0
% 0.26/0.64  thf(fact_8554_dbl__inc__simps_I2_J,axiom,
% 0.26/0.64      ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 0.26/0.64      = one_one_complex ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_simps(2)
% 0.26/0.64  thf(fact_8555_dbl__inc__simps_I2_J,axiom,
% 0.26/0.64      ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 0.26/0.64      = one_one_real ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_simps(2)
% 0.26/0.64  thf(fact_8556_dbl__inc__simps_I2_J,axiom,
% 0.26/0.64      ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 0.26/0.64      = one_one_rat ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_simps(2)
% 0.26/0.64  thf(fact_8557_dbl__inc__simps_I2_J,axiom,
% 0.26/0.64      ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 0.26/0.64      = one_one_int ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_simps(2)
% 0.26/0.64  thf(fact_8558_dbl__inc__simps_I4_J,axiom,
% 0.26/0.64      ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.26/0.64      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_simps(4)
% 0.26/0.64  thf(fact_8559_dbl__inc__simps_I4_J,axiom,
% 0.26/0.64      ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.64      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_simps(4)
% 0.26/0.64  thf(fact_8560_dbl__inc__simps_I4_J,axiom,
% 0.26/0.64      ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.26/0.64      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_simps(4)
% 0.26/0.64  thf(fact_8561_dbl__inc__simps_I4_J,axiom,
% 0.26/0.64      ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.26/0.64      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_simps(4)
% 0.26/0.64  thf(fact_8562_dbl__inc__simps_I4_J,axiom,
% 0.26/0.64      ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.26/0.64      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_simps(4)
% 0.26/0.64  thf(fact_8563_dbl__inc__simps_I5_J,axiom,
% 0.26/0.64      ! [K: num] :
% 0.26/0.64        ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 0.26/0.64        = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_simps(5)
% 0.26/0.64  thf(fact_8564_dbl__inc__simps_I5_J,axiom,
% 0.26/0.64      ! [K: num] :
% 0.26/0.64        ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 0.26/0.64        = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_simps(5)
% 0.26/0.64  thf(fact_8565_dbl__inc__simps_I5_J,axiom,
% 0.26/0.64      ! [K: num] :
% 0.26/0.64        ( ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) )
% 0.26/0.64        = ( numeral_numeral_rat @ ( bit1 @ K ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_simps(5)
% 0.26/0.64  thf(fact_8566_dbl__inc__simps_I5_J,axiom,
% 0.26/0.64      ! [K: num] :
% 0.26/0.64        ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 0.26/0.64        = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_simps(5)
% 0.26/0.64  thf(fact_8567_dbl__dec__simps_I1_J,axiom,
% 0.26/0.64      ! [K: num] :
% 0.26/0.64        ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 0.26/0.64        = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_dec_simps(1)
% 0.26/0.64  thf(fact_8568_dbl__dec__simps_I1_J,axiom,
% 0.26/0.64      ! [K: num] :
% 0.26/0.64        ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.26/0.64        = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_dec_simps(1)
% 0.26/0.64  thf(fact_8569_dbl__dec__simps_I1_J,axiom,
% 0.26/0.64      ! [K: num] :
% 0.26/0.64        ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 0.26/0.64        = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_dec_simps(1)
% 0.26/0.64  thf(fact_8570_dbl__dec__simps_I1_J,axiom,
% 0.26/0.64      ! [K: num] :
% 0.26/0.64        ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.26/0.64        = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_dec_simps(1)
% 0.26/0.64  thf(fact_8571_dbl__dec__simps_I1_J,axiom,
% 0.26/0.64      ! [K: num] :
% 0.26/0.64        ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.26/0.64        = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_dec_simps(1)
% 0.26/0.64  thf(fact_8572_dbl__inc__simps_I1_J,axiom,
% 0.26/0.64      ! [K: num] :
% 0.26/0.64        ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 0.26/0.64        = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_simps(1)
% 0.26/0.64  thf(fact_8573_dbl__inc__simps_I1_J,axiom,
% 0.26/0.64      ! [K: num] :
% 0.26/0.64        ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.26/0.64        = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_simps(1)
% 0.26/0.64  thf(fact_8574_dbl__inc__simps_I1_J,axiom,
% 0.26/0.64      ! [K: num] :
% 0.26/0.64        ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 0.26/0.64        = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_simps(1)
% 0.26/0.64  thf(fact_8575_dbl__inc__simps_I1_J,axiom,
% 0.26/0.64      ! [K: num] :
% 0.26/0.64        ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.26/0.64        = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_simps(1)
% 0.26/0.64  thf(fact_8576_dbl__inc__simps_I1_J,axiom,
% 0.26/0.64      ! [K: num] :
% 0.26/0.64        ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.26/0.64        = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_simps(1)
% 0.26/0.64  thf(fact_8577_cos__arccos,axiom,
% 0.26/0.64      ! [Y3: real] :
% 0.26/0.64        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 0.26/0.64       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 0.26/0.64         => ( ( cos_real @ ( arccos @ Y3 ) )
% 0.26/0.64            = Y3 ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % cos_arccos
% 0.26/0.64  thf(fact_8578_arccos__0,axiom,
% 0.26/0.64      ( ( arccos @ zero_zero_real )
% 0.26/0.64      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % arccos_0
% 0.26/0.64  thf(fact_8579_of__nat__gbinomial,axiom,
% 0.26/0.64      ! [N: nat,K: nat] :
% 0.26/0.64        ( ( semiri8010041392384452111omplex @ ( gbinomial_nat @ N @ K ) )
% 0.26/0.64        = ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ K ) ) ).
% 0.26/0.64  
% 0.26/0.64  % of_nat_gbinomial
% 0.26/0.64  thf(fact_8580_of__nat__gbinomial,axiom,
% 0.26/0.64      ! [N: nat,K: nat] :
% 0.26/0.64        ( ( semiri5074537144036343181t_real @ ( gbinomial_nat @ N @ K ) )
% 0.26/0.64        = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K ) ) ).
% 0.26/0.64  
% 0.26/0.64  % of_nat_gbinomial
% 0.26/0.64  thf(fact_8581_of__nat__gbinomial,axiom,
% 0.26/0.64      ! [N: nat,K: nat] :
% 0.26/0.64        ( ( semiri681578069525770553at_rat @ ( gbinomial_nat @ N @ K ) )
% 0.26/0.64        = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K ) ) ).
% 0.26/0.64  
% 0.26/0.64  % of_nat_gbinomial
% 0.26/0.64  thf(fact_8582_binomial__gbinomial,axiom,
% 0.26/0.64      ! [N: nat,K: nat] :
% 0.26/0.64        ( ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) )
% 0.26/0.64        = ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ K ) ) ).
% 0.26/0.64  
% 0.26/0.64  % binomial_gbinomial
% 0.26/0.64  thf(fact_8583_binomial__gbinomial,axiom,
% 0.26/0.64      ! [N: nat,K: nat] :
% 0.26/0.64        ( ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) )
% 0.26/0.64        = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K ) ) ).
% 0.26/0.64  
% 0.26/0.64  % binomial_gbinomial
% 0.26/0.64  thf(fact_8584_binomial__gbinomial,axiom,
% 0.26/0.64      ! [N: nat,K: nat] :
% 0.26/0.64        ( ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) )
% 0.26/0.64        = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K ) ) ).
% 0.26/0.64  
% 0.26/0.64  % binomial_gbinomial
% 0.26/0.64  thf(fact_8585_gbinomial__of__nat__symmetric,axiom,
% 0.26/0.64      ! [K: nat,N: nat] :
% 0.26/0.64        ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.64       => ( ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ K )
% 0.26/0.64          = ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_of_nat_symmetric
% 0.26/0.64  thf(fact_8586_gbinomial__of__nat__symmetric,axiom,
% 0.26/0.64      ! [K: nat,N: nat] :
% 0.26/0.64        ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.64       => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K )
% 0.26/0.64          = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_of_nat_symmetric
% 0.26/0.64  thf(fact_8587_gbinomial__of__nat__symmetric,axiom,
% 0.26/0.64      ! [K: nat,N: nat] :
% 0.26/0.64        ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.64       => ( ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K )
% 0.26/0.64          = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_of_nat_symmetric
% 0.26/0.64  thf(fact_8588_arccos__le__arccos,axiom,
% 0.26/0.64      ! [X3: real,Y3: real] :
% 0.26/0.64        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.26/0.64       => ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.26/0.64         => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 0.26/0.64           => ( ord_less_eq_real @ ( arccos @ Y3 ) @ ( arccos @ X3 ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % arccos_le_arccos
% 0.26/0.64  thf(fact_8589_arccos__eq__iff,axiom,
% 0.26/0.64      ! [X3: real,Y3: real] :
% 0.26/0.64        ( ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.26/0.64          & ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real ) )
% 0.26/0.64       => ( ( ( arccos @ X3 )
% 0.26/0.64            = ( arccos @ Y3 ) )
% 0.26/0.64          = ( X3 = Y3 ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % arccos_eq_iff
% 0.26/0.64  thf(fact_8590_arccos__le__mono,axiom,
% 0.26/0.64      ! [X3: real,Y3: real] :
% 0.26/0.64        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.26/0.64       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 0.26/0.64         => ( ( ord_less_eq_real @ ( arccos @ X3 ) @ ( arccos @ Y3 ) )
% 0.26/0.64            = ( ord_less_eq_real @ Y3 @ X3 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % arccos_le_mono
% 0.26/0.64  thf(fact_8591_gbinomial__absorb__comp,axiom,
% 0.26/0.64      ! [A: complex,K: nat] :
% 0.26/0.64        ( ( times_times_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ A @ K ) )
% 0.26/0.64        = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_absorb_comp
% 0.26/0.64  thf(fact_8592_gbinomial__absorb__comp,axiom,
% 0.26/0.64      ! [A: real,K: nat] :
% 0.26/0.64        ( ( times_times_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ A @ K ) )
% 0.26/0.64        = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_absorb_comp
% 0.26/0.64  thf(fact_8593_gbinomial__absorb__comp,axiom,
% 0.26/0.64      ! [A: rat,K: nat] :
% 0.26/0.64        ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 0.26/0.64        = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_absorb_comp
% 0.26/0.64  thf(fact_8594_gbinomial__mult__1,axiom,
% 0.26/0.64      ! [A: complex,K: nat] :
% 0.26/0.64        ( ( times_times_complex @ A @ ( gbinomial_complex @ A @ K ) )
% 0.26/0.64        = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_mult_1
% 0.26/0.64  thf(fact_8595_gbinomial__mult__1,axiom,
% 0.26/0.64      ! [A: real,K: nat] :
% 0.26/0.64        ( ( times_times_real @ A @ ( gbinomial_real @ A @ K ) )
% 0.26/0.64        = ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ K ) @ ( gbinomial_real @ A @ K ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_mult_1
% 0.26/0.64  thf(fact_8596_gbinomial__mult__1,axiom,
% 0.26/0.64      ! [A: rat,K: nat] :
% 0.26/0.64        ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 0.26/0.64        = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_mult_1
% 0.26/0.64  thf(fact_8597_gbinomial__mult__1_H,axiom,
% 0.26/0.64      ! [A: complex,K: nat] :
% 0.26/0.64        ( ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ A )
% 0.26/0.64        = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_mult_1'
% 0.26/0.64  thf(fact_8598_gbinomial__mult__1_H,axiom,
% 0.26/0.64      ! [A: real,K: nat] :
% 0.26/0.64        ( ( times_times_real @ ( gbinomial_real @ A @ K ) @ A )
% 0.26/0.64        = ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ K ) @ ( gbinomial_real @ A @ K ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_mult_1'
% 0.26/0.64  thf(fact_8599_gbinomial__mult__1_H,axiom,
% 0.26/0.64      ! [A: rat,K: nat] :
% 0.26/0.64        ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 0.26/0.64        = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_mult_1'
% 0.26/0.64  thf(fact_8600_gbinomial__ge__n__over__k__pow__k,axiom,
% 0.26/0.64      ! [K: nat,A: real] :
% 0.26/0.64        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A )
% 0.26/0.64       => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_ge_n_over_k_pow_k
% 0.26/0.64  thf(fact_8601_gbinomial__ge__n__over__k__pow__k,axiom,
% 0.26/0.64      ! [K: nat,A: rat] :
% 0.26/0.64        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 0.26/0.64       => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_ge_n_over_k_pow_k
% 0.26/0.64  thf(fact_8602_dbl__inc__def,axiom,
% 0.26/0.64      ( neg_nu8557863876264182079omplex
% 0.26/0.64      = ( ^ [X: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X @ X ) @ one_one_complex ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_def
% 0.26/0.64  thf(fact_8603_dbl__inc__def,axiom,
% 0.26/0.64      ( neg_nu8295874005876285629c_real
% 0.26/0.64      = ( ^ [X: real] : ( plus_plus_real @ ( plus_plus_real @ X @ X ) @ one_one_real ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_def
% 0.26/0.64  thf(fact_8604_dbl__inc__def,axiom,
% 0.26/0.64      ( neg_nu5219082963157363817nc_rat
% 0.26/0.64      = ( ^ [X: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_def
% 0.26/0.64  thf(fact_8605_dbl__inc__def,axiom,
% 0.26/0.64      ( neg_nu5851722552734809277nc_int
% 0.26/0.64      = ( ^ [X: int] : ( plus_plus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % dbl_inc_def
% 0.26/0.64  thf(fact_8606_arccos__lbound,axiom,
% 0.26/0.64      ! [Y3: real] :
% 0.26/0.64        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 0.26/0.64       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 0.26/0.64         => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y3 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % arccos_lbound
% 0.26/0.64  thf(fact_8607_arccos__less__arccos,axiom,
% 0.26/0.64      ! [X3: real,Y3: real] :
% 0.26/0.64        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.26/0.64       => ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.64         => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 0.26/0.64           => ( ord_less_real @ ( arccos @ Y3 ) @ ( arccos @ X3 ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % arccos_less_arccos
% 0.26/0.64  thf(fact_8608_arccos__less__mono,axiom,
% 0.26/0.64      ! [X3: real,Y3: real] :
% 0.26/0.64        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.26/0.64       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 0.26/0.64         => ( ( ord_less_real @ ( arccos @ X3 ) @ ( arccos @ Y3 ) )
% 0.26/0.64            = ( ord_less_real @ Y3 @ X3 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % arccos_less_mono
% 0.26/0.64  thf(fact_8609_arccos__ubound,axiom,
% 0.26/0.64      ! [Y3: real] :
% 0.26/0.64        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 0.26/0.64       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 0.26/0.64         => ( ord_less_eq_real @ ( arccos @ Y3 ) @ pi ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % arccos_ubound
% 0.26/0.64  thf(fact_8610_arccos__cos,axiom,
% 0.26/0.64      ! [X3: real] :
% 0.26/0.64        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.64       => ( ( ord_less_eq_real @ X3 @ pi )
% 0.26/0.64         => ( ( arccos @ ( cos_real @ X3 ) )
% 0.26/0.64            = X3 ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % arccos_cos
% 0.26/0.64  thf(fact_8611_cos__arccos__abs,axiom,
% 0.26/0.64      ! [Y3: real] :
% 0.26/0.64        ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 0.26/0.64       => ( ( cos_real @ ( arccos @ Y3 ) )
% 0.26/0.64          = Y3 ) ) ).
% 0.26/0.64  
% 0.26/0.64  % cos_arccos_abs
% 0.26/0.64  thf(fact_8612_arccos__cos__eq__abs,axiom,
% 0.26/0.64      ! [Theta: real] :
% 0.26/0.64        ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 0.26/0.64       => ( ( arccos @ ( cos_real @ Theta ) )
% 0.26/0.64          = ( abs_abs_real @ Theta ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % arccos_cos_eq_abs
% 0.26/0.64  thf(fact_8613_Suc__times__gbinomial,axiom,
% 0.26/0.64      ! [K: nat,A: complex] :
% 0.26/0.64        ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) )
% 0.26/0.64        = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % Suc_times_gbinomial
% 0.26/0.64  thf(fact_8614_Suc__times__gbinomial,axiom,
% 0.26/0.64      ! [K: nat,A: real] :
% 0.26/0.64        ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) ) )
% 0.26/0.64        = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % Suc_times_gbinomial
% 0.26/0.64  thf(fact_8615_Suc__times__gbinomial,axiom,
% 0.26/0.64      ! [K: nat,A: rat] :
% 0.26/0.64        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 0.26/0.64        = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % Suc_times_gbinomial
% 0.26/0.64  thf(fact_8616_gbinomial__absorption,axiom,
% 0.26/0.64      ! [K: nat,A: complex] :
% 0.26/0.64        ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) )
% 0.26/0.64        = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_absorption
% 0.26/0.64  thf(fact_8617_gbinomial__absorption,axiom,
% 0.26/0.64      ! [K: nat,A: real] :
% 0.26/0.64        ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) )
% 0.26/0.64        = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_absorption
% 0.26/0.64  thf(fact_8618_gbinomial__absorption,axiom,
% 0.26/0.64      ! [K: nat,A: rat] :
% 0.26/0.64        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 0.26/0.64        = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_absorption
% 0.26/0.64  thf(fact_8619_gbinomial__trinomial__revision,axiom,
% 0.26/0.64      ! [K: nat,M: nat,A: complex] :
% 0.26/0.64        ( ( ord_less_eq_nat @ K @ M )
% 0.26/0.64       => ( ( times_times_complex @ ( gbinomial_complex @ A @ M ) @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ M ) @ K ) )
% 0.26/0.64          = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_trinomial_revision
% 0.26/0.64  thf(fact_8620_gbinomial__trinomial__revision,axiom,
% 0.26/0.64      ! [K: nat,M: nat,A: real] :
% 0.26/0.64        ( ( ord_less_eq_nat @ K @ M )
% 0.26/0.64       => ( ( times_times_real @ ( gbinomial_real @ A @ M ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M ) @ K ) )
% 0.26/0.64          = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_trinomial_revision
% 0.26/0.64  thf(fact_8621_gbinomial__trinomial__revision,axiom,
% 0.26/0.64      ! [K: nat,M: nat,A: rat] :
% 0.26/0.64        ( ( ord_less_eq_nat @ K @ M )
% 0.26/0.64       => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 0.26/0.64          = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_trinomial_revision
% 0.26/0.64  thf(fact_8622_gbinomial__parallel__sum,axiom,
% 0.26/0.64      ! [A: complex,N: nat] :
% 0.26/0.64        ( ( groups2073611262835488442omplex
% 0.26/0.64          @ ^ [K3: nat] : ( gbinomial_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K3 ) ) @ K3 )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64        = ( gbinomial_complex @ ( plus_plus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N ) ) @ one_one_complex ) @ N ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_parallel_sum
% 0.26/0.64  thf(fact_8623_gbinomial__parallel__sum,axiom,
% 0.26/0.64      ! [A: rat,N: nat] :
% 0.26/0.64        ( ( groups2906978787729119204at_rat
% 0.26/0.64          @ ^ [K3: nat] : ( gbinomial_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K3 ) ) @ K3 )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64        = ( gbinomial_rat @ ( plus_plus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) @ one_one_rat ) @ N ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_parallel_sum
% 0.26/0.64  thf(fact_8624_gbinomial__parallel__sum,axiom,
% 0.26/0.64      ! [A: real,N: nat] :
% 0.26/0.64        ( ( groups6591440286371151544t_real
% 0.26/0.64          @ ^ [K3: nat] : ( gbinomial_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K3 ) ) @ K3 )
% 0.26/0.64          @ ( set_ord_atMost_nat @ N ) )
% 0.26/0.64        = ( gbinomial_real @ ( plus_plus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) @ one_one_real ) @ N ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_parallel_sum
% 0.26/0.64  thf(fact_8625_arccos__lt__bounded,axiom,
% 0.26/0.64      ! [Y3: real] :
% 0.26/0.64        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 0.26/0.64       => ( ( ord_less_real @ Y3 @ one_one_real )
% 0.26/0.64         => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y3 ) )
% 0.26/0.64            & ( ord_less_real @ ( arccos @ Y3 ) @ pi ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % arccos_lt_bounded
% 0.26/0.64  thf(fact_8626_arccos__bounded,axiom,
% 0.26/0.64      ! [Y3: real] :
% 0.26/0.64        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 0.26/0.64       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 0.26/0.64         => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y3 ) )
% 0.26/0.64            & ( ord_less_eq_real @ ( arccos @ Y3 ) @ pi ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % arccos_bounded
% 0.26/0.64  thf(fact_8627_gbinomial__factors,axiom,
% 0.26/0.64      ! [A: complex,K: nat] :
% 0.26/0.64        ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 0.26/0.64        = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_factors
% 0.26/0.64  thf(fact_8628_gbinomial__factors,axiom,
% 0.26/0.64      ! [A: real,K: nat] :
% 0.26/0.64        ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 0.26/0.64        = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_factors
% 0.26/0.64  thf(fact_8629_gbinomial__factors,axiom,
% 0.26/0.64      ! [A: rat,K: nat] :
% 0.26/0.64        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 0.26/0.64        = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_factors
% 0.26/0.64  thf(fact_8630_gbinomial__rec,axiom,
% 0.26/0.64      ! [A: complex,K: nat] :
% 0.26/0.64        ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 0.26/0.64        = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_rec
% 0.26/0.64  thf(fact_8631_gbinomial__rec,axiom,
% 0.26/0.64      ! [A: real,K: nat] :
% 0.26/0.64        ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 0.26/0.64        = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_rec
% 0.26/0.64  thf(fact_8632_gbinomial__rec,axiom,
% 0.26/0.64      ! [A: rat,K: nat] :
% 0.26/0.64        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 0.26/0.64        = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_rec
% 0.26/0.64  thf(fact_8633_gbinomial__index__swap,axiom,
% 0.26/0.64      ! [K: nat,N: nat] :
% 0.26/0.64        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ one_one_complex ) @ K ) )
% 0.26/0.64        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_index_swap
% 0.26/0.64  thf(fact_8634_gbinomial__index__swap,axiom,
% 0.26/0.64      ! [K: nat,N: nat] :
% 0.26/0.64        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ one_one_real ) @ K ) )
% 0.26/0.64        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_index_swap
% 0.26/0.64  thf(fact_8635_gbinomial__index__swap,axiom,
% 0.26/0.64      ! [K: nat,N: nat] :
% 0.26/0.64        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ one_one_rat ) @ K ) )
% 0.26/0.64        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ N ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_index_swap
% 0.26/0.64  thf(fact_8636_gbinomial__negated__upper,axiom,
% 0.26/0.64      ( gbinomial_rat
% 0.26/0.64      = ( ^ [A4: rat,K3: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K3 ) @ A4 ) @ one_one_rat ) @ K3 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % gbinomial_negated_upper
% 0.26/0.64  thf(fact_8637_sin__arccos__nonzero,axiom,
% 0.26/0.64      ! [X3: real] :
% 0.26/0.64        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.26/0.64       => ( ( ord_less_real @ X3 @ one_one_real )
% 0.26/0.64         => ( ( sin_real @ ( arccos @ X3 ) )
% 0.26/0.64           != zero_zero_real ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % sin_arccos_nonzero
% 0.26/0.64  thf(fact_8638_arccos__cos2,axiom,
% 0.26/0.64      ! [X3: real] :
% 0.26/0.64        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 0.26/0.64       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X3 )
% 0.26/0.64         => ( ( arccos @ ( cos_real @ X3 ) )
% 0.26/0.64            = ( uminus_uminus_real @ X3 ) ) ) ) ).
% 0.26/0.64  
% 0.26/0.64  % arccos_cos2
% 0.26/0.64  thf(fact_8639_arccos__minus,axiom,
% 0.26/0.64      ! [X3: real] :
% 0.26/0.64        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.26/0.65       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 0.26/0.65         => ( ( arccos @ ( uminus_uminus_real @ X3 ) )
% 0.26/0.65            = ( minus_minus_real @ pi @ ( arccos @ X3 ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % arccos_minus
% 0.26/0.65  thf(fact_8640_arccos,axiom,
% 0.26/0.65      ! [Y3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 0.26/0.65       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 0.26/0.65         => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y3 ) )
% 0.26/0.65            & ( ord_less_eq_real @ ( arccos @ Y3 ) @ pi )
% 0.26/0.65            & ( ( cos_real @ ( arccos @ Y3 ) )
% 0.26/0.65              = Y3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % arccos
% 0.26/0.65  thf(fact_8641_arccos__minus__abs,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.26/0.65       => ( ( arccos @ ( uminus_uminus_real @ X3 ) )
% 0.26/0.65          = ( minus_minus_real @ pi @ ( arccos @ X3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % arccos_minus_abs
% 0.26/0.65  thf(fact_8642_arccos__le__pi2,axiom,
% 0.26/0.65      ! [Y3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.65       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 0.26/0.65         => ( ord_less_eq_real @ ( arccos @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % arccos_le_pi2
% 0.26/0.65  thf(fact_8643_arccos__cos__eq__abs__2pi,axiom,
% 0.26/0.65      ! [Theta: real] :
% 0.26/0.65        ~ ! [K2: int] :
% 0.26/0.65            ( ( arccos @ ( cos_real @ Theta ) )
% 0.26/0.65           != ( abs_abs_real @ ( minus_minus_real @ Theta @ ( times_times_real @ ( ring_1_of_int_real @ K2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % arccos_cos_eq_abs_2pi
% 0.26/0.65  thf(fact_8644_sin__arccos,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.26/0.65       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 0.26/0.65         => ( ( sin_real @ ( arccos @ X3 ) )
% 0.26/0.65            = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sin_arccos
% 0.26/0.65  thf(fact_8645_Maclaurin__minus__cos__expansion,axiom,
% 0.26/0.65      ! [N: nat,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_real @ X3 @ zero_zero_real )
% 0.26/0.65         => ? [T3: real] :
% 0.26/0.65              ( ( ord_less_real @ X3 @ T3 )
% 0.26/0.65              & ( ord_less_real @ T3 @ zero_zero_real )
% 0.26/0.65              & ( ( cos_real @ X3 )
% 0.26/0.65                = ( plus_plus_real
% 0.26/0.65                  @ ( groups6591440286371151544t_real
% 0.26/0.65                    @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 0.26/0.65                    @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.65                  @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Maclaurin_minus_cos_expansion
% 0.26/0.65  thf(fact_8646_Maclaurin__cos__expansion2,axiom,
% 0.26/0.65      ! [X3: real,N: nat] :
% 0.26/0.65        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65         => ? [T3: real] :
% 0.26/0.65              ( ( ord_less_real @ zero_zero_real @ T3 )
% 0.26/0.65              & ( ord_less_real @ T3 @ X3 )
% 0.26/0.65              & ( ( cos_real @ X3 )
% 0.26/0.65                = ( plus_plus_real
% 0.26/0.65                  @ ( groups6591440286371151544t_real
% 0.26/0.65                    @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 0.26/0.65                    @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.65                  @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Maclaurin_cos_expansion2
% 0.26/0.65  thf(fact_8647_Maclaurin__cos__expansion,axiom,
% 0.26/0.65      ! [X3: real,N: nat] :
% 0.26/0.65      ? [T3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 0.26/0.65        & ( ( cos_real @ X3 )
% 0.26/0.65          = ( plus_plus_real
% 0.26/0.65            @ ( groups6591440286371151544t_real
% 0.26/0.65              @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 0.26/0.65              @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.65            @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Maclaurin_cos_expansion
% 0.26/0.65  thf(fact_8648_infinite__int__iff__unbounded,axiom,
% 0.26/0.65      ! [S2: set_int] :
% 0.26/0.65        ( ( ~ ( finite_finite_int @ S2 ) )
% 0.26/0.65        = ( ! [M3: int] :
% 0.26/0.65            ? [N3: int] :
% 0.26/0.65              ( ( ord_less_int @ M3 @ ( abs_abs_int @ N3 ) )
% 0.26/0.65              & ( member_int @ N3 @ S2 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % infinite_int_iff_unbounded
% 0.26/0.65  thf(fact_8649_square__fact__le__2__fact,axiom,
% 0.26/0.65      ! [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 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % square_fact_le_2_fact
% 0.26/0.65  thf(fact_8650_infinite__nat__iff__unbounded,axiom,
% 0.26/0.65      ! [S2: set_nat] :
% 0.26/0.65        ( ( ~ ( finite_finite_nat @ S2 ) )
% 0.26/0.65        = ( ! [M3: nat] :
% 0.26/0.65            ? [N3: nat] :
% 0.26/0.65              ( ( ord_less_nat @ M3 @ N3 )
% 0.26/0.65              & ( member_nat @ N3 @ S2 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % infinite_nat_iff_unbounded
% 0.26/0.65  thf(fact_8651_unbounded__k__infinite,axiom,
% 0.26/0.65      ! [K: nat,S2: set_nat] :
% 0.26/0.65        ( ! [M4: nat] :
% 0.26/0.65            ( ( ord_less_nat @ K @ M4 )
% 0.26/0.65           => ? [N8: nat] :
% 0.26/0.65                ( ( ord_less_nat @ M4 @ N8 )
% 0.26/0.65                & ( member_nat @ N8 @ S2 ) ) )
% 0.26/0.65       => ~ ( finite_finite_nat @ S2 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % unbounded_k_infinite
% 0.26/0.65  thf(fact_8652_infinite__nat__iff__unbounded__le,axiom,
% 0.26/0.65      ! [S2: set_nat] :
% 0.26/0.65        ( ( ~ ( finite_finite_nat @ S2 ) )
% 0.26/0.65        = ( ! [M3: nat] :
% 0.26/0.65            ? [N3: nat] :
% 0.26/0.65              ( ( ord_less_eq_nat @ M3 @ N3 )
% 0.26/0.65              & ( member_nat @ N3 @ S2 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % infinite_nat_iff_unbounded_le
% 0.26/0.65  thf(fact_8653_Maclaurin__lemma,axiom,
% 0.26/0.65      ! [H2: real,F: real > real,J: nat > real,N: nat] :
% 0.26/0.65        ( ( ord_less_real @ zero_zero_real @ H2 )
% 0.26/0.65       => ? [B6: real] :
% 0.26/0.65            ( ( F @ H2 )
% 0.26/0.65            = ( plus_plus_real
% 0.26/0.65              @ ( groups6591440286371151544t_real
% 0.26/0.65                @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 0.26/0.65                @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.65              @ ( times_times_real @ B6 @ ( divide_divide_real @ ( power_power_real @ H2 @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Maclaurin_lemma
% 0.26/0.65  thf(fact_8654_cos__coeff__def,axiom,
% 0.26/0.65      ( cos_coeff
% 0.26/0.65      = ( ^ [N3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N3 ) ) @ zero_zero_real ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cos_coeff_def
% 0.26/0.65  thf(fact_8655_infinite__int__iff__unbounded__le,axiom,
% 0.26/0.65      ! [S2: set_int] :
% 0.26/0.65        ( ( ~ ( finite_finite_int @ S2 ) )
% 0.26/0.65        = ( ! [M3: int] :
% 0.26/0.65            ? [N3: int] :
% 0.26/0.65              ( ( ord_less_eq_int @ M3 @ ( abs_abs_int @ N3 ) )
% 0.26/0.65              & ( member_int @ N3 @ S2 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % infinite_int_iff_unbounded_le
% 0.26/0.65  thf(fact_8656_Maclaurin__sin__expansion3,axiom,
% 0.26/0.65      ! [N: nat,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.65         => ? [T3: real] :
% 0.26/0.65              ( ( ord_less_real @ zero_zero_real @ T3 )
% 0.26/0.65              & ( ord_less_real @ T3 @ X3 )
% 0.26/0.65              & ( ( sin_real @ X3 )
% 0.26/0.65                = ( plus_plus_real
% 0.26/0.65                  @ ( groups6591440286371151544t_real
% 0.26/0.65                    @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 0.26/0.65                    @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.65                  @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Maclaurin_sin_expansion3
% 0.26/0.65  thf(fact_8657_Maclaurin__sin__expansion4,axiom,
% 0.26/0.65      ! [X3: real,N: nat] :
% 0.26/0.65        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ? [T3: real] :
% 0.26/0.65            ( ( ord_less_real @ zero_zero_real @ T3 )
% 0.26/0.65            & ( ord_less_eq_real @ T3 @ X3 )
% 0.26/0.65            & ( ( sin_real @ X3 )
% 0.26/0.65              = ( plus_plus_real
% 0.26/0.65                @ ( groups6591440286371151544t_real
% 0.26/0.65                  @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 0.26/0.65                  @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.65                @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Maclaurin_sin_expansion4
% 0.26/0.65  thf(fact_8658_Maclaurin__sin__expansion2,axiom,
% 0.26/0.65      ! [X3: real,N: nat] :
% 0.26/0.65      ? [T3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 0.26/0.65        & ( ( sin_real @ X3 )
% 0.26/0.65          = ( plus_plus_real
% 0.26/0.65            @ ( groups6591440286371151544t_real
% 0.26/0.65              @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 0.26/0.65              @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.65            @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Maclaurin_sin_expansion2
% 0.26/0.65  thf(fact_8659_Maclaurin__sin__expansion,axiom,
% 0.26/0.65      ! [X3: real,N: nat] :
% 0.26/0.65      ? [T3: real] :
% 0.26/0.65        ( ( sin_real @ X3 )
% 0.26/0.65        = ( plus_plus_real
% 0.26/0.65          @ ( groups6591440286371151544t_real
% 0.26/0.65            @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 0.26/0.65            @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.65          @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Maclaurin_sin_expansion
% 0.26/0.65  thf(fact_8660_sin__coeff__0,axiom,
% 0.26/0.65      ( ( sin_coeff @ zero_zero_nat )
% 0.26/0.65      = zero_zero_real ) ).
% 0.26/0.65  
% 0.26/0.65  % sin_coeff_0
% 0.26/0.65  thf(fact_8661_fact__ge__self,axiom,
% 0.26/0.65      ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % fact_ge_self
% 0.26/0.65  thf(fact_8662_fact__mono__nat,axiom,
% 0.26/0.65      ! [M: nat,N: nat] :
% 0.26/0.65        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.65       => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % fact_mono_nat
% 0.26/0.65  thf(fact_8663_fact__less__mono__nat,axiom,
% 0.26/0.65      ! [M: nat,N: nat] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.65       => ( ( ord_less_nat @ M @ N )
% 0.26/0.65         => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % fact_less_mono_nat
% 0.26/0.65  thf(fact_8664_fact__ge__Suc__0__nat,axiom,
% 0.26/0.65      ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % fact_ge_Suc_0_nat
% 0.26/0.65  thf(fact_8665_dvd__fact,axiom,
% 0.26/0.65      ! [M: nat,N: nat] :
% 0.26/0.65        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 0.26/0.65       => ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.65         => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % dvd_fact
% 0.26/0.65  thf(fact_8666_fact__diff__Suc,axiom,
% 0.26/0.65      ! [N: nat,M: nat] :
% 0.26/0.65        ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.26/0.65       => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) )
% 0.26/0.65          = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % fact_diff_Suc
% 0.26/0.65  thf(fact_8667_fact__div__fact__le__pow,axiom,
% 0.26/0.65      ! [R2: nat,N: nat] :
% 0.26/0.65        ( ( ord_less_eq_nat @ R2 @ N )
% 0.26/0.65       => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R2 ) ) ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % fact_div_fact_le_pow
% 0.26/0.65  thf(fact_8668_binomial__fact__lemma,axiom,
% 0.26/0.65      ! [K: nat,N: nat] :
% 0.26/0.65        ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.65       => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 0.26/0.65          = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % binomial_fact_lemma
% 0.26/0.65  thf(fact_8669_fact__eq__fact__times,axiom,
% 0.26/0.65      ! [N: nat,M: nat] :
% 0.26/0.65        ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.65       => ( ( semiri1408675320244567234ct_nat @ M )
% 0.26/0.65          = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 0.26/0.65            @ ( groups708209901874060359at_nat
% 0.26/0.65              @ ^ [X: nat] : X
% 0.26/0.65              @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % fact_eq_fact_times
% 0.26/0.65  thf(fact_8670_binomial__altdef__nat,axiom,
% 0.26/0.65      ! [K: nat,N: nat] :
% 0.26/0.65        ( ( ord_less_eq_nat @ K @ N )
% 0.26/0.65       => ( ( binomial @ N @ K )
% 0.26/0.65          = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % binomial_altdef_nat
% 0.26/0.65  thf(fact_8671_fact__div__fact,axiom,
% 0.26/0.65      ! [N: nat,M: nat] :
% 0.26/0.65        ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.65       => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 0.26/0.65          = ( groups708209901874060359at_nat
% 0.26/0.65            @ ^ [X: nat] : X
% 0.26/0.65            @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % fact_div_fact
% 0.26/0.65  thf(fact_8672_sin__coeff__Suc,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( sin_coeff @ ( suc @ N ) )
% 0.26/0.65        = ( divide_divide_real @ ( cos_coeff @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sin_coeff_Suc
% 0.26/0.65  thf(fact_8673_cos__coeff__Suc,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( cos_coeff @ ( suc @ N ) )
% 0.26/0.65        = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cos_coeff_Suc
% 0.26/0.65  thf(fact_8674_binomial__code,axiom,
% 0.26/0.65      ( binomial
% 0.26/0.65      = ( ^ [N3: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N3 @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N3 @ ( minus_minus_nat @ N3 @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N3 @ K3 ) @ one_one_nat ) @ N3 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % binomial_code
% 0.26/0.65  thf(fact_8675_sin__coeff__def,axiom,
% 0.26/0.65      ( sin_coeff
% 0.26/0.65      = ( ^ [N3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N3 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N3 ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sin_coeff_def
% 0.26/0.65  thf(fact_8676_Maclaurin__exp__lt,axiom,
% 0.26/0.65      ! [X3: real,N: nat] :
% 0.26/0.65        ( ( X3 != zero_zero_real )
% 0.26/0.65       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65         => ? [T3: real] :
% 0.26/0.65              ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 0.26/0.65              & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 0.26/0.65              & ( ( exp_real @ X3 )
% 0.26/0.65                = ( plus_plus_real
% 0.26/0.65                  @ ( groups6591440286371151544t_real
% 0.26/0.65                    @ ^ [M3: nat] : ( divide_divide_real @ ( power_power_real @ X3 @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) )
% 0.26/0.65                    @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.65                  @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Maclaurin_exp_lt
% 0.26/0.65  thf(fact_8677_sin__paired,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( sums_real
% 0.26/0.65        @ ^ [N3: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 0.26/0.65        @ ( sin_real @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sin_paired
% 0.26/0.65  thf(fact_8678_VEBT__internal_Oheight_Osimps_I1_J,axiom,
% 0.26/0.65      ! [A: $o,B: $o] :
% 0.26/0.65        ( ( vEBT_VEBT_height @ ( vEBT_Leaf @ A @ B ) )
% 0.26/0.65        = zero_zero_nat ) ).
% 0.26/0.65  
% 0.26/0.65  % VEBT_internal.height.simps(1)
% 0.26/0.65  thf(fact_8679_exp__less__cancel__iff,axiom,
% 0.26/0.65      ! [X3: real,Y3: real] :
% 0.26/0.65        ( ( ord_less_real @ ( exp_real @ X3 ) @ ( exp_real @ Y3 ) )
% 0.26/0.65        = ( ord_less_real @ X3 @ Y3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_less_cancel_iff
% 0.26/0.65  thf(fact_8680_exp__less__mono,axiom,
% 0.26/0.65      ! [X3: real,Y3: real] :
% 0.26/0.65        ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.65       => ( ord_less_real @ ( exp_real @ X3 ) @ ( exp_real @ Y3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_less_mono
% 0.26/0.65  thf(fact_8681_exp__le__cancel__iff,axiom,
% 0.26/0.65      ! [X3: real,Y3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ ( exp_real @ X3 ) @ ( exp_real @ Y3 ) )
% 0.26/0.65        = ( ord_less_eq_real @ X3 @ Y3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_le_cancel_iff
% 0.26/0.65  thf(fact_8682_exp__eq__one__iff,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ( exp_real @ X3 )
% 0.26/0.65          = one_one_real )
% 0.26/0.65        = ( X3 = zero_zero_real ) ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_eq_one_iff
% 0.26/0.65  thf(fact_8683_exp__less__one__iff,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_real @ ( exp_real @ X3 ) @ one_one_real )
% 0.26/0.65        = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_less_one_iff
% 0.26/0.65  thf(fact_8684_one__less__exp__iff,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_real @ one_one_real @ ( exp_real @ X3 ) )
% 0.26/0.65        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % one_less_exp_iff
% 0.26/0.65  thf(fact_8685_exp__le__one__iff,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ ( exp_real @ X3 ) @ one_one_real )
% 0.26/0.65        = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_le_one_iff
% 0.26/0.65  thf(fact_8686_one__le__exp__iff,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X3 ) )
% 0.26/0.65        = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % one_le_exp_iff
% 0.26/0.65  thf(fact_8687_exp__ln,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ( exp_real @ ( ln_ln_real @ X3 ) )
% 0.26/0.65          = X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_ln
% 0.26/0.65  thf(fact_8688_exp__ln__iff,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ( exp_real @ ( ln_ln_real @ X3 ) )
% 0.26/0.65          = X3 )
% 0.26/0.65        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_ln_iff
% 0.26/0.65  thf(fact_8689_exp__less__cancel,axiom,
% 0.26/0.65      ! [X3: real,Y3: real] :
% 0.26/0.65        ( ( ord_less_real @ ( exp_real @ X3 ) @ ( exp_real @ Y3 ) )
% 0.26/0.65       => ( ord_less_real @ X3 @ Y3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_less_cancel
% 0.26/0.65  thf(fact_8690_not__exp__less__zero,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ~ ( ord_less_real @ ( exp_real @ X3 ) @ zero_zero_real ) ).
% 0.26/0.65  
% 0.26/0.65  % not_exp_less_zero
% 0.26/0.65  thf(fact_8691_exp__gt__zero,axiom,
% 0.26/0.65      ! [X3: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_gt_zero
% 0.26/0.65  thf(fact_8692_exp__total,axiom,
% 0.26/0.65      ! [Y3: real] :
% 0.26/0.65        ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.26/0.65       => ? [X4: real] :
% 0.26/0.65            ( ( exp_real @ X4 )
% 0.26/0.65            = Y3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_total
% 0.26/0.65  thf(fact_8693_not__exp__le__zero,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ~ ( ord_less_eq_real @ ( exp_real @ X3 ) @ zero_zero_real ) ).
% 0.26/0.65  
% 0.26/0.65  % not_exp_le_zero
% 0.26/0.65  thf(fact_8694_exp__ge__zero,axiom,
% 0.26/0.65      ! [X3: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_ge_zero
% 0.26/0.65  thf(fact_8695_exp__gt__one,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ord_less_real @ one_one_real @ ( exp_real @ X3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_gt_one
% 0.26/0.65  thf(fact_8696_exp__ge__add__one__self,axiom,
% 0.26/0.65      ! [X3: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X3 ) @ ( exp_real @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_ge_add_one_self
% 0.26/0.65  thf(fact_8697_exp__ge__add__one__self__aux,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X3 ) @ ( exp_real @ X3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_ge_add_one_self_aux
% 0.26/0.65  thf(fact_8698_lemma__exp__total,axiom,
% 0.26/0.65      ! [Y3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ one_one_real @ Y3 )
% 0.26/0.65       => ? [X4: real] :
% 0.26/0.65            ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.26/0.65            & ( ord_less_eq_real @ X4 @ ( minus_minus_real @ Y3 @ one_one_real ) )
% 0.26/0.65            & ( ( exp_real @ X4 )
% 0.26/0.65              = Y3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % lemma_exp_total
% 0.26/0.65  thf(fact_8699_ln__ge__iff,axiom,
% 0.26/0.65      ! [X3: real,Y3: real] :
% 0.26/0.65        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ( ord_less_eq_real @ Y3 @ ( ln_ln_real @ X3 ) )
% 0.26/0.65          = ( ord_less_eq_real @ ( exp_real @ Y3 ) @ X3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % ln_ge_iff
% 0.26/0.65  thf(fact_8700_ln__x__over__x__mono,axiom,
% 0.26/0.65      ! [X3: real,Y3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X3 )
% 0.26/0.65       => ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.26/0.65         => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y3 ) @ Y3 ) @ ( divide_divide_real @ ( ln_ln_real @ X3 ) @ X3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % ln_x_over_x_mono
% 0.26/0.65  thf(fact_8701_exp__le,axiom,
% 0.26/0.65      ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_le
% 0.26/0.65  thf(fact_8702_exp__half__le2,axiom,
% 0.26/0.65      ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_half_le2
% 0.26/0.65  thf(fact_8703_power__half__series,axiom,
% 0.26/0.65      ( sums_real
% 0.26/0.65      @ ^ [N3: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N3 ) )
% 0.26/0.65      @ one_one_real ) ).
% 0.26/0.65  
% 0.26/0.65  % power_half_series
% 0.26/0.65  thf(fact_8704_sums__if_H,axiom,
% 0.26/0.65      ! [G: nat > real,X3: real] :
% 0.26/0.65        ( ( sums_real @ G @ X3 )
% 0.26/0.65       => ( sums_real
% 0.26/0.65          @ ^ [N3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ zero_zero_real @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.65          @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sums_if'
% 0.26/0.65  thf(fact_8705_sums__if,axiom,
% 0.26/0.65      ! [G: nat > real,X3: real,F: nat > real,Y3: real] :
% 0.26/0.65        ( ( sums_real @ G @ X3 )
% 0.26/0.65       => ( ( sums_real @ F @ Y3 )
% 0.26/0.65         => ( sums_real
% 0.26/0.65            @ ^ [N3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ ( F @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.65            @ ( plus_plus_real @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sums_if
% 0.26/0.65  thf(fact_8706_exp__bound,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 0.26/0.65         => ( ord_less_eq_real @ ( exp_real @ X3 ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X3 ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_bound
% 0.26/0.65  thf(fact_8707_real__exp__bound__lemma,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.65         => ( ord_less_eq_real @ ( exp_real @ X3 ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_exp_bound_lemma
% 0.26/0.65  thf(fact_8708_exp__ge__one__plus__x__over__n__power__n,axiom,
% 0.26/0.65      ! [N: nat,X3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X3 )
% 0.26/0.65       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65         => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X3 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_ge_one_plus_x_over_n_power_n
% 0.26/0.65  thf(fact_8709_exp__ge__one__minus__x__over__n__power__n,axiom,
% 0.26/0.65      ! [X3: real,N: nat] :
% 0.26/0.65        ( ( ord_less_eq_real @ X3 @ ( semiri5074537144036343181t_real @ N ) )
% 0.26/0.65       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65         => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X3 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ ( uminus_uminus_real @ X3 ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_ge_one_minus_x_over_n_power_n
% 0.26/0.65  thf(fact_8710_Maclaurin__exp__le,axiom,
% 0.26/0.65      ! [X3: real,N: nat] :
% 0.26/0.65      ? [T3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 0.26/0.65        & ( ( exp_real @ X3 )
% 0.26/0.65          = ( plus_plus_real
% 0.26/0.65            @ ( groups6591440286371151544t_real
% 0.26/0.65              @ ^ [M3: nat] : ( divide_divide_real @ ( power_power_real @ X3 @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) )
% 0.26/0.65              @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.65            @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Maclaurin_exp_le
% 0.26/0.65  thf(fact_8711_exp__lower__Taylor__quadratic,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X3 ) @ ( divide_divide_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_lower_Taylor_quadratic
% 0.26/0.65  thf(fact_8712_log__base__10__eq2,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.26/0.65          = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % log_base_10_eq2
% 0.26/0.65  thf(fact_8713_tanh__real__altdef,axiom,
% 0.26/0.65      ( tanh_real
% 0.26/0.65      = ( ^ [X: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % tanh_real_altdef
% 0.26/0.65  thf(fact_8714_cos__paired,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( sums_real
% 0.26/0.65        @ ^ [N3: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) @ ( power_power_real @ X3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 0.26/0.65        @ ( cos_real @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cos_paired
% 0.26/0.65  thf(fact_8715_log__base__10__eq1,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.26/0.65          = ( 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 @ X3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % log_base_10_eq1
% 0.26/0.65  thf(fact_8716_Maclaurin__sin__bound,axiom,
% 0.26/0.65      ! [X3: real,N: nat] :
% 0.26/0.65        ( ord_less_eq_real
% 0.26/0.65        @ ( abs_abs_real
% 0.26/0.65          @ ( minus_minus_real @ ( sin_real @ X3 )
% 0.26/0.65            @ ( groups6591440286371151544t_real
% 0.26/0.65              @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 0.26/0.65              @ ( set_ord_lessThan_nat @ N ) ) ) )
% 0.26/0.65        @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X3 ) @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Maclaurin_sin_bound
% 0.26/0.65  thf(fact_8717_divmod__BitM__2__eq,axiom,
% 0.26/0.65      ! [M: num] :
% 0.26/0.65        ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 0.26/0.65        = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 0.26/0.65  
% 0.26/0.65  % divmod_BitM_2_eq
% 0.26/0.65  thf(fact_8718_pred__numeral__simps_I2_J,axiom,
% 0.26/0.65      ! [K: num] :
% 0.26/0.65        ( ( pred_numeral @ ( bit0 @ K ) )
% 0.26/0.65        = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % pred_numeral_simps(2)
% 0.26/0.65  thf(fact_8719_real__sqrt__inverse,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( sqrt @ ( inverse_inverse_real @ X3 ) )
% 0.26/0.65        = ( inverse_inverse_real @ ( sqrt @ X3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_sqrt_inverse
% 0.26/0.65  thf(fact_8720_semiring__norm_I26_J,axiom,
% 0.26/0.65      ( ( bitM @ one )
% 0.26/0.65      = one ) ).
% 0.26/0.65  
% 0.26/0.65  % semiring_norm(26)
% 0.26/0.65  thf(fact_8721_divide__real__def,axiom,
% 0.26/0.65      ( divide_divide_real
% 0.26/0.65      = ( ^ [X: real,Y: real] : ( times_times_real @ X @ ( inverse_inverse_real @ Y ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % divide_real_def
% 0.26/0.65  thf(fact_8722_semiring__norm_I28_J,axiom,
% 0.26/0.65      ! [N: num] :
% 0.26/0.65        ( ( bitM @ ( bit1 @ N ) )
% 0.26/0.65        = ( bit1 @ ( bit0 @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % semiring_norm(28)
% 0.26/0.65  thf(fact_8723_semiring__norm_I27_J,axiom,
% 0.26/0.65      ! [N: num] :
% 0.26/0.65        ( ( bitM @ ( bit0 @ N ) )
% 0.26/0.65        = ( bit1 @ ( bitM @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % semiring_norm(27)
% 0.26/0.65  thf(fact_8724_inc__BitM__eq,axiom,
% 0.26/0.65      ! [N: num] :
% 0.26/0.65        ( ( inc @ ( bitM @ N ) )
% 0.26/0.65        = ( bit0 @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % inc_BitM_eq
% 0.26/0.65  thf(fact_8725_BitM__inc__eq,axiom,
% 0.26/0.65      ! [N: num] :
% 0.26/0.65        ( ( bitM @ ( inc @ N ) )
% 0.26/0.65        = ( bit1 @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % BitM_inc_eq
% 0.26/0.65  thf(fact_8726_inverse__powr,axiom,
% 0.26/0.65      ! [Y3: real,A: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.65       => ( ( powr_real @ ( inverse_inverse_real @ Y3 ) @ A )
% 0.26/0.65          = ( inverse_inverse_real @ ( powr_real @ Y3 @ A ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % inverse_powr
% 0.26/0.65  thf(fact_8727_eval__nat__numeral_I2_J,axiom,
% 0.26/0.65      ! [N: num] :
% 0.26/0.65        ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 0.26/0.65        = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % eval_nat_numeral(2)
% 0.26/0.65  thf(fact_8728_BitM__plus__one,axiom,
% 0.26/0.65      ! [N: num] :
% 0.26/0.65        ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 0.26/0.65        = ( bit0 @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % BitM_plus_one
% 0.26/0.65  thf(fact_8729_one__plus__BitM,axiom,
% 0.26/0.65      ! [N: num] :
% 0.26/0.65        ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 0.26/0.65        = ( bit0 @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % one_plus_BitM
% 0.26/0.65  thf(fact_8730_forall__pos__mono__1,axiom,
% 0.26/0.65      ! [P: real > $o,E2: real] :
% 0.26/0.65        ( ! [D6: real,E: real] :
% 0.26/0.65            ( ( ord_less_real @ D6 @ E )
% 0.26/0.65           => ( ( P @ D6 )
% 0.26/0.65             => ( P @ E ) ) )
% 0.26/0.65       => ( ! [N2: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) )
% 0.26/0.65         => ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.26/0.65           => ( P @ E2 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % forall_pos_mono_1
% 0.26/0.65  thf(fact_8731_forall__pos__mono,axiom,
% 0.26/0.65      ! [P: real > $o,E2: real] :
% 0.26/0.65        ( ! [D6: real,E: real] :
% 0.26/0.65            ( ( ord_less_real @ D6 @ E )
% 0.26/0.65           => ( ( P @ D6 )
% 0.26/0.65             => ( P @ E ) ) )
% 0.26/0.65       => ( ! [N2: nat] :
% 0.26/0.65              ( ( N2 != zero_zero_nat )
% 0.26/0.65             => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) )
% 0.26/0.65         => ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.26/0.65           => ( P @ E2 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % forall_pos_mono
% 0.26/0.65  thf(fact_8732_real__arch__inverse,axiom,
% 0.26/0.65      ! [E2: real] :
% 0.26/0.65        ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.26/0.65        = ( ? [N3: nat] :
% 0.26/0.65              ( ( N3 != zero_zero_nat )
% 0.26/0.65              & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) )
% 0.26/0.65              & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) @ E2 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_arch_inverse
% 0.26/0.65  thf(fact_8733_sqrt__divide__self__eq,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ( divide_divide_real @ ( sqrt @ X3 ) @ X3 )
% 0.26/0.65          = ( inverse_inverse_real @ ( sqrt @ X3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sqrt_divide_self_eq
% 0.26/0.65  thf(fact_8734_ln__inverse,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ( ln_ln_real @ ( inverse_inverse_real @ X3 ) )
% 0.26/0.65          = ( uminus_uminus_real @ ( ln_ln_real @ X3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % ln_inverse
% 0.26/0.65  thf(fact_8735_log__inverse,axiom,
% 0.26/0.65      ! [A: real,X3: real] :
% 0.26/0.65        ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.65       => ( ( A != one_one_real )
% 0.26/0.65         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.65           => ( ( log @ A @ ( inverse_inverse_real @ X3 ) )
% 0.26/0.65              = ( uminus_uminus_real @ ( log @ A @ X3 ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % log_inverse
% 0.26/0.65  thf(fact_8736_exp__plus__inverse__exp,axiom,
% 0.26/0.65      ! [X3: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X3 ) @ ( inverse_inverse_real @ ( exp_real @ X3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_plus_inverse_exp
% 0.26/0.65  thf(fact_8737_plus__inverse__ge__2,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X3 @ ( inverse_inverse_real @ X3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % plus_inverse_ge_2
% 0.26/0.65  thf(fact_8738_real__inv__sqrt__pow2,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.65          = ( inverse_inverse_real @ X3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_inv_sqrt_pow2
% 0.26/0.65  thf(fact_8739_tan__cot,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 ) )
% 0.26/0.65        = ( inverse_inverse_real @ ( tan_real @ X3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % tan_cot
% 0.26/0.65  thf(fact_8740_real__le__x__sinh,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ord_less_eq_real @ X3 @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X3 ) @ ( inverse_inverse_real @ ( exp_real @ X3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_le_x_sinh
% 0.26/0.65  thf(fact_8741_real__le__abs__sinh,axiom,
% 0.26/0.65      ! [X3: real] : ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X3 ) @ ( inverse_inverse_real @ ( exp_real @ X3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_le_abs_sinh
% 0.26/0.65  thf(fact_8742_powr__real__of__int,axiom,
% 0.26/0.65      ! [X3: real,N: int] :
% 0.26/0.65        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 0.26/0.65           => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ N ) )
% 0.26/0.65              = ( power_power_real @ X3 @ ( nat2 @ N ) ) ) )
% 0.26/0.65          & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 0.26/0.65           => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ N ) )
% 0.26/0.65              = ( inverse_inverse_real @ ( power_power_real @ X3 @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % powr_real_of_int
% 0.26/0.65  thf(fact_8743_or__minus__numerals_I5_J,axiom,
% 0.26/0.65      ! [N: num] :
% 0.26/0.65        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 0.26/0.65        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % or_minus_numerals(5)
% 0.26/0.65  thf(fact_8744_or__minus__numerals_I1_J,axiom,
% 0.26/0.65      ! [N: num] :
% 0.26/0.65        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.26/0.65        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % or_minus_numerals(1)
% 0.26/0.65  thf(fact_8745_sinh__real__zero__iff,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ( sinh_real @ X3 )
% 0.26/0.65          = zero_zero_real )
% 0.26/0.65        = ( X3 = zero_zero_real ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sinh_real_zero_iff
% 0.26/0.65  thf(fact_8746_sinh__real__less__iff,axiom,
% 0.26/0.65      ! [X3: real,Y3: real] :
% 0.26/0.65        ( ( ord_less_real @ ( sinh_real @ X3 ) @ ( sinh_real @ Y3 ) )
% 0.26/0.65        = ( ord_less_real @ X3 @ Y3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sinh_real_less_iff
% 0.26/0.65  thf(fact_8747_sinh__real__le__iff,axiom,
% 0.26/0.65      ! [X3: real,Y3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ ( sinh_real @ X3 ) @ ( sinh_real @ Y3 ) )
% 0.26/0.65        = ( ord_less_eq_real @ X3 @ Y3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sinh_real_le_iff
% 0.26/0.65  thf(fact_8748_sinh__real__pos__iff,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X3 ) )
% 0.26/0.65        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sinh_real_pos_iff
% 0.26/0.65  thf(fact_8749_sinh__real__neg__iff,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_real @ ( sinh_real @ X3 ) @ zero_zero_real )
% 0.26/0.65        = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sinh_real_neg_iff
% 0.26/0.65  thf(fact_8750_sinh__real__nonpos__iff,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ ( sinh_real @ X3 ) @ zero_zero_real )
% 0.26/0.65        = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sinh_real_nonpos_iff
% 0.26/0.65  thf(fact_8751_sinh__real__nonneg__iff,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X3 ) )
% 0.26/0.65        = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sinh_real_nonneg_iff
% 0.26/0.65  thf(fact_8752_or__minus__numerals_I8_J,axiom,
% 0.26/0.65      ! [N: num,M: num] :
% 0.26/0.65        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 0.26/0.65        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % or_minus_numerals(8)
% 0.26/0.65  thf(fact_8753_or__minus__numerals_I4_J,axiom,
% 0.26/0.65      ! [M: num,N: num] :
% 0.26/0.65        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.26/0.65        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % or_minus_numerals(4)
% 0.26/0.65  thf(fact_8754_or__minus__numerals_I3_J,axiom,
% 0.26/0.65      ! [M: num,N: num] :
% 0.26/0.65        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.26/0.65        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % or_minus_numerals(3)
% 0.26/0.65  thf(fact_8755_or__minus__numerals_I7_J,axiom,
% 0.26/0.65      ! [N: num,M: num] :
% 0.26/0.65        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 0.26/0.65        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % or_minus_numerals(7)
% 0.26/0.65  thf(fact_8756_or__not__num__neg_Osimps_I1_J,axiom,
% 0.26/0.65      ( ( bit_or_not_num_neg @ one @ one )
% 0.26/0.65      = one ) ).
% 0.26/0.65  
% 0.26/0.65  % or_not_num_neg.simps(1)
% 0.26/0.65  thf(fact_8757_sinh__le__cosh__real,axiom,
% 0.26/0.65      ! [X3: real] : ( ord_less_eq_real @ ( sinh_real @ X3 ) @ ( cosh_real @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sinh_le_cosh_real
% 0.26/0.65  thf(fact_8758_sinh__less__cosh__real,axiom,
% 0.26/0.65      ! [X3: real] : ( ord_less_real @ ( sinh_real @ X3 ) @ ( cosh_real @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sinh_less_cosh_real
% 0.26/0.65  thf(fact_8759_cosh__real__nonzero,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( cosh_real @ X3 )
% 0.26/0.65       != zero_zero_real ) ).
% 0.26/0.65  
% 0.26/0.65  % cosh_real_nonzero
% 0.26/0.65  thf(fact_8760_cosh__real__pos,axiom,
% 0.26/0.65      ! [X3: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cosh_real_pos
% 0.26/0.65  thf(fact_8761_cosh__real__nonpos__le__iff,axiom,
% 0.26/0.65      ! [X3: real,Y3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 0.26/0.65       => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 0.26/0.65         => ( ( ord_less_eq_real @ ( cosh_real @ X3 ) @ ( cosh_real @ Y3 ) )
% 0.26/0.65            = ( ord_less_eq_real @ Y3 @ X3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cosh_real_nonpos_le_iff
% 0.26/0.65  thf(fact_8762_cosh__real__nonneg__le__iff,axiom,
% 0.26/0.65      ! [X3: real,Y3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.65         => ( ( ord_less_eq_real @ ( cosh_real @ X3 ) @ ( cosh_real @ Y3 ) )
% 0.26/0.65            = ( ord_less_eq_real @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cosh_real_nonneg_le_iff
% 0.26/0.65  thf(fact_8763_cosh__real__nonneg,axiom,
% 0.26/0.65      ! [X3: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cosh_real_nonneg
% 0.26/0.65  thf(fact_8764_cosh__real__ge__1,axiom,
% 0.26/0.65      ! [X3: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cosh_real_ge_1
% 0.26/0.65  thf(fact_8765_or__not__num__neg_Osimps_I4_J,axiom,
% 0.26/0.65      ! [N: num] :
% 0.26/0.65        ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ one )
% 0.26/0.65        = ( bit0 @ one ) ) ).
% 0.26/0.65  
% 0.26/0.65  % or_not_num_neg.simps(4)
% 0.26/0.65  thf(fact_8766_or__not__num__neg_Osimps_I6_J,axiom,
% 0.26/0.65      ! [N: num,M: num] :
% 0.26/0.65        ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit1 @ M ) )
% 0.26/0.65        = ( bit0 @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % or_not_num_neg.simps(6)
% 0.26/0.65  thf(fact_8767_or__not__num__neg_Osimps_I3_J,axiom,
% 0.26/0.65      ! [M: num] :
% 0.26/0.65        ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 0.26/0.65        = ( bit1 @ M ) ) ).
% 0.26/0.65  
% 0.26/0.65  % or_not_num_neg.simps(3)
% 0.26/0.65  thf(fact_8768_or__not__num__neg_Osimps_I7_J,axiom,
% 0.26/0.65      ! [N: num] :
% 0.26/0.65        ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ one )
% 0.26/0.65        = one ) ).
% 0.26/0.65  
% 0.26/0.65  % or_not_num_neg.simps(7)
% 0.26/0.65  thf(fact_8769_or__not__num__neg_Osimps_I5_J,axiom,
% 0.26/0.65      ! [N: num,M: num] :
% 0.26/0.65        ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit0 @ M ) )
% 0.26/0.65        = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % or_not_num_neg.simps(5)
% 0.26/0.65  thf(fact_8770_or__not__num__neg_Osimps_I9_J,axiom,
% 0.26/0.65      ! [N: num,M: num] :
% 0.26/0.65        ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit1 @ M ) )
% 0.26/0.65        = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % or_not_num_neg.simps(9)
% 0.26/0.65  thf(fact_8771_cosh__real__strict__mono,axiom,
% 0.26/0.65      ! [X3: real,Y3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.65         => ( ord_less_real @ ( cosh_real @ X3 ) @ ( cosh_real @ Y3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cosh_real_strict_mono
% 0.26/0.65  thf(fact_8772_cosh__real__nonneg__less__iff,axiom,
% 0.26/0.65      ! [X3: real,Y3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.65         => ( ( ord_less_real @ ( cosh_real @ X3 ) @ ( cosh_real @ Y3 ) )
% 0.26/0.65            = ( ord_less_real @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cosh_real_nonneg_less_iff
% 0.26/0.65  thf(fact_8773_cosh__real__nonpos__less__iff,axiom,
% 0.26/0.65      ! [X3: real,Y3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 0.26/0.65       => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 0.26/0.65         => ( ( ord_less_real @ ( cosh_real @ X3 ) @ ( cosh_real @ Y3 ) )
% 0.26/0.65            = ( ord_less_real @ Y3 @ X3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cosh_real_nonpos_less_iff
% 0.26/0.65  thf(fact_8774_arcosh__cosh__real,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ( arcosh_real @ ( cosh_real @ X3 ) )
% 0.26/0.65          = X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % arcosh_cosh_real
% 0.26/0.65  thf(fact_8775_or__not__num__neg_Osimps_I2_J,axiom,
% 0.26/0.65      ! [M: num] :
% 0.26/0.65        ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 0.26/0.65        = ( bit1 @ M ) ) ).
% 0.26/0.65  
% 0.26/0.65  % or_not_num_neg.simps(2)
% 0.26/0.65  thf(fact_8776_or__not__num__neg_Osimps_I8_J,axiom,
% 0.26/0.65      ! [N: num,M: num] :
% 0.26/0.65        ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit0 @ M ) )
% 0.26/0.65        = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % or_not_num_neg.simps(8)
% 0.26/0.65  thf(fact_8777_or__not__num__neg_Oelims,axiom,
% 0.26/0.65      ! [X3: num,Xa: num,Y3: num] :
% 0.26/0.65        ( ( ( bit_or_not_num_neg @ X3 @ Xa )
% 0.26/0.65          = Y3 )
% 0.26/0.65       => ( ( ( X3 = one )
% 0.26/0.65           => ( ( Xa = one )
% 0.26/0.65             => ( Y3 != one ) ) )
% 0.26/0.65         => ( ( ( X3 = one )
% 0.26/0.65             => ! [M4: num] :
% 0.26/0.65                  ( ( Xa
% 0.26/0.65                    = ( bit0 @ M4 ) )
% 0.26/0.65                 => ( Y3
% 0.26/0.65                   != ( bit1 @ M4 ) ) ) )
% 0.26/0.65           => ( ( ( X3 = one )
% 0.26/0.65               => ! [M4: num] :
% 0.26/0.65                    ( ( Xa
% 0.26/0.65                      = ( bit1 @ M4 ) )
% 0.26/0.65                   => ( Y3
% 0.26/0.65                     != ( bit1 @ M4 ) ) ) )
% 0.26/0.65             => ( ( ? [N2: num] :
% 0.26/0.65                      ( X3
% 0.26/0.65                      = ( bit0 @ N2 ) )
% 0.26/0.65                 => ( ( Xa = one )
% 0.26/0.65                   => ( Y3
% 0.26/0.65                     != ( bit0 @ one ) ) ) )
% 0.26/0.65               => ( ! [N2: num] :
% 0.26/0.65                      ( ( X3
% 0.26/0.65                        = ( bit0 @ N2 ) )
% 0.26/0.65                     => ! [M4: num] :
% 0.26/0.65                          ( ( Xa
% 0.26/0.65                            = ( bit0 @ M4 ) )
% 0.26/0.65                         => ( Y3
% 0.26/0.65                           != ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) ) ) )
% 0.26/0.65                 => ( ! [N2: num] :
% 0.26/0.65                        ( ( X3
% 0.26/0.65                          = ( bit0 @ N2 ) )
% 0.26/0.65                       => ! [M4: num] :
% 0.26/0.65                            ( ( Xa
% 0.26/0.65                              = ( bit1 @ M4 ) )
% 0.26/0.65                           => ( Y3
% 0.26/0.65                             != ( bit0 @ ( bit_or_not_num_neg @ N2 @ M4 ) ) ) ) )
% 0.26/0.65                   => ( ( ? [N2: num] :
% 0.26/0.65                            ( X3
% 0.26/0.65                            = ( bit1 @ N2 ) )
% 0.26/0.65                       => ( ( Xa = one )
% 0.26/0.65                         => ( Y3 != one ) ) )
% 0.26/0.65                     => ( ! [N2: num] :
% 0.26/0.65                            ( ( X3
% 0.26/0.65                              = ( bit1 @ N2 ) )
% 0.26/0.65                           => ! [M4: num] :
% 0.26/0.65                                ( ( Xa
% 0.26/0.65                                  = ( bit0 @ M4 ) )
% 0.26/0.65                               => ( Y3
% 0.26/0.65                                 != ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) ) ) )
% 0.26/0.65                       => ~ ! [N2: num] :
% 0.26/0.65                              ( ( X3
% 0.26/0.65                                = ( bit1 @ N2 ) )
% 0.26/0.65                             => ! [M4: num] :
% 0.26/0.65                                  ( ( Xa
% 0.26/0.65                                    = ( bit1 @ M4 ) )
% 0.26/0.65                                 => ( Y3
% 0.26/0.65                                   != ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % or_not_num_neg.elims
% 0.26/0.65  thf(fact_8778_numeral__or__not__num__eq,axiom,
% 0.26/0.65      ! [M: num,N: num] :
% 0.26/0.65        ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) )
% 0.26/0.65        = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % numeral_or_not_num_eq
% 0.26/0.65  thf(fact_8779_int__numeral__not__or__num__neg,axiom,
% 0.26/0.65      ! [M: num,N: num] :
% 0.26/0.65        ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.65        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N @ M ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % int_numeral_not_or_num_neg
% 0.26/0.65  thf(fact_8780_int__numeral__or__not__num__neg,axiom,
% 0.26/0.65      ! [M: num,N: num] :
% 0.26/0.65        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.65        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % int_numeral_or_not_num_neg
% 0.26/0.65  thf(fact_8781_complex__inverse,axiom,
% 0.26/0.65      ! [A: real,B: real] :
% 0.26/0.65        ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 0.26/0.65        = ( 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 ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % complex_inverse
% 0.26/0.65  thf(fact_8782_cosh__ln__real,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ( cosh_real @ ( ln_ln_real @ X3 ) )
% 0.26/0.65          = ( divide_divide_real @ ( plus_plus_real @ X3 @ ( inverse_inverse_real @ X3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cosh_ln_real
% 0.26/0.65  thf(fact_8783_sinh__ln__real,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ( sinh_real @ ( ln_ln_real @ X3 ) )
% 0.26/0.65          = ( divide_divide_real @ ( minus_minus_real @ X3 @ ( inverse_inverse_real @ X3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sinh_ln_real
% 0.26/0.65  thf(fact_8784_concat__bit__Suc,axiom,
% 0.26/0.65      ! [N: nat,K: int,L: int] :
% 0.26/0.65        ( ( bit_concat_bit @ ( suc @ N ) @ K @ L )
% 0.26/0.65        = ( 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 ) ) ) @ L ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % concat_bit_Suc
% 0.26/0.65  thf(fact_8785_cot__less__zero,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 )
% 0.26/0.65       => ( ( ord_less_real @ X3 @ zero_zero_real )
% 0.26/0.65         => ( ord_less_real @ ( cot_real @ X3 ) @ zero_zero_real ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cot_less_zero
% 0.26/0.65  thf(fact_8786_i__even__power,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.65        = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % i_even_power
% 0.26/0.65  thf(fact_8787_concat__bit__0,axiom,
% 0.26/0.65      ! [K: int,L: int] :
% 0.26/0.65        ( ( bit_concat_bit @ zero_zero_nat @ K @ L )
% 0.26/0.65        = L ) ).
% 0.26/0.65  
% 0.26/0.65  % concat_bit_0
% 0.26/0.65  thf(fact_8788_concat__bit__nonnegative__iff,axiom,
% 0.26/0.65      ! [N: nat,K: int,L: int] :
% 0.26/0.65        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L ) )
% 0.26/0.65        = ( ord_less_eq_int @ zero_zero_int @ L ) ) ).
% 0.26/0.65  
% 0.26/0.65  % concat_bit_nonnegative_iff
% 0.26/0.65  thf(fact_8789_concat__bit__negative__iff,axiom,
% 0.26/0.65      ! [N: nat,K: int,L: int] :
% 0.26/0.65        ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L ) @ zero_zero_int )
% 0.26/0.65        = ( ord_less_int @ L @ zero_zero_int ) ) ).
% 0.26/0.65  
% 0.26/0.65  % concat_bit_negative_iff
% 0.26/0.65  thf(fact_8790_concat__bit__of__zero__2,axiom,
% 0.26/0.65      ! [N: nat,K: int] :
% 0.26/0.65        ( ( bit_concat_bit @ N @ K @ zero_zero_int )
% 0.26/0.65        = ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 0.26/0.65  
% 0.26/0.65  % concat_bit_of_zero_2
% 0.26/0.65  thf(fact_8791_cot__pi,axiom,
% 0.26/0.65      ( ( cot_real @ pi )
% 0.26/0.65      = zero_zero_real ) ).
% 0.26/0.65  
% 0.26/0.65  % cot_pi
% 0.26/0.65  thf(fact_8792_cot__npi,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 0.26/0.65        = zero_zero_real ) ).
% 0.26/0.65  
% 0.26/0.65  % cot_npi
% 0.26/0.65  thf(fact_8793_cot__periodic,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( cot_real @ ( plus_plus_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.26/0.65        = ( cot_real @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cot_periodic
% 0.26/0.65  thf(fact_8794_power2__i,axiom,
% 0.26/0.65      ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.65      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.26/0.65  
% 0.26/0.65  % power2_i
% 0.26/0.65  thf(fact_8795_exp__two__pi__i,axiom,
% 0.26/0.65      ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 0.26/0.65      = one_one_complex ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_two_pi_i
% 0.26/0.65  thf(fact_8796_exp__two__pi__i_H,axiom,
% 0.26/0.65      ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 0.26/0.65      = one_one_complex ) ).
% 0.26/0.65  
% 0.26/0.65  % exp_two_pi_i'
% 0.26/0.65  thf(fact_8797_complex__i__not__zero,axiom,
% 0.26/0.65      imaginary_unit != zero_zero_complex ).
% 0.26/0.65  
% 0.26/0.65  % complex_i_not_zero
% 0.26/0.65  thf(fact_8798_concat__bit__assoc,axiom,
% 0.26/0.65      ! [N: nat,K: int,M: nat,L: int,R2: int] :
% 0.26/0.65        ( ( bit_concat_bit @ N @ K @ ( bit_concat_bit @ M @ L @ R2 ) )
% 0.26/0.65        = ( bit_concat_bit @ ( plus_plus_nat @ M @ N ) @ ( bit_concat_bit @ N @ K @ L ) @ R2 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % concat_bit_assoc
% 0.26/0.65  thf(fact_8799_concat__bit__eq__iff,axiom,
% 0.26/0.65      ! [N: nat,K: int,L: int,R2: int,S: int] :
% 0.26/0.65        ( ( ( bit_concat_bit @ N @ K @ L )
% 0.26/0.65          = ( bit_concat_bit @ N @ R2 @ S ) )
% 0.26/0.65        = ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.26/0.65            = ( bit_se2923211474154528505it_int @ N @ R2 ) )
% 0.26/0.65          & ( L = S ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % concat_bit_eq_iff
% 0.26/0.65  thf(fact_8800_concat__bit__take__bit__eq,axiom,
% 0.26/0.65      ! [N: nat,B: int] :
% 0.26/0.65        ( ( bit_concat_bit @ N @ ( bit_se2923211474154528505it_int @ N @ B ) )
% 0.26/0.65        = ( bit_concat_bit @ N @ B ) ) ).
% 0.26/0.65  
% 0.26/0.65  % concat_bit_take_bit_eq
% 0.26/0.65  thf(fact_8801_imaginary__unit_Ocode,axiom,
% 0.26/0.65      ( imaginary_unit
% 0.26/0.65      = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 0.26/0.65  
% 0.26/0.65  % imaginary_unit.code
% 0.26/0.65  thf(fact_8802_Complex__eq__i,axiom,
% 0.26/0.65      ! [X3: real,Y3: real] :
% 0.26/0.65        ( ( ( complex2 @ X3 @ Y3 )
% 0.26/0.65          = imaginary_unit )
% 0.26/0.65        = ( ( X3 = zero_zero_real )
% 0.26/0.65          & ( Y3 = one_one_real ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Complex_eq_i
% 0.26/0.65  thf(fact_8803_i__complex__of__real,axiom,
% 0.26/0.65      ! [R2: real] :
% 0.26/0.65        ( ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ R2 ) )
% 0.26/0.65        = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % i_complex_of_real
% 0.26/0.65  thf(fact_8804_complex__of__real__i,axiom,
% 0.26/0.65      ! [R2: real] :
% 0.26/0.65        ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ imaginary_unit )
% 0.26/0.65        = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % complex_of_real_i
% 0.26/0.65  thf(fact_8805_divmod__step__nat__def,axiom,
% 0.26/0.65      ( unique5026877609467782581ep_nat
% 0.26/0.65      = ( ^ [L2: num] :
% 0.26/0.65            ( produc2626176000494625587at_nat
% 0.26/0.65            @ ^ [Q5: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % divmod_step_nat_def
% 0.26/0.65  thf(fact_8806_divmod__step__int__def,axiom,
% 0.26/0.65      ( unique5024387138958732305ep_int
% 0.26/0.65      = ( ^ [L2: num] :
% 0.26/0.65            ( produc4245557441103728435nt_int
% 0.26/0.65            @ ^ [Q5: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % divmod_step_int_def
% 0.26/0.65  thf(fact_8807_cot__gt__zero,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.65         => ( ord_less_real @ zero_zero_real @ ( cot_real @ X3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cot_gt_zero
% 0.26/0.65  thf(fact_8808_tan__cot_H,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 ) )
% 0.26/0.65        = ( cot_real @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % tan_cot'
% 0.26/0.65  thf(fact_8809_Arg__minus__ii,axiom,
% 0.26/0.65      ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 0.26/0.65      = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Arg_minus_ii
% 0.26/0.65  thf(fact_8810_csqrt__ii,axiom,
% 0.26/0.65      ( ( csqrt @ imaginary_unit )
% 0.26/0.65      = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % csqrt_ii
% 0.26/0.65  thf(fact_8811_Arg__ii,axiom,
% 0.26/0.65      ( ( arg @ imaginary_unit )
% 0.26/0.65      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Arg_ii
% 0.26/0.65  thf(fact_8812_cis__minus__pi__half,axiom,
% 0.26/0.65      ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.26/0.65      = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cis_minus_pi_half
% 0.26/0.65  thf(fact_8813_csqrt__eq__0,axiom,
% 0.26/0.65      ! [Z: complex] :
% 0.26/0.65        ( ( ( csqrt @ Z )
% 0.26/0.65          = zero_zero_complex )
% 0.26/0.65        = ( Z = zero_zero_complex ) ) ).
% 0.26/0.65  
% 0.26/0.65  % csqrt_eq_0
% 0.26/0.65  thf(fact_8814_csqrt__0,axiom,
% 0.26/0.65      ( ( csqrt @ zero_zero_complex )
% 0.26/0.65      = zero_zero_complex ) ).
% 0.26/0.65  
% 0.26/0.65  % csqrt_0
% 0.26/0.65  thf(fact_8815_cis__zero,axiom,
% 0.26/0.65      ( ( cis @ zero_zero_real )
% 0.26/0.65      = one_one_complex ) ).
% 0.26/0.65  
% 0.26/0.65  % cis_zero
% 0.26/0.65  thf(fact_8816_power2__csqrt,axiom,
% 0.26/0.65      ! [Z: complex] :
% 0.26/0.65        ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.65        = Z ) ).
% 0.26/0.65  
% 0.26/0.65  % power2_csqrt
% 0.26/0.65  thf(fact_8817_cis__pi__half,axiom,
% 0.26/0.65      ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.65      = imaginary_unit ) ).
% 0.26/0.65  
% 0.26/0.65  % cis_pi_half
% 0.26/0.65  thf(fact_8818_cis__2pi,axiom,
% 0.26/0.65      ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.26/0.65      = one_one_complex ) ).
% 0.26/0.65  
% 0.26/0.65  % cis_2pi
% 0.26/0.65  thf(fact_8819_cis__neq__zero,axiom,
% 0.26/0.65      ! [A: real] :
% 0.26/0.65        ( ( cis @ A )
% 0.26/0.65       != zero_zero_complex ) ).
% 0.26/0.65  
% 0.26/0.65  % cis_neq_zero
% 0.26/0.65  thf(fact_8820_Arg__zero,axiom,
% 0.26/0.65      ( ( arg @ zero_zero_complex )
% 0.26/0.65      = zero_zero_real ) ).
% 0.26/0.65  
% 0.26/0.65  % Arg_zero
% 0.26/0.65  thf(fact_8821_DeMoivre,axiom,
% 0.26/0.65      ! [A: real,N: nat] :
% 0.26/0.65        ( ( power_power_complex @ ( cis @ A ) @ N )
% 0.26/0.65        = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % DeMoivre
% 0.26/0.65  thf(fact_8822_of__real__sqrt,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ( real_V4546457046886955230omplex @ ( sqrt @ X3 ) )
% 0.26/0.65          = ( csqrt @ ( real_V4546457046886955230omplex @ X3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % of_real_sqrt
% 0.26/0.65  thf(fact_8823_Arg__bounded,axiom,
% 0.26/0.65      ! [Z: complex] :
% 0.26/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 0.26/0.65        & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Arg_bounded
% 0.26/0.65  thf(fact_8824_divmod__nat__if,axiom,
% 0.26/0.65      ( divmod_nat
% 0.26/0.65      = ( ^ [M3: nat,N3: nat] :
% 0.26/0.65            ( if_Pro6206227464963214023at_nat
% 0.26/0.65            @ ( ( N3 = zero_zero_nat )
% 0.26/0.65              | ( ord_less_nat @ M3 @ N3 ) )
% 0.26/0.65            @ ( product_Pair_nat_nat @ zero_zero_nat @ M3 )
% 0.26/0.65            @ ( produc2626176000494625587at_nat
% 0.26/0.65              @ ^ [Q5: nat] : ( product_Pair_nat_nat @ ( suc @ Q5 ) )
% 0.26/0.65              @ ( divmod_nat @ ( minus_minus_nat @ M3 @ N3 ) @ N3 ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % divmod_nat_if
% 0.26/0.65  thf(fact_8825_bij__betw__roots__unity,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( bij_betw_nat_complex
% 0.26/0.65          @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.26/0.65          @ ( set_ord_lessThan_nat @ N )
% 0.26/0.65          @ ( collect_complex
% 0.26/0.65            @ ^ [Z6: complex] :
% 0.26/0.65                ( ( power_power_complex @ Z6 @ N )
% 0.26/0.65                = one_one_complex ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % bij_betw_roots_unity
% 0.26/0.65  thf(fact_8826_nat__of__bool,axiom,
% 0.26/0.65      ! [P: $o] :
% 0.26/0.65        ( ( nat2 @ ( zero_n2684676970156552555ol_int @ P ) )
% 0.26/0.65        = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 0.26/0.65  
% 0.26/0.65  % nat_of_bool
% 0.26/0.65  thf(fact_8827_Suc__0__mod__eq,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.26/0.65        = ( zero_n2687167440665602831ol_nat
% 0.26/0.65          @ ( N
% 0.26/0.65           != ( suc @ zero_zero_nat ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Suc_0_mod_eq
% 0.26/0.65  thf(fact_8828_take__bit__of__Suc__0,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.26/0.65        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % take_bit_of_Suc_0
% 0.26/0.65  thf(fact_8829_Divides_Oadjust__div__eq,axiom,
% 0.26/0.65      ! [Q3: int,R2: int] :
% 0.26/0.65        ( ( adjust_div @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 0.26/0.65        = ( plus_plus_int @ Q3 @ ( zero_n2684676970156552555ol_int @ ( R2 != zero_zero_int ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Divides.adjust_div_eq
% 0.26/0.65  thf(fact_8830_Divides_Oadjust__div__def,axiom,
% 0.26/0.65      ( adjust_div
% 0.26/0.65      = ( produc8211389475949308722nt_int
% 0.26/0.65        @ ^ [Q5: int,R5: int] : ( plus_plus_int @ Q5 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Divides.adjust_div_def
% 0.26/0.65  thf(fact_8831_not__int__rec,axiom,
% 0.26/0.65      ( bit_ri7919022796975470100ot_int
% 0.26/0.65      = ( ^ [K3: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % not_int_rec
% 0.26/0.65  thf(fact_8832_or__Suc__0__eq,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.26/0.65        = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % or_Suc_0_eq
% 0.26/0.65  thf(fact_8833_Suc__0__or__eq,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.26/0.65        = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Suc_0_or_eq
% 0.26/0.65  thf(fact_8834_or__int__rec,axiom,
% 0.26/0.65      ( bit_se1409905431419307370or_int
% 0.26/0.65      = ( ^ [K3: int,L2: int] :
% 0.26/0.65            ( plus_plus_int
% 0.26/0.65            @ ( zero_n2684676970156552555ol_int
% 0.26/0.65              @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 0.26/0.65                | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 0.26/0.65            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % or_int_rec
% 0.26/0.65  thf(fact_8835_xor__nat__rec,axiom,
% 0.26/0.65      ( bit_se6528837805403552850or_nat
% 0.26/0.65      = ( ^ [M3: nat,N3: nat] :
% 0.26/0.65            ( plus_plus_nat
% 0.26/0.65            @ ( zero_n2687167440665602831ol_nat
% 0.26/0.65              @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 0.26/0.65               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 0.26/0.65            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % xor_nat_rec
% 0.26/0.65  thf(fact_8836_or__nat__rec,axiom,
% 0.26/0.65      ( bit_se1412395901928357646or_nat
% 0.26/0.65      = ( ^ [M3: nat,N3: nat] :
% 0.26/0.65            ( plus_plus_nat
% 0.26/0.65            @ ( zero_n2687167440665602831ol_nat
% 0.26/0.65              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 0.26/0.65                | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 0.26/0.65            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % or_nat_rec
% 0.26/0.65  thf(fact_8837_xor__int__rec,axiom,
% 0.26/0.65      ( bit_se6526347334894502574or_int
% 0.26/0.65      = ( ^ [K3: int,L2: int] :
% 0.26/0.65            ( plus_plus_int
% 0.26/0.65            @ ( zero_n2684676970156552555ol_int
% 0.26/0.65              @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 0.26/0.65               != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 0.26/0.65            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % xor_int_rec
% 0.26/0.65  thf(fact_8838_xor__Suc__0__eq,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.26/0.65        = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.26/0.65          @ ( zero_n2687167440665602831ol_nat
% 0.26/0.65            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % xor_Suc_0_eq
% 0.26/0.65  thf(fact_8839_Suc__0__xor__eq,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.26/0.65        = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.26/0.65          @ ( zero_n2687167440665602831ol_nat
% 0.26/0.65            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Suc_0_xor_eq
% 0.26/0.65  thf(fact_8840_and__int_Osimps,axiom,
% 0.26/0.65      ( bit_se725231765392027082nd_int
% 0.26/0.65      = ( ^ [K3: int,L2: int] :
% 0.26/0.65            ( if_int
% 0.26/0.65            @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.26/0.65              & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.26/0.65            @ ( uminus_uminus_int
% 0.26/0.65              @ ( zero_n2684676970156552555ol_int
% 0.26/0.65                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 0.26/0.65                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 0.26/0.65            @ ( plus_plus_int
% 0.26/0.65              @ ( zero_n2684676970156552555ol_int
% 0.26/0.65                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 0.26/0.65                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 0.26/0.65              @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % and_int.simps
% 0.26/0.65  thf(fact_8841_and__int_Oelims,axiom,
% 0.26/0.65      ! [X3: int,Xa: int,Y3: int] :
% 0.26/0.65        ( ( ( bit_se725231765392027082nd_int @ X3 @ Xa )
% 0.26/0.65          = Y3 )
% 0.26/0.65       => ( ( ( ( member_int @ X3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.26/0.65              & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.26/0.65           => ( Y3
% 0.26/0.65              = ( uminus_uminus_int
% 0.26/0.65                @ ( zero_n2684676970156552555ol_int
% 0.26/0.65                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 )
% 0.26/0.65                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 0.26/0.65          & ( ~ ( ( member_int @ X3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.26/0.65                & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.26/0.65           => ( Y3
% 0.26/0.65              = ( plus_plus_int
% 0.26/0.65                @ ( zero_n2684676970156552555ol_int
% 0.26/0.65                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 )
% 0.26/0.65                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 0.26/0.65                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % and_int.elims
% 0.26/0.65  thf(fact_8842_int__ge__less__than2__def,axiom,
% 0.26/0.65      ( int_ge_less_than2
% 0.26/0.65      = ( ^ [D4: int] :
% 0.26/0.65            ( collec213857154873943460nt_int
% 0.26/0.65            @ ( produc4947309494688390418_int_o
% 0.26/0.65              @ ^ [Z7: int,Z6: int] :
% 0.26/0.65                  ( ( ord_less_eq_int @ D4 @ Z6 )
% 0.26/0.65                  & ( ord_less_int @ Z7 @ Z6 ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % int_ge_less_than2_def
% 0.26/0.65  thf(fact_8843_int__ge__less__than__def,axiom,
% 0.26/0.65      ( int_ge_less_than
% 0.26/0.65      = ( ^ [D4: int] :
% 0.26/0.65            ( collec213857154873943460nt_int
% 0.26/0.65            @ ( produc4947309494688390418_int_o
% 0.26/0.65              @ ^ [Z7: int,Z6: int] :
% 0.26/0.65                  ( ( ord_less_eq_int @ D4 @ Z7 )
% 0.26/0.65                  & ( ord_less_int @ Z7 @ Z6 ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % int_ge_less_than_def
% 0.26/0.65  thf(fact_8844_and__nonnegative__int__iff,axiom,
% 0.26/0.65      ! [K: int,L: int] :
% 0.26/0.65        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 0.26/0.65        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.26/0.65          | ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % and_nonnegative_int_iff
% 0.26/0.65  thf(fact_8845_and__negative__int__iff,axiom,
% 0.26/0.65      ! [K: int,L: int] :
% 0.26/0.65        ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ zero_zero_int )
% 0.26/0.65        = ( ( ord_less_int @ K @ zero_zero_int )
% 0.26/0.65          & ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % and_negative_int_iff
% 0.26/0.65  thf(fact_8846_and__minus__numerals_I2_J,axiom,
% 0.26/0.65      ! [N: num] :
% 0.26/0.65        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.26/0.65        = one_one_int ) ).
% 0.26/0.65  
% 0.26/0.65  % and_minus_numerals(2)
% 0.26/0.65  thf(fact_8847_and__minus__numerals_I6_J,axiom,
% 0.26/0.65      ! [N: num] :
% 0.26/0.65        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 0.26/0.65        = one_one_int ) ).
% 0.26/0.65  
% 0.26/0.65  % and_minus_numerals(6)
% 0.26/0.65  thf(fact_8848_and__minus__numerals_I1_J,axiom,
% 0.26/0.65      ! [N: num] :
% 0.26/0.65        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.26/0.65        = zero_zero_int ) ).
% 0.26/0.65  
% 0.26/0.65  % and_minus_numerals(1)
% 0.26/0.65  thf(fact_8849_and__minus__numerals_I5_J,axiom,
% 0.26/0.65      ! [N: num] :
% 0.26/0.65        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 0.26/0.65        = zero_zero_int ) ).
% 0.26/0.65  
% 0.26/0.65  % and_minus_numerals(5)
% 0.26/0.65  thf(fact_8850_and__minus__minus__numerals,axiom,
% 0.26/0.65      ! [M: num,N: num] :
% 0.26/0.65        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.65        = ( 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 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % and_minus_minus_numerals
% 0.26/0.65  thf(fact_8851_or__minus__minus__numerals,axiom,
% 0.26/0.65      ! [M: num,N: num] :
% 0.26/0.65        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.65        = ( 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 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % or_minus_minus_numerals
% 0.26/0.65  thf(fact_8852_AND__upper2_H,axiom,
% 0.26/0.65      ! [Y3: int,Z: int,X3: int] :
% 0.26/0.65        ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 0.26/0.65       => ( ( ord_less_eq_int @ Y3 @ Z )
% 0.26/0.65         => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X3 @ Y3 ) @ Z ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % AND_upper2'
% 0.26/0.65  thf(fact_8853_AND__upper1_H,axiom,
% 0.26/0.65      ! [Y3: int,Z: int,Ya: int] :
% 0.26/0.65        ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 0.26/0.65       => ( ( ord_less_eq_int @ Y3 @ Z )
% 0.26/0.65         => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y3 @ Ya ) @ Z ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % AND_upper1'
% 0.26/0.65  thf(fact_8854_AND__upper2,axiom,
% 0.26/0.65      ! [Y3: int,X3: int] :
% 0.26/0.65        ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 0.26/0.65       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X3 @ Y3 ) @ Y3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % AND_upper2
% 0.26/0.65  thf(fact_8855_AND__upper1,axiom,
% 0.26/0.65      ! [X3: int,Y3: int] :
% 0.26/0.65        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.26/0.65       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X3 @ Y3 ) @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % AND_upper1
% 0.26/0.65  thf(fact_8856_AND__lower,axiom,
% 0.26/0.65      ! [X3: int,Y3: int] :
% 0.26/0.65        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.26/0.65       => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X3 @ Y3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % AND_lower
% 0.26/0.65  thf(fact_8857_plus__and__or,axiom,
% 0.26/0.65      ! [X3: int,Y3: int] :
% 0.26/0.65        ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X3 @ Y3 ) @ ( bit_se1409905431419307370or_int @ X3 @ Y3 ) )
% 0.26/0.65        = ( plus_plus_int @ X3 @ Y3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % plus_and_or
% 0.26/0.65  thf(fact_8858_or__int__def,axiom,
% 0.26/0.65      ( bit_se1409905431419307370or_int
% 0.26/0.65      = ( ^ [K3: int,L2: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ ( bit_ri7919022796975470100ot_int @ L2 ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % or_int_def
% 0.26/0.65  thf(fact_8859_and__less__eq,axiom,
% 0.26/0.65      ! [L: int,K: int] :
% 0.26/0.65        ( ( ord_less_int @ L @ zero_zero_int )
% 0.26/0.65       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 0.26/0.65  
% 0.26/0.65  % and_less_eq
% 0.26/0.65  thf(fact_8860_AND__upper1_H_H,axiom,
% 0.26/0.65      ! [Y3: int,Z: int,Ya: int] :
% 0.26/0.65        ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 0.26/0.65       => ( ( ord_less_int @ Y3 @ Z )
% 0.26/0.65         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y3 @ Ya ) @ Z ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % AND_upper1''
% 0.26/0.65  thf(fact_8861_AND__upper2_H_H,axiom,
% 0.26/0.65      ! [Y3: int,Z: int,X3: int] :
% 0.26/0.65        ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 0.26/0.65       => ( ( ord_less_int @ Y3 @ Z )
% 0.26/0.65         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X3 @ Y3 ) @ Z ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % AND_upper2''
% 0.26/0.65  thf(fact_8862_and__not__numerals_I1_J,axiom,
% 0.26/0.65      ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.26/0.65      = zero_zero_int ) ).
% 0.26/0.65  
% 0.26/0.65  % and_not_numerals(1)
% 0.26/0.65  thf(fact_8863_xor__int__def,axiom,
% 0.26/0.65      ( bit_se6526347334894502574or_int
% 0.26/0.65      = ( ^ [K3: int,L2: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ L2 ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ L2 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % xor_int_def
% 0.26/0.65  thf(fact_8864_even__and__iff__int,axiom,
% 0.26/0.65      ! [K: int,L: int] :
% 0.26/0.65        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 0.26/0.65        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 0.26/0.65          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % even_and_iff_int
% 0.26/0.65  thf(fact_8865_and__not__numerals_I2_J,axiom,
% 0.26/0.65      ! [N: num] :
% 0.26/0.65        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.26/0.65        = one_one_int ) ).
% 0.26/0.65  
% 0.26/0.65  % and_not_numerals(2)
% 0.26/0.65  thf(fact_8866_and__not__numerals_I4_J,axiom,
% 0.26/0.65      ! [M: num] :
% 0.26/0.65        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.26/0.65        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % and_not_numerals(4)
% 0.26/0.65  thf(fact_8867_and__not__numerals_I5_J,axiom,
% 0.26/0.65      ! [M: num,N: num] :
% 0.26/0.65        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.26/0.65        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % and_not_numerals(5)
% 0.26/0.65  thf(fact_8868_and__not__numerals_I7_J,axiom,
% 0.26/0.65      ! [M: num] :
% 0.26/0.65        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.26/0.65        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % and_not_numerals(7)
% 0.26/0.65  thf(fact_8869_and__not__numerals_I3_J,axiom,
% 0.26/0.65      ! [N: num] :
% 0.26/0.65        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.26/0.65        = zero_zero_int ) ).
% 0.26/0.65  
% 0.26/0.65  % and_not_numerals(3)
% 0.26/0.65  thf(fact_8870_and__not__numerals_I9_J,axiom,
% 0.26/0.65      ! [M: num,N: num] :
% 0.26/0.65        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.26/0.65        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % and_not_numerals(9)
% 0.26/0.65  thf(fact_8871_and__not__numerals_I6_J,axiom,
% 0.26/0.65      ! [M: num,N: num] :
% 0.26/0.65        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.26/0.65        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % and_not_numerals(6)
% 0.26/0.65  thf(fact_8872_and__int__rec,axiom,
% 0.26/0.65      ( bit_se725231765392027082nd_int
% 0.26/0.65      = ( ^ [K3: int,L2: int] :
% 0.26/0.65            ( plus_plus_int
% 0.26/0.65            @ ( zero_n2684676970156552555ol_int
% 0.26/0.65              @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 0.26/0.65                & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 0.26/0.65            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % and_int_rec
% 0.26/0.65  thf(fact_8873_and__not__numerals_I8_J,axiom,
% 0.26/0.65      ! [M: num,N: num] :
% 0.26/0.65        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.26/0.65        = ( 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 ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % and_not_numerals(8)
% 0.26/0.65  thf(fact_8874_and__int__unfold,axiom,
% 0.26/0.65      ( bit_se725231765392027082nd_int
% 0.26/0.65      = ( ^ [K3: int,L2: int] :
% 0.26/0.65            ( if_int
% 0.26/0.65            @ ( ( K3 = zero_zero_int )
% 0.26/0.65              | ( L2 = zero_zero_int ) )
% 0.26/0.65            @ zero_zero_int
% 0.26/0.65            @ ( if_int
% 0.26/0.65              @ ( K3
% 0.26/0.65                = ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.65              @ L2
% 0.26/0.65              @ ( if_int
% 0.26/0.65                @ ( L2
% 0.26/0.65                  = ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.65                @ K3
% 0.26/0.65                @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % and_int_unfold
% 0.26/0.65  thf(fact_8875_bij__betw__nth__root__unity,axiom,
% 0.26/0.65      ! [C: complex,N: nat] :
% 0.26/0.65        ( ( C != zero_zero_complex )
% 0.26/0.65       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65         => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 0.26/0.65            @ ( collect_complex
% 0.26/0.65              @ ^ [Z6: complex] :
% 0.26/0.65                  ( ( power_power_complex @ Z6 @ N )
% 0.26/0.65                  = one_one_complex ) )
% 0.26/0.65            @ ( collect_complex
% 0.26/0.65              @ ^ [Z6: complex] :
% 0.26/0.65                  ( ( power_power_complex @ Z6 @ N )
% 0.26/0.65                  = C ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % bij_betw_nth_root_unity
% 0.26/0.65  thf(fact_8876_and__int_Opsimps,axiom,
% 0.26/0.65      ! [K: int,L: int] :
% 0.26/0.65        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 0.26/0.65       => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.26/0.65              & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.26/0.65           => ( ( bit_se725231765392027082nd_int @ K @ L )
% 0.26/0.65              = ( uminus_uminus_int
% 0.26/0.65                @ ( zero_n2684676970156552555ol_int
% 0.26/0.65                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 0.26/0.65                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 0.26/0.65          & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.26/0.65                & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.26/0.65           => ( ( bit_se725231765392027082nd_int @ K @ L )
% 0.26/0.65              = ( plus_plus_int
% 0.26/0.65                @ ( zero_n2684676970156552555ol_int
% 0.26/0.65                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 0.26/0.65                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 0.26/0.65                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % and_int.psimps
% 0.26/0.65  thf(fact_8877_and__int_Opelims,axiom,
% 0.26/0.65      ! [X3: int,Xa: int,Y3: int] :
% 0.26/0.65        ( ( ( bit_se725231765392027082nd_int @ X3 @ Xa )
% 0.26/0.65          = Y3 )
% 0.26/0.65       => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X3 @ Xa ) )
% 0.26/0.65         => ~ ( ( ( ( ( member_int @ X3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.26/0.65                    & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.26/0.65                 => ( Y3
% 0.26/0.65                    = ( uminus_uminus_int
% 0.26/0.65                      @ ( zero_n2684676970156552555ol_int
% 0.26/0.65                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 )
% 0.26/0.65                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 0.26/0.65                & ( ~ ( ( member_int @ X3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.26/0.65                      & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.26/0.65                 => ( Y3
% 0.26/0.65                    = ( plus_plus_int
% 0.26/0.65                      @ ( zero_n2684676970156552555ol_int
% 0.26/0.65                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 )
% 0.26/0.65                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 0.26/0.65                      @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.26/0.65             => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X3 @ Xa ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % and_int.pelims
% 0.26/0.65  thf(fact_8878_vebt__buildup_Opelims,axiom,
% 0.26/0.65      ! [X3: nat,Y3: vEBT_VEBT] :
% 0.26/0.65        ( ( ( vEBT_vebt_buildup @ X3 )
% 0.26/0.65          = Y3 )
% 0.26/0.65       => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X3 )
% 0.26/0.65         => ( ( ( X3 = zero_zero_nat )
% 0.26/0.65             => ( ( Y3
% 0.26/0.65                  = ( vEBT_Leaf @ $false @ $false ) )
% 0.26/0.65               => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 0.26/0.65           => ( ( ( X3
% 0.26/0.65                  = ( suc @ zero_zero_nat ) )
% 0.26/0.65               => ( ( Y3
% 0.26/0.65                    = ( vEBT_Leaf @ $false @ $false ) )
% 0.26/0.65                 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 0.26/0.65             => ~ ! [Va: nat] :
% 0.26/0.65                    ( ( X3
% 0.26/0.65                      = ( suc @ ( suc @ Va ) ) )
% 0.26/0.65                   => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.26/0.65                         => ( Y3
% 0.26/0.65                            = ( 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 ) ) ) ) ) ) )
% 0.26/0.65                        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.26/0.65                         => ( Y3
% 0.26/0.65                            = ( 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 ) ) ) ) ) ) ) ) )
% 0.26/0.65                     => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % vebt_buildup.pelims
% 0.26/0.65  thf(fact_8879_real__root__zero,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( root @ N @ zero_zero_real )
% 0.26/0.65        = zero_zero_real ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_zero
% 0.26/0.65  thf(fact_8880_real__root__Suc__0,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( root @ ( suc @ zero_zero_nat ) @ X3 )
% 0.26/0.65        = X3 ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_Suc_0
% 0.26/0.65  thf(fact_8881_real__root__eq__iff,axiom,
% 0.26/0.65      ! [N: nat,X3: real,Y3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ( root @ N @ X3 )
% 0.26/0.65            = ( root @ N @ Y3 ) )
% 0.26/0.65          = ( X3 = Y3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_eq_iff
% 0.26/0.65  thf(fact_8882_root__0,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( root @ zero_zero_nat @ X3 )
% 0.26/0.65        = zero_zero_real ) ).
% 0.26/0.65  
% 0.26/0.65  % root_0
% 0.26/0.65  thf(fact_8883_real__root__eq__0__iff,axiom,
% 0.26/0.65      ! [N: nat,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ( root @ N @ X3 )
% 0.26/0.65            = zero_zero_real )
% 0.26/0.65          = ( X3 = zero_zero_real ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_eq_0_iff
% 0.26/0.65  thf(fact_8884_real__root__less__iff,axiom,
% 0.26/0.65      ! [N: nat,X3: real,Y3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_real @ ( root @ N @ X3 ) @ ( root @ N @ Y3 ) )
% 0.26/0.65          = ( ord_less_real @ X3 @ Y3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_less_iff
% 0.26/0.65  thf(fact_8885_real__root__le__iff,axiom,
% 0.26/0.65      ! [N: nat,X3: real,Y3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_eq_real @ ( root @ N @ X3 ) @ ( root @ N @ Y3 ) )
% 0.26/0.65          = ( ord_less_eq_real @ X3 @ Y3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_le_iff
% 0.26/0.65  thf(fact_8886_real__root__eq__1__iff,axiom,
% 0.26/0.65      ! [N: nat,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ( root @ N @ X3 )
% 0.26/0.65            = one_one_real )
% 0.26/0.65          = ( X3 = one_one_real ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_eq_1_iff
% 0.26/0.65  thf(fact_8887_real__root__one,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( root @ N @ one_one_real )
% 0.26/0.65          = one_one_real ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_one
% 0.26/0.65  thf(fact_8888_real__root__lt__0__iff,axiom,
% 0.26/0.65      ! [N: nat,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_real @ ( root @ N @ X3 ) @ zero_zero_real )
% 0.26/0.65          = ( ord_less_real @ X3 @ zero_zero_real ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_lt_0_iff
% 0.26/0.65  thf(fact_8889_real__root__gt__0__iff,axiom,
% 0.26/0.65      ! [N: nat,Y3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y3 ) )
% 0.26/0.65          = ( ord_less_real @ zero_zero_real @ Y3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_gt_0_iff
% 0.26/0.65  thf(fact_8890_real__root__le__0__iff,axiom,
% 0.26/0.65      ! [N: nat,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_eq_real @ ( root @ N @ X3 ) @ zero_zero_real )
% 0.26/0.65          = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_le_0_iff
% 0.26/0.65  thf(fact_8891_real__root__ge__0__iff,axiom,
% 0.26/0.65      ! [N: nat,Y3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y3 ) )
% 0.26/0.65          = ( ord_less_eq_real @ zero_zero_real @ Y3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_ge_0_iff
% 0.26/0.65  thf(fact_8892_real__root__lt__1__iff,axiom,
% 0.26/0.65      ! [N: nat,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_real @ ( root @ N @ X3 ) @ one_one_real )
% 0.26/0.65          = ( ord_less_real @ X3 @ one_one_real ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_lt_1_iff
% 0.26/0.65  thf(fact_8893_real__root__gt__1__iff,axiom,
% 0.26/0.65      ! [N: nat,Y3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y3 ) )
% 0.26/0.65          = ( ord_less_real @ one_one_real @ Y3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_gt_1_iff
% 0.26/0.65  thf(fact_8894_real__root__le__1__iff,axiom,
% 0.26/0.65      ! [N: nat,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_eq_real @ ( root @ N @ X3 ) @ one_one_real )
% 0.26/0.65          = ( ord_less_eq_real @ X3 @ one_one_real ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_le_1_iff
% 0.26/0.65  thf(fact_8895_real__root__ge__1__iff,axiom,
% 0.26/0.65      ! [N: nat,Y3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y3 ) )
% 0.26/0.65          = ( ord_less_eq_real @ one_one_real @ Y3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_ge_1_iff
% 0.26/0.65  thf(fact_8896_and__nat__numerals_I3_J,axiom,
% 0.26/0.65      ! [X3: num] :
% 0.26/0.65        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 0.26/0.65        = zero_zero_nat ) ).
% 0.26/0.65  
% 0.26/0.65  % and_nat_numerals(3)
% 0.26/0.65  thf(fact_8897_and__nat__numerals_I1_J,axiom,
% 0.26/0.65      ! [Y3: num] :
% 0.26/0.65        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 0.26/0.65        = zero_zero_nat ) ).
% 0.26/0.65  
% 0.26/0.65  % and_nat_numerals(1)
% 0.26/0.65  thf(fact_8898_real__root__pow__pos2,axiom,
% 0.26/0.65      ! [N: nat,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.65         => ( ( power_power_real @ ( root @ N @ X3 ) @ N )
% 0.26/0.65            = X3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_pow_pos2
% 0.26/0.65  thf(fact_8899_and__nat__numerals_I4_J,axiom,
% 0.26/0.65      ! [X3: num] :
% 0.26/0.65        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 0.26/0.65        = one_one_nat ) ).
% 0.26/0.65  
% 0.26/0.65  % and_nat_numerals(4)
% 0.26/0.65  thf(fact_8900_and__nat__numerals_I2_J,axiom,
% 0.26/0.65      ! [Y3: num] :
% 0.26/0.65        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 0.26/0.65        = one_one_nat ) ).
% 0.26/0.65  
% 0.26/0.65  % and_nat_numerals(2)
% 0.26/0.65  thf(fact_8901_Suc__0__and__eq,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.26/0.65        = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Suc_0_and_eq
% 0.26/0.65  thf(fact_8902_and__Suc__0__eq,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.26/0.65        = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % and_Suc_0_eq
% 0.26/0.65  thf(fact_8903_real__root__mult,axiom,
% 0.26/0.65      ! [N: nat,X3: real,Y3: real] :
% 0.26/0.65        ( ( root @ N @ ( times_times_real @ X3 @ Y3 ) )
% 0.26/0.65        = ( times_times_real @ ( root @ N @ X3 ) @ ( root @ N @ Y3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_mult
% 0.26/0.65  thf(fact_8904_real__root__divide,axiom,
% 0.26/0.65      ! [N: nat,X3: real,Y3: real] :
% 0.26/0.65        ( ( root @ N @ ( divide_divide_real @ X3 @ Y3 ) )
% 0.26/0.65        = ( divide_divide_real @ ( root @ N @ X3 ) @ ( root @ N @ Y3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_divide
% 0.26/0.65  thf(fact_8905_real__root__mult__exp,axiom,
% 0.26/0.65      ! [M: nat,N: nat,X3: real] :
% 0.26/0.65        ( ( root @ ( times_times_nat @ M @ N ) @ X3 )
% 0.26/0.65        = ( root @ M @ ( root @ N @ X3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_mult_exp
% 0.26/0.65  thf(fact_8906_real__root__minus,axiom,
% 0.26/0.65      ! [N: nat,X3: real] :
% 0.26/0.65        ( ( root @ N @ ( uminus_uminus_real @ X3 ) )
% 0.26/0.65        = ( uminus_uminus_real @ ( root @ N @ X3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_minus
% 0.26/0.65  thf(fact_8907_real__root__commute,axiom,
% 0.26/0.65      ! [M: nat,N: nat,X3: real] :
% 0.26/0.65        ( ( root @ M @ ( root @ N @ X3 ) )
% 0.26/0.65        = ( root @ N @ ( root @ M @ X3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_commute
% 0.26/0.65  thf(fact_8908_real__root__inverse,axiom,
% 0.26/0.65      ! [N: nat,X3: real] :
% 0.26/0.65        ( ( root @ N @ ( inverse_inverse_real @ X3 ) )
% 0.26/0.65        = ( inverse_inverse_real @ ( root @ N @ X3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_inverse
% 0.26/0.65  thf(fact_8909_real__root__pos__pos__le,axiom,
% 0.26/0.65      ! [X3: real,N: nat] :
% 0.26/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.65       => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_pos_pos_le
% 0.26/0.65  thf(fact_8910_real__root__less__mono,axiom,
% 0.26/0.65      ! [N: nat,X3: real,Y3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.65         => ( ord_less_real @ ( root @ N @ X3 ) @ ( root @ N @ Y3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_less_mono
% 0.26/0.65  thf(fact_8911_real__root__le__mono,axiom,
% 0.26/0.65      ! [N: nat,X3: real,Y3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.26/0.65         => ( ord_less_eq_real @ ( root @ N @ X3 ) @ ( root @ N @ Y3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_le_mono
% 0.26/0.65  thf(fact_8912_real__root__power,axiom,
% 0.26/0.65      ! [N: nat,X3: real,K: nat] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( root @ N @ ( power_power_real @ X3 @ K ) )
% 0.26/0.65          = ( power_power_real @ ( root @ N @ X3 ) @ K ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_power
% 0.26/0.65  thf(fact_8913_real__root__abs,axiom,
% 0.26/0.65      ! [N: nat,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( root @ N @ ( abs_abs_real @ X3 ) )
% 0.26/0.65          = ( abs_abs_real @ ( root @ N @ X3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_abs
% 0.26/0.65  thf(fact_8914_and__nat__def,axiom,
% 0.26/0.65      ( bit_se727722235901077358nd_nat
% 0.26/0.65      = ( ^ [M3: nat,N3: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % and_nat_def
% 0.26/0.65  thf(fact_8915_real__root__gt__zero,axiom,
% 0.26/0.65      ! [N: nat,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.65         => ( ord_less_real @ zero_zero_real @ ( root @ N @ X3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_gt_zero
% 0.26/0.65  thf(fact_8916_real__root__strict__decreasing,axiom,
% 0.26/0.65      ! [N: nat,N4: nat,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_nat @ N @ N4 )
% 0.26/0.65         => ( ( ord_less_real @ one_one_real @ X3 )
% 0.26/0.65           => ( ord_less_real @ ( root @ N4 @ X3 ) @ ( root @ N @ X3 ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_strict_decreasing
% 0.26/0.65  thf(fact_8917_sqrt__def,axiom,
% 0.26/0.65      ( sqrt
% 0.26/0.65      = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sqrt_def
% 0.26/0.65  thf(fact_8918_root__abs__power,axiom,
% 0.26/0.65      ! [N: nat,Y3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y3 @ N ) ) )
% 0.26/0.65          = ( abs_abs_real @ Y3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % root_abs_power
% 0.26/0.65  thf(fact_8919_real__root__pos__pos,axiom,
% 0.26/0.65      ! [N: nat,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.65         => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_pos_pos
% 0.26/0.65  thf(fact_8920_real__root__strict__increasing,axiom,
% 0.26/0.65      ! [N: nat,N4: nat,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_nat @ N @ N4 )
% 0.26/0.65         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.65           => ( ( ord_less_real @ X3 @ one_one_real )
% 0.26/0.65             => ( ord_less_real @ ( root @ N @ X3 ) @ ( root @ N4 @ X3 ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_strict_increasing
% 0.26/0.65  thf(fact_8921_real__root__decreasing,axiom,
% 0.26/0.65      ! [N: nat,N4: nat,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_eq_nat @ N @ N4 )
% 0.26/0.65         => ( ( ord_less_eq_real @ one_one_real @ X3 )
% 0.26/0.65           => ( ord_less_eq_real @ ( root @ N4 @ X3 ) @ ( root @ N @ X3 ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_decreasing
% 0.26/0.65  thf(fact_8922_real__root__pow__pos,axiom,
% 0.26/0.65      ! [N: nat,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.65         => ( ( power_power_real @ ( root @ N @ X3 ) @ N )
% 0.26/0.65            = X3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_pow_pos
% 0.26/0.65  thf(fact_8923_odd__real__root__pow,axiom,
% 0.26/0.65      ! [N: nat,X3: real] :
% 0.26/0.65        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.65       => ( ( power_power_real @ ( root @ N @ X3 ) @ N )
% 0.26/0.65          = X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % odd_real_root_pow
% 0.26/0.65  thf(fact_8924_odd__real__root__unique,axiom,
% 0.26/0.65      ! [N: nat,Y3: real,X3: real] :
% 0.26/0.65        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.65       => ( ( ( power_power_real @ Y3 @ N )
% 0.26/0.65            = X3 )
% 0.26/0.65         => ( ( root @ N @ X3 )
% 0.26/0.65            = Y3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % odd_real_root_unique
% 0.26/0.65  thf(fact_8925_odd__real__root__power__cancel,axiom,
% 0.26/0.65      ! [N: nat,X3: real] :
% 0.26/0.65        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.65       => ( ( root @ N @ ( power_power_real @ X3 @ N ) )
% 0.26/0.65          = X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % odd_real_root_power_cancel
% 0.26/0.65  thf(fact_8926_real__root__power__cancel,axiom,
% 0.26/0.65      ! [N: nat,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.65         => ( ( root @ N @ ( power_power_real @ X3 @ N ) )
% 0.26/0.65            = X3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_power_cancel
% 0.26/0.65  thf(fact_8927_real__root__pos__unique,axiom,
% 0.26/0.65      ! [N: nat,Y3: real,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 0.26/0.65         => ( ( ( power_power_real @ Y3 @ N )
% 0.26/0.65              = X3 )
% 0.26/0.65           => ( ( root @ N @ X3 )
% 0.26/0.65              = Y3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_pos_unique
% 0.26/0.65  thf(fact_8928_real__root__increasing,axiom,
% 0.26/0.65      ! [N: nat,N4: nat,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_eq_nat @ N @ N4 )
% 0.26/0.65         => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.65           => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 0.26/0.65             => ( ord_less_eq_real @ ( root @ N @ X3 ) @ ( root @ N4 @ X3 ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % real_root_increasing
% 0.26/0.65  thf(fact_8929_log__root,axiom,
% 0.26/0.65      ! [N: nat,A: real,B: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.26/0.65         => ( ( log @ B @ ( root @ N @ A ) )
% 0.26/0.65            = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % log_root
% 0.26/0.65  thf(fact_8930_log__base__root,axiom,
% 0.26/0.65      ! [N: nat,B: real,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.26/0.65         => ( ( log @ ( root @ N @ B ) @ X3 )
% 0.26/0.65            = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X3 ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % log_base_root
% 0.26/0.65  thf(fact_8931_ln__root,axiom,
% 0.26/0.65      ! [N: nat,B: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.26/0.65         => ( ( ln_ln_real @ ( root @ N @ B ) )
% 0.26/0.65            = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % ln_root
% 0.26/0.65  thf(fact_8932_and__nat__unfold,axiom,
% 0.26/0.65      ( bit_se727722235901077358nd_nat
% 0.26/0.65      = ( ^ [M3: nat,N3: nat] :
% 0.26/0.65            ( if_nat
% 0.26/0.65            @ ( ( M3 = zero_zero_nat )
% 0.26/0.65              | ( N3 = zero_zero_nat ) )
% 0.26/0.65            @ zero_zero_nat
% 0.26/0.65            @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N3 @ ( 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 @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % and_nat_unfold
% 0.26/0.65  thf(fact_8933_root__powr__inverse,axiom,
% 0.26/0.65      ! [N: nat,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.65         => ( ( root @ N @ X3 )
% 0.26/0.65            = ( powr_real @ X3 @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % root_powr_inverse
% 0.26/0.65  thf(fact_8934_and__nat__rec,axiom,
% 0.26/0.65      ( bit_se727722235901077358nd_nat
% 0.26/0.65      = ( ^ [M3: nat,N3: nat] :
% 0.26/0.65            ( plus_plus_nat
% 0.26/0.65            @ ( zero_n2687167440665602831ol_nat
% 0.26/0.65              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 0.26/0.65                & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 0.26/0.65            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % and_nat_rec
% 0.26/0.65  thf(fact_8935_and__int_Opinduct,axiom,
% 0.26/0.65      ! [A0: int,A1: int,P: int > int > $o] :
% 0.26/0.65        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 0.26/0.65       => ( ! [K2: int,L4: int] :
% 0.26/0.65              ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L4 ) )
% 0.26/0.65             => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.26/0.65                      & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.26/0.65                 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.26/0.65               => ( P @ K2 @ L4 ) ) )
% 0.26/0.65         => ( P @ A0 @ A1 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % and_int.pinduct
% 0.26/0.65  thf(fact_8936_upto_Opinduct,axiom,
% 0.26/0.65      ! [A0: int,A1: int,P: int > int > $o] :
% 0.26/0.65        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 0.26/0.65       => ( ! [I3: int,J2: int] :
% 0.26/0.65              ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I3 @ J2 ) )
% 0.26/0.65             => ( ( ( ord_less_eq_int @ I3 @ J2 )
% 0.26/0.65                 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) )
% 0.26/0.65               => ( P @ I3 @ J2 ) ) )
% 0.26/0.65         => ( P @ A0 @ A1 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % upto.pinduct
% 0.26/0.65  thf(fact_8937_set__decode__0,axiom,
% 0.26/0.65      ! [X3: nat] :
% 0.26/0.65        ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X3 ) )
% 0.26/0.65        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % set_decode_0
% 0.26/0.65  thf(fact_8938_set__decode__Suc,axiom,
% 0.26/0.65      ! [N: nat,X3: nat] :
% 0.26/0.65        ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X3 ) )
% 0.26/0.65        = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % set_decode_Suc
% 0.26/0.65  thf(fact_8939_set__decode__zero,axiom,
% 0.26/0.65      ( ( nat_set_decode @ zero_zero_nat )
% 0.26/0.65      = bot_bot_set_nat ) ).
% 0.26/0.65  
% 0.26/0.65  % set_decode_zero
% 0.26/0.65  thf(fact_8940_subset__decode__imp__le,axiom,
% 0.26/0.65      ! [M: nat,N: nat] :
% 0.26/0.65        ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 0.26/0.65       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % subset_decode_imp_le
% 0.26/0.65  thf(fact_8941_set__decode__plus__power__2,axiom,
% 0.26/0.65      ! [N: nat,Z: nat] :
% 0.26/0.65        ( ~ ( member_nat @ N @ ( nat_set_decode @ Z ) )
% 0.26/0.65       => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z ) )
% 0.26/0.65          = ( insert_nat @ N @ ( nat_set_decode @ Z ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % set_decode_plus_power_2
% 0.26/0.65  thf(fact_8942_set__decode__def,axiom,
% 0.26/0.65      ( nat_set_decode
% 0.26/0.65      = ( ^ [X: nat] :
% 0.26/0.65            ( collect_nat
% 0.26/0.65            @ ^ [N3: nat] :
% 0.26/0.65                ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % set_decode_def
% 0.26/0.65  thf(fact_8943_arctan__def,axiom,
% 0.26/0.65      ( arctan
% 0.26/0.65      = ( ^ [Y: real] :
% 0.26/0.65            ( the_real
% 0.26/0.65            @ ^ [X: real] :
% 0.26/0.65                ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.26/0.65                & ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.65                & ( ( tan_real @ X )
% 0.26/0.65                  = Y ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % arctan_def
% 0.26/0.65  thf(fact_8944_arcsin__def,axiom,
% 0.26/0.65      ( arcsin
% 0.26/0.65      = ( ^ [Y: real] :
% 0.26/0.65            ( the_real
% 0.26/0.65            @ ^ [X: real] :
% 0.26/0.65                ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.26/0.65                & ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.65                & ( ( sin_real @ X )
% 0.26/0.65                  = Y ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % arcsin_def
% 0.26/0.65  thf(fact_8945_ln__neg__is__const,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 0.26/0.65       => ( ( ln_ln_real @ X3 )
% 0.26/0.65          = ( the_real
% 0.26/0.65            @ ^ [X: real] : $false ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % ln_neg_is_const
% 0.26/0.65  thf(fact_8946_arccos__def,axiom,
% 0.26/0.65      ( arccos
% 0.26/0.65      = ( ^ [Y: real] :
% 0.26/0.65            ( the_real
% 0.26/0.65            @ ^ [X: real] :
% 0.26/0.65                ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.26/0.65                & ( ord_less_eq_real @ X @ pi )
% 0.26/0.65                & ( ( cos_real @ X )
% 0.26/0.65                  = Y ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % arccos_def
% 0.26/0.65  thf(fact_8947_pi__half,axiom,
% 0.26/0.65      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.26/0.65      = ( the_real
% 0.26/0.65        @ ^ [X: real] :
% 0.26/0.65            ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.26/0.65            & ( ord_less_eq_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.26/0.65            & ( ( cos_real @ X )
% 0.26/0.65              = zero_zero_real ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % pi_half
% 0.26/0.65  thf(fact_8948_pi__def,axiom,
% 0.26/0.65      ( pi
% 0.26/0.65      = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 0.26/0.65        @ ( the_real
% 0.26/0.65          @ ^ [X: real] :
% 0.26/0.65              ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.26/0.65              & ( ord_less_eq_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.26/0.65              & ( ( cos_real @ X )
% 0.26/0.65                = zero_zero_real ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % pi_def
% 0.26/0.65  thf(fact_8949_modulo__int__def,axiom,
% 0.26/0.65      ( modulo_modulo_int
% 0.26/0.65      = ( ^ [K3: int,L2: int] :
% 0.26/0.65            ( if_int @ ( L2 = zero_zero_int ) @ K3
% 0.26/0.65            @ ( if_int
% 0.26/0.65              @ ( ( sgn_sgn_int @ K3 )
% 0.26/0.65                = ( sgn_sgn_int @ L2 ) )
% 0.26/0.65              @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) )
% 0.26/0.65              @ ( times_times_int @ ( sgn_sgn_int @ L2 )
% 0.26/0.65                @ ( minus_minus_int
% 0.26/0.65                  @ ( times_times_int @ ( abs_abs_int @ L2 )
% 0.26/0.65                    @ ( zero_n2684676970156552555ol_int
% 0.26/0.65                      @ ~ ( dvd_dvd_int @ L2 @ K3 ) ) )
% 0.26/0.65                  @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % modulo_int_def
% 0.26/0.65  thf(fact_8950_signed__take__bit__eq__take__bit__minus,axiom,
% 0.26/0.65      ( bit_ri631733984087533419it_int
% 0.26/0.65      = ( ^ [N3: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N3 ) @ K3 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N3 ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % signed_take_bit_eq_take_bit_minus
% 0.26/0.65  thf(fact_8951_divide__int__def,axiom,
% 0.26/0.65      ( divide_divide_int
% 0.26/0.65      = ( ^ [K3: int,L2: int] :
% 0.26/0.65            ( if_int @ ( L2 = zero_zero_int ) @ zero_zero_int
% 0.26/0.65            @ ( if_int
% 0.26/0.65              @ ( ( sgn_sgn_int @ K3 )
% 0.26/0.65                = ( sgn_sgn_int @ L2 ) )
% 0.26/0.65              @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) )
% 0.26/0.65              @ ( uminus_uminus_int
% 0.26/0.65                @ ( semiri1314217659103216013at_int
% 0.26/0.65                  @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) )
% 0.26/0.65                    @ ( zero_n2687167440665602831ol_nat
% 0.26/0.65                      @ ~ ( dvd_dvd_int @ L2 @ K3 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % divide_int_def
% 0.26/0.65  thf(fact_8952_modulo__int__unfold,axiom,
% 0.26/0.65      ! [L: int,K: int,N: nat,M: nat] :
% 0.26/0.65        ( ( ( ( ( sgn_sgn_int @ L )
% 0.26/0.65              = zero_zero_int )
% 0.26/0.65            | ( ( sgn_sgn_int @ K )
% 0.26/0.65              = zero_zero_int )
% 0.26/0.65            | ( N = zero_zero_nat ) )
% 0.26/0.65         => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.26/0.65            = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 0.26/0.65        & ( ~ ( ( ( sgn_sgn_int @ L )
% 0.26/0.65                = zero_zero_int )
% 0.26/0.65              | ( ( sgn_sgn_int @ K )
% 0.26/0.65                = zero_zero_int )
% 0.26/0.65              | ( N = zero_zero_nat ) )
% 0.26/0.65         => ( ( ( ( sgn_sgn_int @ K )
% 0.26/0.65                = ( sgn_sgn_int @ L ) )
% 0.26/0.65             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.26/0.65                = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 0.26/0.65            & ( ( ( sgn_sgn_int @ K )
% 0.26/0.65               != ( sgn_sgn_int @ L ) )
% 0.26/0.65             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.26/0.65                = ( times_times_int @ ( sgn_sgn_int @ L )
% 0.26/0.65                  @ ( minus_minus_int
% 0.26/0.65                    @ ( semiri1314217659103216013at_int
% 0.26/0.65                      @ ( times_times_nat @ N
% 0.26/0.65                        @ ( zero_n2687167440665602831ol_nat
% 0.26/0.65                          @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 0.26/0.65                    @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % modulo_int_unfold
% 0.26/0.65  thf(fact_8953_dvd__mult__sgn__iff,axiom,
% 0.26/0.65      ! [L: int,K: int,R2: int] :
% 0.26/0.65        ( ( dvd_dvd_int @ L @ ( times_times_int @ K @ ( sgn_sgn_int @ R2 ) ) )
% 0.26/0.65        = ( ( dvd_dvd_int @ L @ K )
% 0.26/0.65          | ( R2 = zero_zero_int ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % dvd_mult_sgn_iff
% 0.26/0.65  thf(fact_8954_dvd__sgn__mult__iff,axiom,
% 0.26/0.65      ! [L: int,R2: int,K: int] :
% 0.26/0.65        ( ( dvd_dvd_int @ L @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ K ) )
% 0.26/0.65        = ( ( dvd_dvd_int @ L @ K )
% 0.26/0.65          | ( R2 = zero_zero_int ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % dvd_sgn_mult_iff
% 0.26/0.65  thf(fact_8955_mult__sgn__dvd__iff,axiom,
% 0.26/0.65      ! [L: int,R2: int,K: int] :
% 0.26/0.65        ( ( dvd_dvd_int @ ( times_times_int @ L @ ( sgn_sgn_int @ R2 ) ) @ K )
% 0.26/0.65        = ( ( dvd_dvd_int @ L @ K )
% 0.26/0.65          & ( ( R2 = zero_zero_int )
% 0.26/0.65           => ( K = zero_zero_int ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % mult_sgn_dvd_iff
% 0.26/0.65  thf(fact_8956_sgn__mult__dvd__iff,axiom,
% 0.26/0.65      ! [R2: int,L: int,K: int] :
% 0.26/0.65        ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ L ) @ K )
% 0.26/0.65        = ( ( dvd_dvd_int @ L @ K )
% 0.26/0.65          & ( ( R2 = zero_zero_int )
% 0.26/0.65           => ( K = zero_zero_int ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sgn_mult_dvd_iff
% 0.26/0.65  thf(fact_8957_signed__take__bit__nonnegative__iff,axiom,
% 0.26/0.65      ! [N: nat,K: int] :
% 0.26/0.65        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 0.26/0.65        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % signed_take_bit_nonnegative_iff
% 0.26/0.65  thf(fact_8958_signed__take__bit__negative__iff,axiom,
% 0.26/0.65      ! [N: nat,K: int] :
% 0.26/0.65        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 0.26/0.65        = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % signed_take_bit_negative_iff
% 0.26/0.65  thf(fact_8959_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 0.26/0.65      ! [W: num,N: nat] :
% 0.26/0.65        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N ) )
% 0.26/0.65        = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % bit_minus_numeral_Bit0_Suc_iff
% 0.26/0.65  thf(fact_8960_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 0.26/0.65      ! [W: num,N: nat] :
% 0.26/0.65        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N ) )
% 0.26/0.65        = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % bit_minus_numeral_Bit1_Suc_iff
% 0.26/0.65  thf(fact_8961_bit__minus__numeral__int_I1_J,axiom,
% 0.26/0.65      ! [W: num,N: num] :
% 0.26/0.65        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 0.26/0.65        = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % bit_minus_numeral_int(1)
% 0.26/0.65  thf(fact_8962_bit__minus__numeral__int_I2_J,axiom,
% 0.26/0.65      ! [W: num,N: num] :
% 0.26/0.65        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 0.26/0.65        = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % bit_minus_numeral_int(2)
% 0.26/0.65  thf(fact_8963_bit__and__int__iff,axiom,
% 0.26/0.65      ! [K: int,L: int,N: nat] :
% 0.26/0.65        ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ N )
% 0.26/0.65        = ( ( bit_se1146084159140164899it_int @ K @ N )
% 0.26/0.65          & ( bit_se1146084159140164899it_int @ L @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % bit_and_int_iff
% 0.26/0.65  thf(fact_8964_bit__xor__int__iff,axiom,
% 0.26/0.65      ! [K: int,L: int,N: nat] :
% 0.26/0.65        ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ N )
% 0.26/0.65        = ( ( bit_se1146084159140164899it_int @ K @ N )
% 0.26/0.65         != ( bit_se1146084159140164899it_int @ L @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % bit_xor_int_iff
% 0.26/0.65  thf(fact_8965_bit__not__int__iff,axiom,
% 0.26/0.65      ! [K: int,N: nat] :
% 0.26/0.65        ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N )
% 0.26/0.65        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % bit_not_int_iff
% 0.26/0.65  thf(fact_8966_bit__or__int__iff,axiom,
% 0.26/0.65      ! [K: int,L: int,N: nat] :
% 0.26/0.65        ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ N )
% 0.26/0.65        = ( ( bit_se1146084159140164899it_int @ K @ N )
% 0.26/0.65          | ( bit_se1146084159140164899it_int @ L @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % bit_or_int_iff
% 0.26/0.65  thf(fact_8967_int__sgnE,axiom,
% 0.26/0.65      ! [K: int] :
% 0.26/0.65        ~ ! [N2: nat,L4: int] :
% 0.26/0.65            ( K
% 0.26/0.65           != ( times_times_int @ ( sgn_sgn_int @ L4 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % int_sgnE
% 0.26/0.65  thf(fact_8968_bit__not__int__iff_H,axiom,
% 0.26/0.65      ! [K: int,N: nat] :
% 0.26/0.65        ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 0.26/0.65        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % bit_not_int_iff'
% 0.26/0.65  thf(fact_8969_sgn__mod,axiom,
% 0.26/0.65      ! [L: int,K: int] :
% 0.26/0.65        ( ( L != zero_zero_int )
% 0.26/0.65       => ( ~ ( dvd_dvd_int @ L @ K )
% 0.26/0.65         => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L ) )
% 0.26/0.65            = ( sgn_sgn_int @ L ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sgn_mod
% 0.26/0.65  thf(fact_8970_zsgn__def,axiom,
% 0.26/0.65      ( sgn_sgn_int
% 0.26/0.65      = ( ^ [I4: int] : ( if_int @ ( I4 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I4 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % zsgn_def
% 0.26/0.65  thf(fact_8971_div__sgn__abs__cancel,axiom,
% 0.26/0.65      ! [V: int,K: int,L: int] :
% 0.26/0.65        ( ( V != zero_zero_int )
% 0.26/0.65       => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ K ) ) @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ L ) ) )
% 0.26/0.65          = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % div_sgn_abs_cancel
% 0.26/0.65  thf(fact_8972_bit__imp__take__bit__positive,axiom,
% 0.26/0.65      ! [N: nat,M: nat,K: int] :
% 0.26/0.65        ( ( ord_less_nat @ N @ M )
% 0.26/0.65       => ( ( bit_se1146084159140164899it_int @ K @ N )
% 0.26/0.65         => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % bit_imp_take_bit_positive
% 0.26/0.65  thf(fact_8973_bit__concat__bit__iff,axiom,
% 0.26/0.65      ! [M: nat,K: int,L: int,N: nat] :
% 0.26/0.65        ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L ) @ N )
% 0.26/0.65        = ( ( ( ord_less_nat @ N @ M )
% 0.26/0.65            & ( bit_se1146084159140164899it_int @ K @ N ) )
% 0.26/0.65          | ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.65            & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % bit_concat_bit_iff
% 0.26/0.65  thf(fact_8974_bit__minus__int__iff,axiom,
% 0.26/0.65      ! [K: int,N: nat] :
% 0.26/0.65        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 0.26/0.65        = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % bit_minus_int_iff
% 0.26/0.65  thf(fact_8975_signed__take__bit__eq__concat__bit,axiom,
% 0.26/0.65      ( bit_ri631733984087533419it_int
% 0.26/0.65      = ( ^ [N3: nat,K3: int] : ( bit_concat_bit @ N3 @ K3 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N3 ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % signed_take_bit_eq_concat_bit
% 0.26/0.65  thf(fact_8976_int__bit__bound,axiom,
% 0.26/0.65      ! [K: int] :
% 0.26/0.65        ~ ! [N2: nat] :
% 0.26/0.65            ( ! [M2: nat] :
% 0.26/0.65                ( ( ord_less_eq_nat @ N2 @ M2 )
% 0.26/0.65               => ( ( bit_se1146084159140164899it_int @ K @ M2 )
% 0.26/0.65                  = ( bit_se1146084159140164899it_int @ K @ N2 ) ) )
% 0.26/0.65           => ~ ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.26/0.65               => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 0.26/0.65                  = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % int_bit_bound
% 0.26/0.65  thf(fact_8977_bit__int__def,axiom,
% 0.26/0.65      ( bit_se1146084159140164899it_int
% 0.26/0.65      = ( ^ [K3: int,N3: nat] :
% 0.26/0.65            ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % bit_int_def
% 0.26/0.65  thf(fact_8978_eucl__rel__int__remainderI,axiom,
% 0.26/0.65      ! [R2: int,L: int,K: int,Q3: int] :
% 0.26/0.65        ( ( ( sgn_sgn_int @ R2 )
% 0.26/0.65          = ( sgn_sgn_int @ L ) )
% 0.26/0.65       => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L ) )
% 0.26/0.65         => ( ( K
% 0.26/0.65              = ( plus_plus_int @ ( times_times_int @ Q3 @ L ) @ R2 ) )
% 0.26/0.65           => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % eucl_rel_int_remainderI
% 0.26/0.65  thf(fact_8979_eucl__rel__int_Osimps,axiom,
% 0.26/0.65      ( eucl_rel_int
% 0.26/0.65      = ( ^ [A12: int,A23: int,A32: product_prod_int_int] :
% 0.26/0.65            ( ? [K3: int] :
% 0.26/0.65                ( ( A12 = K3 )
% 0.26/0.65                & ( A23 = zero_zero_int )
% 0.26/0.65                & ( A32
% 0.26/0.65                  = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 0.26/0.65            | ? [L2: int,K3: int,Q5: int] :
% 0.26/0.65                ( ( A12 = K3 )
% 0.26/0.65                & ( A23 = L2 )
% 0.26/0.65                & ( A32
% 0.26/0.65                  = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 0.26/0.65                & ( L2 != zero_zero_int )
% 0.26/0.65                & ( K3
% 0.26/0.65                  = ( times_times_int @ Q5 @ L2 ) ) )
% 0.26/0.65            | ? [R5: int,L2: int,K3: int,Q5: int] :
% 0.26/0.65                ( ( A12 = K3 )
% 0.26/0.65                & ( A23 = L2 )
% 0.26/0.65                & ( A32
% 0.26/0.65                  = ( product_Pair_int_int @ Q5 @ R5 ) )
% 0.26/0.65                & ( ( sgn_sgn_int @ R5 )
% 0.26/0.65                  = ( sgn_sgn_int @ L2 ) )
% 0.26/0.65                & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L2 ) )
% 0.26/0.65                & ( K3
% 0.26/0.65                  = ( plus_plus_int @ ( times_times_int @ Q5 @ L2 ) @ R5 ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % eucl_rel_int.simps
% 0.26/0.65  thf(fact_8980_eucl__rel__int_Ocases,axiom,
% 0.26/0.65      ! [A1: int,A22: int,A33: product_prod_int_int] :
% 0.26/0.65        ( ( eucl_rel_int @ A1 @ A22 @ A33 )
% 0.26/0.65       => ( ( ( A22 = zero_zero_int )
% 0.26/0.65           => ( A33
% 0.26/0.65             != ( product_Pair_int_int @ zero_zero_int @ A1 ) ) )
% 0.26/0.65         => ( ! [Q4: int] :
% 0.26/0.65                ( ( A33
% 0.26/0.65                  = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 0.26/0.65               => ( ( A22 != zero_zero_int )
% 0.26/0.65                 => ( A1
% 0.26/0.65                   != ( times_times_int @ Q4 @ A22 ) ) ) )
% 0.26/0.65           => ~ ! [R: int,Q4: int] :
% 0.26/0.65                  ( ( A33
% 0.26/0.65                    = ( product_Pair_int_int @ Q4 @ R ) )
% 0.26/0.65                 => ( ( ( sgn_sgn_int @ R )
% 0.26/0.65                      = ( sgn_sgn_int @ A22 ) )
% 0.26/0.65                   => ( ( ord_less_int @ ( abs_abs_int @ R ) @ ( abs_abs_int @ A22 ) )
% 0.26/0.65                     => ( A1
% 0.26/0.65                       != ( plus_plus_int @ ( times_times_int @ Q4 @ A22 ) @ R ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % eucl_rel_int.cases
% 0.26/0.65  thf(fact_8981_div__noneq__sgn__abs,axiom,
% 0.26/0.65      ! [L: int,K: int] :
% 0.26/0.65        ( ( L != zero_zero_int )
% 0.26/0.65       => ( ( ( sgn_sgn_int @ K )
% 0.26/0.65           != ( sgn_sgn_int @ L ) )
% 0.26/0.65         => ( ( divide_divide_int @ K @ L )
% 0.26/0.65            = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) )
% 0.26/0.65              @ ( zero_n2684676970156552555ol_int
% 0.26/0.65                @ ~ ( dvd_dvd_int @ L @ K ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % div_noneq_sgn_abs
% 0.26/0.65  thf(fact_8982_set__bit__eq,axiom,
% 0.26/0.65      ( bit_se7879613467334960850it_int
% 0.26/0.65      = ( ^ [N3: nat,K3: int] :
% 0.26/0.65            ( plus_plus_int @ K3
% 0.26/0.65            @ ( times_times_int
% 0.26/0.65              @ ( zero_n2684676970156552555ol_int
% 0.26/0.65                @ ~ ( bit_se1146084159140164899it_int @ K3 @ N3 ) )
% 0.26/0.65              @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % set_bit_eq
% 0.26/0.65  thf(fact_8983_unset__bit__eq,axiom,
% 0.26/0.65      ( bit_se4203085406695923979it_int
% 0.26/0.65      = ( ^ [N3: nat,K3: int] : ( minus_minus_int @ K3 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N3 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % unset_bit_eq
% 0.26/0.65  thf(fact_8984_take__bit__Suc__from__most,axiom,
% 0.26/0.65      ! [N: nat,K: int] :
% 0.26/0.65        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 0.26/0.65        = ( 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 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % take_bit_Suc_from_most
% 0.26/0.65  thf(fact_8985_divide__int__unfold,axiom,
% 0.26/0.65      ! [L: int,K: int,N: nat,M: nat] :
% 0.26/0.65        ( ( ( ( ( sgn_sgn_int @ L )
% 0.26/0.65              = zero_zero_int )
% 0.26/0.65            | ( ( sgn_sgn_int @ K )
% 0.26/0.65              = zero_zero_int )
% 0.26/0.65            | ( N = zero_zero_nat ) )
% 0.26/0.65         => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.26/0.65            = zero_zero_int ) )
% 0.26/0.65        & ( ~ ( ( ( sgn_sgn_int @ L )
% 0.26/0.65                = zero_zero_int )
% 0.26/0.65              | ( ( sgn_sgn_int @ K )
% 0.26/0.65                = zero_zero_int )
% 0.26/0.65              | ( N = zero_zero_nat ) )
% 0.26/0.65         => ( ( ( ( sgn_sgn_int @ K )
% 0.26/0.65                = ( sgn_sgn_int @ L ) )
% 0.26/0.65             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.26/0.65                = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 0.26/0.65            & ( ( ( sgn_sgn_int @ K )
% 0.26/0.65               != ( sgn_sgn_int @ L ) )
% 0.26/0.65             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.26/0.65                = ( uminus_uminus_int
% 0.26/0.65                  @ ( semiri1314217659103216013at_int
% 0.26/0.65                    @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 0.26/0.65                      @ ( zero_n2687167440665602831ol_nat
% 0.26/0.65                        @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % divide_int_unfold
% 0.26/0.65  thf(fact_8986_num_Osize__gen_I3_J,axiom,
% 0.26/0.65      ! [X32: num] :
% 0.26/0.65        ( ( size_num @ ( bit1 @ X32 ) )
% 0.26/0.65        = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % num.size_gen(3)
% 0.26/0.65  thf(fact_8987_num_Osize__gen_I2_J,axiom,
% 0.26/0.65      ! [X2: num] :
% 0.26/0.65        ( ( size_num @ ( bit0 @ X2 ) )
% 0.26/0.65        = ( plus_plus_nat @ ( size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % num.size_gen(2)
% 0.26/0.65  thf(fact_8988_arctan__inverse,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( X3 != zero_zero_real )
% 0.26/0.65       => ( ( arctan @ ( divide_divide_real @ one_one_real @ X3 ) )
% 0.26/0.65          = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X3 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % arctan_inverse
% 0.26/0.65  thf(fact_8989_mask__nat__positive__iff,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 0.26/0.65        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % mask_nat_positive_iff
% 0.26/0.65  thf(fact_8990_sgn__le__0__iff,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ ( sgn_sgn_real @ X3 ) @ zero_zero_real )
% 0.26/0.65        = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sgn_le_0_iff
% 0.26/0.65  thf(fact_8991_zero__le__sgn__iff,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X3 ) )
% 0.26/0.65        = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % zero_le_sgn_iff
% 0.26/0.65  thf(fact_8992_nat__mask__eq,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N ) )
% 0.26/0.65        = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % nat_mask_eq
% 0.26/0.65  thf(fact_8993_less__eq__mask,axiom,
% 0.26/0.65      ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % less_eq_mask
% 0.26/0.65  thf(fact_8994_not__bit__Suc__0__Suc,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % not_bit_Suc_0_Suc
% 0.26/0.65  thf(fact_8995_bit__Suc__0__iff,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.26/0.65        = ( N = zero_zero_nat ) ) ).
% 0.26/0.65  
% 0.26/0.65  % bit_Suc_0_iff
% 0.26/0.65  thf(fact_8996_mask__nonnegative__int,axiom,
% 0.26/0.65      ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % mask_nonnegative_int
% 0.26/0.65  thf(fact_8997_not__mask__negative__int,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 0.26/0.65  
% 0.26/0.65  % not_mask_negative_int
% 0.26/0.65  thf(fact_8998_not__bit__Suc__0__numeral,axiom,
% 0.26/0.65      ! [N: num] :
% 0.26/0.65        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % not_bit_Suc_0_numeral
% 0.26/0.65  thf(fact_8999_sgn__root,axiom,
% 0.26/0.65      ! [N: nat,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( sgn_sgn_real @ ( root @ N @ X3 ) )
% 0.26/0.65          = ( sgn_sgn_real @ X3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sgn_root
% 0.26/0.65  thf(fact_9000_less__mask,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.26/0.65       => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % less_mask
% 0.26/0.65  thf(fact_9001_cis__Arg,axiom,
% 0.26/0.65      ! [Z: complex] :
% 0.26/0.65        ( ( Z != zero_zero_complex )
% 0.26/0.65       => ( ( cis @ ( arg @ Z ) )
% 0.26/0.65          = ( sgn_sgn_complex @ Z ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cis_Arg
% 0.26/0.65  thf(fact_9002_sgn__real__def,axiom,
% 0.26/0.65      ( sgn_sgn_real
% 0.26/0.65      = ( ^ [A4: real] : ( if_real @ ( A4 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A4 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sgn_real_def
% 0.26/0.65  thf(fact_9003_bit__nat__iff,axiom,
% 0.26/0.65      ! [K: int,N: nat] :
% 0.26/0.65        ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 0.26/0.65        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.26/0.65          & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % bit_nat_iff
% 0.26/0.65  thf(fact_9004_sgn__power__injE,axiom,
% 0.26/0.65      ! [A: real,N: nat,X3: real,B: real] :
% 0.26/0.65        ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 0.26/0.65          = X3 )
% 0.26/0.65       => ( ( X3
% 0.26/0.65            = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 0.26/0.65         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65           => ( A = B ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sgn_power_injE
% 0.26/0.65  thf(fact_9005_take__bit__eq__mask__iff,axiom,
% 0.26/0.65      ! [N: nat,K: int] :
% 0.26/0.65        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.26/0.65          = ( bit_se2000444600071755411sk_int @ N ) )
% 0.26/0.65        = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 0.26/0.65          = zero_zero_int ) ) ).
% 0.26/0.65  
% 0.26/0.65  % take_bit_eq_mask_iff
% 0.26/0.65  thf(fact_9006_num_Osize__gen_I1_J,axiom,
% 0.26/0.65      ( ( size_num @ one )
% 0.26/0.65      = zero_zero_nat ) ).
% 0.26/0.65  
% 0.26/0.65  % num.size_gen(1)
% 0.26/0.65  thf(fact_9007_Suc__mask__eq__exp,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 0.26/0.65        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Suc_mask_eq_exp
% 0.26/0.65  thf(fact_9008_mask__nat__less__exp,axiom,
% 0.26/0.65      ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % mask_nat_less_exp
% 0.26/0.65  thf(fact_9009_bit__nat__def,axiom,
% 0.26/0.65      ( bit_se1148574629649215175it_nat
% 0.26/0.65      = ( ^ [M3: nat,N3: nat] :
% 0.26/0.65            ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % bit_nat_def
% 0.26/0.65  thf(fact_9010_sgn__power__root,axiom,
% 0.26/0.65      ! [N: nat,X3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X3 ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X3 ) ) @ N ) )
% 0.26/0.65          = X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sgn_power_root
% 0.26/0.65  thf(fact_9011_root__sgn__power,axiom,
% 0.26/0.65      ! [N: nat,Y3: real] :
% 0.26/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65       => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y3 ) @ ( power_power_real @ ( abs_abs_real @ Y3 ) @ N ) ) )
% 0.26/0.65          = Y3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % root_sgn_power
% 0.26/0.65  thf(fact_9012_cis__Arg__unique,axiom,
% 0.26/0.65      ! [Z: complex,X3: real] :
% 0.26/0.65        ( ( ( sgn_sgn_complex @ Z )
% 0.26/0.65          = ( cis @ X3 ) )
% 0.26/0.65       => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X3 )
% 0.26/0.65         => ( ( ord_less_eq_real @ X3 @ pi )
% 0.26/0.65           => ( ( arg @ Z )
% 0.26/0.65              = X3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cis_Arg_unique
% 0.26/0.65  thf(fact_9013_split__root,axiom,
% 0.26/0.65      ! [P: real > $o,N: nat,X3: real] :
% 0.26/0.65        ( ( P @ ( root @ N @ X3 ) )
% 0.26/0.65        = ( ( ( N = zero_zero_nat )
% 0.26/0.65           => ( P @ zero_zero_real ) )
% 0.26/0.65          & ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.65           => ! [Y: real] :
% 0.26/0.65                ( ( ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 0.26/0.65                  = X3 )
% 0.26/0.65               => ( P @ Y ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % split_root
% 0.26/0.65  thf(fact_9014_mask__nat__def,axiom,
% 0.26/0.65      ( bit_se2002935070580805687sk_nat
% 0.26/0.65      = ( ^ [N3: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % mask_nat_def
% 0.26/0.65  thf(fact_9015_mask__half__int,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.65        = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % mask_half_int
% 0.26/0.65  thf(fact_9016_mask__int__def,axiom,
% 0.26/0.65      ( bit_se2000444600071755411sk_int
% 0.26/0.65      = ( ^ [N3: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) @ one_one_int ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % mask_int_def
% 0.26/0.65  thf(fact_9017_Arg__correct,axiom,
% 0.26/0.65      ! [Z: complex] :
% 0.26/0.65        ( ( Z != zero_zero_complex )
% 0.26/0.65       => ( ( ( sgn_sgn_complex @ Z )
% 0.26/0.65            = ( cis @ ( arg @ Z ) ) )
% 0.26/0.65          & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 0.26/0.65          & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Arg_correct
% 0.26/0.65  thf(fact_9018_take__bit__eq__mask__iff__exp__dvd,axiom,
% 0.26/0.65      ! [N: nat,K: int] :
% 0.26/0.65        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.26/0.65          = ( bit_se2000444600071755411sk_int @ N ) )
% 0.26/0.65        = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % take_bit_eq_mask_iff_exp_dvd
% 0.26/0.65  thf(fact_9019_Arg__def,axiom,
% 0.26/0.65      ( arg
% 0.26/0.65      = ( ^ [Z6: complex] :
% 0.26/0.65            ( if_real @ ( Z6 = zero_zero_complex ) @ zero_zero_real
% 0.26/0.65            @ ( fChoice_real
% 0.26/0.65              @ ^ [A4: real] :
% 0.26/0.65                  ( ( ( sgn_sgn_complex @ Z6 )
% 0.26/0.65                    = ( cis @ A4 ) )
% 0.26/0.65                  & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A4 )
% 0.26/0.65                  & ( ord_less_eq_real @ A4 @ pi ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Arg_def
% 0.26/0.65  thf(fact_9020_cis__multiple__2pi,axiom,
% 0.26/0.65      ! [N: real] :
% 0.26/0.65        ( ( member_real @ N @ ring_1_Ints_real )
% 0.26/0.65       => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 0.26/0.65          = one_one_complex ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cis_multiple_2pi
% 0.26/0.65  thf(fact_9021_horner__sum__of__bool__2__less,axiom,
% 0.26/0.65      ! [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 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % horner_sum_of_bool_2_less
% 0.26/0.65  thf(fact_9022_push__bit__nonnegative__int__iff,axiom,
% 0.26/0.65      ! [N: nat,K: int] :
% 0.26/0.65        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 0.26/0.65        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.26/0.65  
% 0.26/0.65  % push_bit_nonnegative_int_iff
% 0.26/0.65  thf(fact_9023_push__bit__negative__int__iff,axiom,
% 0.26/0.65      ! [N: nat,K: int] :
% 0.26/0.65        ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 0.26/0.65        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.26/0.65  
% 0.26/0.65  % push_bit_negative_int_iff
% 0.26/0.65  thf(fact_9024_concat__bit__of__zero__1,axiom,
% 0.26/0.65      ! [N: nat,L: int] :
% 0.26/0.65        ( ( bit_concat_bit @ N @ zero_zero_int @ L )
% 0.26/0.65        = ( bit_se545348938243370406it_int @ N @ L ) ) ).
% 0.26/0.65  
% 0.26/0.65  % concat_bit_of_zero_1
% 0.26/0.65  thf(fact_9025_push__bit__of__Suc__0,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.26/0.65        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % push_bit_of_Suc_0
% 0.26/0.65  thf(fact_9026_push__bit__nat__eq,axiom,
% 0.26/0.65      ! [N: nat,K: int] :
% 0.26/0.65        ( ( bit_se547839408752420682it_nat @ N @ ( nat2 @ K ) )
% 0.26/0.65        = ( nat2 @ ( bit_se545348938243370406it_int @ N @ K ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % push_bit_nat_eq
% 0.26/0.65  thf(fact_9027_set__bit__nat__def,axiom,
% 0.26/0.65      ( bit_se7882103937844011126it_nat
% 0.26/0.65      = ( ^ [M3: nat,N3: nat] : ( bit_se1412395901928357646or_nat @ N3 @ ( bit_se547839408752420682it_nat @ M3 @ one_one_nat ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % set_bit_nat_def
% 0.26/0.65  thf(fact_9028_flip__bit__nat__def,axiom,
% 0.26/0.65      ( bit_se2161824704523386999it_nat
% 0.26/0.65      = ( ^ [M3: nat,N3: nat] : ( bit_se6528837805403552850or_nat @ N3 @ ( bit_se547839408752420682it_nat @ M3 @ one_one_nat ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % flip_bit_nat_def
% 0.26/0.65  thf(fact_9029_bit__push__bit__iff__int,axiom,
% 0.26/0.65      ! [M: nat,K: int,N: nat] :
% 0.26/0.65        ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 0.26/0.65        = ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.65          & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % bit_push_bit_iff_int
% 0.26/0.65  thf(fact_9030_bit__push__bit__iff__nat,axiom,
% 0.26/0.65      ! [M: nat,Q3: nat,N: nat] :
% 0.26/0.65        ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q3 ) @ N )
% 0.26/0.65        = ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.65          & ( bit_se1148574629649215175it_nat @ Q3 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % bit_push_bit_iff_nat
% 0.26/0.65  thf(fact_9031_concat__bit__eq,axiom,
% 0.26/0.65      ( bit_concat_bit
% 0.26/0.65      = ( ^ [N3: nat,K3: int,L2: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N3 @ K3 ) @ ( bit_se545348938243370406it_int @ N3 @ L2 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % concat_bit_eq
% 0.26/0.65  thf(fact_9032_concat__bit__def,axiom,
% 0.26/0.65      ( bit_concat_bit
% 0.26/0.65      = ( ^ [N3: nat,K3: int,L2: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N3 @ K3 ) @ ( bit_se545348938243370406it_int @ N3 @ L2 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % concat_bit_def
% 0.26/0.65  thf(fact_9033_set__bit__int__def,axiom,
% 0.26/0.65      ( bit_se7879613467334960850it_int
% 0.26/0.65      = ( ^ [N3: nat,K3: int] : ( bit_se1409905431419307370or_int @ K3 @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % set_bit_int_def
% 0.26/0.65  thf(fact_9034_flip__bit__int__def,axiom,
% 0.26/0.65      ( bit_se2159334234014336723it_int
% 0.26/0.65      = ( ^ [N3: nat,K3: int] : ( bit_se6526347334894502574or_int @ K3 @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % flip_bit_int_def
% 0.26/0.65  thf(fact_9035_sin__times__pi__eq__0,axiom,
% 0.26/0.65      ! [X3: real] :
% 0.26/0.65        ( ( ( sin_real @ ( times_times_real @ X3 @ pi ) )
% 0.26/0.65          = zero_zero_real )
% 0.26/0.65        = ( member_real @ X3 @ ring_1_Ints_real ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sin_times_pi_eq_0
% 0.26/0.65  thf(fact_9036_unset__bit__int__def,axiom,
% 0.26/0.65      ( bit_se4203085406695923979it_int
% 0.26/0.65      = ( ^ [N3: nat,K3: int] : ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % unset_bit_int_def
% 0.26/0.65  thf(fact_9037_push__bit__nat__def,axiom,
% 0.26/0.65      ( bit_se547839408752420682it_nat
% 0.26/0.65      = ( ^ [N3: nat,M3: nat] : ( times_times_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % push_bit_nat_def
% 0.26/0.65  thf(fact_9038_push__bit__int__def,axiom,
% 0.26/0.65      ( bit_se545348938243370406it_int
% 0.26/0.65      = ( ^ [N3: nat,K3: int] : ( times_times_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % push_bit_int_def
% 0.26/0.65  thf(fact_9039_push__bit__minus__one,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.65        = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % push_bit_minus_one
% 0.26/0.65  thf(fact_9040_sin__integer__2pi,axiom,
% 0.26/0.65      ! [N: real] :
% 0.26/0.65        ( ( member_real @ N @ ring_1_Ints_real )
% 0.26/0.65       => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 0.26/0.65          = zero_zero_real ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sin_integer_2pi
% 0.26/0.65  thf(fact_9041_cos__integer__2pi,axiom,
% 0.26/0.65      ! [N: real] :
% 0.26/0.65        ( ( member_real @ N @ ring_1_Ints_real )
% 0.26/0.65       => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 0.26/0.65          = one_one_real ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cos_integer_2pi
% 0.26/0.65  thf(fact_9042_int__of__nat__def,axiom,
% 0.26/0.65      code_T6385005292777649522of_nat = semiri1314217659103216013at_int ).
% 0.26/0.65  
% 0.26/0.65  % int_of_nat_def
% 0.26/0.65  thf(fact_9043_Cauchy__iff2,axiom,
% 0.26/0.65      ( topolo4055970368930404560y_real
% 0.26/0.65      = ( ^ [X8: nat > real] :
% 0.26/0.65          ! [J3: nat] :
% 0.26/0.65          ? [M9: nat] :
% 0.26/0.65          ! [M3: nat] :
% 0.26/0.65            ( ( ord_less_eq_nat @ M9 @ M3 )
% 0.26/0.65           => ! [N3: nat] :
% 0.26/0.65                ( ( ord_less_eq_nat @ M9 @ N3 )
% 0.26/0.65               => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X8 @ M3 ) @ ( X8 @ N3 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Cauchy_iff2
% 0.26/0.65  thf(fact_9044_Sum__Ico__nat,axiom,
% 0.26/0.65      ! [M: nat,N: nat] :
% 0.26/0.65        ( ( groups3542108847815614940at_nat
% 0.26/0.65          @ ^ [X: nat] : X
% 0.26/0.65          @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 0.26/0.65        = ( 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 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Sum_Ico_nat
% 0.26/0.65  thf(fact_9045_ex__nat__less__eq,axiom,
% 0.26/0.65      ! [N: nat,P: nat > $o] :
% 0.26/0.65        ( ( ? [M3: nat] :
% 0.26/0.65              ( ( ord_less_nat @ M3 @ N )
% 0.26/0.65              & ( P @ M3 ) ) )
% 0.26/0.65        = ( ? [X: nat] :
% 0.26/0.65              ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.26/0.65              & ( P @ X ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % ex_nat_less_eq
% 0.26/0.65  thf(fact_9046_all__nat__less__eq,axiom,
% 0.26/0.65      ! [N: nat,P: nat > $o] :
% 0.26/0.65        ( ( ! [M3: nat] :
% 0.26/0.65              ( ( ord_less_nat @ M3 @ N )
% 0.26/0.65             => ( P @ M3 ) ) )
% 0.26/0.65        = ( ! [X: nat] :
% 0.26/0.65              ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.26/0.65             => ( P @ X ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % all_nat_less_eq
% 0.26/0.65  thf(fact_9047_lessThan__atLeast0,axiom,
% 0.26/0.65      ( set_ord_lessThan_nat
% 0.26/0.65      = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 0.26/0.65  
% 0.26/0.65  % lessThan_atLeast0
% 0.26/0.65  thf(fact_9048_atLeastLessThan0,axiom,
% 0.26/0.65      ! [M: nat] :
% 0.26/0.65        ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 0.26/0.65        = bot_bot_set_nat ) ).
% 0.26/0.65  
% 0.26/0.65  % atLeastLessThan0
% 0.26/0.65  thf(fact_9049_atLeast0__lessThan__Suc,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.26/0.65        = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % atLeast0_lessThan_Suc
% 0.26/0.65  thf(fact_9050_subset__eq__atLeast0__lessThan__finite,axiom,
% 0.26/0.65      ! [N4: set_nat,N: nat] :
% 0.26/0.65        ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.26/0.65       => ( finite_finite_nat @ N4 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % subset_eq_atLeast0_lessThan_finite
% 0.26/0.65  thf(fact_9051_atLeastLessThanSuc,axiom,
% 0.26/0.65      ! [M: nat,N: nat] :
% 0.26/0.65        ( ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.65         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 0.26/0.65            = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 0.26/0.65        & ( ~ ( ord_less_eq_nat @ M @ N )
% 0.26/0.65         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 0.26/0.65            = bot_bot_set_nat ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % atLeastLessThanSuc
% 0.26/0.65  thf(fact_9052_prod__Suc__fact,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.26/0.65        = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % prod_Suc_fact
% 0.26/0.65  thf(fact_9053_prod__Suc__Suc__fact,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.26/0.65        = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % prod_Suc_Suc_fact
% 0.26/0.65  thf(fact_9054_atLeastLessThan__nat__numeral,axiom,
% 0.26/0.65      ! [M: nat,K: num] :
% 0.26/0.65        ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 0.26/0.65         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 0.26/0.65            = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 0.26/0.65        & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 0.26/0.65         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 0.26/0.65            = bot_bot_set_nat ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % atLeastLessThan_nat_numeral
% 0.26/0.65  thf(fact_9055_atLeast1__lessThan__eq__remove0,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.26/0.65        = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % atLeast1_lessThan_eq_remove0
% 0.26/0.65  thf(fact_9056_sum__power2,axiom,
% 0.26/0.65      ! [K: nat] :
% 0.26/0.65        ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 0.26/0.65        = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sum_power2
% 0.26/0.65  thf(fact_9057_Chebyshev__sum__upper__nat,axiom,
% 0.26/0.65      ! [N: nat,A: nat > nat,B: nat > nat] :
% 0.26/0.65        ( ! [I3: nat,J2: nat] :
% 0.26/0.65            ( ( ord_less_eq_nat @ I3 @ J2 )
% 0.26/0.65           => ( ( ord_less_nat @ J2 @ N )
% 0.26/0.65             => ( ord_less_eq_nat @ ( A @ I3 ) @ ( A @ J2 ) ) ) )
% 0.26/0.65       => ( ! [I3: nat,J2: nat] :
% 0.26/0.65              ( ( ord_less_eq_nat @ I3 @ J2 )
% 0.26/0.65             => ( ( ord_less_nat @ J2 @ N )
% 0.26/0.65               => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I3 ) ) ) )
% 0.26/0.65         => ( ord_less_eq_nat
% 0.26/0.65            @ ( times_times_nat @ N
% 0.26/0.65              @ ( groups3542108847815614940at_nat
% 0.26/0.65                @ ^ [I4: nat] : ( times_times_nat @ ( A @ I4 ) @ ( B @ I4 ) )
% 0.26/0.65                @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 0.26/0.65            @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Chebyshev_sum_upper_nat
% 0.26/0.65  thf(fact_9058_finite__atLeastZeroLessThan__int,axiom,
% 0.26/0.65      ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 0.26/0.65  
% 0.26/0.65  % finite_atLeastZeroLessThan_int
% 0.26/0.65  thf(fact_9059_VEBT_Osize_I3_J,axiom,
% 0.26/0.65      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 0.26/0.65        ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 0.26/0.65        = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % VEBT.size(3)
% 0.26/0.65  thf(fact_9060_valid__eq,axiom,
% 0.26/0.65      vEBT_VEBT_valid = vEBT_invar_vebt ).
% 0.26/0.65  
% 0.26/0.65  % valid_eq
% 0.26/0.65  thf(fact_9061_valid__eq1,axiom,
% 0.26/0.65      ! [T: vEBT_VEBT,D3: nat] :
% 0.26/0.65        ( ( vEBT_invar_vebt @ T @ D3 )
% 0.26/0.65       => ( vEBT_VEBT_valid @ T @ D3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % valid_eq1
% 0.26/0.65  thf(fact_9062_valid__eq2,axiom,
% 0.26/0.65      ! [T: vEBT_VEBT,D3: nat] :
% 0.26/0.65        ( ( vEBT_VEBT_valid @ T @ D3 )
% 0.26/0.65       => ( vEBT_invar_vebt @ T @ D3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % valid_eq2
% 0.26/0.65  thf(fact_9063_VEBT_Osize__gen_I1_J,axiom,
% 0.26/0.65      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 0.26/0.65        ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 0.26/0.65        = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % VEBT.size_gen(1)
% 0.26/0.65  thf(fact_9064_Code__Target__Int_Opositive__def,axiom,
% 0.26/0.65      code_Target_positive = numeral_numeral_int ).
% 0.26/0.65  
% 0.26/0.65  % Code_Target_Int.positive_def
% 0.26/0.65  thf(fact_9065_VEBT_Osize__gen_I2_J,axiom,
% 0.26/0.65      ! [X21: $o,X222: $o] :
% 0.26/0.65        ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 0.26/0.65        = zero_zero_nat ) ).
% 0.26/0.65  
% 0.26/0.65  % VEBT.size_gen(2)
% 0.26/0.65  thf(fact_9066_csqrt_Osimps_I1_J,axiom,
% 0.26/0.65      ! [Z: complex] :
% 0.26/0.65        ( ( re @ ( csqrt @ Z ) )
% 0.26/0.65        = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % csqrt.simps(1)
% 0.26/0.65  thf(fact_9067_divmod__step__integer__def,axiom,
% 0.26/0.65      ( unique4921790084139445826nteger
% 0.26/0.65      = ( ^ [L2: num] :
% 0.26/0.65            ( produc6916734918728496179nteger
% 0.26/0.65            @ ^ [Q5: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % divmod_step_integer_def
% 0.26/0.65  thf(fact_9068_complex__Re__of__nat,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( re @ ( semiri8010041392384452111omplex @ N ) )
% 0.26/0.65        = ( semiri5074537144036343181t_real @ N ) ) ).
% 0.26/0.65  
% 0.26/0.65  % complex_Re_of_nat
% 0.26/0.65  thf(fact_9069_complex__Re__numeral,axiom,
% 0.26/0.65      ! [V: num] :
% 0.26/0.65        ( ( re @ ( numera6690914467698888265omplex @ V ) )
% 0.26/0.65        = ( numeral_numeral_real @ V ) ) ).
% 0.26/0.65  
% 0.26/0.65  % complex_Re_numeral
% 0.26/0.65  thf(fact_9070_Re__divide__of__nat,axiom,
% 0.26/0.65      ! [Z: complex,N: nat] :
% 0.26/0.65        ( ( re @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N ) ) )
% 0.26/0.65        = ( divide_divide_real @ ( re @ Z ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Re_divide_of_nat
% 0.26/0.65  thf(fact_9071_Re__divide__numeral,axiom,
% 0.26/0.65      ! [Z: complex,W: num] :
% 0.26/0.65        ( ( re @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 0.26/0.65        = ( divide_divide_real @ ( re @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Re_divide_numeral
% 0.26/0.65  thf(fact_9072_cos__Arg__i__mult__zero,axiom,
% 0.26/0.65      ! [Y3: complex] :
% 0.26/0.65        ( ( Y3 != zero_zero_complex )
% 0.26/0.65       => ( ( ( re @ Y3 )
% 0.26/0.65            = zero_zero_real )
% 0.26/0.65         => ( ( cos_real @ ( arg @ Y3 ) )
% 0.26/0.65            = zero_zero_real ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cos_Arg_i_mult_zero
% 0.26/0.65  thf(fact_9073_sgn__integer__code,axiom,
% 0.26/0.65      ( sgn_sgn_Code_integer
% 0.26/0.65      = ( ^ [K3: code_integer] : ( if_Code_integer @ ( K3 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sgn_integer_code
% 0.26/0.65  thf(fact_9074_times__integer__code_I2_J,axiom,
% 0.26/0.65      ! [L: code_integer] :
% 0.26/0.65        ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L )
% 0.26/0.65        = zero_z3403309356797280102nteger ) ).
% 0.26/0.65  
% 0.26/0.65  % times_integer_code(2)
% 0.26/0.65  thf(fact_9075_times__integer__code_I1_J,axiom,
% 0.26/0.65      ! [K: code_integer] :
% 0.26/0.65        ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 0.26/0.65        = zero_z3403309356797280102nteger ) ).
% 0.26/0.65  
% 0.26/0.65  % times_integer_code(1)
% 0.26/0.65  thf(fact_9076_minus__integer__code_I2_J,axiom,
% 0.26/0.65      ! [L: code_integer] :
% 0.26/0.65        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L )
% 0.26/0.65        = ( uminus1351360451143612070nteger @ L ) ) ).
% 0.26/0.65  
% 0.26/0.65  % minus_integer_code(2)
% 0.26/0.65  thf(fact_9077_minus__integer__code_I1_J,axiom,
% 0.26/0.65      ! [K: code_integer] :
% 0.26/0.65        ( ( minus_8373710615458151222nteger @ K @ zero_z3403309356797280102nteger )
% 0.26/0.65        = K ) ).
% 0.26/0.65  
% 0.26/0.65  % minus_integer_code(1)
% 0.26/0.65  thf(fact_9078_less__eq__integer__code_I1_J,axiom,
% 0.26/0.65      ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 0.26/0.65  
% 0.26/0.65  % less_eq_integer_code(1)
% 0.26/0.65  thf(fact_9079_plus__integer__code_I2_J,axiom,
% 0.26/0.65      ! [L: code_integer] :
% 0.26/0.65        ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L )
% 0.26/0.65        = L ) ).
% 0.26/0.65  
% 0.26/0.65  % plus_integer_code(2)
% 0.26/0.65  thf(fact_9080_plus__integer__code_I1_J,axiom,
% 0.26/0.65      ! [K: code_integer] :
% 0.26/0.65        ( ( plus_p5714425477246183910nteger @ K @ zero_z3403309356797280102nteger )
% 0.26/0.65        = K ) ).
% 0.26/0.65  
% 0.26/0.65  % plus_integer_code(1)
% 0.26/0.65  thf(fact_9081_imaginary__unit_Osimps_I1_J,axiom,
% 0.26/0.65      ( ( re @ imaginary_unit )
% 0.26/0.65      = zero_zero_real ) ).
% 0.26/0.65  
% 0.26/0.65  % imaginary_unit.simps(1)
% 0.26/0.65  thf(fact_9082_complex__Re__le__cmod,axiom,
% 0.26/0.65      ! [X3: complex] : ( ord_less_eq_real @ ( re @ X3 ) @ ( real_V1022390504157884413omplex @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % complex_Re_le_cmod
% 0.26/0.65  thf(fact_9083_zero__complex_Osimps_I1_J,axiom,
% 0.26/0.65      ( ( re @ zero_zero_complex )
% 0.26/0.65      = zero_zero_real ) ).
% 0.26/0.65  
% 0.26/0.65  % zero_complex.simps(1)
% 0.26/0.65  thf(fact_9084_abs__Re__le__cmod,axiom,
% 0.26/0.65      ! [X3: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X3 ) ) @ ( real_V1022390504157884413omplex @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % abs_Re_le_cmod
% 0.26/0.65  thf(fact_9085_Re__csqrt,axiom,
% 0.26/0.65      ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Re_csqrt
% 0.26/0.65  thf(fact_9086_zero__natural_Orsp,axiom,
% 0.26/0.65      zero_zero_nat = zero_zero_nat ).
% 0.26/0.65  
% 0.26/0.65  % zero_natural.rsp
% 0.26/0.65  thf(fact_9087_zero__integer_Orsp,axiom,
% 0.26/0.65      zero_zero_int = zero_zero_int ).
% 0.26/0.65  
% 0.26/0.65  % zero_integer.rsp
% 0.26/0.65  thf(fact_9088_cmod__plus__Re__le__0__iff,axiom,
% 0.26/0.65      ! [Z: complex] :
% 0.26/0.65        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 0.26/0.65        = ( ( re @ Z )
% 0.26/0.65          = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cmod_plus_Re_le_0_iff
% 0.26/0.65  thf(fact_9089_cos__n__Re__cis__pow__n,axiom,
% 0.26/0.65      ! [N: nat,A: real] :
% 0.26/0.65        ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 0.26/0.65        = ( re @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cos_n_Re_cis_pow_n
% 0.26/0.65  thf(fact_9090_csqrt_Ocode,axiom,
% 0.26/0.65      ( csqrt
% 0.26/0.65      = ( ^ [Z6: complex] :
% 0.26/0.65            ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z6 ) @ ( re @ Z6 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.65            @ ( times_times_real
% 0.26/0.65              @ ( if_real
% 0.26/0.65                @ ( ( im @ Z6 )
% 0.26/0.65                  = zero_zero_real )
% 0.26/0.65                @ one_one_real
% 0.26/0.65                @ ( sgn_sgn_real @ ( im @ Z6 ) ) )
% 0.26/0.65              @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z6 ) @ ( re @ Z6 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % csqrt.code
% 0.26/0.65  thf(fact_9091_csqrt_Osimps_I2_J,axiom,
% 0.26/0.65      ! [Z: complex] :
% 0.26/0.65        ( ( im @ ( csqrt @ Z ) )
% 0.26/0.65        = ( times_times_real
% 0.26/0.65          @ ( if_real
% 0.26/0.65            @ ( ( im @ Z )
% 0.26/0.65              = zero_zero_real )
% 0.26/0.65            @ one_one_real
% 0.26/0.65            @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 0.26/0.65          @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % csqrt.simps(2)
% 0.26/0.65  thf(fact_9092_integer__of__int__code,axiom,
% 0.26/0.65      ( code_integer_of_int
% 0.26/0.65      = ( ^ [K3: int] :
% 0.26/0.65            ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 0.26/0.65            @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 0.26/0.65              @ ( if_Code_integer
% 0.26/0.65                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.26/0.65                  = zero_zero_int )
% 0.26/0.65                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.26/0.65                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % integer_of_int_code
% 0.26/0.65  thf(fact_9093_complex__Im__fact,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( im @ ( semiri5044797733671781792omplex @ N ) )
% 0.26/0.65        = zero_zero_real ) ).
% 0.26/0.65  
% 0.26/0.65  % complex_Im_fact
% 0.26/0.65  thf(fact_9094_complex__Im__of__int,axiom,
% 0.26/0.65      ! [Z: int] :
% 0.26/0.65        ( ( im @ ( ring_17405671764205052669omplex @ Z ) )
% 0.26/0.65        = zero_zero_real ) ).
% 0.26/0.65  
% 0.26/0.65  % complex_Im_of_int
% 0.26/0.65  thf(fact_9095_Im__complex__of__real,axiom,
% 0.26/0.65      ! [Z: real] :
% 0.26/0.65        ( ( im @ ( real_V4546457046886955230omplex @ Z ) )
% 0.26/0.65        = zero_zero_real ) ).
% 0.26/0.65  
% 0.26/0.65  % Im_complex_of_real
% 0.26/0.65  thf(fact_9096_Im__power__real,axiom,
% 0.26/0.65      ! [X3: complex,N: nat] :
% 0.26/0.65        ( ( ( im @ X3 )
% 0.26/0.65          = zero_zero_real )
% 0.26/0.65       => ( ( im @ ( power_power_complex @ X3 @ N ) )
% 0.26/0.65          = zero_zero_real ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Im_power_real
% 0.26/0.65  thf(fact_9097_complex__Im__numeral,axiom,
% 0.26/0.65      ! [V: num] :
% 0.26/0.65        ( ( im @ ( numera6690914467698888265omplex @ V ) )
% 0.26/0.65        = zero_zero_real ) ).
% 0.26/0.65  
% 0.26/0.65  % complex_Im_numeral
% 0.26/0.65  thf(fact_9098_complex__Im__of__nat,axiom,
% 0.26/0.65      ! [N: nat] :
% 0.26/0.65        ( ( im @ ( semiri8010041392384452111omplex @ N ) )
% 0.26/0.65        = zero_zero_real ) ).
% 0.26/0.65  
% 0.26/0.65  % complex_Im_of_nat
% 0.26/0.65  thf(fact_9099_Re__power__real,axiom,
% 0.26/0.65      ! [X3: complex,N: nat] :
% 0.26/0.65        ( ( ( im @ X3 )
% 0.26/0.65          = zero_zero_real )
% 0.26/0.65       => ( ( re @ ( power_power_complex @ X3 @ N ) )
% 0.26/0.65          = ( power_power_real @ ( re @ X3 ) @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Re_power_real
% 0.26/0.65  thf(fact_9100_Im__divide__numeral,axiom,
% 0.26/0.65      ! [Z: complex,W: num] :
% 0.26/0.65        ( ( im @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 0.26/0.65        = ( divide_divide_real @ ( im @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Im_divide_numeral
% 0.26/0.65  thf(fact_9101_Im__divide__of__nat,axiom,
% 0.26/0.65      ! [Z: complex,N: nat] :
% 0.26/0.65        ( ( im @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N ) ) )
% 0.26/0.65        = ( divide_divide_real @ ( im @ Z ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Im_divide_of_nat
% 0.26/0.65  thf(fact_9102_csqrt__of__real__nonneg,axiom,
% 0.26/0.65      ! [X3: complex] :
% 0.26/0.65        ( ( ( im @ X3 )
% 0.26/0.65          = zero_zero_real )
% 0.26/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X3 ) )
% 0.26/0.65         => ( ( csqrt @ X3 )
% 0.26/0.65            = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X3 ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % csqrt_of_real_nonneg
% 0.26/0.65  thf(fact_9103_csqrt__minus,axiom,
% 0.26/0.65      ! [X3: complex] :
% 0.26/0.65        ( ( ( ord_less_real @ ( im @ X3 ) @ zero_zero_real )
% 0.26/0.65          | ( ( ( im @ X3 )
% 0.26/0.65              = zero_zero_real )
% 0.26/0.65            & ( ord_less_eq_real @ zero_zero_real @ ( re @ X3 ) ) ) )
% 0.26/0.65       => ( ( csqrt @ ( uminus1482373934393186551omplex @ X3 ) )
% 0.26/0.65          = ( times_times_complex @ imaginary_unit @ ( csqrt @ X3 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % csqrt_minus
% 0.26/0.65  thf(fact_9104_csqrt__of__real__nonpos,axiom,
% 0.26/0.65      ! [X3: complex] :
% 0.26/0.65        ( ( ( im @ X3 )
% 0.26/0.65          = zero_zero_real )
% 0.26/0.65       => ( ( ord_less_eq_real @ ( re @ X3 ) @ zero_zero_real )
% 0.26/0.65         => ( ( csqrt @ X3 )
% 0.26/0.65            = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X3 ) ) ) ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % csqrt_of_real_nonpos
% 0.26/0.65  thf(fact_9105_zero__integer__def,axiom,
% 0.26/0.65      ( zero_z3403309356797280102nteger
% 0.26/0.65      = ( code_integer_of_int @ zero_zero_int ) ) ).
% 0.26/0.65  
% 0.26/0.65  % zero_integer_def
% 0.26/0.65  thf(fact_9106_uminus__integer__code_I1_J,axiom,
% 0.26/0.65      ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 0.26/0.65      = zero_z3403309356797280102nteger ) ).
% 0.26/0.65  
% 0.26/0.65  % uminus_integer_code(1)
% 0.26/0.65  thf(fact_9107_abs__integer__code,axiom,
% 0.26/0.65      ( abs_abs_Code_integer
% 0.26/0.65      = ( ^ [K3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K3 ) @ K3 ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % abs_integer_code
% 0.26/0.65  thf(fact_9108_less__integer__code_I1_J,axiom,
% 0.26/0.65      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 0.26/0.65  
% 0.26/0.65  % less_integer_code(1)
% 0.26/0.65  thf(fact_9109_less__integer_Oabs__eq,axiom,
% 0.26/0.65      ! [Xa: int,X3: int] :
% 0.26/0.65        ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X3 ) )
% 0.26/0.65        = ( ord_less_int @ Xa @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % less_integer.abs_eq
% 0.26/0.65  thf(fact_9110_zero__complex_Osimps_I2_J,axiom,
% 0.26/0.65      ( ( im @ zero_zero_complex )
% 0.26/0.65      = zero_zero_real ) ).
% 0.26/0.65  
% 0.26/0.65  % zero_complex.simps(2)
% 0.26/0.65  thf(fact_9111_one__complex_Osimps_I2_J,axiom,
% 0.26/0.65      ( ( im @ one_one_complex )
% 0.26/0.65      = zero_zero_real ) ).
% 0.26/0.65  
% 0.26/0.65  % one_complex.simps(2)
% 0.26/0.65  thf(fact_9112_less__eq__integer_Oabs__eq,axiom,
% 0.26/0.65      ! [Xa: int,X3: int] :
% 0.26/0.65        ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X3 ) )
% 0.26/0.65        = ( ord_less_eq_int @ Xa @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % less_eq_integer.abs_eq
% 0.26/0.65  thf(fact_9113_complex__is__Int__iff,axiom,
% 0.26/0.65      ! [Z: complex] :
% 0.26/0.65        ( ( member_complex @ Z @ ring_1_Ints_complex )
% 0.26/0.65        = ( ( ( im @ Z )
% 0.26/0.65            = zero_zero_real )
% 0.26/0.65          & ? [I4: int] :
% 0.26/0.65              ( ( re @ Z )
% 0.26/0.65              = ( ring_1_of_int_real @ I4 ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % complex_is_Int_iff
% 0.26/0.65  thf(fact_9114_abs__Im__le__cmod,axiom,
% 0.26/0.65      ! [X3: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X3 ) ) @ ( real_V1022390504157884413omplex @ X3 ) ) ).
% 0.26/0.65  
% 0.26/0.65  % abs_Im_le_cmod
% 0.26/0.65  thf(fact_9115_Im__eq__0,axiom,
% 0.26/0.65      ! [Z: complex] :
% 0.26/0.65        ( ( ( abs_abs_real @ ( re @ Z ) )
% 0.26/0.65          = ( real_V1022390504157884413omplex @ Z ) )
% 0.26/0.65       => ( ( im @ Z )
% 0.26/0.65          = zero_zero_real ) ) ).
% 0.26/0.65  
% 0.26/0.65  % Im_eq_0
% 0.26/0.65  thf(fact_9116_cmod__eq__Im,axiom,
% 0.26/0.65      ! [Z: complex] :
% 0.26/0.65        ( ( ( re @ Z )
% 0.26/0.65          = zero_zero_real )
% 0.26/0.65       => ( ( real_V1022390504157884413omplex @ Z )
% 0.26/0.65          = ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cmod_eq_Im
% 0.26/0.65  thf(fact_9117_cmod__eq__Re,axiom,
% 0.26/0.65      ! [Z: complex] :
% 0.26/0.65        ( ( ( im @ Z )
% 0.26/0.65          = zero_zero_real )
% 0.26/0.65       => ( ( real_V1022390504157884413omplex @ Z )
% 0.26/0.65          = ( abs_abs_real @ ( re @ Z ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cmod_eq_Re
% 0.26/0.65  thf(fact_9118_cmod__Re__le__iff,axiom,
% 0.26/0.65      ! [X3: complex,Y3: complex] :
% 0.26/0.65        ( ( ( im @ X3 )
% 0.26/0.65          = ( im @ Y3 ) )
% 0.26/0.65       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y3 ) )
% 0.26/0.65          = ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X3 ) ) @ ( abs_abs_real @ ( re @ Y3 ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cmod_Re_le_iff
% 0.26/0.65  thf(fact_9119_cmod__Im__le__iff,axiom,
% 0.26/0.65      ! [X3: complex,Y3: complex] :
% 0.26/0.65        ( ( ( re @ X3 )
% 0.26/0.65          = ( re @ Y3 ) )
% 0.26/0.65       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y3 ) )
% 0.26/0.65          = ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X3 ) ) @ ( abs_abs_real @ ( im @ Y3 ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cmod_Im_le_iff
% 0.26/0.65  thf(fact_9120_csqrt__principal,axiom,
% 0.26/0.65      ! [Z: complex] :
% 0.26/0.65        ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 0.26/0.65        | ( ( ( re @ ( csqrt @ Z ) )
% 0.26/0.65            = zero_zero_real )
% 0.26/0.65          & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % csqrt_principal
% 0.26/0.65  thf(fact_9121_cmod__le,axiom,
% 0.26/0.65      ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % cmod_le
% 0.26/0.65  thf(fact_9122_sin__n__Im__cis__pow__n,axiom,
% 0.26/0.65      ! [N: nat,A: real] :
% 0.26/0.65        ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 0.26/0.65        = ( im @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 0.26/0.65  
% 0.26/0.65  % sin_n_Im_cis_pow_n
% 0.26/0.65  thf(fact_9123_cmod__power2,axiom,
% 0.26/0.65      ! [Z: complex] :
% 0.26/0.65        ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.65        = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % cmod_power2
% 0.26/0.66  thf(fact_9124_Im__power2,axiom,
% 0.26/0.66      ! [X3: complex] :
% 0.26/0.66        ( ( im @ ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.66        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X3 ) ) @ ( im @ X3 ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Im_power2
% 0.26/0.66  thf(fact_9125_Re__power2,axiom,
% 0.26/0.66      ! [X3: complex] :
% 0.26/0.66        ( ( re @ ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.66        = ( minus_minus_real @ ( power_power_real @ ( re @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Re_power2
% 0.26/0.66  thf(fact_9126_complex__eq__0,axiom,
% 0.26/0.66      ! [Z: complex] :
% 0.26/0.66        ( ( Z = zero_zero_complex )
% 0.26/0.66        = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.66          = zero_zero_real ) ) ).
% 0.26/0.66  
% 0.26/0.66  % complex_eq_0
% 0.26/0.66  thf(fact_9127_norm__complex__def,axiom,
% 0.26/0.66      ( real_V1022390504157884413omplex
% 0.26/0.66      = ( ^ [Z6: complex] : ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( re @ Z6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % norm_complex_def
% 0.26/0.66  thf(fact_9128_inverse__complex_Osimps_I1_J,axiom,
% 0.26/0.66      ! [X3: complex] :
% 0.26/0.66        ( ( re @ ( invers8013647133539491842omplex @ X3 ) )
% 0.26/0.66        = ( 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 ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % inverse_complex.simps(1)
% 0.26/0.66  thf(fact_9129_complex__neq__0,axiom,
% 0.26/0.66      ! [Z: complex] :
% 0.26/0.66        ( ( Z != zero_zero_complex )
% 0.26/0.66        = ( 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 ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % complex_neq_0
% 0.26/0.66  thf(fact_9130_Re__divide,axiom,
% 0.26/0.66      ! [X3: complex,Y3: complex] :
% 0.26/0.66        ( ( re @ ( divide1717551699836669952omplex @ X3 @ Y3 ) )
% 0.26/0.66        = ( 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 ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Re_divide
% 0.26/0.66  thf(fact_9131_csqrt__unique,axiom,
% 0.26/0.66      ! [W: complex,Z: complex] :
% 0.26/0.66        ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.26/0.66          = Z )
% 0.26/0.66       => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 0.26/0.66            | ( ( ( re @ W )
% 0.26/0.66                = zero_zero_real )
% 0.26/0.66              & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 0.26/0.66         => ( ( csqrt @ Z )
% 0.26/0.66            = W ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % csqrt_unique
% 0.26/0.66  thf(fact_9132_csqrt__square,axiom,
% 0.26/0.66      ! [B: complex] :
% 0.26/0.66        ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 0.26/0.66          | ( ( ( re @ B )
% 0.26/0.66              = zero_zero_real )
% 0.26/0.66            & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 0.26/0.66       => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.66          = B ) ) ).
% 0.26/0.66  
% 0.26/0.66  % csqrt_square
% 0.26/0.66  thf(fact_9133_inverse__complex_Osimps_I2_J,axiom,
% 0.26/0.66      ! [X3: complex] :
% 0.26/0.66        ( ( im @ ( invers8013647133539491842omplex @ X3 ) )
% 0.26/0.66        = ( 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 ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % inverse_complex.simps(2)
% 0.26/0.66  thf(fact_9134_Im__divide,axiom,
% 0.26/0.66      ! [X3: complex,Y3: complex] :
% 0.26/0.66        ( ( im @ ( divide1717551699836669952omplex @ X3 @ Y3 ) )
% 0.26/0.66        = ( 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 ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Im_divide
% 0.26/0.66  thf(fact_9135_complex__abs__le__norm,axiom,
% 0.26/0.66      ! [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 ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % complex_abs_le_norm
% 0.26/0.66  thf(fact_9136_complex__unit__circle,axiom,
% 0.26/0.66      ! [Z: complex] :
% 0.26/0.66        ( ( Z != zero_zero_complex )
% 0.26/0.66       => ( ( 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 ) ) ) )
% 0.26/0.66          = one_one_real ) ) ).
% 0.26/0.66  
% 0.26/0.66  % complex_unit_circle
% 0.26/0.66  thf(fact_9137_inverse__complex_Ocode,axiom,
% 0.26/0.66      ( invers8013647133539491842omplex
% 0.26/0.66      = ( ^ [X: complex] : ( complex2 @ ( divide_divide_real @ ( re @ X ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % inverse_complex.code
% 0.26/0.66  thf(fact_9138_Complex__divide,axiom,
% 0.26/0.66      ( divide1717551699836669952omplex
% 0.26/0.66      = ( ^ [X: complex,Y: complex] : ( complex2 @ ( 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 ) ) ) ) ) @ ( 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 ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Complex_divide
% 0.26/0.66  thf(fact_9139_Im__Reals__divide,axiom,
% 0.26/0.66      ! [R2: complex,Z: complex] :
% 0.26/0.66        ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 0.26/0.66       => ( ( im @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 0.26/0.66          = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R2 ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Im_Reals_divide
% 0.26/0.66  thf(fact_9140_Re__Reals__divide,axiom,
% 0.26/0.66      ! [R2: complex,Z: complex] :
% 0.26/0.66        ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 0.26/0.66       => ( ( re @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 0.26/0.66          = ( divide_divide_real @ ( times_times_real @ ( re @ R2 ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Re_Reals_divide
% 0.26/0.66  thf(fact_9141_complex__mult__cnj,axiom,
% 0.26/0.66      ! [Z: complex] :
% 0.26/0.66        ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 0.26/0.66        = ( 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 ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % complex_mult_cnj
% 0.26/0.66  thf(fact_9142_complex__cnj__zero,axiom,
% 0.26/0.66      ( ( cnj @ zero_zero_complex )
% 0.26/0.66      = zero_zero_complex ) ).
% 0.26/0.66  
% 0.26/0.66  % complex_cnj_zero
% 0.26/0.66  thf(fact_9143_complex__cnj__zero__iff,axiom,
% 0.26/0.66      ! [Z: complex] :
% 0.26/0.66        ( ( ( cnj @ Z )
% 0.26/0.66          = zero_zero_complex )
% 0.26/0.66        = ( Z = zero_zero_complex ) ) ).
% 0.26/0.66  
% 0.26/0.66  % complex_cnj_zero_iff
% 0.26/0.66  thf(fact_9144_complex__cnj__power,axiom,
% 0.26/0.66      ! [X3: complex,N: nat] :
% 0.26/0.66        ( ( cnj @ ( power_power_complex @ X3 @ N ) )
% 0.26/0.66        = ( power_power_complex @ ( cnj @ X3 ) @ N ) ) ).
% 0.26/0.66  
% 0.26/0.66  % complex_cnj_power
% 0.26/0.66  thf(fact_9145_complex__In__mult__cnj__zero,axiom,
% 0.26/0.66      ! [Z: complex] :
% 0.26/0.66        ( ( im @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 0.26/0.66        = zero_zero_real ) ).
% 0.26/0.66  
% 0.26/0.66  % complex_In_mult_cnj_zero
% 0.26/0.66  thf(fact_9146_imaginary__eq__real__iff,axiom,
% 0.26/0.66      ! [Y3: complex,X3: complex] :
% 0.26/0.66        ( ( member_complex @ Y3 @ real_V2521375963428798218omplex )
% 0.26/0.66       => ( ( member_complex @ X3 @ real_V2521375963428798218omplex )
% 0.26/0.66         => ( ( ( times_times_complex @ imaginary_unit @ Y3 )
% 0.26/0.66              = X3 )
% 0.26/0.66            = ( ( X3 = zero_zero_complex )
% 0.26/0.66              & ( Y3 = zero_zero_complex ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % imaginary_eq_real_iff
% 0.26/0.66  thf(fact_9147_real__eq__imaginary__iff,axiom,
% 0.26/0.66      ! [Y3: complex,X3: complex] :
% 0.26/0.66        ( ( member_complex @ Y3 @ real_V2521375963428798218omplex )
% 0.26/0.66       => ( ( member_complex @ X3 @ real_V2521375963428798218omplex )
% 0.26/0.66         => ( ( X3
% 0.26/0.66              = ( times_times_complex @ imaginary_unit @ Y3 ) )
% 0.26/0.66            = ( ( X3 = zero_zero_complex )
% 0.26/0.66              & ( Y3 = zero_zero_complex ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % real_eq_imaginary_iff
% 0.26/0.66  thf(fact_9148_complex__is__Real__iff,axiom,
% 0.26/0.66      ! [Z: complex] :
% 0.26/0.66        ( ( member_complex @ Z @ real_V2521375963428798218omplex )
% 0.26/0.66        = ( ( im @ Z )
% 0.26/0.66          = zero_zero_real ) ) ).
% 0.26/0.66  
% 0.26/0.66  % complex_is_Real_iff
% 0.26/0.66  thf(fact_9149_Complex__in__Reals,axiom,
% 0.26/0.66      ! [X3: real] : ( member_complex @ ( complex2 @ X3 @ zero_zero_real ) @ real_V2521375963428798218omplex ) ).
% 0.26/0.66  
% 0.26/0.66  % Complex_in_Reals
% 0.26/0.66  thf(fact_9150_Re__complex__div__eq__0,axiom,
% 0.26/0.66      ! [A: complex,B: complex] :
% 0.26/0.66        ( ( ( re @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.26/0.66          = zero_zero_real )
% 0.26/0.66        = ( ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 0.26/0.66          = zero_zero_real ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Re_complex_div_eq_0
% 0.26/0.66  thf(fact_9151_Im__complex__div__eq__0,axiom,
% 0.26/0.66      ! [A: complex,B: complex] :
% 0.26/0.66        ( ( ( im @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.26/0.66          = zero_zero_real )
% 0.26/0.66        = ( ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 0.26/0.66          = zero_zero_real ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Im_complex_div_eq_0
% 0.26/0.66  thf(fact_9152_Re__complex__div__lt__0,axiom,
% 0.26/0.66      ! [A: complex,B: complex] :
% 0.26/0.66        ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 0.26/0.66        = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Re_complex_div_lt_0
% 0.26/0.66  thf(fact_9153_Re__complex__div__gt__0,axiom,
% 0.26/0.66      ! [A: complex,B: complex] :
% 0.26/0.66        ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.26/0.66        = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Re_complex_div_gt_0
% 0.26/0.66  thf(fact_9154_Re__complex__div__ge__0,axiom,
% 0.26/0.66      ! [A: complex,B: complex] :
% 0.26/0.66        ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.26/0.66        = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Re_complex_div_ge_0
% 0.26/0.66  thf(fact_9155_Re__complex__div__le__0,axiom,
% 0.26/0.66      ! [A: complex,B: complex] :
% 0.26/0.66        ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 0.26/0.66        = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Re_complex_div_le_0
% 0.26/0.66  thf(fact_9156_Im__complex__div__lt__0,axiom,
% 0.26/0.66      ! [A: complex,B: complex] :
% 0.26/0.66        ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 0.26/0.66        = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Im_complex_div_lt_0
% 0.26/0.66  thf(fact_9157_Im__complex__div__gt__0,axiom,
% 0.26/0.66      ! [A: complex,B: complex] :
% 0.26/0.66        ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.26/0.66        = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Im_complex_div_gt_0
% 0.26/0.66  thf(fact_9158_Im__complex__div__ge__0,axiom,
% 0.26/0.66      ! [A: complex,B: complex] :
% 0.26/0.66        ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.26/0.66        = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Im_complex_div_ge_0
% 0.26/0.66  thf(fact_9159_Im__complex__div__le__0,axiom,
% 0.26/0.66      ! [A: complex,B: complex] :
% 0.26/0.66        ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 0.26/0.66        = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Im_complex_div_le_0
% 0.26/0.66  thf(fact_9160_complex__mod__mult__cnj,axiom,
% 0.26/0.66      ! [Z: complex] :
% 0.26/0.66        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 0.26/0.66        = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % complex_mod_mult_cnj
% 0.26/0.66  thf(fact_9161_complex__div__gt__0,axiom,
% 0.26/0.66      ! [A: complex,B: complex] :
% 0.26/0.66        ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.26/0.66          = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 0.26/0.66        & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.26/0.66          = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % complex_div_gt_0
% 0.26/0.66  thf(fact_9162_complex__norm__square,axiom,
% 0.26/0.66      ! [Z: complex] :
% 0.26/0.66        ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.66        = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % complex_norm_square
% 0.26/0.66  thf(fact_9163_complex__add__cnj,axiom,
% 0.26/0.66      ! [Z: complex] :
% 0.26/0.66        ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 0.26/0.66        = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % complex_add_cnj
% 0.26/0.66  thf(fact_9164_complex__diff__cnj,axiom,
% 0.26/0.66      ! [Z: complex] :
% 0.26/0.66        ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 0.26/0.66        = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 0.26/0.66  
% 0.26/0.66  % complex_diff_cnj
% 0.26/0.66  thf(fact_9165_complex__div__cnj,axiom,
% 0.26/0.66      ( divide1717551699836669952omplex
% 0.26/0.66      = ( ^ [A4: complex,B3: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A4 @ ( cnj @ B3 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % complex_div_cnj
% 0.26/0.66  thf(fact_9166_cnj__add__mult__eq__Re,axiom,
% 0.26/0.66      ! [Z: complex,W: complex] :
% 0.26/0.66        ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 0.26/0.66        = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % cnj_add_mult_eq_Re
% 0.26/0.66  thf(fact_9167_int__of__integer__code,axiom,
% 0.26/0.66      ( code_int_of_integer
% 0.26/0.66      = ( ^ [K3: code_integer] :
% 0.26/0.66            ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 0.26/0.66            @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 0.26/0.66              @ ( produc1553301316500091796er_int
% 0.26/0.66                @ ^ [L2: code_integer,J3: code_integer] : ( if_int @ ( J3 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ one_one_int ) )
% 0.26/0.66                @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % int_of_integer_code
% 0.26/0.66  thf(fact_9168_num__of__integer__code,axiom,
% 0.26/0.66      ( code_num_of_integer
% 0.26/0.66      = ( ^ [K3: code_integer] :
% 0.26/0.66            ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 0.26/0.66            @ ( produc7336495610019696514er_num
% 0.26/0.66              @ ^ [L2: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ one ) )
% 0.26/0.66              @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % num_of_integer_code
% 0.26/0.66  thf(fact_9169_setceilmax,axiom,
% 0.26/0.66      ! [S: vEBT_VEBT,M: nat,Listy: list_VEBT_VEBT,N: nat] :
% 0.26/0.66        ( ( vEBT_invar_vebt @ S @ M )
% 0.26/0.66       => ( ! [X4: vEBT_VEBT] :
% 0.26/0.66              ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Listy ) )
% 0.26/0.66             => ( vEBT_invar_vebt @ X4 @ N ) )
% 0.26/0.66         => ( ( M
% 0.26/0.66              = ( suc @ N ) )
% 0.26/0.66           => ( ! [X4: vEBT_VEBT] :
% 0.26/0.66                  ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Listy ) )
% 0.26/0.66                 => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ X4 ) )
% 0.26/0.66                    = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 0.26/0.66             => ( ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ S ) )
% 0.26/0.66                  = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) )
% 0.26/0.66               => ( ( semiri1314217659103216013at_int @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ S @ ( set_VEBT_VEBT2 @ Listy ) ) ) ) )
% 0.26/0.66                  = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % setceilmax
% 0.26/0.66  thf(fact_9170_height__compose__list,axiom,
% 0.26/0.66      ! [T: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.26/0.66        ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.26/0.66       => ( ord_less_eq_nat @ ( vEBT_VEBT_height @ T ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary @ ( set_VEBT_VEBT2 @ TreeList2 ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % height_compose_list
% 0.26/0.66  thf(fact_9171_int__of__integer__of__nat,axiom,
% 0.26/0.66      ! [N: nat] :
% 0.26/0.66        ( ( code_int_of_integer @ ( semiri4939895301339042750nteger @ N ) )
% 0.26/0.66        = ( semiri1314217659103216013at_int @ N ) ) ).
% 0.26/0.66  
% 0.26/0.66  % int_of_integer_of_nat
% 0.26/0.66  thf(fact_9172_max__ins__scaled,axiom,
% 0.26/0.66      ! [N: nat,X14: vEBT_VEBT,M: nat,X13: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( vEBT_VEBT_height @ X14 ) ) @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ ( lattic8265883725875713057ax_nat @ ( insert_nat @ ( vEBT_VEBT_height @ X14 ) @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % max_ins_scaled
% 0.26/0.66  thf(fact_9173_height__i__max,axiom,
% 0.26/0.66      ! [I: nat,X13: list_VEBT_VEBT,Foo: nat] :
% 0.26/0.66        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 0.26/0.66       => ( ord_less_eq_nat @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I ) ) @ ( ord_max_nat @ Foo @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % height_i_max
% 0.26/0.66  thf(fact_9174_max__idx__list,axiom,
% 0.26/0.66      ! [I: nat,X13: list_VEBT_VEBT,N: nat,X14: vEBT_VEBT] :
% 0.26/0.66        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 0.26/0.66       => ( ord_less_eq_nat @ ( times_times_nat @ N @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I ) ) ) @ ( suc @ ( suc @ ( times_times_nat @ N @ ( ord_max_nat @ ( vEBT_VEBT_height @ X14 ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % max_idx_list
% 0.26/0.66  thf(fact_9175_zero__integer_Orep__eq,axiom,
% 0.26/0.66      ( ( code_int_of_integer @ zero_z3403309356797280102nteger )
% 0.26/0.66      = zero_zero_int ) ).
% 0.26/0.66  
% 0.26/0.66  % zero_integer.rep_eq
% 0.26/0.66  thf(fact_9176_int__of__integer__numeral,axiom,
% 0.26/0.66      ! [K: num] :
% 0.26/0.66        ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 0.26/0.66        = ( numeral_numeral_int @ K ) ) ).
% 0.26/0.66  
% 0.26/0.66  % int_of_integer_numeral
% 0.26/0.66  thf(fact_9177_Max__divisors__self__nat,axiom,
% 0.26/0.66      ! [N: nat] :
% 0.26/0.66        ( ( N != zero_zero_nat )
% 0.26/0.66       => ( ( lattic8265883725875713057ax_nat
% 0.26/0.66            @ ( collect_nat
% 0.26/0.66              @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ N ) ) )
% 0.26/0.66          = N ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Max_divisors_self_nat
% 0.26/0.66  thf(fact_9178_integer__less__iff,axiom,
% 0.26/0.66      ( ord_le6747313008572928689nteger
% 0.26/0.66      = ( ^ [K3: code_integer,L2: code_integer] : ( ord_less_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % integer_less_iff
% 0.26/0.66  thf(fact_9179_less__integer_Orep__eq,axiom,
% 0.26/0.66      ( ord_le6747313008572928689nteger
% 0.26/0.66      = ( ^ [X: code_integer,Xa4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % less_integer.rep_eq
% 0.26/0.66  thf(fact_9180_integer__less__eq__iff,axiom,
% 0.26/0.66      ( ord_le3102999989581377725nteger
% 0.26/0.66      = ( ^ [K3: code_integer,L2: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % integer_less_eq_iff
% 0.26/0.66  thf(fact_9181_less__eq__integer_Orep__eq,axiom,
% 0.26/0.66      ( ord_le3102999989581377725nteger
% 0.26/0.66      = ( ^ [X: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % less_eq_integer.rep_eq
% 0.26/0.66  thf(fact_9182_VEBT__internal_Oheight_Oelims,axiom,
% 0.26/0.66      ! [X3: vEBT_VEBT,Y3: nat] :
% 0.26/0.66        ( ( ( vEBT_VEBT_height @ X3 )
% 0.26/0.66          = Y3 )
% 0.26/0.66       => ( ( ? [A5: $o,B4: $o] :
% 0.26/0.66                ( X3
% 0.26/0.66                = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.66           => ( Y3 != zero_zero_nat ) )
% 0.26/0.66         => ~ ! [Uu: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.66                ( ( X3
% 0.26/0.66                  = ( vEBT_Node @ Uu @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.26/0.66               => ( Y3
% 0.26/0.66                 != ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % VEBT_internal.height.elims
% 0.26/0.66  thf(fact_9183_divide__nat__def,axiom,
% 0.26/0.66      ( divide_divide_nat
% 0.26/0.66      = ( ^ [M3: nat,N3: nat] :
% 0.26/0.66            ( if_nat @ ( N3 = zero_zero_nat ) @ zero_zero_nat
% 0.26/0.66            @ ( lattic8265883725875713057ax_nat
% 0.26/0.66              @ ( collect_nat
% 0.26/0.66                @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N3 ) @ M3 ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % divide_nat_def
% 0.26/0.66  thf(fact_9184_nat__of__integer__code,axiom,
% 0.26/0.66      ( code_nat_of_integer
% 0.26/0.66      = ( ^ [K3: code_integer] :
% 0.26/0.66            ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 0.26/0.66            @ ( produc1555791787009142072er_nat
% 0.26/0.66              @ ^ [L2: code_integer,J3: code_integer] : ( if_nat @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ one_one_nat ) )
% 0.26/0.66              @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % nat_of_integer_code
% 0.26/0.66  thf(fact_9185_VEBT__internal_Oheight_Opelims,axiom,
% 0.26/0.66      ! [X3: vEBT_VEBT,Y3: nat] :
% 0.26/0.66        ( ( ( vEBT_VEBT_height @ X3 )
% 0.26/0.66          = Y3 )
% 0.26/0.66       => ( ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ X3 )
% 0.26/0.66         => ( ! [A5: $o,B4: $o] :
% 0.26/0.66                ( ( X3
% 0.26/0.66                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.66               => ( ( Y3 = zero_zero_nat )
% 0.26/0.66                 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Leaf @ A5 @ B4 ) ) ) )
% 0.26/0.66           => ~ ! [Uu: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.66                  ( ( X3
% 0.26/0.66                    = ( vEBT_Node @ Uu @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.26/0.66                 => ( ( Y3
% 0.26/0.66                      = ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList3 ) ) ) ) ) )
% 0.26/0.66                   => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Node @ Uu @ Deg2 @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % VEBT_internal.height.pelims
% 0.26/0.66  thf(fact_9186_bij__betw__Suc,axiom,
% 0.26/0.66      ! [M7: set_nat,N4: set_nat] :
% 0.26/0.66        ( ( bij_betw_nat_nat @ suc @ M7 @ N4 )
% 0.26/0.66        = ( ( image_nat_nat @ suc @ M7 )
% 0.26/0.66          = N4 ) ) ).
% 0.26/0.66  
% 0.26/0.66  % bij_betw_Suc
% 0.26/0.66  thf(fact_9187_Max__divisors__self__int,axiom,
% 0.26/0.66      ! [N: int] :
% 0.26/0.66        ( ( N != zero_zero_int )
% 0.26/0.66       => ( ( lattic8263393255366662781ax_int
% 0.26/0.66            @ ( collect_int
% 0.26/0.66              @ ^ [D4: int] : ( dvd_dvd_int @ D4 @ N ) ) )
% 0.26/0.66          = ( abs_abs_int @ N ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Max_divisors_self_int
% 0.26/0.66  thf(fact_9188_of__nat__of__integer,axiom,
% 0.26/0.66      ! [K: code_integer] :
% 0.26/0.66        ( ( semiri4939895301339042750nteger @ ( code_nat_of_integer @ K ) )
% 0.26/0.66        = ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ K ) ) ).
% 0.26/0.66  
% 0.26/0.66  % of_nat_of_integer
% 0.26/0.66  thf(fact_9189_nat__of__integer__non__positive,axiom,
% 0.26/0.66      ! [K: code_integer] :
% 0.26/0.66        ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 0.26/0.66       => ( ( code_nat_of_integer @ K )
% 0.26/0.66          = zero_zero_nat ) ) ).
% 0.26/0.66  
% 0.26/0.66  % nat_of_integer_non_positive
% 0.26/0.66  thf(fact_9190_zero__notin__Suc__image,axiom,
% 0.26/0.66      ! [A3: set_nat] :
% 0.26/0.66        ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A3 ) ) ).
% 0.26/0.66  
% 0.26/0.66  % zero_notin_Suc_image
% 0.26/0.66  thf(fact_9191_image__int__atLeastAtMost,axiom,
% 0.26/0.66      ! [A: nat,B: nat] :
% 0.26/0.66        ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.26/0.66        = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % image_int_atLeastAtMost
% 0.26/0.66  thf(fact_9192_image__int__atLeastLessThan,axiom,
% 0.26/0.66      ! [A: nat,B: nat] :
% 0.26/0.66        ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 0.26/0.66        = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % image_int_atLeastLessThan
% 0.26/0.66  thf(fact_9193_nat__of__integer__code__post_I1_J,axiom,
% 0.26/0.66      ( ( code_nat_of_integer @ zero_z3403309356797280102nteger )
% 0.26/0.66      = zero_zero_nat ) ).
% 0.26/0.66  
% 0.26/0.66  % nat_of_integer_code_post(1)
% 0.26/0.66  thf(fact_9194_nat__of__integer_Orep__eq,axiom,
% 0.26/0.66      ( code_nat_of_integer
% 0.26/0.66      = ( ^ [X: code_integer] : ( nat2 @ ( code_int_of_integer @ X ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % nat_of_integer.rep_eq
% 0.26/0.66  thf(fact_9195_nat__of__integer_Oabs__eq,axiom,
% 0.26/0.66      ! [X3: int] :
% 0.26/0.66        ( ( code_nat_of_integer @ ( code_integer_of_int @ X3 ) )
% 0.26/0.66        = ( nat2 @ X3 ) ) ).
% 0.26/0.66  
% 0.26/0.66  % nat_of_integer.abs_eq
% 0.26/0.66  thf(fact_9196_nat__of__integer__code__post_I3_J,axiom,
% 0.26/0.66      ! [K: num] :
% 0.26/0.66        ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 0.26/0.66        = ( numeral_numeral_nat @ K ) ) ).
% 0.26/0.66  
% 0.26/0.66  % nat_of_integer_code_post(3)
% 0.26/0.66  thf(fact_9197_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 0.26/0.66      ! [N: nat] :
% 0.26/0.66        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.26/0.66        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % atLeast0_atMost_Suc_eq_insert_0
% 0.26/0.66  thf(fact_9198_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 0.26/0.66      ! [N: nat] :
% 0.26/0.66        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.26/0.66        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % atLeast0_lessThan_Suc_eq_insert_0
% 0.26/0.66  thf(fact_9199_lessThan__Suc__eq__insert__0,axiom,
% 0.26/0.66      ! [N: nat] :
% 0.26/0.66        ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 0.26/0.66        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % lessThan_Suc_eq_insert_0
% 0.26/0.66  thf(fact_9200_atMost__Suc__eq__insert__0,axiom,
% 0.26/0.66      ! [N: nat] :
% 0.26/0.66        ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 0.26/0.66        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % atMost_Suc_eq_insert_0
% 0.26/0.66  thf(fact_9201_image__add__int__atLeastLessThan,axiom,
% 0.26/0.66      ! [L: int,U: int] :
% 0.26/0.66        ( ( image_int_int
% 0.26/0.66          @ ^ [X: int] : ( plus_plus_int @ X @ L )
% 0.26/0.66          @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 0.26/0.66        = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 0.26/0.66  
% 0.26/0.66  % image_add_int_atLeastLessThan
% 0.26/0.66  thf(fact_9202_image__atLeastZeroLessThan__int,axiom,
% 0.26/0.66      ! [U: int] :
% 0.26/0.66        ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.26/0.66       => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 0.26/0.66          = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % image_atLeastZeroLessThan_int
% 0.26/0.66  thf(fact_9203_image__minus__const__atLeastLessThan__nat,axiom,
% 0.26/0.66      ! [C: nat,Y3: nat,X3: nat] :
% 0.26/0.66        ( ( ( ord_less_nat @ C @ Y3 )
% 0.26/0.66         => ( ( image_nat_nat
% 0.26/0.66              @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 0.26/0.66              @ ( set_or4665077453230672383an_nat @ X3 @ Y3 ) )
% 0.26/0.66            = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X3 @ C ) @ ( minus_minus_nat @ Y3 @ C ) ) ) )
% 0.26/0.66        & ( ~ ( ord_less_nat @ C @ Y3 )
% 0.26/0.66         => ( ( ( ord_less_nat @ X3 @ Y3 )
% 0.26/0.66             => ( ( image_nat_nat
% 0.26/0.66                  @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 0.26/0.66                  @ ( set_or4665077453230672383an_nat @ X3 @ Y3 ) )
% 0.26/0.66                = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 0.26/0.66            & ( ~ ( ord_less_nat @ X3 @ Y3 )
% 0.26/0.66             => ( ( image_nat_nat
% 0.26/0.66                  @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 0.26/0.66                  @ ( set_or4665077453230672383an_nat @ X3 @ Y3 ) )
% 0.26/0.66                = bot_bot_set_nat ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % image_minus_const_atLeastLessThan_nat
% 0.26/0.66  thf(fact_9204_vebt__maxt_Opelims,axiom,
% 0.26/0.66      ! [X3: vEBT_VEBT,Y3: option_nat] :
% 0.26/0.66        ( ( ( vEBT_vebt_maxt @ X3 )
% 0.26/0.66          = Y3 )
% 0.26/0.66       => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X3 )
% 0.26/0.66         => ( ! [A5: $o,B4: $o] :
% 0.26/0.66                ( ( X3
% 0.26/0.66                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.66               => ( ( ( B4
% 0.26/0.66                     => ( Y3
% 0.26/0.66                        = ( some_nat @ one_one_nat ) ) )
% 0.26/0.66                    & ( ~ B4
% 0.26/0.66                     => ( ( A5
% 0.26/0.66                         => ( Y3
% 0.26/0.66                            = ( some_nat @ zero_zero_nat ) ) )
% 0.26/0.66                        & ( ~ A5
% 0.26/0.66                         => ( Y3 = none_nat ) ) ) ) )
% 0.26/0.66                 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A5 @ B4 ) ) ) )
% 0.26/0.66           => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.26/0.66                  ( ( X3
% 0.26/0.66                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.26/0.66                 => ( ( Y3 = none_nat )
% 0.26/0.66                   => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) ) ) )
% 0.26/0.66             => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.26/0.66                    ( ( X3
% 0.26/0.66                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 0.26/0.66                   => ( ( Y3
% 0.26/0.66                        = ( some_nat @ Ma2 ) )
% 0.26/0.66                     => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % vebt_maxt.pelims
% 0.26/0.66  thf(fact_9205_vebt__mint_Opelims,axiom,
% 0.26/0.66      ! [X3: vEBT_VEBT,Y3: option_nat] :
% 0.26/0.66        ( ( ( vEBT_vebt_mint @ X3 )
% 0.26/0.66          = Y3 )
% 0.26/0.66       => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X3 )
% 0.26/0.66         => ( ! [A5: $o,B4: $o] :
% 0.26/0.66                ( ( X3
% 0.26/0.66                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.66               => ( ( ( A5
% 0.26/0.66                     => ( Y3
% 0.26/0.66                        = ( some_nat @ zero_zero_nat ) ) )
% 0.26/0.66                    & ( ~ A5
% 0.26/0.66                     => ( ( B4
% 0.26/0.66                         => ( Y3
% 0.26/0.66                            = ( some_nat @ one_one_nat ) ) )
% 0.26/0.66                        & ( ~ B4
% 0.26/0.66                         => ( Y3 = none_nat ) ) ) ) )
% 0.26/0.66                 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A5 @ B4 ) ) ) )
% 0.26/0.66           => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.26/0.66                  ( ( X3
% 0.26/0.66                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.26/0.66                 => ( ( Y3 = none_nat )
% 0.26/0.66                   => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) ) ) )
% 0.26/0.66             => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.26/0.66                    ( ( X3
% 0.26/0.66                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 0.26/0.66                   => ( ( Y3
% 0.26/0.66                        = ( some_nat @ Mi2 ) )
% 0.26/0.66                     => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % vebt_mint.pelims
% 0.26/0.66  thf(fact_9206_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Opelims,axiom,
% 0.26/0.66      ! [X3: vEBT_VEBT,Y3: nat] :
% 0.26/0.66        ( ( ( vEBT_T_m_i_n_t @ X3 )
% 0.26/0.66          = Y3 )
% 0.26/0.66       => ( ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ X3 )
% 0.26/0.66         => ( ! [A5: $o,B4: $o] :
% 0.26/0.66                ( ( X3
% 0.26/0.66                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.66               => ( ( Y3
% 0.26/0.66                    = ( plus_plus_nat @ one_one_nat @ ( if_nat @ A5 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 0.26/0.66                 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Leaf @ A5 @ B4 ) ) ) )
% 0.26/0.66           => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.26/0.66                  ( ( X3
% 0.26/0.66                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.26/0.66                 => ( ( Y3 = one_one_nat )
% 0.26/0.66                   => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) ) ) )
% 0.26/0.66             => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.26/0.66                    ( ( X3
% 0.26/0.66                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 0.26/0.66                   => ( ( Y3 = one_one_nat )
% 0.26/0.66                     => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.pelims
% 0.26/0.66  thf(fact_9207_card__Collect__less__nat,axiom,
% 0.26/0.66      ! [N: nat] :
% 0.26/0.66        ( ( finite_card_nat
% 0.26/0.66          @ ( collect_nat
% 0.26/0.66            @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N ) ) )
% 0.26/0.66        = N ) ).
% 0.26/0.66  
% 0.26/0.66  % card_Collect_less_nat
% 0.26/0.66  thf(fact_9208_card__Collect__le__nat,axiom,
% 0.26/0.66      ! [N: nat] :
% 0.26/0.66        ( ( finite_card_nat
% 0.26/0.66          @ ( collect_nat
% 0.26/0.66            @ ^ [I4: nat] : ( ord_less_eq_nat @ I4 @ N ) ) )
% 0.26/0.66        = ( suc @ N ) ) ).
% 0.26/0.66  
% 0.26/0.66  % card_Collect_le_nat
% 0.26/0.66  thf(fact_9209_card__atLeastLessThan__int,axiom,
% 0.26/0.66      ! [L: int,U: int] :
% 0.26/0.66        ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L @ U ) )
% 0.26/0.66        = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % card_atLeastLessThan_int
% 0.26/0.66  thf(fact_9210_card__atLeastAtMost__int,axiom,
% 0.26/0.66      ! [L: int,U: int] :
% 0.26/0.66        ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 0.26/0.66        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % card_atLeastAtMost_int
% 0.26/0.66  thf(fact_9211_nat_Odisc__eq__case_I2_J,axiom,
% 0.26/0.66      ! [Nat: nat] :
% 0.26/0.66        ( ( Nat != zero_zero_nat )
% 0.26/0.66        = ( case_nat_o @ $false
% 0.26/0.66          @ ^ [Uu3: nat] : $true
% 0.26/0.66          @ Nat ) ) ).
% 0.26/0.66  
% 0.26/0.66  % nat.disc_eq_case(2)
% 0.26/0.66  thf(fact_9212_nat_Odisc__eq__case_I1_J,axiom,
% 0.26/0.66      ! [Nat: nat] :
% 0.26/0.66        ( ( Nat = zero_zero_nat )
% 0.26/0.66        = ( case_nat_o @ $true
% 0.26/0.66          @ ^ [Uu3: nat] : $false
% 0.26/0.66          @ Nat ) ) ).
% 0.26/0.66  
% 0.26/0.66  % nat.disc_eq_case(1)
% 0.26/0.66  thf(fact_9213_card__less__Suc2,axiom,
% 0.26/0.66      ! [M7: set_nat,I: nat] :
% 0.26/0.66        ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 0.26/0.66       => ( ( finite_card_nat
% 0.26/0.66            @ ( collect_nat
% 0.26/0.66              @ ^ [K3: nat] :
% 0.26/0.66                  ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 0.26/0.66                  & ( ord_less_nat @ K3 @ I ) ) ) )
% 0.26/0.66          = ( finite_card_nat
% 0.26/0.66            @ ( collect_nat
% 0.26/0.66              @ ^ [K3: nat] :
% 0.26/0.66                  ( ( member_nat @ K3 @ M7 )
% 0.26/0.66                  & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % card_less_Suc2
% 0.26/0.66  thf(fact_9214_card__less__Suc,axiom,
% 0.26/0.66      ! [M7: set_nat,I: nat] :
% 0.26/0.66        ( ( member_nat @ zero_zero_nat @ M7 )
% 0.26/0.66       => ( ( suc
% 0.26/0.66            @ ( finite_card_nat
% 0.26/0.66              @ ( collect_nat
% 0.26/0.66                @ ^ [K3: nat] :
% 0.26/0.66                    ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 0.26/0.66                    & ( ord_less_nat @ K3 @ I ) ) ) ) )
% 0.26/0.66          = ( finite_card_nat
% 0.26/0.66            @ ( collect_nat
% 0.26/0.66              @ ^ [K3: nat] :
% 0.26/0.66                  ( ( member_nat @ K3 @ M7 )
% 0.26/0.66                  & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % card_less_Suc
% 0.26/0.66  thf(fact_9215_card__less,axiom,
% 0.26/0.66      ! [M7: set_nat,I: nat] :
% 0.26/0.66        ( ( member_nat @ zero_zero_nat @ M7 )
% 0.26/0.66       => ( ( finite_card_nat
% 0.26/0.66            @ ( collect_nat
% 0.26/0.66              @ ^ [K3: nat] :
% 0.26/0.66                  ( ( member_nat @ K3 @ M7 )
% 0.26/0.66                  & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) )
% 0.26/0.66         != zero_zero_nat ) ) ).
% 0.26/0.66  
% 0.26/0.66  % card_less
% 0.26/0.66  thf(fact_9216_card__atLeastZeroLessThan__int,axiom,
% 0.26/0.66      ! [U: int] :
% 0.26/0.66        ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 0.26/0.66        = ( nat2 @ U ) ) ).
% 0.26/0.66  
% 0.26/0.66  % card_atLeastZeroLessThan_int
% 0.26/0.66  thf(fact_9217_less__eq__nat_Osimps_I2_J,axiom,
% 0.26/0.66      ! [M: nat,N: nat] :
% 0.26/0.66        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.26/0.66        = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 0.26/0.66  
% 0.26/0.66  % less_eq_nat.simps(2)
% 0.26/0.66  thf(fact_9218_max__Suc2,axiom,
% 0.26/0.66      ! [M: nat,N: nat] :
% 0.26/0.66        ( ( ord_max_nat @ M @ ( suc @ N ) )
% 0.26/0.66        = ( case_nat_nat @ ( suc @ N )
% 0.26/0.66          @ ^ [M5: nat] : ( suc @ ( ord_max_nat @ M5 @ N ) )
% 0.26/0.66          @ M ) ) ).
% 0.26/0.66  
% 0.26/0.66  % max_Suc2
% 0.26/0.66  thf(fact_9219_max__Suc1,axiom,
% 0.26/0.66      ! [N: nat,M: nat] :
% 0.26/0.66        ( ( ord_max_nat @ ( suc @ N ) @ M )
% 0.26/0.66        = ( case_nat_nat @ ( suc @ N )
% 0.26/0.66          @ ^ [M5: nat] : ( suc @ ( ord_max_nat @ N @ M5 ) )
% 0.26/0.66          @ M ) ) ).
% 0.26/0.66  
% 0.26/0.66  % max_Suc1
% 0.26/0.66  thf(fact_9220_card__le__Suc__Max,axiom,
% 0.26/0.66      ! [S2: set_nat] :
% 0.26/0.66        ( ( finite_finite_nat @ S2 )
% 0.26/0.66       => ( ord_less_eq_nat @ ( finite_card_nat @ S2 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S2 ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % card_le_Suc_Max
% 0.26/0.66  thf(fact_9221_subset__eq__atLeast0__lessThan__card,axiom,
% 0.26/0.66      ! [N4: set_nat,N: nat] :
% 0.26/0.66        ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.26/0.66       => ( ord_less_eq_nat @ ( finite_card_nat @ N4 ) @ N ) ) ).
% 0.26/0.66  
% 0.26/0.66  % subset_eq_atLeast0_lessThan_card
% 0.26/0.66  thf(fact_9222_card__sum__le__nat__sum,axiom,
% 0.26/0.66      ! [S2: set_nat] :
% 0.26/0.66        ( ord_less_eq_nat
% 0.26/0.66        @ ( groups3542108847815614940at_nat
% 0.26/0.66          @ ^ [X: nat] : X
% 0.26/0.66          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S2 ) ) )
% 0.26/0.66        @ ( groups3542108847815614940at_nat
% 0.26/0.66          @ ^ [X: nat] : X
% 0.26/0.66          @ S2 ) ) ).
% 0.26/0.66  
% 0.26/0.66  % card_sum_le_nat_sum
% 0.26/0.66  thf(fact_9223_card__nth__roots,axiom,
% 0.26/0.66      ! [C: complex,N: nat] :
% 0.26/0.66        ( ( C != zero_zero_complex )
% 0.26/0.66       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.66         => ( ( finite_card_complex
% 0.26/0.66              @ ( collect_complex
% 0.26/0.66                @ ^ [Z6: complex] :
% 0.26/0.66                    ( ( power_power_complex @ Z6 @ N )
% 0.26/0.66                    = C ) ) )
% 0.26/0.66            = N ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % card_nth_roots
% 0.26/0.66  thf(fact_9224_card__roots__unity__eq,axiom,
% 0.26/0.66      ! [N: nat] :
% 0.26/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.66       => ( ( finite_card_complex
% 0.26/0.66            @ ( collect_complex
% 0.26/0.66              @ ^ [Z6: complex] :
% 0.26/0.66                  ( ( power_power_complex @ Z6 @ N )
% 0.26/0.66                  = one_one_complex ) ) )
% 0.26/0.66          = N ) ) ).
% 0.26/0.66  
% 0.26/0.66  % card_roots_unity_eq
% 0.26/0.66  thf(fact_9225_diff__Suc,axiom,
% 0.26/0.66      ! [M: nat,N: nat] :
% 0.26/0.66        ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 0.26/0.66        = ( case_nat_nat @ zero_zero_nat
% 0.26/0.66          @ ^ [K3: nat] : K3
% 0.26/0.66          @ ( minus_minus_nat @ M @ N ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % diff_Suc
% 0.26/0.66  thf(fact_9226_floor__real__def,axiom,
% 0.26/0.66      ( archim6058952711729229775r_real
% 0.26/0.66      = ( ^ [X: real] :
% 0.26/0.66            ( the_int
% 0.26/0.66            @ ^ [Z6: int] :
% 0.26/0.66                ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z6 ) @ X )
% 0.26/0.66                & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z6 @ one_one_int ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % floor_real_def
% 0.26/0.66  thf(fact_9227_pred__def,axiom,
% 0.26/0.66      ( pred
% 0.26/0.66      = ( case_nat_nat @ zero_zero_nat
% 0.26/0.66        @ ^ [X23: nat] : X23 ) ) ).
% 0.26/0.66  
% 0.26/0.66  % pred_def
% 0.26/0.66  thf(fact_9228_bezw__0,axiom,
% 0.26/0.66      ! [X3: nat] :
% 0.26/0.66        ( ( bezw @ X3 @ zero_zero_nat )
% 0.26/0.66        = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 0.26/0.66  
% 0.26/0.66  % bezw_0
% 0.26/0.66  thf(fact_9229_drop__bit__numeral__minus__bit1,axiom,
% 0.26/0.66      ! [L: num,K: num] :
% 0.26/0.66        ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.26/0.66        = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % drop_bit_numeral_minus_bit1
% 0.26/0.66  thf(fact_9230_drop__bit__nonnegative__int__iff,axiom,
% 0.26/0.66      ! [N: nat,K: int] :
% 0.26/0.66        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 0.26/0.66        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.26/0.66  
% 0.26/0.66  % drop_bit_nonnegative_int_iff
% 0.26/0.66  thf(fact_9231_drop__bit__negative__int__iff,axiom,
% 0.26/0.66      ! [N: nat,K: int] :
% 0.26/0.66        ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 0.26/0.66        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.26/0.66  
% 0.26/0.66  % drop_bit_negative_int_iff
% 0.26/0.66  thf(fact_9232_drop__bit__minus__one,axiom,
% 0.26/0.66      ! [N: nat] :
% 0.26/0.66        ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 0.26/0.66        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.26/0.66  
% 0.26/0.66  % drop_bit_minus_one
% 0.26/0.66  thf(fact_9233_drop__bit__Suc__minus__bit0,axiom,
% 0.26/0.66      ! [N: nat,K: num] :
% 0.26/0.66        ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.26/0.66        = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % drop_bit_Suc_minus_bit0
% 0.26/0.66  thf(fact_9234_drop__bit__numeral__minus__bit0,axiom,
% 0.26/0.66      ! [L: num,K: num] :
% 0.26/0.66        ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.26/0.66        = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % drop_bit_numeral_minus_bit0
% 0.26/0.66  thf(fact_9235_drop__bit__Suc__minus__bit1,axiom,
% 0.26/0.66      ! [N: nat,K: num] :
% 0.26/0.66        ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.26/0.66        = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % drop_bit_Suc_minus_bit1
% 0.26/0.66  thf(fact_9236_drop__bit__push__bit__int,axiom,
% 0.26/0.66      ! [M: nat,N: nat,K: int] :
% 0.26/0.66        ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N @ K ) )
% 0.26/0.66        = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N @ M ) @ K ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % drop_bit_push_bit_int
% 0.26/0.66  thf(fact_9237_drop__bit__int__def,axiom,
% 0.26/0.66      ( bit_se8568078237143864401it_int
% 0.26/0.66      = ( ^ [N3: nat,K3: int] : ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % drop_bit_int_def
% 0.26/0.66  thf(fact_9238_Suc__0__mod__numeral,axiom,
% 0.26/0.66      ! [K: num] :
% 0.26/0.66        ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 0.26/0.66        = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Suc_0_mod_numeral
% 0.26/0.66  thf(fact_9239_Suc__0__div__numeral,axiom,
% 0.26/0.66      ! [K: num] :
% 0.26/0.66        ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 0.26/0.66        = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Suc_0_div_numeral
% 0.26/0.66  thf(fact_9240_prod__decode__aux_Osimps,axiom,
% 0.26/0.66      ( nat_prod_decode_aux
% 0.26/0.66      = ( ^ [K3: nat,M3: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M3 @ K3 ) @ ( product_Pair_nat_nat @ M3 @ ( minus_minus_nat @ K3 @ M3 ) ) @ ( nat_prod_decode_aux @ ( suc @ K3 ) @ ( minus_minus_nat @ M3 @ ( suc @ K3 ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % prod_decode_aux.simps
% 0.26/0.66  thf(fact_9241_drop__bit__of__Suc__0,axiom,
% 0.26/0.66      ! [N: nat] :
% 0.26/0.66        ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.26/0.66        = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % drop_bit_of_Suc_0
% 0.26/0.66  thf(fact_9242_drop__bit__nat__eq,axiom,
% 0.26/0.66      ! [N: nat,K: int] :
% 0.26/0.66        ( ( bit_se8570568707652914677it_nat @ N @ ( nat2 @ K ) )
% 0.26/0.66        = ( nat2 @ ( bit_se8568078237143864401it_int @ N @ K ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % drop_bit_nat_eq
% 0.26/0.66  thf(fact_9243_drop__bit__nat__def,axiom,
% 0.26/0.66      ( bit_se8570568707652914677it_nat
% 0.26/0.66      = ( ^ [N3: nat,M3: nat] : ( divide_divide_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % drop_bit_nat_def
% 0.26/0.66  thf(fact_9244_prod__decode__aux_Oelims,axiom,
% 0.26/0.66      ! [X3: nat,Xa: nat,Y3: product_prod_nat_nat] :
% 0.26/0.66        ( ( ( nat_prod_decode_aux @ X3 @ Xa )
% 0.26/0.66          = Y3 )
% 0.26/0.66       => ( ( ( ord_less_eq_nat @ Xa @ X3 )
% 0.26/0.66           => ( Y3
% 0.26/0.66              = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X3 @ Xa ) ) ) )
% 0.26/0.66          & ( ~ ( ord_less_eq_nat @ Xa @ X3 )
% 0.26/0.66           => ( Y3
% 0.26/0.66              = ( nat_prod_decode_aux @ ( suc @ X3 ) @ ( minus_minus_nat @ Xa @ ( suc @ X3 ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % prod_decode_aux.elims
% 0.26/0.66  thf(fact_9245_finite__enumerate,axiom,
% 0.26/0.66      ! [S2: set_nat] :
% 0.26/0.66        ( ( finite_finite_nat @ S2 )
% 0.26/0.66       => ? [R: nat > nat] :
% 0.26/0.66            ( ( strict1292158309912662752at_nat @ R @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S2 ) ) )
% 0.26/0.66            & ! [N8: nat] :
% 0.26/0.66                ( ( ord_less_nat @ N8 @ ( finite_card_nat @ S2 ) )
% 0.26/0.66               => ( member_nat @ ( R @ N8 ) @ S2 ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % finite_enumerate
% 0.26/0.66  thf(fact_9246_bezw__non__0,axiom,
% 0.26/0.66      ! [Y3: nat,X3: nat] :
% 0.26/0.66        ( ( ord_less_nat @ zero_zero_nat @ Y3 )
% 0.26/0.66       => ( ( bezw @ X3 @ Y3 )
% 0.26/0.66          = ( 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 ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % bezw_non_0
% 0.26/0.66  thf(fact_9247_bezw_Oelims,axiom,
% 0.26/0.66      ! [X3: nat,Xa: nat,Y3: product_prod_int_int] :
% 0.26/0.66        ( ( ( bezw @ X3 @ Xa )
% 0.26/0.66          = Y3 )
% 0.26/0.66       => ( ( ( Xa = zero_zero_nat )
% 0.26/0.66           => ( Y3
% 0.26/0.66              = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 0.26/0.66          & ( ( Xa != zero_zero_nat )
% 0.26/0.66           => ( Y3
% 0.26/0.66              = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X3 @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X3 @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X3 @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X3 @ Xa ) ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % bezw.elims
% 0.26/0.66  thf(fact_9248_bezw_Osimps,axiom,
% 0.26/0.66      ( bezw
% 0.26/0.66      = ( ^ [X: nat,Y: nat] : ( if_Pro3027730157355071871nt_int @ ( Y = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ 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 ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % bezw.simps
% 0.26/0.66  thf(fact_9249_one__mod__minus__numeral,axiom,
% 0.26/0.66      ! [N: num] :
% 0.26/0.66        ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.66        = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % one_mod_minus_numeral
% 0.26/0.66  thf(fact_9250_minus__one__mod__numeral,axiom,
% 0.26/0.66      ! [N: num] :
% 0.26/0.66        ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.66        = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % minus_one_mod_numeral
% 0.26/0.66  thf(fact_9251_numeral__mod__minus__numeral,axiom,
% 0.26/0.66      ! [M: num,N: num] :
% 0.26/0.66        ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.66        = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % numeral_mod_minus_numeral
% 0.26/0.66  thf(fact_9252_minus__numeral__mod__numeral,axiom,
% 0.26/0.66      ! [M: num,N: num] :
% 0.26/0.66        ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.66        = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % minus_numeral_mod_numeral
% 0.26/0.66  thf(fact_9253_Divides_Oadjust__mod__def,axiom,
% 0.26/0.66      ( adjust_mod
% 0.26/0.66      = ( ^ [L2: int,R5: int] : ( if_int @ ( R5 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L2 @ R5 ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Divides.adjust_mod_def
% 0.26/0.66  thf(fact_9254_bezw_Opelims,axiom,
% 0.26/0.66      ! [X3: nat,Xa: nat,Y3: product_prod_int_int] :
% 0.26/0.66        ( ( ( bezw @ X3 @ Xa )
% 0.26/0.66          = Y3 )
% 0.26/0.66       => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X3 @ Xa ) )
% 0.26/0.66         => ~ ( ( ( ( Xa = zero_zero_nat )
% 0.26/0.66                 => ( Y3
% 0.26/0.66                    = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 0.26/0.66                & ( ( Xa != zero_zero_nat )
% 0.26/0.66                 => ( Y3
% 0.26/0.66                    = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X3 @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X3 @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X3 @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X3 @ Xa ) ) ) ) ) ) ) )
% 0.26/0.66             => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X3 @ Xa ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % bezw.pelims
% 0.26/0.66  thf(fact_9255_prod__decode__aux_Opelims,axiom,
% 0.26/0.66      ! [X3: nat,Xa: nat,Y3: product_prod_nat_nat] :
% 0.26/0.66        ( ( ( nat_prod_decode_aux @ X3 @ Xa )
% 0.26/0.66          = Y3 )
% 0.26/0.66       => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X3 @ Xa ) )
% 0.26/0.66         => ~ ( ( ( ( ord_less_eq_nat @ Xa @ X3 )
% 0.26/0.66                 => ( Y3
% 0.26/0.66                    = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X3 @ Xa ) ) ) )
% 0.26/0.66                & ( ~ ( ord_less_eq_nat @ Xa @ X3 )
% 0.26/0.66                 => ( Y3
% 0.26/0.66                    = ( nat_prod_decode_aux @ ( suc @ X3 ) @ ( minus_minus_nat @ Xa @ ( suc @ X3 ) ) ) ) ) )
% 0.26/0.66             => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X3 @ Xa ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % prod_decode_aux.pelims
% 0.26/0.66  thf(fact_9256_bit__cut__integer__code,axiom,
% 0.26/0.66      ( code_bit_cut_integer
% 0.26/0.66      = ( ^ [K3: code_integer] :
% 0.26/0.66            ( if_Pro5737122678794959658eger_o @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 0.26/0.66            @ ( produc9125791028180074456eger_o
% 0.26/0.66              @ ^ [R5: code_integer,S6: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S6 ) ) @ ( S6 = one_one_Code_integer ) )
% 0.26/0.66              @ ( code_divmod_abs @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % bit_cut_integer_code
% 0.26/0.66  thf(fact_9257_divmod__abs__code_I6_J,axiom,
% 0.26/0.66      ! [J: code_integer] :
% 0.26/0.66        ( ( code_divmod_abs @ zero_z3403309356797280102nteger @ J )
% 0.26/0.66        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ) ).
% 0.26/0.66  
% 0.26/0.66  % divmod_abs_code(6)
% 0.26/0.66  thf(fact_9258_divmod__abs__code_I5_J,axiom,
% 0.26/0.66      ! [J: code_integer] :
% 0.26/0.66        ( ( code_divmod_abs @ J @ zero_z3403309356797280102nteger )
% 0.26/0.66        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ J ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % divmod_abs_code(5)
% 0.26/0.66  thf(fact_9259_bit__cut__integer__def,axiom,
% 0.26/0.66      ( code_bit_cut_integer
% 0.26/0.66      = ( ^ [K3: code_integer] :
% 0.26/0.66            ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.26/0.66            @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K3 ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % bit_cut_integer_def
% 0.26/0.66  thf(fact_9260_divmod__integer__code,axiom,
% 0.26/0.66      ( code_divmod_integer
% 0.26/0.66      = ( ^ [K3: code_integer,L2: code_integer] :
% 0.26/0.66            ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.26/0.66            @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L2 )
% 0.26/0.66              @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ ( code_divmod_abs @ K3 @ L2 )
% 0.26/0.66                @ ( produc6916734918728496179nteger
% 0.26/0.66                  @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L2 @ S6 ) ) )
% 0.26/0.66                  @ ( code_divmod_abs @ K3 @ L2 ) ) )
% 0.26/0.66              @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 0.26/0.66                @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 0.26/0.66                  @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K3 @ L2 )
% 0.26/0.66                    @ ( produc6916734918728496179nteger
% 0.26/0.66                      @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L2 ) @ S6 ) ) )
% 0.26/0.66                      @ ( code_divmod_abs @ K3 @ L2 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % divmod_integer_code
% 0.26/0.66  thf(fact_9261_card__greaterThanLessThan__int,axiom,
% 0.26/0.66      ! [L: int,U: int] :
% 0.26/0.66        ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 0.26/0.66        = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % card_greaterThanLessThan_int
% 0.26/0.66  thf(fact_9262_xor__minus__numerals_I1_J,axiom,
% 0.26/0.66      ! [N: num,K: int] :
% 0.26/0.66        ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ K )
% 0.26/0.66        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N @ one ) @ K ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % xor_minus_numerals(1)
% 0.26/0.66  thf(fact_9263_xor__minus__numerals_I2_J,axiom,
% 0.26/0.66      ! [K: int,N: num] :
% 0.26/0.66        ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.66        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N @ one ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % xor_minus_numerals(2)
% 0.26/0.66  thf(fact_9264_sub__BitM__One__eq,axiom,
% 0.26/0.66      ! [N: num] :
% 0.26/0.66        ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 0.26/0.66        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % sub_BitM_One_eq
% 0.26/0.66  thf(fact_9265_divmod__integer__eq__cases,axiom,
% 0.26/0.66      ( code_divmod_integer
% 0.26/0.66      = ( ^ [K3: code_integer,L2: code_integer] :
% 0.26/0.66            ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.26/0.66            @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 0.26/0.66              @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L2
% 0.26/0.66                @ ( if_Pro6119634080678213985nteger
% 0.26/0.66                  @ ( ( sgn_sgn_Code_integer @ K3 )
% 0.26/0.66                    = ( sgn_sgn_Code_integer @ L2 ) )
% 0.26/0.66                  @ ( code_divmod_abs @ K3 @ L2 )
% 0.26/0.66                  @ ( produc6916734918728496179nteger
% 0.26/0.66                    @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L2 ) @ S6 ) ) )
% 0.26/0.66                    @ ( code_divmod_abs @ K3 @ L2 ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % divmod_integer_eq_cases
% 0.26/0.66  thf(fact_9266_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 0.26/0.66      ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 0.26/0.66      @ ^ [X: nat,Y: nat] : ( ord_less_eq_nat @ Y @ X )
% 0.26/0.66      @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X ) ) ).
% 0.26/0.66  
% 0.26/0.66  % max_nat.semilattice_neutr_order_axioms
% 0.26/0.66  thf(fact_9267_Suc__funpow,axiom,
% 0.26/0.66      ! [N: nat] :
% 0.26/0.66        ( ( compow_nat_nat @ N @ suc )
% 0.26/0.66        = ( plus_plus_nat @ N ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Suc_funpow
% 0.26/0.66  thf(fact_9268_infinite__int__iff__infinite__nat__abs,axiom,
% 0.26/0.66      ! [S2: set_int] :
% 0.26/0.66        ( ( ~ ( finite_finite_int @ S2 ) )
% 0.26/0.66        = ( ~ ( finite_finite_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ S2 ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % infinite_int_iff_infinite_nat_abs
% 0.26/0.66  thf(fact_9269_Code__Target__Int_Onegative__def,axiom,
% 0.26/0.66      ( code_Target_negative
% 0.26/0.66      = ( comp_int_int_num @ uminus_uminus_int @ numeral_numeral_int ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Code_Target_Int.negative_def
% 0.26/0.66  thf(fact_9270_measure__function__int,axiom,
% 0.26/0.66      fun_is_measure_int @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) ).
% 0.26/0.66  
% 0.26/0.66  % measure_function_int
% 0.26/0.66  thf(fact_9271_times__int_Oabs__eq,axiom,
% 0.26/0.66      ! [Xa: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 0.26/0.66        ( ( times_times_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X3 ) )
% 0.26/0.66        = ( abs_Integ
% 0.26/0.66          @ ( produc27273713700761075at_nat
% 0.26/0.66            @ ^ [X: nat,Y: nat] :
% 0.26/0.66                ( produc2626176000494625587at_nat
% 0.26/0.66                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) )
% 0.26/0.66            @ Xa
% 0.26/0.66            @ X3 ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % times_int.abs_eq
% 0.26/0.66  thf(fact_9272_int_Oabs__induct,axiom,
% 0.26/0.66      ! [P: int > $o,X3: int] :
% 0.26/0.66        ( ! [Y4: product_prod_nat_nat] : ( P @ ( abs_Integ @ Y4 ) )
% 0.26/0.66       => ( P @ X3 ) ) ).
% 0.26/0.66  
% 0.26/0.66  % int.abs_induct
% 0.26/0.66  thf(fact_9273_eq__Abs__Integ,axiom,
% 0.26/0.66      ! [Z: int] :
% 0.26/0.66        ~ ! [X4: nat,Y4: nat] :
% 0.26/0.66            ( Z
% 0.26/0.66           != ( abs_Integ @ ( product_Pair_nat_nat @ X4 @ Y4 ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % eq_Abs_Integ
% 0.26/0.66  thf(fact_9274_nat_Oabs__eq,axiom,
% 0.26/0.66      ! [X3: product_prod_nat_nat] :
% 0.26/0.66        ( ( nat2 @ ( abs_Integ @ X3 ) )
% 0.26/0.66        = ( produc6842872674320459806at_nat @ minus_minus_nat @ X3 ) ) ).
% 0.26/0.66  
% 0.26/0.66  % nat.abs_eq
% 0.26/0.66  thf(fact_9275_zero__int__def,axiom,
% 0.26/0.66      ( zero_zero_int
% 0.26/0.66      = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % zero_int_def
% 0.26/0.66  thf(fact_9276_int__def,axiom,
% 0.26/0.66      ( semiri1314217659103216013at_int
% 0.26/0.66      = ( ^ [N3: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N3 @ zero_zero_nat ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % int_def
% 0.26/0.66  thf(fact_9277_uminus__int_Oabs__eq,axiom,
% 0.26/0.66      ! [X3: product_prod_nat_nat] :
% 0.26/0.66        ( ( uminus_uminus_int @ ( abs_Integ @ X3 ) )
% 0.26/0.66        = ( abs_Integ
% 0.26/0.66          @ ( produc2626176000494625587at_nat
% 0.26/0.66            @ ^ [X: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X )
% 0.26/0.66            @ X3 ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % uminus_int.abs_eq
% 0.26/0.66  thf(fact_9278_one__int__def,axiom,
% 0.26/0.66      ( one_one_int
% 0.26/0.66      = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % one_int_def
% 0.26/0.66  thf(fact_9279_less__int_Oabs__eq,axiom,
% 0.26/0.66      ! [Xa: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 0.26/0.66        ( ( ord_less_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X3 ) )
% 0.26/0.66        = ( produc8739625826339149834_nat_o
% 0.26/0.66          @ ^ [X: nat,Y: nat] :
% 0.26/0.66              ( produc6081775807080527818_nat_o
% 0.26/0.66              @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) )
% 0.26/0.66          @ Xa
% 0.26/0.66          @ X3 ) ) ).
% 0.26/0.66  
% 0.26/0.66  % less_int.abs_eq
% 0.26/0.66  thf(fact_9280_less__eq__int_Oabs__eq,axiom,
% 0.26/0.66      ! [Xa: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 0.26/0.66        ( ( ord_less_eq_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X3 ) )
% 0.26/0.66        = ( produc8739625826339149834_nat_o
% 0.26/0.66          @ ^ [X: nat,Y: nat] :
% 0.26/0.66              ( produc6081775807080527818_nat_o
% 0.26/0.66              @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) )
% 0.26/0.66          @ Xa
% 0.26/0.66          @ X3 ) ) ).
% 0.26/0.66  
% 0.26/0.66  % less_eq_int.abs_eq
% 0.26/0.66  thf(fact_9281_plus__int_Oabs__eq,axiom,
% 0.26/0.66      ! [Xa: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 0.26/0.66        ( ( plus_plus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X3 ) )
% 0.26/0.66        = ( abs_Integ
% 0.26/0.66          @ ( produc27273713700761075at_nat
% 0.26/0.66            @ ^ [X: nat,Y: nat] :
% 0.26/0.66                ( produc2626176000494625587at_nat
% 0.26/0.66                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) )
% 0.26/0.66            @ Xa
% 0.26/0.66            @ X3 ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % plus_int.abs_eq
% 0.26/0.66  thf(fact_9282_minus__int_Oabs__eq,axiom,
% 0.26/0.66      ! [Xa: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 0.26/0.66        ( ( minus_minus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X3 ) )
% 0.26/0.66        = ( abs_Integ
% 0.26/0.66          @ ( produc27273713700761075at_nat
% 0.26/0.66            @ ^ [X: nat,Y: nat] :
% 0.26/0.66                ( produc2626176000494625587at_nat
% 0.26/0.66                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) )
% 0.26/0.66            @ Xa
% 0.26/0.66            @ X3 ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % minus_int.abs_eq
% 0.26/0.66  thf(fact_9283_num__of__nat_Osimps_I2_J,axiom,
% 0.26/0.66      ! [N: nat] :
% 0.26/0.66        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.66         => ( ( num_of_nat @ ( suc @ N ) )
% 0.26/0.66            = ( inc @ ( num_of_nat @ N ) ) ) )
% 0.26/0.66        & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.66         => ( ( num_of_nat @ ( suc @ N ) )
% 0.26/0.66            = one ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % num_of_nat.simps(2)
% 0.26/0.66  thf(fact_9284_Gcd__remove0__nat,axiom,
% 0.26/0.66      ! [M7: set_nat] :
% 0.26/0.66        ( ( finite_finite_nat @ M7 )
% 0.26/0.66       => ( ( gcd_Gcd_nat @ M7 )
% 0.26/0.66          = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M7 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Gcd_remove0_nat
% 0.26/0.66  thf(fact_9285_pow_Osimps_I3_J,axiom,
% 0.26/0.66      ! [X3: num,Y3: num] :
% 0.26/0.66        ( ( pow @ X3 @ ( bit1 @ Y3 ) )
% 0.26/0.66        = ( times_times_num @ ( sqr @ ( pow @ X3 @ Y3 ) ) @ X3 ) ) ).
% 0.26/0.66  
% 0.26/0.66  % pow.simps(3)
% 0.26/0.66  thf(fact_9286_num__of__nat__numeral__eq,axiom,
% 0.26/0.66      ! [Q3: num] :
% 0.26/0.66        ( ( num_of_nat @ ( numeral_numeral_nat @ Q3 ) )
% 0.26/0.66        = Q3 ) ).
% 0.26/0.66  
% 0.26/0.66  % num_of_nat_numeral_eq
% 0.26/0.66  thf(fact_9287_sqr_Osimps_I2_J,axiom,
% 0.26/0.66      ! [N: num] :
% 0.26/0.66        ( ( sqr @ ( bit0 @ N ) )
% 0.26/0.66        = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % sqr.simps(2)
% 0.26/0.66  thf(fact_9288_sqr_Osimps_I1_J,axiom,
% 0.26/0.66      ( ( sqr @ one )
% 0.26/0.66      = one ) ).
% 0.26/0.66  
% 0.26/0.66  % sqr.simps(1)
% 0.26/0.66  thf(fact_9289_sqr__conv__mult,axiom,
% 0.26/0.66      ( sqr
% 0.26/0.66      = ( ^ [X: num] : ( times_times_num @ X @ X ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % sqr_conv_mult
% 0.26/0.66  thf(fact_9290_num__of__nat_Osimps_I1_J,axiom,
% 0.26/0.66      ( ( num_of_nat @ zero_zero_nat )
% 0.26/0.66      = one ) ).
% 0.26/0.66  
% 0.26/0.66  % num_of_nat.simps(1)
% 0.26/0.66  thf(fact_9291_numeral__num__of__nat,axiom,
% 0.26/0.66      ! [N: nat] :
% 0.26/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.66       => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 0.26/0.66          = N ) ) ).
% 0.26/0.66  
% 0.26/0.66  % numeral_num_of_nat
% 0.26/0.66  thf(fact_9292_num__of__nat__One,axiom,
% 0.26/0.66      ! [N: nat] :
% 0.26/0.66        ( ( ord_less_eq_nat @ N @ one_one_nat )
% 0.26/0.66       => ( ( num_of_nat @ N )
% 0.26/0.66          = one ) ) ).
% 0.26/0.66  
% 0.26/0.66  % num_of_nat_One
% 0.26/0.66  thf(fact_9293_pow_Osimps_I2_J,axiom,
% 0.26/0.66      ! [X3: num,Y3: num] :
% 0.26/0.66        ( ( pow @ X3 @ ( bit0 @ Y3 ) )
% 0.26/0.66        = ( sqr @ ( pow @ X3 @ Y3 ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % pow.simps(2)
% 0.26/0.66  thf(fact_9294_num__of__integer_Orep__eq,axiom,
% 0.26/0.66      ( code_num_of_integer
% 0.26/0.66      = ( ^ [X: code_integer] : ( num_of_nat @ ( nat2 @ ( code_int_of_integer @ X ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % num_of_integer.rep_eq
% 0.26/0.66  thf(fact_9295_num__of__integer_Oabs__eq,axiom,
% 0.26/0.66      ! [X3: int] :
% 0.26/0.66        ( ( code_num_of_integer @ ( code_integer_of_int @ X3 ) )
% 0.26/0.66        = ( num_of_nat @ ( nat2 @ X3 ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % num_of_integer.abs_eq
% 0.26/0.66  thf(fact_9296_num__of__nat__double,axiom,
% 0.26/0.66      ! [N: nat] :
% 0.26/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.66       => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 0.26/0.66          = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % num_of_nat_double
% 0.26/0.66  thf(fact_9297_num__of__nat__plus__distrib,axiom,
% 0.26/0.66      ! [M: nat,N: nat] :
% 0.26/0.66        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.66       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.66         => ( ( num_of_nat @ ( plus_plus_nat @ M @ N ) )
% 0.26/0.66            = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % num_of_nat_plus_distrib
% 0.26/0.66  thf(fact_9298_sqr_Osimps_I3_J,axiom,
% 0.26/0.66      ! [N: num] :
% 0.26/0.66        ( ( sqr @ ( bit1 @ N ) )
% 0.26/0.66        = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % sqr.simps(3)
% 0.26/0.66  thf(fact_9299_Gcd__int__def,axiom,
% 0.26/0.66      ( gcd_Gcd_int
% 0.26/0.66      = ( ^ [K7: set_int] : ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ K7 ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Gcd_int_def
% 0.26/0.66  thf(fact_9300_less__eq__int_Orep__eq,axiom,
% 0.26/0.66      ( ord_less_eq_int
% 0.26/0.66      = ( ^ [X: int,Xa4: int] :
% 0.26/0.66            ( produc8739625826339149834_nat_o
% 0.26/0.66            @ ^ [Y: nat,Z6: nat] :
% 0.26/0.66                ( produc6081775807080527818_nat_o
% 0.26/0.66                @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y @ V4 ) @ ( plus_plus_nat @ U2 @ Z6 ) ) )
% 0.26/0.66            @ ( rep_Integ @ X )
% 0.26/0.66            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % less_eq_int.rep_eq
% 0.26/0.66  thf(fact_9301_less__int_Orep__eq,axiom,
% 0.26/0.66      ( ord_less_int
% 0.26/0.66      = ( ^ [X: int,Xa4: int] :
% 0.26/0.66            ( produc8739625826339149834_nat_o
% 0.26/0.66            @ ^ [Y: nat,Z6: nat] :
% 0.26/0.66                ( produc6081775807080527818_nat_o
% 0.26/0.66                @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y @ V4 ) @ ( plus_plus_nat @ U2 @ Z6 ) ) )
% 0.26/0.66            @ ( rep_Integ @ X )
% 0.26/0.66            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % less_int.rep_eq
% 0.26/0.66  thf(fact_9302_Gcd__int__eq,axiom,
% 0.26/0.66      ! [N4: set_nat] :
% 0.26/0.66        ( ( gcd_Gcd_int @ ( image_nat_int @ semiri1314217659103216013at_int @ N4 ) )
% 0.26/0.66        = ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ N4 ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Gcd_int_eq
% 0.26/0.66  thf(fact_9303_Gcd__nat__abs__eq,axiom,
% 0.26/0.66      ! [K5: set_int] :
% 0.26/0.66        ( ( gcd_Gcd_nat
% 0.26/0.66          @ ( image_int_nat
% 0.26/0.66            @ ^ [K3: int] : ( nat2 @ ( abs_abs_int @ K3 ) )
% 0.26/0.66            @ K5 ) )
% 0.26/0.66        = ( nat2 @ ( gcd_Gcd_int @ K5 ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Gcd_nat_abs_eq
% 0.26/0.66  thf(fact_9304_Gcd__int__greater__eq__0,axiom,
% 0.26/0.66      ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K5 ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Gcd_int_greater_eq_0
% 0.26/0.66  thf(fact_9305_nat_Orep__eq,axiom,
% 0.26/0.66      ( nat2
% 0.26/0.66      = ( ^ [X: int] : ( produc6842872674320459806at_nat @ minus_minus_nat @ ( rep_Integ @ X ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % nat.rep_eq
% 0.26/0.66  thf(fact_9306_Gcd__eq__Max,axiom,
% 0.26/0.66      ! [M7: set_nat] :
% 0.26/0.66        ( ( finite_finite_nat @ M7 )
% 0.26/0.66       => ( ( M7 != bot_bot_set_nat )
% 0.26/0.66         => ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 0.26/0.66           => ( ( gcd_Gcd_nat @ M7 )
% 0.26/0.66              = ( lattic8265883725875713057ax_nat
% 0.26/0.66                @ ( comple7806235888213564991et_nat
% 0.26/0.66                  @ ( image_nat_set_nat
% 0.26/0.66                    @ ^ [M3: nat] :
% 0.26/0.66                        ( collect_nat
% 0.26/0.66                        @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M3 ) )
% 0.26/0.66                    @ M7 ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Gcd_eq_Max
% 0.26/0.66  thf(fact_9307_uminus__int__def,axiom,
% 0.26/0.66      ( uminus_uminus_int
% 0.26/0.66      = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 0.26/0.66        @ ( produc2626176000494625587at_nat
% 0.26/0.66          @ ^ [X: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % uminus_int_def
% 0.26/0.66  thf(fact_9308_Inf__nat__def1,axiom,
% 0.26/0.66      ! [K5: set_nat] :
% 0.26/0.66        ( ( K5 != bot_bot_set_nat )
% 0.26/0.66       => ( member_nat @ ( complete_Inf_Inf_nat @ K5 ) @ K5 ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Inf_nat_def1
% 0.26/0.66  thf(fact_9309_times__int__def,axiom,
% 0.26/0.66      ( times_times_int
% 0.26/0.66      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.26/0.66        @ ( produc27273713700761075at_nat
% 0.26/0.66          @ ^ [X: nat,Y: nat] :
% 0.26/0.66              ( produc2626176000494625587at_nat
% 0.26/0.66              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % times_int_def
% 0.26/0.66  thf(fact_9310_minus__int__def,axiom,
% 0.26/0.66      ( minus_minus_int
% 0.26/0.66      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.26/0.66        @ ( produc27273713700761075at_nat
% 0.26/0.66          @ ^ [X: nat,Y: nat] :
% 0.26/0.66              ( produc2626176000494625587at_nat
% 0.26/0.66              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % minus_int_def
% 0.26/0.66  thf(fact_9311_plus__int__def,axiom,
% 0.26/0.66      ( plus_plus_int
% 0.26/0.66      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.26/0.66        @ ( produc27273713700761075at_nat
% 0.26/0.66          @ ^ [X: nat,Y: nat] :
% 0.26/0.66              ( produc2626176000494625587at_nat
% 0.26/0.66              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % plus_int_def
% 0.26/0.66  thf(fact_9312_Sup__nat__empty,axiom,
% 0.26/0.66      ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 0.26/0.66      = zero_zero_nat ) ).
% 0.26/0.66  
% 0.26/0.66  % Sup_nat_empty
% 0.26/0.66  thf(fact_9313_Inf__real__def,axiom,
% 0.26/0.66      ( comple4887499456419720421f_real
% 0.26/0.66      = ( ^ [X8: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X8 ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Inf_real_def
% 0.26/0.66  thf(fact_9314_Inf__int__def,axiom,
% 0.26/0.66      ( complete_Inf_Inf_int
% 0.26/0.66      = ( ^ [X8: set_int] : ( uminus_uminus_int @ ( complete_Sup_Sup_int @ ( image_int_int @ uminus_uminus_int @ X8 ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Inf_int_def
% 0.26/0.66  thf(fact_9315_suminf__eq__SUP__real,axiom,
% 0.26/0.66      ! [X9: nat > real] :
% 0.26/0.66        ( ( summable_real @ X9 )
% 0.26/0.66       => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X9 @ I3 ) )
% 0.26/0.66         => ( ( suminf_real @ X9 )
% 0.26/0.66            = ( comple1385675409528146559p_real
% 0.26/0.66              @ ( image_nat_real
% 0.26/0.66                @ ^ [I4: nat] : ( groups6591440286371151544t_real @ X9 @ ( set_ord_lessThan_nat @ I4 ) )
% 0.26/0.66                @ top_top_set_nat ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % suminf_eq_SUP_real
% 0.26/0.66  thf(fact_9316_Sup__nat__def,axiom,
% 0.26/0.66      ( complete_Sup_Sup_nat
% 0.26/0.66      = ( ^ [X8: set_nat] : ( if_nat @ ( X8 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X8 ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Sup_nat_def
% 0.26/0.66  thf(fact_9317_binomial__def,axiom,
% 0.26/0.66      ( binomial
% 0.26/0.66      = ( ^ [N3: nat,K3: nat] :
% 0.26/0.66            ( finite_card_set_nat
% 0.26/0.66            @ ( collect_set_nat
% 0.26/0.66              @ ^ [K7: set_nat] :
% 0.26/0.66                  ( ( member_set_nat @ K7 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N3 ) ) )
% 0.26/0.66                  & ( ( finite_card_nat @ K7 )
% 0.26/0.66                    = K3 ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % binomial_def
% 0.26/0.66  thf(fact_9318_range__mod,axiom,
% 0.26/0.66      ! [N: nat] :
% 0.26/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.66       => ( ( image_nat_nat
% 0.26/0.66            @ ^ [M3: nat] : ( modulo_modulo_nat @ M3 @ N )
% 0.26/0.66            @ top_top_set_nat )
% 0.26/0.66          = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % range_mod
% 0.26/0.66  thf(fact_9319_UNIV__nat__eq,axiom,
% 0.26/0.66      ( top_top_set_nat
% 0.26/0.66      = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % UNIV_nat_eq
% 0.26/0.66  thf(fact_9320_card__UNIV__bool,axiom,
% 0.26/0.66      ( ( finite_card_o @ top_top_set_o )
% 0.26/0.66      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % card_UNIV_bool
% 0.26/0.66  thf(fact_9321_range__mult,axiom,
% 0.26/0.66      ! [A: real] :
% 0.26/0.66        ( ( ( A = zero_zero_real )
% 0.26/0.66         => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 0.26/0.66            = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 0.26/0.66        & ( ( A != zero_zero_real )
% 0.26/0.66         => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 0.26/0.66            = top_top_set_real ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % range_mult
% 0.26/0.66  thf(fact_9322_infinite__UNIV__int,axiom,
% 0.26/0.66      ~ ( finite_finite_int @ top_top_set_int ) ).
% 0.26/0.66  
% 0.26/0.66  % infinite_UNIV_int
% 0.26/0.66  thf(fact_9323_int__in__range__abs,axiom,
% 0.26/0.66      ! [N: nat] : ( member_int @ ( semiri1314217659103216013at_int @ N ) @ ( image_int_int @ abs_abs_int @ top_top_set_int ) ) ).
% 0.26/0.66  
% 0.26/0.66  % int_in_range_abs
% 0.26/0.66  thf(fact_9324_root__def,axiom,
% 0.26/0.66      ( root
% 0.26/0.66      = ( ^ [N3: nat,X: real] :
% 0.26/0.66            ( if_real @ ( N3 = zero_zero_nat ) @ zero_zero_real
% 0.26/0.66            @ ( the_in5290026491893676941l_real @ top_top_set_real
% 0.26/0.66              @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N3 ) )
% 0.26/0.66              @ X ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % root_def
% 0.26/0.66  thf(fact_9325_card__UNIV__char,axiom,
% 0.26/0.66      ( ( finite_card_char @ top_top_set_char )
% 0.26/0.66      = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % card_UNIV_char
% 0.26/0.66  thf(fact_9326_UNIV__char__of__nat,axiom,
% 0.26/0.66      ( top_top_set_char
% 0.26/0.66      = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % UNIV_char_of_nat
% 0.26/0.66  thf(fact_9327_char_Osize_I2_J,axiom,
% 0.26/0.66      ! [X15: $o,X2: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 0.26/0.66        ( ( size_size_char @ ( char2 @ X15 @ X2 @ X32 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 0.26/0.66        = zero_zero_nat ) ).
% 0.26/0.66  
% 0.26/0.66  % char.size(2)
% 0.26/0.66  thf(fact_9328_nat__of__char__less__256,axiom,
% 0.26/0.66      ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % nat_of_char_less_256
% 0.26/0.66  thf(fact_9329_range__nat__of__char,axiom,
% 0.26/0.66      ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 0.26/0.66      = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % range_nat_of_char
% 0.26/0.66  thf(fact_9330_integer__of__char__code,axiom,
% 0.26/0.66      ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B7: $o] :
% 0.26/0.66        ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B7 ) )
% 0.26/0.66        = ( 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 @ B7 ) @ ( 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 ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % integer_of_char_code
% 0.26/0.66  thf(fact_9331_char_Osize__gen,axiom,
% 0.26/0.66      ! [X15: $o,X2: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 0.26/0.66        ( ( size_char @ ( char2 @ X15 @ X2 @ X32 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 0.26/0.66        = zero_zero_nat ) ).
% 0.26/0.66  
% 0.26/0.66  % char.size_gen
% 0.26/0.66  thf(fact_9332_String_Ochar__of__ascii__of,axiom,
% 0.26/0.66      ! [C: char] :
% 0.26/0.66        ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 0.26/0.66        = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % String.char_of_ascii_of
% 0.26/0.66  thf(fact_9333_DERIV__even__real__root,axiom,
% 0.26/0.66      ! [N: nat,X3: real] :
% 0.26/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.66       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.66         => ( ( ord_less_real @ X3 @ zero_zero_real )
% 0.26/0.66           => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ ( power_power_real @ ( root @ N @ X3 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_even_real_root
% 0.26/0.66  thf(fact_9334_DERIV__real__root__generic,axiom,
% 0.26/0.66      ! [N: nat,X3: real,D5: real] :
% 0.26/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.66       => ( ( X3 != zero_zero_real )
% 0.26/0.66         => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.66             => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.66               => ( D5
% 0.26/0.66                  = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X3 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 0.26/0.66           => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.66               => ( ( ord_less_real @ X3 @ zero_zero_real )
% 0.26/0.66                 => ( D5
% 0.26/0.66                    = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X3 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 0.26/0.66             => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.66                 => ( D5
% 0.26/0.66                    = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X3 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 0.26/0.66               => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_real_root_generic
% 0.26/0.66  thf(fact_9335_DERIV__arctan__series,axiom,
% 0.26/0.66      ! [X3: real] :
% 0.26/0.66        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.26/0.66       => ( has_fi5821293074295781190e_real
% 0.26/0.66          @ ^ [X10: real] :
% 0.26/0.66              ( suminf_real
% 0.26/0.66              @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X10 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 0.26/0.66          @ ( suminf_real
% 0.26/0.66            @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( power_power_real @ X3 @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.66          @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_arctan_series
% 0.26/0.66  thf(fact_9336_has__real__derivative__neg__dec__left,axiom,
% 0.26/0.66      ! [F: real > real,L: real,X3: real,S2: set_real] :
% 0.26/0.66        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ S2 ) )
% 0.26/0.66       => ( ( ord_less_real @ L @ zero_zero_real )
% 0.26/0.66         => ? [D6: real] :
% 0.26/0.66              ( ( ord_less_real @ zero_zero_real @ D6 )
% 0.26/0.66              & ! [H4: real] :
% 0.26/0.66                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.26/0.66                 => ( ( member_real @ ( minus_minus_real @ X3 @ H4 ) @ S2 )
% 0.26/0.66                   => ( ( ord_less_real @ H4 @ D6 )
% 0.26/0.66                     => ( ord_less_real @ ( F @ X3 ) @ ( F @ ( minus_minus_real @ X3 @ H4 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % has_real_derivative_neg_dec_left
% 0.26/0.66  thf(fact_9337_has__real__derivative__pos__inc__left,axiom,
% 0.26/0.66      ! [F: real > real,L: real,X3: real,S2: set_real] :
% 0.26/0.66        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ S2 ) )
% 0.26/0.66       => ( ( ord_less_real @ zero_zero_real @ L )
% 0.26/0.66         => ? [D6: real] :
% 0.26/0.66              ( ( ord_less_real @ zero_zero_real @ D6 )
% 0.26/0.66              & ! [H4: real] :
% 0.26/0.66                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.26/0.66                 => ( ( member_real @ ( minus_minus_real @ X3 @ H4 ) @ S2 )
% 0.26/0.66                   => ( ( ord_less_real @ H4 @ D6 )
% 0.26/0.66                     => ( ord_less_real @ ( F @ ( minus_minus_real @ X3 @ H4 ) ) @ ( F @ X3 ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % has_real_derivative_pos_inc_left
% 0.26/0.66  thf(fact_9338_has__real__derivative__pos__inc__right,axiom,
% 0.26/0.66      ! [F: real > real,L: real,X3: real,S2: set_real] :
% 0.26/0.66        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ S2 ) )
% 0.26/0.66       => ( ( ord_less_real @ zero_zero_real @ L )
% 0.26/0.66         => ? [D6: real] :
% 0.26/0.66              ( ( ord_less_real @ zero_zero_real @ D6 )
% 0.26/0.66              & ! [H4: real] :
% 0.26/0.66                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.26/0.66                 => ( ( member_real @ ( plus_plus_real @ X3 @ H4 ) @ S2 )
% 0.26/0.66                   => ( ( ord_less_real @ H4 @ D6 )
% 0.26/0.66                     => ( ord_less_real @ ( F @ X3 ) @ ( F @ ( plus_plus_real @ X3 @ H4 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % has_real_derivative_pos_inc_right
% 0.26/0.66  thf(fact_9339_has__real__derivative__neg__dec__right,axiom,
% 0.26/0.66      ! [F: real > real,L: real,X3: real,S2: set_real] :
% 0.26/0.66        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ S2 ) )
% 0.26/0.66       => ( ( ord_less_real @ L @ zero_zero_real )
% 0.26/0.66         => ? [D6: real] :
% 0.26/0.66              ( ( ord_less_real @ zero_zero_real @ D6 )
% 0.26/0.66              & ! [H4: real] :
% 0.26/0.66                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.26/0.66                 => ( ( member_real @ ( plus_plus_real @ X3 @ H4 ) @ S2 )
% 0.26/0.66                   => ( ( ord_less_real @ H4 @ D6 )
% 0.26/0.66                     => ( ord_less_real @ ( F @ ( plus_plus_real @ X3 @ H4 ) ) @ ( F @ X3 ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % has_real_derivative_neg_dec_right
% 0.26/0.66  thf(fact_9340_DERIV__isconst3,axiom,
% 0.26/0.66      ! [A: real,B: real,X3: real,Y3: real,F: real > real] :
% 0.26/0.66        ( ( ord_less_real @ A @ B )
% 0.26/0.66       => ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.26/0.66         => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.26/0.66           => ( ! [X4: real] :
% 0.26/0.66                  ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.26/0.66                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 0.26/0.66             => ( ( F @ X3 )
% 0.26/0.66                = ( F @ Y3 ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_isconst3
% 0.26/0.66  thf(fact_9341_DERIV__isconst__all,axiom,
% 0.26/0.66      ! [F: real > real,X3: real,Y3: real] :
% 0.26/0.66        ( ! [X4: real] : ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.26/0.66       => ( ( F @ X3 )
% 0.26/0.66          = ( F @ Y3 ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_isconst_all
% 0.26/0.66  thf(fact_9342_DERIV__neg__dec__right,axiom,
% 0.26/0.66      ! [F: real > real,L: real,X3: real] :
% 0.26/0.66        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66       => ( ( ord_less_real @ L @ zero_zero_real )
% 0.26/0.66         => ? [D6: real] :
% 0.26/0.66              ( ( ord_less_real @ zero_zero_real @ D6 )
% 0.26/0.66              & ! [H4: real] :
% 0.26/0.66                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.26/0.66                 => ( ( ord_less_real @ H4 @ D6 )
% 0.26/0.66                   => ( ord_less_real @ ( F @ ( plus_plus_real @ X3 @ H4 ) ) @ ( F @ X3 ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_neg_dec_right
% 0.26/0.66  thf(fact_9343_DERIV__pos__inc__right,axiom,
% 0.26/0.66      ! [F: real > real,L: real,X3: real] :
% 0.26/0.66        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66       => ( ( ord_less_real @ zero_zero_real @ L )
% 0.26/0.66         => ? [D6: real] :
% 0.26/0.66              ( ( ord_less_real @ zero_zero_real @ D6 )
% 0.26/0.66              & ! [H4: real] :
% 0.26/0.66                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.26/0.66                 => ( ( ord_less_real @ H4 @ D6 )
% 0.26/0.66                   => ( ord_less_real @ ( F @ X3 ) @ ( F @ ( plus_plus_real @ X3 @ H4 ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_pos_inc_right
% 0.26/0.66  thf(fact_9344_DERIV__pos__inc__left,axiom,
% 0.26/0.66      ! [F: real > real,L: real,X3: real] :
% 0.26/0.66        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66       => ( ( ord_less_real @ zero_zero_real @ L )
% 0.26/0.66         => ? [D6: real] :
% 0.26/0.66              ( ( ord_less_real @ zero_zero_real @ D6 )
% 0.26/0.66              & ! [H4: real] :
% 0.26/0.66                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.26/0.66                 => ( ( ord_less_real @ H4 @ D6 )
% 0.26/0.66                   => ( ord_less_real @ ( F @ ( minus_minus_real @ X3 @ H4 ) ) @ ( F @ X3 ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_pos_inc_left
% 0.26/0.66  thf(fact_9345_DERIV__neg__dec__left,axiom,
% 0.26/0.66      ! [F: real > real,L: real,X3: real] :
% 0.26/0.66        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66       => ( ( ord_less_real @ L @ zero_zero_real )
% 0.26/0.66         => ? [D6: real] :
% 0.26/0.66              ( ( ord_less_real @ zero_zero_real @ D6 )
% 0.26/0.66              & ! [H4: real] :
% 0.26/0.66                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.26/0.66                 => ( ( ord_less_real @ H4 @ D6 )
% 0.26/0.66                   => ( ord_less_real @ ( F @ X3 ) @ ( F @ ( minus_minus_real @ X3 @ H4 ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_neg_dec_left
% 0.26/0.66  thf(fact_9346_DERIV__nonneg__imp__nondecreasing,axiom,
% 0.26/0.66      ! [A: real,B: real,F: real > real] :
% 0.26/0.66        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.66       => ( ! [X4: real] :
% 0.26/0.66              ( ( ord_less_eq_real @ A @ X4 )
% 0.26/0.66             => ( ( ord_less_eq_real @ X4 @ B )
% 0.26/0.66               => ? [Y6: real] :
% 0.26/0.66                    ( ( has_fi5821293074295781190e_real @ F @ Y6 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.26/0.66                    & ( ord_less_eq_real @ zero_zero_real @ Y6 ) ) ) )
% 0.26/0.66         => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_nonneg_imp_nondecreasing
% 0.26/0.66  thf(fact_9347_DERIV__nonpos__imp__nonincreasing,axiom,
% 0.26/0.66      ! [A: real,B: real,F: real > real] :
% 0.26/0.66        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.66       => ( ! [X4: real] :
% 0.26/0.66              ( ( ord_less_eq_real @ A @ X4 )
% 0.26/0.66             => ( ( ord_less_eq_real @ X4 @ B )
% 0.26/0.66               => ? [Y6: real] :
% 0.26/0.66                    ( ( has_fi5821293074295781190e_real @ F @ Y6 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.26/0.66                    & ( ord_less_eq_real @ Y6 @ zero_zero_real ) ) ) )
% 0.26/0.66         => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_nonpos_imp_nonincreasing
% 0.26/0.66  thf(fact_9348_deriv__nonneg__imp__mono,axiom,
% 0.26/0.66      ! [A: real,B: real,G: real > real,G2: real > real] :
% 0.26/0.66        ( ! [X4: real] :
% 0.26/0.66            ( ( member_real @ X4 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 0.26/0.66           => ( has_fi5821293074295781190e_real @ G @ ( G2 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 0.26/0.66       => ( ! [X4: real] :
% 0.26/0.66              ( ( member_real @ X4 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 0.26/0.66             => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X4 ) ) )
% 0.26/0.66         => ( ( ord_less_eq_real @ A @ B )
% 0.26/0.66           => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % deriv_nonneg_imp_mono
% 0.26/0.66  thf(fact_9349_DERIV__neg__imp__decreasing,axiom,
% 0.26/0.66      ! [A: real,B: real,F: real > real] :
% 0.26/0.66        ( ( ord_less_real @ A @ B )
% 0.26/0.66       => ( ! [X4: real] :
% 0.26/0.66              ( ( ord_less_eq_real @ A @ X4 )
% 0.26/0.66             => ( ( ord_less_eq_real @ X4 @ B )
% 0.26/0.66               => ? [Y6: real] :
% 0.26/0.66                    ( ( has_fi5821293074295781190e_real @ F @ Y6 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.26/0.66                    & ( ord_less_real @ Y6 @ zero_zero_real ) ) ) )
% 0.26/0.66         => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_neg_imp_decreasing
% 0.26/0.66  thf(fact_9350_DERIV__pos__imp__increasing,axiom,
% 0.26/0.66      ! [A: real,B: real,F: real > real] :
% 0.26/0.66        ( ( ord_less_real @ A @ B )
% 0.26/0.66       => ( ! [X4: real] :
% 0.26/0.66              ( ( ord_less_eq_real @ A @ X4 )
% 0.26/0.66             => ( ( ord_less_eq_real @ X4 @ B )
% 0.26/0.66               => ? [Y6: real] :
% 0.26/0.66                    ( ( has_fi5821293074295781190e_real @ F @ Y6 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.26/0.66                    & ( ord_less_real @ zero_zero_real @ Y6 ) ) ) )
% 0.26/0.66         => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_pos_imp_increasing
% 0.26/0.66  thf(fact_9351_MVT2,axiom,
% 0.26/0.66      ! [A: real,B: real,F: real > real,F5: real > real] :
% 0.26/0.66        ( ( ord_less_real @ A @ B )
% 0.26/0.66       => ( ! [X4: real] :
% 0.26/0.66              ( ( ord_less_eq_real @ A @ X4 )
% 0.26/0.66             => ( ( ord_less_eq_real @ X4 @ B )
% 0.26/0.66               => ( has_fi5821293074295781190e_real @ F @ ( F5 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 0.26/0.66         => ? [Z3: real] :
% 0.26/0.66              ( ( ord_less_real @ A @ Z3 )
% 0.26/0.66              & ( ord_less_real @ Z3 @ B )
% 0.26/0.66              & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 0.26/0.66                = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F5 @ Z3 ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % MVT2
% 0.26/0.66  thf(fact_9352_DERIV__local__const,axiom,
% 0.26/0.66      ! [F: real > real,L: real,X3: real,D3: real] :
% 0.26/0.66        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66       => ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.26/0.66         => ( ! [Y4: real] :
% 0.26/0.66                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y4 ) ) @ D3 )
% 0.26/0.66               => ( ( F @ X3 )
% 0.26/0.66                  = ( F @ Y4 ) ) )
% 0.26/0.66           => ( L = zero_zero_real ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_local_const
% 0.26/0.66  thf(fact_9353_DERIV__ln,axiom,
% 0.26/0.66      ! [X3: real] :
% 0.26/0.66        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.66       => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_ln
% 0.26/0.66  thf(fact_9354_DERIV__const__average,axiom,
% 0.26/0.66      ! [A: real,B: real,V: real > real,K: real] :
% 0.26/0.66        ( ( A != B )
% 0.26/0.66       => ( ! [X4: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.26/0.66         => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.26/0.66            = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_const_average
% 0.26/0.66  thf(fact_9355_DERIV__local__max,axiom,
% 0.26/0.66      ! [F: real > real,L: real,X3: real,D3: real] :
% 0.26/0.66        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66       => ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.26/0.66         => ( ! [Y4: real] :
% 0.26/0.66                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y4 ) ) @ D3 )
% 0.26/0.66               => ( ord_less_eq_real @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 0.26/0.66           => ( L = zero_zero_real ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_local_max
% 0.26/0.66  thf(fact_9356_DERIV__local__min,axiom,
% 0.26/0.66      ! [F: real > real,L: real,X3: real,D3: real] :
% 0.26/0.66        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66       => ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.26/0.66         => ( ! [Y4: real] :
% 0.26/0.66                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y4 ) ) @ D3 )
% 0.26/0.66               => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.26/0.66           => ( L = zero_zero_real ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_local_min
% 0.26/0.66  thf(fact_9357_DERIV__ln__divide,axiom,
% 0.26/0.66      ! [X3: real] :
% 0.26/0.66        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.66       => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_ln_divide
% 0.26/0.66  thf(fact_9358_DERIV__pow,axiom,
% 0.26/0.66      ! [N: nat,X3: real,S: set_real] :
% 0.26/0.66        ( has_fi5821293074295781190e_real
% 0.26/0.66        @ ^ [X: real] : ( power_power_real @ X @ N )
% 0.26/0.66        @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X3 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 0.26/0.66        @ ( topolo2177554685111907308n_real @ X3 @ S ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_pow
% 0.26/0.66  thf(fact_9359_DERIV__fun__pow,axiom,
% 0.26/0.66      ! [G: real > real,M: real,X3: real,N: nat] :
% 0.26/0.66        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66       => ( has_fi5821293074295781190e_real
% 0.26/0.66          @ ^ [X: real] : ( power_power_real @ ( G @ X ) @ N )
% 0.26/0.66          @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G @ X3 ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M )
% 0.26/0.66          @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_fun_pow
% 0.26/0.66  thf(fact_9360_has__real__derivative__powr,axiom,
% 0.26/0.66      ! [Z: real,R2: real] :
% 0.26/0.66        ( ( ord_less_real @ zero_zero_real @ Z )
% 0.26/0.66       => ( has_fi5821293074295781190e_real
% 0.26/0.66          @ ^ [Z6: real] : ( powr_real @ Z6 @ R2 )
% 0.26/0.66          @ ( times_times_real @ R2 @ ( powr_real @ Z @ ( minus_minus_real @ R2 @ one_one_real ) ) )
% 0.26/0.66          @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % has_real_derivative_powr
% 0.26/0.66  thf(fact_9361_DERIV__series_H,axiom,
% 0.26/0.66      ! [F: real > nat > real,F5: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 0.26/0.66        ( ! [N2: nat] :
% 0.26/0.66            ( has_fi5821293074295781190e_real
% 0.26/0.66            @ ^ [X: real] : ( F @ X @ N2 )
% 0.26/0.66            @ ( F5 @ X0 @ N2 )
% 0.26/0.66            @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 0.26/0.66       => ( ! [X4: real] :
% 0.26/0.66              ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.26/0.66             => ( summable_real @ ( F @ X4 ) ) )
% 0.26/0.66         => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.26/0.66           => ( ( summable_real @ ( F5 @ X0 ) )
% 0.26/0.66             => ( ( summable_real @ L5 )
% 0.26/0.66               => ( ! [N2: nat,X4: real,Y4: real] :
% 0.26/0.66                      ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.26/0.66                     => ( ( member_real @ Y4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.26/0.66                       => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X4 @ N2 ) @ ( F @ Y4 @ N2 ) ) ) @ ( times_times_real @ ( L5 @ N2 ) @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y4 ) ) ) ) ) )
% 0.26/0.66                 => ( has_fi5821293074295781190e_real
% 0.26/0.66                    @ ^ [X: real] : ( suminf_real @ ( F @ X ) )
% 0.26/0.66                    @ ( suminf_real @ ( F5 @ X0 ) )
% 0.26/0.66                    @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_series'
% 0.26/0.66  thf(fact_9362_DERIV__fun__powr,axiom,
% 0.26/0.66      ! [G: real > real,M: real,X3: real,R2: real] :
% 0.26/0.66        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66       => ( ( ord_less_real @ zero_zero_real @ ( G @ X3 ) )
% 0.26/0.66         => ( has_fi5821293074295781190e_real
% 0.26/0.66            @ ^ [X: real] : ( powr_real @ ( G @ X ) @ R2 )
% 0.26/0.66            @ ( times_times_real @ ( times_times_real @ R2 @ ( powr_real @ ( G @ X3 ) @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 0.26/0.66            @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_fun_powr
% 0.26/0.66  thf(fact_9363_DERIV__log,axiom,
% 0.26/0.66      ! [X3: real,B: real] :
% 0.26/0.66        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.66       => ( has_fi5821293074295781190e_real @ ( log @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X3 ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_log
% 0.26/0.66  thf(fact_9364_DERIV__powr,axiom,
% 0.26/0.66      ! [G: real > real,M: real,X3: real,F: real > real,R2: real] :
% 0.26/0.66        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66       => ( ( ord_less_real @ zero_zero_real @ ( G @ X3 ) )
% 0.26/0.66         => ( ( has_fi5821293074295781190e_real @ F @ R2 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66           => ( has_fi5821293074295781190e_real
% 0.26/0.66              @ ^ [X: real] : ( powr_real @ ( G @ X ) @ ( F @ X ) )
% 0.26/0.66              @ ( times_times_real @ ( powr_real @ ( G @ X3 ) @ ( F @ X3 ) ) @ ( plus_plus_real @ ( times_times_real @ R2 @ ( ln_ln_real @ ( G @ X3 ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X3 ) ) @ ( G @ X3 ) ) ) )
% 0.26/0.66              @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_powr
% 0.26/0.66  thf(fact_9365_DERIV__real__sqrt,axiom,
% 0.26/0.66      ! [X3: real] :
% 0.26/0.66        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.66       => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_real_sqrt
% 0.26/0.66  thf(fact_9366_DERIV__arctan,axiom,
% 0.26/0.66      ! [X3: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_arctan
% 0.26/0.66  thf(fact_9367_arsinh__real__has__field__derivative,axiom,
% 0.26/0.66      ! [X3: real,A3: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ A3 ) ) ).
% 0.26/0.66  
% 0.26/0.66  % arsinh_real_has_field_derivative
% 0.26/0.66  thf(fact_9368_DERIV__real__sqrt__generic,axiom,
% 0.26/0.66      ! [X3: real,D5: real] :
% 0.26/0.66        ( ( X3 != zero_zero_real )
% 0.26/0.66       => ( ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.66           => ( D5
% 0.26/0.66              = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.26/0.66         => ( ( ( ord_less_real @ X3 @ zero_zero_real )
% 0.26/0.66             => ( D5
% 0.26/0.66                = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.26/0.66           => ( has_fi5821293074295781190e_real @ sqrt @ D5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_real_sqrt_generic
% 0.26/0.66  thf(fact_9369_arcosh__real__has__field__derivative,axiom,
% 0.26/0.66      ! [X3: real,A3: set_real] :
% 0.26/0.66        ( ( ord_less_real @ one_one_real @ X3 )
% 0.26/0.66       => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ A3 ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % arcosh_real_has_field_derivative
% 0.26/0.66  thf(fact_9370_artanh__real__has__field__derivative,axiom,
% 0.26/0.66      ! [X3: real,A3: set_real] :
% 0.26/0.66        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.26/0.66       => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ A3 ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % artanh_real_has_field_derivative
% 0.26/0.66  thf(fact_9371_DERIV__power__series_H,axiom,
% 0.26/0.66      ! [R3: real,F: nat > real,X0: real] :
% 0.26/0.66        ( ! [X4: real] :
% 0.26/0.66            ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R3 ) @ R3 ) )
% 0.26/0.66           => ( summable_real
% 0.26/0.66              @ ^ [N3: nat] : ( times_times_real @ ( times_times_real @ ( F @ N3 ) @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ ( power_power_real @ X4 @ N3 ) ) ) )
% 0.26/0.66       => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R3 ) @ R3 ) )
% 0.26/0.66         => ( ( ord_less_real @ zero_zero_real @ R3 )
% 0.26/0.66           => ( has_fi5821293074295781190e_real
% 0.26/0.66              @ ^ [X: real] :
% 0.26/0.66                  ( suminf_real
% 0.26/0.66                  @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ X @ ( suc @ N3 ) ) ) )
% 0.26/0.66              @ ( suminf_real
% 0.26/0.66                @ ^ [N3: nat] : ( times_times_real @ ( times_times_real @ ( F @ N3 ) @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ ( power_power_real @ X0 @ N3 ) ) )
% 0.26/0.66              @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_power_series'
% 0.26/0.66  thf(fact_9372_DERIV__real__root,axiom,
% 0.26/0.66      ! [N: nat,X3: real] :
% 0.26/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.66       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.26/0.66         => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X3 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_real_root
% 0.26/0.66  thf(fact_9373_DERIV__arccos,axiom,
% 0.26/0.66      ! [X3: real] :
% 0.26/0.66        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.26/0.66       => ( ( ord_less_real @ X3 @ one_one_real )
% 0.26/0.66         => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_arccos
% 0.26/0.66  thf(fact_9374_DERIV__arcsin,axiom,
% 0.26/0.66      ! [X3: real] :
% 0.26/0.66        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.26/0.66       => ( ( ord_less_real @ X3 @ one_one_real )
% 0.26/0.66         => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_arcsin
% 0.26/0.66  thf(fact_9375_Maclaurin__all__le__objl,axiom,
% 0.26/0.66      ! [Diff: nat > real > real,F: real > real,X3: real,N: nat] :
% 0.26/0.66        ( ( ( ( Diff @ zero_zero_nat )
% 0.26/0.66            = F )
% 0.26/0.66          & ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 0.26/0.66       => ? [T3: real] :
% 0.26/0.66            ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 0.26/0.66            & ( ( F @ X3 )
% 0.26/0.66              = ( plus_plus_real
% 0.26/0.66                @ ( groups6591440286371151544t_real
% 0.26/0.66                  @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X3 @ M3 ) )
% 0.26/0.66                  @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.66                @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Maclaurin_all_le_objl
% 0.26/0.66  thf(fact_9376_Maclaurin__all__le,axiom,
% 0.26/0.66      ! [Diff: nat > real > real,F: real > real,X3: real,N: nat] :
% 0.26/0.66        ( ( ( Diff @ zero_zero_nat )
% 0.26/0.66          = F )
% 0.26/0.66       => ( ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.26/0.66         => ? [T3: real] :
% 0.26/0.66              ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 0.26/0.66              & ( ( F @ X3 )
% 0.26/0.66                = ( plus_plus_real
% 0.26/0.66                  @ ( groups6591440286371151544t_real
% 0.26/0.66                    @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X3 @ M3 ) )
% 0.26/0.66                    @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.66                  @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Maclaurin_all_le
% 0.26/0.66  thf(fact_9377_DERIV__odd__real__root,axiom,
% 0.26/0.66      ! [N: nat,X3: real] :
% 0.26/0.66        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.66       => ( ( X3 != zero_zero_real )
% 0.26/0.66         => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X3 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_odd_real_root
% 0.26/0.66  thf(fact_9378_Maclaurin,axiom,
% 0.26/0.66      ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 0.26/0.66        ( ( ord_less_real @ zero_zero_real @ H2 )
% 0.26/0.66       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.66         => ( ( ( Diff @ zero_zero_nat )
% 0.26/0.66              = F )
% 0.26/0.66           => ( ! [M4: nat,T3: real] :
% 0.26/0.66                  ( ( ( ord_less_nat @ M4 @ N )
% 0.26/0.66                    & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 0.26/0.66                    & ( ord_less_eq_real @ T3 @ H2 ) )
% 0.26/0.66                 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 0.26/0.66             => ? [T3: real] :
% 0.26/0.66                  ( ( ord_less_real @ zero_zero_real @ T3 )
% 0.26/0.66                  & ( ord_less_real @ T3 @ H2 )
% 0.26/0.66                  & ( ( F @ H2 )
% 0.26/0.66                    = ( plus_plus_real
% 0.26/0.66                      @ ( groups6591440286371151544t_real
% 0.26/0.66                        @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 0.26/0.66                        @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.66                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Maclaurin
% 0.26/0.66  thf(fact_9379_Maclaurin2,axiom,
% 0.26/0.66      ! [H2: real,Diff: nat > real > real,F: real > real,N: nat] :
% 0.26/0.66        ( ( ord_less_real @ zero_zero_real @ H2 )
% 0.26/0.66       => ( ( ( Diff @ zero_zero_nat )
% 0.26/0.66            = F )
% 0.26/0.66         => ( ! [M4: nat,T3: real] :
% 0.26/0.66                ( ( ( ord_less_nat @ M4 @ N )
% 0.26/0.66                  & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 0.26/0.66                  & ( ord_less_eq_real @ T3 @ H2 ) )
% 0.26/0.66               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 0.26/0.66           => ? [T3: real] :
% 0.26/0.66                ( ( ord_less_real @ zero_zero_real @ T3 )
% 0.26/0.66                & ( ord_less_eq_real @ T3 @ H2 )
% 0.26/0.66                & ( ( F @ H2 )
% 0.26/0.66                  = ( plus_plus_real
% 0.26/0.66                    @ ( groups6591440286371151544t_real
% 0.26/0.66                      @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 0.26/0.66                      @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.66                    @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Maclaurin2
% 0.26/0.66  thf(fact_9380_Maclaurin__minus,axiom,
% 0.26/0.66      ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 0.26/0.66        ( ( ord_less_real @ H2 @ zero_zero_real )
% 0.26/0.66       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.66         => ( ( ( Diff @ zero_zero_nat )
% 0.26/0.66              = F )
% 0.26/0.66           => ( ! [M4: nat,T3: real] :
% 0.26/0.66                  ( ( ( ord_less_nat @ M4 @ N )
% 0.26/0.66                    & ( ord_less_eq_real @ H2 @ T3 )
% 0.26/0.66                    & ( ord_less_eq_real @ T3 @ zero_zero_real ) )
% 0.26/0.66                 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 0.26/0.66             => ? [T3: real] :
% 0.26/0.66                  ( ( ord_less_real @ H2 @ T3 )
% 0.26/0.66                  & ( ord_less_real @ T3 @ zero_zero_real )
% 0.26/0.66                  & ( ( F @ H2 )
% 0.26/0.66                    = ( plus_plus_real
% 0.26/0.66                      @ ( groups6591440286371151544t_real
% 0.26/0.66                        @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 0.26/0.66                        @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.66                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Maclaurin_minus
% 0.26/0.66  thf(fact_9381_Maclaurin__all__lt,axiom,
% 0.26/0.66      ! [Diff: nat > real > real,F: real > real,N: nat,X3: real] :
% 0.26/0.66        ( ( ( Diff @ zero_zero_nat )
% 0.26/0.66          = F )
% 0.26/0.66       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.66         => ( ( X3 != zero_zero_real )
% 0.26/0.66           => ( ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.26/0.66             => ? [T3: real] :
% 0.26/0.66                  ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 0.26/0.66                  & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 0.26/0.66                  & ( ( F @ X3 )
% 0.26/0.66                    = ( plus_plus_real
% 0.26/0.66                      @ ( groups6591440286371151544t_real
% 0.26/0.66                        @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X3 @ M3 ) )
% 0.26/0.66                        @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.66                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Maclaurin_all_lt
% 0.26/0.66  thf(fact_9382_Maclaurin__bi__le,axiom,
% 0.26/0.66      ! [Diff: nat > real > real,F: real > real,N: nat,X3: real] :
% 0.26/0.66        ( ( ( Diff @ zero_zero_nat )
% 0.26/0.66          = F )
% 0.26/0.66       => ( ! [M4: nat,T3: real] :
% 0.26/0.66              ( ( ( ord_less_nat @ M4 @ N )
% 0.26/0.66                & ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) ) )
% 0.26/0.66             => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 0.26/0.66         => ? [T3: real] :
% 0.26/0.66              ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 0.26/0.66              & ( ( F @ X3 )
% 0.26/0.66                = ( plus_plus_real
% 0.26/0.66                  @ ( groups6591440286371151544t_real
% 0.26/0.66                    @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X3 @ M3 ) )
% 0.26/0.66                    @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.66                  @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Maclaurin_bi_le
% 0.26/0.66  thf(fact_9383_Taylor__down,axiom,
% 0.26/0.66      ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 0.26/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.66       => ( ( ( Diff @ zero_zero_nat )
% 0.26/0.66            = F )
% 0.26/0.66         => ( ! [M4: nat,T3: real] :
% 0.26/0.66                ( ( ( ord_less_nat @ M4 @ N )
% 0.26/0.66                  & ( ord_less_eq_real @ A @ T3 )
% 0.26/0.66                  & ( ord_less_eq_real @ T3 @ B ) )
% 0.26/0.66               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 0.26/0.66           => ( ( ord_less_real @ A @ C )
% 0.26/0.66             => ( ( ord_less_eq_real @ C @ B )
% 0.26/0.66               => ? [T3: real] :
% 0.26/0.66                    ( ( ord_less_real @ A @ T3 )
% 0.26/0.66                    & ( ord_less_real @ T3 @ C )
% 0.26/0.66                    & ( ( F @ A )
% 0.26/0.66                      = ( plus_plus_real
% 0.26/0.66                        @ ( groups6591440286371151544t_real
% 0.26/0.66                          @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M3 ) )
% 0.26/0.66                          @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.66                        @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Taylor_down
% 0.26/0.66  thf(fact_9384_Taylor__up,axiom,
% 0.26/0.66      ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 0.26/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.66       => ( ( ( Diff @ zero_zero_nat )
% 0.26/0.66            = F )
% 0.26/0.66         => ( ! [M4: nat,T3: real] :
% 0.26/0.66                ( ( ( ord_less_nat @ M4 @ N )
% 0.26/0.66                  & ( ord_less_eq_real @ A @ T3 )
% 0.26/0.66                  & ( ord_less_eq_real @ T3 @ B ) )
% 0.26/0.66               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 0.26/0.66           => ( ( ord_less_eq_real @ A @ C )
% 0.26/0.66             => ( ( ord_less_real @ C @ B )
% 0.26/0.66               => ? [T3: real] :
% 0.26/0.66                    ( ( ord_less_real @ C @ T3 )
% 0.26/0.66                    & ( ord_less_real @ T3 @ B )
% 0.26/0.66                    & ( ( F @ B )
% 0.26/0.66                      = ( plus_plus_real
% 0.26/0.66                        @ ( groups6591440286371151544t_real
% 0.26/0.66                          @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M3 ) )
% 0.26/0.66                          @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.66                        @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Taylor_up
% 0.26/0.66  thf(fact_9385_Taylor,axiom,
% 0.26/0.66      ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X3: real] :
% 0.26/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.66       => ( ( ( Diff @ zero_zero_nat )
% 0.26/0.66            = F )
% 0.26/0.66         => ( ! [M4: nat,T3: real] :
% 0.26/0.66                ( ( ( ord_less_nat @ M4 @ N )
% 0.26/0.66                  & ( ord_less_eq_real @ A @ T3 )
% 0.26/0.66                  & ( ord_less_eq_real @ T3 @ B ) )
% 0.26/0.66               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 0.26/0.66           => ( ( ord_less_eq_real @ A @ C )
% 0.26/0.66             => ( ( ord_less_eq_real @ C @ B )
% 0.26/0.66               => ( ( ord_less_eq_real @ A @ X3 )
% 0.26/0.66                 => ( ( ord_less_eq_real @ X3 @ B )
% 0.26/0.66                   => ( ( X3 != C )
% 0.26/0.66                     => ? [T3: real] :
% 0.26/0.66                          ( ( ( ord_less_real @ X3 @ C )
% 0.26/0.66                           => ( ( ord_less_real @ X3 @ T3 )
% 0.26/0.66                              & ( ord_less_real @ T3 @ C ) ) )
% 0.26/0.66                          & ( ~ ( ord_less_real @ X3 @ C )
% 0.26/0.66                           => ( ( ord_less_real @ C @ T3 )
% 0.26/0.66                              & ( ord_less_real @ T3 @ X3 ) ) )
% 0.26/0.66                          & ( ( F @ X3 )
% 0.26/0.66                            = ( plus_plus_real
% 0.26/0.66                              @ ( groups6591440286371151544t_real
% 0.26/0.66                                @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ X3 @ C ) @ M3 ) )
% 0.26/0.66                                @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.66                              @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X3 @ C ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Taylor
% 0.26/0.66  thf(fact_9386_Maclaurin__lemma2,axiom,
% 0.26/0.66      ! [N: nat,H2: real,Diff: nat > real > real,K: nat,B5: real] :
% 0.26/0.66        ( ! [M4: nat,T3: real] :
% 0.26/0.66            ( ( ( ord_less_nat @ M4 @ N )
% 0.26/0.66              & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 0.26/0.66              & ( ord_less_eq_real @ T3 @ H2 ) )
% 0.26/0.66           => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 0.26/0.66       => ( ( N
% 0.26/0.66            = ( suc @ K ) )
% 0.26/0.66         => ! [M2: nat,T6: real] :
% 0.26/0.66              ( ( ( ord_less_nat @ M2 @ N )
% 0.26/0.66                & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.26/0.66                & ( ord_less_eq_real @ T6 @ H2 ) )
% 0.26/0.66             => ( has_fi5821293074295781190e_real
% 0.26/0.66                @ ^ [U2: real] :
% 0.26/0.66                    ( minus_minus_real @ ( Diff @ M2 @ U2 )
% 0.26/0.66                    @ ( plus_plus_real
% 0.26/0.66                      @ ( groups6591440286371151544t_real
% 0.26/0.66                        @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M2 @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ U2 @ P5 ) )
% 0.26/0.66                        @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M2 ) ) )
% 0.26/0.66                      @ ( times_times_real @ B5 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N @ M2 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) )
% 0.26/0.66                @ ( minus_minus_real @ ( Diff @ ( suc @ M2 ) @ T6 )
% 0.26/0.66                  @ ( plus_plus_real
% 0.26/0.66                    @ ( groups6591440286371151544t_real
% 0.26/0.66                      @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M2 ) @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ T6 @ P5 ) )
% 0.26/0.66                      @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) )
% 0.26/0.66                    @ ( times_times_real @ B5 @ ( divide_divide_real @ ( power_power_real @ T6 @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) ) ) ) )
% 0.26/0.66                @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Maclaurin_lemma2
% 0.26/0.66  thf(fact_9387_isCont__Lb__Ub,axiom,
% 0.26/0.66      ! [A: real,B: real,F: real > real] :
% 0.26/0.66        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.66       => ( ! [X4: real] :
% 0.26/0.66              ( ( ( ord_less_eq_real @ A @ X4 )
% 0.26/0.66                & ( ord_less_eq_real @ X4 @ B ) )
% 0.26/0.66             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ F ) )
% 0.26/0.66         => ? [L6: real,M8: real] :
% 0.26/0.66              ( ! [X6: real] :
% 0.26/0.66                  ( ( ( ord_less_eq_real @ A @ X6 )
% 0.26/0.66                    & ( ord_less_eq_real @ X6 @ B ) )
% 0.26/0.66                 => ( ( ord_less_eq_real @ L6 @ ( F @ X6 ) )
% 0.26/0.66                    & ( ord_less_eq_real @ ( F @ X6 ) @ M8 ) ) )
% 0.26/0.66              & ! [Y6: real] :
% 0.26/0.66                  ( ( ( ord_less_eq_real @ L6 @ Y6 )
% 0.26/0.66                    & ( ord_less_eq_real @ Y6 @ M8 ) )
% 0.26/0.66                 => ? [X4: real] :
% 0.26/0.66                      ( ( ord_less_eq_real @ A @ X4 )
% 0.26/0.66                      & ( ord_less_eq_real @ X4 @ B )
% 0.26/0.66                      & ( ( F @ X4 )
% 0.26/0.66                        = Y6 ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % isCont_Lb_Ub
% 0.26/0.66  thf(fact_9388_LIM__fun__gt__zero,axiom,
% 0.26/0.66      ! [F: real > real,L: real,C: real] :
% 0.26/0.66        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 0.26/0.66       => ( ( ord_less_real @ zero_zero_real @ L )
% 0.26/0.66         => ? [R: real] :
% 0.26/0.66              ( ( ord_less_real @ zero_zero_real @ R )
% 0.26/0.66              & ! [X6: real] :
% 0.26/0.66                  ( ( ( X6 != C )
% 0.26/0.66                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X6 ) ) @ R ) )
% 0.26/0.66                 => ( ord_less_real @ zero_zero_real @ ( F @ X6 ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % LIM_fun_gt_zero
% 0.26/0.66  thf(fact_9389_LIM__fun__not__zero,axiom,
% 0.26/0.66      ! [F: real > real,L: real,C: real] :
% 0.26/0.66        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 0.26/0.66       => ( ( L != zero_zero_real )
% 0.26/0.66         => ? [R: real] :
% 0.26/0.66              ( ( ord_less_real @ zero_zero_real @ R )
% 0.26/0.66              & ! [X6: real] :
% 0.26/0.66                  ( ( ( X6 != C )
% 0.26/0.66                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X6 ) ) @ R ) )
% 0.26/0.66                 => ( ( F @ X6 )
% 0.26/0.66                   != zero_zero_real ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % LIM_fun_not_zero
% 0.26/0.66  thf(fact_9390_LIM__fun__less__zero,axiom,
% 0.26/0.66      ! [F: real > real,L: real,C: real] :
% 0.26/0.66        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 0.26/0.66       => ( ( ord_less_real @ L @ zero_zero_real )
% 0.26/0.66         => ? [R: real] :
% 0.26/0.66              ( ( ord_less_real @ zero_zero_real @ R )
% 0.26/0.66              & ! [X6: real] :
% 0.26/0.66                  ( ( ( X6 != C )
% 0.26/0.66                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X6 ) ) @ R ) )
% 0.26/0.66                 => ( ord_less_real @ ( F @ X6 ) @ zero_zero_real ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % LIM_fun_less_zero
% 0.26/0.66  thf(fact_9391_isCont__real__sqrt,axiom,
% 0.26/0.66      ! [X3: real] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ sqrt ) ).
% 0.26/0.66  
% 0.26/0.66  % isCont_real_sqrt
% 0.26/0.66  thf(fact_9392_isCont__real__root,axiom,
% 0.26/0.66      ! [X3: real,N: nat] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ ( root @ N ) ) ).
% 0.26/0.66  
% 0.26/0.66  % isCont_real_root
% 0.26/0.66  thf(fact_9393_isCont__inverse__function2,axiom,
% 0.26/0.66      ! [A: real,X3: real,B: real,G: real > real,F: real > real] :
% 0.26/0.66        ( ( ord_less_real @ A @ X3 )
% 0.26/0.66       => ( ( ord_less_real @ X3 @ B )
% 0.26/0.66         => ( ! [Z3: real] :
% 0.26/0.66                ( ( ord_less_eq_real @ A @ Z3 )
% 0.26/0.66               => ( ( ord_less_eq_real @ Z3 @ B )
% 0.26/0.66                 => ( ( G @ ( F @ Z3 ) )
% 0.26/0.66                    = Z3 ) ) )
% 0.26/0.66           => ( ! [Z3: real] :
% 0.26/0.66                  ( ( ord_less_eq_real @ A @ Z3 )
% 0.26/0.66                 => ( ( ord_less_eq_real @ Z3 @ B )
% 0.26/0.66                   => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 0.26/0.66             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X3 ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % isCont_inverse_function2
% 0.26/0.66  thf(fact_9394_isCont__ln,axiom,
% 0.26/0.66      ! [X3: real] :
% 0.26/0.66        ( ( X3 != zero_zero_real )
% 0.26/0.66       => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ ln_ln_real ) ) ).
% 0.26/0.66  
% 0.26/0.66  % isCont_ln
% 0.26/0.66  thf(fact_9395_isCont__arcosh,axiom,
% 0.26/0.66      ! [X3: real] :
% 0.26/0.66        ( ( ord_less_real @ one_one_real @ X3 )
% 0.26/0.66       => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ arcosh_real ) ) ).
% 0.26/0.66  
% 0.26/0.66  % isCont_arcosh
% 0.26/0.66  thf(fact_9396_LIM__cos__div__sin,axiom,
% 0.26/0.66      ( filterlim_real_real
% 0.26/0.66      @ ^ [X: real] : ( divide_divide_real @ ( cos_real @ X ) @ ( sin_real @ X ) )
% 0.26/0.66      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.26/0.66      @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 0.26/0.66  
% 0.26/0.66  % LIM_cos_div_sin
% 0.26/0.66  thf(fact_9397_DERIV__inverse__function,axiom,
% 0.26/0.66      ! [F: real > real,D5: real,G: real > real,X3: real,A: real,B: real] :
% 0.26/0.66        ( ( has_fi5821293074295781190e_real @ F @ D5 @ ( topolo2177554685111907308n_real @ ( G @ X3 ) @ top_top_set_real ) )
% 0.26/0.66       => ( ( D5 != zero_zero_real )
% 0.26/0.66         => ( ( ord_less_real @ A @ X3 )
% 0.26/0.66           => ( ( ord_less_real @ X3 @ B )
% 0.26/0.66             => ( ! [Y4: real] :
% 0.26/0.66                    ( ( ord_less_real @ A @ Y4 )
% 0.26/0.66                   => ( ( ord_less_real @ Y4 @ B )
% 0.26/0.66                     => ( ( F @ ( G @ Y4 ) )
% 0.26/0.66                        = Y4 ) ) )
% 0.26/0.66               => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ G )
% 0.26/0.66                 => ( has_fi5821293074295781190e_real @ G @ ( inverse_inverse_real @ D5 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_inverse_function
% 0.26/0.66  thf(fact_9398_isCont__arccos,axiom,
% 0.26/0.66      ! [X3: real] :
% 0.26/0.66        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.26/0.66       => ( ( ord_less_real @ X3 @ one_one_real )
% 0.26/0.66         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ arccos ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % isCont_arccos
% 0.26/0.66  thf(fact_9399_isCont__arcsin,axiom,
% 0.26/0.66      ! [X3: real] :
% 0.26/0.66        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.26/0.66       => ( ( ord_less_real @ X3 @ one_one_real )
% 0.26/0.66         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ arcsin ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % isCont_arcsin
% 0.26/0.66  thf(fact_9400_LIM__less__bound,axiom,
% 0.26/0.66      ! [B: real,X3: real,F: real > real] :
% 0.26/0.66        ( ( ord_less_real @ B @ X3 )
% 0.26/0.66       => ( ! [X4: real] :
% 0.26/0.66              ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ B @ X3 ) )
% 0.26/0.66             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.26/0.66         => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F )
% 0.26/0.66           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % LIM_less_bound
% 0.26/0.66  thf(fact_9401_isCont__artanh,axiom,
% 0.26/0.66      ! [X3: real] :
% 0.26/0.66        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.26/0.66       => ( ( ord_less_real @ X3 @ one_one_real )
% 0.26/0.66         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ artanh_real ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % isCont_artanh
% 0.26/0.66  thf(fact_9402_isCont__inverse__function,axiom,
% 0.26/0.66      ! [D3: real,X3: real,G: real > real,F: real > real] :
% 0.26/0.66        ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.26/0.66       => ( ! [Z3: real] :
% 0.26/0.66              ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X3 ) ) @ D3 )
% 0.26/0.66             => ( ( G @ ( F @ Z3 ) )
% 0.26/0.66                = Z3 ) )
% 0.26/0.66         => ( ! [Z3: real] :
% 0.26/0.66                ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X3 ) ) @ D3 )
% 0.26/0.66               => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) )
% 0.26/0.66           => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X3 ) @ top_top_set_real ) @ G ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % isCont_inverse_function
% 0.26/0.66  thf(fact_9403_GMVT_H,axiom,
% 0.26/0.66      ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F5: real > real] :
% 0.26/0.66        ( ( ord_less_real @ A @ B )
% 0.26/0.66       => ( ! [Z3: real] :
% 0.26/0.66              ( ( ord_less_eq_real @ A @ Z3 )
% 0.26/0.66             => ( ( ord_less_eq_real @ Z3 @ B )
% 0.26/0.66               => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 0.26/0.66         => ( ! [Z3: real] :
% 0.26/0.66                ( ( ord_less_eq_real @ A @ Z3 )
% 0.26/0.66               => ( ( ord_less_eq_real @ Z3 @ B )
% 0.26/0.66                 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ G ) ) )
% 0.26/0.66           => ( ! [Z3: real] :
% 0.26/0.66                  ( ( ord_less_real @ A @ Z3 )
% 0.26/0.66                 => ( ( ord_less_real @ Z3 @ B )
% 0.26/0.66                   => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 0.26/0.66             => ( ! [Z3: real] :
% 0.26/0.66                    ( ( ord_less_real @ A @ Z3 )
% 0.26/0.66                   => ( ( ord_less_real @ Z3 @ B )
% 0.26/0.66                     => ( has_fi5821293074295781190e_real @ F @ ( F5 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 0.26/0.66               => ? [C2: real] :
% 0.26/0.66                    ( ( ord_less_real @ A @ C2 )
% 0.26/0.66                    & ( ord_less_real @ C2 @ B )
% 0.26/0.66                    & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C2 ) )
% 0.26/0.66                      = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F5 @ C2 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % GMVT'
% 0.26/0.66  thf(fact_9404_summable__Leibniz_I2_J,axiom,
% 0.26/0.66      ! [A: nat > real] :
% 0.26/0.66        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.26/0.66       => ( ( topolo6980174941875973593q_real @ A )
% 0.26/0.66         => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 0.26/0.66           => ! [N8: nat] :
% 0.26/0.66                ( member_real
% 0.26/0.66                @ ( suminf_real
% 0.26/0.66                  @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 0.26/0.66                @ ( set_or1222579329274155063t_real
% 0.26/0.66                  @ ( groups6591440286371151544t_real
% 0.26/0.66                    @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 0.26/0.66                    @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) ) )
% 0.26/0.66                  @ ( groups6591440286371151544t_real
% 0.26/0.66                    @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 0.26/0.66                    @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % summable_Leibniz(2)
% 0.26/0.66  thf(fact_9405_summable__Leibniz_I3_J,axiom,
% 0.26/0.66      ! [A: nat > real] :
% 0.26/0.66        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.26/0.66       => ( ( topolo6980174941875973593q_real @ A )
% 0.26/0.66         => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 0.26/0.66           => ! [N8: nat] :
% 0.26/0.66                ( member_real
% 0.26/0.66                @ ( suminf_real
% 0.26/0.66                  @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 0.26/0.66                @ ( set_or1222579329274155063t_real
% 0.26/0.66                  @ ( groups6591440286371151544t_real
% 0.26/0.66                    @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 0.26/0.66                    @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) @ one_one_nat ) ) )
% 0.26/0.66                  @ ( groups6591440286371151544t_real
% 0.26/0.66                    @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 0.26/0.66                    @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % summable_Leibniz(3)
% 0.26/0.66  thf(fact_9406_summable__Leibniz_H_I4_J,axiom,
% 0.26/0.66      ! [A: nat > real,N: nat] :
% 0.26/0.66        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.26/0.66       => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 0.26/0.66         => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 0.26/0.66           => ( ord_less_eq_real
% 0.26/0.66              @ ( suminf_real
% 0.26/0.66                @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 0.26/0.66              @ ( groups6591440286371151544t_real
% 0.26/0.66                @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 0.26/0.66                @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % summable_Leibniz'(4)
% 0.26/0.66  thf(fact_9407_mult__nat__left__at__top,axiom,
% 0.26/0.66      ! [C: nat] :
% 0.26/0.66        ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.26/0.66       => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 0.26/0.66  
% 0.26/0.66  % mult_nat_left_at_top
% 0.26/0.66  thf(fact_9408_mult__nat__right__at__top,axiom,
% 0.26/0.66      ! [C: nat] :
% 0.26/0.66        ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.26/0.66       => ( filterlim_nat_nat
% 0.26/0.66          @ ^ [X: nat] : ( times_times_nat @ X @ C )
% 0.26/0.66          @ at_top_nat
% 0.26/0.66          @ at_top_nat ) ) ).
% 0.26/0.66  
% 0.26/0.66  % mult_nat_right_at_top
% 0.26/0.66  thf(fact_9409_monoseq__convergent,axiom,
% 0.26/0.66      ! [X9: nat > real,B5: real] :
% 0.26/0.66        ( ( topolo6980174941875973593q_real @ X9 )
% 0.26/0.66       => ( ! [I3: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X9 @ I3 ) ) @ B5 )
% 0.26/0.66         => ~ ! [L6: real] :
% 0.26/0.66                ~ ( filterlim_nat_real @ X9 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % monoseq_convergent
% 0.26/0.66  thf(fact_9410_LIMSEQ__root,axiom,
% 0.26/0.66      ( filterlim_nat_real
% 0.26/0.66      @ ^ [N3: nat] : ( root @ N3 @ ( semiri5074537144036343181t_real @ N3 ) )
% 0.26/0.66      @ ( topolo2815343760600316023s_real @ one_one_real )
% 0.26/0.66      @ at_top_nat ) ).
% 0.26/0.66  
% 0.26/0.66  % LIMSEQ_root
% 0.26/0.66  thf(fact_9411_nested__sequence__unique,axiom,
% 0.26/0.66      ! [F: nat > real,G: nat > real] :
% 0.26/0.66        ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.66       => ( ! [N2: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N2 ) ) @ ( G @ N2 ) )
% 0.26/0.66         => ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 0.26/0.66           => ( ( filterlim_nat_real
% 0.26/0.66                @ ^ [N3: nat] : ( minus_minus_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 0.26/0.66                @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.26/0.66                @ at_top_nat )
% 0.26/0.66             => ? [L4: real] :
% 0.26/0.66                  ( ! [N8: nat] : ( ord_less_eq_real @ ( F @ N8 ) @ L4 )
% 0.26/0.66                  & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 0.26/0.66                  & ! [N8: nat] : ( ord_less_eq_real @ L4 @ ( G @ N8 ) )
% 0.26/0.66                  & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % nested_sequence_unique
% 0.26/0.66  thf(fact_9412_LIMSEQ__inverse__zero,axiom,
% 0.26/0.66      ! [X9: nat > real] :
% 0.26/0.66        ( ! [R: real] :
% 0.26/0.66          ? [N6: nat] :
% 0.26/0.66          ! [N2: nat] :
% 0.26/0.66            ( ( ord_less_eq_nat @ N6 @ N2 )
% 0.26/0.66           => ( ord_less_real @ R @ ( X9 @ N2 ) ) )
% 0.26/0.66       => ( filterlim_nat_real
% 0.26/0.66          @ ^ [N3: nat] : ( inverse_inverse_real @ ( X9 @ N3 ) )
% 0.26/0.66          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.26/0.66          @ at_top_nat ) ) ).
% 0.26/0.66  
% 0.26/0.66  % LIMSEQ_inverse_zero
% 0.26/0.66  thf(fact_9413_lim__inverse__n_H,axiom,
% 0.26/0.66      ( filterlim_nat_real
% 0.26/0.66      @ ^ [N3: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N3 ) )
% 0.26/0.66      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.26/0.66      @ at_top_nat ) ).
% 0.26/0.66  
% 0.26/0.66  % lim_inverse_n'
% 0.26/0.66  thf(fact_9414_LIMSEQ__root__const,axiom,
% 0.26/0.66      ! [C: real] :
% 0.26/0.66        ( ( ord_less_real @ zero_zero_real @ C )
% 0.26/0.66       => ( filterlim_nat_real
% 0.26/0.66          @ ^ [N3: nat] : ( root @ N3 @ C )
% 0.26/0.66          @ ( topolo2815343760600316023s_real @ one_one_real )
% 0.26/0.66          @ at_top_nat ) ) ).
% 0.26/0.66  
% 0.26/0.66  % LIMSEQ_root_const
% 0.26/0.66  thf(fact_9415_LIMSEQ__inverse__real__of__nat,axiom,
% 0.26/0.66      ( filterlim_nat_real
% 0.26/0.66      @ ^ [N3: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) )
% 0.26/0.66      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.26/0.66      @ at_top_nat ) ).
% 0.26/0.66  
% 0.26/0.66  % LIMSEQ_inverse_real_of_nat
% 0.26/0.66  thf(fact_9416_LIMSEQ__inverse__real__of__nat__add,axiom,
% 0.26/0.66      ! [R2: real] :
% 0.26/0.66        ( filterlim_nat_real
% 0.26/0.66        @ ^ [N3: nat] : ( plus_plus_real @ R2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 0.26/0.66        @ ( topolo2815343760600316023s_real @ R2 )
% 0.26/0.66        @ at_top_nat ) ).
% 0.26/0.66  
% 0.26/0.66  % LIMSEQ_inverse_real_of_nat_add
% 0.26/0.66  thf(fact_9417_increasing__LIMSEQ,axiom,
% 0.26/0.66      ! [F: nat > real,L: real] :
% 0.26/0.66        ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.66       => ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ L )
% 0.26/0.66         => ( ! [E: real] :
% 0.26/0.66                ( ( ord_less_real @ zero_zero_real @ E )
% 0.26/0.66               => ? [N8: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F @ N8 ) @ E ) ) )
% 0.26/0.66           => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % increasing_LIMSEQ
% 0.26/0.66  thf(fact_9418_LIMSEQ__realpow__zero,axiom,
% 0.26/0.66      ! [X3: real] :
% 0.26/0.66        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.66       => ( ( ord_less_real @ X3 @ one_one_real )
% 0.26/0.66         => ( filterlim_nat_real @ ( power_power_real @ X3 ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % LIMSEQ_realpow_zero
% 0.26/0.66  thf(fact_9419_LIMSEQ__divide__realpow__zero,axiom,
% 0.26/0.66      ! [X3: real,A: real] :
% 0.26/0.66        ( ( ord_less_real @ one_one_real @ X3 )
% 0.26/0.66       => ( filterlim_nat_real
% 0.26/0.66          @ ^ [N3: nat] : ( divide_divide_real @ A @ ( power_power_real @ X3 @ N3 ) )
% 0.26/0.66          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.26/0.66          @ at_top_nat ) ) ).
% 0.26/0.66  
% 0.26/0.66  % LIMSEQ_divide_realpow_zero
% 0.26/0.66  thf(fact_9420_LIMSEQ__abs__realpow__zero2,axiom,
% 0.26/0.66      ! [C: real] :
% 0.26/0.66        ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 0.26/0.66       => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 0.26/0.66  
% 0.26/0.66  % LIMSEQ_abs_realpow_zero2
% 0.26/0.66  thf(fact_9421_LIMSEQ__abs__realpow__zero,axiom,
% 0.26/0.66      ! [C: real] :
% 0.26/0.66        ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 0.26/0.66       => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 0.26/0.66  
% 0.26/0.66  % LIMSEQ_abs_realpow_zero
% 0.26/0.66  thf(fact_9422_LIMSEQ__inverse__realpow__zero,axiom,
% 0.26/0.66      ! [X3: real] :
% 0.26/0.66        ( ( ord_less_real @ one_one_real @ X3 )
% 0.26/0.66       => ( filterlim_nat_real
% 0.26/0.66          @ ^ [N3: nat] : ( inverse_inverse_real @ ( power_power_real @ X3 @ N3 ) )
% 0.26/0.66          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.26/0.66          @ at_top_nat ) ) ).
% 0.26/0.66  
% 0.26/0.66  % LIMSEQ_inverse_realpow_zero
% 0.26/0.66  thf(fact_9423_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 0.26/0.66      ! [R2: real] :
% 0.26/0.66        ( filterlim_nat_real
% 0.26/0.66        @ ^ [N3: nat] : ( plus_plus_real @ R2 @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) ) )
% 0.26/0.66        @ ( topolo2815343760600316023s_real @ R2 )
% 0.26/0.66        @ at_top_nat ) ).
% 0.26/0.66  
% 0.26/0.66  % LIMSEQ_inverse_real_of_nat_add_minus
% 0.26/0.66  thf(fact_9424_tendsto__exp__limit__sequentially,axiom,
% 0.26/0.66      ! [X3: real] :
% 0.26/0.66        ( filterlim_nat_real
% 0.26/0.66        @ ^ [N3: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X3 @ ( semiri5074537144036343181t_real @ N3 ) ) ) @ N3 )
% 0.26/0.66        @ ( topolo2815343760600316023s_real @ ( exp_real @ X3 ) )
% 0.26/0.66        @ at_top_nat ) ).
% 0.26/0.66  
% 0.26/0.66  % tendsto_exp_limit_sequentially
% 0.26/0.66  thf(fact_9425_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 0.26/0.66      ! [R2: real] :
% 0.26/0.66        ( filterlim_nat_real
% 0.26/0.66        @ ^ [N3: nat] : ( times_times_real @ R2 @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) ) ) )
% 0.26/0.66        @ ( topolo2815343760600316023s_real @ R2 )
% 0.26/0.66        @ at_top_nat ) ).
% 0.26/0.66  
% 0.26/0.66  % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 0.26/0.66  thf(fact_9426_summable__Leibniz_I1_J,axiom,
% 0.26/0.66      ! [A: nat > real] :
% 0.26/0.66        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.26/0.66       => ( ( topolo6980174941875973593q_real @ A )
% 0.26/0.66         => ( summable_real
% 0.26/0.66            @ ^ [N3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( A @ N3 ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % summable_Leibniz(1)
% 0.26/0.66  thf(fact_9427_summable,axiom,
% 0.26/0.66      ! [A: nat > real] :
% 0.26/0.66        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.26/0.66       => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 0.26/0.66         => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 0.26/0.66           => ( summable_real
% 0.26/0.66              @ ^ [N3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( A @ N3 ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % summable
% 0.26/0.66  thf(fact_9428_cos__diff__limit__1,axiom,
% 0.26/0.66      ! [Theta: nat > real,Theta2: real] :
% 0.26/0.66        ( ( filterlim_nat_real
% 0.26/0.66          @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 0.26/0.66          @ ( topolo2815343760600316023s_real @ one_one_real )
% 0.26/0.66          @ at_top_nat )
% 0.26/0.66       => ~ ! [K2: nat > int] :
% 0.26/0.66              ~ ( filterlim_nat_real
% 0.26/0.66                @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K2 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.26/0.66                @ ( topolo2815343760600316023s_real @ Theta2 )
% 0.26/0.66                @ at_top_nat ) ) ).
% 0.26/0.66  
% 0.26/0.66  % cos_diff_limit_1
% 0.26/0.66  thf(fact_9429_cos__limit__1,axiom,
% 0.26/0.66      ! [Theta: nat > real] :
% 0.26/0.66        ( ( filterlim_nat_real
% 0.26/0.66          @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 0.26/0.66          @ ( topolo2815343760600316023s_real @ one_one_real )
% 0.26/0.66          @ at_top_nat )
% 0.26/0.66       => ? [K2: nat > int] :
% 0.26/0.66            ( filterlim_nat_real
% 0.26/0.66            @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K2 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.26/0.66            @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.26/0.66            @ at_top_nat ) ) ).
% 0.26/0.66  
% 0.26/0.66  % cos_limit_1
% 0.26/0.66  thf(fact_9430_summable__Leibniz_I4_J,axiom,
% 0.26/0.66      ! [A: nat > real] :
% 0.26/0.66        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.26/0.66       => ( ( topolo6980174941875973593q_real @ A )
% 0.26/0.66         => ( filterlim_nat_real
% 0.26/0.66            @ ^ [N3: nat] :
% 0.26/0.66                ( groups6591440286371151544t_real
% 0.26/0.66                @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 0.26/0.66                @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 0.26/0.66            @ ( topolo2815343760600316023s_real
% 0.26/0.66              @ ( suminf_real
% 0.26/0.66                @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 0.26/0.66            @ at_top_nat ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % summable_Leibniz(4)
% 0.26/0.66  thf(fact_9431_zeroseq__arctan__series,axiom,
% 0.26/0.66      ! [X3: real] :
% 0.26/0.66        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.26/0.66       => ( filterlim_nat_real
% 0.26/0.66          @ ^ [N3: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 0.26/0.66          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.26/0.66          @ at_top_nat ) ) ).
% 0.26/0.66  
% 0.26/0.66  % zeroseq_arctan_series
% 0.26/0.66  thf(fact_9432_summable__Leibniz_H_I3_J,axiom,
% 0.26/0.66      ! [A: nat > real] :
% 0.26/0.66        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.26/0.66       => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 0.26/0.66         => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 0.26/0.66           => ( filterlim_nat_real
% 0.26/0.66              @ ^ [N3: nat] :
% 0.26/0.66                  ( groups6591440286371151544t_real
% 0.26/0.66                  @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 0.26/0.66                  @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 0.26/0.66              @ ( topolo2815343760600316023s_real
% 0.26/0.66                @ ( suminf_real
% 0.26/0.66                  @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 0.26/0.66              @ at_top_nat ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % summable_Leibniz'(3)
% 0.26/0.66  thf(fact_9433_summable__Leibniz_H_I2_J,axiom,
% 0.26/0.66      ! [A: nat > real,N: nat] :
% 0.26/0.66        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.26/0.66       => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 0.26/0.66         => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 0.26/0.66           => ( ord_less_eq_real
% 0.26/0.66              @ ( groups6591440286371151544t_real
% 0.26/0.66                @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 0.26/0.66                @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.26/0.66              @ ( suminf_real
% 0.26/0.66                @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % summable_Leibniz'(2)
% 0.26/0.66  thf(fact_9434_sums__alternating__upper__lower,axiom,
% 0.26/0.66      ! [A: nat > real] :
% 0.26/0.66        ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 0.26/0.66       => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 0.26/0.66         => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.26/0.66           => ? [L4: real] :
% 0.26/0.66                ( ! [N8: nat] :
% 0.26/0.66                    ( ord_less_eq_real
% 0.26/0.66                    @ ( groups6591440286371151544t_real
% 0.26/0.66                      @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 0.26/0.66                      @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) ) )
% 0.26/0.66                    @ L4 )
% 0.26/0.66                & ( filterlim_nat_real
% 0.26/0.66                  @ ^ [N3: nat] :
% 0.26/0.66                      ( groups6591440286371151544t_real
% 0.26/0.66                      @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 0.26/0.66                      @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 0.26/0.66                  @ ( topolo2815343760600316023s_real @ L4 )
% 0.26/0.66                  @ at_top_nat )
% 0.26/0.66                & ! [N8: nat] :
% 0.26/0.66                    ( ord_less_eq_real @ L4
% 0.26/0.66                    @ ( groups6591440286371151544t_real
% 0.26/0.66                      @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 0.26/0.66                      @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) @ one_one_nat ) ) ) )
% 0.26/0.66                & ( filterlim_nat_real
% 0.26/0.66                  @ ^ [N3: nat] :
% 0.26/0.66                      ( groups6591440286371151544t_real
% 0.26/0.66                      @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 0.26/0.66                      @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 0.26/0.66                  @ ( topolo2815343760600316023s_real @ L4 )
% 0.26/0.66                  @ at_top_nat ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % sums_alternating_upper_lower
% 0.26/0.66  thf(fact_9435_summable__Leibniz_I5_J,axiom,
% 0.26/0.66      ! [A: nat > real] :
% 0.26/0.66        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.26/0.66       => ( ( topolo6980174941875973593q_real @ A )
% 0.26/0.66         => ( filterlim_nat_real
% 0.26/0.66            @ ^ [N3: nat] :
% 0.26/0.66                ( groups6591440286371151544t_real
% 0.26/0.66                @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 0.26/0.66                @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 0.26/0.66            @ ( topolo2815343760600316023s_real
% 0.26/0.66              @ ( suminf_real
% 0.26/0.66                @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 0.26/0.66            @ at_top_nat ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % summable_Leibniz(5)
% 0.26/0.66  thf(fact_9436_summable__Leibniz_H_I5_J,axiom,
% 0.26/0.66      ! [A: nat > real] :
% 0.26/0.66        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.26/0.66       => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 0.26/0.66         => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 0.26/0.66           => ( filterlim_nat_real
% 0.26/0.66              @ ^ [N3: nat] :
% 0.26/0.66                  ( groups6591440286371151544t_real
% 0.26/0.66                  @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 0.26/0.66                  @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 0.26/0.66              @ ( topolo2815343760600316023s_real
% 0.26/0.66                @ ( suminf_real
% 0.26/0.66                  @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 0.26/0.66              @ at_top_nat ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % summable_Leibniz'(5)
% 0.26/0.66  thf(fact_9437_tendsto__exp__limit__at__right,axiom,
% 0.26/0.66      ! [X3: real] :
% 0.26/0.66        ( filterlim_real_real
% 0.26/0.66        @ ^ [Y: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X3 @ Y ) ) @ ( divide_divide_real @ one_one_real @ Y ) )
% 0.26/0.66        @ ( topolo2815343760600316023s_real @ ( exp_real @ X3 ) )
% 0.26/0.66        @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % tendsto_exp_limit_at_right
% 0.26/0.66  thf(fact_9438_tendsto__arcosh__at__left__1,axiom,
% 0.26/0.66      filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 0.26/0.66  
% 0.26/0.66  % tendsto_arcosh_at_left_1
% 0.26/0.66  thf(fact_9439_filterlim__tan__at__right,axiom,
% 0.26/0.66      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 ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % filterlim_tan_at_right
% 0.26/0.66  thf(fact_9440_greaterThan__0,axiom,
% 0.26/0.66      ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 0.26/0.66      = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 0.26/0.66  
% 0.26/0.66  % greaterThan_0
% 0.26/0.66  thf(fact_9441_exp__at__bot,axiom,
% 0.26/0.66      filterlim_real_real @ exp_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_bot_real ).
% 0.26/0.66  
% 0.26/0.66  % exp_at_bot
% 0.26/0.66  thf(fact_9442_filterlim__inverse__at__bot__neg,axiom,
% 0.26/0.66      filterlim_real_real @ inverse_inverse_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5984915006950818249n_real @ zero_zero_real ) ) ).
% 0.26/0.66  
% 0.26/0.66  % filterlim_inverse_at_bot_neg
% 0.26/0.66  thf(fact_9443_ln__at__0,axiom,
% 0.26/0.66      filterlim_real_real @ ln_ln_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 0.26/0.66  
% 0.26/0.66  % ln_at_0
% 0.26/0.66  thf(fact_9444_DERIV__pos__imp__increasing__at__bot,axiom,
% 0.26/0.66      ! [B: real,F: real > real,Flim: real] :
% 0.26/0.66        ( ! [X4: real] :
% 0.26/0.66            ( ( ord_less_eq_real @ X4 @ B )
% 0.26/0.66           => ? [Y6: real] :
% 0.26/0.66                ( ( has_fi5821293074295781190e_real @ F @ Y6 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.26/0.66                & ( ord_less_real @ zero_zero_real @ Y6 ) ) )
% 0.26/0.66       => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 0.26/0.66         => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_pos_imp_increasing_at_bot
% 0.26/0.66  thf(fact_9445_filterlim__pow__at__bot__odd,axiom,
% 0.26/0.66      ! [N: nat,F: real > real,F4: filter_real] :
% 0.26/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.66       => ( ( filterlim_real_real @ F @ at_bot_real @ F4 )
% 0.26/0.66         => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.66           => ( filterlim_real_real
% 0.26/0.66              @ ^ [X: real] : ( power_power_real @ ( F @ X ) @ N )
% 0.26/0.66              @ at_bot_real
% 0.26/0.66              @ F4 ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % filterlim_pow_at_bot_odd
% 0.26/0.66  thf(fact_9446_tendsto__arctan__at__bot,axiom,
% 0.26/0.66      filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 0.26/0.66  
% 0.26/0.66  % tendsto_arctan_at_bot
% 0.26/0.66  thf(fact_9447_filterlim__pow__at__bot__even,axiom,
% 0.26/0.66      ! [N: nat,F: real > real,F4: filter_real] :
% 0.26/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.66       => ( ( filterlim_real_real @ F @ at_bot_real @ F4 )
% 0.26/0.66         => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.26/0.66           => ( filterlim_real_real
% 0.26/0.66              @ ^ [X: real] : ( power_power_real @ ( F @ X ) @ N )
% 0.26/0.66              @ at_top_real
% 0.26/0.66              @ F4 ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % filterlim_pow_at_bot_even
% 0.26/0.66  thf(fact_9448_rat__inverse__code,axiom,
% 0.26/0.66      ! [P6: rat] :
% 0.26/0.66        ( ( quotient_of @ ( inverse_inverse_rat @ P6 ) )
% 0.26/0.66        = ( produc4245557441103728435nt_int
% 0.26/0.66          @ ^ [A4: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( A4 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A4 ) @ B3 ) @ ( abs_abs_int @ A4 ) ) )
% 0.26/0.66          @ ( quotient_of @ P6 ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % rat_inverse_code
% 0.26/0.66  thf(fact_9449_rat__zero__code,axiom,
% 0.26/0.66      ( ( quotient_of @ zero_zero_rat )
% 0.26/0.66      = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 0.26/0.66  
% 0.26/0.66  % rat_zero_code
% 0.26/0.66  thf(fact_9450_quotient__of__number_I3_J,axiom,
% 0.26/0.66      ! [K: num] :
% 0.26/0.66        ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 0.26/0.66        = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 0.26/0.66  
% 0.26/0.66  % quotient_of_number(3)
% 0.26/0.66  thf(fact_9451_quotient__of__number_I5_J,axiom,
% 0.26/0.66      ! [K: num] :
% 0.26/0.66        ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.26/0.66        = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 0.26/0.66  
% 0.26/0.66  % quotient_of_number(5)
% 0.26/0.66  thf(fact_9452_sqrt__at__top,axiom,
% 0.26/0.66      filterlim_real_real @ sqrt @ at_top_real @ at_top_real ).
% 0.26/0.66  
% 0.26/0.66  % sqrt_at_top
% 0.26/0.66  thf(fact_9453_quotient__of__denom__pos,axiom,
% 0.26/0.66      ! [R2: rat,P6: int,Q3: int] :
% 0.26/0.66        ( ( ( quotient_of @ R2 )
% 0.26/0.66          = ( product_Pair_int_int @ P6 @ Q3 ) )
% 0.26/0.66       => ( ord_less_int @ zero_zero_int @ Q3 ) ) ).
% 0.26/0.66  
% 0.26/0.66  % quotient_of_denom_pos
% 0.26/0.66  thf(fact_9454_filterlim__real__sequentially,axiom,
% 0.26/0.66      filterlim_nat_real @ semiri5074537144036343181t_real @ at_top_real @ at_top_nat ).
% 0.26/0.66  
% 0.26/0.66  % filterlim_real_sequentially
% 0.26/0.66  thf(fact_9455_quotient__of__denom__pos_H,axiom,
% 0.26/0.66      ! [R2: rat] : ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ ( quotient_of @ R2 ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % quotient_of_denom_pos'
% 0.26/0.66  thf(fact_9456_filterlim__real__at__infinity__sequentially,axiom,
% 0.26/0.66      filterlim_nat_real @ semiri5074537144036343181t_real @ at_infinity_real @ at_top_nat ).
% 0.26/0.66  
% 0.26/0.66  % filterlim_real_at_infinity_sequentially
% 0.26/0.66  thf(fact_9457_rat__less__eq__code,axiom,
% 0.26/0.66      ( ord_less_eq_rat
% 0.26/0.66      = ( ^ [P5: rat,Q5: rat] :
% 0.26/0.66            ( produc4947309494688390418_int_o
% 0.26/0.66            @ ^ [A4: int,C3: int] :
% 0.26/0.66                ( produc4947309494688390418_int_o
% 0.26/0.66                @ ^ [B3: int,D4: int] : ( ord_less_eq_int @ ( times_times_int @ A4 @ D4 ) @ ( times_times_int @ C3 @ B3 ) )
% 0.26/0.66                @ ( quotient_of @ Q5 ) )
% 0.26/0.66            @ ( quotient_of @ P5 ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % rat_less_eq_code
% 0.26/0.66  thf(fact_9458_rat__less__code,axiom,
% 0.26/0.66      ( ord_less_rat
% 0.26/0.66      = ( ^ [P5: rat,Q5: rat] :
% 0.26/0.66            ( produc4947309494688390418_int_o
% 0.26/0.66            @ ^ [A4: int,C3: int] :
% 0.26/0.66                ( produc4947309494688390418_int_o
% 0.26/0.66                @ ^ [B3: int,D4: int] : ( ord_less_int @ ( times_times_int @ A4 @ D4 ) @ ( times_times_int @ C3 @ B3 ) )
% 0.26/0.66                @ ( quotient_of @ Q5 ) )
% 0.26/0.66            @ ( quotient_of @ P5 ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % rat_less_code
% 0.26/0.66  thf(fact_9459_ln__x__over__x__tendsto__0,axiom,
% 0.26/0.66      ( filterlim_real_real
% 0.26/0.66      @ ^ [X: real] : ( divide_divide_real @ ( ln_ln_real @ X ) @ X )
% 0.26/0.66      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.26/0.66      @ at_top_real ) ).
% 0.26/0.66  
% 0.26/0.66  % ln_x_over_x_tendsto_0
% 0.26/0.66  thf(fact_9460_filterlim__inverse__at__top__right,axiom,
% 0.26/0.66      filterlim_real_real @ inverse_inverse_real @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 0.26/0.66  
% 0.26/0.66  % filterlim_inverse_at_top_right
% 0.26/0.66  thf(fact_9461_filterlim__inverse__at__right__top,axiom,
% 0.26/0.66      filterlim_real_real @ inverse_inverse_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) @ at_top_real ).
% 0.26/0.66  
% 0.26/0.66  % filterlim_inverse_at_right_top
% 0.26/0.66  thf(fact_9462_tendsto__power__div__exp__0,axiom,
% 0.26/0.66      ! [K: nat] :
% 0.26/0.66        ( filterlim_real_real
% 0.26/0.66        @ ^ [X: real] : ( divide_divide_real @ ( power_power_real @ X @ K ) @ ( exp_real @ X ) )
% 0.26/0.66        @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.26/0.66        @ at_top_real ) ).
% 0.26/0.66  
% 0.26/0.66  % tendsto_power_div_exp_0
% 0.26/0.66  thf(fact_9463_filterlim__tan__at__left,axiom,
% 0.26/0.66      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 ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % filterlim_tan_at_left
% 0.26/0.66  thf(fact_9464_tendsto__arctan__at__top,axiom,
% 0.26/0.66      filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 0.26/0.66  
% 0.26/0.66  % tendsto_arctan_at_top
% 0.26/0.66  thf(fact_9465_DERIV__neg__imp__decreasing__at__top,axiom,
% 0.26/0.66      ! [B: real,F: real > real,Flim: real] :
% 0.26/0.66        ( ! [X4: real] :
% 0.26/0.66            ( ( ord_less_eq_real @ B @ X4 )
% 0.26/0.66           => ? [Y6: real] :
% 0.26/0.66                ( ( has_fi5821293074295781190e_real @ F @ Y6 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.26/0.66                & ( ord_less_real @ Y6 @ zero_zero_real ) ) )
% 0.26/0.66       => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 0.26/0.66         => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % DERIV_neg_imp_decreasing_at_top
% 0.26/0.66  thf(fact_9466_lhopital__left__at__top,axiom,
% 0.26/0.66      ! [G: real > real,X3: real,G2: real > real,F: real > real,F5: real > real,Y3: real] :
% 0.26/0.66        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 0.26/0.66       => ( ( eventually_real
% 0.26/0.66            @ ^ [X: real] :
% 0.26/0.66                ( ( G2 @ X )
% 0.26/0.66               != zero_zero_real )
% 0.26/0.66            @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 0.26/0.66         => ( ( eventually_real
% 0.26/0.66              @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.26/0.66              @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 0.26/0.66           => ( ( eventually_real
% 0.26/0.66                @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.26/0.66                @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 0.26/0.66             => ( ( filterlim_real_real
% 0.26/0.66                  @ ^ [X: real] : ( divide_divide_real @ ( F5 @ X ) @ ( G2 @ X ) )
% 0.26/0.66                  @ ( topolo2815343760600316023s_real @ Y3 )
% 0.26/0.66                  @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 0.26/0.66               => ( filterlim_real_real
% 0.26/0.66                  @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 0.26/0.66                  @ ( topolo2815343760600316023s_real @ Y3 )
% 0.26/0.66                  @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % lhopital_left_at_top
% 0.26/0.66  thf(fact_9467_lhopital__right__at__top,axiom,
% 0.26/0.66      ! [G: real > real,X3: real,G2: real > real,F: real > real,F5: real > real,Y3: real] :
% 0.26/0.66        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 0.26/0.66       => ( ( eventually_real
% 0.26/0.66            @ ^ [X: real] :
% 0.26/0.66                ( ( G2 @ X )
% 0.26/0.66               != zero_zero_real )
% 0.26/0.66            @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 0.26/0.66         => ( ( eventually_real
% 0.26/0.66              @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.26/0.66              @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 0.26/0.66           => ( ( eventually_real
% 0.26/0.66                @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.26/0.66                @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 0.26/0.66             => ( ( filterlim_real_real
% 0.26/0.66                  @ ^ [X: real] : ( divide_divide_real @ ( F5 @ X ) @ ( G2 @ X ) )
% 0.26/0.66                  @ ( topolo2815343760600316023s_real @ Y3 )
% 0.26/0.66                  @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 0.26/0.66               => ( filterlim_real_real
% 0.26/0.66                  @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 0.26/0.66                  @ ( topolo2815343760600316023s_real @ Y3 )
% 0.26/0.66                  @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % lhopital_right_at_top
% 0.26/0.66  thf(fact_9468_obtain__pos__sum,axiom,
% 0.26/0.66      ! [R2: rat] :
% 0.26/0.66        ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 0.26/0.66       => ~ ! [S3: rat] :
% 0.26/0.66              ( ( ord_less_rat @ zero_zero_rat @ S3 )
% 0.26/0.66             => ! [T3: rat] :
% 0.26/0.66                  ( ( ord_less_rat @ zero_zero_rat @ T3 )
% 0.26/0.66                 => ( R2
% 0.26/0.66                   != ( plus_plus_rat @ S3 @ T3 ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % obtain_pos_sum
% 0.26/0.66  thf(fact_9469_sgn__rat__def,axiom,
% 0.26/0.66      ( sgn_sgn_rat
% 0.26/0.66      = ( ^ [A4: rat] : ( if_rat @ ( A4 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A4 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % sgn_rat_def
% 0.26/0.66  thf(fact_9470_abs__rat__def,axiom,
% 0.26/0.66      ( abs_abs_rat
% 0.26/0.66      = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % abs_rat_def
% 0.26/0.66  thf(fact_9471_eventually__at__right__to__0,axiom,
% 0.26/0.66      ! [P: real > $o,A: real] :
% 0.26/0.66        ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 0.26/0.66        = ( eventually_real
% 0.26/0.66          @ ^ [X: real] : ( P @ ( plus_plus_real @ X @ A ) )
% 0.26/0.66          @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % eventually_at_right_to_0
% 0.26/0.66  thf(fact_9472_eventually__at__right__real,axiom,
% 0.26/0.66      ! [A: real,B: real] :
% 0.26/0.66        ( ( ord_less_real @ A @ B )
% 0.26/0.66       => ( eventually_real
% 0.26/0.66          @ ^ [X: real] : ( member_real @ X @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.26/0.66          @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % eventually_at_right_real
% 0.26/0.66  thf(fact_9473_eventually__at__left__real,axiom,
% 0.26/0.66      ! [B: real,A: real] :
% 0.26/0.66        ( ( ord_less_real @ B @ A )
% 0.26/0.66       => ( eventually_real
% 0.26/0.66          @ ^ [X: real] : ( member_real @ X @ ( set_or1633881224788618240n_real @ B @ A ) )
% 0.26/0.66          @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % eventually_at_left_real
% 0.26/0.66  thf(fact_9474_eventually__at__top__to__right,axiom,
% 0.26/0.66      ! [P: real > $o] :
% 0.26/0.66        ( ( eventually_real @ P @ at_top_real )
% 0.26/0.66        = ( eventually_real
% 0.26/0.66          @ ^ [X: real] : ( P @ ( inverse_inverse_real @ X ) )
% 0.26/0.66          @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % eventually_at_top_to_right
% 0.26/0.66  thf(fact_9475_eventually__at__right__to__top,axiom,
% 0.26/0.66      ! [P: real > $o] :
% 0.26/0.66        ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.26/0.66        = ( eventually_real
% 0.26/0.66          @ ^ [X: real] : ( P @ ( inverse_inverse_real @ X ) )
% 0.26/0.66          @ at_top_real ) ) ).
% 0.26/0.66  
% 0.26/0.66  % eventually_at_right_to_top
% 0.26/0.66  thf(fact_9476_lhopital,axiom,
% 0.26/0.66      ! [F: real > real,X3: real,G: real > real,G2: real > real,F5: real > real,F4: filter_real] :
% 0.26/0.66        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66       => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66         => ( ( eventually_real
% 0.26/0.66              @ ^ [X: real] :
% 0.26/0.66                  ( ( G @ X )
% 0.26/0.66                 != zero_zero_real )
% 0.26/0.66              @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66           => ( ( eventually_real
% 0.26/0.66                @ ^ [X: real] :
% 0.26/0.66                    ( ( G2 @ X )
% 0.26/0.66                   != zero_zero_real )
% 0.26/0.66                @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66             => ( ( eventually_real
% 0.26/0.66                  @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.26/0.66                  @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66               => ( ( eventually_real
% 0.26/0.66                    @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.26/0.66                    @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66                 => ( ( filterlim_real_real
% 0.26/0.66                      @ ^ [X: real] : ( divide_divide_real @ ( F5 @ X ) @ ( G2 @ X ) )
% 0.26/0.66                      @ F4
% 0.26/0.66                      @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66                   => ( filterlim_real_real
% 0.26/0.66                      @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 0.26/0.66                      @ F4
% 0.26/0.66                      @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % lhopital
% 0.26/0.66  thf(fact_9477_lhopital__at__top,axiom,
% 0.26/0.66      ! [G: real > real,X3: real,G2: real > real,F: real > real,F5: real > real,Y3: real] :
% 0.26/0.66        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66       => ( ( eventually_real
% 0.26/0.66            @ ^ [X: real] :
% 0.26/0.66                ( ( G2 @ X )
% 0.26/0.66               != zero_zero_real )
% 0.26/0.66            @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66         => ( ( eventually_real
% 0.26/0.66              @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.26/0.66              @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66           => ( ( eventually_real
% 0.26/0.66                @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.26/0.66                @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66             => ( ( filterlim_real_real
% 0.26/0.66                  @ ^ [X: real] : ( divide_divide_real @ ( F5 @ X ) @ ( G2 @ X ) )
% 0.26/0.66                  @ ( topolo2815343760600316023s_real @ Y3 )
% 0.26/0.66                  @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.26/0.66               => ( filterlim_real_real
% 0.26/0.66                  @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 0.26/0.66                  @ ( topolo2815343760600316023s_real @ Y3 )
% 0.26/0.66                  @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % lhopital_at_top
% 0.26/0.66  thf(fact_9478_lhospital__at__top__at__top,axiom,
% 0.26/0.66      ! [G: real > real,G2: real > real,F: real > real,F5: real > real,X3: real] :
% 0.26/0.66        ( ( filterlim_real_real @ G @ at_top_real @ at_top_real )
% 0.26/0.66       => ( ( eventually_real
% 0.26/0.66            @ ^ [X: real] :
% 0.26/0.66                ( ( G2 @ X )
% 0.26/0.66               != zero_zero_real )
% 0.26/0.66            @ at_top_real )
% 0.26/0.66         => ( ( eventually_real
% 0.26/0.66              @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.26/0.66              @ at_top_real )
% 0.26/0.66           => ( ( eventually_real
% 0.26/0.66                @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.26/0.66                @ at_top_real )
% 0.26/0.66             => ( ( filterlim_real_real
% 0.26/0.66                  @ ^ [X: real] : ( divide_divide_real @ ( F5 @ X ) @ ( G2 @ X ) )
% 0.26/0.66                  @ ( topolo2815343760600316023s_real @ X3 )
% 0.26/0.66                  @ at_top_real )
% 0.26/0.66               => ( filterlim_real_real
% 0.26/0.66                  @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 0.26/0.66                  @ ( topolo2815343760600316023s_real @ X3 )
% 0.26/0.66                  @ at_top_real ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % lhospital_at_top_at_top
% 0.26/0.66  thf(fact_9479_lhopital__right,axiom,
% 0.26/0.66      ! [F: real > real,X3: real,G: real > real,G2: real > real,F5: real > real,F4: filter_real] :
% 0.26/0.66        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 0.26/0.66       => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 0.26/0.66         => ( ( eventually_real
% 0.26/0.66              @ ^ [X: real] :
% 0.26/0.66                  ( ( G @ X )
% 0.26/0.66                 != zero_zero_real )
% 0.26/0.66              @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 0.26/0.66           => ( ( eventually_real
% 0.26/0.66                @ ^ [X: real] :
% 0.26/0.66                    ( ( G2 @ X )
% 0.26/0.66                   != zero_zero_real )
% 0.26/0.66                @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 0.26/0.66             => ( ( eventually_real
% 0.26/0.66                  @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.26/0.66                  @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 0.26/0.66               => ( ( eventually_real
% 0.26/0.66                    @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.26/0.66                    @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 0.26/0.66                 => ( ( filterlim_real_real
% 0.26/0.66                      @ ^ [X: real] : ( divide_divide_real @ ( F5 @ X ) @ ( G2 @ X ) )
% 0.26/0.66                      @ F4
% 0.26/0.66                      @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 0.26/0.66                   => ( filterlim_real_real
% 0.26/0.66                      @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 0.26/0.66                      @ F4
% 0.26/0.66                      @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % lhopital_right
% 0.26/0.66  thf(fact_9480_lhopital__right__0,axiom,
% 0.26/0.66      ! [F0: real > real,G0: real > real,G2: real > real,F5: real > real,F4: filter_real] :
% 0.26/0.66        ( ( filterlim_real_real @ F0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.26/0.66       => ( ( filterlim_real_real @ G0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.26/0.66         => ( ( eventually_real
% 0.26/0.66              @ ^ [X: real] :
% 0.26/0.66                  ( ( G0 @ X )
% 0.26/0.66                 != zero_zero_real )
% 0.26/0.66              @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.26/0.66           => ( ( eventually_real
% 0.26/0.66                @ ^ [X: real] :
% 0.26/0.66                    ( ( G2 @ X )
% 0.26/0.66                   != zero_zero_real )
% 0.26/0.66                @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.26/0.66             => ( ( eventually_real
% 0.26/0.66                  @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F0 @ ( F5 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.26/0.66                  @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.26/0.66               => ( ( eventually_real
% 0.26/0.66                    @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G0 @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.26/0.66                    @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.26/0.66                 => ( ( filterlim_real_real
% 0.26/0.66                      @ ^ [X: real] : ( divide_divide_real @ ( F5 @ X ) @ ( G2 @ X ) )
% 0.26/0.66                      @ F4
% 0.26/0.66                      @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.26/0.66                   => ( filterlim_real_real
% 0.26/0.66                      @ ^ [X: real] : ( divide_divide_real @ ( F0 @ X ) @ ( G0 @ X ) )
% 0.26/0.66                      @ F4
% 0.26/0.66                      @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % lhopital_right_0
% 0.26/0.66  thf(fact_9481_lhopital__left,axiom,
% 0.26/0.66      ! [F: real > real,X3: real,G: real > real,G2: real > real,F5: real > real,F4: filter_real] :
% 0.26/0.66        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 0.26/0.66       => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 0.26/0.66         => ( ( eventually_real
% 0.26/0.66              @ ^ [X: real] :
% 0.26/0.66                  ( ( G @ X )
% 0.26/0.66                 != zero_zero_real )
% 0.26/0.66              @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 0.26/0.66           => ( ( eventually_real
% 0.26/0.66                @ ^ [X: real] :
% 0.26/0.66                    ( ( G2 @ X )
% 0.26/0.66                   != zero_zero_real )
% 0.26/0.66                @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 0.26/0.66             => ( ( eventually_real
% 0.26/0.66                  @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.26/0.66                  @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 0.26/0.66               => ( ( eventually_real
% 0.26/0.66                    @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.26/0.66                    @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 0.26/0.66                 => ( ( filterlim_real_real
% 0.26/0.66                      @ ^ [X: real] : ( divide_divide_real @ ( F5 @ X ) @ ( G2 @ X ) )
% 0.26/0.66                      @ F4
% 0.26/0.66                      @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 0.26/0.66                   => ( filterlim_real_real
% 0.26/0.66                      @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 0.26/0.66                      @ F4
% 0.26/0.66                      @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % lhopital_left
% 0.26/0.66  thf(fact_9482_lhopital__right__0__at__top,axiom,
% 0.26/0.66      ! [G: real > real,G2: real > real,F: real > real,F5: real > real,X3: real] :
% 0.26/0.66        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.26/0.66       => ( ( eventually_real
% 0.26/0.66            @ ^ [X: real] :
% 0.26/0.66                ( ( G2 @ X )
% 0.26/0.66               != zero_zero_real )
% 0.26/0.66            @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.26/0.66         => ( ( eventually_real
% 0.26/0.66              @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.26/0.66              @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.26/0.66           => ( ( eventually_real
% 0.26/0.66                @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.26/0.66                @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.26/0.66             => ( ( filterlim_real_real
% 0.26/0.66                  @ ^ [X: real] : ( divide_divide_real @ ( F5 @ X ) @ ( G2 @ X ) )
% 0.26/0.66                  @ ( topolo2815343760600316023s_real @ X3 )
% 0.26/0.66                  @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.26/0.66               => ( filterlim_real_real
% 0.26/0.66                  @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 0.26/0.66                  @ ( topolo2815343760600316023s_real @ X3 )
% 0.26/0.66                  @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % lhopital_right_0_at_top
% 0.26/0.66  thf(fact_9483_filterlim__int__sequentially,axiom,
% 0.26/0.66      filterlim_nat_int @ semiri1314217659103216013at_int @ at_top_int @ at_top_nat ).
% 0.26/0.66  
% 0.26/0.66  % filterlim_int_sequentially
% 0.26/0.66  thf(fact_9484_filterlim__nat__sequentially,axiom,
% 0.26/0.66      filterlim_int_nat @ nat2 @ at_top_nat @ at_top_int ).
% 0.26/0.66  
% 0.26/0.66  % filterlim_nat_sequentially
% 0.26/0.66  thf(fact_9485_eventually__sequentiallyI,axiom,
% 0.26/0.66      ! [C: nat,P: nat > $o] :
% 0.26/0.66        ( ! [X4: nat] :
% 0.26/0.66            ( ( ord_less_eq_nat @ C @ X4 )
% 0.26/0.66           => ( P @ X4 ) )
% 0.26/0.66       => ( eventually_nat @ P @ at_top_nat ) ) ).
% 0.26/0.66  
% 0.26/0.66  % eventually_sequentiallyI
% 0.26/0.66  thf(fact_9486_eventually__sequentially,axiom,
% 0.26/0.66      ! [P: nat > $o] :
% 0.26/0.66        ( ( eventually_nat @ P @ at_top_nat )
% 0.26/0.66        = ( ? [N9: nat] :
% 0.26/0.66            ! [N3: nat] :
% 0.26/0.66              ( ( ord_less_eq_nat @ N9 @ N3 )
% 0.26/0.66             => ( P @ N3 ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % eventually_sequentially
% 0.26/0.66  thf(fact_9487_le__sequentially,axiom,
% 0.26/0.66      ! [F4: filter_nat] :
% 0.26/0.66        ( ( ord_le2510731241096832064er_nat @ F4 @ at_top_nat )
% 0.26/0.66        = ( ! [N9: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N9 ) @ F4 ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % le_sequentially
% 0.26/0.66  thf(fact_9488_decseq__bounded,axiom,
% 0.26/0.66      ! [X9: nat > real,B5: real] :
% 0.26/0.66        ( ( order_9091379641038594480t_real @ X9 )
% 0.26/0.66       => ( ! [I3: nat] : ( ord_less_eq_real @ B5 @ ( X9 @ I3 ) )
% 0.26/0.66         => ( bfun_nat_real @ X9 @ at_top_nat ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % decseq_bounded
% 0.26/0.66  thf(fact_9489_decseq__convergent,axiom,
% 0.26/0.66      ! [X9: nat > real,B5: real] :
% 0.26/0.66        ( ( order_9091379641038594480t_real @ X9 )
% 0.26/0.66       => ( ! [I3: nat] : ( ord_less_eq_real @ B5 @ ( X9 @ I3 ) )
% 0.26/0.66         => ~ ! [L6: real] :
% 0.26/0.66                ( ( filterlim_nat_real @ X9 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 0.26/0.66               => ~ ! [I2: nat] : ( ord_less_eq_real @ L6 @ ( X9 @ I2 ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % decseq_convergent
% 0.26/0.66  thf(fact_9490_Bseq__realpow,axiom,
% 0.26/0.66      ! [X3: real] :
% 0.26/0.66        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.66       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 0.26/0.66         => ( bfun_nat_real @ ( power_power_real @ X3 ) @ at_top_nat ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Bseq_realpow
% 0.26/0.66  thf(fact_9491_Frct__code__post_I5_J,axiom,
% 0.26/0.66      ! [K: num] :
% 0.26/0.66        ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 0.26/0.66        = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Frct_code_post(5)
% 0.26/0.66  thf(fact_9492_GreatestI__ex__nat,axiom,
% 0.26/0.66      ! [P: nat > $o,B: nat] :
% 0.26/0.66        ( ? [X_12: nat] : ( P @ X_12 )
% 0.26/0.66       => ( ! [Y4: nat] :
% 0.26/0.66              ( ( P @ Y4 )
% 0.26/0.66             => ( ord_less_eq_nat @ Y4 @ B ) )
% 0.26/0.66         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % GreatestI_ex_nat
% 0.26/0.66  thf(fact_9493_Greatest__le__nat,axiom,
% 0.26/0.66      ! [P: nat > $o,K: nat,B: nat] :
% 0.26/0.66        ( ( P @ K )
% 0.26/0.66       => ( ! [Y4: nat] :
% 0.26/0.66              ( ( P @ Y4 )
% 0.26/0.66             => ( ord_less_eq_nat @ Y4 @ B ) )
% 0.26/0.66         => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Greatest_le_nat
% 0.26/0.66  thf(fact_9494_GreatestI__nat,axiom,
% 0.26/0.66      ! [P: nat > $o,K: nat,B: nat] :
% 0.26/0.66        ( ( P @ K )
% 0.26/0.66       => ( ! [Y4: nat] :
% 0.26/0.66              ( ( P @ Y4 )
% 0.26/0.66             => ( ord_less_eq_nat @ Y4 @ B ) )
% 0.26/0.66         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % GreatestI_nat
% 0.26/0.66  thf(fact_9495_Frct__code__post_I2_J,axiom,
% 0.26/0.66      ! [A: int] :
% 0.26/0.66        ( ( frct @ ( product_Pair_int_int @ A @ zero_zero_int ) )
% 0.26/0.66        = zero_zero_rat ) ).
% 0.26/0.66  
% 0.26/0.66  % Frct_code_post(2)
% 0.26/0.66  thf(fact_9496_Frct__code__post_I1_J,axiom,
% 0.26/0.66      ! [A: int] :
% 0.26/0.66        ( ( frct @ ( product_Pair_int_int @ zero_zero_int @ A ) )
% 0.26/0.66        = zero_zero_rat ) ).
% 0.26/0.66  
% 0.26/0.66  % Frct_code_post(1)
% 0.26/0.66  thf(fact_9497_Frct__code__post_I6_J,axiom,
% 0.26/0.66      ! [K: num,L: num] :
% 0.26/0.66        ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L ) ) )
% 0.26/0.66        = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Frct_code_post(6)
% 0.26/0.66  thf(fact_9498_Frct__code__post_I4_J,axiom,
% 0.26/0.66      ! [K: num] :
% 0.26/0.66        ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 0.26/0.66        = ( numeral_numeral_rat @ K ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Frct_code_post(4)
% 0.26/0.66  thf(fact_9499_GMVT,axiom,
% 0.26/0.66      ! [A: real,B: real,F: real > real,G: real > real] :
% 0.26/0.66        ( ( ord_less_real @ A @ B )
% 0.26/0.66       => ( ! [X4: real] :
% 0.26/0.66              ( ( ( ord_less_eq_real @ A @ X4 )
% 0.26/0.66                & ( ord_less_eq_real @ X4 @ B ) )
% 0.26/0.66             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ F ) )
% 0.26/0.66         => ( ! [X4: real] :
% 0.26/0.66                ( ( ( ord_less_real @ A @ X4 )
% 0.26/0.66                  & ( ord_less_real @ X4 @ B ) )
% 0.26/0.66               => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 0.26/0.66           => ( ! [X4: real] :
% 0.26/0.66                  ( ( ( ord_less_eq_real @ A @ X4 )
% 0.26/0.66                    & ( ord_less_eq_real @ X4 @ B ) )
% 0.26/0.66                 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ G ) )
% 0.26/0.66             => ( ! [X4: real] :
% 0.26/0.66                    ( ( ( ord_less_real @ A @ X4 )
% 0.26/0.66                      & ( ord_less_real @ X4 @ B ) )
% 0.26/0.66                   => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 0.26/0.66               => ? [G_c: real,F_c: real,C2: real] :
% 0.26/0.66                    ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 0.26/0.66                    & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 0.26/0.66                    & ( ord_less_real @ A @ C2 )
% 0.26/0.66                    & ( ord_less_real @ C2 @ B )
% 0.26/0.66                    & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 0.26/0.66                      = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % GMVT
% 0.26/0.66  thf(fact_9500_atLeast__0,axiom,
% 0.26/0.66      ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 0.26/0.66      = top_top_set_nat ) ).
% 0.26/0.66  
% 0.26/0.66  % atLeast_0
% 0.26/0.66  thf(fact_9501_card__greaterThanAtMost__int,axiom,
% 0.26/0.66      ! [L: int,U: int] :
% 0.26/0.66        ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L @ U ) )
% 0.26/0.66        = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % card_greaterThanAtMost_int
% 0.26/0.66  thf(fact_9502_normalize__negative,axiom,
% 0.26/0.66      ! [Q3: int,P6: int] :
% 0.26/0.66        ( ( ord_less_int @ Q3 @ zero_zero_int )
% 0.26/0.66       => ( ( normalize @ ( product_Pair_int_int @ P6 @ Q3 ) )
% 0.26/0.66          = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P6 ) @ ( uminus_uminus_int @ Q3 ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % normalize_negative
% 0.26/0.66  thf(fact_9503_MVT,axiom,
% 0.26/0.66      ! [A: real,B: real,F: real > real] :
% 0.26/0.66        ( ( ord_less_real @ A @ B )
% 0.26/0.66       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.26/0.66         => ( ! [X4: real] :
% 0.26/0.66                ( ( ord_less_real @ A @ X4 )
% 0.26/0.66               => ( ( ord_less_real @ X4 @ B )
% 0.26/0.66                 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 0.26/0.66           => ? [L4: real,Z3: real] :
% 0.26/0.66                ( ( ord_less_real @ A @ Z3 )
% 0.26/0.66                & ( ord_less_real @ Z3 @ B )
% 0.26/0.66                & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) )
% 0.26/0.66                & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 0.26/0.66                  = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % MVT
% 0.26/0.66  thf(fact_9504_normalize__denom__zero,axiom,
% 0.26/0.66      ! [P6: int] :
% 0.26/0.66        ( ( normalize @ ( product_Pair_int_int @ P6 @ zero_zero_int ) )
% 0.26/0.66        = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 0.26/0.66  
% 0.26/0.66  % normalize_denom_zero
% 0.26/0.66  thf(fact_9505_continuous__on__arcosh_H,axiom,
% 0.26/0.66      ! [A3: set_real,F: real > real] :
% 0.26/0.66        ( ( topolo5044208981011980120l_real @ A3 @ F )
% 0.26/0.66       => ( ! [X4: real] :
% 0.26/0.66              ( ( member_real @ X4 @ A3 )
% 0.26/0.66             => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 0.26/0.66         => ( topolo5044208981011980120l_real @ A3
% 0.26/0.66            @ ^ [X: real] : ( arcosh_real @ ( F @ X ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % continuous_on_arcosh'
% 0.26/0.66  thf(fact_9506_continuous__image__closed__interval,axiom,
% 0.26/0.66      ! [A: real,B: real,F: real > real] :
% 0.26/0.66        ( ( ord_less_eq_real @ A @ B )
% 0.26/0.66       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.26/0.66         => ? [C2: real,D6: real] :
% 0.26/0.66              ( ( ( image_real_real @ F @ ( set_or1222579329274155063t_real @ A @ B ) )
% 0.26/0.66                = ( set_or1222579329274155063t_real @ C2 @ D6 ) )
% 0.26/0.66              & ( ord_less_eq_real @ C2 @ D6 ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % continuous_image_closed_interval
% 0.26/0.66  thf(fact_9507_Rolle__deriv,axiom,
% 0.26/0.66      ! [A: real,B: real,F: real > real,F5: real > real > real] :
% 0.26/0.66        ( ( ord_less_real @ A @ B )
% 0.26/0.66       => ( ( ( F @ A )
% 0.26/0.66            = ( F @ B ) )
% 0.26/0.66         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.26/0.66           => ( ! [X4: real] :
% 0.26/0.66                  ( ( ord_less_real @ A @ X4 )
% 0.26/0.66                 => ( ( ord_less_real @ X4 @ B )
% 0.26/0.66                   => ( has_de1759254742604945161l_real @ F @ ( F5 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 0.26/0.66             => ? [Z3: real] :
% 0.26/0.66                  ( ( ord_less_real @ A @ Z3 )
% 0.26/0.66                  & ( ord_less_real @ Z3 @ B )
% 0.26/0.66                  & ( ( F5 @ Z3 )
% 0.26/0.66                    = ( ^ [V4: real] : zero_zero_real ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % Rolle_deriv
% 0.26/0.66  thf(fact_9508_mvt,axiom,
% 0.26/0.66      ! [A: real,B: real,F: real > real,F5: real > real > real] :
% 0.26/0.66        ( ( ord_less_real @ A @ B )
% 0.26/0.66       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.26/0.66         => ( ! [X4: real] :
% 0.26/0.66                ( ( ord_less_real @ A @ X4 )
% 0.26/0.66               => ( ( ord_less_real @ X4 @ B )
% 0.26/0.66                 => ( has_de1759254742604945161l_real @ F @ ( F5 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 0.26/0.66           => ~ ! [Xi: real] :
% 0.26/0.66                  ( ( ord_less_real @ A @ Xi )
% 0.26/0.66                 => ( ( ord_less_real @ Xi @ B )
% 0.26/0.66                   => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 0.26/0.66                     != ( F5 @ Xi @ ( minus_minus_real @ B @ A ) ) ) ) ) ) ) ) ).
% 0.26/0.66  
% 0.26/0.66  % mvt
% 0.26/0.66  thf(fact_9509_normalize__denom__pos,axiom,
% 0.26/0.67      ! [R2: product_prod_int_int,P6: int,Q3: int] :
% 0.26/0.67        ( ( ( normalize @ R2 )
% 0.26/0.67          = ( product_Pair_int_int @ P6 @ Q3 ) )
% 0.26/0.67       => ( ord_less_int @ zero_zero_int @ Q3 ) ) ).
% 0.26/0.67  
% 0.26/0.67  % normalize_denom_pos
% 0.26/0.67  thf(fact_9510_normalize__crossproduct,axiom,
% 0.26/0.67      ! [Q3: int,S: int,P6: int,R2: int] :
% 0.26/0.67        ( ( Q3 != zero_zero_int )
% 0.26/0.67       => ( ( S != zero_zero_int )
% 0.26/0.67         => ( ( ( normalize @ ( product_Pair_int_int @ P6 @ Q3 ) )
% 0.26/0.67              = ( normalize @ ( product_Pair_int_int @ R2 @ S ) ) )
% 0.26/0.67           => ( ( times_times_int @ P6 @ S )
% 0.26/0.67              = ( times_times_int @ R2 @ Q3 ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % normalize_crossproduct
% 0.26/0.67  thf(fact_9511_DERIV__pos__imp__increasing__open,axiom,
% 0.26/0.67      ! [A: real,B: real,F: real > real] :
% 0.26/0.67        ( ( ord_less_real @ A @ B )
% 0.26/0.67       => ( ! [X4: real] :
% 0.26/0.67              ( ( ord_less_real @ A @ X4 )
% 0.26/0.67             => ( ( ord_less_real @ X4 @ B )
% 0.26/0.67               => ? [Y6: real] :
% 0.26/0.67                    ( ( has_fi5821293074295781190e_real @ F @ Y6 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.26/0.67                    & ( ord_less_real @ zero_zero_real @ Y6 ) ) ) )
% 0.26/0.67         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.26/0.67           => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % DERIV_pos_imp_increasing_open
% 0.26/0.67  thf(fact_9512_DERIV__neg__imp__decreasing__open,axiom,
% 0.26/0.67      ! [A: real,B: real,F: real > real] :
% 0.26/0.67        ( ( ord_less_real @ A @ B )
% 0.26/0.67       => ( ! [X4: real] :
% 0.26/0.67              ( ( ord_less_real @ A @ X4 )
% 0.26/0.67             => ( ( ord_less_real @ X4 @ B )
% 0.26/0.67               => ? [Y6: real] :
% 0.26/0.67                    ( ( has_fi5821293074295781190e_real @ F @ Y6 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.26/0.67                    & ( ord_less_real @ Y6 @ zero_zero_real ) ) ) )
% 0.26/0.67         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.26/0.67           => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % DERIV_neg_imp_decreasing_open
% 0.26/0.67  thf(fact_9513_DERIV__isconst__end,axiom,
% 0.26/0.67      ! [A: real,B: real,F: real > real] :
% 0.26/0.67        ( ( ord_less_real @ A @ B )
% 0.26/0.67       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.26/0.67         => ( ! [X4: real] :
% 0.26/0.67                ( ( ord_less_real @ A @ X4 )
% 0.26/0.67               => ( ( ord_less_real @ X4 @ B )
% 0.26/0.67                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 0.26/0.67           => ( ( F @ B )
% 0.26/0.67              = ( F @ A ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % DERIV_isconst_end
% 0.26/0.67  thf(fact_9514_DERIV__isconst2,axiom,
% 0.26/0.67      ! [A: real,B: real,F: real > real,X3: real] :
% 0.26/0.67        ( ( ord_less_real @ A @ B )
% 0.26/0.67       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.26/0.67         => ( ! [X4: real] :
% 0.26/0.67                ( ( ord_less_real @ A @ X4 )
% 0.26/0.67               => ( ( ord_less_real @ X4 @ B )
% 0.26/0.67                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 0.26/0.67           => ( ( ord_less_eq_real @ A @ X3 )
% 0.26/0.67             => ( ( ord_less_eq_real @ X3 @ B )
% 0.26/0.67               => ( ( F @ X3 )
% 0.26/0.67                  = ( F @ A ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % DERIV_isconst2
% 0.26/0.67  thf(fact_9515_Rolle,axiom,
% 0.26/0.67      ! [A: real,B: real,F: real > real] :
% 0.26/0.67        ( ( ord_less_real @ A @ B )
% 0.26/0.67       => ( ( ( F @ A )
% 0.26/0.67            = ( F @ B ) )
% 0.26/0.67         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.26/0.67           => ( ! [X4: real] :
% 0.26/0.67                  ( ( ord_less_real @ A @ X4 )
% 0.26/0.67                 => ( ( ord_less_real @ X4 @ B )
% 0.26/0.67                   => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 0.26/0.67             => ? [Z3: real] :
% 0.26/0.67                  ( ( ord_less_real @ A @ Z3 )
% 0.26/0.67                  & ( ord_less_real @ Z3 @ B )
% 0.26/0.67                  & ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Rolle
% 0.26/0.67  thf(fact_9516_normalize__def,axiom,
% 0.26/0.67      ( normalize
% 0.26/0.67      = ( ^ [P5: product_prod_int_int] :
% 0.26/0.67            ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P5 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P5 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P5 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) )
% 0.26/0.67            @ ( if_Pro3027730157355071871nt_int
% 0.26/0.67              @ ( ( product_snd_int_int @ P5 )
% 0.26/0.67                = zero_zero_int )
% 0.26/0.67              @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.26/0.67              @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P5 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P5 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % normalize_def
% 0.26/0.67  thf(fact_9517_gcd__pos__int,axiom,
% 0.26/0.67      ! [M: int,N: int] :
% 0.26/0.67        ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M @ N ) )
% 0.26/0.67        = ( ( M != zero_zero_int )
% 0.26/0.67          | ( N != zero_zero_int ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_pos_int
% 0.26/0.67  thf(fact_9518_gcd__neg__numeral__2__int,axiom,
% 0.26/0.67      ! [X3: int,N: num] :
% 0.26/0.67        ( ( gcd_gcd_int @ X3 @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.67        = ( gcd_gcd_int @ X3 @ ( numeral_numeral_int @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_neg_numeral_2_int
% 0.26/0.67  thf(fact_9519_gcd__neg__numeral__1__int,axiom,
% 0.26/0.67      ! [N: num,X3: int] :
% 0.26/0.67        ( ( gcd_gcd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ X3 )
% 0.26/0.67        = ( gcd_gcd_int @ ( numeral_numeral_int @ N ) @ X3 ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_neg_numeral_1_int
% 0.26/0.67  thf(fact_9520_gcd__0__int,axiom,
% 0.26/0.67      ! [X3: int] :
% 0.26/0.67        ( ( gcd_gcd_int @ X3 @ zero_zero_int )
% 0.26/0.67        = ( abs_abs_int @ X3 ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_0_int
% 0.26/0.67  thf(fact_9521_gcd__0__left__int,axiom,
% 0.26/0.67      ! [X3: int] :
% 0.26/0.67        ( ( gcd_gcd_int @ zero_zero_int @ X3 )
% 0.26/0.67        = ( abs_abs_int @ X3 ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_0_left_int
% 0.26/0.67  thf(fact_9522_gcd__ge__0__int,axiom,
% 0.26/0.67      ! [X3: int,Y3: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X3 @ Y3 ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_ge_0_int
% 0.26/0.67  thf(fact_9523_gcd__le1__int,axiom,
% 0.26/0.67      ! [A: int,B: int] :
% 0.26/0.67        ( ( ord_less_int @ zero_zero_int @ A )
% 0.26/0.67       => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_le1_int
% 0.26/0.67  thf(fact_9524_gcd__le2__int,axiom,
% 0.26/0.67      ! [B: int,A: int] :
% 0.26/0.67        ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.67       => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_le2_int
% 0.26/0.67  thf(fact_9525_gcd__cases__int,axiom,
% 0.26/0.67      ! [X3: int,Y3: int,P: int > $o] :
% 0.26/0.67        ( ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.26/0.67         => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 0.26/0.67           => ( P @ ( gcd_gcd_int @ X3 @ Y3 ) ) ) )
% 0.26/0.67       => ( ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.26/0.67           => ( ( ord_less_eq_int @ Y3 @ zero_zero_int )
% 0.26/0.67             => ( P @ ( gcd_gcd_int @ X3 @ ( uminus_uminus_int @ Y3 ) ) ) ) )
% 0.26/0.67         => ( ( ( ord_less_eq_int @ X3 @ zero_zero_int )
% 0.26/0.67             => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 0.26/0.67               => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X3 ) @ Y3 ) ) ) )
% 0.26/0.67           => ( ( ( ord_less_eq_int @ X3 @ zero_zero_int )
% 0.26/0.67               => ( ( ord_less_eq_int @ Y3 @ zero_zero_int )
% 0.26/0.67                 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X3 ) @ ( uminus_uminus_int @ Y3 ) ) ) ) )
% 0.26/0.67             => ( P @ ( gcd_gcd_int @ X3 @ Y3 ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_cases_int
% 0.26/0.67  thf(fact_9526_gcd__unique__int,axiom,
% 0.26/0.67      ! [D3: int,A: int,B: int] :
% 0.26/0.67        ( ( ( ord_less_eq_int @ zero_zero_int @ D3 )
% 0.26/0.67          & ( dvd_dvd_int @ D3 @ A )
% 0.26/0.67          & ( dvd_dvd_int @ D3 @ B )
% 0.26/0.67          & ! [E3: int] :
% 0.26/0.67              ( ( ( dvd_dvd_int @ E3 @ A )
% 0.26/0.67                & ( dvd_dvd_int @ E3 @ B ) )
% 0.26/0.67             => ( dvd_dvd_int @ E3 @ D3 ) ) )
% 0.26/0.67        = ( D3
% 0.26/0.67          = ( gcd_gcd_int @ A @ B ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_unique_int
% 0.26/0.67  thf(fact_9527_gcd__non__0__int,axiom,
% 0.26/0.67      ! [Y3: int,X3: int] :
% 0.26/0.67        ( ( ord_less_int @ zero_zero_int @ Y3 )
% 0.26/0.67       => ( ( gcd_gcd_int @ X3 @ Y3 )
% 0.26/0.67          = ( gcd_gcd_int @ Y3 @ ( modulo_modulo_int @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_non_0_int
% 0.26/0.67  thf(fact_9528_gcd__code__int,axiom,
% 0.26/0.67      ( gcd_gcd_int
% 0.26/0.67      = ( ^ [K3: int,L2: int] : ( abs_abs_int @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( gcd_gcd_int @ L2 @ ( modulo_modulo_int @ ( abs_abs_int @ K3 ) @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_code_int
% 0.26/0.67  thf(fact_9529_gcd__is__Max__divisors__int,axiom,
% 0.26/0.67      ! [N: int,M: int] :
% 0.26/0.67        ( ( N != zero_zero_int )
% 0.26/0.67       => ( ( gcd_gcd_int @ M @ N )
% 0.26/0.67          = ( lattic8263393255366662781ax_int
% 0.26/0.67            @ ( collect_int
% 0.26/0.67              @ ^ [D4: int] :
% 0.26/0.67                  ( ( dvd_dvd_int @ D4 @ M )
% 0.26/0.67                  & ( dvd_dvd_int @ D4 @ N ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_is_Max_divisors_int
% 0.26/0.67  thf(fact_9530_range__abs__Nats,axiom,
% 0.26/0.67      ( ( image_int_int @ abs_abs_int @ top_top_set_int )
% 0.26/0.67      = semiring_1_Nats_int ) ).
% 0.26/0.67  
% 0.26/0.67  % range_abs_Nats
% 0.26/0.67  thf(fact_9531_gcd__nat_Oeq__neutr__iff,axiom,
% 0.26/0.67      ! [A: nat,B: nat] :
% 0.26/0.67        ( ( ( gcd_gcd_nat @ A @ B )
% 0.26/0.67          = zero_zero_nat )
% 0.26/0.67        = ( ( A = zero_zero_nat )
% 0.26/0.67          & ( B = zero_zero_nat ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_nat.eq_neutr_iff
% 0.26/0.67  thf(fact_9532_gcd__nat_Oleft__neutral,axiom,
% 0.26/0.67      ! [A: nat] :
% 0.26/0.67        ( ( gcd_gcd_nat @ zero_zero_nat @ A )
% 0.26/0.67        = A ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_nat.left_neutral
% 0.26/0.67  thf(fact_9533_gcd__nat_Oneutr__eq__iff,axiom,
% 0.26/0.67      ! [A: nat,B: nat] :
% 0.26/0.67        ( ( zero_zero_nat
% 0.26/0.67          = ( gcd_gcd_nat @ A @ B ) )
% 0.26/0.67        = ( ( A = zero_zero_nat )
% 0.26/0.67          & ( B = zero_zero_nat ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_nat.neutr_eq_iff
% 0.26/0.67  thf(fact_9534_gcd__nat_Oright__neutral,axiom,
% 0.26/0.67      ! [A: nat] :
% 0.26/0.67        ( ( gcd_gcd_nat @ A @ zero_zero_nat )
% 0.26/0.67        = A ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_nat.right_neutral
% 0.26/0.67  thf(fact_9535_gcd__0__nat,axiom,
% 0.26/0.67      ! [X3: nat] :
% 0.26/0.67        ( ( gcd_gcd_nat @ X3 @ zero_zero_nat )
% 0.26/0.67        = X3 ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_0_nat
% 0.26/0.67  thf(fact_9536_gcd__0__left__nat,axiom,
% 0.26/0.67      ! [X3: nat] :
% 0.26/0.67        ( ( gcd_gcd_nat @ zero_zero_nat @ X3 )
% 0.26/0.67        = X3 ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_0_left_nat
% 0.26/0.67  thf(fact_9537_gcd__Suc__0,axiom,
% 0.26/0.67      ! [M: nat] :
% 0.26/0.67        ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.26/0.67        = ( suc @ zero_zero_nat ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_Suc_0
% 0.26/0.67  thf(fact_9538_gcd__pos__nat,axiom,
% 0.26/0.67      ! [M: nat,N: nat] :
% 0.26/0.67        ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N ) )
% 0.26/0.67        = ( ( M != zero_zero_nat )
% 0.26/0.67          | ( N != zero_zero_nat ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_pos_nat
% 0.26/0.67  thf(fact_9539_gcd__int__int__eq,axiom,
% 0.26/0.67      ! [M: nat,N: nat] :
% 0.26/0.67        ( ( gcd_gcd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.67        = ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ M @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_int_int_eq
% 0.26/0.67  thf(fact_9540_gcd__nat__abs__right__eq,axiom,
% 0.26/0.67      ! [N: nat,K: int] :
% 0.26/0.67        ( ( gcd_gcd_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 0.26/0.67        = ( nat2 @ ( gcd_gcd_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_nat_abs_right_eq
% 0.26/0.67  thf(fact_9541_gcd__nat__abs__left__eq,axiom,
% 0.26/0.67      ! [K: int,N: nat] :
% 0.26/0.67        ( ( gcd_gcd_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 0.26/0.67        = ( nat2 @ ( gcd_gcd_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_nat_abs_left_eq
% 0.26/0.67  thf(fact_9542_gcd__non__0__nat,axiom,
% 0.26/0.67      ! [Y3: nat,X3: nat] :
% 0.26/0.67        ( ( Y3 != zero_zero_nat )
% 0.26/0.67       => ( ( gcd_gcd_nat @ X3 @ Y3 )
% 0.26/0.67          = ( gcd_gcd_nat @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_non_0_nat
% 0.26/0.67  thf(fact_9543_gcd__nat_Osimps,axiom,
% 0.26/0.67      ( gcd_gcd_nat
% 0.26/0.67      = ( ^ [X: nat,Y: nat] : ( if_nat @ ( Y = zero_zero_nat ) @ X @ ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_nat.simps
% 0.26/0.67  thf(fact_9544_gcd__nat_Oelims,axiom,
% 0.26/0.67      ! [X3: nat,Xa: nat,Y3: nat] :
% 0.26/0.67        ( ( ( gcd_gcd_nat @ X3 @ Xa )
% 0.26/0.67          = Y3 )
% 0.26/0.67       => ( ( ( Xa = zero_zero_nat )
% 0.26/0.67           => ( Y3 = X3 ) )
% 0.26/0.67          & ( ( Xa != zero_zero_nat )
% 0.26/0.67           => ( Y3
% 0.26/0.67              = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X3 @ Xa ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_nat.elims
% 0.26/0.67  thf(fact_9545_gcd__diff1__nat,axiom,
% 0.26/0.67      ! [N: nat,M: nat] :
% 0.26/0.67        ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.67       => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 0.26/0.67          = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_diff1_nat
% 0.26/0.67  thf(fact_9546_gcd__diff2__nat,axiom,
% 0.26/0.67      ! [M: nat,N: nat] :
% 0.26/0.67        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.67       => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M ) @ N )
% 0.26/0.67          = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_diff2_nat
% 0.26/0.67  thf(fact_9547_gcd__le2__nat,axiom,
% 0.26/0.67      ! [B: nat,A: nat] :
% 0.26/0.67        ( ( B != zero_zero_nat )
% 0.26/0.67       => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_le2_nat
% 0.26/0.67  thf(fact_9548_gcd__le1__nat,axiom,
% 0.26/0.67      ! [A: nat,B: nat] :
% 0.26/0.67        ( ( A != zero_zero_nat )
% 0.26/0.67       => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_le1_nat
% 0.26/0.67  thf(fact_9549_mono__Suc,axiom,
% 0.26/0.67      order_mono_nat_nat @ suc ).
% 0.26/0.67  
% 0.26/0.67  % mono_Suc
% 0.26/0.67  thf(fact_9550_gcd__code__integer,axiom,
% 0.26/0.67      ( gcd_gcd_Code_integer
% 0.26/0.67      = ( ^ [K3: code_integer,L2: code_integer] : ( abs_abs_Code_integer @ ( if_Code_integer @ ( L2 = zero_z3403309356797280102nteger ) @ K3 @ ( gcd_gcd_Code_integer @ L2 @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L2 ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_code_integer
% 0.26/0.67  thf(fact_9551_mono__times__nat,axiom,
% 0.26/0.67      ! [N: nat] :
% 0.26/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.67       => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % mono_times_nat
% 0.26/0.67  thf(fact_9552_bezout__nat,axiom,
% 0.26/0.67      ! [A: nat,B: nat] :
% 0.26/0.67        ( ( A != zero_zero_nat )
% 0.26/0.67       => ? [X4: nat,Y4: nat] :
% 0.26/0.67            ( ( times_times_nat @ A @ X4 )
% 0.26/0.67            = ( plus_plus_nat @ ( times_times_nat @ B @ Y4 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % bezout_nat
% 0.26/0.67  thf(fact_9553_bezout__gcd__nat_H,axiom,
% 0.26/0.67      ! [B: nat,A: nat] :
% 0.26/0.67      ? [X4: nat,Y4: nat] :
% 0.26/0.67        ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y4 ) @ ( times_times_nat @ A @ X4 ) )
% 0.26/0.67          & ( ( minus_minus_nat @ ( times_times_nat @ A @ X4 ) @ ( times_times_nat @ B @ Y4 ) )
% 0.26/0.67            = ( gcd_gcd_nat @ A @ B ) ) )
% 0.26/0.67        | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y4 ) @ ( times_times_nat @ B @ X4 ) )
% 0.26/0.67          & ( ( minus_minus_nat @ ( times_times_nat @ B @ X4 ) @ ( times_times_nat @ A @ Y4 ) )
% 0.26/0.67            = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % bezout_gcd_nat'
% 0.26/0.67  thf(fact_9554_incseq__bounded,axiom,
% 0.26/0.67      ! [X9: nat > real,B5: real] :
% 0.26/0.67        ( ( order_mono_nat_real @ X9 )
% 0.26/0.67       => ( ! [I3: nat] : ( ord_less_eq_real @ ( X9 @ I3 ) @ B5 )
% 0.26/0.67         => ( bfun_nat_real @ X9 @ at_top_nat ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % incseq_bounded
% 0.26/0.67  thf(fact_9555_incseq__convergent,axiom,
% 0.26/0.67      ! [X9: nat > real,B5: real] :
% 0.26/0.67        ( ( order_mono_nat_real @ X9 )
% 0.26/0.67       => ( ! [I3: nat] : ( ord_less_eq_real @ ( X9 @ I3 ) @ B5 )
% 0.26/0.67         => ~ ! [L6: real] :
% 0.26/0.67                ( ( filterlim_nat_real @ X9 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 0.26/0.67               => ~ ! [I2: nat] : ( ord_less_eq_real @ ( X9 @ I2 ) @ L6 ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % incseq_convergent
% 0.26/0.67  thf(fact_9556_gcd__int__def,axiom,
% 0.26/0.67      ( gcd_gcd_int
% 0.26/0.67      = ( ^ [X: int,Y: int] : ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ ( nat2 @ ( abs_abs_int @ X ) ) @ ( nat2 @ ( abs_abs_int @ Y ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_int_def
% 0.26/0.67  thf(fact_9557_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 0.26/0.67      ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 0.26/0.67      @ ^ [M3: nat,N3: nat] :
% 0.26/0.67          ( ( dvd_dvd_nat @ M3 @ N3 )
% 0.26/0.67          & ( M3 != N3 ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_nat.semilattice_neutr_order_axioms
% 0.26/0.67  thf(fact_9558_gcd__is__Max__divisors__nat,axiom,
% 0.26/0.67      ! [N: nat,M: nat] :
% 0.26/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.67       => ( ( gcd_gcd_nat @ M @ N )
% 0.26/0.67          = ( lattic8265883725875713057ax_nat
% 0.26/0.67            @ ( collect_nat
% 0.26/0.67              @ ^ [D4: nat] :
% 0.26/0.67                  ( ( dvd_dvd_nat @ D4 @ M )
% 0.26/0.67                  & ( dvd_dvd_nat @ D4 @ N ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_is_Max_divisors_nat
% 0.26/0.67  thf(fact_9559_mono__ge2__power__minus__self,axiom,
% 0.26/0.67      ! [K: nat] :
% 0.26/0.67        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.26/0.67       => ( order_mono_nat_nat
% 0.26/0.67          @ ^ [M3: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M3 ) @ M3 ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % mono_ge2_power_minus_self
% 0.26/0.67  thf(fact_9560_bezw__aux,axiom,
% 0.26/0.67      ! [X3: nat,Y3: nat] :
% 0.26/0.67        ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X3 @ Y3 ) )
% 0.26/0.67        = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X3 @ Y3 ) ) @ ( semiri1314217659103216013at_int @ X3 ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X3 @ Y3 ) ) @ ( semiri1314217659103216013at_int @ Y3 ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % bezw_aux
% 0.26/0.67  thf(fact_9561_gcd__nat_Opelims,axiom,
% 0.26/0.67      ! [X3: nat,Xa: nat,Y3: nat] :
% 0.26/0.67        ( ( ( gcd_gcd_nat @ X3 @ Xa )
% 0.26/0.67          = Y3 )
% 0.26/0.67       => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X3 @ Xa ) )
% 0.26/0.67         => ~ ( ( ( ( Xa = zero_zero_nat )
% 0.26/0.67                 => ( Y3 = X3 ) )
% 0.26/0.67                & ( ( Xa != zero_zero_nat )
% 0.26/0.67                 => ( Y3
% 0.26/0.67                    = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X3 @ Xa ) ) ) ) )
% 0.26/0.67             => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X3 @ Xa ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % gcd_nat.pelims
% 0.26/0.67  thf(fact_9562_complex__is__Nat__iff,axiom,
% 0.26/0.67      ! [Z: complex] :
% 0.26/0.67        ( ( member_complex @ Z @ semiri3842193898606819883omplex )
% 0.26/0.67        = ( ( ( im @ Z )
% 0.26/0.67            = zero_zero_real )
% 0.26/0.67          & ? [I4: nat] :
% 0.26/0.67              ( ( re @ Z )
% 0.26/0.67              = ( semiri5074537144036343181t_real @ I4 ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % complex_is_Nat_iff
% 0.26/0.67  thf(fact_9563_tendsto__at__topI__sequentially__real,axiom,
% 0.26/0.67      ! [F: real > real,Y3: real] :
% 0.26/0.67        ( ( order_mono_real_real @ F )
% 0.26/0.67       => ( ( filterlim_nat_real
% 0.26/0.67            @ ^ [N3: nat] : ( F @ ( semiri5074537144036343181t_real @ N3 ) )
% 0.26/0.67            @ ( topolo2815343760600316023s_real @ Y3 )
% 0.26/0.67            @ at_top_nat )
% 0.26/0.67         => ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Y3 ) @ at_top_real ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % tendsto_at_topI_sequentially_real
% 0.26/0.67  thf(fact_9564_nonneg__incseq__Bseq__subseq__iff,axiom,
% 0.26/0.67      ! [F: nat > real,G: nat > nat] :
% 0.26/0.67        ( ! [X4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 0.26/0.67       => ( ( order_mono_nat_real @ F )
% 0.26/0.67         => ( ( order_5726023648592871131at_nat @ G )
% 0.26/0.67           => ( ( bfun_nat_real
% 0.26/0.67                @ ^ [X: nat] : ( F @ ( G @ X ) )
% 0.26/0.67                @ at_top_nat )
% 0.26/0.67              = ( bfun_nat_real @ F @ at_top_nat ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % nonneg_incseq_Bseq_subseq_iff
% 0.26/0.67  thf(fact_9565_inj__sgn__power,axiom,
% 0.26/0.67      ! [N: nat] :
% 0.26/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.67       => ( inj_on_real_real
% 0.26/0.67          @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 0.26/0.67          @ top_top_set_real ) ) ).
% 0.26/0.67  
% 0.26/0.67  % inj_sgn_power
% 0.26/0.67  thf(fact_9566_strict__mono__imp__increasing,axiom,
% 0.26/0.67      ! [F: nat > nat,N: nat] :
% 0.26/0.67        ( ( order_5726023648592871131at_nat @ F )
% 0.26/0.67       => ( ord_less_eq_nat @ N @ ( F @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % strict_mono_imp_increasing
% 0.26/0.67  thf(fact_9567_log__inj,axiom,
% 0.26/0.67      ! [B: real] :
% 0.26/0.67        ( ( ord_less_real @ one_one_real @ B )
% 0.26/0.67       => ( inj_on_real_real @ ( log @ B ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % log_inj
% 0.26/0.67  thf(fact_9568_inj__on__diff__nat,axiom,
% 0.26/0.67      ! [N4: set_nat,K: nat] :
% 0.26/0.67        ( ! [N2: nat] :
% 0.26/0.67            ( ( member_nat @ N2 @ N4 )
% 0.26/0.67           => ( ord_less_eq_nat @ K @ N2 ) )
% 0.26/0.67       => ( inj_on_nat_nat
% 0.26/0.67          @ ^ [N3: nat] : ( minus_minus_nat @ N3 @ K )
% 0.26/0.67          @ N4 ) ) ).
% 0.26/0.67  
% 0.26/0.67  % inj_on_diff_nat
% 0.26/0.67  thf(fact_9569_inj__Suc,axiom,
% 0.26/0.67      ! [N4: set_nat] : ( inj_on_nat_nat @ suc @ N4 ) ).
% 0.26/0.67  
% 0.26/0.67  % inj_Suc
% 0.26/0.67  thf(fact_9570_summable__reindex,axiom,
% 0.26/0.67      ! [F: nat > real,G: nat > nat] :
% 0.26/0.67        ( ( summable_real @ F )
% 0.26/0.67       => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 0.26/0.67         => ( ! [X4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 0.26/0.67           => ( summable_real @ ( comp_nat_real_nat @ F @ G ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % summable_reindex
% 0.26/0.67  thf(fact_9571_suminf__reindex__mono,axiom,
% 0.26/0.67      ! [F: nat > real,G: nat > nat] :
% 0.26/0.67        ( ( summable_real @ F )
% 0.26/0.67       => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 0.26/0.67         => ( ! [X4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 0.26/0.67           => ( ord_less_eq_real @ ( suminf_real @ ( comp_nat_real_nat @ F @ G ) ) @ ( suminf_real @ F ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % suminf_reindex_mono
% 0.26/0.67  thf(fact_9572_powr__real__of__int_H,axiom,
% 0.26/0.67      ! [X3: real,N: int] :
% 0.26/0.67        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.67       => ( ( ( X3 != zero_zero_real )
% 0.26/0.67            | ( ord_less_int @ zero_zero_int @ N ) )
% 0.26/0.67         => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ N ) )
% 0.26/0.67            = ( power_int_real @ X3 @ N ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % powr_real_of_int'
% 0.26/0.67  thf(fact_9573_inj__on__char__of__nat,axiom,
% 0.26/0.67      inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % inj_on_char_of_nat
% 0.26/0.67  thf(fact_9574_suminf__reindex,axiom,
% 0.26/0.67      ! [F: nat > real,G: nat > nat] :
% 0.26/0.67        ( ( summable_real @ F )
% 0.26/0.67       => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 0.26/0.67         => ( ! [X4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 0.26/0.67           => ( ! [X4: nat] :
% 0.26/0.67                  ( ~ ( member_nat @ X4 @ ( image_nat_nat @ G @ top_top_set_nat ) )
% 0.26/0.67                 => ( ( F @ X4 )
% 0.26/0.67                    = zero_zero_real ) )
% 0.26/0.67             => ( ( suminf_real @ ( comp_nat_real_nat @ F @ G ) )
% 0.26/0.67                = ( suminf_real @ F ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % suminf_reindex
% 0.26/0.67  thf(fact_9575_pos__deriv__imp__strict__mono,axiom,
% 0.26/0.67      ! [F: real > real,F5: real > real] :
% 0.26/0.67        ( ! [X4: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.26/0.67       => ( ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( F5 @ X4 ) )
% 0.26/0.67         => ( order_7092887310737990675l_real @ F ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % pos_deriv_imp_strict_mono
% 0.26/0.67  thf(fact_9576_integer__of__num__triv_I2_J,axiom,
% 0.26/0.67      ( ( code_integer_of_num @ ( bit0 @ one ) )
% 0.26/0.67      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % integer_of_num_triv(2)
% 0.26/0.67  thf(fact_9577_integer__of__num__triv_I1_J,axiom,
% 0.26/0.67      ( ( code_integer_of_num @ one )
% 0.26/0.67      = one_one_Code_integer ) ).
% 0.26/0.67  
% 0.26/0.67  % integer_of_num_triv(1)
% 0.26/0.67  thf(fact_9578_integer__of__num_I2_J,axiom,
% 0.26/0.67      ! [N: num] :
% 0.26/0.67        ( ( code_integer_of_num @ ( bit0 @ N ) )
% 0.26/0.67        = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % integer_of_num(2)
% 0.26/0.67  thf(fact_9579_atLeastLessThan__add__Un,axiom,
% 0.26/0.67      ! [I: nat,J: nat,K: nat] :
% 0.26/0.67        ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.67       => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 0.26/0.67          = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % atLeastLessThan_add_Un
% 0.26/0.67  thf(fact_9580_sup__nat__def,axiom,
% 0.26/0.67      sup_sup_nat = ord_max_nat ).
% 0.26/0.67  
% 0.26/0.67  % sup_nat_def
% 0.26/0.67  thf(fact_9581_sup__enat__def,axiom,
% 0.26/0.67      sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 0.26/0.67  
% 0.26/0.67  % sup_enat_def
% 0.26/0.67  thf(fact_9582_sup__int__def,axiom,
% 0.26/0.67      sup_sup_int = ord_max_int ).
% 0.26/0.67  
% 0.26/0.67  % sup_int_def
% 0.26/0.67  thf(fact_9583_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 0.26/0.67      ! [X3: vEBT_VEBT,Xa: nat,Y3: $o] :
% 0.26/0.67        ( ( ( vEBT_VEBT_valid @ X3 @ Xa )
% 0.26/0.67          = Y3 )
% 0.26/0.67       => ( ( ? [Uu: $o,Uv: $o] :
% 0.26/0.67                ( X3
% 0.26/0.67                = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.26/0.67           => ( Y3
% 0.26/0.67              = ( Xa != one_one_nat ) ) )
% 0.26/0.67         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.67                ( ( X3
% 0.26/0.67                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.26/0.67               => ( Y3
% 0.26/0.67                  = ( ~ ( ( Deg2 = Xa )
% 0.26/0.67                        & ! [X: vEBT_VEBT] :
% 0.26/0.67                            ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.67                           => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.67                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.67                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.26/0.67                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.67                        & ( case_o184042715313410164at_nat
% 0.26/0.67                          @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 0.26/0.67                            & ! [X: vEBT_VEBT] :
% 0.26/0.67                                ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.67                               => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 0.26/0.67                          @ ( produc6081775807080527818_nat_o
% 0.26/0.67                            @ ^ [Mi3: nat,Ma3: nat] :
% 0.26/0.67                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.26/0.67                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.26/0.67                                & ! [I4: nat] :
% 0.26/0.67                                    ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.67                                   => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X8 ) )
% 0.26/0.67                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 0.26/0.67                                & ( ( Mi3 = Ma3 )
% 0.26/0.67                                 => ! [X: vEBT_VEBT] :
% 0.26/0.67                                      ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.67                                     => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 0.26/0.67                                & ( ( Mi3 != Ma3 )
% 0.26/0.67                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 0.26/0.67                                    & ! [X: nat] :
% 0.26/0.67                                        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.26/0.67                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 0.26/0.67                                         => ( ( ord_less_nat @ Mi3 @ X )
% 0.26/0.67                                            & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 0.26/0.67                          @ Mima ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % VEBT_internal.valid'.elims(1)
% 0.26/0.67  thf(fact_9584_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 0.26/0.67      ! [X3: vEBT_VEBT,Xa: nat] :
% 0.26/0.67        ( ( vEBT_VEBT_valid @ X3 @ Xa )
% 0.26/0.67       => ( ( ? [Uu: $o,Uv: $o] :
% 0.26/0.67                ( X3
% 0.26/0.67                = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.26/0.67           => ( Xa != one_one_nat ) )
% 0.26/0.67         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.67                ( ( X3
% 0.26/0.67                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.26/0.67               => ~ ( ( Deg2 = Xa )
% 0.26/0.67                    & ! [X6: vEBT_VEBT] :
% 0.26/0.67                        ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.67                       => ( vEBT_VEBT_valid @ X6 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.67                    & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.67                    & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.26/0.67                      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.67                    & ( case_o184042715313410164at_nat
% 0.26/0.67                      @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 0.26/0.67                        & ! [X: vEBT_VEBT] :
% 0.26/0.67                            ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.67                           => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 0.26/0.67                      @ ( produc6081775807080527818_nat_o
% 0.26/0.67                        @ ^ [Mi3: nat,Ma3: nat] :
% 0.26/0.67                            ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.26/0.67                            & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.26/0.67                            & ! [I4: nat] :
% 0.26/0.67                                ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.67                               => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X8 ) )
% 0.26/0.67                                  = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 0.26/0.67                            & ( ( Mi3 = Ma3 )
% 0.26/0.67                             => ! [X: vEBT_VEBT] :
% 0.26/0.67                                  ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.67                                 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 0.26/0.67                            & ( ( Mi3 != Ma3 )
% 0.26/0.67                             => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 0.26/0.67                                & ! [X: nat] :
% 0.26/0.67                                    ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.26/0.67                                   => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 0.26/0.67                                     => ( ( ord_less_nat @ Mi3 @ X )
% 0.26/0.67                                        & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 0.26/0.67                      @ Mima ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % VEBT_internal.valid'.elims(2)
% 0.26/0.67  thf(fact_9585_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 0.26/0.67      ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg3: nat] :
% 0.26/0.67        ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList2 @ Summary ) @ Deg3 )
% 0.26/0.67        = ( ( Deg = Deg3 )
% 0.26/0.67          & ! [X: vEBT_VEBT] :
% 0.26/0.67              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.26/0.67             => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.67          & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.67          & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.26/0.67            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.67          & ( case_o184042715313410164at_nat
% 0.26/0.67            @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X8 )
% 0.26/0.67              & ! [X: vEBT_VEBT] :
% 0.26/0.67                  ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.26/0.67                 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 0.26/0.67            @ ( produc6081775807080527818_nat_o
% 0.26/0.67              @ ^ [Mi3: nat,Ma3: nat] :
% 0.26/0.67                  ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.26/0.67                  & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.26/0.67                  & ! [I4: nat] :
% 0.26/0.67                      ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.67                     => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X8 ) )
% 0.26/0.67                        = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 0.26/0.67                  & ( ( Mi3 = Ma3 )
% 0.26/0.67                   => ! [X: vEBT_VEBT] :
% 0.26/0.67                        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.26/0.67                       => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 0.26/0.67                  & ( ( Mi3 != Ma3 )
% 0.26/0.67                   => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 0.26/0.67                      & ! [X: nat] :
% 0.26/0.67                          ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.26/0.67                         => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 0.26/0.67                           => ( ( ord_less_nat @ Mi3 @ X )
% 0.26/0.67                              & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 0.26/0.67            @ Mima2 ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % VEBT_internal.valid'.simps(2)
% 0.26/0.67  thf(fact_9586_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 0.26/0.67      ! [X3: vEBT_VEBT,Xa: nat] :
% 0.26/0.67        ( ~ ( vEBT_VEBT_valid @ X3 @ Xa )
% 0.26/0.67       => ( ( ? [Uu: $o,Uv: $o] :
% 0.26/0.67                ( X3
% 0.26/0.67                = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.26/0.67           => ( Xa = one_one_nat ) )
% 0.26/0.67         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.67                ( ( X3
% 0.26/0.67                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.26/0.67               => ( ( Deg2 = Xa )
% 0.26/0.67                  & ! [X4: vEBT_VEBT] :
% 0.26/0.67                      ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.67                     => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.67                  & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.67                  & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.26/0.67                    = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.67                  & ( case_o184042715313410164at_nat
% 0.26/0.67                    @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 0.26/0.67                      & ! [X: vEBT_VEBT] :
% 0.26/0.67                          ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.67                         => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 0.26/0.67                    @ ( produc6081775807080527818_nat_o
% 0.26/0.67                      @ ^ [Mi3: nat,Ma3: nat] :
% 0.26/0.67                          ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.26/0.67                          & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.26/0.67                          & ! [I4: nat] :
% 0.26/0.67                              ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.67                             => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X8 ) )
% 0.26/0.67                                = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 0.26/0.67                          & ( ( Mi3 = Ma3 )
% 0.26/0.67                           => ! [X: vEBT_VEBT] :
% 0.26/0.67                                ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.67                               => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 0.26/0.67                          & ( ( Mi3 != Ma3 )
% 0.26/0.67                           => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 0.26/0.67                              & ! [X: nat] :
% 0.26/0.67                                  ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.26/0.67                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 0.26/0.67                                   => ( ( ord_less_nat @ Mi3 @ X )
% 0.26/0.67                                      & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 0.26/0.67                    @ Mima ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % VEBT_internal.valid'.elims(3)
% 0.26/0.67  thf(fact_9587_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 0.26/0.67      ! [X3: vEBT_VEBT,Xa: nat,Y3: $o] :
% 0.26/0.67        ( ( ( vEBT_VEBT_valid @ X3 @ Xa )
% 0.26/0.67          = Y3 )
% 0.26/0.67       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.67         => ( ! [Uu: $o,Uv: $o] :
% 0.26/0.67                ( ( X3
% 0.26/0.67                  = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.26/0.67               => ( ( Y3
% 0.26/0.67                    = ( Xa = one_one_nat ) )
% 0.26/0.67                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa ) ) ) )
% 0.26/0.67           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.67                  ( ( X3
% 0.26/0.67                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.26/0.67                 => ( ( Y3
% 0.26/0.67                      = ( ( Deg2 = Xa )
% 0.26/0.67                        & ! [X: vEBT_VEBT] :
% 0.26/0.67                            ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.67                           => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.67                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.67                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.26/0.67                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.67                        & ( case_o184042715313410164at_nat
% 0.26/0.67                          @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 0.26/0.67                            & ! [X: vEBT_VEBT] :
% 0.26/0.67                                ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.67                               => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 0.26/0.67                          @ ( produc6081775807080527818_nat_o
% 0.26/0.67                            @ ^ [Mi3: nat,Ma3: nat] :
% 0.26/0.67                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.26/0.67                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.26/0.67                                & ! [I4: nat] :
% 0.26/0.67                                    ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.67                                   => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X8 ) )
% 0.26/0.67                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 0.26/0.67                                & ( ( Mi3 = Ma3 )
% 0.26/0.67                                 => ! [X: vEBT_VEBT] :
% 0.26/0.67                                      ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.67                                     => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 0.26/0.67                                & ( ( Mi3 != Ma3 )
% 0.26/0.67                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 0.26/0.67                                    & ! [X: nat] :
% 0.26/0.67                                        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.26/0.67                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 0.26/0.67                                         => ( ( ord_less_nat @ Mi3 @ X )
% 0.26/0.67                                            & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 0.26/0.67                          @ Mima ) ) )
% 0.26/0.67                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % VEBT_internal.valid'.pelims(1)
% 0.26/0.67  thf(fact_9588_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 0.26/0.67      ! [X3: vEBT_VEBT,Xa: nat] :
% 0.26/0.67        ( ( vEBT_VEBT_valid @ X3 @ Xa )
% 0.26/0.67       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.67         => ( ! [Uu: $o,Uv: $o] :
% 0.26/0.67                ( ( X3
% 0.26/0.67                  = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.26/0.67               => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa ) )
% 0.26/0.67                 => ( Xa != one_one_nat ) ) )
% 0.26/0.67           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.67                  ( ( X3
% 0.26/0.67                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.26/0.67                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa ) )
% 0.26/0.67                   => ~ ( ( Deg2 = Xa )
% 0.26/0.67                        & ! [X6: vEBT_VEBT] :
% 0.26/0.67                            ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.67                           => ( vEBT_VEBT_valid @ X6 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.67                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.67                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.26/0.67                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.67                        & ( case_o184042715313410164at_nat
% 0.26/0.67                          @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 0.26/0.67                            & ! [X: vEBT_VEBT] :
% 0.26/0.67                                ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.67                               => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 0.26/0.67                          @ ( produc6081775807080527818_nat_o
% 0.26/0.67                            @ ^ [Mi3: nat,Ma3: nat] :
% 0.26/0.67                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.26/0.67                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.26/0.67                                & ! [I4: nat] :
% 0.26/0.67                                    ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.67                                   => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X8 ) )
% 0.26/0.67                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 0.26/0.67                                & ( ( Mi3 = Ma3 )
% 0.26/0.67                                 => ! [X: vEBT_VEBT] :
% 0.26/0.67                                      ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.67                                     => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 0.26/0.67                                & ( ( Mi3 != Ma3 )
% 0.26/0.67                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 0.26/0.67                                    & ! [X: nat] :
% 0.26/0.67                                        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.26/0.67                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 0.26/0.67                                         => ( ( ord_less_nat @ Mi3 @ X )
% 0.26/0.67                                            & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 0.26/0.67                          @ Mima ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % VEBT_internal.valid'.pelims(2)
% 0.26/0.67  thf(fact_9589_Sup__int__def,axiom,
% 0.26/0.67      ( complete_Sup_Sup_int
% 0.26/0.67      = ( ^ [X8: set_int] :
% 0.26/0.67            ( the_int
% 0.26/0.67            @ ^ [X: int] :
% 0.26/0.67                ( ( member_int @ X @ X8 )
% 0.26/0.67                & ! [Y: int] :
% 0.26/0.67                    ( ( member_int @ Y @ X8 )
% 0.26/0.67                   => ( ord_less_eq_int @ Y @ X ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Sup_int_def
% 0.26/0.67  thf(fact_9590_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 0.26/0.67      ! [X3: vEBT_VEBT,Xa: nat] :
% 0.26/0.67        ( ~ ( vEBT_VEBT_valid @ X3 @ Xa )
% 0.26/0.67       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 0.26/0.67         => ( ! [Uu: $o,Uv: $o] :
% 0.26/0.67                ( ( X3
% 0.26/0.67                  = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.26/0.67               => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa ) )
% 0.26/0.67                 => ( Xa = one_one_nat ) ) )
% 0.26/0.67           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.67                  ( ( X3
% 0.26/0.67                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.26/0.67                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa ) )
% 0.26/0.67                   => ( ( Deg2 = Xa )
% 0.26/0.67                      & ! [X4: vEBT_VEBT] :
% 0.26/0.67                          ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.67                         => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.67                      & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.67                      & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.26/0.67                        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.67                      & ( case_o184042715313410164at_nat
% 0.26/0.67                        @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 0.26/0.67                          & ! [X: vEBT_VEBT] :
% 0.26/0.67                              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.67                             => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 0.26/0.67                        @ ( produc6081775807080527818_nat_o
% 0.26/0.67                          @ ^ [Mi3: nat,Ma3: nat] :
% 0.26/0.67                              ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.26/0.67                              & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.26/0.67                              & ! [I4: nat] :
% 0.26/0.67                                  ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.67                                 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X8 ) )
% 0.26/0.67                                    = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 0.26/0.67                              & ( ( Mi3 = Ma3 )
% 0.26/0.67                               => ! [X: vEBT_VEBT] :
% 0.26/0.67                                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.26/0.67                                   => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 0.26/0.67                              & ( ( Mi3 != Ma3 )
% 0.26/0.67                               => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 0.26/0.67                                  & ! [X: nat] :
% 0.26/0.67                                      ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.26/0.67                                     => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 0.26/0.67                                       => ( ( ord_less_nat @ Mi3 @ X )
% 0.26/0.67                                          & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 0.26/0.67                        @ Mima ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % VEBT_internal.valid'.pelims(3)
% 0.26/0.67  thf(fact_9591_take__bit__numeral__minus__numeral__int,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.67        = ( case_option_int_num @ zero_zero_int
% 0.26/0.67          @ ^ [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 ) ) )
% 0.26/0.67          @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % take_bit_numeral_minus_numeral_int
% 0.26/0.67  thf(fact_9592_take__bit__num__simps_I1_J,axiom,
% 0.26/0.67      ! [M: num] :
% 0.26/0.67        ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 0.26/0.67        = none_num ) ).
% 0.26/0.67  
% 0.26/0.67  % take_bit_num_simps(1)
% 0.26/0.67  thf(fact_9593_take__bit__num__simps_I2_J,axiom,
% 0.26/0.67      ! [N: nat] :
% 0.26/0.67        ( ( bit_take_bit_num @ ( suc @ N ) @ one )
% 0.26/0.67        = ( some_num @ one ) ) ).
% 0.26/0.67  
% 0.26/0.67  % take_bit_num_simps(2)
% 0.26/0.67  thf(fact_9594_take__bit__num__simps_I5_J,axiom,
% 0.26/0.67      ! [R2: num] :
% 0.26/0.67        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ one )
% 0.26/0.67        = ( some_num @ one ) ) ).
% 0.26/0.67  
% 0.26/0.67  % take_bit_num_simps(5)
% 0.26/0.67  thf(fact_9595_take__bit__num__simps_I3_J,axiom,
% 0.26/0.67      ! [N: nat,M: num] :
% 0.26/0.67        ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M ) )
% 0.26/0.67        = ( case_o6005452278849405969um_num @ none_num
% 0.26/0.67          @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 0.26/0.67          @ ( bit_take_bit_num @ N @ M ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % take_bit_num_simps(3)
% 0.26/0.67  thf(fact_9596_take__bit__num__simps_I4_J,axiom,
% 0.26/0.67      ! [N: nat,M: num] :
% 0.26/0.67        ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M ) )
% 0.26/0.67        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % take_bit_num_simps(4)
% 0.26/0.67  thf(fact_9597_take__bit__num__simps_I6_J,axiom,
% 0.26/0.67      ! [R2: num,M: num] :
% 0.26/0.67        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit0 @ M ) )
% 0.26/0.67        = ( case_o6005452278849405969um_num @ none_num
% 0.26/0.67          @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 0.26/0.67          @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % take_bit_num_simps(6)
% 0.26/0.67  thf(fact_9598_take__bit__num__simps_I7_J,axiom,
% 0.26/0.67      ! [R2: num,M: num] :
% 0.26/0.67        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit1 @ M ) )
% 0.26/0.67        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % take_bit_num_simps(7)
% 0.26/0.67  thf(fact_9599_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 0.26/0.67      ! [N: nat,M: num] :
% 0.26/0.67        ( ( bit_take_bit_num @ N @ ( bit0 @ M ) )
% 0.26/0.67        = ( case_nat_option_num @ none_num
% 0.26/0.67          @ ^ [N3: nat] :
% 0.26/0.67              ( case_o6005452278849405969um_num @ none_num
% 0.26/0.67              @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 0.26/0.67              @ ( bit_take_bit_num @ N3 @ M ) )
% 0.26/0.67          @ N ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Code_Abstract_Nat.take_bit_num_code(2)
% 0.26/0.67  thf(fact_9600_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 0.26/0.67      ! [N: nat] :
% 0.26/0.67        ( ( bit_take_bit_num @ N @ one )
% 0.26/0.67        = ( case_nat_option_num @ none_num
% 0.26/0.67          @ ^ [N3: nat] : ( some_num @ one )
% 0.26/0.67          @ N ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Code_Abstract_Nat.take_bit_num_code(1)
% 0.26/0.67  thf(fact_9601_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 0.26/0.67      ! [N: nat,M: num] :
% 0.26/0.67        ( ( bit_take_bit_num @ N @ ( bit1 @ M ) )
% 0.26/0.67        = ( case_nat_option_num @ none_num
% 0.26/0.67          @ ^ [N3: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N3 @ M ) ) )
% 0.26/0.67          @ N ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Code_Abstract_Nat.take_bit_num_code(3)
% 0.26/0.67  thf(fact_9602_take__bit__num__def,axiom,
% 0.26/0.67      ( bit_take_bit_num
% 0.26/0.67      = ( ^ [N3: nat,M3: num] :
% 0.26/0.67            ( if_option_num
% 0.26/0.67            @ ( ( bit_se2925701944663578781it_nat @ N3 @ ( numeral_numeral_nat @ M3 ) )
% 0.26/0.67              = zero_zero_nat )
% 0.26/0.67            @ none_num
% 0.26/0.67            @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N3 @ ( numeral_numeral_nat @ M3 ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % take_bit_num_def
% 0.26/0.67  thf(fact_9603_and__minus__numerals_I3_J,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.26/0.67        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_minus_numerals(3)
% 0.26/0.67  thf(fact_9604_and__minus__numerals_I7_J,axiom,
% 0.26/0.67      ! [N: num,M: num] :
% 0.26/0.67        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 0.26/0.67        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_minus_numerals(7)
% 0.26/0.67  thf(fact_9605_and__minus__numerals_I4_J,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.26/0.67        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_minus_numerals(4)
% 0.26/0.67  thf(fact_9606_and__minus__numerals_I8_J,axiom,
% 0.26/0.67      ! [N: num,M: num] :
% 0.26/0.67        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 0.26/0.67        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_minus_numerals(8)
% 0.26/0.67  thf(fact_9607_and__not__num_Osimps_I1_J,axiom,
% 0.26/0.67      ( ( bit_and_not_num @ one @ one )
% 0.26/0.67      = none_num ) ).
% 0.26/0.67  
% 0.26/0.67  % and_not_num.simps(1)
% 0.26/0.67  thf(fact_9608_and__not__num_Osimps_I4_J,axiom,
% 0.26/0.67      ! [M: num] :
% 0.26/0.67        ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 0.26/0.67        = ( some_num @ ( bit0 @ M ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_not_num.simps(4)
% 0.26/0.67  thf(fact_9609_and__not__num_Osimps_I2_J,axiom,
% 0.26/0.67      ! [N: num] :
% 0.26/0.67        ( ( bit_and_not_num @ one @ ( bit0 @ N ) )
% 0.26/0.67        = ( some_num @ one ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_not_num.simps(2)
% 0.26/0.67  thf(fact_9610_and__not__num_Osimps_I3_J,axiom,
% 0.26/0.67      ! [N: num] :
% 0.26/0.67        ( ( bit_and_not_num @ one @ ( bit1 @ N ) )
% 0.26/0.67        = none_num ) ).
% 0.26/0.67  
% 0.26/0.67  % and_not_num.simps(3)
% 0.26/0.67  thf(fact_9611_and__not__num_Osimps_I7_J,axiom,
% 0.26/0.67      ! [M: num] :
% 0.26/0.67        ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 0.26/0.67        = ( some_num @ ( bit0 @ M ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_not_num.simps(7)
% 0.26/0.67  thf(fact_9612_and__not__num__eq__Some__iff,axiom,
% 0.26/0.67      ! [M: num,N: num,Q3: num] :
% 0.26/0.67        ( ( ( bit_and_not_num @ M @ N )
% 0.26/0.67          = ( some_num @ Q3 ) )
% 0.26/0.67        = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.67          = ( numeral_numeral_int @ Q3 ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_not_num_eq_Some_iff
% 0.26/0.67  thf(fact_9613_and__not__num_Osimps_I8_J,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.26/0.67        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.26/0.67          @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 0.26/0.67          @ ( bit_and_not_num @ M @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_not_num.simps(8)
% 0.26/0.67  thf(fact_9614_and__not__num__eq__None__iff,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( ( bit_and_not_num @ M @ N )
% 0.26/0.67          = none_num )
% 0.26/0.67        = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.67          = zero_zero_int ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_not_num_eq_None_iff
% 0.26/0.67  thf(fact_9615_int__numeral__not__and__num,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.67        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N @ M ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % int_numeral_not_and_num
% 0.26/0.67  thf(fact_9616_int__numeral__and__not__num,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.67        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % int_numeral_and_not_num
% 0.26/0.67  thf(fact_9617_Bit__Operations_Otake__bit__num__code,axiom,
% 0.26/0.67      ( bit_take_bit_num
% 0.26/0.67      = ( ^ [N3: nat,M3: num] :
% 0.26/0.67            ( produc478579273971653890on_num
% 0.26/0.67            @ ^ [A4: nat,X: num] :
% 0.26/0.67                ( case_nat_option_num @ none_num
% 0.26/0.67                @ ^ [O: nat] :
% 0.26/0.67                    ( case_num_option_num @ ( some_num @ one )
% 0.26/0.67                    @ ^ [P5: num] :
% 0.26/0.67                        ( case_o6005452278849405969um_num @ none_num
% 0.26/0.67                        @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 0.26/0.67                        @ ( bit_take_bit_num @ O @ P5 ) )
% 0.26/0.67                    @ ^ [P5: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P5 ) ) )
% 0.26/0.67                    @ X )
% 0.26/0.67                @ A4 )
% 0.26/0.67            @ ( product_Pair_nat_num @ N3 @ M3 ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Bit_Operations.take_bit_num_code
% 0.26/0.67  thf(fact_9618_Rats__eq__int__div__nat,axiom,
% 0.26/0.67      ( field_5140801741446780682s_real
% 0.26/0.67      = ( collect_real
% 0.26/0.67        @ ^ [Uu3: real] :
% 0.26/0.67          ? [I4: int,N3: nat] :
% 0.26/0.67            ( ( Uu3
% 0.26/0.67              = ( divide_divide_real @ ( ring_1_of_int_real @ I4 ) @ ( semiri5074537144036343181t_real @ N3 ) ) )
% 0.26/0.67            & ( N3 != zero_zero_nat ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Rats_eq_int_div_nat
% 0.26/0.67  thf(fact_9619_Rats__abs__iff,axiom,
% 0.26/0.67      ! [X3: real] :
% 0.26/0.67        ( ( member_real @ ( abs_abs_real @ X3 ) @ field_5140801741446780682s_real )
% 0.26/0.67        = ( member_real @ X3 @ field_5140801741446780682s_real ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Rats_abs_iff
% 0.26/0.67  thf(fact_9620_Rats__dense__in__real,axiom,
% 0.26/0.67      ! [X3: real,Y3: real] :
% 0.26/0.67        ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.67       => ? [X4: real] :
% 0.26/0.67            ( ( member_real @ X4 @ field_5140801741446780682s_real )
% 0.26/0.67            & ( ord_less_real @ X3 @ X4 )
% 0.26/0.67            & ( ord_less_real @ X4 @ Y3 ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Rats_dense_in_real
% 0.26/0.67  thf(fact_9621_Rats__no__bot__less,axiom,
% 0.26/0.67      ! [X3: real] :
% 0.26/0.67      ? [X4: real] :
% 0.26/0.67        ( ( member_real @ X4 @ field_5140801741446780682s_real )
% 0.26/0.67        & ( ord_less_real @ X4 @ X3 ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Rats_no_bot_less
% 0.26/0.67  thf(fact_9622_Rats__no__top__le,axiom,
% 0.26/0.67      ! [X3: real] :
% 0.26/0.67      ? [X4: real] :
% 0.26/0.67        ( ( member_real @ X4 @ field_5140801741446780682s_real )
% 0.26/0.67        & ( ord_less_eq_real @ X3 @ X4 ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Rats_no_top_le
% 0.26/0.67  thf(fact_9623_Rats__eq__int__div__int,axiom,
% 0.26/0.67      ( field_5140801741446780682s_real
% 0.26/0.67      = ( collect_real
% 0.26/0.67        @ ^ [Uu3: real] :
% 0.26/0.67          ? [I4: int,J3: int] :
% 0.26/0.67            ( ( Uu3
% 0.26/0.67              = ( divide_divide_real @ ( ring_1_of_int_real @ I4 ) @ ( ring_1_of_int_real @ J3 ) ) )
% 0.26/0.67            & ( J3 != zero_zero_int ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Rats_eq_int_div_int
% 0.26/0.67  thf(fact_9624_and__not__num_Oelims,axiom,
% 0.26/0.67      ! [X3: num,Xa: num,Y3: option_num] :
% 0.26/0.67        ( ( ( bit_and_not_num @ X3 @ Xa )
% 0.26/0.67          = Y3 )
% 0.26/0.67       => ( ( ( X3 = one )
% 0.26/0.67           => ( ( Xa = one )
% 0.26/0.67             => ( Y3 != none_num ) ) )
% 0.26/0.67         => ( ( ( X3 = one )
% 0.26/0.67             => ( ? [N2: num] :
% 0.26/0.67                    ( Xa
% 0.26/0.67                    = ( bit0 @ N2 ) )
% 0.26/0.67               => ( Y3
% 0.26/0.67                 != ( some_num @ one ) ) ) )
% 0.26/0.67           => ( ( ( X3 = one )
% 0.26/0.67               => ( ? [N2: num] :
% 0.26/0.67                      ( Xa
% 0.26/0.67                      = ( bit1 @ N2 ) )
% 0.26/0.67                 => ( Y3 != none_num ) ) )
% 0.26/0.67             => ( ! [M4: num] :
% 0.26/0.67                    ( ( X3
% 0.26/0.67                      = ( bit0 @ M4 ) )
% 0.26/0.67                   => ( ( Xa = one )
% 0.26/0.67                     => ( Y3
% 0.26/0.67                       != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 0.26/0.67               => ( ! [M4: num] :
% 0.26/0.67                      ( ( X3
% 0.26/0.67                        = ( bit0 @ M4 ) )
% 0.26/0.67                     => ! [N2: num] :
% 0.26/0.67                          ( ( Xa
% 0.26/0.67                            = ( bit0 @ N2 ) )
% 0.26/0.67                         => ( Y3
% 0.26/0.67                           != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) )
% 0.26/0.67                 => ( ! [M4: num] :
% 0.26/0.67                        ( ( X3
% 0.26/0.67                          = ( bit0 @ M4 ) )
% 0.26/0.67                       => ! [N2: num] :
% 0.26/0.67                            ( ( Xa
% 0.26/0.67                              = ( bit1 @ N2 ) )
% 0.26/0.67                           => ( Y3
% 0.26/0.67                             != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) )
% 0.26/0.67                   => ( ! [M4: num] :
% 0.26/0.67                          ( ( X3
% 0.26/0.67                            = ( bit1 @ M4 ) )
% 0.26/0.67                         => ( ( Xa = one )
% 0.26/0.67                           => ( Y3
% 0.26/0.67                             != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 0.26/0.67                     => ( ! [M4: num] :
% 0.26/0.67                            ( ( X3
% 0.26/0.67                              = ( bit1 @ M4 ) )
% 0.26/0.67                           => ! [N2: num] :
% 0.26/0.67                                ( ( Xa
% 0.26/0.67                                  = ( bit0 @ N2 ) )
% 0.26/0.67                               => ( Y3
% 0.26/0.67                                 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.26/0.67                                    @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 0.26/0.67                                    @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) )
% 0.26/0.67                       => ~ ! [M4: num] :
% 0.26/0.67                              ( ( X3
% 0.26/0.67                                = ( bit1 @ M4 ) )
% 0.26/0.67                             => ! [N2: num] :
% 0.26/0.67                                  ( ( Xa
% 0.26/0.67                                    = ( bit1 @ N2 ) )
% 0.26/0.67                                 => ( Y3
% 0.26/0.67                                   != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_not_num.elims
% 0.26/0.67  thf(fact_9625_xor__num_Osimps_I6_J,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.26/0.67        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % xor_num.simps(6)
% 0.26/0.67  thf(fact_9626_xor__num_Osimps_I9_J,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.26/0.67        = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % xor_num.simps(9)
% 0.26/0.67  thf(fact_9627_xor__num_Osimps_I5_J,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.26/0.67        = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % xor_num.simps(5)
% 0.26/0.67  thf(fact_9628_and__not__num_Osimps_I5_J,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.26/0.67        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_not_num.simps(5)
% 0.26/0.67  thf(fact_9629_and__not__num_Osimps_I6_J,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.26/0.67        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_not_num.simps(6)
% 0.26/0.67  thf(fact_9630_and__not__num_Osimps_I9_J,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.26/0.67        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_not_num.simps(9)
% 0.26/0.67  thf(fact_9631_xor__num_Osimps_I1_J,axiom,
% 0.26/0.67      ( ( bit_un2480387367778600638or_num @ one @ one )
% 0.26/0.67      = none_num ) ).
% 0.26/0.67  
% 0.26/0.67  % xor_num.simps(1)
% 0.26/0.67  thf(fact_9632_xor__num_Oelims,axiom,
% 0.26/0.67      ! [X3: num,Xa: num,Y3: option_num] :
% 0.26/0.67        ( ( ( bit_un2480387367778600638or_num @ X3 @ Xa )
% 0.26/0.67          = Y3 )
% 0.26/0.67       => ( ( ( X3 = one )
% 0.26/0.67           => ( ( Xa = one )
% 0.26/0.67             => ( Y3 != none_num ) ) )
% 0.26/0.67         => ( ( ( X3 = one )
% 0.26/0.67             => ! [N2: num] :
% 0.26/0.67                  ( ( Xa
% 0.26/0.67                    = ( bit0 @ N2 ) )
% 0.26/0.67                 => ( Y3
% 0.26/0.67                   != ( some_num @ ( bit1 @ N2 ) ) ) ) )
% 0.26/0.67           => ( ( ( X3 = one )
% 0.26/0.67               => ! [N2: num] :
% 0.26/0.67                    ( ( Xa
% 0.26/0.67                      = ( bit1 @ N2 ) )
% 0.26/0.67                   => ( Y3
% 0.26/0.67                     != ( some_num @ ( bit0 @ N2 ) ) ) ) )
% 0.26/0.67             => ( ! [M4: num] :
% 0.26/0.67                    ( ( X3
% 0.26/0.67                      = ( bit0 @ M4 ) )
% 0.26/0.67                   => ( ( Xa = one )
% 0.26/0.67                     => ( Y3
% 0.26/0.67                       != ( some_num @ ( bit1 @ M4 ) ) ) ) )
% 0.26/0.67               => ( ! [M4: num] :
% 0.26/0.67                      ( ( X3
% 0.26/0.67                        = ( bit0 @ M4 ) )
% 0.26/0.67                     => ! [N2: num] :
% 0.26/0.67                          ( ( Xa
% 0.26/0.67                            = ( bit0 @ N2 ) )
% 0.26/0.67                         => ( Y3
% 0.26/0.67                           != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) ) )
% 0.26/0.67                 => ( ! [M4: num] :
% 0.26/0.67                        ( ( X3
% 0.26/0.67                          = ( bit0 @ M4 ) )
% 0.26/0.67                       => ! [N2: num] :
% 0.26/0.67                            ( ( Xa
% 0.26/0.67                              = ( bit1 @ N2 ) )
% 0.26/0.67                           => ( Y3
% 0.26/0.67                             != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) ) ) )
% 0.26/0.67                   => ( ! [M4: num] :
% 0.26/0.67                          ( ( X3
% 0.26/0.67                            = ( bit1 @ M4 ) )
% 0.26/0.67                         => ( ( Xa = one )
% 0.26/0.67                           => ( Y3
% 0.26/0.67                             != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 0.26/0.67                     => ( ! [M4: num] :
% 0.26/0.67                            ( ( X3
% 0.26/0.67                              = ( bit1 @ M4 ) )
% 0.26/0.67                           => ! [N2: num] :
% 0.26/0.67                                ( ( Xa
% 0.26/0.67                                  = ( bit0 @ N2 ) )
% 0.26/0.67                               => ( Y3
% 0.26/0.67                                 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) ) ) )
% 0.26/0.67                       => ~ ! [M4: num] :
% 0.26/0.67                              ( ( X3
% 0.26/0.67                                = ( bit1 @ M4 ) )
% 0.26/0.67                             => ! [N2: num] :
% 0.26/0.67                                  ( ( Xa
% 0.26/0.67                                    = ( bit1 @ N2 ) )
% 0.26/0.67                                 => ( Y3
% 0.26/0.67                                   != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % xor_num.elims
% 0.26/0.67  thf(fact_9633_xor__num_Osimps_I7_J,axiom,
% 0.26/0.67      ! [M: num] :
% 0.26/0.67        ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ one )
% 0.26/0.67        = ( some_num @ ( bit0 @ M ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % xor_num.simps(7)
% 0.26/0.67  thf(fact_9634_xor__num_Osimps_I4_J,axiom,
% 0.26/0.67      ! [M: num] :
% 0.26/0.67        ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ one )
% 0.26/0.67        = ( some_num @ ( bit1 @ M ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % xor_num.simps(4)
% 0.26/0.67  thf(fact_9635_xor__num_Osimps_I3_J,axiom,
% 0.26/0.67      ! [N: num] :
% 0.26/0.67        ( ( bit_un2480387367778600638or_num @ one @ ( bit1 @ N ) )
% 0.26/0.67        = ( some_num @ ( bit0 @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % xor_num.simps(3)
% 0.26/0.67  thf(fact_9636_xor__num_Osimps_I2_J,axiom,
% 0.26/0.67      ! [N: num] :
% 0.26/0.67        ( ( bit_un2480387367778600638or_num @ one @ ( bit0 @ N ) )
% 0.26/0.67        = ( some_num @ ( bit1 @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % xor_num.simps(2)
% 0.26/0.67  thf(fact_9637_xor__num_Osimps_I8_J,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.26/0.67        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % xor_num.simps(8)
% 0.26/0.67  thf(fact_9638_and__num_Oelims,axiom,
% 0.26/0.67      ! [X3: num,Xa: num,Y3: option_num] :
% 0.26/0.67        ( ( ( bit_un7362597486090784418nd_num @ X3 @ Xa )
% 0.26/0.67          = Y3 )
% 0.26/0.67       => ( ( ( X3 = one )
% 0.26/0.67           => ( ( Xa = one )
% 0.26/0.67             => ( Y3
% 0.26/0.67               != ( some_num @ one ) ) ) )
% 0.26/0.67         => ( ( ( X3 = one )
% 0.26/0.67             => ( ? [N2: num] :
% 0.26/0.67                    ( Xa
% 0.26/0.67                    = ( bit0 @ N2 ) )
% 0.26/0.67               => ( Y3 != none_num ) ) )
% 0.26/0.67           => ( ( ( X3 = one )
% 0.26/0.67               => ( ? [N2: num] :
% 0.26/0.67                      ( Xa
% 0.26/0.67                      = ( bit1 @ N2 ) )
% 0.26/0.67                 => ( Y3
% 0.26/0.67                   != ( some_num @ one ) ) ) )
% 0.26/0.67             => ( ( ? [M4: num] :
% 0.26/0.67                      ( X3
% 0.26/0.67                      = ( bit0 @ M4 ) )
% 0.26/0.67                 => ( ( Xa = one )
% 0.26/0.67                   => ( Y3 != none_num ) ) )
% 0.26/0.67               => ( ! [M4: num] :
% 0.26/0.67                      ( ( X3
% 0.26/0.67                        = ( bit0 @ M4 ) )
% 0.26/0.67                     => ! [N2: num] :
% 0.26/0.67                          ( ( Xa
% 0.26/0.67                            = ( bit0 @ N2 ) )
% 0.26/0.67                         => ( Y3
% 0.26/0.67                           != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) )
% 0.26/0.67                 => ( ! [M4: num] :
% 0.26/0.67                        ( ( X3
% 0.26/0.67                          = ( bit0 @ M4 ) )
% 0.26/0.67                       => ! [N2: num] :
% 0.26/0.67                            ( ( Xa
% 0.26/0.67                              = ( bit1 @ N2 ) )
% 0.26/0.67                           => ( Y3
% 0.26/0.67                             != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) )
% 0.26/0.67                   => ( ( ? [M4: num] :
% 0.26/0.67                            ( X3
% 0.26/0.67                            = ( bit1 @ M4 ) )
% 0.26/0.67                       => ( ( Xa = one )
% 0.26/0.67                         => ( Y3
% 0.26/0.67                           != ( some_num @ one ) ) ) )
% 0.26/0.67                     => ( ! [M4: num] :
% 0.26/0.67                            ( ( X3
% 0.26/0.67                              = ( bit1 @ M4 ) )
% 0.26/0.67                           => ! [N2: num] :
% 0.26/0.67                                ( ( Xa
% 0.26/0.67                                  = ( bit0 @ N2 ) )
% 0.26/0.67                               => ( Y3
% 0.26/0.67                                 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) )
% 0.26/0.67                       => ~ ! [M4: num] :
% 0.26/0.67                              ( ( X3
% 0.26/0.67                                = ( bit1 @ M4 ) )
% 0.26/0.67                             => ! [N2: num] :
% 0.26/0.67                                  ( ( Xa
% 0.26/0.67                                    = ( bit1 @ N2 ) )
% 0.26/0.67                                 => ( Y3
% 0.26/0.67                                   != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.26/0.67                                      @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 0.26/0.67                                      @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_num.elims
% 0.26/0.67  thf(fact_9639_xor__num__dict,axiom,
% 0.26/0.67      bit_un2480387367778600638or_num = bit_un6178654185764691216or_num ).
% 0.26/0.67  
% 0.26/0.67  % xor_num_dict
% 0.26/0.67  thf(fact_9640_and__num_Osimps_I1_J,axiom,
% 0.26/0.67      ( ( bit_un7362597486090784418nd_num @ one @ one )
% 0.26/0.67      = ( some_num @ one ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_num.simps(1)
% 0.26/0.67  thf(fact_9641_and__num_Osimps_I5_J,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.26/0.67        = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_num.simps(5)
% 0.26/0.67  thf(fact_9642_and__num_Osimps_I7_J,axiom,
% 0.26/0.67      ! [M: num] :
% 0.26/0.67        ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ one )
% 0.26/0.67        = ( some_num @ one ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_num.simps(7)
% 0.26/0.67  thf(fact_9643_and__num_Osimps_I3_J,axiom,
% 0.26/0.67      ! [N: num] :
% 0.26/0.67        ( ( bit_un7362597486090784418nd_num @ one @ ( bit1 @ N ) )
% 0.26/0.67        = ( some_num @ one ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_num.simps(3)
% 0.26/0.67  thf(fact_9644_and__num_Osimps_I2_J,axiom,
% 0.26/0.67      ! [N: num] :
% 0.26/0.67        ( ( bit_un7362597486090784418nd_num @ one @ ( bit0 @ N ) )
% 0.26/0.67        = none_num ) ).
% 0.26/0.67  
% 0.26/0.67  % and_num.simps(2)
% 0.26/0.67  thf(fact_9645_and__num_Osimps_I4_J,axiom,
% 0.26/0.67      ! [M: num] :
% 0.26/0.67        ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ one )
% 0.26/0.67        = none_num ) ).
% 0.26/0.67  
% 0.26/0.67  % and_num.simps(4)
% 0.26/0.67  thf(fact_9646_and__num_Osimps_I8_J,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.26/0.67        = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_num.simps(8)
% 0.26/0.67  thf(fact_9647_and__num_Osimps_I6_J,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.26/0.67        = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_num.simps(6)
% 0.26/0.67  thf(fact_9648_and__num_Osimps_I9_J,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.26/0.67        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.26/0.67          @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 0.26/0.67          @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_num.simps(9)
% 0.26/0.67  thf(fact_9649_and__num__dict,axiom,
% 0.26/0.67      bit_un7362597486090784418nd_num = bit_un1837492267222099188nd_num ).
% 0.26/0.67  
% 0.26/0.67  % and_num_dict
% 0.26/0.67  thf(fact_9650_of__nat__eq__id,axiom,
% 0.26/0.67      semiri1316708129612266289at_nat = id_nat ).
% 0.26/0.67  
% 0.26/0.67  % of_nat_eq_id
% 0.26/0.67  thf(fact_9651_less__eq__int__def,axiom,
% 0.26/0.67      ( ord_less_eq_int
% 0.26/0.67      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 0.26/0.67        @ ( produc8739625826339149834_nat_o
% 0.26/0.67          @ ^ [X: nat,Y: nat] :
% 0.26/0.67              ( produc6081775807080527818_nat_o
% 0.26/0.67              @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % less_eq_int_def
% 0.26/0.67  thf(fact_9652_less__int__def,axiom,
% 0.26/0.67      ( ord_less_int
% 0.26/0.67      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 0.26/0.67        @ ( produc8739625826339149834_nat_o
% 0.26/0.67          @ ^ [X: nat,Y: nat] :
% 0.26/0.67              ( produc6081775807080527818_nat_o
% 0.26/0.67              @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % less_int_def
% 0.26/0.67  thf(fact_9653_nat__def,axiom,
% 0.26/0.67      ( nat2
% 0.26/0.67      = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % nat_def
% 0.26/0.67  thf(fact_9654_min__Suc__Suc,axiom,
% 0.26/0.67      ! [M: nat,N: nat] :
% 0.26/0.67        ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.26/0.67        = ( suc @ ( ord_min_nat @ M @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % min_Suc_Suc
% 0.26/0.67  thf(fact_9655_min__0L,axiom,
% 0.26/0.67      ! [N: nat] :
% 0.26/0.67        ( ( ord_min_nat @ zero_zero_nat @ N )
% 0.26/0.67        = zero_zero_nat ) ).
% 0.26/0.67  
% 0.26/0.67  % min_0L
% 0.26/0.67  thf(fact_9656_min__0R,axiom,
% 0.26/0.67      ! [N: nat] :
% 0.26/0.67        ( ( ord_min_nat @ N @ zero_zero_nat )
% 0.26/0.67        = zero_zero_nat ) ).
% 0.26/0.67  
% 0.26/0.67  % min_0R
% 0.26/0.67  thf(fact_9657_min__enat__simps_I3_J,axiom,
% 0.26/0.67      ! [Q3: extended_enat] :
% 0.26/0.67        ( ( ord_mi8085742599997312461d_enat @ zero_z5237406670263579293d_enat @ Q3 )
% 0.26/0.67        = zero_z5237406670263579293d_enat ) ).
% 0.26/0.67  
% 0.26/0.67  % min_enat_simps(3)
% 0.26/0.67  thf(fact_9658_min__enat__simps_I2_J,axiom,
% 0.26/0.67      ! [Q3: extended_enat] :
% 0.26/0.67        ( ( ord_mi8085742599997312461d_enat @ Q3 @ zero_z5237406670263579293d_enat )
% 0.26/0.67        = zero_z5237406670263579293d_enat ) ).
% 0.26/0.67  
% 0.26/0.67  % min_enat_simps(2)
% 0.26/0.67  thf(fact_9659_min__numeral__Suc,axiom,
% 0.26/0.67      ! [K: num,N: nat] :
% 0.26/0.67        ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 0.26/0.67        = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % min_numeral_Suc
% 0.26/0.67  thf(fact_9660_min__Suc__numeral,axiom,
% 0.26/0.67      ! [N: nat,K: num] :
% 0.26/0.67        ( ( ord_min_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 0.26/0.67        = ( suc @ ( ord_min_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % min_Suc_numeral
% 0.26/0.67  thf(fact_9661_concat__bit__assoc__sym,axiom,
% 0.26/0.67      ! [M: nat,N: nat,K: int,L: int,R2: int] :
% 0.26/0.67        ( ( bit_concat_bit @ M @ ( bit_concat_bit @ N @ K @ L ) @ R2 )
% 0.26/0.67        = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_concat_bit @ ( minus_minus_nat @ M @ N ) @ L @ R2 ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % concat_bit_assoc_sym
% 0.26/0.67  thf(fact_9662_min__diff,axiom,
% 0.26/0.67      ! [M: nat,I: nat,N: nat] :
% 0.26/0.67        ( ( ord_min_nat @ ( minus_minus_nat @ M @ I ) @ ( minus_minus_nat @ N @ I ) )
% 0.26/0.67        = ( minus_minus_nat @ ( ord_min_nat @ M @ N ) @ I ) ) ).
% 0.26/0.67  
% 0.26/0.67  % min_diff
% 0.26/0.67  thf(fact_9663_nat__mult__min__right,axiom,
% 0.26/0.67      ! [M: nat,N: nat,Q3: nat] :
% 0.26/0.67        ( ( times_times_nat @ M @ ( ord_min_nat @ N @ Q3 ) )
% 0.26/0.67        = ( ord_min_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % nat_mult_min_right
% 0.26/0.67  thf(fact_9664_nat__mult__min__left,axiom,
% 0.26/0.67      ! [M: nat,N: nat,Q3: nat] :
% 0.26/0.67        ( ( times_times_nat @ ( ord_min_nat @ M @ N ) @ Q3 )
% 0.26/0.67        = ( ord_min_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N @ Q3 ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % nat_mult_min_left
% 0.26/0.67  thf(fact_9665_take__bit__concat__bit__eq,axiom,
% 0.26/0.67      ! [M: nat,N: nat,K: int,L: int] :
% 0.26/0.67        ( ( bit_se2923211474154528505it_int @ M @ ( bit_concat_bit @ N @ K @ L ) )
% 0.26/0.67        = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N ) @ L ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % take_bit_concat_bit_eq
% 0.26/0.67  thf(fact_9666_min__Suc2,axiom,
% 0.26/0.67      ! [M: nat,N: nat] :
% 0.26/0.67        ( ( ord_min_nat @ M @ ( suc @ N ) )
% 0.26/0.67        = ( case_nat_nat @ zero_zero_nat
% 0.26/0.67          @ ^ [M5: nat] : ( suc @ ( ord_min_nat @ M5 @ N ) )
% 0.26/0.67          @ M ) ) ).
% 0.26/0.67  
% 0.26/0.67  % min_Suc2
% 0.26/0.67  thf(fact_9667_min__Suc1,axiom,
% 0.26/0.67      ! [N: nat,M: nat] :
% 0.26/0.67        ( ( ord_min_nat @ ( suc @ N ) @ M )
% 0.26/0.67        = ( case_nat_nat @ zero_zero_nat
% 0.26/0.67          @ ^ [M5: nat] : ( suc @ ( ord_min_nat @ N @ M5 ) )
% 0.26/0.67          @ M ) ) ).
% 0.26/0.67  
% 0.26/0.67  % min_Suc1
% 0.26/0.67  thf(fact_9668_inf__int__def,axiom,
% 0.26/0.67      inf_inf_int = ord_min_int ).
% 0.26/0.67  
% 0.26/0.67  % inf_int_def
% 0.26/0.67  thf(fact_9669_inf__nat__def,axiom,
% 0.26/0.67      inf_inf_nat = ord_min_nat ).
% 0.26/0.67  
% 0.26/0.67  % inf_nat_def
% 0.26/0.67  thf(fact_9670_inf__enat__def,axiom,
% 0.26/0.67      inf_in1870772243966228564d_enat = ord_mi8085742599997312461d_enat ).
% 0.26/0.67  
% 0.26/0.67  % inf_enat_def
% 0.26/0.67  thf(fact_9671_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 0.26/0.67      ! [N: nat,J: nat,I: nat] :
% 0.26/0.67        ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I ) )
% 0.26/0.67       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N )
% 0.26/0.67          = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % nth_sorted_list_of_set_greaterThanAtMost
% 0.26/0.67  thf(fact_9672_and__not__num_Opelims,axiom,
% 0.26/0.67      ! [X3: num,Xa: num,Y3: option_num] :
% 0.26/0.67        ( ( ( bit_and_not_num @ X3 @ Xa )
% 0.26/0.67          = Y3 )
% 0.26/0.67       => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X3 @ Xa ) )
% 0.26/0.67         => ( ( ( X3 = one )
% 0.26/0.67             => ( ( Xa = one )
% 0.26/0.67               => ( ( Y3 = none_num )
% 0.26/0.67                 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.26/0.67           => ( ( ( X3 = one )
% 0.26/0.67               => ! [N2: num] :
% 0.26/0.67                    ( ( Xa
% 0.26/0.67                      = ( bit0 @ N2 ) )
% 0.26/0.67                   => ( ( Y3
% 0.26/0.67                        = ( some_num @ one ) )
% 0.26/0.67                     => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) ) ) ) )
% 0.26/0.67             => ( ( ( X3 = one )
% 0.26/0.67                 => ! [N2: num] :
% 0.26/0.67                      ( ( Xa
% 0.26/0.67                        = ( bit1 @ N2 ) )
% 0.26/0.67                     => ( ( Y3 = none_num )
% 0.26/0.67                       => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) ) ) ) )
% 0.26/0.67               => ( ! [M4: num] :
% 0.26/0.67                      ( ( X3
% 0.26/0.67                        = ( bit0 @ M4 ) )
% 0.26/0.67                     => ( ( Xa = one )
% 0.26/0.67                       => ( ( Y3
% 0.26/0.67                            = ( some_num @ ( bit0 @ M4 ) ) )
% 0.26/0.67                         => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 0.26/0.67                 => ( ! [M4: num] :
% 0.26/0.67                        ( ( X3
% 0.26/0.67                          = ( bit0 @ M4 ) )
% 0.26/0.67                       => ! [N2: num] :
% 0.26/0.67                            ( ( Xa
% 0.26/0.67                              = ( bit0 @ N2 ) )
% 0.26/0.67                           => ( ( Y3
% 0.26/0.67                                = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 0.26/0.67                             => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 0.26/0.67                   => ( ! [M4: num] :
% 0.26/0.67                          ( ( X3
% 0.26/0.67                            = ( bit0 @ M4 ) )
% 0.26/0.67                         => ! [N2: num] :
% 0.26/0.67                              ( ( Xa
% 0.26/0.67                                = ( bit1 @ N2 ) )
% 0.26/0.67                             => ( ( Y3
% 0.26/0.67                                  = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 0.26/0.67                               => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) )
% 0.26/0.67                     => ( ! [M4: num] :
% 0.26/0.67                            ( ( X3
% 0.26/0.67                              = ( bit1 @ M4 ) )
% 0.26/0.67                           => ( ( Xa = one )
% 0.26/0.67                             => ( ( Y3
% 0.26/0.67                                  = ( some_num @ ( bit0 @ M4 ) ) )
% 0.26/0.67                               => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 0.26/0.67                       => ( ! [M4: num] :
% 0.26/0.67                              ( ( X3
% 0.26/0.67                                = ( bit1 @ M4 ) )
% 0.26/0.67                             => ! [N2: num] :
% 0.26/0.67                                  ( ( Xa
% 0.26/0.67                                    = ( bit0 @ N2 ) )
% 0.26/0.67                                 => ( ( Y3
% 0.26/0.67                                      = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.26/0.67                                        @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 0.26/0.67                                        @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 0.26/0.67                                   => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 0.26/0.67                         => ~ ! [M4: num] :
% 0.26/0.67                                ( ( X3
% 0.26/0.67                                  = ( bit1 @ M4 ) )
% 0.26/0.67                               => ! [N2: num] :
% 0.26/0.67                                    ( ( Xa
% 0.26/0.67                                      = ( bit1 @ N2 ) )
% 0.26/0.67                                   => ( ( Y3
% 0.26/0.67                                        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 0.26/0.67                                     => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_not_num.pelims
% 0.26/0.67  thf(fact_9673_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 0.26/0.67      ! [N: nat,J: nat,I: nat] :
% 0.26/0.67        ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 0.26/0.67       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N )
% 0.26/0.67          = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % nth_sorted_list_of_set_greaterThanLessThan
% 0.26/0.67  thf(fact_9674_and__num_Opelims,axiom,
% 0.26/0.67      ! [X3: num,Xa: num,Y3: option_num] :
% 0.26/0.67        ( ( ( bit_un7362597486090784418nd_num @ X3 @ Xa )
% 0.26/0.67          = Y3 )
% 0.26/0.67       => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X3 @ Xa ) )
% 0.26/0.67         => ( ( ( X3 = one )
% 0.26/0.67             => ( ( Xa = one )
% 0.26/0.67               => ( ( Y3
% 0.26/0.67                    = ( some_num @ one ) )
% 0.26/0.67                 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.26/0.67           => ( ( ( X3 = one )
% 0.26/0.67               => ! [N2: num] :
% 0.26/0.67                    ( ( Xa
% 0.26/0.67                      = ( bit0 @ N2 ) )
% 0.26/0.67                   => ( ( Y3 = none_num )
% 0.26/0.67                     => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) ) ) ) )
% 0.26/0.67             => ( ( ( X3 = one )
% 0.26/0.67                 => ! [N2: num] :
% 0.26/0.67                      ( ( Xa
% 0.26/0.67                        = ( bit1 @ N2 ) )
% 0.26/0.67                     => ( ( Y3
% 0.26/0.67                          = ( some_num @ one ) )
% 0.26/0.67                       => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) ) ) ) )
% 0.26/0.67               => ( ! [M4: num] :
% 0.26/0.67                      ( ( X3
% 0.26/0.67                        = ( bit0 @ M4 ) )
% 0.26/0.67                     => ( ( Xa = one )
% 0.26/0.67                       => ( ( Y3 = none_num )
% 0.26/0.67                         => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 0.26/0.67                 => ( ! [M4: num] :
% 0.26/0.67                        ( ( X3
% 0.26/0.67                          = ( bit0 @ M4 ) )
% 0.26/0.67                       => ! [N2: num] :
% 0.26/0.67                            ( ( Xa
% 0.26/0.67                              = ( bit0 @ N2 ) )
% 0.26/0.67                           => ( ( Y3
% 0.26/0.67                                = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 0.26/0.67                             => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 0.26/0.67                   => ( ! [M4: num] :
% 0.26/0.67                          ( ( X3
% 0.26/0.67                            = ( bit0 @ M4 ) )
% 0.26/0.67                         => ! [N2: num] :
% 0.26/0.67                              ( ( Xa
% 0.26/0.67                                = ( bit1 @ N2 ) )
% 0.26/0.67                             => ( ( Y3
% 0.26/0.67                                  = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 0.26/0.67                               => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) )
% 0.26/0.67                     => ( ! [M4: num] :
% 0.26/0.67                            ( ( X3
% 0.26/0.67                              = ( bit1 @ M4 ) )
% 0.26/0.67                           => ( ( Xa = one )
% 0.26/0.67                             => ( ( Y3
% 0.26/0.67                                  = ( some_num @ one ) )
% 0.26/0.67                               => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 0.26/0.67                       => ( ! [M4: num] :
% 0.26/0.67                              ( ( X3
% 0.26/0.67                                = ( bit1 @ M4 ) )
% 0.26/0.67                             => ! [N2: num] :
% 0.26/0.67                                  ( ( Xa
% 0.26/0.67                                    = ( bit0 @ N2 ) )
% 0.26/0.67                                 => ( ( Y3
% 0.26/0.67                                      = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 0.26/0.67                                   => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 0.26/0.67                         => ~ ! [M4: num] :
% 0.26/0.67                                ( ( X3
% 0.26/0.67                                  = ( bit1 @ M4 ) )
% 0.26/0.67                               => ! [N2: num] :
% 0.26/0.67                                    ( ( Xa
% 0.26/0.67                                      = ( bit1 @ N2 ) )
% 0.26/0.67                                   => ( ( Y3
% 0.26/0.67                                        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.26/0.67                                          @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 0.26/0.67                                          @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 0.26/0.67                                     => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % and_num.pelims
% 0.26/0.67  thf(fact_9675_xor__num_Opelims,axiom,
% 0.26/0.67      ! [X3: num,Xa: num,Y3: option_num] :
% 0.26/0.67        ( ( ( bit_un2480387367778600638or_num @ X3 @ Xa )
% 0.26/0.67          = Y3 )
% 0.26/0.67       => ( ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ X3 @ Xa ) )
% 0.26/0.67         => ( ( ( X3 = one )
% 0.26/0.67             => ( ( Xa = one )
% 0.26/0.67               => ( ( Y3 = none_num )
% 0.26/0.67                 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.26/0.67           => ( ( ( X3 = one )
% 0.26/0.67               => ! [N2: num] :
% 0.26/0.67                    ( ( Xa
% 0.26/0.67                      = ( bit0 @ N2 ) )
% 0.26/0.67                   => ( ( Y3
% 0.26/0.67                        = ( some_num @ ( bit1 @ N2 ) ) )
% 0.26/0.67                     => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) ) ) ) )
% 0.26/0.67             => ( ( ( X3 = one )
% 0.26/0.67                 => ! [N2: num] :
% 0.26/0.67                      ( ( Xa
% 0.26/0.67                        = ( bit1 @ N2 ) )
% 0.26/0.67                     => ( ( Y3
% 0.26/0.67                          = ( some_num @ ( bit0 @ N2 ) ) )
% 0.26/0.67                       => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) ) ) ) )
% 0.26/0.67               => ( ! [M4: num] :
% 0.26/0.67                      ( ( X3
% 0.26/0.67                        = ( bit0 @ M4 ) )
% 0.26/0.67                     => ( ( Xa = one )
% 0.26/0.67                       => ( ( Y3
% 0.26/0.67                            = ( some_num @ ( bit1 @ M4 ) ) )
% 0.26/0.67                         => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 0.26/0.67                 => ( ! [M4: num] :
% 0.26/0.67                        ( ( X3
% 0.26/0.67                          = ( bit0 @ M4 ) )
% 0.26/0.67                       => ! [N2: num] :
% 0.26/0.67                            ( ( Xa
% 0.26/0.67                              = ( bit0 @ N2 ) )
% 0.26/0.67                           => ( ( Y3
% 0.26/0.67                                = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) )
% 0.26/0.67                             => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 0.26/0.67                   => ( ! [M4: num] :
% 0.26/0.67                          ( ( X3
% 0.26/0.67                            = ( bit0 @ M4 ) )
% 0.26/0.67                         => ! [N2: num] :
% 0.26/0.67                              ( ( Xa
% 0.26/0.67                                = ( bit1 @ N2 ) )
% 0.26/0.67                             => ( ( Y3
% 0.26/0.67                                  = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) )
% 0.26/0.67                               => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) )
% 0.26/0.67                     => ( ! [M4: num] :
% 0.26/0.67                            ( ( X3
% 0.26/0.67                              = ( bit1 @ M4 ) )
% 0.26/0.67                           => ( ( Xa = one )
% 0.26/0.67                             => ( ( Y3
% 0.26/0.67                                  = ( some_num @ ( bit0 @ M4 ) ) )
% 0.26/0.67                               => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 0.26/0.67                       => ( ! [M4: num] :
% 0.26/0.67                              ( ( X3
% 0.26/0.67                                = ( bit1 @ M4 ) )
% 0.26/0.67                             => ! [N2: num] :
% 0.26/0.67                                  ( ( Xa
% 0.26/0.67                                    = ( bit0 @ N2 ) )
% 0.26/0.67                                 => ( ( Y3
% 0.26/0.67                                      = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) )
% 0.26/0.67                                   => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 0.26/0.67                         => ~ ! [M4: num] :
% 0.26/0.67                                ( ( X3
% 0.26/0.67                                  = ( bit1 @ M4 ) )
% 0.26/0.67                               => ! [N2: num] :
% 0.26/0.67                                    ( ( Xa
% 0.26/0.67                                      = ( bit1 @ N2 ) )
% 0.26/0.67                                   => ( ( Y3
% 0.26/0.67                                        = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) )
% 0.26/0.67                                     => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % xor_num.pelims
% 0.26/0.67  thf(fact_9676_or__not__num__neg_Opelims,axiom,
% 0.26/0.67      ! [X3: num,Xa: num,Y3: num] :
% 0.26/0.67        ( ( ( bit_or_not_num_neg @ X3 @ Xa )
% 0.26/0.67          = Y3 )
% 0.26/0.67       => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X3 @ Xa ) )
% 0.26/0.67         => ( ( ( X3 = one )
% 0.26/0.67             => ( ( Xa = one )
% 0.26/0.67               => ( ( Y3 = one )
% 0.26/0.67                 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.26/0.67           => ( ( ( X3 = one )
% 0.26/0.67               => ! [M4: num] :
% 0.26/0.67                    ( ( Xa
% 0.26/0.67                      = ( bit0 @ M4 ) )
% 0.26/0.67                   => ( ( Y3
% 0.26/0.67                        = ( bit1 @ M4 ) )
% 0.26/0.67                     => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M4 ) ) ) ) ) )
% 0.26/0.67             => ( ( ( X3 = one )
% 0.26/0.67                 => ! [M4: num] :
% 0.26/0.67                      ( ( Xa
% 0.26/0.67                        = ( bit1 @ M4 ) )
% 0.26/0.67                     => ( ( Y3
% 0.26/0.67                          = ( bit1 @ M4 ) )
% 0.26/0.67                       => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M4 ) ) ) ) ) )
% 0.26/0.67               => ( ! [N2: num] :
% 0.26/0.67                      ( ( X3
% 0.26/0.67                        = ( bit0 @ N2 ) )
% 0.26/0.67                     => ( ( Xa = one )
% 0.26/0.67                       => ( ( Y3
% 0.26/0.67                            = ( bit0 @ one ) )
% 0.26/0.67                         => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N2 ) @ one ) ) ) ) )
% 0.26/0.67                 => ( ! [N2: num] :
% 0.26/0.67                        ( ( X3
% 0.26/0.67                          = ( bit0 @ N2 ) )
% 0.26/0.67                       => ! [M4: num] :
% 0.26/0.67                            ( ( Xa
% 0.26/0.67                              = ( bit0 @ M4 ) )
% 0.26/0.67                           => ( ( Y3
% 0.26/0.67                                = ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) )
% 0.26/0.67                             => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N2 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 0.26/0.67                   => ( ! [N2: num] :
% 0.26/0.67                          ( ( X3
% 0.26/0.67                            = ( bit0 @ N2 ) )
% 0.26/0.67                         => ! [M4: num] :
% 0.26/0.67                              ( ( Xa
% 0.26/0.67                                = ( bit1 @ M4 ) )
% 0.26/0.67                             => ( ( Y3
% 0.26/0.67                                  = ( bit0 @ ( bit_or_not_num_neg @ N2 @ M4 ) ) )
% 0.26/0.67                               => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N2 ) @ ( bit1 @ M4 ) ) ) ) ) )
% 0.26/0.67                     => ( ! [N2: num] :
% 0.26/0.67                            ( ( X3
% 0.26/0.67                              = ( bit1 @ N2 ) )
% 0.26/0.67                           => ( ( Xa = one )
% 0.26/0.67                             => ( ( Y3 = one )
% 0.26/0.67                               => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N2 ) @ one ) ) ) ) )
% 0.26/0.67                       => ( ! [N2: num] :
% 0.26/0.67                              ( ( X3
% 0.26/0.67                                = ( bit1 @ N2 ) )
% 0.26/0.67                             => ! [M4: num] :
% 0.26/0.67                                  ( ( Xa
% 0.26/0.67                                    = ( bit0 @ M4 ) )
% 0.26/0.67                                 => ( ( Y3
% 0.26/0.67                                      = ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) )
% 0.26/0.67                                   => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N2 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 0.26/0.67                         => ~ ! [N2: num] :
% 0.26/0.67                                ( ( X3
% 0.26/0.67                                  = ( bit1 @ N2 ) )
% 0.26/0.67                               => ! [M4: num] :
% 0.26/0.67                                    ( ( Xa
% 0.26/0.67                                      = ( bit1 @ M4 ) )
% 0.26/0.67                                   => ( ( Y3
% 0.26/0.67                                        = ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) )
% 0.26/0.67                                     => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N2 ) @ ( bit1 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % or_not_num_neg.pelims
% 0.26/0.67  thf(fact_9677_xor__num__rel__dict,axiom,
% 0.26/0.67      bit_un2901131394128224187um_rel = bit_un3595099601533988841um_rel ).
% 0.26/0.67  
% 0.26/0.67  % xor_num_rel_dict
% 0.26/0.67  thf(fact_9678_and__num__rel__dict,axiom,
% 0.26/0.67      bit_un4731106466462545111um_rel = bit_un5425074673868309765um_rel ).
% 0.26/0.67  
% 0.26/0.67  % and_num_rel_dict
% 0.26/0.67  thf(fact_9679_card__length__sum__list__rec,axiom,
% 0.26/0.67      ! [M: nat,N4: nat] :
% 0.26/0.67        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 0.26/0.67       => ( ( finite_card_list_nat
% 0.26/0.67            @ ( collect_list_nat
% 0.26/0.67              @ ^ [L2: list_nat] :
% 0.26/0.67                  ( ( ( size_size_list_nat @ L2 )
% 0.26/0.67                    = M )
% 0.26/0.67                  & ( ( groups4561878855575611511st_nat @ L2 )
% 0.26/0.67                    = N4 ) ) ) )
% 0.26/0.67          = ( plus_plus_nat
% 0.26/0.67            @ ( finite_card_list_nat
% 0.26/0.67              @ ( collect_list_nat
% 0.26/0.67                @ ^ [L2: list_nat] :
% 0.26/0.67                    ( ( ( size_size_list_nat @ L2 )
% 0.26/0.67                      = ( minus_minus_nat @ M @ one_one_nat ) )
% 0.26/0.67                    & ( ( groups4561878855575611511st_nat @ L2 )
% 0.26/0.67                      = N4 ) ) ) )
% 0.26/0.67            @ ( finite_card_list_nat
% 0.26/0.67              @ ( collect_list_nat
% 0.26/0.67                @ ^ [L2: list_nat] :
% 0.26/0.67                    ( ( ( size_size_list_nat @ L2 )
% 0.26/0.67                      = M )
% 0.26/0.67                    & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 0.26/0.67                      = N4 ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % card_length_sum_list_rec
% 0.26/0.67  thf(fact_9680_Code__Target__Nat_ONat_Oabs__eq,axiom,
% 0.26/0.67      ! [X3: int] :
% 0.26/0.67        ( ( code_Target_Nat @ ( code_integer_of_int @ X3 ) )
% 0.26/0.67        = ( nat2 @ X3 ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Code_Target_Nat.Nat.abs_eq
% 0.26/0.67  thf(fact_9681_Code__Target__Nat_ONat_Orep__eq,axiom,
% 0.26/0.67      ( code_Target_Nat
% 0.26/0.67      = ( ^ [X: code_integer] : ( nat2 @ ( code_int_of_integer @ X ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Code_Target_Nat.Nat.rep_eq
% 0.26/0.67  thf(fact_9682_sorted__list__of__set__greaterThanAtMost,axiom,
% 0.26/0.67      ! [I: nat,J: nat] :
% 0.26/0.67        ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 0.26/0.67       => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 0.26/0.67          = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % sorted_list_of_set_greaterThanAtMost
% 0.26/0.67  thf(fact_9683_sorted__list__of__set__greaterThanLessThan,axiom,
% 0.26/0.67      ! [I: nat,J: nat] :
% 0.26/0.67        ( ( ord_less_nat @ ( suc @ I ) @ J )
% 0.26/0.67       => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) )
% 0.26/0.67          = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % sorted_list_of_set_greaterThanLessThan
% 0.26/0.67  thf(fact_9684_upto__aux__rec,axiom,
% 0.26/0.67      ( upto_aux
% 0.26/0.67      = ( ^ [I4: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I4 ) @ Js @ ( upto_aux @ I4 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upto_aux_rec
% 0.26/0.67  thf(fact_9685_upto_Opsimps,axiom,
% 0.26/0.67      ! [I: int,J: int] :
% 0.26/0.67        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 0.26/0.67       => ( ( ( ord_less_eq_int @ I @ J )
% 0.26/0.67           => ( ( upto @ I @ J )
% 0.26/0.67              = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 0.26/0.67          & ( ~ ( ord_less_eq_int @ I @ J )
% 0.26/0.67           => ( ( upto @ I @ J )
% 0.26/0.67              = nil_int ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upto.psimps
% 0.26/0.67  thf(fact_9686_upto_Opelims,axiom,
% 0.26/0.67      ! [X3: int,Xa: int,Y3: list_int] :
% 0.26/0.67        ( ( ( upto @ X3 @ Xa )
% 0.26/0.67          = Y3 )
% 0.26/0.67       => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X3 @ Xa ) )
% 0.26/0.67         => ~ ( ( ( ( ord_less_eq_int @ X3 @ Xa )
% 0.26/0.67                 => ( Y3
% 0.26/0.67                    = ( cons_int @ X3 @ ( upto @ ( plus_plus_int @ X3 @ one_one_int ) @ Xa ) ) ) )
% 0.26/0.67                & ( ~ ( ord_less_eq_int @ X3 @ Xa )
% 0.26/0.67                 => ( Y3 = nil_int ) ) )
% 0.26/0.67             => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X3 @ Xa ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upto.pelims
% 0.26/0.67  thf(fact_9687_upto__Nil,axiom,
% 0.26/0.67      ! [I: int,J: int] :
% 0.26/0.67        ( ( ( upto @ I @ J )
% 0.26/0.67          = nil_int )
% 0.26/0.67        = ( ord_less_int @ J @ I ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upto_Nil
% 0.26/0.67  thf(fact_9688_upto__Nil2,axiom,
% 0.26/0.67      ! [I: int,J: int] :
% 0.26/0.67        ( ( nil_int
% 0.26/0.67          = ( upto @ I @ J ) )
% 0.26/0.67        = ( ord_less_int @ J @ I ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upto_Nil2
% 0.26/0.67  thf(fact_9689_upto__empty,axiom,
% 0.26/0.67      ! [J: int,I: int] :
% 0.26/0.67        ( ( ord_less_int @ J @ I )
% 0.26/0.67       => ( ( upto @ I @ J )
% 0.26/0.67          = nil_int ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upto_empty
% 0.26/0.67  thf(fact_9690_nth__upto,axiom,
% 0.26/0.67      ! [I: int,K: nat,J: int] :
% 0.26/0.67        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 0.26/0.67       => ( ( nth_int @ ( upto @ I @ J ) @ K )
% 0.26/0.67          = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % nth_upto
% 0.26/0.67  thf(fact_9691_length__upto,axiom,
% 0.26/0.67      ! [I: int,J: int] :
% 0.26/0.67        ( ( size_size_list_int @ ( upto @ I @ J ) )
% 0.26/0.67        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % length_upto
% 0.26/0.67  thf(fact_9692_upto__rec__numeral_I1_J,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.67         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.67            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 0.26/0.67        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.67         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.67            = nil_int ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upto_rec_numeral(1)
% 0.26/0.67  thf(fact_9693_upto__rec__numeral_I2_J,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.67         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.67            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 0.26/0.67        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.67         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.67            = nil_int ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upto_rec_numeral(2)
% 0.26/0.67  thf(fact_9694_upto__rec__numeral_I3_J,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.67         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.67            = ( 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 ) ) ) ) )
% 0.26/0.67        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.67         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.26/0.67            = nil_int ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upto_rec_numeral(3)
% 0.26/0.67  thf(fact_9695_upto__rec__numeral_I4_J,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.67         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.67            = ( 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 ) ) ) ) ) )
% 0.26/0.67        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.67         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.26/0.67            = nil_int ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upto_rec_numeral(4)
% 0.26/0.67  thf(fact_9696_upto__split2,axiom,
% 0.26/0.67      ! [I: int,J: int,K: int] :
% 0.26/0.67        ( ( ord_less_eq_int @ I @ J )
% 0.26/0.67       => ( ( ord_less_eq_int @ J @ K )
% 0.26/0.67         => ( ( upto @ I @ K )
% 0.26/0.67            = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upto_split2
% 0.26/0.67  thf(fact_9697_upto__split1,axiom,
% 0.26/0.67      ! [I: int,J: int,K: int] :
% 0.26/0.67        ( ( ord_less_eq_int @ I @ J )
% 0.26/0.67       => ( ( ord_less_eq_int @ J @ K )
% 0.26/0.67         => ( ( upto @ I @ K )
% 0.26/0.67            = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upto_split1
% 0.26/0.67  thf(fact_9698_upto_Oelims,axiom,
% 0.26/0.67      ! [X3: int,Xa: int,Y3: list_int] :
% 0.26/0.67        ( ( ( upto @ X3 @ Xa )
% 0.26/0.67          = Y3 )
% 0.26/0.67       => ( ( ( ord_less_eq_int @ X3 @ Xa )
% 0.26/0.67           => ( Y3
% 0.26/0.67              = ( cons_int @ X3 @ ( upto @ ( plus_plus_int @ X3 @ one_one_int ) @ Xa ) ) ) )
% 0.26/0.67          & ( ~ ( ord_less_eq_int @ X3 @ Xa )
% 0.26/0.67           => ( Y3 = nil_int ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upto.elims
% 0.26/0.67  thf(fact_9699_upto_Osimps,axiom,
% 0.26/0.67      ( upto
% 0.26/0.67      = ( ^ [I4: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I4 @ J3 ) @ ( cons_int @ I4 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upto.simps
% 0.26/0.67  thf(fact_9700_upto__rec1,axiom,
% 0.26/0.67      ! [I: int,J: int] :
% 0.26/0.67        ( ( ord_less_eq_int @ I @ J )
% 0.26/0.67       => ( ( upto @ I @ J )
% 0.26/0.67          = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upto_rec1
% 0.26/0.67  thf(fact_9701_upto__rec2,axiom,
% 0.26/0.67      ! [I: int,J: int] :
% 0.26/0.67        ( ( ord_less_eq_int @ I @ J )
% 0.26/0.67       => ( ( upto @ I @ J )
% 0.26/0.67          = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upto_rec2
% 0.26/0.67  thf(fact_9702_upto__split3,axiom,
% 0.26/0.67      ! [I: int,J: int,K: int] :
% 0.26/0.67        ( ( ord_less_eq_int @ I @ J )
% 0.26/0.67       => ( ( ord_less_eq_int @ J @ K )
% 0.26/0.67         => ( ( upto @ I @ K )
% 0.26/0.67            = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upto_split3
% 0.26/0.67  thf(fact_9703_le__enumerate,axiom,
% 0.26/0.67      ! [S2: set_nat,N: nat] :
% 0.26/0.67        ( ~ ( finite_finite_nat @ S2 )
% 0.26/0.67       => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S2 @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % le_enumerate
% 0.26/0.67  thf(fact_9704_finite__le__enumerate,axiom,
% 0.26/0.67      ! [S2: set_nat,N: nat] :
% 0.26/0.67        ( ( finite_finite_nat @ S2 )
% 0.26/0.67       => ( ( ord_less_nat @ N @ ( finite_card_nat @ S2 ) )
% 0.26/0.67         => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S2 @ N ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % finite_le_enumerate
% 0.26/0.67  thf(fact_9705_DeMoivre2,axiom,
% 0.26/0.67      ! [R2: real,A: real,N: nat] :
% 0.26/0.67        ( ( power_power_complex @ ( rcis @ R2 @ A ) @ N )
% 0.26/0.67        = ( rcis @ ( power_power_real @ R2 @ N ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % DeMoivre2
% 0.26/0.67  thf(fact_9706_Least__eq__0,axiom,
% 0.26/0.67      ! [P: nat > $o] :
% 0.26/0.67        ( ( P @ zero_zero_nat )
% 0.26/0.67       => ( ( ord_Least_nat @ P )
% 0.26/0.67          = zero_zero_nat ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Least_eq_0
% 0.26/0.67  thf(fact_9707_rcis__zero__arg,axiom,
% 0.26/0.67      ! [R2: real] :
% 0.26/0.67        ( ( rcis @ R2 @ zero_zero_real )
% 0.26/0.67        = ( real_V4546457046886955230omplex @ R2 ) ) ).
% 0.26/0.67  
% 0.26/0.67  % rcis_zero_arg
% 0.26/0.67  thf(fact_9708_rcis__zero__mod,axiom,
% 0.26/0.67      ! [A: real] :
% 0.26/0.67        ( ( rcis @ zero_zero_real @ A )
% 0.26/0.67        = zero_zero_complex ) ).
% 0.26/0.67  
% 0.26/0.67  % rcis_zero_mod
% 0.26/0.67  thf(fact_9709_rcis__eq__zero__iff,axiom,
% 0.26/0.67      ! [R2: real,A: real] :
% 0.26/0.67        ( ( ( rcis @ R2 @ A )
% 0.26/0.67          = zero_zero_complex )
% 0.26/0.67        = ( R2 = zero_zero_real ) ) ).
% 0.26/0.67  
% 0.26/0.67  % rcis_eq_zero_iff
% 0.26/0.67  thf(fact_9710_Least__Suc2,axiom,
% 0.26/0.67      ! [P: nat > $o,N: nat,Q: nat > $o,M: nat] :
% 0.26/0.67        ( ( P @ N )
% 0.26/0.67       => ( ( Q @ M )
% 0.26/0.67         => ( ~ ( P @ zero_zero_nat )
% 0.26/0.67           => ( ! [K2: nat] :
% 0.26/0.67                  ( ( P @ ( suc @ K2 ) )
% 0.26/0.67                  = ( Q @ K2 ) )
% 0.26/0.67             => ( ( ord_Least_nat @ P )
% 0.26/0.67                = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Least_Suc2
% 0.26/0.67  thf(fact_9711_Least__Suc,axiom,
% 0.26/0.67      ! [P: nat > $o,N: nat] :
% 0.26/0.67        ( ( P @ N )
% 0.26/0.67       => ( ~ ( P @ zero_zero_nat )
% 0.26/0.67         => ( ( ord_Least_nat @ P )
% 0.26/0.67            = ( suc
% 0.26/0.67              @ ( ord_Least_nat
% 0.26/0.67                @ ^ [M3: nat] : ( P @ ( suc @ M3 ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Least_Suc
% 0.26/0.67  thf(fact_9712_Inf__nat__def,axiom,
% 0.26/0.67      ( complete_Inf_Inf_nat
% 0.26/0.67      = ( ^ [X8: set_nat] :
% 0.26/0.67            ( ord_Least_nat
% 0.26/0.67            @ ^ [N3: nat] : ( member_nat @ N3 @ X8 ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Inf_nat_def
% 0.26/0.67  thf(fact_9713_Sup__real__def,axiom,
% 0.26/0.67      ( comple1385675409528146559p_real
% 0.26/0.67      = ( ^ [X8: set_real] :
% 0.26/0.67            ( ord_Least_real
% 0.26/0.67            @ ^ [Z6: real] :
% 0.26/0.67              ! [X: real] :
% 0.26/0.67                ( ( member_real @ X @ X8 )
% 0.26/0.67               => ( ord_less_eq_real @ X @ Z6 ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Sup_real_def
% 0.26/0.67  thf(fact_9714_Code__Target__Nat_ONat__def,axiom,
% 0.26/0.67      ( code_Target_Nat
% 0.26/0.67      = ( map_fu6539832666145259331at_nat @ code_int_of_integer @ id_nat @ nat2 ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Code_Target_Nat.Nat_def
% 0.26/0.67  thf(fact_9715_sum__list__upt,axiom,
% 0.26/0.67      ! [M: nat,N: nat] :
% 0.26/0.67        ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.67       => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 0.26/0.67          = ( groups3542108847815614940at_nat
% 0.26/0.67            @ ^ [X: nat] : X
% 0.26/0.67            @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % sum_list_upt
% 0.26/0.67  thf(fact_9716_hd__upt,axiom,
% 0.26/0.67      ! [I: nat,J: nat] :
% 0.26/0.67        ( ( ord_less_nat @ I @ J )
% 0.26/0.67       => ( ( hd_nat @ ( upt @ I @ J ) )
% 0.26/0.67          = I ) ) ).
% 0.26/0.67  
% 0.26/0.67  % hd_upt
% 0.26/0.67  thf(fact_9717_upt__conv__Nil,axiom,
% 0.26/0.67      ! [J: nat,I: nat] :
% 0.26/0.67        ( ( ord_less_eq_nat @ J @ I )
% 0.26/0.67       => ( ( upt @ I @ J )
% 0.26/0.67          = nil_nat ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upt_conv_Nil
% 0.26/0.67  thf(fact_9718_upt__eq__Nil__conv,axiom,
% 0.26/0.67      ! [I: nat,J: nat] :
% 0.26/0.67        ( ( ( upt @ I @ J )
% 0.26/0.67          = nil_nat )
% 0.26/0.67        = ( ( J = zero_zero_nat )
% 0.26/0.67          | ( ord_less_eq_nat @ J @ I ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upt_eq_Nil_conv
% 0.26/0.67  thf(fact_9719_take__upt,axiom,
% 0.26/0.67      ! [I: nat,M: nat,N: nat] :
% 0.26/0.67        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ M ) @ N )
% 0.26/0.67       => ( ( take_nat @ M @ ( upt @ I @ N ) )
% 0.26/0.67          = ( upt @ I @ ( plus_plus_nat @ I @ M ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % take_upt
% 0.26/0.67  thf(fact_9720_nth__upt,axiom,
% 0.26/0.67      ! [I: nat,K: nat,J: nat] :
% 0.26/0.67        ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J )
% 0.26/0.67       => ( ( nth_nat @ ( upt @ I @ J ) @ K )
% 0.26/0.67          = ( plus_plus_nat @ I @ K ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % nth_upt
% 0.26/0.67  thf(fact_9721_upt__rec__numeral,axiom,
% 0.26/0.67      ! [M: num,N: num] :
% 0.26/0.67        ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.26/0.67         => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.26/0.67            = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 0.26/0.67        & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.26/0.67         => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.26/0.67            = nil_nat ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upt_rec_numeral
% 0.26/0.67  thf(fact_9722_upt__add__eq__append,axiom,
% 0.26/0.67      ! [I: nat,J: nat,K: nat] :
% 0.26/0.67        ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.67       => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 0.26/0.67          = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upt_add_eq_append
% 0.26/0.67  thf(fact_9723_atLeast__upt,axiom,
% 0.26/0.67      ( set_ord_lessThan_nat
% 0.26/0.67      = ( ^ [N3: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N3 ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % atLeast_upt
% 0.26/0.67  thf(fact_9724_upt__0,axiom,
% 0.26/0.67      ! [I: nat] :
% 0.26/0.67        ( ( upt @ I @ zero_zero_nat )
% 0.26/0.67        = nil_nat ) ).
% 0.26/0.67  
% 0.26/0.67  % upt_0
% 0.26/0.67  thf(fact_9725_atMost__upto,axiom,
% 0.26/0.67      ( set_ord_atMost_nat
% 0.26/0.67      = ( ^ [N3: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N3 ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % atMost_upto
% 0.26/0.67  thf(fact_9726_upt__rec,axiom,
% 0.26/0.67      ( upt
% 0.26/0.67      = ( ^ [I4: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I4 @ J3 ) @ ( cons_nat @ I4 @ ( upt @ ( suc @ I4 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upt_rec
% 0.26/0.67  thf(fact_9727_upt__conv__Cons,axiom,
% 0.26/0.67      ! [I: nat,J: nat] :
% 0.26/0.67        ( ( ord_less_nat @ I @ J )
% 0.26/0.67       => ( ( upt @ I @ J )
% 0.26/0.67          = ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upt_conv_Cons
% 0.26/0.67  thf(fact_9728_upt__Suc,axiom,
% 0.26/0.67      ! [I: nat,J: nat] :
% 0.26/0.67        ( ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.67         => ( ( upt @ I @ ( suc @ J ) )
% 0.26/0.67            = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 0.26/0.67        & ( ~ ( ord_less_eq_nat @ I @ J )
% 0.26/0.67         => ( ( upt @ I @ ( suc @ J ) )
% 0.26/0.67            = nil_nat ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upt_Suc
% 0.26/0.67  thf(fact_9729_upt__Suc__append,axiom,
% 0.26/0.67      ! [I: nat,J: nat] :
% 0.26/0.67        ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.67       => ( ( upt @ I @ ( suc @ J ) )
% 0.26/0.67          = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upt_Suc_append
% 0.26/0.67  thf(fact_9730_upt__eq__Cons__conv,axiom,
% 0.26/0.67      ! [I: nat,J: nat,X3: nat,Xs2: list_nat] :
% 0.26/0.67        ( ( ( upt @ I @ J )
% 0.26/0.67          = ( cons_nat @ X3 @ Xs2 ) )
% 0.26/0.67        = ( ( ord_less_nat @ I @ J )
% 0.26/0.67          & ( I = X3 )
% 0.26/0.67          & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 0.26/0.67            = Xs2 ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % upt_eq_Cons_conv
% 0.26/0.67  thf(fact_9731_nat__of__integer__def,axiom,
% 0.26/0.67      ( code_nat_of_integer
% 0.26/0.67      = ( map_fu6539832666145259331at_nat @ code_int_of_integer @ id_nat @ nat2 ) ) ).
% 0.26/0.67  
% 0.26/0.67  % nat_of_integer_def
% 0.26/0.67  thf(fact_9732_sorted__upt,axiom,
% 0.26/0.67      ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N ) ) ).
% 0.26/0.67  
% 0.26/0.67  % sorted_upt
% 0.26/0.67  thf(fact_9733_sorted__wrt__upt,axiom,
% 0.26/0.67      ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N ) ) ).
% 0.26/0.67  
% 0.26/0.67  % sorted_wrt_upt
% 0.26/0.67  thf(fact_9734_map__add__upt,axiom,
% 0.26/0.67      ! [N: nat,M: nat] :
% 0.26/0.67        ( ( map_nat_nat
% 0.26/0.67          @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ N )
% 0.26/0.67          @ ( upt @ zero_zero_nat @ M ) )
% 0.26/0.67        = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % map_add_upt
% 0.26/0.67  thf(fact_9735_map__decr__upt,axiom,
% 0.26/0.67      ! [M: nat,N: nat] :
% 0.26/0.67        ( ( map_nat_nat
% 0.26/0.67          @ ^ [N3: nat] : ( minus_minus_nat @ N3 @ ( suc @ zero_zero_nat ) )
% 0.26/0.67          @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 0.26/0.67        = ( upt @ M @ N ) ) ).
% 0.26/0.67  
% 0.26/0.67  % map_decr_upt
% 0.26/0.67  thf(fact_9736_sorted__wrt__less__idx,axiom,
% 0.26/0.67      ! [Ns: list_nat,I: nat] :
% 0.26/0.67        ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 0.26/0.67       => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ns ) )
% 0.26/0.67         => ( ord_less_eq_nat @ I @ ( nth_nat @ Ns @ I ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % sorted_wrt_less_idx
% 0.26/0.67  thf(fact_9737_sorted__upto,axiom,
% 0.26/0.67      ! [M: int,N: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M @ N ) ) ).
% 0.26/0.67  
% 0.26/0.67  % sorted_upto
% 0.26/0.67  thf(fact_9738_sorted__wrt__upto,axiom,
% 0.26/0.67      ! [I: int,J: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I @ J ) ) ).
% 0.26/0.67  
% 0.26/0.67  % sorted_wrt_upto
% 0.26/0.67  thf(fact_9739_num__of__integer__def,axiom,
% 0.26/0.67      ( code_num_of_integer
% 0.26/0.67      = ( map_fu1227494855608507351um_num @ code_int_of_integer @ id_num @ ( comp_nat_num_int @ num_of_nat @ nat2 ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % num_of_integer_def
% 0.26/0.67  thf(fact_9740_last__upt,axiom,
% 0.26/0.67      ! [I: nat,J: nat] :
% 0.26/0.67        ( ( ord_less_nat @ I @ J )
% 0.26/0.67       => ( ( last_nat @ ( upt @ I @ J ) )
% 0.26/0.67          = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % last_upt
% 0.26/0.67  thf(fact_9741_uniformity__real__def,axiom,
% 0.26/0.67      ( topolo1511823702728130853y_real
% 0.26/0.67      = ( comple2936214249959783750l_real
% 0.26/0.67        @ ( image_2178119161166701260l_real
% 0.26/0.67          @ ^ [E3: real] :
% 0.26/0.67              ( princi6114159922880469582l_real
% 0.26/0.67              @ ( collec3799799289383736868l_real
% 0.26/0.67                @ ( produc5414030515140494994real_o
% 0.26/0.67                  @ ^ [X: real,Y: real] : ( ord_less_real @ ( real_V975177566351809787t_real @ X @ Y ) @ E3 ) ) ) )
% 0.26/0.67          @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % uniformity_real_def
% 0.26/0.67  thf(fact_9742_uniformity__complex__def,axiom,
% 0.26/0.67      ( topolo896644834953643431omplex
% 0.26/0.67      = ( comple8358262395181532106omplex
% 0.26/0.67        @ ( image_5971271580939081552omplex
% 0.26/0.67          @ ^ [E3: real] :
% 0.26/0.67              ( princi3496590319149328850omplex
% 0.26/0.67              @ ( collec8663557070575231912omplex
% 0.26/0.67                @ ( produc6771430404735790350plex_o
% 0.26/0.67                  @ ^ [X: complex,Y: complex] : ( ord_less_real @ ( real_V3694042436643373181omplex @ X @ Y ) @ E3 ) ) ) )
% 0.26/0.67          @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % uniformity_complex_def
% 0.26/0.67  thf(fact_9743_zero__rat__def,axiom,
% 0.26/0.67      ( zero_zero_rat
% 0.26/0.67      = ( abs_Rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % zero_rat_def
% 0.26/0.67  thf(fact_9744_inverse__rat_Oabs__eq,axiom,
% 0.26/0.67      ! [X3: product_prod_int_int] :
% 0.26/0.67        ( ( ratrel @ X3 @ X3 )
% 0.26/0.67       => ( ( inverse_inverse_rat @ ( abs_Rat @ X3 ) )
% 0.26/0.67          = ( abs_Rat
% 0.26/0.67            @ ( if_Pro3027730157355071871nt_int
% 0.26/0.67              @ ( ( product_fst_int_int @ X3 )
% 0.26/0.67                = zero_zero_int )
% 0.26/0.67              @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.26/0.67              @ ( product_Pair_int_int @ ( product_snd_int_int @ X3 ) @ ( product_fst_int_int @ X3 ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % inverse_rat.abs_eq
% 0.26/0.67  thf(fact_9745_ratrel__iff,axiom,
% 0.26/0.67      ( ratrel
% 0.26/0.67      = ( ^ [X: product_prod_int_int,Y: product_prod_int_int] :
% 0.26/0.67            ( ( ( product_snd_int_int @ X )
% 0.26/0.67             != zero_zero_int )
% 0.26/0.67            & ( ( product_snd_int_int @ Y )
% 0.26/0.67             != zero_zero_int )
% 0.26/0.67            & ( ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y ) )
% 0.26/0.67              = ( times_times_int @ ( product_fst_int_int @ Y ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % ratrel_iff
% 0.26/0.67  thf(fact_9746_zero__rat_Orsp,axiom,
% 0.26/0.67      ratrel @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ).
% 0.26/0.67  
% 0.26/0.67  % zero_rat.rsp
% 0.26/0.67  thf(fact_9747_ratrel__def,axiom,
% 0.26/0.67      ( ratrel
% 0.26/0.67      = ( ^ [X: product_prod_int_int,Y: product_prod_int_int] :
% 0.26/0.67            ( ( ( product_snd_int_int @ X )
% 0.26/0.67             != zero_zero_int )
% 0.26/0.67            & ( ( product_snd_int_int @ Y )
% 0.26/0.67             != zero_zero_int )
% 0.26/0.67            & ( ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y ) )
% 0.26/0.67              = ( times_times_int @ ( product_fst_int_int @ Y ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % ratrel_def
% 0.26/0.67  thf(fact_9748_Rat_Opositive_Oabs__eq,axiom,
% 0.26/0.67      ! [X3: product_prod_int_int] :
% 0.26/0.67        ( ( ratrel @ X3 @ X3 )
% 0.26/0.67       => ( ( positive @ ( abs_Rat @ X3 ) )
% 0.26/0.67          = ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Rat.positive.abs_eq
% 0.26/0.67  thf(fact_9749_Rat_Opositive__zero,axiom,
% 0.26/0.67      ~ ( positive @ zero_zero_rat ) ).
% 0.26/0.67  
% 0.26/0.67  % Rat.positive_zero
% 0.26/0.67  thf(fact_9750_Rat_Opositive__minus,axiom,
% 0.26/0.67      ! [X3: rat] :
% 0.26/0.67        ( ~ ( positive @ X3 )
% 0.26/0.67       => ( ( X3 != zero_zero_rat )
% 0.26/0.67         => ( positive @ ( uminus_uminus_rat @ X3 ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Rat.positive_minus
% 0.26/0.67  thf(fact_9751_Rat_Opositive_Orep__eq,axiom,
% 0.26/0.67      ( positive
% 0.26/0.67      = ( ^ [X: rat] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ ( rep_Rat @ X ) ) @ ( product_snd_int_int @ ( rep_Rat @ X ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Rat.positive.rep_eq
% 0.26/0.67  thf(fact_9752_Rat_Opositive__def,axiom,
% 0.26/0.67      ( positive
% 0.26/0.67      = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 0.26/0.67        @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Rat.positive_def
% 0.26/0.67  thf(fact_9753_inverse__rat__def,axiom,
% 0.26/0.67      ( inverse_inverse_rat
% 0.26/0.67      = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 0.26/0.67        @ ^ [X: product_prod_int_int] :
% 0.26/0.67            ( if_Pro3027730157355071871nt_int
% 0.26/0.67            @ ( ( product_fst_int_int @ X )
% 0.26/0.67              = zero_zero_int )
% 0.26/0.67            @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.26/0.67            @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % inverse_rat_def
% 0.26/0.67  thf(fact_9754_of__rat__dense,axiom,
% 0.26/0.67      ! [X3: real,Y3: real] :
% 0.26/0.67        ( ( ord_less_real @ X3 @ Y3 )
% 0.26/0.67       => ? [Q4: rat] :
% 0.26/0.67            ( ( ord_less_real @ X3 @ ( field_7254667332652039916t_real @ Q4 ) )
% 0.26/0.67            & ( ord_less_real @ ( field_7254667332652039916t_real @ Q4 ) @ Y3 ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % of_rat_dense
% 0.26/0.67  thf(fact_9755_Rat_Opositive_Orsp,axiom,
% 0.26/0.67      ( bNF_re8699439704749558557nt_o_o @ ratrel
% 0.26/0.67      @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 )
% 0.26/0.67      @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) )
% 0.26/0.67      @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Rat.positive.rsp
% 0.26/0.67  thf(fact_9756_inverse__rat_Orsp,axiom,
% 0.26/0.67      ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 0.26/0.67      @ ^ [X: product_prod_int_int] :
% 0.26/0.67          ( if_Pro3027730157355071871nt_int
% 0.26/0.67          @ ( ( product_fst_int_int @ X )
% 0.26/0.67            = zero_zero_int )
% 0.26/0.67          @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.26/0.67          @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) )
% 0.26/0.67      @ ^ [X: product_prod_int_int] :
% 0.26/0.67          ( if_Pro3027730157355071871nt_int
% 0.26/0.67          @ ( ( product_fst_int_int @ X )
% 0.26/0.67            = zero_zero_int )
% 0.26/0.67          @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.26/0.67          @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % inverse_rat.rsp
% 0.26/0.67  thf(fact_9757_Fract_Orsp,axiom,
% 0.26/0.67      ( bNF_re157797125943740599nt_int
% 0.26/0.67      @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 0.26/0.67      @ ( bNF_re6250860962936578807nt_int
% 0.26/0.67        @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 0.26/0.67        @ ratrel )
% 0.26/0.67      @ ^ [A4: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( B3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A4 @ B3 ) )
% 0.26/0.67      @ ^ [A4: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( B3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A4 @ B3 ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Fract.rsp
% 0.26/0.67  thf(fact_9758_integer__of__natural_Orsp,axiom,
% 0.26/0.67      ( bNF_re6650684261131312217nt_int
% 0.26/0.67      @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 0.26/0.67      @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 0.26/0.67      @ semiri1314217659103216013at_int
% 0.26/0.67      @ semiri1314217659103216013at_int ) ).
% 0.26/0.67  
% 0.26/0.67  % integer_of_natural.rsp
% 0.26/0.67  thf(fact_9759_natural__of__integer_Orsp,axiom,
% 0.26/0.67      ( bNF_re3715656647883201625at_nat
% 0.26/0.67      @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 0.26/0.67      @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 0.26/0.67      @ nat2
% 0.26/0.67      @ nat2 ) ).
% 0.26/0.67  
% 0.26/0.67  % natural_of_integer.rsp
% 0.26/0.67  thf(fact_9760_sub_Orsp,axiom,
% 0.26/0.67      ( bNF_re8402795839162346335um_int
% 0.26/0.67      @ ^ [Y5: num,Z2: num] : ( Y5 = Z2 )
% 0.26/0.67      @ ( bNF_re1822329894187522285nt_int
% 0.26/0.67        @ ^ [Y5: num,Z2: num] : ( Y5 = Z2 )
% 0.26/0.67        @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 0.26/0.67      @ ^ [M3: num,N3: num] : ( minus_minus_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N3 ) )
% 0.26/0.67      @ ^ [M3: num,N3: num] : ( minus_minus_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N3 ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % sub.rsp
% 0.26/0.67  thf(fact_9761_less__integer_Orsp,axiom,
% 0.26/0.67      ( bNF_re3403563459893282935_int_o
% 0.26/0.67      @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 0.26/0.67      @ ( bNF_re5089333283451836215nt_o_o
% 0.26/0.67        @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 0.26/0.67        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 0.26/0.67      @ ord_less_int
% 0.26/0.67      @ ord_less_int ) ).
% 0.26/0.67  
% 0.26/0.67  % less_integer.rsp
% 0.26/0.67  thf(fact_9762_less__natural_Orsp,axiom,
% 0.26/0.67      ( bNF_re578469030762574527_nat_o
% 0.26/0.67      @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 0.26/0.67      @ ( bNF_re4705727531993890431at_o_o
% 0.26/0.67        @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 0.26/0.67        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 0.26/0.67      @ ord_less_nat
% 0.26/0.67      @ ord_less_nat ) ).
% 0.26/0.67  
% 0.26/0.67  % less_natural.rsp
% 0.26/0.67  thf(fact_9763_less__eq__integer_Orsp,axiom,
% 0.26/0.67      ( bNF_re3403563459893282935_int_o
% 0.26/0.67      @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 0.26/0.67      @ ( bNF_re5089333283451836215nt_o_o
% 0.26/0.67        @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 0.26/0.67        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 0.26/0.67      @ ord_less_eq_int
% 0.26/0.67      @ ord_less_eq_int ) ).
% 0.26/0.67  
% 0.26/0.67  % less_eq_integer.rsp
% 0.26/0.67  thf(fact_9764_less__eq__natural_Orsp,axiom,
% 0.26/0.67      ( bNF_re578469030762574527_nat_o
% 0.26/0.67      @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 0.26/0.67      @ ( bNF_re4705727531993890431at_o_o
% 0.26/0.67        @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 0.26/0.67        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 0.26/0.67      @ ord_less_eq_nat
% 0.26/0.67      @ ord_less_eq_nat ) ).
% 0.26/0.67  
% 0.26/0.67  % less_eq_natural.rsp
% 0.26/0.67  thf(fact_9765_num__of__integer_Orsp,axiom,
% 0.26/0.67      ( bNF_re7626690874201225453um_num
% 0.26/0.67      @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 0.26/0.67      @ ^ [Y5: num,Z2: num] : ( Y5 = Z2 )
% 0.26/0.67      @ ( comp_nat_num_int @ num_of_nat @ nat2 )
% 0.26/0.67      @ ( comp_nat_num_int @ num_of_nat @ nat2 ) ) ).
% 0.26/0.67  
% 0.26/0.67  % num_of_integer.rsp
% 0.26/0.67  thf(fact_9766_inverse__rat_Otransfer,axiom,
% 0.26/0.67      ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 0.26/0.67      @ ^ [X: product_prod_int_int] :
% 0.26/0.67          ( if_Pro3027730157355071871nt_int
% 0.26/0.67          @ ( ( product_fst_int_int @ X )
% 0.26/0.67            = zero_zero_int )
% 0.26/0.67          @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.26/0.67          @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) )
% 0.26/0.67      @ inverse_inverse_rat ) ).
% 0.26/0.67  
% 0.26/0.67  % inverse_rat.transfer
% 0.26/0.67  thf(fact_9767_Rat_Opositive_Otransfer,axiom,
% 0.26/0.67      ( bNF_re1494630372529172596at_o_o @ pcr_rat
% 0.26/0.67      @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 )
% 0.26/0.67      @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) )
% 0.26/0.67      @ positive ) ).
% 0.26/0.67  
% 0.26/0.67  % Rat.positive.transfer
% 0.26/0.67  thf(fact_9768_zero__rat_Otransfer,axiom,
% 0.26/0.67      pcr_rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ zero_zero_rat ).
% 0.26/0.67  
% 0.26/0.67  % zero_rat.transfer
% 0.26/0.67  thf(fact_9769_times__int_Otransfer,axiom,
% 0.26/0.67      ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 0.26/0.67      @ ( produc27273713700761075at_nat
% 0.26/0.67        @ ^ [X: nat,Y: nat] :
% 0.26/0.67            ( produc2626176000494625587at_nat
% 0.26/0.67            @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) )
% 0.26/0.67      @ times_times_int ) ).
% 0.26/0.67  
% 0.26/0.67  % times_int.transfer
% 0.26/0.67  thf(fact_9770_zero__int_Otransfer,axiom,
% 0.26/0.67      pcr_int @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ zero_zero_int ).
% 0.26/0.67  
% 0.26/0.67  % zero_int.transfer
% 0.26/0.67  thf(fact_9771_int__transfer,axiom,
% 0.26/0.67      ( bNF_re6830278522597306478at_int
% 0.26/0.67      @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 0.26/0.67      @ pcr_int
% 0.26/0.67      @ ^ [N3: nat] : ( product_Pair_nat_nat @ N3 @ zero_zero_nat )
% 0.26/0.67      @ semiri1314217659103216013at_int ) ).
% 0.26/0.67  
% 0.26/0.67  % int_transfer
% 0.26/0.67  thf(fact_9772_uminus__int_Otransfer,axiom,
% 0.26/0.67      ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 0.26/0.67      @ ( produc2626176000494625587at_nat
% 0.26/0.67        @ ^ [X: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X ) )
% 0.26/0.67      @ uminus_uminus_int ) ).
% 0.26/0.67  
% 0.26/0.67  % uminus_int.transfer
% 0.26/0.67  thf(fact_9773_nat_Otransfer,axiom,
% 0.26/0.67      ( bNF_re4555766996558763186at_nat @ pcr_int
% 0.26/0.67      @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 0.26/0.67      @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 0.26/0.67      @ nat2 ) ).
% 0.26/0.67  
% 0.26/0.67  % nat.transfer
% 0.26/0.67  thf(fact_9774_one__int_Otransfer,axiom,
% 0.26/0.67      pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 0.26/0.67  
% 0.26/0.67  % one_int.transfer
% 0.26/0.67  thf(fact_9775_less__int_Otransfer,axiom,
% 0.26/0.67      ( bNF_re717283939379294677_int_o @ pcr_int
% 0.26/0.67      @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 0.26/0.67        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 0.26/0.67      @ ( produc8739625826339149834_nat_o
% 0.26/0.67        @ ^ [X: nat,Y: nat] :
% 0.26/0.67            ( produc6081775807080527818_nat_o
% 0.26/0.67            @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 0.26/0.67      @ ord_less_int ) ).
% 0.26/0.67  
% 0.26/0.67  % less_int.transfer
% 0.26/0.67  thf(fact_9776_less__eq__int_Otransfer,axiom,
% 0.26/0.67      ( bNF_re717283939379294677_int_o @ pcr_int
% 0.26/0.67      @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 0.26/0.67        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 0.26/0.67      @ ( produc8739625826339149834_nat_o
% 0.26/0.67        @ ^ [X: nat,Y: nat] :
% 0.26/0.67            ( produc6081775807080527818_nat_o
% 0.26/0.67            @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 0.26/0.67      @ ord_less_eq_int ) ).
% 0.26/0.67  
% 0.26/0.67  % less_eq_int.transfer
% 0.26/0.67  thf(fact_9777_plus__int_Otransfer,axiom,
% 0.26/0.67      ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 0.26/0.67      @ ( produc27273713700761075at_nat
% 0.26/0.67        @ ^ [X: nat,Y: nat] :
% 0.26/0.67            ( produc2626176000494625587at_nat
% 0.26/0.67            @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) )
% 0.26/0.67      @ plus_plus_int ) ).
% 0.26/0.67  
% 0.26/0.67  % plus_int.transfer
% 0.26/0.67  thf(fact_9778_minus__int_Otransfer,axiom,
% 0.26/0.67      ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 0.26/0.67      @ ( produc27273713700761075at_nat
% 0.26/0.67        @ ^ [X: nat,Y: nat] :
% 0.26/0.67            ( produc2626176000494625587at_nat
% 0.26/0.67            @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) )
% 0.26/0.67      @ minus_minus_int ) ).
% 0.26/0.67  
% 0.26/0.67  % minus_int.transfer
% 0.26/0.67  thf(fact_9779_times__int_Orsp,axiom,
% 0.26/0.67      ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 0.26/0.67      @ ( produc27273713700761075at_nat
% 0.26/0.67        @ ^ [X: nat,Y: nat] :
% 0.26/0.67            ( produc2626176000494625587at_nat
% 0.26/0.67            @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) )
% 0.26/0.67      @ ( produc27273713700761075at_nat
% 0.26/0.67        @ ^ [X: nat,Y: nat] :
% 0.26/0.67            ( produc2626176000494625587at_nat
% 0.26/0.67            @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % times_int.rsp
% 0.26/0.67  thf(fact_9780_Real_Opositive_Orsp,axiom,
% 0.26/0.67      ( bNF_re728719798268516973at_o_o @ realrel
% 0.26/0.67      @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 )
% 0.26/0.67      @ ^ [X8: nat > rat] :
% 0.26/0.67        ? [R5: rat] :
% 0.26/0.67          ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 0.26/0.67          & ? [K3: nat] :
% 0.26/0.67            ! [N3: nat] :
% 0.26/0.67              ( ( ord_less_eq_nat @ K3 @ N3 )
% 0.26/0.67             => ( ord_less_rat @ R5 @ ( X8 @ N3 ) ) ) )
% 0.26/0.67      @ ^ [X8: nat > rat] :
% 0.26/0.67        ? [R5: rat] :
% 0.26/0.67          ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 0.26/0.67          & ? [K3: nat] :
% 0.26/0.67            ! [N3: nat] :
% 0.26/0.67              ( ( ord_less_eq_nat @ K3 @ N3 )
% 0.26/0.67             => ( ord_less_rat @ R5 @ ( X8 @ N3 ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Real.positive.rsp
% 0.26/0.67  thf(fact_9781_intrel__iff,axiom,
% 0.26/0.67      ! [X3: nat,Y3: nat,U: nat,V: nat] :
% 0.26/0.67        ( ( intrel @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ ( product_Pair_nat_nat @ U @ V ) )
% 0.26/0.67        = ( ( plus_plus_nat @ X3 @ V )
% 0.26/0.67          = ( plus_plus_nat @ U @ Y3 ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % intrel_iff
% 0.26/0.67  thf(fact_9782_plus__real_Orsp,axiom,
% 0.26/0.67      ( bNF_re1962705104956426057at_rat @ realrel @ ( bNF_re895249473297799549at_rat @ realrel @ realrel )
% 0.26/0.67      @ ^ [X8: nat > rat,Y7: nat > rat,N3: nat] : ( plus_plus_rat @ ( X8 @ N3 ) @ ( Y7 @ N3 ) )
% 0.26/0.67      @ ^ [X8: nat > rat,Y7: nat > rat,N3: nat] : ( plus_plus_rat @ ( X8 @ N3 ) @ ( Y7 @ N3 ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % plus_real.rsp
% 0.26/0.67  thf(fact_9783_int_Orel__eq__transfer,axiom,
% 0.26/0.67      ( bNF_re717283939379294677_int_o @ pcr_int
% 0.26/0.67      @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 0.26/0.67        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 0.26/0.67      @ intrel
% 0.26/0.67      @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) ) ).
% 0.26/0.67  
% 0.26/0.67  % int.rel_eq_transfer
% 0.26/0.67  thf(fact_9784_times__real_Orsp,axiom,
% 0.26/0.67      ( bNF_re1962705104956426057at_rat @ realrel @ ( bNF_re895249473297799549at_rat @ realrel @ realrel )
% 0.26/0.67      @ ^ [X8: nat > rat,Y7: nat > rat,N3: nat] : ( times_times_rat @ ( X8 @ N3 ) @ ( Y7 @ N3 ) )
% 0.26/0.67      @ ^ [X8: nat > rat,Y7: nat > rat,N3: nat] : ( times_times_rat @ ( X8 @ N3 ) @ ( Y7 @ N3 ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % times_real.rsp
% 0.26/0.67  thf(fact_9785_uminus__real_Orsp,axiom,
% 0.26/0.67      ( bNF_re895249473297799549at_rat @ realrel @ realrel
% 0.26/0.67      @ ^ [X8: nat > rat,N3: nat] : ( uminus_uminus_rat @ ( X8 @ N3 ) )
% 0.26/0.67      @ ^ [X8: nat > rat,N3: nat] : ( uminus_uminus_rat @ ( X8 @ N3 ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % uminus_real.rsp
% 0.26/0.67  thf(fact_9786_one__real_Orsp,axiom,
% 0.26/0.67      ( realrel
% 0.26/0.67      @ ^ [N3: nat] : one_one_rat
% 0.26/0.67      @ ^ [N3: nat] : one_one_rat ) ).
% 0.26/0.67  
% 0.26/0.67  % one_real.rsp
% 0.26/0.67  thf(fact_9787_int_Oabs__eq__iff,axiom,
% 0.26/0.67      ! [X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.26/0.67        ( ( ( abs_Integ @ X3 )
% 0.26/0.67          = ( abs_Integ @ Y3 ) )
% 0.26/0.67        = ( intrel @ X3 @ Y3 ) ) ).
% 0.26/0.67  
% 0.26/0.67  % int.abs_eq_iff
% 0.26/0.67  thf(fact_9788_zero__real_Orsp,axiom,
% 0.26/0.67      ( realrel
% 0.26/0.67      @ ^ [N3: nat] : zero_zero_rat
% 0.26/0.67      @ ^ [N3: nat] : zero_zero_rat ) ).
% 0.26/0.67  
% 0.26/0.67  % zero_real.rsp
% 0.26/0.67  thf(fact_9789_zero__int_Orsp,axiom,
% 0.26/0.67      intrel @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.26/0.67  
% 0.26/0.67  % zero_int.rsp
% 0.26/0.67  thf(fact_9790_uminus__int_Orsp,axiom,
% 0.26/0.67      ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 0.26/0.67      @ ( produc2626176000494625587at_nat
% 0.26/0.67        @ ^ [X: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X ) )
% 0.26/0.67      @ ( produc2626176000494625587at_nat
% 0.26/0.67        @ ^ [X: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % uminus_int.rsp
% 0.26/0.67  thf(fact_9791_nat_Orsp,axiom,
% 0.26/0.67      ( bNF_re8246922863344978751at_nat @ intrel
% 0.26/0.67      @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 0.26/0.67      @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 0.26/0.67      @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ).
% 0.26/0.67  
% 0.26/0.67  % nat.rsp
% 0.26/0.67  thf(fact_9792_one__int_Orsp,axiom,
% 0.26/0.67      intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.26/0.67  
% 0.26/0.67  % one_int.rsp
% 0.26/0.67  thf(fact_9793_intrel__def,axiom,
% 0.26/0.67      ( intrel
% 0.26/0.67      = ( produc8739625826339149834_nat_o
% 0.26/0.67        @ ^ [X: nat,Y: nat] :
% 0.26/0.67            ( produc6081775807080527818_nat_o
% 0.26/0.67            @ ^ [U2: nat,V4: nat] :
% 0.26/0.67                ( ( plus_plus_nat @ X @ V4 )
% 0.26/0.67                = ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % intrel_def
% 0.26/0.67  thf(fact_9794_less__int_Orsp,axiom,
% 0.26/0.67      ( bNF_re4202695980764964119_nat_o @ intrel
% 0.26/0.67      @ ( bNF_re3666534408544137501at_o_o @ intrel
% 0.26/0.67        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 0.26/0.67      @ ( produc8739625826339149834_nat_o
% 0.26/0.67        @ ^ [X: nat,Y: nat] :
% 0.26/0.67            ( produc6081775807080527818_nat_o
% 0.26/0.67            @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 0.26/0.67      @ ( produc8739625826339149834_nat_o
% 0.26/0.67        @ ^ [X: nat,Y: nat] :
% 0.26/0.67            ( produc6081775807080527818_nat_o
% 0.26/0.67            @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % less_int.rsp
% 0.26/0.67  thf(fact_9795_less__eq__int_Orsp,axiom,
% 0.26/0.67      ( bNF_re4202695980764964119_nat_o @ intrel
% 0.26/0.67      @ ( bNF_re3666534408544137501at_o_o @ intrel
% 0.26/0.67        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 0.26/0.67      @ ( produc8739625826339149834_nat_o
% 0.26/0.67        @ ^ [X: nat,Y: nat] :
% 0.26/0.67            ( produc6081775807080527818_nat_o
% 0.26/0.67            @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 0.26/0.67      @ ( produc8739625826339149834_nat_o
% 0.26/0.67        @ ^ [X: nat,Y: nat] :
% 0.26/0.67            ( produc6081775807080527818_nat_o
% 0.26/0.67            @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % less_eq_int.rsp
% 0.26/0.67  thf(fact_9796_plus__int_Orsp,axiom,
% 0.26/0.67      ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 0.26/0.67      @ ( produc27273713700761075at_nat
% 0.26/0.67        @ ^ [X: nat,Y: nat] :
% 0.26/0.67            ( produc2626176000494625587at_nat
% 0.26/0.67            @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) )
% 0.26/0.67      @ ( produc27273713700761075at_nat
% 0.26/0.67        @ ^ [X: nat,Y: nat] :
% 0.26/0.67            ( produc2626176000494625587at_nat
% 0.26/0.67            @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % plus_int.rsp
% 0.26/0.67  thf(fact_9797_minus__int_Orsp,axiom,
% 0.26/0.67      ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 0.26/0.67      @ ( produc27273713700761075at_nat
% 0.26/0.67        @ ^ [X: nat,Y: nat] :
% 0.26/0.67            ( produc2626176000494625587at_nat
% 0.26/0.67            @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) )
% 0.26/0.67      @ ( produc27273713700761075at_nat
% 0.26/0.67        @ ^ [X: nat,Y: nat] :
% 0.26/0.67            ( produc2626176000494625587at_nat
% 0.26/0.67            @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % minus_int.rsp
% 0.26/0.67  thf(fact_9798_int_Obi__total,axiom,
% 0.26/0.67      bi_tot896582865486249351at_int @ pcr_int ).
% 0.26/0.67  
% 0.26/0.67  % int.bi_total
% 0.26/0.67  thf(fact_9799_inverse__real_Orsp,axiom,
% 0.26/0.67      ( bNF_re895249473297799549at_rat @ realrel @ realrel
% 0.26/0.67      @ ^ [X8: nat > rat] :
% 0.26/0.67          ( if_nat_rat @ ( vanishes @ X8 )
% 0.26/0.67          @ ^ [N3: nat] : zero_zero_rat
% 0.26/0.67          @ ^ [N3: nat] : ( inverse_inverse_rat @ ( X8 @ N3 ) ) )
% 0.26/0.67      @ ^ [X8: nat > rat] :
% 0.26/0.67          ( if_nat_rat @ ( vanishes @ X8 )
% 0.26/0.67          @ ^ [N3: nat] : zero_zero_rat
% 0.26/0.67          @ ^ [N3: nat] : ( inverse_inverse_rat @ ( X8 @ N3 ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % inverse_real.rsp
% 0.26/0.67  thf(fact_9800_vanishes__mult__bounded,axiom,
% 0.26/0.67      ! [X9: nat > rat,Y8: nat > rat] :
% 0.26/0.67        ( ? [A7: rat] :
% 0.26/0.67            ( ( ord_less_rat @ zero_zero_rat @ A7 )
% 0.26/0.67            & ! [N2: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X9 @ N2 ) ) @ A7 ) )
% 0.26/0.67       => ( ( vanishes @ Y8 )
% 0.26/0.67         => ( vanishes
% 0.26/0.67            @ ^ [N3: nat] : ( times_times_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % vanishes_mult_bounded
% 0.26/0.67  thf(fact_9801_vanishes__const,axiom,
% 0.26/0.67      ! [C: rat] :
% 0.26/0.67        ( ( vanishes
% 0.26/0.67          @ ^ [N3: nat] : C )
% 0.26/0.67        = ( C = zero_zero_rat ) ) ).
% 0.26/0.67  
% 0.26/0.67  % vanishes_const
% 0.26/0.67  thf(fact_9802_vanishes__add,axiom,
% 0.26/0.67      ! [X9: nat > rat,Y8: nat > rat] :
% 0.26/0.67        ( ( vanishes @ X9 )
% 0.26/0.67       => ( ( vanishes @ Y8 )
% 0.26/0.67         => ( vanishes
% 0.26/0.67            @ ^ [N3: nat] : ( plus_plus_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % vanishes_add
% 0.26/0.67  thf(fact_9803_vanishes__diff,axiom,
% 0.26/0.67      ! [X9: nat > rat,Y8: nat > rat] :
% 0.26/0.67        ( ( vanishes @ X9 )
% 0.26/0.67       => ( ( vanishes @ Y8 )
% 0.26/0.67         => ( vanishes
% 0.26/0.67            @ ^ [N3: nat] : ( minus_minus_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % vanishes_diff
% 0.26/0.67  thf(fact_9804_vanishes__minus,axiom,
% 0.26/0.67      ! [X9: nat > rat] :
% 0.26/0.67        ( ( vanishes @ X9 )
% 0.26/0.67       => ( vanishes
% 0.26/0.67          @ ^ [N3: nat] : ( uminus_uminus_rat @ ( X9 @ N3 ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % vanishes_minus
% 0.26/0.67  thf(fact_9805_vanishes__def,axiom,
% 0.26/0.67      ( vanishes
% 0.26/0.67      = ( ^ [X8: nat > rat] :
% 0.26/0.67          ! [R5: rat] :
% 0.26/0.67            ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 0.26/0.67           => ? [K3: nat] :
% 0.26/0.67              ! [N3: nat] :
% 0.26/0.67                ( ( ord_less_eq_nat @ K3 @ N3 )
% 0.26/0.67               => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N3 ) ) @ R5 ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % vanishes_def
% 0.26/0.67  thf(fact_9806_vanishesI,axiom,
% 0.26/0.67      ! [X9: nat > rat] :
% 0.26/0.67        ( ! [R: rat] :
% 0.26/0.67            ( ( ord_less_rat @ zero_zero_rat @ R )
% 0.26/0.67           => ? [K4: nat] :
% 0.26/0.67              ! [N2: nat] :
% 0.26/0.67                ( ( ord_less_eq_nat @ K4 @ N2 )
% 0.26/0.67               => ( ord_less_rat @ ( abs_abs_rat @ ( X9 @ N2 ) ) @ R ) ) )
% 0.26/0.67       => ( vanishes @ X9 ) ) ).
% 0.26/0.67  
% 0.26/0.67  % vanishesI
% 0.26/0.67  thf(fact_9807_vanishesD,axiom,
% 0.26/0.67      ! [X9: nat > rat,R2: rat] :
% 0.26/0.67        ( ( vanishes @ X9 )
% 0.26/0.67       => ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 0.26/0.67         => ? [K2: nat] :
% 0.26/0.67            ! [N8: nat] :
% 0.26/0.67              ( ( ord_less_eq_nat @ K2 @ N8 )
% 0.26/0.67             => ( ord_less_rat @ ( abs_abs_rat @ ( X9 @ N8 ) ) @ R2 ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % vanishesD
% 0.26/0.67  thf(fact_9808_inverse__real_Otransfer,axiom,
% 0.26/0.67      ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real
% 0.26/0.67      @ ^ [X8: nat > rat] :
% 0.26/0.67          ( if_nat_rat @ ( vanishes @ X8 )
% 0.26/0.67          @ ^ [N3: nat] : zero_zero_rat
% 0.26/0.67          @ ^ [N3: nat] : ( inverse_inverse_rat @ ( X8 @ N3 ) ) )
% 0.26/0.67      @ inverse_inverse_real ) ).
% 0.26/0.67  
% 0.26/0.67  % inverse_real.transfer
% 0.26/0.67  thf(fact_9809_inverse__real_Oabs__eq,axiom,
% 0.26/0.67      ! [X3: nat > rat] :
% 0.26/0.67        ( ( realrel @ X3 @ X3 )
% 0.26/0.67       => ( ( inverse_inverse_real @ ( real2 @ X3 ) )
% 0.26/0.67          = ( real2
% 0.26/0.67            @ ( if_nat_rat @ ( vanishes @ X3 )
% 0.26/0.67              @ ^ [N3: nat] : zero_zero_rat
% 0.26/0.67              @ ^ [N3: nat] : ( inverse_inverse_rat @ ( X3 @ N3 ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % inverse_real.abs_eq
% 0.26/0.67  thf(fact_9810_real_Oabs__induct,axiom,
% 0.26/0.67      ! [P: real > $o,X3: real] :
% 0.26/0.67        ( ! [Y4: nat > rat] :
% 0.26/0.67            ( ( realrel @ Y4 @ Y4 )
% 0.26/0.67           => ( P @ ( real2 @ Y4 ) ) )
% 0.26/0.67       => ( P @ X3 ) ) ).
% 0.26/0.67  
% 0.26/0.67  % real.abs_induct
% 0.26/0.67  thf(fact_9811_of__rat__Real,axiom,
% 0.26/0.67      ( field_7254667332652039916t_real
% 0.26/0.67      = ( ^ [X: rat] :
% 0.26/0.67            ( real2
% 0.26/0.67            @ ^ [N3: nat] : X ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % of_rat_Real
% 0.26/0.67  thf(fact_9812_zero__real__def,axiom,
% 0.26/0.67      ( zero_zero_real
% 0.26/0.67      = ( real2
% 0.26/0.67        @ ^ [N3: nat] : zero_zero_rat ) ) ).
% 0.26/0.67  
% 0.26/0.67  % zero_real_def
% 0.26/0.67  thf(fact_9813_one__real__def,axiom,
% 0.26/0.67      ( one_one_real
% 0.26/0.67      = ( real2
% 0.26/0.67        @ ^ [N3: nat] : one_one_rat ) ) ).
% 0.26/0.67  
% 0.26/0.67  % one_real_def
% 0.26/0.67  thf(fact_9814_real_Orel__eq__transfer,axiom,
% 0.26/0.67      ( bNF_re4521903465945308077real_o @ pcr_real
% 0.26/0.67      @ ( bNF_re4297313714947099218al_o_o @ pcr_real
% 0.26/0.67        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 0.26/0.67      @ realrel
% 0.26/0.67      @ ^ [Y5: real,Z2: real] : ( Y5 = Z2 ) ) ).
% 0.26/0.67  
% 0.26/0.67  % real.rel_eq_transfer
% 0.26/0.67  thf(fact_9815_of__int__Real,axiom,
% 0.26/0.67      ( ring_1_of_int_real
% 0.26/0.67      = ( ^ [X: int] :
% 0.26/0.67            ( real2
% 0.26/0.67            @ ^ [N3: nat] : ( ring_1_of_int_rat @ X ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % of_int_Real
% 0.26/0.67  thf(fact_9816_zero__real_Otransfer,axiom,
% 0.26/0.67      ( pcr_real
% 0.26/0.67      @ ^ [N3: nat] : zero_zero_rat
% 0.26/0.67      @ zero_zero_real ) ).
% 0.26/0.67  
% 0.26/0.67  % zero_real.transfer
% 0.26/0.67  thf(fact_9817_one__real_Otransfer,axiom,
% 0.26/0.67      ( pcr_real
% 0.26/0.67      @ ^ [N3: nat] : one_one_rat
% 0.26/0.67      @ one_one_real ) ).
% 0.26/0.67  
% 0.26/0.67  % one_real.transfer
% 0.26/0.67  thf(fact_9818_of__nat__Real,axiom,
% 0.26/0.67      ( semiri5074537144036343181t_real
% 0.26/0.67      = ( ^ [X: nat] :
% 0.26/0.67            ( real2
% 0.26/0.67            @ ^ [N3: nat] : ( semiri681578069525770553at_rat @ X ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % of_nat_Real
% 0.26/0.67  thf(fact_9819_uminus__real_Otransfer,axiom,
% 0.26/0.67      ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real
% 0.26/0.67      @ ^ [X8: nat > rat,N3: nat] : ( uminus_uminus_rat @ ( X8 @ N3 ) )
% 0.26/0.67      @ uminus_uminus_real ) ).
% 0.26/0.67  
% 0.26/0.67  % uminus_real.transfer
% 0.26/0.67  thf(fact_9820_plus__real_Otransfer,axiom,
% 0.26/0.67      ( bNF_re4695409256820837752l_real @ pcr_real @ ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real )
% 0.26/0.67      @ ^ [X8: nat > rat,Y7: nat > rat,N3: nat] : ( plus_plus_rat @ ( X8 @ N3 ) @ ( Y7 @ N3 ) )
% 0.26/0.67      @ plus_plus_real ) ).
% 0.26/0.67  
% 0.26/0.67  % plus_real.transfer
% 0.26/0.67  thf(fact_9821_uminus__real_Oabs__eq,axiom,
% 0.26/0.67      ! [X3: nat > rat] :
% 0.26/0.67        ( ( realrel @ X3 @ X3 )
% 0.26/0.67       => ( ( uminus_uminus_real @ ( real2 @ X3 ) )
% 0.26/0.67          = ( real2
% 0.26/0.67            @ ^ [N3: nat] : ( uminus_uminus_rat @ ( X3 @ N3 ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % uminus_real.abs_eq
% 0.26/0.67  thf(fact_9822_times__real_Otransfer,axiom,
% 0.26/0.67      ( bNF_re4695409256820837752l_real @ pcr_real @ ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real )
% 0.26/0.67      @ ^ [X8: nat > rat,Y7: nat > rat,N3: nat] : ( times_times_rat @ ( X8 @ N3 ) @ ( Y7 @ N3 ) )
% 0.26/0.67      @ times_times_real ) ).
% 0.26/0.67  
% 0.26/0.67  % times_real.transfer
% 0.26/0.67  thf(fact_9823_plus__real_Oabs__eq,axiom,
% 0.26/0.67      ! [Xa: nat > rat,X3: nat > rat] :
% 0.26/0.67        ( ( realrel @ Xa @ Xa )
% 0.26/0.67       => ( ( realrel @ X3 @ X3 )
% 0.26/0.67         => ( ( plus_plus_real @ ( real2 @ Xa ) @ ( real2 @ X3 ) )
% 0.26/0.67            = ( real2
% 0.26/0.67              @ ^ [N3: nat] : ( plus_plus_rat @ ( Xa @ N3 ) @ ( X3 @ N3 ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % plus_real.abs_eq
% 0.26/0.67  thf(fact_9824_times__real_Oabs__eq,axiom,
% 0.26/0.67      ! [Xa: nat > rat,X3: nat > rat] :
% 0.26/0.67        ( ( realrel @ Xa @ Xa )
% 0.26/0.67       => ( ( realrel @ X3 @ X3 )
% 0.26/0.67         => ( ( times_times_real @ ( real2 @ Xa ) @ ( real2 @ X3 ) )
% 0.26/0.67            = ( real2
% 0.26/0.67              @ ^ [N3: nat] : ( times_times_rat @ ( Xa @ N3 ) @ ( X3 @ N3 ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % times_real.abs_eq
% 0.26/0.67  thf(fact_9825_Real_Opositive_Otransfer,axiom,
% 0.26/0.67      ( bNF_re4297313714947099218al_o_o @ pcr_real
% 0.26/0.67      @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 )
% 0.26/0.67      @ ^ [X8: nat > rat] :
% 0.26/0.67        ? [R5: rat] :
% 0.26/0.67          ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 0.26/0.67          & ? [K3: nat] :
% 0.26/0.67            ! [N3: nat] :
% 0.26/0.67              ( ( ord_less_eq_nat @ K3 @ N3 )
% 0.26/0.67             => ( ord_less_rat @ R5 @ ( X8 @ N3 ) ) ) )
% 0.26/0.67      @ positive2 ) ).
% 0.26/0.67  
% 0.26/0.67  % Real.positive.transfer
% 0.26/0.67  thf(fact_9826_Real_Opositive_Oabs__eq,axiom,
% 0.26/0.67      ! [X3: nat > rat] :
% 0.26/0.67        ( ( realrel @ X3 @ X3 )
% 0.26/0.67       => ( ( positive2 @ ( real2 @ X3 ) )
% 0.26/0.67          = ( ? [R5: rat] :
% 0.26/0.67                ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 0.26/0.67                & ? [K3: nat] :
% 0.26/0.67                  ! [N3: nat] :
% 0.26/0.67                    ( ( ord_less_eq_nat @ K3 @ N3 )
% 0.26/0.67                   => ( ord_less_rat @ R5 @ ( X3 @ N3 ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Real.positive.abs_eq
% 0.26/0.67  thf(fact_9827_Real_Opositive__mult,axiom,
% 0.26/0.67      ! [X3: real,Y3: real] :
% 0.26/0.67        ( ( positive2 @ X3 )
% 0.26/0.67       => ( ( positive2 @ Y3 )
% 0.26/0.67         => ( positive2 @ ( times_times_real @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Real.positive_mult
% 0.26/0.67  thf(fact_9828_Real_Opositive__add,axiom,
% 0.26/0.67      ! [X3: real,Y3: real] :
% 0.26/0.67        ( ( positive2 @ X3 )
% 0.26/0.67       => ( ( positive2 @ Y3 )
% 0.26/0.67         => ( positive2 @ ( plus_plus_real @ X3 @ Y3 ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Real.positive_add
% 0.26/0.67  thf(fact_9829_Real_Opositive__zero,axiom,
% 0.26/0.67      ~ ( positive2 @ zero_zero_real ) ).
% 0.26/0.67  
% 0.26/0.67  % Real.positive_zero
% 0.26/0.67  thf(fact_9830_Real_Opositive__minus,axiom,
% 0.26/0.67      ! [X3: real] :
% 0.26/0.67        ( ~ ( positive2 @ X3 )
% 0.26/0.67       => ( ( X3 != zero_zero_real )
% 0.26/0.67         => ( positive2 @ ( uminus_uminus_real @ X3 ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Real.positive_minus
% 0.26/0.67  thf(fact_9831_less__real__def,axiom,
% 0.26/0.67      ( ord_less_real
% 0.26/0.67      = ( ^ [X: real,Y: real] : ( positive2 @ ( minus_minus_real @ Y @ X ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % less_real_def
% 0.26/0.67  thf(fact_9832_le__Real,axiom,
% 0.26/0.67      ! [X9: nat > rat,Y8: nat > rat] :
% 0.26/0.67        ( ( cauchy @ X9 )
% 0.26/0.67       => ( ( cauchy @ Y8 )
% 0.26/0.67         => ( ( ord_less_eq_real @ ( real2 @ X9 ) @ ( real2 @ Y8 ) )
% 0.26/0.67            = ( ! [R5: rat] :
% 0.26/0.67                  ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 0.26/0.67                 => ? [K3: nat] :
% 0.26/0.67                    ! [N3: nat] :
% 0.26/0.67                      ( ( ord_less_eq_nat @ K3 @ N3 )
% 0.26/0.67                     => ( ord_less_eq_rat @ ( X9 @ N3 ) @ ( plus_plus_rat @ ( Y8 @ N3 ) @ R5 ) ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % le_Real
% 0.26/0.67  thf(fact_9833_Real_Opositive_Orep__eq,axiom,
% 0.26/0.67      ( positive2
% 0.26/0.67      = ( ^ [X: real] :
% 0.26/0.67          ? [R5: rat] :
% 0.26/0.67            ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 0.26/0.67            & ? [K3: nat] :
% 0.26/0.67              ! [N3: nat] :
% 0.26/0.67                ( ( ord_less_eq_nat @ K3 @ N3 )
% 0.26/0.67               => ( ord_less_rat @ R5 @ ( rep_real @ X @ N3 ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Real.positive.rep_eq
% 0.26/0.67  thf(fact_9834_realrel__refl,axiom,
% 0.26/0.67      ! [X9: nat > rat] :
% 0.26/0.67        ( ( cauchy @ X9 )
% 0.26/0.67       => ( realrel @ X9 @ X9 ) ) ).
% 0.26/0.67  
% 0.26/0.67  % realrel_refl
% 0.26/0.67  thf(fact_9835_cauchy__minus,axiom,
% 0.26/0.67      ! [X9: nat > rat] :
% 0.26/0.67        ( ( cauchy @ X9 )
% 0.26/0.67       => ( cauchy
% 0.26/0.67          @ ^ [N3: nat] : ( uminus_uminus_rat @ ( X9 @ N3 ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % cauchy_minus
% 0.26/0.67  thf(fact_9836_cauchy__const,axiom,
% 0.26/0.67      ! [X3: rat] :
% 0.26/0.67        ( cauchy
% 0.26/0.67        @ ^ [N3: nat] : X3 ) ).
% 0.26/0.67  
% 0.26/0.67  % cauchy_const
% 0.26/0.67  thf(fact_9837_cauchy__add,axiom,
% 0.26/0.67      ! [X9: nat > rat,Y8: nat > rat] :
% 0.26/0.67        ( ( cauchy @ X9 )
% 0.26/0.67       => ( ( cauchy @ Y8 )
% 0.26/0.67         => ( cauchy
% 0.26/0.67            @ ^ [N3: nat] : ( plus_plus_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % cauchy_add
% 0.26/0.67  thf(fact_9838_cauchy__mult,axiom,
% 0.26/0.67      ! [X9: nat > rat,Y8: nat > rat] :
% 0.26/0.67        ( ( cauchy @ X9 )
% 0.26/0.67       => ( ( cauchy @ Y8 )
% 0.26/0.67         => ( cauchy
% 0.26/0.67            @ ^ [N3: nat] : ( times_times_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % cauchy_mult
% 0.26/0.67  thf(fact_9839_Real__induct,axiom,
% 0.26/0.67      ! [P: real > $o,X3: real] :
% 0.26/0.67        ( ! [X16: nat > rat] :
% 0.26/0.67            ( ( cauchy @ X16 )
% 0.26/0.67           => ( P @ ( real2 @ X16 ) ) )
% 0.26/0.67       => ( P @ X3 ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Real_induct
% 0.26/0.67  thf(fact_9840_cauchy__diff,axiom,
% 0.26/0.67      ! [X9: nat > rat,Y8: nat > rat] :
% 0.26/0.67        ( ( cauchy @ X9 )
% 0.26/0.67       => ( ( cauchy @ Y8 )
% 0.26/0.67         => ( cauchy
% 0.26/0.67            @ ^ [N3: nat] : ( minus_minus_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % cauchy_diff
% 0.26/0.67  thf(fact_9841_cr__real__eq,axiom,
% 0.26/0.67      ( pcr_real
% 0.26/0.67      = ( ^ [X: nat > rat,Y: real] :
% 0.26/0.67            ( ( cauchy @ X )
% 0.26/0.67            & ( ( real2 @ X )
% 0.26/0.67              = Y ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % cr_real_eq
% 0.26/0.67  thf(fact_9842_cauchy__inverse,axiom,
% 0.26/0.67      ! [X9: nat > rat] :
% 0.26/0.67        ( ( cauchy @ X9 )
% 0.26/0.67       => ( ~ ( vanishes @ X9 )
% 0.26/0.67         => ( cauchy
% 0.26/0.67            @ ^ [N3: nat] : ( inverse_inverse_rat @ ( X9 @ N3 ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % cauchy_inverse
% 0.26/0.67  thf(fact_9843_cauchy__imp__bounded,axiom,
% 0.26/0.67      ! [X9: nat > rat] :
% 0.26/0.67        ( ( cauchy @ X9 )
% 0.26/0.67       => ? [B4: rat] :
% 0.26/0.67            ( ( ord_less_rat @ zero_zero_rat @ B4 )
% 0.26/0.67            & ! [N8: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X9 @ N8 ) ) @ B4 ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % cauchy_imp_bounded
% 0.26/0.67  thf(fact_9844_less__RealD,axiom,
% 0.26/0.67      ! [Y8: nat > rat,X3: real] :
% 0.26/0.67        ( ( cauchy @ Y8 )
% 0.26/0.67       => ( ( ord_less_real @ X3 @ ( real2 @ Y8 ) )
% 0.26/0.67         => ? [N2: nat] : ( ord_less_real @ X3 @ ( field_7254667332652039916t_real @ ( Y8 @ N2 ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % less_RealD
% 0.26/0.67  thf(fact_9845_le__RealI,axiom,
% 0.26/0.67      ! [Y8: nat > rat,X3: real] :
% 0.26/0.67        ( ( cauchy @ Y8 )
% 0.26/0.67       => ( ! [N2: nat] : ( ord_less_eq_real @ X3 @ ( field_7254667332652039916t_real @ ( Y8 @ N2 ) ) )
% 0.26/0.67         => ( ord_less_eq_real @ X3 @ ( real2 @ Y8 ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % le_RealI
% 0.26/0.67  thf(fact_9846_Real__leI,axiom,
% 0.26/0.67      ! [X9: nat > rat,Y3: real] :
% 0.26/0.67        ( ( cauchy @ X9 )
% 0.26/0.67       => ( ! [N2: nat] : ( ord_less_eq_real @ ( field_7254667332652039916t_real @ ( X9 @ N2 ) ) @ Y3 )
% 0.26/0.67         => ( ord_less_eq_real @ ( real2 @ X9 ) @ Y3 ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Real_leI
% 0.26/0.67  thf(fact_9847_minus__Real,axiom,
% 0.26/0.67      ! [X9: nat > rat] :
% 0.26/0.67        ( ( cauchy @ X9 )
% 0.26/0.67       => ( ( uminus_uminus_real @ ( real2 @ X9 ) )
% 0.26/0.67          = ( real2
% 0.26/0.67            @ ^ [N3: nat] : ( uminus_uminus_rat @ ( X9 @ N3 ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % minus_Real
% 0.26/0.67  thf(fact_9848_add__Real,axiom,
% 0.26/0.67      ! [X9: nat > rat,Y8: nat > rat] :
% 0.26/0.67        ( ( cauchy @ X9 )
% 0.26/0.67       => ( ( cauchy @ Y8 )
% 0.26/0.67         => ( ( plus_plus_real @ ( real2 @ X9 ) @ ( real2 @ Y8 ) )
% 0.26/0.67            = ( real2
% 0.26/0.67              @ ^ [N3: nat] : ( plus_plus_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % add_Real
% 0.26/0.67  thf(fact_9849_mult__Real,axiom,
% 0.26/0.67      ! [X9: nat > rat,Y8: nat > rat] :
% 0.26/0.67        ( ( cauchy @ X9 )
% 0.26/0.67       => ( ( cauchy @ Y8 )
% 0.26/0.67         => ( ( times_times_real @ ( real2 @ X9 ) @ ( real2 @ Y8 ) )
% 0.26/0.67            = ( real2
% 0.26/0.67              @ ^ [N3: nat] : ( times_times_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % mult_Real
% 0.26/0.67  thf(fact_9850_diff__Real,axiom,
% 0.26/0.67      ! [X9: nat > rat,Y8: nat > rat] :
% 0.26/0.67        ( ( cauchy @ X9 )
% 0.26/0.67       => ( ( cauchy @ Y8 )
% 0.26/0.67         => ( ( minus_minus_real @ ( real2 @ X9 ) @ ( real2 @ Y8 ) )
% 0.26/0.67            = ( real2
% 0.26/0.67              @ ^ [N3: nat] : ( minus_minus_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % diff_Real
% 0.26/0.67  thf(fact_9851_realrelI,axiom,
% 0.26/0.67      ! [X9: nat > rat,Y8: nat > rat] :
% 0.26/0.67        ( ( cauchy @ X9 )
% 0.26/0.67       => ( ( cauchy @ Y8 )
% 0.26/0.67         => ( ( vanishes
% 0.26/0.67              @ ^ [N3: nat] : ( minus_minus_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) )
% 0.26/0.67           => ( realrel @ X9 @ Y8 ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % realrelI
% 0.26/0.67  thf(fact_9852_eq__Real,axiom,
% 0.26/0.67      ! [X9: nat > rat,Y8: nat > rat] :
% 0.26/0.67        ( ( cauchy @ X9 )
% 0.26/0.67       => ( ( cauchy @ Y8 )
% 0.26/0.67         => ( ( ( real2 @ X9 )
% 0.26/0.67              = ( real2 @ Y8 ) )
% 0.26/0.67            = ( vanishes
% 0.26/0.67              @ ^ [N3: nat] : ( minus_minus_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % eq_Real
% 0.26/0.67  thf(fact_9853_vanishes__diff__inverse,axiom,
% 0.26/0.67      ! [X9: nat > rat,Y8: nat > rat] :
% 0.26/0.67        ( ( cauchy @ X9 )
% 0.26/0.67       => ( ~ ( vanishes @ X9 )
% 0.26/0.67         => ( ( cauchy @ Y8 )
% 0.26/0.67           => ( ~ ( vanishes @ Y8 )
% 0.26/0.67             => ( ( vanishes
% 0.26/0.67                  @ ^ [N3: nat] : ( minus_minus_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) )
% 0.26/0.67               => ( vanishes
% 0.26/0.67                  @ ^ [N3: nat] : ( minus_minus_rat @ ( inverse_inverse_rat @ ( X9 @ N3 ) ) @ ( inverse_inverse_rat @ ( Y8 @ N3 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % vanishes_diff_inverse
% 0.26/0.67  thf(fact_9854_realrel__def,axiom,
% 0.26/0.67      ( realrel
% 0.26/0.67      = ( ^ [X8: nat > rat,Y7: nat > rat] :
% 0.26/0.67            ( ( cauchy @ X8 )
% 0.26/0.67            & ( cauchy @ Y7 )
% 0.26/0.67            & ( vanishes
% 0.26/0.67              @ ^ [N3: nat] : ( minus_minus_rat @ ( X8 @ N3 ) @ ( Y7 @ N3 ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % realrel_def
% 0.26/0.67  thf(fact_9855_cauchy__not__vanishes__cases,axiom,
% 0.26/0.67      ! [X9: nat > rat] :
% 0.26/0.67        ( ( cauchy @ X9 )
% 0.26/0.67       => ( ~ ( vanishes @ X9 )
% 0.26/0.67         => ? [B4: rat] :
% 0.26/0.67              ( ( ord_less_rat @ zero_zero_rat @ B4 )
% 0.26/0.67              & ? [K2: nat] :
% 0.26/0.67                  ( ! [N8: nat] :
% 0.26/0.67                      ( ( ord_less_eq_nat @ K2 @ N8 )
% 0.26/0.67                     => ( ord_less_rat @ B4 @ ( uminus_uminus_rat @ ( X9 @ N8 ) ) ) )
% 0.26/0.67                  | ! [N8: nat] :
% 0.26/0.67                      ( ( ord_less_eq_nat @ K2 @ N8 )
% 0.26/0.67                     => ( ord_less_rat @ B4 @ ( X9 @ N8 ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % cauchy_not_vanishes_cases
% 0.26/0.67  thf(fact_9856_positive__Real,axiom,
% 0.26/0.67      ! [X9: nat > rat] :
% 0.26/0.67        ( ( cauchy @ X9 )
% 0.26/0.67       => ( ( positive2 @ ( real2 @ X9 ) )
% 0.26/0.67          = ( ? [R5: rat] :
% 0.26/0.67                ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 0.26/0.67                & ? [K3: nat] :
% 0.26/0.67                  ! [N3: nat] :
% 0.26/0.67                    ( ( ord_less_eq_nat @ K3 @ N3 )
% 0.26/0.67                   => ( ord_less_rat @ R5 @ ( X9 @ N3 ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % positive_Real
% 0.26/0.67  thf(fact_9857_cauchy__not__vanishes,axiom,
% 0.26/0.67      ! [X9: nat > rat] :
% 0.26/0.67        ( ( cauchy @ X9 )
% 0.26/0.67       => ( ~ ( vanishes @ X9 )
% 0.26/0.67         => ? [B4: rat] :
% 0.26/0.67              ( ( ord_less_rat @ zero_zero_rat @ B4 )
% 0.26/0.67              & ? [K2: nat] :
% 0.26/0.67                ! [N8: nat] :
% 0.26/0.67                  ( ( ord_less_eq_nat @ K2 @ N8 )
% 0.26/0.67                 => ( ord_less_rat @ B4 @ ( abs_abs_rat @ ( X9 @ N8 ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % cauchy_not_vanishes
% 0.26/0.67  thf(fact_9858_cauchy__def,axiom,
% 0.26/0.67      ( cauchy
% 0.26/0.67      = ( ^ [X8: nat > rat] :
% 0.26/0.67          ! [R5: rat] :
% 0.26/0.67            ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 0.26/0.67           => ? [K3: nat] :
% 0.26/0.67              ! [M3: nat] :
% 0.26/0.67                ( ( ord_less_eq_nat @ K3 @ M3 )
% 0.26/0.67               => ! [N3: nat] :
% 0.26/0.67                    ( ( ord_less_eq_nat @ K3 @ N3 )
% 0.26/0.67                   => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M3 ) @ ( X8 @ N3 ) ) ) @ R5 ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % cauchy_def
% 0.26/0.67  thf(fact_9859_cauchyI,axiom,
% 0.26/0.67      ! [X9: nat > rat] :
% 0.26/0.67        ( ! [R: rat] :
% 0.26/0.67            ( ( ord_less_rat @ zero_zero_rat @ R )
% 0.26/0.67           => ? [K4: nat] :
% 0.26/0.67              ! [M4: nat] :
% 0.26/0.67                ( ( ord_less_eq_nat @ K4 @ M4 )
% 0.26/0.67               => ! [N2: nat] :
% 0.26/0.67                    ( ( ord_less_eq_nat @ K4 @ N2 )
% 0.26/0.67                   => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X9 @ M4 ) @ ( X9 @ N2 ) ) ) @ R ) ) ) )
% 0.26/0.67       => ( cauchy @ X9 ) ) ).
% 0.26/0.67  
% 0.26/0.67  % cauchyI
% 0.26/0.67  thf(fact_9860_cauchyD,axiom,
% 0.26/0.67      ! [X9: nat > rat,R2: rat] :
% 0.26/0.67        ( ( cauchy @ X9 )
% 0.26/0.67       => ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 0.26/0.67         => ? [K2: nat] :
% 0.26/0.67            ! [M2: nat] :
% 0.26/0.67              ( ( ord_less_eq_nat @ K2 @ M2 )
% 0.26/0.67             => ! [N8: nat] :
% 0.26/0.67                  ( ( ord_less_eq_nat @ K2 @ N8 )
% 0.26/0.67                 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X9 @ M2 ) @ ( X9 @ N8 ) ) ) @ R2 ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % cauchyD
% 0.26/0.67  thf(fact_9861_inverse__Real,axiom,
% 0.26/0.67      ! [X9: nat > rat] :
% 0.26/0.67        ( ( cauchy @ X9 )
% 0.26/0.67       => ( ( ( vanishes @ X9 )
% 0.26/0.67           => ( ( inverse_inverse_real @ ( real2 @ X9 ) )
% 0.26/0.67              = zero_zero_real ) )
% 0.26/0.67          & ( ~ ( vanishes @ X9 )
% 0.26/0.67           => ( ( inverse_inverse_real @ ( real2 @ X9 ) )
% 0.26/0.67              = ( real2
% 0.26/0.67                @ ^ [N3: nat] : ( inverse_inverse_rat @ ( X9 @ N3 ) ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % inverse_Real
% 0.26/0.67  thf(fact_9862_not__positive__Real,axiom,
% 0.26/0.67      ! [X9: nat > rat] :
% 0.26/0.67        ( ( cauchy @ X9 )
% 0.26/0.67       => ( ( ~ ( positive2 @ ( real2 @ X9 ) ) )
% 0.26/0.67          = ( ! [R5: rat] :
% 0.26/0.67                ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 0.26/0.67               => ? [K3: nat] :
% 0.26/0.67                  ! [N3: nat] :
% 0.26/0.67                    ( ( ord_less_eq_nat @ K3 @ N3 )
% 0.26/0.67                   => ( ord_less_eq_rat @ ( X9 @ N3 ) @ R5 ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % not_positive_Real
% 0.26/0.67  thf(fact_9863_Real_Opositive__def,axiom,
% 0.26/0.67      ( positive2
% 0.26/0.67      = ( map_fu1856342031159181835at_o_o @ rep_real @ id_o
% 0.26/0.67        @ ^ [X8: nat > rat] :
% 0.26/0.67          ? [R5: rat] :
% 0.26/0.67            ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 0.26/0.67            & ? [K3: nat] :
% 0.26/0.67              ! [N3: nat] :
% 0.26/0.67                ( ( ord_less_eq_nat @ K3 @ N3 )
% 0.26/0.67               => ( ord_less_rat @ R5 @ ( X8 @ N3 ) ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Real.positive_def
% 0.26/0.67  thf(fact_9864_inverse__real__def,axiom,
% 0.26/0.67      ( inverse_inverse_real
% 0.26/0.67      = ( map_fu7146612038024189824t_real @ rep_real @ real2
% 0.26/0.67        @ ^ [X8: nat > rat] :
% 0.26/0.67            ( if_nat_rat @ ( vanishes @ X8 )
% 0.26/0.67            @ ^ [N3: nat] : zero_zero_rat
% 0.26/0.67            @ ^ [N3: nat] : ( inverse_inverse_rat @ ( X8 @ N3 ) ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % inverse_real_def
% 0.26/0.67  thf(fact_9865_uminus__real__def,axiom,
% 0.26/0.67      ( uminus_uminus_real
% 0.26/0.67      = ( map_fu7146612038024189824t_real @ rep_real @ real2
% 0.26/0.67        @ ^ [X8: nat > rat,N3: nat] : ( uminus_uminus_rat @ ( X8 @ N3 ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % uminus_real_def
% 0.26/0.67  thf(fact_9866_times__real__def,axiom,
% 0.26/0.67      ( times_times_real
% 0.26/0.67      = ( map_fu1532550112467129777l_real @ rep_real @ ( map_fu7146612038024189824t_real @ rep_real @ real2 )
% 0.26/0.67        @ ^ [X8: nat > rat,Y7: nat > rat,N3: nat] : ( times_times_rat @ ( X8 @ N3 ) @ ( Y7 @ N3 ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % times_real_def
% 0.26/0.67  thf(fact_9867_plus__real__def,axiom,
% 0.26/0.67      ( plus_plus_real
% 0.26/0.67      = ( map_fu1532550112467129777l_real @ rep_real @ ( map_fu7146612038024189824t_real @ rep_real @ real2 )
% 0.26/0.67        @ ^ [X8: nat > rat,Y7: nat > rat,N3: nat] : ( plus_plus_rat @ ( X8 @ N3 ) @ ( Y7 @ N3 ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % plus_real_def
% 0.26/0.67  thf(fact_9868_cr__real__def,axiom,
% 0.26/0.67      ( cr_real
% 0.26/0.67      = ( ^ [X: nat > rat,Y: real] :
% 0.26/0.67            ( ( realrel @ X @ X )
% 0.26/0.67            & ( ( real2 @ X )
% 0.26/0.67              = Y ) ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % cr_real_def
% 0.26/0.67  thf(fact_9869_Bseq__monoseq__convergent_H__dec,axiom,
% 0.26/0.67      ! [F: nat > real,M7: nat] :
% 0.26/0.67        ( ( bfun_nat_real
% 0.26/0.67          @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ M7 ) )
% 0.26/0.67          @ at_top_nat )
% 0.26/0.67       => ( ! [M4: nat,N2: nat] :
% 0.26/0.67              ( ( ord_less_eq_nat @ M7 @ M4 )
% 0.26/0.67             => ( ( ord_less_eq_nat @ M4 @ N2 )
% 0.26/0.67               => ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ M4 ) ) ) )
% 0.26/0.67         => ( topolo7531315842566124627t_real @ F ) ) ) ).
% 0.26/0.67  
% 0.26/0.67  % Bseq_monoseq_convergent'_dec
% 0.26/0.67  thf(fact_9870_real_Opcr__cr__eq,axiom,
% 0.26/0.67      pcr_real = cr_real ).
% 0.26/0.67  
% 0.26/0.67  % real.pcr_cr_eq
% 0.26/0.67  thf(fact_9871_Bseq__mono__convergent,axiom,
% 0.26/0.67      ! [X9: nat > real] :
% 0.26/0.67        ( ( bfun_nat_real @ X9 @ at_top_nat )
% 0.26/0.67       => ( ! [M4: nat,N2: nat] :
% 0.26/0.67              ( ( ord_less_eq_nat @ M4 @ N2 )
% 0.26/0.67             => ( ord_less_eq_real @ ( X9 @ M4 ) @ ( X9 @ N2 ) ) )
% 0.26/0.67         => ( topolo7531315842566124627t_real @ X9 ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Bseq_mono_convergent
% 0.26/0.68  thf(fact_9872_convergent__realpow,axiom,
% 0.26/0.68      ! [X3: real] :
% 0.26/0.68        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.26/0.68       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 0.26/0.68         => ( topolo7531315842566124627t_real @ ( power_power_real @ X3 ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % convergent_realpow
% 0.26/0.68  thf(fact_9873_Bseq__monoseq__convergent_H__inc,axiom,
% 0.26/0.68      ! [F: nat > real,M7: nat] :
% 0.26/0.68        ( ( bfun_nat_real
% 0.26/0.68          @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ M7 ) )
% 0.26/0.68          @ at_top_nat )
% 0.26/0.68       => ( ! [M4: nat,N2: nat] :
% 0.26/0.68              ( ( ord_less_eq_nat @ M7 @ M4 )
% 0.26/0.68             => ( ( ord_less_eq_nat @ M4 @ N2 )
% 0.26/0.68               => ( ord_less_eq_real @ ( F @ M4 ) @ ( F @ N2 ) ) ) )
% 0.26/0.68         => ( topolo7531315842566124627t_real @ F ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Bseq_monoseq_convergent'_inc
% 0.26/0.68  thf(fact_9874_at__right__to__0,axiom,
% 0.26/0.68      ! [A: real] :
% 0.26/0.68        ( ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) )
% 0.26/0.68        = ( filtermap_real_real
% 0.26/0.68          @ ^ [X: real] : ( plus_plus_real @ X @ A )
% 0.26/0.68          @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % at_right_to_0
% 0.26/0.68  thf(fact_9875_at__right__to__top,axiom,
% 0.26/0.68      ( ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) )
% 0.26/0.68      = ( filtermap_real_real @ inverse_inverse_real @ at_top_real ) ) ).
% 0.26/0.68  
% 0.26/0.68  % at_right_to_top
% 0.26/0.68  thf(fact_9876_at__top__to__right,axiom,
% 0.26/0.68      ( at_top_real
% 0.26/0.68      = ( filtermap_real_real @ inverse_inverse_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % at_top_to_right
% 0.26/0.68  thf(fact_9877_filtermap__ln__at__right,axiom,
% 0.26/0.68      ( ( filtermap_real_real @ ln_ln_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.26/0.68      = at_bot_real ) ).
% 0.26/0.68  
% 0.26/0.68  % filtermap_ln_at_right
% 0.26/0.68  thf(fact_9878_pair__lessI2,axiom,
% 0.26/0.68      ! [A: nat,B: nat,S: nat,T: nat] :
% 0.26/0.68        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.68       => ( ( ord_less_nat @ S @ T )
% 0.26/0.68         => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % pair_lessI2
% 0.26/0.68  thf(fact_9879_pair__less__iff1,axiom,
% 0.26/0.68      ! [X3: nat,Y3: nat,Z: nat] :
% 0.26/0.68        ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ ( product_Pair_nat_nat @ X3 @ Z ) ) @ fun_pair_less )
% 0.26/0.68        = ( ord_less_nat @ Y3 @ Z ) ) ).
% 0.26/0.68  
% 0.26/0.68  % pair_less_iff1
% 0.26/0.68  thf(fact_9880_pair__lessI1,axiom,
% 0.26/0.68      ! [A: nat,B: nat,S: nat,T: nat] :
% 0.26/0.68        ( ( ord_less_nat @ A @ B )
% 0.26/0.68       => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ).
% 0.26/0.68  
% 0.26/0.68  % pair_lessI1
% 0.26/0.68  thf(fact_9881_gcd__nat_Oordering__top__axioms,axiom,
% 0.26/0.68      ( ordering_top_nat @ dvd_dvd_nat
% 0.26/0.68      @ ^ [M3: nat,N3: nat] :
% 0.26/0.68          ( ( dvd_dvd_nat @ M3 @ N3 )
% 0.26/0.68          & ( M3 != N3 ) )
% 0.26/0.68      @ zero_zero_nat ) ).
% 0.26/0.68  
% 0.26/0.68  % gcd_nat.ordering_top_axioms
% 0.26/0.68  thf(fact_9882_bot__nat__0_Oordering__top__axioms,axiom,
% 0.26/0.68      ( ordering_top_nat
% 0.26/0.68      @ ^ [X: nat,Y: nat] : ( ord_less_eq_nat @ Y @ X )
% 0.26/0.68      @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X )
% 0.26/0.68      @ zero_zero_nat ) ).
% 0.26/0.68  
% 0.26/0.68  % bot_nat_0.ordering_top_axioms
% 0.26/0.68  thf(fact_9883_pair__leqI2,axiom,
% 0.26/0.68      ! [A: nat,B: nat,S: nat,T: nat] :
% 0.26/0.68        ( ( ord_less_eq_nat @ A @ B )
% 0.26/0.68       => ( ( ord_less_eq_nat @ S @ T )
% 0.26/0.68         => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % pair_leqI2
% 0.26/0.68  thf(fact_9884_pair__leqI1,axiom,
% 0.26/0.68      ! [A: nat,B: nat,S: nat,T: nat] :
% 0.26/0.68        ( ( ord_less_nat @ A @ B )
% 0.26/0.68       => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ).
% 0.26/0.68  
% 0.26/0.68  % pair_leqI1
% 0.26/0.68  thf(fact_9885_wmax__insertI,axiom,
% 0.26/0.68      ! [Y3: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat,X3: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat] :
% 0.26/0.68        ( ( member8440522571783428010at_nat @ Y3 @ YS )
% 0.26/0.68       => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y3 ) @ fun_pair_leq )
% 0.26/0.68         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_max_weak )
% 0.26/0.68           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X3 @ XS ) @ YS ) @ fun_max_weak ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % wmax_insertI
% 0.26/0.68  thf(fact_9886_wmin__insertI,axiom,
% 0.26/0.68      ! [X3: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y3: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 0.26/0.68        ( ( member8440522571783428010at_nat @ X3 @ XS )
% 0.26/0.68       => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y3 ) @ fun_pair_leq )
% 0.26/0.68         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_weak )
% 0.26/0.68           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y3 @ YS ) ) @ fun_min_weak ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % wmin_insertI
% 0.26/0.68  thf(fact_9887_wmin__emptyI,axiom,
% 0.26/0.68      ! [X9: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X9 @ bot_bo2099793752762293965at_nat ) @ fun_min_weak ) ).
% 0.26/0.68  
% 0.26/0.68  % wmin_emptyI
% 0.26/0.68  thf(fact_9888_wmax__emptyI,axiom,
% 0.26/0.68      ! [X9: set_Pr1261947904930325089at_nat] :
% 0.26/0.68        ( ( finite6177210948735845034at_nat @ X9 )
% 0.26/0.68       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ X9 ) @ fun_max_weak ) ) ).
% 0.26/0.68  
% 0.26/0.68  % wmax_emptyI
% 0.26/0.68  thf(fact_9889_smax__insertI,axiom,
% 0.26/0.68      ! [Y3: product_prod_nat_nat,Y8: set_Pr1261947904930325089at_nat,X3: product_prod_nat_nat,X9: set_Pr1261947904930325089at_nat] :
% 0.26/0.68        ( ( member8440522571783428010at_nat @ Y3 @ Y8 )
% 0.26/0.68       => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y3 ) @ fun_pair_less )
% 0.26/0.68         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X9 @ Y8 ) @ fun_max_strict )
% 0.26/0.68           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X3 @ X9 ) @ Y8 ) @ fun_max_strict ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % smax_insertI
% 0.26/0.68  thf(fact_9890_smin__insertI,axiom,
% 0.26/0.68      ! [X3: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y3: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 0.26/0.68        ( ( member8440522571783428010at_nat @ X3 @ XS )
% 0.26/0.68       => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y3 ) @ fun_pair_less )
% 0.26/0.68         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_strict )
% 0.26/0.68           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y3 @ YS ) ) @ fun_min_strict ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % smin_insertI
% 0.26/0.68  thf(fact_9891_smax__emptyI,axiom,
% 0.26/0.68      ! [Y8: set_Pr1261947904930325089at_nat] :
% 0.26/0.68        ( ( finite6177210948735845034at_nat @ Y8 )
% 0.26/0.68       => ( ( Y8 != bot_bo2099793752762293965at_nat )
% 0.26/0.68         => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ Y8 ) @ fun_max_strict ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % smax_emptyI
% 0.26/0.68  thf(fact_9892_smin__emptyI,axiom,
% 0.26/0.68      ! [X9: set_Pr1261947904930325089at_nat] :
% 0.26/0.68        ( ( X9 != bot_bo2099793752762293965at_nat )
% 0.26/0.68       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X9 @ bot_bo2099793752762293965at_nat ) @ fun_min_strict ) ) ).
% 0.26/0.68  
% 0.26/0.68  % smin_emptyI
% 0.26/0.68  thf(fact_9893_min__weak__def,axiom,
% 0.26/0.68      ( fun_min_weak
% 0.26/0.68      = ( sup_su5525570899277871387at_nat @ ( min_ex6901939911449802026at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % min_weak_def
% 0.26/0.68  thf(fact_9894_max__weak__def,axiom,
% 0.26/0.68      ( fun_max_weak
% 0.26/0.68      = ( sup_su5525570899277871387at_nat @ ( max_ex8135407076693332796at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % max_weak_def
% 0.26/0.68  thf(fact_9895_max__strict__def,axiom,
% 0.26/0.68      ( fun_max_strict
% 0.26/0.68      = ( max_ex8135407076693332796at_nat @ fun_pair_less ) ) ).
% 0.26/0.68  
% 0.26/0.68  % max_strict_def
% 0.26/0.68  thf(fact_9896_min__strict__def,axiom,
% 0.26/0.68      ( fun_min_strict
% 0.26/0.68      = ( min_ex6901939911449802026at_nat @ fun_pair_less ) ) ).
% 0.26/0.68  
% 0.26/0.68  % min_strict_def
% 0.26/0.68  thf(fact_9897_min__rpair__set,axiom,
% 0.26/0.68      fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_min_strict @ fun_min_weak ) ).
% 0.26/0.68  
% 0.26/0.68  % min_rpair_set
% 0.26/0.68  thf(fact_9898_max__rpair__set,axiom,
% 0.26/0.68      fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_max_strict @ fun_max_weak ) ).
% 0.26/0.68  
% 0.26/0.68  % max_rpair_set
% 0.26/0.68  thf(fact_9899_pred__nat__trancl__eq__le,axiom,
% 0.26/0.68      ! [M: nat,N: nat] :
% 0.26/0.68        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 0.26/0.68        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.68  
% 0.26/0.68  % pred_nat_trancl_eq_le
% 0.26/0.68  thf(fact_9900_less__eq,axiom,
% 0.26/0.68      ! [M: nat,N: nat] :
% 0.26/0.68        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 0.26/0.68        = ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.68  
% 0.26/0.68  % less_eq
% 0.26/0.68  thf(fact_9901_euclidean__size__int__def,axiom,
% 0.26/0.68      ( euclid4774559944035922753ze_int
% 0.26/0.68      = ( comp_int_nat_int @ nat2 @ abs_abs_int ) ) ).
% 0.26/0.68  
% 0.26/0.68  % euclidean_size_int_def
% 0.26/0.68  thf(fact_9902_division__segment__eq__sgn,axiom,
% 0.26/0.68      ! [K: int] :
% 0.26/0.68        ( ( K != zero_zero_int )
% 0.26/0.68       => ( ( euclid3395696857347342551nt_int @ K )
% 0.26/0.68          = ( sgn_sgn_int @ K ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % division_segment_eq_sgn
% 0.26/0.68  thf(fact_9903_division__segment__int__def,axiom,
% 0.26/0.68      ( euclid3395696857347342551nt_int
% 0.26/0.68      = ( ^ [K3: int] : ( if_int @ ( ord_less_eq_int @ zero_zero_int @ K3 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % division_segment_int_def
% 0.26/0.68  thf(fact_9904_rat__number__expand_I5_J,axiom,
% 0.26/0.68      ! [K: num] :
% 0.26/0.68        ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) )
% 0.26/0.68        = ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 0.26/0.68  
% 0.26/0.68  % rat_number_expand(5)
% 0.26/0.68  thf(fact_9905_less__rat,axiom,
% 0.26/0.68      ! [B: int,D3: int,A: int,C: int] :
% 0.26/0.68        ( ( B != zero_zero_int )
% 0.26/0.68       => ( ( D3 != zero_zero_int )
% 0.26/0.68         => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D3 ) )
% 0.26/0.68            = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A @ D3 ) @ ( times_times_int @ B @ D3 ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % less_rat
% 0.26/0.68  thf(fact_9906_add__rat,axiom,
% 0.26/0.68      ! [B: int,D3: int,A: int,C: int] :
% 0.26/0.68        ( ( B != zero_zero_int )
% 0.26/0.68       => ( ( D3 != zero_zero_int )
% 0.26/0.68         => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D3 ) )
% 0.26/0.68            = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D3 ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D3 ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % add_rat
% 0.26/0.68  thf(fact_9907_le__rat,axiom,
% 0.26/0.68      ! [B: int,D3: int,A: int,C: int] :
% 0.26/0.68        ( ( B != zero_zero_int )
% 0.26/0.68       => ( ( D3 != zero_zero_int )
% 0.26/0.68         => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C @ D3 ) )
% 0.26/0.68            = ( ord_less_eq_int @ ( times_times_int @ ( times_times_int @ A @ D3 ) @ ( times_times_int @ B @ D3 ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D3 ) ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % le_rat
% 0.26/0.68  thf(fact_9908_diff__rat,axiom,
% 0.26/0.68      ! [B: int,D3: int,A: int,C: int] :
% 0.26/0.68        ( ( B != zero_zero_int )
% 0.26/0.68       => ( ( D3 != zero_zero_int )
% 0.26/0.68         => ( ( minus_minus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D3 ) )
% 0.26/0.68            = ( fract @ ( minus_minus_int @ ( times_times_int @ A @ D3 ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D3 ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % diff_rat
% 0.26/0.68  thf(fact_9909_eq__rat_I1_J,axiom,
% 0.26/0.68      ! [B: int,D3: int,A: int,C: int] :
% 0.26/0.68        ( ( B != zero_zero_int )
% 0.26/0.68       => ( ( D3 != zero_zero_int )
% 0.26/0.68         => ( ( ( fract @ A @ B )
% 0.26/0.68              = ( fract @ C @ D3 ) )
% 0.26/0.68            = ( ( times_times_int @ A @ D3 )
% 0.26/0.68              = ( times_times_int @ C @ B ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % eq_rat(1)
% 0.26/0.68  thf(fact_9910_mult__rat__cancel,axiom,
% 0.26/0.68      ! [C: int,A: int,B: int] :
% 0.26/0.68        ( ( C != zero_zero_int )
% 0.26/0.68       => ( ( fract @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.26/0.68          = ( fract @ A @ B ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % mult_rat_cancel
% 0.26/0.68  thf(fact_9911_eq__rat_I2_J,axiom,
% 0.26/0.68      ! [A: int] :
% 0.26/0.68        ( ( fract @ A @ zero_zero_int )
% 0.26/0.68        = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 0.26/0.68  
% 0.26/0.68  % eq_rat(2)
% 0.26/0.68  thf(fact_9912_eq__rat_I3_J,axiom,
% 0.26/0.68      ! [A: int,C: int] :
% 0.26/0.68        ( ( fract @ zero_zero_int @ A )
% 0.26/0.68        = ( fract @ zero_zero_int @ C ) ) ).
% 0.26/0.68  
% 0.26/0.68  % eq_rat(3)
% 0.26/0.68  thf(fact_9913_rat__number__collapse_I6_J,axiom,
% 0.26/0.68      ! [K: int] :
% 0.26/0.68        ( ( fract @ K @ zero_zero_int )
% 0.26/0.68        = zero_zero_rat ) ).
% 0.26/0.68  
% 0.26/0.68  % rat_number_collapse(6)
% 0.26/0.68  thf(fact_9914_rat__number__collapse_I1_J,axiom,
% 0.26/0.68      ! [K: int] :
% 0.26/0.68        ( ( fract @ zero_zero_int @ K )
% 0.26/0.68        = zero_zero_rat ) ).
% 0.26/0.68  
% 0.26/0.68  % rat_number_collapse(1)
% 0.26/0.68  thf(fact_9915_Rat__induct__pos,axiom,
% 0.26/0.68      ! [P: rat > $o,Q3: rat] :
% 0.26/0.68        ( ! [A5: int,B4: int] :
% 0.26/0.68            ( ( ord_less_int @ zero_zero_int @ B4 )
% 0.26/0.68           => ( P @ ( fract @ A5 @ B4 ) ) )
% 0.26/0.68       => ( P @ Q3 ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Rat_induct_pos
% 0.26/0.68  thf(fact_9916_Zero__rat__def,axiom,
% 0.26/0.68      ( zero_zero_rat
% 0.26/0.68      = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Zero_rat_def
% 0.26/0.68  thf(fact_9917_rat__number__expand_I3_J,axiom,
% 0.26/0.68      ( numeral_numeral_rat
% 0.26/0.68      = ( ^ [K3: num] : ( fract @ ( numeral_numeral_int @ K3 ) @ one_one_int ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % rat_number_expand(3)
% 0.26/0.68  thf(fact_9918_rat__number__collapse_I3_J,axiom,
% 0.26/0.68      ! [W: num] :
% 0.26/0.68        ( ( fract @ ( numeral_numeral_int @ W ) @ one_one_int )
% 0.26/0.68        = ( numeral_numeral_rat @ W ) ) ).
% 0.26/0.68  
% 0.26/0.68  % rat_number_collapse(3)
% 0.26/0.68  thf(fact_9919_Fract__of__nat__eq,axiom,
% 0.26/0.68      ! [K: nat] :
% 0.26/0.68        ( ( fract @ ( semiri1314217659103216013at_int @ K ) @ one_one_int )
% 0.26/0.68        = ( semiri681578069525770553at_rat @ K ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Fract_of_nat_eq
% 0.26/0.68  thf(fact_9920_Fract__less__zero__iff,axiom,
% 0.26/0.68      ! [B: int,A: int] :
% 0.26/0.68        ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.68       => ( ( ord_less_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 0.26/0.68          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Fract_less_zero_iff
% 0.26/0.68  thf(fact_9921_zero__less__Fract__iff,axiom,
% 0.26/0.68      ! [B: int,A: int] :
% 0.26/0.68        ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.68       => ( ( ord_less_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 0.26/0.68          = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % zero_less_Fract_iff
% 0.26/0.68  thf(fact_9922_Fract_Oabs__eq,axiom,
% 0.26/0.68      ( fract
% 0.26/0.68      = ( ^ [Xa4: int,X: int] : ( abs_Rat @ ( if_Pro3027730157355071871nt_int @ ( X = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ Xa4 @ X ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Fract.abs_eq
% 0.26/0.68  thf(fact_9923_positive__rat,axiom,
% 0.26/0.68      ! [A: int,B: int] :
% 0.26/0.68        ( ( positive @ ( fract @ A @ B ) )
% 0.26/0.68        = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % positive_rat
% 0.26/0.68  thf(fact_9924_Fract__less__one__iff,axiom,
% 0.26/0.68      ! [B: int,A: int] :
% 0.26/0.68        ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.68       => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 0.26/0.68          = ( ord_less_int @ A @ B ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Fract_less_one_iff
% 0.26/0.68  thf(fact_9925_one__less__Fract__iff,axiom,
% 0.26/0.68      ! [B: int,A: int] :
% 0.26/0.68        ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.68       => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 0.26/0.68          = ( ord_less_int @ B @ A ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % one_less_Fract_iff
% 0.26/0.68  thf(fact_9926_Fract__add__one,axiom,
% 0.26/0.68      ! [N: int,M: int] :
% 0.26/0.68        ( ( N != zero_zero_int )
% 0.26/0.68       => ( ( fract @ ( plus_plus_int @ M @ N ) @ N )
% 0.26/0.68          = ( plus_plus_rat @ ( fract @ M @ N ) @ one_one_rat ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Fract_add_one
% 0.26/0.68  thf(fact_9927_Fract_Otransfer,axiom,
% 0.26/0.68      ( bNF_re3461391660133120880nt_rat
% 0.26/0.68      @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 0.26/0.68      @ ( bNF_re2214769303045360666nt_rat
% 0.26/0.68        @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 0.26/0.68        @ pcr_rat )
% 0.26/0.68      @ ^ [A4: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( B3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A4 @ B3 ) )
% 0.26/0.68      @ fract ) ).
% 0.26/0.68  
% 0.26/0.68  % Fract.transfer
% 0.26/0.68  thf(fact_9928_Fract__le__zero__iff,axiom,
% 0.26/0.68      ! [B: int,A: int] :
% 0.26/0.68        ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.68       => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 0.26/0.68          = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Fract_le_zero_iff
% 0.26/0.68  thf(fact_9929_zero__le__Fract__iff,axiom,
% 0.26/0.68      ! [B: int,A: int] :
% 0.26/0.68        ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.68       => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 0.26/0.68          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % zero_le_Fract_iff
% 0.26/0.68  thf(fact_9930_Fract__le__one__iff,axiom,
% 0.26/0.68      ! [B: int,A: int] :
% 0.26/0.68        ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.68       => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 0.26/0.68          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Fract_le_one_iff
% 0.26/0.68  thf(fact_9931_one__le__Fract__iff,axiom,
% 0.26/0.68      ! [B: int,A: int] :
% 0.26/0.68        ( ( ord_less_int @ zero_zero_int @ B )
% 0.26/0.68       => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 0.26/0.68          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % one_le_Fract_iff
% 0.26/0.68  thf(fact_9932_rat__number__collapse_I4_J,axiom,
% 0.26/0.68      ! [W: num] :
% 0.26/0.68        ( ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ one_one_int )
% 0.26/0.68        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % rat_number_collapse(4)
% 0.26/0.68  thf(fact_9933_quotient__of__def,axiom,
% 0.26/0.68      ( quotient_of
% 0.26/0.68      = ( ^ [X: rat] :
% 0.26/0.68            ( the_Pr4378521158711661632nt_int
% 0.26/0.68            @ ^ [Pair: product_prod_int_int] :
% 0.26/0.68                ( ( X
% 0.26/0.68                  = ( fract @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) )
% 0.26/0.68                & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Pair ) )
% 0.26/0.68                & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % quotient_of_def
% 0.26/0.68  thf(fact_9934_less__eq__enat__def,axiom,
% 0.26/0.68      ( ord_le2932123472753598470d_enat
% 0.26/0.68      = ( ^ [M3: extended_enat] :
% 0.26/0.68            ( extended_case_enat_o
% 0.26/0.68            @ ^ [N1: nat] :
% 0.26/0.68                ( extended_case_enat_o
% 0.26/0.68                @ ^ [M1: nat] : ( ord_less_eq_nat @ M1 @ N1 )
% 0.26/0.68                @ $false
% 0.26/0.68                @ M3 )
% 0.26/0.68            @ $true ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % less_eq_enat_def
% 0.26/0.68  thf(fact_9935_normalize__stable,axiom,
% 0.26/0.68      ! [Q3: int,P6: int] :
% 0.26/0.68        ( ( ord_less_int @ zero_zero_int @ Q3 )
% 0.26/0.68       => ( ( algebr932160517623751201me_int @ P6 @ Q3 )
% 0.26/0.68         => ( ( normalize @ ( product_Pair_int_int @ P6 @ Q3 ) )
% 0.26/0.68            = ( product_Pair_int_int @ P6 @ Q3 ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % normalize_stable
% 0.26/0.68  thf(fact_9936_Rat__cases,axiom,
% 0.26/0.68      ! [Q3: rat] :
% 0.26/0.68        ~ ! [A5: int,B4: int] :
% 0.26/0.68            ( ( Q3
% 0.26/0.68              = ( fract @ A5 @ B4 ) )
% 0.26/0.68           => ( ( ord_less_int @ zero_zero_int @ B4 )
% 0.26/0.68             => ~ ( algebr932160517623751201me_int @ A5 @ B4 ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Rat_cases
% 0.26/0.68  thf(fact_9937_Rat__induct,axiom,
% 0.26/0.68      ! [P: rat > $o,Q3: rat] :
% 0.26/0.68        ( ! [A5: int,B4: int] :
% 0.26/0.68            ( ( ord_less_int @ zero_zero_int @ B4 )
% 0.26/0.68           => ( ( algebr932160517623751201me_int @ A5 @ B4 )
% 0.26/0.68             => ( P @ ( fract @ A5 @ B4 ) ) ) )
% 0.26/0.68       => ( P @ Q3 ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Rat_induct
% 0.26/0.68  thf(fact_9938_Rat__cases__nonzero,axiom,
% 0.26/0.68      ! [Q3: rat] :
% 0.26/0.68        ( ! [A5: int,B4: int] :
% 0.26/0.68            ( ( Q3
% 0.26/0.68              = ( fract @ A5 @ B4 ) )
% 0.26/0.68           => ( ( ord_less_int @ zero_zero_int @ B4 )
% 0.26/0.68             => ( ( A5 != zero_zero_int )
% 0.26/0.68               => ~ ( algebr932160517623751201me_int @ A5 @ B4 ) ) ) )
% 0.26/0.68       => ( Q3 = zero_zero_rat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Rat_cases_nonzero
% 0.26/0.68  thf(fact_9939_quotient__of__unique,axiom,
% 0.26/0.68      ! [R2: rat] :
% 0.26/0.68      ? [X4: product_prod_int_int] :
% 0.26/0.68        ( ( R2
% 0.26/0.68          = ( fract @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) )
% 0.26/0.68        & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ X4 ) )
% 0.26/0.68        & ( algebr932160517623751201me_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) )
% 0.26/0.68        & ! [Y6: product_prod_int_int] :
% 0.26/0.68            ( ( ( R2
% 0.26/0.68                = ( fract @ ( product_fst_int_int @ Y6 ) @ ( product_snd_int_int @ Y6 ) ) )
% 0.26/0.68              & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Y6 ) )
% 0.26/0.68              & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Y6 ) @ ( product_snd_int_int @ Y6 ) ) )
% 0.26/0.68           => ( Y6 = X4 ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % quotient_of_unique
% 0.26/0.68  thf(fact_9940_less__enat__def,axiom,
% 0.26/0.68      ( ord_le72135733267957522d_enat
% 0.26/0.68      = ( ^ [M3: extended_enat,N3: extended_enat] :
% 0.26/0.68            ( extended_case_enat_o
% 0.26/0.68            @ ^ [M1: nat] : ( extended_case_enat_o @ ( ord_less_nat @ M1 ) @ $true @ N3 )
% 0.26/0.68            @ $false
% 0.26/0.68            @ M3 ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % less_enat_def
% 0.26/0.68  thf(fact_9941_set__encode__vimage__Suc,axiom,
% 0.26/0.68      ! [A3: set_nat] :
% 0.26/0.68        ( ( nat_set_encode @ ( vimage_nat_nat @ suc @ A3 ) )
% 0.26/0.68        = ( divide_divide_nat @ ( nat_set_encode @ A3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % set_encode_vimage_Suc
% 0.26/0.68  thf(fact_9942_set__decode__div__2,axiom,
% 0.26/0.68      ! [X3: nat] :
% 0.26/0.68        ( ( nat_set_decode @ ( divide_divide_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.26/0.68        = ( vimage_nat_nat @ suc @ ( nat_set_decode @ X3 ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % set_decode_div_2
% 0.26/0.68  thf(fact_9943_coprime__int__iff,axiom,
% 0.26/0.68      ! [M: nat,N: nat] :
% 0.26/0.68        ( ( algebr932160517623751201me_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.68        = ( algebr934650988132801477me_nat @ M @ N ) ) ).
% 0.26/0.68  
% 0.26/0.68  % coprime_int_iff
% 0.26/0.68  thf(fact_9944_coprime__nat__abs__right__iff,axiom,
% 0.26/0.68      ! [N: nat,K: int] :
% 0.26/0.68        ( ( algebr934650988132801477me_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 0.26/0.68        = ( algebr932160517623751201me_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ).
% 0.26/0.68  
% 0.26/0.68  % coprime_nat_abs_right_iff
% 0.26/0.68  thf(fact_9945_coprime__nat__abs__left__iff,axiom,
% 0.26/0.68      ! [K: int,N: nat] :
% 0.26/0.68        ( ( algebr934650988132801477me_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 0.26/0.68        = ( algebr932160517623751201me_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % coprime_nat_abs_left_iff
% 0.26/0.68  thf(fact_9946_coprime__Suc__0__left,axiom,
% 0.26/0.68      ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ zero_zero_nat ) @ N ) ).
% 0.26/0.68  
% 0.26/0.68  % coprime_Suc_0_left
% 0.26/0.68  thf(fact_9947_coprime__Suc__0__right,axiom,
% 0.26/0.68      ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ zero_zero_nat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % coprime_Suc_0_right
% 0.26/0.68  thf(fact_9948_vimage__Suc__insert__0,axiom,
% 0.26/0.68      ! [A3: set_nat] :
% 0.26/0.68        ( ( vimage_nat_nat @ suc @ ( insert_nat @ zero_zero_nat @ A3 ) )
% 0.26/0.68        = ( vimage_nat_nat @ suc @ A3 ) ) ).
% 0.26/0.68  
% 0.26/0.68  % vimage_Suc_insert_0
% 0.26/0.68  thf(fact_9949_coprime__diff__one__right__nat,axiom,
% 0.26/0.68      ! [N: nat] :
% 0.26/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.68       => ( algebr934650988132801477me_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % coprime_diff_one_right_nat
% 0.26/0.68  thf(fact_9950_coprime__diff__one__left__nat,axiom,
% 0.26/0.68      ! [N: nat] :
% 0.26/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.68       => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ N ) ) ).
% 0.26/0.68  
% 0.26/0.68  % coprime_diff_one_left_nat
% 0.26/0.68  thf(fact_9951_Rats__abs__nat__div__natE,axiom,
% 0.26/0.68      ! [X3: real] :
% 0.26/0.68        ( ( member_real @ X3 @ field_5140801741446780682s_real )
% 0.26/0.68       => ~ ! [M4: nat,N2: nat] :
% 0.26/0.68              ( ( N2 != zero_zero_nat )
% 0.26/0.68             => ( ( ( abs_abs_real @ X3 )
% 0.26/0.68                  = ( divide_divide_real @ ( semiri5074537144036343181t_real @ M4 ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 0.26/0.68               => ~ ( algebr934650988132801477me_nat @ M4 @ N2 ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Rats_abs_nat_div_natE
% 0.26/0.68  thf(fact_9952_transp__realrel,axiom,
% 0.26/0.68      transp_nat_rat @ realrel ).
% 0.26/0.68  
% 0.26/0.68  % transp_realrel
% 0.26/0.68  thf(fact_9953_bdd__above__nat,axiom,
% 0.26/0.68      condit2214826472909112428ve_nat = finite_finite_nat ).
% 0.26/0.68  
% 0.26/0.68  % bdd_above_nat
% 0.26/0.68  thf(fact_9954_num__of__integer_Otransfer,axiom,
% 0.26/0.68      ( bNF_re6718328864250387230um_num @ code_pcr_integer
% 0.26/0.68      @ ^ [Y5: num,Z2: num] : ( Y5 = Z2 )
% 0.26/0.68      @ ( comp_nat_num_int @ num_of_nat @ nat2 )
% 0.26/0.68      @ code_num_of_integer ) ).
% 0.26/0.68  
% 0.26/0.68  % num_of_integer.transfer
% 0.26/0.68  thf(fact_9955_compute__powr__real,axiom,
% 0.26/0.68      ( powr_real2
% 0.26/0.68      = ( ^ [B3: real,I4: real] :
% 0.26/0.68            ( if_real @ ( ord_less_eq_real @ B3 @ zero_zero_real )
% 0.26/0.68            @ ( abort_real @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.68              @ ^ [Uu3: product_unit] : ( powr_real2 @ B3 @ I4 ) )
% 0.26/0.68            @ ( if_real
% 0.26/0.68              @ ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ I4 ) )
% 0.26/0.68                = I4 )
% 0.26/0.68              @ ( if_real @ ( ord_less_eq_real @ zero_zero_real @ I4 ) @ ( power_power_real @ B3 @ ( nat2 @ ( archim6058952711729229775r_real @ I4 ) ) ) @ ( divide_divide_real @ one_one_real @ ( power_power_real @ B3 @ ( nat2 @ ( archim6058952711729229775r_real @ ( uminus_uminus_real @ I4 ) ) ) ) ) )
% 0.26/0.68              @ ( abort_real @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $true @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.26/0.68                @ ^ [Uu3: product_unit] : ( powr_real2 @ B3 @ I4 ) ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % compute_powr_real
% 0.26/0.68  thf(fact_9956_less__eq__integer_Otransfer,axiom,
% 0.26/0.68      ( bNF_re6321650412969554871eger_o @ code_pcr_integer
% 0.26/0.68      @ ( bNF_re6574881592172037608er_o_o @ code_pcr_integer
% 0.26/0.68        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 0.26/0.68      @ ord_less_eq_int
% 0.26/0.68      @ ord_le3102999989581377725nteger ) ).
% 0.26/0.68  
% 0.26/0.68  % less_eq_integer.transfer
% 0.26/0.68  thf(fact_9957_Code__Target__Nat_ONat_Otransfer,axiom,
% 0.26/0.68      ( bNF_re2807294637932363402at_nat @ code_pcr_integer
% 0.26/0.68      @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 0.26/0.68      @ nat2
% 0.26/0.68      @ code_Target_Nat ) ).
% 0.26/0.68  
% 0.26/0.68  % Code_Target_Nat.Nat.transfer
% 0.26/0.68  thf(fact_9958_nat__of__integer_Otransfer,axiom,
% 0.26/0.68      ( bNF_re2807294637932363402at_nat @ code_pcr_integer
% 0.26/0.68      @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 0.26/0.68      @ nat2
% 0.26/0.68      @ code_nat_of_integer ) ).
% 0.26/0.68  
% 0.26/0.68  % nat_of_integer.transfer
% 0.26/0.68  thf(fact_9959_less__integer_Otransfer,axiom,
% 0.26/0.68      ( bNF_re6321650412969554871eger_o @ code_pcr_integer
% 0.26/0.68      @ ( bNF_re6574881592172037608er_o_o @ code_pcr_integer
% 0.26/0.68        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 0.26/0.68      @ ord_less_int
% 0.26/0.68      @ ord_le6747313008572928689nteger ) ).
% 0.26/0.68  
% 0.26/0.68  % less_integer.transfer
% 0.26/0.68  thf(fact_9960_zero__integer_Otransfer,axiom,
% 0.26/0.68      code_pcr_integer @ zero_zero_int @ zero_z3403309356797280102nteger ).
% 0.26/0.68  
% 0.26/0.68  % zero_integer.transfer
% 0.26/0.68  thf(fact_9961_String_Oempty__neq__Literal,axiom,
% 0.26/0.68      ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,S: literal] :
% 0.26/0.68        ( zero_zero_literal
% 0.26/0.68       != ( literal2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ S ) ) ).
% 0.26/0.68  
% 0.26/0.68  % String.empty_neq_Literal
% 0.26/0.68  thf(fact_9962_int__of__integer__integer__of__nat,axiom,
% 0.26/0.68      ! [N: nat] :
% 0.26/0.68        ( ( code_int_of_integer @ ( code_integer_of_nat @ N ) )
% 0.26/0.68        = ( semiri1314217659103216013at_int @ N ) ) ).
% 0.26/0.68  
% 0.26/0.68  % int_of_integer_integer_of_nat
% 0.26/0.68  thf(fact_9963_integer__of__nat_Orep__eq,axiom,
% 0.26/0.68      ! [X3: nat] :
% 0.26/0.68        ( ( code_int_of_integer @ ( code_integer_of_nat @ X3 ) )
% 0.26/0.68        = ( semiri1314217659103216013at_int @ X3 ) ) ).
% 0.26/0.68  
% 0.26/0.68  % integer_of_nat.rep_eq
% 0.26/0.68  thf(fact_9964_integer__of__nat__0,axiom,
% 0.26/0.68      ( ( code_integer_of_nat @ zero_zero_nat )
% 0.26/0.68      = zero_z3403309356797280102nteger ) ).
% 0.26/0.68  
% 0.26/0.68  % integer_of_nat_0
% 0.26/0.68  thf(fact_9965_integer__of__nat_Oabs__eq,axiom,
% 0.26/0.68      ( code_integer_of_nat
% 0.26/0.68      = ( ^ [X: nat] : ( code_integer_of_int @ ( semiri1314217659103216013at_int @ X ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % integer_of_nat.abs_eq
% 0.26/0.68  thf(fact_9966_integer__of__nat_Otransfer,axiom,
% 0.26/0.68      ( bNF_re4153400068438556298nteger
% 0.26/0.68      @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 0.26/0.68      @ code_pcr_integer
% 0.26/0.68      @ semiri1314217659103216013at_int
% 0.26/0.68      @ code_integer_of_nat ) ).
% 0.26/0.68  
% 0.26/0.68  % integer_of_nat.transfer
% 0.26/0.68  thf(fact_9967_integer__of__nat__numeral,axiom,
% 0.26/0.68      ! [N: num] :
% 0.26/0.68        ( ( code_integer_of_nat @ ( numeral_numeral_nat @ N ) )
% 0.26/0.68        = ( numera6620942414471956472nteger @ N ) ) ).
% 0.26/0.68  
% 0.26/0.68  % integer_of_nat_numeral
% 0.26/0.68  thf(fact_9968_divmod__nat__code,axiom,
% 0.26/0.68      ( divmod_nat
% 0.26/0.68      = ( ^ [M3: nat,N3: nat] :
% 0.26/0.68            ( produc8678311845419106900er_nat @ code_nat_of_integer @ code_nat_of_integer
% 0.26/0.68            @ ( if_Pro6119634080678213985nteger
% 0.26/0.68              @ ( ( code_integer_of_nat @ M3 )
% 0.26/0.68                = zero_z3403309356797280102nteger )
% 0.26/0.68              @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.26/0.68              @ ( if_Pro6119634080678213985nteger
% 0.26/0.68                @ ( ( code_integer_of_nat @ N3 )
% 0.26/0.68                  = zero_z3403309356797280102nteger )
% 0.26/0.68                @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( code_integer_of_nat @ M3 ) )
% 0.26/0.68                @ ( code_divmod_abs @ ( code_integer_of_nat @ M3 ) @ ( code_integer_of_nat @ N3 ) ) ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % divmod_nat_code
% 0.26/0.68  thf(fact_9969_integer__of__nat__def,axiom,
% 0.26/0.68      ( code_integer_of_nat
% 0.26/0.68      = ( map_fu6290471996055670595nteger @ id_nat @ code_integer_of_int @ semiri1314217659103216013at_int ) ) ).
% 0.26/0.68  
% 0.26/0.68  % integer_of_nat_def
% 0.26/0.68  thf(fact_9970_pairs__le__eq__Sigma,axiom,
% 0.26/0.68      ! [M: nat] :
% 0.26/0.68        ( ( collec3392354462482085612at_nat
% 0.26/0.68          @ ( produc6081775807080527818_nat_o
% 0.26/0.68            @ ^ [I4: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I4 @ J3 ) @ M ) ) )
% 0.26/0.68        = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M )
% 0.26/0.68          @ ^ [R5: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ R5 ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % pairs_le_eq_Sigma
% 0.26/0.68  thf(fact_9971_numeral__le__enat__iff,axiom,
% 0.26/0.68      ! [M: num,N: nat] :
% 0.26/0.68        ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( extended_enat2 @ N ) )
% 0.26/0.68        = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 0.26/0.68  
% 0.26/0.68  % numeral_le_enat_iff
% 0.26/0.68  thf(fact_9972_enat_Oinject,axiom,
% 0.26/0.68      ! [Nat: nat,Nat2: nat] :
% 0.26/0.68        ( ( ( extended_enat2 @ Nat )
% 0.26/0.68          = ( extended_enat2 @ Nat2 ) )
% 0.26/0.68        = ( Nat = Nat2 ) ) ).
% 0.26/0.68  
% 0.26/0.68  % enat.inject
% 0.26/0.68  thf(fact_9973_enat__ord__simps_I2_J,axiom,
% 0.26/0.68      ! [M: nat,N: nat] :
% 0.26/0.68        ( ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 0.26/0.68        = ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.68  
% 0.26/0.68  % enat_ord_simps(2)
% 0.26/0.68  thf(fact_9974_plus__enat__simps_I1_J,axiom,
% 0.26/0.68      ! [M: nat,N: nat] :
% 0.26/0.68        ( ( plus_p3455044024723400733d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 0.26/0.68        = ( extended_enat2 @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % plus_enat_simps(1)
% 0.26/0.68  thf(fact_9975_enat__ord__simps_I1_J,axiom,
% 0.26/0.68      ! [M: nat,N: nat] :
% 0.26/0.68        ( ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 0.26/0.68        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.68  
% 0.26/0.68  % enat_ord_simps(1)
% 0.26/0.68  thf(fact_9976_idiff__enat__0__right,axiom,
% 0.26/0.68      ! [N: extended_enat] :
% 0.26/0.68        ( ( minus_3235023915231533773d_enat @ N @ ( extended_enat2 @ zero_zero_nat ) )
% 0.26/0.68        = N ) ).
% 0.26/0.68  
% 0.26/0.68  % idiff_enat_0_right
% 0.26/0.68  thf(fact_9977_idiff__enat__0,axiom,
% 0.26/0.68      ! [N: extended_enat] :
% 0.26/0.68        ( ( minus_3235023915231533773d_enat @ ( extended_enat2 @ zero_zero_nat ) @ N )
% 0.26/0.68        = ( extended_enat2 @ zero_zero_nat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % idiff_enat_0
% 0.26/0.68  thf(fact_9978_idiff__enat__enat,axiom,
% 0.26/0.68      ! [A: nat,B: nat] :
% 0.26/0.68        ( ( minus_3235023915231533773d_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
% 0.26/0.68        = ( extended_enat2 @ ( minus_minus_nat @ A @ B ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % idiff_enat_enat
% 0.26/0.68  thf(fact_9979_times__enat__simps_I1_J,axiom,
% 0.26/0.68      ! [M: nat,N: nat] :
% 0.26/0.68        ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 0.26/0.68        = ( extended_enat2 @ ( times_times_nat @ M @ N ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % times_enat_simps(1)
% 0.26/0.68  thf(fact_9980_max__enat__simps_I1_J,axiom,
% 0.26/0.68      ! [M: nat,N: nat] :
% 0.26/0.68        ( ( ord_ma741700101516333627d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 0.26/0.68        = ( extended_enat2 @ ( ord_max_nat @ M @ N ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % max_enat_simps(1)
% 0.26/0.68  thf(fact_9981_min__enat__simps_I1_J,axiom,
% 0.26/0.68      ! [M: nat,N: nat] :
% 0.26/0.68        ( ( ord_mi8085742599997312461d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 0.26/0.68        = ( extended_enat2 @ ( ord_min_nat @ M @ N ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % min_enat_simps(1)
% 0.26/0.68  thf(fact_9982_numeral__less__enat__iff,axiom,
% 0.26/0.68      ! [M: num,N: nat] :
% 0.26/0.68        ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( extended_enat2 @ N ) )
% 0.26/0.68        = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 0.26/0.68  
% 0.26/0.68  % numeral_less_enat_iff
% 0.26/0.68  thf(fact_9983_finite__enat__bounded,axiom,
% 0.26/0.68      ! [A3: set_Extended_enat,N: nat] :
% 0.26/0.68        ( ! [Y4: extended_enat] :
% 0.26/0.68            ( ( member_Extended_enat @ Y4 @ A3 )
% 0.26/0.68           => ( ord_le2932123472753598470d_enat @ Y4 @ ( extended_enat2 @ N ) ) )
% 0.26/0.68       => ( finite4001608067531595151d_enat @ A3 ) ) ).
% 0.26/0.68  
% 0.26/0.68  % finite_enat_bounded
% 0.26/0.68  thf(fact_9984_enat__ile,axiom,
% 0.26/0.68      ! [N: extended_enat,M: nat] :
% 0.26/0.68        ( ( ord_le2932123472753598470d_enat @ N @ ( extended_enat2 @ M ) )
% 0.26/0.68       => ? [K2: nat] :
% 0.26/0.68            ( N
% 0.26/0.68            = ( extended_enat2 @ K2 ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % enat_ile
% 0.26/0.68  thf(fact_9985_enat__iless,axiom,
% 0.26/0.68      ! [N: extended_enat,M: nat] :
% 0.26/0.68        ( ( ord_le72135733267957522d_enat @ N @ ( extended_enat2 @ M ) )
% 0.26/0.68       => ? [K2: nat] :
% 0.26/0.68            ( N
% 0.26/0.68            = ( extended_enat2 @ K2 ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % enat_iless
% 0.26/0.68  thf(fact_9986_less__enatE,axiom,
% 0.26/0.68      ! [N: extended_enat,M: nat] :
% 0.26/0.68        ( ( ord_le72135733267957522d_enat @ N @ ( extended_enat2 @ M ) )
% 0.26/0.68       => ~ ! [K2: nat] :
% 0.26/0.68              ( ( N
% 0.26/0.68                = ( extended_enat2 @ K2 ) )
% 0.26/0.68             => ~ ( ord_less_nat @ K2 @ M ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % less_enatE
% 0.26/0.68  thf(fact_9987_numeral__eq__enat,axiom,
% 0.26/0.68      ( numera1916890842035813515d_enat
% 0.26/0.68      = ( ^ [K3: num] : ( extended_enat2 @ ( numeral_numeral_nat @ K3 ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % numeral_eq_enat
% 0.26/0.68  thf(fact_9988_one__enat__def,axiom,
% 0.26/0.68      ( one_on7984719198319812577d_enat
% 0.26/0.68      = ( extended_enat2 @ one_one_nat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % one_enat_def
% 0.26/0.68  thf(fact_9989_enat__1__iff_I1_J,axiom,
% 0.26/0.68      ! [X3: nat] :
% 0.26/0.68        ( ( ( extended_enat2 @ X3 )
% 0.26/0.68          = one_on7984719198319812577d_enat )
% 0.26/0.68        = ( X3 = one_one_nat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % enat_1_iff(1)
% 0.26/0.68  thf(fact_9990_enat__1__iff_I2_J,axiom,
% 0.26/0.68      ! [X3: nat] :
% 0.26/0.68        ( ( one_on7984719198319812577d_enat
% 0.26/0.68          = ( extended_enat2 @ X3 ) )
% 0.26/0.68        = ( X3 = one_one_nat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % enat_1_iff(2)
% 0.26/0.68  thf(fact_9991_of__nat__eq__enat,axiom,
% 0.26/0.68      semiri4216267220026989637d_enat = extended_enat2 ).
% 0.26/0.68  
% 0.26/0.68  % of_nat_eq_enat
% 0.26/0.68  thf(fact_9992_zero__enat__def,axiom,
% 0.26/0.68      ( zero_z5237406670263579293d_enat
% 0.26/0.68      = ( extended_enat2 @ zero_zero_nat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % zero_enat_def
% 0.26/0.68  thf(fact_9993_enat__0__iff_I1_J,axiom,
% 0.26/0.68      ! [X3: nat] :
% 0.26/0.68        ( ( ( extended_enat2 @ X3 )
% 0.26/0.68          = zero_z5237406670263579293d_enat )
% 0.26/0.68        = ( X3 = zero_zero_nat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % enat_0_iff(1)
% 0.26/0.68  thf(fact_9994_enat__0__iff_I2_J,axiom,
% 0.26/0.68      ! [X3: nat] :
% 0.26/0.68        ( ( zero_z5237406670263579293d_enat
% 0.26/0.68          = ( extended_enat2 @ X3 ) )
% 0.26/0.68        = ( X3 = zero_zero_nat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % enat_0_iff(2)
% 0.26/0.68  thf(fact_9995_Suc__ile__eq,axiom,
% 0.26/0.68      ! [M: nat,N: extended_enat] :
% 0.26/0.68        ( ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ ( suc @ M ) ) @ N )
% 0.26/0.68        = ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M ) @ N ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Suc_ile_eq
% 0.26/0.68  thf(fact_9996_iadd__le__enat__iff,axiom,
% 0.26/0.68      ! [X3: extended_enat,Y3: extended_enat,N: nat] :
% 0.26/0.68        ( ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ X3 @ Y3 ) @ ( extended_enat2 @ N ) )
% 0.26/0.68        = ( ? [Y9: nat,X10: nat] :
% 0.26/0.68              ( ( X3
% 0.26/0.68                = ( extended_enat2 @ X10 ) )
% 0.26/0.68              & ( Y3
% 0.26/0.68                = ( extended_enat2 @ Y9 ) )
% 0.26/0.68              & ( ord_less_eq_nat @ ( plus_plus_nat @ X10 @ Y9 ) @ N ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % iadd_le_enat_iff
% 0.26/0.68  thf(fact_9997_elimnum,axiom,
% 0.26/0.68      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 0.26/0.68        ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 0.26/0.68       => ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.26/0.68          = ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % elimnum
% 0.26/0.68  thf(fact_9998_VEBT__internal_Oelim__dead_Osimps_I3_J,axiom,
% 0.26/0.68      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,L: nat] :
% 0.26/0.68        ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ ( extended_enat2 @ L ) )
% 0.26/0.68        = ( vEBT_Node @ Info @ Deg
% 0.26/0.68          @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.68            @ ( map_VE8901447254227204932T_VEBT
% 0.26/0.68              @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.68              @ TreeList2 ) )
% 0.26/0.68          @ ( vEBT_VEBT_elim_dead @ Summary @ ( extended_enat2 @ ( divide_divide_nat @ L @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % VEBT_internal.elim_dead.simps(3)
% 0.26/0.68  thf(fact_9999_VEBT__internal_Oelim__dead_Oelims,axiom,
% 0.26/0.68      ! [X3: vEBT_VEBT,Xa: extended_enat,Y3: vEBT_VEBT] :
% 0.26/0.68        ( ( ( vEBT_VEBT_elim_dead @ X3 @ Xa )
% 0.26/0.68          = Y3 )
% 0.26/0.68       => ( ! [A5: $o,B4: $o] :
% 0.26/0.68              ( ( X3
% 0.26/0.68                = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.68             => ( Y3
% 0.26/0.68               != ( vEBT_Leaf @ A5 @ B4 ) ) )
% 0.26/0.68         => ( ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.68                ( ( X3
% 0.26/0.68                  = ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.26/0.68               => ( ( Xa = extend5688581933313929465d_enat )
% 0.26/0.68                 => ( Y3
% 0.26/0.68                   != ( vEBT_Node @ Info2 @ Deg2
% 0.26/0.68                      @ ( map_VE8901447254227204932T_VEBT
% 0.26/0.68                        @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.68                        @ TreeList3 )
% 0.26/0.68                      @ ( vEBT_VEBT_elim_dead @ Summary2 @ extend5688581933313929465d_enat ) ) ) ) )
% 0.26/0.68           => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.68                  ( ( X3
% 0.26/0.68                    = ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.26/0.68                 => ! [L4: nat] :
% 0.26/0.68                      ( ( Xa
% 0.26/0.68                        = ( extended_enat2 @ L4 ) )
% 0.26/0.68                     => ( Y3
% 0.26/0.68                       != ( vEBT_Node @ Info2 @ Deg2
% 0.26/0.68                          @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.68                            @ ( map_VE8901447254227204932T_VEBT
% 0.26/0.68                              @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.68                              @ TreeList3 ) )
% 0.26/0.68                          @ ( vEBT_VEBT_elim_dead @ Summary2 @ ( extended_enat2 @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % VEBT_internal.elim_dead.elims
% 0.26/0.68  thf(fact_10000_VEBT__internal_Oelim__dead_Osimps_I2_J,axiom,
% 0.26/0.68      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.26/0.68        ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ extend5688581933313929465d_enat )
% 0.26/0.68        = ( vEBT_Node @ Info @ Deg
% 0.26/0.68          @ ( map_VE8901447254227204932T_VEBT
% 0.26/0.68            @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.68            @ TreeList2 )
% 0.26/0.68          @ ( vEBT_VEBT_elim_dead @ Summary @ extend5688581933313929465d_enat ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % VEBT_internal.elim_dead.simps(2)
% 0.26/0.68  thf(fact_10001_elimcomplete,axiom,
% 0.26/0.68      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 0.26/0.68        ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 0.26/0.68       => ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ extend5688581933313929465d_enat )
% 0.26/0.68          = ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % elimcomplete
% 0.26/0.68  thf(fact_10002_not__enat__eq,axiom,
% 0.26/0.68      ! [X3: extended_enat] :
% 0.26/0.68        ( ( ! [Y: nat] :
% 0.26/0.68              ( X3
% 0.26/0.68             != ( extended_enat2 @ Y ) ) )
% 0.26/0.68        = ( X3 = extend5688581933313929465d_enat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % not_enat_eq
% 0.26/0.68  thf(fact_10003_not__infinity__eq,axiom,
% 0.26/0.68      ! [X3: extended_enat] :
% 0.26/0.68        ( ( X3 != extend5688581933313929465d_enat )
% 0.26/0.68        = ( ? [I4: nat] :
% 0.26/0.68              ( X3
% 0.26/0.68              = ( extended_enat2 @ I4 ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % not_infinity_eq
% 0.26/0.68  thf(fact_10004_enat__ord__simps_I6_J,axiom,
% 0.26/0.68      ! [Q3: extended_enat] :
% 0.26/0.68        ~ ( ord_le72135733267957522d_enat @ extend5688581933313929465d_enat @ Q3 ) ).
% 0.26/0.68  
% 0.26/0.68  % enat_ord_simps(6)
% 0.26/0.68  thf(fact_10005_enat__ord__simps_I4_J,axiom,
% 0.26/0.68      ! [Q3: extended_enat] :
% 0.26/0.68        ( ( ord_le72135733267957522d_enat @ Q3 @ extend5688581933313929465d_enat )
% 0.26/0.68        = ( Q3 != extend5688581933313929465d_enat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % enat_ord_simps(4)
% 0.26/0.68  thf(fact_10006_plus__enat__simps_I3_J,axiom,
% 0.26/0.68      ! [Q3: extended_enat] :
% 0.26/0.68        ( ( plus_p3455044024723400733d_enat @ Q3 @ extend5688581933313929465d_enat )
% 0.26/0.68        = extend5688581933313929465d_enat ) ).
% 0.26/0.68  
% 0.26/0.68  % plus_enat_simps(3)
% 0.26/0.68  thf(fact_10007_plus__enat__simps_I2_J,axiom,
% 0.26/0.68      ! [Q3: extended_enat] :
% 0.26/0.68        ( ( plus_p3455044024723400733d_enat @ extend5688581933313929465d_enat @ Q3 )
% 0.26/0.68        = extend5688581933313929465d_enat ) ).
% 0.26/0.68  
% 0.26/0.68  % plus_enat_simps(2)
% 0.26/0.68  thf(fact_10008_enat__ord__code_I3_J,axiom,
% 0.26/0.68      ! [Q3: extended_enat] : ( ord_le2932123472753598470d_enat @ Q3 @ extend5688581933313929465d_enat ) ).
% 0.26/0.68  
% 0.26/0.68  % enat_ord_code(3)
% 0.26/0.68  thf(fact_10009_enat__ord__simps_I5_J,axiom,
% 0.26/0.68      ! [Q3: extended_enat] :
% 0.26/0.68        ( ( ord_le2932123472753598470d_enat @ extend5688581933313929465d_enat @ Q3 )
% 0.26/0.68        = ( Q3 = extend5688581933313929465d_enat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % enat_ord_simps(5)
% 0.26/0.68  thf(fact_10010_idiff__infinity,axiom,
% 0.26/0.68      ! [N: extended_enat] :
% 0.26/0.68        ( ( minus_3235023915231533773d_enat @ extend5688581933313929465d_enat @ N )
% 0.26/0.68        = extend5688581933313929465d_enat ) ).
% 0.26/0.68  
% 0.26/0.68  % idiff_infinity
% 0.26/0.68  thf(fact_10011_times__enat__simps_I2_J,axiom,
% 0.26/0.68      ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ extend5688581933313929465d_enat )
% 0.26/0.68      = extend5688581933313929465d_enat ) ).
% 0.26/0.68  
% 0.26/0.68  % times_enat_simps(2)
% 0.26/0.68  thf(fact_10012_max__enat__simps_I5_J,axiom,
% 0.26/0.68      ! [Q3: extended_enat] :
% 0.26/0.68        ( ( ord_ma741700101516333627d_enat @ extend5688581933313929465d_enat @ Q3 )
% 0.26/0.68        = extend5688581933313929465d_enat ) ).
% 0.26/0.68  
% 0.26/0.68  % max_enat_simps(5)
% 0.26/0.68  thf(fact_10013_max__enat__simps_I4_J,axiom,
% 0.26/0.68      ! [Q3: extended_enat] :
% 0.26/0.68        ( ( ord_ma741700101516333627d_enat @ Q3 @ extend5688581933313929465d_enat )
% 0.26/0.68        = extend5688581933313929465d_enat ) ).
% 0.26/0.68  
% 0.26/0.68  % max_enat_simps(4)
% 0.26/0.68  thf(fact_10014_min__enat__simps_I4_J,axiom,
% 0.26/0.68      ! [Q3: extended_enat] :
% 0.26/0.68        ( ( ord_mi8085742599997312461d_enat @ Q3 @ extend5688581933313929465d_enat )
% 0.26/0.68        = Q3 ) ).
% 0.26/0.68  
% 0.26/0.68  % min_enat_simps(4)
% 0.26/0.68  thf(fact_10015_min__enat__simps_I5_J,axiom,
% 0.26/0.68      ! [Q3: extended_enat] :
% 0.26/0.68        ( ( ord_mi8085742599997312461d_enat @ extend5688581933313929465d_enat @ Q3 )
% 0.26/0.68        = Q3 ) ).
% 0.26/0.68  
% 0.26/0.68  % min_enat_simps(5)
% 0.26/0.68  thf(fact_10016_idiff__self,axiom,
% 0.26/0.68      ! [N: extended_enat] :
% 0.26/0.68        ( ( N != extend5688581933313929465d_enat )
% 0.26/0.68       => ( ( minus_3235023915231533773d_enat @ N @ N )
% 0.26/0.68          = zero_z5237406670263579293d_enat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % idiff_self
% 0.26/0.68  thf(fact_10017_add__diff__cancel__enat,axiom,
% 0.26/0.68      ! [X3: extended_enat,Y3: extended_enat] :
% 0.26/0.68        ( ( X3 != extend5688581933313929465d_enat )
% 0.26/0.68       => ( ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X3 @ Y3 ) @ X3 )
% 0.26/0.68          = Y3 ) ) ).
% 0.26/0.68  
% 0.26/0.68  % add_diff_cancel_enat
% 0.26/0.68  thf(fact_10018_idiff__infinity__right,axiom,
% 0.26/0.68      ! [A: nat] :
% 0.26/0.68        ( ( minus_3235023915231533773d_enat @ ( extended_enat2 @ A ) @ extend5688581933313929465d_enat )
% 0.26/0.68        = zero_z5237406670263579293d_enat ) ).
% 0.26/0.68  
% 0.26/0.68  % idiff_infinity_right
% 0.26/0.68  thf(fact_10019_times__enat__simps_I3_J,axiom,
% 0.26/0.68      ! [N: nat] :
% 0.26/0.68        ( ( ( N = zero_zero_nat )
% 0.26/0.68         => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) )
% 0.26/0.68            = zero_z5237406670263579293d_enat ) )
% 0.26/0.68        & ( ( N != zero_zero_nat )
% 0.26/0.68         => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) )
% 0.26/0.68            = extend5688581933313929465d_enat ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % times_enat_simps(3)
% 0.26/0.68  thf(fact_10020_times__enat__simps_I4_J,axiom,
% 0.26/0.68      ! [M: nat] :
% 0.26/0.68        ( ( ( M = zero_zero_nat )
% 0.26/0.68         => ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M ) @ extend5688581933313929465d_enat )
% 0.26/0.68            = zero_z5237406670263579293d_enat ) )
% 0.26/0.68        & ( ( M != zero_zero_nat )
% 0.26/0.68         => ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M ) @ extend5688581933313929465d_enat )
% 0.26/0.68            = extend5688581933313929465d_enat ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % times_enat_simps(4)
% 0.26/0.68  thf(fact_10021_Sup__enat__def,axiom,
% 0.26/0.68      ( comple4398354569131411667d_enat
% 0.26/0.68      = ( ^ [A8: set_Extended_enat] : ( if_Extended_enat @ ( A8 = bot_bo7653980558646680370d_enat ) @ zero_z5237406670263579293d_enat @ ( if_Extended_enat @ ( finite4001608067531595151d_enat @ A8 ) @ ( lattic921264341876707157d_enat @ A8 ) @ extend5688581933313929465d_enat ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Sup_enat_def
% 0.26/0.68  thf(fact_10022_enat__add__left__cancel__le,axiom,
% 0.26/0.68      ! [A: extended_enat,B: extended_enat,C: extended_enat] :
% 0.26/0.68        ( ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) @ ( plus_p3455044024723400733d_enat @ A @ C ) )
% 0.26/0.68        = ( ( A = extend5688581933313929465d_enat )
% 0.26/0.68          | ( ord_le2932123472753598470d_enat @ B @ C ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % enat_add_left_cancel_le
% 0.26/0.68  thf(fact_10023_enat__ord__simps_I3_J,axiom,
% 0.26/0.68      ! [Q3: extended_enat] : ( ord_le2932123472753598470d_enat @ Q3 @ extend5688581933313929465d_enat ) ).
% 0.26/0.68  
% 0.26/0.68  % enat_ord_simps(3)
% 0.26/0.68  thf(fact_10024_enat__add__left__cancel__less,axiom,
% 0.26/0.68      ! [A: extended_enat,B: extended_enat,C: extended_enat] :
% 0.26/0.68        ( ( ord_le72135733267957522d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) @ ( plus_p3455044024723400733d_enat @ A @ C ) )
% 0.26/0.68        = ( ( A != extend5688581933313929465d_enat )
% 0.26/0.68          & ( ord_le72135733267957522d_enat @ B @ C ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % enat_add_left_cancel_less
% 0.26/0.68  thf(fact_10025_enat__add__left__cancel,axiom,
% 0.26/0.68      ! [A: extended_enat,B: extended_enat,C: extended_enat] :
% 0.26/0.68        ( ( ( plus_p3455044024723400733d_enat @ A @ B )
% 0.26/0.68          = ( plus_p3455044024723400733d_enat @ A @ C ) )
% 0.26/0.68        = ( ( A = extend5688581933313929465d_enat )
% 0.26/0.68          | ( B = C ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % enat_add_left_cancel
% 0.26/0.68  thf(fact_10026_plus__eq__infty__iff__enat,axiom,
% 0.26/0.68      ! [M: extended_enat,N: extended_enat] :
% 0.26/0.68        ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 0.26/0.68          = extend5688581933313929465d_enat )
% 0.26/0.68        = ( ( M = extend5688581933313929465d_enat )
% 0.26/0.68          | ( N = extend5688581933313929465d_enat ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % plus_eq_infty_iff_enat
% 0.26/0.68  thf(fact_10027_infinity__ne__i1,axiom,
% 0.26/0.68      extend5688581933313929465d_enat != one_on7984719198319812577d_enat ).
% 0.26/0.68  
% 0.26/0.68  % infinity_ne_i1
% 0.26/0.68  thf(fact_10028_top__enat__def,axiom,
% 0.26/0.68      top_to3028658606643905974d_enat = extend5688581933313929465d_enat ).
% 0.26/0.68  
% 0.26/0.68  % top_enat_def
% 0.26/0.68  thf(fact_10029_numeral__ne__infinity,axiom,
% 0.26/0.68      ! [K: num] :
% 0.26/0.68        ( ( numera1916890842035813515d_enat @ K )
% 0.26/0.68       != extend5688581933313929465d_enat ) ).
% 0.26/0.68  
% 0.26/0.68  % numeral_ne_infinity
% 0.26/0.68  thf(fact_10030_Inf__enat__def,axiom,
% 0.26/0.68      ( comple2295165028678016749d_enat
% 0.26/0.68      = ( ^ [A8: set_Extended_enat] :
% 0.26/0.68            ( if_Extended_enat @ ( A8 = bot_bo7653980558646680370d_enat ) @ extend5688581933313929465d_enat
% 0.26/0.68            @ ( ord_Le1955565732374568822d_enat
% 0.26/0.68              @ ^ [X: extended_enat] : ( member_Extended_enat @ X @ A8 ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Inf_enat_def
% 0.26/0.68  thf(fact_10031_infinity__ne__i0,axiom,
% 0.26/0.68      extend5688581933313929465d_enat != zero_z5237406670263579293d_enat ).
% 0.26/0.68  
% 0.26/0.68  % infinity_ne_i0
% 0.26/0.68  thf(fact_10032_imult__is__infinity,axiom,
% 0.26/0.68      ! [A: extended_enat,B: extended_enat] :
% 0.26/0.68        ( ( ( times_7803423173614009249d_enat @ A @ B )
% 0.26/0.68          = extend5688581933313929465d_enat )
% 0.26/0.68        = ( ( ( A = extend5688581933313929465d_enat )
% 0.26/0.68            & ( B != zero_z5237406670263579293d_enat ) )
% 0.26/0.68          | ( ( B = extend5688581933313929465d_enat )
% 0.26/0.68            & ( A != zero_z5237406670263579293d_enat ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % imult_is_infinity
% 0.26/0.68  thf(fact_10033_enat__ord__code_I4_J,axiom,
% 0.26/0.68      ! [M: nat] : ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M ) @ extend5688581933313929465d_enat ) ).
% 0.26/0.68  
% 0.26/0.68  % enat_ord_code(4)
% 0.26/0.68  thf(fact_10034_less__infinityE,axiom,
% 0.26/0.68      ! [N: extended_enat] :
% 0.26/0.68        ( ( ord_le72135733267957522d_enat @ N @ extend5688581933313929465d_enat )
% 0.26/0.68       => ~ ! [K2: nat] :
% 0.26/0.68              ( N
% 0.26/0.68             != ( extended_enat2 @ K2 ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % less_infinityE
% 0.26/0.68  thf(fact_10035_infinity__ilessE,axiom,
% 0.26/0.68      ! [M: nat] :
% 0.26/0.68        ~ ( ord_le72135733267957522d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ M ) ) ).
% 0.26/0.68  
% 0.26/0.68  % infinity_ilessE
% 0.26/0.68  thf(fact_10036_enat_Odistinct_I2_J,axiom,
% 0.26/0.68      ! [Nat: nat] :
% 0.26/0.68        ( extend5688581933313929465d_enat
% 0.26/0.68       != ( extended_enat2 @ Nat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % enat.distinct(2)
% 0.26/0.68  thf(fact_10037_enat_Odistinct_I1_J,axiom,
% 0.26/0.68      ! [Nat: nat] :
% 0.26/0.68        ( ( extended_enat2 @ Nat )
% 0.26/0.68       != extend5688581933313929465d_enat ) ).
% 0.26/0.68  
% 0.26/0.68  % enat.distinct(1)
% 0.26/0.68  thf(fact_10038_enat_Oexhaust,axiom,
% 0.26/0.68      ! [Y3: extended_enat] :
% 0.26/0.68        ( ! [Nat3: nat] :
% 0.26/0.68            ( Y3
% 0.26/0.68           != ( extended_enat2 @ Nat3 ) )
% 0.26/0.68       => ( Y3 = extend5688581933313929465d_enat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % enat.exhaust
% 0.26/0.68  thf(fact_10039_enat2__cases,axiom,
% 0.26/0.68      ! [Y3: extended_enat,Ya: extended_enat] :
% 0.26/0.68        ( ( ? [Nat3: nat] :
% 0.26/0.68              ( Y3
% 0.26/0.68              = ( extended_enat2 @ Nat3 ) )
% 0.26/0.68         => ! [Nata: nat] :
% 0.26/0.68              ( Ya
% 0.26/0.68             != ( extended_enat2 @ Nata ) ) )
% 0.26/0.68       => ( ( ? [Nat3: nat] :
% 0.26/0.68                ( Y3
% 0.26/0.68                = ( extended_enat2 @ Nat3 ) )
% 0.26/0.68           => ( Ya != extend5688581933313929465d_enat ) )
% 0.26/0.68         => ( ( ( Y3 = extend5688581933313929465d_enat )
% 0.26/0.68             => ! [Nat3: nat] :
% 0.26/0.68                  ( Ya
% 0.26/0.68                 != ( extended_enat2 @ Nat3 ) ) )
% 0.26/0.68           => ~ ( ( Y3 = extend5688581933313929465d_enat )
% 0.26/0.68               => ( Ya != extend5688581933313929465d_enat ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % enat2_cases
% 0.26/0.68  thf(fact_10040_enat3__cases,axiom,
% 0.26/0.68      ! [Y3: extended_enat,Ya: extended_enat,Yb: extended_enat] :
% 0.26/0.68        ( ( ? [Nat3: nat] :
% 0.26/0.68              ( Y3
% 0.26/0.68              = ( extended_enat2 @ Nat3 ) )
% 0.26/0.68         => ( ? [Nata: nat] :
% 0.26/0.68                ( Ya
% 0.26/0.68                = ( extended_enat2 @ Nata ) )
% 0.26/0.68           => ! [Natb: nat] :
% 0.26/0.68                ( Yb
% 0.26/0.68               != ( extended_enat2 @ Natb ) ) ) )
% 0.26/0.68       => ( ( ? [Nat3: nat] :
% 0.26/0.68                ( Y3
% 0.26/0.68                = ( extended_enat2 @ Nat3 ) )
% 0.26/0.68           => ( ? [Nata: nat] :
% 0.26/0.68                  ( Ya
% 0.26/0.68                  = ( extended_enat2 @ Nata ) )
% 0.26/0.68             => ( Yb != extend5688581933313929465d_enat ) ) )
% 0.26/0.68         => ( ( ? [Nat3: nat] :
% 0.26/0.68                  ( Y3
% 0.26/0.68                  = ( extended_enat2 @ Nat3 ) )
% 0.26/0.68             => ( ( Ya = extend5688581933313929465d_enat )
% 0.26/0.68               => ! [Nata: nat] :
% 0.26/0.68                    ( Yb
% 0.26/0.68                   != ( extended_enat2 @ Nata ) ) ) )
% 0.26/0.68           => ( ( ? [Nat3: nat] :
% 0.26/0.68                    ( Y3
% 0.26/0.68                    = ( extended_enat2 @ Nat3 ) )
% 0.26/0.68               => ( ( Ya = extend5688581933313929465d_enat )
% 0.26/0.68                 => ( Yb != extend5688581933313929465d_enat ) ) )
% 0.26/0.68             => ( ( ( Y3 = extend5688581933313929465d_enat )
% 0.26/0.68                 => ( ? [Nat3: nat] :
% 0.26/0.68                        ( Ya
% 0.26/0.68                        = ( extended_enat2 @ Nat3 ) )
% 0.26/0.68                   => ! [Nata: nat] :
% 0.26/0.68                        ( Yb
% 0.26/0.68                       != ( extended_enat2 @ Nata ) ) ) )
% 0.26/0.68               => ( ( ( Y3 = extend5688581933313929465d_enat )
% 0.26/0.68                   => ( ? [Nat3: nat] :
% 0.26/0.68                          ( Ya
% 0.26/0.68                          = ( extended_enat2 @ Nat3 ) )
% 0.26/0.68                     => ( Yb != extend5688581933313929465d_enat ) ) )
% 0.26/0.68                 => ( ( ( Y3 = extend5688581933313929465d_enat )
% 0.26/0.68                     => ( ( Ya = extend5688581933313929465d_enat )
% 0.26/0.68                       => ! [Nat3: nat] :
% 0.26/0.68                            ( Yb
% 0.26/0.68                           != ( extended_enat2 @ Nat3 ) ) ) )
% 0.26/0.68                   => ~ ( ( Y3 = extend5688581933313929465d_enat )
% 0.26/0.68                       => ( ( Ya = extend5688581933313929465d_enat )
% 0.26/0.68                         => ( Yb != extend5688581933313929465d_enat ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % enat3_cases
% 0.26/0.68  thf(fact_10041_enat__ex__split,axiom,
% 0.26/0.68      ( ( ^ [P2: extended_enat > $o] :
% 0.26/0.68          ? [X5: extended_enat] : ( P2 @ X5 ) )
% 0.26/0.68      = ( ^ [P3: extended_enat > $o] :
% 0.26/0.68            ( ( P3 @ extend5688581933313929465d_enat )
% 0.26/0.68            | ? [X: nat] : ( P3 @ ( extended_enat2 @ X ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % enat_ex_split
% 0.26/0.68  thf(fact_10042_infinity__ileE,axiom,
% 0.26/0.68      ! [M: nat] :
% 0.26/0.68        ~ ( ord_le2932123472753598470d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ M ) ) ).
% 0.26/0.68  
% 0.26/0.68  % infinity_ileE
% 0.26/0.68  thf(fact_10043_enat__ord__code_I5_J,axiom,
% 0.26/0.68      ! [N: nat] :
% 0.26/0.68        ~ ( ord_le2932123472753598470d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) ) ).
% 0.26/0.68  
% 0.26/0.68  % enat_ord_code(5)
% 0.26/0.68  thf(fact_10044_plus__enat__def,axiom,
% 0.26/0.68      ( plus_p3455044024723400733d_enat
% 0.26/0.68      = ( ^ [M3: extended_enat,N3: extended_enat] :
% 0.26/0.68            ( extend3600170679010898289d_enat
% 0.26/0.68            @ ^ [O: nat] :
% 0.26/0.68                ( extend3600170679010898289d_enat
% 0.26/0.68                @ ^ [P5: nat] : ( extended_enat2 @ ( plus_plus_nat @ O @ P5 ) )
% 0.26/0.68                @ extend5688581933313929465d_enat
% 0.26/0.68                @ N3 )
% 0.26/0.68            @ extend5688581933313929465d_enat
% 0.26/0.68            @ M3 ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % plus_enat_def
% 0.26/0.68  thf(fact_10045_imult__infinity__right,axiom,
% 0.26/0.68      ! [N: extended_enat] :
% 0.26/0.68        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 0.26/0.68       => ( ( times_7803423173614009249d_enat @ N @ extend5688581933313929465d_enat )
% 0.26/0.68          = extend5688581933313929465d_enat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % imult_infinity_right
% 0.26/0.68  thf(fact_10046_imult__infinity,axiom,
% 0.26/0.68      ! [N: extended_enat] :
% 0.26/0.68        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 0.26/0.68       => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ N )
% 0.26/0.68          = extend5688581933313929465d_enat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % imult_infinity
% 0.26/0.68  thf(fact_10047_diff__enat__def,axiom,
% 0.26/0.68      ( minus_3235023915231533773d_enat
% 0.26/0.68      = ( ^ [A4: extended_enat,B3: extended_enat] :
% 0.26/0.68            ( extend3600170679010898289d_enat
% 0.26/0.68            @ ^ [X: nat] :
% 0.26/0.68                ( extend3600170679010898289d_enat
% 0.26/0.68                @ ^ [Y: nat] : ( extended_enat2 @ ( minus_minus_nat @ X @ Y ) )
% 0.26/0.68                @ zero_z5237406670263579293d_enat
% 0.26/0.68                @ B3 )
% 0.26/0.68            @ extend5688581933313929465d_enat
% 0.26/0.68            @ A4 ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % diff_enat_def
% 0.26/0.68  thf(fact_10048_times__enat__def,axiom,
% 0.26/0.68      ( times_7803423173614009249d_enat
% 0.26/0.68      = ( ^ [M3: extended_enat,N3: extended_enat] :
% 0.26/0.68            ( extend3600170679010898289d_enat
% 0.26/0.68            @ ^ [O: nat] :
% 0.26/0.68                ( extend3600170679010898289d_enat
% 0.26/0.68                @ ^ [P5: nat] : ( extended_enat2 @ ( times_times_nat @ O @ P5 ) )
% 0.26/0.68                @ ( if_Extended_enat @ ( O = zero_zero_nat ) @ zero_z5237406670263579293d_enat @ extend5688581933313929465d_enat )
% 0.26/0.68                @ N3 )
% 0.26/0.68            @ ( if_Extended_enat @ ( N3 = zero_z5237406670263579293d_enat ) @ zero_z5237406670263579293d_enat @ extend5688581933313929465d_enat )
% 0.26/0.68            @ M3 ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % times_enat_def
% 0.26/0.68  thf(fact_10049_VEBT__internal_Oelim__dead_Opelims,axiom,
% 0.26/0.68      ! [X3: vEBT_VEBT,Xa: extended_enat,Y3: vEBT_VEBT] :
% 0.26/0.68        ( ( ( vEBT_VEBT_elim_dead @ X3 @ Xa )
% 0.26/0.68          = Y3 )
% 0.26/0.68       => ( ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ X3 @ Xa ) )
% 0.26/0.68         => ( ! [A5: $o,B4: $o] :
% 0.26/0.68                ( ( X3
% 0.26/0.68                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.68               => ( ( Y3
% 0.26/0.68                    = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.26/0.68                 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) ) ) )
% 0.26/0.68           => ( ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.68                  ( ( X3
% 0.26/0.68                    = ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.26/0.68                 => ( ( Xa = extend5688581933313929465d_enat )
% 0.26/0.68                   => ( ( Y3
% 0.26/0.68                        = ( vEBT_Node @ Info2 @ Deg2
% 0.26/0.68                          @ ( map_VE8901447254227204932T_VEBT
% 0.26/0.68                            @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.68                            @ TreeList3 )
% 0.26/0.68                          @ ( vEBT_VEBT_elim_dead @ Summary2 @ extend5688581933313929465d_enat ) ) )
% 0.26/0.68                     => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary2 ) @ extend5688581933313929465d_enat ) ) ) ) )
% 0.26/0.68             => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.26/0.68                    ( ( X3
% 0.26/0.68                      = ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.26/0.68                   => ! [L4: nat] :
% 0.26/0.68                        ( ( Xa
% 0.26/0.68                          = ( extended_enat2 @ L4 ) )
% 0.26/0.68                       => ( ( Y3
% 0.26/0.68                            = ( vEBT_Node @ Info2 @ Deg2
% 0.26/0.68                              @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.26/0.68                                @ ( map_VE8901447254227204932T_VEBT
% 0.26/0.68                                  @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.26/0.68                                  @ TreeList3 ) )
% 0.26/0.68                              @ ( vEBT_VEBT_elim_dead @ Summary2 @ ( extended_enat2 @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.26/0.68                         => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary2 ) @ ( extended_enat2 @ L4 ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % VEBT_internal.elim_dead.pelims
% 0.26/0.68  thf(fact_10050_the__enat_Osimps,axiom,
% 0.26/0.68      ! [N: nat] :
% 0.26/0.68        ( ( extended_the_enat @ ( extended_enat2 @ N ) )
% 0.26/0.68        = N ) ).
% 0.26/0.68  
% 0.26/0.68  % the_enat.simps
% 0.26/0.68  thf(fact_10051_eSuc__Max,axiom,
% 0.26/0.68      ! [A3: set_Extended_enat] :
% 0.26/0.68        ( ( finite4001608067531595151d_enat @ A3 )
% 0.26/0.68       => ( ( A3 != bot_bo7653980558646680370d_enat )
% 0.26/0.68         => ( ( extended_eSuc @ ( lattic921264341876707157d_enat @ A3 ) )
% 0.26/0.68            = ( lattic921264341876707157d_enat @ ( image_80655429650038917d_enat @ extended_eSuc @ A3 ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % eSuc_Max
% 0.26/0.68  thf(fact_10052_eSuc__inject,axiom,
% 0.26/0.68      ! [M: extended_enat,N: extended_enat] :
% 0.26/0.68        ( ( ( extended_eSuc @ M )
% 0.26/0.68          = ( extended_eSuc @ N ) )
% 0.26/0.68        = ( M = N ) ) ).
% 0.26/0.68  
% 0.26/0.68  % eSuc_inject
% 0.26/0.68  thf(fact_10053_eSuc__infinity,axiom,
% 0.26/0.68      ( ( extended_eSuc @ extend5688581933313929465d_enat )
% 0.26/0.68      = extend5688581933313929465d_enat ) ).
% 0.26/0.68  
% 0.26/0.68  % eSuc_infinity
% 0.26/0.68  thf(fact_10054_eSuc__mono,axiom,
% 0.26/0.68      ! [N: extended_enat,M: extended_enat] :
% 0.26/0.68        ( ( ord_le72135733267957522d_enat @ ( extended_eSuc @ N ) @ ( extended_eSuc @ M ) )
% 0.26/0.68        = ( ord_le72135733267957522d_enat @ N @ M ) ) ).
% 0.26/0.68  
% 0.26/0.68  % eSuc_mono
% 0.26/0.68  thf(fact_10055_eSuc__ile__mono,axiom,
% 0.26/0.68      ! [N: extended_enat,M: extended_enat] :
% 0.26/0.68        ( ( ord_le2932123472753598470d_enat @ ( extended_eSuc @ N ) @ ( extended_eSuc @ M ) )
% 0.26/0.68        = ( ord_le2932123472753598470d_enat @ N @ M ) ) ).
% 0.26/0.68  
% 0.26/0.68  % eSuc_ile_mono
% 0.26/0.68  thf(fact_10056_eSuc__minus__eSuc,axiom,
% 0.26/0.68      ! [N: extended_enat,M: extended_enat] :
% 0.26/0.68        ( ( minus_3235023915231533773d_enat @ ( extended_eSuc @ N ) @ ( extended_eSuc @ M ) )
% 0.26/0.68        = ( minus_3235023915231533773d_enat @ N @ M ) ) ).
% 0.26/0.68  
% 0.26/0.68  % eSuc_minus_eSuc
% 0.26/0.68  thf(fact_10057_iless__eSuc0,axiom,
% 0.26/0.68      ! [N: extended_enat] :
% 0.26/0.68        ( ( ord_le72135733267957522d_enat @ N @ ( extended_eSuc @ zero_z5237406670263579293d_enat ) )
% 0.26/0.68        = ( N = zero_z5237406670263579293d_enat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % iless_eSuc0
% 0.26/0.68  thf(fact_10058_eSuc__minus__1,axiom,
% 0.26/0.68      ! [N: extended_enat] :
% 0.26/0.68        ( ( minus_3235023915231533773d_enat @ ( extended_eSuc @ N ) @ one_on7984719198319812577d_enat )
% 0.26/0.68        = N ) ).
% 0.26/0.68  
% 0.26/0.68  % eSuc_minus_1
% 0.26/0.68  thf(fact_10059_eSuc__numeral,axiom,
% 0.26/0.68      ! [K: num] :
% 0.26/0.68        ( ( extended_eSuc @ ( numera1916890842035813515d_enat @ K ) )
% 0.26/0.68        = ( numera1916890842035813515d_enat @ ( plus_plus_num @ K @ one ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % eSuc_numeral
% 0.26/0.68  thf(fact_10060_iless__Suc__eq,axiom,
% 0.26/0.68      ! [M: nat,N: extended_enat] :
% 0.26/0.68        ( ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M ) @ ( extended_eSuc @ N ) )
% 0.26/0.68        = ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ M ) @ N ) ) ).
% 0.26/0.68  
% 0.26/0.68  % iless_Suc_eq
% 0.26/0.68  thf(fact_10061_ile__eSuc,axiom,
% 0.26/0.68      ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ N @ ( extended_eSuc @ N ) ) ).
% 0.26/0.68  
% 0.26/0.68  % ile_eSuc
% 0.26/0.68  thf(fact_10062_ileI1,axiom,
% 0.26/0.68      ! [M: extended_enat,N: extended_enat] :
% 0.26/0.68        ( ( ord_le72135733267957522d_enat @ M @ N )
% 0.26/0.68       => ( ord_le2932123472753598470d_enat @ ( extended_eSuc @ M ) @ N ) ) ).
% 0.26/0.68  
% 0.26/0.68  % ileI1
% 0.26/0.68  thf(fact_10063_eSuc__plus__1,axiom,
% 0.26/0.68      ( extended_eSuc
% 0.26/0.68      = ( ^ [N3: extended_enat] : ( plus_p3455044024723400733d_enat @ N3 @ one_on7984719198319812577d_enat ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % eSuc_plus_1
% 0.26/0.68  thf(fact_10064_plus__1__eSuc_I1_J,axiom,
% 0.26/0.68      ! [Q3: extended_enat] :
% 0.26/0.68        ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ Q3 )
% 0.26/0.68        = ( extended_eSuc @ Q3 ) ) ).
% 0.26/0.68  
% 0.26/0.68  % plus_1_eSuc(1)
% 0.26/0.68  thf(fact_10065_plus__1__eSuc_I2_J,axiom,
% 0.26/0.68      ! [Q3: extended_enat] :
% 0.26/0.68        ( ( plus_p3455044024723400733d_enat @ Q3 @ one_on7984719198319812577d_enat )
% 0.26/0.68        = ( extended_eSuc @ Q3 ) ) ).
% 0.26/0.68  
% 0.26/0.68  % plus_1_eSuc(2)
% 0.26/0.68  thf(fact_10066_mono__eSuc,axiom,
% 0.26/0.68      order_4130057895858720880d_enat @ extended_eSuc ).
% 0.26/0.68  
% 0.26/0.68  % mono_eSuc
% 0.26/0.68  thf(fact_10067_iadd__Suc,axiom,
% 0.26/0.68      ! [M: extended_enat,N: extended_enat] :
% 0.26/0.68        ( ( plus_p3455044024723400733d_enat @ ( extended_eSuc @ M ) @ N )
% 0.26/0.68        = ( extended_eSuc @ ( plus_p3455044024723400733d_enat @ M @ N ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % iadd_Suc
% 0.26/0.68  thf(fact_10068_iadd__Suc__right,axiom,
% 0.26/0.68      ! [M: extended_enat,N: extended_enat] :
% 0.26/0.68        ( ( plus_p3455044024723400733d_enat @ M @ ( extended_eSuc @ N ) )
% 0.26/0.68        = ( extended_eSuc @ ( plus_p3455044024723400733d_enat @ M @ N ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % iadd_Suc_right
% 0.26/0.68  thf(fact_10069_eSuc__max,axiom,
% 0.26/0.68      ! [X3: extended_enat,Y3: extended_enat] :
% 0.26/0.68        ( ( extended_eSuc @ ( ord_ma741700101516333627d_enat @ X3 @ Y3 ) )
% 0.26/0.68        = ( ord_ma741700101516333627d_enat @ ( extended_eSuc @ X3 ) @ ( extended_eSuc @ Y3 ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % eSuc_max
% 0.26/0.68  thf(fact_10070_mult__eSuc__right,axiom,
% 0.26/0.68      ! [M: extended_enat,N: extended_enat] :
% 0.26/0.68        ( ( times_7803423173614009249d_enat @ M @ ( extended_eSuc @ N ) )
% 0.26/0.68        = ( plus_p3455044024723400733d_enat @ M @ ( times_7803423173614009249d_enat @ M @ N ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % mult_eSuc_right
% 0.26/0.68  thf(fact_10071_mult__eSuc,axiom,
% 0.26/0.68      ! [M: extended_enat,N: extended_enat] :
% 0.26/0.68        ( ( times_7803423173614009249d_enat @ ( extended_eSuc @ M ) @ N )
% 0.26/0.68        = ( plus_p3455044024723400733d_enat @ N @ ( times_7803423173614009249d_enat @ M @ N ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % mult_eSuc
% 0.26/0.68  thf(fact_10072_zero__ne__eSuc,axiom,
% 0.26/0.68      ! [N: extended_enat] :
% 0.26/0.68        ( zero_z5237406670263579293d_enat
% 0.26/0.68       != ( extended_eSuc @ N ) ) ).
% 0.26/0.68  
% 0.26/0.68  % zero_ne_eSuc
% 0.26/0.68  thf(fact_10073_i0__iless__eSuc,axiom,
% 0.26/0.68      ! [N: extended_enat] : ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( extended_eSuc @ N ) ) ).
% 0.26/0.68  
% 0.26/0.68  % i0_iless_eSuc
% 0.26/0.68  thf(fact_10074_one__eSuc,axiom,
% 0.26/0.68      ( one_on7984719198319812577d_enat
% 0.26/0.68      = ( extended_eSuc @ zero_z5237406670263579293d_enat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % one_eSuc
% 0.26/0.68  thf(fact_10075_not__eSuc__ilei0,axiom,
% 0.26/0.68      ! [N: extended_enat] :
% 0.26/0.68        ~ ( ord_le2932123472753598470d_enat @ ( extended_eSuc @ N ) @ zero_z5237406670263579293d_enat ) ).
% 0.26/0.68  
% 0.26/0.68  % not_eSuc_ilei0
% 0.26/0.68  thf(fact_10076_enat__eSuc__iff,axiom,
% 0.26/0.68      ! [Y3: nat,X3: extended_enat] :
% 0.26/0.68        ( ( ( extended_enat2 @ Y3 )
% 0.26/0.68          = ( extended_eSuc @ X3 ) )
% 0.26/0.68        = ( ? [N3: nat] :
% 0.26/0.68              ( ( Y3
% 0.26/0.68                = ( suc @ N3 ) )
% 0.26/0.68              & ( ( extended_enat2 @ N3 )
% 0.26/0.68                = X3 ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % enat_eSuc_iff
% 0.26/0.68  thf(fact_10077_eSuc__enat__iff,axiom,
% 0.26/0.68      ! [X3: extended_enat,Y3: nat] :
% 0.26/0.68        ( ( ( extended_eSuc @ X3 )
% 0.26/0.68          = ( extended_enat2 @ Y3 ) )
% 0.26/0.68        = ( ? [N3: nat] :
% 0.26/0.68              ( ( Y3
% 0.26/0.68                = ( suc @ N3 ) )
% 0.26/0.68              & ( X3
% 0.26/0.68                = ( extended_enat2 @ N3 ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % eSuc_enat_iff
% 0.26/0.68  thf(fact_10078_eSuc__enat,axiom,
% 0.26/0.68      ! [N: nat] :
% 0.26/0.68        ( ( extended_eSuc @ ( extended_enat2 @ N ) )
% 0.26/0.68        = ( extended_enat2 @ ( suc @ N ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % eSuc_enat
% 0.26/0.68  thf(fact_10079_eSuc__Sup,axiom,
% 0.26/0.68      ! [A3: set_Extended_enat] :
% 0.26/0.68        ( ( A3 != bot_bo7653980558646680370d_enat )
% 0.26/0.68       => ( ( extended_eSuc @ ( comple4398354569131411667d_enat @ A3 ) )
% 0.26/0.68          = ( comple4398354569131411667d_enat @ ( image_80655429650038917d_enat @ extended_eSuc @ A3 ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % eSuc_Sup
% 0.26/0.68  thf(fact_10080_eSuc__def,axiom,
% 0.26/0.68      ( extended_eSuc
% 0.26/0.68      = ( extend3600170679010898289d_enat
% 0.26/0.68        @ ^ [N3: nat] : ( extended_enat2 @ ( suc @ N3 ) )
% 0.26/0.68        @ extend5688581933313929465d_enat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % eSuc_def
% 0.26/0.68  thf(fact_10081_sub_Otransfer,axiom,
% 0.26/0.68      ( bNF_re7876454716742015248nteger
% 0.26/0.68      @ ^ [Y5: num,Z2: num] : ( Y5 = Z2 )
% 0.26/0.68      @ ( bNF_re6501075790457514782nteger
% 0.26/0.68        @ ^ [Y5: num,Z2: num] : ( Y5 = Z2 )
% 0.26/0.68        @ code_pcr_integer )
% 0.26/0.68      @ ^ [M3: num,N3: num] : ( minus_minus_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N3 ) )
% 0.26/0.68      @ code_sub ) ).
% 0.26/0.68  
% 0.26/0.68  % sub.transfer
% 0.26/0.68  thf(fact_10082_Code__Numeral_Osub__code_I1_J,axiom,
% 0.26/0.68      ( ( code_sub @ one @ one )
% 0.26/0.68      = zero_z3403309356797280102nteger ) ).
% 0.26/0.68  
% 0.26/0.68  % Code_Numeral.sub_code(1)
% 0.26/0.68  thf(fact_10083_sub_Orep__eq,axiom,
% 0.26/0.68      ! [X3: num,Xa: num] :
% 0.26/0.68        ( ( code_int_of_integer @ ( code_sub @ X3 @ Xa ) )
% 0.26/0.68        = ( minus_minus_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Xa ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % sub.rep_eq
% 0.26/0.68  thf(fact_10084_sub_Oabs__eq,axiom,
% 0.26/0.68      ( code_sub
% 0.26/0.68      = ( ^ [Xa4: num,X: num] : ( code_integer_of_int @ ( minus_minus_int @ ( numeral_numeral_int @ Xa4 ) @ ( numeral_numeral_int @ X ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % sub.abs_eq
% 0.26/0.68  thf(fact_10085_Code__Numeral_Osub__code_I9_J,axiom,
% 0.26/0.68      ! [M: num,N: num] :
% 0.26/0.68        ( ( code_sub @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.26/0.68        = ( minus_8373710615458151222nteger @ ( code_dup @ ( code_sub @ M @ N ) ) @ one_one_Code_integer ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Code_Numeral.sub_code(9)
% 0.26/0.68  thf(fact_10086_Code__Numeral_Osub__code_I8_J,axiom,
% 0.26/0.68      ! [M: num,N: num] :
% 0.26/0.68        ( ( code_sub @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.26/0.68        = ( plus_p5714425477246183910nteger @ ( code_dup @ ( code_sub @ M @ N ) ) @ one_one_Code_integer ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Code_Numeral.sub_code(8)
% 0.26/0.68  thf(fact_10087_Code__Numeral_Odup__code_I1_J,axiom,
% 0.26/0.68      ( ( code_dup @ zero_z3403309356797280102nteger )
% 0.26/0.68      = zero_z3403309356797280102nteger ) ).
% 0.26/0.68  
% 0.26/0.68  % Code_Numeral.dup_code(1)
% 0.26/0.68  thf(fact_10088_Code__Numeral_Osub__code_I6_J,axiom,
% 0.26/0.68      ! [M: num,N: num] :
% 0.26/0.68        ( ( code_sub @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.26/0.68        = ( code_dup @ ( code_sub @ M @ N ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Code_Numeral.sub_code(6)
% 0.26/0.68  thf(fact_10089_Code__Numeral_Osub__code_I4_J,axiom,
% 0.26/0.68      ! [N: num] :
% 0.26/0.68        ( ( code_sub @ one @ ( bit0 @ N ) )
% 0.26/0.68        = ( code_Neg @ ( bitM @ N ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Code_Numeral.sub_code(4)
% 0.26/0.68  thf(fact_10090_less__than__iff,axiom,
% 0.26/0.68      ! [X3: nat,Y3: nat] :
% 0.26/0.68        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ less_than )
% 0.26/0.68        = ( ord_less_nat @ X3 @ Y3 ) ) ).
% 0.26/0.68  
% 0.26/0.68  % less_than_iff
% 0.26/0.68  thf(fact_10091_Code__Numeral_Odup__code_I3_J,axiom,
% 0.26/0.68      ! [N: num] :
% 0.26/0.68        ( ( code_dup @ ( code_Neg @ N ) )
% 0.26/0.68        = ( code_Neg @ ( bit0 @ N ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Code_Numeral.dup_code(3)
% 0.26/0.68  thf(fact_10092_less__eq__integer__code_I7_J,axiom,
% 0.26/0.68      ! [K: num] : ( ord_le3102999989581377725nteger @ ( code_Neg @ K ) @ zero_z3403309356797280102nteger ) ).
% 0.26/0.68  
% 0.26/0.68  % less_eq_integer_code(7)
% 0.26/0.68  thf(fact_10093_less__eq__integer__code_I3_J,axiom,
% 0.26/0.68      ! [L: num] :
% 0.26/0.68        ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( code_Neg @ L ) ) ).
% 0.26/0.68  
% 0.26/0.68  % less_eq_integer_code(3)
% 0.26/0.68  thf(fact_10094_less__integer__code_I3_J,axiom,
% 0.26/0.68      ! [L: num] :
% 0.26/0.68        ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( code_Neg @ L ) ) ).
% 0.26/0.68  
% 0.26/0.68  % less_integer_code(3)
% 0.26/0.68  thf(fact_10095_less__integer__code_I7_J,axiom,
% 0.26/0.68      ! [K: num] : ( ord_le6747313008572928689nteger @ ( code_Neg @ K ) @ zero_z3403309356797280102nteger ) ).
% 0.26/0.68  
% 0.26/0.68  % less_integer_code(7)
% 0.26/0.68  thf(fact_10096_less__integer__code_I9_J,axiom,
% 0.26/0.68      ! [K: num,L: num] :
% 0.26/0.68        ( ( ord_le6747313008572928689nteger @ ( code_Neg @ K ) @ ( code_Neg @ L ) )
% 0.26/0.68        = ( ord_less_num @ L @ K ) ) ).
% 0.26/0.68  
% 0.26/0.68  % less_integer_code(9)
% 0.26/0.68  thf(fact_10097_less__eq__integer__code_I9_J,axiom,
% 0.26/0.68      ! [K: num,L: num] :
% 0.26/0.68        ( ( ord_le3102999989581377725nteger @ ( code_Neg @ K ) @ ( code_Neg @ L ) )
% 0.26/0.68        = ( ord_less_eq_num @ L @ K ) ) ).
% 0.26/0.68  
% 0.26/0.68  % less_eq_integer_code(9)
% 0.26/0.68  thf(fact_10098_Code__Numeral_Osub__code_I5_J,axiom,
% 0.26/0.68      ! [N: num] :
% 0.26/0.68        ( ( code_sub @ one @ ( bit1 @ N ) )
% 0.26/0.68        = ( code_Neg @ ( bit0 @ N ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Code_Numeral.sub_code(5)
% 0.26/0.68  thf(fact_10099_pair__less__def,axiom,
% 0.26/0.68      ( fun_pair_less
% 0.26/0.68      = ( lex_prod_nat_nat @ less_than @ less_than ) ) ).
% 0.26/0.68  
% 0.26/0.68  % pair_less_def
% 0.26/0.68  thf(fact_10100_Gcd__nat__set__eq__fold,axiom,
% 0.26/0.68      ! [Xs2: list_nat] :
% 0.26/0.68        ( ( gcd_Gcd_nat @ ( set_nat2 @ Xs2 ) )
% 0.26/0.68        = ( fold_nat_nat @ gcd_gcd_nat @ Xs2 @ zero_zero_nat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Gcd_nat_set_eq_fold
% 0.26/0.68  thf(fact_10101_Quotient__real,axiom,
% 0.26/0.68      quotie3684837364556693515t_real @ realrel @ real2 @ rep_real @ cr_real ).
% 0.26/0.68  
% 0.26/0.68  % Quotient_real
% 0.26/0.68  thf(fact_10102_Code__Numeral_Osub__code_I2_J,axiom,
% 0.26/0.68      ! [M: num] :
% 0.26/0.68        ( ( code_sub @ ( bit0 @ M ) @ one )
% 0.26/0.68        = ( code_Pos @ ( bitM @ M ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Code_Numeral.sub_code(2)
% 0.26/0.68  thf(fact_10103_Code__Numeral_Odup__code_I2_J,axiom,
% 0.26/0.68      ! [N: num] :
% 0.26/0.68        ( ( code_dup @ ( code_Pos @ N ) )
% 0.26/0.68        = ( code_Pos @ ( bit0 @ N ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Code_Numeral.dup_code(2)
% 0.26/0.68  thf(fact_10104_less__eq__integer__code_I4_J,axiom,
% 0.26/0.68      ! [K: num] :
% 0.26/0.68        ~ ( ord_le3102999989581377725nteger @ ( code_Pos @ K ) @ zero_z3403309356797280102nteger ) ).
% 0.26/0.68  
% 0.26/0.68  % less_eq_integer_code(4)
% 0.26/0.68  thf(fact_10105_less__eq__integer__code_I2_J,axiom,
% 0.26/0.68      ! [L: num] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( code_Pos @ L ) ) ).
% 0.26/0.68  
% 0.26/0.68  % less_eq_integer_code(2)
% 0.26/0.68  thf(fact_10106_less__integer__code_I2_J,axiom,
% 0.26/0.68      ! [L: num] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( code_Pos @ L ) ) ).
% 0.26/0.68  
% 0.26/0.68  % less_integer_code(2)
% 0.26/0.68  thf(fact_10107_less__integer__code_I4_J,axiom,
% 0.26/0.68      ! [K: num] :
% 0.26/0.68        ~ ( ord_le6747313008572928689nteger @ ( code_Pos @ K ) @ zero_z3403309356797280102nteger ) ).
% 0.26/0.68  
% 0.26/0.68  % less_integer_code(4)
% 0.26/0.68  thf(fact_10108_less__integer__code_I5_J,axiom,
% 0.26/0.68      ! [K: num,L: num] :
% 0.26/0.68        ( ( ord_le6747313008572928689nteger @ ( code_Pos @ K ) @ ( code_Pos @ L ) )
% 0.26/0.68        = ( ord_less_num @ K @ L ) ) ).
% 0.26/0.68  
% 0.26/0.68  % less_integer_code(5)
% 0.26/0.68  thf(fact_10109_one__integer__code,axiom,
% 0.26/0.68      ( one_one_Code_integer
% 0.26/0.68      = ( code_Pos @ one ) ) ).
% 0.26/0.68  
% 0.26/0.68  % one_integer_code
% 0.26/0.68  thf(fact_10110_Pos__fold_I2_J,axiom,
% 0.26/0.68      ! [K: num] :
% 0.26/0.68        ( ( numera6620942414471956472nteger @ ( bit0 @ K ) )
% 0.26/0.68        = ( code_Pos @ ( bit0 @ K ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Pos_fold(2)
% 0.26/0.68  thf(fact_10111_Pos__fold_I1_J,axiom,
% 0.26/0.68      ( ( numera6620942414471956472nteger @ one )
% 0.26/0.68      = ( code_Pos @ one ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Pos_fold(1)
% 0.26/0.68  thf(fact_10112_less__eq__integer__code_I5_J,axiom,
% 0.26/0.68      ! [K: num,L: num] :
% 0.26/0.68        ( ( ord_le3102999989581377725nteger @ ( code_Pos @ K ) @ ( code_Pos @ L ) )
% 0.26/0.68        = ( ord_less_eq_num @ K @ L ) ) ).
% 0.26/0.68  
% 0.26/0.68  % less_eq_integer_code(5)
% 0.26/0.68  thf(fact_10113_Gcd__int__set__eq__fold,axiom,
% 0.26/0.68      ! [Xs2: list_int] :
% 0.26/0.68        ( ( gcd_Gcd_int @ ( set_int2 @ Xs2 ) )
% 0.26/0.68        = ( fold_int_int @ gcd_gcd_int @ Xs2 @ zero_zero_int ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Gcd_int_set_eq_fold
% 0.26/0.68  thf(fact_10114_Code__Numeral_Osub__code_I3_J,axiom,
% 0.26/0.68      ! [M: num] :
% 0.26/0.68        ( ( code_sub @ ( bit1 @ M ) @ one )
% 0.26/0.68        = ( code_Pos @ ( bit0 @ M ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Code_Numeral.sub_code(3)
% 0.26/0.68  thf(fact_10115_cr__int__def,axiom,
% 0.26/0.68      ( cr_int
% 0.26/0.68      = ( ^ [X: product_prod_nat_nat] :
% 0.26/0.68            ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 0.26/0.68            @ ( abs_Integ @ X ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % cr_int_def
% 0.26/0.68  thf(fact_10116_int_Opcr__cr__eq,axiom,
% 0.26/0.68      pcr_int = cr_int ).
% 0.26/0.68  
% 0.26/0.68  % int.pcr_cr_eq
% 0.26/0.68  thf(fact_10117_Quotient__int,axiom,
% 0.26/0.68      quotie1194848508323700631at_int @ intrel @ abs_Integ @ rep_Integ @ cr_int ).
% 0.26/0.68  
% 0.26/0.68  % Quotient_int
% 0.26/0.68  thf(fact_10118_gcd__nat_Osemilattice__neutr__axioms,axiom,
% 0.26/0.68      semila9081495762789891438tr_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 0.26/0.68  
% 0.26/0.68  % gcd_nat.semilattice_neutr_axioms
% 0.26/0.68  thf(fact_10119_max__nat_Osemilattice__neutr__axioms,axiom,
% 0.26/0.68      semila9081495762789891438tr_nat @ ord_max_nat @ zero_zero_nat ).
% 0.26/0.68  
% 0.26/0.68  % max_nat.semilattice_neutr_axioms
% 0.26/0.68  thf(fact_10120_natLess__def,axiom,
% 0.26/0.68      ( bNF_Ca8459412986667044542atLess
% 0.26/0.68      = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % natLess_def
% 0.26/0.68  thf(fact_10121_Restr__natLeq,axiom,
% 0.26/0.68      ! [N: nat] :
% 0.26/0.68        ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 0.26/0.68          @ ( produc457027306803732586at_nat
% 0.26/0.68            @ ( collect_nat
% 0.26/0.68              @ ^ [X: nat] : ( ord_less_nat @ X @ N ) )
% 0.26/0.68            @ ^ [Uu3: nat] :
% 0.26/0.68                ( collect_nat
% 0.26/0.68                @ ^ [X: nat] : ( ord_less_nat @ X @ N ) ) ) )
% 0.26/0.68        = ( collec3392354462482085612at_nat
% 0.26/0.68          @ ( produc6081775807080527818_nat_o
% 0.26/0.68            @ ^ [X: nat,Y: nat] :
% 0.26/0.68                ( ( ord_less_nat @ X @ N )
% 0.26/0.68                & ( ord_less_nat @ Y @ N )
% 0.26/0.68                & ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Restr_natLeq
% 0.26/0.68  thf(fact_10122_natLeq__def,axiom,
% 0.26/0.68      ( bNF_Ca8665028551170535155natLeq
% 0.26/0.68      = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_eq_nat ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % natLeq_def
% 0.26/0.68  thf(fact_10123_Restr__natLeq2,axiom,
% 0.26/0.68      ! [N: nat] :
% 0.26/0.68        ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 0.26/0.68          @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 0.26/0.68            @ ^ [Uu3: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N ) ) )
% 0.26/0.68        = ( collec3392354462482085612at_nat
% 0.26/0.68          @ ( produc6081775807080527818_nat_o
% 0.26/0.68            @ ^ [X: nat,Y: nat] :
% 0.26/0.68                ( ( ord_less_nat @ X @ N )
% 0.26/0.68                & ( ord_less_nat @ Y @ N )
% 0.26/0.68                & ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Restr_natLeq2
% 0.26/0.68  thf(fact_10124_natLeq__underS__less,axiom,
% 0.26/0.68      ! [N: nat] :
% 0.26/0.68        ( ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 0.26/0.68        = ( collect_nat
% 0.26/0.68          @ ^ [X: nat] : ( ord_less_nat @ X @ N ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % natLeq_underS_less
% 0.26/0.68  thf(fact_10125_gcd__nat_Omonoid__axioms,axiom,
% 0.26/0.68      monoid_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 0.26/0.68  
% 0.26/0.68  % gcd_nat.monoid_axioms
% 0.26/0.68  thf(fact_10126_max__nat_Omonoid__axioms,axiom,
% 0.26/0.68      monoid_nat @ ord_max_nat @ zero_zero_nat ).
% 0.26/0.68  
% 0.26/0.68  % max_nat.monoid_axioms
% 0.26/0.68  thf(fact_10127_infinity__enat__def,axiom,
% 0.26/0.68      ( extend5688581933313929465d_enat
% 0.26/0.68      = ( extended_Abs_enat @ none_nat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % infinity_enat_def
% 0.26/0.68  thf(fact_10128_Abs__enat__cases,axiom,
% 0.26/0.68      ! [X3: extended_enat] :
% 0.26/0.68        ~ ! [Y4: option_nat] :
% 0.26/0.68            ( ( X3
% 0.26/0.68              = ( extended_Abs_enat @ Y4 ) )
% 0.26/0.68           => ~ ( member_option_nat @ Y4 @ top_to8920198386146353926on_nat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Abs_enat_cases
% 0.26/0.68  thf(fact_10129_Abs__enat__induct,axiom,
% 0.26/0.68      ! [P: extended_enat > $o,X3: extended_enat] :
% 0.26/0.68        ( ! [Y4: option_nat] :
% 0.26/0.68            ( ( member_option_nat @ Y4 @ top_to8920198386146353926on_nat )
% 0.26/0.68           => ( P @ ( extended_Abs_enat @ Y4 ) ) )
% 0.26/0.68       => ( P @ X3 ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Abs_enat_induct
% 0.26/0.68  thf(fact_10130_Abs__enat__inject,axiom,
% 0.26/0.68      ! [X3: option_nat,Y3: option_nat] :
% 0.26/0.68        ( ( member_option_nat @ X3 @ top_to8920198386146353926on_nat )
% 0.26/0.68       => ( ( member_option_nat @ Y3 @ top_to8920198386146353926on_nat )
% 0.26/0.68         => ( ( ( extended_Abs_enat @ X3 )
% 0.26/0.68              = ( extended_Abs_enat @ Y3 ) )
% 0.26/0.68            = ( X3 = Y3 ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Abs_enat_inject
% 0.26/0.68  thf(fact_10131_enat__def,axiom,
% 0.26/0.68      ( extended_enat2
% 0.26/0.68      = ( ^ [N3: nat] : ( extended_Abs_enat @ ( some_nat @ N3 ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % enat_def
% 0.26/0.68  thf(fact_10132_Abs__enat__inverse,axiom,
% 0.26/0.68      ! [Y3: option_nat] :
% 0.26/0.68        ( ( member_option_nat @ Y3 @ top_to8920198386146353926on_nat )
% 0.26/0.68       => ( ( extended_Rep_enat @ ( extended_Abs_enat @ Y3 ) )
% 0.26/0.68          = Y3 ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Abs_enat_inverse
% 0.26/0.68  thf(fact_10133_Rep__enat__induct,axiom,
% 0.26/0.68      ! [Y3: option_nat,P: option_nat > $o] :
% 0.26/0.68        ( ( member_option_nat @ Y3 @ top_to8920198386146353926on_nat )
% 0.26/0.68       => ( ! [X4: extended_enat] : ( P @ ( extended_Rep_enat @ X4 ) )
% 0.26/0.68         => ( P @ Y3 ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Rep_enat_induct
% 0.26/0.68  thf(fact_10134_Rep__enat__cases,axiom,
% 0.26/0.68      ! [Y3: option_nat] :
% 0.26/0.68        ( ( member_option_nat @ Y3 @ top_to8920198386146353926on_nat )
% 0.26/0.68       => ~ ! [X4: extended_enat] :
% 0.26/0.68              ( Y3
% 0.26/0.68             != ( extended_Rep_enat @ X4 ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Rep_enat_cases
% 0.26/0.68  thf(fact_10135_Rep__enat,axiom,
% 0.26/0.68      ! [X3: extended_enat] : ( member_option_nat @ ( extended_Rep_enat @ X3 ) @ top_to8920198386146353926on_nat ) ).
% 0.26/0.68  
% 0.26/0.68  % Rep_enat
% 0.26/0.68  thf(fact_10136_Rep__enat__inject,axiom,
% 0.26/0.68      ! [X3: extended_enat,Y3: extended_enat] :
% 0.26/0.68        ( ( ( extended_Rep_enat @ X3 )
% 0.26/0.68          = ( extended_Rep_enat @ Y3 ) )
% 0.26/0.68        = ( X3 = Y3 ) ) ).
% 0.26/0.68  
% 0.26/0.68  % Rep_enat_inject
% 0.26/0.68  thf(fact_10137_Rep__enat__inverse,axiom,
% 0.26/0.68      ! [X3: extended_enat] :
% 0.26/0.68        ( ( extended_Abs_enat @ ( extended_Rep_enat @ X3 ) )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  % Rep_enat_inverse
% 0.26/0.68  thf(fact_10138_type__definition__enat,axiom,
% 0.26/0.68      type_d7649664348572268762on_nat @ extended_Rep_enat @ extended_Abs_enat @ top_to8920198386146353926on_nat ).
% 0.26/0.68  
% 0.26/0.68  % type_definition_enat
% 0.26/0.68  thf(fact_10139_list__encode_Oelims,axiom,
% 0.26/0.68      ! [X3: list_nat,Y3: nat] :
% 0.26/0.68        ( ( ( nat_list_encode @ X3 )
% 0.26/0.68          = Y3 )
% 0.26/0.68       => ( ( ( X3 = nil_nat )
% 0.26/0.68           => ( Y3 != zero_zero_nat ) )
% 0.26/0.68         => ~ ! [X4: nat,Xs3: list_nat] :
% 0.26/0.68                ( ( X3
% 0.26/0.68                  = ( cons_nat @ X4 @ Xs3 ) )
% 0.26/0.68               => ( Y3
% 0.26/0.68                 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs3 ) ) ) ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % list_encode.elims
% 0.26/0.68  thf(fact_10140_le__prod__encode__1,axiom,
% 0.26/0.68      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % le_prod_encode_1
% 0.26/0.68  thf(fact_10141_le__prod__encode__2,axiom,
% 0.26/0.68      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % le_prod_encode_2
% 0.26/0.68  thf(fact_10142_list__encode_Osimps_I1_J,axiom,
% 0.26/0.68      ( ( nat_list_encode @ nil_nat )
% 0.26/0.68      = zero_zero_nat ) ).
% 0.26/0.68  
% 0.26/0.68  % list_encode.simps(1)
% 0.26/0.68  thf(fact_10143_list__encode_Opelims,axiom,
% 0.26/0.68      ! [X3: list_nat,Y3: nat] :
% 0.26/0.68        ( ( ( nat_list_encode @ X3 )
% 0.26/0.68          = Y3 )
% 0.26/0.68       => ( ( accp_list_nat @ nat_list_encode_rel @ X3 )
% 0.26/0.68         => ( ( ( X3 = nil_nat )
% 0.26/0.68             => ( ( Y3 = zero_zero_nat )
% 0.26/0.68               => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 0.26/0.68           => ~ ! [X4: nat,Xs3: list_nat] :
% 0.26/0.68                  ( ( X3
% 0.26/0.68                    = ( cons_nat @ X4 @ Xs3 ) )
% 0.26/0.68                 => ( ( Y3
% 0.26/0.68                      = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs3 ) ) ) ) )
% 0.26/0.68                   => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X4 @ Xs3 ) ) ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % list_encode.pelims
% 0.26/0.68  thf(fact_10144_wf__less,axiom,
% 0.26/0.68      wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % wf_less
% 0.26/0.68  thf(fact_10145_wf__pair__less,axiom,
% 0.26/0.68      wf_Pro7803398752247294826at_nat @ fun_pair_less ).
% 0.26/0.68  
% 0.26/0.68  % wf_pair_less
% 0.26/0.68  thf(fact_10146_wf__int__ge__less__than2,axiom,
% 0.26/0.68      ! [D3: int] : ( wf_int @ ( int_ge_less_than2 @ D3 ) ) ).
% 0.26/0.68  
% 0.26/0.68  % wf_int_ge_less_than2
% 0.26/0.68  thf(fact_10147_wf__int__ge__less__than,axiom,
% 0.26/0.68      ! [D3: int] : ( wf_int @ ( int_ge_less_than @ D3 ) ) ).
% 0.26/0.68  
% 0.26/0.68  % wf_int_ge_less_than
% 0.26/0.68  thf(fact_10148_prod__decode__def,axiom,
% 0.26/0.68      ( nat_prod_decode
% 0.26/0.68      = ( nat_prod_decode_aux @ zero_zero_nat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % prod_decode_def
% 0.26/0.68  thf(fact_10149_max__nat_Ocomm__monoid__axioms,axiom,
% 0.26/0.68      comm_monoid_nat @ ord_max_nat @ zero_zero_nat ).
% 0.26/0.68  
% 0.26/0.68  % max_nat.comm_monoid_axioms
% 0.26/0.68  thf(fact_10150_gcd__nat_Ocomm__monoid__axioms,axiom,
% 0.26/0.68      comm_monoid_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 0.26/0.68  
% 0.26/0.68  % gcd_nat.comm_monoid_axioms
% 0.26/0.68  thf(fact_10151_list__decode_Opinduct,axiom,
% 0.26/0.68      ! [A0: nat,P: nat > $o] :
% 0.26/0.68        ( ( accp_nat @ nat_list_decode_rel @ A0 )
% 0.26/0.68       => ( ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 0.26/0.68           => ( P @ zero_zero_nat ) )
% 0.26/0.68         => ( ! [N2: nat] :
% 0.26/0.68                ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N2 ) )
% 0.26/0.68               => ( ! [X6: nat,Y6: nat] :
% 0.26/0.68                      ( ( ( product_Pair_nat_nat @ X6 @ Y6 )
% 0.26/0.68                        = ( nat_prod_decode @ N2 ) )
% 0.26/0.68                     => ( P @ Y6 ) )
% 0.26/0.68                 => ( P @ ( suc @ N2 ) ) ) )
% 0.26/0.68           => ( P @ A0 ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % list_decode.pinduct
% 0.26/0.68  thf(fact_10152_list__decode_Oelims,axiom,
% 0.26/0.68      ! [X3: nat,Y3: list_nat] :
% 0.26/0.68        ( ( ( nat_list_decode @ X3 )
% 0.26/0.68          = Y3 )
% 0.26/0.68       => ( ( ( X3 = zero_zero_nat )
% 0.26/0.68           => ( Y3 != nil_nat ) )
% 0.26/0.68         => ~ ! [N2: nat] :
% 0.26/0.68                ( ( X3
% 0.26/0.68                  = ( suc @ N2 ) )
% 0.26/0.68               => ( Y3
% 0.26/0.68                 != ( produc2761476792215241774st_nat
% 0.26/0.68                    @ ^ [X: nat,Y: nat] : ( cons_nat @ X @ ( nat_list_decode @ Y ) )
% 0.26/0.68                    @ ( nat_prod_decode @ N2 ) ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % list_decode.elims
% 0.26/0.68  thf(fact_10153_list__decode_Opsimps_I1_J,axiom,
% 0.26/0.68      ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 0.26/0.68     => ( ( nat_list_decode @ zero_zero_nat )
% 0.26/0.68        = nil_nat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % list_decode.psimps(1)
% 0.26/0.68  thf(fact_10154_list__decode_Osimps_I1_J,axiom,
% 0.26/0.68      ( ( nat_list_decode @ zero_zero_nat )
% 0.26/0.68      = nil_nat ) ).
% 0.26/0.68  
% 0.26/0.68  % list_decode.simps(1)
% 0.26/0.68  thf(fact_10155_list__decode_Opelims,axiom,
% 0.26/0.68      ! [X3: nat,Y3: list_nat] :
% 0.26/0.68        ( ( ( nat_list_decode @ X3 )
% 0.26/0.68          = Y3 )
% 0.26/0.68       => ( ( accp_nat @ nat_list_decode_rel @ X3 )
% 0.26/0.68         => ( ( ( X3 = zero_zero_nat )
% 0.26/0.68             => ( ( Y3 = nil_nat )
% 0.26/0.68               => ~ ( accp_nat @ nat_list_decode_rel @ zero_zero_nat ) ) )
% 0.26/0.68           => ~ ! [N2: nat] :
% 0.26/0.68                  ( ( X3
% 0.26/0.68                    = ( suc @ N2 ) )
% 0.26/0.68                 => ( ( Y3
% 0.26/0.68                      = ( produc2761476792215241774st_nat
% 0.26/0.68                        @ ^ [X: nat,Y: nat] : ( cons_nat @ X @ ( nat_list_decode @ Y ) )
% 0.26/0.68                        @ ( nat_prod_decode @ N2 ) ) )
% 0.26/0.68                   => ~ ( accp_nat @ nat_list_decode_rel @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % list_decode.pelims
% 0.26/0.68  thf(fact_10156_times__num__def,axiom,
% 0.26/0.68      ( times_times_num
% 0.26/0.68      = ( ^ [M3: num,N3: num] : ( num_of_nat @ ( times_times_nat @ ( nat_of_num @ M3 ) @ ( nat_of_num @ N3 ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % times_num_def
% 0.26/0.68  thf(fact_10157_less__eq__num__def,axiom,
% 0.26/0.68      ( ord_less_eq_num
% 0.26/0.68      = ( ^ [M3: num,N3: num] : ( ord_less_eq_nat @ ( nat_of_num @ M3 ) @ ( nat_of_num @ N3 ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % less_eq_num_def
% 0.26/0.68  thf(fact_10158_nat__of__num_Osimps_I3_J,axiom,
% 0.26/0.68      ! [X3: num] :
% 0.26/0.68        ( ( nat_of_num @ ( bit1 @ X3 ) )
% 0.26/0.68        = ( suc @ ( plus_plus_nat @ ( nat_of_num @ X3 ) @ ( nat_of_num @ X3 ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % nat_of_num.simps(3)
% 0.26/0.68  thf(fact_10159_nat__of__num__pos,axiom,
% 0.26/0.68      ! [X3: num] : ( ord_less_nat @ zero_zero_nat @ ( nat_of_num @ X3 ) ) ).
% 0.26/0.68  
% 0.26/0.68  % nat_of_num_pos
% 0.26/0.68  thf(fact_10160_nat__of__num__neq__0,axiom,
% 0.26/0.68      ! [X3: num] :
% 0.26/0.68        ( ( nat_of_num @ X3 )
% 0.26/0.68       != zero_zero_nat ) ).
% 0.26/0.68  
% 0.26/0.68  % nat_of_num_neq_0
% 0.26/0.68  thf(fact_10161_nat__of__num__add,axiom,
% 0.26/0.68      ! [X3: num,Y3: num] :
% 0.26/0.68        ( ( nat_of_num @ ( plus_plus_num @ X3 @ Y3 ) )
% 0.26/0.68        = ( plus_plus_nat @ ( nat_of_num @ X3 ) @ ( nat_of_num @ Y3 ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % nat_of_num_add
% 0.26/0.68  thf(fact_10162_nat__of__num__numeral,axiom,
% 0.26/0.68      nat_of_num = numeral_numeral_nat ).
% 0.26/0.68  
% 0.26/0.68  % nat_of_num_numeral
% 0.26/0.68  thf(fact_10163_nat__of__num__inverse,axiom,
% 0.26/0.68      ! [X3: num] :
% 0.26/0.68        ( ( num_of_nat @ ( nat_of_num @ X3 ) )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  % nat_of_num_inverse
% 0.26/0.68  thf(fact_10164_num__eq__iff,axiom,
% 0.26/0.68      ( ( ^ [Y5: num,Z2: num] : ( Y5 = Z2 ) )
% 0.26/0.68      = ( ^ [X: num,Y: num] :
% 0.26/0.68            ( ( nat_of_num @ X )
% 0.26/0.68            = ( nat_of_num @ Y ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % num_eq_iff
% 0.26/0.68  thf(fact_10165_nat__of__num__code_I1_J,axiom,
% 0.26/0.68      ( ( nat_of_num @ one )
% 0.26/0.68      = one_one_nat ) ).
% 0.26/0.68  
% 0.26/0.68  % nat_of_num_code(1)
% 0.26/0.68  thf(fact_10166_nat__of__num_Osimps_I2_J,axiom,
% 0.26/0.68      ! [X3: num] :
% 0.26/0.68        ( ( nat_of_num @ ( bit0 @ X3 ) )
% 0.26/0.68        = ( plus_plus_nat @ ( nat_of_num @ X3 ) @ ( nat_of_num @ X3 ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % nat_of_num.simps(2)
% 0.26/0.68  thf(fact_10167_nat__of__num__inc,axiom,
% 0.26/0.68      ! [X3: num] :
% 0.26/0.68        ( ( nat_of_num @ ( inc @ X3 ) )
% 0.26/0.68        = ( suc @ ( nat_of_num @ X3 ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % nat_of_num_inc
% 0.26/0.68  thf(fact_10168_less__num__def,axiom,
% 0.26/0.68      ( ord_less_num
% 0.26/0.68      = ( ^ [M3: num,N3: num] : ( ord_less_nat @ ( nat_of_num @ M3 ) @ ( nat_of_num @ N3 ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % less_num_def
% 0.26/0.68  thf(fact_10169_nat__of__num__code_I2_J,axiom,
% 0.26/0.68      ! [N: num] :
% 0.26/0.68        ( ( nat_of_num @ ( bit0 @ N ) )
% 0.26/0.68        = ( plus_plus_nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % nat_of_num_code(2)
% 0.26/0.68  thf(fact_10170_nat__of__num__mult,axiom,
% 0.26/0.68      ! [X3: num,Y3: num] :
% 0.26/0.68        ( ( nat_of_num @ ( times_times_num @ X3 @ Y3 ) )
% 0.26/0.68        = ( times_times_nat @ ( nat_of_num @ X3 ) @ ( nat_of_num @ Y3 ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % nat_of_num_mult
% 0.26/0.68  thf(fact_10171_nat__of__num__sqr,axiom,
% 0.26/0.68      ! [X3: num] :
% 0.26/0.68        ( ( nat_of_num @ ( sqr @ X3 ) )
% 0.26/0.68        = ( times_times_nat @ ( nat_of_num @ X3 ) @ ( nat_of_num @ X3 ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % nat_of_num_sqr
% 0.26/0.68  thf(fact_10172_nat__of__num_Osimps_I1_J,axiom,
% 0.26/0.68      ( ( nat_of_num @ one )
% 0.26/0.68      = ( suc @ zero_zero_nat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % nat_of_num.simps(1)
% 0.26/0.68  thf(fact_10173_num__of__nat__inverse,axiom,
% 0.26/0.68      ! [N: nat] :
% 0.26/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.68       => ( ( nat_of_num @ ( num_of_nat @ N ) )
% 0.26/0.68          = N ) ) ).
% 0.26/0.68  
% 0.26/0.68  % num_of_nat_inverse
% 0.26/0.68  thf(fact_10174_nat__of__num__code_I3_J,axiom,
% 0.26/0.68      ! [N: num] :
% 0.26/0.68        ( ( nat_of_num @ ( bit1 @ N ) )
% 0.26/0.68        = ( suc @ ( plus_plus_nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % nat_of_num_code(3)
% 0.26/0.68  thf(fact_10175_plus__num__def,axiom,
% 0.26/0.68      ( plus_plus_num
% 0.26/0.68      = ( ^ [M3: num,N3: num] : ( num_of_nat @ ( plus_plus_nat @ ( nat_of_num @ M3 ) @ ( nat_of_num @ N3 ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % plus_num_def
% 0.26/0.68  thf(fact_10176_or__num_Oelims,axiom,
% 0.26/0.68      ! [X3: num,Xa: num,Y3: num] :
% 0.26/0.68        ( ( ( bit_un6697907153464112080or_num @ X3 @ Xa )
% 0.26/0.68          = Y3 )
% 0.26/0.68       => ( ( ( X3 = one )
% 0.26/0.68           => ( ( Xa = one )
% 0.26/0.68             => ( Y3 != one ) ) )
% 0.26/0.68         => ( ( ( X3 = one )
% 0.26/0.68             => ! [N2: num] :
% 0.26/0.68                  ( ( Xa
% 0.26/0.68                    = ( bit0 @ N2 ) )
% 0.26/0.68                 => ( Y3
% 0.26/0.68                   != ( bit1 @ N2 ) ) ) )
% 0.26/0.68           => ( ( ( X3 = one )
% 0.26/0.68               => ! [N2: num] :
% 0.26/0.68                    ( ( Xa
% 0.26/0.68                      = ( bit1 @ N2 ) )
% 0.26/0.68                   => ( Y3
% 0.26/0.68                     != ( bit1 @ N2 ) ) ) )
% 0.26/0.68             => ( ! [M4: num] :
% 0.26/0.68                    ( ( X3
% 0.26/0.68                      = ( bit0 @ M4 ) )
% 0.26/0.68                   => ( ( Xa = one )
% 0.26/0.68                     => ( Y3
% 0.26/0.68                       != ( bit1 @ M4 ) ) ) )
% 0.26/0.68               => ( ! [M4: num] :
% 0.26/0.68                      ( ( X3
% 0.26/0.68                        = ( bit0 @ M4 ) )
% 0.26/0.68                     => ! [N2: num] :
% 0.26/0.68                          ( ( Xa
% 0.26/0.68                            = ( bit0 @ N2 ) )
% 0.26/0.68                         => ( Y3
% 0.26/0.68                           != ( bit0 @ ( bit_un6697907153464112080or_num @ M4 @ N2 ) ) ) ) )
% 0.26/0.68                 => ( ! [M4: num] :
% 0.26/0.68                        ( ( X3
% 0.26/0.68                          = ( bit0 @ M4 ) )
% 0.26/0.68                       => ! [N2: num] :
% 0.26/0.68                            ( ( Xa
% 0.26/0.68                              = ( bit1 @ N2 ) )
% 0.26/0.68                           => ( Y3
% 0.26/0.68                             != ( bit1 @ ( bit_un6697907153464112080or_num @ M4 @ N2 ) ) ) ) )
% 0.26/0.68                   => ( ! [M4: num] :
% 0.26/0.68                          ( ( X3
% 0.26/0.68                            = ( bit1 @ M4 ) )
% 0.26/0.68                         => ( ( Xa = one )
% 0.26/0.68                           => ( Y3
% 0.26/0.68                             != ( bit1 @ M4 ) ) ) )
% 0.26/0.68                     => ( ! [M4: num] :
% 0.26/0.68                            ( ( X3
% 0.26/0.68                              = ( bit1 @ M4 ) )
% 0.26/0.68                           => ! [N2: num] :
% 0.26/0.68                                ( ( Xa
% 0.26/0.68                                  = ( bit0 @ N2 ) )
% 0.26/0.68                               => ( Y3
% 0.26/0.68                                 != ( bit1 @ ( bit_un6697907153464112080or_num @ M4 @ N2 ) ) ) ) )
% 0.26/0.68                       => ~ ! [M4: num] :
% 0.26/0.68                              ( ( X3
% 0.26/0.68                                = ( bit1 @ M4 ) )
% 0.26/0.68                             => ! [N2: num] :
% 0.26/0.68                                  ( ( Xa
% 0.26/0.68                                    = ( bit1 @ N2 ) )
% 0.26/0.68                                 => ( Y3
% 0.26/0.68                                   != ( bit1 @ ( bit_un6697907153464112080or_num @ M4 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % or_num.elims
% 0.26/0.68  thf(fact_10177_or__num_Osimps_I2_J,axiom,
% 0.26/0.68      ! [N: num] :
% 0.26/0.68        ( ( bit_un6697907153464112080or_num @ one @ ( bit0 @ N ) )
% 0.26/0.68        = ( bit1 @ N ) ) ).
% 0.26/0.68  
% 0.26/0.68  % or_num.simps(2)
% 0.26/0.68  thf(fact_10178_or__num_Osimps_I6_J,axiom,
% 0.26/0.68      ! [M: num,N: num] :
% 0.26/0.68        ( ( bit_un6697907153464112080or_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.26/0.68        = ( bit1 @ ( bit_un6697907153464112080or_num @ M @ N ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % or_num.simps(6)
% 0.26/0.68  thf(fact_10179_or__num_Osimps_I8_J,axiom,
% 0.26/0.68      ! [M: num,N: num] :
% 0.26/0.68        ( ( bit_un6697907153464112080or_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.26/0.68        = ( bit1 @ ( bit_un6697907153464112080or_num @ M @ N ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % or_num.simps(8)
% 0.26/0.68  thf(fact_10180_or__num_Osimps_I3_J,axiom,
% 0.26/0.68      ! [N: num] :
% 0.26/0.68        ( ( bit_un6697907153464112080or_num @ one @ ( bit1 @ N ) )
% 0.26/0.68        = ( bit1 @ N ) ) ).
% 0.26/0.68  
% 0.26/0.68  % or_num.simps(3)
% 0.26/0.68  thf(fact_10181_or__num_Osimps_I7_J,axiom,
% 0.26/0.68      ! [M: num] :
% 0.26/0.68        ( ( bit_un6697907153464112080or_num @ ( bit1 @ M ) @ one )
% 0.26/0.68        = ( bit1 @ M ) ) ).
% 0.26/0.68  
% 0.26/0.68  % or_num.simps(7)
% 0.26/0.68  thf(fact_10182_or__num_Osimps_I9_J,axiom,
% 0.26/0.68      ! [M: num,N: num] :
% 0.26/0.68        ( ( bit_un6697907153464112080or_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.26/0.68        = ( bit1 @ ( bit_un6697907153464112080or_num @ M @ N ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % or_num.simps(9)
% 0.26/0.68  thf(fact_10183_or__num_Osimps_I1_J,axiom,
% 0.26/0.68      ( ( bit_un6697907153464112080or_num @ one @ one )
% 0.26/0.68      = one ) ).
% 0.26/0.68  
% 0.26/0.68  % or_num.simps(1)
% 0.26/0.68  thf(fact_10184_or__num_Osimps_I5_J,axiom,
% 0.26/0.68      ! [M: num,N: num] :
% 0.26/0.68        ( ( bit_un6697907153464112080or_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.26/0.68        = ( bit0 @ ( bit_un6697907153464112080or_num @ M @ N ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % or_num.simps(5)
% 0.26/0.68  thf(fact_10185_or__num_Osimps_I4_J,axiom,
% 0.26/0.68      ! [M: num] :
% 0.26/0.68        ( ( bit_un6697907153464112080or_num @ ( bit0 @ M ) @ one )
% 0.26/0.68        = ( bit1 @ M ) ) ).
% 0.26/0.68  
% 0.26/0.68  % or_num.simps(4)
% 0.26/0.68  thf(fact_10186_or__num_Opelims,axiom,
% 0.26/0.68      ! [X3: num,Xa: num,Y3: num] :
% 0.26/0.68        ( ( ( bit_un6697907153464112080or_num @ X3 @ Xa )
% 0.26/0.68          = Y3 )
% 0.26/0.68       => ( ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ X3 @ Xa ) )
% 0.26/0.68         => ( ( ( X3 = one )
% 0.26/0.68             => ( ( Xa = one )
% 0.26/0.68               => ( ( Y3 = one )
% 0.26/0.68                 => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.26/0.68           => ( ( ( X3 = one )
% 0.26/0.68               => ! [N2: num] :
% 0.26/0.68                    ( ( Xa
% 0.26/0.68                      = ( bit0 @ N2 ) )
% 0.26/0.68                   => ( ( Y3
% 0.26/0.68                        = ( bit1 @ N2 ) )
% 0.26/0.68                     => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) ) ) ) )
% 0.26/0.68             => ( ( ( X3 = one )
% 0.26/0.68                 => ! [N2: num] :
% 0.26/0.68                      ( ( Xa
% 0.26/0.68                        = ( bit1 @ N2 ) )
% 0.26/0.68                     => ( ( Y3
% 0.26/0.68                          = ( bit1 @ N2 ) )
% 0.26/0.68                       => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) ) ) ) )
% 0.26/0.68               => ( ! [M4: num] :
% 0.26/0.68                      ( ( X3
% 0.26/0.68                        = ( bit0 @ M4 ) )
% 0.26/0.68                     => ( ( Xa = one )
% 0.26/0.68                       => ( ( Y3
% 0.26/0.68                            = ( bit1 @ M4 ) )
% 0.26/0.68                         => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 0.26/0.68                 => ( ! [M4: num] :
% 0.26/0.68                        ( ( X3
% 0.26/0.68                          = ( bit0 @ M4 ) )
% 0.26/0.68                       => ! [N2: num] :
% 0.26/0.68                            ( ( Xa
% 0.26/0.68                              = ( bit0 @ N2 ) )
% 0.26/0.68                           => ( ( Y3
% 0.26/0.68                                = ( bit0 @ ( bit_un6697907153464112080or_num @ M4 @ N2 ) ) )
% 0.26/0.68                             => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 0.26/0.68                   => ( ! [M4: num] :
% 0.26/0.68                          ( ( X3
% 0.26/0.68                            = ( bit0 @ M4 ) )
% 0.26/0.68                         => ! [N2: num] :
% 0.26/0.68                              ( ( Xa
% 0.26/0.68                                = ( bit1 @ N2 ) )
% 0.26/0.68                             => ( ( Y3
% 0.26/0.68                                  = ( bit1 @ ( bit_un6697907153464112080or_num @ M4 @ N2 ) ) )
% 0.26/0.68                               => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) )
% 0.26/0.68                     => ( ! [M4: num] :
% 0.26/0.68                            ( ( X3
% 0.26/0.68                              = ( bit1 @ M4 ) )
% 0.26/0.68                           => ( ( Xa = one )
% 0.26/0.68                             => ( ( Y3
% 0.26/0.68                                  = ( bit1 @ M4 ) )
% 0.26/0.68                               => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 0.26/0.68                       => ( ! [M4: num] :
% 0.26/0.68                              ( ( X3
% 0.26/0.68                                = ( bit1 @ M4 ) )
% 0.26/0.68                             => ! [N2: num] :
% 0.26/0.68                                  ( ( Xa
% 0.26/0.68                                    = ( bit0 @ N2 ) )
% 0.26/0.68                                 => ( ( Y3
% 0.26/0.68                                      = ( bit1 @ ( bit_un6697907153464112080or_num @ M4 @ N2 ) ) )
% 0.26/0.68                                   => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 0.26/0.68                         => ~ ! [M4: num] :
% 0.26/0.68                                ( ( X3
% 0.26/0.68                                  = ( bit1 @ M4 ) )
% 0.26/0.68                               => ! [N2: num] :
% 0.26/0.68                                    ( ( Xa
% 0.26/0.68                                      = ( bit1 @ N2 ) )
% 0.26/0.68                                   => ( ( Y3
% 0.26/0.68                                        = ( bit1 @ ( bit_un6697907153464112080or_num @ M4 @ N2 ) ) )
% 0.26/0.68                                     => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % or_num.pelims
% 0.26/0.68  thf(fact_10187_or__num__dict,axiom,
% 0.26/0.68      bit_un6697907153464112080or_num = bit_un2785000775030745342or_num ).
% 0.26/0.68  
% 0.26/0.68  % or_num_dict
% 0.26/0.68  thf(fact_10188_or__num__rel__dict,axiom,
% 0.26/0.68      bit_un4773296044027857193um_rel = bit_un6909899581280750971um_rel ).
% 0.26/0.68  
% 0.26/0.68  % or_num_rel_dict
% 0.26/0.68  thf(fact_10189_unit__factor__simps_I1_J,axiom,
% 0.26/0.68      ( ( unit_f2748546683901255202or_nat @ zero_zero_nat )
% 0.26/0.68      = zero_zero_nat ) ).
% 0.26/0.68  
% 0.26/0.68  % unit_factor_simps(1)
% 0.26/0.68  thf(fact_10190_unit__factor__nat__def,axiom,
% 0.26/0.68      ( unit_f2748546683901255202or_nat
% 0.26/0.68      = ( ^ [N3: nat] : ( if_nat @ ( N3 = zero_zero_nat ) @ zero_zero_nat @ one_one_nat ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % unit_factor_nat_def
% 0.26/0.68  thf(fact_10191_VEBT__internal_Ogreater_Osimps,axiom,
% 0.26/0.68      ( vEBT_VEBT_greater
% 0.26/0.68      = ( vEBT_V2881884560877996034ft_nat
% 0.26/0.68        @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % VEBT_internal.greater.simps
% 0.26/0.68  thf(fact_10192_VEBT__internal_Ogreater_Oelims_I1_J,axiom,
% 0.26/0.68      ! [X3: option_nat,Xa: option_nat,Y3: $o] :
% 0.26/0.68        ( ( ( vEBT_VEBT_greater @ X3 @ Xa )
% 0.26/0.68          = Y3 )
% 0.26/0.68       => ( Y3
% 0.26/0.68          = ( vEBT_V2881884560877996034ft_nat
% 0.26/0.68            @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X )
% 0.26/0.68            @ X3
% 0.26/0.68            @ Xa ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % VEBT_internal.greater.elims(1)
% 0.26/0.68  thf(fact_10193_VEBT__internal_Ogreater_Oelims_I2_J,axiom,
% 0.26/0.68      ! [X3: option_nat,Xa: option_nat] :
% 0.26/0.68        ( ( vEBT_VEBT_greater @ X3 @ Xa )
% 0.26/0.68       => ( vEBT_V2881884560877996034ft_nat
% 0.26/0.68          @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X )
% 0.26/0.68          @ X3
% 0.26/0.68          @ Xa ) ) ).
% 0.26/0.68  
% 0.26/0.68  % VEBT_internal.greater.elims(2)
% 0.26/0.68  thf(fact_10194_VEBT__internal_Ogreater_Oelims_I3_J,axiom,
% 0.26/0.68      ! [X3: option_nat,Xa: option_nat] :
% 0.26/0.68        ( ~ ( vEBT_VEBT_greater @ X3 @ Xa )
% 0.26/0.68       => ~ ( vEBT_V2881884560877996034ft_nat
% 0.26/0.68            @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X )
% 0.26/0.68            @ X3
% 0.26/0.68            @ Xa ) ) ).
% 0.26/0.68  
% 0.26/0.68  % VEBT_internal.greater.elims(3)
% 0.26/0.68  thf(fact_10195_VEBT__internal_Oless_Osimps,axiom,
% 0.26/0.68      ( vEBT_VEBT_less
% 0.26/0.68      = ( vEBT_V2881884560877996034ft_nat @ ord_less_nat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % VEBT_internal.less.simps
% 0.26/0.68  thf(fact_10196_VEBT__internal_Oless_Oelims_I1_J,axiom,
% 0.26/0.68      ! [X3: option_nat,Xa: option_nat,Y3: $o] :
% 0.26/0.68        ( ( ( vEBT_VEBT_less @ X3 @ Xa )
% 0.26/0.68          = Y3 )
% 0.26/0.68       => ( Y3
% 0.26/0.68          = ( vEBT_V2881884560877996034ft_nat @ ord_less_nat @ X3 @ Xa ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % VEBT_internal.less.elims(1)
% 0.26/0.68  thf(fact_10197_VEBT__internal_Oless_Oelims_I2_J,axiom,
% 0.26/0.68      ! [X3: option_nat,Xa: option_nat] :
% 0.26/0.68        ( ( vEBT_VEBT_less @ X3 @ Xa )
% 0.26/0.68       => ( vEBT_V2881884560877996034ft_nat @ ord_less_nat @ X3 @ Xa ) ) ).
% 0.26/0.68  
% 0.26/0.68  % VEBT_internal.less.elims(2)
% 0.26/0.68  thf(fact_10198_VEBT__internal_Oless_Oelims_I3_J,axiom,
% 0.26/0.68      ! [X3: option_nat,Xa: option_nat] :
% 0.26/0.68        ( ~ ( vEBT_VEBT_less @ X3 @ Xa )
% 0.26/0.68       => ~ ( vEBT_V2881884560877996034ft_nat @ ord_less_nat @ X3 @ Xa ) ) ).
% 0.26/0.68  
% 0.26/0.68  % VEBT_internal.less.elims(3)
% 0.26/0.68  thf(fact_10199_VEBT__internal_Olesseq_Oelims_I3_J,axiom,
% 0.26/0.68      ! [X3: option_nat,Xa: option_nat] :
% 0.26/0.68        ( ~ ( vEBT_VEBT_lesseq @ X3 @ Xa )
% 0.26/0.68       => ~ ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat @ X3 @ Xa ) ) ).
% 0.26/0.68  
% 0.26/0.68  % VEBT_internal.lesseq.elims(3)
% 0.26/0.68  thf(fact_10200_VEBT__internal_Olesseq_Oelims_I2_J,axiom,
% 0.26/0.68      ! [X3: option_nat,Xa: option_nat] :
% 0.26/0.68        ( ( vEBT_VEBT_lesseq @ X3 @ Xa )
% 0.26/0.68       => ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat @ X3 @ Xa ) ) ).
% 0.26/0.68  
% 0.26/0.68  % VEBT_internal.lesseq.elims(2)
% 0.26/0.68  thf(fact_10201_VEBT__internal_Olesseq_Oelims_I1_J,axiom,
% 0.26/0.68      ! [X3: option_nat,Xa: option_nat,Y3: $o] :
% 0.26/0.68        ( ( ( vEBT_VEBT_lesseq @ X3 @ Xa )
% 0.26/0.68          = Y3 )
% 0.26/0.68       => ( Y3
% 0.26/0.68          = ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat @ X3 @ Xa ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % VEBT_internal.lesseq.elims(1)
% 0.26/0.68  thf(fact_10202_VEBT__internal_Olesseq_Osimps,axiom,
% 0.26/0.68      ( vEBT_VEBT_lesseq
% 0.26/0.68      = ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat ) ) ).
% 0.26/0.68  
% 0.26/0.68  % VEBT_internal.lesseq.simps
% 0.26/0.68  thf(fact_10203_lcm__0__iff__nat,axiom,
% 0.26/0.68      ! [M: nat,N: nat] :
% 0.26/0.68        ( ( ( gcd_lcm_nat @ M @ N )
% 0.26/0.68          = zero_zero_nat )
% 0.26/0.68        = ( ( M = zero_zero_nat )
% 0.26/0.68          | ( N = zero_zero_nat ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % lcm_0_iff_nat
% 0.26/0.68  thf(fact_10204_lcm__0__iff__int,axiom,
% 0.26/0.68      ! [M: int,N: int] :
% 0.26/0.68        ( ( ( gcd_lcm_int @ M @ N )
% 0.26/0.68          = zero_zero_int )
% 0.26/0.68        = ( ( M = zero_zero_int )
% 0.26/0.68          | ( N = zero_zero_int ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % lcm_0_iff_int
% 0.26/0.68  thf(fact_10205_lcm__int__int__eq,axiom,
% 0.26/0.68      ! [M: nat,N: nat] :
% 0.26/0.68        ( ( gcd_lcm_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.26/0.68        = ( semiri1314217659103216013at_int @ ( gcd_lcm_nat @ M @ N ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % lcm_int_int_eq
% 0.26/0.68  thf(fact_10206_lcm__1__iff__nat,axiom,
% 0.26/0.68      ! [M: nat,N: nat] :
% 0.26/0.68        ( ( ( gcd_lcm_nat @ M @ N )
% 0.26/0.68          = ( suc @ zero_zero_nat ) )
% 0.26/0.68        = ( ( M
% 0.26/0.68            = ( suc @ zero_zero_nat ) )
% 0.26/0.68          & ( N
% 0.26/0.68            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % lcm_1_iff_nat
% 0.26/0.68  thf(fact_10207_lcm__nat__abs__left__eq,axiom,
% 0.26/0.68      ! [K: int,N: nat] :
% 0.26/0.68        ( ( gcd_lcm_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 0.26/0.68        = ( nat2 @ ( gcd_lcm_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  % lcm_nat_abs_left_eq
% 0.26/0.68  
% 0.26/0.68  % Helper facts (44)
% 0.26/0.68  thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 0.26/0.68      ! [X3: int,Y3: int] :
% 0.26/0.68        ( ( if_int @ $false @ X3 @ Y3 )
% 0.26/0.68        = Y3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 0.26/0.68      ! [X3: int,Y3: int] :
% 0.26/0.68        ( ( if_int @ $true @ X3 @ Y3 )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 0.26/0.68      ! [X3: nat,Y3: nat] :
% 0.26/0.68        ( ( if_nat @ $false @ X3 @ Y3 )
% 0.26/0.68        = Y3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 0.26/0.68      ! [X3: nat,Y3: nat] :
% 0.26/0.68        ( ( if_nat @ $true @ X3 @ Y3 )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 0.26/0.68      ! [X3: num,Y3: num] :
% 0.26/0.68        ( ( if_num @ $false @ X3 @ Y3 )
% 0.26/0.68        = Y3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 0.26/0.68      ! [X3: num,Y3: num] :
% 0.26/0.68        ( ( if_num @ $true @ X3 @ Y3 )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 0.26/0.68      ! [X3: rat,Y3: rat] :
% 0.26/0.68        ( ( if_rat @ $false @ X3 @ Y3 )
% 0.26/0.68        = Y3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 0.26/0.68      ! [X3: rat,Y3: rat] :
% 0.26/0.68        ( ( if_rat @ $true @ X3 @ Y3 )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 0.26/0.68      ! [X3: real,Y3: real] :
% 0.26/0.68        ( ( if_real @ $false @ X3 @ Y3 )
% 0.26/0.68        = Y3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 0.26/0.68      ! [X3: real,Y3: real] :
% 0.26/0.68        ( ( if_real @ $true @ X3 @ Y3 )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 0.26/0.68      ! [P: real > $o] :
% 0.26/0.68        ( ( P @ ( fChoice_real @ P ) )
% 0.26/0.68        = ( ? [X8: real] : ( P @ X8 ) ) ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 0.26/0.68      ! [X3: complex,Y3: complex] :
% 0.26/0.68        ( ( if_complex @ $false @ X3 @ Y3 )
% 0.26/0.68        = Y3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 0.26/0.68      ! [X3: complex,Y3: complex] :
% 0.26/0.68        ( ( if_complex @ $true @ X3 @ Y3 )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 0.26/0.68      ! [X3: extended_enat,Y3: extended_enat] :
% 0.26/0.68        ( ( if_Extended_enat @ $false @ X3 @ Y3 )
% 0.26/0.68        = Y3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 0.26/0.68      ! [X3: extended_enat,Y3: extended_enat] :
% 0.26/0.68        ( ( if_Extended_enat @ $true @ X3 @ Y3 )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 0.26/0.68      ! [X3: code_integer,Y3: code_integer] :
% 0.26/0.68        ( ( if_Code_integer @ $false @ X3 @ Y3 )
% 0.26/0.68        = Y3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 0.26/0.68      ! [X3: code_integer,Y3: code_integer] :
% 0.26/0.68        ( ( if_Code_integer @ $true @ X3 @ Y3 )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 0.26/0.68      ! [X3: set_int,Y3: set_int] :
% 0.26/0.68        ( ( if_set_int @ $false @ X3 @ Y3 )
% 0.26/0.68        = Y3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 0.26/0.68      ! [X3: set_int,Y3: set_int] :
% 0.26/0.68        ( ( if_set_int @ $true @ X3 @ Y3 )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_2_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 0.26/0.68      ! [X3: set_nat,Y3: set_nat] :
% 0.26/0.68        ( ( if_set_nat @ $false @ X3 @ Y3 )
% 0.26/0.68        = Y3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_1_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 0.26/0.68      ! [X3: set_nat,Y3: set_nat] :
% 0.26/0.68        ( ( if_set_nat @ $true @ X3 @ Y3 )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 0.26/0.68      ! [X3: vEBT_VEBT,Y3: vEBT_VEBT] :
% 0.26/0.68        ( ( if_VEBT_VEBT @ $false @ X3 @ Y3 )
% 0.26/0.68        = Y3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 0.26/0.68      ! [X3: vEBT_VEBT,Y3: vEBT_VEBT] :
% 0.26/0.68        ( ( if_VEBT_VEBT @ $true @ X3 @ Y3 )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 0.26/0.68      ! [X3: list_int,Y3: list_int] :
% 0.26/0.68        ( ( if_list_int @ $false @ X3 @ Y3 )
% 0.26/0.68        = Y3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 0.26/0.68      ! [X3: list_int,Y3: list_int] :
% 0.26/0.68        ( ( if_list_int @ $true @ X3 @ Y3 )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 0.26/0.68      ! [X3: list_nat,Y3: list_nat] :
% 0.26/0.68        ( ( if_list_nat @ $false @ X3 @ Y3 )
% 0.26/0.68        = Y3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 0.26/0.68      ! [X3: list_nat,Y3: list_nat] :
% 0.26/0.68        ( ( if_list_nat @ $true @ X3 @ Y3 )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.26/0.68      ! [X3: int > int,Y3: int > int] :
% 0.26/0.68        ( ( if_int_int @ $false @ X3 @ Y3 )
% 0.26/0.68        = Y3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.26/0.68      ! [X3: int > int,Y3: int > int] :
% 0.26/0.68        ( ( if_int_int @ $true @ X3 @ Y3 )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_2_1_If_001_062_It__Nat__Onat_Mt__Rat__Orat_J_T,axiom,
% 0.26/0.68      ! [X3: nat > rat,Y3: nat > rat] :
% 0.26/0.68        ( ( if_nat_rat @ $false @ X3 @ Y3 )
% 0.26/0.68        = Y3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_1_1_If_001_062_It__Nat__Onat_Mt__Rat__Orat_J_T,axiom,
% 0.26/0.68      ! [X3: nat > rat,Y3: nat > rat] :
% 0.26/0.68        ( ( if_nat_rat @ $true @ X3 @ Y3 )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 0.26/0.68      ! [X3: option_nat,Y3: option_nat] :
% 0.26/0.68        ( ( if_option_nat @ $false @ X3 @ Y3 )
% 0.26/0.68        = Y3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 0.26/0.68      ! [X3: option_nat,Y3: option_nat] :
% 0.26/0.68        ( ( if_option_nat @ $true @ X3 @ Y3 )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 0.26/0.68      ! [X3: option_num,Y3: option_num] :
% 0.26/0.68        ( ( if_option_num @ $false @ X3 @ Y3 )
% 0.26/0.68        = Y3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 0.26/0.68      ! [X3: option_num,Y3: option_num] :
% 0.26/0.68        ( ( if_option_num @ $true @ X3 @ Y3 )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.26/0.68      ! [X3: product_prod_int_int,Y3: product_prod_int_int] :
% 0.26/0.68        ( ( if_Pro3027730157355071871nt_int @ $false @ X3 @ Y3 )
% 0.26/0.68        = Y3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.26/0.68      ! [X3: product_prod_int_int,Y3: product_prod_int_int] :
% 0.26/0.68        ( ( if_Pro3027730157355071871nt_int @ $true @ X3 @ Y3 )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.26/0.68      ! [X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.26/0.68        ( ( if_Pro6206227464963214023at_nat @ $false @ X3 @ Y3 )
% 0.26/0.68        = Y3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.26/0.68      ! [X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.26/0.68        ( ( if_Pro6206227464963214023at_nat @ $true @ X3 @ Y3 )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 0.26/0.68      ! [X3: produc6271795597528267376eger_o,Y3: produc6271795597528267376eger_o] :
% 0.26/0.68        ( ( if_Pro5737122678794959658eger_o @ $false @ X3 @ Y3 )
% 0.26/0.68        = Y3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 0.26/0.68      ! [X3: produc6271795597528267376eger_o,Y3: produc6271795597528267376eger_o] :
% 0.26/0.68        ( ( if_Pro5737122678794959658eger_o @ $true @ X3 @ Y3 )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.26/0.68      ! [P: $o] :
% 0.26/0.68        ( ( P = $true )
% 0.26/0.68        | ( P = $false ) ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.26/0.68      ! [X3: produc8923325533196201883nteger,Y3: produc8923325533196201883nteger] :
% 0.26/0.68        ( ( if_Pro6119634080678213985nteger @ $false @ X3 @ Y3 )
% 0.26/0.68        = Y3 ) ).
% 0.26/0.68  
% 0.26/0.68  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.26/0.68      ! [X3: produc8923325533196201883nteger,Y3: produc8923325533196201883nteger] :
% 0.26/0.68        ( ( if_Pro6119634080678213985nteger @ $true @ X3 @ Y3 )
% 0.26/0.68        = X3 ) ).
% 0.26/0.68  
% 0.26/0.68  % Conjectures (1)
% 0.26/0.68  thf(conj_0,conjecture,
% 0.26/0.68      ord_less_nat @ x @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 0.26/0.68  
% 0.26/0.68  %------------------------------------------------------------------------------
% 0.26/0.68  ------------------------
% 11.21/4.15  ---- Embedded in THF ---
% 11.21/4.15  %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 11.21/4.15  %%% Generated on Tue Feb 24 08:40:38 EST 2026
% 11.21/4.15  %%% using '$$dhol' embedding, version 1.3.0.
% 11.21/4.15  %%% Logic specification used:
% 11.21/4.15  %%% thf(spec, logic, $$dhol).
% 11.21/4.15  
% 11.21/4.15  % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.i3enffnfiD/DTF2DTF27763.p
% See solution above
% 11.25/4.20  ------------------------
% 15.48/8.45  ---- Cleaned THF ---
% 15.48/8.45  thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
% 15.48/8.45      produc1319942482725812455at_nat: $tType ).
% 15.48/8.45  
% 15.48/8.45  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,
% 15.48/8.45      produc5542196010084753463at_nat: $tType ).
% 15.48/8.45  
% 15.48/8.45  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,
% 15.48/8.45      produc5491161045314408544at_nat: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 15.48/8.45      list_P5464809261938338413at_nat: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 15.48/8.45      set_Pr4329608150637261639at_nat: $tType ).
% 15.48/8.45  
% 15.48/8.45  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,
% 15.48/8.45      produc1193250871479095198on_num: $tType ).
% 15.48/8.45  
% 15.48/8.45  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,
% 15.48/8.45      produc8306885398267862888on_nat: $tType ).
% 15.48/8.45  
% 15.48/8.45  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,
% 15.48/8.45      produc6121120109295599847at_nat: $tType ).
% 15.48/8.45  
% 15.48/8.45  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,
% 15.48/8.45      produc7036089656553540234on_num: $tType ).
% 15.48/8.45  
% 15.48/8.45  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,
% 15.48/8.45      produc2233624965454879586on_nat: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 15.48/8.45      produc3843707927480180839at_nat: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 15.48/8.45      set_Pr8693737435421807431at_nat: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 15.48/8.45      produc859450856879609959at_nat: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__Set__Oset_It__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J_J,type,
% 15.48/8.45      set_fi4554929511873752355omplex: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 15.48/8.45      list_P7413028617227757229T_VEBT: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J,type,
% 15.48/8.45      produc3447558737645232053on_num: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J,type,
% 15.48/8.45      produc4953844613479565601on_nat: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__Set__Oset_It__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J_J,type,
% 15.48/8.45      set_fi7789364187291644575l_real: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 15.48/8.45      filter6041513312241820739omplex: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 15.48/8.45      list_P7037539587688870467BT_nat: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
% 15.48/8.45      list_P4547456442757143711BT_int: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__Set__Oset_It__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 15.48/8.45      set_li5450038453877631591at_nat: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 15.48/8.45      produc8243902056947475879T_VEBT: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 15.48/8.45      set_Pr5085853215250843933omplex: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 15.48/8.45      produc8923325533196201883nteger: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Extended____Nat__Oenat_J,type,
% 15.48/8.45      produc7272778201969148633d_enat: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 15.48/8.45      list_P3126845725202233233VEBT_o: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 15.48/8.45      list_P7495141550334521929T_VEBT: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 15.48/8.45      filter2146258269922977983l_real: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 15.48/8.45      option4927543243414619207at_nat: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 15.48/8.45      set_Pr6218003697084177305l_real: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J_J,type,
% 15.48/8.45      list_P3744719386663036955um_num: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_J,type,
% 15.48/8.45      list_P1726324292696863441at_num: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 15.48/8.45      list_P6011104703257516679at_nat: $tType ).
% 15.48/8.45  
% 15.48/8.45  thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 15.48/8.45      produc9072475918466114483BT_nat: $tType ).
% 15.48/8.45  
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% 15.48/8.45      bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 15.48/8.45      bNF_re3715656647883201625at_nat: ( int > int > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( int > nat ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum,type,
% 15.48/8.45      bNF_re7626690874201225453um_num: ( int > int > $o ) > ( num > num > $o ) > ( int > num ) > ( int > num ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 15.48/8.45      bNF_re6250860962936578807nt_int: ( int > int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 15.48/8.45      bNF_re2214769303045360666nt_rat: ( int > int > $o ) > ( product_prod_int_int > rat > $o ) > ( int > product_prod_int_int ) > ( int > rat ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 15.48/8.45      bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
% 15.48/8.45      bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 15.48/8.45      bNF_re4153400068438556298nteger: ( nat > nat > $o ) > ( int > code_integer > $o ) > ( nat > int ) > ( nat > code_integer ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
% 15.48/8.45      bNF_re6650684261131312217nt_int: ( nat > nat > $o ) > ( int > int > $o ) > ( nat > int ) > ( nat > int ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 15.48/8.45      bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001_062_It__Num__Onum_Mt__Int__Oint_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
% 15.48/8.45      bNF_re7876454716742015248nteger: ( num > num > $o ) > ( ( num > int ) > ( num > code_integer ) > $o ) > ( num > num > int ) > ( num > num > code_integer ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001_062_It__Num__Onum_Mt__Int__Oint_J_001_062_It__Num__Onum_Mt__Int__Oint_J,type,
% 15.48/8.45      bNF_re8402795839162346335um_int: ( num > num > $o ) > ( ( num > int ) > ( num > int ) > $o ) > ( num > num > int ) > ( num > num > int ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 15.48/8.45      bNF_re6501075790457514782nteger: ( num > num > $o ) > ( int > code_integer > $o ) > ( num > int ) > ( num > code_integer ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Int__Oint,type,
% 15.48/8.45      bNF_re1822329894187522285nt_int: ( num > num > $o ) > ( int > int > $o ) > ( num > int ) > ( num > int ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001_Eo,type,
% 15.48/8.45      bNF_re8699439704749558557nt_o_o: ( product_prod_int_int > product_prod_int_int > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 15.48/8.45      bNF_re7145576690424134365nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001_Eo_001_Eo,type,
% 15.48/8.45      bNF_re1494630372529172596at_o_o: ( product_prod_int_int > rat > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( rat > $o ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 15.48/8.45      bNF_re8279943556446156061nt_rat: ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_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,
% 15.48/8.45      bNF_re717283939379294677_int_o: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_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,
% 15.48/8.45      bNF_re7408651293131936558nt_int: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_Eo_001_Eo,type,
% 15.48/8.45      bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 15.48/8.45      bNF_re4555766996558763186at_nat: ( product_prod_nat_nat > int > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 15.48/8.45      bNF_re7400052026677387805at_int: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_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__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 15.48/8.45      bNF_re4202695980764964119_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_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__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 15.48/8.45      bNF_re3099431351363272937at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 15.48/8.45      bNF_re3666534408544137501at_o_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 15.48/8.45      bNF_re8246922863344978751at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > nat ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 15.48/8.45      bNF_re2241393799969408733at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Binomial_Obinomial,type,
% 15.48/8.45      binomial: nat > nat > nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Binomial_Ogbinomial_001t__Complex__Ocomplex,type,
% 15.48/8.45      gbinomial_complex: complex > nat > complex ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Binomial_Ogbinomial_001t__Int__Oint,type,
% 15.48/8.45      gbinomial_int: int > nat > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Binomial_Ogbinomial_001t__Nat__Onat,type,
% 15.48/8.45      gbinomial_nat: nat > nat > nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Binomial_Ogbinomial_001t__Rat__Orat,type,
% 15.48/8.45      gbinomial_rat: rat > nat > rat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Binomial_Ogbinomial_001t__Real__Oreal,type,
% 15.48/8.45      gbinomial_real: real > nat > real ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Oand__int__rel,type,
% 15.48/8.45      bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Oand__not__num,type,
% 15.48/8.45      bit_and_not_num: num > num > option_num ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Oand__not__num__rel,type,
% 15.48/8.45      bit_and_not_num_rel: product_prod_num_num > product_prod_num_num > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Oconcat__bit,type,
% 15.48/8.45      bit_concat_bit: nat > int > int > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Oor__not__num__neg,type,
% 15.48/8.45      bit_or_not_num_neg: num > num > num ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Oor__not__num__neg__rel,type,
% 15.48/8.45      bit_or3848514188828904588eg_rel: product_prod_num_num > product_prod_num_num > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Oring__bit__operations__class_Onot_001t__Code____Numeral__Ointeger,type,
% 15.48/8.45      bit_ri7632146776885996613nteger: code_integer > code_integer ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Oring__bit__operations__class_Onot_001t__Int__Oint,type,
% 15.48/8.45      bit_ri7919022796975470100ot_int: int > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Code____Numeral__Ointeger,type,
% 15.48/8.45      bit_ri6519982836138164636nteger: nat > code_integer > code_integer ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Int__Oint,type,
% 15.48/8.45      bit_ri631733984087533419it_int: nat > int > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Int__Oint,type,
% 15.48/8.45      bit_se725231765392027082nd_int: int > int > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Nat__Onat,type,
% 15.48/8.45      bit_se727722235901077358nd_nat: nat > nat > nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Int__Oint,type,
% 15.48/8.45      bit_se8568078237143864401it_int: nat > int > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Nat__Onat,type,
% 15.48/8.45      bit_se8570568707652914677it_nat: nat > nat > nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Code____Numeral__Ointeger,type,
% 15.48/8.45      bit_se1345352211410354436nteger: nat > code_integer > code_integer ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Int__Oint,type,
% 15.48/8.45      bit_se2159334234014336723it_int: nat > int > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Nat__Onat,type,
% 15.48/8.45      bit_se2161824704523386999it_nat: nat > nat > nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Int__Oint,type,
% 15.48/8.45      bit_se2000444600071755411sk_int: nat > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Nat__Onat,type,
% 15.48/8.45      bit_se2002935070580805687sk_nat: nat > nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Code____Numeral__Ointeger,type,
% 15.48/8.45      bit_se1080825931792720795nteger: code_integer > code_integer > code_integer ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Int__Oint,type,
% 15.48/8.45      bit_se1409905431419307370or_int: int > int > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Nat__Onat,type,
% 15.48/8.45      bit_se1412395901928357646or_nat: nat > nat > nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Int__Oint,type,
% 15.48/8.45      bit_se545348938243370406it_int: nat > int > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Nat__Onat,type,
% 15.48/8.45      bit_se547839408752420682it_nat: nat > nat > nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Code____Numeral__Ointeger,type,
% 15.48/8.45      bit_se2793503036327961859nteger: nat > code_integer > code_integer ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Int__Oint,type,
% 15.48/8.45      bit_se7879613467334960850it_int: nat > int > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Nat__Onat,type,
% 15.48/8.45      bit_se7882103937844011126it_nat: nat > nat > nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Code____Numeral__Ointeger,type,
% 15.48/8.45      bit_se1745604003318907178nteger: nat > code_integer > code_integer ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Int__Oint,type,
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% 15.48/8.45  
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% 15.48/8.45  thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal,type,
% 15.48/8.45      inverse_inverse_real: real > real ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Filter_Oat__bot_001t__Real__Oreal,type,
% 15.48/8.45      at_bot_real: filter_real ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Filter_Oat__top_001t__Int__Oint,type,
% 15.48/8.45      at_top_int: filter_int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Filter_Oat__top_001t__Nat__Onat,type,
% 15.48/8.45      at_top_nat: filter_nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Filter_Oat__top_001t__Real__Oreal,type,
% 15.48/8.45      at_top_real: filter_real ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Filter_Oeventually_001t__Nat__Onat,type,
% 15.48/8.45      eventually_nat: ( nat > $o ) > filter_nat > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Filter_Oeventually_001t__Real__Oreal,type,
% 15.48/8.45      eventually_real: ( real > $o ) > filter_real > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Filter_Ofilterlim_001t__Int__Oint_001t__Nat__Onat,type,
% 15.48/8.45      filterlim_int_nat: ( int > nat ) > filter_nat > filter_int > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Int__Oint,type,
% 15.48/8.45      filterlim_nat_int: ( nat > int ) > filter_int > filter_nat > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Nat__Onat,type,
% 15.48/8.45      filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Real__Oreal,type,
% 15.48/8.45      filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Filter_Ofilterlim_001t__Real__Oreal_001t__Real__Oreal,type,
% 15.48/8.45      filterlim_real_real: ( real > real ) > filter_real > filter_real > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Filter_Ofiltermap_001t__Real__Oreal_001t__Real__Oreal,type,
% 15.48/8.45      filtermap_real_real: ( real > real ) > filter_real > filter_real ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Filter_Oprincipal_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
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% 15.48/8.45  thf(sy_c_Finite__Set_Ocard_001_Eo,type,
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% 15.48/8.45  thf(sy_c_Finite__Set_Ocard_001t__Complex__Ocomplex,type,
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% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Finite__Set_Ocard_001t__Int__Oint,type,
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% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Finite__Set_Ocard_001t__List__Olist_It__Nat__Onat_J,type,
% 15.48/8.45      finite_card_list_nat: set_list_nat > nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Finite__Set_Ocard_001t__Nat__Onat,type,
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% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Finite__Set_Ocard_001t__Set__Oset_It__Nat__Onat_J,type,
% 15.48/8.45      finite_card_set_nat: set_set_nat > nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Finite__Set_Ocard_001t__String__Ochar,type,
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% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Finite__Set_Ofinite_001_Eo,type,
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% 15.48/8.45  thf(sy_c_Finite__Set_Ofinite_001t__Complex__Ocomplex,type,
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% 15.48/8.45  
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% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_I_Eo_J,type,
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% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Complex__Ocomplex_J,type,
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% 15.48/8.45  
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% 15.48/8.45  thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Nat__Onat_J,type,
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% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum,type,
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% 15.48/8.45  thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Real__Oreal_001t__Nat__Onat,type,
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% 15.48/8.45      id_o: $o > $o ).
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% 15.48/8.45  thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__String__Ochar,type,
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% 15.48/8.45  thf(sy_c_Fun_Oinj__on_001t__Real__Oreal_001t__Real__Oreal,type,
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% 15.48/8.45  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,
% 15.48/8.45      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 ).
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% 15.48/8.45      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 ).
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% 15.48/8.45      gcd_Gcd_nat: set_nat > nat ).
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% 15.48/8.45  thf(sy_c_GCD_Obezw,type,
% 15.48/8.45      bezw: nat > nat > product_prod_int_int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_GCD_Obezw__rel,type,
% 15.48/8.45      bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Code____Numeral__Ointeger,type,
% 15.48/8.45      gcd_gcd_Code_integer: code_integer > code_integer > code_integer ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Int__Oint,type,
% 15.48/8.45      gcd_gcd_int: int > int > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Nat__Onat,type,
% 15.48/8.45      gcd_gcd_nat: nat > nat > nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_GCD_Ogcd__class_Olcm_001t__Int__Oint,type,
% 15.48/8.45      gcd_lcm_int: int > int > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_GCD_Ogcd__class_Olcm_001t__Nat__Onat,type,
% 15.48/8.45      gcd_lcm_nat: nat > nat > nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_GCD_Ogcd__nat__rel,type,
% 15.48/8.45      gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Oabs__class_Oabs_001t__Code____Numeral__Ointeger,type,
% 15.48/8.45      abs_abs_Code_integer: code_integer > code_integer ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint,type,
% 15.48/8.45      abs_abs_int: int > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Oabs__class_Oabs_001t__Rat__Orat,type,
% 15.48/8.45      abs_abs_rat: rat > rat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal,type,
% 15.48/8.45      abs_abs_real: real > real ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Ocomm__monoid_001t__Nat__Onat,type,
% 15.48/8.45      comm_monoid_nat: ( nat > nat > nat ) > nat > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Ominus__class_Ominus_001t__Code____Numeral__Ointeger,type,
% 15.48/8.45      minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Ominus__class_Ominus_001t__Complex__Ocomplex,type,
% 15.48/8.45      minus_minus_complex: complex > complex > complex ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Ominus__class_Ominus_001t__Extended____Nat__Oenat,type,
% 15.48/8.45      minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint,type,
% 15.48/8.45      minus_minus_int: int > int > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 15.48/8.45      minus_minus_nat: nat > nat > nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Ominus__class_Ominus_001t__Rat__Orat,type,
% 15.48/8.45      minus_minus_rat: rat > rat > rat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal,type,
% 15.48/8.45      minus_minus_real: real > real > real ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 15.48/8.45      minus_811609699411566653omplex: set_complex > set_complex > set_complex ).
% 15.48/8.45  
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% 15.48/8.45      minus_925952699566721837d_enat: set_Extended_enat > set_Extended_enat > set_Extended_enat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Int__Oint_J,type,
% 15.48/8.45      minus_minus_set_int: set_int > set_int > set_int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Nat__Onat_J,type,
% 15.48/8.45      minus_minus_set_nat: set_nat > set_nat > set_nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Real__Oreal_J,type,
% 15.48/8.45      minus_minus_set_real: set_real > set_real > set_real ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Omonoid_001t__Nat__Onat,type,
% 15.48/8.45      monoid_nat: ( nat > nat > nat ) > nat > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Oone__class_Oone_001t__Code____Numeral__Ointeger,type,
% 15.48/8.45      one_one_Code_integer: code_integer ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex,type,
% 15.48/8.45      one_one_complex: complex ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Oone__class_Oone_001t__Extended____Nat__Oenat,type,
% 15.48/8.45      one_on7984719198319812577d_enat: extended_enat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
% 15.48/8.45      one_one_int: int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 15.48/8.45      one_one_nat: nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Oone__class_Oone_001t__Rat__Orat,type,
% 15.48/8.45      one_one_rat: rat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal,type,
% 15.48/8.45      one_one_real: real ).
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% 15.48/8.45  thf(sy_c_Groups_Oplus__class_Oplus_001t__Code____Numeral__Ointeger,type,
% 15.48/8.45      plus_p5714425477246183910nteger: code_integer > code_integer > code_integer ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Oplus__class_Oplus_001t__Complex__Ocomplex,type,
% 15.48/8.45      plus_plus_complex: complex > complex > complex ).
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% 15.48/8.45  thf(sy_c_Groups_Oplus__class_Oplus_001t__Extended____Nat__Oenat,type,
% 15.48/8.45      plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Oplus__class_Oplus_001t__Int__Oint,type,
% 15.48/8.45      plus_plus_int: int > int > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 15.48/8.45      plus_plus_nat: nat > nat > nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Oplus__class_Oplus_001t__Num__Onum,type,
% 15.48/8.45      plus_plus_num: num > num > num ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Oplus__class_Oplus_001t__Rat__Orat,type,
% 15.48/8.45      plus_plus_rat: rat > rat > rat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal,type,
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% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Oplus__class_Oplus_001t__String__Oliteral,type,
% 15.48/8.45      plus_plus_literal: literal > literal > literal ).
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% 15.48/8.45      sgn_sgn_Code_integer: code_integer > code_integer ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Osgn__class_Osgn_001t__Complex__Ocomplex,type,
% 15.48/8.45      sgn_sgn_complex: complex > complex ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Osgn__class_Osgn_001t__Int__Oint,type,
% 15.48/8.45      sgn_sgn_int: int > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Osgn__class_Osgn_001t__Rat__Orat,type,
% 15.48/8.45      sgn_sgn_rat: rat > rat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Osgn__class_Osgn_001t__Real__Oreal,type,
% 15.48/8.45      sgn_sgn_real: real > real ).
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% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Otimes__class_Otimes_001t__Complex__Ocomplex,type,
% 15.48/8.45      times_times_complex: complex > complex > complex ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Otimes__class_Otimes_001t__Extended____Nat__Oenat,type,
% 15.48/8.45      times_7803423173614009249d_enat: extended_enat > extended_enat > extended_enat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Otimes__class_Otimes_001t__Int__Oint,type,
% 15.48/8.45      times_times_int: int > int > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat,type,
% 15.48/8.45      times_times_nat: nat > nat > nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Otimes__class_Otimes_001t__Num__Onum,type,
% 15.48/8.45      times_times_num: num > num > num ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Otimes__class_Otimes_001t__Rat__Orat,type,
% 15.48/8.45      times_times_rat: rat > rat > rat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Otimes__class_Otimes_001t__Real__Oreal,type,
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% 15.48/8.45  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Code____Numeral__Ointeger,type,
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% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Complex__Ocomplex,type,
% 15.48/8.45      uminus1482373934393186551omplex: complex > complex ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Int__Oint,type,
% 15.48/8.45      uminus_uminus_int: int > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Rat__Orat,type,
% 15.48/8.45      uminus_uminus_rat: rat > rat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal,type,
% 15.48/8.45      uminus_uminus_real: real > real ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Nat__Onat_J,type,
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% 15.48/8.45  thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 15.48/8.45      zero_zero_nat: nat ).
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% 15.48/8.45  thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
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% 15.48/8.45  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Int__Oint,type,
% 15.48/8.45      inf_inf_int: int > int > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
% 15.48/8.45      inf_inf_nat: nat > nat > nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 15.48/8.45      inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Lattices_Osemilattice__neutr_001t__Nat__Onat,type,
% 15.48/8.45      semila9081495762789891438tr_nat: ( nat > nat > nat ) > nat > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 15.48/8.45      semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Lattices_Osup__class_Osup_001t__Extended____Nat__Oenat,type,
% 15.48/8.45      sup_su3973961784419623482d_enat: extended_enat > extended_enat > extended_enat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Lattices_Osup__class_Osup_001t__Int__Oint,type,
% 15.48/8.45      sup_sup_int: int > int > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 15.48/8.45      sup_sup_nat: nat > nat > nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 15.48/8.45      sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 15.48/8.45      sup_su5525570899277871387at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Extended____Nat__Oenat,type,
% 15.48/8.45      lattic921264341876707157d_enat: set_Extended_enat > extended_enat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Int__Oint,type,
% 15.48/8.45      lattic8263393255366662781ax_int: set_int > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 15.48/8.45      lattic8265883725875713057ax_nat: set_nat > nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Lifting_OQuotient_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal,type,
% 15.48/8.45      quotie3684837364556693515t_real: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > real ) > ( real > nat > rat ) > ( ( nat > rat ) > real > $o ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Lifting_OQuotient_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 15.48/8.45      quotie1194848508323700631at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int > $o ) > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Limits_OBfun_001t__Nat__Onat_001t__Real__Oreal,type,
% 15.48/8.45      bfun_nat_real: ( nat > real ) > filter_nat > $o ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_Limits_Oat__infinity_001t__Real__Oreal,type,
% 15.48/8.45      at_infinity_real: filter_real ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 15.48/8.45      append_int: list_int > list_int > list_int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 15.48/8.45      append_nat: list_nat > list_nat > list_nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_List_Ofold_001t__Int__Oint_001t__Int__Oint,type,
% 15.48/8.45      fold_int_int: ( int > int > int ) > list_int > int > int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_List_Ofold_001t__Nat__Onat_001t__Nat__Onat,type,
% 15.48/8.45      fold_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_List_Olast_001t__Nat__Onat,type,
% 15.48/8.45      last_nat: list_nat > nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 15.48/8.45      linord2614967742042102400et_nat: set_nat > list_nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 15.48/8.45      cons_int: int > list_int > list_int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 15.48/8.45      cons_nat: nat > list_nat > list_nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 15.48/8.45      nil_int: list_int ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 15.48/8.45      nil_nat: list_nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
% 15.48/8.45      hd_nat: list_nat > nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 15.48/8.45      map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 15.48/8.45  
% 15.48/8.45  thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 15.48/8.46      map_VE8901447254227204932T_VEBT: ( vEBT_VEBT > vEBT_VEBT ) > list_VEBT_VEBT > list_VEBT_VEBT ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Olist_Oset_001_Eo,type,
% 15.48/8.46      set_o2: list_o > set_o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 15.48/8.46      set_complex2: list_complex > set_complex ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Olist_Oset_001t__Extended____Nat__Oenat,type,
% 15.48/8.46      set_Extended_enat2: list_Extended_enat > set_Extended_enat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 15.48/8.46      set_int2: list_int > set_int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 15.48/8.46      set_nat2: list_nat > set_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Olist_Oset_001t__Option__Ooption_It__Nat__Onat_J,type,
% 15.48/8.46      set_option_nat2: list_option_nat > set_option_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 15.48/8.46      set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 15.48/8.46      set_Pr3765526544606949372at_nat: list_P5464809261938338413at_nat > set_Pr4329608150637261639at_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 15.48/8.46      set_real2: list_real > set_real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Olist_Oset_001t__Set__Oset_It__Nat__Onat_J,type,
% 15.48/8.46      set_set_nat2: list_set_nat > set_set_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 15.48/8.46      set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 15.48/8.46      size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Olist__update_001_Eo,type,
% 15.48/8.46      list_update_o: list_o > nat > $o > list_o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Olist__update_001t__Int__Oint,type,
% 15.48/8.46      list_update_int: list_int > nat > int > list_int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 15.48/8.46      list_update_nat: list_nat > nat > nat > list_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Olist__update_001t__Option__Ooption_It__Nat__Onat_J,type,
% 15.48/8.46      list_u3411377215356412978on_nat: list_option_nat > nat > option_nat > list_option_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Olist__update_001t__Real__Oreal,type,
% 15.48/8.46      list_update_real: list_real > nat > real > list_real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Olist__update_001t__Set__Oset_It__Nat__Onat_J,type,
% 15.48/8.46      list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Olist__update_001t__VEBT____Definitions__OVEBT,type,
% 15.48/8.46      list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Onth_001_Eo,type,
% 15.48/8.46      nth_o: list_o > nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Onth_001t__Int__Oint,type,
% 15.48/8.46      nth_int: list_int > nat > int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 15.48/8.46      nth_nat: list_nat > nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Onth_001t__Num__Onum,type,
% 15.48/8.46      nth_num: list_num > nat > num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Onth_001t__Option__Ooption_It__Nat__Onat_J,type,
% 15.48/8.46      nth_option_nat: list_option_nat > nat > option_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 15.48/8.46      nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 15.48/8.46      nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 15.48/8.46      nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 15.48/8.46      nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
% 15.48/8.46      nth_Pr8326237132889035090at_num: list_P1726324292696863441at_num > nat > product_prod_nat_num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 15.48/8.46      nth_Pr6456567536196504476um_num: list_P3744719386663036955um_num > nat > product_prod_num_num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 15.48/8.46      nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 15.48/8.46      nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 15.48/8.46      nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 15.48/8.46      nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 15.48/8.46      nth_real: list_real > nat > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 15.48/8.46      nth_set_nat: list_set_nat > nat > set_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 15.48/8.46      nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 15.48/8.46      product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 15.48/8.46      product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 15.48/8.46      product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 15.48/8.46      product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Num__Onum,type,
% 15.48/8.46      product_nat_num: list_nat > list_num > list_P1726324292696863441at_num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oproduct_001t__Num__Onum_001t__Num__Onum,type,
% 15.48/8.46      product_num_num: list_num > list_num > list_P3744719386663036955um_num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 15.48/8.46      product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 15.48/8.46      produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 15.48/8.46      produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 15.48/8.46      produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oreplicate_001t__Extended____Nat__Oenat,type,
% 15.48/8.46      replic7216382294607269926d_enat: nat > extended_enat > list_Extended_enat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 15.48/8.46      replicate_int: nat > int > list_int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 15.48/8.46      replicate_nat: nat > nat > list_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oreplicate_001t__Option__Ooption_It__Nat__Onat_J,type,
% 15.48/8.46      replicate_option_nat: nat > option_nat > list_option_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oreplicate_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 15.48/8.46      replic4235873036481779905at_nat: nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oreplicate_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 15.48/8.46      replic2264142908078655527at_nat: nat > produc3843707927480180839at_nat > list_P5464809261938338413at_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 15.48/8.46      replicate_real: nat > real > list_real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oreplicate_001t__Set__Oset_It__Nat__Onat_J,type,
% 15.48/8.46      replicate_set_nat: nat > set_nat > list_set_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 15.48/8.46      replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 15.48/8.46      sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 15.48/8.46      sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 15.48/8.46      take_nat: nat > list_nat > list_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Otake_001t__VEBT____Definitions__OVEBT,type,
% 15.48/8.46      take_VEBT_VEBT: nat > list_VEBT_VEBT > list_VEBT_VEBT ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oupt,type,
% 15.48/8.46      upt: nat > nat > list_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oupto,type,
% 15.48/8.46      upto: int > int > list_int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oupto__aux,type,
% 15.48/8.46      upto_aux: int > int > list_int > list_int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_List_Oupto__rel,type,
% 15.48/8.46      upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_OSuc,type,
% 15.48/8.46      suc: nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 15.48/8.46      compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 15.48/8.46      case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 15.48/8.46      case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 15.48/8.46      case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Onat_Opred,type,
% 15.48/8.46      pred: nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osemiring__1__class_ONats_001t__Complex__Ocomplex,type,
% 15.48/8.46      semiri3842193898606819883omplex: set_complex ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osemiring__1__class_ONats_001t__Int__Oint,type,
% 15.48/8.46      semiring_1_Nats_int: set_int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 15.48/8.46      semiri4939895301339042750nteger: nat > code_integer ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 15.48/8.46      semiri8010041392384452111omplex: nat > complex ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
% 15.48/8.46      semiri4216267220026989637d_enat: nat > extended_enat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 15.48/8.46      semiri1314217659103216013at_int: nat > int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 15.48/8.46      semiri1316708129612266289at_nat: nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 15.48/8.46      semiri681578069525770553at_rat: nat > rat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 15.48/8.46      semiri5074537144036343181t_real: nat > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 15.48/8.46      size_size_list_o: list_o > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 15.48/8.46      size_s3451745648224563538omplex: list_complex > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Extended____Nat__Oenat_J,type,
% 15.48/8.46      size_s3941691890525107288d_enat: list_Extended_enat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 15.48/8.46      size_size_list_int: list_int > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 15.48/8.46      size_size_list_nat: list_nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
% 15.48/8.46      size_size_list_num: list_num > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Option__Ooption_It__Nat__Onat_J_J,type,
% 15.48/8.46      size_s6086282163384603972on_nat: list_option_nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 15.48/8.46      size_s5460976970255530739at_nat: list_P6011104703257516679at_nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 15.48/8.46      size_size_list_real: list_real > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 15.48/8.46      size_s3254054031482475050et_nat: list_set_nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 15.48/8.46      size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 15.48/8.46      size_size_num: num > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Nat__Onat_J,type,
% 15.48/8.46      size_size_option_nat: option_nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
% 15.48/8.46      size_size_option_num: option_num > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 15.48/8.46      size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osize__class_Osize_001t__String__Ochar,type,
% 15.48/8.46      size_size_char: char > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 15.48/8.46      size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat__Bijection_Olist__decode,type,
% 15.48/8.46      nat_list_decode: nat > list_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat__Bijection_Olist__decode__rel,type,
% 15.48/8.46      nat_list_decode_rel: nat > nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat__Bijection_Olist__encode,type,
% 15.48/8.46      nat_list_encode: list_nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 15.48/8.46      nat_list_encode_rel: list_nat > list_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat__Bijection_Oprod__decode,type,
% 15.48/8.46      nat_prod_decode: nat > product_prod_nat_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 15.48/8.46      nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 15.48/8.46      nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 15.48/8.46      nat_prod_encode: product_prod_nat_nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat__Bijection_Oset__decode,type,
% 15.48/8.46      nat_set_decode: nat > set_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat__Bijection_Oset__encode,type,
% 15.48/8.46      nat_set_encode: set_nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Nat__Bijection_Otriangle,type,
% 15.48/8.46      nat_triangle: nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_NthRoot_Oroot,type,
% 15.48/8.46      root: nat > real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_NthRoot_Osqrt,type,
% 15.48/8.46      sqrt: real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_OBitM,type,
% 15.48/8.46      bitM: num > num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Oinc,type,
% 15.48/8.46      inc: num > num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Onat__of__num,type,
% 15.48/8.46      nat_of_num: num > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 15.48/8.46      neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 15.48/8.46      neg_nu7009210354673126013omplex: complex > complex ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 15.48/8.46      neg_numeral_dbl_int: int > int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 15.48/8.46      neg_numeral_dbl_rat: rat > rat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 15.48/8.46      neg_numeral_dbl_real: real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 15.48/8.46      neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 15.48/8.46      neg_nu6511756317524482435omplex: complex > complex ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 15.48/8.46      neg_nu3811975205180677377ec_int: int > int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 15.48/8.46      neg_nu3179335615603231917ec_rat: rat > rat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 15.48/8.46      neg_nu6075765906172075777c_real: real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
% 15.48/8.46      neg_nu5831290666863070958nteger: code_integer > code_integer ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 15.48/8.46      neg_nu8557863876264182079omplex: complex > complex ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 15.48/8.46      neg_nu5851722552734809277nc_int: int > int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 15.48/8.46      neg_nu5219082963157363817nc_rat: rat > rat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
% 15.48/8.46      neg_nu8295874005876285629c_real: real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 15.48/8.46      neg_numeral_sub_int: num > num > int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Onum_OBit0,type,
% 15.48/8.46      bit0: num > num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Onum_OBit1,type,
% 15.48/8.46      bit1: num > num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Onum_OOne,type,
% 15.48/8.46      one: num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
% 15.48/8.46      case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Onum_Osize__num,type,
% 15.48/8.46      size_num: num > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Onum__of__nat,type,
% 15.48/8.46      num_of_nat: nat > num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 15.48/8.46      numera6620942414471956472nteger: num > code_integer ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex,type,
% 15.48/8.46      numera6690914467698888265omplex: num > complex ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Nat__Oenat,type,
% 15.48/8.46      numera1916890842035813515d_enat: num > extended_enat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
% 15.48/8.46      numeral_numeral_int: num > int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
% 15.48/8.46      numeral_numeral_nat: num > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
% 15.48/8.46      numeral_numeral_rat: num > rat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal,type,
% 15.48/8.46      numeral_numeral_real: num > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Opow,type,
% 15.48/8.46      pow: num > num > num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Opred__numeral,type,
% 15.48/8.46      pred_numeral: num > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Num_Osqr,type,
% 15.48/8.46      sqr: num > num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Option_Ooption_ONone_001t__Nat__Onat,type,
% 15.48/8.46      none_nat: option_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Option_Ooption_ONone_001t__Num__Onum,type,
% 15.48/8.46      none_num: option_num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 15.48/8.46      none_P5556105721700978146at_nat: option4927543243414619207at_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Option_Ooption_OSome_001t__Nat__Onat,type,
% 15.48/8.46      some_nat: nat > option_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Option_Ooption_OSome_001t__Num__Onum,type,
% 15.48/8.46      some_num: num > option_num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 15.48/8.46      some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 15.48/8.46      case_o184042715313410164at_nat: $o > ( product_prod_nat_nat > $o ) > option4927543243414619207at_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Option_Ooption_Ocase__option_001t__Int__Oint_001t__Num__Onum,type,
% 15.48/8.46      case_option_int_num: int > ( num > int ) > option_num > int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Num__Onum,type,
% 15.48/8.46      case_option_num_num: num > ( num > num ) > option_num > num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
% 15.48/8.46      case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Num__Onum,type,
% 15.48/8.46      map_option_num_num: ( num > num ) > option_num > option_num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Option_Ooption_Othe_001t__Nat__Onat,type,
% 15.48/8.46      the_nat: option_nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Option_Ooption_Othe_001t__Num__Onum,type,
% 15.48/8.46      the_num: option_num > num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Option_Ooption_Othe_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 15.48/8.46      the_Pr8591224930841456533at_nat: option4927543243414619207at_nat > product_prod_nat_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Order__Relation_OunderS_001t__Nat__Onat,type,
% 15.48/8.46      order_underS_nat: set_Pr1261947904930325089at_nat > nat > set_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Orderings_Obot__class_Obot_001t__Extended____Nat__Oenat,type,
% 15.48/8.46      bot_bo4199563552545308370d_enat: extended_enat ).
% 15.48/8.46  
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% 15.48/8.46  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,
% 15.48/8.46      produc3994169339658061776at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > produc6121120109295599847at_nat > produc5491161045314408544at_nat ).
% 15.48/8.46  
% 15.48/8.46  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,
% 15.48/8.46      produc2899441246263362727at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > produc6121120109295599847at_nat > produc5542196010084753463at_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_OPair_001_Eo_001_Eo,type,
% 15.48/8.46      product_Pair_o_o: $o > $o > product_prod_o_o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_OPair_001_Eo_001t__Int__Oint,type,
% 15.48/8.46      product_Pair_o_int: $o > int > product_prod_o_int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_OPair_001_Eo_001t__Nat__Onat,type,
% 15.48/8.46      product_Pair_o_nat: $o > nat > product_prod_o_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_OPair_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 15.48/8.46      produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001_Eo,type,
% 15.48/8.46      produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 15.48/8.46      produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Int__Oint,type,
% 15.48/8.46      product_Pair_int_int: int > int > product_prod_int_int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 15.48/8.46      product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Num__Onum,type,
% 15.48/8.46      product_Pair_nat_num: nat > num > product_prod_nat_num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_OPair_001t__Num__Onum_001t__Num__Onum,type,
% 15.48/8.46      product_Pair_num_num: num > num > product_prod_num_num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Nat__Onat_J_001t__Option__Ooption_It__Nat__Onat_J,type,
% 15.48/8.46      produc5098337634421038937on_nat: option_nat > option_nat > produc4953844613479565601on_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Num__Onum_J,type,
% 15.48/8.46      produc8585076106096196333on_num: option_num > option_num > produc3447558737645232053on_num ).
% 15.48/8.46  
% 15.48/8.46  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,
% 15.48/8.46      produc488173922507101015at_nat: option4927543243414619207at_nat > option4927543243414619207at_nat > produc6121120109295599847at_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 15.48/8.46      produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 15.48/8.46      produc2922128104949294807at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 15.48/8.46      produc9060074326276436823at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > produc1319942482725812455at_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 15.48/8.46      produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Extended____Nat__Oenat,type,
% 15.48/8.46      produc581526299967858633d_enat: vEBT_VEBT > extended_enat > produc7272778201969148633d_enat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 15.48/8.46      produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 15.48/8.46      produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 15.48/8.46      produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Nat__Onat,type,
% 15.48/8.46      produc457027306803732586at_nat: set_nat > ( nat > set_nat ) > set_Pr1261947904930325089at_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 15.48/8.46      produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_Omap__prod_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 15.48/8.46      produc8678311845419106900er_nat: ( code_integer > nat ) > ( code_integer > nat ) > produc8923325533196201883nteger > product_prod_nat_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 15.48/8.46      produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 15.48/8.46      produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 15.48/8.46      produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).
% 15.48/8.46  
% 15.48/8.46  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,
% 15.48/8.46      produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).
% 15.48/8.46  
% 15.48/8.46  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,
% 15.48/8.46      produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Complex__Ocomplex_001t__Complex__Ocomplex_001_Eo,type,
% 15.48/8.46      produc6771430404735790350plex_o: ( complex > complex > $o ) > produc4411394909380815293omplex > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 15.48/8.46      produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 15.48/8.46      produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
% 15.48/8.46  
% 15.48/8.46  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,
% 15.48/8.46      produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
% 15.48/8.46  
% 15.48/8.46  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,
% 15.48/8.46      produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  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,
% 15.48/8.46      produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 15.48/8.46      produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J,type,
% 15.48/8.46      produc2761476792215241774st_nat: ( nat > nat > list_nat ) > product_prod_nat_nat > list_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 15.48/8.46      produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
% 15.48/8.46  
% 15.48/8.46  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,
% 15.48/8.46      produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
% 15.48/8.46      produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Real__Oreal_001t__Real__Oreal_001_Eo,type,
% 15.48/8.46      produc5414030515140494994real_o: ( real > real > $o ) > produc2422161461964618553l_real > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
% 15.48/8.46      product_fst_int_int: product_prod_int_int > int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
% 15.48/8.46      product_fst_nat_nat: product_prod_nat_nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
% 15.48/8.46      product_snd_int_int: product_prod_int_int > int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 15.48/8.46      product_snd_nat_nat: product_prod_nat_nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Rat_OAbs__Rat,type,
% 15.48/8.46      abs_Rat: product_prod_int_int > rat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Rat_OFract,type,
% 15.48/8.46      fract: int > int > rat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Rat_OFrct,type,
% 15.48/8.46      frct: product_prod_int_int > rat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Rat_ORep__Rat,type,
% 15.48/8.46      rep_Rat: rat > product_prod_int_int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Rat_Ofield__char__0__class_ORats_001t__Real__Oreal,type,
% 15.48/8.46      field_5140801741446780682s_real: set_real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Rat_Ofield__char__0__class_Oof__rat_001t__Real__Oreal,type,
% 15.48/8.46      field_7254667332652039916t_real: rat > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Rat_Onormalize,type,
% 15.48/8.46      normalize: product_prod_int_int > product_prod_int_int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Rat_Opcr__rat,type,
% 15.48/8.46      pcr_rat: product_prod_int_int > rat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Rat_Opositive,type,
% 15.48/8.46      positive: rat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Rat_Oquotient__of,type,
% 15.48/8.46      quotient_of: rat > product_prod_int_int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Rat_Oratrel,type,
% 15.48/8.46      ratrel: product_prod_int_int > product_prod_int_int > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Real_OReal,type,
% 15.48/8.46      real2: ( nat > rat ) > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Real_Ocauchy,type,
% 15.48/8.46      cauchy: ( nat > rat ) > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Real_Ocr__real,type,
% 15.48/8.46      cr_real: ( nat > rat ) > real > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Real_Opcr__real,type,
% 15.48/8.46      pcr_real: ( nat > rat ) > real > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Real_Opositive,type,
% 15.48/8.46      positive2: real > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Real_Orealrel,type,
% 15.48/8.46      realrel: ( nat > rat ) > ( nat > rat ) > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Real_Orep__real,type,
% 15.48/8.46      rep_real: real > nat > rat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Real_Ovanishes,type,
% 15.48/8.46      vanishes: ( nat > rat ) > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Real__Vector__Spaces_OReals_001t__Complex__Ocomplex,type,
% 15.48/8.46      real_V2521375963428798218omplex: set_complex ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Complex__Ocomplex,type,
% 15.48/8.46      real_V3694042436643373181omplex: complex > complex > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Real__Oreal,type,
% 15.48/8.46      real_V975177566351809787t_real: real > real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
% 15.48/8.46      real_V1022390504157884413omplex: complex > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal,type,
% 15.48/8.46      real_V7735802525324610683m_real: real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
% 15.48/8.46      real_V4546457046886955230omplex: real > complex ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Real__Oreal,type,
% 15.48/8.46      real_V1803761363581548252l_real: real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Relation_Otransp_001_062_It__Nat__Onat_Mt__Rat__Orat_J,type,
% 15.48/8.46      transp_nat_rat: ( ( nat > rat ) > ( nat > rat ) > $o ) > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Rings_Oalgebraic__semidom__class_Ocoprime_001t__Int__Oint,type,
% 15.48/8.46      algebr932160517623751201me_int: int > int > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Rings_Oalgebraic__semidom__class_Ocoprime_001t__Nat__Onat,type,
% 15.48/8.46      algebr934650988132801477me_nat: nat > nat > $o ).
% 15.48/8.46  
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% 15.48/8.46  thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
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% 15.48/8.46  thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex,type,
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% 15.48/8.46  
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% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
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% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Rings_Odvd__class_Odvd_001t__Rat__Orat,type,
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% 15.48/8.46  thf(sy_c_Rings_Odvd__class_Odvd_001t__Real__Oreal,type,
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% 15.48/8.46  thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
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% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Rings_Ounit__factor__class_Ounit__factor_001t__Nat__Onat,type,
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% 15.48/8.46  
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% 15.48/8.46  
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% 15.48/8.46  
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% 15.48/8.46      summable_complex: ( nat > complex ) > $o ).
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% 15.48/8.46  
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% 15.48/8.46  
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% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__String__Ochar,type,
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% 15.48/8.46  thf(sy_c_Set_Oimage_001t__String__Ochar_001t__Nat__Onat,type,
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% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Nat__Onat_J,type,
% 15.48/8.46      set_or4236626031148496127et_nat: set_nat > set_set_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
% 15.48/8.46      set_or6656581121297822940st_int: int > int > set_int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
% 15.48/8.46      set_or6659071591806873216st_nat: nat > nat > set_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
% 15.48/8.46      set_or5832277885323065728an_int: int > int > set_int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
% 15.48/8.46      set_or5834768355832116004an_nat: nat > nat > set_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
% 15.48/8.46      set_or1633881224788618240n_real: real > real > set_real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
% 15.48/8.46      set_or1210151606488870762an_nat: nat > set_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
% 15.48/8.46      set_or5849166863359141190n_real: real > set_real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
% 15.48/8.46      set_ord_lessThan_int: int > set_int ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 15.48/8.46      set_ord_lessThan_nat: nat > set_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Num__Onum,type,
% 15.48/8.46      set_ord_lessThan_num: num > set_num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Rat__Orat,type,
% 15.48/8.46      set_ord_lessThan_rat: rat > set_rat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
% 15.48/8.46      set_or5984915006950818249n_real: real > set_real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Set__Oset_It__Nat__Onat_J,type,
% 15.48/8.46      set_or890127255671739683et_nat: set_nat > set_set_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_String_OCode_Oabort_001t__Real__Oreal,type,
% 15.48/8.46      abort_real: literal > ( product_unit > real ) > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_String_OLiteral,type,
% 15.48/8.46      literal2: $o > $o > $o > $o > $o > $o > $o > literal > literal ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_String_Oascii__of,type,
% 15.48/8.46      ascii_of: char > char ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_String_Ochar_OChar,type,
% 15.48/8.46      char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_String_Ochar_Osize__char,type,
% 15.48/8.46      size_char: char > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_String_Ocomm__semiring__1__class_Oof__char_001t__Nat__Onat,type,
% 15.48/8.46      comm_s629917340098488124ar_nat: char > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_String_Ointeger__of__char,type,
% 15.48/8.46      integer_of_char: char > code_integer ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
% 15.48/8.46      unique3096191561947761185of_nat: nat > char ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 15.48/8.46      topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 15.48/8.46      topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 15.48/8.46      topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 15.48/8.46      topolo2177554685111907308n_real: real > set_real > filter_real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Topological__Spaces_Otopological__space__class_Oconvergent_001t__Real__Oreal,type,
% 15.48/8.46      topolo7531315842566124627t_real: ( nat > real ) > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 15.48/8.46      topolo2815343760600316023s_real: real > filter_real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 15.48/8.46      topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Complex__Ocomplex,type,
% 15.48/8.46      topolo896644834953643431omplex: filter6041513312241820739omplex ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Real__Oreal,type,
% 15.48/8.46      topolo1511823702728130853y_real: filter2146258269922977983l_real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Oarccos,type,
% 15.48/8.46      arccos: real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 15.48/8.46      arcosh_real: real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Oarcsin,type,
% 15.48/8.46      arcsin: real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Oarctan,type,
% 15.48/8.46      arctan: real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 15.48/8.46      arsinh_real: real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 15.48/8.46      artanh_real: real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Ocos_001t__Complex__Ocomplex,type,
% 15.48/8.46      cos_complex: complex > complex ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 15.48/8.46      cos_real: real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Ocos__coeff,type,
% 15.48/8.46      cos_coeff: nat > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 15.48/8.46      cosh_real: real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 15.48/8.46      cot_real: real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 15.48/8.46      exp_complex: complex > complex ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 15.48/8.46      exp_real: real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 15.48/8.46      ln_ln_real: real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Olog,type,
% 15.48/8.46      log: real > real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Opi,type,
% 15.48/8.46      pi: real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 15.48/8.46      powr_real: real > real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Opowr__real,type,
% 15.48/8.46      powr_real2: real > real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Osin_001t__Complex__Ocomplex,type,
% 15.48/8.46      sin_complex: complex > complex ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 15.48/8.46      sin_real: real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Osin__coeff,type,
% 15.48/8.46      sin_coeff: nat > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 15.48/8.46      sinh_real: real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Otan_001t__Complex__Ocomplex,type,
% 15.48/8.46      tan_complex: complex > complex ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 15.48/8.46      tan_real: real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 15.48/8.46      tanh_real: real > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transfer_Obi__total_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 15.48/8.46      bi_tot896582865486249351at_int: ( product_prod_nat_nat > int > $o ) > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
% 15.48/8.46      transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 15.48/8.46      transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Typedef_Otype__definition_001t__Extended____Nat__Oenat_001t__Option__Ooption_It__Nat__Onat_J,type,
% 15.48/8.46      type_d7649664348572268762on_nat: ( extended_enat > option_nat ) > ( option_nat > extended_enat ) > set_option_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t,type,
% 15.48/8.46      vEBT_T_i_n_s_e_r_t: vEBT_VEBT > nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H,type,
% 15.48/8.46      vEBT_T_i_n_s_e_r_t2: vEBT_VEBT > nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H__rel,type,
% 15.48/8.46      vEBT_T5076183648494686801_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t__rel,type,
% 15.48/8.46      vEBT_T9217963907923527482_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t,type,
% 15.48/8.46      vEBT_T_m_a_x_t: vEBT_VEBT > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r,type,
% 15.48/8.46      vEBT_T_m_e_m_b_e_r: vEBT_VEBT > nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H,type,
% 15.48/8.46      vEBT_T_m_e_m_b_e_r2: vEBT_VEBT > nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H__rel,type,
% 15.48/8.46      vEBT_T8099345112685741742_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r__rel,type,
% 15.48/8.46      vEBT_T5837161174952499735_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l,type,
% 15.48/8.46      vEBT_T_m_i_n_N_u_l_l: vEBT_VEBT > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t,type,
% 15.48/8.46      vEBT_T_m_i_n_t: vEBT_VEBT > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t__rel,type,
% 15.48/8.46      vEBT_T_m_i_n_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d,type,
% 15.48/8.46      vEBT_T_p_r_e_d: vEBT_VEBT > nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H,type,
% 15.48/8.46      vEBT_T_p_r_e_d2: vEBT_VEBT > nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H__rel,type,
% 15.48/8.46      vEBT_T_p_r_e_d_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d__rel,type,
% 15.48/8.46      vEBT_T_p_r_e_d_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c,type,
% 15.48/8.46      vEBT_T_s_u_c_c: vEBT_VEBT > nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H,type,
% 15.48/8.46      vEBT_T_s_u_c_c2: vEBT_VEBT > nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H__rel,type,
% 15.48/8.46      vEBT_T_s_u_c_c_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c__rel,type,
% 15.48/8.46      vEBT_T_s_u_c_c_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 15.48/8.46      vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 15.48/8.46      vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 15.48/8.46      vEBT_size_VEBT: vEBT_VEBT > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 15.48/8.46      vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oelim__dead,type,
% 15.48/8.46      vEBT_VEBT_elim_dead: vEBT_VEBT > extended_enat > vEBT_VEBT ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oelim__dead__rel,type,
% 15.48/8.46      vEBT_V312737461966249ad_rel: produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 15.48/8.46      vEBT_VEBT_high: nat > nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 15.48/8.46      vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 15.48/8.46      vEBT_VEBT_low: nat > nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 15.48/8.46      vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 15.48/8.46      vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 15.48/8.46      vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 15.48/8.46      vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 15.48/8.46      vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 15.48/8.46      vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 15.48/8.46      vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 15.48/8.46      vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 15.48/8.46      vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 15.48/8.46      vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__DeleteBounds_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e,type,
% 15.48/8.46      vEBT_T_d_e_l_e_t_e: vEBT_VEBT > nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__DeleteBounds_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e__rel,type,
% 15.48/8.46      vEBT_T8441311223069195367_e_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Delete_Ovebt__delete,type,
% 15.48/8.46      vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Delete_Ovebt__delete__rel,type,
% 15.48/8.46      vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Height_OVEBT__internal_Oheight,type,
% 15.48/8.46      vEBT_VEBT_height: vEBT_VEBT > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Height_OVEBT__internal_Oheight__rel,type,
% 15.48/8.46      vEBT_VEBT_height_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 15.48/8.46      vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 15.48/8.46      vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 15.48/8.46      vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 15.48/8.46      vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 15.48/8.46      vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Member_Ovebt__member,type,
% 15.48/8.46      vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 15.48/8.46      vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 15.48/8.46      vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 15.48/8.46      vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 15.48/8.46      vEBT_VEBT_less: option_nat > option_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 15.48/8.46      vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 15.48/8.46      vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
% 15.48/8.46      vEBT_VEBT_min_in_set: set_nat > nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Omul,type,
% 15.48/8.46      vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__comp__shift_001t__Nat__Onat,type,
% 15.48/8.46      vEBT_V2881884560877996034ft_nat: ( nat > nat > $o ) > option_nat > option_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Nat__Onat,type,
% 15.48/8.46      vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Num__Onum,type,
% 15.48/8.46      vEBT_V819420779217536731ft_num: ( num > num > num ) > option_num > option_num > option_num ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 15.48/8.46      vEBT_V1502963449132264192at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__MinMax_OVEBT__internal_Opower,type,
% 15.48/8.46      vEBT_VEBT_power: option_nat > option_nat > option_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__MinMax_Ovebt__maxt,type,
% 15.48/8.46      vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__MinMax_Ovebt__maxt__rel,type,
% 15.48/8.46      vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__MinMax_Ovebt__mint,type,
% 15.48/8.46      vEBT_vebt_mint: vEBT_VEBT > option_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__MinMax_Ovebt__mint__rel,type,
% 15.48/8.46      vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Pred_Ois__pred__in__set,type,
% 15.48/8.46      vEBT_is_pred_in_set: set_nat > nat > nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Pred_Ovebt__pred,type,
% 15.48/8.46      vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Pred_Ovebt__pred__rel,type,
% 15.48/8.46      vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Succ_Ois__succ__in__set,type,
% 15.48/8.46      vEBT_is_succ_in_set: set_nat > nat > nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Succ_Ovebt__succ,type,
% 15.48/8.46      vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_VEBT__Succ_Ovebt__succ__rel,type,
% 15.48/8.46      vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 15.48/8.46      accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 15.48/8.46      accp_nat: ( nat > nat > $o ) > nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 15.48/8.46      accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 15.48/8.46      accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 15.48/8.46      accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Extended____Nat__Oenat_J,type,
% 15.48/8.46      accp_P6183159247885693666d_enat: ( produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o ) > produc7272778201969148633d_enat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 15.48/8.46      accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 15.48/8.46      accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Wellfounded_Oless__than,type,
% 15.48/8.46      less_than: set_Pr1261947904930325089at_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Wellfounded_Olex__prod_001t__Nat__Onat_001t__Nat__Onat,type,
% 15.48/8.46      lex_prod_nat_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Wellfounded_Omax__ext_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 15.48/8.46      max_ex8135407076693332796at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Wellfounded_Omin__ext_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 15.48/8.46      min_ex6901939911449802026at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Wellfounded_Opred__nat,type,
% 15.48/8.46      pred_nat: set_Pr1261947904930325089at_nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Wellfounded_Owf_001t__Int__Oint,type,
% 15.48/8.46      wf_int: set_Pr958786334691620121nt_int > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
% 15.48/8.46      wf_nat: set_Pr1261947904930325089at_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_Wellfounded_Owf_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 15.48/8.46      wf_Pro7803398752247294826at_nat: set_Pr8693737435421807431at_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_fChoice_001t__Real__Oreal,type,
% 15.48/8.46      fChoice_real: ( real > $o ) > real ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_member_001_Eo,type,
% 15.48/8.46      member_o: $o > set_o > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_member_001t__Complex__Ocomplex,type,
% 15.48/8.46      member_complex: complex > set_complex > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_member_001t__Extended____Nat__Oenat,type,
% 15.48/8.46      member_Extended_enat: extended_enat > set_Extended_enat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_member_001t__Int__Oint,type,
% 15.48/8.46      member_int: int > set_int > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 15.48/8.46      member_list_o: list_o > set_list_o > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 15.48/8.46      member_list_int: list_int > set_list_int > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 15.48/8.46      member_list_nat: list_nat > set_list_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 15.48/8.46      member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_member_001t__Nat__Onat,type,
% 15.48/8.46      member_nat: nat > set_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_member_001t__Num__Onum,type,
% 15.48/8.46      member_num: num > set_num > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_member_001t__Option__Ooption_It__Nat__Onat_J,type,
% 15.48/8.46      member_option_nat: option_nat > set_option_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 15.48/8.46      member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 15.48/8.46      member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 15.48/8.46      member8757157785044589968at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_member_001t__Rat__Orat,type,
% 15.48/8.46      member_rat: rat > set_rat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_member_001t__Real__Oreal,type,
% 15.48/8.46      member_real: real > set_real > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 15.48/8.46      member_set_nat: set_nat > set_set_nat > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 15.48/8.46      member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_v_deg____,type,
% 15.48/8.46      deg: nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_v_m____,type,
% 15.48/8.46      m: nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_v_ma____,type,
% 15.48/8.46      ma: nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_v_mi____,type,
% 15.48/8.46      mi: nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_v_na____,type,
% 15.48/8.46      na: nat ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_v_summary____,type,
% 15.48/8.46      summary: vEBT_VEBT ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_v_treeList____,type,
% 15.48/8.46      treeList: list_VEBT_VEBT ).
% 15.48/8.46  
% 15.48/8.46  thf(sy_v_x,type,
% 15.48/8.46      x: nat ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_0_False,axiom,
% 15.48/8.46      x != mi ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_1__C5_Ohyps_C_I8_J,axiom,
% 15.48/8.46      ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_2__092_060open_062mi_A_060_Ax_092_060close_062,axiom,
% 15.48/8.46      ord_less_nat @ mi @ x ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_3_less__exp,axiom,
% 15.48/8.46      ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_4_semiring__norm_I85_J,axiom,
% 15.48/8.46      ! [M: num] :
% 15.48/8.46        ( ( bit0 @ M )
% 15.48/8.46       != one ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_5_semiring__norm_I83_J,axiom,
% 15.48/8.46      ! [N: num] :
% 15.48/8.46        ( one
% 15.48/8.46       != ( bit0 @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_6_numeral__less__iff,axiom,
% 15.48/8.46      ! [M: num,N: num] :
% 15.48/8.46        ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 15.48/8.46        = ( ord_less_num @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_7_numeral__less__iff,axiom,
% 15.48/8.46      ! [M: num,N: num] :
% 15.48/8.46        ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 15.48/8.46        = ( ord_less_num @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_8_numeral__less__iff,axiom,
% 15.48/8.46      ! [M: num,N: num] :
% 15.48/8.46        ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 15.48/8.46        = ( ord_less_num @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_9_numeral__less__iff,axiom,
% 15.48/8.46      ! [M: num,N: num] :
% 15.48/8.46        ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 15.48/8.46        = ( ord_less_num @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_10__092_060open_0622_A_092_060le_062_Adeg_092_060close_062,axiom,
% 15.48/8.46      ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_11_verit__eq__simplify_I8_J,axiom,
% 15.48/8.46      ! [X2: num,Y2: num] :
% 15.48/8.46        ( ( ( bit0 @ X2 )
% 15.48/8.46          = ( bit0 @ Y2 ) )
% 15.48/8.46        = ( X2 = Y2 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_12_semiring__norm_I87_J,axiom,
% 15.48/8.46      ! [M: num,N: num] :
% 15.48/8.46        ( ( ( bit0 @ M )
% 15.48/8.46          = ( bit0 @ N ) )
% 15.48/8.46        = ( M = N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_13_numeral__eq__iff,axiom,
% 15.48/8.46      ! [M: num,N: num] :
% 15.48/8.46        ( ( ( numera6690914467698888265omplex @ M )
% 15.48/8.46          = ( numera6690914467698888265omplex @ N ) )
% 15.48/8.46        = ( M = N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_14_numeral__eq__iff,axiom,
% 15.48/8.46      ! [M: num,N: num] :
% 15.48/8.46        ( ( ( numeral_numeral_real @ M )
% 15.48/8.46          = ( numeral_numeral_real @ N ) )
% 15.48/8.46        = ( M = N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_15_numeral__eq__iff,axiom,
% 15.48/8.46      ! [M: num,N: num] :
% 15.48/8.46        ( ( ( numeral_numeral_rat @ M )
% 15.48/8.46          = ( numeral_numeral_rat @ N ) )
% 15.48/8.46        = ( M = N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_16_numeral__eq__iff,axiom,
% 15.48/8.46      ! [M: num,N: num] :
% 15.48/8.46        ( ( ( numeral_numeral_nat @ M )
% 15.48/8.46          = ( numeral_numeral_nat @ N ) )
% 15.48/8.46        = ( M = N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_17_numeral__eq__iff,axiom,
% 15.48/8.46      ! [M: num,N: num] :
% 15.48/8.46        ( ( ( numeral_numeral_int @ M )
% 15.48/8.46          = ( numeral_numeral_int @ N ) )
% 15.48/8.46        = ( M = N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_18_verit__eq__simplify_I10_J,axiom,
% 15.48/8.46      ! [X2: num] :
% 15.48/8.46        ( one
% 15.48/8.46       != ( bit0 @ X2 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_19_local_Opower__def,axiom,
% 15.48/8.46      ( vEBT_VEBT_power
% 15.48/8.46      = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_20__C5_Ohyps_C_I7_J,axiom,
% 15.48/8.46      ord_less_eq_nat @ mi @ ma ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_21__092_060open_062_092_060not_062_A_Ix_A_061_Ami_A_092_060and_062_Ax_A_061_Ama_J_092_060close_062,axiom,
% 15.48/8.46      ~ ( ( x = mi )
% 15.48/8.46        & ( x = ma ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_22_max__in__set__def,axiom,
% 15.48/8.46      ( vEBT_VEBT_max_in_set
% 15.48/8.46      = ( ^ [Xs: set_nat,X: nat] :
% 15.48/8.46            ( ( member_nat @ X @ Xs )
% 15.48/8.46            & ! [Y: nat] :
% 15.48/8.46                ( ( member_nat @ Y @ Xs )
% 15.48/8.46               => ( ord_less_eq_nat @ Y @ X ) ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_23_min__in__set__def,axiom,
% 15.48/8.46      ( vEBT_VEBT_min_in_set
% 15.48/8.46      = ( ^ [Xs: set_nat,X: nat] :
% 15.48/8.46            ( ( member_nat @ X @ Xs )
% 15.48/8.46            & ! [Y: nat] :
% 15.48/8.46                ( ( member_nat @ Y @ Xs )
% 15.48/8.46               => ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_24__092_060open_062x_A_092_060le_062_Ama_A_092_060and_062_Ami_A_092_060le_062_Ax_092_060close_062,axiom,
% 15.48/8.46      ( ( ord_less_eq_nat @ x @ ma )
% 15.48/8.46      & ( ord_less_eq_nat @ mi @ x ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_25_numeral__le__iff,axiom,
% 15.48/8.46      ! [M: num,N: num] :
% 15.48/8.46        ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 15.48/8.46        = ( ord_less_eq_num @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_26_numeral__le__iff,axiom,
% 15.48/8.46      ! [M: num,N: num] :
% 15.48/8.46        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 15.48/8.46        = ( ord_less_eq_num @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_27_numeral__le__iff,axiom,
% 15.48/8.46      ! [M: num,N: num] :
% 15.48/8.46        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 15.48/8.46        = ( ord_less_eq_num @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_28_numeral__le__iff,axiom,
% 15.48/8.46      ! [M: num,N: num] :
% 15.48/8.46        ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 15.48/8.46        = ( ord_less_eq_num @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_29_semiring__norm_I78_J,axiom,
% 15.48/8.46      ! [M: num,N: num] :
% 15.48/8.46        ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 15.48/8.46        = ( ord_less_num @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_30_semiring__norm_I75_J,axiom,
% 15.48/8.46      ! [M: num] :
% 15.48/8.46        ~ ( ord_less_num @ M @ one ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_31_semiring__norm_I76_J,axiom,
% 15.48/8.46      ! [N: num] : ( ord_less_num @ one @ ( bit0 @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_32_verit__comp__simplify1_I2_J,axiom,
% 15.48/8.46      ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_33_verit__comp__simplify1_I2_J,axiom,
% 15.48/8.46      ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_34_verit__comp__simplify1_I2_J,axiom,
% 15.48/8.46      ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_35_verit__comp__simplify1_I2_J,axiom,
% 15.48/8.46      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_36_verit__comp__simplify1_I2_J,axiom,
% 15.48/8.46      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_37_verit__la__disequality,axiom,
% 15.48/8.46      ! [A: rat,B: rat] :
% 15.48/8.46        ( ( A = B )
% 15.48/8.46        | ~ ( ord_less_eq_rat @ A @ B )
% 15.48/8.46        | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_38_verit__la__disequality,axiom,
% 15.48/8.46      ! [A: num,B: num] :
% 15.48/8.46        ( ( A = B )
% 15.48/8.46        | ~ ( ord_less_eq_num @ A @ B )
% 15.48/8.46        | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_39_verit__la__disequality,axiom,
% 15.48/8.46      ! [A: nat,B: nat] :
% 15.48/8.46        ( ( A = B )
% 15.48/8.46        | ~ ( ord_less_eq_nat @ A @ B )
% 15.48/8.46        | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_40_verit__la__disequality,axiom,
% 15.48/8.46      ! [A: int,B: int] :
% 15.48/8.46        ( ( A = B )
% 15.48/8.46        | ~ ( ord_less_eq_int @ A @ B )
% 15.48/8.46        | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_41_verit__comp__simplify1_I3_J,axiom,
% 15.48/8.46      ! [B2: real,A2: real] :
% 15.48/8.46        ( ( ~ ( ord_less_eq_real @ B2 @ A2 ) )
% 15.48/8.46        = ( ord_less_real @ A2 @ B2 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_42_verit__comp__simplify1_I3_J,axiom,
% 15.48/8.46      ! [B2: rat,A2: rat] :
% 15.48/8.46        ( ( ~ ( ord_less_eq_rat @ B2 @ A2 ) )
% 15.48/8.46        = ( ord_less_rat @ A2 @ B2 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_43_verit__comp__simplify1_I3_J,axiom,
% 15.48/8.46      ! [B2: num,A2: num] :
% 15.48/8.46        ( ( ~ ( ord_less_eq_num @ B2 @ A2 ) )
% 15.48/8.46        = ( ord_less_num @ A2 @ B2 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_44_verit__comp__simplify1_I3_J,axiom,
% 15.48/8.46      ! [B2: nat,A2: nat] :
% 15.48/8.46        ( ( ~ ( ord_less_eq_nat @ B2 @ A2 ) )
% 15.48/8.46        = ( ord_less_nat @ A2 @ B2 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_45_verit__comp__simplify1_I3_J,axiom,
% 15.48/8.46      ! [B2: int,A2: int] :
% 15.48/8.46        ( ( ~ ( ord_less_eq_int @ B2 @ A2 ) )
% 15.48/8.46        = ( ord_less_int @ A2 @ B2 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_46_power2__nat__le__imp__le,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 15.48/8.46       => ( ord_less_eq_nat @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_47_power2__nat__le__eq__le,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.48/8.46        = ( ord_less_eq_nat @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_48_self__le__ge2__pow,axiom,
% 15.48/8.46      ! [K: nat,M: nat] :
% 15.48/8.46        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 15.48/8.46       => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_49_verit__comp__simplify1_I1_J,axiom,
% 15.48/8.46      ! [A: real] :
% 15.48/8.46        ~ ( ord_less_real @ A @ A ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_50_verit__comp__simplify1_I1_J,axiom,
% 15.48/8.46      ! [A: rat] :
% 15.48/8.46        ~ ( ord_less_rat @ A @ A ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_51_verit__comp__simplify1_I1_J,axiom,
% 15.48/8.46      ! [A: num] :
% 15.48/8.46        ~ ( ord_less_num @ A @ A ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_52_verit__comp__simplify1_I1_J,axiom,
% 15.48/8.46      ! [A: nat] :
% 15.48/8.46        ~ ( ord_less_nat @ A @ A ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_53_verit__comp__simplify1_I1_J,axiom,
% 15.48/8.46      ! [A: int] :
% 15.48/8.46        ~ ( ord_less_int @ A @ A ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_54_enat__ord__number_I2_J,axiom,
% 15.48/8.46      ! [M: num,N: num] :
% 15.48/8.46        ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 15.48/8.46        = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_55_power__numeral,axiom,
% 15.48/8.46      ! [K: num,L: num] :
% 15.48/8.46        ( ( power_power_complex @ ( numera6690914467698888265omplex @ K ) @ ( numeral_numeral_nat @ L ) )
% 15.48/8.46        = ( numera6690914467698888265omplex @ ( pow @ K @ L ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_56_power__numeral,axiom,
% 15.48/8.46      ! [K: num,L: num] :
% 15.48/8.46        ( ( power_power_real @ ( numeral_numeral_real @ K ) @ ( numeral_numeral_nat @ L ) )
% 15.48/8.46        = ( numeral_numeral_real @ ( pow @ K @ L ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_57_power__numeral,axiom,
% 15.48/8.46      ! [K: num,L: num] :
% 15.48/8.46        ( ( power_power_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_nat @ L ) )
% 15.48/8.46        = ( numeral_numeral_rat @ ( pow @ K @ L ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_58_power__numeral,axiom,
% 15.48/8.46      ! [K: num,L: num] :
% 15.48/8.46        ( ( power_power_nat @ ( numeral_numeral_nat @ K ) @ ( numeral_numeral_nat @ L ) )
% 15.48/8.46        = ( numeral_numeral_nat @ ( pow @ K @ L ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_59_power__numeral,axiom,
% 15.48/8.46      ! [K: num,L: num] :
% 15.48/8.46        ( ( power_power_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_nat @ L ) )
% 15.48/8.46        = ( numeral_numeral_int @ ( pow @ K @ L ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_60_order__refl,axiom,
% 15.48/8.46      ! [X3: set_nat] : ( ord_less_eq_set_nat @ X3 @ X3 ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_61_order__refl,axiom,
% 15.48/8.46      ! [X3: rat] : ( ord_less_eq_rat @ X3 @ X3 ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_62_order__refl,axiom,
% 15.48/8.46      ! [X3: num] : ( ord_less_eq_num @ X3 @ X3 ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_63_order__refl,axiom,
% 15.48/8.46      ! [X3: nat] : ( ord_less_eq_nat @ X3 @ X3 ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_64_order__refl,axiom,
% 15.48/8.46      ! [X3: int] : ( ord_less_eq_int @ X3 @ X3 ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_65_dual__order_Orefl,axiom,
% 15.48/8.46      ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_66_dual__order_Orefl,axiom,
% 15.48/8.46      ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_67_dual__order_Orefl,axiom,
% 15.48/8.46      ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_68_dual__order_Orefl,axiom,
% 15.48/8.46      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_69_dual__order_Orefl,axiom,
% 15.48/8.46      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_70_power__shift,axiom,
% 15.48/8.46      ! [X3: nat,Y3: nat,Z: nat] :
% 15.48/8.46        ( ( ( power_power_nat @ X3 @ Y3 )
% 15.48/8.46          = Z )
% 15.48/8.46        = ( ( vEBT_VEBT_power @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) )
% 15.48/8.46          = ( some_nat @ Z ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_71_of__nat__le__numeral__power__cancel__iff,axiom,
% 15.48/8.46      ! [X3: nat,I: num,N: nat] :
% 15.48/8.46        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 15.48/8.46        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_72_of__nat__le__numeral__power__cancel__iff,axiom,
% 15.48/8.46      ! [X3: nat,I: num,N: nat] :
% 15.48/8.46        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 15.48/8.46        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_73_of__nat__le__numeral__power__cancel__iff,axiom,
% 15.48/8.46      ! [X3: nat,I: num,N: nat] :
% 15.48/8.46        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 15.48/8.46        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_74_of__nat__le__numeral__power__cancel__iff,axiom,
% 15.48/8.46      ! [X3: nat,I: num,N: nat] :
% 15.48/8.46        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 15.48/8.46        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_75_numeral__power__le__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [I: num,N: nat,X3: nat] :
% 15.48/8.46        ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X3 ) )
% 15.48/8.46        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_76_numeral__power__le__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [I: num,N: nat,X3: nat] :
% 15.48/8.46        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X3 ) )
% 15.48/8.46        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_77_numeral__power__le__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [I: num,N: nat,X3: nat] :
% 15.48/8.46        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X3 ) )
% 15.48/8.46        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_78_numeral__power__le__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [I: num,N: nat,X3: nat] :
% 15.48/8.46        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X3 ) )
% 15.48/8.46        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_79_of__nat__less__numeral__power__cancel__iff,axiom,
% 15.48/8.46      ! [X3: nat,I: num,N: nat] :
% 15.48/8.46        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 15.48/8.46        = ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_80_of__nat__less__numeral__power__cancel__iff,axiom,
% 15.48/8.46      ! [X3: nat,I: num,N: nat] :
% 15.48/8.46        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 15.48/8.46        = ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_81_of__nat__less__numeral__power__cancel__iff,axiom,
% 15.48/8.46      ! [X3: nat,I: num,N: nat] :
% 15.48/8.46        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 15.48/8.46        = ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_82_of__nat__less__numeral__power__cancel__iff,axiom,
% 15.48/8.46      ! [X3: nat,I: num,N: nat] :
% 15.48/8.46        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 15.48/8.46        = ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_83_numeral__power__less__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [I: num,N: nat,X3: nat] :
% 15.48/8.46        ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X3 ) )
% 15.48/8.46        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_84_numeral__power__less__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [I: num,N: nat,X3: nat] :
% 15.48/8.46        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X3 ) )
% 15.48/8.46        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_85_numeral__power__less__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [I: num,N: nat,X3: nat] :
% 15.48/8.46        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X3 ) )
% 15.48/8.46        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_86_numeral__power__less__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [I: num,N: nat,X3: nat] :
% 15.48/8.46        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X3 ) )
% 15.48/8.46        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_87_nat__descend__induct,axiom,
% 15.48/8.46      ! [N: nat,P: nat > $o,M: nat] :
% 15.48/8.46        ( ! [K2: nat] :
% 15.48/8.46            ( ( ord_less_nat @ N @ K2 )
% 15.48/8.46           => ( P @ K2 ) )
% 15.48/8.46       => ( ! [K2: nat] :
% 15.48/8.46              ( ( ord_less_eq_nat @ K2 @ N )
% 15.48/8.46             => ( ! [I2: nat] :
% 15.48/8.46                    ( ( ord_less_nat @ K2 @ I2 )
% 15.48/8.46                   => ( P @ I2 ) )
% 15.48/8.46               => ( P @ K2 ) ) )
% 15.48/8.46         => ( P @ M ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_88_less__mono__imp__le__mono,axiom,
% 15.48/8.46      ! [F: nat > nat,I: nat,J: nat] :
% 15.48/8.46        ( ! [I3: nat,J2: nat] :
% 15.48/8.46            ( ( ord_less_nat @ I3 @ J2 )
% 15.48/8.46           => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 15.48/8.46       => ( ( ord_less_eq_nat @ I @ J )
% 15.48/8.46         => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_89_of__nat__eq__iff,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ( semiri8010041392384452111omplex @ M )
% 15.48/8.46          = ( semiri8010041392384452111omplex @ N ) )
% 15.48/8.46        = ( M = N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_90_of__nat__eq__iff,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ( semiri5074537144036343181t_real @ M )
% 15.48/8.46          = ( semiri5074537144036343181t_real @ N ) )
% 15.48/8.46        = ( M = N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_91_of__nat__eq__iff,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ( semiri681578069525770553at_rat @ M )
% 15.48/8.46          = ( semiri681578069525770553at_rat @ N ) )
% 15.48/8.46        = ( M = N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_92_of__nat__eq__iff,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ( semiri1316708129612266289at_nat @ M )
% 15.48/8.46          = ( semiri1316708129612266289at_nat @ N ) )
% 15.48/8.46        = ( M = N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_93_of__nat__eq__iff,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ( semiri1314217659103216013at_int @ M )
% 15.48/8.46          = ( semiri1314217659103216013at_int @ N ) )
% 15.48/8.46        = ( M = N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_94_semiring__norm_I71_J,axiom,
% 15.48/8.46      ! [M: num,N: num] :
% 15.48/8.46        ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 15.48/8.46        = ( ord_less_eq_num @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_95_mem__Collect__eq,axiom,
% 15.48/8.46      ! [A: option_nat,P: option_nat > $o] :
% 15.48/8.46        ( ( member_option_nat @ A @ ( collect_option_nat @ P ) )
% 15.48/8.46        = ( P @ A ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_96_mem__Collect__eq,axiom,
% 15.48/8.46      ! [A: real,P: real > $o] :
% 15.48/8.46        ( ( member_real @ A @ ( collect_real @ P ) )
% 15.48/8.46        = ( P @ A ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_97_mem__Collect__eq,axiom,
% 15.48/8.46      ! [A: list_nat,P: list_nat > $o] :
% 15.48/8.46        ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 15.48/8.46        = ( P @ A ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_98_mem__Collect__eq,axiom,
% 15.48/8.46      ! [A: set_nat,P: set_nat > $o] :
% 15.48/8.46        ( ( member_set_nat @ A @ ( collect_set_nat @ P ) )
% 15.48/8.46        = ( P @ A ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_99_mem__Collect__eq,axiom,
% 15.48/8.46      ! [A: nat,P: nat > $o] :
% 15.48/8.46        ( ( member_nat @ A @ ( collect_nat @ P ) )
% 15.48/8.46        = ( P @ A ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_100_mem__Collect__eq,axiom,
% 15.48/8.46      ! [A: int,P: int > $o] :
% 15.48/8.46        ( ( member_int @ A @ ( collect_int @ P ) )
% 15.48/8.46        = ( P @ A ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_101_Collect__mem__eq,axiom,
% 15.48/8.46      ! [A3: set_option_nat] :
% 15.48/8.46        ( ( collect_option_nat
% 15.48/8.46          @ ^ [X: option_nat] : ( member_option_nat @ X @ A3 ) )
% 15.48/8.46        = A3 ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_102_Collect__mem__eq,axiom,
% 15.48/8.46      ! [A3: set_real] :
% 15.48/8.46        ( ( collect_real
% 15.48/8.46          @ ^ [X: real] : ( member_real @ X @ A3 ) )
% 15.48/8.46        = A3 ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_103_Collect__mem__eq,axiom,
% 15.48/8.46      ! [A3: set_list_nat] :
% 15.48/8.46        ( ( collect_list_nat
% 15.48/8.46          @ ^ [X: list_nat] : ( member_list_nat @ X @ A3 ) )
% 15.48/8.46        = A3 ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_104_Collect__mem__eq,axiom,
% 15.48/8.46      ! [A3: set_set_nat] :
% 15.48/8.46        ( ( collect_set_nat
% 15.48/8.46          @ ^ [X: set_nat] : ( member_set_nat @ X @ A3 ) )
% 15.48/8.46        = A3 ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_105_Collect__mem__eq,axiom,
% 15.48/8.46      ! [A3: set_nat] :
% 15.48/8.46        ( ( collect_nat
% 15.48/8.46          @ ^ [X: nat] : ( member_nat @ X @ A3 ) )
% 15.48/8.46        = A3 ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_106_Collect__mem__eq,axiom,
% 15.48/8.46      ! [A3: set_int] :
% 15.48/8.46        ( ( collect_int
% 15.48/8.46          @ ^ [X: int] : ( member_int @ X @ A3 ) )
% 15.48/8.46        = A3 ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_107_Collect__cong,axiom,
% 15.48/8.46      ! [P: real > $o,Q: real > $o] :
% 15.48/8.46        ( ! [X4: real] :
% 15.48/8.46            ( ( P @ X4 )
% 15.48/8.46            = ( Q @ X4 ) )
% 15.48/8.46       => ( ( collect_real @ P )
% 15.48/8.46          = ( collect_real @ Q ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_108_Collect__cong,axiom,
% 15.48/8.46      ! [P: list_nat > $o,Q: list_nat > $o] :
% 15.48/8.46        ( ! [X4: list_nat] :
% 15.48/8.46            ( ( P @ X4 )
% 15.48/8.46            = ( Q @ X4 ) )
% 15.48/8.46       => ( ( collect_list_nat @ P )
% 15.48/8.46          = ( collect_list_nat @ Q ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_109_Collect__cong,axiom,
% 15.48/8.46      ! [P: set_nat > $o,Q: set_nat > $o] :
% 15.48/8.46        ( ! [X4: set_nat] :
% 15.48/8.46            ( ( P @ X4 )
% 15.48/8.46            = ( Q @ X4 ) )
% 15.48/8.46       => ( ( collect_set_nat @ P )
% 15.48/8.46          = ( collect_set_nat @ Q ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_110_Collect__cong,axiom,
% 15.48/8.46      ! [P: nat > $o,Q: nat > $o] :
% 15.48/8.46        ( ! [X4: nat] :
% 15.48/8.46            ( ( P @ X4 )
% 15.48/8.46            = ( Q @ X4 ) )
% 15.48/8.46       => ( ( collect_nat @ P )
% 15.48/8.46          = ( collect_nat @ Q ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_111_Collect__cong,axiom,
% 15.48/8.46      ! [P: int > $o,Q: int > $o] :
% 15.48/8.46        ( ! [X4: int] :
% 15.48/8.46            ( ( P @ X4 )
% 15.48/8.46            = ( Q @ X4 ) )
% 15.48/8.46       => ( ( collect_int @ P )
% 15.48/8.46          = ( collect_int @ Q ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_112_semiring__norm_I68_J,axiom,
% 15.48/8.46      ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_113_of__nat__numeral,axiom,
% 15.48/8.46      ! [N: num] :
% 15.48/8.46        ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N ) )
% 15.48/8.46        = ( numera6690914467698888265omplex @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_114_of__nat__numeral,axiom,
% 15.48/8.46      ! [N: num] :
% 15.48/8.46        ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 15.48/8.46        = ( numeral_numeral_real @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_115_of__nat__numeral,axiom,
% 15.48/8.46      ! [N: num] :
% 15.48/8.46        ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N ) )
% 15.48/8.46        = ( numeral_numeral_rat @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_116_of__nat__numeral,axiom,
% 15.48/8.46      ! [N: num] :
% 15.48/8.46        ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 15.48/8.46        = ( numeral_numeral_nat @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_117_of__nat__numeral,axiom,
% 15.48/8.46      ! [N: num] :
% 15.48/8.46        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 15.48/8.46        = ( numeral_numeral_int @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_118_of__nat__less__iff,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 15.48/8.46        = ( ord_less_nat @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_119_of__nat__less__iff,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 15.48/8.46        = ( ord_less_nat @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_120_of__nat__less__iff,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 15.48/8.46        = ( ord_less_nat @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_121_of__nat__less__iff,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 15.48/8.46        = ( ord_less_nat @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_122_of__nat__le__iff,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 15.48/8.46        = ( ord_less_eq_nat @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_123_of__nat__le__iff,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 15.48/8.46        = ( ord_less_eq_nat @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_124_of__nat__le__iff,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 15.48/8.46        = ( ord_less_eq_nat @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_125_of__nat__le__iff,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 15.48/8.46        = ( ord_less_eq_nat @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_126_of__nat__power,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N ) )
% 15.48/8.46        = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_127_of__nat__power,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N ) )
% 15.48/8.46        = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_128_of__nat__power,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( semiri681578069525770553at_rat @ ( power_power_nat @ M @ N ) )
% 15.48/8.46        = ( power_power_rat @ ( semiri681578069525770553at_rat @ M ) @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_129_of__nat__power,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N ) )
% 15.48/8.46        = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_130_of__nat__power,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N ) )
% 15.48/8.46        = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_131_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 15.48/8.46      ! [B: nat,W: nat,X3: nat] :
% 15.48/8.46        ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 15.48/8.46          = ( semiri8010041392384452111omplex @ X3 ) )
% 15.48/8.46        = ( ( power_power_nat @ B @ W )
% 15.48/8.46          = X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_132_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 15.48/8.46      ! [B: nat,W: nat,X3: nat] :
% 15.48/8.46        ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 15.48/8.46          = ( semiri5074537144036343181t_real @ X3 ) )
% 15.48/8.46        = ( ( power_power_nat @ B @ W )
% 15.48/8.46          = X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_133_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 15.48/8.46      ! [B: nat,W: nat,X3: nat] :
% 15.48/8.46        ( ( ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W )
% 15.48/8.46          = ( semiri681578069525770553at_rat @ X3 ) )
% 15.48/8.46        = ( ( power_power_nat @ B @ W )
% 15.48/8.46          = X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_134_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 15.48/8.46      ! [B: nat,W: nat,X3: nat] :
% 15.48/8.46        ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 15.48/8.46          = ( semiri1316708129612266289at_nat @ X3 ) )
% 15.48/8.46        = ( ( power_power_nat @ B @ W )
% 15.48/8.46          = X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_135_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 15.48/8.46      ! [B: nat,W: nat,X3: nat] :
% 15.48/8.46        ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 15.48/8.46          = ( semiri1314217659103216013at_int @ X3 ) )
% 15.48/8.46        = ( ( power_power_nat @ B @ W )
% 15.48/8.46          = X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_136_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [X3: nat,B: nat,W: nat] :
% 15.48/8.46        ( ( ( semiri8010041392384452111omplex @ X3 )
% 15.48/8.46          = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 15.48/8.46        = ( X3
% 15.48/8.46          = ( power_power_nat @ B @ W ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_137_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [X3: nat,B: nat,W: nat] :
% 15.48/8.46        ( ( ( semiri5074537144036343181t_real @ X3 )
% 15.48/8.46          = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 15.48/8.46        = ( X3
% 15.48/8.46          = ( power_power_nat @ B @ W ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_138_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [X3: nat,B: nat,W: nat] :
% 15.48/8.46        ( ( ( semiri681578069525770553at_rat @ X3 )
% 15.48/8.46          = ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 15.48/8.46        = ( X3
% 15.48/8.46          = ( power_power_nat @ B @ W ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_139_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [X3: nat,B: nat,W: nat] :
% 15.48/8.46        ( ( ( semiri1316708129612266289at_nat @ X3 )
% 15.48/8.46          = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 15.48/8.46        = ( X3
% 15.48/8.46          = ( power_power_nat @ B @ W ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_140_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [X3: nat,B: nat,W: nat] :
% 15.48/8.46        ( ( ( semiri1314217659103216013at_int @ X3 )
% 15.48/8.46          = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 15.48/8.46        = ( X3
% 15.48/8.46          = ( power_power_nat @ B @ W ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_141_semiring__norm_I69_J,axiom,
% 15.48/8.46      ! [M: num] :
% 15.48/8.46        ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_142_enat__ord__number_I1_J,axiom,
% 15.48/8.46      ! [M: num,N: num] :
% 15.48/8.46        ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 15.48/8.46        = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_143_lesseq__shift,axiom,
% 15.48/8.46      ( ord_less_eq_nat
% 15.48/8.46      = ( ^ [X: nat,Y: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X ) @ ( some_nat @ Y ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_144_numeral__power__eq__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [X3: num,N: nat,Y3: nat] :
% 15.48/8.46        ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X3 ) @ N )
% 15.48/8.46          = ( semiri8010041392384452111omplex @ Y3 ) )
% 15.48/8.46        = ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N )
% 15.48/8.46          = Y3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_145_numeral__power__eq__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [X3: num,N: nat,Y3: nat] :
% 15.48/8.46        ( ( ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N )
% 15.48/8.46          = ( semiri5074537144036343181t_real @ Y3 ) )
% 15.48/8.46        = ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N )
% 15.48/8.46          = Y3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_146_numeral__power__eq__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [X3: num,N: nat,Y3: nat] :
% 15.48/8.46        ( ( ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N )
% 15.48/8.46          = ( semiri681578069525770553at_rat @ Y3 ) )
% 15.48/8.46        = ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N )
% 15.48/8.46          = Y3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_147_numeral__power__eq__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [X3: num,N: nat,Y3: nat] :
% 15.48/8.46        ( ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N )
% 15.48/8.46          = ( semiri1316708129612266289at_nat @ Y3 ) )
% 15.48/8.46        = ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N )
% 15.48/8.46          = Y3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_148_numeral__power__eq__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [X3: num,N: nat,Y3: nat] :
% 15.48/8.46        ( ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N )
% 15.48/8.46          = ( semiri1314217659103216013at_int @ Y3 ) )
% 15.48/8.46        = ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N )
% 15.48/8.46          = Y3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_149_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 15.48/8.46      ! [Y3: nat,X3: num,N: nat] :
% 15.48/8.46        ( ( ( semiri8010041392384452111omplex @ Y3 )
% 15.48/8.46          = ( power_power_complex @ ( numera6690914467698888265omplex @ X3 ) @ N ) )
% 15.48/8.46        = ( Y3
% 15.48/8.46          = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_150_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 15.48/8.46      ! [Y3: nat,X3: num,N: nat] :
% 15.48/8.46        ( ( ( semiri5074537144036343181t_real @ Y3 )
% 15.48/8.46          = ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N ) )
% 15.48/8.46        = ( Y3
% 15.48/8.46          = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_151_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 15.48/8.46      ! [Y3: nat,X3: num,N: nat] :
% 15.48/8.46        ( ( ( semiri681578069525770553at_rat @ Y3 )
% 15.48/8.46          = ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N ) )
% 15.48/8.46        = ( Y3
% 15.48/8.46          = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_152_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 15.48/8.46      ! [Y3: nat,X3: num,N: nat] :
% 15.48/8.46        ( ( ( semiri1316708129612266289at_nat @ Y3 )
% 15.48/8.46          = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) )
% 15.48/8.46        = ( Y3
% 15.48/8.46          = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_153_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 15.48/8.46      ! [Y3: nat,X3: num,N: nat] :
% 15.48/8.46        ( ( ( semiri1314217659103216013at_int @ Y3 )
% 15.48/8.46          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) )
% 15.48/8.46        = ( Y3
% 15.48/8.46          = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_154_of__nat__less__of__nat__power__cancel__iff,axiom,
% 15.48/8.46      ! [B: nat,W: nat,X3: nat] :
% 15.48/8.46        ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X3 ) )
% 15.48/8.46        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_155_of__nat__less__of__nat__power__cancel__iff,axiom,
% 15.48/8.46      ! [B: nat,W: nat,X3: nat] :
% 15.48/8.46        ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X3 ) )
% 15.48/8.46        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_156_of__nat__less__of__nat__power__cancel__iff,axiom,
% 15.48/8.46      ! [B: nat,W: nat,X3: nat] :
% 15.48/8.46        ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X3 ) )
% 15.48/8.46        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_157_of__nat__less__of__nat__power__cancel__iff,axiom,
% 15.48/8.46      ! [B: nat,W: nat,X3: nat] :
% 15.48/8.46        ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X3 ) )
% 15.48/8.46        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_158_of__nat__power__less__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [X3: nat,B: nat,W: nat] :
% 15.48/8.46        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 15.48/8.46        = ( ord_less_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_159_of__nat__power__less__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [X3: nat,B: nat,W: nat] :
% 15.48/8.46        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 15.48/8.46        = ( ord_less_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_160_of__nat__power__less__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [X3: nat,B: nat,W: nat] :
% 15.48/8.46        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 15.48/8.46        = ( ord_less_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_161_of__nat__power__less__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [X3: nat,B: nat,W: nat] :
% 15.48/8.46        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 15.48/8.46        = ( ord_less_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_162_of__nat__le__of__nat__power__cancel__iff,axiom,
% 15.48/8.46      ! [B: nat,W: nat,X3: nat] :
% 15.48/8.46        ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X3 ) )
% 15.48/8.46        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_163_of__nat__le__of__nat__power__cancel__iff,axiom,
% 15.48/8.46      ! [B: nat,W: nat,X3: nat] :
% 15.48/8.46        ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X3 ) )
% 15.48/8.46        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_164_of__nat__le__of__nat__power__cancel__iff,axiom,
% 15.48/8.46      ! [B: nat,W: nat,X3: nat] :
% 15.48/8.46        ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X3 ) )
% 15.48/8.46        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_165_of__nat__le__of__nat__power__cancel__iff,axiom,
% 15.48/8.46      ! [B: nat,W: nat,X3: nat] :
% 15.48/8.46        ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X3 ) )
% 15.48/8.46        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_166_of__nat__power__le__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [X3: nat,B: nat,W: nat] :
% 15.48/8.46        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 15.48/8.46        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_167_of__nat__power__le__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [X3: nat,B: nat,W: nat] :
% 15.48/8.46        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 15.48/8.46        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_168_of__nat__power__le__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [X3: nat,B: nat,W: nat] :
% 15.48/8.46        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 15.48/8.46        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_169_of__nat__power__le__of__nat__cancel__iff,axiom,
% 15.48/8.46      ! [X3: nat,B: nat,W: nat] :
% 15.48/8.46        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 15.48/8.46        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_170_enat__less__induct,axiom,
% 15.48/8.46      ! [P: extended_enat > $o,N: extended_enat] :
% 15.48/8.46        ( ! [N2: extended_enat] :
% 15.48/8.46            ( ! [M2: extended_enat] :
% 15.48/8.46                ( ( ord_le72135733267957522d_enat @ M2 @ N2 )
% 15.48/8.46               => ( P @ M2 ) )
% 15.48/8.46           => ( P @ N2 ) )
% 15.48/8.46       => ( P @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_171_nat__int__comparison_I3_J,axiom,
% 15.48/8.46      ( ord_less_eq_nat
% 15.48/8.46      = ( ^ [A4: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_172_int__ops_I3_J,axiom,
% 15.48/8.46      ! [N: num] :
% 15.48/8.46        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 15.48/8.46        = ( numeral_numeral_int @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_173_nat__int__comparison_I2_J,axiom,
% 15.48/8.46      ( ord_less_nat
% 15.48/8.46      = ( ^ [A4: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_174_le__num__One__iff,axiom,
% 15.48/8.46      ! [X3: num] :
% 15.48/8.46        ( ( ord_less_eq_num @ X3 @ one )
% 15.48/8.46        = ( X3 = one ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_175_less__imp__of__nat__less,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ord_less_nat @ M @ N )
% 15.48/8.46       => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_176_less__imp__of__nat__less,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ord_less_nat @ M @ N )
% 15.48/8.46       => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_177_less__imp__of__nat__less,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ord_less_nat @ M @ N )
% 15.48/8.46       => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_178_less__imp__of__nat__less,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ord_less_nat @ M @ N )
% 15.48/8.46       => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_179_of__nat__less__imp__less,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 15.48/8.46       => ( ord_less_nat @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_180_of__nat__less__imp__less,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 15.48/8.46       => ( ord_less_nat @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_181_of__nat__less__imp__less,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 15.48/8.46       => ( ord_less_nat @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_182_of__nat__less__imp__less,axiom,
% 15.48/8.46      ! [M: nat,N: nat] :
% 15.48/8.46        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 15.48/8.46       => ( ord_less_nat @ M @ N ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_183_of__nat__mono,axiom,
% 15.48/8.46      ! [I: nat,J: nat] :
% 15.48/8.46        ( ( ord_less_eq_nat @ I @ J )
% 15.48/8.46       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_184_of__nat__mono,axiom,
% 15.48/8.46      ! [I: nat,J: nat] :
% 15.48/8.46        ( ( ord_less_eq_nat @ I @ J )
% 15.48/8.46       => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_185_of__nat__mono,axiom,
% 15.48/8.46      ! [I: nat,J: nat] :
% 15.48/8.46        ( ( ord_less_eq_nat @ I @ J )
% 15.48/8.46       => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_186_of__nat__mono,axiom,
% 15.48/8.46      ! [I: nat,J: nat] :
% 15.48/8.46        ( ( ord_less_eq_nat @ I @ J )
% 15.48/8.46       => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_187_pow_Osimps_I1_J,axiom,
% 15.48/8.46      ! [X3: num] :
% 15.48/8.46        ( ( pow @ X3 @ one )
% 15.48/8.46        = X3 ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_188_order__antisym__conv,axiom,
% 15.48/8.46      ! [Y3: set_nat,X3: set_nat] :
% 15.48/8.46        ( ( ord_less_eq_set_nat @ Y3 @ X3 )
% 15.48/8.46       => ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 15.48/8.46          = ( X3 = Y3 ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_189_order__antisym__conv,axiom,
% 15.48/8.46      ! [Y3: rat,X3: rat] :
% 15.48/8.46        ( ( ord_less_eq_rat @ Y3 @ X3 )
% 15.48/8.46       => ( ( ord_less_eq_rat @ X3 @ Y3 )
% 15.48/8.46          = ( X3 = Y3 ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_190_order__antisym__conv,axiom,
% 15.48/8.46      ! [Y3: num,X3: num] :
% 15.48/8.46        ( ( ord_less_eq_num @ Y3 @ X3 )
% 15.48/8.46       => ( ( ord_less_eq_num @ X3 @ Y3 )
% 15.48/8.46          = ( X3 = Y3 ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_191_order__antisym__conv,axiom,
% 15.48/8.46      ! [Y3: nat,X3: nat] :
% 15.48/8.46        ( ( ord_less_eq_nat @ Y3 @ X3 )
% 15.48/8.46       => ( ( ord_less_eq_nat @ X3 @ Y3 )
% 15.48/8.46          = ( X3 = Y3 ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_192_order__antisym__conv,axiom,
% 15.48/8.46      ! [Y3: int,X3: int] :
% 15.48/8.46        ( ( ord_less_eq_int @ Y3 @ X3 )
% 15.48/8.46       => ( ( ord_less_eq_int @ X3 @ Y3 )
% 15.48/8.46          = ( X3 = Y3 ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_193_linorder__le__cases,axiom,
% 15.48/8.46      ! [X3: rat,Y3: rat] :
% 15.48/8.46        ( ~ ( ord_less_eq_rat @ X3 @ Y3 )
% 15.48/8.46       => ( ord_less_eq_rat @ Y3 @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_194_linorder__le__cases,axiom,
% 15.48/8.46      ! [X3: num,Y3: num] :
% 15.48/8.46        ( ~ ( ord_less_eq_num @ X3 @ Y3 )
% 15.48/8.46       => ( ord_less_eq_num @ Y3 @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_195_linorder__le__cases,axiom,
% 15.48/8.46      ! [X3: nat,Y3: nat] :
% 15.48/8.46        ( ~ ( ord_less_eq_nat @ X3 @ Y3 )
% 15.48/8.46       => ( ord_less_eq_nat @ Y3 @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_196_linorder__le__cases,axiom,
% 15.48/8.46      ! [X3: int,Y3: int] :
% 15.48/8.46        ( ~ ( ord_less_eq_int @ X3 @ Y3 )
% 15.48/8.46       => ( ord_less_eq_int @ Y3 @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_197_ord__le__eq__subst,axiom,
% 15.48/8.46      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 15.48/8.46        ( ( ord_less_eq_rat @ A @ B )
% 15.48/8.46       => ( ( ( F @ B )
% 15.48/8.46            = C )
% 15.48/8.46         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_198_ord__le__eq__subst,axiom,
% 15.48/8.46      ! [A: rat,B: rat,F: rat > num,C: num] :
% 15.48/8.46        ( ( ord_less_eq_rat @ A @ B )
% 15.48/8.46       => ( ( ( F @ B )
% 15.48/8.46            = C )
% 15.48/8.46         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_199_ord__le__eq__subst,axiom,
% 15.48/8.46      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 15.48/8.46        ( ( ord_less_eq_rat @ A @ B )
% 15.48/8.46       => ( ( ( F @ B )
% 15.48/8.46            = C )
% 15.48/8.46         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_200_ord__le__eq__subst,axiom,
% 15.48/8.46      ! [A: rat,B: rat,F: rat > int,C: int] :
% 15.48/8.46        ( ( ord_less_eq_rat @ A @ B )
% 15.48/8.46       => ( ( ( F @ B )
% 15.48/8.46            = C )
% 15.48/8.46         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_201_ord__le__eq__subst,axiom,
% 15.48/8.46      ! [A: num,B: num,F: num > rat,C: rat] :
% 15.48/8.46        ( ( ord_less_eq_num @ A @ B )
% 15.48/8.46       => ( ( ( F @ B )
% 15.48/8.46            = C )
% 15.48/8.46         => ( ! [X4: num,Y4: num] :
% 15.48/8.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_202_ord__le__eq__subst,axiom,
% 15.48/8.46      ! [A: num,B: num,F: num > num,C: num] :
% 15.48/8.46        ( ( ord_less_eq_num @ A @ B )
% 15.48/8.46       => ( ( ( F @ B )
% 15.48/8.46            = C )
% 15.48/8.46         => ( ! [X4: num,Y4: num] :
% 15.48/8.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_203_ord__le__eq__subst,axiom,
% 15.48/8.46      ! [A: num,B: num,F: num > nat,C: nat] :
% 15.48/8.46        ( ( ord_less_eq_num @ A @ B )
% 15.48/8.46       => ( ( ( F @ B )
% 15.48/8.46            = C )
% 15.48/8.46         => ( ! [X4: num,Y4: num] :
% 15.48/8.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_204_ord__le__eq__subst,axiom,
% 15.48/8.46      ! [A: num,B: num,F: num > int,C: int] :
% 15.48/8.46        ( ( ord_less_eq_num @ A @ B )
% 15.48/8.46       => ( ( ( F @ B )
% 15.48/8.46            = C )
% 15.48/8.46         => ( ! [X4: num,Y4: num] :
% 15.48/8.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_205_ord__le__eq__subst,axiom,
% 15.48/8.46      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 15.48/8.46        ( ( ord_less_eq_nat @ A @ B )
% 15.48/8.46       => ( ( ( F @ B )
% 15.48/8.46            = C )
% 15.48/8.46         => ( ! [X4: nat,Y4: nat] :
% 15.48/8.46                ( ( ord_less_eq_nat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_206_ord__le__eq__subst,axiom,
% 15.48/8.46      ! [A: nat,B: nat,F: nat > num,C: num] :
% 15.48/8.46        ( ( ord_less_eq_nat @ A @ B )
% 15.48/8.46       => ( ( ( F @ B )
% 15.48/8.46            = C )
% 15.48/8.46         => ( ! [X4: nat,Y4: nat] :
% 15.48/8.46                ( ( ord_less_eq_nat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_207_ord__eq__le__subst,axiom,
% 15.48/8.46      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 15.48/8.46        ( ( A
% 15.48/8.46          = ( F @ B ) )
% 15.48/8.46       => ( ( ord_less_eq_rat @ B @ C )
% 15.48/8.46         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_208_ord__eq__le__subst,axiom,
% 15.48/8.46      ! [A: num,F: rat > num,B: rat,C: rat] :
% 15.48/8.46        ( ( A
% 15.48/8.46          = ( F @ B ) )
% 15.48/8.46       => ( ( ord_less_eq_rat @ B @ C )
% 15.48/8.46         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_209_ord__eq__le__subst,axiom,
% 15.48/8.46      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 15.48/8.46        ( ( A
% 15.48/8.46          = ( F @ B ) )
% 15.48/8.46       => ( ( ord_less_eq_rat @ B @ C )
% 15.48/8.46         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_210_ord__eq__le__subst,axiom,
% 15.48/8.46      ! [A: int,F: rat > int,B: rat,C: rat] :
% 15.48/8.46        ( ( A
% 15.48/8.46          = ( F @ B ) )
% 15.48/8.46       => ( ( ord_less_eq_rat @ B @ C )
% 15.48/8.46         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_211_ord__eq__le__subst,axiom,
% 15.48/8.46      ! [A: rat,F: num > rat,B: num,C: num] :
% 15.48/8.46        ( ( A
% 15.48/8.46          = ( F @ B ) )
% 15.48/8.46       => ( ( ord_less_eq_num @ B @ C )
% 15.48/8.46         => ( ! [X4: num,Y4: num] :
% 15.48/8.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_212_ord__eq__le__subst,axiom,
% 15.48/8.46      ! [A: num,F: num > num,B: num,C: num] :
% 15.48/8.46        ( ( A
% 15.48/8.46          = ( F @ B ) )
% 15.48/8.46       => ( ( ord_less_eq_num @ B @ C )
% 15.48/8.46         => ( ! [X4: num,Y4: num] :
% 15.48/8.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_213_ord__eq__le__subst,axiom,
% 15.48/8.46      ! [A: nat,F: num > nat,B: num,C: num] :
% 15.48/8.46        ( ( A
% 15.48/8.46          = ( F @ B ) )
% 15.48/8.46       => ( ( ord_less_eq_num @ B @ C )
% 15.48/8.46         => ( ! [X4: num,Y4: num] :
% 15.48/8.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_214_ord__eq__le__subst,axiom,
% 15.48/8.46      ! [A: int,F: num > int,B: num,C: num] :
% 15.48/8.46        ( ( A
% 15.48/8.46          = ( F @ B ) )
% 15.48/8.46       => ( ( ord_less_eq_num @ B @ C )
% 15.48/8.46         => ( ! [X4: num,Y4: num] :
% 15.48/8.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_215_ord__eq__le__subst,axiom,
% 15.48/8.46      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 15.48/8.46        ( ( A
% 15.48/8.46          = ( F @ B ) )
% 15.48/8.46       => ( ( ord_less_eq_nat @ B @ C )
% 15.48/8.46         => ( ! [X4: nat,Y4: nat] :
% 15.48/8.46                ( ( ord_less_eq_nat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_216_ord__eq__le__subst,axiom,
% 15.48/8.46      ! [A: num,F: nat > num,B: nat,C: nat] :
% 15.48/8.46        ( ( A
% 15.48/8.46          = ( F @ B ) )
% 15.48/8.46       => ( ( ord_less_eq_nat @ B @ C )
% 15.48/8.46         => ( ! [X4: nat,Y4: nat] :
% 15.48/8.46                ( ( ord_less_eq_nat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_217_linorder__linear,axiom,
% 15.48/8.46      ! [X3: rat,Y3: rat] :
% 15.48/8.46        ( ( ord_less_eq_rat @ X3 @ Y3 )
% 15.48/8.46        | ( ord_less_eq_rat @ Y3 @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_218_linorder__linear,axiom,
% 15.48/8.46      ! [X3: num,Y3: num] :
% 15.48/8.46        ( ( ord_less_eq_num @ X3 @ Y3 )
% 15.48/8.46        | ( ord_less_eq_num @ Y3 @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_219_linorder__linear,axiom,
% 15.48/8.46      ! [X3: nat,Y3: nat] :
% 15.48/8.46        ( ( ord_less_eq_nat @ X3 @ Y3 )
% 15.48/8.46        | ( ord_less_eq_nat @ Y3 @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_220_linorder__linear,axiom,
% 15.48/8.46      ! [X3: int,Y3: int] :
% 15.48/8.46        ( ( ord_less_eq_int @ X3 @ Y3 )
% 15.48/8.46        | ( ord_less_eq_int @ Y3 @ X3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_221_order__eq__refl,axiom,
% 15.48/8.46      ! [X3: set_nat,Y3: set_nat] :
% 15.48/8.46        ( ( X3 = Y3 )
% 15.48/8.46       => ( ord_less_eq_set_nat @ X3 @ Y3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_222_order__eq__refl,axiom,
% 15.48/8.46      ! [X3: rat,Y3: rat] :
% 15.48/8.46        ( ( X3 = Y3 )
% 15.48/8.46       => ( ord_less_eq_rat @ X3 @ Y3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_223_order__eq__refl,axiom,
% 15.48/8.46      ! [X3: num,Y3: num] :
% 15.48/8.46        ( ( X3 = Y3 )
% 15.48/8.46       => ( ord_less_eq_num @ X3 @ Y3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_224_order__eq__refl,axiom,
% 15.48/8.46      ! [X3: nat,Y3: nat] :
% 15.48/8.46        ( ( X3 = Y3 )
% 15.48/8.46       => ( ord_less_eq_nat @ X3 @ Y3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_225_order__eq__refl,axiom,
% 15.48/8.46      ! [X3: int,Y3: int] :
% 15.48/8.46        ( ( X3 = Y3 )
% 15.48/8.46       => ( ord_less_eq_int @ X3 @ Y3 ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_226_order__subst2,axiom,
% 15.48/8.46      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 15.48/8.46        ( ( ord_less_eq_rat @ A @ B )
% 15.48/8.46       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 15.48/8.46         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_227_order__subst2,axiom,
% 15.48/8.46      ! [A: rat,B: rat,F: rat > num,C: num] :
% 15.48/8.46        ( ( ord_less_eq_rat @ A @ B )
% 15.48/8.46       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 15.48/8.46         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_228_order__subst2,axiom,
% 15.48/8.46      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 15.48/8.46        ( ( ord_less_eq_rat @ A @ B )
% 15.48/8.46       => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 15.48/8.46         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_229_order__subst2,axiom,
% 15.48/8.46      ! [A: rat,B: rat,F: rat > int,C: int] :
% 15.48/8.46        ( ( ord_less_eq_rat @ A @ B )
% 15.48/8.46       => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 15.48/8.46         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_230_order__subst2,axiom,
% 15.48/8.46      ! [A: num,B: num,F: num > rat,C: rat] :
% 15.48/8.46        ( ( ord_less_eq_num @ A @ B )
% 15.48/8.46       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 15.48/8.46         => ( ! [X4: num,Y4: num] :
% 15.48/8.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_231_order__subst2,axiom,
% 15.48/8.46      ! [A: num,B: num,F: num > num,C: num] :
% 15.48/8.46        ( ( ord_less_eq_num @ A @ B )
% 15.48/8.46       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 15.48/8.46         => ( ! [X4: num,Y4: num] :
% 15.48/8.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_232_order__subst2,axiom,
% 15.48/8.46      ! [A: num,B: num,F: num > nat,C: nat] :
% 15.48/8.46        ( ( ord_less_eq_num @ A @ B )
% 15.48/8.46       => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 15.48/8.46         => ( ! [X4: num,Y4: num] :
% 15.48/8.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_233_order__subst2,axiom,
% 15.48/8.46      ! [A: num,B: num,F: num > int,C: int] :
% 15.48/8.46        ( ( ord_less_eq_num @ A @ B )
% 15.48/8.46       => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 15.48/8.46         => ( ! [X4: num,Y4: num] :
% 15.48/8.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_234_order__subst2,axiom,
% 15.48/8.46      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 15.48/8.46        ( ( ord_less_eq_nat @ A @ B )
% 15.48/8.46       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 15.48/8.46         => ( ! [X4: nat,Y4: nat] :
% 15.48/8.46                ( ( ord_less_eq_nat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_235_order__subst2,axiom,
% 15.48/8.46      ! [A: nat,B: nat,F: nat > num,C: num] :
% 15.48/8.46        ( ( ord_less_eq_nat @ A @ B )
% 15.48/8.46       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 15.48/8.46         => ( ! [X4: nat,Y4: nat] :
% 15.48/8.46                ( ( ord_less_eq_nat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_236_order__subst1,axiom,
% 15.48/8.46      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 15.48/8.46        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 15.48/8.46       => ( ( ord_less_eq_rat @ B @ C )
% 15.48/8.46         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_237_order__subst1,axiom,
% 15.48/8.46      ! [A: rat,F: num > rat,B: num,C: num] :
% 15.48/8.46        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 15.48/8.46       => ( ( ord_less_eq_num @ B @ C )
% 15.48/8.46         => ( ! [X4: num,Y4: num] :
% 15.48/8.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_238_order__subst1,axiom,
% 15.48/8.46      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 15.48/8.46        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 15.48/8.46       => ( ( ord_less_eq_nat @ B @ C )
% 15.48/8.46         => ( ! [X4: nat,Y4: nat] :
% 15.48/8.46                ( ( ord_less_eq_nat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_239_order__subst1,axiom,
% 15.48/8.46      ! [A: rat,F: int > rat,B: int,C: int] :
% 15.48/8.46        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 15.48/8.46       => ( ( ord_less_eq_int @ B @ C )
% 15.48/8.46         => ( ! [X4: int,Y4: int] :
% 15.48/8.46                ( ( ord_less_eq_int @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_240_order__subst1,axiom,
% 15.48/8.46      ! [A: num,F: rat > num,B: rat,C: rat] :
% 15.48/8.46        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 15.48/8.46       => ( ( ord_less_eq_rat @ B @ C )
% 15.48/8.46         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_241_order__subst1,axiom,
% 15.48/8.46      ! [A: num,F: num > num,B: num,C: num] :
% 15.48/8.46        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 15.48/8.46       => ( ( ord_less_eq_num @ B @ C )
% 15.48/8.46         => ( ! [X4: num,Y4: num] :
% 15.48/8.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_242_order__subst1,axiom,
% 15.48/8.46      ! [A: num,F: nat > num,B: nat,C: nat] :
% 15.48/8.46        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 15.48/8.46       => ( ( ord_less_eq_nat @ B @ C )
% 15.48/8.46         => ( ! [X4: nat,Y4: nat] :
% 15.48/8.46                ( ( ord_less_eq_nat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_243_order__subst1,axiom,
% 15.48/8.46      ! [A: num,F: int > num,B: int,C: int] :
% 15.48/8.46        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 15.48/8.46       => ( ( ord_less_eq_int @ B @ C )
% 15.48/8.46         => ( ! [X4: int,Y4: int] :
% 15.48/8.46                ( ( ord_less_eq_int @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_244_order__subst1,axiom,
% 15.48/8.46      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 15.48/8.46        ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 15.48/8.46       => ( ( ord_less_eq_rat @ B @ C )
% 15.48/8.46         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.46                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_245_order__subst1,axiom,
% 15.48/8.46      ! [A: nat,F: num > nat,B: num,C: num] :
% 15.48/8.46        ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 15.48/8.46       => ( ( ord_less_eq_num @ B @ C )
% 15.48/8.46         => ( ! [X4: num,Y4: num] :
% 15.48/8.46                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.46               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.46           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_246_Orderings_Oorder__eq__iff,axiom,
% 15.48/8.46      ( ( ^ [Y5: set_nat,Z2: set_nat] : ( Y5 = Z2 ) )
% 15.48/8.46      = ( ^ [A4: set_nat,B3: set_nat] :
% 15.48/8.46            ( ( ord_less_eq_set_nat @ A4 @ B3 )
% 15.48/8.46            & ( ord_less_eq_set_nat @ B3 @ A4 ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_247_Orderings_Oorder__eq__iff,axiom,
% 15.48/8.46      ( ( ^ [Y5: rat,Z2: rat] : ( Y5 = Z2 ) )
% 15.48/8.46      = ( ^ [A4: rat,B3: rat] :
% 15.48/8.46            ( ( ord_less_eq_rat @ A4 @ B3 )
% 15.48/8.46            & ( ord_less_eq_rat @ B3 @ A4 ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_248_Orderings_Oorder__eq__iff,axiom,
% 15.48/8.46      ( ( ^ [Y5: num,Z2: num] : ( Y5 = Z2 ) )
% 15.48/8.46      = ( ^ [A4: num,B3: num] :
% 15.48/8.46            ( ( ord_less_eq_num @ A4 @ B3 )
% 15.48/8.46            & ( ord_less_eq_num @ B3 @ A4 ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_249_Orderings_Oorder__eq__iff,axiom,
% 15.48/8.46      ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 15.48/8.46      = ( ^ [A4: nat,B3: nat] :
% 15.48/8.46            ( ( ord_less_eq_nat @ A4 @ B3 )
% 15.48/8.46            & ( ord_less_eq_nat @ B3 @ A4 ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_250_Orderings_Oorder__eq__iff,axiom,
% 15.48/8.46      ( ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 15.48/8.46      = ( ^ [A4: int,B3: int] :
% 15.48/8.46            ( ( ord_less_eq_int @ A4 @ B3 )
% 15.48/8.46            & ( ord_less_eq_int @ B3 @ A4 ) ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_251_antisym,axiom,
% 15.48/8.46      ! [A: set_nat,B: set_nat] :
% 15.48/8.46        ( ( ord_less_eq_set_nat @ A @ B )
% 15.48/8.46       => ( ( ord_less_eq_set_nat @ B @ A )
% 15.48/8.46         => ( A = B ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_252_antisym,axiom,
% 15.48/8.46      ! [A: rat,B: rat] :
% 15.48/8.46        ( ( ord_less_eq_rat @ A @ B )
% 15.48/8.46       => ( ( ord_less_eq_rat @ B @ A )
% 15.48/8.46         => ( A = B ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_253_antisym,axiom,
% 15.48/8.46      ! [A: num,B: num] :
% 15.48/8.46        ( ( ord_less_eq_num @ A @ B )
% 15.48/8.46       => ( ( ord_less_eq_num @ B @ A )
% 15.48/8.46         => ( A = B ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_254_antisym,axiom,
% 15.48/8.46      ! [A: nat,B: nat] :
% 15.48/8.46        ( ( ord_less_eq_nat @ A @ B )
% 15.48/8.46       => ( ( ord_less_eq_nat @ B @ A )
% 15.48/8.46         => ( A = B ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_255_antisym,axiom,
% 15.48/8.46      ! [A: int,B: int] :
% 15.48/8.46        ( ( ord_less_eq_int @ A @ B )
% 15.48/8.46       => ( ( ord_less_eq_int @ B @ A )
% 15.48/8.46         => ( A = B ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_256_dual__order_Otrans,axiom,
% 15.48/8.46      ! [B: set_nat,A: set_nat,C: set_nat] :
% 15.48/8.46        ( ( ord_less_eq_set_nat @ B @ A )
% 15.48/8.46       => ( ( ord_less_eq_set_nat @ C @ B )
% 15.48/8.46         => ( ord_less_eq_set_nat @ C @ A ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_257_dual__order_Otrans,axiom,
% 15.48/8.46      ! [B: rat,A: rat,C: rat] :
% 15.48/8.46        ( ( ord_less_eq_rat @ B @ A )
% 15.48/8.46       => ( ( ord_less_eq_rat @ C @ B )
% 15.48/8.46         => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_258_dual__order_Otrans,axiom,
% 15.48/8.46      ! [B: num,A: num,C: num] :
% 15.48/8.46        ( ( ord_less_eq_num @ B @ A )
% 15.48/8.46       => ( ( ord_less_eq_num @ C @ B )
% 15.48/8.46         => ( ord_less_eq_num @ C @ A ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_259_dual__order_Otrans,axiom,
% 15.48/8.46      ! [B: nat,A: nat,C: nat] :
% 15.48/8.46        ( ( ord_less_eq_nat @ B @ A )
% 15.48/8.46       => ( ( ord_less_eq_nat @ C @ B )
% 15.48/8.46         => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_260_dual__order_Otrans,axiom,
% 15.48/8.46      ! [B: int,A: int,C: int] :
% 15.48/8.46        ( ( ord_less_eq_int @ B @ A )
% 15.48/8.46       => ( ( ord_less_eq_int @ C @ B )
% 15.48/8.46         => ( ord_less_eq_int @ C @ A ) ) ) ).
% 15.48/8.46  
% 15.48/8.46  thf(fact_261_dual__order_Oantisym,axiom,
% 15.48/8.46      ! [B: set_nat,A: set_nat] :
% 15.48/8.46        ( ( ord_less_eq_set_nat @ B @ A )
% 15.48/8.46       => ( ( ord_less_eq_set_nat @ A @ B )
% 15.48/8.46         => ( A = B ) ) ) ).
% 15.48/8.46  
% 15.48/8.47  thf(fact_262_dual__order_Oantisym,axiom,
% 15.48/8.47      ! [B: rat,A: rat] :
% 15.48/8.47        ( ( ord_less_eq_rat @ B @ A )
% 15.48/8.47       => ( ( ord_less_eq_rat @ A @ B )
% 15.48/8.47         => ( A = B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_263_dual__order_Oantisym,axiom,
% 15.48/8.47      ! [B: num,A: num] :
% 15.48/8.47        ( ( ord_less_eq_num @ B @ A )
% 15.48/8.47       => ( ( ord_less_eq_num @ A @ B )
% 15.48/8.47         => ( A = B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_264_dual__order_Oantisym,axiom,
% 15.48/8.47      ! [B: nat,A: nat] :
% 15.48/8.47        ( ( ord_less_eq_nat @ B @ A )
% 15.48/8.47       => ( ( ord_less_eq_nat @ A @ B )
% 15.48/8.47         => ( A = B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_265_dual__order_Oantisym,axiom,
% 15.48/8.47      ! [B: int,A: int] :
% 15.48/8.47        ( ( ord_less_eq_int @ B @ A )
% 15.48/8.47       => ( ( ord_less_eq_int @ A @ B )
% 15.48/8.47         => ( A = B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_266_dual__order_Oeq__iff,axiom,
% 15.48/8.47      ( ( ^ [Y5: set_nat,Z2: set_nat] : ( Y5 = Z2 ) )
% 15.48/8.47      = ( ^ [A4: set_nat,B3: set_nat] :
% 15.48/8.47            ( ( ord_less_eq_set_nat @ B3 @ A4 )
% 15.48/8.47            & ( ord_less_eq_set_nat @ A4 @ B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_267_dual__order_Oeq__iff,axiom,
% 15.48/8.47      ( ( ^ [Y5: rat,Z2: rat] : ( Y5 = Z2 ) )
% 15.48/8.47      = ( ^ [A4: rat,B3: rat] :
% 15.48/8.47            ( ( ord_less_eq_rat @ B3 @ A4 )
% 15.48/8.47            & ( ord_less_eq_rat @ A4 @ B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_268_dual__order_Oeq__iff,axiom,
% 15.48/8.47      ( ( ^ [Y5: num,Z2: num] : ( Y5 = Z2 ) )
% 15.48/8.47      = ( ^ [A4: num,B3: num] :
% 15.48/8.47            ( ( ord_less_eq_num @ B3 @ A4 )
% 15.48/8.47            & ( ord_less_eq_num @ A4 @ B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_269_dual__order_Oeq__iff,axiom,
% 15.48/8.47      ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 15.48/8.47      = ( ^ [A4: nat,B3: nat] :
% 15.48/8.47            ( ( ord_less_eq_nat @ B3 @ A4 )
% 15.48/8.47            & ( ord_less_eq_nat @ A4 @ B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_270_dual__order_Oeq__iff,axiom,
% 15.48/8.47      ( ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 15.48/8.47      = ( ^ [A4: int,B3: int] :
% 15.48/8.47            ( ( ord_less_eq_int @ B3 @ A4 )
% 15.48/8.47            & ( ord_less_eq_int @ A4 @ B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_271_linorder__wlog,axiom,
% 15.48/8.47      ! [P: rat > rat > $o,A: rat,B: rat] :
% 15.48/8.47        ( ! [A5: rat,B4: rat] :
% 15.48/8.47            ( ( ord_less_eq_rat @ A5 @ B4 )
% 15.48/8.47           => ( P @ A5 @ B4 ) )
% 15.48/8.47       => ( ! [A5: rat,B4: rat] :
% 15.48/8.47              ( ( P @ B4 @ A5 )
% 15.48/8.47             => ( P @ A5 @ B4 ) )
% 15.48/8.47         => ( P @ A @ B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_272_linorder__wlog,axiom,
% 15.48/8.47      ! [P: num > num > $o,A: num,B: num] :
% 15.48/8.47        ( ! [A5: num,B4: num] :
% 15.48/8.47            ( ( ord_less_eq_num @ A5 @ B4 )
% 15.48/8.47           => ( P @ A5 @ B4 ) )
% 15.48/8.47       => ( ! [A5: num,B4: num] :
% 15.48/8.47              ( ( P @ B4 @ A5 )
% 15.48/8.47             => ( P @ A5 @ B4 ) )
% 15.48/8.47         => ( P @ A @ B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_273_linorder__wlog,axiom,
% 15.48/8.47      ! [P: nat > nat > $o,A: nat,B: nat] :
% 15.48/8.47        ( ! [A5: nat,B4: nat] :
% 15.48/8.47            ( ( ord_less_eq_nat @ A5 @ B4 )
% 15.48/8.47           => ( P @ A5 @ B4 ) )
% 15.48/8.47       => ( ! [A5: nat,B4: nat] :
% 15.48/8.47              ( ( P @ B4 @ A5 )
% 15.48/8.47             => ( P @ A5 @ B4 ) )
% 15.48/8.47         => ( P @ A @ B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_274_linorder__wlog,axiom,
% 15.48/8.47      ! [P: int > int > $o,A: int,B: int] :
% 15.48/8.47        ( ! [A5: int,B4: int] :
% 15.48/8.47            ( ( ord_less_eq_int @ A5 @ B4 )
% 15.48/8.47           => ( P @ A5 @ B4 ) )
% 15.48/8.47       => ( ! [A5: int,B4: int] :
% 15.48/8.47              ( ( P @ B4 @ A5 )
% 15.48/8.47             => ( P @ A5 @ B4 ) )
% 15.48/8.47         => ( P @ A @ B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_275_order__trans,axiom,
% 15.48/8.47      ! [X3: set_nat,Y3: set_nat,Z: set_nat] :
% 15.48/8.47        ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_eq_set_nat @ Y3 @ Z )
% 15.48/8.47         => ( ord_less_eq_set_nat @ X3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_276_order__trans,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat,Z: rat] :
% 15.48/8.47        ( ( ord_less_eq_rat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_eq_rat @ Y3 @ Z )
% 15.48/8.47         => ( ord_less_eq_rat @ X3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_277_order__trans,axiom,
% 15.48/8.47      ! [X3: num,Y3: num,Z: num] :
% 15.48/8.47        ( ( ord_less_eq_num @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_eq_num @ Y3 @ Z )
% 15.48/8.47         => ( ord_less_eq_num @ X3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_278_order__trans,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat,Z: nat] :
% 15.48/8.47        ( ( ord_less_eq_nat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_eq_nat @ Y3 @ Z )
% 15.48/8.47         => ( ord_less_eq_nat @ X3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_279_order__trans,axiom,
% 15.48/8.47      ! [X3: int,Y3: int,Z: int] :
% 15.48/8.47        ( ( ord_less_eq_int @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_eq_int @ Y3 @ Z )
% 15.48/8.47         => ( ord_less_eq_int @ X3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_280_order_Otrans,axiom,
% 15.48/8.47      ! [A: set_nat,B: set_nat,C: set_nat] :
% 15.48/8.47        ( ( ord_less_eq_set_nat @ A @ B )
% 15.48/8.47       => ( ( ord_less_eq_set_nat @ B @ C )
% 15.48/8.47         => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_281_order_Otrans,axiom,
% 15.48/8.47      ! [A: rat,B: rat,C: rat] :
% 15.48/8.47        ( ( ord_less_eq_rat @ A @ B )
% 15.48/8.47       => ( ( ord_less_eq_rat @ B @ C )
% 15.48/8.47         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_282_order_Otrans,axiom,
% 15.48/8.47      ! [A: num,B: num,C: num] :
% 15.48/8.47        ( ( ord_less_eq_num @ A @ B )
% 15.48/8.47       => ( ( ord_less_eq_num @ B @ C )
% 15.48/8.47         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_283_order_Otrans,axiom,
% 15.48/8.47      ! [A: nat,B: nat,C: nat] :
% 15.48/8.47        ( ( ord_less_eq_nat @ A @ B )
% 15.48/8.47       => ( ( ord_less_eq_nat @ B @ C )
% 15.48/8.47         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_284_order_Otrans,axiom,
% 15.48/8.47      ! [A: int,B: int,C: int] :
% 15.48/8.47        ( ( ord_less_eq_int @ A @ B )
% 15.48/8.47       => ( ( ord_less_eq_int @ B @ C )
% 15.48/8.47         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_285_order__antisym,axiom,
% 15.48/8.47      ! [X3: set_nat,Y3: set_nat] :
% 15.48/8.47        ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_eq_set_nat @ Y3 @ X3 )
% 15.48/8.47         => ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_286_order__antisym,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat] :
% 15.48/8.47        ( ( ord_less_eq_rat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_eq_rat @ Y3 @ X3 )
% 15.48/8.47         => ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_287_order__antisym,axiom,
% 15.48/8.47      ! [X3: num,Y3: num] :
% 15.48/8.47        ( ( ord_less_eq_num @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_eq_num @ Y3 @ X3 )
% 15.48/8.47         => ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_288_order__antisym,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat] :
% 15.48/8.47        ( ( ord_less_eq_nat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_eq_nat @ Y3 @ X3 )
% 15.48/8.47         => ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_289_order__antisym,axiom,
% 15.48/8.47      ! [X3: int,Y3: int] :
% 15.48/8.47        ( ( ord_less_eq_int @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_eq_int @ Y3 @ X3 )
% 15.48/8.47         => ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_290_ord__le__eq__trans,axiom,
% 15.48/8.47      ! [A: set_nat,B: set_nat,C: set_nat] :
% 15.48/8.47        ( ( ord_less_eq_set_nat @ A @ B )
% 15.48/8.47       => ( ( B = C )
% 15.48/8.47         => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_291_ord__le__eq__trans,axiom,
% 15.48/8.47      ! [A: rat,B: rat,C: rat] :
% 15.48/8.47        ( ( ord_less_eq_rat @ A @ B )
% 15.48/8.47       => ( ( B = C )
% 15.48/8.47         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_292_ord__le__eq__trans,axiom,
% 15.48/8.47      ! [A: num,B: num,C: num] :
% 15.48/8.47        ( ( ord_less_eq_num @ A @ B )
% 15.48/8.47       => ( ( B = C )
% 15.48/8.47         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_293_ord__le__eq__trans,axiom,
% 15.48/8.47      ! [A: nat,B: nat,C: nat] :
% 15.48/8.47        ( ( ord_less_eq_nat @ A @ B )
% 15.48/8.47       => ( ( B = C )
% 15.48/8.47         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_294_ord__le__eq__trans,axiom,
% 15.48/8.47      ! [A: int,B: int,C: int] :
% 15.48/8.47        ( ( ord_less_eq_int @ A @ B )
% 15.48/8.47       => ( ( B = C )
% 15.48/8.47         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_295_ord__eq__le__trans,axiom,
% 15.48/8.47      ! [A: set_nat,B: set_nat,C: set_nat] :
% 15.48/8.47        ( ( A = B )
% 15.48/8.47       => ( ( ord_less_eq_set_nat @ B @ C )
% 15.48/8.47         => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_296_ord__eq__le__trans,axiom,
% 15.48/8.47      ! [A: rat,B: rat,C: rat] :
% 15.48/8.47        ( ( A = B )
% 15.48/8.47       => ( ( ord_less_eq_rat @ B @ C )
% 15.48/8.47         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_297_ord__eq__le__trans,axiom,
% 15.48/8.47      ! [A: num,B: num,C: num] :
% 15.48/8.47        ( ( A = B )
% 15.48/8.47       => ( ( ord_less_eq_num @ B @ C )
% 15.48/8.47         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_298_ord__eq__le__trans,axiom,
% 15.48/8.47      ! [A: nat,B: nat,C: nat] :
% 15.48/8.47        ( ( A = B )
% 15.48/8.47       => ( ( ord_less_eq_nat @ B @ C )
% 15.48/8.47         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_299_ord__eq__le__trans,axiom,
% 15.48/8.47      ! [A: int,B: int,C: int] :
% 15.48/8.47        ( ( A = B )
% 15.48/8.47       => ( ( ord_less_eq_int @ B @ C )
% 15.48/8.47         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_300_order__class_Oorder__eq__iff,axiom,
% 15.48/8.47      ( ( ^ [Y5: set_nat,Z2: set_nat] : ( Y5 = Z2 ) )
% 15.48/8.47      = ( ^ [X: set_nat,Y: set_nat] :
% 15.48/8.47            ( ( ord_less_eq_set_nat @ X @ Y )
% 15.48/8.47            & ( ord_less_eq_set_nat @ Y @ X ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_301_order__class_Oorder__eq__iff,axiom,
% 15.48/8.47      ( ( ^ [Y5: rat,Z2: rat] : ( Y5 = Z2 ) )
% 15.48/8.47      = ( ^ [X: rat,Y: rat] :
% 15.48/8.47            ( ( ord_less_eq_rat @ X @ Y )
% 15.48/8.47            & ( ord_less_eq_rat @ Y @ X ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_302_order__class_Oorder__eq__iff,axiom,
% 15.48/8.47      ( ( ^ [Y5: num,Z2: num] : ( Y5 = Z2 ) )
% 15.48/8.47      = ( ^ [X: num,Y: num] :
% 15.48/8.47            ( ( ord_less_eq_num @ X @ Y )
% 15.48/8.47            & ( ord_less_eq_num @ Y @ X ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_303_order__class_Oorder__eq__iff,axiom,
% 15.48/8.47      ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 15.48/8.47      = ( ^ [X: nat,Y: nat] :
% 15.48/8.47            ( ( ord_less_eq_nat @ X @ Y )
% 15.48/8.47            & ( ord_less_eq_nat @ Y @ X ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_304_order__class_Oorder__eq__iff,axiom,
% 15.48/8.47      ( ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 15.48/8.47      = ( ^ [X: int,Y: int] :
% 15.48/8.47            ( ( ord_less_eq_int @ X @ Y )
% 15.48/8.47            & ( ord_less_eq_int @ Y @ X ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_305_le__cases3,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat,Z: rat] :
% 15.48/8.47        ( ( ( ord_less_eq_rat @ X3 @ Y3 )
% 15.48/8.47         => ~ ( ord_less_eq_rat @ Y3 @ Z ) )
% 15.48/8.47       => ( ( ( ord_less_eq_rat @ Y3 @ X3 )
% 15.48/8.47           => ~ ( ord_less_eq_rat @ X3 @ Z ) )
% 15.48/8.47         => ( ( ( ord_less_eq_rat @ X3 @ Z )
% 15.48/8.47             => ~ ( ord_less_eq_rat @ Z @ Y3 ) )
% 15.48/8.47           => ( ( ( ord_less_eq_rat @ Z @ Y3 )
% 15.48/8.47               => ~ ( ord_less_eq_rat @ Y3 @ X3 ) )
% 15.48/8.47             => ( ( ( ord_less_eq_rat @ Y3 @ Z )
% 15.48/8.47                 => ~ ( ord_less_eq_rat @ Z @ X3 ) )
% 15.48/8.47               => ~ ( ( ord_less_eq_rat @ Z @ X3 )
% 15.48/8.47                   => ~ ( ord_less_eq_rat @ X3 @ Y3 ) ) ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_306_le__cases3,axiom,
% 15.48/8.47      ! [X3: num,Y3: num,Z: num] :
% 15.48/8.47        ( ( ( ord_less_eq_num @ X3 @ Y3 )
% 15.48/8.47         => ~ ( ord_less_eq_num @ Y3 @ Z ) )
% 15.48/8.47       => ( ( ( ord_less_eq_num @ Y3 @ X3 )
% 15.48/8.47           => ~ ( ord_less_eq_num @ X3 @ Z ) )
% 15.48/8.47         => ( ( ( ord_less_eq_num @ X3 @ Z )
% 15.48/8.47             => ~ ( ord_less_eq_num @ Z @ Y3 ) )
% 15.48/8.47           => ( ( ( ord_less_eq_num @ Z @ Y3 )
% 15.48/8.47               => ~ ( ord_less_eq_num @ Y3 @ X3 ) )
% 15.48/8.47             => ( ( ( ord_less_eq_num @ Y3 @ Z )
% 15.48/8.47                 => ~ ( ord_less_eq_num @ Z @ X3 ) )
% 15.48/8.47               => ~ ( ( ord_less_eq_num @ Z @ X3 )
% 15.48/8.47                   => ~ ( ord_less_eq_num @ X3 @ Y3 ) ) ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_307_le__cases3,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat,Z: nat] :
% 15.48/8.47        ( ( ( ord_less_eq_nat @ X3 @ Y3 )
% 15.48/8.47         => ~ ( ord_less_eq_nat @ Y3 @ Z ) )
% 15.48/8.47       => ( ( ( ord_less_eq_nat @ Y3 @ X3 )
% 15.48/8.47           => ~ ( ord_less_eq_nat @ X3 @ Z ) )
% 15.48/8.47         => ( ( ( ord_less_eq_nat @ X3 @ Z )
% 15.48/8.47             => ~ ( ord_less_eq_nat @ Z @ Y3 ) )
% 15.48/8.47           => ( ( ( ord_less_eq_nat @ Z @ Y3 )
% 15.48/8.47               => ~ ( ord_less_eq_nat @ Y3 @ X3 ) )
% 15.48/8.47             => ( ( ( ord_less_eq_nat @ Y3 @ Z )
% 15.48/8.47                 => ~ ( ord_less_eq_nat @ Z @ X3 ) )
% 15.48/8.47               => ~ ( ( ord_less_eq_nat @ Z @ X3 )
% 15.48/8.47                   => ~ ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_308_le__cases3,axiom,
% 15.48/8.47      ! [X3: int,Y3: int,Z: int] :
% 15.48/8.47        ( ( ( ord_less_eq_int @ X3 @ Y3 )
% 15.48/8.47         => ~ ( ord_less_eq_int @ Y3 @ Z ) )
% 15.48/8.47       => ( ( ( ord_less_eq_int @ Y3 @ X3 )
% 15.48/8.47           => ~ ( ord_less_eq_int @ X3 @ Z ) )
% 15.48/8.47         => ( ( ( ord_less_eq_int @ X3 @ Z )
% 15.48/8.47             => ~ ( ord_less_eq_int @ Z @ Y3 ) )
% 15.48/8.47           => ( ( ( ord_less_eq_int @ Z @ Y3 )
% 15.48/8.47               => ~ ( ord_less_eq_int @ Y3 @ X3 ) )
% 15.48/8.47             => ( ( ( ord_less_eq_int @ Y3 @ Z )
% 15.48/8.47                 => ~ ( ord_less_eq_int @ Z @ X3 ) )
% 15.48/8.47               => ~ ( ( ord_less_eq_int @ Z @ X3 )
% 15.48/8.47                   => ~ ( ord_less_eq_int @ X3 @ Y3 ) ) ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_309_nle__le,axiom,
% 15.48/8.47      ! [A: rat,B: rat] :
% 15.48/8.47        ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 15.48/8.47        = ( ( ord_less_eq_rat @ B @ A )
% 15.48/8.47          & ( B != A ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_310_nle__le,axiom,
% 15.48/8.47      ! [A: num,B: num] :
% 15.48/8.47        ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 15.48/8.47        = ( ( ord_less_eq_num @ B @ A )
% 15.48/8.47          & ( B != A ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_311_nle__le,axiom,
% 15.48/8.47      ! [A: nat,B: nat] :
% 15.48/8.47        ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 15.48/8.47        = ( ( ord_less_eq_nat @ B @ A )
% 15.48/8.47          & ( B != A ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_312_nle__le,axiom,
% 15.48/8.47      ! [A: int,B: int] :
% 15.48/8.47        ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 15.48/8.47        = ( ( ord_less_eq_int @ B @ A )
% 15.48/8.47          & ( B != A ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_313_lt__ex,axiom,
% 15.48/8.47      ! [X3: real] :
% 15.48/8.47      ? [Y4: real] : ( ord_less_real @ Y4 @ X3 ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_314_lt__ex,axiom,
% 15.48/8.47      ! [X3: rat] :
% 15.48/8.47      ? [Y4: rat] : ( ord_less_rat @ Y4 @ X3 ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_315_lt__ex,axiom,
% 15.48/8.47      ! [X3: int] :
% 15.48/8.47      ? [Y4: int] : ( ord_less_int @ Y4 @ X3 ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_316_gt__ex,axiom,
% 15.48/8.47      ! [X3: real] :
% 15.48/8.47      ? [X_1: real] : ( ord_less_real @ X3 @ X_1 ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_317_gt__ex,axiom,
% 15.48/8.47      ! [X3: rat] :
% 15.48/8.47      ? [X_1: rat] : ( ord_less_rat @ X3 @ X_1 ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_318_gt__ex,axiom,
% 15.48/8.47      ! [X3: nat] :
% 15.48/8.47      ? [X_1: nat] : ( ord_less_nat @ X3 @ X_1 ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_319_gt__ex,axiom,
% 15.48/8.47      ! [X3: int] :
% 15.48/8.47      ? [X_1: int] : ( ord_less_int @ X3 @ X_1 ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_320_dense,axiom,
% 15.48/8.47      ! [X3: real,Y3: real] :
% 15.48/8.47        ( ( ord_less_real @ X3 @ Y3 )
% 15.48/8.47       => ? [Z3: real] :
% 15.48/8.47            ( ( ord_less_real @ X3 @ Z3 )
% 15.48/8.47            & ( ord_less_real @ Z3 @ Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_321_dense,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat] :
% 15.48/8.47        ( ( ord_less_rat @ X3 @ Y3 )
% 15.48/8.47       => ? [Z3: rat] :
% 15.48/8.47            ( ( ord_less_rat @ X3 @ Z3 )
% 15.48/8.47            & ( ord_less_rat @ Z3 @ Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_322_less__imp__neq,axiom,
% 15.48/8.47      ! [X3: real,Y3: real] :
% 15.48/8.47        ( ( ord_less_real @ X3 @ Y3 )
% 15.48/8.47       => ( X3 != Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_323_less__imp__neq,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat] :
% 15.48/8.47        ( ( ord_less_rat @ X3 @ Y3 )
% 15.48/8.47       => ( X3 != Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_324_less__imp__neq,axiom,
% 15.48/8.47      ! [X3: num,Y3: num] :
% 15.48/8.47        ( ( ord_less_num @ X3 @ Y3 )
% 15.48/8.47       => ( X3 != Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_325_less__imp__neq,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat] :
% 15.48/8.47        ( ( ord_less_nat @ X3 @ Y3 )
% 15.48/8.47       => ( X3 != Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_326_less__imp__neq,axiom,
% 15.48/8.47      ! [X3: int,Y3: int] :
% 15.48/8.47        ( ( ord_less_int @ X3 @ Y3 )
% 15.48/8.47       => ( X3 != Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_327_order_Oasym,axiom,
% 15.48/8.47      ! [A: real,B: real] :
% 15.48/8.47        ( ( ord_less_real @ A @ B )
% 15.48/8.47       => ~ ( ord_less_real @ B @ A ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_328_order_Oasym,axiom,
% 15.48/8.47      ! [A: rat,B: rat] :
% 15.48/8.47        ( ( ord_less_rat @ A @ B )
% 15.48/8.47       => ~ ( ord_less_rat @ B @ A ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_329_order_Oasym,axiom,
% 15.48/8.47      ! [A: num,B: num] :
% 15.48/8.47        ( ( ord_less_num @ A @ B )
% 15.48/8.47       => ~ ( ord_less_num @ B @ A ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_330_order_Oasym,axiom,
% 15.48/8.47      ! [A: nat,B: nat] :
% 15.48/8.47        ( ( ord_less_nat @ A @ B )
% 15.48/8.47       => ~ ( ord_less_nat @ B @ A ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_331_order_Oasym,axiom,
% 15.48/8.47      ! [A: int,B: int] :
% 15.48/8.47        ( ( ord_less_int @ A @ B )
% 15.48/8.47       => ~ ( ord_less_int @ B @ A ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_332_ord__eq__less__trans,axiom,
% 15.48/8.47      ! [A: real,B: real,C: real] :
% 15.48/8.47        ( ( A = B )
% 15.48/8.47       => ( ( ord_less_real @ B @ C )
% 15.48/8.47         => ( ord_less_real @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_333_ord__eq__less__trans,axiom,
% 15.48/8.47      ! [A: rat,B: rat,C: rat] :
% 15.48/8.47        ( ( A = B )
% 15.48/8.47       => ( ( ord_less_rat @ B @ C )
% 15.48/8.47         => ( ord_less_rat @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_334_ord__eq__less__trans,axiom,
% 15.48/8.47      ! [A: num,B: num,C: num] :
% 15.48/8.47        ( ( A = B )
% 15.48/8.47       => ( ( ord_less_num @ B @ C )
% 15.48/8.47         => ( ord_less_num @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_335_ord__eq__less__trans,axiom,
% 15.48/8.47      ! [A: nat,B: nat,C: nat] :
% 15.48/8.47        ( ( A = B )
% 15.48/8.47       => ( ( ord_less_nat @ B @ C )
% 15.48/8.47         => ( ord_less_nat @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_336_ord__eq__less__trans,axiom,
% 15.48/8.47      ! [A: int,B: int,C: int] :
% 15.48/8.47        ( ( A = B )
% 15.48/8.47       => ( ( ord_less_int @ B @ C )
% 15.48/8.47         => ( ord_less_int @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_337_ord__less__eq__trans,axiom,
% 15.48/8.47      ! [A: real,B: real,C: real] :
% 15.48/8.47        ( ( ord_less_real @ A @ B )
% 15.48/8.47       => ( ( B = C )
% 15.48/8.47         => ( ord_less_real @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_338_ord__less__eq__trans,axiom,
% 15.48/8.47      ! [A: rat,B: rat,C: rat] :
% 15.48/8.47        ( ( ord_less_rat @ A @ B )
% 15.48/8.47       => ( ( B = C )
% 15.48/8.47         => ( ord_less_rat @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_339_ord__less__eq__trans,axiom,
% 15.48/8.47      ! [A: num,B: num,C: num] :
% 15.48/8.47        ( ( ord_less_num @ A @ B )
% 15.48/8.47       => ( ( B = C )
% 15.48/8.47         => ( ord_less_num @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_340_ord__less__eq__trans,axiom,
% 15.48/8.47      ! [A: nat,B: nat,C: nat] :
% 15.48/8.47        ( ( ord_less_nat @ A @ B )
% 15.48/8.47       => ( ( B = C )
% 15.48/8.47         => ( ord_less_nat @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_341_ord__less__eq__trans,axiom,
% 15.48/8.47      ! [A: int,B: int,C: int] :
% 15.48/8.47        ( ( ord_less_int @ A @ B )
% 15.48/8.47       => ( ( B = C )
% 15.48/8.47         => ( ord_less_int @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_342_less__induct,axiom,
% 15.48/8.47      ! [P: nat > $o,A: nat] :
% 15.48/8.47        ( ! [X4: nat] :
% 15.48/8.47            ( ! [Y6: nat] :
% 15.48/8.47                ( ( ord_less_nat @ Y6 @ X4 )
% 15.48/8.47               => ( P @ Y6 ) )
% 15.48/8.47           => ( P @ X4 ) )
% 15.48/8.47       => ( P @ A ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_343_antisym__conv3,axiom,
% 15.48/8.47      ! [Y3: real,X3: real] :
% 15.48/8.47        ( ~ ( ord_less_real @ Y3 @ X3 )
% 15.48/8.47       => ( ( ~ ( ord_less_real @ X3 @ Y3 ) )
% 15.48/8.47          = ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_344_antisym__conv3,axiom,
% 15.48/8.47      ! [Y3: rat,X3: rat] :
% 15.48/8.47        ( ~ ( ord_less_rat @ Y3 @ X3 )
% 15.48/8.47       => ( ( ~ ( ord_less_rat @ X3 @ Y3 ) )
% 15.48/8.47          = ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_345_antisym__conv3,axiom,
% 15.48/8.47      ! [Y3: num,X3: num] :
% 15.48/8.47        ( ~ ( ord_less_num @ Y3 @ X3 )
% 15.48/8.47       => ( ( ~ ( ord_less_num @ X3 @ Y3 ) )
% 15.48/8.47          = ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_346_antisym__conv3,axiom,
% 15.48/8.47      ! [Y3: nat,X3: nat] :
% 15.48/8.47        ( ~ ( ord_less_nat @ Y3 @ X3 )
% 15.48/8.47       => ( ( ~ ( ord_less_nat @ X3 @ Y3 ) )
% 15.48/8.47          = ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_347_antisym__conv3,axiom,
% 15.48/8.47      ! [Y3: int,X3: int] :
% 15.48/8.47        ( ~ ( ord_less_int @ Y3 @ X3 )
% 15.48/8.47       => ( ( ~ ( ord_less_int @ X3 @ Y3 ) )
% 15.48/8.47          = ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_348_linorder__cases,axiom,
% 15.48/8.47      ! [X3: real,Y3: real] :
% 15.48/8.47        ( ~ ( ord_less_real @ X3 @ Y3 )
% 15.48/8.47       => ( ( X3 != Y3 )
% 15.48/8.47         => ( ord_less_real @ Y3 @ X3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_349_linorder__cases,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat] :
% 15.48/8.47        ( ~ ( ord_less_rat @ X3 @ Y3 )
% 15.48/8.47       => ( ( X3 != Y3 )
% 15.48/8.47         => ( ord_less_rat @ Y3 @ X3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_350_linorder__cases,axiom,
% 15.48/8.47      ! [X3: num,Y3: num] :
% 15.48/8.47        ( ~ ( ord_less_num @ X3 @ Y3 )
% 15.48/8.47       => ( ( X3 != Y3 )
% 15.48/8.47         => ( ord_less_num @ Y3 @ X3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_351_linorder__cases,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat] :
% 15.48/8.47        ( ~ ( ord_less_nat @ X3 @ Y3 )
% 15.48/8.47       => ( ( X3 != Y3 )
% 15.48/8.47         => ( ord_less_nat @ Y3 @ X3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_352_linorder__cases,axiom,
% 15.48/8.47      ! [X3: int,Y3: int] :
% 15.48/8.47        ( ~ ( ord_less_int @ X3 @ Y3 )
% 15.48/8.47       => ( ( X3 != Y3 )
% 15.48/8.47         => ( ord_less_int @ Y3 @ X3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_353_dual__order_Oasym,axiom,
% 15.48/8.47      ! [B: real,A: real] :
% 15.48/8.47        ( ( ord_less_real @ B @ A )
% 15.48/8.47       => ~ ( ord_less_real @ A @ B ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_354_dual__order_Oasym,axiom,
% 15.48/8.47      ! [B: rat,A: rat] :
% 15.48/8.47        ( ( ord_less_rat @ B @ A )
% 15.48/8.47       => ~ ( ord_less_rat @ A @ B ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_355_dual__order_Oasym,axiom,
% 15.48/8.47      ! [B: num,A: num] :
% 15.48/8.47        ( ( ord_less_num @ B @ A )
% 15.48/8.47       => ~ ( ord_less_num @ A @ B ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_356_dual__order_Oasym,axiom,
% 15.48/8.47      ! [B: nat,A: nat] :
% 15.48/8.47        ( ( ord_less_nat @ B @ A )
% 15.48/8.47       => ~ ( ord_less_nat @ A @ B ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_357_dual__order_Oasym,axiom,
% 15.48/8.47      ! [B: int,A: int] :
% 15.48/8.47        ( ( ord_less_int @ B @ A )
% 15.48/8.47       => ~ ( ord_less_int @ A @ B ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_358_dual__order_Oirrefl,axiom,
% 15.48/8.47      ! [A: real] :
% 15.48/8.47        ~ ( ord_less_real @ A @ A ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_359_dual__order_Oirrefl,axiom,
% 15.48/8.47      ! [A: rat] :
% 15.48/8.47        ~ ( ord_less_rat @ A @ A ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_360_dual__order_Oirrefl,axiom,
% 15.48/8.47      ! [A: num] :
% 15.48/8.47        ~ ( ord_less_num @ A @ A ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_361_dual__order_Oirrefl,axiom,
% 15.48/8.47      ! [A: nat] :
% 15.48/8.47        ~ ( ord_less_nat @ A @ A ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_362_dual__order_Oirrefl,axiom,
% 15.48/8.47      ! [A: int] :
% 15.48/8.47        ~ ( ord_less_int @ A @ A ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_363_exists__least__iff,axiom,
% 15.48/8.47      ( ( ^ [P2: nat > $o] :
% 15.48/8.47          ? [X5: nat] : ( P2 @ X5 ) )
% 15.48/8.47      = ( ^ [P3: nat > $o] :
% 15.48/8.47          ? [N3: nat] :
% 15.48/8.47            ( ( P3 @ N3 )
% 15.48/8.47            & ! [M3: nat] :
% 15.48/8.47                ( ( ord_less_nat @ M3 @ N3 )
% 15.48/8.47               => ~ ( P3 @ M3 ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_364_linorder__less__wlog,axiom,
% 15.48/8.47      ! [P: real > real > $o,A: real,B: real] :
% 15.48/8.47        ( ! [A5: real,B4: real] :
% 15.48/8.47            ( ( ord_less_real @ A5 @ B4 )
% 15.48/8.47           => ( P @ A5 @ B4 ) )
% 15.48/8.47       => ( ! [A5: real] : ( P @ A5 @ A5 )
% 15.48/8.47         => ( ! [A5: real,B4: real] :
% 15.48/8.47                ( ( P @ B4 @ A5 )
% 15.48/8.47               => ( P @ A5 @ B4 ) )
% 15.48/8.47           => ( P @ A @ B ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_365_linorder__less__wlog,axiom,
% 15.48/8.47      ! [P: rat > rat > $o,A: rat,B: rat] :
% 15.48/8.47        ( ! [A5: rat,B4: rat] :
% 15.48/8.47            ( ( ord_less_rat @ A5 @ B4 )
% 15.48/8.47           => ( P @ A5 @ B4 ) )
% 15.48/8.47       => ( ! [A5: rat] : ( P @ A5 @ A5 )
% 15.48/8.47         => ( ! [A5: rat,B4: rat] :
% 15.48/8.47                ( ( P @ B4 @ A5 )
% 15.48/8.47               => ( P @ A5 @ B4 ) )
% 15.48/8.47           => ( P @ A @ B ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_366_linorder__less__wlog,axiom,
% 15.48/8.47      ! [P: num > num > $o,A: num,B: num] :
% 15.48/8.47        ( ! [A5: num,B4: num] :
% 15.48/8.47            ( ( ord_less_num @ A5 @ B4 )
% 15.48/8.47           => ( P @ A5 @ B4 ) )
% 15.48/8.47       => ( ! [A5: num] : ( P @ A5 @ A5 )
% 15.48/8.47         => ( ! [A5: num,B4: num] :
% 15.48/8.47                ( ( P @ B4 @ A5 )
% 15.48/8.47               => ( P @ A5 @ B4 ) )
% 15.48/8.47           => ( P @ A @ B ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_367_linorder__less__wlog,axiom,
% 15.48/8.47      ! [P: nat > nat > $o,A: nat,B: nat] :
% 15.48/8.47        ( ! [A5: nat,B4: nat] :
% 15.48/8.47            ( ( ord_less_nat @ A5 @ B4 )
% 15.48/8.47           => ( P @ A5 @ B4 ) )
% 15.48/8.47       => ( ! [A5: nat] : ( P @ A5 @ A5 )
% 15.48/8.47         => ( ! [A5: nat,B4: nat] :
% 15.48/8.47                ( ( P @ B4 @ A5 )
% 15.48/8.47               => ( P @ A5 @ B4 ) )
% 15.48/8.47           => ( P @ A @ B ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_368_linorder__less__wlog,axiom,
% 15.48/8.47      ! [P: int > int > $o,A: int,B: int] :
% 15.48/8.47        ( ! [A5: int,B4: int] :
% 15.48/8.47            ( ( ord_less_int @ A5 @ B4 )
% 15.48/8.47           => ( P @ A5 @ B4 ) )
% 15.48/8.47       => ( ! [A5: int] : ( P @ A5 @ A5 )
% 15.48/8.47         => ( ! [A5: int,B4: int] :
% 15.48/8.47                ( ( P @ B4 @ A5 )
% 15.48/8.47               => ( P @ A5 @ B4 ) )
% 15.48/8.47           => ( P @ A @ B ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_369_order_Ostrict__trans,axiom,
% 15.48/8.47      ! [A: real,B: real,C: real] :
% 15.48/8.47        ( ( ord_less_real @ A @ B )
% 15.48/8.47       => ( ( ord_less_real @ B @ C )
% 15.48/8.47         => ( ord_less_real @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_370_order_Ostrict__trans,axiom,
% 15.48/8.47      ! [A: rat,B: rat,C: rat] :
% 15.48/8.47        ( ( ord_less_rat @ A @ B )
% 15.48/8.47       => ( ( ord_less_rat @ B @ C )
% 15.48/8.47         => ( ord_less_rat @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_371_order_Ostrict__trans,axiom,
% 15.48/8.47      ! [A: num,B: num,C: num] :
% 15.48/8.47        ( ( ord_less_num @ A @ B )
% 15.48/8.47       => ( ( ord_less_num @ B @ C )
% 15.48/8.47         => ( ord_less_num @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_372_order_Ostrict__trans,axiom,
% 15.48/8.47      ! [A: nat,B: nat,C: nat] :
% 15.48/8.47        ( ( ord_less_nat @ A @ B )
% 15.48/8.47       => ( ( ord_less_nat @ B @ C )
% 15.48/8.47         => ( ord_less_nat @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_373_order_Ostrict__trans,axiom,
% 15.48/8.47      ! [A: int,B: int,C: int] :
% 15.48/8.47        ( ( ord_less_int @ A @ B )
% 15.48/8.47       => ( ( ord_less_int @ B @ C )
% 15.48/8.47         => ( ord_less_int @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_374_not__less__iff__gr__or__eq,axiom,
% 15.48/8.47      ! [X3: real,Y3: real] :
% 15.48/8.47        ( ( ~ ( ord_less_real @ X3 @ Y3 ) )
% 15.48/8.47        = ( ( ord_less_real @ Y3 @ X3 )
% 15.48/8.47          | ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_375_not__less__iff__gr__or__eq,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat] :
% 15.48/8.47        ( ( ~ ( ord_less_rat @ X3 @ Y3 ) )
% 15.48/8.47        = ( ( ord_less_rat @ Y3 @ X3 )
% 15.48/8.47          | ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_376_not__less__iff__gr__or__eq,axiom,
% 15.48/8.47      ! [X3: num,Y3: num] :
% 15.48/8.47        ( ( ~ ( ord_less_num @ X3 @ Y3 ) )
% 15.48/8.47        = ( ( ord_less_num @ Y3 @ X3 )
% 15.48/8.47          | ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_377_not__less__iff__gr__or__eq,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat] :
% 15.48/8.47        ( ( ~ ( ord_less_nat @ X3 @ Y3 ) )
% 15.48/8.47        = ( ( ord_less_nat @ Y3 @ X3 )
% 15.48/8.47          | ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_378_not__less__iff__gr__or__eq,axiom,
% 15.48/8.47      ! [X3: int,Y3: int] :
% 15.48/8.47        ( ( ~ ( ord_less_int @ X3 @ Y3 ) )
% 15.48/8.47        = ( ( ord_less_int @ Y3 @ X3 )
% 15.48/8.47          | ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_379_dual__order_Ostrict__trans,axiom,
% 15.48/8.47      ! [B: real,A: real,C: real] :
% 15.48/8.47        ( ( ord_less_real @ B @ A )
% 15.48/8.47       => ( ( ord_less_real @ C @ B )
% 15.48/8.47         => ( ord_less_real @ C @ A ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_380_dual__order_Ostrict__trans,axiom,
% 15.48/8.47      ! [B: rat,A: rat,C: rat] :
% 15.48/8.47        ( ( ord_less_rat @ B @ A )
% 15.48/8.47       => ( ( ord_less_rat @ C @ B )
% 15.48/8.47         => ( ord_less_rat @ C @ A ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_381_dual__order_Ostrict__trans,axiom,
% 15.48/8.47      ! [B: num,A: num,C: num] :
% 15.48/8.47        ( ( ord_less_num @ B @ A )
% 15.48/8.47       => ( ( ord_less_num @ C @ B )
% 15.48/8.47         => ( ord_less_num @ C @ A ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_382_dual__order_Ostrict__trans,axiom,
% 15.48/8.47      ! [B: nat,A: nat,C: nat] :
% 15.48/8.47        ( ( ord_less_nat @ B @ A )
% 15.48/8.47       => ( ( ord_less_nat @ C @ B )
% 15.48/8.47         => ( ord_less_nat @ C @ A ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_383_dual__order_Ostrict__trans,axiom,
% 15.48/8.47      ! [B: int,A: int,C: int] :
% 15.48/8.47        ( ( ord_less_int @ B @ A )
% 15.48/8.47       => ( ( ord_less_int @ C @ B )
% 15.48/8.47         => ( ord_less_int @ C @ A ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_384_order_Ostrict__implies__not__eq,axiom,
% 15.48/8.47      ! [A: real,B: real] :
% 15.48/8.47        ( ( ord_less_real @ A @ B )
% 15.48/8.47       => ( A != B ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_385_order_Ostrict__implies__not__eq,axiom,
% 15.48/8.47      ! [A: rat,B: rat] :
% 15.48/8.47        ( ( ord_less_rat @ A @ B )
% 15.48/8.47       => ( A != B ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_386_order_Ostrict__implies__not__eq,axiom,
% 15.48/8.47      ! [A: num,B: num] :
% 15.48/8.47        ( ( ord_less_num @ A @ B )
% 15.48/8.47       => ( A != B ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_387_order_Ostrict__implies__not__eq,axiom,
% 15.48/8.47      ! [A: nat,B: nat] :
% 15.48/8.47        ( ( ord_less_nat @ A @ B )
% 15.48/8.47       => ( A != B ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_388_order_Ostrict__implies__not__eq,axiom,
% 15.48/8.47      ! [A: int,B: int] :
% 15.48/8.47        ( ( ord_less_int @ A @ B )
% 15.48/8.47       => ( A != B ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_389_dual__order_Ostrict__implies__not__eq,axiom,
% 15.48/8.47      ! [B: real,A: real] :
% 15.48/8.47        ( ( ord_less_real @ B @ A )
% 15.48/8.47       => ( A != B ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_390_dual__order_Ostrict__implies__not__eq,axiom,
% 15.48/8.47      ! [B: rat,A: rat] :
% 15.48/8.47        ( ( ord_less_rat @ B @ A )
% 15.48/8.47       => ( A != B ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_391_dual__order_Ostrict__implies__not__eq,axiom,
% 15.48/8.47      ! [B: num,A: num] :
% 15.48/8.47        ( ( ord_less_num @ B @ A )
% 15.48/8.47       => ( A != B ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_392_dual__order_Ostrict__implies__not__eq,axiom,
% 15.48/8.47      ! [B: nat,A: nat] :
% 15.48/8.47        ( ( ord_less_nat @ B @ A )
% 15.48/8.47       => ( A != B ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_393_dual__order_Ostrict__implies__not__eq,axiom,
% 15.48/8.47      ! [B: int,A: int] :
% 15.48/8.47        ( ( ord_less_int @ B @ A )
% 15.48/8.47       => ( A != B ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_394_linorder__neqE,axiom,
% 15.48/8.47      ! [X3: real,Y3: real] :
% 15.48/8.47        ( ( X3 != Y3 )
% 15.48/8.47       => ( ~ ( ord_less_real @ X3 @ Y3 )
% 15.48/8.47         => ( ord_less_real @ Y3 @ X3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_395_linorder__neqE,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat] :
% 15.48/8.47        ( ( X3 != Y3 )
% 15.48/8.47       => ( ~ ( ord_less_rat @ X3 @ Y3 )
% 15.48/8.47         => ( ord_less_rat @ Y3 @ X3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_396_linorder__neqE,axiom,
% 15.48/8.47      ! [X3: num,Y3: num] :
% 15.48/8.47        ( ( X3 != Y3 )
% 15.48/8.47       => ( ~ ( ord_less_num @ X3 @ Y3 )
% 15.48/8.47         => ( ord_less_num @ Y3 @ X3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_397_linorder__neqE,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat] :
% 15.48/8.47        ( ( X3 != Y3 )
% 15.48/8.47       => ( ~ ( ord_less_nat @ X3 @ Y3 )
% 15.48/8.47         => ( ord_less_nat @ Y3 @ X3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_398_linorder__neqE,axiom,
% 15.48/8.47      ! [X3: int,Y3: int] :
% 15.48/8.47        ( ( X3 != Y3 )
% 15.48/8.47       => ( ~ ( ord_less_int @ X3 @ Y3 )
% 15.48/8.47         => ( ord_less_int @ Y3 @ X3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_399_order__less__asym,axiom,
% 15.48/8.47      ! [X3: real,Y3: real] :
% 15.48/8.47        ( ( ord_less_real @ X3 @ Y3 )
% 15.48/8.47       => ~ ( ord_less_real @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_400_order__less__asym,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat] :
% 15.48/8.47        ( ( ord_less_rat @ X3 @ Y3 )
% 15.48/8.47       => ~ ( ord_less_rat @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_401_order__less__asym,axiom,
% 15.48/8.47      ! [X3: num,Y3: num] :
% 15.48/8.47        ( ( ord_less_num @ X3 @ Y3 )
% 15.48/8.47       => ~ ( ord_less_num @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_402_order__less__asym,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat] :
% 15.48/8.47        ( ( ord_less_nat @ X3 @ Y3 )
% 15.48/8.47       => ~ ( ord_less_nat @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_403_order__less__asym,axiom,
% 15.48/8.47      ! [X3: int,Y3: int] :
% 15.48/8.47        ( ( ord_less_int @ X3 @ Y3 )
% 15.48/8.47       => ~ ( ord_less_int @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_404_linorder__neq__iff,axiom,
% 15.48/8.47      ! [X3: real,Y3: real] :
% 15.48/8.47        ( ( X3 != Y3 )
% 15.48/8.47        = ( ( ord_less_real @ X3 @ Y3 )
% 15.48/8.47          | ( ord_less_real @ Y3 @ X3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_405_linorder__neq__iff,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat] :
% 15.48/8.47        ( ( X3 != Y3 )
% 15.48/8.47        = ( ( ord_less_rat @ X3 @ Y3 )
% 15.48/8.47          | ( ord_less_rat @ Y3 @ X3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_406_linorder__neq__iff,axiom,
% 15.48/8.47      ! [X3: num,Y3: num] :
% 15.48/8.47        ( ( X3 != Y3 )
% 15.48/8.47        = ( ( ord_less_num @ X3 @ Y3 )
% 15.48/8.47          | ( ord_less_num @ Y3 @ X3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_407_linorder__neq__iff,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat] :
% 15.48/8.47        ( ( X3 != Y3 )
% 15.48/8.47        = ( ( ord_less_nat @ X3 @ Y3 )
% 15.48/8.47          | ( ord_less_nat @ Y3 @ X3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_408_linorder__neq__iff,axiom,
% 15.48/8.47      ! [X3: int,Y3: int] :
% 15.48/8.47        ( ( X3 != Y3 )
% 15.48/8.47        = ( ( ord_less_int @ X3 @ Y3 )
% 15.48/8.47          | ( ord_less_int @ Y3 @ X3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_409_order__less__asym_H,axiom,
% 15.48/8.47      ! [A: real,B: real] :
% 15.48/8.47        ( ( ord_less_real @ A @ B )
% 15.48/8.47       => ~ ( ord_less_real @ B @ A ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_410_order__less__asym_H,axiom,
% 15.48/8.47      ! [A: rat,B: rat] :
% 15.48/8.47        ( ( ord_less_rat @ A @ B )
% 15.48/8.47       => ~ ( ord_less_rat @ B @ A ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_411_order__less__asym_H,axiom,
% 15.48/8.47      ! [A: num,B: num] :
% 15.48/8.47        ( ( ord_less_num @ A @ B )
% 15.48/8.47       => ~ ( ord_less_num @ B @ A ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_412_order__less__asym_H,axiom,
% 15.48/8.47      ! [A: nat,B: nat] :
% 15.48/8.47        ( ( ord_less_nat @ A @ B )
% 15.48/8.47       => ~ ( ord_less_nat @ B @ A ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_413_order__less__asym_H,axiom,
% 15.48/8.47      ! [A: int,B: int] :
% 15.48/8.47        ( ( ord_less_int @ A @ B )
% 15.48/8.47       => ~ ( ord_less_int @ B @ A ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_414_order__less__trans,axiom,
% 15.48/8.47      ! [X3: real,Y3: real,Z: real] :
% 15.48/8.47        ( ( ord_less_real @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_real @ Y3 @ Z )
% 15.48/8.47         => ( ord_less_real @ X3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_415_order__less__trans,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat,Z: rat] :
% 15.48/8.47        ( ( ord_less_rat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_rat @ Y3 @ Z )
% 15.48/8.47         => ( ord_less_rat @ X3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_416_order__less__trans,axiom,
% 15.48/8.47      ! [X3: num,Y3: num,Z: num] :
% 15.48/8.47        ( ( ord_less_num @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_num @ Y3 @ Z )
% 15.48/8.47         => ( ord_less_num @ X3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_417_order__less__trans,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat,Z: nat] :
% 15.48/8.47        ( ( ord_less_nat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_nat @ Y3 @ Z )
% 15.48/8.47         => ( ord_less_nat @ X3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_418_order__less__trans,axiom,
% 15.48/8.47      ! [X3: int,Y3: int,Z: int] :
% 15.48/8.47        ( ( ord_less_int @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_int @ Y3 @ Z )
% 15.48/8.47         => ( ord_less_int @ X3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_419_ord__eq__less__subst,axiom,
% 15.48/8.47      ! [A: real,F: real > real,B: real,C: real] :
% 15.48/8.47        ( ( A
% 15.48/8.47          = ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_real @ B @ C )
% 15.48/8.47         => ( ! [X4: real,Y4: real] :
% 15.48/8.47                ( ( ord_less_real @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_420_ord__eq__less__subst,axiom,
% 15.48/8.47      ! [A: rat,F: real > rat,B: real,C: real] :
% 15.48/8.47        ( ( A
% 15.48/8.47          = ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_real @ B @ C )
% 15.48/8.47         => ( ! [X4: real,Y4: real] :
% 15.48/8.47                ( ( ord_less_real @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_421_ord__eq__less__subst,axiom,
% 15.48/8.47      ! [A: num,F: real > num,B: real,C: real] :
% 15.48/8.47        ( ( A
% 15.48/8.47          = ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_real @ B @ C )
% 15.48/8.47         => ( ! [X4: real,Y4: real] :
% 15.48/8.47                ( ( ord_less_real @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_422_ord__eq__less__subst,axiom,
% 15.48/8.47      ! [A: nat,F: real > nat,B: real,C: real] :
% 15.48/8.47        ( ( A
% 15.48/8.47          = ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_real @ B @ C )
% 15.48/8.47         => ( ! [X4: real,Y4: real] :
% 15.48/8.47                ( ( ord_less_real @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_423_ord__eq__less__subst,axiom,
% 15.48/8.47      ! [A: int,F: real > int,B: real,C: real] :
% 15.48/8.47        ( ( A
% 15.48/8.47          = ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_real @ B @ C )
% 15.48/8.47         => ( ! [X4: real,Y4: real] :
% 15.48/8.47                ( ( ord_less_real @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_424_ord__eq__less__subst,axiom,
% 15.48/8.47      ! [A: real,F: rat > real,B: rat,C: rat] :
% 15.48/8.47        ( ( A
% 15.48/8.47          = ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_rat @ B @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_425_ord__eq__less__subst,axiom,
% 15.48/8.47      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 15.48/8.47        ( ( A
% 15.48/8.47          = ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_rat @ B @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_426_ord__eq__less__subst,axiom,
% 15.48/8.47      ! [A: num,F: rat > num,B: rat,C: rat] :
% 15.48/8.47        ( ( A
% 15.48/8.47          = ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_rat @ B @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_427_ord__eq__less__subst,axiom,
% 15.48/8.47      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 15.48/8.47        ( ( A
% 15.48/8.47          = ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_rat @ B @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_428_ord__eq__less__subst,axiom,
% 15.48/8.47      ! [A: int,F: rat > int,B: rat,C: rat] :
% 15.48/8.47        ( ( A
% 15.48/8.47          = ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_rat @ B @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_429_ord__less__eq__subst,axiom,
% 15.48/8.47      ! [A: real,B: real,F: real > real,C: real] :
% 15.48/8.47        ( ( ord_less_real @ A @ B )
% 15.48/8.47       => ( ( ( F @ B )
% 15.48/8.47            = C )
% 15.48/8.47         => ( ! [X4: real,Y4: real] :
% 15.48/8.47                ( ( ord_less_real @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_430_ord__less__eq__subst,axiom,
% 15.48/8.47      ! [A: real,B: real,F: real > rat,C: rat] :
% 15.48/8.47        ( ( ord_less_real @ A @ B )
% 15.48/8.47       => ( ( ( F @ B )
% 15.48/8.47            = C )
% 15.48/8.47         => ( ! [X4: real,Y4: real] :
% 15.48/8.47                ( ( ord_less_real @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_431_ord__less__eq__subst,axiom,
% 15.48/8.47      ! [A: real,B: real,F: real > num,C: num] :
% 15.48/8.47        ( ( ord_less_real @ A @ B )
% 15.48/8.47       => ( ( ( F @ B )
% 15.48/8.47            = C )
% 15.48/8.47         => ( ! [X4: real,Y4: real] :
% 15.48/8.47                ( ( ord_less_real @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_432_ord__less__eq__subst,axiom,
% 15.48/8.47      ! [A: real,B: real,F: real > nat,C: nat] :
% 15.48/8.47        ( ( ord_less_real @ A @ B )
% 15.48/8.47       => ( ( ( F @ B )
% 15.48/8.47            = C )
% 15.48/8.47         => ( ! [X4: real,Y4: real] :
% 15.48/8.47                ( ( ord_less_real @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_433_ord__less__eq__subst,axiom,
% 15.48/8.47      ! [A: real,B: real,F: real > int,C: int] :
% 15.48/8.47        ( ( ord_less_real @ A @ B )
% 15.48/8.47       => ( ( ( F @ B )
% 15.48/8.47            = C )
% 15.48/8.47         => ( ! [X4: real,Y4: real] :
% 15.48/8.47                ( ( ord_less_real @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_434_ord__less__eq__subst,axiom,
% 15.48/8.47      ! [A: rat,B: rat,F: rat > real,C: real] :
% 15.48/8.47        ( ( ord_less_rat @ A @ B )
% 15.48/8.47       => ( ( ( F @ B )
% 15.48/8.47            = C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_435_ord__less__eq__subst,axiom,
% 15.48/8.47      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 15.48/8.47        ( ( ord_less_rat @ A @ B )
% 15.48/8.47       => ( ( ( F @ B )
% 15.48/8.47            = C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_436_ord__less__eq__subst,axiom,
% 15.48/8.47      ! [A: rat,B: rat,F: rat > num,C: num] :
% 15.48/8.47        ( ( ord_less_rat @ A @ B )
% 15.48/8.47       => ( ( ( F @ B )
% 15.48/8.47            = C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_437_ord__less__eq__subst,axiom,
% 15.48/8.47      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 15.48/8.47        ( ( ord_less_rat @ A @ B )
% 15.48/8.47       => ( ( ( F @ B )
% 15.48/8.47            = C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_438_ord__less__eq__subst,axiom,
% 15.48/8.47      ! [A: rat,B: rat,F: rat > int,C: int] :
% 15.48/8.47        ( ( ord_less_rat @ A @ B )
% 15.48/8.47       => ( ( ( F @ B )
% 15.48/8.47            = C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_439_order__less__irrefl,axiom,
% 15.48/8.47      ! [X3: real] :
% 15.48/8.47        ~ ( ord_less_real @ X3 @ X3 ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_440_order__less__irrefl,axiom,
% 15.48/8.47      ! [X3: rat] :
% 15.48/8.47        ~ ( ord_less_rat @ X3 @ X3 ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_441_order__less__irrefl,axiom,
% 15.48/8.47      ! [X3: num] :
% 15.48/8.47        ~ ( ord_less_num @ X3 @ X3 ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_442_order__less__irrefl,axiom,
% 15.48/8.47      ! [X3: nat] :
% 15.48/8.47        ~ ( ord_less_nat @ X3 @ X3 ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_443_order__less__irrefl,axiom,
% 15.48/8.47      ! [X3: int] :
% 15.48/8.47        ~ ( ord_less_int @ X3 @ X3 ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_444_order__less__subst1,axiom,
% 15.48/8.47      ! [A: real,F: real > real,B: real,C: real] :
% 15.48/8.47        ( ( ord_less_real @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_real @ B @ C )
% 15.48/8.47         => ( ! [X4: real,Y4: real] :
% 15.48/8.47                ( ( ord_less_real @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_445_order__less__subst1,axiom,
% 15.48/8.47      ! [A: real,F: rat > real,B: rat,C: rat] :
% 15.48/8.47        ( ( ord_less_real @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_rat @ B @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_446_order__less__subst1,axiom,
% 15.48/8.47      ! [A: real,F: num > real,B: num,C: num] :
% 15.48/8.47        ( ( ord_less_real @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_num @ B @ C )
% 15.48/8.47         => ( ! [X4: num,Y4: num] :
% 15.48/8.47                ( ( ord_less_num @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_447_order__less__subst1,axiom,
% 15.48/8.47      ! [A: real,F: nat > real,B: nat,C: nat] :
% 15.48/8.47        ( ( ord_less_real @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_nat @ B @ C )
% 15.48/8.47         => ( ! [X4: nat,Y4: nat] :
% 15.48/8.47                ( ( ord_less_nat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_448_order__less__subst1,axiom,
% 15.48/8.47      ! [A: real,F: int > real,B: int,C: int] :
% 15.48/8.47        ( ( ord_less_real @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_int @ B @ C )
% 15.48/8.47         => ( ! [X4: int,Y4: int] :
% 15.48/8.47                ( ( ord_less_int @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_449_order__less__subst1,axiom,
% 15.48/8.47      ! [A: rat,F: real > rat,B: real,C: real] :
% 15.48/8.47        ( ( ord_less_rat @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_real @ B @ C )
% 15.48/8.47         => ( ! [X4: real,Y4: real] :
% 15.48/8.47                ( ( ord_less_real @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_450_order__less__subst1,axiom,
% 15.48/8.47      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 15.48/8.47        ( ( ord_less_rat @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_rat @ B @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_451_order__less__subst1,axiom,
% 15.48/8.47      ! [A: rat,F: num > rat,B: num,C: num] :
% 15.48/8.47        ( ( ord_less_rat @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_num @ B @ C )
% 15.48/8.47         => ( ! [X4: num,Y4: num] :
% 15.48/8.47                ( ( ord_less_num @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_452_order__less__subst1,axiom,
% 15.48/8.47      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 15.48/8.47        ( ( ord_less_rat @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_nat @ B @ C )
% 15.48/8.47         => ( ! [X4: nat,Y4: nat] :
% 15.48/8.47                ( ( ord_less_nat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_453_order__less__subst1,axiom,
% 15.48/8.47      ! [A: rat,F: int > rat,B: int,C: int] :
% 15.48/8.47        ( ( ord_less_rat @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_int @ B @ C )
% 15.48/8.47         => ( ! [X4: int,Y4: int] :
% 15.48/8.47                ( ( ord_less_int @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_454_order__less__subst2,axiom,
% 15.48/8.47      ! [A: real,B: real,F: real > real,C: real] :
% 15.48/8.47        ( ( ord_less_real @ A @ B )
% 15.48/8.47       => ( ( ord_less_real @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: real,Y4: real] :
% 15.48/8.47                ( ( ord_less_real @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_455_order__less__subst2,axiom,
% 15.48/8.47      ! [A: real,B: real,F: real > rat,C: rat] :
% 15.48/8.47        ( ( ord_less_real @ A @ B )
% 15.48/8.47       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: real,Y4: real] :
% 15.48/8.47                ( ( ord_less_real @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_456_order__less__subst2,axiom,
% 15.48/8.47      ! [A: real,B: real,F: real > num,C: num] :
% 15.48/8.47        ( ( ord_less_real @ A @ B )
% 15.48/8.47       => ( ( ord_less_num @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: real,Y4: real] :
% 15.48/8.47                ( ( ord_less_real @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_457_order__less__subst2,axiom,
% 15.48/8.47      ! [A: real,B: real,F: real > nat,C: nat] :
% 15.48/8.47        ( ( ord_less_real @ A @ B )
% 15.48/8.47       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: real,Y4: real] :
% 15.48/8.47                ( ( ord_less_real @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_458_order__less__subst2,axiom,
% 15.48/8.47      ! [A: real,B: real,F: real > int,C: int] :
% 15.48/8.47        ( ( ord_less_real @ A @ B )
% 15.48/8.47       => ( ( ord_less_int @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: real,Y4: real] :
% 15.48/8.47                ( ( ord_less_real @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_459_order__less__subst2,axiom,
% 15.48/8.47      ! [A: rat,B: rat,F: rat > real,C: real] :
% 15.48/8.47        ( ( ord_less_rat @ A @ B )
% 15.48/8.47       => ( ( ord_less_real @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_460_order__less__subst2,axiom,
% 15.48/8.47      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 15.48/8.47        ( ( ord_less_rat @ A @ B )
% 15.48/8.47       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_461_order__less__subst2,axiom,
% 15.48/8.47      ! [A: rat,B: rat,F: rat > num,C: num] :
% 15.48/8.47        ( ( ord_less_rat @ A @ B )
% 15.48/8.47       => ( ( ord_less_num @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_462_order__less__subst2,axiom,
% 15.48/8.47      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 15.48/8.47        ( ( ord_less_rat @ A @ B )
% 15.48/8.47       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_463_order__less__subst2,axiom,
% 15.48/8.47      ! [A: rat,B: rat,F: rat > int,C: int] :
% 15.48/8.47        ( ( ord_less_rat @ A @ B )
% 15.48/8.47       => ( ( ord_less_int @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_464_order__less__not__sym,axiom,
% 15.48/8.47      ! [X3: real,Y3: real] :
% 15.48/8.47        ( ( ord_less_real @ X3 @ Y3 )
% 15.48/8.47       => ~ ( ord_less_real @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_465_order__less__not__sym,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat] :
% 15.48/8.47        ( ( ord_less_rat @ X3 @ Y3 )
% 15.48/8.47       => ~ ( ord_less_rat @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_466_order__less__not__sym,axiom,
% 15.48/8.47      ! [X3: num,Y3: num] :
% 15.48/8.47        ( ( ord_less_num @ X3 @ Y3 )
% 15.48/8.47       => ~ ( ord_less_num @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_467_order__less__not__sym,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat] :
% 15.48/8.47        ( ( ord_less_nat @ X3 @ Y3 )
% 15.48/8.47       => ~ ( ord_less_nat @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_468_order__less__not__sym,axiom,
% 15.48/8.47      ! [X3: int,Y3: int] :
% 15.48/8.47        ( ( ord_less_int @ X3 @ Y3 )
% 15.48/8.47       => ~ ( ord_less_int @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_469_order__less__imp__triv,axiom,
% 15.48/8.47      ! [X3: real,Y3: real,P: $o] :
% 15.48/8.47        ( ( ord_less_real @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_real @ Y3 @ X3 )
% 15.48/8.47         => P ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_470_order__less__imp__triv,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat,P: $o] :
% 15.48/8.47        ( ( ord_less_rat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_rat @ Y3 @ X3 )
% 15.48/8.47         => P ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_471_order__less__imp__triv,axiom,
% 15.48/8.47      ! [X3: num,Y3: num,P: $o] :
% 15.48/8.47        ( ( ord_less_num @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_num @ Y3 @ X3 )
% 15.48/8.47         => P ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_472_order__less__imp__triv,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat,P: $o] :
% 15.48/8.47        ( ( ord_less_nat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_nat @ Y3 @ X3 )
% 15.48/8.47         => P ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_473_order__less__imp__triv,axiom,
% 15.48/8.47      ! [X3: int,Y3: int,P: $o] :
% 15.48/8.47        ( ( ord_less_int @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_int @ Y3 @ X3 )
% 15.48/8.47         => P ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_474_linorder__less__linear,axiom,
% 15.48/8.47      ! [X3: real,Y3: real] :
% 15.48/8.47        ( ( ord_less_real @ X3 @ Y3 )
% 15.48/8.47        | ( X3 = Y3 )
% 15.48/8.47        | ( ord_less_real @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_475_linorder__less__linear,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat] :
% 15.48/8.47        ( ( ord_less_rat @ X3 @ Y3 )
% 15.48/8.47        | ( X3 = Y3 )
% 15.48/8.47        | ( ord_less_rat @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_476_linorder__less__linear,axiom,
% 15.48/8.47      ! [X3: num,Y3: num] :
% 15.48/8.47        ( ( ord_less_num @ X3 @ Y3 )
% 15.48/8.47        | ( X3 = Y3 )
% 15.48/8.47        | ( ord_less_num @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_477_linorder__less__linear,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat] :
% 15.48/8.47        ( ( ord_less_nat @ X3 @ Y3 )
% 15.48/8.47        | ( X3 = Y3 )
% 15.48/8.47        | ( ord_less_nat @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_478_linorder__less__linear,axiom,
% 15.48/8.47      ! [X3: int,Y3: int] :
% 15.48/8.47        ( ( ord_less_int @ X3 @ Y3 )
% 15.48/8.47        | ( X3 = Y3 )
% 15.48/8.47        | ( ord_less_int @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_479_order__less__imp__not__eq,axiom,
% 15.48/8.47      ! [X3: real,Y3: real] :
% 15.48/8.47        ( ( ord_less_real @ X3 @ Y3 )
% 15.48/8.47       => ( X3 != Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_480_order__less__imp__not__eq,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat] :
% 15.48/8.47        ( ( ord_less_rat @ X3 @ Y3 )
% 15.48/8.47       => ( X3 != Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_481_order__less__imp__not__eq,axiom,
% 15.48/8.47      ! [X3: num,Y3: num] :
% 15.48/8.47        ( ( ord_less_num @ X3 @ Y3 )
% 15.48/8.47       => ( X3 != Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_482_order__less__imp__not__eq,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat] :
% 15.48/8.47        ( ( ord_less_nat @ X3 @ Y3 )
% 15.48/8.47       => ( X3 != Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_483_order__less__imp__not__eq,axiom,
% 15.48/8.47      ! [X3: int,Y3: int] :
% 15.48/8.47        ( ( ord_less_int @ X3 @ Y3 )
% 15.48/8.47       => ( X3 != Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_484_order__less__imp__not__eq2,axiom,
% 15.48/8.47      ! [X3: real,Y3: real] :
% 15.48/8.47        ( ( ord_less_real @ X3 @ Y3 )
% 15.48/8.47       => ( Y3 != X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_485_order__less__imp__not__eq2,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat] :
% 15.48/8.47        ( ( ord_less_rat @ X3 @ Y3 )
% 15.48/8.47       => ( Y3 != X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_486_order__less__imp__not__eq2,axiom,
% 15.48/8.47      ! [X3: num,Y3: num] :
% 15.48/8.47        ( ( ord_less_num @ X3 @ Y3 )
% 15.48/8.47       => ( Y3 != X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_487_order__less__imp__not__eq2,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat] :
% 15.48/8.47        ( ( ord_less_nat @ X3 @ Y3 )
% 15.48/8.47       => ( Y3 != X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_488_order__less__imp__not__eq2,axiom,
% 15.48/8.47      ! [X3: int,Y3: int] :
% 15.48/8.47        ( ( ord_less_int @ X3 @ Y3 )
% 15.48/8.47       => ( Y3 != X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_489_order__less__imp__not__less,axiom,
% 15.48/8.47      ! [X3: real,Y3: real] :
% 15.48/8.47        ( ( ord_less_real @ X3 @ Y3 )
% 15.48/8.47       => ~ ( ord_less_real @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_490_order__less__imp__not__less,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat] :
% 15.48/8.47        ( ( ord_less_rat @ X3 @ Y3 )
% 15.48/8.47       => ~ ( ord_less_rat @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_491_order__less__imp__not__less,axiom,
% 15.48/8.47      ! [X3: num,Y3: num] :
% 15.48/8.47        ( ( ord_less_num @ X3 @ Y3 )
% 15.48/8.47       => ~ ( ord_less_num @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_492_order__less__imp__not__less,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat] :
% 15.48/8.47        ( ( ord_less_nat @ X3 @ Y3 )
% 15.48/8.47       => ~ ( ord_less_nat @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_493_order__less__imp__not__less,axiom,
% 15.48/8.47      ! [X3: int,Y3: int] :
% 15.48/8.47        ( ( ord_less_int @ X3 @ Y3 )
% 15.48/8.47       => ~ ( ord_less_int @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_494_nat__neq__iff,axiom,
% 15.48/8.47      ! [M: nat,N: nat] :
% 15.48/8.47        ( ( M != N )
% 15.48/8.47        = ( ( ord_less_nat @ M @ N )
% 15.48/8.47          | ( ord_less_nat @ N @ M ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_495_less__not__refl,axiom,
% 15.48/8.47      ! [N: nat] :
% 15.48/8.47        ~ ( ord_less_nat @ N @ N ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_496_less__not__refl2,axiom,
% 15.48/8.47      ! [N: nat,M: nat] :
% 15.48/8.47        ( ( ord_less_nat @ N @ M )
% 15.48/8.47       => ( M != N ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_497_less__not__refl3,axiom,
% 15.48/8.47      ! [S: nat,T: nat] :
% 15.48/8.47        ( ( ord_less_nat @ S @ T )
% 15.48/8.47       => ( S != T ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_498_less__irrefl__nat,axiom,
% 15.48/8.47      ! [N: nat] :
% 15.48/8.47        ~ ( ord_less_nat @ N @ N ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_499_nat__less__induct,axiom,
% 15.48/8.47      ! [P: nat > $o,N: nat] :
% 15.48/8.47        ( ! [N2: nat] :
% 15.48/8.47            ( ! [M2: nat] :
% 15.48/8.47                ( ( ord_less_nat @ M2 @ N2 )
% 15.48/8.47               => ( P @ M2 ) )
% 15.48/8.47           => ( P @ N2 ) )
% 15.48/8.47       => ( P @ N ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_500_infinite__descent,axiom,
% 15.48/8.47      ! [P: nat > $o,N: nat] :
% 15.48/8.47        ( ! [N2: nat] :
% 15.48/8.47            ( ~ ( P @ N2 )
% 15.48/8.47           => ? [M2: nat] :
% 15.48/8.47                ( ( ord_less_nat @ M2 @ N2 )
% 15.48/8.47                & ~ ( P @ M2 ) ) )
% 15.48/8.47       => ( P @ N ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_501_linorder__neqE__nat,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat] :
% 15.48/8.47        ( ( X3 != Y3 )
% 15.48/8.47       => ( ~ ( ord_less_nat @ X3 @ Y3 )
% 15.48/8.47         => ( ord_less_nat @ Y3 @ X3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_502_Nat_Oex__has__greatest__nat,axiom,
% 15.48/8.47      ! [P: nat > $o,K: nat,B: nat] :
% 15.48/8.47        ( ( P @ K )
% 15.48/8.47       => ( ! [Y4: nat] :
% 15.48/8.47              ( ( P @ Y4 )
% 15.48/8.47             => ( ord_less_eq_nat @ Y4 @ B ) )
% 15.48/8.47         => ? [X4: nat] :
% 15.48/8.47              ( ( P @ X4 )
% 15.48/8.47              & ! [Y6: nat] :
% 15.48/8.47                  ( ( P @ Y6 )
% 15.48/8.47                 => ( ord_less_eq_nat @ Y6 @ X4 ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_503_nat__le__linear,axiom,
% 15.48/8.47      ! [M: nat,N: nat] :
% 15.48/8.47        ( ( ord_less_eq_nat @ M @ N )
% 15.48/8.47        | ( ord_less_eq_nat @ N @ M ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_504_le__antisym,axiom,
% 15.48/8.47      ! [M: nat,N: nat] :
% 15.48/8.47        ( ( ord_less_eq_nat @ M @ N )
% 15.48/8.47       => ( ( ord_less_eq_nat @ N @ M )
% 15.48/8.47         => ( M = N ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_505_eq__imp__le,axiom,
% 15.48/8.47      ! [M: nat,N: nat] :
% 15.48/8.47        ( ( M = N )
% 15.48/8.47       => ( ord_less_eq_nat @ M @ N ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_506_le__trans,axiom,
% 15.48/8.47      ! [I: nat,J: nat,K: nat] :
% 15.48/8.47        ( ( ord_less_eq_nat @ I @ J )
% 15.48/8.47       => ( ( ord_less_eq_nat @ J @ K )
% 15.48/8.47         => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_507_le__refl,axiom,
% 15.48/8.47      ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_508_leD,axiom,
% 15.48/8.47      ! [Y3: real,X3: real] :
% 15.48/8.47        ( ( ord_less_eq_real @ Y3 @ X3 )
% 15.48/8.47       => ~ ( ord_less_real @ X3 @ Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_509_leD,axiom,
% 15.48/8.47      ! [Y3: set_nat,X3: set_nat] :
% 15.48/8.47        ( ( ord_less_eq_set_nat @ Y3 @ X3 )
% 15.48/8.47       => ~ ( ord_less_set_nat @ X3 @ Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_510_leD,axiom,
% 15.48/8.47      ! [Y3: rat,X3: rat] :
% 15.48/8.47        ( ( ord_less_eq_rat @ Y3 @ X3 )
% 15.48/8.47       => ~ ( ord_less_rat @ X3 @ Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_511_leD,axiom,
% 15.48/8.47      ! [Y3: num,X3: num] :
% 15.48/8.47        ( ( ord_less_eq_num @ Y3 @ X3 )
% 15.48/8.47       => ~ ( ord_less_num @ X3 @ Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_512_leD,axiom,
% 15.48/8.47      ! [Y3: nat,X3: nat] :
% 15.48/8.47        ( ( ord_less_eq_nat @ Y3 @ X3 )
% 15.48/8.47       => ~ ( ord_less_nat @ X3 @ Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_513_leD,axiom,
% 15.48/8.47      ! [Y3: int,X3: int] :
% 15.48/8.47        ( ( ord_less_eq_int @ Y3 @ X3 )
% 15.48/8.47       => ~ ( ord_less_int @ X3 @ Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_514_leI,axiom,
% 15.48/8.47      ! [X3: real,Y3: real] :
% 15.48/8.47        ( ~ ( ord_less_real @ X3 @ Y3 )
% 15.48/8.47       => ( ord_less_eq_real @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_515_leI,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat] :
% 15.48/8.47        ( ~ ( ord_less_rat @ X3 @ Y3 )
% 15.48/8.47       => ( ord_less_eq_rat @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_516_leI,axiom,
% 15.48/8.47      ! [X3: num,Y3: num] :
% 15.48/8.47        ( ~ ( ord_less_num @ X3 @ Y3 )
% 15.48/8.47       => ( ord_less_eq_num @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_517_leI,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat] :
% 15.48/8.47        ( ~ ( ord_less_nat @ X3 @ Y3 )
% 15.48/8.47       => ( ord_less_eq_nat @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_518_leI,axiom,
% 15.48/8.47      ! [X3: int,Y3: int] :
% 15.48/8.47        ( ~ ( ord_less_int @ X3 @ Y3 )
% 15.48/8.47       => ( ord_less_eq_int @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_519_nless__le,axiom,
% 15.48/8.47      ! [A: real,B: real] :
% 15.48/8.47        ( ( ~ ( ord_less_real @ A @ B ) )
% 15.48/8.47        = ( ~ ( ord_less_eq_real @ A @ B )
% 15.48/8.47          | ( A = B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_520_nless__le,axiom,
% 15.48/8.47      ! [A: set_nat,B: set_nat] :
% 15.48/8.47        ( ( ~ ( ord_less_set_nat @ A @ B ) )
% 15.48/8.47        = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 15.48/8.47          | ( A = B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_521_nless__le,axiom,
% 15.48/8.47      ! [A: rat,B: rat] :
% 15.48/8.47        ( ( ~ ( ord_less_rat @ A @ B ) )
% 15.48/8.47        = ( ~ ( ord_less_eq_rat @ A @ B )
% 15.48/8.47          | ( A = B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_522_nless__le,axiom,
% 15.48/8.47      ! [A: num,B: num] :
% 15.48/8.47        ( ( ~ ( ord_less_num @ A @ B ) )
% 15.48/8.47        = ( ~ ( ord_less_eq_num @ A @ B )
% 15.48/8.47          | ( A = B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_523_nless__le,axiom,
% 15.48/8.47      ! [A: nat,B: nat] :
% 15.48/8.47        ( ( ~ ( ord_less_nat @ A @ B ) )
% 15.48/8.47        = ( ~ ( ord_less_eq_nat @ A @ B )
% 15.48/8.47          | ( A = B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_524_nless__le,axiom,
% 15.48/8.47      ! [A: int,B: int] :
% 15.48/8.47        ( ( ~ ( ord_less_int @ A @ B ) )
% 15.48/8.47        = ( ~ ( ord_less_eq_int @ A @ B )
% 15.48/8.47          | ( A = B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_525_antisym__conv1,axiom,
% 15.48/8.47      ! [X3: real,Y3: real] :
% 15.48/8.47        ( ~ ( ord_less_real @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_eq_real @ X3 @ Y3 )
% 15.48/8.47          = ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_526_antisym__conv1,axiom,
% 15.48/8.47      ! [X3: set_nat,Y3: set_nat] :
% 15.48/8.47        ( ~ ( ord_less_set_nat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 15.48/8.47          = ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_527_antisym__conv1,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat] :
% 15.48/8.47        ( ~ ( ord_less_rat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_eq_rat @ X3 @ Y3 )
% 15.48/8.47          = ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_528_antisym__conv1,axiom,
% 15.48/8.47      ! [X3: num,Y3: num] :
% 15.48/8.47        ( ~ ( ord_less_num @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_eq_num @ X3 @ Y3 )
% 15.48/8.47          = ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_529_antisym__conv1,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat] :
% 15.48/8.47        ( ~ ( ord_less_nat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_eq_nat @ X3 @ Y3 )
% 15.48/8.47          = ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_530_antisym__conv1,axiom,
% 15.48/8.47      ! [X3: int,Y3: int] :
% 15.48/8.47        ( ~ ( ord_less_int @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_eq_int @ X3 @ Y3 )
% 15.48/8.47          = ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_531_antisym__conv2,axiom,
% 15.48/8.47      ! [X3: real,Y3: real] :
% 15.48/8.47        ( ( ord_less_eq_real @ X3 @ Y3 )
% 15.48/8.47       => ( ( ~ ( ord_less_real @ X3 @ Y3 ) )
% 15.48/8.47          = ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_532_antisym__conv2,axiom,
% 15.48/8.47      ! [X3: set_nat,Y3: set_nat] :
% 15.48/8.47        ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ~ ( ord_less_set_nat @ X3 @ Y3 ) )
% 15.48/8.47          = ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_533_antisym__conv2,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat] :
% 15.48/8.47        ( ( ord_less_eq_rat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ~ ( ord_less_rat @ X3 @ Y3 ) )
% 15.48/8.47          = ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_534_antisym__conv2,axiom,
% 15.48/8.47      ! [X3: num,Y3: num] :
% 15.48/8.47        ( ( ord_less_eq_num @ X3 @ Y3 )
% 15.48/8.47       => ( ( ~ ( ord_less_num @ X3 @ Y3 ) )
% 15.48/8.47          = ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_535_antisym__conv2,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat] :
% 15.48/8.47        ( ( ord_less_eq_nat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ~ ( ord_less_nat @ X3 @ Y3 ) )
% 15.48/8.47          = ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_536_antisym__conv2,axiom,
% 15.48/8.47      ! [X3: int,Y3: int] :
% 15.48/8.47        ( ( ord_less_eq_int @ X3 @ Y3 )
% 15.48/8.47       => ( ( ~ ( ord_less_int @ X3 @ Y3 ) )
% 15.48/8.47          = ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_537_dense__ge,axiom,
% 15.48/8.47      ! [Z: real,Y3: real] :
% 15.48/8.47        ( ! [X4: real] :
% 15.48/8.47            ( ( ord_less_real @ Z @ X4 )
% 15.48/8.47           => ( ord_less_eq_real @ Y3 @ X4 ) )
% 15.48/8.47       => ( ord_less_eq_real @ Y3 @ Z ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_538_dense__ge,axiom,
% 15.48/8.47      ! [Z: rat,Y3: rat] :
% 15.48/8.47        ( ! [X4: rat] :
% 15.48/8.47            ( ( ord_less_rat @ Z @ X4 )
% 15.48/8.47           => ( ord_less_eq_rat @ Y3 @ X4 ) )
% 15.48/8.47       => ( ord_less_eq_rat @ Y3 @ Z ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_539_dense__le,axiom,
% 15.48/8.47      ! [Y3: real,Z: real] :
% 15.48/8.47        ( ! [X4: real] :
% 15.48/8.47            ( ( ord_less_real @ X4 @ Y3 )
% 15.48/8.47           => ( ord_less_eq_real @ X4 @ Z ) )
% 15.48/8.47       => ( ord_less_eq_real @ Y3 @ Z ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_540_dense__le,axiom,
% 15.48/8.47      ! [Y3: rat,Z: rat] :
% 15.48/8.47        ( ! [X4: rat] :
% 15.48/8.47            ( ( ord_less_rat @ X4 @ Y3 )
% 15.48/8.47           => ( ord_less_eq_rat @ X4 @ Z ) )
% 15.48/8.47       => ( ord_less_eq_rat @ Y3 @ Z ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_541_less__le__not__le,axiom,
% 15.48/8.47      ( ord_less_real
% 15.48/8.47      = ( ^ [X: real,Y: real] :
% 15.48/8.47            ( ( ord_less_eq_real @ X @ Y )
% 15.48/8.47            & ~ ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_542_less__le__not__le,axiom,
% 15.48/8.47      ( ord_less_set_nat
% 15.48/8.47      = ( ^ [X: set_nat,Y: set_nat] :
% 15.48/8.47            ( ( ord_less_eq_set_nat @ X @ Y )
% 15.48/8.47            & ~ ( ord_less_eq_set_nat @ Y @ X ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_543_less__le__not__le,axiom,
% 15.48/8.47      ( ord_less_rat
% 15.48/8.47      = ( ^ [X: rat,Y: rat] :
% 15.48/8.47            ( ( ord_less_eq_rat @ X @ Y )
% 15.48/8.47            & ~ ( ord_less_eq_rat @ Y @ X ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_544_less__le__not__le,axiom,
% 15.48/8.47      ( ord_less_num
% 15.48/8.47      = ( ^ [X: num,Y: num] :
% 15.48/8.47            ( ( ord_less_eq_num @ X @ Y )
% 15.48/8.47            & ~ ( ord_less_eq_num @ Y @ X ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_545_less__le__not__le,axiom,
% 15.48/8.47      ( ord_less_nat
% 15.48/8.47      = ( ^ [X: nat,Y: nat] :
% 15.48/8.47            ( ( ord_less_eq_nat @ X @ Y )
% 15.48/8.47            & ~ ( ord_less_eq_nat @ Y @ X ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_546_less__le__not__le,axiom,
% 15.48/8.47      ( ord_less_int
% 15.48/8.47      = ( ^ [X: int,Y: int] :
% 15.48/8.47            ( ( ord_less_eq_int @ X @ Y )
% 15.48/8.47            & ~ ( ord_less_eq_int @ Y @ X ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_547_not__le__imp__less,axiom,
% 15.48/8.47      ! [Y3: real,X3: real] :
% 15.48/8.47        ( ~ ( ord_less_eq_real @ Y3 @ X3 )
% 15.48/8.47       => ( ord_less_real @ X3 @ Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_548_not__le__imp__less,axiom,
% 15.48/8.47      ! [Y3: rat,X3: rat] :
% 15.48/8.47        ( ~ ( ord_less_eq_rat @ Y3 @ X3 )
% 15.48/8.47       => ( ord_less_rat @ X3 @ Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_549_not__le__imp__less,axiom,
% 15.48/8.47      ! [Y3: num,X3: num] :
% 15.48/8.47        ( ~ ( ord_less_eq_num @ Y3 @ X3 )
% 15.48/8.47       => ( ord_less_num @ X3 @ Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_550_not__le__imp__less,axiom,
% 15.48/8.47      ! [Y3: nat,X3: nat] :
% 15.48/8.47        ( ~ ( ord_less_eq_nat @ Y3 @ X3 )
% 15.48/8.47       => ( ord_less_nat @ X3 @ Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_551_not__le__imp__less,axiom,
% 15.48/8.47      ! [Y3: int,X3: int] :
% 15.48/8.47        ( ~ ( ord_less_eq_int @ Y3 @ X3 )
% 15.48/8.47       => ( ord_less_int @ X3 @ Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_552_order_Oorder__iff__strict,axiom,
% 15.48/8.47      ( ord_less_eq_real
% 15.48/8.47      = ( ^ [A4: real,B3: real] :
% 15.48/8.47            ( ( ord_less_real @ A4 @ B3 )
% 15.48/8.47            | ( A4 = B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_553_order_Oorder__iff__strict,axiom,
% 15.48/8.47      ( ord_less_eq_set_nat
% 15.48/8.47      = ( ^ [A4: set_nat,B3: set_nat] :
% 15.48/8.47            ( ( ord_less_set_nat @ A4 @ B3 )
% 15.48/8.47            | ( A4 = B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_554_order_Oorder__iff__strict,axiom,
% 15.48/8.47      ( ord_less_eq_rat
% 15.48/8.47      = ( ^ [A4: rat,B3: rat] :
% 15.48/8.47            ( ( ord_less_rat @ A4 @ B3 )
% 15.48/8.47            | ( A4 = B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_555_order_Oorder__iff__strict,axiom,
% 15.48/8.47      ( ord_less_eq_num
% 15.48/8.47      = ( ^ [A4: num,B3: num] :
% 15.48/8.47            ( ( ord_less_num @ A4 @ B3 )
% 15.48/8.47            | ( A4 = B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_556_order_Oorder__iff__strict,axiom,
% 15.48/8.47      ( ord_less_eq_nat
% 15.48/8.47      = ( ^ [A4: nat,B3: nat] :
% 15.48/8.47            ( ( ord_less_nat @ A4 @ B3 )
% 15.48/8.47            | ( A4 = B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_557_order_Oorder__iff__strict,axiom,
% 15.48/8.47      ( ord_less_eq_int
% 15.48/8.47      = ( ^ [A4: int,B3: int] :
% 15.48/8.47            ( ( ord_less_int @ A4 @ B3 )
% 15.48/8.47            | ( A4 = B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_558_order_Ostrict__iff__order,axiom,
% 15.48/8.47      ( ord_less_real
% 15.48/8.47      = ( ^ [A4: real,B3: real] :
% 15.48/8.47            ( ( ord_less_eq_real @ A4 @ B3 )
% 15.48/8.47            & ( A4 != B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_559_order_Ostrict__iff__order,axiom,
% 15.48/8.47      ( ord_less_set_nat
% 15.48/8.47      = ( ^ [A4: set_nat,B3: set_nat] :
% 15.48/8.47            ( ( ord_less_eq_set_nat @ A4 @ B3 )
% 15.48/8.47            & ( A4 != B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_560_order_Ostrict__iff__order,axiom,
% 15.48/8.47      ( ord_less_rat
% 15.48/8.47      = ( ^ [A4: rat,B3: rat] :
% 15.48/8.47            ( ( ord_less_eq_rat @ A4 @ B3 )
% 15.48/8.47            & ( A4 != B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_561_order_Ostrict__iff__order,axiom,
% 15.48/8.47      ( ord_less_num
% 15.48/8.47      = ( ^ [A4: num,B3: num] :
% 15.48/8.47            ( ( ord_less_eq_num @ A4 @ B3 )
% 15.48/8.47            & ( A4 != B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_562_order_Ostrict__iff__order,axiom,
% 15.48/8.47      ( ord_less_nat
% 15.48/8.47      = ( ^ [A4: nat,B3: nat] :
% 15.48/8.47            ( ( ord_less_eq_nat @ A4 @ B3 )
% 15.48/8.47            & ( A4 != B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_563_order_Ostrict__iff__order,axiom,
% 15.48/8.47      ( ord_less_int
% 15.48/8.47      = ( ^ [A4: int,B3: int] :
% 15.48/8.47            ( ( ord_less_eq_int @ A4 @ B3 )
% 15.48/8.47            & ( A4 != B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_564_order_Ostrict__trans1,axiom,
% 15.48/8.47      ! [A: real,B: real,C: real] :
% 15.48/8.47        ( ( ord_less_eq_real @ A @ B )
% 15.48/8.47       => ( ( ord_less_real @ B @ C )
% 15.48/8.47         => ( ord_less_real @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_565_order_Ostrict__trans1,axiom,
% 15.48/8.47      ! [A: set_nat,B: set_nat,C: set_nat] :
% 15.48/8.47        ( ( ord_less_eq_set_nat @ A @ B )
% 15.48/8.47       => ( ( ord_less_set_nat @ B @ C )
% 15.48/8.47         => ( ord_less_set_nat @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_566_order_Ostrict__trans1,axiom,
% 15.48/8.47      ! [A: rat,B: rat,C: rat] :
% 15.48/8.47        ( ( ord_less_eq_rat @ A @ B )
% 15.48/8.47       => ( ( ord_less_rat @ B @ C )
% 15.48/8.47         => ( ord_less_rat @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_567_order_Ostrict__trans1,axiom,
% 15.48/8.47      ! [A: num,B: num,C: num] :
% 15.48/8.47        ( ( ord_less_eq_num @ A @ B )
% 15.48/8.47       => ( ( ord_less_num @ B @ C )
% 15.48/8.47         => ( ord_less_num @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_568_order_Ostrict__trans1,axiom,
% 15.48/8.47      ! [A: nat,B: nat,C: nat] :
% 15.48/8.47        ( ( ord_less_eq_nat @ A @ B )
% 15.48/8.47       => ( ( ord_less_nat @ B @ C )
% 15.48/8.47         => ( ord_less_nat @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_569_order_Ostrict__trans1,axiom,
% 15.48/8.47      ! [A: int,B: int,C: int] :
% 15.48/8.47        ( ( ord_less_eq_int @ A @ B )
% 15.48/8.47       => ( ( ord_less_int @ B @ C )
% 15.48/8.47         => ( ord_less_int @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_570_order_Ostrict__trans2,axiom,
% 15.48/8.47      ! [A: real,B: real,C: real] :
% 15.48/8.47        ( ( ord_less_real @ A @ B )
% 15.48/8.47       => ( ( ord_less_eq_real @ B @ C )
% 15.48/8.47         => ( ord_less_real @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_571_order_Ostrict__trans2,axiom,
% 15.48/8.47      ! [A: set_nat,B: set_nat,C: set_nat] :
% 15.48/8.47        ( ( ord_less_set_nat @ A @ B )
% 15.48/8.47       => ( ( ord_less_eq_set_nat @ B @ C )
% 15.48/8.47         => ( ord_less_set_nat @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_572_order_Ostrict__trans2,axiom,
% 15.48/8.47      ! [A: rat,B: rat,C: rat] :
% 15.48/8.47        ( ( ord_less_rat @ A @ B )
% 15.48/8.47       => ( ( ord_less_eq_rat @ B @ C )
% 15.48/8.47         => ( ord_less_rat @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_573_order_Ostrict__trans2,axiom,
% 15.48/8.47      ! [A: num,B: num,C: num] :
% 15.48/8.47        ( ( ord_less_num @ A @ B )
% 15.48/8.47       => ( ( ord_less_eq_num @ B @ C )
% 15.48/8.47         => ( ord_less_num @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_574_order_Ostrict__trans2,axiom,
% 15.48/8.47      ! [A: nat,B: nat,C: nat] :
% 15.48/8.47        ( ( ord_less_nat @ A @ B )
% 15.48/8.47       => ( ( ord_less_eq_nat @ B @ C )
% 15.48/8.47         => ( ord_less_nat @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_575_order_Ostrict__trans2,axiom,
% 15.48/8.47      ! [A: int,B: int,C: int] :
% 15.48/8.47        ( ( ord_less_int @ A @ B )
% 15.48/8.47       => ( ( ord_less_eq_int @ B @ C )
% 15.48/8.47         => ( ord_less_int @ A @ C ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_576_order_Ostrict__iff__not,axiom,
% 15.48/8.47      ( ord_less_real
% 15.48/8.47      = ( ^ [A4: real,B3: real] :
% 15.48/8.47            ( ( ord_less_eq_real @ A4 @ B3 )
% 15.48/8.47            & ~ ( ord_less_eq_real @ B3 @ A4 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_577_order_Ostrict__iff__not,axiom,
% 15.48/8.47      ( ord_less_set_nat
% 15.48/8.47      = ( ^ [A4: set_nat,B3: set_nat] :
% 15.48/8.47            ( ( ord_less_eq_set_nat @ A4 @ B3 )
% 15.48/8.47            & ~ ( ord_less_eq_set_nat @ B3 @ A4 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_578_order_Ostrict__iff__not,axiom,
% 15.48/8.47      ( ord_less_rat
% 15.48/8.47      = ( ^ [A4: rat,B3: rat] :
% 15.48/8.47            ( ( ord_less_eq_rat @ A4 @ B3 )
% 15.48/8.47            & ~ ( ord_less_eq_rat @ B3 @ A4 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_579_order_Ostrict__iff__not,axiom,
% 15.48/8.47      ( ord_less_num
% 15.48/8.47      = ( ^ [A4: num,B3: num] :
% 15.48/8.47            ( ( ord_less_eq_num @ A4 @ B3 )
% 15.48/8.47            & ~ ( ord_less_eq_num @ B3 @ A4 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_580_order_Ostrict__iff__not,axiom,
% 15.48/8.47      ( ord_less_nat
% 15.48/8.47      = ( ^ [A4: nat,B3: nat] :
% 15.48/8.47            ( ( ord_less_eq_nat @ A4 @ B3 )
% 15.48/8.47            & ~ ( ord_less_eq_nat @ B3 @ A4 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_581_order_Ostrict__iff__not,axiom,
% 15.48/8.47      ( ord_less_int
% 15.48/8.47      = ( ^ [A4: int,B3: int] :
% 15.48/8.47            ( ( ord_less_eq_int @ A4 @ B3 )
% 15.48/8.47            & ~ ( ord_less_eq_int @ B3 @ A4 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_582_dense__ge__bounded,axiom,
% 15.48/8.47      ! [Z: real,X3: real,Y3: real] :
% 15.48/8.47        ( ( ord_less_real @ Z @ X3 )
% 15.48/8.47       => ( ! [W2: real] :
% 15.48/8.47              ( ( ord_less_real @ Z @ W2 )
% 15.48/8.47             => ( ( ord_less_real @ W2 @ X3 )
% 15.48/8.47               => ( ord_less_eq_real @ Y3 @ W2 ) ) )
% 15.48/8.47         => ( ord_less_eq_real @ Y3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_583_dense__ge__bounded,axiom,
% 15.48/8.47      ! [Z: rat,X3: rat,Y3: rat] :
% 15.48/8.47        ( ( ord_less_rat @ Z @ X3 )
% 15.48/8.47       => ( ! [W2: rat] :
% 15.48/8.47              ( ( ord_less_rat @ Z @ W2 )
% 15.48/8.47             => ( ( ord_less_rat @ W2 @ X3 )
% 15.48/8.47               => ( ord_less_eq_rat @ Y3 @ W2 ) ) )
% 15.48/8.47         => ( ord_less_eq_rat @ Y3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_584_dense__le__bounded,axiom,
% 15.48/8.47      ! [X3: real,Y3: real,Z: real] :
% 15.48/8.47        ( ( ord_less_real @ X3 @ Y3 )
% 15.48/8.47       => ( ! [W2: real] :
% 15.48/8.47              ( ( ord_less_real @ X3 @ W2 )
% 15.48/8.47             => ( ( ord_less_real @ W2 @ Y3 )
% 15.48/8.47               => ( ord_less_eq_real @ W2 @ Z ) ) )
% 15.48/8.47         => ( ord_less_eq_real @ Y3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_585_dense__le__bounded,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat,Z: rat] :
% 15.48/8.47        ( ( ord_less_rat @ X3 @ Y3 )
% 15.48/8.47       => ( ! [W2: rat] :
% 15.48/8.47              ( ( ord_less_rat @ X3 @ W2 )
% 15.48/8.47             => ( ( ord_less_rat @ W2 @ Y3 )
% 15.48/8.47               => ( ord_less_eq_rat @ W2 @ Z ) ) )
% 15.48/8.47         => ( ord_less_eq_rat @ Y3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_586_dual__order_Oorder__iff__strict,axiom,
% 15.48/8.47      ( ord_less_eq_real
% 15.48/8.47      = ( ^ [B3: real,A4: real] :
% 15.48/8.47            ( ( ord_less_real @ B3 @ A4 )
% 15.48/8.47            | ( A4 = B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_587_dual__order_Oorder__iff__strict,axiom,
% 15.48/8.47      ( ord_less_eq_set_nat
% 15.48/8.47      = ( ^ [B3: set_nat,A4: set_nat] :
% 15.48/8.47            ( ( ord_less_set_nat @ B3 @ A4 )
% 15.48/8.47            | ( A4 = B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_588_dual__order_Oorder__iff__strict,axiom,
% 15.48/8.47      ( ord_less_eq_rat
% 15.48/8.47      = ( ^ [B3: rat,A4: rat] :
% 15.48/8.47            ( ( ord_less_rat @ B3 @ A4 )
% 15.48/8.47            | ( A4 = B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_589_dual__order_Oorder__iff__strict,axiom,
% 15.48/8.47      ( ord_less_eq_num
% 15.48/8.47      = ( ^ [B3: num,A4: num] :
% 15.48/8.47            ( ( ord_less_num @ B3 @ A4 )
% 15.48/8.47            | ( A4 = B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_590_dual__order_Oorder__iff__strict,axiom,
% 15.48/8.47      ( ord_less_eq_nat
% 15.48/8.47      = ( ^ [B3: nat,A4: nat] :
% 15.48/8.47            ( ( ord_less_nat @ B3 @ A4 )
% 15.48/8.47            | ( A4 = B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_591_dual__order_Oorder__iff__strict,axiom,
% 15.48/8.47      ( ord_less_eq_int
% 15.48/8.47      = ( ^ [B3: int,A4: int] :
% 15.48/8.47            ( ( ord_less_int @ B3 @ A4 )
% 15.48/8.47            | ( A4 = B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_592_dual__order_Ostrict__iff__order,axiom,
% 15.48/8.47      ( ord_less_real
% 15.48/8.47      = ( ^ [B3: real,A4: real] :
% 15.48/8.47            ( ( ord_less_eq_real @ B3 @ A4 )
% 15.48/8.47            & ( A4 != B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_593_dual__order_Ostrict__iff__order,axiom,
% 15.48/8.47      ( ord_less_set_nat
% 15.48/8.47      = ( ^ [B3: set_nat,A4: set_nat] :
% 15.48/8.47            ( ( ord_less_eq_set_nat @ B3 @ A4 )
% 15.48/8.47            & ( A4 != B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_594_dual__order_Ostrict__iff__order,axiom,
% 15.48/8.47      ( ord_less_rat
% 15.48/8.47      = ( ^ [B3: rat,A4: rat] :
% 15.48/8.47            ( ( ord_less_eq_rat @ B3 @ A4 )
% 15.48/8.47            & ( A4 != B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_595_dual__order_Ostrict__iff__order,axiom,
% 15.48/8.47      ( ord_less_num
% 15.48/8.47      = ( ^ [B3: num,A4: num] :
% 15.48/8.47            ( ( ord_less_eq_num @ B3 @ A4 )
% 15.48/8.47            & ( A4 != B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_596_dual__order_Ostrict__iff__order,axiom,
% 15.48/8.47      ( ord_less_nat
% 15.48/8.47      = ( ^ [B3: nat,A4: nat] :
% 15.48/8.47            ( ( ord_less_eq_nat @ B3 @ A4 )
% 15.48/8.47            & ( A4 != B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_597_dual__order_Ostrict__iff__order,axiom,
% 15.48/8.47      ( ord_less_int
% 15.48/8.47      = ( ^ [B3: int,A4: int] :
% 15.48/8.47            ( ( ord_less_eq_int @ B3 @ A4 )
% 15.48/8.47            & ( A4 != B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_598_dual__order_Ostrict__trans1,axiom,
% 15.48/8.47      ! [B: real,A: real,C: real] :
% 15.48/8.47        ( ( ord_less_eq_real @ B @ A )
% 15.48/8.47       => ( ( ord_less_real @ C @ B )
% 15.48/8.47         => ( ord_less_real @ C @ A ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_599_dual__order_Ostrict__trans1,axiom,
% 15.48/8.47      ! [B: set_nat,A: set_nat,C: set_nat] :
% 15.48/8.47        ( ( ord_less_eq_set_nat @ B @ A )
% 15.48/8.47       => ( ( ord_less_set_nat @ C @ B )
% 15.48/8.47         => ( ord_less_set_nat @ C @ A ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_600_dual__order_Ostrict__trans1,axiom,
% 15.48/8.47      ! [B: rat,A: rat,C: rat] :
% 15.48/8.47        ( ( ord_less_eq_rat @ B @ A )
% 15.48/8.47       => ( ( ord_less_rat @ C @ B )
% 15.48/8.47         => ( ord_less_rat @ C @ A ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_601_dual__order_Ostrict__trans1,axiom,
% 15.48/8.47      ! [B: num,A: num,C: num] :
% 15.48/8.47        ( ( ord_less_eq_num @ B @ A )
% 15.48/8.47       => ( ( ord_less_num @ C @ B )
% 15.48/8.47         => ( ord_less_num @ C @ A ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_602_dual__order_Ostrict__trans1,axiom,
% 15.48/8.47      ! [B: nat,A: nat,C: nat] :
% 15.48/8.47        ( ( ord_less_eq_nat @ B @ A )
% 15.48/8.47       => ( ( ord_less_nat @ C @ B )
% 15.48/8.47         => ( ord_less_nat @ C @ A ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_603_dual__order_Ostrict__trans1,axiom,
% 15.48/8.47      ! [B: int,A: int,C: int] :
% 15.48/8.47        ( ( ord_less_eq_int @ B @ A )
% 15.48/8.47       => ( ( ord_less_int @ C @ B )
% 15.48/8.47         => ( ord_less_int @ C @ A ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_604_dual__order_Ostrict__trans2,axiom,
% 15.48/8.47      ! [B: real,A: real,C: real] :
% 15.48/8.47        ( ( ord_less_real @ B @ A )
% 15.48/8.47       => ( ( ord_less_eq_real @ C @ B )
% 15.48/8.47         => ( ord_less_real @ C @ A ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_605_dual__order_Ostrict__trans2,axiom,
% 15.48/8.47      ! [B: set_nat,A: set_nat,C: set_nat] :
% 15.48/8.47        ( ( ord_less_set_nat @ B @ A )
% 15.48/8.47       => ( ( ord_less_eq_set_nat @ C @ B )
% 15.48/8.47         => ( ord_less_set_nat @ C @ A ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_606_dual__order_Ostrict__trans2,axiom,
% 15.48/8.47      ! [B: rat,A: rat,C: rat] :
% 15.48/8.47        ( ( ord_less_rat @ B @ A )
% 15.48/8.47       => ( ( ord_less_eq_rat @ C @ B )
% 15.48/8.47         => ( ord_less_rat @ C @ A ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_607_dual__order_Ostrict__trans2,axiom,
% 15.48/8.47      ! [B: num,A: num,C: num] :
% 15.48/8.47        ( ( ord_less_num @ B @ A )
% 15.48/8.47       => ( ( ord_less_eq_num @ C @ B )
% 15.48/8.47         => ( ord_less_num @ C @ A ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_608_dual__order_Ostrict__trans2,axiom,
% 15.48/8.47      ! [B: nat,A: nat,C: nat] :
% 15.48/8.47        ( ( ord_less_nat @ B @ A )
% 15.48/8.47       => ( ( ord_less_eq_nat @ C @ B )
% 15.48/8.47         => ( ord_less_nat @ C @ A ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_609_dual__order_Ostrict__trans2,axiom,
% 15.48/8.47      ! [B: int,A: int,C: int] :
% 15.48/8.47        ( ( ord_less_int @ B @ A )
% 15.48/8.47       => ( ( ord_less_eq_int @ C @ B )
% 15.48/8.47         => ( ord_less_int @ C @ A ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_610_dual__order_Ostrict__iff__not,axiom,
% 15.48/8.47      ( ord_less_real
% 15.48/8.47      = ( ^ [B3: real,A4: real] :
% 15.48/8.47            ( ( ord_less_eq_real @ B3 @ A4 )
% 15.48/8.47            & ~ ( ord_less_eq_real @ A4 @ B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_611_dual__order_Ostrict__iff__not,axiom,
% 15.48/8.47      ( ord_less_set_nat
% 15.48/8.47      = ( ^ [B3: set_nat,A4: set_nat] :
% 15.48/8.47            ( ( ord_less_eq_set_nat @ B3 @ A4 )
% 15.48/8.47            & ~ ( ord_less_eq_set_nat @ A4 @ B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_612_dual__order_Ostrict__iff__not,axiom,
% 15.48/8.47      ( ord_less_rat
% 15.48/8.47      = ( ^ [B3: rat,A4: rat] :
% 15.48/8.47            ( ( ord_less_eq_rat @ B3 @ A4 )
% 15.48/8.47            & ~ ( ord_less_eq_rat @ A4 @ B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_613_dual__order_Ostrict__iff__not,axiom,
% 15.48/8.47      ( ord_less_num
% 15.48/8.47      = ( ^ [B3: num,A4: num] :
% 15.48/8.47            ( ( ord_less_eq_num @ B3 @ A4 )
% 15.48/8.47            & ~ ( ord_less_eq_num @ A4 @ B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_614_dual__order_Ostrict__iff__not,axiom,
% 15.48/8.47      ( ord_less_nat
% 15.48/8.47      = ( ^ [B3: nat,A4: nat] :
% 15.48/8.47            ( ( ord_less_eq_nat @ B3 @ A4 )
% 15.48/8.47            & ~ ( ord_less_eq_nat @ A4 @ B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_615_dual__order_Ostrict__iff__not,axiom,
% 15.48/8.47      ( ord_less_int
% 15.48/8.47      = ( ^ [B3: int,A4: int] :
% 15.48/8.47            ( ( ord_less_eq_int @ B3 @ A4 )
% 15.48/8.47            & ~ ( ord_less_eq_int @ A4 @ B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_616_order_Ostrict__implies__order,axiom,
% 15.48/8.47      ! [A: real,B: real] :
% 15.48/8.47        ( ( ord_less_real @ A @ B )
% 15.48/8.47       => ( ord_less_eq_real @ A @ B ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_617_order_Ostrict__implies__order,axiom,
% 15.48/8.47      ! [A: set_nat,B: set_nat] :
% 15.48/8.47        ( ( ord_less_set_nat @ A @ B )
% 15.48/8.47       => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_618_order_Ostrict__implies__order,axiom,
% 15.48/8.47      ! [A: rat,B: rat] :
% 15.48/8.47        ( ( ord_less_rat @ A @ B )
% 15.48/8.47       => ( ord_less_eq_rat @ A @ B ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_619_order_Ostrict__implies__order,axiom,
% 15.48/8.47      ! [A: num,B: num] :
% 15.48/8.47        ( ( ord_less_num @ A @ B )
% 15.48/8.47       => ( ord_less_eq_num @ A @ B ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_620_order_Ostrict__implies__order,axiom,
% 15.48/8.47      ! [A: nat,B: nat] :
% 15.48/8.47        ( ( ord_less_nat @ A @ B )
% 15.48/8.47       => ( ord_less_eq_nat @ A @ B ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_621_order_Ostrict__implies__order,axiom,
% 15.48/8.47      ! [A: int,B: int] :
% 15.48/8.47        ( ( ord_less_int @ A @ B )
% 15.48/8.47       => ( ord_less_eq_int @ A @ B ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_622_dual__order_Ostrict__implies__order,axiom,
% 15.48/8.47      ! [B: real,A: real] :
% 15.48/8.47        ( ( ord_less_real @ B @ A )
% 15.48/8.47       => ( ord_less_eq_real @ B @ A ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_623_dual__order_Ostrict__implies__order,axiom,
% 15.48/8.47      ! [B: set_nat,A: set_nat] :
% 15.48/8.47        ( ( ord_less_set_nat @ B @ A )
% 15.48/8.47       => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_624_dual__order_Ostrict__implies__order,axiom,
% 15.48/8.47      ! [B: rat,A: rat] :
% 15.48/8.47        ( ( ord_less_rat @ B @ A )
% 15.48/8.47       => ( ord_less_eq_rat @ B @ A ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_625_dual__order_Ostrict__implies__order,axiom,
% 15.48/8.47      ! [B: num,A: num] :
% 15.48/8.47        ( ( ord_less_num @ B @ A )
% 15.48/8.47       => ( ord_less_eq_num @ B @ A ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_626_dual__order_Ostrict__implies__order,axiom,
% 15.48/8.47      ! [B: nat,A: nat] :
% 15.48/8.47        ( ( ord_less_nat @ B @ A )
% 15.48/8.47       => ( ord_less_eq_nat @ B @ A ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_627_dual__order_Ostrict__implies__order,axiom,
% 15.48/8.47      ! [B: int,A: int] :
% 15.48/8.47        ( ( ord_less_int @ B @ A )
% 15.48/8.47       => ( ord_less_eq_int @ B @ A ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_628_order__le__less,axiom,
% 15.48/8.47      ( ord_less_eq_real
% 15.48/8.47      = ( ^ [X: real,Y: real] :
% 15.48/8.47            ( ( ord_less_real @ X @ Y )
% 15.48/8.47            | ( X = Y ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_629_order__le__less,axiom,
% 15.48/8.47      ( ord_less_eq_set_nat
% 15.48/8.47      = ( ^ [X: set_nat,Y: set_nat] :
% 15.48/8.47            ( ( ord_less_set_nat @ X @ Y )
% 15.48/8.47            | ( X = Y ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_630_order__le__less,axiom,
% 15.48/8.47      ( ord_less_eq_rat
% 15.48/8.47      = ( ^ [X: rat,Y: rat] :
% 15.48/8.47            ( ( ord_less_rat @ X @ Y )
% 15.48/8.47            | ( X = Y ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_631_order__le__less,axiom,
% 15.48/8.47      ( ord_less_eq_num
% 15.48/8.47      = ( ^ [X: num,Y: num] :
% 15.48/8.47            ( ( ord_less_num @ X @ Y )
% 15.48/8.47            | ( X = Y ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_632_order__le__less,axiom,
% 15.48/8.47      ( ord_less_eq_nat
% 15.48/8.47      = ( ^ [X: nat,Y: nat] :
% 15.48/8.47            ( ( ord_less_nat @ X @ Y )
% 15.48/8.47            | ( X = Y ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_633_order__le__less,axiom,
% 15.48/8.47      ( ord_less_eq_int
% 15.48/8.47      = ( ^ [X: int,Y: int] :
% 15.48/8.47            ( ( ord_less_int @ X @ Y )
% 15.48/8.47            | ( X = Y ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_634_order__less__le,axiom,
% 15.48/8.47      ( ord_less_real
% 15.48/8.47      = ( ^ [X: real,Y: real] :
% 15.48/8.47            ( ( ord_less_eq_real @ X @ Y )
% 15.48/8.47            & ( X != Y ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_635_order__less__le,axiom,
% 15.48/8.47      ( ord_less_set_nat
% 15.48/8.47      = ( ^ [X: set_nat,Y: set_nat] :
% 15.48/8.47            ( ( ord_less_eq_set_nat @ X @ Y )
% 15.48/8.47            & ( X != Y ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_636_order__less__le,axiom,
% 15.48/8.47      ( ord_less_rat
% 15.48/8.47      = ( ^ [X: rat,Y: rat] :
% 15.48/8.47            ( ( ord_less_eq_rat @ X @ Y )
% 15.48/8.47            & ( X != Y ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_637_order__less__le,axiom,
% 15.48/8.47      ( ord_less_num
% 15.48/8.47      = ( ^ [X: num,Y: num] :
% 15.48/8.47            ( ( ord_less_eq_num @ X @ Y )
% 15.48/8.47            & ( X != Y ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_638_order__less__le,axiom,
% 15.48/8.47      ( ord_less_nat
% 15.48/8.47      = ( ^ [X: nat,Y: nat] :
% 15.48/8.47            ( ( ord_less_eq_nat @ X @ Y )
% 15.48/8.47            & ( X != Y ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_639_order__less__le,axiom,
% 15.48/8.47      ( ord_less_int
% 15.48/8.47      = ( ^ [X: int,Y: int] :
% 15.48/8.47            ( ( ord_less_eq_int @ X @ Y )
% 15.48/8.47            & ( X != Y ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_640_linorder__not__le,axiom,
% 15.48/8.47      ! [X3: real,Y3: real] :
% 15.48/8.47        ( ( ~ ( ord_less_eq_real @ X3 @ Y3 ) )
% 15.48/8.47        = ( ord_less_real @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_641_linorder__not__le,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat] :
% 15.48/8.47        ( ( ~ ( ord_less_eq_rat @ X3 @ Y3 ) )
% 15.48/8.47        = ( ord_less_rat @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_642_linorder__not__le,axiom,
% 15.48/8.47      ! [X3: num,Y3: num] :
% 15.48/8.47        ( ( ~ ( ord_less_eq_num @ X3 @ Y3 ) )
% 15.48/8.47        = ( ord_less_num @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_643_linorder__not__le,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat] :
% 15.48/8.47        ( ( ~ ( ord_less_eq_nat @ X3 @ Y3 ) )
% 15.48/8.47        = ( ord_less_nat @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_644_linorder__not__le,axiom,
% 15.48/8.47      ! [X3: int,Y3: int] :
% 15.48/8.47        ( ( ~ ( ord_less_eq_int @ X3 @ Y3 ) )
% 15.48/8.47        = ( ord_less_int @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_645_linorder__not__less,axiom,
% 15.48/8.47      ! [X3: real,Y3: real] :
% 15.48/8.47        ( ( ~ ( ord_less_real @ X3 @ Y3 ) )
% 15.48/8.47        = ( ord_less_eq_real @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_646_linorder__not__less,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat] :
% 15.48/8.47        ( ( ~ ( ord_less_rat @ X3 @ Y3 ) )
% 15.48/8.47        = ( ord_less_eq_rat @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_647_linorder__not__less,axiom,
% 15.48/8.47      ! [X3: num,Y3: num] :
% 15.48/8.47        ( ( ~ ( ord_less_num @ X3 @ Y3 ) )
% 15.48/8.47        = ( ord_less_eq_num @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_648_linorder__not__less,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat] :
% 15.48/8.47        ( ( ~ ( ord_less_nat @ X3 @ Y3 ) )
% 15.48/8.47        = ( ord_less_eq_nat @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_649_linorder__not__less,axiom,
% 15.48/8.47      ! [X3: int,Y3: int] :
% 15.48/8.47        ( ( ~ ( ord_less_int @ X3 @ Y3 ) )
% 15.48/8.47        = ( ord_less_eq_int @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_650_order__less__imp__le,axiom,
% 15.48/8.47      ! [X3: real,Y3: real] :
% 15.48/8.47        ( ( ord_less_real @ X3 @ Y3 )
% 15.48/8.47       => ( ord_less_eq_real @ X3 @ Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_651_order__less__imp__le,axiom,
% 15.48/8.47      ! [X3: set_nat,Y3: set_nat] :
% 15.48/8.47        ( ( ord_less_set_nat @ X3 @ Y3 )
% 15.48/8.47       => ( ord_less_eq_set_nat @ X3 @ Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_652_order__less__imp__le,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat] :
% 15.48/8.47        ( ( ord_less_rat @ X3 @ Y3 )
% 15.48/8.47       => ( ord_less_eq_rat @ X3 @ Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_653_order__less__imp__le,axiom,
% 15.48/8.47      ! [X3: num,Y3: num] :
% 15.48/8.47        ( ( ord_less_num @ X3 @ Y3 )
% 15.48/8.47       => ( ord_less_eq_num @ X3 @ Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_654_order__less__imp__le,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat] :
% 15.48/8.47        ( ( ord_less_nat @ X3 @ Y3 )
% 15.48/8.47       => ( ord_less_eq_nat @ X3 @ Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_655_order__less__imp__le,axiom,
% 15.48/8.47      ! [X3: int,Y3: int] :
% 15.48/8.47        ( ( ord_less_int @ X3 @ Y3 )
% 15.48/8.47       => ( ord_less_eq_int @ X3 @ Y3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_656_order__le__neq__trans,axiom,
% 15.48/8.47      ! [A: real,B: real] :
% 15.48/8.47        ( ( ord_less_eq_real @ A @ B )
% 15.48/8.47       => ( ( A != B )
% 15.48/8.47         => ( ord_less_real @ A @ B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_657_order__le__neq__trans,axiom,
% 15.48/8.47      ! [A: set_nat,B: set_nat] :
% 15.48/8.47        ( ( ord_less_eq_set_nat @ A @ B )
% 15.48/8.47       => ( ( A != B )
% 15.48/8.47         => ( ord_less_set_nat @ A @ B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_658_order__le__neq__trans,axiom,
% 15.48/8.47      ! [A: rat,B: rat] :
% 15.48/8.47        ( ( ord_less_eq_rat @ A @ B )
% 15.48/8.47       => ( ( A != B )
% 15.48/8.47         => ( ord_less_rat @ A @ B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_659_order__le__neq__trans,axiom,
% 15.48/8.47      ! [A: num,B: num] :
% 15.48/8.47        ( ( ord_less_eq_num @ A @ B )
% 15.48/8.47       => ( ( A != B )
% 15.48/8.47         => ( ord_less_num @ A @ B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_660_order__le__neq__trans,axiom,
% 15.48/8.47      ! [A: nat,B: nat] :
% 15.48/8.47        ( ( ord_less_eq_nat @ A @ B )
% 15.48/8.47       => ( ( A != B )
% 15.48/8.47         => ( ord_less_nat @ A @ B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_661_order__le__neq__trans,axiom,
% 15.48/8.47      ! [A: int,B: int] :
% 15.48/8.47        ( ( ord_less_eq_int @ A @ B )
% 15.48/8.47       => ( ( A != B )
% 15.48/8.47         => ( ord_less_int @ A @ B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_662_order__neq__le__trans,axiom,
% 15.48/8.47      ! [A: real,B: real] :
% 15.48/8.47        ( ( A != B )
% 15.48/8.47       => ( ( ord_less_eq_real @ A @ B )
% 15.48/8.47         => ( ord_less_real @ A @ B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_663_order__neq__le__trans,axiom,
% 15.48/8.47      ! [A: set_nat,B: set_nat] :
% 15.48/8.47        ( ( A != B )
% 15.48/8.47       => ( ( ord_less_eq_set_nat @ A @ B )
% 15.48/8.47         => ( ord_less_set_nat @ A @ B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_664_order__neq__le__trans,axiom,
% 15.48/8.47      ! [A: rat,B: rat] :
% 15.48/8.47        ( ( A != B )
% 15.48/8.47       => ( ( ord_less_eq_rat @ A @ B )
% 15.48/8.47         => ( ord_less_rat @ A @ B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_665_order__neq__le__trans,axiom,
% 15.48/8.47      ! [A: num,B: num] :
% 15.48/8.47        ( ( A != B )
% 15.48/8.47       => ( ( ord_less_eq_num @ A @ B )
% 15.48/8.47         => ( ord_less_num @ A @ B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_666_order__neq__le__trans,axiom,
% 15.48/8.47      ! [A: nat,B: nat] :
% 15.48/8.47        ( ( A != B )
% 15.48/8.47       => ( ( ord_less_eq_nat @ A @ B )
% 15.48/8.47         => ( ord_less_nat @ A @ B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_667_order__neq__le__trans,axiom,
% 15.48/8.47      ! [A: int,B: int] :
% 15.48/8.47        ( ( A != B )
% 15.48/8.47       => ( ( ord_less_eq_int @ A @ B )
% 15.48/8.47         => ( ord_less_int @ A @ B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_668_order__le__less__trans,axiom,
% 15.48/8.47      ! [X3: real,Y3: real,Z: real] :
% 15.48/8.47        ( ( ord_less_eq_real @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_real @ Y3 @ Z )
% 15.48/8.47         => ( ord_less_real @ X3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_669_order__le__less__trans,axiom,
% 15.48/8.47      ! [X3: set_nat,Y3: set_nat,Z: set_nat] :
% 15.48/8.47        ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_set_nat @ Y3 @ Z )
% 15.48/8.47         => ( ord_less_set_nat @ X3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_670_order__le__less__trans,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat,Z: rat] :
% 15.48/8.47        ( ( ord_less_eq_rat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_rat @ Y3 @ Z )
% 15.48/8.47         => ( ord_less_rat @ X3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_671_order__le__less__trans,axiom,
% 15.48/8.47      ! [X3: num,Y3: num,Z: num] :
% 15.48/8.47        ( ( ord_less_eq_num @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_num @ Y3 @ Z )
% 15.48/8.47         => ( ord_less_num @ X3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_672_order__le__less__trans,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat,Z: nat] :
% 15.48/8.47        ( ( ord_less_eq_nat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_nat @ Y3 @ Z )
% 15.48/8.47         => ( ord_less_nat @ X3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_673_order__le__less__trans,axiom,
% 15.48/8.47      ! [X3: int,Y3: int,Z: int] :
% 15.48/8.47        ( ( ord_less_eq_int @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_int @ Y3 @ Z )
% 15.48/8.47         => ( ord_less_int @ X3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_674_order__less__le__trans,axiom,
% 15.48/8.47      ! [X3: real,Y3: real,Z: real] :
% 15.48/8.47        ( ( ord_less_real @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_eq_real @ Y3 @ Z )
% 15.48/8.47         => ( ord_less_real @ X3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_675_order__less__le__trans,axiom,
% 15.48/8.47      ! [X3: set_nat,Y3: set_nat,Z: set_nat] :
% 15.48/8.47        ( ( ord_less_set_nat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_eq_set_nat @ Y3 @ Z )
% 15.48/8.47         => ( ord_less_set_nat @ X3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_676_order__less__le__trans,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat,Z: rat] :
% 15.48/8.47        ( ( ord_less_rat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_eq_rat @ Y3 @ Z )
% 15.48/8.47         => ( ord_less_rat @ X3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_677_order__less__le__trans,axiom,
% 15.48/8.47      ! [X3: num,Y3: num,Z: num] :
% 15.48/8.47        ( ( ord_less_num @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_eq_num @ Y3 @ Z )
% 15.48/8.47         => ( ord_less_num @ X3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_678_order__less__le__trans,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat,Z: nat] :
% 15.48/8.47        ( ( ord_less_nat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_eq_nat @ Y3 @ Z )
% 15.48/8.47         => ( ord_less_nat @ X3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_679_order__less__le__trans,axiom,
% 15.48/8.47      ! [X3: int,Y3: int,Z: int] :
% 15.48/8.47        ( ( ord_less_int @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_eq_int @ Y3 @ Z )
% 15.48/8.47         => ( ord_less_int @ X3 @ Z ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_680_order__le__less__subst1,axiom,
% 15.48/8.47      ! [A: real,F: real > real,B: real,C: real] :
% 15.48/8.47        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_real @ B @ C )
% 15.48/8.47         => ( ! [X4: real,Y4: real] :
% 15.48/8.47                ( ( ord_less_real @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_681_order__le__less__subst1,axiom,
% 15.48/8.47      ! [A: real,F: rat > real,B: rat,C: rat] :
% 15.48/8.47        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_rat @ B @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_682_order__le__less__subst1,axiom,
% 15.48/8.47      ! [A: real,F: num > real,B: num,C: num] :
% 15.48/8.47        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_num @ B @ C )
% 15.48/8.47         => ( ! [X4: num,Y4: num] :
% 15.48/8.47                ( ( ord_less_num @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_683_order__le__less__subst1,axiom,
% 15.48/8.47      ! [A: real,F: nat > real,B: nat,C: nat] :
% 15.48/8.47        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_nat @ B @ C )
% 15.48/8.47         => ( ! [X4: nat,Y4: nat] :
% 15.48/8.47                ( ( ord_less_nat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_684_order__le__less__subst1,axiom,
% 15.48/8.47      ! [A: real,F: int > real,B: int,C: int] :
% 15.48/8.47        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_int @ B @ C )
% 15.48/8.47         => ( ! [X4: int,Y4: int] :
% 15.48/8.47                ( ( ord_less_int @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_685_order__le__less__subst1,axiom,
% 15.48/8.47      ! [A: rat,F: real > rat,B: real,C: real] :
% 15.48/8.47        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_real @ B @ C )
% 15.48/8.47         => ( ! [X4: real,Y4: real] :
% 15.48/8.47                ( ( ord_less_real @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_686_order__le__less__subst1,axiom,
% 15.48/8.47      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 15.48/8.47        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_rat @ B @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_687_order__le__less__subst1,axiom,
% 15.48/8.47      ! [A: rat,F: num > rat,B: num,C: num] :
% 15.48/8.47        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_num @ B @ C )
% 15.48/8.47         => ( ! [X4: num,Y4: num] :
% 15.48/8.47                ( ( ord_less_num @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_688_order__le__less__subst1,axiom,
% 15.48/8.47      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 15.48/8.47        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_nat @ B @ C )
% 15.48/8.47         => ( ! [X4: nat,Y4: nat] :
% 15.48/8.47                ( ( ord_less_nat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_689_order__le__less__subst1,axiom,
% 15.48/8.47      ! [A: rat,F: int > rat,B: int,C: int] :
% 15.48/8.47        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_int @ B @ C )
% 15.48/8.47         => ( ! [X4: int,Y4: int] :
% 15.48/8.47                ( ( ord_less_int @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_690_order__le__less__subst2,axiom,
% 15.48/8.47      ! [A: rat,B: rat,F: rat > real,C: real] :
% 15.48/8.47        ( ( ord_less_eq_rat @ A @ B )
% 15.48/8.47       => ( ( ord_less_real @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_691_order__le__less__subst2,axiom,
% 15.48/8.47      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 15.48/8.47        ( ( ord_less_eq_rat @ A @ B )
% 15.48/8.47       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_692_order__le__less__subst2,axiom,
% 15.48/8.47      ! [A: rat,B: rat,F: rat > num,C: num] :
% 15.48/8.47        ( ( ord_less_eq_rat @ A @ B )
% 15.48/8.47       => ( ( ord_less_num @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_693_order__le__less__subst2,axiom,
% 15.48/8.47      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 15.48/8.47        ( ( ord_less_eq_rat @ A @ B )
% 15.48/8.47       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_694_order__le__less__subst2,axiom,
% 15.48/8.47      ! [A: rat,B: rat,F: rat > int,C: int] :
% 15.48/8.47        ( ( ord_less_eq_rat @ A @ B )
% 15.48/8.47       => ( ( ord_less_int @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_695_order__le__less__subst2,axiom,
% 15.48/8.47      ! [A: num,B: num,F: num > real,C: real] :
% 15.48/8.47        ( ( ord_less_eq_num @ A @ B )
% 15.48/8.47       => ( ( ord_less_real @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: num,Y4: num] :
% 15.48/8.47                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_696_order__le__less__subst2,axiom,
% 15.48/8.47      ! [A: num,B: num,F: num > rat,C: rat] :
% 15.48/8.47        ( ( ord_less_eq_num @ A @ B )
% 15.48/8.47       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: num,Y4: num] :
% 15.48/8.47                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_697_order__le__less__subst2,axiom,
% 15.48/8.47      ! [A: num,B: num,F: num > num,C: num] :
% 15.48/8.47        ( ( ord_less_eq_num @ A @ B )
% 15.48/8.47       => ( ( ord_less_num @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: num,Y4: num] :
% 15.48/8.47                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_698_order__le__less__subst2,axiom,
% 15.48/8.47      ! [A: num,B: num,F: num > nat,C: nat] :
% 15.48/8.47        ( ( ord_less_eq_num @ A @ B )
% 15.48/8.47       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: num,Y4: num] :
% 15.48/8.47                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_699_order__le__less__subst2,axiom,
% 15.48/8.47      ! [A: num,B: num,F: num > int,C: int] :
% 15.48/8.47        ( ( ord_less_eq_num @ A @ B )
% 15.48/8.47       => ( ( ord_less_int @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: num,Y4: num] :
% 15.48/8.47                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_700_order__less__le__subst1,axiom,
% 15.48/8.47      ! [A: real,F: rat > real,B: rat,C: rat] :
% 15.48/8.47        ( ( ord_less_real @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_eq_rat @ B @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_701_order__less__le__subst1,axiom,
% 15.48/8.47      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 15.48/8.47        ( ( ord_less_rat @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_eq_rat @ B @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_702_order__less__le__subst1,axiom,
% 15.48/8.47      ! [A: num,F: rat > num,B: rat,C: rat] :
% 15.48/8.47        ( ( ord_less_num @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_eq_rat @ B @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_703_order__less__le__subst1,axiom,
% 15.48/8.47      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 15.48/8.47        ( ( ord_less_nat @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_eq_rat @ B @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_704_order__less__le__subst1,axiom,
% 15.48/8.47      ! [A: int,F: rat > int,B: rat,C: rat] :
% 15.48/8.47        ( ( ord_less_int @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_eq_rat @ B @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_eq_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_705_order__less__le__subst1,axiom,
% 15.48/8.47      ! [A: real,F: num > real,B: num,C: num] :
% 15.48/8.47        ( ( ord_less_real @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_eq_num @ B @ C )
% 15.48/8.47         => ( ! [X4: num,Y4: num] :
% 15.48/8.47                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_706_order__less__le__subst1,axiom,
% 15.48/8.47      ! [A: rat,F: num > rat,B: num,C: num] :
% 15.48/8.47        ( ( ord_less_rat @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_eq_num @ B @ C )
% 15.48/8.47         => ( ! [X4: num,Y4: num] :
% 15.48/8.47                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_707_order__less__le__subst1,axiom,
% 15.48/8.47      ! [A: num,F: num > num,B: num,C: num] :
% 15.48/8.47        ( ( ord_less_num @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_eq_num @ B @ C )
% 15.48/8.47         => ( ! [X4: num,Y4: num] :
% 15.48/8.47                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_708_order__less__le__subst1,axiom,
% 15.48/8.47      ! [A: nat,F: num > nat,B: num,C: num] :
% 15.48/8.47        ( ( ord_less_nat @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_eq_num @ B @ C )
% 15.48/8.47         => ( ! [X4: num,Y4: num] :
% 15.48/8.47                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_709_order__less__le__subst1,axiom,
% 15.48/8.47      ! [A: int,F: num > int,B: num,C: num] :
% 15.48/8.47        ( ( ord_less_int @ A @ ( F @ B ) )
% 15.48/8.47       => ( ( ord_less_eq_num @ B @ C )
% 15.48/8.47         => ( ! [X4: num,Y4: num] :
% 15.48/8.47                ( ( ord_less_eq_num @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_710_order__less__le__subst2,axiom,
% 15.48/8.47      ! [A: real,B: real,F: real > real,C: real] :
% 15.48/8.47        ( ( ord_less_real @ A @ B )
% 15.48/8.47       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: real,Y4: real] :
% 15.48/8.47                ( ( ord_less_real @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_711_order__less__le__subst2,axiom,
% 15.48/8.47      ! [A: rat,B: rat,F: rat > real,C: real] :
% 15.48/8.47        ( ( ord_less_rat @ A @ B )
% 15.48/8.47       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_712_order__less__le__subst2,axiom,
% 15.48/8.47      ! [A: num,B: num,F: num > real,C: real] :
% 15.48/8.47        ( ( ord_less_num @ A @ B )
% 15.48/8.47       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: num,Y4: num] :
% 15.48/8.47                ( ( ord_less_num @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_713_order__less__le__subst2,axiom,
% 15.48/8.47      ! [A: nat,B: nat,F: nat > real,C: real] :
% 15.48/8.47        ( ( ord_less_nat @ A @ B )
% 15.48/8.47       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: nat,Y4: nat] :
% 15.48/8.47                ( ( ord_less_nat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_714_order__less__le__subst2,axiom,
% 15.48/8.47      ! [A: int,B: int,F: int > real,C: real] :
% 15.48/8.47        ( ( ord_less_int @ A @ B )
% 15.48/8.47       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: int,Y4: int] :
% 15.48/8.47                ( ( ord_less_int @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_715_order__less__le__subst2,axiom,
% 15.48/8.47      ! [A: real,B: real,F: real > rat,C: rat] :
% 15.48/8.47        ( ( ord_less_real @ A @ B )
% 15.48/8.47       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: real,Y4: real] :
% 15.48/8.47                ( ( ord_less_real @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_716_order__less__le__subst2,axiom,
% 15.48/8.47      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 15.48/8.47        ( ( ord_less_rat @ A @ B )
% 15.48/8.47       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: rat,Y4: rat] :
% 15.48/8.47                ( ( ord_less_rat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_717_order__less__le__subst2,axiom,
% 15.48/8.47      ! [A: num,B: num,F: num > rat,C: rat] :
% 15.48/8.47        ( ( ord_less_num @ A @ B )
% 15.48/8.47       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: num,Y4: num] :
% 15.48/8.47                ( ( ord_less_num @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_718_order__less__le__subst2,axiom,
% 15.48/8.47      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 15.48/8.47        ( ( ord_less_nat @ A @ B )
% 15.48/8.47       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: nat,Y4: nat] :
% 15.48/8.47                ( ( ord_less_nat @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_719_order__less__le__subst2,axiom,
% 15.48/8.47      ! [A: int,B: int,F: int > rat,C: rat] :
% 15.48/8.47        ( ( ord_less_int @ A @ B )
% 15.48/8.47       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 15.48/8.47         => ( ! [X4: int,Y4: int] :
% 15.48/8.47                ( ( ord_less_int @ X4 @ Y4 )
% 15.48/8.47               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 15.48/8.47           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_720_linorder__le__less__linear,axiom,
% 15.48/8.47      ! [X3: real,Y3: real] :
% 15.48/8.47        ( ( ord_less_eq_real @ X3 @ Y3 )
% 15.48/8.47        | ( ord_less_real @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_721_linorder__le__less__linear,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat] :
% 15.48/8.47        ( ( ord_less_eq_rat @ X3 @ Y3 )
% 15.48/8.47        | ( ord_less_rat @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_722_linorder__le__less__linear,axiom,
% 15.48/8.47      ! [X3: num,Y3: num] :
% 15.48/8.47        ( ( ord_less_eq_num @ X3 @ Y3 )
% 15.48/8.47        | ( ord_less_num @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_723_linorder__le__less__linear,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat] :
% 15.48/8.47        ( ( ord_less_eq_nat @ X3 @ Y3 )
% 15.48/8.47        | ( ord_less_nat @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_724_linorder__le__less__linear,axiom,
% 15.48/8.47      ! [X3: int,Y3: int] :
% 15.48/8.47        ( ( ord_less_eq_int @ X3 @ Y3 )
% 15.48/8.47        | ( ord_less_int @ Y3 @ X3 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_725_order__le__imp__less__or__eq,axiom,
% 15.48/8.47      ! [X3: real,Y3: real] :
% 15.48/8.47        ( ( ord_less_eq_real @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_real @ X3 @ Y3 )
% 15.48/8.47          | ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_726_order__le__imp__less__or__eq,axiom,
% 15.48/8.47      ! [X3: set_nat,Y3: set_nat] :
% 15.48/8.47        ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_set_nat @ X3 @ Y3 )
% 15.48/8.47          | ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_727_order__le__imp__less__or__eq,axiom,
% 15.48/8.47      ! [X3: rat,Y3: rat] :
% 15.48/8.47        ( ( ord_less_eq_rat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_rat @ X3 @ Y3 )
% 15.48/8.47          | ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_728_order__le__imp__less__or__eq,axiom,
% 15.48/8.47      ! [X3: num,Y3: num] :
% 15.48/8.47        ( ( ord_less_eq_num @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_num @ X3 @ Y3 )
% 15.48/8.47          | ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_729_order__le__imp__less__or__eq,axiom,
% 15.48/8.47      ! [X3: nat,Y3: nat] :
% 15.48/8.47        ( ( ord_less_eq_nat @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_nat @ X3 @ Y3 )
% 15.48/8.47          | ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_730_order__le__imp__less__or__eq,axiom,
% 15.48/8.47      ! [X3: int,Y3: int] :
% 15.48/8.47        ( ( ord_less_eq_int @ X3 @ Y3 )
% 15.48/8.47       => ( ( ord_less_int @ X3 @ Y3 )
% 15.48/8.47          | ( X3 = Y3 ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_731_nat__less__le,axiom,
% 15.48/8.47      ( ord_less_nat
% 15.48/8.47      = ( ^ [M3: nat,N3: nat] :
% 15.48/8.47            ( ( ord_less_eq_nat @ M3 @ N3 )
% 15.48/8.47            & ( M3 != N3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_732_less__imp__le__nat,axiom,
% 15.48/8.47      ! [M: nat,N: nat] :
% 15.48/8.47        ( ( ord_less_nat @ M @ N )
% 15.48/8.47       => ( ord_less_eq_nat @ M @ N ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_733_le__eq__less__or__eq,axiom,
% 15.48/8.47      ( ord_less_eq_nat
% 15.48/8.47      = ( ^ [M3: nat,N3: nat] :
% 15.48/8.47            ( ( ord_less_nat @ M3 @ N3 )
% 15.48/8.47            | ( M3 = N3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_734_less__or__eq__imp__le,axiom,
% 15.48/8.47      ! [M: nat,N: nat] :
% 15.48/8.47        ( ( ( ord_less_nat @ M @ N )
% 15.48/8.47          | ( M = N ) )
% 15.48/8.47       => ( ord_less_eq_nat @ M @ N ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_735_le__neq__implies__less,axiom,
% 15.48/8.47      ! [M: nat,N: nat] :
% 15.48/8.47        ( ( ord_less_eq_nat @ M @ N )
% 15.48/8.47       => ( ( M != N )
% 15.48/8.47         => ( ord_less_nat @ M @ N ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_736_of__nat__less__two__power,axiom,
% 15.48/8.47      ! [N: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_737_of__nat__less__two__power,axiom,
% 15.48/8.47      ! [N: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_738_of__nat__less__two__power,axiom,
% 15.48/8.47      ! [N: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_739_numeral__le__real__of__nat__iff,axiom,
% 15.48/8.47      ! [N: num,M: nat] :
% 15.48/8.47        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M ) )
% 15.48/8.47        = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_740_numeral__less__real__of__nat__iff,axiom,
% 15.48/8.47      ! [W: num,N: nat] :
% 15.48/8.47        ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N ) )
% 15.48/8.47        = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_741_real__of__nat__less__numeral__iff,axiom,
% 15.48/8.47      ! [N: nat,W: num] :
% 15.48/8.47        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W ) )
% 15.48/8.47        = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_742_greater__shift,axiom,
% 15.48/8.47      ( ord_less_nat
% 15.48/8.47      = ( ^ [Y: nat,X: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X ) @ ( some_nat @ Y ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_743_less__shift,axiom,
% 15.48/8.47      ( ord_less_nat
% 15.48/8.47      = ( ^ [X: nat,Y: nat] : ( vEBT_VEBT_less @ ( some_nat @ X ) @ ( some_nat @ Y ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_744_option_Oinject,axiom,
% 15.48/8.47      ! [X2: nat,Y2: nat] :
% 15.48/8.47        ( ( ( some_nat @ X2 )
% 15.48/8.47          = ( some_nat @ Y2 ) )
% 15.48/8.47        = ( X2 = Y2 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_745_option_Oinject,axiom,
% 15.48/8.47      ! [X2: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 15.48/8.47        ( ( ( some_P7363390416028606310at_nat @ X2 )
% 15.48/8.47          = ( some_P7363390416028606310at_nat @ Y2 ) )
% 15.48/8.47        = ( X2 = Y2 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_746_option_Oinject,axiom,
% 15.48/8.47      ! [X2: num,Y2: num] :
% 15.48/8.47        ( ( ( some_num @ X2 )
% 15.48/8.47          = ( some_num @ Y2 ) )
% 15.48/8.47        = ( X2 = Y2 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_747_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 15.48/8.47      ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 15.48/8.47        ( ( vEBT_V1502963449132264192at_nat @ F @ ( some_P7363390416028606310at_nat @ A ) @ ( some_P7363390416028606310at_nat @ B ) )
% 15.48/8.47        = ( some_P7363390416028606310at_nat @ ( F @ A @ B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_748_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 15.48/8.47      ! [F: num > num > num,A: num,B: num] :
% 15.48/8.47        ( ( vEBT_V819420779217536731ft_num @ F @ ( some_num @ A ) @ ( some_num @ B ) )
% 15.48/8.47        = ( some_num @ ( F @ A @ B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_749_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 15.48/8.47      ! [F: nat > nat > nat,A: nat,B: nat] :
% 15.48/8.47        ( ( vEBT_V4262088993061758097ft_nat @ F @ ( some_nat @ A ) @ ( some_nat @ B ) )
% 15.48/8.47        = ( some_nat @ ( F @ A @ B ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_750_int__eq__iff__numeral,axiom,
% 15.48/8.47      ! [M: nat,V: num] :
% 15.48/8.47        ( ( ( semiri1314217659103216013at_int @ M )
% 15.48/8.47          = ( numeral_numeral_int @ V ) )
% 15.48/8.47        = ( M
% 15.48/8.47          = ( numeral_numeral_nat @ V ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_751_reals__Archimedean2,axiom,
% 15.48/8.47      ! [X3: real] :
% 15.48/8.47      ? [N2: nat] : ( ord_less_real @ X3 @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_752_reals__Archimedean2,axiom,
% 15.48/8.47      ! [X3: rat] :
% 15.48/8.47      ? [N2: nat] : ( ord_less_rat @ X3 @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_753_real__arch__simple,axiom,
% 15.48/8.47      ! [X3: real] :
% 15.48/8.47      ? [N2: nat] : ( ord_less_eq_real @ X3 @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_754_real__arch__simple,axiom,
% 15.48/8.47      ! [X3: rat] :
% 15.48/8.47      ? [N2: nat] : ( ord_less_eq_rat @ X3 @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_755_minf_I8_J,axiom,
% 15.48/8.47      ! [T: real] :
% 15.48/8.47      ? [Z3: real] :
% 15.48/8.47      ! [X6: real] :
% 15.48/8.47        ( ( ord_less_real @ X6 @ Z3 )
% 15.48/8.47       => ~ ( ord_less_eq_real @ T @ X6 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_756_minf_I8_J,axiom,
% 15.48/8.47      ! [T: rat] :
% 15.48/8.47      ? [Z3: rat] :
% 15.48/8.47      ! [X6: rat] :
% 15.48/8.47        ( ( ord_less_rat @ X6 @ Z3 )
% 15.48/8.47       => ~ ( ord_less_eq_rat @ T @ X6 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_757_minf_I8_J,axiom,
% 15.48/8.47      ! [T: num] :
% 15.48/8.47      ? [Z3: num] :
% 15.48/8.47      ! [X6: num] :
% 15.48/8.47        ( ( ord_less_num @ X6 @ Z3 )
% 15.48/8.47       => ~ ( ord_less_eq_num @ T @ X6 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_758_minf_I8_J,axiom,
% 15.48/8.47      ! [T: nat] :
% 15.48/8.47      ? [Z3: nat] :
% 15.48/8.47      ! [X6: nat] :
% 15.48/8.47        ( ( ord_less_nat @ X6 @ Z3 )
% 15.48/8.47       => ~ ( ord_less_eq_nat @ T @ X6 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_759_minf_I8_J,axiom,
% 15.48/8.47      ! [T: int] :
% 15.48/8.47      ? [Z3: int] :
% 15.48/8.47      ! [X6: int] :
% 15.48/8.47        ( ( ord_less_int @ X6 @ Z3 )
% 15.48/8.47       => ~ ( ord_less_eq_int @ T @ X6 ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_760_nat__int__comparison_I1_J,axiom,
% 15.48/8.47      ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 15.48/8.47      = ( ^ [A4: nat,B3: nat] :
% 15.48/8.47            ( ( semiri1314217659103216013at_int @ A4 )
% 15.48/8.47            = ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_761_int__if,axiom,
% 15.48/8.47      ! [P: $o,A: nat,B: nat] :
% 15.48/8.47        ( ( P
% 15.48/8.47         => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 15.48/8.47            = ( semiri1314217659103216013at_int @ A ) ) )
% 15.48/8.47        & ( ~ P
% 15.48/8.47         => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 15.48/8.47            = ( semiri1314217659103216013at_int @ B ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_762_complete__real,axiom,
% 15.48/8.47      ! [S2: set_real] :
% 15.48/8.47        ( ? [X6: real] : ( member_real @ X6 @ S2 )
% 15.48/8.47       => ( ? [Z4: real] :
% 15.48/8.47            ! [X4: real] :
% 15.48/8.47              ( ( member_real @ X4 @ S2 )
% 15.48/8.47             => ( ord_less_eq_real @ X4 @ Z4 ) )
% 15.48/8.47         => ? [Y4: real] :
% 15.48/8.47              ( ! [X6: real] :
% 15.48/8.47                  ( ( member_real @ X6 @ S2 )
% 15.48/8.47                 => ( ord_less_eq_real @ X6 @ Y4 ) )
% 15.48/8.47              & ! [Z4: real] :
% 15.48/8.47                  ( ! [X4: real] :
% 15.48/8.47                      ( ( member_real @ X4 @ S2 )
% 15.48/8.47                     => ( ord_less_eq_real @ X4 @ Z4 ) )
% 15.48/8.47                 => ( ord_less_eq_real @ Y4 @ Z4 ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_763_verit__la__generic,axiom,
% 15.48/8.47      ! [A: int,X3: int] :
% 15.48/8.47        ( ( ord_less_eq_int @ A @ X3 )
% 15.48/8.47        | ( A = X3 )
% 15.48/8.47        | ( ord_less_eq_int @ X3 @ A ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_764_less__eq__real__def,axiom,
% 15.48/8.47      ( ord_less_eq_real
% 15.48/8.47      = ( ^ [X: real,Y: real] :
% 15.48/8.47            ( ( ord_less_real @ X @ Y )
% 15.48/8.47            | ( X = Y ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_765_int__int__eq,axiom,
% 15.48/8.47      ! [M: nat,N: nat] :
% 15.48/8.47        ( ( ( semiri1314217659103216013at_int @ M )
% 15.48/8.47          = ( semiri1314217659103216013at_int @ N ) )
% 15.48/8.47        = ( M = N ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_766_pinf_I1_J,axiom,
% 15.48/8.47      ! [P: real > $o,P4: real > $o,Q: real > $o,Q2: real > $o] :
% 15.48/8.47        ( ? [Z4: real] :
% 15.48/8.47          ! [X4: real] :
% 15.48/8.47            ( ( ord_less_real @ Z4 @ X4 )
% 15.48/8.47           => ( ( P @ X4 )
% 15.48/8.47              = ( P4 @ X4 ) ) )
% 15.48/8.47       => ( ? [Z4: real] :
% 15.48/8.47            ! [X4: real] :
% 15.48/8.47              ( ( ord_less_real @ Z4 @ X4 )
% 15.48/8.47             => ( ( Q @ X4 )
% 15.48/8.47                = ( Q2 @ X4 ) ) )
% 15.48/8.47         => ? [Z3: real] :
% 15.48/8.47            ! [X6: real] :
% 15.48/8.47              ( ( ord_less_real @ Z3 @ X6 )
% 15.48/8.47             => ( ( ( P @ X6 )
% 15.48/8.47                  & ( Q @ X6 ) )
% 15.48/8.47                = ( ( P4 @ X6 )
% 15.48/8.47                  & ( Q2 @ X6 ) ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_767_pinf_I1_J,axiom,
% 15.48/8.47      ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 15.48/8.47        ( ? [Z4: rat] :
% 15.48/8.47          ! [X4: rat] :
% 15.48/8.47            ( ( ord_less_rat @ Z4 @ X4 )
% 15.48/8.47           => ( ( P @ X4 )
% 15.48/8.47              = ( P4 @ X4 ) ) )
% 15.48/8.47       => ( ? [Z4: rat] :
% 15.48/8.47            ! [X4: rat] :
% 15.48/8.47              ( ( ord_less_rat @ Z4 @ X4 )
% 15.48/8.47             => ( ( Q @ X4 )
% 15.48/8.47                = ( Q2 @ X4 ) ) )
% 15.48/8.47         => ? [Z3: rat] :
% 15.48/8.47            ! [X6: rat] :
% 15.48/8.47              ( ( ord_less_rat @ Z3 @ X6 )
% 15.48/8.47             => ( ( ( P @ X6 )
% 15.48/8.47                  & ( Q @ X6 ) )
% 15.48/8.47                = ( ( P4 @ X6 )
% 15.48/8.47                  & ( Q2 @ X6 ) ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_768_pinf_I1_J,axiom,
% 15.48/8.47      ! [P: num > $o,P4: num > $o,Q: num > $o,Q2: num > $o] :
% 15.48/8.47        ( ? [Z4: num] :
% 15.48/8.47          ! [X4: num] :
% 15.48/8.47            ( ( ord_less_num @ Z4 @ X4 )
% 15.48/8.47           => ( ( P @ X4 )
% 15.48/8.47              = ( P4 @ X4 ) ) )
% 15.48/8.47       => ( ? [Z4: num] :
% 15.48/8.47            ! [X4: num] :
% 15.48/8.47              ( ( ord_less_num @ Z4 @ X4 )
% 15.48/8.47             => ( ( Q @ X4 )
% 15.48/8.47                = ( Q2 @ X4 ) ) )
% 15.48/8.47         => ? [Z3: num] :
% 15.48/8.47            ! [X6: num] :
% 15.48/8.47              ( ( ord_less_num @ Z3 @ X6 )
% 15.48/8.47             => ( ( ( P @ X6 )
% 15.48/8.47                  & ( Q @ X6 ) )
% 15.48/8.47                = ( ( P4 @ X6 )
% 15.48/8.47                  & ( Q2 @ X6 ) ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_769_pinf_I1_J,axiom,
% 15.48/8.47      ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 15.48/8.47        ( ? [Z4: nat] :
% 15.48/8.47          ! [X4: nat] :
% 15.48/8.47            ( ( ord_less_nat @ Z4 @ X4 )
% 15.48/8.47           => ( ( P @ X4 )
% 15.48/8.47              = ( P4 @ X4 ) ) )
% 15.48/8.47       => ( ? [Z4: nat] :
% 15.48/8.47            ! [X4: nat] :
% 15.48/8.47              ( ( ord_less_nat @ Z4 @ X4 )
% 15.48/8.47             => ( ( Q @ X4 )
% 15.48/8.47                = ( Q2 @ X4 ) ) )
% 15.48/8.47         => ? [Z3: nat] :
% 15.48/8.47            ! [X6: nat] :
% 15.48/8.47              ( ( ord_less_nat @ Z3 @ X6 )
% 15.48/8.47             => ( ( ( P @ X6 )
% 15.48/8.47                  & ( Q @ X6 ) )
% 15.48/8.47                = ( ( P4 @ X6 )
% 15.48/8.47                  & ( Q2 @ X6 ) ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_770_pinf_I1_J,axiom,
% 15.48/8.47      ! [P: int > $o,P4: int > $o,Q: int > $o,Q2: int > $o] :
% 15.48/8.47        ( ? [Z4: int] :
% 15.48/8.47          ! [X4: int] :
% 15.48/8.47            ( ( ord_less_int @ Z4 @ X4 )
% 15.48/8.47           => ( ( P @ X4 )
% 15.48/8.47              = ( P4 @ X4 ) ) )
% 15.48/8.47       => ( ? [Z4: int] :
% 15.48/8.47            ! [X4: int] :
% 15.48/8.47              ( ( ord_less_int @ Z4 @ X4 )
% 15.48/8.47             => ( ( Q @ X4 )
% 15.48/8.47                = ( Q2 @ X4 ) ) )
% 15.48/8.47         => ? [Z3: int] :
% 15.48/8.47            ! [X6: int] :
% 15.48/8.47              ( ( ord_less_int @ Z3 @ X6 )
% 15.48/8.47             => ( ( ( P @ X6 )
% 15.48/8.47                  & ( Q @ X6 ) )
% 15.48/8.47                = ( ( P4 @ X6 )
% 15.48/8.47                  & ( Q2 @ X6 ) ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_771_pinf_I2_J,axiom,
% 15.48/8.47      ! [P: real > $o,P4: real > $o,Q: real > $o,Q2: real > $o] :
% 15.48/8.47        ( ? [Z4: real] :
% 15.48/8.47          ! [X4: real] :
% 15.48/8.47            ( ( ord_less_real @ Z4 @ X4 )
% 15.48/8.47           => ( ( P @ X4 )
% 15.48/8.47              = ( P4 @ X4 ) ) )
% 15.48/8.47       => ( ? [Z4: real] :
% 15.48/8.47            ! [X4: real] :
% 15.48/8.47              ( ( ord_less_real @ Z4 @ X4 )
% 15.48/8.47             => ( ( Q @ X4 )
% 15.48/8.47                = ( Q2 @ X4 ) ) )
% 15.48/8.47         => ? [Z3: real] :
% 15.48/8.47            ! [X6: real] :
% 15.48/8.47              ( ( ord_less_real @ Z3 @ X6 )
% 15.48/8.47             => ( ( ( P @ X6 )
% 15.48/8.47                  | ( Q @ X6 ) )
% 15.48/8.47                = ( ( P4 @ X6 )
% 15.48/8.47                  | ( Q2 @ X6 ) ) ) ) ) ) ).
% 15.48/8.47  
% 15.48/8.47  thf(fact_772_pinf_I2_J,axiom,
% 15.48/8.47      ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 15.48/8.47        ( ? [Z4: rat] :
% 15.48/8.47          ! [X4: rat] :
% 15.48/8.47            ( ( ord_less_rat @ Z4 @ X4 )
% 15.48/8.47           => ( ( P @ X4 )
% 15.48/8.47              = ( P4 @ X4 ) ) )
% 15.48/8.47       => ( ? [Z4: rat] :
% 15.48/8.47            ! [X4: rat] :
% 15.48/8.47              ( ( ord_less_rat @ Z4 @ X4 )
% 15.48/8.47             => ( ( Q @ X4 )
% 15.48/8.47                = ( Q2 @ X4 ) ) )
% 15.48/8.47         => ? [Z3: rat] :
% 15.48/8.47            ! [X6: rat] :
% 15.48/8.48              ( ( ord_less_rat @ Z3 @ X6 )
% 15.48/8.48             => ( ( ( P @ X6 )
% 15.48/8.48                  | ( Q @ X6 ) )
% 15.48/8.48                = ( ( P4 @ X6 )
% 15.48/8.48                  | ( Q2 @ X6 ) ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_773_pinf_I2_J,axiom,
% 15.48/8.48      ! [P: num > $o,P4: num > $o,Q: num > $o,Q2: num > $o] :
% 15.48/8.48        ( ? [Z4: num] :
% 15.48/8.48          ! [X4: num] :
% 15.48/8.48            ( ( ord_less_num @ Z4 @ X4 )
% 15.48/8.48           => ( ( P @ X4 )
% 15.48/8.48              = ( P4 @ X4 ) ) )
% 15.48/8.48       => ( ? [Z4: num] :
% 15.48/8.48            ! [X4: num] :
% 15.48/8.48              ( ( ord_less_num @ Z4 @ X4 )
% 15.48/8.48             => ( ( Q @ X4 )
% 15.48/8.48                = ( Q2 @ X4 ) ) )
% 15.48/8.48         => ? [Z3: num] :
% 15.48/8.48            ! [X6: num] :
% 15.48/8.48              ( ( ord_less_num @ Z3 @ X6 )
% 15.48/8.48             => ( ( ( P @ X6 )
% 15.48/8.48                  | ( Q @ X6 ) )
% 15.48/8.48                = ( ( P4 @ X6 )
% 15.48/8.48                  | ( Q2 @ X6 ) ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_774_pinf_I2_J,axiom,
% 15.48/8.48      ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 15.48/8.48        ( ? [Z4: nat] :
% 15.48/8.48          ! [X4: nat] :
% 15.48/8.48            ( ( ord_less_nat @ Z4 @ X4 )
% 15.48/8.48           => ( ( P @ X4 )
% 15.48/8.48              = ( P4 @ X4 ) ) )
% 15.48/8.48       => ( ? [Z4: nat] :
% 15.48/8.48            ! [X4: nat] :
% 15.48/8.48              ( ( ord_less_nat @ Z4 @ X4 )
% 15.48/8.48             => ( ( Q @ X4 )
% 15.48/8.48                = ( Q2 @ X4 ) ) )
% 15.48/8.48         => ? [Z3: nat] :
% 15.48/8.48            ! [X6: nat] :
% 15.48/8.48              ( ( ord_less_nat @ Z3 @ X6 )
% 15.48/8.48             => ( ( ( P @ X6 )
% 15.48/8.48                  | ( Q @ X6 ) )
% 15.48/8.48                = ( ( P4 @ X6 )
% 15.48/8.48                  | ( Q2 @ X6 ) ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_775_pinf_I2_J,axiom,
% 15.48/8.48      ! [P: int > $o,P4: int > $o,Q: int > $o,Q2: int > $o] :
% 15.48/8.48        ( ? [Z4: int] :
% 15.48/8.48          ! [X4: int] :
% 15.48/8.48            ( ( ord_less_int @ Z4 @ X4 )
% 15.48/8.48           => ( ( P @ X4 )
% 15.48/8.48              = ( P4 @ X4 ) ) )
% 15.48/8.48       => ( ? [Z4: int] :
% 15.48/8.48            ! [X4: int] :
% 15.48/8.48              ( ( ord_less_int @ Z4 @ X4 )
% 15.48/8.48             => ( ( Q @ X4 )
% 15.48/8.48                = ( Q2 @ X4 ) ) )
% 15.48/8.48         => ? [Z3: int] :
% 15.48/8.48            ! [X6: int] :
% 15.48/8.48              ( ( ord_less_int @ Z3 @ X6 )
% 15.48/8.48             => ( ( ( P @ X6 )
% 15.48/8.48                  | ( Q @ X6 ) )
% 15.48/8.48                = ( ( P4 @ X6 )
% 15.48/8.48                  | ( Q2 @ X6 ) ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_776_pinf_I3_J,axiom,
% 15.48/8.48      ! [T: real] :
% 15.48/8.48      ? [Z3: real] :
% 15.48/8.48      ! [X6: real] :
% 15.48/8.48        ( ( ord_less_real @ Z3 @ X6 )
% 15.48/8.48       => ( X6 != T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_777_pinf_I3_J,axiom,
% 15.48/8.48      ! [T: rat] :
% 15.48/8.48      ? [Z3: rat] :
% 15.48/8.48      ! [X6: rat] :
% 15.48/8.48        ( ( ord_less_rat @ Z3 @ X6 )
% 15.48/8.48       => ( X6 != T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_778_pinf_I3_J,axiom,
% 15.48/8.48      ! [T: num] :
% 15.48/8.48      ? [Z3: num] :
% 15.48/8.48      ! [X6: num] :
% 15.48/8.48        ( ( ord_less_num @ Z3 @ X6 )
% 15.48/8.48       => ( X6 != T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_779_pinf_I3_J,axiom,
% 15.48/8.48      ! [T: nat] :
% 15.48/8.48      ? [Z3: nat] :
% 15.48/8.48      ! [X6: nat] :
% 15.48/8.48        ( ( ord_less_nat @ Z3 @ X6 )
% 15.48/8.48       => ( X6 != T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_780_pinf_I3_J,axiom,
% 15.48/8.48      ! [T: int] :
% 15.48/8.48      ? [Z3: int] :
% 15.48/8.48      ! [X6: int] :
% 15.48/8.48        ( ( ord_less_int @ Z3 @ X6 )
% 15.48/8.48       => ( X6 != T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_781_pinf_I4_J,axiom,
% 15.48/8.48      ! [T: real] :
% 15.48/8.48      ? [Z3: real] :
% 15.48/8.48      ! [X6: real] :
% 15.48/8.48        ( ( ord_less_real @ Z3 @ X6 )
% 15.48/8.48       => ( X6 != T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_782_pinf_I4_J,axiom,
% 15.48/8.48      ! [T: rat] :
% 15.48/8.48      ? [Z3: rat] :
% 15.48/8.48      ! [X6: rat] :
% 15.48/8.48        ( ( ord_less_rat @ Z3 @ X6 )
% 15.48/8.48       => ( X6 != T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_783_pinf_I4_J,axiom,
% 15.48/8.48      ! [T: num] :
% 15.48/8.48      ? [Z3: num] :
% 15.48/8.48      ! [X6: num] :
% 15.48/8.48        ( ( ord_less_num @ Z3 @ X6 )
% 15.48/8.48       => ( X6 != T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_784_pinf_I4_J,axiom,
% 15.48/8.48      ! [T: nat] :
% 15.48/8.48      ? [Z3: nat] :
% 15.48/8.48      ! [X6: nat] :
% 15.48/8.48        ( ( ord_less_nat @ Z3 @ X6 )
% 15.48/8.48       => ( X6 != T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_785_pinf_I4_J,axiom,
% 15.48/8.48      ! [T: int] :
% 15.48/8.48      ? [Z3: int] :
% 15.48/8.48      ! [X6: int] :
% 15.48/8.48        ( ( ord_less_int @ Z3 @ X6 )
% 15.48/8.48       => ( X6 != T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_786_pinf_I5_J,axiom,
% 15.48/8.48      ! [T: real] :
% 15.48/8.48      ? [Z3: real] :
% 15.48/8.48      ! [X6: real] :
% 15.48/8.48        ( ( ord_less_real @ Z3 @ X6 )
% 15.48/8.48       => ~ ( ord_less_real @ X6 @ T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_787_pinf_I5_J,axiom,
% 15.48/8.48      ! [T: rat] :
% 15.48/8.48      ? [Z3: rat] :
% 15.48/8.48      ! [X6: rat] :
% 15.48/8.48        ( ( ord_less_rat @ Z3 @ X6 )
% 15.48/8.48       => ~ ( ord_less_rat @ X6 @ T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_788_pinf_I5_J,axiom,
% 15.48/8.48      ! [T: num] :
% 15.48/8.48      ? [Z3: num] :
% 15.48/8.48      ! [X6: num] :
% 15.48/8.48        ( ( ord_less_num @ Z3 @ X6 )
% 15.48/8.48       => ~ ( ord_less_num @ X6 @ T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_789_pinf_I5_J,axiom,
% 15.48/8.48      ! [T: nat] :
% 15.48/8.48      ? [Z3: nat] :
% 15.48/8.48      ! [X6: nat] :
% 15.48/8.48        ( ( ord_less_nat @ Z3 @ X6 )
% 15.48/8.48       => ~ ( ord_less_nat @ X6 @ T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_790_pinf_I5_J,axiom,
% 15.48/8.48      ! [T: int] :
% 15.48/8.48      ? [Z3: int] :
% 15.48/8.48      ! [X6: int] :
% 15.48/8.48        ( ( ord_less_int @ Z3 @ X6 )
% 15.48/8.48       => ~ ( ord_less_int @ X6 @ T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_791_pinf_I7_J,axiom,
% 15.48/8.48      ! [T: real] :
% 15.48/8.48      ? [Z3: real] :
% 15.48/8.48      ! [X6: real] :
% 15.48/8.48        ( ( ord_less_real @ Z3 @ X6 )
% 15.48/8.48       => ( ord_less_real @ T @ X6 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_792_pinf_I7_J,axiom,
% 15.48/8.48      ! [T: rat] :
% 15.48/8.48      ? [Z3: rat] :
% 15.48/8.48      ! [X6: rat] :
% 15.48/8.48        ( ( ord_less_rat @ Z3 @ X6 )
% 15.48/8.48       => ( ord_less_rat @ T @ X6 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_793_pinf_I7_J,axiom,
% 15.48/8.48      ! [T: num] :
% 15.48/8.48      ? [Z3: num] :
% 15.48/8.48      ! [X6: num] :
% 15.48/8.48        ( ( ord_less_num @ Z3 @ X6 )
% 15.48/8.48       => ( ord_less_num @ T @ X6 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_794_pinf_I7_J,axiom,
% 15.48/8.48      ! [T: nat] :
% 15.48/8.48      ? [Z3: nat] :
% 15.48/8.48      ! [X6: nat] :
% 15.48/8.48        ( ( ord_less_nat @ Z3 @ X6 )
% 15.48/8.48       => ( ord_less_nat @ T @ X6 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_795_pinf_I7_J,axiom,
% 15.48/8.48      ! [T: int] :
% 15.48/8.48      ? [Z3: int] :
% 15.48/8.48      ! [X6: int] :
% 15.48/8.48        ( ( ord_less_int @ Z3 @ X6 )
% 15.48/8.48       => ( ord_less_int @ T @ X6 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_796_minf_I1_J,axiom,
% 15.48/8.48      ! [P: real > $o,P4: real > $o,Q: real > $o,Q2: real > $o] :
% 15.48/8.48        ( ? [Z4: real] :
% 15.48/8.48          ! [X4: real] :
% 15.48/8.48            ( ( ord_less_real @ X4 @ Z4 )
% 15.48/8.48           => ( ( P @ X4 )
% 15.48/8.48              = ( P4 @ X4 ) ) )
% 15.48/8.48       => ( ? [Z4: real] :
% 15.48/8.48            ! [X4: real] :
% 15.48/8.48              ( ( ord_less_real @ X4 @ Z4 )
% 15.48/8.48             => ( ( Q @ X4 )
% 15.48/8.48                = ( Q2 @ X4 ) ) )
% 15.48/8.48         => ? [Z3: real] :
% 15.48/8.48            ! [X6: real] :
% 15.48/8.48              ( ( ord_less_real @ X6 @ Z3 )
% 15.48/8.48             => ( ( ( P @ X6 )
% 15.48/8.48                  & ( Q @ X6 ) )
% 15.48/8.48                = ( ( P4 @ X6 )
% 15.48/8.48                  & ( Q2 @ X6 ) ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_797_minf_I1_J,axiom,
% 15.48/8.48      ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 15.48/8.48        ( ? [Z4: rat] :
% 15.48/8.48          ! [X4: rat] :
% 15.48/8.48            ( ( ord_less_rat @ X4 @ Z4 )
% 15.48/8.48           => ( ( P @ X4 )
% 15.48/8.48              = ( P4 @ X4 ) ) )
% 15.48/8.48       => ( ? [Z4: rat] :
% 15.48/8.48            ! [X4: rat] :
% 15.48/8.48              ( ( ord_less_rat @ X4 @ Z4 )
% 15.48/8.48             => ( ( Q @ X4 )
% 15.48/8.48                = ( Q2 @ X4 ) ) )
% 15.48/8.48         => ? [Z3: rat] :
% 15.48/8.48            ! [X6: rat] :
% 15.48/8.48              ( ( ord_less_rat @ X6 @ Z3 )
% 15.48/8.48             => ( ( ( P @ X6 )
% 15.48/8.48                  & ( Q @ X6 ) )
% 15.48/8.48                = ( ( P4 @ X6 )
% 15.48/8.48                  & ( Q2 @ X6 ) ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_798_minf_I1_J,axiom,
% 15.48/8.48      ! [P: num > $o,P4: num > $o,Q: num > $o,Q2: num > $o] :
% 15.48/8.48        ( ? [Z4: num] :
% 15.48/8.48          ! [X4: num] :
% 15.48/8.48            ( ( ord_less_num @ X4 @ Z4 )
% 15.48/8.48           => ( ( P @ X4 )
% 15.48/8.48              = ( P4 @ X4 ) ) )
% 15.48/8.48       => ( ? [Z4: num] :
% 15.48/8.48            ! [X4: num] :
% 15.48/8.48              ( ( ord_less_num @ X4 @ Z4 )
% 15.48/8.48             => ( ( Q @ X4 )
% 15.48/8.48                = ( Q2 @ X4 ) ) )
% 15.48/8.48         => ? [Z3: num] :
% 15.48/8.48            ! [X6: num] :
% 15.48/8.48              ( ( ord_less_num @ X6 @ Z3 )
% 15.48/8.48             => ( ( ( P @ X6 )
% 15.48/8.48                  & ( Q @ X6 ) )
% 15.48/8.48                = ( ( P4 @ X6 )
% 15.48/8.48                  & ( Q2 @ X6 ) ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_799_minf_I1_J,axiom,
% 15.48/8.48      ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 15.48/8.48        ( ? [Z4: nat] :
% 15.48/8.48          ! [X4: nat] :
% 15.48/8.48            ( ( ord_less_nat @ X4 @ Z4 )
% 15.48/8.48           => ( ( P @ X4 )
% 15.48/8.48              = ( P4 @ X4 ) ) )
% 15.48/8.48       => ( ? [Z4: nat] :
% 15.48/8.48            ! [X4: nat] :
% 15.48/8.48              ( ( ord_less_nat @ X4 @ Z4 )
% 15.48/8.48             => ( ( Q @ X4 )
% 15.48/8.48                = ( Q2 @ X4 ) ) )
% 15.48/8.48         => ? [Z3: nat] :
% 15.48/8.48            ! [X6: nat] :
% 15.48/8.48              ( ( ord_less_nat @ X6 @ Z3 )
% 15.48/8.48             => ( ( ( P @ X6 )
% 15.48/8.48                  & ( Q @ X6 ) )
% 15.48/8.48                = ( ( P4 @ X6 )
% 15.48/8.48                  & ( Q2 @ X6 ) ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_800_minf_I1_J,axiom,
% 15.48/8.48      ! [P: int > $o,P4: int > $o,Q: int > $o,Q2: int > $o] :
% 15.48/8.48        ( ? [Z4: int] :
% 15.48/8.48          ! [X4: int] :
% 15.48/8.48            ( ( ord_less_int @ X4 @ Z4 )
% 15.48/8.48           => ( ( P @ X4 )
% 15.48/8.48              = ( P4 @ X4 ) ) )
% 15.48/8.48       => ( ? [Z4: int] :
% 15.48/8.48            ! [X4: int] :
% 15.48/8.48              ( ( ord_less_int @ X4 @ Z4 )
% 15.48/8.48             => ( ( Q @ X4 )
% 15.48/8.48                = ( Q2 @ X4 ) ) )
% 15.48/8.48         => ? [Z3: int] :
% 15.48/8.48            ! [X6: int] :
% 15.48/8.48              ( ( ord_less_int @ X6 @ Z3 )
% 15.48/8.48             => ( ( ( P @ X6 )
% 15.48/8.48                  & ( Q @ X6 ) )
% 15.48/8.48                = ( ( P4 @ X6 )
% 15.48/8.48                  & ( Q2 @ X6 ) ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_801_minf_I2_J,axiom,
% 15.48/8.48      ! [P: real > $o,P4: real > $o,Q: real > $o,Q2: real > $o] :
% 15.48/8.48        ( ? [Z4: real] :
% 15.48/8.48          ! [X4: real] :
% 15.48/8.48            ( ( ord_less_real @ X4 @ Z4 )
% 15.48/8.48           => ( ( P @ X4 )
% 15.48/8.48              = ( P4 @ X4 ) ) )
% 15.48/8.48       => ( ? [Z4: real] :
% 15.48/8.48            ! [X4: real] :
% 15.48/8.48              ( ( ord_less_real @ X4 @ Z4 )
% 15.48/8.48             => ( ( Q @ X4 )
% 15.48/8.48                = ( Q2 @ X4 ) ) )
% 15.48/8.48         => ? [Z3: real] :
% 15.48/8.48            ! [X6: real] :
% 15.48/8.48              ( ( ord_less_real @ X6 @ Z3 )
% 15.48/8.48             => ( ( ( P @ X6 )
% 15.48/8.48                  | ( Q @ X6 ) )
% 15.48/8.48                = ( ( P4 @ X6 )
% 15.48/8.48                  | ( Q2 @ X6 ) ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_802_minf_I2_J,axiom,
% 15.48/8.48      ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 15.48/8.48        ( ? [Z4: rat] :
% 15.48/8.48          ! [X4: rat] :
% 15.48/8.48            ( ( ord_less_rat @ X4 @ Z4 )
% 15.48/8.48           => ( ( P @ X4 )
% 15.48/8.48              = ( P4 @ X4 ) ) )
% 15.48/8.48       => ( ? [Z4: rat] :
% 15.48/8.48            ! [X4: rat] :
% 15.48/8.48              ( ( ord_less_rat @ X4 @ Z4 )
% 15.48/8.48             => ( ( Q @ X4 )
% 15.48/8.48                = ( Q2 @ X4 ) ) )
% 15.48/8.48         => ? [Z3: rat] :
% 15.48/8.48            ! [X6: rat] :
% 15.48/8.48              ( ( ord_less_rat @ X6 @ Z3 )
% 15.48/8.48             => ( ( ( P @ X6 )
% 15.48/8.48                  | ( Q @ X6 ) )
% 15.48/8.48                = ( ( P4 @ X6 )
% 15.48/8.48                  | ( Q2 @ X6 ) ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_803_minf_I2_J,axiom,
% 15.48/8.48      ! [P: num > $o,P4: num > $o,Q: num > $o,Q2: num > $o] :
% 15.48/8.48        ( ? [Z4: num] :
% 15.48/8.48          ! [X4: num] :
% 15.48/8.48            ( ( ord_less_num @ X4 @ Z4 )
% 15.48/8.48           => ( ( P @ X4 )
% 15.48/8.48              = ( P4 @ X4 ) ) )
% 15.48/8.48       => ( ? [Z4: num] :
% 15.48/8.48            ! [X4: num] :
% 15.48/8.48              ( ( ord_less_num @ X4 @ Z4 )
% 15.48/8.48             => ( ( Q @ X4 )
% 15.48/8.48                = ( Q2 @ X4 ) ) )
% 15.48/8.48         => ? [Z3: num] :
% 15.48/8.48            ! [X6: num] :
% 15.48/8.48              ( ( ord_less_num @ X6 @ Z3 )
% 15.48/8.48             => ( ( ( P @ X6 )
% 15.48/8.48                  | ( Q @ X6 ) )
% 15.48/8.48                = ( ( P4 @ X6 )
% 15.48/8.48                  | ( Q2 @ X6 ) ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_804_minf_I2_J,axiom,
% 15.48/8.48      ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 15.48/8.48        ( ? [Z4: nat] :
% 15.48/8.48          ! [X4: nat] :
% 15.48/8.48            ( ( ord_less_nat @ X4 @ Z4 )
% 15.48/8.48           => ( ( P @ X4 )
% 15.48/8.48              = ( P4 @ X4 ) ) )
% 15.48/8.48       => ( ? [Z4: nat] :
% 15.48/8.48            ! [X4: nat] :
% 15.48/8.48              ( ( ord_less_nat @ X4 @ Z4 )
% 15.48/8.48             => ( ( Q @ X4 )
% 15.48/8.48                = ( Q2 @ X4 ) ) )
% 15.48/8.48         => ? [Z3: nat] :
% 15.48/8.48            ! [X6: nat] :
% 15.48/8.48              ( ( ord_less_nat @ X6 @ Z3 )
% 15.48/8.48             => ( ( ( P @ X6 )
% 15.48/8.48                  | ( Q @ X6 ) )
% 15.48/8.48                = ( ( P4 @ X6 )
% 15.48/8.48                  | ( Q2 @ X6 ) ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_805_minf_I2_J,axiom,
% 15.48/8.48      ! [P: int > $o,P4: int > $o,Q: int > $o,Q2: int > $o] :
% 15.48/8.48        ( ? [Z4: int] :
% 15.48/8.48          ! [X4: int] :
% 15.48/8.48            ( ( ord_less_int @ X4 @ Z4 )
% 15.48/8.48           => ( ( P @ X4 )
% 15.48/8.48              = ( P4 @ X4 ) ) )
% 15.48/8.48       => ( ? [Z4: int] :
% 15.48/8.48            ! [X4: int] :
% 15.48/8.48              ( ( ord_less_int @ X4 @ Z4 )
% 15.48/8.48             => ( ( Q @ X4 )
% 15.48/8.48                = ( Q2 @ X4 ) ) )
% 15.48/8.48         => ? [Z3: int] :
% 15.48/8.48            ! [X6: int] :
% 15.48/8.48              ( ( ord_less_int @ X6 @ Z3 )
% 15.48/8.48             => ( ( ( P @ X6 )
% 15.48/8.48                  | ( Q @ X6 ) )
% 15.48/8.48                = ( ( P4 @ X6 )
% 15.48/8.48                  | ( Q2 @ X6 ) ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_806_minf_I3_J,axiom,
% 15.48/8.48      ! [T: real] :
% 15.48/8.48      ? [Z3: real] :
% 15.48/8.48      ! [X6: real] :
% 15.48/8.48        ( ( ord_less_real @ X6 @ Z3 )
% 15.48/8.48       => ( X6 != T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_807_minf_I3_J,axiom,
% 15.48/8.48      ! [T: rat] :
% 15.48/8.48      ? [Z3: rat] :
% 15.48/8.48      ! [X6: rat] :
% 15.48/8.48        ( ( ord_less_rat @ X6 @ Z3 )
% 15.48/8.48       => ( X6 != T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_808_minf_I3_J,axiom,
% 15.48/8.48      ! [T: num] :
% 15.48/8.48      ? [Z3: num] :
% 15.48/8.48      ! [X6: num] :
% 15.48/8.48        ( ( ord_less_num @ X6 @ Z3 )
% 15.48/8.48       => ( X6 != T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_809_minf_I3_J,axiom,
% 15.48/8.48      ! [T: nat] :
% 15.48/8.48      ? [Z3: nat] :
% 15.48/8.48      ! [X6: nat] :
% 15.48/8.48        ( ( ord_less_nat @ X6 @ Z3 )
% 15.48/8.48       => ( X6 != T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_810_minf_I3_J,axiom,
% 15.48/8.48      ! [T: int] :
% 15.48/8.48      ? [Z3: int] :
% 15.48/8.48      ! [X6: int] :
% 15.48/8.48        ( ( ord_less_int @ X6 @ Z3 )
% 15.48/8.48       => ( X6 != T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_811_minf_I4_J,axiom,
% 15.48/8.48      ! [T: real] :
% 15.48/8.48      ? [Z3: real] :
% 15.48/8.48      ! [X6: real] :
% 15.48/8.48        ( ( ord_less_real @ X6 @ Z3 )
% 15.48/8.48       => ( X6 != T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_812_minf_I4_J,axiom,
% 15.48/8.48      ! [T: rat] :
% 15.48/8.48      ? [Z3: rat] :
% 15.48/8.48      ! [X6: rat] :
% 15.48/8.48        ( ( ord_less_rat @ X6 @ Z3 )
% 15.48/8.48       => ( X6 != T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_813_minf_I4_J,axiom,
% 15.48/8.48      ! [T: num] :
% 15.48/8.48      ? [Z3: num] :
% 15.48/8.48      ! [X6: num] :
% 15.48/8.48        ( ( ord_less_num @ X6 @ Z3 )
% 15.48/8.48       => ( X6 != T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_814_minf_I4_J,axiom,
% 15.48/8.48      ! [T: nat] :
% 15.48/8.48      ? [Z3: nat] :
% 15.48/8.48      ! [X6: nat] :
% 15.48/8.48        ( ( ord_less_nat @ X6 @ Z3 )
% 15.48/8.48       => ( X6 != T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_815_minf_I4_J,axiom,
% 15.48/8.48      ! [T: int] :
% 15.48/8.48      ? [Z3: int] :
% 15.48/8.48      ! [X6: int] :
% 15.48/8.48        ( ( ord_less_int @ X6 @ Z3 )
% 15.48/8.48       => ( X6 != T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_816_minf_I5_J,axiom,
% 15.48/8.48      ! [T: real] :
% 15.48/8.48      ? [Z3: real] :
% 15.48/8.48      ! [X6: real] :
% 15.48/8.48        ( ( ord_less_real @ X6 @ Z3 )
% 15.48/8.48       => ( ord_less_real @ X6 @ T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_817_minf_I5_J,axiom,
% 15.48/8.48      ! [T: rat] :
% 15.48/8.48      ? [Z3: rat] :
% 15.48/8.48      ! [X6: rat] :
% 15.48/8.48        ( ( ord_less_rat @ X6 @ Z3 )
% 15.48/8.48       => ( ord_less_rat @ X6 @ T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_818_minf_I5_J,axiom,
% 15.48/8.48      ! [T: num] :
% 15.48/8.48      ? [Z3: num] :
% 15.48/8.48      ! [X6: num] :
% 15.48/8.48        ( ( ord_less_num @ X6 @ Z3 )
% 15.48/8.48       => ( ord_less_num @ X6 @ T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_819_minf_I5_J,axiom,
% 15.48/8.48      ! [T: nat] :
% 15.48/8.48      ? [Z3: nat] :
% 15.48/8.48      ! [X6: nat] :
% 15.48/8.48        ( ( ord_less_nat @ X6 @ Z3 )
% 15.48/8.48       => ( ord_less_nat @ X6 @ T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_820_minf_I5_J,axiom,
% 15.48/8.48      ! [T: int] :
% 15.48/8.48      ? [Z3: int] :
% 15.48/8.48      ! [X6: int] :
% 15.48/8.48        ( ( ord_less_int @ X6 @ Z3 )
% 15.48/8.48       => ( ord_less_int @ X6 @ T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_821_minf_I7_J,axiom,
% 15.48/8.48      ! [T: real] :
% 15.48/8.48      ? [Z3: real] :
% 15.48/8.48      ! [X6: real] :
% 15.48/8.48        ( ( ord_less_real @ X6 @ Z3 )
% 15.48/8.48       => ~ ( ord_less_real @ T @ X6 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_822_minf_I7_J,axiom,
% 15.48/8.48      ! [T: rat] :
% 15.48/8.48      ? [Z3: rat] :
% 15.48/8.48      ! [X6: rat] :
% 15.48/8.48        ( ( ord_less_rat @ X6 @ Z3 )
% 15.48/8.48       => ~ ( ord_less_rat @ T @ X6 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_823_minf_I7_J,axiom,
% 15.48/8.48      ! [T: num] :
% 15.48/8.48      ? [Z3: num] :
% 15.48/8.48      ! [X6: num] :
% 15.48/8.48        ( ( ord_less_num @ X6 @ Z3 )
% 15.48/8.48       => ~ ( ord_less_num @ T @ X6 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_824_minf_I7_J,axiom,
% 15.48/8.48      ! [T: nat] :
% 15.48/8.48      ? [Z3: nat] :
% 15.48/8.48      ! [X6: nat] :
% 15.48/8.48        ( ( ord_less_nat @ X6 @ Z3 )
% 15.48/8.48       => ~ ( ord_less_nat @ T @ X6 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_825_minf_I7_J,axiom,
% 15.48/8.48      ! [T: int] :
% 15.48/8.48      ? [Z3: int] :
% 15.48/8.48      ! [X6: int] :
% 15.48/8.48        ( ( ord_less_int @ X6 @ Z3 )
% 15.48/8.48       => ~ ( ord_less_int @ T @ X6 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_826_zle__int,axiom,
% 15.48/8.48      ! [M: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 15.48/8.48        = ( ord_less_eq_nat @ M @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_827_pinf_I6_J,axiom,
% 15.48/8.48      ! [T: real] :
% 15.48/8.48      ? [Z3: real] :
% 15.48/8.48      ! [X6: real] :
% 15.48/8.48        ( ( ord_less_real @ Z3 @ X6 )
% 15.48/8.48       => ~ ( ord_less_eq_real @ X6 @ T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_828_pinf_I6_J,axiom,
% 15.48/8.48      ! [T: rat] :
% 15.48/8.48      ? [Z3: rat] :
% 15.48/8.48      ! [X6: rat] :
% 15.48/8.48        ( ( ord_less_rat @ Z3 @ X6 )
% 15.48/8.48       => ~ ( ord_less_eq_rat @ X6 @ T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_829_pinf_I6_J,axiom,
% 15.48/8.48      ! [T: num] :
% 15.48/8.48      ? [Z3: num] :
% 15.48/8.48      ! [X6: num] :
% 15.48/8.48        ( ( ord_less_num @ Z3 @ X6 )
% 15.48/8.48       => ~ ( ord_less_eq_num @ X6 @ T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_830_pinf_I6_J,axiom,
% 15.48/8.48      ! [T: nat] :
% 15.48/8.48      ? [Z3: nat] :
% 15.48/8.48      ! [X6: nat] :
% 15.48/8.48        ( ( ord_less_nat @ Z3 @ X6 )
% 15.48/8.48       => ~ ( ord_less_eq_nat @ X6 @ T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_831_pinf_I6_J,axiom,
% 15.48/8.48      ! [T: int] :
% 15.48/8.48      ? [Z3: int] :
% 15.48/8.48      ! [X6: int] :
% 15.48/8.48        ( ( ord_less_int @ Z3 @ X6 )
% 15.48/8.48       => ~ ( ord_less_eq_int @ X6 @ T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_832_pinf_I8_J,axiom,
% 15.48/8.48      ! [T: real] :
% 15.48/8.48      ? [Z3: real] :
% 15.48/8.48      ! [X6: real] :
% 15.48/8.48        ( ( ord_less_real @ Z3 @ X6 )
% 15.48/8.48       => ( ord_less_eq_real @ T @ X6 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_833_pinf_I8_J,axiom,
% 15.48/8.48      ! [T: rat] :
% 15.48/8.48      ? [Z3: rat] :
% 15.48/8.48      ! [X6: rat] :
% 15.48/8.48        ( ( ord_less_rat @ Z3 @ X6 )
% 15.48/8.48       => ( ord_less_eq_rat @ T @ X6 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_834_pinf_I8_J,axiom,
% 15.48/8.48      ! [T: num] :
% 15.48/8.48      ? [Z3: num] :
% 15.48/8.48      ! [X6: num] :
% 15.48/8.48        ( ( ord_less_num @ Z3 @ X6 )
% 15.48/8.48       => ( ord_less_eq_num @ T @ X6 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_835_pinf_I8_J,axiom,
% 15.48/8.48      ! [T: nat] :
% 15.48/8.48      ? [Z3: nat] :
% 15.48/8.48      ! [X6: nat] :
% 15.48/8.48        ( ( ord_less_nat @ Z3 @ X6 )
% 15.48/8.48       => ( ord_less_eq_nat @ T @ X6 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_836_pinf_I8_J,axiom,
% 15.48/8.48      ! [T: int] :
% 15.48/8.48      ? [Z3: int] :
% 15.48/8.48      ! [X6: int] :
% 15.48/8.48        ( ( ord_less_int @ Z3 @ X6 )
% 15.48/8.48       => ( ord_less_eq_int @ T @ X6 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_837_minf_I6_J,axiom,
% 15.48/8.48      ! [T: real] :
% 15.48/8.48      ? [Z3: real] :
% 15.48/8.48      ! [X6: real] :
% 15.48/8.48        ( ( ord_less_real @ X6 @ Z3 )
% 15.48/8.48       => ( ord_less_eq_real @ X6 @ T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_838_minf_I6_J,axiom,
% 15.48/8.48      ! [T: rat] :
% 15.48/8.48      ? [Z3: rat] :
% 15.48/8.48      ! [X6: rat] :
% 15.48/8.48        ( ( ord_less_rat @ X6 @ Z3 )
% 15.48/8.48       => ( ord_less_eq_rat @ X6 @ T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_839_minf_I6_J,axiom,
% 15.48/8.48      ! [T: num] :
% 15.48/8.48      ? [Z3: num] :
% 15.48/8.48      ! [X6: num] :
% 15.48/8.48        ( ( ord_less_num @ X6 @ Z3 )
% 15.48/8.48       => ( ord_less_eq_num @ X6 @ T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_840_minf_I6_J,axiom,
% 15.48/8.48      ! [T: nat] :
% 15.48/8.48      ? [Z3: nat] :
% 15.48/8.48      ! [X6: nat] :
% 15.48/8.48        ( ( ord_less_nat @ X6 @ Z3 )
% 15.48/8.48       => ( ord_less_eq_nat @ X6 @ T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_841_minf_I6_J,axiom,
% 15.48/8.48      ! [T: int] :
% 15.48/8.48      ? [Z3: int] :
% 15.48/8.48      ! [X6: int] :
% 15.48/8.48        ( ( ord_less_int @ X6 @ Z3 )
% 15.48/8.48       => ( ord_less_eq_int @ X6 @ T ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_842_complete__interval,axiom,
% 15.48/8.48      ! [A: real,B: real,P: real > $o] :
% 15.48/8.48        ( ( ord_less_real @ A @ B )
% 15.48/8.48       => ( ( P @ A )
% 15.48/8.48         => ( ~ ( P @ B )
% 15.48/8.48           => ? [C2: real] :
% 15.48/8.48                ( ( ord_less_eq_real @ A @ C2 )
% 15.48/8.48                & ( ord_less_eq_real @ C2 @ B )
% 15.48/8.48                & ! [X6: real] :
% 15.48/8.48                    ( ( ( ord_less_eq_real @ A @ X6 )
% 15.48/8.48                      & ( ord_less_real @ X6 @ C2 ) )
% 15.48/8.48                   => ( P @ X6 ) )
% 15.48/8.48                & ! [D: real] :
% 15.48/8.48                    ( ! [X4: real] :
% 15.48/8.48                        ( ( ( ord_less_eq_real @ A @ X4 )
% 15.48/8.48                          & ( ord_less_real @ X4 @ D ) )
% 15.48/8.48                       => ( P @ X4 ) )
% 15.48/8.48                   => ( ord_less_eq_real @ D @ C2 ) ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_843_complete__interval,axiom,
% 15.48/8.48      ! [A: nat,B: nat,P: nat > $o] :
% 15.48/8.48        ( ( ord_less_nat @ A @ B )
% 15.48/8.48       => ( ( P @ A )
% 15.48/8.48         => ( ~ ( P @ B )
% 15.48/8.48           => ? [C2: nat] :
% 15.48/8.48                ( ( ord_less_eq_nat @ A @ C2 )
% 15.48/8.48                & ( ord_less_eq_nat @ C2 @ B )
% 15.48/8.48                & ! [X6: nat] :
% 15.48/8.48                    ( ( ( ord_less_eq_nat @ A @ X6 )
% 15.48/8.48                      & ( ord_less_nat @ X6 @ C2 ) )
% 15.48/8.48                   => ( P @ X6 ) )
% 15.48/8.48                & ! [D: nat] :
% 15.48/8.48                    ( ! [X4: nat] :
% 15.48/8.48                        ( ( ( ord_less_eq_nat @ A @ X4 )
% 15.48/8.48                          & ( ord_less_nat @ X4 @ D ) )
% 15.48/8.48                       => ( P @ X4 ) )
% 15.48/8.48                   => ( ord_less_eq_nat @ D @ C2 ) ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_844_complete__interval,axiom,
% 15.48/8.48      ! [A: int,B: int,P: int > $o] :
% 15.48/8.48        ( ( ord_less_int @ A @ B )
% 15.48/8.48       => ( ( P @ A )
% 15.48/8.48         => ( ~ ( P @ B )
% 15.48/8.48           => ? [C2: int] :
% 15.48/8.48                ( ( ord_less_eq_int @ A @ C2 )
% 15.48/8.48                & ( ord_less_eq_int @ C2 @ B )
% 15.48/8.48                & ! [X6: int] :
% 15.48/8.48                    ( ( ( ord_less_eq_int @ A @ X6 )
% 15.48/8.48                      & ( ord_less_int @ X6 @ C2 ) )
% 15.48/8.48                   => ( P @ X6 ) )
% 15.48/8.48                & ! [D: int] :
% 15.48/8.48                    ( ! [X4: int] :
% 15.48/8.48                        ( ( ( ord_less_eq_int @ A @ X4 )
% 15.48/8.48                          & ( ord_less_int @ X4 @ D ) )
% 15.48/8.48                       => ( P @ X4 ) )
% 15.48/8.48                   => ( ord_less_eq_int @ D @ C2 ) ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_845_zero__less__power2,axiom,
% 15.48/8.48      ! [A: real] :
% 15.48/8.48        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.48/8.48        = ( A != zero_zero_real ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_846_zero__less__power2,axiom,
% 15.48/8.48      ! [A: rat] :
% 15.48/8.48        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.48/8.48        = ( A != zero_zero_rat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_847_zero__less__power2,axiom,
% 15.48/8.48      ! [A: int] :
% 15.48/8.48        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.48/8.48        = ( A != zero_zero_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_848_power2__eq__iff__nonneg,axiom,
% 15.48/8.48      ! [X3: real,Y3: real] :
% 15.48/8.48        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.48/8.48       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.48/8.48         => ( ( ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.48              = ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.48/8.48            = ( X3 = Y3 ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_849_power2__eq__iff__nonneg,axiom,
% 15.48/8.48      ! [X3: rat,Y3: rat] :
% 15.48/8.48        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 15.48/8.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 15.48/8.48         => ( ( ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.48              = ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.48/8.48            = ( X3 = Y3 ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_850_power2__eq__iff__nonneg,axiom,
% 15.48/8.48      ! [X3: nat,Y3: nat] :
% 15.48/8.48        ( ( ord_less_eq_nat @ zero_zero_nat @ X3 )
% 15.48/8.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 15.48/8.48         => ( ( ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.48              = ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.48/8.48            = ( X3 = Y3 ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_851_power2__eq__iff__nonneg,axiom,
% 15.48/8.48      ! [X3: int,Y3: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 15.48/8.48       => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 15.48/8.48         => ( ( ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.48              = ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.48/8.48            = ( X3 = Y3 ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_852_power2__less__eq__zero__iff,axiom,
% 15.48/8.48      ! [A: real] :
% 15.48/8.48        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 15.48/8.48        = ( A = zero_zero_real ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_853_power2__less__eq__zero__iff,axiom,
% 15.48/8.48      ! [A: rat] :
% 15.48/8.48        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 15.48/8.48        = ( A = zero_zero_rat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_854_power2__less__eq__zero__iff,axiom,
% 15.48/8.48      ! [A: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 15.48/8.48        = ( A = zero_zero_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_855_power2__less__imp__less,axiom,
% 15.48/8.48      ! [X3: real,Y3: real] :
% 15.48/8.48        ( ( ord_less_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.48/8.48       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.48/8.48         => ( ord_less_real @ X3 @ Y3 ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_856_power2__less__imp__less,axiom,
% 15.48/8.48      ! [X3: rat,Y3: rat] :
% 15.48/8.48        ( ( ord_less_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.48/8.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 15.48/8.48         => ( ord_less_rat @ X3 @ Y3 ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_857_power2__less__imp__less,axiom,
% 15.48/8.48      ! [X3: nat,Y3: nat] :
% 15.48/8.48        ( ( ord_less_nat @ ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.48/8.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 15.48/8.48         => ( ord_less_nat @ X3 @ Y3 ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_858_power2__less__imp__less,axiom,
% 15.48/8.48      ! [X3: int,Y3: int] :
% 15.48/8.48        ( ( ord_less_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.48/8.48       => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 15.48/8.48         => ( ord_less_int @ X3 @ Y3 ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_859_nat__le__numeral__power__cancel__iff,axiom,
% 15.48/8.48      ! [A: int,X3: num,N: nat] :
% 15.48/8.48        ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) )
% 15.48/8.48        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_860_numeral__power__le__nat__cancel__iff,axiom,
% 15.48/8.48      ! [X3: num,N: nat,A: int] :
% 15.48/8.48        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) @ ( nat2 @ A ) )
% 15.48/8.48        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_861_numeral__power__less__nat__cancel__iff,axiom,
% 15.48/8.48      ! [X3: num,N: nat,A: int] :
% 15.48/8.48        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) @ ( nat2 @ A ) )
% 15.48/8.48        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_862_nat__less__numeral__power__cancel__iff,axiom,
% 15.48/8.48      ! [A: int,X3: num,N: nat] :
% 15.48/8.48        ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) )
% 15.48/8.48        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_863_of__int__less__numeral__power__cancel__iff,axiom,
% 15.48/8.48      ! [A: int,X3: num,N: nat] :
% 15.48/8.48        ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N ) )
% 15.48/8.48        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_864_of__int__less__numeral__power__cancel__iff,axiom,
% 15.48/8.48      ! [A: int,X3: num,N: nat] :
% 15.48/8.48        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N ) )
% 15.48/8.48        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_865_of__int__less__numeral__power__cancel__iff,axiom,
% 15.48/8.48      ! [A: int,X3: num,N: nat] :
% 15.48/8.48        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) )
% 15.48/8.48        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_866_numeral__power__less__of__int__cancel__iff,axiom,
% 15.48/8.48      ! [X3: num,N: nat,A: int] :
% 15.48/8.48        ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 15.48/8.48        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_867_numeral__power__less__of__int__cancel__iff,axiom,
% 15.48/8.48      ! [X3: num,N: nat,A: int] :
% 15.48/8.48        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 15.48/8.48        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_868_numeral__power__less__of__int__cancel__iff,axiom,
% 15.48/8.48      ! [X3: num,N: nat,A: int] :
% 15.48/8.48        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 15.48/8.48        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_869_bot__nat__0_Onot__eq__extremum,axiom,
% 15.48/8.48      ! [A: nat] :
% 15.48/8.48        ( ( A != zero_zero_nat )
% 15.48/8.48        = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_870_neq0__conv,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( N != zero_zero_nat )
% 15.48/8.48        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_871_less__nat__zero__code,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_872_le0,axiom,
% 15.48/8.48      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_873_bot__nat__0_Oextremum,axiom,
% 15.48/8.48      ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_874_of__int__eq__iff,axiom,
% 15.48/8.48      ! [W: int,Z: int] :
% 15.48/8.48        ( ( ( ring_1_of_int_real @ W )
% 15.48/8.48          = ( ring_1_of_int_real @ Z ) )
% 15.48/8.48        = ( W = Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_875_of__int__eq__iff,axiom,
% 15.48/8.48      ! [W: int,Z: int] :
% 15.48/8.48        ( ( ( ring_17405671764205052669omplex @ W )
% 15.48/8.48          = ( ring_17405671764205052669omplex @ Z ) )
% 15.48/8.48        = ( W = Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_876_of__int__eq__iff,axiom,
% 15.48/8.48      ! [W: int,Z: int] :
% 15.48/8.48        ( ( ( ring_1_of_int_rat @ W )
% 15.48/8.48          = ( ring_1_of_int_rat @ Z ) )
% 15.48/8.48        = ( W = Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_877_i0__less,axiom,
% 15.48/8.48      ! [N: extended_enat] :
% 15.48/8.48        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 15.48/8.48        = ( N != zero_z5237406670263579293d_enat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_878_of__nat__eq__0__iff,axiom,
% 15.48/8.48      ! [M: nat] :
% 15.48/8.48        ( ( ( semiri8010041392384452111omplex @ M )
% 15.48/8.48          = zero_zero_complex )
% 15.48/8.48        = ( M = zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_879_of__nat__eq__0__iff,axiom,
% 15.48/8.48      ! [M: nat] :
% 15.48/8.48        ( ( ( semiri5074537144036343181t_real @ M )
% 15.48/8.48          = zero_zero_real )
% 15.48/8.48        = ( M = zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_880_of__nat__eq__0__iff,axiom,
% 15.48/8.48      ! [M: nat] :
% 15.48/8.48        ( ( ( semiri681578069525770553at_rat @ M )
% 15.48/8.48          = zero_zero_rat )
% 15.48/8.48        = ( M = zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_881_of__nat__eq__0__iff,axiom,
% 15.48/8.48      ! [M: nat] :
% 15.48/8.48        ( ( ( semiri1316708129612266289at_nat @ M )
% 15.48/8.48          = zero_zero_nat )
% 15.48/8.48        = ( M = zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_882_of__nat__eq__0__iff,axiom,
% 15.48/8.48      ! [M: nat] :
% 15.48/8.48        ( ( ( semiri1314217659103216013at_int @ M )
% 15.48/8.48          = zero_zero_int )
% 15.48/8.48        = ( M = zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_883_of__nat__0__eq__iff,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( zero_zero_complex
% 15.48/8.48          = ( semiri8010041392384452111omplex @ N ) )
% 15.48/8.48        = ( zero_zero_nat = N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_884_of__nat__0__eq__iff,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( zero_zero_real
% 15.48/8.48          = ( semiri5074537144036343181t_real @ N ) )
% 15.48/8.48        = ( zero_zero_nat = N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_885_of__nat__0__eq__iff,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( zero_zero_rat
% 15.48/8.48          = ( semiri681578069525770553at_rat @ N ) )
% 15.48/8.48        = ( zero_zero_nat = N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_886_of__nat__0__eq__iff,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( zero_zero_nat
% 15.48/8.48          = ( semiri1316708129612266289at_nat @ N ) )
% 15.48/8.48        = ( zero_zero_nat = N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_887_of__nat__0__eq__iff,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( zero_zero_int
% 15.48/8.48          = ( semiri1314217659103216013at_int @ N ) )
% 15.48/8.48        = ( zero_zero_nat = N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_888_of__nat__0,axiom,
% 15.48/8.48      ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 15.48/8.48      = zero_zero_complex ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_889_of__nat__0,axiom,
% 15.48/8.48      ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 15.48/8.48      = zero_zero_real ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_890_of__nat__0,axiom,
% 15.48/8.48      ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 15.48/8.48      = zero_zero_rat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_891_of__nat__0,axiom,
% 15.48/8.48      ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 15.48/8.48      = zero_zero_nat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_892_of__nat__0,axiom,
% 15.48/8.48      ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 15.48/8.48      = zero_zero_int ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_893_of__int__0,axiom,
% 15.48/8.48      ( ( ring_1_of_int_int @ zero_zero_int )
% 15.48/8.48      = zero_zero_int ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_894_of__int__0,axiom,
% 15.48/8.48      ( ( ring_1_of_int_real @ zero_zero_int )
% 15.48/8.48      = zero_zero_real ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_895_of__int__0,axiom,
% 15.48/8.48      ( ( ring_17405671764205052669omplex @ zero_zero_int )
% 15.48/8.48      = zero_zero_complex ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_896_of__int__0,axiom,
% 15.48/8.48      ( ( ring_1_of_int_rat @ zero_zero_int )
% 15.48/8.48      = zero_zero_rat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_897_of__int__0__eq__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( zero_zero_int
% 15.48/8.48          = ( ring_1_of_int_int @ Z ) )
% 15.48/8.48        = ( Z = zero_zero_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_898_of__int__0__eq__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( zero_zero_real
% 15.48/8.48          = ( ring_1_of_int_real @ Z ) )
% 15.48/8.48        = ( Z = zero_zero_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_899_of__int__0__eq__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( zero_zero_complex
% 15.48/8.48          = ( ring_17405671764205052669omplex @ Z ) )
% 15.48/8.48        = ( Z = zero_zero_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_900_of__int__0__eq__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( zero_zero_rat
% 15.48/8.48          = ( ring_1_of_int_rat @ Z ) )
% 15.48/8.48        = ( Z = zero_zero_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_901_of__int__eq__0__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ( ring_1_of_int_int @ Z )
% 15.48/8.48          = zero_zero_int )
% 15.48/8.48        = ( Z = zero_zero_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_902_of__int__eq__0__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ( ring_1_of_int_real @ Z )
% 15.48/8.48          = zero_zero_real )
% 15.48/8.48        = ( Z = zero_zero_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_903_of__int__eq__0__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ( ring_17405671764205052669omplex @ Z )
% 15.48/8.48          = zero_zero_complex )
% 15.48/8.48        = ( Z = zero_zero_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_904_of__int__eq__0__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ( ring_1_of_int_rat @ Z )
% 15.48/8.48          = zero_zero_rat )
% 15.48/8.48        = ( Z = zero_zero_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_905_nat__zero__less__power__iff,axiom,
% 15.48/8.48      ! [X3: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X3 @ N ) )
% 15.48/8.48        = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 15.48/8.48          | ( N = zero_zero_nat ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_906_nat__le__0,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 15.48/8.48       => ( ( nat2 @ Z )
% 15.48/8.48          = zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_907_nat__0__iff,axiom,
% 15.48/8.48      ! [I: int] :
% 15.48/8.48        ( ( ( nat2 @ I )
% 15.48/8.48          = zero_zero_nat )
% 15.48/8.48        = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_908_nat__int,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( nat2 @ ( semiri1314217659103216013at_int @ N ) )
% 15.48/8.48        = N ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_909_of__nat__le__0__iff,axiom,
% 15.48/8.48      ! [M: nat] :
% 15.48/8.48        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 15.48/8.48        = ( M = zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_910_of__nat__le__0__iff,axiom,
% 15.48/8.48      ! [M: nat] :
% 15.48/8.48        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 15.48/8.48        = ( M = zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_911_of__nat__le__0__iff,axiom,
% 15.48/8.48      ! [M: nat] :
% 15.48/8.48        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 15.48/8.48        = ( M = zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_912_of__nat__le__0__iff,axiom,
% 15.48/8.48      ! [M: nat] :
% 15.48/8.48        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 15.48/8.48        = ( M = zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_913_power__zero__numeral,axiom,
% 15.48/8.48      ! [K: num] :
% 15.48/8.48        ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 15.48/8.48        = zero_zero_rat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_914_power__zero__numeral,axiom,
% 15.48/8.48      ! [K: num] :
% 15.48/8.48        ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 15.48/8.48        = zero_zero_nat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_915_power__zero__numeral,axiom,
% 15.48/8.48      ! [K: num] :
% 15.48/8.48        ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 15.48/8.48        = zero_zero_int ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_916_power__zero__numeral,axiom,
% 15.48/8.48      ! [K: num] :
% 15.48/8.48        ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 15.48/8.48        = zero_zero_real ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_917_power__zero__numeral,axiom,
% 15.48/8.48      ! [K: num] :
% 15.48/8.48        ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 15.48/8.48        = zero_zero_complex ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_918_power__eq__0__iff,axiom,
% 15.48/8.48      ! [A: rat,N: nat] :
% 15.48/8.48        ( ( ( power_power_rat @ A @ N )
% 15.48/8.48          = zero_zero_rat )
% 15.48/8.48        = ( ( A = zero_zero_rat )
% 15.48/8.48          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_919_power__eq__0__iff,axiom,
% 15.48/8.48      ! [A: nat,N: nat] :
% 15.48/8.48        ( ( ( power_power_nat @ A @ N )
% 15.48/8.48          = zero_zero_nat )
% 15.48/8.48        = ( ( A = zero_zero_nat )
% 15.48/8.48          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_920_power__eq__0__iff,axiom,
% 15.48/8.48      ! [A: int,N: nat] :
% 15.48/8.48        ( ( ( power_power_int @ A @ N )
% 15.48/8.48          = zero_zero_int )
% 15.48/8.48        = ( ( A = zero_zero_int )
% 15.48/8.48          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_921_power__eq__0__iff,axiom,
% 15.48/8.48      ! [A: real,N: nat] :
% 15.48/8.48        ( ( ( power_power_real @ A @ N )
% 15.48/8.48          = zero_zero_real )
% 15.48/8.48        = ( ( A = zero_zero_real )
% 15.48/8.48          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_922_power__eq__0__iff,axiom,
% 15.48/8.48      ! [A: complex,N: nat] :
% 15.48/8.48        ( ( ( power_power_complex @ A @ N )
% 15.48/8.48          = zero_zero_complex )
% 15.48/8.48        = ( ( A = zero_zero_complex )
% 15.48/8.48          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_923_of__int__numeral,axiom,
% 15.48/8.48      ! [K: num] :
% 15.48/8.48        ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 15.48/8.48        = ( numera6690914467698888265omplex @ K ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_924_of__int__numeral,axiom,
% 15.48/8.48      ! [K: num] :
% 15.48/8.48        ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 15.48/8.48        = ( numeral_numeral_real @ K ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_925_of__int__numeral,axiom,
% 15.48/8.48      ! [K: num] :
% 15.48/8.48        ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 15.48/8.48        = ( numeral_numeral_rat @ K ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_926_of__int__numeral,axiom,
% 15.48/8.48      ! [K: num] :
% 15.48/8.48        ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 15.48/8.48        = ( numeral_numeral_int @ K ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_927_of__int__eq__numeral__iff,axiom,
% 15.48/8.48      ! [Z: int,N: num] :
% 15.48/8.48        ( ( ( ring_17405671764205052669omplex @ Z )
% 15.48/8.48          = ( numera6690914467698888265omplex @ N ) )
% 15.48/8.48        = ( Z
% 15.48/8.48          = ( numeral_numeral_int @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_928_of__int__eq__numeral__iff,axiom,
% 15.48/8.48      ! [Z: int,N: num] :
% 15.48/8.48        ( ( ( ring_1_of_int_real @ Z )
% 15.48/8.48          = ( numeral_numeral_real @ N ) )
% 15.48/8.48        = ( Z
% 15.48/8.48          = ( numeral_numeral_int @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_929_of__int__eq__numeral__iff,axiom,
% 15.48/8.48      ! [Z: int,N: num] :
% 15.48/8.48        ( ( ( ring_1_of_int_rat @ Z )
% 15.48/8.48          = ( numeral_numeral_rat @ N ) )
% 15.48/8.48        = ( Z
% 15.48/8.48          = ( numeral_numeral_int @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_930_of__int__eq__numeral__iff,axiom,
% 15.48/8.48      ! [Z: int,N: num] :
% 15.48/8.48        ( ( ( ring_1_of_int_int @ Z )
% 15.48/8.48          = ( numeral_numeral_int @ N ) )
% 15.48/8.48        = ( Z
% 15.48/8.48          = ( numeral_numeral_int @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_931_of__int__le__iff,axiom,
% 15.48/8.48      ! [W: int,Z: int] :
% 15.48/8.48        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 15.48/8.48        = ( ord_less_eq_int @ W @ Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_932_of__int__le__iff,axiom,
% 15.48/8.48      ! [W: int,Z: int] :
% 15.48/8.48        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 15.48/8.48        = ( ord_less_eq_int @ W @ Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_933_of__int__le__iff,axiom,
% 15.48/8.48      ! [W: int,Z: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 15.48/8.48        = ( ord_less_eq_int @ W @ Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_934_of__int__less__iff,axiom,
% 15.48/8.48      ! [W: int,Z: int] :
% 15.48/8.48        ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 15.48/8.48        = ( ord_less_int @ W @ Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_935_of__int__less__iff,axiom,
% 15.48/8.48      ! [W: int,Z: int] :
% 15.48/8.48        ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 15.48/8.48        = ( ord_less_int @ W @ Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_936_of__int__less__iff,axiom,
% 15.48/8.48      ! [W: int,Z: int] :
% 15.48/8.48        ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 15.48/8.48        = ( ord_less_int @ W @ Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_937_nat__numeral,axiom,
% 15.48/8.48      ! [K: num] :
% 15.48/8.48        ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 15.48/8.48        = ( numeral_numeral_nat @ K ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_938_zero__less__nat__eq,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 15.48/8.48        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_939_zless__nat__conj,axiom,
% 15.48/8.48      ! [W: int,Z: int] :
% 15.48/8.48        ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 15.48/8.48        = ( ( ord_less_int @ zero_zero_int @ Z )
% 15.48/8.48          & ( ord_less_int @ W @ Z ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_940_of__int__of__nat__eq,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ring_17405671764205052669omplex @ ( semiri1314217659103216013at_int @ N ) )
% 15.48/8.48        = ( semiri8010041392384452111omplex @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_941_of__int__of__nat__eq,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ring_1_of_int_real @ ( semiri1314217659103216013at_int @ N ) )
% 15.48/8.48        = ( semiri5074537144036343181t_real @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_942_of__int__of__nat__eq,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ring_1_of_int_rat @ ( semiri1314217659103216013at_int @ N ) )
% 15.48/8.48        = ( semiri681578069525770553at_rat @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_943_of__int__of__nat__eq,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ring_1_of_int_int @ ( semiri1314217659103216013at_int @ N ) )
% 15.48/8.48        = ( semiri1314217659103216013at_int @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_944_int__nat__eq,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 15.48/8.48         => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 15.48/8.48            = Z ) )
% 15.48/8.48        & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 15.48/8.48         => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 15.48/8.48            = zero_zero_int ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_945_of__int__power,axiom,
% 15.48/8.48      ! [Z: int,N: nat] :
% 15.48/8.48        ( ( ring_1_of_int_rat @ ( power_power_int @ Z @ N ) )
% 15.48/8.48        = ( power_power_rat @ ( ring_1_of_int_rat @ Z ) @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_946_of__int__power,axiom,
% 15.48/8.48      ! [Z: int,N: nat] :
% 15.48/8.48        ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N ) )
% 15.48/8.48        = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_947_of__int__power,axiom,
% 15.48/8.48      ! [Z: int,N: nat] :
% 15.48/8.48        ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N ) )
% 15.48/8.48        = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_948_of__int__power,axiom,
% 15.48/8.48      ! [Z: int,N: nat] :
% 15.48/8.48        ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N ) )
% 15.48/8.48        = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_949_of__int__eq__of__int__power__cancel__iff,axiom,
% 15.48/8.48      ! [B: int,W: nat,X3: int] :
% 15.48/8.48        ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W )
% 15.48/8.48          = ( ring_1_of_int_rat @ X3 ) )
% 15.48/8.48        = ( ( power_power_int @ B @ W )
% 15.48/8.48          = X3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_950_of__int__eq__of__int__power__cancel__iff,axiom,
% 15.48/8.48      ! [B: int,W: nat,X3: int] :
% 15.48/8.48        ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W )
% 15.48/8.48          = ( ring_1_of_int_int @ X3 ) )
% 15.48/8.48        = ( ( power_power_int @ B @ W )
% 15.48/8.48          = X3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_951_of__int__eq__of__int__power__cancel__iff,axiom,
% 15.48/8.48      ! [B: int,W: nat,X3: int] :
% 15.48/8.48        ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
% 15.48/8.48          = ( ring_1_of_int_real @ X3 ) )
% 15.48/8.48        = ( ( power_power_int @ B @ W )
% 15.48/8.48          = X3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_952_of__int__eq__of__int__power__cancel__iff,axiom,
% 15.48/8.48      ! [B: int,W: nat,X3: int] :
% 15.48/8.48        ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W )
% 15.48/8.48          = ( ring_17405671764205052669omplex @ X3 ) )
% 15.48/8.48        = ( ( power_power_int @ B @ W )
% 15.48/8.48          = X3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_953_of__int__power__eq__of__int__cancel__iff,axiom,
% 15.48/8.48      ! [X3: int,B: int,W: nat] :
% 15.48/8.48        ( ( ( ring_1_of_int_rat @ X3 )
% 15.48/8.48          = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 15.48/8.48        = ( X3
% 15.48/8.48          = ( power_power_int @ B @ W ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_954_of__int__power__eq__of__int__cancel__iff,axiom,
% 15.48/8.48      ! [X3: int,B: int,W: nat] :
% 15.48/8.48        ( ( ( ring_1_of_int_int @ X3 )
% 15.48/8.48          = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 15.48/8.48        = ( X3
% 15.48/8.48          = ( power_power_int @ B @ W ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_955_of__int__power__eq__of__int__cancel__iff,axiom,
% 15.48/8.48      ! [X3: int,B: int,W: nat] :
% 15.48/8.48        ( ( ( ring_1_of_int_real @ X3 )
% 15.48/8.48          = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 15.48/8.48        = ( X3
% 15.48/8.48          = ( power_power_int @ B @ W ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_956_of__int__power__eq__of__int__cancel__iff,axiom,
% 15.48/8.48      ! [X3: int,B: int,W: nat] :
% 15.48/8.48        ( ( ( ring_17405671764205052669omplex @ X3 )
% 15.48/8.48          = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W ) )
% 15.48/8.48        = ( X3
% 15.48/8.48          = ( power_power_int @ B @ W ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_957_power__mono__iff,axiom,
% 15.48/8.48      ! [A: real,B: real,N: nat] :
% 15.48/8.48        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.48/8.48       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 15.48/8.48         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48           => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 15.48/8.48              = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_958_power__mono__iff,axiom,
% 15.48/8.48      ! [A: rat,B: rat,N: nat] :
% 15.48/8.48        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.48/8.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 15.48/8.48         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48           => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 15.48/8.48              = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_959_power__mono__iff,axiom,
% 15.48/8.48      ! [A: nat,B: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.48/8.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 15.48/8.48         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48           => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 15.48/8.48              = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_960_power__mono__iff,axiom,
% 15.48/8.48      ! [A: int,B: int,N: nat] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.48/8.48       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 15.48/8.48         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48           => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 15.48/8.48              = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_961_of__nat__0__less__iff,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 15.48/8.48        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_962_of__nat__0__less__iff,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 15.48/8.48        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_963_of__nat__0__less__iff,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 15.48/8.48        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_964_of__nat__0__less__iff,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 15.48/8.48        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_965_of__int__le__0__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 15.48/8.48        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_966_of__int__le__0__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 15.48/8.48        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_967_of__int__le__0__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 15.48/8.48        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_968_of__int__0__le__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 15.48/8.48        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_969_of__int__0__le__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 15.48/8.48        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_970_of__int__0__le__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 15.48/8.48        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_971_of__int__less__0__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 15.48/8.48        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_972_of__int__less__0__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 15.48/8.48        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_973_of__int__less__0__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 15.48/8.48        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_974_of__int__0__less__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 15.48/8.48        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_975_of__int__0__less__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 15.48/8.48        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_976_of__int__0__less__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 15.48/8.48        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_977_of__nat__nat,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 15.48/8.48       => ( ( semiri8010041392384452111omplex @ ( nat2 @ Z ) )
% 15.48/8.48          = ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_978_of__nat__nat,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 15.48/8.48       => ( ( semiri5074537144036343181t_real @ ( nat2 @ Z ) )
% 15.48/8.48          = ( ring_1_of_int_real @ Z ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_979_of__nat__nat,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 15.48/8.48       => ( ( semiri681578069525770553at_rat @ ( nat2 @ Z ) )
% 15.48/8.48          = ( ring_1_of_int_rat @ Z ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_980_of__nat__nat,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 15.48/8.48       => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 15.48/8.48          = ( ring_1_of_int_int @ Z ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_981_zero__eq__power2,axiom,
% 15.48/8.48      ! [A: rat] :
% 15.48/8.48        ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.48          = zero_zero_rat )
% 15.48/8.48        = ( A = zero_zero_rat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_982_zero__eq__power2,axiom,
% 15.48/8.48      ! [A: nat] :
% 15.48/8.48        ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.48          = zero_zero_nat )
% 15.48/8.48        = ( A = zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_983_zero__eq__power2,axiom,
% 15.48/8.48      ! [A: int] :
% 15.48/8.48        ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.48          = zero_zero_int )
% 15.48/8.48        = ( A = zero_zero_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_984_zero__eq__power2,axiom,
% 15.48/8.48      ! [A: real] :
% 15.48/8.48        ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.48          = zero_zero_real )
% 15.48/8.48        = ( A = zero_zero_real ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_985_zero__eq__power2,axiom,
% 15.48/8.48      ! [A: complex] :
% 15.48/8.48        ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.48          = zero_zero_complex )
% 15.48/8.48        = ( A = zero_zero_complex ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_986_of__nat__zero__less__power__iff,axiom,
% 15.48/8.48      ! [X3: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X3 ) @ N ) )
% 15.48/8.48        = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 15.48/8.48          | ( N = zero_zero_nat ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_987_of__nat__zero__less__power__iff,axiom,
% 15.48/8.48      ! [X3: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X3 ) @ N ) )
% 15.48/8.48        = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 15.48/8.48          | ( N = zero_zero_nat ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_988_of__nat__zero__less__power__iff,axiom,
% 15.48/8.48      ! [X3: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ N ) )
% 15.48/8.48        = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 15.48/8.48          | ( N = zero_zero_nat ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_989_of__nat__zero__less__power__iff,axiom,
% 15.48/8.48      ! [X3: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X3 ) @ N ) )
% 15.48/8.48        = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 15.48/8.48          | ( N = zero_zero_nat ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_990_of__int__numeral__le__iff,axiom,
% 15.48/8.48      ! [N: num,Z: int] :
% 15.48/8.48        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 15.48/8.48        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_991_of__int__numeral__le__iff,axiom,
% 15.48/8.48      ! [N: num,Z: int] :
% 15.48/8.48        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 15.48/8.48        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_992_of__int__numeral__le__iff,axiom,
% 15.48/8.48      ! [N: num,Z: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 15.48/8.48        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_993_of__int__le__numeral__iff,axiom,
% 15.48/8.48      ! [Z: int,N: num] :
% 15.48/8.48        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 15.48/8.48        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_994_of__int__le__numeral__iff,axiom,
% 15.48/8.48      ! [Z: int,N: num] :
% 15.48/8.48        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 15.48/8.48        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_995_of__int__le__numeral__iff,axiom,
% 15.48/8.48      ! [Z: int,N: num] :
% 15.48/8.48        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 15.48/8.48        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_996_of__int__less__numeral__iff,axiom,
% 15.48/8.48      ! [Z: int,N: num] :
% 15.48/8.48        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 15.48/8.48        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_997_of__int__less__numeral__iff,axiom,
% 15.48/8.48      ! [Z: int,N: num] :
% 15.48/8.48        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 15.48/8.48        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_998_of__int__less__numeral__iff,axiom,
% 15.48/8.48      ! [Z: int,N: num] :
% 15.48/8.48        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 15.48/8.48        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_999_of__int__numeral__less__iff,axiom,
% 15.48/8.48      ! [N: num,Z: int] :
% 15.48/8.48        ( ( ord_less_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 15.48/8.48        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1000_of__int__numeral__less__iff,axiom,
% 15.48/8.48      ! [N: num,Z: int] :
% 15.48/8.48        ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 15.48/8.48        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1001_of__int__numeral__less__iff,axiom,
% 15.48/8.48      ! [N: num,Z: int] :
% 15.48/8.48        ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 15.48/8.48        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1002_numeral__power__eq__of__int__cancel__iff,axiom,
% 15.48/8.48      ! [X3: num,N: nat,Y3: int] :
% 15.48/8.48        ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X3 ) @ N )
% 15.48/8.48          = ( ring_17405671764205052669omplex @ Y3 ) )
% 15.48/8.48        = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N )
% 15.48/8.48          = Y3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1003_numeral__power__eq__of__int__cancel__iff,axiom,
% 15.48/8.48      ! [X3: num,N: nat,Y3: int] :
% 15.48/8.48        ( ( ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N )
% 15.48/8.48          = ( ring_1_of_int_real @ Y3 ) )
% 15.48/8.48        = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N )
% 15.48/8.48          = Y3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1004_numeral__power__eq__of__int__cancel__iff,axiom,
% 15.48/8.48      ! [X3: num,N: nat,Y3: int] :
% 15.48/8.48        ( ( ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N )
% 15.48/8.48          = ( ring_1_of_int_rat @ Y3 ) )
% 15.48/8.48        = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N )
% 15.48/8.48          = Y3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1005_numeral__power__eq__of__int__cancel__iff,axiom,
% 15.48/8.48      ! [X3: num,N: nat,Y3: int] :
% 15.48/8.48        ( ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N )
% 15.48/8.48          = ( ring_1_of_int_int @ Y3 ) )
% 15.48/8.48        = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N )
% 15.48/8.48          = Y3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1006_of__int__eq__numeral__power__cancel__iff,axiom,
% 15.48/8.48      ! [Y3: int,X3: num,N: nat] :
% 15.48/8.48        ( ( ( ring_17405671764205052669omplex @ Y3 )
% 15.48/8.48          = ( power_power_complex @ ( numera6690914467698888265omplex @ X3 ) @ N ) )
% 15.48/8.48        = ( Y3
% 15.48/8.48          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1007_of__int__eq__numeral__power__cancel__iff,axiom,
% 15.48/8.48      ! [Y3: int,X3: num,N: nat] :
% 15.48/8.48        ( ( ( ring_1_of_int_real @ Y3 )
% 15.48/8.48          = ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N ) )
% 15.48/8.48        = ( Y3
% 15.48/8.48          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1008_of__int__eq__numeral__power__cancel__iff,axiom,
% 15.48/8.48      ! [Y3: int,X3: num,N: nat] :
% 15.48/8.48        ( ( ( ring_1_of_int_rat @ Y3 )
% 15.48/8.48          = ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N ) )
% 15.48/8.48        = ( Y3
% 15.48/8.48          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1009_of__int__eq__numeral__power__cancel__iff,axiom,
% 15.48/8.48      ! [Y3: int,X3: num,N: nat] :
% 15.48/8.48        ( ( ( ring_1_of_int_int @ Y3 )
% 15.48/8.48          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) )
% 15.48/8.48        = ( Y3
% 15.48/8.48          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1010_of__int__power__le__of__int__cancel__iff,axiom,
% 15.48/8.48      ! [X3: int,B: int,W: nat] :
% 15.48/8.48        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X3 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 15.48/8.48        = ( ord_less_eq_int @ X3 @ ( power_power_int @ B @ W ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1011_of__int__power__le__of__int__cancel__iff,axiom,
% 15.48/8.48      ! [X3: int,B: int,W: nat] :
% 15.48/8.48        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X3 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 15.48/8.48        = ( ord_less_eq_int @ X3 @ ( power_power_int @ B @ W ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1012_of__int__power__le__of__int__cancel__iff,axiom,
% 15.48/8.48      ! [X3: int,B: int,W: nat] :
% 15.48/8.48        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X3 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 15.48/8.48        = ( ord_less_eq_int @ X3 @ ( power_power_int @ B @ W ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1013_of__int__le__of__int__power__cancel__iff,axiom,
% 15.48/8.48      ! [B: int,W: nat,X3: int] :
% 15.48/8.48        ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X3 ) )
% 15.48/8.48        = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1014_of__int__le__of__int__power__cancel__iff,axiom,
% 15.48/8.48      ! [B: int,W: nat,X3: int] :
% 15.48/8.48        ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X3 ) )
% 15.48/8.48        = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1015_of__int__le__of__int__power__cancel__iff,axiom,
% 15.48/8.48      ! [B: int,W: nat,X3: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X3 ) )
% 15.48/8.48        = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1016_of__int__less__of__int__power__cancel__iff,axiom,
% 15.48/8.48      ! [B: int,W: nat,X3: int] :
% 15.48/8.48        ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X3 ) )
% 15.48/8.48        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1017_of__int__less__of__int__power__cancel__iff,axiom,
% 15.48/8.48      ! [B: int,W: nat,X3: int] :
% 15.48/8.48        ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X3 ) )
% 15.48/8.48        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1018_of__int__less__of__int__power__cancel__iff,axiom,
% 15.48/8.48      ! [B: int,W: nat,X3: int] :
% 15.48/8.48        ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X3 ) )
% 15.48/8.48        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1019_of__int__power__less__of__int__cancel__iff,axiom,
% 15.48/8.48      ! [X3: int,B: int,W: nat] :
% 15.48/8.48        ( ( ord_less_real @ ( ring_1_of_int_real @ X3 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 15.48/8.48        = ( ord_less_int @ X3 @ ( power_power_int @ B @ W ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1020_of__int__power__less__of__int__cancel__iff,axiom,
% 15.48/8.48      ! [X3: int,B: int,W: nat] :
% 15.48/8.48        ( ( ord_less_rat @ ( ring_1_of_int_rat @ X3 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 15.48/8.48        = ( ord_less_int @ X3 @ ( power_power_int @ B @ W ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1021_of__int__power__less__of__int__cancel__iff,axiom,
% 15.48/8.48      ! [X3: int,B: int,W: nat] :
% 15.48/8.48        ( ( ord_less_int @ ( ring_1_of_int_int @ X3 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 15.48/8.48        = ( ord_less_int @ X3 @ ( power_power_int @ B @ W ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1022_nat__eq__numeral__power__cancel__iff,axiom,
% 15.48/8.48      ! [Y3: int,X3: num,N: nat] :
% 15.48/8.48        ( ( ( nat2 @ Y3 )
% 15.48/8.48          = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) )
% 15.48/8.48        = ( Y3
% 15.48/8.48          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1023_numeral__power__eq__nat__cancel__iff,axiom,
% 15.48/8.48      ! [X3: num,N: nat,Y3: int] :
% 15.48/8.48        ( ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N )
% 15.48/8.48          = ( nat2 @ Y3 ) )
% 15.48/8.48        = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N )
% 15.48/8.48          = Y3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1024_numeral__power__le__of__int__cancel__iff,axiom,
% 15.48/8.48      ! [X3: num,N: nat,A: int] :
% 15.48/8.48        ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 15.48/8.48        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1025_numeral__power__le__of__int__cancel__iff,axiom,
% 15.48/8.48      ! [X3: num,N: nat,A: int] :
% 15.48/8.48        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 15.48/8.48        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1026_numeral__power__le__of__int__cancel__iff,axiom,
% 15.48/8.48      ! [X3: num,N: nat,A: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 15.48/8.48        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1027_of__int__le__numeral__power__cancel__iff,axiom,
% 15.48/8.48      ! [A: int,X3: num,N: nat] :
% 15.48/8.48        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N ) )
% 15.48/8.48        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1028_of__int__le__numeral__power__cancel__iff,axiom,
% 15.48/8.48      ! [A: int,X3: num,N: nat] :
% 15.48/8.48        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N ) )
% 15.48/8.48        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1029_of__int__le__numeral__power__cancel__iff,axiom,
% 15.48/8.48      ! [A: int,X3: num,N: nat] :
% 15.48/8.48        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) )
% 15.48/8.48        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1030_nat__zero__as__int,axiom,
% 15.48/8.48      ( zero_zero_nat
% 15.48/8.48      = ( nat2 @ zero_zero_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1031_eq__nat__nat__iff,axiom,
% 15.48/8.48      ! [Z: int,Z5: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 15.48/8.48       => ( ( ord_less_eq_int @ zero_zero_int @ Z5 )
% 15.48/8.48         => ( ( ( nat2 @ Z )
% 15.48/8.48              = ( nat2 @ Z5 ) )
% 15.48/8.48            = ( Z = Z5 ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1032_all__nat,axiom,
% 15.48/8.48      ( ( ^ [P2: nat > $o] :
% 15.48/8.48          ! [X5: nat] : ( P2 @ X5 ) )
% 15.48/8.48      = ( ^ [P3: nat > $o] :
% 15.48/8.48          ! [X: int] :
% 15.48/8.48            ( ( ord_less_eq_int @ zero_zero_int @ X )
% 15.48/8.48           => ( P3 @ ( nat2 @ X ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1033_ex__nat,axiom,
% 15.48/8.48      ( ( ^ [P2: nat > $o] :
% 15.48/8.48          ? [X5: nat] : ( P2 @ X5 ) )
% 15.48/8.48      = ( ^ [P3: nat > $o] :
% 15.48/8.48          ? [X: int] :
% 15.48/8.48            ( ( ord_less_eq_int @ zero_zero_int @ X )
% 15.48/8.48            & ( P3 @ ( nat2 @ X ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1034_int__ops_I1_J,axiom,
% 15.48/8.48      ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 15.48/8.48      = zero_zero_int ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1035_of__int__nonneg,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 15.48/8.48       => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1036_of__int__nonneg,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 15.48/8.48       => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1037_of__int__nonneg,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 15.48/8.48       => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1038_of__int__pos,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_int @ zero_zero_int @ Z )
% 15.48/8.48       => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1039_of__int__pos,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_int @ zero_zero_int @ Z )
% 15.48/8.48       => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1040_of__int__pos,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_int @ zero_zero_int @ Z )
% 15.48/8.48       => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1041_nat__eq__iff2,axiom,
% 15.48/8.48      ! [M: nat,W: int] :
% 15.48/8.48        ( ( M
% 15.48/8.48          = ( nat2 @ W ) )
% 15.48/8.48        = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 15.48/8.48           => ( W
% 15.48/8.48              = ( semiri1314217659103216013at_int @ M ) ) )
% 15.48/8.48          & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 15.48/8.48           => ( M = zero_zero_nat ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1042_nat__eq__iff,axiom,
% 15.48/8.48      ! [W: int,M: nat] :
% 15.48/8.48        ( ( ( nat2 @ W )
% 15.48/8.48          = M )
% 15.48/8.48        = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 15.48/8.48           => ( W
% 15.48/8.48              = ( semiri1314217659103216013at_int @ M ) ) )
% 15.48/8.48          & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 15.48/8.48           => ( M = zero_zero_nat ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1043_split__nat,axiom,
% 15.48/8.48      ! [P: nat > $o,I: int] :
% 15.48/8.48        ( ( P @ ( nat2 @ I ) )
% 15.48/8.48        = ( ! [N3: nat] :
% 15.48/8.48              ( ( I
% 15.48/8.48                = ( semiri1314217659103216013at_int @ N3 ) )
% 15.48/8.48             => ( P @ N3 ) )
% 15.48/8.48          & ( ( ord_less_int @ I @ zero_zero_int )
% 15.48/8.48           => ( P @ zero_zero_nat ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1044_nat__mono__iff,axiom,
% 15.48/8.48      ! [Z: int,W: int] :
% 15.48/8.48        ( ( ord_less_int @ zero_zero_int @ Z )
% 15.48/8.48       => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 15.48/8.48          = ( ord_less_int @ W @ Z ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1045_nat__power__eq,axiom,
% 15.48/8.48      ! [Z: int,N: nat] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 15.48/8.48       => ( ( nat2 @ ( power_power_int @ Z @ N ) )
% 15.48/8.48          = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1046_int__eq__iff,axiom,
% 15.48/8.48      ! [M: nat,Z: int] :
% 15.48/8.48        ( ( ( semiri1314217659103216013at_int @ M )
% 15.48/8.48          = Z )
% 15.48/8.48        = ( ( M
% 15.48/8.48            = ( nat2 @ Z ) )
% 15.48/8.48          & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1047_nat__0__le,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 15.48/8.48       => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 15.48/8.48          = Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1048_ex__le__of__int,axiom,
% 15.48/8.48      ! [X3: real] :
% 15.48/8.48      ? [Z3: int] : ( ord_less_eq_real @ X3 @ ( ring_1_of_int_real @ Z3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1049_ex__le__of__int,axiom,
% 15.48/8.48      ! [X3: rat] :
% 15.48/8.48      ? [Z3: int] : ( ord_less_eq_rat @ X3 @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1050_ex__less__of__int,axiom,
% 15.48/8.48      ! [X3: real] :
% 15.48/8.48      ? [Z3: int] : ( ord_less_real @ X3 @ ( ring_1_of_int_real @ Z3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1051_ex__less__of__int,axiom,
% 15.48/8.48      ! [X3: rat] :
% 15.48/8.48      ? [Z3: int] : ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1052_ex__of__int__less,axiom,
% 15.48/8.48      ! [X3: real] :
% 15.48/8.48      ? [Z3: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z3 ) @ X3 ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1053_ex__of__int__less,axiom,
% 15.48/8.48      ! [X3: rat] :
% 15.48/8.48      ? [Z3: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z3 ) @ X3 ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1054_zero__power,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48       => ( ( power_power_rat @ zero_zero_rat @ N )
% 15.48/8.48          = zero_zero_rat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1055_zero__power,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48       => ( ( power_power_nat @ zero_zero_nat @ N )
% 15.48/8.48          = zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1056_zero__power,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48       => ( ( power_power_int @ zero_zero_int @ N )
% 15.48/8.48          = zero_zero_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1057_zero__power,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48       => ( ( power_power_real @ zero_zero_real @ N )
% 15.48/8.48          = zero_zero_real ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1058_zero__power,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48       => ( ( power_power_complex @ zero_zero_complex @ N )
% 15.48/8.48          = zero_zero_complex ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1059_le__numeral__extra_I3_J,axiom,
% 15.48/8.48      ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1060_le__numeral__extra_I3_J,axiom,
% 15.48/8.48      ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1061_le__numeral__extra_I3_J,axiom,
% 15.48/8.48      ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1062_le__numeral__extra_I3_J,axiom,
% 15.48/8.48      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1063_less__numeral__extra_I3_J,axiom,
% 15.48/8.48      ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1064_less__numeral__extra_I3_J,axiom,
% 15.48/8.48      ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1065_less__numeral__extra_I3_J,axiom,
% 15.48/8.48      ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1066_less__numeral__extra_I3_J,axiom,
% 15.48/8.48      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1067_field__lbound__gt__zero,axiom,
% 15.48/8.48      ! [D1: real,D2: real] :
% 15.48/8.48        ( ( ord_less_real @ zero_zero_real @ D1 )
% 15.48/8.48       => ( ( ord_less_real @ zero_zero_real @ D2 )
% 15.48/8.48         => ? [E: real] :
% 15.48/8.48              ( ( ord_less_real @ zero_zero_real @ E )
% 15.48/8.48              & ( ord_less_real @ E @ D1 )
% 15.48/8.48              & ( ord_less_real @ E @ D2 ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1068_field__lbound__gt__zero,axiom,
% 15.48/8.48      ! [D1: rat,D2: rat] :
% 15.48/8.48        ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 15.48/8.48       => ( ( ord_less_rat @ zero_zero_rat @ D2 )
% 15.48/8.48         => ? [E: rat] :
% 15.48/8.48              ( ( ord_less_rat @ zero_zero_rat @ E )
% 15.48/8.48              & ( ord_less_rat @ E @ D1 )
% 15.48/8.48              & ( ord_less_rat @ E @ D2 ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1069_zero__neq__numeral,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ( zero_zero_complex
% 15.48/8.48       != ( numera6690914467698888265omplex @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1070_zero__neq__numeral,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ( zero_zero_real
% 15.48/8.48       != ( numeral_numeral_real @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1071_zero__neq__numeral,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ( zero_zero_rat
% 15.48/8.48       != ( numeral_numeral_rat @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1072_zero__neq__numeral,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ( zero_zero_nat
% 15.48/8.48       != ( numeral_numeral_nat @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1073_zero__neq__numeral,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ( zero_zero_int
% 15.48/8.48       != ( numeral_numeral_int @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1074_power__not__zero,axiom,
% 15.48/8.48      ! [A: rat,N: nat] :
% 15.48/8.48        ( ( A != zero_zero_rat )
% 15.48/8.48       => ( ( power_power_rat @ A @ N )
% 15.48/8.48         != zero_zero_rat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1075_power__not__zero,axiom,
% 15.48/8.48      ! [A: nat,N: nat] :
% 15.48/8.48        ( ( A != zero_zero_nat )
% 15.48/8.48       => ( ( power_power_nat @ A @ N )
% 15.48/8.48         != zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1076_power__not__zero,axiom,
% 15.48/8.48      ! [A: int,N: nat] :
% 15.48/8.48        ( ( A != zero_zero_int )
% 15.48/8.48       => ( ( power_power_int @ A @ N )
% 15.48/8.48         != zero_zero_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1077_power__not__zero,axiom,
% 15.48/8.48      ! [A: real,N: nat] :
% 15.48/8.48        ( ( A != zero_zero_real )
% 15.48/8.48       => ( ( power_power_real @ A @ N )
% 15.48/8.48         != zero_zero_real ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1078_power__not__zero,axiom,
% 15.48/8.48      ! [A: complex,N: nat] :
% 15.48/8.48        ( ( A != zero_zero_complex )
% 15.48/8.48       => ( ( power_power_complex @ A @ N )
% 15.48/8.48         != zero_zero_complex ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1079_bot__nat__0_Oextremum__strict,axiom,
% 15.48/8.48      ! [A: nat] :
% 15.48/8.48        ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1080_gr0I,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( N != zero_zero_nat )
% 15.48/8.48       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1081_not__gr0,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 15.48/8.48        = ( N = zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1082_not__less0,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1083_less__zeroE,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1084_gr__implies__not0,axiom,
% 15.48/8.48      ! [M: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_nat @ M @ N )
% 15.48/8.48       => ( N != zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1085_infinite__descent0,axiom,
% 15.48/8.48      ! [P: nat > $o,N: nat] :
% 15.48/8.48        ( ( P @ zero_zero_nat )
% 15.48/8.48       => ( ! [N2: nat] :
% 15.48/8.48              ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 15.48/8.48             => ( ~ ( P @ N2 )
% 15.48/8.48               => ? [M2: nat] :
% 15.48/8.48                    ( ( ord_less_nat @ M2 @ N2 )
% 15.48/8.48                    & ~ ( P @ M2 ) ) ) )
% 15.48/8.48         => ( P @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1086_le__0__eq,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 15.48/8.48        = ( N = zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1087_bot__nat__0_Oextremum__uniqueI,axiom,
% 15.48/8.48      ! [A: nat] :
% 15.48/8.48        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 15.48/8.48       => ( A = zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1088_bot__nat__0_Oextremum__unique,axiom,
% 15.48/8.48      ! [A: nat] :
% 15.48/8.48        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 15.48/8.48        = ( A = zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1089_less__eq__nat_Osimps_I1_J,axiom,
% 15.48/8.48      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1090_conj__le__cong,axiom,
% 15.48/8.48      ! [X3: int,X7: int,P: $o,P4: $o] :
% 15.48/8.48        ( ( X3 = X7 )
% 15.48/8.48       => ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 15.48/8.48           => ( P = P4 ) )
% 15.48/8.48         => ( ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 15.48/8.48              & P )
% 15.48/8.48            = ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 15.48/8.48              & P4 ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1091_imp__le__cong,axiom,
% 15.48/8.48      ! [X3: int,X7: int,P: $o,P4: $o] :
% 15.48/8.48        ( ( X3 = X7 )
% 15.48/8.48       => ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 15.48/8.48           => ( P = P4 ) )
% 15.48/8.48         => ( ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 15.48/8.48             => P )
% 15.48/8.48            = ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 15.48/8.48             => P4 ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1092_less__eq__int__code_I1_J,axiom,
% 15.48/8.48      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1093_less__int__code_I1_J,axiom,
% 15.48/8.48      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1094_not__iless0,axiom,
% 15.48/8.48      ! [N: extended_enat] :
% 15.48/8.48        ~ ( ord_le72135733267957522d_enat @ N @ zero_z5237406670263579293d_enat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1095_nat__less__eq__zless,axiom,
% 15.48/8.48      ! [W: int,Z: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ W )
% 15.48/8.48       => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 15.48/8.48          = ( ord_less_int @ W @ Z ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1096_nat__le__eq__zle,axiom,
% 15.48/8.48      ! [W: int,Z: int] :
% 15.48/8.48        ( ( ( ord_less_int @ zero_zero_int @ W )
% 15.48/8.48          | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 15.48/8.48       => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 15.48/8.48          = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1097_le__nat__iff,axiom,
% 15.48/8.48      ! [K: int,N: nat] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 15.48/8.48       => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 15.48/8.48          = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1098_ile0__eq,axiom,
% 15.48/8.48      ! [N: extended_enat] :
% 15.48/8.48        ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 15.48/8.48        = ( N = zero_z5237406670263579293d_enat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1099_i0__lb,axiom,
% 15.48/8.48      ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1100_power__eq__iff__eq__base,axiom,
% 15.48/8.48      ! [N: nat,A: real,B: real] :
% 15.48/8.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.48/8.48         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 15.48/8.48           => ( ( ( power_power_real @ A @ N )
% 15.48/8.48                = ( power_power_real @ B @ N ) )
% 15.48/8.48              = ( A = B ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1101_power__eq__iff__eq__base,axiom,
% 15.48/8.48      ! [N: nat,A: rat,B: rat] :
% 15.48/8.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.48/8.48         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 15.48/8.48           => ( ( ( power_power_rat @ A @ N )
% 15.48/8.48                = ( power_power_rat @ B @ N ) )
% 15.48/8.48              = ( A = B ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1102_power__eq__iff__eq__base,axiom,
% 15.48/8.48      ! [N: nat,A: nat,B: nat] :
% 15.48/8.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.48/8.48         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 15.48/8.48           => ( ( ( power_power_nat @ A @ N )
% 15.48/8.48                = ( power_power_nat @ B @ N ) )
% 15.48/8.48              = ( A = B ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1103_power__eq__iff__eq__base,axiom,
% 15.48/8.48      ! [N: nat,A: int,B: int] :
% 15.48/8.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.48/8.48         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 15.48/8.48           => ( ( ( power_power_int @ A @ N )
% 15.48/8.48                = ( power_power_int @ B @ N ) )
% 15.48/8.48              = ( A = B ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1104_power__eq__imp__eq__base,axiom,
% 15.48/8.48      ! [A: real,N: nat,B: real] :
% 15.48/8.48        ( ( ( power_power_real @ A @ N )
% 15.48/8.48          = ( power_power_real @ B @ N ) )
% 15.48/8.48       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.48/8.48         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 15.48/8.48           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48             => ( A = B ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1105_power__eq__imp__eq__base,axiom,
% 15.48/8.48      ! [A: rat,N: nat,B: rat] :
% 15.48/8.48        ( ( ( power_power_rat @ A @ N )
% 15.48/8.48          = ( power_power_rat @ B @ N ) )
% 15.48/8.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.48/8.48         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 15.48/8.48           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48             => ( A = B ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1106_power__eq__imp__eq__base,axiom,
% 15.48/8.48      ! [A: nat,N: nat,B: nat] :
% 15.48/8.48        ( ( ( power_power_nat @ A @ N )
% 15.48/8.48          = ( power_power_nat @ B @ N ) )
% 15.48/8.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.48/8.48         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 15.48/8.48           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48             => ( A = B ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1107_power__eq__imp__eq__base,axiom,
% 15.48/8.48      ! [A: int,N: nat,B: int] :
% 15.48/8.48        ( ( ( power_power_int @ A @ N )
% 15.48/8.48          = ( power_power_int @ B @ N ) )
% 15.48/8.48       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.48/8.48         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 15.48/8.48           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48             => ( A = B ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1108_zero__less__imp__eq__int,axiom,
% 15.48/8.48      ! [K: int] :
% 15.48/8.48        ( ( ord_less_int @ zero_zero_int @ K )
% 15.48/8.48       => ? [N2: nat] :
% 15.48/8.48            ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 15.48/8.48            & ( K
% 15.48/8.48              = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1109_pos__int__cases,axiom,
% 15.48/8.48      ! [K: int] :
% 15.48/8.48        ( ( ord_less_int @ zero_zero_int @ K )
% 15.48/8.48       => ~ ! [N2: nat] :
% 15.48/8.48              ( ( K
% 15.48/8.48                = ( semiri1314217659103216013at_int @ N2 ) )
% 15.48/8.48             => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1110_nat__numeral__as__int,axiom,
% 15.48/8.48      ( numeral_numeral_nat
% 15.48/8.48      = ( ^ [I4: num] : ( nat2 @ ( numeral_numeral_int @ I4 ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1111_nat__less__iff,axiom,
% 15.48/8.48      ! [W: int,M: nat] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ W )
% 15.48/8.48       => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 15.48/8.48          = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1112_nat__mono,axiom,
% 15.48/8.48      ! [X3: int,Y3: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ X3 @ Y3 )
% 15.48/8.48       => ( ord_less_eq_nat @ ( nat2 @ X3 ) @ ( nat2 @ Y3 ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1113_power__strict__mono,axiom,
% 15.48/8.48      ! [A: real,B: real,N: nat] :
% 15.48/8.48        ( ( ord_less_real @ A @ B )
% 15.48/8.48       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.48/8.48         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48           => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1114_power__strict__mono,axiom,
% 15.48/8.48      ! [A: rat,B: rat,N: nat] :
% 15.48/8.48        ( ( ord_less_rat @ A @ B )
% 15.48/8.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.48/8.48         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48           => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1115_power__strict__mono,axiom,
% 15.48/8.48      ! [A: nat,B: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_nat @ A @ B )
% 15.48/8.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.48/8.48         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48           => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1116_power__strict__mono,axiom,
% 15.48/8.48      ! [A: int,B: int,N: nat] :
% 15.48/8.48        ( ( ord_less_int @ A @ B )
% 15.48/8.48       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.48/8.48         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48           => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1117_not__numeral__le__zero,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1118_not__numeral__le__zero,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1119_not__numeral__le__zero,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1120_not__numeral__le__zero,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1121_zero__le__numeral,axiom,
% 15.48/8.48      ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1122_zero__le__numeral,axiom,
% 15.48/8.48      ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1123_zero__le__numeral,axiom,
% 15.48/8.48      ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1124_zero__le__numeral,axiom,
% 15.48/8.48      ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1125_zero__less__numeral,axiom,
% 15.48/8.48      ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1126_zero__less__numeral,axiom,
% 15.48/8.48      ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1127_zero__less__numeral,axiom,
% 15.48/8.48      ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1128_zero__less__numeral,axiom,
% 15.48/8.48      ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1129_not__numeral__less__zero,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1130_not__numeral__less__zero,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1131_not__numeral__less__zero,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1132_not__numeral__less__zero,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1133_zero__le__power,axiom,
% 15.48/8.48      ! [A: real,N: nat] :
% 15.48/8.48        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.48/8.48       => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1134_zero__le__power,axiom,
% 15.48/8.48      ! [A: rat,N: nat] :
% 15.48/8.48        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.48/8.48       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1135_zero__le__power,axiom,
% 15.48/8.48      ! [A: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.48/8.48       => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1136_zero__le__power,axiom,
% 15.48/8.48      ! [A: int,N: nat] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.48/8.48       => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1137_power__mono,axiom,
% 15.48/8.48      ! [A: real,B: real,N: nat] :
% 15.48/8.48        ( ( ord_less_eq_real @ A @ B )
% 15.48/8.48       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.48/8.48         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1138_power__mono,axiom,
% 15.48/8.48      ! [A: rat,B: rat,N: nat] :
% 15.48/8.48        ( ( ord_less_eq_rat @ A @ B )
% 15.48/8.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.48/8.48         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1139_power__mono,axiom,
% 15.48/8.48      ! [A: nat,B: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_eq_nat @ A @ B )
% 15.48/8.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.48/8.48         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1140_power__mono,axiom,
% 15.48/8.48      ! [A: int,B: int,N: nat] :
% 15.48/8.48        ( ( ord_less_eq_int @ A @ B )
% 15.48/8.48       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.48/8.48         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1141_zero__less__power,axiom,
% 15.48/8.48      ! [A: real,N: nat] :
% 15.48/8.48        ( ( ord_less_real @ zero_zero_real @ A )
% 15.48/8.48       => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1142_zero__less__power,axiom,
% 15.48/8.48      ! [A: rat,N: nat] :
% 15.48/8.48        ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.48/8.48       => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1143_zero__less__power,axiom,
% 15.48/8.48      ! [A: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_nat @ zero_zero_nat @ A )
% 15.48/8.48       => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1144_zero__less__power,axiom,
% 15.48/8.48      ! [A: int,N: nat] :
% 15.48/8.48        ( ( ord_less_int @ zero_zero_int @ A )
% 15.48/8.48       => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1145_of__nat__0__le__iff,axiom,
% 15.48/8.48      ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1146_of__nat__0__le__iff,axiom,
% 15.48/8.48      ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1147_of__nat__0__le__iff,axiom,
% 15.48/8.48      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1148_of__nat__0__le__iff,axiom,
% 15.48/8.48      ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1149_of__nat__less__0__iff,axiom,
% 15.48/8.48      ! [M: nat] :
% 15.48/8.48        ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1150_of__nat__less__0__iff,axiom,
% 15.48/8.48      ! [M: nat] :
% 15.48/8.48        ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1151_of__nat__less__0__iff,axiom,
% 15.48/8.48      ! [M: nat] :
% 15.48/8.48        ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1152_of__nat__less__0__iff,axiom,
% 15.48/8.48      ! [M: nat] :
% 15.48/8.48        ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1153_ex__least__nat__le,axiom,
% 15.48/8.48      ! [P: nat > $o,N: nat] :
% 15.48/8.48        ( ( P @ N )
% 15.48/8.48       => ( ~ ( P @ zero_zero_nat )
% 15.48/8.48         => ? [K2: nat] :
% 15.48/8.48              ( ( ord_less_eq_nat @ K2 @ N )
% 15.48/8.48              & ! [I2: nat] :
% 15.48/8.48                  ( ( ord_less_nat @ I2 @ K2 )
% 15.48/8.48                 => ~ ( P @ I2 ) )
% 15.48/8.48              & ( P @ K2 ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1154_nat__power__less__imp__less,axiom,
% 15.48/8.48      ! [I: nat,M: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_nat @ zero_zero_nat @ I )
% 15.48/8.48       => ( ( ord_less_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 15.48/8.48         => ( ord_less_nat @ M @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1155_zero__le__imp__eq__int,axiom,
% 15.48/8.48      ! [K: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 15.48/8.48       => ? [N2: nat] :
% 15.48/8.48            ( K
% 15.48/8.48            = ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1156_nonneg__int__cases,axiom,
% 15.48/8.48      ! [K: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 15.48/8.48       => ~ ! [N2: nat] :
% 15.48/8.48              ( K
% 15.48/8.48             != ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1157_zless__nat__eq__int__zless,axiom,
% 15.48/8.48      ! [M: nat,Z: int] :
% 15.48/8.48        ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 15.48/8.48        = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1158_nat__le__iff,axiom,
% 15.48/8.48      ! [X3: int,N: nat] :
% 15.48/8.48        ( ( ord_less_eq_nat @ ( nat2 @ X3 ) @ N )
% 15.48/8.48        = ( ord_less_eq_int @ X3 @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1159_ex__gt__or__lt,axiom,
% 15.48/8.48      ! [A: real] :
% 15.48/8.48      ? [B4: real] :
% 15.48/8.48        ( ( ord_less_real @ A @ B4 )
% 15.48/8.48        | ( ord_less_real @ B4 @ A ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1160_power__less__imp__less__base,axiom,
% 15.48/8.48      ! [A: real,N: nat,B: real] :
% 15.48/8.48        ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 15.48/8.48       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 15.48/8.48         => ( ord_less_real @ A @ B ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1161_power__less__imp__less__base,axiom,
% 15.48/8.48      ! [A: rat,N: nat,B: rat] :
% 15.48/8.48        ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 15.48/8.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 15.48/8.48         => ( ord_less_rat @ A @ B ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1162_power__less__imp__less__base,axiom,
% 15.48/8.48      ! [A: nat,N: nat,B: nat] :
% 15.48/8.48        ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 15.48/8.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 15.48/8.48         => ( ord_less_nat @ A @ B ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1163_power__less__imp__less__base,axiom,
% 15.48/8.48      ! [A: int,N: nat,B: int] :
% 15.48/8.48        ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 15.48/8.48       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 15.48/8.48         => ( ord_less_int @ A @ B ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1164_of__nat__less__of__int__iff,axiom,
% 15.48/8.48      ! [N: nat,X3: int] :
% 15.48/8.48        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( ring_1_of_int_real @ X3 ) )
% 15.48/8.48        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1165_of__nat__less__of__int__iff,axiom,
% 15.48/8.48      ! [N: nat,X3: int] :
% 15.48/8.48        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X3 ) )
% 15.48/8.48        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1166_of__nat__less__of__int__iff,axiom,
% 15.48/8.48      ! [N: nat,X3: int] :
% 15.48/8.48        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X3 ) )
% 15.48/8.48        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1167_zero__power2,axiom,
% 15.48/8.48      ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.48      = zero_zero_rat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1168_zero__power2,axiom,
% 15.48/8.48      ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.48      = zero_zero_nat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1169_zero__power2,axiom,
% 15.48/8.48      ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.48      = zero_zero_int ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1170_zero__power2,axiom,
% 15.48/8.48      ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.48      = zero_zero_real ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1171_zero__power2,axiom,
% 15.48/8.48      ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.48      = zero_zero_complex ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1172_zero__le__power2,axiom,
% 15.48/8.48      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1173_zero__le__power2,axiom,
% 15.48/8.48      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1174_zero__le__power2,axiom,
% 15.48/8.48      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1175_power2__eq__imp__eq,axiom,
% 15.48/8.48      ! [X3: real,Y3: real] :
% 15.48/8.48        ( ( ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.48          = ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.48/8.48       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.48/8.48         => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.48/8.48           => ( X3 = Y3 ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1176_power2__eq__imp__eq,axiom,
% 15.48/8.48      ! [X3: rat,Y3: rat] :
% 15.48/8.48        ( ( ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.48          = ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.48/8.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 15.48/8.48         => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 15.48/8.48           => ( X3 = Y3 ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1177_power2__eq__imp__eq,axiom,
% 15.48/8.48      ! [X3: nat,Y3: nat] :
% 15.48/8.48        ( ( ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.48          = ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.48/8.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ X3 )
% 15.48/8.48         => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 15.48/8.48           => ( X3 = Y3 ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1178_power2__eq__imp__eq,axiom,
% 15.48/8.48      ! [X3: int,Y3: int] :
% 15.48/8.48        ( ( ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.48          = ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.48/8.48       => ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 15.48/8.48         => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 15.48/8.48           => ( X3 = Y3 ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1179_power2__le__imp__le,axiom,
% 15.48/8.48      ! [X3: real,Y3: real] :
% 15.48/8.48        ( ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.48/8.48       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.48/8.48         => ( ord_less_eq_real @ X3 @ Y3 ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1180_power2__le__imp__le,axiom,
% 15.48/8.48      ! [X3: rat,Y3: rat] :
% 15.48/8.48        ( ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.48/8.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 15.48/8.48         => ( ord_less_eq_rat @ X3 @ Y3 ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1181_power2__le__imp__le,axiom,
% 15.48/8.48      ! [X3: nat,Y3: nat] :
% 15.48/8.48        ( ( ord_less_eq_nat @ ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.48/8.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 15.48/8.48         => ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1182_power2__le__imp__le,axiom,
% 15.48/8.48      ! [X3: int,Y3: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.48/8.48       => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 15.48/8.48         => ( ord_less_eq_int @ X3 @ Y3 ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1183_power2__less__0,axiom,
% 15.48/8.48      ! [A: real] :
% 15.48/8.48        ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1184_power2__less__0,axiom,
% 15.48/8.48      ! [A: rat] :
% 15.48/8.48        ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1185_power2__less__0,axiom,
% 15.48/8.48      ! [A: int] :
% 15.48/8.48        ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1186_not__exp__less__eq__0__int,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1187_not__gr__zero,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 15.48/8.48        = ( N = zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1188_le__zero__eq,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 15.48/8.48        = ( N = zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1189_pos2,axiom,
% 15.48/8.48      ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1190_realpow__pos__nth__unique,axiom,
% 15.48/8.48      ! [N: nat,A: real] :
% 15.48/8.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48       => ( ( ord_less_real @ zero_zero_real @ A )
% 15.48/8.48         => ? [X4: real] :
% 15.48/8.48              ( ( ord_less_real @ zero_zero_real @ X4 )
% 15.48/8.48              & ( ( power_power_real @ X4 @ N )
% 15.48/8.48                = A )
% 15.48/8.48              & ! [Y6: real] :
% 15.48/8.48                  ( ( ( ord_less_real @ zero_zero_real @ Y6 )
% 15.48/8.48                    & ( ( power_power_real @ Y6 @ N )
% 15.48/8.48                      = A ) )
% 15.48/8.48                 => ( Y6 = X4 ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1191_realpow__pos__nth,axiom,
% 15.48/8.48      ! [N: nat,A: real] :
% 15.48/8.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48       => ( ( ord_less_real @ zero_zero_real @ A )
% 15.48/8.48         => ? [R: real] :
% 15.48/8.48              ( ( ord_less_real @ zero_zero_real @ R )
% 15.48/8.48              & ( ( power_power_real @ R @ N )
% 15.48/8.48                = A ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1192_gr__zeroI,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( N != zero_zero_nat )
% 15.48/8.48       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1193_not__less__zero,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1194_gr__implies__not__zero,axiom,
% 15.48/8.48      ! [M: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_nat @ M @ N )
% 15.48/8.48       => ( N != zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1195_zero__less__iff__neq__zero,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.48        = ( N != zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1196_zero__reorient,axiom,
% 15.48/8.48      ! [X3: literal] :
% 15.48/8.48        ( ( zero_zero_literal = X3 )
% 15.48/8.48        = ( X3 = zero_zero_literal ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1197_zero__reorient,axiom,
% 15.48/8.48      ! [X3: real] :
% 15.48/8.48        ( ( zero_zero_real = X3 )
% 15.48/8.48        = ( X3 = zero_zero_real ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1198_zero__reorient,axiom,
% 15.48/8.48      ! [X3: rat] :
% 15.48/8.48        ( ( zero_zero_rat = X3 )
% 15.48/8.48        = ( X3 = zero_zero_rat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1199_zero__reorient,axiom,
% 15.48/8.48      ! [X3: nat] :
% 15.48/8.48        ( ( zero_zero_nat = X3 )
% 15.48/8.48        = ( X3 = zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1200_zero__reorient,axiom,
% 15.48/8.48      ! [X3: int] :
% 15.48/8.48        ( ( zero_zero_int = X3 )
% 15.48/8.48        = ( X3 = zero_zero_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1201_zero__le,axiom,
% 15.48/8.48      ! [X3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X3 ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1202_log2__of__power__le,axiom,
% 15.48/8.48      ! [M: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.48/8.48       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 15.48/8.48         => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1203_take__bit__int__eq__self__iff,axiom,
% 15.48/8.48      ! [N: nat,K: int] :
% 15.48/8.48        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 15.48/8.48          = K )
% 15.48/8.48        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 15.48/8.48          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1204_take__bit__int__eq__self,axiom,
% 15.48/8.48      ! [K: int,N: nat] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 15.48/8.48       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 15.48/8.48         => ( ( bit_se2923211474154528505it_int @ N @ K )
% 15.48/8.48            = K ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1205_XOR__upper,axiom,
% 15.48/8.48      ! [X3: int,N: nat,Y3: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 15.48/8.48       => ( ( ord_less_int @ X3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 15.48/8.48         => ( ( ord_less_int @ Y3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 15.48/8.48           => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X3 @ Y3 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1206_power__le__zero__eq__numeral,axiom,
% 15.48/8.48      ! [A: real,W: num] :
% 15.48/8.48        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 15.48/8.48        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 15.48/8.48          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.48/8.48              & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 15.48/8.48            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.48/8.48              & ( A = zero_zero_real ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1207_power__le__zero__eq__numeral,axiom,
% 15.48/8.48      ! [A: rat,W: num] :
% 15.48/8.48        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 15.48/8.48        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 15.48/8.48          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.48/8.48              & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 15.48/8.48            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.48/8.48              & ( A = zero_zero_rat ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1208_power__le__zero__eq__numeral,axiom,
% 15.48/8.48      ! [A: int,W: num] :
% 15.48/8.48        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 15.48/8.48        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 15.48/8.48          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.48/8.48              & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 15.48/8.48            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.48/8.48              & ( A = zero_zero_int ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1209_OR__upper,axiom,
% 15.48/8.48      ! [X3: int,N: nat,Y3: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 15.48/8.48       => ( ( ord_less_int @ X3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 15.48/8.48         => ( ( ord_less_int @ Y3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 15.48/8.48           => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X3 @ Y3 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1210_real__sqrt__pow2__iff,axiom,
% 15.48/8.48      ! [X3: real] :
% 15.48/8.48        ( ( ( power_power_real @ ( sqrt @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.48          = X3 )
% 15.48/8.48        = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1211_real__sqrt__pow2,axiom,
% 15.48/8.48      ! [X3: real] :
% 15.48/8.48        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.48/8.48       => ( ( power_power_real @ ( sqrt @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.48          = X3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1212_real__less__lsqrt,axiom,
% 15.48/8.48      ! [X3: real,Y3: real] :
% 15.48/8.48        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.48/8.48       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.48/8.48         => ( ( ord_less_real @ X3 @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.48/8.48           => ( ord_less_real @ ( sqrt @ X3 ) @ Y3 ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1213_power__decreasing__iff,axiom,
% 15.48/8.48      ! [B: real,M: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_real @ zero_zero_real @ B )
% 15.48/8.48       => ( ( ord_less_real @ B @ one_one_real )
% 15.48/8.48         => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 15.48/8.48            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1214_power__decreasing__iff,axiom,
% 15.48/8.48      ! [B: rat,M: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_rat @ zero_zero_rat @ B )
% 15.48/8.48       => ( ( ord_less_rat @ B @ one_one_rat )
% 15.48/8.48         => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 15.48/8.48            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1215_power__decreasing__iff,axiom,
% 15.48/8.48      ! [B: nat,M: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_nat @ zero_zero_nat @ B )
% 15.48/8.48       => ( ( ord_less_nat @ B @ one_one_nat )
% 15.48/8.48         => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 15.48/8.48            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1216_power__decreasing__iff,axiom,
% 15.48/8.48      ! [B: int,M: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_int @ zero_zero_int @ B )
% 15.48/8.48       => ( ( ord_less_int @ B @ one_one_int )
% 15.48/8.48         => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 15.48/8.48            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1217_log2__of__power__less,axiom,
% 15.48/8.48      ! [M: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.48/8.48       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 15.48/8.48         => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1218_power__one__right,axiom,
% 15.48/8.48      ! [A: nat] :
% 15.48/8.48        ( ( power_power_nat @ A @ one_one_nat )
% 15.48/8.48        = A ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1219_power__one__right,axiom,
% 15.48/8.48      ! [A: int] :
% 15.48/8.48        ( ( power_power_int @ A @ one_one_nat )
% 15.48/8.48        = A ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1220_power__one__right,axiom,
% 15.48/8.48      ! [A: real] :
% 15.48/8.48        ( ( power_power_real @ A @ one_one_nat )
% 15.48/8.48        = A ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1221_power__one__right,axiom,
% 15.48/8.48      ! [A: complex] :
% 15.48/8.48        ( ( power_power_complex @ A @ one_one_nat )
% 15.48/8.48        = A ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1222_nat__dvd__1__iff__1,axiom,
% 15.48/8.48      ! [M: nat] :
% 15.48/8.48        ( ( dvd_dvd_nat @ M @ one_one_nat )
% 15.48/8.48        = ( M = one_one_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1223_or_Oidem,axiom,
% 15.48/8.48      ! [A: int] :
% 15.48/8.48        ( ( bit_se1409905431419307370or_int @ A @ A )
% 15.48/8.48        = A ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1224_or_Oidem,axiom,
% 15.48/8.48      ! [A: nat] :
% 15.48/8.48        ( ( bit_se1412395901928357646or_nat @ A @ A )
% 15.48/8.48        = A ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1225_or_Oleft__idem,axiom,
% 15.48/8.48      ! [A: int,B: int] :
% 15.48/8.48        ( ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 15.48/8.48        = ( bit_se1409905431419307370or_int @ A @ B ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1226_or_Oleft__idem,axiom,
% 15.48/8.48      ! [A: nat,B: nat] :
% 15.48/8.48        ( ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 15.48/8.48        = ( bit_se1412395901928357646or_nat @ A @ B ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1227_or_Oright__idem,axiom,
% 15.48/8.48      ! [A: int,B: int] :
% 15.48/8.48        ( ( bit_se1409905431419307370or_int @ ( bit_se1409905431419307370or_int @ A @ B ) @ B )
% 15.48/8.48        = ( bit_se1409905431419307370or_int @ A @ B ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1228_or_Oright__idem,axiom,
% 15.48/8.48      ! [A: nat,B: nat] :
% 15.48/8.48        ( ( bit_se1412395901928357646or_nat @ ( bit_se1412395901928357646or_nat @ A @ B ) @ B )
% 15.48/8.48        = ( bit_se1412395901928357646or_nat @ A @ B ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1229_real__sqrt__one,axiom,
% 15.48/8.48      ( ( sqrt @ one_one_real )
% 15.48/8.48      = one_one_real ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1230_real__sqrt__eq__iff,axiom,
% 15.48/8.48      ! [X3: real,Y3: real] :
% 15.48/8.48        ( ( ( sqrt @ X3 )
% 15.48/8.48          = ( sqrt @ Y3 ) )
% 15.48/8.48        = ( X3 = Y3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1231_real__sqrt__eq__1__iff,axiom,
% 15.48/8.48      ! [X3: real] :
% 15.48/8.48        ( ( ( sqrt @ X3 )
% 15.48/8.48          = one_one_real )
% 15.48/8.48        = ( X3 = one_one_real ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1232_bit_Oxor__left__self,axiom,
% 15.48/8.48      ! [X3: int,Y3: int] :
% 15.48/8.48        ( ( bit_se6526347334894502574or_int @ X3 @ ( bit_se6526347334894502574or_int @ X3 @ Y3 ) )
% 15.48/8.48        = Y3 ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1233_power__one,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( power_power_rat @ one_one_rat @ N )
% 15.48/8.48        = one_one_rat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1234_power__one,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( power_power_nat @ one_one_nat @ N )
% 15.48/8.48        = one_one_nat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1235_power__one,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( power_power_int @ one_one_int @ N )
% 15.48/8.48        = one_one_int ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1236_power__one,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( power_power_real @ one_one_real @ N )
% 15.48/8.48        = one_one_real ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1237_power__one,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( power_power_complex @ one_one_complex @ N )
% 15.48/8.48        = one_one_complex ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1238_of__nat__eq__1__iff,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ( semiri8010041392384452111omplex @ N )
% 15.48/8.48          = one_one_complex )
% 15.48/8.48        = ( N = one_one_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1239_of__nat__eq__1__iff,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ( semiri5074537144036343181t_real @ N )
% 15.48/8.48          = one_one_real )
% 15.48/8.48        = ( N = one_one_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1240_of__nat__eq__1__iff,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ( semiri681578069525770553at_rat @ N )
% 15.48/8.48          = one_one_rat )
% 15.48/8.48        = ( N = one_one_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1241_of__nat__eq__1__iff,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ( semiri1316708129612266289at_nat @ N )
% 15.48/8.48          = one_one_nat )
% 15.48/8.48        = ( N = one_one_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1242_of__nat__eq__1__iff,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ( semiri1314217659103216013at_int @ N )
% 15.48/8.48          = one_one_int )
% 15.48/8.48        = ( N = one_one_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1243_of__nat__1__eq__iff,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( one_one_complex
% 15.48/8.48          = ( semiri8010041392384452111omplex @ N ) )
% 15.48/8.48        = ( N = one_one_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1244_of__nat__1__eq__iff,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( one_one_real
% 15.48/8.48          = ( semiri5074537144036343181t_real @ N ) )
% 15.48/8.48        = ( N = one_one_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1245_of__nat__1__eq__iff,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( one_one_rat
% 15.48/8.48          = ( semiri681578069525770553at_rat @ N ) )
% 15.48/8.48        = ( N = one_one_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1246_of__nat__1__eq__iff,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( one_one_nat
% 15.48/8.48          = ( semiri1316708129612266289at_nat @ N ) )
% 15.48/8.48        = ( N = one_one_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1247_of__nat__1__eq__iff,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( one_one_int
% 15.48/8.48          = ( semiri1314217659103216013at_int @ N ) )
% 15.48/8.48        = ( N = one_one_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1248_of__nat__1,axiom,
% 15.48/8.48      ( ( semiri8010041392384452111omplex @ one_one_nat )
% 15.48/8.48      = one_one_complex ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1249_of__nat__1,axiom,
% 15.48/8.48      ( ( semiri5074537144036343181t_real @ one_one_nat )
% 15.48/8.48      = one_one_real ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1250_of__nat__1,axiom,
% 15.48/8.48      ( ( semiri681578069525770553at_rat @ one_one_nat )
% 15.48/8.48      = one_one_rat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1251_of__nat__1,axiom,
% 15.48/8.48      ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 15.48/8.48      = one_one_nat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1252_of__nat__1,axiom,
% 15.48/8.48      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 15.48/8.48      = one_one_int ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1253_less__one,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( ord_less_nat @ N @ one_one_nat )
% 15.48/8.48        = ( N = zero_zero_nat ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1254_of__int__1,axiom,
% 15.48/8.48      ( ( ring_1_of_int_int @ one_one_int )
% 15.48/8.48      = one_one_int ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1255_of__int__1,axiom,
% 15.48/8.48      ( ( ring_1_of_int_real @ one_one_int )
% 15.48/8.48      = one_one_real ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1256_of__int__1,axiom,
% 15.48/8.48      ( ( ring_17405671764205052669omplex @ one_one_int )
% 15.48/8.48      = one_one_complex ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1257_of__int__1,axiom,
% 15.48/8.48      ( ( ring_1_of_int_rat @ one_one_int )
% 15.48/8.48      = one_one_rat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1258_of__int__eq__1__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ( ring_1_of_int_int @ Z )
% 15.48/8.48          = one_one_int )
% 15.48/8.48        = ( Z = one_one_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1259_of__int__eq__1__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ( ring_1_of_int_real @ Z )
% 15.48/8.48          = one_one_real )
% 15.48/8.48        = ( Z = one_one_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1260_of__int__eq__1__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ( ring_17405671764205052669omplex @ Z )
% 15.48/8.48          = one_one_complex )
% 15.48/8.48        = ( Z = one_one_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1261_of__int__eq__1__iff,axiom,
% 15.48/8.48      ! [Z: int] :
% 15.48/8.48        ( ( ( ring_1_of_int_rat @ Z )
% 15.48/8.48          = one_one_rat )
% 15.48/8.48        = ( Z = one_one_int ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1262_take__bit__of__0,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( bit_se2923211474154528505it_int @ N @ zero_zero_int )
% 15.48/8.48        = zero_zero_int ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1263_take__bit__of__0,axiom,
% 15.48/8.48      ! [N: nat] :
% 15.48/8.48        ( ( bit_se2925701944663578781it_nat @ N @ zero_zero_nat )
% 15.48/8.48        = zero_zero_nat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1264_or_Oright__neutral,axiom,
% 15.48/8.48      ! [A: int] :
% 15.48/8.48        ( ( bit_se1409905431419307370or_int @ A @ zero_zero_int )
% 15.48/8.48        = A ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1265_or_Oright__neutral,axiom,
% 15.48/8.48      ! [A: nat] :
% 15.48/8.48        ( ( bit_se1412395901928357646or_nat @ A @ zero_zero_nat )
% 15.48/8.48        = A ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1266_or_Oleft__neutral,axiom,
% 15.48/8.48      ! [A: int] :
% 15.48/8.48        ( ( bit_se1409905431419307370or_int @ zero_zero_int @ A )
% 15.48/8.48        = A ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1267_or_Oleft__neutral,axiom,
% 15.48/8.48      ! [A: nat] :
% 15.48/8.48        ( ( bit_se1412395901928357646or_nat @ zero_zero_nat @ A )
% 15.48/8.48        = A ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1268_xor_Oright__neutral,axiom,
% 15.48/8.48      ! [A: int] :
% 15.48/8.48        ( ( bit_se6526347334894502574or_int @ A @ zero_zero_int )
% 15.48/8.48        = A ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1269_xor_Oright__neutral,axiom,
% 15.48/8.48      ! [A: nat] :
% 15.48/8.48        ( ( bit_se6528837805403552850or_nat @ A @ zero_zero_nat )
% 15.48/8.48        = A ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1270_xor_Oleft__neutral,axiom,
% 15.48/8.48      ! [A: int] :
% 15.48/8.48        ( ( bit_se6526347334894502574or_int @ zero_zero_int @ A )
% 15.48/8.48        = A ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1271_xor_Oleft__neutral,axiom,
% 15.48/8.48      ! [A: nat] :
% 15.48/8.48        ( ( bit_se6528837805403552850or_nat @ zero_zero_nat @ A )
% 15.48/8.48        = A ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1272_xor__self__eq,axiom,
% 15.48/8.48      ! [A: int] :
% 15.48/8.48        ( ( bit_se6526347334894502574or_int @ A @ A )
% 15.48/8.48        = zero_zero_int ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1273_xor__self__eq,axiom,
% 15.48/8.48      ! [A: nat] :
% 15.48/8.48        ( ( bit_se6528837805403552850or_nat @ A @ A )
% 15.48/8.48        = zero_zero_nat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1274_bit_Oxor__self,axiom,
% 15.48/8.48      ! [X3: int] :
% 15.48/8.48        ( ( bit_se6526347334894502574or_int @ X3 @ X3 )
% 15.48/8.48        = zero_zero_int ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1275_real__sqrt__zero,axiom,
% 15.48/8.48      ( ( sqrt @ zero_zero_real )
% 15.48/8.48      = zero_zero_real ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1276_real__sqrt__eq__zero__cancel__iff,axiom,
% 15.48/8.48      ! [X3: real] :
% 15.48/8.48        ( ( ( sqrt @ X3 )
% 15.48/8.48          = zero_zero_real )
% 15.48/8.48        = ( X3 = zero_zero_real ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1277_real__sqrt__lt__1__iff,axiom,
% 15.48/8.48      ! [X3: real] :
% 15.48/8.48        ( ( ord_less_real @ ( sqrt @ X3 ) @ one_one_real )
% 15.48/8.48        = ( ord_less_real @ X3 @ one_one_real ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1278_real__sqrt__gt__1__iff,axiom,
% 15.48/8.48      ! [Y3: real] :
% 15.48/8.48        ( ( ord_less_real @ one_one_real @ ( sqrt @ Y3 ) )
% 15.48/8.48        = ( ord_less_real @ one_one_real @ Y3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1279_real__sqrt__less__iff,axiom,
% 15.48/8.48      ! [X3: real,Y3: real] :
% 15.48/8.48        ( ( ord_less_real @ ( sqrt @ X3 ) @ ( sqrt @ Y3 ) )
% 15.48/8.48        = ( ord_less_real @ X3 @ Y3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1280_real__sqrt__ge__1__iff,axiom,
% 15.48/8.48      ! [Y3: real] :
% 15.48/8.48        ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y3 ) )
% 15.48/8.48        = ( ord_less_eq_real @ one_one_real @ Y3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1281_real__sqrt__le__1__iff,axiom,
% 15.48/8.48      ! [X3: real] :
% 15.48/8.48        ( ( ord_less_eq_real @ ( sqrt @ X3 ) @ one_one_real )
% 15.48/8.48        = ( ord_less_eq_real @ X3 @ one_one_real ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1282_real__sqrt__le__iff,axiom,
% 15.48/8.48      ! [X3: real,Y3: real] :
% 15.48/8.48        ( ( ord_less_eq_real @ ( sqrt @ X3 ) @ ( sqrt @ Y3 ) )
% 15.48/8.48        = ( ord_less_eq_real @ X3 @ Y3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1283_log__one,axiom,
% 15.48/8.48      ! [A: real] :
% 15.48/8.48        ( ( log @ A @ one_one_real )
% 15.48/8.48        = zero_zero_real ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1284_take__bit__or,axiom,
% 15.48/8.48      ! [N: nat,A: int,B: int] :
% 15.48/8.48        ( ( bit_se2923211474154528505it_int @ N @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 15.48/8.48        = ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1285_take__bit__or,axiom,
% 15.48/8.48      ! [N: nat,A: nat,B: nat] :
% 15.48/8.48        ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 15.48/8.48        = ( bit_se1412395901928357646or_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1286_take__bit__xor,axiom,
% 15.48/8.48      ! [N: nat,A: int,B: int] :
% 15.48/8.48        ( ( bit_se2923211474154528505it_int @ N @ ( bit_se6526347334894502574or_int @ A @ B ) )
% 15.48/8.48        = ( bit_se6526347334894502574or_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1287_take__bit__xor,axiom,
% 15.48/8.48      ! [N: nat,A: nat,B: nat] :
% 15.48/8.48        ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se6528837805403552850or_nat @ A @ B ) )
% 15.48/8.48        = ( bit_se6528837805403552850or_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1288_numeral__eq__one__iff,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ( ( ( numera6690914467698888265omplex @ N )
% 15.48/8.48          = one_one_complex )
% 15.48/8.48        = ( N = one ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1289_numeral__eq__one__iff,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ( ( ( numeral_numeral_real @ N )
% 15.48/8.48          = one_one_real )
% 15.48/8.48        = ( N = one ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1290_numeral__eq__one__iff,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ( ( ( numeral_numeral_rat @ N )
% 15.48/8.48          = one_one_rat )
% 15.48/8.48        = ( N = one ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1291_numeral__eq__one__iff,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ( ( ( numeral_numeral_nat @ N )
% 15.48/8.48          = one_one_nat )
% 15.48/8.48        = ( N = one ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1292_numeral__eq__one__iff,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ( ( ( numeral_numeral_int @ N )
% 15.48/8.48          = one_one_int )
% 15.48/8.48        = ( N = one ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1293_one__eq__numeral__iff,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ( ( one_one_complex
% 15.48/8.48          = ( numera6690914467698888265omplex @ N ) )
% 15.48/8.48        = ( one = N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1294_one__eq__numeral__iff,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ( ( one_one_real
% 15.48/8.48          = ( numeral_numeral_real @ N ) )
% 15.48/8.48        = ( one = N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1295_one__eq__numeral__iff,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ( ( one_one_rat
% 15.48/8.48          = ( numeral_numeral_rat @ N ) )
% 15.48/8.48        = ( one = N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1296_one__eq__numeral__iff,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ( ( one_one_nat
% 15.48/8.48          = ( numeral_numeral_nat @ N ) )
% 15.48/8.48        = ( one = N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1297_one__eq__numeral__iff,axiom,
% 15.48/8.48      ! [N: num] :
% 15.48/8.48        ( ( one_one_int
% 15.48/8.48          = ( numeral_numeral_int @ N ) )
% 15.48/8.48        = ( one = N ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1298_power__inject__exp,axiom,
% 15.48/8.48      ! [A: real,M: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_real @ one_one_real @ A )
% 15.48/8.48       => ( ( ( power_power_real @ A @ M )
% 15.48/8.48            = ( power_power_real @ A @ N ) )
% 15.48/8.48          = ( M = N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1299_power__inject__exp,axiom,
% 15.48/8.48      ! [A: rat,M: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_rat @ one_one_rat @ A )
% 15.48/8.48       => ( ( ( power_power_rat @ A @ M )
% 15.48/8.48            = ( power_power_rat @ A @ N ) )
% 15.48/8.48          = ( M = N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1300_power__inject__exp,axiom,
% 15.48/8.48      ! [A: nat,M: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_nat @ one_one_nat @ A )
% 15.48/8.48       => ( ( ( power_power_nat @ A @ M )
% 15.48/8.48            = ( power_power_nat @ A @ N ) )
% 15.48/8.48          = ( M = N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1301_power__inject__exp,axiom,
% 15.48/8.48      ! [A: int,M: nat,N: nat] :
% 15.48/8.48        ( ( ord_less_int @ one_one_int @ A )
% 15.48/8.48       => ( ( ( power_power_int @ A @ M )
% 15.48/8.48            = ( power_power_int @ A @ N ) )
% 15.48/8.48          = ( M = N ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1302_take__bit__0,axiom,
% 15.48/8.48      ! [A: int] :
% 15.48/8.48        ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 15.48/8.48        = zero_zero_int ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1303_take__bit__0,axiom,
% 15.48/8.48      ! [A: nat] :
% 15.48/8.48        ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 15.48/8.48        = zero_zero_nat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1304_take__bit__numeral__1,axiom,
% 15.48/8.48      ! [L: num] :
% 15.48/8.48        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ one_one_int )
% 15.48/8.48        = one_one_int ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1305_take__bit__numeral__1,axiom,
% 15.48/8.48      ! [L: num] :
% 15.48/8.48        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ one_one_nat )
% 15.48/8.48        = one_one_nat ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1306_real__sqrt__gt__0__iff,axiom,
% 15.48/8.48      ! [Y3: real] :
% 15.48/8.48        ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y3 ) )
% 15.48/8.48        = ( ord_less_real @ zero_zero_real @ Y3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1307_real__sqrt__lt__0__iff,axiom,
% 15.48/8.48      ! [X3: real] :
% 15.48/8.48        ( ( ord_less_real @ ( sqrt @ X3 ) @ zero_zero_real )
% 15.48/8.48        = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1308_real__sqrt__ge__0__iff,axiom,
% 15.48/8.48      ! [Y3: real] :
% 15.48/8.48        ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y3 ) )
% 15.48/8.48        = ( ord_less_eq_real @ zero_zero_real @ Y3 ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1309_real__sqrt__le__0__iff,axiom,
% 15.48/8.48      ! [X3: real] :
% 15.48/8.48        ( ( ord_less_eq_real @ ( sqrt @ X3 ) @ zero_zero_real )
% 15.48/8.48        = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1310_zero__less__log__cancel__iff,axiom,
% 15.48/8.48      ! [A: real,X3: real] :
% 15.48/8.48        ( ( ord_less_real @ one_one_real @ A )
% 15.48/8.48       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.48/8.48         => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X3 ) )
% 15.48/8.48            = ( ord_less_real @ one_one_real @ X3 ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1311_log__less__zero__cancel__iff,axiom,
% 15.48/8.48      ! [A: real,X3: real] :
% 15.48/8.48        ( ( ord_less_real @ one_one_real @ A )
% 15.48/8.48       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.48/8.48         => ( ( ord_less_real @ ( log @ A @ X3 ) @ zero_zero_real )
% 15.48/8.48            = ( ord_less_real @ X3 @ one_one_real ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1312_one__less__log__cancel__iff,axiom,
% 15.48/8.48      ! [A: real,X3: real] :
% 15.48/8.48        ( ( ord_less_real @ one_one_real @ A )
% 15.48/8.48       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.48/8.48         => ( ( ord_less_real @ one_one_real @ ( log @ A @ X3 ) )
% 15.48/8.48            = ( ord_less_real @ A @ X3 ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1313_log__less__one__cancel__iff,axiom,
% 15.48/8.48      ! [A: real,X3: real] :
% 15.48/8.48        ( ( ord_less_real @ one_one_real @ A )
% 15.48/8.48       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.48/8.48         => ( ( ord_less_real @ ( log @ A @ X3 ) @ one_one_real )
% 15.48/8.48            = ( ord_less_real @ X3 @ A ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1314_log__less__cancel__iff,axiom,
% 15.48/8.48      ! [A: real,X3: real,Y3: real] :
% 15.48/8.48        ( ( ord_less_real @ one_one_real @ A )
% 15.48/8.48       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.48/8.48         => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.48/8.48           => ( ( ord_less_real @ ( log @ A @ X3 ) @ ( log @ A @ Y3 ) )
% 15.48/8.48              = ( ord_less_real @ X3 @ Y3 ) ) ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1315_log__eq__one,axiom,
% 15.48/8.48      ! [A: real] :
% 15.48/8.48        ( ( ord_less_real @ zero_zero_real @ A )
% 15.48/8.48       => ( ( A != one_one_real )
% 15.48/8.48         => ( ( log @ A @ A )
% 15.48/8.48            = one_one_real ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1316_or__nonnegative__int__iff,axiom,
% 15.48/8.48      ! [K: int,L: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 15.48/8.48        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 15.48/8.48          & ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1317_or__negative__int__iff,axiom,
% 15.48/8.48      ! [K: int,L: int] :
% 15.48/8.48        ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ zero_zero_int )
% 15.48/8.48        = ( ( ord_less_int @ K @ zero_zero_int )
% 15.48/8.48          | ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 15.48/8.48  
% 15.48/8.48  thf(fact_1318_xor__nonnegative__int__iff,axiom,
% 15.48/8.48      ! [K: int,L: int] :
% 15.48/8.48        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 15.48/8.49        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 15.48/8.49          = ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1319_xor__negative__int__iff,axiom,
% 15.48/8.49      ! [K: int,L: int] :
% 15.48/8.49        ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ zero_zero_int )
% 15.48/8.49        = ( ( ord_less_int @ K @ zero_zero_int )
% 15.48/8.49         != ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1320_power__strict__increasing__iff,axiom,
% 15.48/8.49      ! [B: real,X3: nat,Y3: nat] :
% 15.48/8.49        ( ( ord_less_real @ one_one_real @ B )
% 15.48/8.49       => ( ( ord_less_real @ ( power_power_real @ B @ X3 ) @ ( power_power_real @ B @ Y3 ) )
% 15.48/8.49          = ( ord_less_nat @ X3 @ Y3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1321_power__strict__increasing__iff,axiom,
% 15.48/8.49      ! [B: rat,X3: nat,Y3: nat] :
% 15.48/8.49        ( ( ord_less_rat @ one_one_rat @ B )
% 15.48/8.49       => ( ( ord_less_rat @ ( power_power_rat @ B @ X3 ) @ ( power_power_rat @ B @ Y3 ) )
% 15.48/8.49          = ( ord_less_nat @ X3 @ Y3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1322_power__strict__increasing__iff,axiom,
% 15.48/8.49      ! [B: nat,X3: nat,Y3: nat] :
% 15.48/8.49        ( ( ord_less_nat @ one_one_nat @ B )
% 15.48/8.49       => ( ( ord_less_nat @ ( power_power_nat @ B @ X3 ) @ ( power_power_nat @ B @ Y3 ) )
% 15.48/8.49          = ( ord_less_nat @ X3 @ Y3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1323_power__strict__increasing__iff,axiom,
% 15.48/8.49      ! [B: int,X3: nat,Y3: nat] :
% 15.48/8.49        ( ( ord_less_int @ one_one_int @ B )
% 15.48/8.49       => ( ( ord_less_int @ ( power_power_int @ B @ X3 ) @ ( power_power_int @ B @ Y3 ) )
% 15.48/8.49          = ( ord_less_nat @ X3 @ Y3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1324_take__bit__of__1__eq__0__iff,axiom,
% 15.48/8.49      ! [N: nat] :
% 15.48/8.49        ( ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 15.48/8.49          = zero_zero_int )
% 15.48/8.49        = ( N = zero_zero_nat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1325_take__bit__of__1__eq__0__iff,axiom,
% 15.48/8.49      ! [N: nat] :
% 15.48/8.49        ( ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 15.48/8.49          = zero_zero_nat )
% 15.48/8.49        = ( N = zero_zero_nat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1326_of__int__le__1__iff,axiom,
% 15.48/8.49      ! [Z: int] :
% 15.48/8.49        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 15.48/8.49        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1327_of__int__le__1__iff,axiom,
% 15.48/8.49      ! [Z: int] :
% 15.48/8.49        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 15.48/8.49        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1328_of__int__le__1__iff,axiom,
% 15.48/8.49      ! [Z: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 15.48/8.49        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1329_of__int__1__le__iff,axiom,
% 15.48/8.49      ! [Z: int] :
% 15.48/8.49        ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 15.48/8.49        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1330_of__int__1__le__iff,axiom,
% 15.48/8.49      ! [Z: int] :
% 15.48/8.49        ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 15.48/8.49        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1331_of__int__1__le__iff,axiom,
% 15.48/8.49      ! [Z: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 15.48/8.49        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1332_of__int__less__1__iff,axiom,
% 15.48/8.49      ! [Z: int] :
% 15.48/8.49        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 15.48/8.49        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1333_of__int__less__1__iff,axiom,
% 15.48/8.49      ! [Z: int] :
% 15.48/8.49        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 15.48/8.49        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1334_of__int__less__1__iff,axiom,
% 15.48/8.49      ! [Z: int] :
% 15.48/8.49        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 15.48/8.49        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1335_of__int__1__less__iff,axiom,
% 15.48/8.49      ! [Z: int] :
% 15.48/8.49        ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 15.48/8.49        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1336_of__int__1__less__iff,axiom,
% 15.48/8.49      ! [Z: int] :
% 15.48/8.49        ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 15.48/8.49        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1337_of__int__1__less__iff,axiom,
% 15.48/8.49      ! [Z: int] :
% 15.48/8.49        ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 15.48/8.49        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1338_real__sqrt__four,axiom,
% 15.48/8.49      ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 15.48/8.49      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1339_zero__le__log__cancel__iff,axiom,
% 15.48/8.49      ! [A: real,X3: real] :
% 15.48/8.49        ( ( ord_less_real @ one_one_real @ A )
% 15.48/8.49       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.48/8.49         => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X3 ) )
% 15.48/8.49            = ( ord_less_eq_real @ one_one_real @ X3 ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1340_log__le__zero__cancel__iff,axiom,
% 15.48/8.49      ! [A: real,X3: real] :
% 15.48/8.49        ( ( ord_less_real @ one_one_real @ A )
% 15.48/8.49       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.48/8.49         => ( ( ord_less_eq_real @ ( log @ A @ X3 ) @ zero_zero_real )
% 15.48/8.49            = ( ord_less_eq_real @ X3 @ one_one_real ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1341_one__le__log__cancel__iff,axiom,
% 15.48/8.49      ! [A: real,X3: real] :
% 15.48/8.49        ( ( ord_less_real @ one_one_real @ A )
% 15.48/8.49       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.48/8.49         => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X3 ) )
% 15.48/8.49            = ( ord_less_eq_real @ A @ X3 ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1342_log__le__one__cancel__iff,axiom,
% 15.48/8.49      ! [A: real,X3: real] :
% 15.48/8.49        ( ( ord_less_real @ one_one_real @ A )
% 15.48/8.49       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.48/8.49         => ( ( ord_less_eq_real @ ( log @ A @ X3 ) @ one_one_real )
% 15.48/8.49            = ( ord_less_eq_real @ X3 @ A ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1343_log__le__cancel__iff,axiom,
% 15.48/8.49      ! [A: real,X3: real,Y3: real] :
% 15.48/8.49        ( ( ord_less_real @ one_one_real @ A )
% 15.48/8.49       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.48/8.49         => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.48/8.49           => ( ( ord_less_eq_real @ ( log @ A @ X3 ) @ ( log @ A @ Y3 ) )
% 15.48/8.49              = ( ord_less_eq_real @ X3 @ Y3 ) ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1344_of__nat__nat__take__bit__eq,axiom,
% 15.48/8.49      ! [N: nat,K: int] :
% 15.48/8.49        ( ( semiri8010041392384452111omplex @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 15.48/8.49        = ( ring_17405671764205052669omplex @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1345_of__nat__nat__take__bit__eq,axiom,
% 15.48/8.49      ! [N: nat,K: int] :
% 15.48/8.49        ( ( semiri5074537144036343181t_real @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 15.48/8.49        = ( ring_1_of_int_real @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1346_of__nat__nat__take__bit__eq,axiom,
% 15.48/8.49      ! [N: nat,K: int] :
% 15.48/8.49        ( ( semiri681578069525770553at_rat @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 15.48/8.49        = ( ring_1_of_int_rat @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1347_of__nat__nat__take__bit__eq,axiom,
% 15.48/8.49      ! [N: nat,K: int] :
% 15.48/8.49        ( ( semiri1314217659103216013at_int @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 15.48/8.49        = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1348_power__strict__decreasing__iff,axiom,
% 15.48/8.49      ! [B: real,M: nat,N: nat] :
% 15.48/8.49        ( ( ord_less_real @ zero_zero_real @ B )
% 15.48/8.49       => ( ( ord_less_real @ B @ one_one_real )
% 15.48/8.49         => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 15.48/8.49            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1349_power__strict__decreasing__iff,axiom,
% 15.48/8.49      ! [B: rat,M: nat,N: nat] :
% 15.48/8.49        ( ( ord_less_rat @ zero_zero_rat @ B )
% 15.48/8.49       => ( ( ord_less_rat @ B @ one_one_rat )
% 15.48/8.49         => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 15.48/8.49            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1350_power__strict__decreasing__iff,axiom,
% 15.48/8.49      ! [B: nat,M: nat,N: nat] :
% 15.48/8.49        ( ( ord_less_nat @ zero_zero_nat @ B )
% 15.48/8.49       => ( ( ord_less_nat @ B @ one_one_nat )
% 15.48/8.49         => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 15.48/8.49            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1351_power__strict__decreasing__iff,axiom,
% 15.48/8.49      ! [B: int,M: nat,N: nat] :
% 15.48/8.49        ( ( ord_less_int @ zero_zero_int @ B )
% 15.48/8.49       => ( ( ord_less_int @ B @ one_one_int )
% 15.48/8.49         => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 15.48/8.49            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1352_power__increasing__iff,axiom,
% 15.48/8.49      ! [B: real,X3: nat,Y3: nat] :
% 15.48/8.49        ( ( ord_less_real @ one_one_real @ B )
% 15.48/8.49       => ( ( ord_less_eq_real @ ( power_power_real @ B @ X3 ) @ ( power_power_real @ B @ Y3 ) )
% 15.48/8.49          = ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1353_power__increasing__iff,axiom,
% 15.48/8.49      ! [B: rat,X3: nat,Y3: nat] :
% 15.48/8.49        ( ( ord_less_rat @ one_one_rat @ B )
% 15.48/8.49       => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X3 ) @ ( power_power_rat @ B @ Y3 ) )
% 15.48/8.49          = ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1354_power__increasing__iff,axiom,
% 15.48/8.49      ! [B: nat,X3: nat,Y3: nat] :
% 15.48/8.49        ( ( ord_less_nat @ one_one_nat @ B )
% 15.48/8.49       => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X3 ) @ ( power_power_nat @ B @ Y3 ) )
% 15.48/8.49          = ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1355_power__increasing__iff,axiom,
% 15.48/8.49      ! [B: int,X3: nat,Y3: nat] :
% 15.48/8.49        ( ( ord_less_int @ one_one_int @ B )
% 15.48/8.49       => ( ( ord_less_eq_int @ ( power_power_int @ B @ X3 ) @ ( power_power_int @ B @ Y3 ) )
% 15.48/8.49          = ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1356_numeral__le__one__iff,axiom,
% 15.48/8.49      ! [N: num] :
% 15.48/8.49        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 15.48/8.49        = ( ord_less_eq_num @ N @ one ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1357_numeral__le__one__iff,axiom,
% 15.48/8.49      ! [N: num] :
% 15.48/8.49        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 15.48/8.49        = ( ord_less_eq_num @ N @ one ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1358_numeral__le__one__iff,axiom,
% 15.48/8.49      ! [N: num] :
% 15.48/8.49        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 15.48/8.49        = ( ord_less_eq_num @ N @ one ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1359_numeral__le__one__iff,axiom,
% 15.48/8.49      ! [N: num] :
% 15.48/8.49        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 15.48/8.49        = ( ord_less_eq_num @ N @ one ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1360_one__less__numeral__iff,axiom,
% 15.48/8.49      ! [N: num] :
% 15.48/8.49        ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 15.48/8.49        = ( ord_less_num @ one @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1361_one__less__numeral__iff,axiom,
% 15.48/8.49      ! [N: num] :
% 15.48/8.49        ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 15.48/8.49        = ( ord_less_num @ one @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1362_one__less__numeral__iff,axiom,
% 15.48/8.49      ! [N: num] :
% 15.48/8.49        ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 15.48/8.49        = ( ord_less_num @ one @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1363_one__less__numeral__iff,axiom,
% 15.48/8.49      ! [N: num] :
% 15.48/8.49        ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 15.48/8.49        = ( ord_less_num @ one @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1364_log__pow__cancel,axiom,
% 15.48/8.49      ! [A: real,B: nat] :
% 15.48/8.49        ( ( ord_less_real @ zero_zero_real @ A )
% 15.48/8.49       => ( ( A != one_one_real )
% 15.48/8.49         => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 15.48/8.49            = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1365_even__take__bit__eq,axiom,
% 15.48/8.49      ! [N: nat,A: code_integer] :
% 15.48/8.49        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N @ A ) )
% 15.48/8.49        = ( ( N = zero_zero_nat )
% 15.48/8.49          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1366_even__take__bit__eq,axiom,
% 15.48/8.49      ! [N: nat,A: int] :
% 15.48/8.49        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 15.48/8.49        = ( ( N = zero_zero_nat )
% 15.48/8.49          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1367_even__take__bit__eq,axiom,
% 15.48/8.49      ! [N: nat,A: nat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N @ A ) )
% 15.48/8.49        = ( ( N = zero_zero_nat )
% 15.48/8.49          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1368_even__power,axiom,
% 15.48/8.49      ! [A: code_integer,N: nat] :
% 15.48/8.49        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 15.48/8.49        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.48/8.49          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1369_even__power,axiom,
% 15.48/8.49      ! [A: nat,N: nat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N ) )
% 15.48/8.49        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.48/8.49          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1370_even__power,axiom,
% 15.48/8.49      ! [A: int,N: nat] :
% 15.48/8.49        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N ) )
% 15.48/8.49        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.48/8.49          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1371_zero__le__power__eq__numeral,axiom,
% 15.48/8.49      ! [A: real,W: num] :
% 15.48/8.49        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 15.48/8.49        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.48/8.49          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.48/8.49            & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1372_zero__le__power__eq__numeral,axiom,
% 15.48/8.49      ! [A: rat,W: num] :
% 15.48/8.49        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 15.48/8.49        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.48/8.49          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.48/8.49            & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1373_zero__le__power__eq__numeral,axiom,
% 15.48/8.49      ! [A: int,W: num] :
% 15.48/8.49        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 15.48/8.49        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.48/8.49          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.48/8.49            & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1374_power__less__zero__eq,axiom,
% 15.48/8.49      ! [A: real,N: nat] :
% 15.48/8.49        ( ( ord_less_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 15.48/8.49        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49          & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1375_power__less__zero__eq,axiom,
% 15.48/8.49      ! [A: rat,N: nat] :
% 15.48/8.49        ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 15.48/8.49        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49          & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1376_power__less__zero__eq,axiom,
% 15.48/8.49      ! [A: int,N: nat] :
% 15.48/8.49        ( ( ord_less_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 15.48/8.49        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49          & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1377_power__less__zero__eq__numeral,axiom,
% 15.48/8.49      ! [A: real,W: num] :
% 15.48/8.49        ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 15.48/8.49        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.48/8.49          & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1378_power__less__zero__eq__numeral,axiom,
% 15.48/8.49      ! [A: rat,W: num] :
% 15.48/8.49        ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 15.48/8.49        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.48/8.49          & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1379_power__less__zero__eq__numeral,axiom,
% 15.48/8.49      ! [A: int,W: num] :
% 15.48/8.49        ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 15.48/8.49        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.48/8.49          & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1380_even__of__nat,axiom,
% 15.48/8.49      ! [N: nat] :
% 15.48/8.49        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N ) )
% 15.48/8.49        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1381_even__of__nat,axiom,
% 15.48/8.49      ! [N: nat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N ) )
% 15.48/8.49        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1382_even__of__nat,axiom,
% 15.48/8.49      ! [N: nat] :
% 15.48/8.49        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N ) )
% 15.48/8.49        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1383_zero__less__power__eq__numeral,axiom,
% 15.48/8.49      ! [A: real,W: num] :
% 15.48/8.49        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 15.48/8.49        = ( ( ( numeral_numeral_nat @ W )
% 15.48/8.49            = zero_zero_nat )
% 15.48/8.49          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.48/8.49            & ( A != zero_zero_real ) )
% 15.48/8.49          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.48/8.49            & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1384_zero__less__power__eq__numeral,axiom,
% 15.48/8.49      ! [A: rat,W: num] :
% 15.48/8.49        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 15.48/8.49        = ( ( ( numeral_numeral_nat @ W )
% 15.48/8.49            = zero_zero_nat )
% 15.48/8.49          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.48/8.49            & ( A != zero_zero_rat ) )
% 15.48/8.49          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.48/8.49            & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1385_zero__less__power__eq__numeral,axiom,
% 15.48/8.49      ! [A: int,W: num] :
% 15.48/8.49        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 15.48/8.49        = ( ( ( numeral_numeral_nat @ W )
% 15.48/8.49            = zero_zero_nat )
% 15.48/8.49          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.48/8.49            & ( A != zero_zero_int ) )
% 15.48/8.49          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.48/8.49            & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1386_or_Oassoc,axiom,
% 15.48/8.49      ! [A: int,B: int,C: int] :
% 15.48/8.49        ( ( bit_se1409905431419307370or_int @ ( bit_se1409905431419307370or_int @ A @ B ) @ C )
% 15.48/8.49        = ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ B @ C ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1387_or_Oassoc,axiom,
% 15.48/8.49      ! [A: nat,B: nat,C: nat] :
% 15.48/8.49        ( ( bit_se1412395901928357646or_nat @ ( bit_se1412395901928357646or_nat @ A @ B ) @ C )
% 15.48/8.49        = ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ B @ C ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1388_xor_Oassoc,axiom,
% 15.48/8.49      ! [A: int,B: int,C: int] :
% 15.48/8.49        ( ( bit_se6526347334894502574or_int @ ( bit_se6526347334894502574or_int @ A @ B ) @ C )
% 15.48/8.49        = ( bit_se6526347334894502574or_int @ A @ ( bit_se6526347334894502574or_int @ B @ C ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1389_xor_Oassoc,axiom,
% 15.48/8.49      ! [A: nat,B: nat,C: nat] :
% 15.48/8.49        ( ( bit_se6528837805403552850or_nat @ ( bit_se6528837805403552850or_nat @ A @ B ) @ C )
% 15.48/8.49        = ( bit_se6528837805403552850or_nat @ A @ ( bit_se6528837805403552850or_nat @ B @ C ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1390_or_Ocommute,axiom,
% 15.48/8.49      ( bit_se1409905431419307370or_int
% 15.48/8.49      = ( ^ [A4: int,B3: int] : ( bit_se1409905431419307370or_int @ B3 @ A4 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1391_or_Ocommute,axiom,
% 15.48/8.49      ( bit_se1412395901928357646or_nat
% 15.48/8.49      = ( ^ [A4: nat,B3: nat] : ( bit_se1412395901928357646or_nat @ B3 @ A4 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1392_xor_Ocommute,axiom,
% 15.48/8.49      ( bit_se6526347334894502574or_int
% 15.48/8.49      = ( ^ [A4: int,B3: int] : ( bit_se6526347334894502574or_int @ B3 @ A4 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1393_xor_Ocommute,axiom,
% 15.48/8.49      ( bit_se6528837805403552850or_nat
% 15.48/8.49      = ( ^ [A4: nat,B3: nat] : ( bit_se6528837805403552850or_nat @ B3 @ A4 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1394_or_Oleft__commute,axiom,
% 15.48/8.49      ! [B: int,A: int,C: int] :
% 15.48/8.49        ( ( bit_se1409905431419307370or_int @ B @ ( bit_se1409905431419307370or_int @ A @ C ) )
% 15.48/8.49        = ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ B @ C ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1395_or_Oleft__commute,axiom,
% 15.48/8.49      ! [B: nat,A: nat,C: nat] :
% 15.48/8.49        ( ( bit_se1412395901928357646or_nat @ B @ ( bit_se1412395901928357646or_nat @ A @ C ) )
% 15.48/8.49        = ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ B @ C ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1396_xor_Oleft__commute,axiom,
% 15.48/8.49      ! [B: int,A: int,C: int] :
% 15.48/8.49        ( ( bit_se6526347334894502574or_int @ B @ ( bit_se6526347334894502574or_int @ A @ C ) )
% 15.48/8.49        = ( bit_se6526347334894502574or_int @ A @ ( bit_se6526347334894502574or_int @ B @ C ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1397_xor_Oleft__commute,axiom,
% 15.48/8.49      ! [B: nat,A: nat,C: nat] :
% 15.48/8.49        ( ( bit_se6528837805403552850or_nat @ B @ ( bit_se6528837805403552850or_nat @ A @ C ) )
% 15.48/8.49        = ( bit_se6528837805403552850or_nat @ A @ ( bit_se6528837805403552850or_nat @ B @ C ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1398_one__reorient,axiom,
% 15.48/8.49      ! [X3: complex] :
% 15.48/8.49        ( ( one_one_complex = X3 )
% 15.48/8.49        = ( X3 = one_one_complex ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1399_one__reorient,axiom,
% 15.48/8.49      ! [X3: real] :
% 15.48/8.49        ( ( one_one_real = X3 )
% 15.48/8.49        = ( X3 = one_one_real ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1400_one__reorient,axiom,
% 15.48/8.49      ! [X3: rat] :
% 15.48/8.49        ( ( one_one_rat = X3 )
% 15.48/8.49        = ( X3 = one_one_rat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1401_one__reorient,axiom,
% 15.48/8.49      ! [X3: nat] :
% 15.48/8.49        ( ( one_one_nat = X3 )
% 15.48/8.49        = ( X3 = one_one_nat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1402_one__reorient,axiom,
% 15.48/8.49      ! [X3: int] :
% 15.48/8.49        ( ( one_one_int = X3 )
% 15.48/8.49        = ( X3 = one_one_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1403_of__nat__or__eq,axiom,
% 15.48/8.49      ! [M: nat,N: nat] :
% 15.48/8.49        ( ( semiri1314217659103216013at_int @ ( bit_se1412395901928357646or_nat @ M @ N ) )
% 15.48/8.49        = ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1404_of__nat__or__eq,axiom,
% 15.48/8.49      ! [M: nat,N: nat] :
% 15.48/8.49        ( ( semiri1316708129612266289at_nat @ ( bit_se1412395901928357646or_nat @ M @ N ) )
% 15.48/8.49        = ( bit_se1412395901928357646or_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1405_take__bit__of__nat,axiom,
% 15.48/8.49      ! [N: nat,M: nat] :
% 15.48/8.49        ( ( bit_se2923211474154528505it_int @ N @ ( semiri1314217659103216013at_int @ M ) )
% 15.48/8.49        = ( semiri1314217659103216013at_int @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1406_take__bit__of__nat,axiom,
% 15.48/8.49      ! [N: nat,M: nat] :
% 15.48/8.49        ( ( bit_se2925701944663578781it_nat @ N @ ( semiri1316708129612266289at_nat @ M ) )
% 15.48/8.49        = ( semiri1316708129612266289at_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1407_dvd__antisym,axiom,
% 15.48/8.49      ! [M: nat,N: nat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ M @ N )
% 15.48/8.49       => ( ( dvd_dvd_nat @ N @ M )
% 15.48/8.49         => ( M = N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1408_take__bit__of__int,axiom,
% 15.48/8.49      ! [N: nat,K: int] :
% 15.48/8.49        ( ( bit_se2923211474154528505it_int @ N @ ( ring_1_of_int_int @ K ) )
% 15.48/8.49        = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1409_of__int__or__eq,axiom,
% 15.48/8.49      ! [K: int,L: int] :
% 15.48/8.49        ( ( ring_1_of_int_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 15.48/8.49        = ( bit_se1409905431419307370or_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1410_of__nat__xor__eq,axiom,
% 15.48/8.49      ! [M: nat,N: nat] :
% 15.48/8.49        ( ( semiri1314217659103216013at_int @ ( bit_se6528837805403552850or_nat @ M @ N ) )
% 15.48/8.49        = ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1411_of__nat__xor__eq,axiom,
% 15.48/8.49      ! [M: nat,N: nat] :
% 15.48/8.49        ( ( semiri1316708129612266289at_nat @ ( bit_se6528837805403552850or_nat @ M @ N ) )
% 15.48/8.49        = ( bit_se6528837805403552850or_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1412_real__sqrt__ge__one,axiom,
% 15.48/8.49      ! [X3: real] :
% 15.48/8.49        ( ( ord_less_eq_real @ one_one_real @ X3 )
% 15.48/8.49       => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1413_of__int__xor__eq,axiom,
% 15.48/8.49      ! [K: int,L: int] :
% 15.48/8.49        ( ( ring_1_of_int_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 15.48/8.49        = ( bit_se6526347334894502574or_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1414_int__ops_I2_J,axiom,
% 15.48/8.49      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 15.48/8.49      = one_one_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1415_nat__one__as__int,axiom,
% 15.48/8.49      ( one_one_nat
% 15.48/8.49      = ( nat2 @ one_one_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1416_is__unit__power__iff,axiom,
% 15.48/8.49      ! [A: code_integer,N: nat] :
% 15.48/8.49        ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 15.48/8.49        = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 15.48/8.49          | ( N = zero_zero_nat ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1417_is__unit__power__iff,axiom,
% 15.48/8.49      ! [A: nat,N: nat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 15.48/8.49        = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 15.48/8.49          | ( N = zero_zero_nat ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1418_is__unit__power__iff,axiom,
% 15.48/8.49      ! [A: int,N: nat] :
% 15.48/8.49        ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 15.48/8.49        = ( ( dvd_dvd_int @ A @ one_one_int )
% 15.48/8.49          | ( N = zero_zero_nat ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1419_bit_Odisj__zero__right,axiom,
% 15.48/8.49      ! [X3: int] :
% 15.48/8.49        ( ( bit_se1409905431419307370or_int @ X3 @ zero_zero_int )
% 15.48/8.49        = X3 ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1420_or__eq__0__iff,axiom,
% 15.48/8.49      ! [A: int,B: int] :
% 15.48/8.49        ( ( ( bit_se1409905431419307370or_int @ A @ B )
% 15.48/8.49          = zero_zero_int )
% 15.48/8.49        = ( ( A = zero_zero_int )
% 15.48/8.49          & ( B = zero_zero_int ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1421_or__eq__0__iff,axiom,
% 15.48/8.49      ! [A: nat,B: nat] :
% 15.48/8.49        ( ( ( bit_se1412395901928357646or_nat @ A @ B )
% 15.48/8.49          = zero_zero_nat )
% 15.48/8.49        = ( ( A = zero_zero_nat )
% 15.48/8.49          & ( B = zero_zero_nat ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1422_take__bit__tightened,axiom,
% 15.48/8.49      ! [N: nat,A: int,B: int,M: nat] :
% 15.48/8.49        ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 15.48/8.49          = ( bit_se2923211474154528505it_int @ N @ B ) )
% 15.48/8.49       => ( ( ord_less_eq_nat @ M @ N )
% 15.48/8.49         => ( ( bit_se2923211474154528505it_int @ M @ A )
% 15.48/8.49            = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1423_take__bit__tightened,axiom,
% 15.48/8.49      ! [N: nat,A: nat,B: nat,M: nat] :
% 15.48/8.49        ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 15.48/8.49          = ( bit_se2925701944663578781it_nat @ N @ B ) )
% 15.48/8.49       => ( ( ord_less_eq_nat @ M @ N )
% 15.48/8.49         => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 15.48/8.49            = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1424_real__sqrt__less__mono,axiom,
% 15.48/8.49      ! [X3: real,Y3: real] :
% 15.48/8.49        ( ( ord_less_real @ X3 @ Y3 )
% 15.48/8.49       => ( ord_less_real @ ( sqrt @ X3 ) @ ( sqrt @ Y3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1425_real__sqrt__le__mono,axiom,
% 15.48/8.49      ! [X3: real,Y3: real] :
% 15.48/8.49        ( ( ord_less_eq_real @ X3 @ Y3 )
% 15.48/8.49       => ( ord_less_eq_real @ ( sqrt @ X3 ) @ ( sqrt @ Y3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1426_odd__one,axiom,
% 15.48/8.49      ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1427_odd__one,axiom,
% 15.48/8.49      ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1428_odd__one,axiom,
% 15.48/8.49      ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1429_real__sqrt__power,axiom,
% 15.48/8.49      ! [X3: real,K: nat] :
% 15.48/8.49        ( ( sqrt @ ( power_power_real @ X3 @ K ) )
% 15.48/8.49        = ( power_power_real @ ( sqrt @ X3 ) @ K ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1430_less__log__of__power,axiom,
% 15.48/8.49      ! [B: real,N: nat,M: real] :
% 15.48/8.49        ( ( ord_less_real @ ( power_power_real @ B @ N ) @ M )
% 15.48/8.49       => ( ( ord_less_real @ one_one_real @ B )
% 15.48/8.49         => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1431_log__of__power__eq,axiom,
% 15.48/8.49      ! [M: nat,B: real,N: nat] :
% 15.48/8.49        ( ( ( semiri5074537144036343181t_real @ M )
% 15.48/8.49          = ( power_power_real @ B @ N ) )
% 15.48/8.49       => ( ( ord_less_real @ one_one_real @ B )
% 15.48/8.49         => ( ( semiri5074537144036343181t_real @ N )
% 15.48/8.49            = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1432_dvd__power__same,axiom,
% 15.48/8.49      ! [X3: code_integer,Y3: code_integer,N: nat] :
% 15.48/8.49        ( ( dvd_dvd_Code_integer @ X3 @ Y3 )
% 15.48/8.49       => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X3 @ N ) @ ( power_8256067586552552935nteger @ Y3 @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1433_dvd__power__same,axiom,
% 15.48/8.49      ! [X3: nat,Y3: nat,N: nat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ X3 @ Y3 )
% 15.48/8.49       => ( dvd_dvd_nat @ ( power_power_nat @ X3 @ N ) @ ( power_power_nat @ Y3 @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1434_dvd__power__same,axiom,
% 15.48/8.49      ! [X3: int,Y3: int,N: nat] :
% 15.48/8.49        ( ( dvd_dvd_int @ X3 @ Y3 )
% 15.48/8.49       => ( dvd_dvd_int @ ( power_power_int @ X3 @ N ) @ ( power_power_int @ Y3 @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1435_dvd__power__same,axiom,
% 15.48/8.49      ! [X3: real,Y3: real,N: nat] :
% 15.48/8.49        ( ( dvd_dvd_real @ X3 @ Y3 )
% 15.48/8.49       => ( dvd_dvd_real @ ( power_power_real @ X3 @ N ) @ ( power_power_real @ Y3 @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1436_dvd__power__same,axiom,
% 15.48/8.49      ! [X3: complex,Y3: complex,N: nat] :
% 15.48/8.49        ( ( dvd_dvd_complex @ X3 @ Y3 )
% 15.48/8.49       => ( dvd_dvd_complex @ ( power_power_complex @ X3 @ N ) @ ( power_power_complex @ Y3 @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1437_le__numeral__extra_I4_J,axiom,
% 15.48/8.49      ord_less_eq_real @ one_one_real @ one_one_real ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1438_le__numeral__extra_I4_J,axiom,
% 15.48/8.49      ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1439_le__numeral__extra_I4_J,axiom,
% 15.48/8.49      ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1440_le__numeral__extra_I4_J,axiom,
% 15.48/8.49      ord_less_eq_int @ one_one_int @ one_one_int ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1441_less__numeral__extra_I4_J,axiom,
% 15.48/8.49      ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1442_less__numeral__extra_I4_J,axiom,
% 15.48/8.49      ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1443_less__numeral__extra_I4_J,axiom,
% 15.48/8.49      ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1444_less__numeral__extra_I4_J,axiom,
% 15.48/8.49      ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1445_even__or__iff,axiom,
% 15.48/8.49      ! [A: code_integer,B: code_integer] :
% 15.48/8.49        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1080825931792720795nteger @ A @ B ) )
% 15.48/8.49        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.48/8.49          & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1446_even__or__iff,axiom,
% 15.48/8.49      ! [A: int,B: int] :
% 15.48/8.49        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 15.48/8.49        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.48/8.49          & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1447_even__or__iff,axiom,
% 15.48/8.49      ! [A: nat,B: nat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 15.48/8.49        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.48/8.49          & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1448_even__xor__iff,axiom,
% 15.48/8.49      ! [A: code_integer,B: code_integer] :
% 15.48/8.49        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ A @ B ) )
% 15.48/8.49        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.48/8.49          = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1449_even__xor__iff,axiom,
% 15.48/8.49      ! [A: int,B: int] :
% 15.48/8.49        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ A @ B ) )
% 15.48/8.49        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.48/8.49          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1450_even__xor__iff,axiom,
% 15.48/8.49      ! [A: nat,B: nat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ A @ B ) )
% 15.48/8.49        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.48/8.49          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1451_zero__one__enat__neq_I1_J,axiom,
% 15.48/8.49      zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1452_dvd__power__iff,axiom,
% 15.48/8.49      ! [X3: code_integer,M: nat,N: nat] :
% 15.48/8.49        ( ( X3 != zero_z3403309356797280102nteger )
% 15.48/8.49       => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X3 @ M ) @ ( power_8256067586552552935nteger @ X3 @ N ) )
% 15.48/8.49          = ( ( dvd_dvd_Code_integer @ X3 @ one_one_Code_integer )
% 15.48/8.49            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1453_dvd__power__iff,axiom,
% 15.48/8.49      ! [X3: nat,M: nat,N: nat] :
% 15.48/8.49        ( ( X3 != zero_zero_nat )
% 15.48/8.49       => ( ( dvd_dvd_nat @ ( power_power_nat @ X3 @ M ) @ ( power_power_nat @ X3 @ N ) )
% 15.48/8.49          = ( ( dvd_dvd_nat @ X3 @ one_one_nat )
% 15.48/8.49            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1454_dvd__power__iff,axiom,
% 15.48/8.49      ! [X3: int,M: nat,N: nat] :
% 15.48/8.49        ( ( X3 != zero_zero_int )
% 15.48/8.49       => ( ( dvd_dvd_int @ ( power_power_int @ X3 @ M ) @ ( power_power_int @ X3 @ N ) )
% 15.48/8.49          = ( ( dvd_dvd_int @ X3 @ one_one_int )
% 15.48/8.49            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1455_dvd__power,axiom,
% 15.48/8.49      ! [N: nat,X3: code_integer] :
% 15.48/8.49        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.49          | ( X3 = one_one_Code_integer ) )
% 15.48/8.49       => ( dvd_dvd_Code_integer @ X3 @ ( power_8256067586552552935nteger @ X3 @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1456_dvd__power,axiom,
% 15.48/8.49      ! [N: nat,X3: rat] :
% 15.48/8.49        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.49          | ( X3 = one_one_rat ) )
% 15.48/8.49       => ( dvd_dvd_rat @ X3 @ ( power_power_rat @ X3 @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1457_dvd__power,axiom,
% 15.48/8.49      ! [N: nat,X3: nat] :
% 15.48/8.49        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.49          | ( X3 = one_one_nat ) )
% 15.48/8.49       => ( dvd_dvd_nat @ X3 @ ( power_power_nat @ X3 @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1458_dvd__power,axiom,
% 15.48/8.49      ! [N: nat,X3: int] :
% 15.48/8.49        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.49          | ( X3 = one_one_int ) )
% 15.48/8.49       => ( dvd_dvd_int @ X3 @ ( power_power_int @ X3 @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1459_dvd__power,axiom,
% 15.48/8.49      ! [N: nat,X3: real] :
% 15.48/8.49        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.49          | ( X3 = one_one_real ) )
% 15.48/8.49       => ( dvd_dvd_real @ X3 @ ( power_power_real @ X3 @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1460_dvd__power,axiom,
% 15.48/8.49      ! [N: nat,X3: complex] :
% 15.48/8.49        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.49          | ( X3 = one_one_complex ) )
% 15.48/8.49       => ( dvd_dvd_complex @ X3 @ ( power_power_complex @ X3 @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1461_power__dvd__imp__le,axiom,
% 15.48/8.49      ! [I: nat,M: nat,N: nat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 15.48/8.49       => ( ( ord_less_nat @ one_one_nat @ I )
% 15.48/8.49         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1462_le__log__of__power,axiom,
% 15.48/8.49      ! [B: real,N: nat,M: real] :
% 15.48/8.49        ( ( ord_less_eq_real @ ( power_power_real @ B @ N ) @ M )
% 15.48/8.49       => ( ( ord_less_real @ one_one_real @ B )
% 15.48/8.49         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1463_real__sqrt__gt__zero,axiom,
% 15.48/8.49      ! [X3: real] :
% 15.48/8.49        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.48/8.49       => ( ord_less_real @ zero_zero_real @ ( sqrt @ X3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1464_real__sqrt__ge__zero,axiom,
% 15.48/8.49      ! [X3: real] :
% 15.48/8.49        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.48/8.49       => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1465_real__sqrt__eq__zero__cancel,axiom,
% 15.48/8.49      ! [X3: real] :
% 15.48/8.49        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.48/8.49       => ( ( ( sqrt @ X3 )
% 15.48/8.49            = zero_zero_real )
% 15.48/8.49         => ( X3 = zero_zero_real ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1466_log__of__power__less,axiom,
% 15.48/8.49      ! [M: nat,B: real,N: nat] :
% 15.48/8.49        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 15.48/8.49       => ( ( ord_less_real @ one_one_real @ B )
% 15.48/8.49         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 15.48/8.49           => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1467_OR__lower,axiom,
% 15.48/8.49      ! [X3: int,Y3: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 15.48/8.49       => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 15.48/8.49         => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X3 @ Y3 ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1468_or__greater__eq,axiom,
% 15.48/8.49      ! [L: int,K: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ zero_zero_int @ L )
% 15.48/8.49       => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1469_even__numeral,axiom,
% 15.48/8.49      ! [N: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1470_even__numeral,axiom,
% 15.48/8.49      ! [N: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1471_even__numeral,axiom,
% 15.48/8.49      ! [N: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1472_take__bit__tightened__less__eq__int,axiom,
% 15.48/8.49      ! [M: nat,N: nat,K: int] :
% 15.48/8.49        ( ( ord_less_eq_nat @ M @ N )
% 15.48/8.49       => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1473_XOR__lower,axiom,
% 15.48/8.49      ! [X3: int,Y3: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 15.48/8.49       => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 15.48/8.49         => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X3 @ Y3 ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1474_take__bit__nonnegative,axiom,
% 15.48/8.49      ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1475_take__bit__int__less__eq__self__iff,axiom,
% 15.48/8.49      ! [N: nat,K: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 15.48/8.49        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1476_not__take__bit__negative,axiom,
% 15.48/8.49      ! [N: nat,K: int] :
% 15.48/8.49        ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1477_take__bit__int__greater__self__iff,axiom,
% 15.48/8.49      ! [K: int,N: nat] :
% 15.48/8.49        ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 15.48/8.49        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1478_le__imp__power__dvd,axiom,
% 15.48/8.49      ! [M: nat,N: nat,A: code_integer] :
% 15.48/8.49        ( ( ord_less_eq_nat @ M @ N )
% 15.48/8.49       => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1479_le__imp__power__dvd,axiom,
% 15.48/8.49      ! [M: nat,N: nat,A: nat] :
% 15.48/8.49        ( ( ord_less_eq_nat @ M @ N )
% 15.48/8.49       => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1480_le__imp__power__dvd,axiom,
% 15.48/8.49      ! [M: nat,N: nat,A: int] :
% 15.48/8.49        ( ( ord_less_eq_nat @ M @ N )
% 15.48/8.49       => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1481_le__imp__power__dvd,axiom,
% 15.48/8.49      ! [M: nat,N: nat,A: real] :
% 15.48/8.49        ( ( ord_less_eq_nat @ M @ N )
% 15.48/8.49       => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1482_le__imp__power__dvd,axiom,
% 15.48/8.49      ! [M: nat,N: nat,A: complex] :
% 15.48/8.49        ( ( ord_less_eq_nat @ M @ N )
% 15.48/8.49       => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1483_power__le__dvd,axiom,
% 15.48/8.49      ! [A: code_integer,N: nat,B: code_integer,M: nat] :
% 15.48/8.49        ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ B )
% 15.48/8.49       => ( ( ord_less_eq_nat @ M @ N )
% 15.48/8.49         => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1484_power__le__dvd,axiom,
% 15.48/8.49      ! [A: nat,N: nat,B: nat,M: nat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ B )
% 15.48/8.49       => ( ( ord_less_eq_nat @ M @ N )
% 15.48/8.49         => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1485_power__le__dvd,axiom,
% 15.48/8.49      ! [A: int,N: nat,B: int,M: nat] :
% 15.48/8.49        ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ B )
% 15.48/8.49       => ( ( ord_less_eq_nat @ M @ N )
% 15.48/8.49         => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1486_power__le__dvd,axiom,
% 15.48/8.49      ! [A: real,N: nat,B: real,M: nat] :
% 15.48/8.49        ( ( dvd_dvd_real @ ( power_power_real @ A @ N ) @ B )
% 15.48/8.49       => ( ( ord_less_eq_nat @ M @ N )
% 15.48/8.49         => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1487_power__le__dvd,axiom,
% 15.48/8.49      ! [A: complex,N: nat,B: complex,M: nat] :
% 15.48/8.49        ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N ) @ B )
% 15.48/8.49       => ( ( ord_less_eq_nat @ M @ N )
% 15.48/8.49         => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1488_dvd__power__le,axiom,
% 15.48/8.49      ! [X3: code_integer,Y3: code_integer,N: nat,M: nat] :
% 15.48/8.49        ( ( dvd_dvd_Code_integer @ X3 @ Y3 )
% 15.48/8.49       => ( ( ord_less_eq_nat @ N @ M )
% 15.48/8.49         => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X3 @ N ) @ ( power_8256067586552552935nteger @ Y3 @ M ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1489_dvd__power__le,axiom,
% 15.48/8.49      ! [X3: nat,Y3: nat,N: nat,M: nat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ X3 @ Y3 )
% 15.48/8.49       => ( ( ord_less_eq_nat @ N @ M )
% 15.48/8.49         => ( dvd_dvd_nat @ ( power_power_nat @ X3 @ N ) @ ( power_power_nat @ Y3 @ M ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1490_dvd__power__le,axiom,
% 15.48/8.49      ! [X3: int,Y3: int,N: nat,M: nat] :
% 15.48/8.49        ( ( dvd_dvd_int @ X3 @ Y3 )
% 15.48/8.49       => ( ( ord_less_eq_nat @ N @ M )
% 15.48/8.49         => ( dvd_dvd_int @ ( power_power_int @ X3 @ N ) @ ( power_power_int @ Y3 @ M ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1491_dvd__power__le,axiom,
% 15.48/8.49      ! [X3: real,Y3: real,N: nat,M: nat] :
% 15.48/8.49        ( ( dvd_dvd_real @ X3 @ Y3 )
% 15.48/8.49       => ( ( ord_less_eq_nat @ N @ M )
% 15.48/8.49         => ( dvd_dvd_real @ ( power_power_real @ X3 @ N ) @ ( power_power_real @ Y3 @ M ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1492_dvd__power__le,axiom,
% 15.48/8.49      ! [X3: complex,Y3: complex,N: nat,M: nat] :
% 15.48/8.49        ( ( dvd_dvd_complex @ X3 @ Y3 )
% 15.48/8.49       => ( ( ord_less_eq_nat @ N @ M )
% 15.48/8.49         => ( dvd_dvd_complex @ ( power_power_complex @ X3 @ N ) @ ( power_power_complex @ Y3 @ M ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1493_nat__dvd__not__less,axiom,
% 15.48/8.49      ! [M: nat,N: nat] :
% 15.48/8.49        ( ( ord_less_nat @ zero_zero_nat @ M )
% 15.48/8.49       => ( ( ord_less_nat @ M @ N )
% 15.48/8.49         => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1494_less__numeral__extra_I1_J,axiom,
% 15.48/8.49      ord_less_real @ zero_zero_real @ one_one_real ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1495_less__numeral__extra_I1_J,axiom,
% 15.48/8.49      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1496_less__numeral__extra_I1_J,axiom,
% 15.48/8.49      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1497_less__numeral__extra_I1_J,axiom,
% 15.48/8.49      ord_less_int @ zero_zero_int @ one_one_int ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1498_one__le__numeral,axiom,
% 15.48/8.49      ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1499_one__le__numeral,axiom,
% 15.48/8.49      ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1500_one__le__numeral,axiom,
% 15.48/8.49      ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1501_one__le__numeral,axiom,
% 15.48/8.49      ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1502_not__numeral__less__one,axiom,
% 15.48/8.49      ! [N: num] :
% 15.48/8.49        ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1503_not__numeral__less__one,axiom,
% 15.48/8.49      ! [N: num] :
% 15.48/8.49        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1504_not__numeral__less__one,axiom,
% 15.48/8.49      ! [N: num] :
% 15.48/8.49        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1505_not__numeral__less__one,axiom,
% 15.48/8.49      ! [N: num] :
% 15.48/8.49        ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1506_numeral__One,axiom,
% 15.48/8.49      ( ( numera6690914467698888265omplex @ one )
% 15.48/8.49      = one_one_complex ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1507_numeral__One,axiom,
% 15.48/8.49      ( ( numeral_numeral_real @ one )
% 15.48/8.49      = one_one_real ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1508_numeral__One,axiom,
% 15.48/8.49      ( ( numeral_numeral_rat @ one )
% 15.48/8.49      = one_one_rat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1509_numeral__One,axiom,
% 15.48/8.49      ( ( numeral_numeral_nat @ one )
% 15.48/8.49      = one_one_nat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1510_numeral__One,axiom,
% 15.48/8.49      ( ( numeral_numeral_int @ one )
% 15.48/8.49      = one_one_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1511_one__le__power,axiom,
% 15.48/8.49      ! [A: real,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_real @ one_one_real @ A )
% 15.48/8.49       => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1512_one__le__power,axiom,
% 15.48/8.49      ! [A: rat,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 15.48/8.49       => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1513_one__le__power,axiom,
% 15.48/8.49      ! [A: nat,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 15.48/8.49       => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1514_one__le__power,axiom,
% 15.48/8.49      ! [A: int,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_int @ one_one_int @ A )
% 15.48/8.49       => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1515_take__bit__eq__0__iff,axiom,
% 15.48/8.49      ! [N: nat,A: code_integer] :
% 15.48/8.49        ( ( ( bit_se1745604003318907178nteger @ N @ A )
% 15.48/8.49          = zero_z3403309356797280102nteger )
% 15.48/8.49        = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1516_take__bit__eq__0__iff,axiom,
% 15.48/8.49      ! [N: nat,A: int] :
% 15.48/8.49        ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 15.48/8.49          = zero_zero_int )
% 15.48/8.49        = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1517_take__bit__eq__0__iff,axiom,
% 15.48/8.49      ! [N: nat,A: nat] :
% 15.48/8.49        ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 15.48/8.49          = zero_zero_nat )
% 15.48/8.49        = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1518_power__0,axiom,
% 15.48/8.49      ! [A: rat] :
% 15.48/8.49        ( ( power_power_rat @ A @ zero_zero_nat )
% 15.48/8.49        = one_one_rat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1519_power__0,axiom,
% 15.48/8.49      ! [A: nat] :
% 15.48/8.49        ( ( power_power_nat @ A @ zero_zero_nat )
% 15.48/8.49        = one_one_nat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1520_power__0,axiom,
% 15.48/8.49      ! [A: int] :
% 15.48/8.49        ( ( power_power_int @ A @ zero_zero_nat )
% 15.48/8.49        = one_one_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1521_power__0,axiom,
% 15.48/8.49      ! [A: real] :
% 15.48/8.49        ( ( power_power_real @ A @ zero_zero_nat )
% 15.48/8.49        = one_one_real ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1522_power__0,axiom,
% 15.48/8.49      ! [A: complex] :
% 15.48/8.49        ( ( power_power_complex @ A @ zero_zero_nat )
% 15.48/8.49        = one_one_complex ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1523_numerals_I1_J,axiom,
% 15.48/8.49      ( ( numeral_numeral_nat @ one )
% 15.48/8.49      = one_one_nat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1524_real__arch__pow,axiom,
% 15.48/8.49      ! [X3: real,Y3: real] :
% 15.48/8.49        ( ( ord_less_real @ one_one_real @ X3 )
% 15.48/8.49       => ? [N2: nat] : ( ord_less_real @ Y3 @ ( power_power_real @ X3 @ N2 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1525_log__of__power__le,axiom,
% 15.48/8.49      ! [M: nat,B: real,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 15.48/8.49       => ( ( ord_less_real @ one_one_real @ B )
% 15.48/8.49         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 15.48/8.49           => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1526_even__of__int__iff,axiom,
% 15.48/8.49      ! [K: int] :
% 15.48/8.49        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ K ) )
% 15.48/8.49        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1527_even__of__int__iff,axiom,
% 15.48/8.49      ! [K: int] :
% 15.48/8.49        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 15.48/8.49        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1528_even__zero,axiom,
% 15.48/8.49      dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1529_even__zero,axiom,
% 15.48/8.49      dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1530_even__zero,axiom,
% 15.48/8.49      dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1531_dvd__imp__le,axiom,
% 15.48/8.49      ! [K: nat,N: nat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ K @ N )
% 15.48/8.49       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.49         => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1532_power__le__one,axiom,
% 15.48/8.49      ! [A: real,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.48/8.49       => ( ( ord_less_eq_real @ A @ one_one_real )
% 15.48/8.49         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1533_power__le__one,axiom,
% 15.48/8.49      ! [A: rat,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.48/8.49       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 15.48/8.49         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1534_power__le__one,axiom,
% 15.48/8.49      ! [A: nat,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.48/8.49       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 15.48/8.49         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1535_power__le__one,axiom,
% 15.48/8.49      ! [A: int,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.48/8.49       => ( ( ord_less_eq_int @ A @ one_one_int )
% 15.48/8.49         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1536_power__0__left,axiom,
% 15.48/8.49      ! [N: nat] :
% 15.48/8.49        ( ( ( N = zero_zero_nat )
% 15.48/8.49         => ( ( power_power_rat @ zero_zero_rat @ N )
% 15.48/8.49            = one_one_rat ) )
% 15.48/8.49        & ( ( N != zero_zero_nat )
% 15.48/8.49         => ( ( power_power_rat @ zero_zero_rat @ N )
% 15.48/8.49            = zero_zero_rat ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1537_power__0__left,axiom,
% 15.48/8.49      ! [N: nat] :
% 15.48/8.49        ( ( ( N = zero_zero_nat )
% 15.48/8.49         => ( ( power_power_nat @ zero_zero_nat @ N )
% 15.48/8.49            = one_one_nat ) )
% 15.48/8.49        & ( ( N != zero_zero_nat )
% 15.48/8.49         => ( ( power_power_nat @ zero_zero_nat @ N )
% 15.48/8.49            = zero_zero_nat ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1538_power__0__left,axiom,
% 15.48/8.49      ! [N: nat] :
% 15.48/8.49        ( ( ( N = zero_zero_nat )
% 15.48/8.49         => ( ( power_power_int @ zero_zero_int @ N )
% 15.48/8.49            = one_one_int ) )
% 15.48/8.49        & ( ( N != zero_zero_nat )
% 15.48/8.49         => ( ( power_power_int @ zero_zero_int @ N )
% 15.48/8.49            = zero_zero_int ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1539_power__0__left,axiom,
% 15.48/8.49      ! [N: nat] :
% 15.48/8.49        ( ( ( N = zero_zero_nat )
% 15.48/8.49         => ( ( power_power_real @ zero_zero_real @ N )
% 15.48/8.49            = one_one_real ) )
% 15.48/8.49        & ( ( N != zero_zero_nat )
% 15.48/8.49         => ( ( power_power_real @ zero_zero_real @ N )
% 15.48/8.49            = zero_zero_real ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1540_power__0__left,axiom,
% 15.48/8.49      ! [N: nat] :
% 15.48/8.49        ( ( ( N = zero_zero_nat )
% 15.48/8.49         => ( ( power_power_complex @ zero_zero_complex @ N )
% 15.48/8.49            = one_one_complex ) )
% 15.48/8.49        & ( ( N != zero_zero_nat )
% 15.48/8.49         => ( ( power_power_complex @ zero_zero_complex @ N )
% 15.48/8.49            = zero_zero_complex ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1541_power__less__imp__less__exp,axiom,
% 15.48/8.49      ! [A: real,M: nat,N: nat] :
% 15.48/8.49        ( ( ord_less_real @ one_one_real @ A )
% 15.48/8.49       => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 15.48/8.49         => ( ord_less_nat @ M @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1542_power__less__imp__less__exp,axiom,
% 15.48/8.49      ! [A: rat,M: nat,N: nat] :
% 15.48/8.49        ( ( ord_less_rat @ one_one_rat @ A )
% 15.48/8.49       => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 15.48/8.49         => ( ord_less_nat @ M @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1543_power__less__imp__less__exp,axiom,
% 15.48/8.49      ! [A: nat,M: nat,N: nat] :
% 15.48/8.49        ( ( ord_less_nat @ one_one_nat @ A )
% 15.48/8.49       => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 15.48/8.49         => ( ord_less_nat @ M @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1544_power__less__imp__less__exp,axiom,
% 15.48/8.49      ! [A: int,M: nat,N: nat] :
% 15.48/8.49        ( ( ord_less_int @ one_one_int @ A )
% 15.48/8.49       => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 15.48/8.49         => ( ord_less_nat @ M @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1545_power__strict__increasing,axiom,
% 15.48/8.49      ! [N: nat,N4: nat,A: real] :
% 15.48/8.49        ( ( ord_less_nat @ N @ N4 )
% 15.48/8.49       => ( ( ord_less_real @ one_one_real @ A )
% 15.48/8.49         => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1546_power__strict__increasing,axiom,
% 15.48/8.49      ! [N: nat,N4: nat,A: rat] :
% 15.48/8.49        ( ( ord_less_nat @ N @ N4 )
% 15.48/8.49       => ( ( ord_less_rat @ one_one_rat @ A )
% 15.48/8.49         => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1547_power__strict__increasing,axiom,
% 15.48/8.49      ! [N: nat,N4: nat,A: nat] :
% 15.48/8.49        ( ( ord_less_nat @ N @ N4 )
% 15.48/8.49       => ( ( ord_less_nat @ one_one_nat @ A )
% 15.48/8.49         => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1548_power__strict__increasing,axiom,
% 15.48/8.49      ! [N: nat,N4: nat,A: int] :
% 15.48/8.49        ( ( ord_less_nat @ N @ N4 )
% 15.48/8.49       => ( ( ord_less_int @ one_one_int @ A )
% 15.48/8.49         => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1549_power__increasing,axiom,
% 15.48/8.49      ! [N: nat,N4: nat,A: real] :
% 15.48/8.49        ( ( ord_less_eq_nat @ N @ N4 )
% 15.48/8.49       => ( ( ord_less_eq_real @ one_one_real @ A )
% 15.48/8.49         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1550_power__increasing,axiom,
% 15.48/8.49      ! [N: nat,N4: nat,A: rat] :
% 15.48/8.49        ( ( ord_less_eq_nat @ N @ N4 )
% 15.48/8.49       => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 15.48/8.49         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1551_power__increasing,axiom,
% 15.48/8.49      ! [N: nat,N4: nat,A: nat] :
% 15.48/8.49        ( ( ord_less_eq_nat @ N @ N4 )
% 15.48/8.49       => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 15.48/8.49         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1552_power__increasing,axiom,
% 15.48/8.49      ! [N: nat,N4: nat,A: int] :
% 15.48/8.49        ( ( ord_less_eq_nat @ N @ N4 )
% 15.48/8.49       => ( ( ord_less_eq_int @ one_one_int @ A )
% 15.48/8.49         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1553_real__arch__pow__inv,axiom,
% 15.48/8.49      ! [Y3: real,X3: real] :
% 15.48/8.49        ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.48/8.49       => ( ( ord_less_real @ X3 @ one_one_real )
% 15.48/8.49         => ? [N2: nat] : ( ord_less_real @ ( power_power_real @ X3 @ N2 ) @ Y3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1554_int__one__le__iff__zero__less,axiom,
% 15.48/8.49      ! [Z: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ one_one_int @ Z )
% 15.48/8.49        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1555_power__mono__odd,axiom,
% 15.48/8.49      ! [N: nat,A: real,B: real] :
% 15.48/8.49        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49       => ( ( ord_less_eq_real @ A @ B )
% 15.48/8.49         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1556_power__mono__odd,axiom,
% 15.48/8.49      ! [N: nat,A: rat,B: rat] :
% 15.48/8.49        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49       => ( ( ord_less_eq_rat @ A @ B )
% 15.48/8.49         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1557_power__mono__odd,axiom,
% 15.48/8.49      ! [N: nat,A: int,B: int] :
% 15.48/8.49        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49       => ( ( ord_less_eq_int @ A @ B )
% 15.48/8.49         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1558_odd__pos,axiom,
% 15.48/8.49      ! [N: nat] :
% 15.48/8.49        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1559_sqrt2__less__2,axiom,
% 15.48/8.49      ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1560_log2__of__power__eq,axiom,
% 15.48/8.49      ! [M: nat,N: nat] :
% 15.48/8.49        ( ( M
% 15.48/8.49          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.48/8.49       => ( ( semiri5074537144036343181t_real @ N )
% 15.48/8.49          = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1561_power__strict__decreasing,axiom,
% 15.48/8.49      ! [N: nat,N4: nat,A: real] :
% 15.48/8.49        ( ( ord_less_nat @ N @ N4 )
% 15.48/8.49       => ( ( ord_less_real @ zero_zero_real @ A )
% 15.48/8.49         => ( ( ord_less_real @ A @ one_one_real )
% 15.48/8.49           => ( ord_less_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1562_power__strict__decreasing,axiom,
% 15.48/8.49      ! [N: nat,N4: nat,A: rat] :
% 15.48/8.49        ( ( ord_less_nat @ N @ N4 )
% 15.48/8.49       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.48/8.49         => ( ( ord_less_rat @ A @ one_one_rat )
% 15.48/8.49           => ( ord_less_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1563_power__strict__decreasing,axiom,
% 15.48/8.49      ! [N: nat,N4: nat,A: nat] :
% 15.48/8.49        ( ( ord_less_nat @ N @ N4 )
% 15.48/8.49       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 15.48/8.49         => ( ( ord_less_nat @ A @ one_one_nat )
% 15.48/8.49           => ( ord_less_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1564_power__strict__decreasing,axiom,
% 15.48/8.49      ! [N: nat,N4: nat,A: int] :
% 15.48/8.49        ( ( ord_less_nat @ N @ N4 )
% 15.48/8.49       => ( ( ord_less_int @ zero_zero_int @ A )
% 15.48/8.49         => ( ( ord_less_int @ A @ one_one_int )
% 15.48/8.49           => ( ord_less_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1565_power__decreasing,axiom,
% 15.48/8.49      ! [N: nat,N4: nat,A: real] :
% 15.48/8.49        ( ( ord_less_eq_nat @ N @ N4 )
% 15.48/8.49       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.48/8.49         => ( ( ord_less_eq_real @ A @ one_one_real )
% 15.48/8.49           => ( ord_less_eq_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1566_power__decreasing,axiom,
% 15.48/8.49      ! [N: nat,N4: nat,A: rat] :
% 15.48/8.49        ( ( ord_less_eq_nat @ N @ N4 )
% 15.48/8.49       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.48/8.49         => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 15.48/8.49           => ( ord_less_eq_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1567_power__decreasing,axiom,
% 15.48/8.49      ! [N: nat,N4: nat,A: nat] :
% 15.48/8.49        ( ( ord_less_eq_nat @ N @ N4 )
% 15.48/8.49       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.48/8.49         => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 15.48/8.49           => ( ord_less_eq_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1568_power__decreasing,axiom,
% 15.48/8.49      ! [N: nat,N4: nat,A: int] :
% 15.48/8.49        ( ( ord_less_eq_nat @ N @ N4 )
% 15.48/8.49       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.48/8.49         => ( ( ord_less_eq_int @ A @ one_one_int )
% 15.48/8.49           => ( ord_less_eq_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1569_power__le__imp__le__exp,axiom,
% 15.48/8.49      ! [A: real,M: nat,N: nat] :
% 15.48/8.49        ( ( ord_less_real @ one_one_real @ A )
% 15.48/8.49       => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 15.48/8.49         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1570_power__le__imp__le__exp,axiom,
% 15.48/8.49      ! [A: rat,M: nat,N: nat] :
% 15.48/8.49        ( ( ord_less_rat @ one_one_rat @ A )
% 15.48/8.49       => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 15.48/8.49         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1571_power__le__imp__le__exp,axiom,
% 15.48/8.49      ! [A: nat,M: nat,N: nat] :
% 15.48/8.49        ( ( ord_less_nat @ one_one_nat @ A )
% 15.48/8.49       => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 15.48/8.49         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1572_power__le__imp__le__exp,axiom,
% 15.48/8.49      ! [A: int,M: nat,N: nat] :
% 15.48/8.49        ( ( ord_less_int @ one_one_int @ A )
% 15.48/8.49       => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 15.48/8.49         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1573_one__power2,axiom,
% 15.48/8.49      ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.49      = one_one_rat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1574_one__power2,axiom,
% 15.48/8.49      ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.49      = one_one_nat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1575_one__power2,axiom,
% 15.48/8.49      ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.49      = one_one_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1576_one__power2,axiom,
% 15.48/8.49      ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.49      = one_one_real ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1577_one__power2,axiom,
% 15.48/8.49      ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.49      = one_one_complex ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1578_self__le__power,axiom,
% 15.48/8.49      ! [A: real,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_real @ one_one_real @ A )
% 15.48/8.49       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.49         => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1579_self__le__power,axiom,
% 15.48/8.49      ! [A: rat,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 15.48/8.49       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.49         => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1580_self__le__power,axiom,
% 15.48/8.49      ! [A: nat,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 15.48/8.49       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.49         => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1581_self__le__power,axiom,
% 15.48/8.49      ! [A: int,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_int @ one_one_int @ A )
% 15.48/8.49       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.49         => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1582_one__less__power,axiom,
% 15.48/8.49      ! [A: real,N: nat] :
% 15.48/8.49        ( ( ord_less_real @ one_one_real @ A )
% 15.48/8.49       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.49         => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1583_one__less__power,axiom,
% 15.48/8.49      ! [A: rat,N: nat] :
% 15.48/8.49        ( ( ord_less_rat @ one_one_rat @ A )
% 15.48/8.49       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.49         => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1584_one__less__power,axiom,
% 15.48/8.49      ! [A: nat,N: nat] :
% 15.48/8.49        ( ( ord_less_nat @ one_one_nat @ A )
% 15.48/8.49       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.49         => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1585_one__less__power,axiom,
% 15.48/8.49      ! [A: int,N: nat] :
% 15.48/8.49        ( ( ord_less_int @ one_one_int @ A )
% 15.48/8.49       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.49         => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1586_zero__le__power__eq,axiom,
% 15.48/8.49      ! [A: real,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 15.48/8.49        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49            & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1587_zero__le__power__eq,axiom,
% 15.48/8.49      ! [A: rat,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 15.48/8.49        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49            & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1588_zero__le__power__eq,axiom,
% 15.48/8.49      ! [A: int,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 15.48/8.49        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49            & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1589_zero__le__odd__power,axiom,
% 15.48/8.49      ! [N: nat,A: real] :
% 15.48/8.49        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49       => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 15.48/8.49          = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1590_zero__le__odd__power,axiom,
% 15.48/8.49      ! [N: nat,A: rat] :
% 15.48/8.49        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49       => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 15.48/8.49          = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1591_zero__le__odd__power,axiom,
% 15.48/8.49      ! [N: nat,A: int] :
% 15.48/8.49        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49       => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 15.48/8.49          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1592_zero__le__even__power,axiom,
% 15.48/8.49      ! [N: nat,A: real] :
% 15.48/8.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49       => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1593_zero__le__even__power,axiom,
% 15.48/8.49      ! [N: nat,A: rat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1594_zero__le__even__power,axiom,
% 15.48/8.49      ! [N: nat,A: int] :
% 15.48/8.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49       => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1595_real__less__rsqrt,axiom,
% 15.48/8.49      ! [X3: real,Y3: real] :
% 15.48/8.49        ( ( ord_less_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y3 )
% 15.48/8.49       => ( ord_less_real @ X3 @ ( sqrt @ Y3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1596_sqrt__le__D,axiom,
% 15.48/8.49      ! [X3: real,Y3: real] :
% 15.48/8.49        ( ( ord_less_eq_real @ ( sqrt @ X3 ) @ Y3 )
% 15.48/8.49       => ( ord_less_eq_real @ X3 @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1597_real__le__rsqrt,axiom,
% 15.48/8.49      ! [X3: real,Y3: real] :
% 15.48/8.49        ( ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y3 )
% 15.48/8.49       => ( ord_less_eq_real @ X3 @ ( sqrt @ Y3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1598_take__bit__int__less__exp,axiom,
% 15.48/8.49      ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1599_zero__less__power__eq,axiom,
% 15.48/8.49      ! [A: real,N: nat] :
% 15.48/8.49        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 15.48/8.49        = ( ( N = zero_zero_nat )
% 15.48/8.49          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49            & ( A != zero_zero_real ) )
% 15.48/8.49          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49            & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1600_zero__less__power__eq,axiom,
% 15.48/8.49      ! [A: rat,N: nat] :
% 15.48/8.49        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 15.48/8.49        = ( ( N = zero_zero_nat )
% 15.48/8.49          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49            & ( A != zero_zero_rat ) )
% 15.48/8.49          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49            & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1601_zero__less__power__eq,axiom,
% 15.48/8.49      ! [A: int,N: nat] :
% 15.48/8.49        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 15.48/8.49        = ( ( N = zero_zero_nat )
% 15.48/8.49          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49            & ( A != zero_zero_int ) )
% 15.48/8.49          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49            & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1602_dvd__power__iff__le,axiom,
% 15.48/8.49      ! [K: nat,M: nat,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 15.48/8.49       => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 15.48/8.49          = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1603_two__realpow__ge__one,axiom,
% 15.48/8.49      ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1604_real__le__lsqrt,axiom,
% 15.48/8.49      ! [X3: real,Y3: real] :
% 15.48/8.49        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.48/8.49       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.48/8.49         => ( ( ord_less_eq_real @ X3 @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.48/8.49           => ( ord_less_eq_real @ ( sqrt @ X3 ) @ Y3 ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1605_real__sqrt__unique,axiom,
% 15.48/8.49      ! [Y3: real,X3: real] :
% 15.48/8.49        ( ( ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.48/8.49          = X3 )
% 15.48/8.49       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.48/8.49         => ( ( sqrt @ X3 )
% 15.48/8.49            = Y3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1606_less__log2__of__power,axiom,
% 15.48/8.49      ! [N: nat,M: nat] :
% 15.48/8.49        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 15.48/8.49       => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1607_le__log2__of__power,axiom,
% 15.48/8.49      ! [N: nat,M: nat] :
% 15.48/8.49        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 15.48/8.49       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1608_take__bit__int__greater__eq__self__iff,axiom,
% 15.48/8.49      ! [K: int,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 15.48/8.49        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1609_take__bit__int__less__self__iff,axiom,
% 15.48/8.49      ! [N: nat,K: int] :
% 15.48/8.49        ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 15.48/8.49        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1610_power__le__zero__eq,axiom,
% 15.48/8.49      ! [A: real,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 15.48/8.49        = ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.49          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49              & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 15.48/8.49            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49              & ( A = zero_zero_real ) ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1611_power__le__zero__eq,axiom,
% 15.48/8.49      ! [A: rat,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 15.48/8.49        = ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.49          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49              & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 15.48/8.49            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49              & ( A = zero_zero_rat ) ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1612_power__le__zero__eq,axiom,
% 15.48/8.49      ! [A: int,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 15.48/8.49        = ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.49          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49              & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 15.48/8.49            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49              & ( A = zero_zero_int ) ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1613_pow__divides__pow__iff,axiom,
% 15.48/8.49      ! [N: nat,A: nat,B: nat] :
% 15.48/8.49        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.49       => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 15.48/8.49          = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1614_pow__divides__pow__iff,axiom,
% 15.48/8.49      ! [N: nat,A: int,B: int] :
% 15.48/8.49        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.49       => ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 15.48/8.49          = ( dvd_dvd_int @ A @ B ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1615_arcosh__1,axiom,
% 15.48/8.49      ( ( arcosh_real @ one_one_real )
% 15.48/8.49      = zero_zero_real ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1616_dvd__0__left__iff,axiom,
% 15.48/8.49      ! [A: code_integer] :
% 15.48/8.49        ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 15.48/8.49        = ( A = zero_z3403309356797280102nteger ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1617_dvd__0__left__iff,axiom,
% 15.48/8.49      ! [A: real] :
% 15.48/8.49        ( ( dvd_dvd_real @ zero_zero_real @ A )
% 15.48/8.49        = ( A = zero_zero_real ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1618_dvd__0__left__iff,axiom,
% 15.48/8.49      ! [A: rat] :
% 15.48/8.49        ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 15.48/8.49        = ( A = zero_zero_rat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1619_dvd__0__left__iff,axiom,
% 15.48/8.49      ! [A: nat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 15.48/8.49        = ( A = zero_zero_nat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1620_dvd__0__left__iff,axiom,
% 15.48/8.49      ! [A: int] :
% 15.48/8.49        ( ( dvd_dvd_int @ zero_zero_int @ A )
% 15.48/8.49        = ( A = zero_zero_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1621_dvd__0__right,axiom,
% 15.48/8.49      ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ zero_z3403309356797280102nteger ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1622_dvd__0__right,axiom,
% 15.48/8.49      ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1623_dvd__0__right,axiom,
% 15.48/8.49      ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1624_dvd__0__right,axiom,
% 15.48/8.49      ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1625_dvd__0__right,axiom,
% 15.48/8.49      ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1626_artanh__0,axiom,
% 15.48/8.49      ( ( artanh_real @ zero_zero_real )
% 15.48/8.49      = zero_zero_real ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1627_arsinh__0,axiom,
% 15.48/8.49      ( ( arsinh_real @ zero_zero_real )
% 15.48/8.49      = zero_zero_real ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1628_of__nat__dvd__iff,axiom,
% 15.48/8.49      ! [M: nat,N: nat] :
% 15.48/8.49        ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 15.48/8.49        = ( dvd_dvd_nat @ M @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1629_of__nat__dvd__iff,axiom,
% 15.48/8.49      ! [M: nat,N: nat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 15.48/8.49        = ( dvd_dvd_nat @ M @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1630_of__nat__dvd__iff,axiom,
% 15.48/8.49      ! [M: nat,N: nat] :
% 15.48/8.49        ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 15.48/8.49        = ( dvd_dvd_nat @ M @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1631_log__ceil__idem,axiom,
% 15.48/8.49      ! [X3: real] :
% 15.48/8.49        ( ( ord_less_eq_real @ one_one_real @ X3 )
% 15.48/8.49       => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) )
% 15.48/8.49          = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X3 ) ) ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1632_dbl__simps_I3_J,axiom,
% 15.48/8.49      ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 15.48/8.49      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1633_dbl__simps_I3_J,axiom,
% 15.48/8.49      ( ( neg_numeral_dbl_real @ one_one_real )
% 15.48/8.49      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1634_dbl__simps_I3_J,axiom,
% 15.48/8.49      ( ( neg_numeral_dbl_rat @ one_one_rat )
% 15.48/8.49      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1635_dbl__simps_I3_J,axiom,
% 15.48/8.49      ( ( neg_numeral_dbl_int @ one_one_int )
% 15.48/8.49      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1636_dvd__pos__nat,axiom,
% 15.48/8.49      ! [N: nat,M: nat] :
% 15.48/8.49        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.49       => ( ( dvd_dvd_nat @ M @ N )
% 15.48/8.49         => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1637_not__is__unit__0,axiom,
% 15.48/8.49      ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1638_not__is__unit__0,axiom,
% 15.48/8.49      ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1639_not__is__unit__0,axiom,
% 15.48/8.49      ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1640_ceiling__of__int,axiom,
% 15.48/8.49      ! [Z: int] :
% 15.48/8.49        ( ( archim2889992004027027881ng_rat @ ( ring_1_of_int_rat @ Z ) )
% 15.48/8.49        = Z ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1641_ceiling__of__int,axiom,
% 15.48/8.49      ! [Z: int] :
% 15.48/8.49        ( ( archim7802044766580827645g_real @ ( ring_1_of_int_real @ Z ) )
% 15.48/8.49        = Z ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1642_of__int__ceiling__cancel,axiom,
% 15.48/8.49      ! [X3: rat] :
% 15.48/8.49        ( ( ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X3 ) )
% 15.48/8.49          = X3 )
% 15.48/8.49        = ( ? [N3: int] :
% 15.48/8.49              ( X3
% 15.48/8.49              = ( ring_1_of_int_rat @ N3 ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1643_of__int__ceiling__cancel,axiom,
% 15.48/8.49      ! [X3: real] :
% 15.48/8.49        ( ( ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X3 ) )
% 15.48/8.49          = X3 )
% 15.48/8.49        = ( ? [N3: int] :
% 15.48/8.49              ( X3
% 15.48/8.49              = ( ring_1_of_int_real @ N3 ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1644_dbl__simps_I2_J,axiom,
% 15.48/8.49      ( ( neg_numeral_dbl_real @ zero_zero_real )
% 15.48/8.49      = zero_zero_real ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1645_dbl__simps_I2_J,axiom,
% 15.48/8.49      ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 15.48/8.49      = zero_zero_rat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1646_dbl__simps_I2_J,axiom,
% 15.48/8.49      ( ( neg_numeral_dbl_int @ zero_zero_int )
% 15.48/8.49      = zero_zero_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1647_ceiling__zero,axiom,
% 15.48/8.49      ( ( archim2889992004027027881ng_rat @ zero_zero_rat )
% 15.48/8.49      = zero_zero_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1648_ceiling__zero,axiom,
% 15.48/8.49      ( ( archim7802044766580827645g_real @ zero_zero_real )
% 15.48/8.49      = zero_zero_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1649_ceiling__numeral,axiom,
% 15.48/8.49      ! [V: num] :
% 15.48/8.49        ( ( archim7802044766580827645g_real @ ( numeral_numeral_real @ V ) )
% 15.48/8.49        = ( numeral_numeral_int @ V ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1650_ceiling__numeral,axiom,
% 15.48/8.49      ! [V: num] :
% 15.48/8.49        ( ( archim2889992004027027881ng_rat @ ( numeral_numeral_rat @ V ) )
% 15.48/8.49        = ( numeral_numeral_int @ V ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1651_ceiling__one,axiom,
% 15.48/8.49      ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 15.48/8.49      = one_one_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1652_ceiling__one,axiom,
% 15.48/8.49      ( ( archim7802044766580827645g_real @ one_one_real )
% 15.48/8.49      = one_one_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1653_ceiling__of__nat,axiom,
% 15.48/8.49      ! [N: nat] :
% 15.48/8.49        ( ( archim7802044766580827645g_real @ ( semiri5074537144036343181t_real @ N ) )
% 15.48/8.49        = ( semiri1314217659103216013at_int @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1654_ceiling__of__nat,axiom,
% 15.48/8.49      ! [N: nat] :
% 15.48/8.49        ( ( archim2889992004027027881ng_rat @ ( semiri681578069525770553at_rat @ N ) )
% 15.48/8.49        = ( semiri1314217659103216013at_int @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1655_int__dvd__int__iff,axiom,
% 15.48/8.49      ! [M: nat,N: nat] :
% 15.48/8.49        ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 15.48/8.49        = ( dvd_dvd_nat @ M @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1656_dbl__simps_I5_J,axiom,
% 15.48/8.49      ! [K: num] :
% 15.48/8.49        ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 15.48/8.49        = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1657_dbl__simps_I5_J,axiom,
% 15.48/8.49      ! [K: num] :
% 15.48/8.49        ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 15.48/8.49        = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1658_dbl__simps_I5_J,axiom,
% 15.48/8.49      ! [K: num] :
% 15.48/8.49        ( ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) )
% 15.48/8.49        = ( numeral_numeral_rat @ ( bit0 @ K ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1659_dbl__simps_I5_J,axiom,
% 15.48/8.49      ! [K: num] :
% 15.48/8.49        ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 15.48/8.49        = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1660_ceiling__le__zero,axiom,
% 15.48/8.49      ! [X3: real] :
% 15.48/8.49        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X3 ) @ zero_zero_int )
% 15.48/8.49        = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1661_ceiling__le__zero,axiom,
% 15.48/8.49      ! [X3: rat] :
% 15.48/8.49        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X3 ) @ zero_zero_int )
% 15.48/8.49        = ( ord_less_eq_rat @ X3 @ zero_zero_rat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1662_zero__less__ceiling,axiom,
% 15.48/8.49      ! [X3: rat] :
% 15.48/8.49        ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X3 ) )
% 15.48/8.49        = ( ord_less_rat @ zero_zero_rat @ X3 ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1663_zero__less__ceiling,axiom,
% 15.48/8.49      ! [X3: real] :
% 15.48/8.49        ( ( ord_less_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X3 ) )
% 15.48/8.49        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1664_ceiling__le__numeral,axiom,
% 15.48/8.49      ! [X3: real,V: num] :
% 15.48/8.49        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X3 ) @ ( numeral_numeral_int @ V ) )
% 15.48/8.49        = ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ V ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1665_ceiling__le__numeral,axiom,
% 15.48/8.49      ! [X3: rat,V: num] :
% 15.48/8.49        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X3 ) @ ( numeral_numeral_int @ V ) )
% 15.48/8.49        = ( ord_less_eq_rat @ X3 @ ( numeral_numeral_rat @ V ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1666_ceiling__less__one,axiom,
% 15.48/8.49      ! [X3: real] :
% 15.48/8.49        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X3 ) @ one_one_int )
% 15.48/8.49        = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1667_ceiling__less__one,axiom,
% 15.48/8.49      ! [X3: rat] :
% 15.48/8.49        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X3 ) @ one_one_int )
% 15.48/8.49        = ( ord_less_eq_rat @ X3 @ zero_zero_rat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1668_numeral__less__ceiling,axiom,
% 15.48/8.49      ! [V: num,X3: real] :
% 15.48/8.49        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X3 ) )
% 15.48/8.49        = ( ord_less_real @ ( numeral_numeral_real @ V ) @ X3 ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1669_numeral__less__ceiling,axiom,
% 15.48/8.49      ! [V: num,X3: rat] :
% 15.48/8.49        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X3 ) )
% 15.48/8.49        = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X3 ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1670_one__le__ceiling,axiom,
% 15.48/8.49      ! [X3: rat] :
% 15.48/8.49        ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X3 ) )
% 15.48/8.49        = ( ord_less_rat @ zero_zero_rat @ X3 ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1671_one__le__ceiling,axiom,
% 15.48/8.49      ! [X3: real] :
% 15.48/8.49        ( ( ord_less_eq_int @ one_one_int @ ( archim7802044766580827645g_real @ X3 ) )
% 15.48/8.49        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1672_ceiling__le__one,axiom,
% 15.48/8.49      ! [X3: real] :
% 15.48/8.49        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X3 ) @ one_one_int )
% 15.48/8.49        = ( ord_less_eq_real @ X3 @ one_one_real ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1673_ceiling__le__one,axiom,
% 15.48/8.49      ! [X3: rat] :
% 15.48/8.49        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X3 ) @ one_one_int )
% 15.48/8.49        = ( ord_less_eq_rat @ X3 @ one_one_rat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1674_one__less__ceiling,axiom,
% 15.48/8.49      ! [X3: rat] :
% 15.48/8.49        ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X3 ) )
% 15.48/8.49        = ( ord_less_rat @ one_one_rat @ X3 ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1675_one__less__ceiling,axiom,
% 15.48/8.49      ! [X3: real] :
% 15.48/8.49        ( ( ord_less_int @ one_one_int @ ( archim7802044766580827645g_real @ X3 ) )
% 15.48/8.49        = ( ord_less_real @ one_one_real @ X3 ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1676_ceiling__numeral__power,axiom,
% 15.48/8.49      ! [X3: num,N: nat] :
% 15.48/8.49        ( ( archim7802044766580827645g_real @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N ) )
% 15.48/8.49        = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1677_ceiling__numeral__power,axiom,
% 15.48/8.49      ! [X3: num,N: nat] :
% 15.48/8.49        ( ( archim2889992004027027881ng_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N ) )
% 15.48/8.49        = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1678_nat__ceiling__le__eq,axiom,
% 15.48/8.49      ! [X3: real,A: nat] :
% 15.48/8.49        ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X3 ) ) @ A )
% 15.48/8.49        = ( ord_less_eq_real @ X3 @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1679_take__bit__nat__less__eq__self,axiom,
% 15.48/8.49      ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1680_take__bit__tightened__less__eq__nat,axiom,
% 15.48/8.49      ! [M: nat,N: nat,Q3: nat] :
% 15.48/8.49        ( ( ord_less_eq_nat @ M @ N )
% 15.48/8.49       => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q3 ) @ ( bit_se2925701944663578781it_nat @ N @ Q3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1681_ceiling__mono,axiom,
% 15.48/8.49      ! [Y3: real,X3: real] :
% 15.48/8.49        ( ( ord_less_eq_real @ Y3 @ X3 )
% 15.48/8.49       => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ Y3 ) @ ( archim7802044766580827645g_real @ X3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1682_ceiling__mono,axiom,
% 15.48/8.49      ! [Y3: rat,X3: rat] :
% 15.48/8.49        ( ( ord_less_eq_rat @ Y3 @ X3 )
% 15.48/8.49       => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ Y3 ) @ ( archim2889992004027027881ng_rat @ X3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1683_le__of__int__ceiling,axiom,
% 15.48/8.49      ! [X3: real] : ( ord_less_eq_real @ X3 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1684_le__of__int__ceiling,axiom,
% 15.48/8.49      ! [X3: rat] : ( ord_less_eq_rat @ X3 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1685_ceiling__less__cancel,axiom,
% 15.48/8.49      ! [X3: rat,Y3: rat] :
% 15.48/8.49        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X3 ) @ ( archim2889992004027027881ng_rat @ Y3 ) )
% 15.48/8.49       => ( ord_less_rat @ X3 @ Y3 ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1686_ceiling__less__cancel,axiom,
% 15.48/8.49      ! [X3: real,Y3: real] :
% 15.48/8.49        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X3 ) @ ( archim7802044766580827645g_real @ Y3 ) )
% 15.48/8.49       => ( ord_less_real @ X3 @ Y3 ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1687_zdvd__antisym__nonneg,axiom,
% 15.48/8.49      ! [M: int,N: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ zero_zero_int @ M )
% 15.48/8.49       => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 15.48/8.49         => ( ( dvd_dvd_int @ M @ N )
% 15.48/8.49           => ( ( dvd_dvd_int @ N @ M )
% 15.48/8.49             => ( M = N ) ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1688_zdvd__not__zless,axiom,
% 15.48/8.49      ! [M: int,N: int] :
% 15.48/8.49        ( ( ord_less_int @ zero_zero_int @ M )
% 15.48/8.49       => ( ( ord_less_int @ M @ N )
% 15.48/8.49         => ~ ( dvd_dvd_int @ N @ M ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1689_real__nat__ceiling__ge,axiom,
% 15.48/8.49      ! [X3: real] : ( ord_less_eq_real @ X3 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X3 ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1690_of__nat__ceiling,axiom,
% 15.48/8.49      ! [R2: real] : ( ord_less_eq_real @ R2 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ R2 ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1691_of__nat__ceiling,axiom,
% 15.48/8.49      ! [R2: rat] : ( ord_less_eq_rat @ R2 @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim2889992004027027881ng_rat @ R2 ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1692_ceiling__le,axiom,
% 15.48/8.49      ! [X3: real,A: int] :
% 15.48/8.49        ( ( ord_less_eq_real @ X3 @ ( ring_1_of_int_real @ A ) )
% 15.48/8.49       => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X3 ) @ A ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1693_ceiling__le,axiom,
% 15.48/8.49      ! [X3: rat,A: int] :
% 15.48/8.49        ( ( ord_less_eq_rat @ X3 @ ( ring_1_of_int_rat @ A ) )
% 15.48/8.49       => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X3 ) @ A ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1694_ceiling__le__iff,axiom,
% 15.48/8.49      ! [X3: real,Z: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X3 ) @ Z )
% 15.48/8.49        = ( ord_less_eq_real @ X3 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1695_ceiling__le__iff,axiom,
% 15.48/8.49      ! [X3: rat,Z: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X3 ) @ Z )
% 15.48/8.49        = ( ord_less_eq_rat @ X3 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1696_less__ceiling__iff,axiom,
% 15.48/8.49      ! [Z: int,X3: rat] :
% 15.48/8.49        ( ( ord_less_int @ Z @ ( archim2889992004027027881ng_rat @ X3 ) )
% 15.48/8.49        = ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ X3 ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1697_less__ceiling__iff,axiom,
% 15.48/8.49      ! [Z: int,X3: real] :
% 15.48/8.49        ( ( ord_less_int @ Z @ ( archim7802044766580827645g_real @ X3 ) )
% 15.48/8.49        = ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ X3 ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1698_or__nat__def,axiom,
% 15.48/8.49      ( bit_se1412395901928357646or_nat
% 15.48/8.49      = ( ^ [M3: nat,N3: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1699_zdvd__imp__le,axiom,
% 15.48/8.49      ! [Z: int,N: int] :
% 15.48/8.49        ( ( dvd_dvd_int @ Z @ N )
% 15.48/8.49       => ( ( ord_less_int @ zero_zero_int @ N )
% 15.48/8.49         => ( ord_less_eq_int @ Z @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1700_linorder__neqE__linordered__idom,axiom,
% 15.48/8.49      ! [X3: real,Y3: real] :
% 15.48/8.49        ( ( X3 != Y3 )
% 15.48/8.49       => ( ~ ( ord_less_real @ X3 @ Y3 )
% 15.48/8.49         => ( ord_less_real @ Y3 @ X3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1701_linorder__neqE__linordered__idom,axiom,
% 15.48/8.49      ! [X3: rat,Y3: rat] :
% 15.48/8.49        ( ( X3 != Y3 )
% 15.48/8.49       => ( ~ ( ord_less_rat @ X3 @ Y3 )
% 15.48/8.49         => ( ord_less_rat @ Y3 @ X3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1702_linorder__neqE__linordered__idom,axiom,
% 15.48/8.49      ! [X3: int,Y3: int] :
% 15.48/8.49        ( ( X3 != Y3 )
% 15.48/8.49       => ( ~ ( ord_less_int @ X3 @ Y3 )
% 15.48/8.49         => ( ord_less_int @ Y3 @ X3 ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1703_xor__nat__def,axiom,
% 15.48/8.49      ( bit_se6528837805403552850or_nat
% 15.48/8.49      = ( ^ [M3: nat,N3: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1704_take__bit__nat__eq,axiom,
% 15.48/8.49      ! [K: int,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 15.48/8.49       => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 15.48/8.49          = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1705_nat__take__bit__eq,axiom,
% 15.48/8.49      ! [K: int,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 15.48/8.49       => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 15.48/8.49          = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1706_take__bit__nat__eq__self__iff,axiom,
% 15.48/8.49      ! [N: nat,M: nat] :
% 15.48/8.49        ( ( ( bit_se2925701944663578781it_nat @ N @ M )
% 15.48/8.49          = M )
% 15.48/8.49        = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1707_take__bit__nat__less__exp,axiom,
% 15.48/8.49      ! [N: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1708_take__bit__nat__eq__self,axiom,
% 15.48/8.49      ! [M: nat,N: nat] :
% 15.48/8.49        ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.48/8.49       => ( ( bit_se2925701944663578781it_nat @ N @ M )
% 15.48/8.49          = M ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1709_take__bit__nat__less__self__iff,axiom,
% 15.48/8.49      ! [N: nat,M: nat] :
% 15.48/8.49        ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 15.48/8.49        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1710_nat__dvd__iff,axiom,
% 15.48/8.49      ! [Z: int,M: nat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ ( nat2 @ Z ) @ M )
% 15.48/8.49        = ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 15.48/8.49           => ( dvd_dvd_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) )
% 15.48/8.49          & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 15.48/8.49           => ( M = zero_zero_nat ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1711_zero__neq__one,axiom,
% 15.48/8.49      zero_zero_complex != one_one_complex ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1712_zero__neq__one,axiom,
% 15.48/8.49      zero_zero_real != one_one_real ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1713_zero__neq__one,axiom,
% 15.48/8.49      zero_zero_rat != one_one_rat ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1714_zero__neq__one,axiom,
% 15.48/8.49      zero_zero_nat != one_one_nat ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1715_zero__neq__one,axiom,
% 15.48/8.49      zero_zero_int != one_one_int ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1716_dvd__0__left,axiom,
% 15.48/8.49      ! [A: code_integer] :
% 15.48/8.49        ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 15.48/8.49       => ( A = zero_z3403309356797280102nteger ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1717_dvd__0__left,axiom,
% 15.48/8.49      ! [A: real] :
% 15.48/8.49        ( ( dvd_dvd_real @ zero_zero_real @ A )
% 15.48/8.49       => ( A = zero_zero_real ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1718_dvd__0__left,axiom,
% 15.48/8.49      ! [A: rat] :
% 15.48/8.49        ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 15.48/8.49       => ( A = zero_zero_rat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1719_dvd__0__left,axiom,
% 15.48/8.49      ! [A: nat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 15.48/8.49       => ( A = zero_zero_nat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1720_dvd__0__left,axiom,
% 15.48/8.49      ! [A: int] :
% 15.48/8.49        ( ( dvd_dvd_int @ zero_zero_int @ A )
% 15.48/8.49       => ( A = zero_zero_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1721_gcd__nat_Oextremum__uniqueI,axiom,
% 15.48/8.49      ! [A: nat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 15.48/8.49       => ( A = zero_zero_nat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1722_gcd__nat_Onot__eq__extremum,axiom,
% 15.48/8.49      ! [A: nat] :
% 15.48/8.49        ( ( A != zero_zero_nat )
% 15.48/8.49        = ( ( dvd_dvd_nat @ A @ zero_zero_nat )
% 15.48/8.49          & ( A != zero_zero_nat ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1723_gcd__nat_Oextremum__unique,axiom,
% 15.48/8.49      ! [A: nat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 15.48/8.49        = ( A = zero_zero_nat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1724_gcd__nat_Oextremum__strict,axiom,
% 15.48/8.49      ! [A: nat] :
% 15.48/8.49        ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 15.48/8.49          & ( zero_zero_nat != A ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1725_gcd__nat_Oextremum,axiom,
% 15.48/8.49      ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1726_even__nat__iff,axiom,
% 15.48/8.49      ! [K: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 15.48/8.49       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 15.48/8.49          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1727_not__one__le__zero,axiom,
% 15.48/8.49      ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1728_not__one__le__zero,axiom,
% 15.48/8.49      ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1729_not__one__le__zero,axiom,
% 15.48/8.49      ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1730_not__one__le__zero,axiom,
% 15.48/8.49      ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1731_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 15.48/8.49      ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1732_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 15.48/8.49      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1733_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 15.48/8.49      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1734_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 15.48/8.49      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1735_zero__less__one__class_Ozero__le__one,axiom,
% 15.48/8.49      ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1736_zero__less__one__class_Ozero__le__one,axiom,
% 15.48/8.49      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1737_zero__less__one__class_Ozero__le__one,axiom,
% 15.48/8.49      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1738_zero__less__one__class_Ozero__le__one,axiom,
% 15.48/8.49      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1739_not__one__less__zero,axiom,
% 15.48/8.49      ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1740_not__one__less__zero,axiom,
% 15.48/8.49      ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1741_not__one__less__zero,axiom,
% 15.48/8.49      ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1742_not__one__less__zero,axiom,
% 15.48/8.49      ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1743_zero__less__one,axiom,
% 15.48/8.49      ord_less_real @ zero_zero_real @ one_one_real ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1744_zero__less__one,axiom,
% 15.48/8.49      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1745_zero__less__one,axiom,
% 15.48/8.49      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1746_zero__less__one,axiom,
% 15.48/8.49      ord_less_int @ zero_zero_int @ one_one_int ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1747_even__unset__bit__iff,axiom,
% 15.48/8.49      ! [M: nat,A: code_integer] :
% 15.48/8.49        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 15.48/8.49        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.48/8.49          | ( M = zero_zero_nat ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1748_even__unset__bit__iff,axiom,
% 15.48/8.49      ! [M: nat,A: int] :
% 15.48/8.49        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 15.48/8.49        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.48/8.49          | ( M = zero_zero_nat ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1749_even__unset__bit__iff,axiom,
% 15.48/8.49      ! [M: nat,A: nat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 15.48/8.49        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.48/8.49          | ( M = zero_zero_nat ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1750_even__flip__bit__iff,axiom,
% 15.48/8.49      ! [M: nat,A: code_integer] :
% 15.48/8.49        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 15.48/8.49        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.48/8.49         != ( M = zero_zero_nat ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1751_even__flip__bit__iff,axiom,
% 15.48/8.49      ! [M: nat,A: int] :
% 15.48/8.49        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 15.48/8.49        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.48/8.49         != ( M = zero_zero_nat ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1752_even__flip__bit__iff,axiom,
% 15.48/8.49      ! [M: nat,A: nat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 15.48/8.49        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.48/8.49         != ( M = zero_zero_nat ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1753_even__set__bit__iff,axiom,
% 15.48/8.49      ! [M: nat,A: code_integer] :
% 15.48/8.49        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 15.48/8.49        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.48/8.49          & ( M != zero_zero_nat ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1754_even__set__bit__iff,axiom,
% 15.48/8.49      ! [M: nat,A: int] :
% 15.48/8.49        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 15.48/8.49        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.48/8.49          & ( M != zero_zero_nat ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1755_even__set__bit__iff,axiom,
% 15.48/8.49      ! [M: nat,A: nat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 15.48/8.49        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.48/8.49          & ( M != zero_zero_nat ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1756_take__bit__int__greater__eq,axiom,
% 15.48/8.49      ! [K: int,N: nat] :
% 15.48/8.49        ( ( ord_less_int @ K @ zero_zero_int )
% 15.48/8.49       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1757_ln__one,axiom,
% 15.48/8.49      ( ( ln_ln_real @ one_one_real )
% 15.48/8.49      = zero_zero_real ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1758_take__bit__int__less__eq,axiom,
% 15.48/8.49      ! [N: nat,K: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 15.48/8.49       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.48/8.49         => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1759_semiring__parity__class_Oeven__mask__iff,axiom,
% 15.48/8.49      ! [N: nat] :
% 15.48/8.49        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 15.48/8.49        = ( N = zero_zero_nat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1760_semiring__parity__class_Oeven__mask__iff,axiom,
% 15.48/8.49      ! [N: nat] :
% 15.48/8.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 15.48/8.49        = ( N = zero_zero_nat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1761_semiring__parity__class_Oeven__mask__iff,axiom,
% 15.48/8.49      ! [N: nat] :
% 15.48/8.49        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 15.48/8.49        = ( N = zero_zero_nat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1762_real__sqrt__power__even,axiom,
% 15.48/8.49      ! [N: nat,X3: real] :
% 15.48/8.49        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.48/8.49       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.48/8.49         => ( ( power_power_real @ ( sqrt @ X3 ) @ N )
% 15.48/8.49            = ( power_power_real @ X3 @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1763_arsinh__real__aux,axiom,
% 15.48/8.49      ! [X3: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X3 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1764_numeral__le__ceiling,axiom,
% 15.48/8.49      ! [V: num,X3: real] :
% 15.48/8.49        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X3 ) )
% 15.48/8.49        = ( ord_less_real @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X3 ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1765_numeral__le__ceiling,axiom,
% 15.48/8.49      ! [V: num,X3: rat] :
% 15.48/8.49        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X3 ) )
% 15.48/8.49        = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X3 ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1766_add__left__cancel,axiom,
% 15.48/8.49      ! [A: real,B: real,C: real] :
% 15.48/8.49        ( ( ( plus_plus_real @ A @ B )
% 15.48/8.49          = ( plus_plus_real @ A @ C ) )
% 15.48/8.49        = ( B = C ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1767_add__left__cancel,axiom,
% 15.48/8.49      ! [A: rat,B: rat,C: rat] :
% 15.48/8.49        ( ( ( plus_plus_rat @ A @ B )
% 15.48/8.49          = ( plus_plus_rat @ A @ C ) )
% 15.48/8.49        = ( B = C ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1768_add__left__cancel,axiom,
% 15.48/8.49      ! [A: nat,B: nat,C: nat] :
% 15.48/8.49        ( ( ( plus_plus_nat @ A @ B )
% 15.48/8.49          = ( plus_plus_nat @ A @ C ) )
% 15.48/8.49        = ( B = C ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1769_add__left__cancel,axiom,
% 15.48/8.49      ! [A: int,B: int,C: int] :
% 15.48/8.49        ( ( ( plus_plus_int @ A @ B )
% 15.48/8.49          = ( plus_plus_int @ A @ C ) )
% 15.48/8.49        = ( B = C ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1770_add__right__cancel,axiom,
% 15.48/8.49      ! [B: real,A: real,C: real] :
% 15.48/8.49        ( ( ( plus_plus_real @ B @ A )
% 15.48/8.49          = ( plus_plus_real @ C @ A ) )
% 15.48/8.49        = ( B = C ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1771_add__right__cancel,axiom,
% 15.48/8.49      ! [B: rat,A: rat,C: rat] :
% 15.48/8.49        ( ( ( plus_plus_rat @ B @ A )
% 15.48/8.49          = ( plus_plus_rat @ C @ A ) )
% 15.48/8.49        = ( B = C ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1772_add__right__cancel,axiom,
% 15.48/8.49      ! [B: nat,A: nat,C: nat] :
% 15.48/8.49        ( ( ( plus_plus_nat @ B @ A )
% 15.48/8.49          = ( plus_plus_nat @ C @ A ) )
% 15.48/8.49        = ( B = C ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1773_add__right__cancel,axiom,
% 15.48/8.49      ! [B: int,A: int,C: int] :
% 15.48/8.49        ( ( ( plus_plus_int @ B @ A )
% 15.48/8.49          = ( plus_plus_int @ C @ A ) )
% 15.48/8.49        = ( B = C ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1774_diff__self__eq__0,axiom,
% 15.48/8.49      ! [M: nat] :
% 15.48/8.49        ( ( minus_minus_nat @ M @ M )
% 15.48/8.49        = zero_zero_nat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1775_diff__0__eq__0,axiom,
% 15.48/8.49      ! [N: nat] :
% 15.48/8.49        ( ( minus_minus_nat @ zero_zero_nat @ N )
% 15.48/8.49        = zero_zero_nat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1776_diff__diff__cancel,axiom,
% 15.48/8.49      ! [I: nat,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_nat @ I @ N )
% 15.48/8.49       => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 15.48/8.49          = I ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1777_idiff__0__right,axiom,
% 15.48/8.49      ! [N: extended_enat] :
% 15.48/8.49        ( ( minus_3235023915231533773d_enat @ N @ zero_z5237406670263579293d_enat )
% 15.48/8.49        = N ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1778_idiff__0,axiom,
% 15.48/8.49      ! [N: extended_enat] :
% 15.48/8.49        ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N )
% 15.48/8.49        = zero_z5237406670263579293d_enat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1779_power__minus__is__div,axiom,
% 15.48/8.49      ! [B: nat,A: nat] :
% 15.48/8.49        ( ( ord_less_eq_nat @ B @ A )
% 15.48/8.49       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B ) )
% 15.48/8.49          = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1780_add__le__cancel__right,axiom,
% 15.48/8.49      ! [A: real,C: real,B: real] :
% 15.48/8.49        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 15.48/8.49        = ( ord_less_eq_real @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1781_add__le__cancel__right,axiom,
% 15.48/8.49      ! [A: rat,C: rat,B: rat] :
% 15.48/8.49        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 15.48/8.49        = ( ord_less_eq_rat @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1782_add__le__cancel__right,axiom,
% 15.48/8.49      ! [A: nat,C: nat,B: nat] :
% 15.48/8.49        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 15.48/8.49        = ( ord_less_eq_nat @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1783_add__le__cancel__right,axiom,
% 15.48/8.49      ! [A: int,C: int,B: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 15.48/8.49        = ( ord_less_eq_int @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1784_add__le__cancel__left,axiom,
% 15.48/8.49      ! [C: real,A: real,B: real] :
% 15.48/8.49        ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 15.48/8.49        = ( ord_less_eq_real @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1785_add__le__cancel__left,axiom,
% 15.48/8.49      ! [C: rat,A: rat,B: rat] :
% 15.48/8.49        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 15.48/8.49        = ( ord_less_eq_rat @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1786_add__le__cancel__left,axiom,
% 15.48/8.49      ! [C: nat,A: nat,B: nat] :
% 15.48/8.49        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 15.48/8.49        = ( ord_less_eq_nat @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1787_add__le__cancel__left,axiom,
% 15.48/8.49      ! [C: int,A: int,B: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 15.48/8.49        = ( ord_less_eq_int @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1788_double__eq__0__iff,axiom,
% 15.48/8.49      ! [A: real] :
% 15.48/8.49        ( ( ( plus_plus_real @ A @ A )
% 15.48/8.49          = zero_zero_real )
% 15.48/8.49        = ( A = zero_zero_real ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1789_double__eq__0__iff,axiom,
% 15.48/8.49      ! [A: rat] :
% 15.48/8.49        ( ( ( plus_plus_rat @ A @ A )
% 15.48/8.49          = zero_zero_rat )
% 15.48/8.49        = ( A = zero_zero_rat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1790_double__eq__0__iff,axiom,
% 15.48/8.49      ! [A: int] :
% 15.48/8.49        ( ( ( plus_plus_int @ A @ A )
% 15.48/8.49          = zero_zero_int )
% 15.48/8.49        = ( A = zero_zero_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1791_add__0,axiom,
% 15.48/8.49      ! [A: literal] :
% 15.48/8.49        ( ( plus_plus_literal @ zero_zero_literal @ A )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1792_add__0,axiom,
% 15.48/8.49      ! [A: real] :
% 15.48/8.49        ( ( plus_plus_real @ zero_zero_real @ A )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1793_add__0,axiom,
% 15.48/8.49      ! [A: rat] :
% 15.48/8.49        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1794_add__0,axiom,
% 15.48/8.49      ! [A: nat] :
% 15.48/8.49        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1795_add__0,axiom,
% 15.48/8.49      ! [A: int] :
% 15.48/8.49        ( ( plus_plus_int @ zero_zero_int @ A )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1796_zero__eq__add__iff__both__eq__0,axiom,
% 15.48/8.49      ! [X3: nat,Y3: nat] :
% 15.48/8.49        ( ( zero_zero_nat
% 15.48/8.49          = ( plus_plus_nat @ X3 @ Y3 ) )
% 15.48/8.49        = ( ( X3 = zero_zero_nat )
% 15.48/8.49          & ( Y3 = zero_zero_nat ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1797_add__eq__0__iff__both__eq__0,axiom,
% 15.48/8.49      ! [X3: nat,Y3: nat] :
% 15.48/8.49        ( ( ( plus_plus_nat @ X3 @ Y3 )
% 15.48/8.49          = zero_zero_nat )
% 15.48/8.49        = ( ( X3 = zero_zero_nat )
% 15.48/8.49          & ( Y3 = zero_zero_nat ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1798_add__cancel__right__right,axiom,
% 15.48/8.49      ! [A: real,B: real] :
% 15.48/8.49        ( ( A
% 15.48/8.49          = ( plus_plus_real @ A @ B ) )
% 15.48/8.49        = ( B = zero_zero_real ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1799_add__cancel__right__right,axiom,
% 15.48/8.49      ! [A: rat,B: rat] :
% 15.48/8.49        ( ( A
% 15.48/8.49          = ( plus_plus_rat @ A @ B ) )
% 15.48/8.49        = ( B = zero_zero_rat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1800_add__cancel__right__right,axiom,
% 15.48/8.49      ! [A: nat,B: nat] :
% 15.48/8.49        ( ( A
% 15.48/8.49          = ( plus_plus_nat @ A @ B ) )
% 15.48/8.49        = ( B = zero_zero_nat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1801_add__cancel__right__right,axiom,
% 15.48/8.49      ! [A: int,B: int] :
% 15.48/8.49        ( ( A
% 15.48/8.49          = ( plus_plus_int @ A @ B ) )
% 15.48/8.49        = ( B = zero_zero_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1802_add__cancel__right__left,axiom,
% 15.48/8.49      ! [A: real,B: real] :
% 15.48/8.49        ( ( A
% 15.48/8.49          = ( plus_plus_real @ B @ A ) )
% 15.48/8.49        = ( B = zero_zero_real ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1803_add__cancel__right__left,axiom,
% 15.48/8.49      ! [A: rat,B: rat] :
% 15.48/8.49        ( ( A
% 15.48/8.49          = ( plus_plus_rat @ B @ A ) )
% 15.48/8.49        = ( B = zero_zero_rat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1804_add__cancel__right__left,axiom,
% 15.48/8.49      ! [A: nat,B: nat] :
% 15.48/8.49        ( ( A
% 15.48/8.49          = ( plus_plus_nat @ B @ A ) )
% 15.48/8.49        = ( B = zero_zero_nat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1805_add__cancel__right__left,axiom,
% 15.48/8.49      ! [A: int,B: int] :
% 15.48/8.49        ( ( A
% 15.48/8.49          = ( plus_plus_int @ B @ A ) )
% 15.48/8.49        = ( B = zero_zero_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1806_add__cancel__left__right,axiom,
% 15.48/8.49      ! [A: real,B: real] :
% 15.48/8.49        ( ( ( plus_plus_real @ A @ B )
% 15.48/8.49          = A )
% 15.48/8.49        = ( B = zero_zero_real ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1807_add__cancel__left__right,axiom,
% 15.48/8.49      ! [A: rat,B: rat] :
% 15.48/8.49        ( ( ( plus_plus_rat @ A @ B )
% 15.48/8.49          = A )
% 15.48/8.49        = ( B = zero_zero_rat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1808_add__cancel__left__right,axiom,
% 15.48/8.49      ! [A: nat,B: nat] :
% 15.48/8.49        ( ( ( plus_plus_nat @ A @ B )
% 15.48/8.49          = A )
% 15.48/8.49        = ( B = zero_zero_nat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1809_add__cancel__left__right,axiom,
% 15.48/8.49      ! [A: int,B: int] :
% 15.48/8.49        ( ( ( plus_plus_int @ A @ B )
% 15.48/8.49          = A )
% 15.48/8.49        = ( B = zero_zero_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1810_add__cancel__left__left,axiom,
% 15.48/8.49      ! [B: real,A: real] :
% 15.48/8.49        ( ( ( plus_plus_real @ B @ A )
% 15.48/8.49          = A )
% 15.48/8.49        = ( B = zero_zero_real ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1811_add__cancel__left__left,axiom,
% 15.48/8.49      ! [B: rat,A: rat] :
% 15.48/8.49        ( ( ( plus_plus_rat @ B @ A )
% 15.48/8.49          = A )
% 15.48/8.49        = ( B = zero_zero_rat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1812_add__cancel__left__left,axiom,
% 15.48/8.49      ! [B: nat,A: nat] :
% 15.48/8.49        ( ( ( plus_plus_nat @ B @ A )
% 15.48/8.49          = A )
% 15.48/8.49        = ( B = zero_zero_nat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1813_add__cancel__left__left,axiom,
% 15.48/8.49      ! [B: int,A: int] :
% 15.48/8.49        ( ( ( plus_plus_int @ B @ A )
% 15.48/8.49          = A )
% 15.48/8.49        = ( B = zero_zero_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1814_double__zero__sym,axiom,
% 15.48/8.49      ! [A: real] :
% 15.48/8.49        ( ( zero_zero_real
% 15.48/8.49          = ( plus_plus_real @ A @ A ) )
% 15.48/8.49        = ( A = zero_zero_real ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1815_double__zero__sym,axiom,
% 15.48/8.49      ! [A: rat] :
% 15.48/8.49        ( ( zero_zero_rat
% 15.48/8.49          = ( plus_plus_rat @ A @ A ) )
% 15.48/8.49        = ( A = zero_zero_rat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1816_double__zero__sym,axiom,
% 15.48/8.49      ! [A: int] :
% 15.48/8.49        ( ( zero_zero_int
% 15.48/8.49          = ( plus_plus_int @ A @ A ) )
% 15.48/8.49        = ( A = zero_zero_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1817_add_Oright__neutral,axiom,
% 15.48/8.49      ! [A: literal] :
% 15.48/8.49        ( ( plus_plus_literal @ A @ zero_zero_literal )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1818_add_Oright__neutral,axiom,
% 15.48/8.49      ! [A: real] :
% 15.48/8.49        ( ( plus_plus_real @ A @ zero_zero_real )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1819_add_Oright__neutral,axiom,
% 15.48/8.49      ! [A: rat] :
% 15.48/8.49        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1820_add_Oright__neutral,axiom,
% 15.48/8.49      ! [A: nat] :
% 15.48/8.49        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1821_add_Oright__neutral,axiom,
% 15.48/8.49      ! [A: int] :
% 15.48/8.49        ( ( plus_plus_int @ A @ zero_zero_int )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1822_add__less__cancel__left,axiom,
% 15.48/8.49      ! [C: real,A: real,B: real] :
% 15.48/8.49        ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 15.48/8.49        = ( ord_less_real @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1823_add__less__cancel__left,axiom,
% 15.48/8.49      ! [C: rat,A: rat,B: rat] :
% 15.48/8.49        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 15.48/8.49        = ( ord_less_rat @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1824_add__less__cancel__left,axiom,
% 15.48/8.49      ! [C: nat,A: nat,B: nat] :
% 15.48/8.49        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 15.48/8.49        = ( ord_less_nat @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1825_add__less__cancel__left,axiom,
% 15.48/8.49      ! [C: int,A: int,B: int] :
% 15.48/8.49        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 15.48/8.49        = ( ord_less_int @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1826_add__less__cancel__right,axiom,
% 15.48/8.49      ! [A: real,C: real,B: real] :
% 15.48/8.49        ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 15.48/8.49        = ( ord_less_real @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1827_add__less__cancel__right,axiom,
% 15.48/8.49      ! [A: rat,C: rat,B: rat] :
% 15.48/8.49        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 15.48/8.49        = ( ord_less_rat @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1828_add__less__cancel__right,axiom,
% 15.48/8.49      ! [A: nat,C: nat,B: nat] :
% 15.48/8.49        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 15.48/8.49        = ( ord_less_nat @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1829_add__less__cancel__right,axiom,
% 15.48/8.49      ! [A: int,C: int,B: int] :
% 15.48/8.49        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 15.48/8.49        = ( ord_less_int @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1830_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 15.48/8.49      ! [A: real] :
% 15.48/8.49        ( ( minus_minus_real @ A @ A )
% 15.48/8.49        = zero_zero_real ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1831_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 15.48/8.49      ! [A: rat] :
% 15.48/8.49        ( ( minus_minus_rat @ A @ A )
% 15.48/8.49        = zero_zero_rat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1832_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 15.48/8.49      ! [A: nat] :
% 15.48/8.49        ( ( minus_minus_nat @ A @ A )
% 15.48/8.49        = zero_zero_nat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1833_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 15.48/8.49      ! [A: int] :
% 15.48/8.49        ( ( minus_minus_int @ A @ A )
% 15.48/8.49        = zero_zero_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1834_diff__zero,axiom,
% 15.48/8.49      ! [A: real] :
% 15.48/8.49        ( ( minus_minus_real @ A @ zero_zero_real )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1835_diff__zero,axiom,
% 15.48/8.49      ! [A: rat] :
% 15.48/8.49        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1836_diff__zero,axiom,
% 15.48/8.49      ! [A: nat] :
% 15.48/8.49        ( ( minus_minus_nat @ A @ zero_zero_nat )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1837_diff__zero,axiom,
% 15.48/8.49      ! [A: int] :
% 15.48/8.49        ( ( minus_minus_int @ A @ zero_zero_int )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1838_zero__diff,axiom,
% 15.48/8.49      ! [A: nat] :
% 15.48/8.49        ( ( minus_minus_nat @ zero_zero_nat @ A )
% 15.48/8.49        = zero_zero_nat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1839_diff__0__right,axiom,
% 15.48/8.49      ! [A: real] :
% 15.48/8.49        ( ( minus_minus_real @ A @ zero_zero_real )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1840_diff__0__right,axiom,
% 15.48/8.49      ! [A: rat] :
% 15.48/8.49        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1841_diff__0__right,axiom,
% 15.48/8.49      ! [A: int] :
% 15.48/8.49        ( ( minus_minus_int @ A @ zero_zero_int )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1842_diff__self,axiom,
% 15.48/8.49      ! [A: real] :
% 15.48/8.49        ( ( minus_minus_real @ A @ A )
% 15.48/8.49        = zero_zero_real ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1843_diff__self,axiom,
% 15.48/8.49      ! [A: rat] :
% 15.48/8.49        ( ( minus_minus_rat @ A @ A )
% 15.48/8.49        = zero_zero_rat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1844_diff__self,axiom,
% 15.48/8.49      ! [A: int] :
% 15.48/8.49        ( ( minus_minus_int @ A @ A )
% 15.48/8.49        = zero_zero_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1845_bits__div__by__0,axiom,
% 15.48/8.49      ! [A: nat] :
% 15.48/8.49        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 15.48/8.49        = zero_zero_nat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1846_bits__div__by__0,axiom,
% 15.48/8.49      ! [A: int] :
% 15.48/8.49        ( ( divide_divide_int @ A @ zero_zero_int )
% 15.48/8.49        = zero_zero_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1847_bits__div__0,axiom,
% 15.48/8.49      ! [A: nat] :
% 15.48/8.49        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 15.48/8.49        = zero_zero_nat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1848_bits__div__0,axiom,
% 15.48/8.49      ! [A: int] :
% 15.48/8.49        ( ( divide_divide_int @ zero_zero_int @ A )
% 15.48/8.49        = zero_zero_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1849_div__by__0,axiom,
% 15.48/8.49      ! [A: complex] :
% 15.48/8.49        ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 15.48/8.49        = zero_zero_complex ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1850_div__by__0,axiom,
% 15.48/8.49      ! [A: real] :
% 15.48/8.49        ( ( divide_divide_real @ A @ zero_zero_real )
% 15.48/8.49        = zero_zero_real ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1851_div__by__0,axiom,
% 15.48/8.49      ! [A: rat] :
% 15.48/8.49        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 15.48/8.49        = zero_zero_rat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1852_div__by__0,axiom,
% 15.48/8.49      ! [A: nat] :
% 15.48/8.49        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 15.48/8.49        = zero_zero_nat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1853_div__by__0,axiom,
% 15.48/8.49      ! [A: int] :
% 15.48/8.49        ( ( divide_divide_int @ A @ zero_zero_int )
% 15.48/8.49        = zero_zero_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1854_div__0,axiom,
% 15.48/8.49      ! [A: complex] :
% 15.48/8.49        ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 15.48/8.49        = zero_zero_complex ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1855_div__0,axiom,
% 15.48/8.49      ! [A: real] :
% 15.48/8.49        ( ( divide_divide_real @ zero_zero_real @ A )
% 15.48/8.49        = zero_zero_real ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1856_div__0,axiom,
% 15.48/8.49      ! [A: rat] :
% 15.48/8.49        ( ( divide_divide_rat @ zero_zero_rat @ A )
% 15.48/8.49        = zero_zero_rat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1857_div__0,axiom,
% 15.48/8.49      ! [A: nat] :
% 15.48/8.49        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 15.48/8.49        = zero_zero_nat ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1858_div__0,axiom,
% 15.48/8.49      ! [A: int] :
% 15.48/8.49        ( ( divide_divide_int @ zero_zero_int @ A )
% 15.48/8.49        = zero_zero_int ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1859_add__numeral__left,axiom,
% 15.48/8.49      ! [V: num,W: num,Z: complex] :
% 15.48/8.49        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 15.48/8.49        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1860_add__numeral__left,axiom,
% 15.48/8.49      ! [V: num,W: num,Z: real] :
% 15.48/8.49        ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 15.48/8.49        = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1861_add__numeral__left,axiom,
% 15.48/8.49      ! [V: num,W: num,Z: rat] :
% 15.48/8.49        ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 15.48/8.49        = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1862_add__numeral__left,axiom,
% 15.48/8.49      ! [V: num,W: num,Z: nat] :
% 15.48/8.49        ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 15.48/8.49        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1863_add__numeral__left,axiom,
% 15.48/8.49      ! [V: num,W: num,Z: int] :
% 15.48/8.49        ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 15.48/8.49        = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1864_numeral__plus__numeral,axiom,
% 15.48/8.49      ! [M: num,N: num] :
% 15.48/8.49        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 15.48/8.49        = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1865_numeral__plus__numeral,axiom,
% 15.48/8.49      ! [M: num,N: num] :
% 15.48/8.49        ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 15.48/8.49        = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1866_numeral__plus__numeral,axiom,
% 15.48/8.49      ! [M: num,N: num] :
% 15.48/8.49        ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 15.48/8.49        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1867_numeral__plus__numeral,axiom,
% 15.48/8.49      ! [M: num,N: num] :
% 15.48/8.49        ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 15.48/8.49        = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1868_numeral__plus__numeral,axiom,
% 15.48/8.49      ! [M: num,N: num] :
% 15.48/8.49        ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 15.48/8.49        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1869_add__diff__cancel,axiom,
% 15.48/8.49      ! [A: real,B: real] :
% 15.48/8.49        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1870_add__diff__cancel,axiom,
% 15.48/8.49      ! [A: rat,B: rat] :
% 15.48/8.49        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1871_add__diff__cancel,axiom,
% 15.48/8.49      ! [A: int,B: int] :
% 15.48/8.49        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1872_diff__add__cancel,axiom,
% 15.48/8.49      ! [A: real,B: real] :
% 15.48/8.49        ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1873_diff__add__cancel,axiom,
% 15.48/8.49      ! [A: rat,B: rat] :
% 15.48/8.49        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1874_diff__add__cancel,axiom,
% 15.48/8.49      ! [A: int,B: int] :
% 15.48/8.49        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1875_add__diff__cancel__left,axiom,
% 15.48/8.49      ! [C: real,A: real,B: real] :
% 15.48/8.49        ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 15.48/8.49        = ( minus_minus_real @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1876_add__diff__cancel__left,axiom,
% 15.48/8.49      ! [C: rat,A: rat,B: rat] :
% 15.48/8.49        ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 15.48/8.49        = ( minus_minus_rat @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1877_add__diff__cancel__left,axiom,
% 15.48/8.49      ! [C: nat,A: nat,B: nat] :
% 15.48/8.49        ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 15.48/8.49        = ( minus_minus_nat @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1878_add__diff__cancel__left,axiom,
% 15.48/8.49      ! [C: int,A: int,B: int] :
% 15.48/8.49        ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 15.48/8.49        = ( minus_minus_int @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1879_add__diff__cancel__left_H,axiom,
% 15.48/8.49      ! [A: real,B: real] :
% 15.48/8.49        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 15.48/8.49        = B ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1880_add__diff__cancel__left_H,axiom,
% 15.48/8.49      ! [A: rat,B: rat] :
% 15.48/8.49        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 15.48/8.49        = B ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1881_add__diff__cancel__left_H,axiom,
% 15.48/8.49      ! [A: nat,B: nat] :
% 15.48/8.49        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 15.48/8.49        = B ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1882_add__diff__cancel__left_H,axiom,
% 15.48/8.49      ! [A: int,B: int] :
% 15.48/8.49        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 15.48/8.49        = B ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1883_add__diff__cancel__right,axiom,
% 15.48/8.49      ! [A: real,C: real,B: real] :
% 15.48/8.49        ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 15.48/8.49        = ( minus_minus_real @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1884_add__diff__cancel__right,axiom,
% 15.48/8.49      ! [A: rat,C: rat,B: rat] :
% 15.48/8.49        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 15.48/8.49        = ( minus_minus_rat @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1885_add__diff__cancel__right,axiom,
% 15.48/8.49      ! [A: nat,C: nat,B: nat] :
% 15.48/8.49        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 15.48/8.49        = ( minus_minus_nat @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1886_add__diff__cancel__right,axiom,
% 15.48/8.49      ! [A: int,C: int,B: int] :
% 15.48/8.49        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 15.48/8.49        = ( minus_minus_int @ A @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1887_add__diff__cancel__right_H,axiom,
% 15.48/8.49      ! [A: real,B: real] :
% 15.48/8.49        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1888_add__diff__cancel__right_H,axiom,
% 15.48/8.49      ! [A: rat,B: rat] :
% 15.48/8.49        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1889_add__diff__cancel__right_H,axiom,
% 15.48/8.49      ! [A: nat,B: nat] :
% 15.48/8.49        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1890_add__diff__cancel__right_H,axiom,
% 15.48/8.49      ! [A: int,B: int] :
% 15.48/8.49        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1891_bits__div__by__1,axiom,
% 15.48/8.49      ! [A: nat] :
% 15.48/8.49        ( ( divide_divide_nat @ A @ one_one_nat )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1892_bits__div__by__1,axiom,
% 15.48/8.49      ! [A: int] :
% 15.48/8.49        ( ( divide_divide_int @ A @ one_one_int )
% 15.48/8.49        = A ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1893_of__nat__add,axiom,
% 15.48/8.49      ! [M: nat,N: nat] :
% 15.48/8.49        ( ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ N ) )
% 15.48/8.49        = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1894_of__nat__add,axiom,
% 15.48/8.49      ! [M: nat,N: nat] :
% 15.48/8.49        ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N ) )
% 15.48/8.49        = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1895_of__nat__add,axiom,
% 15.48/8.49      ! [M: nat,N: nat] :
% 15.48/8.49        ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 15.48/8.49        = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1896_of__nat__add,axiom,
% 15.48/8.49      ! [M: nat,N: nat] :
% 15.48/8.49        ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 15.48/8.49        = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1897_of__nat__add,axiom,
% 15.48/8.49      ! [M: nat,N: nat] :
% 15.48/8.49        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 15.48/8.49        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1898_zero__less__diff,axiom,
% 15.48/8.49      ! [N: nat,M: nat] :
% 15.48/8.49        ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 15.48/8.49        = ( ord_less_nat @ M @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1899_diff__is__0__eq,axiom,
% 15.48/8.49      ! [M: nat,N: nat] :
% 15.48/8.49        ( ( ( minus_minus_nat @ M @ N )
% 15.48/8.49          = zero_zero_nat )
% 15.48/8.49        = ( ord_less_eq_nat @ M @ N ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1900_diff__is__0__eq_H,axiom,
% 15.48/8.49      ! [M: nat,N: nat] :
% 15.48/8.49        ( ( ord_less_eq_nat @ M @ N )
% 15.48/8.49       => ( ( minus_minus_nat @ M @ N )
% 15.48/8.49          = zero_zero_nat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1901_ln__inj__iff,axiom,
% 15.48/8.49      ! [X3: real,Y3: real] :
% 15.48/8.49        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.48/8.49       => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.48/8.49         => ( ( ( ln_ln_real @ X3 )
% 15.48/8.49              = ( ln_ln_real @ Y3 ) )
% 15.48/8.49            = ( X3 = Y3 ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1902_ln__less__cancel__iff,axiom,
% 15.48/8.49      ! [X3: real,Y3: real] :
% 15.48/8.49        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.48/8.49       => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.48/8.49         => ( ( ord_less_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y3 ) )
% 15.48/8.49            = ( ord_less_real @ X3 @ Y3 ) ) ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1903_unset__bit__nonnegative__int__iff,axiom,
% 15.48/8.49      ! [N: nat,K: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 15.48/8.49        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1904_set__bit__nonnegative__int__iff,axiom,
% 15.48/8.49      ! [N: nat,K: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 15.48/8.49        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1905_flip__bit__nonnegative__int__iff,axiom,
% 15.48/8.49      ! [N: nat,K: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 15.48/8.49        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1906_unset__bit__negative__int__iff,axiom,
% 15.48/8.49      ! [N: nat,K: int] :
% 15.48/8.49        ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 15.48/8.49        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1907_set__bit__negative__int__iff,axiom,
% 15.48/8.49      ! [N: nat,K: int] :
% 15.48/8.49        ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 15.48/8.49        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1908_flip__bit__negative__int__iff,axiom,
% 15.48/8.49      ! [N: nat,K: int] :
% 15.48/8.49        ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 15.48/8.49        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1909_add__le__same__cancel1,axiom,
% 15.48/8.49      ! [B: real,A: real] :
% 15.48/8.49        ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 15.48/8.49        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1910_add__le__same__cancel1,axiom,
% 15.48/8.49      ! [B: rat,A: rat] :
% 15.48/8.49        ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 15.48/8.49        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1911_add__le__same__cancel1,axiom,
% 15.48/8.49      ! [B: nat,A: nat] :
% 15.48/8.49        ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 15.48/8.49        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1912_add__le__same__cancel1,axiom,
% 15.48/8.49      ! [B: int,A: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 15.48/8.49        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1913_add__le__same__cancel2,axiom,
% 15.48/8.49      ! [A: real,B: real] :
% 15.48/8.49        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 15.48/8.49        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1914_add__le__same__cancel2,axiom,
% 15.48/8.49      ! [A: rat,B: rat] :
% 15.48/8.49        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 15.48/8.49        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1915_add__le__same__cancel2,axiom,
% 15.48/8.49      ! [A: nat,B: nat] :
% 15.48/8.49        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 15.48/8.49        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1916_add__le__same__cancel2,axiom,
% 15.48/8.49      ! [A: int,B: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 15.48/8.49        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1917_le__add__same__cancel1,axiom,
% 15.48/8.49      ! [A: real,B: real] :
% 15.48/8.49        ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 15.48/8.49        = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1918_le__add__same__cancel1,axiom,
% 15.48/8.49      ! [A: rat,B: rat] :
% 15.48/8.49        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 15.48/8.49        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1919_le__add__same__cancel1,axiom,
% 15.48/8.49      ! [A: nat,B: nat] :
% 15.48/8.49        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 15.48/8.49        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1920_le__add__same__cancel1,axiom,
% 15.48/8.49      ! [A: int,B: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 15.48/8.49        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1921_le__add__same__cancel2,axiom,
% 15.48/8.49      ! [A: real,B: real] :
% 15.48/8.49        ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 15.48/8.49        = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1922_le__add__same__cancel2,axiom,
% 15.48/8.49      ! [A: rat,B: rat] :
% 15.48/8.49        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 15.48/8.49        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1923_le__add__same__cancel2,axiom,
% 15.48/8.49      ! [A: nat,B: nat] :
% 15.48/8.49        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 15.48/8.49        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1924_le__add__same__cancel2,axiom,
% 15.48/8.49      ! [A: int,B: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 15.48/8.49        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1925_double__add__le__zero__iff__single__add__le__zero,axiom,
% 15.48/8.49      ! [A: real] :
% 15.48/8.49        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 15.48/8.49        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1926_double__add__le__zero__iff__single__add__le__zero,axiom,
% 15.48/8.49      ! [A: rat] :
% 15.48/8.49        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 15.48/8.49        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1927_double__add__le__zero__iff__single__add__le__zero,axiom,
% 15.48/8.49      ! [A: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 15.48/8.49        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1928_zero__le__double__add__iff__zero__le__single__add,axiom,
% 15.48/8.49      ! [A: real] :
% 15.48/8.49        ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 15.48/8.49        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1929_zero__le__double__add__iff__zero__le__single__add,axiom,
% 15.48/8.49      ! [A: rat] :
% 15.48/8.49        ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 15.48/8.49        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1930_zero__le__double__add__iff__zero__le__single__add,axiom,
% 15.48/8.49      ! [A: int] :
% 15.48/8.49        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 15.48/8.49        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1931_add__less__same__cancel1,axiom,
% 15.48/8.49      ! [B: real,A: real] :
% 15.48/8.49        ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 15.48/8.49        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1932_add__less__same__cancel1,axiom,
% 15.48/8.49      ! [B: rat,A: rat] :
% 15.48/8.49        ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 15.48/8.49        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1933_add__less__same__cancel1,axiom,
% 15.48/8.49      ! [B: nat,A: nat] :
% 15.48/8.49        ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 15.48/8.49        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1934_add__less__same__cancel1,axiom,
% 15.48/8.49      ! [B: int,A: int] :
% 15.48/8.49        ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 15.48/8.49        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1935_add__less__same__cancel2,axiom,
% 15.48/8.49      ! [A: real,B: real] :
% 15.48/8.49        ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 15.48/8.49        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1936_add__less__same__cancel2,axiom,
% 15.48/8.49      ! [A: rat,B: rat] :
% 15.48/8.49        ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 15.48/8.49        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1937_add__less__same__cancel2,axiom,
% 15.48/8.49      ! [A: nat,B: nat] :
% 15.48/8.49        ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 15.48/8.49        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1938_add__less__same__cancel2,axiom,
% 15.48/8.49      ! [A: int,B: int] :
% 15.48/8.49        ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 15.48/8.49        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1939_less__add__same__cancel1,axiom,
% 15.48/8.49      ! [A: real,B: real] :
% 15.48/8.49        ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 15.48/8.49        = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1940_less__add__same__cancel1,axiom,
% 15.48/8.49      ! [A: rat,B: rat] :
% 15.48/8.49        ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 15.48/8.49        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1941_less__add__same__cancel1,axiom,
% 15.48/8.49      ! [A: nat,B: nat] :
% 15.48/8.49        ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 15.48/8.49        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1942_less__add__same__cancel1,axiom,
% 15.48/8.49      ! [A: int,B: int] :
% 15.48/8.49        ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 15.48/8.49        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1943_less__add__same__cancel2,axiom,
% 15.48/8.49      ! [A: real,B: real] :
% 15.48/8.49        ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 15.48/8.49        = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1944_less__add__same__cancel2,axiom,
% 15.48/8.49      ! [A: rat,B: rat] :
% 15.48/8.49        ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 15.48/8.49        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1945_less__add__same__cancel2,axiom,
% 15.48/8.49      ! [A: nat,B: nat] :
% 15.48/8.49        ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 15.48/8.49        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1946_less__add__same__cancel2,axiom,
% 15.48/8.49      ! [A: int,B: int] :
% 15.48/8.49        ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 15.48/8.49        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1947_double__add__less__zero__iff__single__add__less__zero,axiom,
% 15.48/8.49      ! [A: real] :
% 15.48/8.49        ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 15.48/8.49        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1948_double__add__less__zero__iff__single__add__less__zero,axiom,
% 15.48/8.49      ! [A: rat] :
% 15.48/8.49        ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 15.48/8.49        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1949_double__add__less__zero__iff__single__add__less__zero,axiom,
% 15.48/8.49      ! [A: int] :
% 15.48/8.49        ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 15.48/8.49        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1950_zero__less__double__add__iff__zero__less__single__add,axiom,
% 15.48/8.49      ! [A: real] :
% 15.48/8.49        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 15.48/8.49        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1951_zero__less__double__add__iff__zero__less__single__add,axiom,
% 15.48/8.49      ! [A: rat] :
% 15.48/8.49        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 15.48/8.49        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 15.48/8.49  
% 15.48/8.49  thf(fact_1952_zero__less__double__add__iff__zero__less__single__add,axiom,
% 15.48/8.49      ! [A: int] :
% 15.48/8.50        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 15.48/8.50        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1953_diff__ge__0__iff__ge,axiom,
% 15.48/8.50      ! [A: real,B: real] :
% 15.48/8.50        ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 15.48/8.50        = ( ord_less_eq_real @ B @ A ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1954_diff__ge__0__iff__ge,axiom,
% 15.48/8.50      ! [A: rat,B: rat] :
% 15.48/8.50        ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 15.48/8.50        = ( ord_less_eq_rat @ B @ A ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1955_diff__ge__0__iff__ge,axiom,
% 15.48/8.50      ! [A: int,B: int] :
% 15.48/8.50        ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 15.48/8.50        = ( ord_less_eq_int @ B @ A ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1956_diff__gt__0__iff__gt,axiom,
% 15.48/8.50      ! [A: real,B: real] :
% 15.48/8.50        ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 15.48/8.50        = ( ord_less_real @ B @ A ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1957_diff__gt__0__iff__gt,axiom,
% 15.48/8.50      ! [A: rat,B: rat] :
% 15.48/8.50        ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 15.48/8.50        = ( ord_less_rat @ B @ A ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1958_diff__gt__0__iff__gt,axiom,
% 15.48/8.50      ! [A: int,B: int] :
% 15.48/8.50        ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 15.48/8.50        = ( ord_less_int @ B @ A ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1959_diff__numeral__special_I9_J,axiom,
% 15.48/8.50      ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 15.48/8.50      = zero_zero_complex ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1960_diff__numeral__special_I9_J,axiom,
% 15.48/8.50      ( ( minus_minus_real @ one_one_real @ one_one_real )
% 15.48/8.50      = zero_zero_real ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1961_diff__numeral__special_I9_J,axiom,
% 15.48/8.50      ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 15.48/8.50      = zero_zero_rat ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1962_diff__numeral__special_I9_J,axiom,
% 15.48/8.50      ( ( minus_minus_int @ one_one_int @ one_one_int )
% 15.48/8.50      = zero_zero_int ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1963_le__add__diff__inverse,axiom,
% 15.48/8.50      ! [B: real,A: real] :
% 15.48/8.50        ( ( ord_less_eq_real @ B @ A )
% 15.48/8.50       => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 15.48/8.50          = A ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1964_le__add__diff__inverse,axiom,
% 15.48/8.50      ! [B: rat,A: rat] :
% 15.48/8.50        ( ( ord_less_eq_rat @ B @ A )
% 15.48/8.50       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 15.48/8.50          = A ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1965_le__add__diff__inverse,axiom,
% 15.48/8.50      ! [B: nat,A: nat] :
% 15.48/8.50        ( ( ord_less_eq_nat @ B @ A )
% 15.48/8.50       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 15.48/8.50          = A ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1966_le__add__diff__inverse,axiom,
% 15.48/8.50      ! [B: int,A: int] :
% 15.48/8.50        ( ( ord_less_eq_int @ B @ A )
% 15.48/8.50       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 15.48/8.50          = A ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1967_le__add__diff__inverse2,axiom,
% 15.48/8.50      ! [B: real,A: real] :
% 15.48/8.50        ( ( ord_less_eq_real @ B @ A )
% 15.48/8.50       => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 15.48/8.50          = A ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1968_le__add__diff__inverse2,axiom,
% 15.48/8.50      ! [B: rat,A: rat] :
% 15.48/8.50        ( ( ord_less_eq_rat @ B @ A )
% 15.48/8.50       => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 15.48/8.50          = A ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1969_le__add__diff__inverse2,axiom,
% 15.48/8.50      ! [B: nat,A: nat] :
% 15.48/8.50        ( ( ord_less_eq_nat @ B @ A )
% 15.48/8.50       => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 15.48/8.50          = A ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1970_le__add__diff__inverse2,axiom,
% 15.48/8.50      ! [B: int,A: int] :
% 15.48/8.50        ( ( ord_less_eq_int @ B @ A )
% 15.48/8.50       => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 15.48/8.50          = A ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1971_diff__add__zero,axiom,
% 15.48/8.50      ! [A: nat,B: nat] :
% 15.48/8.50        ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 15.48/8.50        = zero_zero_nat ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1972_div__self,axiom,
% 15.48/8.50      ! [A: complex] :
% 15.48/8.50        ( ( A != zero_zero_complex )
% 15.48/8.50       => ( ( divide1717551699836669952omplex @ A @ A )
% 15.48/8.50          = one_one_complex ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1973_div__self,axiom,
% 15.48/8.50      ! [A: real] :
% 15.48/8.50        ( ( A != zero_zero_real )
% 15.48/8.50       => ( ( divide_divide_real @ A @ A )
% 15.48/8.50          = one_one_real ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1974_div__self,axiom,
% 15.48/8.50      ! [A: rat] :
% 15.48/8.50        ( ( A != zero_zero_rat )
% 15.48/8.50       => ( ( divide_divide_rat @ A @ A )
% 15.48/8.50          = one_one_rat ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1975_div__self,axiom,
% 15.48/8.50      ! [A: nat] :
% 15.48/8.50        ( ( A != zero_zero_nat )
% 15.48/8.50       => ( ( divide_divide_nat @ A @ A )
% 15.48/8.50          = one_one_nat ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1976_div__self,axiom,
% 15.48/8.50      ! [A: int] :
% 15.48/8.50        ( ( A != zero_zero_int )
% 15.48/8.50       => ( ( divide_divide_int @ A @ A )
% 15.48/8.50          = one_one_int ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1977_ln__le__cancel__iff,axiom,
% 15.48/8.50      ! [X3: real,Y3: real] :
% 15.48/8.50        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.48/8.50       => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.48/8.50         => ( ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y3 ) )
% 15.48/8.50            = ( ord_less_eq_real @ X3 @ Y3 ) ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1978_div__less,axiom,
% 15.48/8.50      ! [M: nat,N: nat] :
% 15.48/8.50        ( ( ord_less_nat @ M @ N )
% 15.48/8.50       => ( ( divide_divide_nat @ M @ N )
% 15.48/8.50          = zero_zero_nat ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1979_ln__less__zero__iff,axiom,
% 15.48/8.50      ! [X3: real] :
% 15.48/8.50        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.48/8.50       => ( ( ord_less_real @ ( ln_ln_real @ X3 ) @ zero_zero_real )
% 15.48/8.50          = ( ord_less_real @ X3 @ one_one_real ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1980_ln__gt__zero__iff,axiom,
% 15.48/8.50      ! [X3: real] :
% 15.48/8.50        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.48/8.50       => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X3 ) )
% 15.48/8.50          = ( ord_less_real @ one_one_real @ X3 ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1981_ln__eq__zero__iff,axiom,
% 15.48/8.50      ! [X3: real] :
% 15.48/8.50        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.48/8.50       => ( ( ( ln_ln_real @ X3 )
% 15.48/8.50            = zero_zero_real )
% 15.48/8.50          = ( X3 = one_one_real ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1982_of__int__add,axiom,
% 15.48/8.50      ! [W: int,Z: int] :
% 15.48/8.50        ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 15.48/8.50        = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1983_of__int__add,axiom,
% 15.48/8.50      ! [W: int,Z: int] :
% 15.48/8.50        ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 15.48/8.50        = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1984_of__int__add,axiom,
% 15.48/8.50      ! [W: int,Z: int] :
% 15.48/8.50        ( ( ring_17405671764205052669omplex @ ( plus_plus_int @ W @ Z ) )
% 15.48/8.50        = ( plus_plus_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1985_of__int__add,axiom,
% 15.48/8.50      ! [W: int,Z: int] :
% 15.48/8.50        ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 15.48/8.50        = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1986_of__int__diff,axiom,
% 15.48/8.50      ! [W: int,Z: int] :
% 15.48/8.50        ( ( ring_17405671764205052669omplex @ ( minus_minus_int @ W @ Z ) )
% 15.48/8.50        = ( minus_minus_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1987_of__int__diff,axiom,
% 15.48/8.50      ! [W: int,Z: int] :
% 15.48/8.50        ( ( ring_1_of_int_real @ ( minus_minus_int @ W @ Z ) )
% 15.48/8.50        = ( minus_minus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1988_of__int__diff,axiom,
% 15.48/8.50      ! [W: int,Z: int] :
% 15.48/8.50        ( ( ring_1_of_int_rat @ ( minus_minus_int @ W @ Z ) )
% 15.48/8.50        = ( minus_minus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1989_of__int__diff,axiom,
% 15.48/8.50      ! [W: int,Z: int] :
% 15.48/8.50        ( ( ring_1_of_int_int @ ( minus_minus_int @ W @ Z ) )
% 15.48/8.50        = ( minus_minus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1990_numeral__plus__one,axiom,
% 15.48/8.50      ! [N: num] :
% 15.48/8.50        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 15.48/8.50        = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1991_numeral__plus__one,axiom,
% 15.48/8.50      ! [N: num] :
% 15.48/8.50        ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 15.48/8.50        = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1992_numeral__plus__one,axiom,
% 15.48/8.50      ! [N: num] :
% 15.48/8.50        ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 15.48/8.50        = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1993_numeral__plus__one,axiom,
% 15.48/8.50      ! [N: num] :
% 15.48/8.50        ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 15.48/8.50        = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1994_numeral__plus__one,axiom,
% 15.48/8.50      ! [N: num] :
% 15.48/8.50        ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 15.48/8.50        = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1995_one__plus__numeral,axiom,
% 15.48/8.50      ! [N: num] :
% 15.48/8.50        ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 15.48/8.50        = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1996_one__plus__numeral,axiom,
% 15.48/8.50      ! [N: num] :
% 15.48/8.50        ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 15.48/8.50        = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1997_one__plus__numeral,axiom,
% 15.48/8.50      ! [N: num] :
% 15.48/8.50        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 15.48/8.50        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1998_one__plus__numeral,axiom,
% 15.48/8.50      ! [N: num] :
% 15.48/8.50        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 15.48/8.50        = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_1999_one__plus__numeral,axiom,
% 15.48/8.50      ! [N: num] :
% 15.48/8.50        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 15.48/8.50        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_2000_ln__le__zero__iff,axiom,
% 15.48/8.50      ! [X3: real] :
% 15.48/8.50        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.48/8.50       => ( ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ zero_zero_real )
% 15.48/8.50          = ( ord_less_eq_real @ X3 @ one_one_real ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_2001_ln__ge__zero__iff,axiom,
% 15.48/8.50      ! [X3: real] :
% 15.48/8.50        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.48/8.50       => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X3 ) )
% 15.48/8.50          = ( ord_less_eq_real @ one_one_real @ X3 ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_2002_diff__nat__numeral,axiom,
% 15.48/8.50      ! [V: num,V2: num] :
% 15.48/8.50        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V2 ) )
% 15.48/8.50        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V2 ) ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_2003_zle__add1__eq__le,axiom,
% 15.48/8.50      ! [W: int,Z: int] :
% 15.48/8.50        ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 15.48/8.50        = ( ord_less_eq_int @ W @ Z ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_2004_ceiling__add__of__int,axiom,
% 15.48/8.50      ! [X3: rat,Z: int] :
% 15.48/8.50        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X3 @ ( ring_1_of_int_rat @ Z ) ) )
% 15.48/8.50        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X3 ) @ Z ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_2005_ceiling__add__of__int,axiom,
% 15.48/8.50      ! [X3: real,Z: int] :
% 15.48/8.50        ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X3 @ ( ring_1_of_int_real @ Z ) ) )
% 15.48/8.50        = ( plus_plus_int @ ( archim7802044766580827645g_real @ X3 ) @ Z ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_2006_zle__diff1__eq,axiom,
% 15.48/8.50      ! [W: int,Z: int] :
% 15.48/8.50        ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 15.48/8.50        = ( ord_less_int @ W @ Z ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_2007_ceiling__diff__of__int,axiom,
% 15.48/8.50      ! [X3: rat,Z: int] :
% 15.48/8.50        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X3 @ ( ring_1_of_int_rat @ Z ) ) )
% 15.48/8.50        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X3 ) @ Z ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_2008_ceiling__diff__of__int,axiom,
% 15.48/8.50      ! [X3: real,Z: int] :
% 15.48/8.50        ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X3 @ ( ring_1_of_int_real @ Z ) ) )
% 15.48/8.50        = ( minus_minus_int @ ( archim7802044766580827645g_real @ X3 ) @ Z ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_2009_one__add__one,axiom,
% 15.48/8.50      ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 15.48/8.50      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_2010_one__add__one,axiom,
% 15.48/8.50      ( ( plus_plus_real @ one_one_real @ one_one_real )
% 15.48/8.50      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_2011_one__add__one,axiom,
% 15.48/8.50      ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 15.48/8.50      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_2012_one__add__one,axiom,
% 15.48/8.50      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 15.48/8.50      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_2013_one__add__one,axiom,
% 15.48/8.50      ( ( plus_plus_int @ one_one_int @ one_one_int )
% 15.48/8.50      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_2014_odd__add,axiom,
% 15.48/8.50      ! [A: code_integer,B: code_integer] :
% 15.48/8.50        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 15.48/8.50        = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 15.48/8.50         != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_2015_odd__add,axiom,
% 15.48/8.50      ! [A: nat,B: nat] :
% 15.48/8.50        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 15.48/8.50        = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 15.48/8.50         != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_2016_odd__add,axiom,
% 15.48/8.50      ! [A: int,B: int] :
% 15.48/8.50        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 15.48/8.50        = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 15.48/8.50         != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_2017_even__add,axiom,
% 15.48/8.50      ! [A: code_integer,B: code_integer] :
% 15.48/8.50        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 15.48/8.50        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.48/8.50          = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_2018_even__add,axiom,
% 15.48/8.50      ! [A: nat,B: nat] :
% 15.48/8.50        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 15.48/8.50        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.48/8.50          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_2019_even__add,axiom,
% 15.48/8.50      ! [A: int,B: int] :
% 15.48/8.50        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 15.48/8.50        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.48/8.50          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_2020_ceiling__add__numeral,axiom,
% 15.48/8.50      ! [X3: real,V: num] :
% 15.48/8.50        ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X3 @ ( numeral_numeral_real @ V ) ) )
% 15.48/8.50        = ( plus_plus_int @ ( archim7802044766580827645g_real @ X3 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 15.48/8.50  
% 15.48/8.50  thf(fact_2021_ceiling__add__numeral,axiom,
% 15.48/8.50      ! [X3: rat,V: num] :
% 15.48/8.50        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X3 @ ( numeral_numeral_rat @ V ) ) )
% 15.55/8.50        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X3 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2022_ceiling__add__one,axiom,
% 15.55/8.50      ! [X3: rat] :
% 15.55/8.50        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X3 @ one_one_rat ) )
% 15.55/8.50        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X3 ) @ one_one_int ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2023_ceiling__add__one,axiom,
% 15.55/8.50      ! [X3: real] :
% 15.55/8.50        ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X3 @ one_one_real ) )
% 15.55/8.50        = ( plus_plus_int @ ( archim7802044766580827645g_real @ X3 ) @ one_one_int ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2024_ceiling__diff__numeral,axiom,
% 15.55/8.50      ! [X3: real,V: num] :
% 15.55/8.50        ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X3 @ ( numeral_numeral_real @ V ) ) )
% 15.55/8.50        = ( minus_minus_int @ ( archim7802044766580827645g_real @ X3 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2025_ceiling__diff__numeral,axiom,
% 15.55/8.50      ! [X3: rat,V: num] :
% 15.55/8.50        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X3 @ ( numeral_numeral_rat @ V ) ) )
% 15.55/8.50        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X3 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2026_ceiling__diff__one,axiom,
% 15.55/8.50      ! [X3: rat] :
% 15.55/8.50        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X3 @ one_one_rat ) )
% 15.55/8.50        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X3 ) @ one_one_int ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2027_ceiling__diff__one,axiom,
% 15.55/8.50      ! [X3: real] :
% 15.55/8.50        ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X3 @ one_one_real ) )
% 15.55/8.50        = ( minus_minus_int @ ( archim7802044766580827645g_real @ X3 ) @ one_one_int ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2028_bits__1__div__2,axiom,
% 15.55/8.50      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.50      = zero_zero_nat ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2029_bits__1__div__2,axiom,
% 15.55/8.50      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.50      = zero_zero_int ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2030_one__div__two__eq__zero,axiom,
% 15.55/8.50      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.50      = zero_zero_nat ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2031_one__div__two__eq__zero,axiom,
% 15.55/8.50      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.50      = zero_zero_int ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2032_sum__power2__eq__zero__iff,axiom,
% 15.55/8.50      ! [X3: rat,Y3: rat] :
% 15.55/8.50        ( ( ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.50          = zero_zero_rat )
% 15.55/8.50        = ( ( X3 = zero_zero_rat )
% 15.55/8.50          & ( Y3 = zero_zero_rat ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2033_sum__power2__eq__zero__iff,axiom,
% 15.55/8.50      ! [X3: int,Y3: int] :
% 15.55/8.50        ( ( ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.50          = zero_zero_int )
% 15.55/8.50        = ( ( X3 = zero_zero_int )
% 15.55/8.50          & ( Y3 = zero_zero_int ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2034_sum__power2__eq__zero__iff,axiom,
% 15.55/8.50      ! [X3: real,Y3: real] :
% 15.55/8.50        ( ( ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.50          = zero_zero_real )
% 15.55/8.50        = ( ( X3 = zero_zero_real )
% 15.55/8.50          & ( Y3 = zero_zero_real ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2035_even__plus__one__iff,axiom,
% 15.55/8.50      ! [A: code_integer] :
% 15.55/8.50        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 15.55/8.50        = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2036_even__plus__one__iff,axiom,
% 15.55/8.50      ! [A: nat] :
% 15.55/8.50        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 15.55/8.50        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2037_even__plus__one__iff,axiom,
% 15.55/8.50      ! [A: int] :
% 15.55/8.50        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 15.55/8.50        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2038_even__diff,axiom,
% 15.55/8.50      ! [A: code_integer,B: code_integer] :
% 15.55/8.50        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 15.55/8.50        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2039_even__diff,axiom,
% 15.55/8.50      ! [A: int,B: int] :
% 15.55/8.50        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 15.55/8.50        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2040_nat__numeral__diff__1,axiom,
% 15.55/8.50      ! [V: num] :
% 15.55/8.50        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 15.55/8.50        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2041_even__succ__div__2,axiom,
% 15.55/8.50      ! [A: code_integer] :
% 15.55/8.50        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.55/8.50       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 15.55/8.50          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2042_even__succ__div__2,axiom,
% 15.55/8.50      ! [A: nat] :
% 15.55/8.50        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.55/8.50       => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.50          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2043_even__succ__div__2,axiom,
% 15.55/8.50      ! [A: int] :
% 15.55/8.50        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.55/8.50       => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.50          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2044_odd__succ__div__two,axiom,
% 15.55/8.50      ! [A: code_integer] :
% 15.55/8.50        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.55/8.50       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 15.55/8.50          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2045_odd__succ__div__two,axiom,
% 15.55/8.50      ! [A: nat] :
% 15.55/8.50        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.55/8.50       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.50          = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2046_odd__succ__div__two,axiom,
% 15.55/8.50      ! [A: int] :
% 15.55/8.50        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.55/8.50       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.50          = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2047_even__succ__div__two,axiom,
% 15.55/8.50      ! [A: code_integer] :
% 15.55/8.50        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.55/8.50       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 15.55/8.50          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2048_even__succ__div__two,axiom,
% 15.55/8.50      ! [A: nat] :
% 15.55/8.50        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.55/8.50       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.50          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2049_even__succ__div__two,axiom,
% 15.55/8.50      ! [A: int] :
% 15.55/8.50        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.55/8.50       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.50          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2050_ceiling__less__numeral,axiom,
% 15.55/8.50      ! [X3: real,V: num] :
% 15.55/8.50        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X3 ) @ ( numeral_numeral_int @ V ) )
% 15.55/8.50        = ( ord_less_eq_real @ X3 @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2051_ceiling__less__numeral,axiom,
% 15.55/8.50      ! [X3: rat,V: num] :
% 15.55/8.50        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X3 ) @ ( numeral_numeral_int @ V ) )
% 15.55/8.50        = ( ord_less_eq_rat @ X3 @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2052_even__succ__div__exp,axiom,
% 15.55/8.50      ! [A: code_integer,N: nat] :
% 15.55/8.50        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.55/8.50       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.50         => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.50            = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2053_even__succ__div__exp,axiom,
% 15.55/8.50      ! [A: nat,N: nat] :
% 15.55/8.50        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.55/8.50       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.50         => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.50            = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2054_even__succ__div__exp,axiom,
% 15.55/8.50      ! [A: int,N: nat] :
% 15.55/8.50        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.55/8.50       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.50         => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.50            = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2055_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 15.55/8.50      ! [A: real,B: real] :
% 15.55/8.50        ( ~ ( ord_less_real @ A @ B )
% 15.55/8.50       => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 15.55/8.50          = A ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2056_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 15.55/8.50      ! [A: rat,B: rat] :
% 15.55/8.50        ( ~ ( ord_less_rat @ A @ B )
% 15.55/8.50       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 15.55/8.50          = A ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2057_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 15.55/8.50      ! [A: nat,B: nat] :
% 15.55/8.50        ( ~ ( ord_less_nat @ A @ B )
% 15.55/8.50       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 15.55/8.50          = A ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2058_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 15.55/8.50      ! [A: int,B: int] :
% 15.55/8.50        ( ~ ( ord_less_int @ A @ B )
% 15.55/8.50       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 15.55/8.50          = A ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2059_add__le__add__imp__diff__le,axiom,
% 15.55/8.50      ! [I: real,K: real,N: real,J: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 15.55/8.50       => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 15.55/8.50         => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 15.55/8.50           => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 15.55/8.50             => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2060_add__le__add__imp__diff__le,axiom,
% 15.55/8.50      ! [I: rat,K: rat,N: rat,J: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 15.55/8.50       => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 15.55/8.50         => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 15.55/8.50           => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 15.55/8.50             => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2061_add__le__add__imp__diff__le,axiom,
% 15.55/8.50      ! [I: nat,K: nat,N: nat,J: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 15.55/8.50       => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 15.55/8.50         => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 15.55/8.50           => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 15.55/8.50             => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2062_add__le__add__imp__diff__le,axiom,
% 15.55/8.50      ! [I: int,K: int,N: int,J: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 15.55/8.50       => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 15.55/8.50         => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 15.55/8.50           => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 15.55/8.50             => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2063_add__le__imp__le__diff,axiom,
% 15.55/8.50      ! [I: real,K: real,N: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 15.55/8.50       => ( ord_less_eq_real @ I @ ( minus_minus_real @ N @ K ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2064_add__le__imp__le__diff,axiom,
% 15.55/8.50      ! [I: rat,K: rat,N: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 15.55/8.50       => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N @ K ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2065_add__le__imp__le__diff,axiom,
% 15.55/8.50      ! [I: nat,K: nat,N: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 15.55/8.50       => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2066_add__le__imp__le__diff,axiom,
% 15.55/8.50      ! [I: int,K: int,N: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 15.55/8.50       => ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2067_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.50       => ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.50         => ( ( ( minus_minus_nat @ B @ A )
% 15.55/8.50              = C )
% 15.55/8.50            = ( B
% 15.55/8.50              = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2068_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 15.55/8.50      ! [A: nat,B: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.50       => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 15.55/8.50          = B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2069_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.50       => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 15.55/8.50          = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2070_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.50       => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 15.55/8.50          = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2071_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.50       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 15.55/8.50          = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2072_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.50       => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 15.55/8.50          = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2073_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.50       => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 15.55/8.50          = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2074_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.50       => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 15.55/8.50          = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2075_le__add__diff,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.50       => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2076_diff__add,axiom,
% 15.55/8.50      ! [A: nat,B: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.50       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 15.55/8.50          = B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2077_le__diff__eq,axiom,
% 15.55/8.50      ! [A: real,C: real,B: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 15.55/8.50        = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2078_le__diff__eq,axiom,
% 15.55/8.50      ! [A: rat,C: rat,B: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 15.55/8.50        = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2079_le__diff__eq,axiom,
% 15.55/8.50      ! [A: int,C: int,B: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 15.55/8.50        = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2080_diff__le__eq,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 15.55/8.50        = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2081_diff__le__eq,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 15.55/8.50        = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2082_diff__le__eq,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 15.55/8.50        = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2083_diff__less__eq,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 15.55/8.50        = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2084_diff__less__eq,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 15.55/8.50        = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2085_diff__less__eq,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 15.55/8.50        = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2086_less__diff__eq,axiom,
% 15.55/8.50      ! [A: real,C: real,B: real] :
% 15.55/8.50        ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 15.55/8.50        = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2087_less__diff__eq,axiom,
% 15.55/8.50      ! [A: rat,C: rat,B: rat] :
% 15.55/8.50        ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 15.55/8.50        = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2088_less__diff__eq,axiom,
% 15.55/8.50      ! [A: int,C: int,B: int] :
% 15.55/8.50        ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 15.55/8.50        = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2089_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 15.55/8.50        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2090_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 15.55/8.50        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2091_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat] :
% 15.55/8.50        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 15.55/8.50        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2092_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 15.55/8.50        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2093_add__mono__thms__linordered__semiring_I4_J,axiom,
% 15.55/8.50      ! [I: real,J: real,K: real,L: real] :
% 15.55/8.50        ( ( ( I = J )
% 15.55/8.50          & ( K = L ) )
% 15.55/8.50       => ( ( plus_plus_real @ I @ K )
% 15.55/8.50          = ( plus_plus_real @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2094_add__mono__thms__linordered__semiring_I4_J,axiom,
% 15.55/8.50      ! [I: rat,J: rat,K: rat,L: rat] :
% 15.55/8.50        ( ( ( I = J )
% 15.55/8.50          & ( K = L ) )
% 15.55/8.50       => ( ( plus_plus_rat @ I @ K )
% 15.55/8.50          = ( plus_plus_rat @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2095_add__mono__thms__linordered__semiring_I4_J,axiom,
% 15.55/8.50      ! [I: nat,J: nat,K: nat,L: nat] :
% 15.55/8.50        ( ( ( I = J )
% 15.55/8.50          & ( K = L ) )
% 15.55/8.50       => ( ( plus_plus_nat @ I @ K )
% 15.55/8.50          = ( plus_plus_nat @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2096_add__mono__thms__linordered__semiring_I4_J,axiom,
% 15.55/8.50      ! [I: int,J: int,K: int,L: int] :
% 15.55/8.50        ( ( ( I = J )
% 15.55/8.50          & ( K = L ) )
% 15.55/8.50       => ( ( plus_plus_int @ I @ K )
% 15.55/8.50          = ( plus_plus_int @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2097_group__cancel_Oadd1,axiom,
% 15.55/8.50      ! [A3: real,K: real,A: real,B: real] :
% 15.55/8.50        ( ( A3
% 15.55/8.50          = ( plus_plus_real @ K @ A ) )
% 15.55/8.50       => ( ( plus_plus_real @ A3 @ B )
% 15.55/8.50          = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2098_group__cancel_Oadd1,axiom,
% 15.55/8.50      ! [A3: rat,K: rat,A: rat,B: rat] :
% 15.55/8.50        ( ( A3
% 15.55/8.50          = ( plus_plus_rat @ K @ A ) )
% 15.55/8.50       => ( ( plus_plus_rat @ A3 @ B )
% 15.55/8.50          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2099_group__cancel_Oadd1,axiom,
% 15.55/8.50      ! [A3: nat,K: nat,A: nat,B: nat] :
% 15.55/8.50        ( ( A3
% 15.55/8.50          = ( plus_plus_nat @ K @ A ) )
% 15.55/8.50       => ( ( plus_plus_nat @ A3 @ B )
% 15.55/8.50          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2100_group__cancel_Oadd1,axiom,
% 15.55/8.50      ! [A3: int,K: int,A: int,B: int] :
% 15.55/8.50        ( ( A3
% 15.55/8.50          = ( plus_plus_int @ K @ A ) )
% 15.55/8.50       => ( ( plus_plus_int @ A3 @ B )
% 15.55/8.50          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2101_group__cancel_Oadd2,axiom,
% 15.55/8.50      ! [B5: real,K: real,B: real,A: real] :
% 15.55/8.50        ( ( B5
% 15.55/8.50          = ( plus_plus_real @ K @ B ) )
% 15.55/8.50       => ( ( plus_plus_real @ A @ B5 )
% 15.55/8.50          = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2102_group__cancel_Oadd2,axiom,
% 15.55/8.50      ! [B5: rat,K: rat,B: rat,A: rat] :
% 15.55/8.50        ( ( B5
% 15.55/8.50          = ( plus_plus_rat @ K @ B ) )
% 15.55/8.50       => ( ( plus_plus_rat @ A @ B5 )
% 15.55/8.50          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2103_group__cancel_Oadd2,axiom,
% 15.55/8.50      ! [B5: nat,K: nat,B: nat,A: nat] :
% 15.55/8.50        ( ( B5
% 15.55/8.50          = ( plus_plus_nat @ K @ B ) )
% 15.55/8.50       => ( ( plus_plus_nat @ A @ B5 )
% 15.55/8.50          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2104_group__cancel_Oadd2,axiom,
% 15.55/8.50      ! [B5: int,K: int,B: int,A: int] :
% 15.55/8.50        ( ( B5
% 15.55/8.50          = ( plus_plus_int @ K @ B ) )
% 15.55/8.50       => ( ( plus_plus_int @ A @ B5 )
% 15.55/8.50          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2105_group__cancel_Osub1,axiom,
% 15.55/8.50      ! [A3: real,K: real,A: real,B: real] :
% 15.55/8.50        ( ( A3
% 15.55/8.50          = ( plus_plus_real @ K @ A ) )
% 15.55/8.50       => ( ( minus_minus_real @ A3 @ B )
% 15.55/8.50          = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2106_group__cancel_Osub1,axiom,
% 15.55/8.50      ! [A3: rat,K: rat,A: rat,B: rat] :
% 15.55/8.50        ( ( A3
% 15.55/8.50          = ( plus_plus_rat @ K @ A ) )
% 15.55/8.50       => ( ( minus_minus_rat @ A3 @ B )
% 15.55/8.50          = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2107_group__cancel_Osub1,axiom,
% 15.55/8.50      ! [A3: int,K: int,A: int,B: int] :
% 15.55/8.50        ( ( A3
% 15.55/8.50          = ( plus_plus_int @ K @ A ) )
% 15.55/8.50       => ( ( minus_minus_int @ A3 @ B )
% 15.55/8.50          = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2108_diff__eq__eq,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( ( minus_minus_real @ A @ B )
% 15.55/8.50          = C )
% 15.55/8.50        = ( A
% 15.55/8.50          = ( plus_plus_real @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2109_diff__eq__eq,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( ( minus_minus_rat @ A @ B )
% 15.55/8.50          = C )
% 15.55/8.50        = ( A
% 15.55/8.50          = ( plus_plus_rat @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2110_diff__eq__eq,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( ( minus_minus_int @ A @ B )
% 15.55/8.50          = C )
% 15.55/8.50        = ( A
% 15.55/8.50          = ( plus_plus_int @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2111_eq__diff__eq,axiom,
% 15.55/8.50      ! [A: real,C: real,B: real] :
% 15.55/8.50        ( ( A
% 15.55/8.50          = ( minus_minus_real @ C @ B ) )
% 15.55/8.50        = ( ( plus_plus_real @ A @ B )
% 15.55/8.50          = C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2112_eq__diff__eq,axiom,
% 15.55/8.50      ! [A: rat,C: rat,B: rat] :
% 15.55/8.50        ( ( A
% 15.55/8.50          = ( minus_minus_rat @ C @ B ) )
% 15.55/8.50        = ( ( plus_plus_rat @ A @ B )
% 15.55/8.50          = C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2113_eq__diff__eq,axiom,
% 15.55/8.50      ! [A: int,C: int,B: int] :
% 15.55/8.50        ( ( A
% 15.55/8.50          = ( minus_minus_int @ C @ B ) )
% 15.55/8.50        = ( ( plus_plus_int @ A @ B )
% 15.55/8.50          = C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2114_add__diff__eq,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 15.55/8.50        = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2115_add__diff__eq,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 15.55/8.50        = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2116_add__diff__eq,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 15.55/8.50        = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2117_diff__diff__eq2,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 15.55/8.50        = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2118_diff__diff__eq2,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 15.55/8.50        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2119_diff__diff__eq2,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 15.55/8.50        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2120_add_Oassoc,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 15.55/8.50        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2121_add_Oassoc,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 15.55/8.50        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2122_add_Oassoc,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat] :
% 15.55/8.50        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 15.55/8.50        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2123_add_Oassoc,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 15.55/8.50        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2124_diff__add__eq,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 15.55/8.50        = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2125_diff__add__eq,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 15.55/8.50        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2126_diff__add__eq,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 15.55/8.50        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2127_add_Oleft__cancel,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( ( plus_plus_real @ A @ B )
% 15.55/8.50          = ( plus_plus_real @ A @ C ) )
% 15.55/8.50        = ( B = C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2128_add_Oleft__cancel,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( ( plus_plus_rat @ A @ B )
% 15.55/8.50          = ( plus_plus_rat @ A @ C ) )
% 15.55/8.50        = ( B = C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2129_add_Oleft__cancel,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( ( plus_plus_int @ A @ B )
% 15.55/8.50          = ( plus_plus_int @ A @ C ) )
% 15.55/8.50        = ( B = C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2130_diff__eq__diff__eq,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real,D3: real] :
% 15.55/8.50        ( ( ( minus_minus_real @ A @ B )
% 15.55/8.50          = ( minus_minus_real @ C @ D3 ) )
% 15.55/8.50       => ( ( A = B )
% 15.55/8.50          = ( C = D3 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2131_diff__eq__diff__eq,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat,D3: rat] :
% 15.55/8.50        ( ( ( minus_minus_rat @ A @ B )
% 15.55/8.50          = ( minus_minus_rat @ C @ D3 ) )
% 15.55/8.50       => ( ( A = B )
% 15.55/8.50          = ( C = D3 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2132_diff__eq__diff__eq,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int,D3: int] :
% 15.55/8.50        ( ( ( minus_minus_int @ A @ B )
% 15.55/8.50          = ( minus_minus_int @ C @ D3 ) )
% 15.55/8.50       => ( ( A = B )
% 15.55/8.50          = ( C = D3 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2133_add_Oright__cancel,axiom,
% 15.55/8.50      ! [B: real,A: real,C: real] :
% 15.55/8.50        ( ( ( plus_plus_real @ B @ A )
% 15.55/8.50          = ( plus_plus_real @ C @ A ) )
% 15.55/8.50        = ( B = C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2134_add_Oright__cancel,axiom,
% 15.55/8.50      ! [B: rat,A: rat,C: rat] :
% 15.55/8.50        ( ( ( plus_plus_rat @ B @ A )
% 15.55/8.50          = ( plus_plus_rat @ C @ A ) )
% 15.55/8.50        = ( B = C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2135_add_Oright__cancel,axiom,
% 15.55/8.50      ! [B: int,A: int,C: int] :
% 15.55/8.50        ( ( ( plus_plus_int @ B @ A )
% 15.55/8.50          = ( plus_plus_int @ C @ A ) )
% 15.55/8.50        = ( B = C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2136_add_Ocommute,axiom,
% 15.55/8.50      ( plus_plus_real
% 15.55/8.50      = ( ^ [A4: real,B3: real] : ( plus_plus_real @ B3 @ A4 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2137_add_Ocommute,axiom,
% 15.55/8.50      ( plus_plus_rat
% 15.55/8.50      = ( ^ [A4: rat,B3: rat] : ( plus_plus_rat @ B3 @ A4 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2138_add_Ocommute,axiom,
% 15.55/8.50      ( plus_plus_nat
% 15.55/8.50      = ( ^ [A4: nat,B3: nat] : ( plus_plus_nat @ B3 @ A4 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2139_add_Ocommute,axiom,
% 15.55/8.50      ( plus_plus_int
% 15.55/8.50      = ( ^ [A4: int,B3: int] : ( plus_plus_int @ B3 @ A4 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2140_add_Oleft__commute,axiom,
% 15.55/8.50      ! [B: real,A: real,C: real] :
% 15.55/8.50        ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 15.55/8.50        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2141_add_Oleft__commute,axiom,
% 15.55/8.50      ! [B: rat,A: rat,C: rat] :
% 15.55/8.50        ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 15.55/8.50        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2142_add_Oleft__commute,axiom,
% 15.55/8.50      ! [B: nat,A: nat,C: nat] :
% 15.55/8.50        ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 15.55/8.50        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2143_add_Oleft__commute,axiom,
% 15.55/8.50      ! [B: int,A: int,C: int] :
% 15.55/8.50        ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 15.55/8.50        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2144_add__left__imp__eq,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( ( plus_plus_real @ A @ B )
% 15.55/8.50          = ( plus_plus_real @ A @ C ) )
% 15.55/8.50       => ( B = C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2145_add__left__imp__eq,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( ( plus_plus_rat @ A @ B )
% 15.55/8.50          = ( plus_plus_rat @ A @ C ) )
% 15.55/8.50       => ( B = C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2146_add__left__imp__eq,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat] :
% 15.55/8.50        ( ( ( plus_plus_nat @ A @ B )
% 15.55/8.50          = ( plus_plus_nat @ A @ C ) )
% 15.55/8.50       => ( B = C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2147_add__left__imp__eq,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( ( plus_plus_int @ A @ B )
% 15.55/8.50          = ( plus_plus_int @ A @ C ) )
% 15.55/8.50       => ( B = C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2148_diff__add__eq__diff__diff__swap,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 15.55/8.50        = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2149_diff__add__eq__diff__diff__swap,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 15.55/8.50        = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2150_diff__add__eq__diff__diff__swap,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 15.55/8.50        = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2151_add__right__imp__eq,axiom,
% 15.55/8.50      ! [B: real,A: real,C: real] :
% 15.55/8.50        ( ( ( plus_plus_real @ B @ A )
% 15.55/8.50          = ( plus_plus_real @ C @ A ) )
% 15.55/8.50       => ( B = C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2152_add__right__imp__eq,axiom,
% 15.55/8.50      ! [B: rat,A: rat,C: rat] :
% 15.55/8.50        ( ( ( plus_plus_rat @ B @ A )
% 15.55/8.50          = ( plus_plus_rat @ C @ A ) )
% 15.55/8.50       => ( B = C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2153_add__right__imp__eq,axiom,
% 15.55/8.50      ! [B: nat,A: nat,C: nat] :
% 15.55/8.50        ( ( ( plus_plus_nat @ B @ A )
% 15.55/8.50          = ( plus_plus_nat @ C @ A ) )
% 15.55/8.50       => ( B = C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2154_add__right__imp__eq,axiom,
% 15.55/8.50      ! [B: int,A: int,C: int] :
% 15.55/8.50        ( ( ( plus_plus_int @ B @ A )
% 15.55/8.50          = ( plus_plus_int @ C @ A ) )
% 15.55/8.50       => ( B = C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2155_add__implies__diff,axiom,
% 15.55/8.50      ! [C: real,B: real,A: real] :
% 15.55/8.50        ( ( ( plus_plus_real @ C @ B )
% 15.55/8.50          = A )
% 15.55/8.50       => ( C
% 15.55/8.50          = ( minus_minus_real @ A @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2156_add__implies__diff,axiom,
% 15.55/8.50      ! [C: rat,B: rat,A: rat] :
% 15.55/8.50        ( ( ( plus_plus_rat @ C @ B )
% 15.55/8.50          = A )
% 15.55/8.50       => ( C
% 15.55/8.50          = ( minus_minus_rat @ A @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2157_add__implies__diff,axiom,
% 15.55/8.50      ! [C: nat,B: nat,A: nat] :
% 15.55/8.50        ( ( ( plus_plus_nat @ C @ B )
% 15.55/8.50          = A )
% 15.55/8.50       => ( C
% 15.55/8.50          = ( minus_minus_nat @ A @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2158_add__implies__diff,axiom,
% 15.55/8.50      ! [C: int,B: int,A: int] :
% 15.55/8.50        ( ( ( plus_plus_int @ C @ B )
% 15.55/8.50          = A )
% 15.55/8.50       => ( C
% 15.55/8.50          = ( minus_minus_int @ A @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2159_diff__right__commute,axiom,
% 15.55/8.50      ! [A: real,C: real,B: real] :
% 15.55/8.50        ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 15.55/8.50        = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2160_diff__right__commute,axiom,
% 15.55/8.50      ! [A: rat,C: rat,B: rat] :
% 15.55/8.50        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 15.55/8.50        = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2161_diff__right__commute,axiom,
% 15.55/8.50      ! [A: nat,C: nat,B: nat] :
% 15.55/8.50        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 15.55/8.50        = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2162_diff__right__commute,axiom,
% 15.55/8.50      ! [A: int,C: int,B: int] :
% 15.55/8.50        ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 15.55/8.50        = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2163_diff__diff__eq,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 15.55/8.50        = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2164_diff__diff__eq,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 15.55/8.50        = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2165_diff__diff__eq,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat] :
% 15.55/8.50        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 15.55/8.50        = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2166_diff__diff__eq,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 15.55/8.50        = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2167_add__diff__add,axiom,
% 15.55/8.50      ! [A: real,C: real,B: real,D3: real] :
% 15.55/8.50        ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D3 ) )
% 15.55/8.50        = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D3 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2168_add__diff__add,axiom,
% 15.55/8.50      ! [A: rat,C: rat,B: rat,D3: rat] :
% 15.55/8.50        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D3 ) )
% 15.55/8.50        = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D3 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2169_add__diff__add,axiom,
% 15.55/8.50      ! [A: int,C: int,B: int,D3: int] :
% 15.55/8.50        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D3 ) )
% 15.55/8.50        = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D3 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2170_is__num__normalize_I1_J,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 15.55/8.50        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2171_is__num__normalize_I1_J,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 15.55/8.50        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2172_is__num__normalize_I1_J,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 15.55/8.50        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2173_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 15.55/8.50      ! [M: nat,N: nat] :
% 15.55/8.50        ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N ) )
% 15.55/8.50        = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2174_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 15.55/8.50      ! [M: nat,N: nat] :
% 15.55/8.50        ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) )
% 15.55/8.50        = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2175_div__add__self2,axiom,
% 15.55/8.50      ! [B: nat,A: nat] :
% 15.55/8.50        ( ( B != zero_zero_nat )
% 15.55/8.50       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 15.55/8.50          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2176_div__add__self2,axiom,
% 15.55/8.50      ! [B: int,A: int] :
% 15.55/8.50        ( ( B != zero_zero_int )
% 15.55/8.50       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 15.55/8.50          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2177_div__add__self1,axiom,
% 15.55/8.50      ! [B: nat,A: nat] :
% 15.55/8.50        ( ( B != zero_zero_nat )
% 15.55/8.50       => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 15.55/8.50          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2178_div__add__self1,axiom,
% 15.55/8.50      ! [B: int,A: int] :
% 15.55/8.50        ( ( B != zero_zero_int )
% 15.55/8.50       => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 15.55/8.50          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2179_of__nat__diff,axiom,
% 15.55/8.50      ! [N: nat,M: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.50       => ( ( semiri8010041392384452111omplex @ ( minus_minus_nat @ M @ N ) )
% 15.55/8.50          = ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2180_of__nat__diff,axiom,
% 15.55/8.50      ! [N: nat,M: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.50       => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N ) )
% 15.55/8.50          = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2181_of__nat__diff,axiom,
% 15.55/8.50      ! [N: nat,M: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.50       => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N ) )
% 15.55/8.50          = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2182_of__nat__diff,axiom,
% 15.55/8.50      ! [N: nat,M: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.50       => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 15.55/8.50          = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2183_of__nat__diff,axiom,
% 15.55/8.50      ! [N: nat,M: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.50       => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 15.55/8.50          = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2184_int__induct,axiom,
% 15.55/8.50      ! [P: int > $o,K: int,I: int] :
% 15.55/8.50        ( ( P @ K )
% 15.55/8.50       => ( ! [I3: int] :
% 15.55/8.50              ( ( ord_less_eq_int @ K @ I3 )
% 15.55/8.50             => ( ( P @ I3 )
% 15.55/8.50               => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 15.55/8.50         => ( ! [I3: int] :
% 15.55/8.50                ( ( ord_less_eq_int @ I3 @ K )
% 15.55/8.50               => ( ( P @ I3 )
% 15.55/8.50                 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 15.55/8.50           => ( P @ I ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2185_int__minus,axiom,
% 15.55/8.50      ! [N: nat,M: nat] :
% 15.55/8.50        ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ M ) )
% 15.55/8.50        = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2186_ceiling__add__le,axiom,
% 15.55/8.50      ! [X3: rat,Y3: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X3 @ Y3 ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X3 ) @ ( archim2889992004027027881ng_rat @ Y3 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2187_ceiling__add__le,axiom,
% 15.55/8.50      ! [X3: real,Y3: real] : ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( plus_plus_real @ X3 @ Y3 ) ) @ ( plus_plus_int @ ( archim7802044766580827645g_real @ X3 ) @ ( archim7802044766580827645g_real @ Y3 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2188_diff__eq__diff__less__eq,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real,D3: real] :
% 15.55/8.50        ( ( ( minus_minus_real @ A @ B )
% 15.55/8.50          = ( minus_minus_real @ C @ D3 ) )
% 15.55/8.50       => ( ( ord_less_eq_real @ A @ B )
% 15.55/8.50          = ( ord_less_eq_real @ C @ D3 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2189_diff__eq__diff__less__eq,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat,D3: rat] :
% 15.55/8.50        ( ( ( minus_minus_rat @ A @ B )
% 15.55/8.50          = ( minus_minus_rat @ C @ D3 ) )
% 15.55/8.50       => ( ( ord_less_eq_rat @ A @ B )
% 15.55/8.50          = ( ord_less_eq_rat @ C @ D3 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2190_diff__eq__diff__less__eq,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int,D3: int] :
% 15.55/8.50        ( ( ( minus_minus_int @ A @ B )
% 15.55/8.50          = ( minus_minus_int @ C @ D3 ) )
% 15.55/8.50       => ( ( ord_less_eq_int @ A @ B )
% 15.55/8.50          = ( ord_less_eq_int @ C @ D3 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2191_diff__right__mono,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.50       => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2192_diff__right__mono,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ A @ B )
% 15.55/8.50       => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2193_diff__right__mono,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ A @ B )
% 15.55/8.50       => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2194_diff__left__mono,axiom,
% 15.55/8.50      ! [B: real,A: real,C: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ B @ A )
% 15.55/8.50       => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2195_diff__left__mono,axiom,
% 15.55/8.50      ! [B: rat,A: rat,C: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ B @ A )
% 15.55/8.50       => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2196_diff__left__mono,axiom,
% 15.55/8.50      ! [B: int,A: int,C: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ B @ A )
% 15.55/8.50       => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2197_diff__mono,axiom,
% 15.55/8.50      ! [A: real,B: real,D3: real,C: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.50       => ( ( ord_less_eq_real @ D3 @ C )
% 15.55/8.50         => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2198_diff__mono,axiom,
% 15.55/8.50      ! [A: rat,B: rat,D3: rat,C: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ A @ B )
% 15.55/8.50       => ( ( ord_less_eq_rat @ D3 @ C )
% 15.55/8.50         => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2199_diff__mono,axiom,
% 15.55/8.50      ! [A: int,B: int,D3: int,C: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ A @ B )
% 15.55/8.50       => ( ( ord_less_eq_int @ D3 @ C )
% 15.55/8.50         => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2200_eq__iff__diff__eq__0,axiom,
% 15.55/8.50      ( ( ^ [Y5: real,Z2: real] : ( Y5 = Z2 ) )
% 15.55/8.50      = ( ^ [A4: real,B3: real] :
% 15.55/8.50            ( ( minus_minus_real @ A4 @ B3 )
% 15.55/8.50            = zero_zero_real ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2201_eq__iff__diff__eq__0,axiom,
% 15.55/8.50      ( ( ^ [Y5: rat,Z2: rat] : ( Y5 = Z2 ) )
% 15.55/8.50      = ( ^ [A4: rat,B3: rat] :
% 15.55/8.50            ( ( minus_minus_rat @ A4 @ B3 )
% 15.55/8.50            = zero_zero_rat ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2202_eq__iff__diff__eq__0,axiom,
% 15.55/8.50      ( ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 15.55/8.50      = ( ^ [A4: int,B3: int] :
% 15.55/8.50            ( ( minus_minus_int @ A4 @ B3 )
% 15.55/8.50            = zero_zero_int ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2203_diff__strict__mono,axiom,
% 15.55/8.50      ! [A: real,B: real,D3: real,C: real] :
% 15.55/8.50        ( ( ord_less_real @ A @ B )
% 15.55/8.50       => ( ( ord_less_real @ D3 @ C )
% 15.55/8.50         => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2204_diff__strict__mono,axiom,
% 15.55/8.50      ! [A: rat,B: rat,D3: rat,C: rat] :
% 15.55/8.50        ( ( ord_less_rat @ A @ B )
% 15.55/8.50       => ( ( ord_less_rat @ D3 @ C )
% 15.55/8.50         => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2205_diff__strict__mono,axiom,
% 15.55/8.50      ! [A: int,B: int,D3: int,C: int] :
% 15.55/8.50        ( ( ord_less_int @ A @ B )
% 15.55/8.50       => ( ( ord_less_int @ D3 @ C )
% 15.55/8.50         => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2206_diff__eq__diff__less,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real,D3: real] :
% 15.55/8.50        ( ( ( minus_minus_real @ A @ B )
% 15.55/8.50          = ( minus_minus_real @ C @ D3 ) )
% 15.55/8.50       => ( ( ord_less_real @ A @ B )
% 15.55/8.50          = ( ord_less_real @ C @ D3 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2207_diff__eq__diff__less,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat,D3: rat] :
% 15.55/8.50        ( ( ( minus_minus_rat @ A @ B )
% 15.55/8.50          = ( minus_minus_rat @ C @ D3 ) )
% 15.55/8.50       => ( ( ord_less_rat @ A @ B )
% 15.55/8.50          = ( ord_less_rat @ C @ D3 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2208_diff__eq__diff__less,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int,D3: int] :
% 15.55/8.50        ( ( ( minus_minus_int @ A @ B )
% 15.55/8.50          = ( minus_minus_int @ C @ D3 ) )
% 15.55/8.50       => ( ( ord_less_int @ A @ B )
% 15.55/8.50          = ( ord_less_int @ C @ D3 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2209_diff__strict__left__mono,axiom,
% 15.55/8.50      ! [B: real,A: real,C: real] :
% 15.55/8.50        ( ( ord_less_real @ B @ A )
% 15.55/8.50       => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2210_diff__strict__left__mono,axiom,
% 15.55/8.50      ! [B: rat,A: rat,C: rat] :
% 15.55/8.50        ( ( ord_less_rat @ B @ A )
% 15.55/8.50       => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2211_diff__strict__left__mono,axiom,
% 15.55/8.50      ! [B: int,A: int,C: int] :
% 15.55/8.50        ( ( ord_less_int @ B @ A )
% 15.55/8.50       => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2212_diff__strict__right__mono,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( ord_less_real @ A @ B )
% 15.55/8.50       => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2213_diff__strict__right__mono,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( ord_less_rat @ A @ B )
% 15.55/8.50       => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2214_diff__strict__right__mono,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( ord_less_int @ A @ B )
% 15.55/8.50       => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2215_add__le__imp__le__right,axiom,
% 15.55/8.50      ! [A: real,C: real,B: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 15.55/8.50       => ( ord_less_eq_real @ A @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2216_add__le__imp__le__right,axiom,
% 15.55/8.50      ! [A: rat,C: rat,B: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 15.55/8.50       => ( ord_less_eq_rat @ A @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2217_add__le__imp__le__right,axiom,
% 15.55/8.50      ! [A: nat,C: nat,B: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 15.55/8.50       => ( ord_less_eq_nat @ A @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2218_add__le__imp__le__right,axiom,
% 15.55/8.50      ! [A: int,C: int,B: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 15.55/8.50       => ( ord_less_eq_int @ A @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2219_add__le__imp__le__left,axiom,
% 15.55/8.50      ! [C: real,A: real,B: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 15.55/8.50       => ( ord_less_eq_real @ A @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2220_add__le__imp__le__left,axiom,
% 15.55/8.50      ! [C: rat,A: rat,B: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 15.55/8.50       => ( ord_less_eq_rat @ A @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2221_add__le__imp__le__left,axiom,
% 15.55/8.50      ! [C: nat,A: nat,B: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 15.55/8.50       => ( ord_less_eq_nat @ A @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2222_add__le__imp__le__left,axiom,
% 15.55/8.50      ! [C: int,A: int,B: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 15.55/8.50       => ( ord_less_eq_int @ A @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2223_le__iff__add,axiom,
% 15.55/8.50      ( ord_less_eq_nat
% 15.55/8.50      = ( ^ [A4: nat,B3: nat] :
% 15.55/8.50          ? [C3: nat] :
% 15.55/8.50            ( B3
% 15.55/8.50            = ( plus_plus_nat @ A4 @ C3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2224_add__right__mono,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.50       => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2225_add__right__mono,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ A @ B )
% 15.55/8.50       => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2226_add__right__mono,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.50       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2227_add__right__mono,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ A @ B )
% 15.55/8.50       => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2228_less__eqE,axiom,
% 15.55/8.50      ! [A: nat,B: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.50       => ~ ! [C2: nat] :
% 15.55/8.50              ( B
% 15.55/8.50             != ( plus_plus_nat @ A @ C2 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2229_add__left__mono,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.50       => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2230_add__left__mono,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ A @ B )
% 15.55/8.50       => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2231_add__left__mono,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.50       => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2232_add__left__mono,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ A @ B )
% 15.55/8.50       => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2233_add__mono,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real,D3: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.50       => ( ( ord_less_eq_real @ C @ D3 )
% 15.55/8.50         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2234_add__mono,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat,D3: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ A @ B )
% 15.55/8.50       => ( ( ord_less_eq_rat @ C @ D3 )
% 15.55/8.50         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2235_add__mono,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat,D3: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.50       => ( ( ord_less_eq_nat @ C @ D3 )
% 15.55/8.50         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2236_add__mono,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int,D3: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ A @ B )
% 15.55/8.50       => ( ( ord_less_eq_int @ C @ D3 )
% 15.55/8.50         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2237_add__mono__thms__linordered__semiring_I1_J,axiom,
% 15.55/8.50      ! [I: real,J: real,K: real,L: real] :
% 15.55/8.50        ( ( ( ord_less_eq_real @ I @ J )
% 15.55/8.50          & ( ord_less_eq_real @ K @ L ) )
% 15.55/8.50       => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2238_add__mono__thms__linordered__semiring_I1_J,axiom,
% 15.55/8.50      ! [I: rat,J: rat,K: rat,L: rat] :
% 15.55/8.50        ( ( ( ord_less_eq_rat @ I @ J )
% 15.55/8.50          & ( ord_less_eq_rat @ K @ L ) )
% 15.55/8.50       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2239_add__mono__thms__linordered__semiring_I1_J,axiom,
% 15.55/8.50      ! [I: nat,J: nat,K: nat,L: nat] :
% 15.55/8.50        ( ( ( ord_less_eq_nat @ I @ J )
% 15.55/8.50          & ( ord_less_eq_nat @ K @ L ) )
% 15.55/8.50       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2240_add__mono__thms__linordered__semiring_I1_J,axiom,
% 15.55/8.50      ! [I: int,J: int,K: int,L: int] :
% 15.55/8.50        ( ( ( ord_less_eq_int @ I @ J )
% 15.55/8.50          & ( ord_less_eq_int @ K @ L ) )
% 15.55/8.50       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2241_add__mono__thms__linordered__semiring_I2_J,axiom,
% 15.55/8.50      ! [I: real,J: real,K: real,L: real] :
% 15.55/8.50        ( ( ( I = J )
% 15.55/8.50          & ( ord_less_eq_real @ K @ L ) )
% 15.55/8.50       => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2242_add__mono__thms__linordered__semiring_I2_J,axiom,
% 15.55/8.50      ! [I: rat,J: rat,K: rat,L: rat] :
% 15.55/8.50        ( ( ( I = J )
% 15.55/8.50          & ( ord_less_eq_rat @ K @ L ) )
% 15.55/8.50       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2243_add__mono__thms__linordered__semiring_I2_J,axiom,
% 15.55/8.50      ! [I: nat,J: nat,K: nat,L: nat] :
% 15.55/8.50        ( ( ( I = J )
% 15.55/8.50          & ( ord_less_eq_nat @ K @ L ) )
% 15.55/8.50       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2244_add__mono__thms__linordered__semiring_I2_J,axiom,
% 15.55/8.50      ! [I: int,J: int,K: int,L: int] :
% 15.55/8.50        ( ( ( I = J )
% 15.55/8.50          & ( ord_less_eq_int @ K @ L ) )
% 15.55/8.50       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2245_add__mono__thms__linordered__semiring_I3_J,axiom,
% 15.55/8.50      ! [I: real,J: real,K: real,L: real] :
% 15.55/8.50        ( ( ( ord_less_eq_real @ I @ J )
% 15.55/8.50          & ( K = L ) )
% 15.55/8.50       => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2246_add__mono__thms__linordered__semiring_I3_J,axiom,
% 15.55/8.50      ! [I: rat,J: rat,K: rat,L: rat] :
% 15.55/8.50        ( ( ( ord_less_eq_rat @ I @ J )
% 15.55/8.50          & ( K = L ) )
% 15.55/8.50       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2247_add__mono__thms__linordered__semiring_I3_J,axiom,
% 15.55/8.50      ! [I: nat,J: nat,K: nat,L: nat] :
% 15.55/8.50        ( ( ( ord_less_eq_nat @ I @ J )
% 15.55/8.50          & ( K = L ) )
% 15.55/8.50       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2248_add__mono__thms__linordered__semiring_I3_J,axiom,
% 15.55/8.50      ! [I: int,J: int,K: int,L: int] :
% 15.55/8.50        ( ( ( ord_less_eq_int @ I @ J )
% 15.55/8.50          & ( K = L ) )
% 15.55/8.50       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2249_verit__sum__simplify,axiom,
% 15.55/8.50      ! [A: real] :
% 15.55/8.50        ( ( plus_plus_real @ A @ zero_zero_real )
% 15.55/8.50        = A ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2250_verit__sum__simplify,axiom,
% 15.55/8.50      ! [A: rat] :
% 15.55/8.50        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 15.55/8.50        = A ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2251_verit__sum__simplify,axiom,
% 15.55/8.50      ! [A: nat] :
% 15.55/8.50        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 15.55/8.50        = A ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2252_verit__sum__simplify,axiom,
% 15.55/8.50      ! [A: int] :
% 15.55/8.50        ( ( plus_plus_int @ A @ zero_zero_int )
% 15.55/8.50        = A ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2253_add_Ogroup__left__neutral,axiom,
% 15.55/8.50      ! [A: real] :
% 15.55/8.50        ( ( plus_plus_real @ zero_zero_real @ A )
% 15.55/8.50        = A ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2254_add_Ogroup__left__neutral,axiom,
% 15.55/8.50      ! [A: rat] :
% 15.55/8.50        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 15.55/8.50        = A ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2255_add_Ogroup__left__neutral,axiom,
% 15.55/8.50      ! [A: int] :
% 15.55/8.50        ( ( plus_plus_int @ zero_zero_int @ A )
% 15.55/8.50        = A ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2256_add_Ocomm__neutral,axiom,
% 15.55/8.50      ! [A: real] :
% 15.55/8.50        ( ( plus_plus_real @ A @ zero_zero_real )
% 15.55/8.50        = A ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2257_add_Ocomm__neutral,axiom,
% 15.55/8.50      ! [A: rat] :
% 15.55/8.50        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 15.55/8.50        = A ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2258_add_Ocomm__neutral,axiom,
% 15.55/8.50      ! [A: nat] :
% 15.55/8.50        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 15.55/8.50        = A ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2259_add_Ocomm__neutral,axiom,
% 15.55/8.50      ! [A: int] :
% 15.55/8.50        ( ( plus_plus_int @ A @ zero_zero_int )
% 15.55/8.50        = A ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2260_comm__monoid__add__class_Oadd__0,axiom,
% 15.55/8.50      ! [A: real] :
% 15.55/8.50        ( ( plus_plus_real @ zero_zero_real @ A )
% 15.55/8.50        = A ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2261_comm__monoid__add__class_Oadd__0,axiom,
% 15.55/8.50      ! [A: rat] :
% 15.55/8.50        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 15.55/8.50        = A ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2262_comm__monoid__add__class_Oadd__0,axiom,
% 15.55/8.50      ! [A: nat] :
% 15.55/8.50        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 15.55/8.50        = A ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2263_comm__monoid__add__class_Oadd__0,axiom,
% 15.55/8.50      ! [A: int] :
% 15.55/8.50        ( ( plus_plus_int @ zero_zero_int @ A )
% 15.55/8.50        = A ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2264_add__mono__thms__linordered__field_I5_J,axiom,
% 15.55/8.50      ! [I: real,J: real,K: real,L: real] :
% 15.55/8.50        ( ( ( ord_less_real @ I @ J )
% 15.55/8.50          & ( ord_less_real @ K @ L ) )
% 15.55/8.50       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2265_add__mono__thms__linordered__field_I5_J,axiom,
% 15.55/8.50      ! [I: rat,J: rat,K: rat,L: rat] :
% 15.55/8.50        ( ( ( ord_less_rat @ I @ J )
% 15.55/8.50          & ( ord_less_rat @ K @ L ) )
% 15.55/8.50       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2266_add__mono__thms__linordered__field_I5_J,axiom,
% 15.55/8.50      ! [I: nat,J: nat,K: nat,L: nat] :
% 15.55/8.50        ( ( ( ord_less_nat @ I @ J )
% 15.55/8.50          & ( ord_less_nat @ K @ L ) )
% 15.55/8.50       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2267_add__mono__thms__linordered__field_I5_J,axiom,
% 15.55/8.50      ! [I: int,J: int,K: int,L: int] :
% 15.55/8.50        ( ( ( ord_less_int @ I @ J )
% 15.55/8.50          & ( ord_less_int @ K @ L ) )
% 15.55/8.50       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2268_add__mono__thms__linordered__field_I2_J,axiom,
% 15.55/8.50      ! [I: real,J: real,K: real,L: real] :
% 15.55/8.50        ( ( ( I = J )
% 15.55/8.50          & ( ord_less_real @ K @ L ) )
% 15.55/8.50       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2269_add__mono__thms__linordered__field_I2_J,axiom,
% 15.55/8.50      ! [I: rat,J: rat,K: rat,L: rat] :
% 15.55/8.50        ( ( ( I = J )
% 15.55/8.50          & ( ord_less_rat @ K @ L ) )
% 15.55/8.50       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2270_add__mono__thms__linordered__field_I2_J,axiom,
% 15.55/8.50      ! [I: nat,J: nat,K: nat,L: nat] :
% 15.55/8.50        ( ( ( I = J )
% 15.55/8.50          & ( ord_less_nat @ K @ L ) )
% 15.55/8.50       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2271_add__mono__thms__linordered__field_I2_J,axiom,
% 15.55/8.50      ! [I: int,J: int,K: int,L: int] :
% 15.55/8.50        ( ( ( I = J )
% 15.55/8.50          & ( ord_less_int @ K @ L ) )
% 15.55/8.50       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2272_add__mono__thms__linordered__field_I1_J,axiom,
% 15.55/8.50      ! [I: real,J: real,K: real,L: real] :
% 15.55/8.50        ( ( ( ord_less_real @ I @ J )
% 15.55/8.50          & ( K = L ) )
% 15.55/8.50       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2273_add__mono__thms__linordered__field_I1_J,axiom,
% 15.55/8.50      ! [I: rat,J: rat,K: rat,L: rat] :
% 15.55/8.50        ( ( ( ord_less_rat @ I @ J )
% 15.55/8.50          & ( K = L ) )
% 15.55/8.50       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2274_add__mono__thms__linordered__field_I1_J,axiom,
% 15.55/8.50      ! [I: nat,J: nat,K: nat,L: nat] :
% 15.55/8.50        ( ( ( ord_less_nat @ I @ J )
% 15.55/8.50          & ( K = L ) )
% 15.55/8.50       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2275_add__mono__thms__linordered__field_I1_J,axiom,
% 15.55/8.50      ! [I: int,J: int,K: int,L: int] :
% 15.55/8.50        ( ( ( ord_less_int @ I @ J )
% 15.55/8.50          & ( K = L ) )
% 15.55/8.50       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2276_add__strict__mono,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real,D3: real] :
% 15.55/8.50        ( ( ord_less_real @ A @ B )
% 15.55/8.50       => ( ( ord_less_real @ C @ D3 )
% 15.55/8.50         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2277_add__strict__mono,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat,D3: rat] :
% 15.55/8.50        ( ( ord_less_rat @ A @ B )
% 15.55/8.50       => ( ( ord_less_rat @ C @ D3 )
% 15.55/8.50         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2278_add__strict__mono,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat,D3: nat] :
% 15.55/8.50        ( ( ord_less_nat @ A @ B )
% 15.55/8.50       => ( ( ord_less_nat @ C @ D3 )
% 15.55/8.50         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2279_add__strict__mono,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int,D3: int] :
% 15.55/8.50        ( ( ord_less_int @ A @ B )
% 15.55/8.50       => ( ( ord_less_int @ C @ D3 )
% 15.55/8.50         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2280_add__strict__left__mono,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( ord_less_real @ A @ B )
% 15.55/8.50       => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2281_add__strict__left__mono,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( ord_less_rat @ A @ B )
% 15.55/8.50       => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2282_add__strict__left__mono,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat] :
% 15.55/8.50        ( ( ord_less_nat @ A @ B )
% 15.55/8.50       => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2283_add__strict__left__mono,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( ord_less_int @ A @ B )
% 15.55/8.50       => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2284_add__strict__right__mono,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( ord_less_real @ A @ B )
% 15.55/8.50       => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2285_add__strict__right__mono,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( ord_less_rat @ A @ B )
% 15.55/8.50       => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2286_add__strict__right__mono,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat] :
% 15.55/8.50        ( ( ord_less_nat @ A @ B )
% 15.55/8.50       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2287_add__strict__right__mono,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( ord_less_int @ A @ B )
% 15.55/8.50       => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2288_add__less__imp__less__left,axiom,
% 15.55/8.50      ! [C: real,A: real,B: real] :
% 15.55/8.50        ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 15.55/8.50       => ( ord_less_real @ A @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2289_add__less__imp__less__left,axiom,
% 15.55/8.50      ! [C: rat,A: rat,B: rat] :
% 15.55/8.50        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 15.55/8.50       => ( ord_less_rat @ A @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2290_add__less__imp__less__left,axiom,
% 15.55/8.50      ! [C: nat,A: nat,B: nat] :
% 15.55/8.50        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 15.55/8.50       => ( ord_less_nat @ A @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2291_add__less__imp__less__left,axiom,
% 15.55/8.50      ! [C: int,A: int,B: int] :
% 15.55/8.50        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 15.55/8.50       => ( ord_less_int @ A @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2292_add__less__imp__less__right,axiom,
% 15.55/8.50      ! [A: real,C: real,B: real] :
% 15.55/8.50        ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 15.55/8.50       => ( ord_less_real @ A @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2293_add__less__imp__less__right,axiom,
% 15.55/8.50      ! [A: rat,C: rat,B: rat] :
% 15.55/8.50        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 15.55/8.50       => ( ord_less_rat @ A @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2294_add__less__imp__less__right,axiom,
% 15.55/8.50      ! [A: nat,C: nat,B: nat] :
% 15.55/8.50        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 15.55/8.50       => ( ord_less_nat @ A @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2295_add__less__imp__less__right,axiom,
% 15.55/8.50      ! [A: int,C: int,B: int] :
% 15.55/8.50        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 15.55/8.50       => ( ord_less_int @ A @ B ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2296_power__divide,axiom,
% 15.55/8.50      ! [A: complex,B: complex,N: nat] :
% 15.55/8.50        ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N )
% 15.55/8.50        = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2297_power__divide,axiom,
% 15.55/8.50      ! [A: real,B: real,N: nat] :
% 15.55/8.50        ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N )
% 15.55/8.50        = ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2298_power__divide,axiom,
% 15.55/8.50      ! [A: rat,B: rat,N: nat] :
% 15.55/8.50        ( ( power_power_rat @ ( divide_divide_rat @ A @ B ) @ N )
% 15.55/8.50        = ( divide_divide_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2299_diffs0__imp__equal,axiom,
% 15.55/8.50      ! [M: nat,N: nat] :
% 15.55/8.50        ( ( ( minus_minus_nat @ M @ N )
% 15.55/8.50          = zero_zero_nat )
% 15.55/8.50       => ( ( ( minus_minus_nat @ N @ M )
% 15.55/8.50            = zero_zero_nat )
% 15.55/8.50         => ( M = N ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2300_minus__nat_Odiff__0,axiom,
% 15.55/8.50      ! [M: nat] :
% 15.55/8.50        ( ( minus_minus_nat @ M @ zero_zero_nat )
% 15.55/8.50        = M ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2301_diff__less__mono2,axiom,
% 15.55/8.50      ! [M: nat,N: nat,L: nat] :
% 15.55/8.50        ( ( ord_less_nat @ M @ N )
% 15.55/8.50       => ( ( ord_less_nat @ M @ L )
% 15.55/8.50         => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2302_less__imp__diff__less,axiom,
% 15.55/8.50      ! [J: nat,K: nat,N: nat] :
% 15.55/8.50        ( ( ord_less_nat @ J @ K )
% 15.55/8.50       => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2303_minus__int__code_I1_J,axiom,
% 15.55/8.50      ! [K: int] :
% 15.55/8.50        ( ( minus_minus_int @ K @ zero_zero_int )
% 15.55/8.50        = K ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2304_diff__le__mono2,axiom,
% 15.55/8.50      ! [M: nat,N: nat,L: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.50       => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2305_le__diff__iff_H,axiom,
% 15.55/8.50      ! [A: nat,C: nat,B: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ A @ C )
% 15.55/8.50       => ( ( ord_less_eq_nat @ B @ C )
% 15.55/8.50         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 15.55/8.50            = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2306_diff__le__self,axiom,
% 15.55/8.50      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2307_diff__le__mono,axiom,
% 15.55/8.50      ! [M: nat,N: nat,L: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.50       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2308_Nat_Odiff__diff__eq,axiom,
% 15.55/8.50      ! [K: nat,M: nat,N: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ K @ M )
% 15.55/8.50       => ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.50         => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 15.55/8.50            = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2309_le__diff__iff,axiom,
% 15.55/8.50      ! [K: nat,M: nat,N: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ K @ M )
% 15.55/8.50       => ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.50         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 15.55/8.50            = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2310_eq__diff__iff,axiom,
% 15.55/8.50      ! [K: nat,M: nat,N: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ K @ M )
% 15.55/8.50       => ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.50         => ( ( ( minus_minus_nat @ M @ K )
% 15.55/8.50              = ( minus_minus_nat @ N @ K ) )
% 15.55/8.50            = ( M = N ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2311_div__le__dividend,axiom,
% 15.55/8.50      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2312_div__le__mono,axiom,
% 15.55/8.50      ! [M: nat,N: nat,K: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.50       => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2313_plus__int__code_I1_J,axiom,
% 15.55/8.50      ! [K: int] :
% 15.55/8.50        ( ( plus_plus_int @ K @ zero_zero_int )
% 15.55/8.50        = K ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2314_plus__int__code_I2_J,axiom,
% 15.55/8.50      ! [L: int] :
% 15.55/8.50        ( ( plus_plus_int @ zero_zero_int @ L )
% 15.55/8.50        = L ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2315_int__diff__cases,axiom,
% 15.55/8.50      ! [Z: int] :
% 15.55/8.50        ~ ! [M4: nat,N2: nat] :
% 15.55/8.50            ( Z
% 15.55/8.50           != ( minus_minus_int @ ( semiri1314217659103216013at_int @ M4 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2316_dvd__diff__nat,axiom,
% 15.55/8.50      ! [K: nat,M: nat,N: nat] :
% 15.55/8.50        ( ( dvd_dvd_nat @ K @ M )
% 15.55/8.50       => ( ( dvd_dvd_nat @ K @ N )
% 15.55/8.50         => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2317_take__bit__add,axiom,
% 15.55/8.50      ! [N: nat,A: int,B: int] :
% 15.55/8.50        ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) )
% 15.55/8.50        = ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ A @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2318_take__bit__add,axiom,
% 15.55/8.50      ! [N: nat,A: nat,B: nat] :
% 15.55/8.50        ( ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) )
% 15.55/8.50        = ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ A @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2319_zdvd__zdiffD,axiom,
% 15.55/8.50      ! [K: int,M: int,N: int] :
% 15.55/8.50        ( ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N ) )
% 15.55/8.50       => ( ( dvd_dvd_int @ K @ N )
% 15.55/8.50         => ( dvd_dvd_int @ K @ M ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2320_take__bit__diff,axiom,
% 15.55/8.50      ! [N: nat,K: int,L: int] :
% 15.55/8.50        ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L ) ) )
% 15.55/8.50        = ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2321_ln__eq__minus__one,axiom,
% 15.55/8.50      ! [X3: real] :
% 15.55/8.50        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.50       => ( ( ( ln_ln_real @ X3 )
% 15.55/8.50            = ( minus_minus_real @ X3 @ one_one_real ) )
% 15.55/8.50         => ( X3 = one_one_real ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2322_ln__add__one__self__le__self,axiom,
% 15.55/8.50      ! [X3: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.50       => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X3 ) ) @ X3 ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2323_artanh__def,axiom,
% 15.55/8.50      ( artanh_real
% 15.55/8.50      = ( ^ [X: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X ) @ ( minus_minus_real @ one_one_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2324_field__sum__of__halves,axiom,
% 15.55/8.50      ! [X3: real] :
% 15.55/8.50        ( ( plus_plus_real @ ( divide_divide_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.50        = X3 ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2325_field__sum__of__halves,axiom,
% 15.55/8.50      ! [X3: rat] :
% 15.55/8.50        ( ( plus_plus_rat @ ( divide_divide_rat @ X3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 15.55/8.50        = X3 ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2326_power__diff,axiom,
% 15.55/8.50      ! [A: complex,N: nat,M: nat] :
% 15.55/8.50        ( ( A != zero_zero_complex )
% 15.55/8.50       => ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.50         => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N ) )
% 15.55/8.50            = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2327_power__diff,axiom,
% 15.55/8.50      ! [A: real,N: nat,M: nat] :
% 15.55/8.50        ( ( A != zero_zero_real )
% 15.55/8.50       => ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.50         => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N ) )
% 15.55/8.50            = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2328_power__diff,axiom,
% 15.55/8.50      ! [A: rat,N: nat,M: nat] :
% 15.55/8.50        ( ( A != zero_zero_rat )
% 15.55/8.50       => ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.50         => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N ) )
% 15.55/8.50            = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2329_power__diff,axiom,
% 15.55/8.50      ! [A: nat,N: nat,M: nat] :
% 15.55/8.50        ( ( A != zero_zero_nat )
% 15.55/8.50       => ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.50         => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) )
% 15.55/8.50            = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2330_power__diff,axiom,
% 15.55/8.50      ! [A: int,N: nat,M: nat] :
% 15.55/8.50        ( ( A != zero_zero_int )
% 15.55/8.50       => ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.50         => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) )
% 15.55/8.50            = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2331_int__ops_I6_J,axiom,
% 15.55/8.50      ! [A: nat,B: nat] :
% 15.55/8.50        ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 15.55/8.50         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 15.55/8.50            = zero_zero_int ) )
% 15.55/8.50        & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 15.55/8.50         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 15.55/8.50            = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2332_nat__diff__distrib,axiom,
% 15.55/8.50      ! [Z5: int,Z: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ zero_zero_int @ Z5 )
% 15.55/8.50       => ( ( ord_less_eq_int @ Z5 @ Z )
% 15.55/8.50         => ( ( nat2 @ ( minus_minus_int @ Z @ Z5 ) )
% 15.55/8.50            = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z5 ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2333_nat__diff__distrib_H,axiom,
% 15.55/8.50      ! [X3: int,Y3: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 15.55/8.50       => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 15.55/8.50         => ( ( nat2 @ ( minus_minus_int @ X3 @ Y3 ) )
% 15.55/8.50            = ( minus_minus_nat @ ( nat2 @ X3 ) @ ( nat2 @ Y3 ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2334_unset__bit__nat__def,axiom,
% 15.55/8.50      ( bit_se4205575877204974255it_nat
% 15.55/8.50      = ( ^ [M3: nat,N3: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M3 @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2335_dbl__def,axiom,
% 15.55/8.50      ( neg_numeral_dbl_real
% 15.55/8.50      = ( ^ [X: real] : ( plus_plus_real @ X @ X ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2336_dbl__def,axiom,
% 15.55/8.50      ( neg_numeral_dbl_rat
% 15.55/8.50      = ( ^ [X: rat] : ( plus_plus_rat @ X @ X ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2337_dbl__def,axiom,
% 15.55/8.50      ( neg_numeral_dbl_int
% 15.55/8.50      = ( ^ [X: int] : ( plus_plus_int @ X @ X ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2338_unset__bit__less__eq,axiom,
% 15.55/8.50      ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2339_set__bit__greater__eq,axiom,
% 15.55/8.50      ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2340_ln__le__minus__one,axiom,
% 15.55/8.50      ! [X3: real] :
% 15.55/8.50        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.50       => ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ ( minus_minus_real @ X3 @ one_one_real ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2341_field__less__half__sum,axiom,
% 15.55/8.50      ! [X3: real,Y3: real] :
% 15.55/8.50        ( ( ord_less_real @ X3 @ Y3 )
% 15.55/8.50       => ( ord_less_real @ X3 @ ( divide_divide_real @ ( plus_plus_real @ X3 @ Y3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2342_field__less__half__sum,axiom,
% 15.55/8.50      ! [X3: rat,Y3: rat] :
% 15.55/8.50        ( ( ord_less_rat @ X3 @ Y3 )
% 15.55/8.50       => ( ord_less_rat @ X3 @ ( divide_divide_rat @ ( plus_plus_rat @ X3 @ Y3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2343_power__diff__power__eq,axiom,
% 15.55/8.50      ! [A: nat,N: nat,M: nat] :
% 15.55/8.50        ( ( A != zero_zero_nat )
% 15.55/8.50       => ( ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.50           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 15.55/8.50              = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 15.55/8.50          & ( ~ ( ord_less_eq_nat @ N @ M )
% 15.55/8.50           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 15.55/8.50              = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2344_power__diff__power__eq,axiom,
% 15.55/8.50      ! [A: int,N: nat,M: nat] :
% 15.55/8.50        ( ( A != zero_zero_int )
% 15.55/8.50       => ( ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.50           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 15.55/8.50              = ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 15.55/8.50          & ( ~ ( ord_less_eq_nat @ N @ M )
% 15.55/8.50           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 15.55/8.50              = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2345_ln__less__self,axiom,
% 15.55/8.50      ! [X3: real] :
% 15.55/8.50        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.50       => ( ord_less_real @ ( ln_ln_real @ X3 ) @ X3 ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2346_zdiff__int__split,axiom,
% 15.55/8.50      ! [P: int > $o,X3: nat,Y3: nat] :
% 15.55/8.50        ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X3 @ Y3 ) ) )
% 15.55/8.50        = ( ( ( ord_less_eq_nat @ Y3 @ X3 )
% 15.55/8.50           => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( semiri1314217659103216013at_int @ Y3 ) ) ) )
% 15.55/8.50          & ( ( ord_less_nat @ X3 @ Y3 )
% 15.55/8.50           => ( P @ zero_zero_int ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2347_even__diff__iff,axiom,
% 15.55/8.50      ! [K: int,L: int] :
% 15.55/8.50        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L ) )
% 15.55/8.50        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2348_le__iff__diff__le__0,axiom,
% 15.55/8.50      ( ord_less_eq_real
% 15.55/8.50      = ( ^ [A4: real,B3: real] : ( ord_less_eq_real @ ( minus_minus_real @ A4 @ B3 ) @ zero_zero_real ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2349_le__iff__diff__le__0,axiom,
% 15.55/8.50      ( ord_less_eq_rat
% 15.55/8.50      = ( ^ [A4: rat,B3: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A4 @ B3 ) @ zero_zero_rat ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2350_le__iff__diff__le__0,axiom,
% 15.55/8.50      ( ord_less_eq_int
% 15.55/8.50      = ( ^ [A4: int,B3: int] : ( ord_less_eq_int @ ( minus_minus_int @ A4 @ B3 ) @ zero_zero_int ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2351_less__iff__diff__less__0,axiom,
% 15.55/8.50      ( ord_less_real
% 15.55/8.50      = ( ^ [A4: real,B3: real] : ( ord_less_real @ ( minus_minus_real @ A4 @ B3 ) @ zero_zero_real ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2352_less__iff__diff__less__0,axiom,
% 15.55/8.50      ( ord_less_rat
% 15.55/8.50      = ( ^ [A4: rat,B3: rat] : ( ord_less_rat @ ( minus_minus_rat @ A4 @ B3 ) @ zero_zero_rat ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2353_less__iff__diff__less__0,axiom,
% 15.55/8.50      ( ord_less_int
% 15.55/8.50      = ( ^ [A4: int,B3: int] : ( ord_less_int @ ( minus_minus_int @ A4 @ B3 ) @ zero_zero_int ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2354_divide__numeral__1,axiom,
% 15.55/8.50      ! [A: complex] :
% 15.55/8.50        ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 15.55/8.50        = A ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2355_divide__numeral__1,axiom,
% 15.55/8.50      ! [A: real] :
% 15.55/8.50        ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 15.55/8.50        = A ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2356_divide__numeral__1,axiom,
% 15.55/8.50      ! [A: rat] :
% 15.55/8.50        ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 15.55/8.50        = A ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2357_add__decreasing,axiom,
% 15.55/8.50      ! [A: real,C: real,B: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 15.55/8.50       => ( ( ord_less_eq_real @ C @ B )
% 15.55/8.50         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2358_add__decreasing,axiom,
% 15.55/8.50      ! [A: rat,C: rat,B: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 15.55/8.50       => ( ( ord_less_eq_rat @ C @ B )
% 15.55/8.50         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2359_add__decreasing,axiom,
% 15.55/8.50      ! [A: nat,C: nat,B: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 15.55/8.50       => ( ( ord_less_eq_nat @ C @ B )
% 15.55/8.50         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2360_add__decreasing,axiom,
% 15.55/8.50      ! [A: int,C: int,B: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 15.55/8.50       => ( ( ord_less_eq_int @ C @ B )
% 15.55/8.50         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2361_add__increasing,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.50       => ( ( ord_less_eq_real @ B @ C )
% 15.55/8.50         => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2362_add__increasing,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.50       => ( ( ord_less_eq_rat @ B @ C )
% 15.55/8.50         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2363_add__increasing,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.55/8.50       => ( ( ord_less_eq_nat @ B @ C )
% 15.55/8.50         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2364_add__increasing,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.50       => ( ( ord_less_eq_int @ B @ C )
% 15.55/8.50         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2365_add__decreasing2,axiom,
% 15.55/8.50      ! [C: real,A: real,B: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ C @ zero_zero_real )
% 15.55/8.50       => ( ( ord_less_eq_real @ A @ B )
% 15.55/8.50         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2366_add__decreasing2,axiom,
% 15.55/8.50      ! [C: rat,A: rat,B: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 15.55/8.50       => ( ( ord_less_eq_rat @ A @ B )
% 15.55/8.50         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2367_add__decreasing2,axiom,
% 15.55/8.50      ! [C: nat,A: nat,B: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 15.55/8.50       => ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.50         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2368_add__decreasing2,axiom,
% 15.55/8.50      ! [C: int,A: int,B: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ C @ zero_zero_int )
% 15.55/8.50       => ( ( ord_less_eq_int @ A @ B )
% 15.55/8.50         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2369_add__increasing2,axiom,
% 15.55/8.50      ! [C: real,B: real,A: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ zero_zero_real @ C )
% 15.55/8.50       => ( ( ord_less_eq_real @ B @ A )
% 15.55/8.50         => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2370_add__increasing2,axiom,
% 15.55/8.50      ! [C: rat,B: rat,A: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 15.55/8.50       => ( ( ord_less_eq_rat @ B @ A )
% 15.55/8.50         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2371_add__increasing2,axiom,
% 15.55/8.50      ! [C: nat,B: nat,A: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 15.55/8.50       => ( ( ord_less_eq_nat @ B @ A )
% 15.55/8.50         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2372_add__increasing2,axiom,
% 15.55/8.50      ! [C: int,B: int,A: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 15.55/8.50       => ( ( ord_less_eq_int @ B @ A )
% 15.55/8.50         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2373_add__nonneg__nonneg,axiom,
% 15.55/8.50      ! [A: real,B: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.50       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 15.55/8.50         => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2374_add__nonneg__nonneg,axiom,
% 15.55/8.50      ! [A: rat,B: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.50       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 15.55/8.50         => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2375_add__nonneg__nonneg,axiom,
% 15.55/8.50      ! [A: nat,B: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.55/8.50       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 15.55/8.50         => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2376_add__nonneg__nonneg,axiom,
% 15.55/8.50      ! [A: int,B: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.50       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 15.55/8.50         => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2377_add__nonpos__nonpos,axiom,
% 15.55/8.50      ! [A: real,B: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 15.55/8.50       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 15.55/8.50         => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2378_add__nonpos__nonpos,axiom,
% 15.55/8.50      ! [A: rat,B: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 15.55/8.50       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 15.55/8.50         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2379_add__nonpos__nonpos,axiom,
% 15.55/8.50      ! [A: nat,B: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 15.55/8.50       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 15.55/8.50         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2380_add__nonpos__nonpos,axiom,
% 15.55/8.50      ! [A: int,B: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 15.55/8.50       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 15.55/8.50         => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2381_add__nonneg__eq__0__iff,axiom,
% 15.55/8.50      ! [X3: real,Y3: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.50       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.50         => ( ( ( plus_plus_real @ X3 @ Y3 )
% 15.55/8.50              = zero_zero_real )
% 15.55/8.50            = ( ( X3 = zero_zero_real )
% 15.55/8.50              & ( Y3 = zero_zero_real ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2382_add__nonneg__eq__0__iff,axiom,
% 15.55/8.50      ! [X3: rat,Y3: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 15.55/8.50       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 15.55/8.50         => ( ( ( plus_plus_rat @ X3 @ Y3 )
% 15.55/8.50              = zero_zero_rat )
% 15.55/8.50            = ( ( X3 = zero_zero_rat )
% 15.55/8.50              & ( Y3 = zero_zero_rat ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2383_add__nonneg__eq__0__iff,axiom,
% 15.55/8.50      ! [X3: nat,Y3: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ zero_zero_nat @ X3 )
% 15.55/8.50       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 15.55/8.50         => ( ( ( plus_plus_nat @ X3 @ Y3 )
% 15.55/8.50              = zero_zero_nat )
% 15.55/8.50            = ( ( X3 = zero_zero_nat )
% 15.55/8.50              & ( Y3 = zero_zero_nat ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2384_add__nonneg__eq__0__iff,axiom,
% 15.55/8.50      ! [X3: int,Y3: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 15.55/8.50       => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 15.55/8.50         => ( ( ( plus_plus_int @ X3 @ Y3 )
% 15.55/8.50              = zero_zero_int )
% 15.55/8.50            = ( ( X3 = zero_zero_int )
% 15.55/8.50              & ( Y3 = zero_zero_int ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2385_add__nonpos__eq__0__iff,axiom,
% 15.55/8.50      ! [X3: real,Y3: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 15.55/8.50       => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 15.55/8.50         => ( ( ( plus_plus_real @ X3 @ Y3 )
% 15.55/8.50              = zero_zero_real )
% 15.55/8.50            = ( ( X3 = zero_zero_real )
% 15.55/8.50              & ( Y3 = zero_zero_real ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2386_add__nonpos__eq__0__iff,axiom,
% 15.55/8.50      ! [X3: rat,Y3: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 15.55/8.50       => ( ( ord_less_eq_rat @ Y3 @ zero_zero_rat )
% 15.55/8.50         => ( ( ( plus_plus_rat @ X3 @ Y3 )
% 15.55/8.50              = zero_zero_rat )
% 15.55/8.50            = ( ( X3 = zero_zero_rat )
% 15.55/8.50              & ( Y3 = zero_zero_rat ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2387_add__nonpos__eq__0__iff,axiom,
% 15.55/8.50      ! [X3: nat,Y3: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ X3 @ zero_zero_nat )
% 15.55/8.50       => ( ( ord_less_eq_nat @ Y3 @ zero_zero_nat )
% 15.55/8.50         => ( ( ( plus_plus_nat @ X3 @ Y3 )
% 15.55/8.50              = zero_zero_nat )
% 15.55/8.50            = ( ( X3 = zero_zero_nat )
% 15.55/8.50              & ( Y3 = zero_zero_nat ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2388_add__nonpos__eq__0__iff,axiom,
% 15.55/8.50      ! [X3: int,Y3: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ X3 @ zero_zero_int )
% 15.55/8.50       => ( ( ord_less_eq_int @ Y3 @ zero_zero_int )
% 15.55/8.50         => ( ( ( plus_plus_int @ X3 @ Y3 )
% 15.55/8.50              = zero_zero_int )
% 15.55/8.50            = ( ( X3 = zero_zero_int )
% 15.55/8.50              & ( Y3 = zero_zero_int ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2389_add__less__le__mono,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real,D3: real] :
% 15.55/8.50        ( ( ord_less_real @ A @ B )
% 15.55/8.50       => ( ( ord_less_eq_real @ C @ D3 )
% 15.55/8.50         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2390_add__less__le__mono,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat,D3: rat] :
% 15.55/8.50        ( ( ord_less_rat @ A @ B )
% 15.55/8.50       => ( ( ord_less_eq_rat @ C @ D3 )
% 15.55/8.50         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2391_add__less__le__mono,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat,D3: nat] :
% 15.55/8.50        ( ( ord_less_nat @ A @ B )
% 15.55/8.50       => ( ( ord_less_eq_nat @ C @ D3 )
% 15.55/8.50         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2392_add__less__le__mono,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int,D3: int] :
% 15.55/8.50        ( ( ord_less_int @ A @ B )
% 15.55/8.50       => ( ( ord_less_eq_int @ C @ D3 )
% 15.55/8.50         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2393_add__le__less__mono,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real,D3: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.50       => ( ( ord_less_real @ C @ D3 )
% 15.55/8.50         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2394_add__le__less__mono,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat,D3: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ A @ B )
% 15.55/8.50       => ( ( ord_less_rat @ C @ D3 )
% 15.55/8.50         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2395_add__le__less__mono,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat,D3: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.50       => ( ( ord_less_nat @ C @ D3 )
% 15.55/8.50         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2396_add__le__less__mono,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int,D3: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ A @ B )
% 15.55/8.50       => ( ( ord_less_int @ C @ D3 )
% 15.55/8.50         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D3 ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2397_add__mono__thms__linordered__field_I3_J,axiom,
% 15.55/8.50      ! [I: real,J: real,K: real,L: real] :
% 15.55/8.50        ( ( ( ord_less_real @ I @ J )
% 15.55/8.50          & ( ord_less_eq_real @ K @ L ) )
% 15.55/8.50       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2398_add__mono__thms__linordered__field_I3_J,axiom,
% 15.55/8.50      ! [I: rat,J: rat,K: rat,L: rat] :
% 15.55/8.50        ( ( ( ord_less_rat @ I @ J )
% 15.55/8.50          & ( ord_less_eq_rat @ K @ L ) )
% 15.55/8.50       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2399_add__mono__thms__linordered__field_I3_J,axiom,
% 15.55/8.50      ! [I: nat,J: nat,K: nat,L: nat] :
% 15.55/8.50        ( ( ( ord_less_nat @ I @ J )
% 15.55/8.50          & ( ord_less_eq_nat @ K @ L ) )
% 15.55/8.50       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2400_add__mono__thms__linordered__field_I3_J,axiom,
% 15.55/8.50      ! [I: int,J: int,K: int,L: int] :
% 15.55/8.50        ( ( ( ord_less_int @ I @ J )
% 15.55/8.50          & ( ord_less_eq_int @ K @ L ) )
% 15.55/8.50       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2401_add__mono__thms__linordered__field_I4_J,axiom,
% 15.55/8.50      ! [I: real,J: real,K: real,L: real] :
% 15.55/8.50        ( ( ( ord_less_eq_real @ I @ J )
% 15.55/8.50          & ( ord_less_real @ K @ L ) )
% 15.55/8.50       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2402_add__mono__thms__linordered__field_I4_J,axiom,
% 15.55/8.50      ! [I: rat,J: rat,K: rat,L: rat] :
% 15.55/8.50        ( ( ( ord_less_eq_rat @ I @ J )
% 15.55/8.50          & ( ord_less_rat @ K @ L ) )
% 15.55/8.50       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2403_add__mono__thms__linordered__field_I4_J,axiom,
% 15.55/8.50      ! [I: nat,J: nat,K: nat,L: nat] :
% 15.55/8.50        ( ( ( ord_less_eq_nat @ I @ J )
% 15.55/8.50          & ( ord_less_nat @ K @ L ) )
% 15.55/8.50       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2404_add__mono__thms__linordered__field_I4_J,axiom,
% 15.55/8.50      ! [I: int,J: int,K: int,L: int] :
% 15.55/8.50        ( ( ( ord_less_eq_int @ I @ J )
% 15.55/8.50          & ( ord_less_int @ K @ L ) )
% 15.55/8.50       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2405_add__neg__neg,axiom,
% 15.55/8.50      ! [A: real,B: real] :
% 15.55/8.50        ( ( ord_less_real @ A @ zero_zero_real )
% 15.55/8.50       => ( ( ord_less_real @ B @ zero_zero_real )
% 15.55/8.50         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2406_add__neg__neg,axiom,
% 15.55/8.50      ! [A: rat,B: rat] :
% 15.55/8.50        ( ( ord_less_rat @ A @ zero_zero_rat )
% 15.55/8.50       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 15.55/8.50         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2407_add__neg__neg,axiom,
% 15.55/8.50      ! [A: nat,B: nat] :
% 15.55/8.50        ( ( ord_less_nat @ A @ zero_zero_nat )
% 15.55/8.50       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 15.55/8.50         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2408_add__neg__neg,axiom,
% 15.55/8.50      ! [A: int,B: int] :
% 15.55/8.50        ( ( ord_less_int @ A @ zero_zero_int )
% 15.55/8.50       => ( ( ord_less_int @ B @ zero_zero_int )
% 15.55/8.50         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2409_add__pos__pos,axiom,
% 15.55/8.50      ! [A: real,B: real] :
% 15.55/8.50        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.50       => ( ( ord_less_real @ zero_zero_real @ B )
% 15.55/8.50         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2410_add__pos__pos,axiom,
% 15.55/8.50      ! [A: rat,B: rat] :
% 15.55/8.50        ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.50       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 15.55/8.50         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2411_add__pos__pos,axiom,
% 15.55/8.50      ! [A: nat,B: nat] :
% 15.55/8.50        ( ( ord_less_nat @ zero_zero_nat @ A )
% 15.55/8.50       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 15.55/8.50         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2412_add__pos__pos,axiom,
% 15.55/8.50      ! [A: int,B: int] :
% 15.55/8.50        ( ( ord_less_int @ zero_zero_int @ A )
% 15.55/8.50       => ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.50         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2413_canonically__ordered__monoid__add__class_OlessE,axiom,
% 15.55/8.50      ! [A: nat,B: nat] :
% 15.55/8.50        ( ( ord_less_nat @ A @ B )
% 15.55/8.50       => ~ ! [C2: nat] :
% 15.55/8.50              ( ( B
% 15.55/8.50                = ( plus_plus_nat @ A @ C2 ) )
% 15.55/8.50             => ( C2 = zero_zero_nat ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2414_pos__add__strict,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.50       => ( ( ord_less_real @ B @ C )
% 15.55/8.50         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2415_pos__add__strict,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.50       => ( ( ord_less_rat @ B @ C )
% 15.55/8.50         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2416_pos__add__strict,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat] :
% 15.55/8.50        ( ( ord_less_nat @ zero_zero_nat @ A )
% 15.55/8.50       => ( ( ord_less_nat @ B @ C )
% 15.55/8.50         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2417_pos__add__strict,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( ord_less_int @ zero_zero_int @ A )
% 15.55/8.50       => ( ( ord_less_int @ B @ C )
% 15.55/8.50         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2418_add__less__zeroD,axiom,
% 15.55/8.50      ! [X3: real,Y3: real] :
% 15.55/8.50        ( ( ord_less_real @ ( plus_plus_real @ X3 @ Y3 ) @ zero_zero_real )
% 15.55/8.50       => ( ( ord_less_real @ X3 @ zero_zero_real )
% 15.55/8.50          | ( ord_less_real @ Y3 @ zero_zero_real ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2419_add__less__zeroD,axiom,
% 15.55/8.50      ! [X3: rat,Y3: rat] :
% 15.55/8.50        ( ( ord_less_rat @ ( plus_plus_rat @ X3 @ Y3 ) @ zero_zero_rat )
% 15.55/8.50       => ( ( ord_less_rat @ X3 @ zero_zero_rat )
% 15.55/8.50          | ( ord_less_rat @ Y3 @ zero_zero_rat ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2420_add__less__zeroD,axiom,
% 15.55/8.50      ! [X3: int,Y3: int] :
% 15.55/8.50        ( ( ord_less_int @ ( plus_plus_int @ X3 @ Y3 ) @ zero_zero_int )
% 15.55/8.50       => ( ( ord_less_int @ X3 @ zero_zero_int )
% 15.55/8.50          | ( ord_less_int @ Y3 @ zero_zero_int ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2421_dvd__div__eq__0__iff,axiom,
% 15.55/8.50      ! [B: code_integer,A: code_integer] :
% 15.55/8.50        ( ( dvd_dvd_Code_integer @ B @ A )
% 15.55/8.50       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 15.55/8.50            = zero_z3403309356797280102nteger )
% 15.55/8.50          = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2422_dvd__div__eq__0__iff,axiom,
% 15.55/8.50      ! [B: complex,A: complex] :
% 15.55/8.50        ( ( dvd_dvd_complex @ B @ A )
% 15.55/8.50       => ( ( ( divide1717551699836669952omplex @ A @ B )
% 15.55/8.50            = zero_zero_complex )
% 15.55/8.50          = ( A = zero_zero_complex ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2423_dvd__div__eq__0__iff,axiom,
% 15.55/8.50      ! [B: real,A: real] :
% 15.55/8.50        ( ( dvd_dvd_real @ B @ A )
% 15.55/8.50       => ( ( ( divide_divide_real @ A @ B )
% 15.55/8.50            = zero_zero_real )
% 15.55/8.50          = ( A = zero_zero_real ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2424_dvd__div__eq__0__iff,axiom,
% 15.55/8.50      ! [B: rat,A: rat] :
% 15.55/8.50        ( ( dvd_dvd_rat @ B @ A )
% 15.55/8.50       => ( ( ( divide_divide_rat @ A @ B )
% 15.55/8.50            = zero_zero_rat )
% 15.55/8.50          = ( A = zero_zero_rat ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2425_dvd__div__eq__0__iff,axiom,
% 15.55/8.50      ! [B: nat,A: nat] :
% 15.55/8.50        ( ( dvd_dvd_nat @ B @ A )
% 15.55/8.50       => ( ( ( divide_divide_nat @ A @ B )
% 15.55/8.50            = zero_zero_nat )
% 15.55/8.50          = ( A = zero_zero_nat ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2426_dvd__div__eq__0__iff,axiom,
% 15.55/8.50      ! [B: int,A: int] :
% 15.55/8.50        ( ( dvd_dvd_int @ B @ A )
% 15.55/8.50       => ( ( ( divide_divide_int @ A @ B )
% 15.55/8.50            = zero_zero_int )
% 15.55/8.50          = ( A = zero_zero_int ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2427_power__one__over,axiom,
% 15.55/8.50      ! [A: complex,N: nat] :
% 15.55/8.50        ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N )
% 15.55/8.50        = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2428_power__one__over,axiom,
% 15.55/8.50      ! [A: real,N: nat] :
% 15.55/8.50        ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N )
% 15.55/8.50        = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2429_power__one__over,axiom,
% 15.55/8.50      ! [A: rat,N: nat] :
% 15.55/8.50        ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 15.55/8.50        = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2430_add__mono1,axiom,
% 15.55/8.50      ! [A: real,B: real] :
% 15.55/8.50        ( ( ord_less_real @ A @ B )
% 15.55/8.50       => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2431_add__mono1,axiom,
% 15.55/8.50      ! [A: rat,B: rat] :
% 15.55/8.50        ( ( ord_less_rat @ A @ B )
% 15.55/8.50       => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2432_add__mono1,axiom,
% 15.55/8.50      ! [A: nat,B: nat] :
% 15.55/8.50        ( ( ord_less_nat @ A @ B )
% 15.55/8.50       => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2433_add__mono1,axiom,
% 15.55/8.50      ! [A: int,B: int] :
% 15.55/8.50        ( ( ord_less_int @ A @ B )
% 15.55/8.50       => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2434_less__add__one,axiom,
% 15.55/8.50      ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2435_less__add__one,axiom,
% 15.55/8.50      ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2436_less__add__one,axiom,
% 15.55/8.50      ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2437_less__add__one,axiom,
% 15.55/8.50      ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2438_numeral__Bit0,axiom,
% 15.55/8.50      ! [N: num] :
% 15.55/8.50        ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 15.55/8.50        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2439_numeral__Bit0,axiom,
% 15.55/8.50      ! [N: num] :
% 15.55/8.50        ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 15.55/8.50        = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2440_numeral__Bit0,axiom,
% 15.55/8.50      ! [N: num] :
% 15.55/8.50        ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 15.55/8.50        = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2441_numeral__Bit0,axiom,
% 15.55/8.50      ! [N: num] :
% 15.55/8.50        ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 15.55/8.50        = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2442_numeral__Bit0,axiom,
% 15.55/8.50      ! [N: num] :
% 15.55/8.50        ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 15.55/8.50        = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2443_one__plus__numeral__commute,axiom,
% 15.55/8.50      ! [X3: num] :
% 15.55/8.50        ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X3 ) )
% 15.55/8.50        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X3 ) @ one_one_complex ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2444_one__plus__numeral__commute,axiom,
% 15.55/8.50      ! [X3: num] :
% 15.55/8.50        ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X3 ) )
% 15.55/8.50        = ( plus_plus_real @ ( numeral_numeral_real @ X3 ) @ one_one_real ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2445_one__plus__numeral__commute,axiom,
% 15.55/8.50      ! [X3: num] :
% 15.55/8.50        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X3 ) )
% 15.55/8.50        = ( plus_plus_rat @ ( numeral_numeral_rat @ X3 ) @ one_one_rat ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2446_one__plus__numeral__commute,axiom,
% 15.55/8.50      ! [X3: num] :
% 15.55/8.50        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X3 ) )
% 15.55/8.50        = ( plus_plus_nat @ ( numeral_numeral_nat @ X3 ) @ one_one_nat ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2447_one__plus__numeral__commute,axiom,
% 15.55/8.50      ! [X3: num] :
% 15.55/8.50        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X3 ) )
% 15.55/8.50        = ( plus_plus_int @ ( numeral_numeral_int @ X3 ) @ one_one_int ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2448_div__power,axiom,
% 15.55/8.50      ! [B: code_integer,A: code_integer,N: nat] :
% 15.55/8.50        ( ( dvd_dvd_Code_integer @ B @ A )
% 15.55/8.50       => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N )
% 15.55/8.50          = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2449_div__power,axiom,
% 15.55/8.50      ! [B: nat,A: nat,N: nat] :
% 15.55/8.50        ( ( dvd_dvd_nat @ B @ A )
% 15.55/8.50       => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N )
% 15.55/8.50          = ( divide_divide_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2450_div__power,axiom,
% 15.55/8.50      ! [B: int,A: int,N: nat] :
% 15.55/8.50        ( ( dvd_dvd_int @ B @ A )
% 15.55/8.50       => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N )
% 15.55/8.50          = ( divide_divide_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2451_pinf_I9_J,axiom,
% 15.55/8.50      ! [D3: code_integer,S: code_integer] :
% 15.55/8.50      ? [Z3: code_integer] :
% 15.55/8.50      ! [X6: code_integer] :
% 15.55/8.50        ( ( ord_le6747313008572928689nteger @ Z3 @ X6 )
% 15.55/8.50       => ( ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ X6 @ S ) )
% 15.55/8.50          = ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ X6 @ S ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2452_pinf_I9_J,axiom,
% 15.55/8.50      ! [D3: real,S: real] :
% 15.55/8.50      ? [Z3: real] :
% 15.55/8.50      ! [X6: real] :
% 15.55/8.50        ( ( ord_less_real @ Z3 @ X6 )
% 15.55/8.50       => ( ( dvd_dvd_real @ D3 @ ( plus_plus_real @ X6 @ S ) )
% 15.55/8.50          = ( dvd_dvd_real @ D3 @ ( plus_plus_real @ X6 @ S ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2453_pinf_I9_J,axiom,
% 15.55/8.50      ! [D3: rat,S: rat] :
% 15.55/8.50      ? [Z3: rat] :
% 15.55/8.50      ! [X6: rat] :
% 15.55/8.50        ( ( ord_less_rat @ Z3 @ X6 )
% 15.55/8.50       => ( ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ X6 @ S ) )
% 15.55/8.50          = ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ X6 @ S ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2454_pinf_I9_J,axiom,
% 15.55/8.50      ! [D3: nat,S: nat] :
% 15.55/8.50      ? [Z3: nat] :
% 15.55/8.50      ! [X6: nat] :
% 15.55/8.50        ( ( ord_less_nat @ Z3 @ X6 )
% 15.55/8.50       => ( ( dvd_dvd_nat @ D3 @ ( plus_plus_nat @ X6 @ S ) )
% 15.55/8.50          = ( dvd_dvd_nat @ D3 @ ( plus_plus_nat @ X6 @ S ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2455_pinf_I9_J,axiom,
% 15.55/8.50      ! [D3: int,S: int] :
% 15.55/8.50      ? [Z3: int] :
% 15.55/8.50      ! [X6: int] :
% 15.55/8.50        ( ( ord_less_int @ Z3 @ X6 )
% 15.55/8.50       => ( ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ S ) )
% 15.55/8.50          = ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ S ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2456_pinf_I10_J,axiom,
% 15.55/8.50      ! [D3: code_integer,S: code_integer] :
% 15.55/8.50      ? [Z3: code_integer] :
% 15.55/8.50      ! [X6: code_integer] :
% 15.55/8.50        ( ( ord_le6747313008572928689nteger @ Z3 @ X6 )
% 15.55/8.50       => ( ( ~ ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ X6 @ S ) ) )
% 15.55/8.50          = ( ~ ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ X6 @ S ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2457_pinf_I10_J,axiom,
% 15.55/8.50      ! [D3: real,S: real] :
% 15.55/8.50      ? [Z3: real] :
% 15.55/8.50      ! [X6: real] :
% 15.55/8.50        ( ( ord_less_real @ Z3 @ X6 )
% 15.55/8.50       => ( ( ~ ( dvd_dvd_real @ D3 @ ( plus_plus_real @ X6 @ S ) ) )
% 15.55/8.50          = ( ~ ( dvd_dvd_real @ D3 @ ( plus_plus_real @ X6 @ S ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2458_pinf_I10_J,axiom,
% 15.55/8.50      ! [D3: rat,S: rat] :
% 15.55/8.50      ? [Z3: rat] :
% 15.55/8.50      ! [X6: rat] :
% 15.55/8.50        ( ( ord_less_rat @ Z3 @ X6 )
% 15.55/8.50       => ( ( ~ ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ X6 @ S ) ) )
% 15.55/8.50          = ( ~ ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ X6 @ S ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2459_pinf_I10_J,axiom,
% 15.55/8.50      ! [D3: nat,S: nat] :
% 15.55/8.50      ? [Z3: nat] :
% 15.55/8.50      ! [X6: nat] :
% 15.55/8.50        ( ( ord_less_nat @ Z3 @ X6 )
% 15.55/8.50       => ( ( ~ ( dvd_dvd_nat @ D3 @ ( plus_plus_nat @ X6 @ S ) ) )
% 15.55/8.50          = ( ~ ( dvd_dvd_nat @ D3 @ ( plus_plus_nat @ X6 @ S ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2460_pinf_I10_J,axiom,
% 15.55/8.50      ! [D3: int,S: int] :
% 15.55/8.50      ? [Z3: int] :
% 15.55/8.50      ! [X6: int] :
% 15.55/8.50        ( ( ord_less_int @ Z3 @ X6 )
% 15.55/8.50       => ( ( ~ ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ S ) ) )
% 15.55/8.50          = ( ~ ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ S ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2461_minf_I9_J,axiom,
% 15.55/8.50      ! [D3: code_integer,S: code_integer] :
% 15.55/8.50      ? [Z3: code_integer] :
% 15.55/8.50      ! [X6: code_integer] :
% 15.55/8.50        ( ( ord_le6747313008572928689nteger @ X6 @ Z3 )
% 15.55/8.50       => ( ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ X6 @ S ) )
% 15.55/8.50          = ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ X6 @ S ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2462_minf_I9_J,axiom,
% 15.55/8.50      ! [D3: real,S: real] :
% 15.55/8.50      ? [Z3: real] :
% 15.55/8.50      ! [X6: real] :
% 15.55/8.50        ( ( ord_less_real @ X6 @ Z3 )
% 15.55/8.50       => ( ( dvd_dvd_real @ D3 @ ( plus_plus_real @ X6 @ S ) )
% 15.55/8.50          = ( dvd_dvd_real @ D3 @ ( plus_plus_real @ X6 @ S ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2463_minf_I9_J,axiom,
% 15.55/8.50      ! [D3: rat,S: rat] :
% 15.55/8.50      ? [Z3: rat] :
% 15.55/8.50      ! [X6: rat] :
% 15.55/8.50        ( ( ord_less_rat @ X6 @ Z3 )
% 15.55/8.50       => ( ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ X6 @ S ) )
% 15.55/8.50          = ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ X6 @ S ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2464_minf_I9_J,axiom,
% 15.55/8.50      ! [D3: nat,S: nat] :
% 15.55/8.50      ? [Z3: nat] :
% 15.55/8.50      ! [X6: nat] :
% 15.55/8.50        ( ( ord_less_nat @ X6 @ Z3 )
% 15.55/8.50       => ( ( dvd_dvd_nat @ D3 @ ( plus_plus_nat @ X6 @ S ) )
% 15.55/8.50          = ( dvd_dvd_nat @ D3 @ ( plus_plus_nat @ X6 @ S ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2465_minf_I9_J,axiom,
% 15.55/8.50      ! [D3: int,S: int] :
% 15.55/8.50      ? [Z3: int] :
% 15.55/8.50      ! [X6: int] :
% 15.55/8.50        ( ( ord_less_int @ X6 @ Z3 )
% 15.55/8.50       => ( ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ S ) )
% 15.55/8.50          = ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ S ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2466_minf_I10_J,axiom,
% 15.55/8.50      ! [D3: code_integer,S: code_integer] :
% 15.55/8.50      ? [Z3: code_integer] :
% 15.55/8.50      ! [X6: code_integer] :
% 15.55/8.50        ( ( ord_le6747313008572928689nteger @ X6 @ Z3 )
% 15.55/8.50       => ( ( ~ ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ X6 @ S ) ) )
% 15.55/8.50          = ( ~ ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ X6 @ S ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2467_minf_I10_J,axiom,
% 15.55/8.50      ! [D3: real,S: real] :
% 15.55/8.50      ? [Z3: real] :
% 15.55/8.50      ! [X6: real] :
% 15.55/8.50        ( ( ord_less_real @ X6 @ Z3 )
% 15.55/8.50       => ( ( ~ ( dvd_dvd_real @ D3 @ ( plus_plus_real @ X6 @ S ) ) )
% 15.55/8.50          = ( ~ ( dvd_dvd_real @ D3 @ ( plus_plus_real @ X6 @ S ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2468_minf_I10_J,axiom,
% 15.55/8.50      ! [D3: rat,S: rat] :
% 15.55/8.50      ? [Z3: rat] :
% 15.55/8.50      ! [X6: rat] :
% 15.55/8.50        ( ( ord_less_rat @ X6 @ Z3 )
% 15.55/8.50       => ( ( ~ ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ X6 @ S ) ) )
% 15.55/8.50          = ( ~ ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ X6 @ S ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2469_minf_I10_J,axiom,
% 15.55/8.50      ! [D3: nat,S: nat] :
% 15.55/8.50      ? [Z3: nat] :
% 15.55/8.50      ! [X6: nat] :
% 15.55/8.50        ( ( ord_less_nat @ X6 @ Z3 )
% 15.55/8.50       => ( ( ~ ( dvd_dvd_nat @ D3 @ ( plus_plus_nat @ X6 @ S ) ) )
% 15.55/8.50          = ( ~ ( dvd_dvd_nat @ D3 @ ( plus_plus_nat @ X6 @ S ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2470_minf_I10_J,axiom,
% 15.55/8.50      ! [D3: int,S: int] :
% 15.55/8.50      ? [Z3: int] :
% 15.55/8.50      ! [X6: int] :
% 15.55/8.50        ( ( ord_less_int @ X6 @ Z3 )
% 15.55/8.50       => ( ( ~ ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ S ) ) )
% 15.55/8.50          = ( ~ ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ S ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2471_ln__one__plus__pos__lower__bound,axiom,
% 15.55/8.50      ! [X3: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.50       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 15.55/8.50         => ( ord_less_eq_real @ ( minus_minus_real @ X3 @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X3 ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2472_diff__less,axiom,
% 15.55/8.50      ! [N: nat,M: nat] :
% 15.55/8.50        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.50       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 15.55/8.50         => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2473_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 15.55/8.50      ! [M: nat,N: nat] :
% 15.55/8.50        ( ( ( divide_divide_nat @ M @ N )
% 15.55/8.50          = zero_zero_nat )
% 15.55/8.50        = ( ( ord_less_nat @ M @ N )
% 15.55/8.50          | ( N = zero_zero_nat ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2474_diff__less__mono,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat] :
% 15.55/8.50        ( ( ord_less_nat @ A @ B )
% 15.55/8.50       => ( ( ord_less_eq_nat @ C @ A )
% 15.55/8.50         => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2475_less__diff__iff,axiom,
% 15.55/8.50      ! [K: nat,M: nat,N: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ K @ M )
% 15.55/8.50       => ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.50         => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 15.55/8.50            = ( ord_less_nat @ M @ N ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2476_arcosh__real__def,axiom,
% 15.55/8.50      ! [X3: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ one_one_real @ X3 )
% 15.55/8.50       => ( ( arcosh_real @ X3 )
% 15.55/8.50          = ( ln_ln_real @ ( plus_plus_real @ X3 @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2477_dvd__minus__self,axiom,
% 15.55/8.50      ! [M: nat,N: nat] :
% 15.55/8.50        ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 15.55/8.50        = ( ( ord_less_nat @ N @ M )
% 15.55/8.50          | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2478_int__le__induct,axiom,
% 15.55/8.50      ! [I: int,K: int,P: int > $o] :
% 15.55/8.50        ( ( ord_less_eq_int @ I @ K )
% 15.55/8.50       => ( ( P @ K )
% 15.55/8.50         => ( ! [I3: int] :
% 15.55/8.50                ( ( ord_less_eq_int @ I3 @ K )
% 15.55/8.50               => ( ( P @ I3 )
% 15.55/8.50                 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 15.55/8.50           => ( P @ I ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2479_int__less__induct,axiom,
% 15.55/8.50      ! [I: int,K: int,P: int > $o] :
% 15.55/8.50        ( ( ord_less_int @ I @ K )
% 15.55/8.50       => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 15.55/8.50         => ( ! [I3: int] :
% 15.55/8.50                ( ( ord_less_int @ I3 @ K )
% 15.55/8.50               => ( ( P @ I3 )
% 15.55/8.50                 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 15.55/8.50           => ( P @ I ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2480_dvd__diffD,axiom,
% 15.55/8.50      ! [K: nat,M: nat,N: nat] :
% 15.55/8.50        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 15.55/8.50       => ( ( dvd_dvd_nat @ K @ N )
% 15.55/8.50         => ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.50           => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2481_dvd__diffD1,axiom,
% 15.55/8.50      ! [K: nat,M: nat,N: nat] :
% 15.55/8.50        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 15.55/8.50       => ( ( dvd_dvd_nat @ K @ M )
% 15.55/8.50         => ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.50           => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2482_less__eq__dvd__minus,axiom,
% 15.55/8.50      ! [M: nat,N: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.50       => ( ( dvd_dvd_nat @ M @ N )
% 15.55/8.50          = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2483_odd__nonzero,axiom,
% 15.55/8.50      ! [Z: int] :
% 15.55/8.50        ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 15.55/8.50       != zero_zero_int ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2484_int__ge__induct,axiom,
% 15.55/8.50      ! [K: int,I: int,P: int > $o] :
% 15.55/8.50        ( ( ord_less_eq_int @ K @ I )
% 15.55/8.50       => ( ( P @ K )
% 15.55/8.50         => ( ! [I3: int] :
% 15.55/8.50                ( ( ord_less_eq_int @ K @ I3 )
% 15.55/8.50               => ( ( P @ I3 )
% 15.55/8.50                 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 15.55/8.50           => ( P @ I ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2485_zless__add1__eq,axiom,
% 15.55/8.50      ! [W: int,Z: int] :
% 15.55/8.50        ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 15.55/8.50        = ( ( ord_less_int @ W @ Z )
% 15.55/8.50          | ( W = Z ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2486_int__gr__induct,axiom,
% 15.55/8.50      ! [K: int,I: int,P: int > $o] :
% 15.55/8.50        ( ( ord_less_int @ K @ I )
% 15.55/8.50       => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 15.55/8.50         => ( ! [I3: int] :
% 15.55/8.50                ( ( ord_less_int @ K @ I3 )
% 15.55/8.50               => ( ( P @ I3 )
% 15.55/8.50                 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 15.55/8.50           => ( P @ I ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2487_zle__iff__zadd,axiom,
% 15.55/8.50      ( ord_less_eq_int
% 15.55/8.50      = ( ^ [W3: int,Z6: int] :
% 15.55/8.50          ? [N3: nat] :
% 15.55/8.50            ( Z6
% 15.55/8.50            = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2488_ln__bound,axiom,
% 15.55/8.50      ! [X3: real] :
% 15.55/8.50        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.50       => ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ X3 ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2489_ln__gt__zero__imp__gt__one,axiom,
% 15.55/8.50      ! [X3: real] :
% 15.55/8.50        ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X3 ) )
% 15.55/8.50       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.50         => ( ord_less_real @ one_one_real @ X3 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2490_ln__less__zero,axiom,
% 15.55/8.50      ! [X3: real] :
% 15.55/8.50        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.50       => ( ( ord_less_real @ X3 @ one_one_real )
% 15.55/8.50         => ( ord_less_real @ ( ln_ln_real @ X3 ) @ zero_zero_real ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2491_ln__gt__zero,axiom,
% 15.55/8.50      ! [X3: real] :
% 15.55/8.50        ( ( ord_less_real @ one_one_real @ X3 )
% 15.55/8.50       => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X3 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2492_ln__ge__zero,axiom,
% 15.55/8.50      ! [X3: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ one_one_real @ X3 )
% 15.55/8.50       => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X3 ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2493_arsinh__real__def,axiom,
% 15.55/8.50      ( arsinh_real
% 15.55/8.50      = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2494_ceiling__eq,axiom,
% 15.55/8.50      ! [N: int,X3: real] :
% 15.55/8.50        ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X3 )
% 15.55/8.50       => ( ( ord_less_eq_real @ X3 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 15.55/8.50         => ( ( archim7802044766580827645g_real @ X3 )
% 15.55/8.50            = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2495_ceiling__eq,axiom,
% 15.55/8.50      ! [N: int,X3: rat] :
% 15.55/8.50        ( ( ord_less_rat @ ( ring_1_of_int_rat @ N ) @ X3 )
% 15.55/8.50       => ( ( ord_less_eq_rat @ X3 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ N ) @ one_one_rat ) )
% 15.55/8.50         => ( ( archim2889992004027027881ng_rat @ X3 )
% 15.55/8.50            = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2496_numeral__Bit0__div__2,axiom,
% 15.55/8.50      ! [N: num] :
% 15.55/8.50        ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.50        = ( numeral_numeral_nat @ N ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2497_numeral__Bit0__div__2,axiom,
% 15.55/8.50      ! [N: num] :
% 15.55/8.50        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.50        = ( numeral_numeral_int @ N ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2498_add__strict__increasing2,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.50       => ( ( ord_less_real @ B @ C )
% 15.55/8.50         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2499_add__strict__increasing2,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.50       => ( ( ord_less_rat @ B @ C )
% 15.55/8.50         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2500_add__strict__increasing2,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.55/8.50       => ( ( ord_less_nat @ B @ C )
% 15.55/8.50         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2501_add__strict__increasing2,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.50       => ( ( ord_less_int @ B @ C )
% 15.55/8.50         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2502_add__strict__increasing,axiom,
% 15.55/8.50      ! [A: real,B: real,C: real] :
% 15.55/8.50        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.50       => ( ( ord_less_eq_real @ B @ C )
% 15.55/8.50         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2503_add__strict__increasing,axiom,
% 15.55/8.50      ! [A: rat,B: rat,C: rat] :
% 15.55/8.50        ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.50       => ( ( ord_less_eq_rat @ B @ C )
% 15.55/8.50         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2504_add__strict__increasing,axiom,
% 15.55/8.50      ! [A: nat,B: nat,C: nat] :
% 15.55/8.50        ( ( ord_less_nat @ zero_zero_nat @ A )
% 15.55/8.50       => ( ( ord_less_eq_nat @ B @ C )
% 15.55/8.50         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2505_add__strict__increasing,axiom,
% 15.55/8.50      ! [A: int,B: int,C: int] :
% 15.55/8.50        ( ( ord_less_int @ zero_zero_int @ A )
% 15.55/8.50       => ( ( ord_less_eq_int @ B @ C )
% 15.55/8.50         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2506_add__pos__nonneg,axiom,
% 15.55/8.50      ! [A: real,B: real] :
% 15.55/8.50        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.50       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 15.55/8.50         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2507_add__pos__nonneg,axiom,
% 15.55/8.50      ! [A: rat,B: rat] :
% 15.55/8.50        ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.50       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 15.55/8.50         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2508_add__pos__nonneg,axiom,
% 15.55/8.50      ! [A: nat,B: nat] :
% 15.55/8.50        ( ( ord_less_nat @ zero_zero_nat @ A )
% 15.55/8.50       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 15.55/8.50         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2509_add__pos__nonneg,axiom,
% 15.55/8.50      ! [A: int,B: int] :
% 15.55/8.50        ( ( ord_less_int @ zero_zero_int @ A )
% 15.55/8.50       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 15.55/8.50         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2510_add__nonpos__neg,axiom,
% 15.55/8.50      ! [A: real,B: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 15.55/8.50       => ( ( ord_less_real @ B @ zero_zero_real )
% 15.55/8.50         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2511_add__nonpos__neg,axiom,
% 15.55/8.50      ! [A: rat,B: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 15.55/8.50       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 15.55/8.50         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2512_add__nonpos__neg,axiom,
% 15.55/8.50      ! [A: nat,B: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 15.55/8.50       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 15.55/8.50         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2513_add__nonpos__neg,axiom,
% 15.55/8.50      ! [A: int,B: int] :
% 15.55/8.50        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 15.55/8.50       => ( ( ord_less_int @ B @ zero_zero_int )
% 15.55/8.50         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2514_add__nonneg__pos,axiom,
% 15.55/8.50      ! [A: real,B: real] :
% 15.55/8.50        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.50       => ( ( ord_less_real @ zero_zero_real @ B )
% 15.55/8.50         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2515_add__nonneg__pos,axiom,
% 15.55/8.50      ! [A: rat,B: rat] :
% 15.55/8.50        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.50       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 15.55/8.50         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 15.55/8.50  
% 15.55/8.50  thf(fact_2516_add__nonneg__pos,axiom,
% 15.55/8.50      ! [A: nat,B: nat] :
% 15.55/8.50        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.55/8.50       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 15.55/8.50         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2517_add__nonneg__pos,axiom,
% 15.55/8.51      ! [A: int,B: int] :
% 15.55/8.51        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.51       => ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.51         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2518_add__neg__nonpos,axiom,
% 15.55/8.51      ! [A: real,B: real] :
% 15.55/8.51        ( ( ord_less_real @ A @ zero_zero_real )
% 15.55/8.51       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 15.55/8.51         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2519_add__neg__nonpos,axiom,
% 15.55/8.51      ! [A: rat,B: rat] :
% 15.55/8.51        ( ( ord_less_rat @ A @ zero_zero_rat )
% 15.55/8.51       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 15.55/8.51         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2520_add__neg__nonpos,axiom,
% 15.55/8.51      ! [A: nat,B: nat] :
% 15.55/8.51        ( ( ord_less_nat @ A @ zero_zero_nat )
% 15.55/8.51       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 15.55/8.51         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2521_add__neg__nonpos,axiom,
% 15.55/8.51      ! [A: int,B: int] :
% 15.55/8.51        ( ( ord_less_int @ A @ zero_zero_int )
% 15.55/8.51       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 15.55/8.51         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2522_unit__div__eq__0__iff,axiom,
% 15.55/8.51      ! [B: code_integer,A: code_integer] :
% 15.55/8.51        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 15.55/8.51       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 15.55/8.51            = zero_z3403309356797280102nteger )
% 15.55/8.51          = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2523_unit__div__eq__0__iff,axiom,
% 15.55/8.51      ! [B: nat,A: nat] :
% 15.55/8.51        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 15.55/8.51       => ( ( ( divide_divide_nat @ A @ B )
% 15.55/8.51            = zero_zero_nat )
% 15.55/8.51          = ( A = zero_zero_nat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2524_unit__div__eq__0__iff,axiom,
% 15.55/8.51      ! [B: int,A: int] :
% 15.55/8.51        ( ( dvd_dvd_int @ B @ one_one_int )
% 15.55/8.51       => ( ( ( divide_divide_int @ A @ B )
% 15.55/8.51            = zero_zero_int )
% 15.55/8.51          = ( A = zero_zero_int ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2525_zero__less__two,axiom,
% 15.55/8.51      ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2526_zero__less__two,axiom,
% 15.55/8.51      ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2527_zero__less__two,axiom,
% 15.55/8.51      ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2528_zero__less__two,axiom,
% 15.55/8.51      ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2529_take__bit__incr__eq,axiom,
% 15.55/8.51      ! [N: nat,K: int] :
% 15.55/8.51        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 15.55/8.51         != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 15.55/8.51       => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 15.55/8.51          = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2530_div__greater__zero__iff,axiom,
% 15.55/8.51      ! [M: nat,N: nat] :
% 15.55/8.51        ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 15.55/8.51        = ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.51          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2531_div__le__mono2,axiom,
% 15.55/8.51      ! [M: nat,N: nat,K: nat] :
% 15.55/8.51        ( ( ord_less_nat @ zero_zero_nat @ M )
% 15.55/8.51       => ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.51         => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2532_div__eq__dividend__iff,axiom,
% 15.55/8.51      ! [M: nat,N: nat] :
% 15.55/8.51        ( ( ord_less_nat @ zero_zero_nat @ M )
% 15.55/8.51       => ( ( ( divide_divide_nat @ M @ N )
% 15.55/8.51            = M )
% 15.55/8.51          = ( N = one_one_nat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2533_div__less__dividend,axiom,
% 15.55/8.51      ! [N: nat,M: nat] :
% 15.55/8.51        ( ( ord_less_nat @ one_one_nat @ N )
% 15.55/8.51       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 15.55/8.51         => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2534_odd__less__0__iff,axiom,
% 15.55/8.51      ! [Z: int] :
% 15.55/8.51        ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 15.55/8.51        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2535_sqrt__add__le__add__sqrt,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.51       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.51         => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X3 @ Y3 ) ) @ ( plus_plus_real @ ( sqrt @ X3 ) @ ( sqrt @ Y3 ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2536_zless__imp__add1__zle,axiom,
% 15.55/8.51      ! [W: int,Z: int] :
% 15.55/8.51        ( ( ord_less_int @ W @ Z )
% 15.55/8.51       => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2537_add1__zle__eq,axiom,
% 15.55/8.51      ! [W: int,Z: int] :
% 15.55/8.51        ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 15.55/8.51        = ( ord_less_int @ W @ Z ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2538_take__bit__decr__eq,axiom,
% 15.55/8.51      ! [N: nat,K: int] :
% 15.55/8.51        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 15.55/8.51         != zero_zero_int )
% 15.55/8.51       => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 15.55/8.51          = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2539_even__mask__div__iff_H,axiom,
% 15.55/8.51      ! [M: nat,N: nat] :
% 15.55/8.51        ( ( 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 ) ) )
% 15.55/8.51        = ( ord_less_eq_nat @ M @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2540_even__mask__div__iff_H,axiom,
% 15.55/8.51      ! [M: nat,N: nat] :
% 15.55/8.51        ( ( 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 ) ) )
% 15.55/8.51        = ( ord_less_eq_nat @ M @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2541_even__mask__div__iff_H,axiom,
% 15.55/8.51      ! [M: nat,N: nat] :
% 15.55/8.51        ( ( 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 ) ) )
% 15.55/8.51        = ( ord_less_eq_nat @ M @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2542_ln__ge__zero__imp__ge__one,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X3 ) )
% 15.55/8.51       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.51         => ( ord_less_eq_real @ one_one_real @ X3 ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2543_even__mask__div__iff,axiom,
% 15.55/8.51      ! [M: nat,N: nat] :
% 15.55/8.51        ( ( 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 ) ) )
% 15.55/8.51        = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 15.55/8.51            = zero_z3403309356797280102nteger )
% 15.55/8.51          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2544_even__mask__div__iff,axiom,
% 15.55/8.51      ! [M: nat,N: nat] :
% 15.55/8.51        ( ( 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 ) ) )
% 15.55/8.51        = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.51            = zero_zero_nat )
% 15.55/8.51          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2545_even__mask__div__iff,axiom,
% 15.55/8.51      ! [M: nat,N: nat] :
% 15.55/8.51        ( ( 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 ) ) )
% 15.55/8.51        = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 15.55/8.51            = zero_zero_int )
% 15.55/8.51          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2546_stable__imp__take__bit__eq,axiom,
% 15.55/8.51      ! [A: code_integer,N: nat] :
% 15.55/8.51        ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 15.55/8.51          = A )
% 15.55/8.51       => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.55/8.51           => ( ( bit_se1745604003318907178nteger @ N @ A )
% 15.55/8.51              = zero_z3403309356797280102nteger ) )
% 15.55/8.51          & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.55/8.51           => ( ( bit_se1745604003318907178nteger @ N @ A )
% 15.55/8.51              = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2547_stable__imp__take__bit__eq,axiom,
% 15.55/8.51      ! [A: int,N: nat] :
% 15.55/8.51        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.51          = A )
% 15.55/8.51       => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.55/8.51           => ( ( bit_se2923211474154528505it_int @ N @ A )
% 15.55/8.51              = zero_zero_int ) )
% 15.55/8.51          & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.55/8.51           => ( ( bit_se2923211474154528505it_int @ N @ A )
% 15.55/8.51              = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2548_stable__imp__take__bit__eq,axiom,
% 15.55/8.51      ! [A: nat,N: nat] :
% 15.55/8.51        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.51          = A )
% 15.55/8.51       => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.55/8.51           => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 15.55/8.51              = zero_zero_nat ) )
% 15.55/8.51          & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.55/8.51           => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 15.55/8.51              = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2549_bit__eq__rec,axiom,
% 15.55/8.51      ( ( ^ [Y5: code_integer,Z2: code_integer] : ( Y5 = Z2 ) )
% 15.55/8.51      = ( ^ [A4: code_integer,B3: code_integer] :
% 15.55/8.51            ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 )
% 15.55/8.51              = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) )
% 15.55/8.51            & ( ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 15.55/8.51              = ( divide6298287555418463151nteger @ B3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2550_bit__eq__rec,axiom,
% 15.55/8.51      ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 15.55/8.51      = ( ^ [A4: nat,B3: nat] :
% 15.55/8.51            ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 )
% 15.55/8.51              = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) )
% 15.55/8.51            & ( ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.51              = ( divide_divide_nat @ B3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2551_bit__eq__rec,axiom,
% 15.55/8.51      ( ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 15.55/8.51      = ( ^ [A4: int,B3: int] :
% 15.55/8.51            ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 )
% 15.55/8.51              = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) )
% 15.55/8.51            & ( ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.51              = ( divide_divide_int @ B3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2552_power2__commute,axiom,
% 15.55/8.51      ! [X3: complex,Y3: complex] :
% 15.55/8.51        ( ( power_power_complex @ ( minus_minus_complex @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.51        = ( power_power_complex @ ( minus_minus_complex @ Y3 @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2553_power2__commute,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( power_power_real @ ( minus_minus_real @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.51        = ( power_power_real @ ( minus_minus_real @ Y3 @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2554_power2__commute,axiom,
% 15.55/8.51      ! [X3: rat,Y3: rat] :
% 15.55/8.51        ( ( power_power_rat @ ( minus_minus_rat @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.51        = ( power_power_rat @ ( minus_minus_rat @ Y3 @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2555_power2__commute,axiom,
% 15.55/8.51      ! [X3: int,Y3: int] :
% 15.55/8.51        ( ( power_power_int @ ( minus_minus_int @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.51        = ( power_power_int @ ( minus_minus_int @ Y3 @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2556_odd__even__add,axiom,
% 15.55/8.51      ! [A: code_integer,B: code_integer] :
% 15.55/8.51        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.55/8.51       => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 15.55/8.51         => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2557_odd__even__add,axiom,
% 15.55/8.51      ! [A: nat,B: nat] :
% 15.55/8.51        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.55/8.51       => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 15.55/8.51         => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2558_odd__even__add,axiom,
% 15.55/8.51      ! [A: int,B: int] :
% 15.55/8.51        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.55/8.51       => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 15.55/8.51         => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2559_of__int__ceiling__diff__one__le,axiom,
% 15.55/8.51      ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R2 ) ) @ one_one_real ) @ R2 ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2560_of__int__ceiling__diff__one__le,axiom,
% 15.55/8.51      ! [R2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R2 ) ) @ one_one_rat ) @ R2 ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2561_floor__exists1,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51      ? [X4: int] :
% 15.55/8.51        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X4 ) @ X3 )
% 15.55/8.51        & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ X4 @ one_one_int ) ) )
% 15.55/8.51        & ! [Y6: int] :
% 15.55/8.51            ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y6 ) @ X3 )
% 15.55/8.51              & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ Y6 @ one_one_int ) ) ) )
% 15.55/8.51           => ( Y6 = X4 ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2562_floor__exists1,axiom,
% 15.55/8.51      ! [X3: rat] :
% 15.55/8.51      ? [X4: int] :
% 15.55/8.51        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X4 ) @ X3 )
% 15.55/8.51        & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ X4 @ one_one_int ) ) )
% 15.55/8.51        & ! [Y6: int] :
% 15.55/8.51            ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y6 ) @ X3 )
% 15.55/8.51              & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y6 @ one_one_int ) ) ) )
% 15.55/8.51           => ( Y6 = X4 ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2563_floor__exists,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51      ? [Z3: int] :
% 15.55/8.51        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z3 ) @ X3 )
% 15.55/8.51        & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2564_floor__exists,axiom,
% 15.55/8.51      ! [X3: rat] :
% 15.55/8.51      ? [Z3: int] :
% 15.55/8.51        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X3 )
% 15.55/8.51        & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2565_take__bit__set__bit__eq,axiom,
% 15.55/8.51      ! [N: nat,M: nat,A: int] :
% 15.55/8.51        ( ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.51         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 15.55/8.51            = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 15.55/8.51        & ( ~ ( ord_less_eq_nat @ N @ M )
% 15.55/8.51         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 15.55/8.51            = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2566_take__bit__set__bit__eq,axiom,
% 15.55/8.51      ! [N: nat,M: nat,A: nat] :
% 15.55/8.51        ( ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.51         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 15.55/8.51            = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 15.55/8.51        & ( ~ ( ord_less_eq_nat @ N @ M )
% 15.55/8.51         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 15.55/8.51            = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2567_take__bit__flip__bit__eq,axiom,
% 15.55/8.51      ! [N: nat,M: nat,A: int] :
% 15.55/8.51        ( ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.51         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 15.55/8.51            = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 15.55/8.51        & ( ~ ( ord_less_eq_nat @ N @ M )
% 15.55/8.51         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 15.55/8.51            = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2568_take__bit__flip__bit__eq,axiom,
% 15.55/8.51      ! [N: nat,M: nat,A: nat] :
% 15.55/8.51        ( ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.51         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 15.55/8.51            = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 15.55/8.51        & ( ~ ( ord_less_eq_nat @ N @ M )
% 15.55/8.51         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 15.55/8.51            = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2569_take__bit__unset__bit__eq,axiom,
% 15.55/8.51      ! [N: nat,M: nat,A: int] :
% 15.55/8.51        ( ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.51         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 15.55/8.51            = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 15.55/8.51        & ( ~ ( ord_less_eq_nat @ N @ M )
% 15.55/8.51         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 15.55/8.51            = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2570_take__bit__unset__bit__eq,axiom,
% 15.55/8.51      ! [N: nat,M: nat,A: nat] :
% 15.55/8.51        ( ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.51         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 15.55/8.51            = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 15.55/8.51        & ( ~ ( ord_less_eq_nat @ N @ M )
% 15.55/8.51         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 15.55/8.51            = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2571_of__int__ceiling__le__add__one,axiom,
% 15.55/8.51      ! [R2: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R2 ) ) @ ( plus_plus_real @ R2 @ one_one_real ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2572_of__int__ceiling__le__add__one,axiom,
% 15.55/8.51      ! [R2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R2 ) ) @ ( plus_plus_rat @ R2 @ one_one_rat ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2573_nat__less__real__le,axiom,
% 15.55/8.51      ( ord_less_nat
% 15.55/8.51      = ( ^ [N3: nat,M3: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N3 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2574_nat__le__real__less,axiom,
% 15.55/8.51      ( ord_less_eq_nat
% 15.55/8.51      = ( ^ [N3: nat,M3: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M3 ) @ one_one_real ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2575_le__imp__0__less,axiom,
% 15.55/8.51      ! [Z: int] :
% 15.55/8.51        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 15.55/8.51       => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2576_int__le__real__less,axiom,
% 15.55/8.51      ( ord_less_eq_int
% 15.55/8.51      = ( ^ [N3: int,M3: int] : ( ord_less_real @ ( ring_1_of_int_real @ N3 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M3 ) @ one_one_real ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2577_int__less__real__le,axiom,
% 15.55/8.51      ( ord_less_int
% 15.55/8.51      = ( ^ [N3: int,M3: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N3 ) @ one_one_real ) @ ( ring_1_of_int_real @ M3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2578_half__gt__zero,axiom,
% 15.55/8.51      ! [A: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.51       => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2579_half__gt__zero,axiom,
% 15.55/8.51      ! [A: rat] :
% 15.55/8.51        ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.51       => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2580_half__gt__zero__iff,axiom,
% 15.55/8.51      ! [A: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.51        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2581_half__gt__zero__iff,axiom,
% 15.55/8.51      ! [A: rat] :
% 15.55/8.51        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 15.55/8.51        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2582_inverse__of__nat__le,axiom,
% 15.55/8.51      ! [N: nat,M: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.51       => ( ( N != zero_zero_nat )
% 15.55/8.51         => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2583_inverse__of__nat__le,axiom,
% 15.55/8.51      ! [N: nat,M: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.51       => ( ( N != zero_zero_nat )
% 15.55/8.51         => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2584_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 15.55/8.51      ! [N: nat,M: nat] :
% 15.55/8.51        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.51         != zero_zero_nat )
% 15.55/8.51       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 15.55/8.51         != zero_zero_nat ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2585_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 15.55/8.51      ! [N: nat,M: nat] :
% 15.55/8.51        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 15.55/8.51         != zero_zero_int )
% 15.55/8.51       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 15.55/8.51         != zero_zero_int ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2586_ceiling__split,axiom,
% 15.55/8.51      ! [P: int > $o,T: real] :
% 15.55/8.51        ( ( P @ ( archim7802044766580827645g_real @ T ) )
% 15.55/8.51        = ( ! [I4: int] :
% 15.55/8.51              ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ I4 ) @ one_one_real ) @ T )
% 15.55/8.51                & ( ord_less_eq_real @ T @ ( ring_1_of_int_real @ I4 ) ) )
% 15.55/8.51             => ( P @ I4 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2587_ceiling__split,axiom,
% 15.55/8.51      ! [P: int > $o,T: rat] :
% 15.55/8.51        ( ( P @ ( archim2889992004027027881ng_rat @ T ) )
% 15.55/8.51        = ( ! [I4: int] :
% 15.55/8.51              ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I4 ) @ one_one_rat ) @ T )
% 15.55/8.51                & ( ord_less_eq_rat @ T @ ( ring_1_of_int_rat @ I4 ) ) )
% 15.55/8.51             => ( P @ I4 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2588_ceiling__eq__iff,axiom,
% 15.55/8.51      ! [X3: real,A: int] :
% 15.55/8.51        ( ( ( archim7802044766580827645g_real @ X3 )
% 15.55/8.51          = A )
% 15.55/8.51        = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ X3 )
% 15.55/8.51          & ( ord_less_eq_real @ X3 @ ( ring_1_of_int_real @ A ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2589_ceiling__eq__iff,axiom,
% 15.55/8.51      ! [X3: rat,A: int] :
% 15.55/8.51        ( ( ( archim2889992004027027881ng_rat @ X3 )
% 15.55/8.51          = A )
% 15.55/8.51        = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X3 )
% 15.55/8.51          & ( ord_less_eq_rat @ X3 @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2590_ceiling__unique,axiom,
% 15.55/8.51      ! [Z: int,X3: real] :
% 15.55/8.51        ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X3 )
% 15.55/8.51       => ( ( ord_less_eq_real @ X3 @ ( ring_1_of_int_real @ Z ) )
% 15.55/8.51         => ( ( archim7802044766580827645g_real @ X3 )
% 15.55/8.51            = Z ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2591_ceiling__unique,axiom,
% 15.55/8.51      ! [Z: int,X3: rat] :
% 15.55/8.51        ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X3 )
% 15.55/8.51       => ( ( ord_less_eq_rat @ X3 @ ( ring_1_of_int_rat @ Z ) )
% 15.55/8.51         => ( ( archim2889992004027027881ng_rat @ X3 )
% 15.55/8.51            = Z ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2592_ceiling__correct,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X3 ) ) @ one_one_real ) @ X3 )
% 15.55/8.51        & ( ord_less_eq_real @ X3 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2593_ceiling__correct,axiom,
% 15.55/8.51      ! [X3: rat] :
% 15.55/8.51        ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X3 ) ) @ one_one_rat ) @ X3 )
% 15.55/8.51        & ( ord_less_eq_rat @ X3 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2594_diff__le__diff__pow,axiom,
% 15.55/8.51      ! [K: nat,M: nat,N: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 15.55/8.51       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2595_ceiling__less__iff,axiom,
% 15.55/8.51      ! [X3: real,Z: int] :
% 15.55/8.51        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X3 ) @ Z )
% 15.55/8.51        = ( ord_less_eq_real @ X3 @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2596_ceiling__less__iff,axiom,
% 15.55/8.51      ! [X3: rat,Z: int] :
% 15.55/8.51        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X3 ) @ Z )
% 15.55/8.51        = ( ord_less_eq_rat @ X3 @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2597_le__ceiling__iff,axiom,
% 15.55/8.51      ! [Z: int,X3: rat] :
% 15.55/8.51        ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X3 ) )
% 15.55/8.51        = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2598_le__ceiling__iff,axiom,
% 15.55/8.51      ! [Z: int,X3: real] :
% 15.55/8.51        ( ( ord_less_eq_int @ Z @ ( archim7802044766580827645g_real @ X3 ) )
% 15.55/8.51        = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2599_sum__power2__ge__zero,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2600_sum__power2__ge__zero,axiom,
% 15.55/8.51      ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2601_sum__power2__ge__zero,axiom,
% 15.55/8.51      ! [X3: int,Y3: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2602_sum__power2__le__zero__iff,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 15.55/8.51        = ( ( X3 = zero_zero_real )
% 15.55/8.51          & ( Y3 = zero_zero_real ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2603_sum__power2__le__zero__iff,axiom,
% 15.55/8.51      ! [X3: rat,Y3: rat] :
% 15.55/8.51        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 15.55/8.51        = ( ( X3 = zero_zero_rat )
% 15.55/8.51          & ( Y3 = zero_zero_rat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2604_sum__power2__le__zero__iff,axiom,
% 15.55/8.51      ! [X3: int,Y3: int] :
% 15.55/8.51        ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 15.55/8.51        = ( ( X3 = zero_zero_int )
% 15.55/8.51          & ( Y3 = zero_zero_int ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2605_not__sum__power2__lt__zero,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2606_not__sum__power2__lt__zero,axiom,
% 15.55/8.51      ! [X3: rat,Y3: rat] :
% 15.55/8.51        ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2607_not__sum__power2__lt__zero,axiom,
% 15.55/8.51      ! [X3: int,Y3: int] :
% 15.55/8.51        ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2608_sum__power2__gt__zero__iff,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.51        = ( ( X3 != zero_zero_real )
% 15.55/8.51          | ( Y3 != zero_zero_real ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2609_sum__power2__gt__zero__iff,axiom,
% 15.55/8.51      ! [X3: rat,Y3: rat] :
% 15.55/8.51        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.51        = ( ( X3 != zero_zero_rat )
% 15.55/8.51          | ( Y3 != zero_zero_rat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2610_sum__power2__gt__zero__iff,axiom,
% 15.55/8.51      ! [X3: int,Y3: int] :
% 15.55/8.51        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.51        = ( ( X3 != zero_zero_int )
% 15.55/8.51          | ( Y3 != zero_zero_int ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2611_real__sqrt__sum__squares__eq__cancel,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.51          = X3 )
% 15.55/8.51       => ( Y3 = zero_zero_real ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2612_real__sqrt__sum__squares__eq__cancel2,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.51          = Y3 )
% 15.55/8.51       => ( X3 = zero_zero_real ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2613_real__sqrt__sum__squares__ge1,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] : ( ord_less_eq_real @ X3 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2614_real__sqrt__sum__squares__ge2,axiom,
% 15.55/8.51      ! [Y3: real,X3: real] : ( ord_less_eq_real @ Y3 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2615_real__sqrt__sum__squares__triangle__ineq,axiom,
% 15.55/8.51      ! [A: real,C: real,B: real,D3: 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 @ D3 ) @ ( 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 @ D3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2616_sqrt__sum__squares__le__sum,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.51       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.51         => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2617_sqrt__even__pow2,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.51       => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.51          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2618_le__divide__eq__1__pos,axiom,
% 15.55/8.51      ! [A: real,B: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.51       => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 15.55/8.51          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2619_le__divide__eq__1__pos,axiom,
% 15.55/8.51      ! [A: rat,B: rat] :
% 15.55/8.51        ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.51       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 15.55/8.51          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2620_le__divide__eq__1__neg,axiom,
% 15.55/8.51      ! [A: real,B: real] :
% 15.55/8.51        ( ( ord_less_real @ A @ zero_zero_real )
% 15.55/8.51       => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 15.55/8.51          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2621_le__divide__eq__1__neg,axiom,
% 15.55/8.51      ! [A: rat,B: rat] :
% 15.55/8.51        ( ( ord_less_rat @ A @ zero_zero_rat )
% 15.55/8.51       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 15.55/8.51          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2622_divide__le__eq__1__pos,axiom,
% 15.55/8.51      ! [A: real,B: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.51       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 15.55/8.51          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2623_divide__le__eq__1__pos,axiom,
% 15.55/8.51      ! [A: rat,B: rat] :
% 15.55/8.51        ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.51       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 15.55/8.51          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2624_divide__le__eq__1__neg,axiom,
% 15.55/8.51      ! [A: real,B: real] :
% 15.55/8.51        ( ( ord_less_real @ A @ zero_zero_real )
% 15.55/8.51       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 15.55/8.51          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2625_divide__le__eq__1__neg,axiom,
% 15.55/8.51      ! [A: rat,B: rat] :
% 15.55/8.51        ( ( ord_less_rat @ A @ zero_zero_rat )
% 15.55/8.51       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 15.55/8.51          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2626_divide__less__0__1__iff,axiom,
% 15.55/8.51      ! [A: real] :
% 15.55/8.51        ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 15.55/8.51        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2627_divide__less__0__1__iff,axiom,
% 15.55/8.51      ! [A: rat] :
% 15.55/8.51        ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 15.55/8.51        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2628_divide__less__eq__1__neg,axiom,
% 15.55/8.51      ! [A: real,B: real] :
% 15.55/8.51        ( ( ord_less_real @ A @ zero_zero_real )
% 15.55/8.51       => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 15.55/8.51          = ( ord_less_real @ A @ B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2629_divide__less__eq__1__neg,axiom,
% 15.55/8.51      ! [A: rat,B: rat] :
% 15.55/8.51        ( ( ord_less_rat @ A @ zero_zero_rat )
% 15.55/8.51       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 15.55/8.51          = ( ord_less_rat @ A @ B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2630_divide__less__eq__1__pos,axiom,
% 15.55/8.51      ! [A: real,B: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.51       => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 15.55/8.51          = ( ord_less_real @ B @ A ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2631_divide__less__eq__1__pos,axiom,
% 15.55/8.51      ! [A: rat,B: rat] :
% 15.55/8.51        ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.51       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 15.55/8.51          = ( ord_less_rat @ B @ A ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2632_less__divide__eq__1__neg,axiom,
% 15.55/8.51      ! [A: real,B: real] :
% 15.55/8.51        ( ( ord_less_real @ A @ zero_zero_real )
% 15.55/8.51       => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 15.55/8.51          = ( ord_less_real @ B @ A ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2633_less__divide__eq__1__neg,axiom,
% 15.55/8.51      ! [A: rat,B: rat] :
% 15.55/8.51        ( ( ord_less_rat @ A @ zero_zero_rat )
% 15.55/8.51       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 15.55/8.51          = ( ord_less_rat @ B @ A ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2634_less__divide__eq__1__pos,axiom,
% 15.55/8.51      ! [A: real,B: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.51       => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 15.55/8.51          = ( ord_less_real @ A @ B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2635_less__divide__eq__1__pos,axiom,
% 15.55/8.51      ! [A: rat,B: rat] :
% 15.55/8.51        ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.51       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 15.55/8.51          = ( ord_less_rat @ A @ B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2636_zero__less__divide__1__iff,axiom,
% 15.55/8.51      ! [A: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 15.55/8.51        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2637_zero__less__divide__1__iff,axiom,
% 15.55/8.51      ! [A: rat] :
% 15.55/8.51        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 15.55/8.51        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2638_pow__sum,axiom,
% 15.55/8.51      ! [A: nat,B: nat] :
% 15.55/8.51        ( ( 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 ) )
% 15.55/8.51        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2639_divide__eq__0__iff,axiom,
% 15.55/8.51      ! [A: complex,B: complex] :
% 15.55/8.51        ( ( ( divide1717551699836669952omplex @ A @ B )
% 15.55/8.51          = zero_zero_complex )
% 15.55/8.51        = ( ( A = zero_zero_complex )
% 15.55/8.51          | ( B = zero_zero_complex ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2640_divide__eq__0__iff,axiom,
% 15.55/8.51      ! [A: real,B: real] :
% 15.55/8.51        ( ( ( divide_divide_real @ A @ B )
% 15.55/8.51          = zero_zero_real )
% 15.55/8.51        = ( ( A = zero_zero_real )
% 15.55/8.51          | ( B = zero_zero_real ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2641_divide__eq__0__iff,axiom,
% 15.55/8.51      ! [A: rat,B: rat] :
% 15.55/8.51        ( ( ( divide_divide_rat @ A @ B )
% 15.55/8.51          = zero_zero_rat )
% 15.55/8.51        = ( ( A = zero_zero_rat )
% 15.55/8.51          | ( B = zero_zero_rat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2642_divide__cancel__left,axiom,
% 15.55/8.51      ! [C: complex,A: complex,B: complex] :
% 15.55/8.51        ( ( ( divide1717551699836669952omplex @ C @ A )
% 15.55/8.51          = ( divide1717551699836669952omplex @ C @ B ) )
% 15.55/8.51        = ( ( C = zero_zero_complex )
% 15.55/8.51          | ( A = B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2643_divide__cancel__left,axiom,
% 15.55/8.51      ! [C: real,A: real,B: real] :
% 15.55/8.51        ( ( ( divide_divide_real @ C @ A )
% 15.55/8.51          = ( divide_divide_real @ C @ B ) )
% 15.55/8.51        = ( ( C = zero_zero_real )
% 15.55/8.51          | ( A = B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2644_divide__cancel__left,axiom,
% 15.55/8.51      ! [C: rat,A: rat,B: rat] :
% 15.55/8.51        ( ( ( divide_divide_rat @ C @ A )
% 15.55/8.51          = ( divide_divide_rat @ C @ B ) )
% 15.55/8.51        = ( ( C = zero_zero_rat )
% 15.55/8.51          | ( A = B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2645_divide__cancel__right,axiom,
% 15.55/8.51      ! [A: complex,C: complex,B: complex] :
% 15.55/8.51        ( ( ( divide1717551699836669952omplex @ A @ C )
% 15.55/8.51          = ( divide1717551699836669952omplex @ B @ C ) )
% 15.55/8.51        = ( ( C = zero_zero_complex )
% 15.55/8.51          | ( A = B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2646_divide__cancel__right,axiom,
% 15.55/8.51      ! [A: real,C: real,B: real] :
% 15.55/8.51        ( ( ( divide_divide_real @ A @ C )
% 15.55/8.51          = ( divide_divide_real @ B @ C ) )
% 15.55/8.51        = ( ( C = zero_zero_real )
% 15.55/8.51          | ( A = B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2647_divide__cancel__right,axiom,
% 15.55/8.51      ! [A: rat,C: rat,B: rat] :
% 15.55/8.51        ( ( ( divide_divide_rat @ A @ C )
% 15.55/8.51          = ( divide_divide_rat @ B @ C ) )
% 15.55/8.51        = ( ( C = zero_zero_rat )
% 15.55/8.51          | ( A = B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2648_division__ring__divide__zero,axiom,
% 15.55/8.51      ! [A: complex] :
% 15.55/8.51        ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 15.55/8.51        = zero_zero_complex ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2649_division__ring__divide__zero,axiom,
% 15.55/8.51      ! [A: real] :
% 15.55/8.51        ( ( divide_divide_real @ A @ zero_zero_real )
% 15.55/8.51        = zero_zero_real ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2650_division__ring__divide__zero,axiom,
% 15.55/8.51      ! [A: rat] :
% 15.55/8.51        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 15.55/8.51        = zero_zero_rat ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2651_add__is__0,axiom,
% 15.55/8.51      ! [M: nat,N: nat] :
% 15.55/8.51        ( ( ( plus_plus_nat @ M @ N )
% 15.55/8.51          = zero_zero_nat )
% 15.55/8.51        = ( ( M = zero_zero_nat )
% 15.55/8.51          & ( N = zero_zero_nat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2652_Nat_Oadd__0__right,axiom,
% 15.55/8.51      ! [M: nat] :
% 15.55/8.51        ( ( plus_plus_nat @ M @ zero_zero_nat )
% 15.55/8.51        = M ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2653_nat__add__left__cancel__less,axiom,
% 15.55/8.51      ! [K: nat,M: nat,N: nat] :
% 15.55/8.51        ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 15.55/8.51        = ( ord_less_nat @ M @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2654_nat__add__left__cancel__le,axiom,
% 15.55/8.51      ! [K: nat,M: nat,N: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 15.55/8.51        = ( ord_less_eq_nat @ M @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2655_diff__diff__left,axiom,
% 15.55/8.51      ! [I: nat,J: nat,K: nat] :
% 15.55/8.51        ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 15.55/8.51        = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2656_semiring__norm_I6_J,axiom,
% 15.55/8.51      ! [M: num,N: num] :
% 15.55/8.51        ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 15.55/8.51        = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2657_divide__eq__1__iff,axiom,
% 15.55/8.51      ! [A: complex,B: complex] :
% 15.55/8.51        ( ( ( divide1717551699836669952omplex @ A @ B )
% 15.55/8.51          = one_one_complex )
% 15.55/8.51        = ( ( B != zero_zero_complex )
% 15.55/8.51          & ( A = B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2658_divide__eq__1__iff,axiom,
% 15.55/8.51      ! [A: real,B: real] :
% 15.55/8.51        ( ( ( divide_divide_real @ A @ B )
% 15.55/8.51          = one_one_real )
% 15.55/8.51        = ( ( B != zero_zero_real )
% 15.55/8.51          & ( A = B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2659_divide__eq__1__iff,axiom,
% 15.55/8.51      ! [A: rat,B: rat] :
% 15.55/8.51        ( ( ( divide_divide_rat @ A @ B )
% 15.55/8.51          = one_one_rat )
% 15.55/8.51        = ( ( B != zero_zero_rat )
% 15.55/8.51          & ( A = B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2660_one__eq__divide__iff,axiom,
% 15.55/8.51      ! [A: complex,B: complex] :
% 15.55/8.51        ( ( one_one_complex
% 15.55/8.51          = ( divide1717551699836669952omplex @ A @ B ) )
% 15.55/8.51        = ( ( B != zero_zero_complex )
% 15.55/8.51          & ( A = B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2661_one__eq__divide__iff,axiom,
% 15.55/8.51      ! [A: real,B: real] :
% 15.55/8.51        ( ( one_one_real
% 15.55/8.51          = ( divide_divide_real @ A @ B ) )
% 15.55/8.51        = ( ( B != zero_zero_real )
% 15.55/8.51          & ( A = B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2662_one__eq__divide__iff,axiom,
% 15.55/8.51      ! [A: rat,B: rat] :
% 15.55/8.51        ( ( one_one_rat
% 15.55/8.51          = ( divide_divide_rat @ A @ B ) )
% 15.55/8.51        = ( ( B != zero_zero_rat )
% 15.55/8.51          & ( A = B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2663_divide__self,axiom,
% 15.55/8.51      ! [A: complex] :
% 15.55/8.51        ( ( A != zero_zero_complex )
% 15.55/8.51       => ( ( divide1717551699836669952omplex @ A @ A )
% 15.55/8.51          = one_one_complex ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2664_divide__self,axiom,
% 15.55/8.51      ! [A: real] :
% 15.55/8.51        ( ( A != zero_zero_real )
% 15.55/8.51       => ( ( divide_divide_real @ A @ A )
% 15.55/8.51          = one_one_real ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2665_divide__self,axiom,
% 15.55/8.51      ! [A: rat] :
% 15.55/8.51        ( ( A != zero_zero_rat )
% 15.55/8.51       => ( ( divide_divide_rat @ A @ A )
% 15.55/8.51          = one_one_rat ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2666_divide__self__if,axiom,
% 15.55/8.51      ! [A: complex] :
% 15.55/8.51        ( ( ( A = zero_zero_complex )
% 15.55/8.51         => ( ( divide1717551699836669952omplex @ A @ A )
% 15.55/8.51            = zero_zero_complex ) )
% 15.55/8.51        & ( ( A != zero_zero_complex )
% 15.55/8.51         => ( ( divide1717551699836669952omplex @ A @ A )
% 15.55/8.51            = one_one_complex ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2667_divide__self__if,axiom,
% 15.55/8.51      ! [A: real] :
% 15.55/8.51        ( ( ( A = zero_zero_real )
% 15.55/8.51         => ( ( divide_divide_real @ A @ A )
% 15.55/8.51            = zero_zero_real ) )
% 15.55/8.51        & ( ( A != zero_zero_real )
% 15.55/8.51         => ( ( divide_divide_real @ A @ A )
% 15.55/8.51            = one_one_real ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2668_divide__self__if,axiom,
% 15.55/8.51      ! [A: rat] :
% 15.55/8.51        ( ( ( A = zero_zero_rat )
% 15.55/8.51         => ( ( divide_divide_rat @ A @ A )
% 15.55/8.51            = zero_zero_rat ) )
% 15.55/8.51        & ( ( A != zero_zero_rat )
% 15.55/8.51         => ( ( divide_divide_rat @ A @ A )
% 15.55/8.51            = one_one_rat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2669_divide__eq__eq__1,axiom,
% 15.55/8.51      ! [B: real,A: real] :
% 15.55/8.51        ( ( ( divide_divide_real @ B @ A )
% 15.55/8.51          = one_one_real )
% 15.55/8.51        = ( ( A != zero_zero_real )
% 15.55/8.51          & ( A = B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2670_divide__eq__eq__1,axiom,
% 15.55/8.51      ! [B: rat,A: rat] :
% 15.55/8.51        ( ( ( divide_divide_rat @ B @ A )
% 15.55/8.51          = one_one_rat )
% 15.55/8.51        = ( ( A != zero_zero_rat )
% 15.55/8.51          & ( A = B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2671_eq__divide__eq__1,axiom,
% 15.55/8.51      ! [B: real,A: real] :
% 15.55/8.51        ( ( one_one_real
% 15.55/8.51          = ( divide_divide_real @ B @ A ) )
% 15.55/8.51        = ( ( A != zero_zero_real )
% 15.55/8.51          & ( A = B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2672_eq__divide__eq__1,axiom,
% 15.55/8.51      ! [B: rat,A: rat] :
% 15.55/8.51        ( ( one_one_rat
% 15.55/8.51          = ( divide_divide_rat @ B @ A ) )
% 15.55/8.51        = ( ( A != zero_zero_rat )
% 15.55/8.51          & ( A = B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2673_one__divide__eq__0__iff,axiom,
% 15.55/8.51      ! [A: real] :
% 15.55/8.51        ( ( ( divide_divide_real @ one_one_real @ A )
% 15.55/8.51          = zero_zero_real )
% 15.55/8.51        = ( A = zero_zero_real ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2674_one__divide__eq__0__iff,axiom,
% 15.55/8.51      ! [A: rat] :
% 15.55/8.51        ( ( ( divide_divide_rat @ one_one_rat @ A )
% 15.55/8.51          = zero_zero_rat )
% 15.55/8.51        = ( A = zero_zero_rat ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2675_zero__eq__1__divide__iff,axiom,
% 15.55/8.51      ! [A: real] :
% 15.55/8.51        ( ( zero_zero_real
% 15.55/8.51          = ( divide_divide_real @ one_one_real @ A ) )
% 15.55/8.51        = ( A = zero_zero_real ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2676_zero__eq__1__divide__iff,axiom,
% 15.55/8.51      ! [A: rat] :
% 15.55/8.51        ( ( zero_zero_rat
% 15.55/8.51          = ( divide_divide_rat @ one_one_rat @ A ) )
% 15.55/8.51        = ( A = zero_zero_rat ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2677_add__gr__0,axiom,
% 15.55/8.51      ! [M: nat,N: nat] :
% 15.55/8.51        ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 15.55/8.51        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 15.55/8.51          | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2678_Nat_Odiff__diff__right,axiom,
% 15.55/8.51      ! [K: nat,J: nat,I: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ K @ J )
% 15.55/8.51       => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 15.55/8.51          = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2679_Nat_Oadd__diff__assoc2,axiom,
% 15.55/8.51      ! [K: nat,J: nat,I: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ K @ J )
% 15.55/8.51       => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 15.55/8.51          = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2680_Nat_Oadd__diff__assoc,axiom,
% 15.55/8.51      ! [K: nat,J: nat,I: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ K @ J )
% 15.55/8.51       => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 15.55/8.51          = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2681_div__neg__neg__trivial,axiom,
% 15.55/8.51      ! [K: int,L: int] :
% 15.55/8.51        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 15.55/8.51       => ( ( ord_less_int @ L @ K )
% 15.55/8.51         => ( ( divide_divide_int @ K @ L )
% 15.55/8.51            = zero_zero_int ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2682_div__pos__pos__trivial,axiom,
% 15.55/8.51      ! [K: int,L: int] :
% 15.55/8.51        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 15.55/8.51       => ( ( ord_less_int @ K @ L )
% 15.55/8.51         => ( ( divide_divide_int @ K @ L )
% 15.55/8.51            = zero_zero_int ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2683_semiring__norm_I2_J,axiom,
% 15.55/8.51      ( ( plus_plus_num @ one @ one )
% 15.55/8.51      = ( bit0 @ one ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2684_zero__le__divide__1__iff,axiom,
% 15.55/8.51      ! [A: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 15.55/8.51        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2685_zero__le__divide__1__iff,axiom,
% 15.55/8.51      ! [A: rat] :
% 15.55/8.51        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 15.55/8.51        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2686_divide__le__0__1__iff,axiom,
% 15.55/8.51      ! [A: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 15.55/8.51        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2687_divide__le__0__1__iff,axiom,
% 15.55/8.51      ! [A: rat] :
% 15.55/8.51        ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 15.55/8.51        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2688_add__self__div__2,axiom,
% 15.55/8.51      ! [M: nat] :
% 15.55/8.51        ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.51        = M ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2689_half__nonnegative__int__iff,axiom,
% 15.55/8.51      ! [K: int] :
% 15.55/8.51        ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 15.55/8.51        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2690_half__negative__int__iff,axiom,
% 15.55/8.51      ! [K: int] :
% 15.55/8.51        ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 15.55/8.51        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2691_even__diff__nat,axiom,
% 15.55/8.51      ! [M: nat,N: nat] :
% 15.55/8.51        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 15.55/8.51        = ( ( ord_less_nat @ M @ N )
% 15.55/8.51          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2692_Nat_Odiff__cancel,axiom,
% 15.55/8.51      ! [K: nat,M: nat,N: nat] :
% 15.55/8.51        ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 15.55/8.51        = ( minus_minus_nat @ M @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2693_diff__cancel2,axiom,
% 15.55/8.51      ! [M: nat,K: nat,N: nat] :
% 15.55/8.51        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 15.55/8.51        = ( minus_minus_nat @ M @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2694_diff__commute,axiom,
% 15.55/8.51      ! [I: nat,J: nat,K: nat] :
% 15.55/8.51        ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 15.55/8.51        = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2695_diff__add__inverse,axiom,
% 15.55/8.51      ! [N: nat,M: nat] :
% 15.55/8.51        ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 15.55/8.51        = M ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2696_diff__add__inverse2,axiom,
% 15.55/8.51      ! [M: nat,N: nat] :
% 15.55/8.51        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 15.55/8.51        = M ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2697_real__of__int__div4,axiom,
% 15.55/8.51      ! [N: int,X3: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X3 ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X3 ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2698_real__of__int__div,axiom,
% 15.55/8.51      ! [D3: int,N: int] :
% 15.55/8.51        ( ( dvd_dvd_int @ D3 @ N )
% 15.55/8.51       => ( ( ring_1_of_int_real @ ( divide_divide_int @ N @ D3 ) )
% 15.55/8.51          = ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ D3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2699_add__One__commute,axiom,
% 15.55/8.51      ! [N: num] :
% 15.55/8.51        ( ( plus_plus_num @ one @ N )
% 15.55/8.51        = ( plus_plus_num @ N @ one ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2700_Euclid__induct,axiom,
% 15.55/8.51      ! [P: nat > nat > $o,A: nat,B: nat] :
% 15.55/8.51        ( ! [A5: nat,B4: nat] :
% 15.55/8.51            ( ( P @ A5 @ B4 )
% 15.55/8.51            = ( P @ B4 @ A5 ) )
% 15.55/8.51       => ( ! [A5: nat] : ( P @ A5 @ zero_zero_nat )
% 15.55/8.51         => ( ! [A5: nat,B4: nat] :
% 15.55/8.51                ( ( P @ A5 @ B4 )
% 15.55/8.51               => ( P @ A5 @ ( plus_plus_nat @ A5 @ B4 ) ) )
% 15.55/8.51           => ( P @ A @ B ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2701_plus__nat_Oadd__0,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( plus_plus_nat @ zero_zero_nat @ N )
% 15.55/8.51        = N ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2702_add__eq__self__zero,axiom,
% 15.55/8.51      ! [M: nat,N: nat] :
% 15.55/8.51        ( ( ( plus_plus_nat @ M @ N )
% 15.55/8.51          = M )
% 15.55/8.51       => ( N = zero_zero_nat ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2703_diff__add__0,axiom,
% 15.55/8.51      ! [N: nat,M: nat] :
% 15.55/8.51        ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 15.55/8.51        = zero_zero_nat ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2704_less__add__eq__less,axiom,
% 15.55/8.51      ! [K: nat,L: nat,M: nat,N: nat] :
% 15.55/8.51        ( ( ord_less_nat @ K @ L )
% 15.55/8.51       => ( ( ( plus_plus_nat @ M @ L )
% 15.55/8.51            = ( plus_plus_nat @ K @ N ) )
% 15.55/8.51         => ( ord_less_nat @ M @ N ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2705_trans__less__add2,axiom,
% 15.55/8.51      ! [I: nat,J: nat,M: nat] :
% 15.55/8.51        ( ( ord_less_nat @ I @ J )
% 15.55/8.51       => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2706_trans__less__add1,axiom,
% 15.55/8.51      ! [I: nat,J: nat,M: nat] :
% 15.55/8.51        ( ( ord_less_nat @ I @ J )
% 15.55/8.51       => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2707_add__less__mono1,axiom,
% 15.55/8.51      ! [I: nat,J: nat,K: nat] :
% 15.55/8.51        ( ( ord_less_nat @ I @ J )
% 15.55/8.51       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2708_not__add__less2,axiom,
% 15.55/8.51      ! [J: nat,I: nat] :
% 15.55/8.51        ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2709_not__add__less1,axiom,
% 15.55/8.51      ! [I: nat,J: nat] :
% 15.55/8.51        ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2710_add__less__mono,axiom,
% 15.55/8.51      ! [I: nat,J: nat,K: nat,L: nat] :
% 15.55/8.51        ( ( ord_less_nat @ I @ J )
% 15.55/8.51       => ( ( ord_less_nat @ K @ L )
% 15.55/8.51         => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2711_add__lessD1,axiom,
% 15.55/8.51      ! [I: nat,J: nat,K: nat] :
% 15.55/8.51        ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 15.55/8.51       => ( ord_less_nat @ I @ K ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2712_add__diff__inverse__nat,axiom,
% 15.55/8.51      ! [M: nat,N: nat] :
% 15.55/8.51        ( ~ ( ord_less_nat @ M @ N )
% 15.55/8.51       => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 15.55/8.51          = M ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2713_less__diff__conv,axiom,
% 15.55/8.51      ! [I: nat,J: nat,K: nat] :
% 15.55/8.51        ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 15.55/8.51        = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2714_add__leE,axiom,
% 15.55/8.51      ! [M: nat,K: nat,N: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 15.55/8.51       => ~ ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.51           => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2715_le__add1,axiom,
% 15.55/8.51      ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2716_le__add2,axiom,
% 15.55/8.51      ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2717_add__leD1,axiom,
% 15.55/8.51      ! [M: nat,K: nat,N: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 15.55/8.51       => ( ord_less_eq_nat @ M @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2718_add__leD2,axiom,
% 15.55/8.51      ! [M: nat,K: nat,N: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 15.55/8.51       => ( ord_less_eq_nat @ K @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2719_le__Suc__ex,axiom,
% 15.55/8.51      ! [K: nat,L: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ K @ L )
% 15.55/8.51       => ? [N2: nat] :
% 15.55/8.51            ( L
% 15.55/8.51            = ( plus_plus_nat @ K @ N2 ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2720_add__le__mono,axiom,
% 15.55/8.51      ! [I: nat,J: nat,K: nat,L: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ I @ J )
% 15.55/8.51       => ( ( ord_less_eq_nat @ K @ L )
% 15.55/8.51         => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2721_add__le__mono1,axiom,
% 15.55/8.51      ! [I: nat,J: nat,K: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ I @ J )
% 15.55/8.51       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2722_trans__le__add1,axiom,
% 15.55/8.51      ! [I: nat,J: nat,M: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ I @ J )
% 15.55/8.51       => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2723_trans__le__add2,axiom,
% 15.55/8.51      ! [I: nat,J: nat,M: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ I @ J )
% 15.55/8.51       => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2724_nat__le__iff__add,axiom,
% 15.55/8.51      ( ord_less_eq_nat
% 15.55/8.51      = ( ^ [M3: nat,N3: nat] :
% 15.55/8.51          ? [K3: nat] :
% 15.55/8.51            ( N3
% 15.55/8.51            = ( plus_plus_nat @ M3 @ K3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2725_Nat_Ole__imp__diff__is__add,axiom,
% 15.55/8.51      ! [I: nat,J: nat,K: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ I @ J )
% 15.55/8.51       => ( ( ( minus_minus_nat @ J @ I )
% 15.55/8.51            = K )
% 15.55/8.51          = ( J
% 15.55/8.51            = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2726_Nat_Odiff__add__assoc2,axiom,
% 15.55/8.51      ! [K: nat,J: nat,I: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ K @ J )
% 15.55/8.51       => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 15.55/8.51          = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2727_Nat_Odiff__add__assoc,axiom,
% 15.55/8.51      ! [K: nat,J: nat,I: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ K @ J )
% 15.55/8.51       => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 15.55/8.51          = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2728_Nat_Ole__diff__conv2,axiom,
% 15.55/8.51      ! [K: nat,J: nat,I: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ K @ J )
% 15.55/8.51       => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 15.55/8.51          = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2729_le__diff__conv,axiom,
% 15.55/8.51      ! [J: nat,K: nat,I: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 15.55/8.51        = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2730_real__sqrt__divide,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( sqrt @ ( divide_divide_real @ X3 @ Y3 ) )
% 15.55/8.51        = ( divide_divide_real @ ( sqrt @ X3 ) @ ( sqrt @ Y3 ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2731_iadd__is__0,axiom,
% 15.55/8.51      ! [M: extended_enat,N: extended_enat] :
% 15.55/8.51        ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 15.55/8.51          = zero_z5237406670263579293d_enat )
% 15.55/8.51        = ( ( M = zero_z5237406670263579293d_enat )
% 15.55/8.51          & ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2732_add__diff__assoc__enat,axiom,
% 15.55/8.51      ! [Z: extended_enat,Y3: extended_enat,X3: extended_enat] :
% 15.55/8.51        ( ( ord_le2932123472753598470d_enat @ Z @ Y3 )
% 15.55/8.51       => ( ( plus_p3455044024723400733d_enat @ X3 @ ( minus_3235023915231533773d_enat @ Y3 @ Z ) )
% 15.55/8.51          = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X3 @ Y3 ) @ Z ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2733_real__of__int__div2,axiom,
% 15.55/8.51      ! [N: int,X3: 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 @ X3 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2734_real__of__int__div3,axiom,
% 15.55/8.51      ! [N: int,X3: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X3 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X3 ) ) ) @ one_one_real ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2735_ln__div,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.51       => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.55/8.51         => ( ( ln_ln_real @ ( divide_divide_real @ X3 @ Y3 ) )
% 15.55/8.51            = ( minus_minus_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y3 ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2736_less__imp__add__positive,axiom,
% 15.55/8.51      ! [I: nat,J: nat] :
% 15.55/8.51        ( ( ord_less_nat @ I @ J )
% 15.55/8.51       => ? [K2: nat] :
% 15.55/8.51            ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 15.55/8.51            & ( ( plus_plus_nat @ I @ K2 )
% 15.55/8.51              = J ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2737_nat__diff__split__asm,axiom,
% 15.55/8.51      ! [P: nat > $o,A: nat,B: nat] :
% 15.55/8.51        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 15.55/8.51        = ( ~ ( ( ( ord_less_nat @ A @ B )
% 15.55/8.51                & ~ ( P @ zero_zero_nat ) )
% 15.55/8.51              | ? [D4: nat] :
% 15.55/8.51                  ( ( A
% 15.55/8.51                    = ( plus_plus_nat @ B @ D4 ) )
% 15.55/8.51                  & ~ ( P @ D4 ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2738_nat__diff__split,axiom,
% 15.55/8.51      ! [P: nat > $o,A: nat,B: nat] :
% 15.55/8.51        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 15.55/8.51        = ( ( ( ord_less_nat @ A @ B )
% 15.55/8.51           => ( P @ zero_zero_nat ) )
% 15.55/8.51          & ! [D4: nat] :
% 15.55/8.51              ( ( A
% 15.55/8.51                = ( plus_plus_nat @ B @ D4 ) )
% 15.55/8.51             => ( P @ D4 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2739_mono__nat__linear__lb,axiom,
% 15.55/8.51      ! [F: nat > nat,M: nat,K: nat] :
% 15.55/8.51        ( ! [M4: nat,N2: nat] :
% 15.55/8.51            ( ( ord_less_nat @ M4 @ N2 )
% 15.55/8.51           => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N2 ) ) )
% 15.55/8.51       => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2740_less__diff__conv2,axiom,
% 15.55/8.51      ! [K: nat,J: nat,I: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ K @ J )
% 15.55/8.51       => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 15.55/8.51          = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2741_int__ops_I5_J,axiom,
% 15.55/8.51      ! [A: nat,B: nat] :
% 15.55/8.51        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 15.55/8.51        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2742_int__plus,axiom,
% 15.55/8.51      ! [N: nat,M: nat] :
% 15.55/8.51        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
% 15.55/8.51        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2743_zadd__int__left,axiom,
% 15.55/8.51      ! [M: nat,N: nat,Z: int] :
% 15.55/8.51        ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z ) )
% 15.55/8.51        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2744_ln__diff__le,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.51       => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.55/8.51         => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y3 ) ) @ ( divide_divide_real @ ( minus_minus_real @ X3 @ Y3 ) @ Y3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2745_linordered__field__no__ub,axiom,
% 15.55/8.51      ! [X6: real] :
% 15.55/8.51      ? [X_1: real] : ( ord_less_real @ X6 @ X_1 ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2746_linordered__field__no__ub,axiom,
% 15.55/8.51      ! [X6: rat] :
% 15.55/8.51      ? [X_1: rat] : ( ord_less_rat @ X6 @ X_1 ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2747_linordered__field__no__lb,axiom,
% 15.55/8.51      ! [X6: real] :
% 15.55/8.51      ? [Y4: real] : ( ord_less_real @ Y4 @ X6 ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2748_linordered__field__no__lb,axiom,
% 15.55/8.51      ! [X6: rat] :
% 15.55/8.51      ? [Y4: rat] : ( ord_less_rat @ Y4 @ X6 ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2749_real__div__sqrt,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.51       => ( ( divide_divide_real @ X3 @ ( sqrt @ X3 ) )
% 15.55/8.51          = ( sqrt @ X3 ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2750_real__of__nat__div4,axiom,
% 15.55/8.51      ! [N: nat,X3: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X3 ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X3 ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2751_real__of__nat__div,axiom,
% 15.55/8.51      ! [D3: nat,N: nat] :
% 15.55/8.51        ( ( dvd_dvd_nat @ D3 @ N )
% 15.55/8.51       => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ D3 ) )
% 15.55/8.51          = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ D3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2752_nat__int__add,axiom,
% 15.55/8.51      ! [A: nat,B: nat] :
% 15.55/8.51        ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 15.55/8.51        = ( plus_plus_nat @ A @ B ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2753_nat__1__add__1,axiom,
% 15.55/8.51      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 15.55/8.51      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2754_real__of__nat__div2,axiom,
% 15.55/8.51      ! [N: nat,X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X3 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2755_nat__div__distrib_H,axiom,
% 15.55/8.51      ! [Y3: int,X3: int] :
% 15.55/8.51        ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 15.55/8.51       => ( ( nat2 @ ( divide_divide_int @ X3 @ Y3 ) )
% 15.55/8.51          = ( divide_divide_nat @ ( nat2 @ X3 ) @ ( nat2 @ Y3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2756_nat__div__distrib,axiom,
% 15.55/8.51      ! [X3: int,Y3: int] :
% 15.55/8.51        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 15.55/8.51       => ( ( nat2 @ ( divide_divide_int @ X3 @ Y3 ) )
% 15.55/8.51          = ( divide_divide_nat @ ( nat2 @ X3 ) @ ( nat2 @ Y3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2757_real__of__nat__div3,axiom,
% 15.55/8.51      ! [N: nat,X3: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X3 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X3 ) ) ) @ one_one_real ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2758_log__base__change,axiom,
% 15.55/8.51      ! [A: real,B: real,X3: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.51       => ( ( A != one_one_real )
% 15.55/8.51         => ( ( log @ B @ X3 )
% 15.55/8.51            = ( divide_divide_real @ ( log @ A @ X3 ) @ ( log @ A @ B ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2759_log__divide,axiom,
% 15.55/8.51      ! [A: real,X3: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.51       => ( ( A != one_one_real )
% 15.55/8.51         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.51           => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.55/8.51             => ( ( log @ A @ ( divide_divide_real @ X3 @ Y3 ) )
% 15.55/8.51                = ( minus_minus_real @ ( log @ A @ X3 ) @ ( log @ A @ Y3 ) ) ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2760_nat__add__distrib,axiom,
% 15.55/8.51      ! [Z: int,Z5: int] :
% 15.55/8.51        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 15.55/8.51       => ( ( ord_less_eq_int @ zero_zero_int @ Z5 )
% 15.55/8.51         => ( ( nat2 @ ( plus_plus_int @ Z @ Z5 ) )
% 15.55/8.51            = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z5 ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2761_exp__add__not__zero__imp__right,axiom,
% 15.55/8.51      ! [M: nat,N: nat] :
% 15.55/8.51        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 15.55/8.51         != zero_zero_nat )
% 15.55/8.51       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.51         != zero_zero_nat ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2762_exp__add__not__zero__imp__right,axiom,
% 15.55/8.51      ! [M: nat,N: nat] :
% 15.55/8.51        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 15.55/8.51         != zero_zero_int )
% 15.55/8.51       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 15.55/8.51         != zero_zero_int ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2763_exp__add__not__zero__imp__left,axiom,
% 15.55/8.51      ! [M: nat,N: nat] :
% 15.55/8.51        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 15.55/8.51         != zero_zero_nat )
% 15.55/8.51       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 15.55/8.51         != zero_zero_nat ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2764_exp__add__not__zero__imp__left,axiom,
% 15.55/8.51      ! [M: nat,N: nat] :
% 15.55/8.51        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 15.55/8.51         != zero_zero_int )
% 15.55/8.51       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 15.55/8.51         != zero_zero_int ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2765_div__exp__eq,axiom,
% 15.55/8.51      ! [A: nat,M: nat,N: nat] :
% 15.55/8.51        ( ( 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 ) )
% 15.55/8.51        = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2766_div__exp__eq,axiom,
% 15.55/8.51      ! [A: int,M: nat,N: nat] :
% 15.55/8.51        ( ( 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 ) )
% 15.55/8.51        = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2767_nat__induct2,axiom,
% 15.55/8.51      ! [P: nat > $o,N: nat] :
% 15.55/8.51        ( ( P @ zero_zero_nat )
% 15.55/8.51       => ( ( P @ one_one_nat )
% 15.55/8.51         => ( ! [N2: nat] :
% 15.55/8.51                ( ( P @ N2 )
% 15.55/8.51               => ( P @ ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.51           => ( P @ N ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2768_log__base__pow,axiom,
% 15.55/8.51      ! [A: real,N: nat,X3: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.51       => ( ( log @ ( power_power_real @ A @ N ) @ X3 )
% 15.55/8.51          = ( divide_divide_real @ ( log @ A @ X3 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2769_lemma__real__divide__sqrt__less,axiom,
% 15.55/8.51      ! [U: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ U )
% 15.55/8.51       => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2770_ln__sqrt,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.51       => ( ( ln_ln_real @ ( sqrt @ X3 ) )
% 15.55/8.51          = ( divide_divide_real @ ( ln_ln_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2771_dvd__field__iff,axiom,
% 15.55/8.51      ( dvd_dvd_real
% 15.55/8.51      = ( ^ [A4: real,B3: real] :
% 15.55/8.51            ( ( A4 = zero_zero_real )
% 15.55/8.51           => ( B3 = zero_zero_real ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2772_dvd__field__iff,axiom,
% 15.55/8.51      ( dvd_dvd_rat
% 15.55/8.51      = ( ^ [A4: rat,B3: rat] :
% 15.55/8.51            ( ( A4 = zero_zero_rat )
% 15.55/8.51           => ( B3 = zero_zero_rat ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2773_ex__power__ivl2,axiom,
% 15.55/8.51      ! [B: nat,K: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 15.55/8.51       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 15.55/8.51         => ? [N2: nat] :
% 15.55/8.51              ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 15.55/8.51              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2774_ex__power__ivl1,axiom,
% 15.55/8.51      ! [B: nat,K: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 15.55/8.51       => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 15.55/8.51         => ? [N2: nat] :
% 15.55/8.51              ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 15.55/8.51              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2775_divide__right__mono__neg,axiom,
% 15.55/8.51      ! [A: real,B: real,C: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.51       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 15.55/8.51         => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2776_divide__right__mono__neg,axiom,
% 15.55/8.51      ! [A: rat,B: rat,C: rat] :
% 15.55/8.51        ( ( ord_less_eq_rat @ A @ B )
% 15.55/8.51       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 15.55/8.51         => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2777_divide__nonpos__nonpos,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 15.55/8.51       => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 15.55/8.51         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2778_divide__nonpos__nonpos,axiom,
% 15.55/8.51      ! [X3: rat,Y3: rat] :
% 15.55/8.51        ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 15.55/8.51       => ( ( ord_less_eq_rat @ Y3 @ zero_zero_rat )
% 15.55/8.51         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2779_divide__nonpos__nonneg,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 15.55/8.51       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.51         => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y3 ) @ zero_zero_real ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2780_divide__nonpos__nonneg,axiom,
% 15.55/8.51      ! [X3: rat,Y3: rat] :
% 15.55/8.51        ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 15.55/8.51       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 15.55/8.51         => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2781_divide__nonneg__nonpos,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.51       => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 15.55/8.51         => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y3 ) @ zero_zero_real ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2782_divide__nonneg__nonpos,axiom,
% 15.55/8.51      ! [X3: rat,Y3: rat] :
% 15.55/8.51        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 15.55/8.51       => ( ( ord_less_eq_rat @ Y3 @ zero_zero_rat )
% 15.55/8.51         => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2783_divide__nonneg__nonneg,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.51       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.51         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2784_divide__nonneg__nonneg,axiom,
% 15.55/8.51      ! [X3: rat,Y3: rat] :
% 15.55/8.51        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 15.55/8.51       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 15.55/8.51         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2785_zero__le__divide__iff,axiom,
% 15.55/8.51      ! [A: real,B: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 15.55/8.51        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.51            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 15.55/8.51          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 15.55/8.51            & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2786_zero__le__divide__iff,axiom,
% 15.55/8.51      ! [A: rat,B: rat] :
% 15.55/8.51        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 15.55/8.51        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.51            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 15.55/8.51          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 15.55/8.51            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2787_divide__right__mono,axiom,
% 15.55/8.51      ! [A: real,B: real,C: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.51       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 15.55/8.51         => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2788_divide__right__mono,axiom,
% 15.55/8.51      ! [A: rat,B: rat,C: rat] :
% 15.55/8.51        ( ( ord_less_eq_rat @ A @ B )
% 15.55/8.51       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 15.55/8.51         => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2789_divide__le__0__iff,axiom,
% 15.55/8.51      ! [A: real,B: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 15.55/8.51        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.51            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 15.55/8.51          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 15.55/8.51            & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2790_divide__le__0__iff,axiom,
% 15.55/8.51      ! [A: rat,B: rat] :
% 15.55/8.51        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 15.55/8.51        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.51            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 15.55/8.51          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 15.55/8.51            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2791_divide__strict__right__mono__neg,axiom,
% 15.55/8.51      ! [B: real,A: real,C: real] :
% 15.55/8.51        ( ( ord_less_real @ B @ A )
% 15.55/8.51       => ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.51         => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2792_divide__strict__right__mono__neg,axiom,
% 15.55/8.51      ! [B: rat,A: rat,C: rat] :
% 15.55/8.51        ( ( ord_less_rat @ B @ A )
% 15.55/8.51       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.51         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2793_divide__strict__right__mono,axiom,
% 15.55/8.51      ! [A: real,B: real,C: real] :
% 15.55/8.51        ( ( ord_less_real @ A @ B )
% 15.55/8.51       => ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.51         => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2794_divide__strict__right__mono,axiom,
% 15.55/8.51      ! [A: rat,B: rat,C: rat] :
% 15.55/8.51        ( ( ord_less_rat @ A @ B )
% 15.55/8.51       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.51         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2795_zero__less__divide__iff,axiom,
% 15.55/8.51      ! [A: real,B: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 15.55/8.51        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.51            & ( ord_less_real @ zero_zero_real @ B ) )
% 15.55/8.51          | ( ( ord_less_real @ A @ zero_zero_real )
% 15.55/8.51            & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2796_zero__less__divide__iff,axiom,
% 15.55/8.51      ! [A: rat,B: rat] :
% 15.55/8.51        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 15.55/8.51        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.51            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 15.55/8.51          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 15.55/8.51            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2797_divide__less__cancel,axiom,
% 15.55/8.51      ! [A: real,C: real,B: real] :
% 15.55/8.51        ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 15.55/8.51        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.51           => ( ord_less_real @ A @ B ) )
% 15.55/8.51          & ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.51           => ( ord_less_real @ B @ A ) )
% 15.55/8.51          & ( C != zero_zero_real ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2798_divide__less__cancel,axiom,
% 15.55/8.51      ! [A: rat,C: rat,B: rat] :
% 15.55/8.51        ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 15.55/8.51        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.51           => ( ord_less_rat @ A @ B ) )
% 15.55/8.51          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.51           => ( ord_less_rat @ B @ A ) )
% 15.55/8.51          & ( C != zero_zero_rat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2799_divide__less__0__iff,axiom,
% 15.55/8.51      ! [A: real,B: real] :
% 15.55/8.51        ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 15.55/8.51        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.51            & ( ord_less_real @ B @ zero_zero_real ) )
% 15.55/8.51          | ( ( ord_less_real @ A @ zero_zero_real )
% 15.55/8.51            & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2800_divide__less__0__iff,axiom,
% 15.55/8.51      ! [A: rat,B: rat] :
% 15.55/8.51        ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 15.55/8.51        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.51            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 15.55/8.51          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 15.55/8.51            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2801_divide__pos__pos,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.51       => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.55/8.51         => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2802_divide__pos__pos,axiom,
% 15.55/8.51      ! [X3: rat,Y3: rat] :
% 15.55/8.51        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 15.55/8.51       => ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 15.55/8.51         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2803_divide__pos__neg,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.51       => ( ( ord_less_real @ Y3 @ zero_zero_real )
% 15.55/8.51         => ( ord_less_real @ ( divide_divide_real @ X3 @ Y3 ) @ zero_zero_real ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2804_divide__pos__neg,axiom,
% 15.55/8.51      ! [X3: rat,Y3: rat] :
% 15.55/8.51        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 15.55/8.51       => ( ( ord_less_rat @ Y3 @ zero_zero_rat )
% 15.55/8.51         => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2805_divide__neg__pos,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_real @ X3 @ zero_zero_real )
% 15.55/8.51       => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.55/8.51         => ( ord_less_real @ ( divide_divide_real @ X3 @ Y3 ) @ zero_zero_real ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2806_divide__neg__pos,axiom,
% 15.55/8.51      ! [X3: rat,Y3: rat] :
% 15.55/8.51        ( ( ord_less_rat @ X3 @ zero_zero_rat )
% 15.55/8.51       => ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 15.55/8.51         => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2807_divide__neg__neg,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_real @ X3 @ zero_zero_real )
% 15.55/8.51       => ( ( ord_less_real @ Y3 @ zero_zero_real )
% 15.55/8.51         => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2808_divide__neg__neg,axiom,
% 15.55/8.51      ! [X3: rat,Y3: rat] :
% 15.55/8.51        ( ( ord_less_rat @ X3 @ zero_zero_rat )
% 15.55/8.51       => ( ( ord_less_rat @ Y3 @ zero_zero_rat )
% 15.55/8.51         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2809_right__inverse__eq,axiom,
% 15.55/8.51      ! [B: complex,A: complex] :
% 15.55/8.51        ( ( B != zero_zero_complex )
% 15.55/8.51       => ( ( ( divide1717551699836669952omplex @ A @ B )
% 15.55/8.51            = one_one_complex )
% 15.55/8.51          = ( A = B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2810_right__inverse__eq,axiom,
% 15.55/8.51      ! [B: real,A: real] :
% 15.55/8.51        ( ( B != zero_zero_real )
% 15.55/8.51       => ( ( ( divide_divide_real @ A @ B )
% 15.55/8.51            = one_one_real )
% 15.55/8.51          = ( A = B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2811_right__inverse__eq,axiom,
% 15.55/8.51      ! [B: rat,A: rat] :
% 15.55/8.51        ( ( B != zero_zero_rat )
% 15.55/8.51       => ( ( ( divide_divide_rat @ A @ B )
% 15.55/8.51            = one_one_rat )
% 15.55/8.51          = ( A = B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2812_sqrt__sum__squares__half__less,axiom,
% 15.55/8.51      ! [X3: real,U: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_real @ X3 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.51       => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.51         => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.51           => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.51             => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2813_ceiling__log2__div2,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.51       => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 15.55/8.51          = ( 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 ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2814_field__le__epsilon,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ! [E: real] :
% 15.55/8.51            ( ( ord_less_real @ zero_zero_real @ E )
% 15.55/8.51           => ( ord_less_eq_real @ X3 @ ( plus_plus_real @ Y3 @ E ) ) )
% 15.55/8.51       => ( ord_less_eq_real @ X3 @ Y3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2815_field__le__epsilon,axiom,
% 15.55/8.51      ! [X3: rat,Y3: rat] :
% 15.55/8.51        ( ! [E: rat] :
% 15.55/8.51            ( ( ord_less_rat @ zero_zero_rat @ E )
% 15.55/8.51           => ( ord_less_eq_rat @ X3 @ ( plus_plus_rat @ Y3 @ E ) ) )
% 15.55/8.51       => ( ord_less_eq_rat @ X3 @ Y3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2816_frac__le,axiom,
% 15.55/8.51      ! [Y3: real,X3: real,W: real,Z: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.51       => ( ( ord_less_eq_real @ X3 @ Y3 )
% 15.55/8.51         => ( ( ord_less_real @ zero_zero_real @ W )
% 15.55/8.51           => ( ( ord_less_eq_real @ W @ Z )
% 15.55/8.51             => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Z ) @ ( divide_divide_real @ Y3 @ W ) ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2817_frac__le,axiom,
% 15.55/8.51      ! [Y3: rat,X3: rat,W: rat,Z: rat] :
% 15.55/8.51        ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 15.55/8.51       => ( ( ord_less_eq_rat @ X3 @ Y3 )
% 15.55/8.51         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 15.55/8.51           => ( ( ord_less_eq_rat @ W @ Z )
% 15.55/8.51             => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Z ) @ ( divide_divide_rat @ Y3 @ W ) ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2818_frac__less,axiom,
% 15.55/8.51      ! [X3: real,Y3: real,W: real,Z: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.51       => ( ( ord_less_real @ X3 @ Y3 )
% 15.55/8.51         => ( ( ord_less_real @ zero_zero_real @ W )
% 15.55/8.51           => ( ( ord_less_eq_real @ W @ Z )
% 15.55/8.51             => ( ord_less_real @ ( divide_divide_real @ X3 @ Z ) @ ( divide_divide_real @ Y3 @ W ) ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2819_frac__less,axiom,
% 15.55/8.51      ! [X3: rat,Y3: rat,W: rat,Z: rat] :
% 15.55/8.51        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 15.55/8.51       => ( ( ord_less_rat @ X3 @ Y3 )
% 15.55/8.51         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 15.55/8.51           => ( ( ord_less_eq_rat @ W @ Z )
% 15.55/8.51             => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Z ) @ ( divide_divide_rat @ Y3 @ W ) ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2820_frac__less2,axiom,
% 15.55/8.51      ! [X3: real,Y3: real,W: real,Z: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.51       => ( ( ord_less_eq_real @ X3 @ Y3 )
% 15.55/8.51         => ( ( ord_less_real @ zero_zero_real @ W )
% 15.55/8.51           => ( ( ord_less_real @ W @ Z )
% 15.55/8.51             => ( ord_less_real @ ( divide_divide_real @ X3 @ Z ) @ ( divide_divide_real @ Y3 @ W ) ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2821_frac__less2,axiom,
% 15.55/8.51      ! [X3: rat,Y3: rat,W: rat,Z: rat] :
% 15.55/8.51        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 15.55/8.51       => ( ( ord_less_eq_rat @ X3 @ Y3 )
% 15.55/8.51         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 15.55/8.51           => ( ( ord_less_rat @ W @ Z )
% 15.55/8.51             => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Z ) @ ( divide_divide_rat @ Y3 @ W ) ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2822_divide__le__cancel,axiom,
% 15.55/8.51      ! [A: real,C: real,B: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 15.55/8.51        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.51           => ( ord_less_eq_real @ A @ B ) )
% 15.55/8.51          & ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.51           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2823_divide__le__cancel,axiom,
% 15.55/8.51      ! [A: rat,C: rat,B: rat] :
% 15.55/8.51        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 15.55/8.51        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.51           => ( ord_less_eq_rat @ A @ B ) )
% 15.55/8.51          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.51           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2824_divide__nonneg__neg,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.51       => ( ( ord_less_real @ Y3 @ zero_zero_real )
% 15.55/8.51         => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y3 ) @ zero_zero_real ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2825_divide__nonneg__neg,axiom,
% 15.55/8.51      ! [X3: rat,Y3: rat] :
% 15.55/8.51        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 15.55/8.51       => ( ( ord_less_rat @ Y3 @ zero_zero_rat )
% 15.55/8.51         => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2826_divide__nonneg__pos,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.51       => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.55/8.51         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2827_divide__nonneg__pos,axiom,
% 15.55/8.51      ! [X3: rat,Y3: rat] :
% 15.55/8.51        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 15.55/8.51       => ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 15.55/8.51         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2828_divide__nonpos__neg,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 15.55/8.51       => ( ( ord_less_real @ Y3 @ zero_zero_real )
% 15.55/8.51         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2829_divide__nonpos__neg,axiom,
% 15.55/8.51      ! [X3: rat,Y3: rat] :
% 15.55/8.51        ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 15.55/8.51       => ( ( ord_less_rat @ Y3 @ zero_zero_rat )
% 15.55/8.51         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2830_divide__nonpos__pos,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 15.55/8.51       => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.55/8.51         => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y3 ) @ zero_zero_real ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2831_divide__nonpos__pos,axiom,
% 15.55/8.51      ! [X3: rat,Y3: rat] :
% 15.55/8.51        ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 15.55/8.51       => ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 15.55/8.51         => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2832_less__divide__eq__1,axiom,
% 15.55/8.51      ! [B: real,A: real] :
% 15.55/8.51        ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 15.55/8.51        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.51            & ( ord_less_real @ A @ B ) )
% 15.55/8.51          | ( ( ord_less_real @ A @ zero_zero_real )
% 15.55/8.51            & ( ord_less_real @ B @ A ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2833_less__divide__eq__1,axiom,
% 15.55/8.51      ! [B: rat,A: rat] :
% 15.55/8.51        ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 15.55/8.51        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.51            & ( ord_less_rat @ A @ B ) )
% 15.55/8.51          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 15.55/8.51            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2834_divide__less__eq__1,axiom,
% 15.55/8.51      ! [B: real,A: real] :
% 15.55/8.51        ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 15.55/8.51        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.51            & ( ord_less_real @ B @ A ) )
% 15.55/8.51          | ( ( ord_less_real @ A @ zero_zero_real )
% 15.55/8.51            & ( ord_less_real @ A @ B ) )
% 15.55/8.51          | ( A = zero_zero_real ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2835_divide__less__eq__1,axiom,
% 15.55/8.51      ! [B: rat,A: rat] :
% 15.55/8.51        ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 15.55/8.51        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.51            & ( ord_less_rat @ B @ A ) )
% 15.55/8.51          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 15.55/8.51            & ( ord_less_rat @ A @ B ) )
% 15.55/8.51          | ( A = zero_zero_rat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2836_gt__half__sum,axiom,
% 15.55/8.51      ! [A: real,B: real] :
% 15.55/8.51        ( ( ord_less_real @ A @ B )
% 15.55/8.51       => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2837_gt__half__sum,axiom,
% 15.55/8.51      ! [A: rat,B: rat] :
% 15.55/8.51        ( ( ord_less_rat @ A @ B )
% 15.55/8.51       => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2838_less__half__sum,axiom,
% 15.55/8.51      ! [A: real,B: real] :
% 15.55/8.51        ( ( ord_less_real @ A @ B )
% 15.55/8.51       => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2839_less__half__sum,axiom,
% 15.55/8.51      ! [A: rat,B: rat] :
% 15.55/8.51        ( ( ord_less_rat @ A @ B )
% 15.55/8.51       => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2840_ceiling__log__nat__eq__if,axiom,
% 15.55/8.51      ! [B: nat,N: nat,K: nat] :
% 15.55/8.51        ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 15.55/8.51       => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 15.55/8.51         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 15.55/8.51           => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 15.55/8.51              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2841_ceiling__log__nat__eq__powr__iff,axiom,
% 15.55/8.51      ! [B: nat,K: nat,N: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 15.55/8.51       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 15.55/8.51         => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 15.55/8.51              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 15.55/8.51            = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 15.55/8.51              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2842_le__divide__eq__1,axiom,
% 15.55/8.51      ! [B: real,A: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 15.55/8.51        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.51            & ( ord_less_eq_real @ A @ B ) )
% 15.55/8.51          | ( ( ord_less_real @ A @ zero_zero_real )
% 15.55/8.51            & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2843_le__divide__eq__1,axiom,
% 15.55/8.51      ! [B: rat,A: rat] :
% 15.55/8.51        ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 15.55/8.51        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.51            & ( ord_less_eq_rat @ A @ B ) )
% 15.55/8.51          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 15.55/8.51            & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2844_divide__le__eq__1,axiom,
% 15.55/8.51      ! [B: real,A: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 15.55/8.51        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.51            & ( ord_less_eq_real @ B @ A ) )
% 15.55/8.51          | ( ( ord_less_real @ A @ zero_zero_real )
% 15.55/8.51            & ( ord_less_eq_real @ A @ B ) )
% 15.55/8.51          | ( A = zero_zero_real ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2845_divide__le__eq__1,axiom,
% 15.55/8.51      ! [B: rat,A: rat] :
% 15.55/8.51        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 15.55/8.51        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.51            & ( ord_less_eq_rat @ B @ A ) )
% 15.55/8.51          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 15.55/8.51            & ( ord_less_eq_rat @ A @ B ) )
% 15.55/8.51          | ( A = zero_zero_rat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2846_real__average__minus__first,axiom,
% 15.55/8.51      ! [A: real,B: real] :
% 15.55/8.51        ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 15.55/8.51        = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2847_real__average__minus__second,axiom,
% 15.55/8.51      ! [B: real,A: real] :
% 15.55/8.51        ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 15.55/8.51        = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2848_add__def,axiom,
% 15.55/8.51      ( vEBT_VEBT_add
% 15.55/8.51      = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2849_div__pos__geq,axiom,
% 15.55/8.51      ! [L: int,K: int] :
% 15.55/8.51        ( ( ord_less_int @ zero_zero_int @ L )
% 15.55/8.51       => ( ( ord_less_eq_int @ L @ K )
% 15.55/8.51         => ( ( divide_divide_int @ K @ L )
% 15.55/8.51            = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2850_ln__2__less__1,axiom,
% 15.55/8.51      ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2851__C5_Ohyps_C_I4_J,axiom,
% 15.55/8.51      ( deg
% 15.55/8.51      = ( plus_plus_nat @ na @ m ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2852_div2__even__ext__nat,axiom,
% 15.55/8.51      ! [X3: nat,Y3: nat] :
% 15.55/8.51        ( ( ( divide_divide_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.51          = ( divide_divide_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.51       => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X3 )
% 15.55/8.51            = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y3 ) )
% 15.55/8.51         => ( X3 = Y3 ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2853_zdiv__numeral__Bit0,axiom,
% 15.55/8.51      ! [V: num,W: num] :
% 15.55/8.51        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 15.55/8.51        = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2854_add__shift,axiom,
% 15.55/8.51      ! [X3: nat,Y3: nat,Z: nat] :
% 15.55/8.51        ( ( ( plus_plus_nat @ X3 @ Y3 )
% 15.55/8.51          = Z )
% 15.55/8.51        = ( ( vEBT_VEBT_add @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) )
% 15.55/8.51          = ( some_nat @ Z ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2855__C5_Ohyps_C_I3_J,axiom,
% 15.55/8.51      ( m
% 15.55/8.51      = ( suc @ na ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2856_div__neg__pos__less0,axiom,
% 15.55/8.51      ! [A: int,B: int] :
% 15.55/8.51        ( ( ord_less_int @ A @ zero_zero_int )
% 15.55/8.51       => ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.51         => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2857_neg__imp__zdiv__neg__iff,axiom,
% 15.55/8.51      ! [B: int,A: int] :
% 15.55/8.51        ( ( ord_less_int @ B @ zero_zero_int )
% 15.55/8.51       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 15.55/8.51          = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2858_pos__imp__zdiv__neg__iff,axiom,
% 15.55/8.51      ! [B: int,A: int] :
% 15.55/8.51        ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.51       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 15.55/8.51          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2859_zdiv__int,axiom,
% 15.55/8.51      ! [A: nat,B: nat] :
% 15.55/8.51        ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 15.55/8.51        = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2860_nonneg1__imp__zdiv__pos__iff,axiom,
% 15.55/8.51      ! [A: int,B: int] :
% 15.55/8.51        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.51       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 15.55/8.51          = ( ( ord_less_eq_int @ B @ A )
% 15.55/8.51            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2861_pos__imp__zdiv__nonneg__iff,axiom,
% 15.55/8.51      ! [B: int,A: int] :
% 15.55/8.51        ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.51       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 15.55/8.51          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2862_neg__imp__zdiv__nonneg__iff,axiom,
% 15.55/8.51      ! [B: int,A: int] :
% 15.55/8.51        ( ( ord_less_int @ B @ zero_zero_int )
% 15.55/8.51       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 15.55/8.51          = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2863_pos__imp__zdiv__pos__iff,axiom,
% 15.55/8.51      ! [K: int,I: int] :
% 15.55/8.51        ( ( ord_less_int @ zero_zero_int @ K )
% 15.55/8.51       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 15.55/8.51          = ( ord_less_eq_int @ K @ I ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2864_div__nonpos__pos__le0,axiom,
% 15.55/8.51      ! [A: int,B: int] :
% 15.55/8.51        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 15.55/8.51       => ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.51         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2865_div__nonneg__neg__le0,axiom,
% 15.55/8.51      ! [A: int,B: int] :
% 15.55/8.51        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.51       => ( ( ord_less_int @ B @ zero_zero_int )
% 15.55/8.51         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2866_div__positive__int,axiom,
% 15.55/8.51      ! [L: int,K: int] :
% 15.55/8.51        ( ( ord_less_eq_int @ L @ K )
% 15.55/8.51       => ( ( ord_less_int @ zero_zero_int @ L )
% 15.55/8.51         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2867_div__int__pos__iff,axiom,
% 15.55/8.51      ! [K: int,L: int] :
% 15.55/8.51        ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 15.55/8.51        = ( ( K = zero_zero_int )
% 15.55/8.51          | ( L = zero_zero_int )
% 15.55/8.51          | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 15.55/8.51            & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 15.55/8.51          | ( ( ord_less_int @ K @ zero_zero_int )
% 15.55/8.51            & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2868_zdiv__mono2__neg,axiom,
% 15.55/8.51      ! [A: int,B2: int,B: int] :
% 15.55/8.51        ( ( ord_less_int @ A @ zero_zero_int )
% 15.55/8.51       => ( ( ord_less_int @ zero_zero_int @ B2 )
% 15.55/8.51         => ( ( ord_less_eq_int @ B2 @ B )
% 15.55/8.51           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B2 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2869_zdiv__mono1__neg,axiom,
% 15.55/8.51      ! [A: int,A2: int,B: int] :
% 15.55/8.51        ( ( ord_less_eq_int @ A @ A2 )
% 15.55/8.51       => ( ( ord_less_int @ B @ zero_zero_int )
% 15.55/8.51         => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2870_zdiv__eq__0__iff,axiom,
% 15.55/8.51      ! [I: int,K: int] :
% 15.55/8.51        ( ( ( divide_divide_int @ I @ K )
% 15.55/8.51          = zero_zero_int )
% 15.55/8.51        = ( ( K = zero_zero_int )
% 15.55/8.51          | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 15.55/8.51            & ( ord_less_int @ I @ K ) )
% 15.55/8.51          | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 15.55/8.51            & ( ord_less_int @ K @ I ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2871_zdiv__mono2,axiom,
% 15.55/8.51      ! [A: int,B2: int,B: int] :
% 15.55/8.51        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.51       => ( ( ord_less_int @ zero_zero_int @ B2 )
% 15.55/8.51         => ( ( ord_less_eq_int @ B2 @ B )
% 15.55/8.51           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B2 ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2872_zdiv__mono1,axiom,
% 15.55/8.51      ! [A: int,A2: int,B: int] :
% 15.55/8.51        ( ( ord_less_eq_int @ A @ A2 )
% 15.55/8.51       => ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.51         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A2 @ B ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2873_int__div__less__self,axiom,
% 15.55/8.51      ! [X3: int,K: int] :
% 15.55/8.51        ( ( ord_less_int @ zero_zero_int @ X3 )
% 15.55/8.51       => ( ( ord_less_int @ one_one_int @ K )
% 15.55/8.51         => ( ord_less_int @ ( divide_divide_int @ X3 @ K ) @ X3 ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2874_div__positive,axiom,
% 15.55/8.51      ! [B: nat,A: nat] :
% 15.55/8.51        ( ( ord_less_nat @ zero_zero_nat @ B )
% 15.55/8.51       => ( ( ord_less_eq_nat @ B @ A )
% 15.55/8.51         => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2875_div__positive,axiom,
% 15.55/8.51      ! [B: int,A: int] :
% 15.55/8.51        ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.51       => ( ( ord_less_eq_int @ B @ A )
% 15.55/8.51         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2876_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 15.55/8.51      ! [A: nat,B: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.55/8.51       => ( ( ord_less_nat @ A @ B )
% 15.55/8.51         => ( ( divide_divide_nat @ A @ B )
% 15.55/8.51            = zero_zero_nat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2877_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 15.55/8.51      ! [A: int,B: int] :
% 15.55/8.51        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.51       => ( ( ord_less_int @ A @ B )
% 15.55/8.51         => ( ( divide_divide_int @ A @ B )
% 15.55/8.51            = zero_zero_int ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2878_discrete,axiom,
% 15.55/8.51      ( ord_less_nat
% 15.55/8.51      = ( ^ [A4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A4 @ one_one_nat ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2879_discrete,axiom,
% 15.55/8.51      ( ord_less_int
% 15.55/8.51      = ( ^ [A4: int] : ( ord_less_eq_int @ ( plus_plus_int @ A4 @ one_one_int ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2880_Bolzano,axiom,
% 15.55/8.51      ! [A: real,B: real,P: real > real > $o] :
% 15.55/8.51        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.51       => ( ! [A5: real,B4: real,C2: real] :
% 15.55/8.51              ( ( P @ A5 @ B4 )
% 15.55/8.51             => ( ( P @ B4 @ C2 )
% 15.55/8.51               => ( ( ord_less_eq_real @ A5 @ B4 )
% 15.55/8.51                 => ( ( ord_less_eq_real @ B4 @ C2 )
% 15.55/8.51                   => ( P @ A5 @ C2 ) ) ) ) )
% 15.55/8.51         => ( ! [X4: real] :
% 15.55/8.51                ( ( ord_less_eq_real @ A @ X4 )
% 15.55/8.51               => ( ( ord_less_eq_real @ X4 @ B )
% 15.55/8.51                 => ? [D: real] :
% 15.55/8.51                      ( ( ord_less_real @ zero_zero_real @ D )
% 15.55/8.51                      & ! [A5: real,B4: real] :
% 15.55/8.51                          ( ( ( ord_less_eq_real @ A5 @ X4 )
% 15.55/8.51                            & ( ord_less_eq_real @ X4 @ B4 )
% 15.55/8.51                            & ( ord_less_real @ ( minus_minus_real @ B4 @ A5 ) @ D ) )
% 15.55/8.51                         => ( P @ A5 @ B4 ) ) ) ) )
% 15.55/8.51           => ( P @ A @ B ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2881_round__unique,axiom,
% 15.55/8.51      ! [X3: real,Y3: int] :
% 15.55/8.51        ( ( ord_less_real @ ( minus_minus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y3 ) )
% 15.55/8.51       => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y3 ) @ ( plus_plus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 15.55/8.51         => ( ( archim8280529875227126926d_real @ X3 )
% 15.55/8.51            = Y3 ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2882_round__unique,axiom,
% 15.55/8.51      ! [X3: rat,Y3: int] :
% 15.55/8.51        ( ( ord_less_rat @ ( minus_minus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y3 ) )
% 15.55/8.51       => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y3 ) @ ( plus_plus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.51         => ( ( archim7778729529865785530nd_rat @ X3 )
% 15.55/8.51            = Y3 ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2883_high__bound__aux,axiom,
% 15.55/8.51      ! [Ma: nat,N: nat,M: nat] :
% 15.55/8.51        ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 15.55/8.51       => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2884_tanh__ln__real,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.51       => ( ( tanh_real @ ( ln_ln_real @ X3 ) )
% 15.55/8.51          = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2885_ceiling__log__eq__powr__iff,axiom,
% 15.55/8.51      ! [X3: real,B: real,K: nat] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.51       => ( ( ord_less_real @ one_one_real @ B )
% 15.55/8.51         => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X3 ) )
% 15.55/8.51              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 15.55/8.51            = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X3 )
% 15.55/8.51              & ( ord_less_eq_real @ X3 @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2886__C5_Ohyps_C_I2_J,axiom,
% 15.55/8.51      ( ( size_s6755466524823107622T_VEBT @ treeList )
% 15.55/8.51      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2887_floor__log__nat__eq__powr__iff,axiom,
% 15.55/8.51      ! [B: nat,K: nat,N: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 15.55/8.51       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 15.55/8.51         => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 15.55/8.51              = ( semiri1314217659103216013at_int @ N ) )
% 15.55/8.51            = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 15.55/8.51              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2888_high__def,axiom,
% 15.55/8.51      ( vEBT_VEBT_high
% 15.55/8.51      = ( ^ [X: nat,N3: nat] : ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2889_even__odd__cases,axiom,
% 15.55/8.51      ! [X3: nat] :
% 15.55/8.51        ( ! [N2: nat] :
% 15.55/8.51            ( X3
% 15.55/8.51           != ( plus_plus_nat @ N2 @ N2 ) )
% 15.55/8.51       => ~ ! [N2: nat] :
% 15.55/8.51              ( X3
% 15.55/8.51             != ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2890_old_Onat_Oinject,axiom,
% 15.55/8.51      ! [Nat: nat,Nat2: nat] :
% 15.55/8.51        ( ( ( suc @ Nat )
% 15.55/8.51          = ( suc @ Nat2 ) )
% 15.55/8.51        = ( Nat = Nat2 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2891_nat_Oinject,axiom,
% 15.55/8.51      ! [X2: nat,Y2: nat] :
% 15.55/8.51        ( ( ( suc @ X2 )
% 15.55/8.51          = ( suc @ Y2 ) )
% 15.55/8.51        = ( X2 = Y2 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2892_Suc__less__eq,axiom,
% 15.55/8.51      ! [M: nat,N: nat] :
% 15.55/8.51        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 15.55/8.51        = ( ord_less_nat @ M @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2893_Suc__mono,axiom,
% 15.55/8.51      ! [M: nat,N: nat] :
% 15.55/8.51        ( ( ord_less_nat @ M @ N )
% 15.55/8.51       => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2894_lessI,axiom,
% 15.55/8.51      ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2895_add__Suc__right,axiom,
% 15.55/8.51      ! [M: nat,N: nat] :
% 15.55/8.51        ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 15.55/8.51        = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2896_Suc__le__mono,axiom,
% 15.55/8.51      ! [N: nat,M: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 15.55/8.51        = ( ord_less_eq_nat @ N @ M ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2897_diff__Suc__Suc,axiom,
% 15.55/8.51      ! [M: nat,N: nat] :
% 15.55/8.51        ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 15.55/8.51        = ( minus_minus_nat @ M @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2898_Suc__diff__diff,axiom,
% 15.55/8.51      ! [M: nat,N: nat,K: nat] :
% 15.55/8.51        ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 15.55/8.51        = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2899_powr__0,axiom,
% 15.55/8.51      ! [Z: real] :
% 15.55/8.51        ( ( powr_real @ zero_zero_real @ Z )
% 15.55/8.51        = zero_zero_real ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2900_powr__eq__0__iff,axiom,
% 15.55/8.51      ! [W: real,Z: real] :
% 15.55/8.51        ( ( ( powr_real @ W @ Z )
% 15.55/8.51          = zero_zero_real )
% 15.55/8.51        = ( W = zero_zero_real ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2901_floor__of__int,axiom,
% 15.55/8.51      ! [Z: int] :
% 15.55/8.51        ( ( archim3151403230148437115or_rat @ ( ring_1_of_int_rat @ Z ) )
% 15.55/8.51        = Z ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2902_floor__of__int,axiom,
% 15.55/8.51      ! [Z: int] :
% 15.55/8.51        ( ( archim6058952711729229775r_real @ ( ring_1_of_int_real @ Z ) )
% 15.55/8.51        = Z ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2903_of__int__floor__cancel,axiom,
% 15.55/8.51      ! [X3: rat] :
% 15.55/8.51        ( ( ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X3 ) )
% 15.55/8.51          = X3 )
% 15.55/8.51        = ( ? [N3: int] :
% 15.55/8.51              ( X3
% 15.55/8.51              = ( ring_1_of_int_rat @ N3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2904_of__int__floor__cancel,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X3 ) )
% 15.55/8.51          = X3 )
% 15.55/8.51        = ( ? [N3: int] :
% 15.55/8.51              ( X3
% 15.55/8.51              = ( ring_1_of_int_real @ N3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2905_tanh__0,axiom,
% 15.55/8.51      ( ( tanh_real @ zero_zero_real )
% 15.55/8.51      = zero_zero_real ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2906_tanh__real__zero__iff,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( ( tanh_real @ X3 )
% 15.55/8.51          = zero_zero_real )
% 15.55/8.51        = ( X3 = zero_zero_real ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2907_tanh__real__less__iff,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_real @ ( tanh_real @ X3 ) @ ( tanh_real @ Y3 ) )
% 15.55/8.51        = ( ord_less_real @ X3 @ Y3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2908_tanh__real__le__iff,axiom,
% 15.55/8.51      ! [X3: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ ( tanh_real @ X3 ) @ ( tanh_real @ Y3 ) )
% 15.55/8.51        = ( ord_less_eq_real @ X3 @ Y3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2909_round__of__int,axiom,
% 15.55/8.51      ! [N: int] :
% 15.55/8.51        ( ( archim8280529875227126926d_real @ ( ring_1_of_int_real @ N ) )
% 15.55/8.51        = N ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2910_round__of__int,axiom,
% 15.55/8.51      ! [N: int] :
% 15.55/8.51        ( ( archim7778729529865785530nd_rat @ ( ring_1_of_int_rat @ N ) )
% 15.55/8.51        = N ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2911_power__0__Suc,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 15.55/8.51        = zero_zero_rat ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2912_power__0__Suc,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 15.55/8.51        = zero_zero_nat ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2913_power__0__Suc,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 15.55/8.51        = zero_zero_int ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2914_power__0__Suc,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 15.55/8.51        = zero_zero_real ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2915_power__0__Suc,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 15.55/8.51        = zero_zero_complex ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2916_power__Suc0__right,axiom,
% 15.55/8.51      ! [A: nat] :
% 15.55/8.51        ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 15.55/8.51        = A ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2917_power__Suc0__right,axiom,
% 15.55/8.51      ! [A: int] :
% 15.55/8.51        ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 15.55/8.51        = A ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2918_power__Suc0__right,axiom,
% 15.55/8.51      ! [A: real] :
% 15.55/8.51        ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 15.55/8.51        = A ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2919_power__Suc0__right,axiom,
% 15.55/8.51      ! [A: complex] :
% 15.55/8.51        ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 15.55/8.51        = A ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2920_zero__less__Suc,axiom,
% 15.55/8.51      ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2921_less__Suc0,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 15.55/8.51        = ( N = zero_zero_nat ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2922_div__by__Suc__0,axiom,
% 15.55/8.51      ! [M: nat] :
% 15.55/8.51        ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 15.55/8.51        = M ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2923_power__Suc__0,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 15.55/8.51        = ( suc @ zero_zero_nat ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2924_nat__power__eq__Suc__0__iff,axiom,
% 15.55/8.51      ! [X3: nat,M: nat] :
% 15.55/8.51        ( ( ( power_power_nat @ X3 @ M )
% 15.55/8.51          = ( suc @ zero_zero_nat ) )
% 15.55/8.51        = ( ( M = zero_zero_nat )
% 15.55/8.51          | ( X3
% 15.55/8.51            = ( suc @ zero_zero_nat ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2925_dvd__1__left,axiom,
% 15.55/8.51      ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2926_dvd__1__iff__1,axiom,
% 15.55/8.51      ! [M: nat] :
% 15.55/8.51        ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 15.55/8.51        = ( M
% 15.55/8.51          = ( suc @ zero_zero_nat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2927_diff__Suc__1,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 15.55/8.51        = N ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2928_take__bit__Suc__1,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ one_one_int )
% 15.55/8.51        = one_one_int ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2929_take__bit__Suc__1,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ one_one_nat )
% 15.55/8.51        = one_one_nat ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2930_powr__zero__eq__one,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( ( X3 = zero_zero_real )
% 15.55/8.51         => ( ( powr_real @ X3 @ zero_zero_real )
% 15.55/8.51            = zero_zero_real ) )
% 15.55/8.51        & ( ( X3 != zero_zero_real )
% 15.55/8.51         => ( ( powr_real @ X3 @ zero_zero_real )
% 15.55/8.51            = one_one_real ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2931_floor__zero,axiom,
% 15.55/8.51      ( ( archim3151403230148437115or_rat @ zero_zero_rat )
% 15.55/8.51      = zero_zero_int ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2932_floor__zero,axiom,
% 15.55/8.51      ( ( archim6058952711729229775r_real @ zero_zero_real )
% 15.55/8.51      = zero_zero_int ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2933_floor__numeral,axiom,
% 15.55/8.51      ! [V: num] :
% 15.55/8.51        ( ( archim3151403230148437115or_rat @ ( numeral_numeral_rat @ V ) )
% 15.55/8.51        = ( numeral_numeral_int @ V ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2934_floor__numeral,axiom,
% 15.55/8.51      ! [V: num] :
% 15.55/8.51        ( ( archim6058952711729229775r_real @ ( numeral_numeral_real @ V ) )
% 15.55/8.51        = ( numeral_numeral_int @ V ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2935_floor__one,axiom,
% 15.55/8.51      ( ( archim3151403230148437115or_rat @ one_one_rat )
% 15.55/8.51      = one_one_int ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2936_floor__one,axiom,
% 15.55/8.51      ( ( archim6058952711729229775r_real @ one_one_real )
% 15.55/8.51      = one_one_int ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2937_powr__gt__zero,axiom,
% 15.55/8.51      ! [X3: real,A: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X3 @ A ) )
% 15.55/8.51        = ( X3 != zero_zero_real ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2938_powr__nonneg__iff,axiom,
% 15.55/8.51      ! [A: real,X3: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ ( powr_real @ A @ X3 ) @ zero_zero_real )
% 15.55/8.51        = ( A = zero_zero_real ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2939_powr__less__cancel__iff,axiom,
% 15.55/8.51      ! [X3: real,A: real,B: real] :
% 15.55/8.51        ( ( ord_less_real @ one_one_real @ X3 )
% 15.55/8.51       => ( ( ord_less_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) )
% 15.55/8.51          = ( ord_less_real @ A @ B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2940_floor__of__nat,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( archim3151403230148437115or_rat @ ( semiri681578069525770553at_rat @ N ) )
% 15.55/8.51        = ( semiri1314217659103216013at_int @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2941_floor__of__nat,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( archim6058952711729229775r_real @ ( semiri5074537144036343181t_real @ N ) )
% 15.55/8.51        = ( semiri1314217659103216013at_int @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2942_round__0,axiom,
% 15.55/8.51      ( ( archim8280529875227126926d_real @ zero_zero_real )
% 15.55/8.51      = zero_zero_int ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2943_round__0,axiom,
% 15.55/8.51      ( ( archim7778729529865785530nd_rat @ zero_zero_rat )
% 15.55/8.51      = zero_zero_int ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2944_tanh__real__pos__iff,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X3 ) )
% 15.55/8.51        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2945_tanh__real__neg__iff,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( ord_less_real @ ( tanh_real @ X3 ) @ zero_zero_real )
% 15.55/8.51        = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2946_tanh__real__nonpos__iff,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ ( tanh_real @ X3 ) @ zero_zero_real )
% 15.55/8.51        = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2947_tanh__real__nonneg__iff,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X3 ) )
% 15.55/8.51        = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2948_round__numeral,axiom,
% 15.55/8.51      ! [N: num] :
% 15.55/8.51        ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N ) )
% 15.55/8.51        = ( numeral_numeral_int @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2949_round__numeral,axiom,
% 15.55/8.51      ! [N: num] :
% 15.55/8.51        ( ( archim7778729529865785530nd_rat @ ( numeral_numeral_rat @ N ) )
% 15.55/8.51        = ( numeral_numeral_int @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2950_round__1,axiom,
% 15.55/8.51      ( ( archim8280529875227126926d_real @ one_one_real )
% 15.55/8.51      = one_one_int ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2951_round__1,axiom,
% 15.55/8.51      ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 15.55/8.51      = one_one_int ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2952_round__of__nat,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( archim8280529875227126926d_real @ ( semiri5074537144036343181t_real @ N ) )
% 15.55/8.51        = ( semiri1314217659103216013at_int @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2953_round__of__nat,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( archim7778729529865785530nd_rat @ ( semiri681578069525770553at_rat @ N ) )
% 15.55/8.51        = ( semiri1314217659103216013at_int @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2954_of__nat__Suc,axiom,
% 15.55/8.51      ! [M: nat] :
% 15.55/8.51        ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 15.55/8.51        = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2955_of__nat__Suc,axiom,
% 15.55/8.51      ! [M: nat] :
% 15.55/8.51        ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 15.55/8.51        = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2956_of__nat__Suc,axiom,
% 15.55/8.51      ! [M: nat] :
% 15.55/8.51        ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 15.55/8.51        = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2957_of__nat__Suc,axiom,
% 15.55/8.51      ! [M: nat] :
% 15.55/8.51        ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 15.55/8.51        = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2958_of__nat__Suc,axiom,
% 15.55/8.51      ! [M: nat] :
% 15.55/8.51        ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 15.55/8.51        = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2959_Suc__pred,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.51       => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 15.55/8.51          = N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2960_diff__Suc__diff__eq2,axiom,
% 15.55/8.51      ! [K: nat,J: nat,I: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ K @ J )
% 15.55/8.51       => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 15.55/8.51          = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2961_diff__Suc__diff__eq1,axiom,
% 15.55/8.51      ! [K: nat,J: nat,I: nat] :
% 15.55/8.51        ( ( ord_less_eq_nat @ K @ J )
% 15.55/8.51       => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 15.55/8.51          = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2962_nat__1,axiom,
% 15.55/8.51      ( ( nat2 @ one_one_int )
% 15.55/8.51      = ( suc @ zero_zero_nat ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2963_Suc__numeral,axiom,
% 15.55/8.51      ! [N: num] :
% 15.55/8.51        ( ( suc @ ( numeral_numeral_nat @ N ) )
% 15.55/8.51        = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2964_powr__eq__one__iff,axiom,
% 15.55/8.51      ! [A: real,X3: real] :
% 15.55/8.51        ( ( ord_less_real @ one_one_real @ A )
% 15.55/8.51       => ( ( ( powr_real @ A @ X3 )
% 15.55/8.51            = one_one_real )
% 15.55/8.51          = ( X3 = zero_zero_real ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2965_powr__one,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.51       => ( ( powr_real @ X3 @ one_one_real )
% 15.55/8.51          = X3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2966_powr__one__gt__zero__iff,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( ( powr_real @ X3 @ one_one_real )
% 15.55/8.51          = X3 )
% 15.55/8.51        = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2967_powr__le__cancel__iff,axiom,
% 15.55/8.51      ! [X3: real,A: real,B: real] :
% 15.55/8.51        ( ( ord_less_real @ one_one_real @ X3 )
% 15.55/8.51       => ( ( ord_less_eq_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) )
% 15.55/8.51          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2968_numeral__powr__numeral__real,axiom,
% 15.55/8.51      ! [M: num,N: num] :
% 15.55/8.51        ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 15.55/8.51        = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2969_floor__diff__of__int,axiom,
% 15.55/8.51      ! [X3: rat,Z: int] :
% 15.55/8.51        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X3 @ ( ring_1_of_int_rat @ Z ) ) )
% 15.55/8.51        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X3 ) @ Z ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2970_floor__diff__of__int,axiom,
% 15.55/8.51      ! [X3: real,Z: int] :
% 15.55/8.51        ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X3 @ ( ring_1_of_int_real @ Z ) ) )
% 15.55/8.51        = ( minus_minus_int @ ( archim6058952711729229775r_real @ X3 ) @ Z ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2971_add__2__eq__Suc_H,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.51        = ( suc @ ( suc @ N ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2972_add__2__eq__Suc,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.51        = ( suc @ ( suc @ N ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2973_Suc__1,axiom,
% 15.55/8.51      ( ( suc @ one_one_nat )
% 15.55/8.51      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2974_div2__Suc__Suc,axiom,
% 15.55/8.51      ! [M: nat] :
% 15.55/8.51        ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.51        = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2975_even__Suc__Suc__iff,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 15.55/8.51        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2976_even__Suc,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 15.55/8.51        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2977_Suc__diff__1,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.51       => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 15.55/8.51          = N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2978_zero__le__floor,axiom,
% 15.55/8.51      ! [X3: rat] :
% 15.55/8.51        ( ( ord_less_eq_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X3 ) )
% 15.55/8.51        = ( ord_less_eq_rat @ zero_zero_rat @ X3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2979_zero__le__floor,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( ord_less_eq_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X3 ) )
% 15.55/8.51        = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2980_floor__less__zero,axiom,
% 15.55/8.51      ! [X3: rat] :
% 15.55/8.51        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X3 ) @ zero_zero_int )
% 15.55/8.51        = ( ord_less_rat @ X3 @ zero_zero_rat ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2981_floor__less__zero,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X3 ) @ zero_zero_int )
% 15.55/8.51        = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2982_numeral__le__floor,axiom,
% 15.55/8.51      ! [V: num,X3: rat] :
% 15.55/8.51        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X3 ) )
% 15.55/8.51        = ( ord_less_eq_rat @ ( numeral_numeral_rat @ V ) @ X3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2983_numeral__le__floor,axiom,
% 15.55/8.51      ! [V: num,X3: real] :
% 15.55/8.51        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X3 ) )
% 15.55/8.51        = ( ord_less_eq_real @ ( numeral_numeral_real @ V ) @ X3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2984_zero__less__floor,axiom,
% 15.55/8.51      ! [X3: rat] :
% 15.55/8.51        ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X3 ) )
% 15.55/8.51        = ( ord_less_eq_rat @ one_one_rat @ X3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2985_zero__less__floor,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( ord_less_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X3 ) )
% 15.55/8.51        = ( ord_less_eq_real @ one_one_real @ X3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2986_floor__le__zero,axiom,
% 15.55/8.51      ! [X3: rat] :
% 15.55/8.51        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X3 ) @ zero_zero_int )
% 15.55/8.51        = ( ord_less_rat @ X3 @ one_one_rat ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2987_floor__le__zero,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X3 ) @ zero_zero_int )
% 15.55/8.51        = ( ord_less_real @ X3 @ one_one_real ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2988_floor__less__numeral,axiom,
% 15.55/8.51      ! [X3: rat,V: num] :
% 15.55/8.51        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X3 ) @ ( numeral_numeral_int @ V ) )
% 15.55/8.51        = ( ord_less_rat @ X3 @ ( numeral_numeral_rat @ V ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2989_floor__less__numeral,axiom,
% 15.55/8.51      ! [X3: real,V: num] :
% 15.55/8.51        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X3 ) @ ( numeral_numeral_int @ V ) )
% 15.55/8.51        = ( ord_less_real @ X3 @ ( numeral_numeral_real @ V ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2990_one__le__floor,axiom,
% 15.55/8.51      ! [X3: rat] :
% 15.55/8.51        ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X3 ) )
% 15.55/8.51        = ( ord_less_eq_rat @ one_one_rat @ X3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2991_one__le__floor,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( ord_less_eq_int @ one_one_int @ ( archim6058952711729229775r_real @ X3 ) )
% 15.55/8.51        = ( ord_less_eq_real @ one_one_real @ X3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2992_floor__less__one,axiom,
% 15.55/8.51      ! [X3: rat] :
% 15.55/8.51        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X3 ) @ one_one_int )
% 15.55/8.51        = ( ord_less_rat @ X3 @ one_one_rat ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2993_floor__less__one,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X3 ) @ one_one_int )
% 15.55/8.51        = ( ord_less_real @ X3 @ one_one_real ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2994_floor__diff__numeral,axiom,
% 15.55/8.51      ! [X3: rat,V: num] :
% 15.55/8.51        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X3 @ ( numeral_numeral_rat @ V ) ) )
% 15.55/8.51        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X3 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2995_floor__diff__numeral,axiom,
% 15.55/8.51      ! [X3: real,V: num] :
% 15.55/8.51        ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X3 @ ( numeral_numeral_real @ V ) ) )
% 15.55/8.51        = ( minus_minus_int @ ( archim6058952711729229775r_real @ X3 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2996_floor__diff__one,axiom,
% 15.55/8.51      ! [X3: rat] :
% 15.55/8.51        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X3 @ one_one_rat ) )
% 15.55/8.51        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X3 ) @ one_one_int ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2997_floor__diff__one,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X3 @ one_one_real ) )
% 15.55/8.51        = ( minus_minus_int @ ( archim6058952711729229775r_real @ X3 ) @ one_one_int ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2998_floor__numeral__power,axiom,
% 15.55/8.51      ! [X3: num,N: nat] :
% 15.55/8.51        ( ( archim3151403230148437115or_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N ) )
% 15.55/8.51        = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_2999_floor__numeral__power,axiom,
% 15.55/8.51      ! [X3: num,N: nat] :
% 15.55/8.51        ( ( archim6058952711729229775r_real @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N ) )
% 15.55/8.51        = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3000_powr__log__cancel,axiom,
% 15.55/8.51      ! [A: real,X3: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.51       => ( ( A != one_one_real )
% 15.55/8.51         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.51           => ( ( powr_real @ A @ ( log @ A @ X3 ) )
% 15.55/8.51              = X3 ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3001_log__powr__cancel,axiom,
% 15.55/8.51      ! [A: real,Y3: real] :
% 15.55/8.51        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.51       => ( ( A != one_one_real )
% 15.55/8.51         => ( ( log @ A @ ( powr_real @ A @ Y3 ) )
% 15.55/8.51            = Y3 ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3002_floor__divide__eq__div__numeral,axiom,
% 15.55/8.51      ! [A: num,B: num] :
% 15.55/8.51        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 15.55/8.51        = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3003_even__Suc__div__two,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.51       => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.51          = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3004_odd__Suc__div__two,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.51       => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.51          = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3005_one__less__nat__eq,axiom,
% 15.55/8.51      ! [Z: int] :
% 15.55/8.51        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 15.55/8.51        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3006_powr__numeral,axiom,
% 15.55/8.51      ! [X3: real,N: num] :
% 15.55/8.51        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.51       => ( ( powr_real @ X3 @ ( numeral_numeral_real @ N ) )
% 15.55/8.51          = ( power_power_real @ X3 @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3007_odd__Suc__minus__one,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.51       => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 15.55/8.51          = N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3008_numeral__less__floor,axiom,
% 15.55/8.51      ! [V: num,X3: rat] :
% 15.55/8.51        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X3 ) )
% 15.55/8.51        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3009_numeral__less__floor,axiom,
% 15.55/8.51      ! [V: num,X3: real] :
% 15.55/8.51        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X3 ) )
% 15.55/8.51        = ( ord_less_eq_real @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3010_floor__le__numeral,axiom,
% 15.55/8.51      ! [X3: rat,V: num] :
% 15.55/8.51        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X3 ) @ ( numeral_numeral_int @ V ) )
% 15.55/8.51        = ( ord_less_rat @ X3 @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3011_floor__le__numeral,axiom,
% 15.55/8.51      ! [X3: real,V: num] :
% 15.55/8.51        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X3 ) @ ( numeral_numeral_int @ V ) )
% 15.55/8.51        = ( ord_less_real @ X3 @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3012_one__less__floor,axiom,
% 15.55/8.51      ! [X3: rat] :
% 15.55/8.51        ( ( ord_less_int @ one_one_int @ ( archim3151403230148437115or_rat @ X3 ) )
% 15.55/8.51        = ( ord_less_eq_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3013_one__less__floor,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( ord_less_int @ one_one_int @ ( archim6058952711729229775r_real @ X3 ) )
% 15.55/8.51        = ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3014_floor__le__one,axiom,
% 15.55/8.51      ! [X3: rat] :
% 15.55/8.51        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X3 ) @ one_one_int )
% 15.55/8.51        = ( ord_less_rat @ X3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3015_floor__le__one,axiom,
% 15.55/8.51      ! [X3: real] :
% 15.55/8.51        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X3 ) @ one_one_int )
% 15.55/8.51        = ( ord_less_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3016_floor__one__divide__eq__div__numeral,axiom,
% 15.55/8.51      ! [B: num] :
% 15.55/8.51        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 15.55/8.51        = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3017_n__not__Suc__n,axiom,
% 15.55/8.51      ! [N: nat] :
% 15.55/8.51        ( N
% 15.55/8.51       != ( suc @ N ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3018_Suc__inject,axiom,
% 15.55/8.51      ! [X3: nat,Y3: nat] :
% 15.55/8.51        ( ( ( suc @ X3 )
% 15.55/8.51          = ( suc @ Y3 ) )
% 15.55/8.51       => ( X3 = Y3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3019_floor__le__round,axiom,
% 15.55/8.51      ! [X3: real] : ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X3 ) @ ( archim8280529875227126926d_real @ X3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3020_size__neq__size__imp__neq,axiom,
% 15.55/8.51      ! [X3: list_VEBT_VEBT,Y3: list_VEBT_VEBT] :
% 15.55/8.51        ( ( ( size_s6755466524823107622T_VEBT @ X3 )
% 15.55/8.51         != ( size_s6755466524823107622T_VEBT @ Y3 ) )
% 15.55/8.51       => ( X3 != Y3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3021_size__neq__size__imp__neq,axiom,
% 15.55/8.51      ! [X3: list_o,Y3: list_o] :
% 15.55/8.51        ( ( ( size_size_list_o @ X3 )
% 15.55/8.51         != ( size_size_list_o @ Y3 ) )
% 15.55/8.51       => ( X3 != Y3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3022_size__neq__size__imp__neq,axiom,
% 15.55/8.51      ! [X3: list_nat,Y3: list_nat] :
% 15.55/8.51        ( ( ( size_size_list_nat @ X3 )
% 15.55/8.51         != ( size_size_list_nat @ Y3 ) )
% 15.55/8.51       => ( X3 != Y3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3023_size__neq__size__imp__neq,axiom,
% 15.55/8.51      ! [X3: list_int,Y3: list_int] :
% 15.55/8.51        ( ( ( size_size_list_int @ X3 )
% 15.55/8.51         != ( size_size_list_int @ Y3 ) )
% 15.55/8.51       => ( X3 != Y3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3024_size__neq__size__imp__neq,axiom,
% 15.55/8.51      ! [X3: num,Y3: num] :
% 15.55/8.51        ( ( ( size_size_num @ X3 )
% 15.55/8.51         != ( size_size_num @ Y3 ) )
% 15.55/8.51       => ( X3 != Y3 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3025_exists__least__lemma,axiom,
% 15.55/8.51      ! [P: nat > $o] :
% 15.55/8.51        ( ~ ( P @ zero_zero_nat )
% 15.55/8.51       => ( ? [X_12: nat] : ( P @ X_12 )
% 15.55/8.51         => ? [N2: nat] :
% 15.55/8.51              ( ~ ( P @ N2 )
% 15.55/8.51              & ( P @ ( suc @ N2 ) ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3026_nat_Odistinct_I1_J,axiom,
% 15.55/8.51      ! [X2: nat] :
% 15.55/8.51        ( zero_zero_nat
% 15.55/8.51       != ( suc @ X2 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3027_old_Onat_Odistinct_I2_J,axiom,
% 15.55/8.51      ! [Nat2: nat] :
% 15.55/8.51        ( ( suc @ Nat2 )
% 15.55/8.51       != zero_zero_nat ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3028_old_Onat_Odistinct_I1_J,axiom,
% 15.55/8.51      ! [Nat2: nat] :
% 15.55/8.51        ( zero_zero_nat
% 15.55/8.51       != ( suc @ Nat2 ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3029_nat_OdiscI,axiom,
% 15.55/8.51      ! [Nat: nat,X2: nat] :
% 15.55/8.51        ( ( Nat
% 15.55/8.51          = ( suc @ X2 ) )
% 15.55/8.51       => ( Nat != zero_zero_nat ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3030_old_Onat_Oexhaust,axiom,
% 15.55/8.51      ! [Y3: nat] :
% 15.55/8.51        ( ( Y3 != zero_zero_nat )
% 15.55/8.51       => ~ ! [Nat3: nat] :
% 15.55/8.51              ( Y3
% 15.55/8.51             != ( suc @ Nat3 ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3031_nat__induct,axiom,
% 15.55/8.51      ! [P: nat > $o,N: nat] :
% 15.55/8.51        ( ( P @ zero_zero_nat )
% 15.55/8.51       => ( ! [N2: nat] :
% 15.55/8.51              ( ( P @ N2 )
% 15.55/8.51             => ( P @ ( suc @ N2 ) ) )
% 15.55/8.51         => ( P @ N ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3032_diff__induct,axiom,
% 15.55/8.51      ! [P: nat > nat > $o,M: nat,N: nat] :
% 15.55/8.51        ( ! [X4: nat] : ( P @ X4 @ zero_zero_nat )
% 15.55/8.51       => ( ! [Y4: nat] : ( P @ zero_zero_nat @ ( suc @ Y4 ) )
% 15.55/8.51         => ( ! [X4: nat,Y4: nat] :
% 15.55/8.51                ( ( P @ X4 @ Y4 )
% 15.55/8.51               => ( P @ ( suc @ X4 ) @ ( suc @ Y4 ) ) )
% 15.55/8.51           => ( P @ M @ N ) ) ) ) ).
% 15.55/8.51  
% 15.55/8.51  thf(fact_3033_zero__induct,axiom,
% 15.55/8.51      ! [P: nat > $o,K: nat] :
% 15.55/8.51        ( ( P @ K )
% 15.55/8.52       => ( ! [N2: nat] :
% 15.55/8.52              ( ( P @ ( suc @ N2 ) )
% 15.55/8.52             => ( P @ N2 ) )
% 15.55/8.52         => ( P @ zero_zero_nat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3034_Suc__neq__Zero,axiom,
% 15.55/8.52      ! [M: nat] :
% 15.55/8.52        ( ( suc @ M )
% 15.55/8.52       != zero_zero_nat ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3035_Zero__neq__Suc,axiom,
% 15.55/8.52      ! [M: nat] :
% 15.55/8.52        ( zero_zero_nat
% 15.55/8.52       != ( suc @ M ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3036_Zero__not__Suc,axiom,
% 15.55/8.52      ! [M: nat] :
% 15.55/8.52        ( zero_zero_nat
% 15.55/8.52       != ( suc @ M ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3037_not0__implies__Suc,axiom,
% 15.55/8.52      ! [N: nat] :
% 15.55/8.52        ( ( N != zero_zero_nat )
% 15.55/8.52       => ? [M4: nat] :
% 15.55/8.52            ( N
% 15.55/8.52            = ( suc @ M4 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3038_list__decode_Ocases,axiom,
% 15.55/8.52      ! [X3: nat] :
% 15.55/8.52        ( ( X3 != zero_zero_nat )
% 15.55/8.52       => ~ ! [N2: nat] :
% 15.55/8.52              ( X3
% 15.55/8.52             != ( suc @ N2 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3039_not__less__less__Suc__eq,axiom,
% 15.55/8.52      ! [N: nat,M: nat] :
% 15.55/8.52        ( ~ ( ord_less_nat @ N @ M )
% 15.55/8.52       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 15.55/8.52          = ( N = M ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3040_strict__inc__induct,axiom,
% 15.55/8.52      ! [I: nat,J: nat,P: nat > $o] :
% 15.55/8.52        ( ( ord_less_nat @ I @ J )
% 15.55/8.52       => ( ! [I3: nat] :
% 15.55/8.52              ( ( J
% 15.55/8.52                = ( suc @ I3 ) )
% 15.55/8.52             => ( P @ I3 ) )
% 15.55/8.52         => ( ! [I3: nat] :
% 15.55/8.52                ( ( ord_less_nat @ I3 @ J )
% 15.55/8.52               => ( ( P @ ( suc @ I3 ) )
% 15.55/8.52                 => ( P @ I3 ) ) )
% 15.55/8.52           => ( P @ I ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3041_less__Suc__induct,axiom,
% 15.55/8.52      ! [I: nat,J: nat,P: nat > nat > $o] :
% 15.55/8.52        ( ( ord_less_nat @ I @ J )
% 15.55/8.52       => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 15.55/8.52         => ( ! [I3: nat,J2: nat,K2: nat] :
% 15.55/8.52                ( ( ord_less_nat @ I3 @ J2 )
% 15.55/8.52               => ( ( ord_less_nat @ J2 @ K2 )
% 15.55/8.52                 => ( ( P @ I3 @ J2 )
% 15.55/8.52                   => ( ( P @ J2 @ K2 )
% 15.55/8.52                     => ( P @ I3 @ K2 ) ) ) ) )
% 15.55/8.52           => ( P @ I @ J ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3042_less__trans__Suc,axiom,
% 15.55/8.52      ! [I: nat,J: nat,K: nat] :
% 15.55/8.52        ( ( ord_less_nat @ I @ J )
% 15.55/8.52       => ( ( ord_less_nat @ J @ K )
% 15.55/8.52         => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3043_Suc__less__SucD,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 15.55/8.52       => ( ord_less_nat @ M @ N ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3044_less__antisym,axiom,
% 15.55/8.52      ! [N: nat,M: nat] :
% 15.55/8.52        ( ~ ( ord_less_nat @ N @ M )
% 15.55/8.52       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 15.55/8.52         => ( M = N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3045_Suc__less__eq2,axiom,
% 15.55/8.52      ! [N: nat,M: nat] :
% 15.55/8.52        ( ( ord_less_nat @ ( suc @ N ) @ M )
% 15.55/8.52        = ( ? [M5: nat] :
% 15.55/8.52              ( ( M
% 15.55/8.52                = ( suc @ M5 ) )
% 15.55/8.52              & ( ord_less_nat @ N @ M5 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3046_All__less__Suc,axiom,
% 15.55/8.52      ! [N: nat,P: nat > $o] :
% 15.55/8.52        ( ( ! [I4: nat] :
% 15.55/8.52              ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 15.55/8.52             => ( P @ I4 ) ) )
% 15.55/8.52        = ( ( P @ N )
% 15.55/8.52          & ! [I4: nat] :
% 15.55/8.52              ( ( ord_less_nat @ I4 @ N )
% 15.55/8.52             => ( P @ I4 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3047_not__less__eq,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ~ ( ord_less_nat @ M @ N ) )
% 15.55/8.52        = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3048_less__Suc__eq,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 15.55/8.52        = ( ( ord_less_nat @ M @ N )
% 15.55/8.52          | ( M = N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3049_Ex__less__Suc,axiom,
% 15.55/8.52      ! [N: nat,P: nat > $o] :
% 15.55/8.52        ( ( ? [I4: nat] :
% 15.55/8.52              ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 15.55/8.52              & ( P @ I4 ) ) )
% 15.55/8.52        = ( ( P @ N )
% 15.55/8.52          | ? [I4: nat] :
% 15.55/8.52              ( ( ord_less_nat @ I4 @ N )
% 15.55/8.52              & ( P @ I4 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3050_less__SucI,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ M @ N )
% 15.55/8.52       => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3051_less__SucE,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 15.55/8.52       => ( ~ ( ord_less_nat @ M @ N )
% 15.55/8.52         => ( M = N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3052_Suc__lessI,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ M @ N )
% 15.55/8.52       => ( ( ( suc @ M )
% 15.55/8.52           != N )
% 15.55/8.52         => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3053_Suc__lessE,axiom,
% 15.55/8.52      ! [I: nat,K: nat] :
% 15.55/8.52        ( ( ord_less_nat @ ( suc @ I ) @ K )
% 15.55/8.52       => ~ ! [J2: nat] :
% 15.55/8.52              ( ( ord_less_nat @ I @ J2 )
% 15.55/8.52             => ( K
% 15.55/8.52               != ( suc @ J2 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3054_Suc__lessD,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ ( suc @ M ) @ N )
% 15.55/8.52       => ( ord_less_nat @ M @ N ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3055_Nat_OlessE,axiom,
% 15.55/8.52      ! [I: nat,K: nat] :
% 15.55/8.52        ( ( ord_less_nat @ I @ K )
% 15.55/8.52       => ( ( K
% 15.55/8.52           != ( suc @ I ) )
% 15.55/8.52         => ~ ! [J2: nat] :
% 15.55/8.52                ( ( ord_less_nat @ I @ J2 )
% 15.55/8.52               => ( K
% 15.55/8.52                 != ( suc @ J2 ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3056_nat__arith_Osuc1,axiom,
% 15.55/8.52      ! [A3: nat,K: nat,A: nat] :
% 15.55/8.52        ( ( A3
% 15.55/8.52          = ( plus_plus_nat @ K @ A ) )
% 15.55/8.52       => ( ( suc @ A3 )
% 15.55/8.52          = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3057_add__Suc,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 15.55/8.52        = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3058_add__Suc__shift,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 15.55/8.52        = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3059_Suc__leD,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 15.55/8.52       => ( ord_less_eq_nat @ M @ N ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3060_le__SucE,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 15.55/8.52       => ( ~ ( ord_less_eq_nat @ M @ N )
% 15.55/8.52         => ( M
% 15.55/8.52            = ( suc @ N ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3061_le__SucI,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.52       => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3062_Suc__le__D,axiom,
% 15.55/8.52      ! [N: nat,M6: nat] :
% 15.55/8.52        ( ( ord_less_eq_nat @ ( suc @ N ) @ M6 )
% 15.55/8.52       => ? [M4: nat] :
% 15.55/8.52            ( M6
% 15.55/8.52            = ( suc @ M4 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3063_le__Suc__eq,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 15.55/8.52        = ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.52          | ( M
% 15.55/8.52            = ( suc @ N ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3064_Suc__n__not__le__n,axiom,
% 15.55/8.52      ! [N: nat] :
% 15.55/8.52        ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3065_not__less__eq__eq,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 15.55/8.52        = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3066_full__nat__induct,axiom,
% 15.55/8.52      ! [P: nat > $o,N: nat] :
% 15.55/8.52        ( ! [N2: nat] :
% 15.55/8.52            ( ! [M2: nat] :
% 15.55/8.52                ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N2 )
% 15.55/8.52               => ( P @ M2 ) )
% 15.55/8.52           => ( P @ N2 ) )
% 15.55/8.52       => ( P @ N ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3067_nat__induct__at__least,axiom,
% 15.55/8.52      ! [M: nat,N: nat,P: nat > $o] :
% 15.55/8.52        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.52       => ( ( P @ M )
% 15.55/8.52         => ( ! [N2: nat] :
% 15.55/8.52                ( ( ord_less_eq_nat @ M @ N2 )
% 15.55/8.52               => ( ( P @ N2 )
% 15.55/8.52                 => ( P @ ( suc @ N2 ) ) ) )
% 15.55/8.52           => ( P @ N ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3068_transitive__stepwise__le,axiom,
% 15.55/8.52      ! [M: nat,N: nat,R3: nat > nat > $o] :
% 15.55/8.52        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.52       => ( ! [X4: nat] : ( R3 @ X4 @ X4 )
% 15.55/8.52         => ( ! [X4: nat,Y4: nat,Z3: nat] :
% 15.55/8.52                ( ( R3 @ X4 @ Y4 )
% 15.55/8.52               => ( ( R3 @ Y4 @ Z3 )
% 15.55/8.52                 => ( R3 @ X4 @ Z3 ) ) )
% 15.55/8.52           => ( ! [N2: nat] : ( R3 @ N2 @ ( suc @ N2 ) )
% 15.55/8.52             => ( R3 @ M @ N ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3069_zero__induct__lemma,axiom,
% 15.55/8.52      ! [P: nat > $o,K: nat,I: nat] :
% 15.55/8.52        ( ( P @ K )
% 15.55/8.52       => ( ! [N2: nat] :
% 15.55/8.52              ( ( P @ ( suc @ N2 ) )
% 15.55/8.52             => ( P @ N2 ) )
% 15.55/8.52         => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3070_floor__eq3,axiom,
% 15.55/8.52      ! [N: nat,X3: real] :
% 15.55/8.52        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X3 )
% 15.55/8.52       => ( ( ord_less_real @ X3 @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 15.55/8.52         => ( ( nat2 @ ( archim6058952711729229775r_real @ X3 ) )
% 15.55/8.52            = N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3071_floor__mono,axiom,
% 15.55/8.52      ! [X3: rat,Y3: rat] :
% 15.55/8.52        ( ( ord_less_eq_rat @ X3 @ Y3 )
% 15.55/8.52       => ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X3 ) @ ( archim3151403230148437115or_rat @ Y3 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3072_floor__mono,axiom,
% 15.55/8.52      ! [X3: real,Y3: real] :
% 15.55/8.52        ( ( ord_less_eq_real @ X3 @ Y3 )
% 15.55/8.52       => ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X3 ) @ ( archim6058952711729229775r_real @ Y3 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3073_of__int__floor__le,axiom,
% 15.55/8.52      ! [X3: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X3 ) ) @ X3 ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3074_of__int__floor__le,axiom,
% 15.55/8.52      ! [X3: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X3 ) ) @ X3 ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3075_floor__less__cancel,axiom,
% 15.55/8.52      ! [X3: rat,Y3: rat] :
% 15.55/8.52        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X3 ) @ ( archim3151403230148437115or_rat @ Y3 ) )
% 15.55/8.52       => ( ord_less_rat @ X3 @ Y3 ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3076_floor__less__cancel,axiom,
% 15.55/8.52      ! [X3: real,Y3: real] :
% 15.55/8.52        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X3 ) @ ( archim6058952711729229775r_real @ Y3 ) )
% 15.55/8.52       => ( ord_less_real @ X3 @ Y3 ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3077_powr__less__mono2__neg,axiom,
% 15.55/8.52      ! [A: real,X3: real,Y3: real] :
% 15.55/8.52        ( ( ord_less_real @ A @ zero_zero_real )
% 15.55/8.52       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.52         => ( ( ord_less_real @ X3 @ Y3 )
% 15.55/8.52           => ( ord_less_real @ ( powr_real @ Y3 @ A ) @ ( powr_real @ X3 @ A ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3078_powr__non__neg,axiom,
% 15.55/8.52      ! [A: real,X3: real] :
% 15.55/8.52        ~ ( ord_less_real @ ( powr_real @ A @ X3 ) @ zero_zero_real ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3079_powr__ge__pzero,axiom,
% 15.55/8.52      ! [X3: real,Y3: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X3 @ Y3 ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3080_powr__mono2,axiom,
% 15.55/8.52      ! [A: real,X3: real,Y3: real] :
% 15.55/8.52        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.52       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.52         => ( ( ord_less_eq_real @ X3 @ Y3 )
% 15.55/8.52           => ( ord_less_eq_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ Y3 @ A ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3081_floor__eq4,axiom,
% 15.55/8.52      ! [N: nat,X3: real] :
% 15.55/8.52        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X3 )
% 15.55/8.52       => ( ( ord_less_real @ X3 @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 15.55/8.52         => ( ( nat2 @ ( archim6058952711729229775r_real @ X3 ) )
% 15.55/8.52            = N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3082_powr__less__mono,axiom,
% 15.55/8.52      ! [A: real,B: real,X3: real] :
% 15.55/8.52        ( ( ord_less_real @ A @ B )
% 15.55/8.52       => ( ( ord_less_real @ one_one_real @ X3 )
% 15.55/8.52         => ( ord_less_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3083_powr__less__cancel,axiom,
% 15.55/8.52      ! [X3: real,A: real,B: real] :
% 15.55/8.52        ( ( ord_less_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) )
% 15.55/8.52       => ( ( ord_less_real @ one_one_real @ X3 )
% 15.55/8.52         => ( ord_less_real @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3084_powr__mono,axiom,
% 15.55/8.52      ! [A: real,B: real,X3: real] :
% 15.55/8.52        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.52       => ( ( ord_less_eq_real @ one_one_real @ X3 )
% 15.55/8.52         => ( ord_less_eq_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3085_floor__le__ceiling,axiom,
% 15.55/8.52      ! [X3: real] : ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X3 ) @ ( archim7802044766580827645g_real @ X3 ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3086_lift__Suc__mono__less__iff,axiom,
% 15.55/8.52      ! [F: nat > real,N: nat,M: nat] :
% 15.55/8.52        ( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 15.55/8.52       => ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
% 15.55/8.52          = ( ord_less_nat @ N @ M ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3087_lift__Suc__mono__less__iff,axiom,
% 15.55/8.52      ! [F: nat > rat,N: nat,M: nat] :
% 15.55/8.52        ( ! [N2: nat] : ( ord_less_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 15.55/8.52       => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 15.55/8.52          = ( ord_less_nat @ N @ M ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3088_lift__Suc__mono__less__iff,axiom,
% 15.55/8.52      ! [F: nat > num,N: nat,M: nat] :
% 15.55/8.52        ( ! [N2: nat] : ( ord_less_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 15.55/8.52       => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 15.55/8.52          = ( ord_less_nat @ N @ M ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3089_lift__Suc__mono__less__iff,axiom,
% 15.55/8.52      ! [F: nat > nat,N: nat,M: nat] :
% 15.55/8.52        ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 15.55/8.52       => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 15.55/8.52          = ( ord_less_nat @ N @ M ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3090_lift__Suc__mono__less__iff,axiom,
% 15.55/8.52      ! [F: nat > int,N: nat,M: nat] :
% 15.55/8.52        ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 15.55/8.52       => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 15.55/8.52          = ( ord_less_nat @ N @ M ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3091_lift__Suc__mono__less,axiom,
% 15.55/8.52      ! [F: nat > real,N: nat,N5: nat] :
% 15.55/8.52        ( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 15.55/8.52       => ( ( ord_less_nat @ N @ N5 )
% 15.55/8.52         => ( ord_less_real @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3092_lift__Suc__mono__less,axiom,
% 15.55/8.52      ! [F: nat > rat,N: nat,N5: nat] :
% 15.55/8.52        ( ! [N2: nat] : ( ord_less_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 15.55/8.52       => ( ( ord_less_nat @ N @ N5 )
% 15.55/8.52         => ( ord_less_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3093_lift__Suc__mono__less,axiom,
% 15.55/8.52      ! [F: nat > num,N: nat,N5: nat] :
% 15.55/8.52        ( ! [N2: nat] : ( ord_less_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 15.55/8.52       => ( ( ord_less_nat @ N @ N5 )
% 15.55/8.52         => ( ord_less_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3094_lift__Suc__mono__less,axiom,
% 15.55/8.52      ! [F: nat > nat,N: nat,N5: nat] :
% 15.55/8.52        ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 15.55/8.52       => ( ( ord_less_nat @ N @ N5 )
% 15.55/8.52         => ( ord_less_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3095_lift__Suc__mono__less,axiom,
% 15.55/8.52      ! [F: nat > int,N: nat,N5: nat] :
% 15.55/8.52        ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 15.55/8.52       => ( ( ord_less_nat @ N @ N5 )
% 15.55/8.52         => ( ord_less_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3096_lift__Suc__mono__le,axiom,
% 15.55/8.52      ! [F: nat > set_nat,N: nat,N5: nat] :
% 15.55/8.52        ( ! [N2: nat] : ( ord_less_eq_set_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 15.55/8.52       => ( ( ord_less_eq_nat @ N @ N5 )
% 15.55/8.52         => ( ord_less_eq_set_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3097_lift__Suc__mono__le,axiom,
% 15.55/8.52      ! [F: nat > rat,N: nat,N5: nat] :
% 15.55/8.52        ( ! [N2: nat] : ( ord_less_eq_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 15.55/8.52       => ( ( ord_less_eq_nat @ N @ N5 )
% 15.55/8.52         => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3098_lift__Suc__mono__le,axiom,
% 15.55/8.52      ! [F: nat > num,N: nat,N5: nat] :
% 15.55/8.52        ( ! [N2: nat] : ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 15.55/8.52       => ( ( ord_less_eq_nat @ N @ N5 )
% 15.55/8.52         => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3099_lift__Suc__mono__le,axiom,
% 15.55/8.52      ! [F: nat > nat,N: nat,N5: nat] :
% 15.55/8.52        ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 15.55/8.52       => ( ( ord_less_eq_nat @ N @ N5 )
% 15.55/8.52         => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3100_lift__Suc__mono__le,axiom,
% 15.55/8.52      ! [F: nat > int,N: nat,N5: nat] :
% 15.55/8.52        ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 15.55/8.52       => ( ( ord_less_eq_nat @ N @ N5 )
% 15.55/8.52         => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3101_lift__Suc__antimono__le,axiom,
% 15.55/8.52      ! [F: nat > set_nat,N: nat,N5: nat] :
% 15.55/8.52        ( ! [N2: nat] : ( ord_less_eq_set_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 15.55/8.52       => ( ( ord_less_eq_nat @ N @ N5 )
% 15.55/8.52         => ( ord_less_eq_set_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3102_lift__Suc__antimono__le,axiom,
% 15.55/8.52      ! [F: nat > rat,N: nat,N5: nat] :
% 15.55/8.52        ( ! [N2: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 15.55/8.52       => ( ( ord_less_eq_nat @ N @ N5 )
% 15.55/8.52         => ( ord_less_eq_rat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3103_lift__Suc__antimono__le,axiom,
% 15.55/8.52      ! [F: nat > num,N: nat,N5: nat] :
% 15.55/8.52        ( ! [N2: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 15.55/8.52       => ( ( ord_less_eq_nat @ N @ N5 )
% 15.55/8.52         => ( ord_less_eq_num @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3104_lift__Suc__antimono__le,axiom,
% 15.55/8.52      ! [F: nat > nat,N: nat,N5: nat] :
% 15.55/8.52        ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 15.55/8.52       => ( ( ord_less_eq_nat @ N @ N5 )
% 15.55/8.52         => ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3105_lift__Suc__antimono__le,axiom,
% 15.55/8.52      ! [F: nat > int,N: nat,N5: nat] :
% 15.55/8.52        ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 15.55/8.52       => ( ( ord_less_eq_nat @ N @ N5 )
% 15.55/8.52         => ( ord_less_eq_int @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3106_of__nat__neq__0,axiom,
% 15.55/8.52      ! [N: nat] :
% 15.55/8.52        ( ( semiri8010041392384452111omplex @ ( suc @ N ) )
% 15.55/8.52       != zero_zero_complex ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3107_of__nat__neq__0,axiom,
% 15.55/8.52      ! [N: nat] :
% 15.55/8.52        ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 15.55/8.52       != zero_zero_real ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3108_of__nat__neq__0,axiom,
% 15.55/8.52      ! [N: nat] :
% 15.55/8.52        ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 15.55/8.52       != zero_zero_rat ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3109_of__nat__neq__0,axiom,
% 15.55/8.52      ! [N: nat] :
% 15.55/8.52        ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 15.55/8.52       != zero_zero_nat ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3110_of__nat__neq__0,axiom,
% 15.55/8.52      ! [N: nat] :
% 15.55/8.52        ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 15.55/8.52       != zero_zero_int ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3111_less__Suc__eq__0__disj,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 15.55/8.52        = ( ( M = zero_zero_nat )
% 15.55/8.52          | ? [J3: nat] :
% 15.55/8.52              ( ( M
% 15.55/8.52                = ( suc @ J3 ) )
% 15.55/8.52              & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3112_gr0__implies__Suc,axiom,
% 15.55/8.52      ! [N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.52       => ? [M4: nat] :
% 15.55/8.52            ( N
% 15.55/8.52            = ( suc @ M4 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3113_All__less__Suc2,axiom,
% 15.55/8.52      ! [N: nat,P: nat > $o] :
% 15.55/8.52        ( ( ! [I4: nat] :
% 15.55/8.52              ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 15.55/8.52             => ( P @ I4 ) ) )
% 15.55/8.52        = ( ( P @ zero_zero_nat )
% 15.55/8.52          & ! [I4: nat] :
% 15.55/8.52              ( ( ord_less_nat @ I4 @ N )
% 15.55/8.52             => ( P @ ( suc @ I4 ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3114_gr0__conv__Suc,axiom,
% 15.55/8.52      ! [N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.52        = ( ? [M3: nat] :
% 15.55/8.52              ( N
% 15.55/8.52              = ( suc @ M3 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3115_Ex__less__Suc2,axiom,
% 15.55/8.52      ! [N: nat,P: nat > $o] :
% 15.55/8.52        ( ( ? [I4: nat] :
% 15.55/8.52              ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 15.55/8.52              & ( P @ I4 ) ) )
% 15.55/8.52        = ( ( P @ zero_zero_nat )
% 15.55/8.52          | ? [I4: nat] :
% 15.55/8.52              ( ( ord_less_nat @ I4 @ N )
% 15.55/8.52              & ( P @ ( suc @ I4 ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3116_one__is__add,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ( suc @ zero_zero_nat )
% 15.55/8.52          = ( plus_plus_nat @ M @ N ) )
% 15.55/8.52        = ( ( ( M
% 15.55/8.52              = ( suc @ zero_zero_nat ) )
% 15.55/8.52            & ( N = zero_zero_nat ) )
% 15.55/8.52          | ( ( M = zero_zero_nat )
% 15.55/8.52            & ( N
% 15.55/8.52              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3117_add__is__1,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ( plus_plus_nat @ M @ N )
% 15.55/8.52          = ( suc @ zero_zero_nat ) )
% 15.55/8.52        = ( ( ( M
% 15.55/8.52              = ( suc @ zero_zero_nat ) )
% 15.55/8.52            & ( N = zero_zero_nat ) )
% 15.55/8.52          | ( ( M = zero_zero_nat )
% 15.55/8.52            & ( N
% 15.55/8.52              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3118_less__natE,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ M @ N )
% 15.55/8.52       => ~ ! [Q4: nat] :
% 15.55/8.52              ( N
% 15.55/8.52             != ( suc @ ( plus_plus_nat @ M @ Q4 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3119_less__add__Suc1,axiom,
% 15.55/8.52      ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3120_less__add__Suc2,axiom,
% 15.55/8.52      ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3121_less__iff__Suc__add,axiom,
% 15.55/8.52      ( ord_less_nat
% 15.55/8.52      = ( ^ [M3: nat,N3: nat] :
% 15.55/8.52          ? [K3: nat] :
% 15.55/8.52            ( N3
% 15.55/8.52            = ( suc @ ( plus_plus_nat @ M3 @ K3 ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3122_less__imp__Suc__add,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ M @ N )
% 15.55/8.52       => ? [K2: nat] :
% 15.55/8.52            ( N
% 15.55/8.52            = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3123_Suc__leI,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ M @ N )
% 15.55/8.52       => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3124_Suc__le__eq,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 15.55/8.52        = ( ord_less_nat @ M @ N ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3125_dec__induct,axiom,
% 15.55/8.52      ! [I: nat,J: nat,P: nat > $o] :
% 15.55/8.52        ( ( ord_less_eq_nat @ I @ J )
% 15.55/8.52       => ( ( P @ I )
% 15.55/8.52         => ( ! [N2: nat] :
% 15.55/8.52                ( ( ord_less_eq_nat @ I @ N2 )
% 15.55/8.52               => ( ( ord_less_nat @ N2 @ J )
% 15.55/8.52                 => ( ( P @ N2 )
% 15.55/8.52                   => ( P @ ( suc @ N2 ) ) ) ) )
% 15.55/8.52           => ( P @ J ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3126_inc__induct,axiom,
% 15.55/8.52      ! [I: nat,J: nat,P: nat > $o] :
% 15.55/8.52        ( ( ord_less_eq_nat @ I @ J )
% 15.55/8.52       => ( ( P @ J )
% 15.55/8.52         => ( ! [N2: nat] :
% 15.55/8.52                ( ( ord_less_eq_nat @ I @ N2 )
% 15.55/8.52               => ( ( ord_less_nat @ N2 @ J )
% 15.55/8.52                 => ( ( P @ ( suc @ N2 ) )
% 15.55/8.52                   => ( P @ N2 ) ) ) )
% 15.55/8.52           => ( P @ I ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3127_Suc__le__lessD,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 15.55/8.52       => ( ord_less_nat @ M @ N ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3128_le__less__Suc__eq,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.52       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 15.55/8.52          = ( N = M ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3129_less__Suc__eq__le,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 15.55/8.52        = ( ord_less_eq_nat @ M @ N ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3130_less__eq__Suc__le,axiom,
% 15.55/8.52      ( ord_less_nat
% 15.55/8.52      = ( ^ [N3: nat] : ( ord_less_eq_nat @ ( suc @ N3 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3131_le__imp__less__Suc,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.52       => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3132_One__nat__def,axiom,
% 15.55/8.52      ( one_one_nat
% 15.55/8.52      = ( suc @ zero_zero_nat ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3133_Suc__eq__plus1,axiom,
% 15.55/8.52      ( suc
% 15.55/8.52      = ( ^ [N3: nat] : ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3134_plus__1__eq__Suc,axiom,
% 15.55/8.52      ( ( plus_plus_nat @ one_one_nat )
% 15.55/8.52      = suc ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3135_Suc__eq__plus1__left,axiom,
% 15.55/8.52      ( suc
% 15.55/8.52      = ( plus_plus_nat @ one_one_nat ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3136_diff__less__Suc,axiom,
% 15.55/8.52      ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3137_Suc__diff__Suc,axiom,
% 15.55/8.52      ! [N: nat,M: nat] :
% 15.55/8.52        ( ( ord_less_nat @ N @ M )
% 15.55/8.52       => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 15.55/8.52          = ( minus_minus_nat @ M @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3138_Suc__div__le__mono,axiom,
% 15.55/8.52      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3139_Suc__diff__le,axiom,
% 15.55/8.52      ! [N: nat,M: nat] :
% 15.55/8.52        ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.52       => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 15.55/8.52          = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3140_diff__Suc__eq__diff__pred,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 15.55/8.52        = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3141_tanh__real__lt__1,axiom,
% 15.55/8.52      ! [X3: real] : ( ord_less_real @ ( tanh_real @ X3 ) @ one_one_real ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3142_le__floor__iff,axiom,
% 15.55/8.52      ! [Z: int,X3: rat] :
% 15.55/8.52        ( ( ord_less_eq_int @ Z @ ( archim3151403230148437115or_rat @ X3 ) )
% 15.55/8.52        = ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X3 ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3143_le__floor__iff,axiom,
% 15.55/8.52      ! [Z: int,X3: real] :
% 15.55/8.52        ( ( ord_less_eq_int @ Z @ ( archim6058952711729229775r_real @ X3 ) )
% 15.55/8.52        = ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X3 ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3144_floor__less__iff,axiom,
% 15.55/8.52      ! [X3: rat,Z: int] :
% 15.55/8.52        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X3 ) @ Z )
% 15.55/8.52        = ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3145_floor__less__iff,axiom,
% 15.55/8.52      ! [X3: real,Z: int] :
% 15.55/8.52        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X3 ) @ Z )
% 15.55/8.52        = ( ord_less_real @ X3 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3146_powr__mono2_H,axiom,
% 15.55/8.52      ! [A: real,X3: real,Y3: real] :
% 15.55/8.52        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 15.55/8.52       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.52         => ( ( ord_less_eq_real @ X3 @ Y3 )
% 15.55/8.52           => ( ord_less_eq_real @ ( powr_real @ Y3 @ A ) @ ( powr_real @ X3 @ A ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3147_powr__less__mono2,axiom,
% 15.55/8.52      ! [A: real,X3: real,Y3: real] :
% 15.55/8.52        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.52       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.52         => ( ( ord_less_real @ X3 @ Y3 )
% 15.55/8.52           => ( ord_less_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ Y3 @ A ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3148_le__floor__add,axiom,
% 15.55/8.52      ! [X3: rat,Y3: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X3 ) @ ( archim3151403230148437115or_rat @ Y3 ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X3 @ Y3 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3149_le__floor__add,axiom,
% 15.55/8.52      ! [X3: real,Y3: real] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X3 ) @ ( archim6058952711729229775r_real @ Y3 ) ) @ ( archim6058952711729229775r_real @ ( plus_plus_real @ X3 @ Y3 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3150_int__add__floor,axiom,
% 15.55/8.52      ! [Z: int,X3: rat] :
% 15.55/8.52        ( ( plus_plus_int @ Z @ ( archim3151403230148437115or_rat @ X3 ) )
% 15.55/8.52        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ X3 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3151_int__add__floor,axiom,
% 15.55/8.52      ! [Z: int,X3: real] :
% 15.55/8.52        ( ( plus_plus_int @ Z @ ( archim6058952711729229775r_real @ X3 ) )
% 15.55/8.52        = ( archim6058952711729229775r_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ X3 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3152_floor__add__int,axiom,
% 15.55/8.52      ! [X3: rat,Z: int] :
% 15.55/8.52        ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X3 ) @ Z )
% 15.55/8.52        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X3 @ ( ring_1_of_int_rat @ Z ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3153_floor__add__int,axiom,
% 15.55/8.52      ! [X3: real,Z: int] :
% 15.55/8.52        ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X3 ) @ Z )
% 15.55/8.52        = ( archim6058952711729229775r_real @ ( plus_plus_real @ X3 @ ( ring_1_of_int_real @ Z ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3154_powr__inj,axiom,
% 15.55/8.52      ! [A: real,X3: real,Y3: real] :
% 15.55/8.52        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.52       => ( ( A != one_one_real )
% 15.55/8.52         => ( ( ( powr_real @ A @ X3 )
% 15.55/8.52              = ( powr_real @ A @ Y3 ) )
% 15.55/8.52            = ( X3 = Y3 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3155_gr__one__powr,axiom,
% 15.55/8.52      ! [X3: real,Y3: real] :
% 15.55/8.52        ( ( ord_less_real @ one_one_real @ X3 )
% 15.55/8.52       => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.55/8.52         => ( ord_less_real @ one_one_real @ ( powr_real @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3156_powr__le1,axiom,
% 15.55/8.52      ! [A: real,X3: real] :
% 15.55/8.52        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.52       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.52         => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 15.55/8.52           => ( ord_less_eq_real @ ( powr_real @ X3 @ A ) @ one_one_real ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3157_powr__mono__both,axiom,
% 15.55/8.52      ! [A: real,B: real,X3: real,Y3: real] :
% 15.55/8.52        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.52       => ( ( ord_less_eq_real @ A @ B )
% 15.55/8.52         => ( ( ord_less_eq_real @ one_one_real @ X3 )
% 15.55/8.52           => ( ( ord_less_eq_real @ X3 @ Y3 )
% 15.55/8.52             => ( ord_less_eq_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ Y3 @ B ) ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3158_ge__one__powr__ge__zero,axiom,
% 15.55/8.52      ! [X3: real,A: real] :
% 15.55/8.52        ( ( ord_less_eq_real @ one_one_real @ X3 )
% 15.55/8.52       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.52         => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X3 @ A ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3159_powr__divide,axiom,
% 15.55/8.52      ! [X3: real,Y3: real,A: real] :
% 15.55/8.52        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.52       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.52         => ( ( powr_real @ ( divide_divide_real @ X3 @ Y3 ) @ A )
% 15.55/8.52            = ( divide_divide_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ Y3 @ A ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3160_floor__divide__of__int__eq,axiom,
% 15.55/8.52      ! [K: int,L: int] :
% 15.55/8.52        ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ K ) @ ( ring_1_of_int_rat @ L ) ) )
% 15.55/8.52        = ( divide_divide_int @ K @ L ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3161_floor__divide__of__int__eq,axiom,
% 15.55/8.52      ! [K: int,L: int] :
% 15.55/8.52        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( ring_1_of_int_real @ K ) @ ( ring_1_of_int_real @ L ) ) )
% 15.55/8.52        = ( divide_divide_int @ K @ L ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3162_floor__power,axiom,
% 15.55/8.52      ! [X3: rat,N: nat] :
% 15.55/8.52        ( ( X3
% 15.55/8.52          = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X3 ) ) )
% 15.55/8.52       => ( ( archim3151403230148437115or_rat @ ( power_power_rat @ X3 @ N ) )
% 15.55/8.52          = ( power_power_int @ ( archim3151403230148437115or_rat @ X3 ) @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3163_floor__power,axiom,
% 15.55/8.52      ! [X3: real,N: nat] :
% 15.55/8.52        ( ( X3
% 15.55/8.52          = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X3 ) ) )
% 15.55/8.52       => ( ( archim6058952711729229775r_real @ ( power_power_real @ X3 @ N ) )
% 15.55/8.52          = ( power_power_int @ ( archim6058952711729229775r_real @ X3 ) @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3164_log__base__powr,axiom,
% 15.55/8.52      ! [A: real,B: real,X3: real] :
% 15.55/8.52        ( ( A != zero_zero_real )
% 15.55/8.52       => ( ( log @ ( powr_real @ A @ B ) @ X3 )
% 15.55/8.52          = ( divide_divide_real @ ( log @ A @ X3 ) @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3165_round__mono,axiom,
% 15.55/8.52      ! [X3: rat,Y3: rat] :
% 15.55/8.52        ( ( ord_less_eq_rat @ X3 @ Y3 )
% 15.55/8.52       => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X3 ) @ ( archim7778729529865785530nd_rat @ Y3 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3166_power__inject__base,axiom,
% 15.55/8.52      ! [A: real,N: nat,B: real] :
% 15.55/8.52        ( ( ( power_power_real @ A @ ( suc @ N ) )
% 15.55/8.52          = ( power_power_real @ B @ ( suc @ N ) ) )
% 15.55/8.52       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.52         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 15.55/8.52           => ( A = B ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3167_power__inject__base,axiom,
% 15.55/8.52      ! [A: rat,N: nat,B: rat] :
% 15.55/8.52        ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 15.55/8.52          = ( power_power_rat @ B @ ( suc @ N ) ) )
% 15.55/8.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.52         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 15.55/8.52           => ( A = B ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3168_power__inject__base,axiom,
% 15.55/8.52      ! [A: nat,N: nat,B: nat] :
% 15.55/8.52        ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 15.55/8.52          = ( power_power_nat @ B @ ( suc @ N ) ) )
% 15.55/8.52       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.55/8.52         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 15.55/8.52           => ( A = B ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3169_power__inject__base,axiom,
% 15.55/8.52      ! [A: int,N: nat,B: int] :
% 15.55/8.52        ( ( ( power_power_int @ A @ ( suc @ N ) )
% 15.55/8.52          = ( power_power_int @ B @ ( suc @ N ) ) )
% 15.55/8.52       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.52         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 15.55/8.52           => ( A = B ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3170_power__le__imp__le__base,axiom,
% 15.55/8.52      ! [A: real,N: nat,B: real] :
% 15.55/8.52        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 15.55/8.52       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 15.55/8.52         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3171_power__le__imp__le__base,axiom,
% 15.55/8.52      ! [A: rat,N: nat,B: rat] :
% 15.55/8.52        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 15.55/8.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 15.55/8.52         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3172_power__le__imp__le__base,axiom,
% 15.55/8.52      ! [A: nat,N: nat,B: nat] :
% 15.55/8.52        ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 15.55/8.52       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 15.55/8.52         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3173_power__le__imp__le__base,axiom,
% 15.55/8.52      ! [A: int,N: nat,B: int] :
% 15.55/8.52        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 15.55/8.52       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 15.55/8.52         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3174_power__gt1,axiom,
% 15.55/8.52      ! [A: real,N: nat] :
% 15.55/8.52        ( ( ord_less_real @ one_one_real @ A )
% 15.55/8.52       => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3175_power__gt1,axiom,
% 15.55/8.52      ! [A: rat,N: nat] :
% 15.55/8.52        ( ( ord_less_rat @ one_one_rat @ A )
% 15.55/8.52       => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3176_power__gt1,axiom,
% 15.55/8.52      ! [A: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ one_one_nat @ A )
% 15.55/8.52       => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3177_power__gt1,axiom,
% 15.55/8.52      ! [A: int,N: nat] :
% 15.55/8.52        ( ( ord_less_int @ one_one_int @ A )
% 15.55/8.52       => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3178_round__def,axiom,
% 15.55/8.52      ( archim7778729529865785530nd_rat
% 15.55/8.52      = ( ^ [X: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3179_round__def,axiom,
% 15.55/8.52      ( archim8280529875227126926d_real
% 15.55/8.52      = ( ^ [X: real] : ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3180_numeral__1__eq__Suc__0,axiom,
% 15.55/8.52      ( ( numeral_numeral_nat @ one )
% 15.55/8.52      = ( suc @ zero_zero_nat ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3181_ex__least__nat__less,axiom,
% 15.55/8.52      ! [P: nat > $o,N: nat] :
% 15.55/8.52        ( ( P @ N )
% 15.55/8.52       => ( ~ ( P @ zero_zero_nat )
% 15.55/8.52         => ? [K2: nat] :
% 15.55/8.52              ( ( ord_less_nat @ K2 @ N )
% 15.55/8.52              & ! [I2: nat] :
% 15.55/8.52                  ( ( ord_less_eq_nat @ I2 @ K2 )
% 15.55/8.52                 => ~ ( P @ I2 ) )
% 15.55/8.52              & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3182_nat__induct__non__zero,axiom,
% 15.55/8.52      ! [N: nat,P: nat > $o] :
% 15.55/8.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.52       => ( ( P @ one_one_nat )
% 15.55/8.52         => ( ! [N2: nat] :
% 15.55/8.52                ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 15.55/8.52               => ( ( P @ N2 )
% 15.55/8.52                 => ( P @ ( suc @ N2 ) ) ) )
% 15.55/8.52           => ( P @ N ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3183_diff__Suc__less,axiom,
% 15.55/8.52      ! [N: nat,I: nat] :
% 15.55/8.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.52       => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3184_power__gt__expt,axiom,
% 15.55/8.52      ! [N: nat,K: nat] :
% 15.55/8.52        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 15.55/8.52       => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3185_realpow__pos__nth2,axiom,
% 15.55/8.52      ! [A: real,N: nat] :
% 15.55/8.52        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.52       => ? [R: real] :
% 15.55/8.52            ( ( ord_less_real @ zero_zero_real @ R )
% 15.55/8.52            & ( ( power_power_real @ R @ ( suc @ N ) )
% 15.55/8.52              = A ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3186_nat__one__le__power,axiom,
% 15.55/8.52      ! [I: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 15.55/8.52       => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3187_ceiling__ge__round,axiom,
% 15.55/8.52      ! [X3: real] : ( ord_less_eq_int @ ( archim8280529875227126926d_real @ X3 ) @ ( archim7802044766580827645g_real @ X3 ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3188_int__Suc,axiom,
% 15.55/8.52      ! [N: nat] :
% 15.55/8.52        ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 15.55/8.52        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3189_int__ops_I4_J,axiom,
% 15.55/8.52      ! [A: nat] :
% 15.55/8.52        ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 15.55/8.52        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3190_zless__iff__Suc__zadd,axiom,
% 15.55/8.52      ( ord_less_int
% 15.55/8.52      = ( ^ [W3: int,Z6: int] :
% 15.55/8.52          ? [N3: nat] :
% 15.55/8.52            ( Z6
% 15.55/8.52            = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3191_of__nat__floor,axiom,
% 15.55/8.52      ! [R2: rat] :
% 15.55/8.52        ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 15.55/8.52       => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim3151403230148437115or_rat @ R2 ) ) ) @ R2 ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3192_of__nat__floor,axiom,
% 15.55/8.52      ! [R2: real] :
% 15.55/8.52        ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 15.55/8.52       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim6058952711729229775r_real @ R2 ) ) ) @ R2 ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3193_one__add__floor,axiom,
% 15.55/8.52      ! [X3: rat] :
% 15.55/8.52        ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X3 ) @ one_one_int )
% 15.55/8.52        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X3 @ one_one_rat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3194_one__add__floor,axiom,
% 15.55/8.52      ! [X3: real] :
% 15.55/8.52        ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X3 ) @ one_one_int )
% 15.55/8.52        = ( archim6058952711729229775r_real @ ( plus_plus_real @ X3 @ one_one_real ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3195_floor__log__eq__powr__iff,axiom,
% 15.55/8.52      ! [X3: real,B: real,K: int] :
% 15.55/8.52        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.52       => ( ( ord_less_real @ one_one_real @ B )
% 15.55/8.52         => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X3 ) )
% 15.55/8.52              = K )
% 15.55/8.52            = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X3 )
% 15.55/8.52              & ( ord_less_real @ X3 @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3196_floor__divide__of__nat__eq,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) )
% 15.55/8.52        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3197_floor__divide__of__nat__eq,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 15.55/8.52        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3198_nat__floor__neg,axiom,
% 15.55/8.52      ! [X3: real] :
% 15.55/8.52        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 15.55/8.52       => ( ( nat2 @ ( archim6058952711729229775r_real @ X3 ) )
% 15.55/8.52          = zero_zero_nat ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3199_powr__realpow,axiom,
% 15.55/8.52      ! [X3: real,N: nat] :
% 15.55/8.52        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.52       => ( ( powr_real @ X3 @ ( semiri5074537144036343181t_real @ N ) )
% 15.55/8.52          = ( power_power_real @ X3 @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3200_powr__less__iff,axiom,
% 15.55/8.52      ! [B: real,X3: real,Y3: real] :
% 15.55/8.52        ( ( ord_less_real @ one_one_real @ B )
% 15.55/8.52       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.52         => ( ( ord_less_real @ ( powr_real @ B @ Y3 ) @ X3 )
% 15.55/8.52            = ( ord_less_real @ Y3 @ ( log @ B @ X3 ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3201_less__powr__iff,axiom,
% 15.55/8.52      ! [B: real,X3: real,Y3: real] :
% 15.55/8.52        ( ( ord_less_real @ one_one_real @ B )
% 15.55/8.52       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.52         => ( ( ord_less_real @ X3 @ ( powr_real @ B @ Y3 ) )
% 15.55/8.52            = ( ord_less_real @ ( log @ B @ X3 ) @ Y3 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3202_log__less__iff,axiom,
% 15.55/8.52      ! [B: real,X3: real,Y3: real] :
% 15.55/8.52        ( ( ord_less_real @ one_one_real @ B )
% 15.55/8.52       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.52         => ( ( ord_less_real @ ( log @ B @ X3 ) @ Y3 )
% 15.55/8.52            = ( ord_less_real @ X3 @ ( powr_real @ B @ Y3 ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3203_less__log__iff,axiom,
% 15.55/8.52      ! [B: real,X3: real,Y3: real] :
% 15.55/8.52        ( ( ord_less_real @ one_one_real @ B )
% 15.55/8.52       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.52         => ( ( ord_less_real @ Y3 @ ( log @ B @ X3 ) )
% 15.55/8.52            = ( ord_less_real @ ( powr_real @ B @ Y3 ) @ X3 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3204_le__nat__floor,axiom,
% 15.55/8.52      ! [X3: nat,A: real] :
% 15.55/8.52        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X3 ) @ A )
% 15.55/8.52       => ( ord_less_eq_nat @ X3 @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3205_ceiling__altdef,axiom,
% 15.55/8.52      ( archim2889992004027027881ng_rat
% 15.55/8.52      = ( ^ [X: rat] :
% 15.55/8.52            ( if_int
% 15.55/8.52            @ ( X
% 15.55/8.52              = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) )
% 15.55/8.52            @ ( archim3151403230148437115or_rat @ X )
% 15.55/8.52            @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3206_ceiling__altdef,axiom,
% 15.55/8.52      ( archim7802044766580827645g_real
% 15.55/8.52      = ( ^ [X: real] :
% 15.55/8.52            ( if_int
% 15.55/8.52            @ ( X
% 15.55/8.52              = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) )
% 15.55/8.52            @ ( archim6058952711729229775r_real @ X )
% 15.55/8.52            @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3207_ceiling__diff__floor__le__1,axiom,
% 15.55/8.52      ! [X3: real] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim7802044766580827645g_real @ X3 ) @ ( archim6058952711729229775r_real @ X3 ) ) @ one_one_int ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3208_floor__eq,axiom,
% 15.55/8.52      ! [N: int,X3: real] :
% 15.55/8.52        ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X3 )
% 15.55/8.52       => ( ( ord_less_real @ X3 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 15.55/8.52         => ( ( archim6058952711729229775r_real @ X3 )
% 15.55/8.52            = N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3209_real__of__int__floor__add__one__gt,axiom,
% 15.55/8.52      ! [R2: real] : ( ord_less_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3210_real__of__int__floor__add__one__ge,axiom,
% 15.55/8.52      ! [R2: real] : ( ord_less_eq_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3211_real__of__int__floor__gt__diff__one,axiom,
% 15.55/8.52      ! [R2: real] : ( ord_less_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3212_real__of__int__floor__ge__diff__one,axiom,
% 15.55/8.52      ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3213_power__Suc__le__self,axiom,
% 15.55/8.52      ! [A: real,N: nat] :
% 15.55/8.52        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.52       => ( ( ord_less_eq_real @ A @ one_one_real )
% 15.55/8.52         => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3214_power__Suc__le__self,axiom,
% 15.55/8.52      ! [A: rat,N: nat] :
% 15.55/8.52        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.52       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 15.55/8.52         => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3215_power__Suc__le__self,axiom,
% 15.55/8.52      ! [A: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.55/8.52       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 15.55/8.52         => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3216_power__Suc__le__self,axiom,
% 15.55/8.52      ! [A: int,N: nat] :
% 15.55/8.52        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.52       => ( ( ord_less_eq_int @ A @ one_one_int )
% 15.55/8.52         => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3217_power__Suc__less__one,axiom,
% 15.55/8.52      ! [A: real,N: nat] :
% 15.55/8.52        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.52       => ( ( ord_less_real @ A @ one_one_real )
% 15.55/8.52         => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3218_power__Suc__less__one,axiom,
% 15.55/8.52      ! [A: rat,N: nat] :
% 15.55/8.52        ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.52       => ( ( ord_less_rat @ A @ one_one_rat )
% 15.55/8.52         => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3219_power__Suc__less__one,axiom,
% 15.55/8.52      ! [A: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ zero_zero_nat @ A )
% 15.55/8.52       => ( ( ord_less_nat @ A @ one_one_nat )
% 15.55/8.52         => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3220_power__Suc__less__one,axiom,
% 15.55/8.52      ! [A: int,N: nat] :
% 15.55/8.52        ( ( ord_less_int @ zero_zero_int @ A )
% 15.55/8.52       => ( ( ord_less_int @ A @ one_one_int )
% 15.55/8.52         => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3221_numeral__2__eq__2,axiom,
% 15.55/8.52      ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 15.55/8.52      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3222_Suc__pred_H,axiom,
% 15.55/8.52      ! [N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.52       => ( N
% 15.55/8.52          = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3223_Suc__diff__eq__diff__pred,axiom,
% 15.55/8.52      ! [N: nat,M: nat] :
% 15.55/8.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.52       => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 15.55/8.52          = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3224_add__eq__if,axiom,
% 15.55/8.52      ( plus_plus_nat
% 15.55/8.52      = ( ^ [M3: nat,N3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N3 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N3 ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3225_div__if,axiom,
% 15.55/8.52      ( divide_divide_nat
% 15.55/8.52      = ( ^ [M3: nat,N3: nat] :
% 15.55/8.52            ( if_nat
% 15.55/8.52            @ ( ( ord_less_nat @ M3 @ N3 )
% 15.55/8.52              | ( N3 = zero_zero_nat ) )
% 15.55/8.52            @ zero_zero_nat
% 15.55/8.52            @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M3 @ N3 ) @ N3 ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3226_div__geq,axiom,
% 15.55/8.52      ! [N: nat,M: nat] :
% 15.55/8.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.52       => ( ~ ( ord_less_nat @ M @ N )
% 15.55/8.52         => ( ( divide_divide_nat @ M @ N )
% 15.55/8.52            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3227_Suc__nat__number__of__add,axiom,
% 15.55/8.52      ! [V: num,N: nat] :
% 15.55/8.52        ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 15.55/8.52        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3228_Suc__as__int,axiom,
% 15.55/8.52      ( suc
% 15.55/8.52      = ( ^ [A4: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A4 ) @ one_one_int ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3229_floor__unique,axiom,
% 15.55/8.52      ! [Z: int,X3: rat] :
% 15.55/8.52        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X3 )
% 15.55/8.52       => ( ( ord_less_rat @ X3 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) )
% 15.55/8.52         => ( ( archim3151403230148437115or_rat @ X3 )
% 15.55/8.52            = Z ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3230_floor__unique,axiom,
% 15.55/8.52      ! [Z: int,X3: real] :
% 15.55/8.52        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X3 )
% 15.55/8.52       => ( ( ord_less_real @ X3 @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) )
% 15.55/8.52         => ( ( archim6058952711729229775r_real @ X3 )
% 15.55/8.52            = Z ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3231_floor__eq__iff,axiom,
% 15.55/8.52      ! [X3: rat,A: int] :
% 15.55/8.52        ( ( ( archim3151403230148437115or_rat @ X3 )
% 15.55/8.52          = A )
% 15.55/8.52        = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X3 )
% 15.55/8.52          & ( ord_less_rat @ X3 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3232_floor__eq__iff,axiom,
% 15.55/8.52      ! [X3: real,A: int] :
% 15.55/8.52        ( ( ( archim6058952711729229775r_real @ X3 )
% 15.55/8.52          = A )
% 15.55/8.52        = ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ X3 )
% 15.55/8.52          & ( ord_less_real @ X3 @ ( plus_plus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3233_floor__split,axiom,
% 15.55/8.52      ! [P: int > $o,T: rat] :
% 15.55/8.52        ( ( P @ ( archim3151403230148437115or_rat @ T ) )
% 15.55/8.52        = ( ! [I4: int] :
% 15.55/8.52              ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I4 ) @ T )
% 15.55/8.52                & ( ord_less_rat @ T @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I4 ) @ one_one_rat ) ) )
% 15.55/8.52             => ( P @ I4 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3234_floor__split,axiom,
% 15.55/8.52      ! [P: int > $o,T: real] :
% 15.55/8.52        ( ( P @ ( archim6058952711729229775r_real @ T ) )
% 15.55/8.52        = ( ! [I4: int] :
% 15.55/8.52              ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ I4 ) @ T )
% 15.55/8.52                & ( ord_less_real @ T @ ( plus_plus_real @ ( ring_1_of_int_real @ I4 ) @ one_one_real ) ) )
% 15.55/8.52             => ( P @ I4 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3235_less__floor__iff,axiom,
% 15.55/8.52      ! [Z: int,X3: rat] :
% 15.55/8.52        ( ( ord_less_int @ Z @ ( archim3151403230148437115or_rat @ X3 ) )
% 15.55/8.52        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X3 ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3236_less__floor__iff,axiom,
% 15.55/8.52      ! [Z: int,X3: real] :
% 15.55/8.52        ( ( ord_less_int @ Z @ ( archim6058952711729229775r_real @ X3 ) )
% 15.55/8.52        = ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X3 ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3237_floor__le__iff,axiom,
% 15.55/8.52      ! [X3: rat,Z: int] :
% 15.55/8.52        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X3 ) @ Z )
% 15.55/8.52        = ( ord_less_rat @ X3 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3238_floor__le__iff,axiom,
% 15.55/8.52      ! [X3: real,Z: int] :
% 15.55/8.52        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X3 ) @ Z )
% 15.55/8.52        = ( ord_less_real @ X3 @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3239_floor__correct,axiom,
% 15.55/8.52      ! [X3: rat] :
% 15.55/8.52        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X3 ) ) @ X3 )
% 15.55/8.52        & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X3 ) @ one_one_int ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3240_floor__correct,axiom,
% 15.55/8.52      ! [X3: real] :
% 15.55/8.52        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X3 ) ) @ X3 )
% 15.55/8.52        & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X3 ) @ one_one_int ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3241_le__log__iff,axiom,
% 15.55/8.52      ! [B: real,X3: real,Y3: real] :
% 15.55/8.52        ( ( ord_less_real @ one_one_real @ B )
% 15.55/8.52       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.52         => ( ( ord_less_eq_real @ Y3 @ ( log @ B @ X3 ) )
% 15.55/8.52            = ( ord_less_eq_real @ ( powr_real @ B @ Y3 ) @ X3 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3242_log__le__iff,axiom,
% 15.55/8.52      ! [B: real,X3: real,Y3: real] :
% 15.55/8.52        ( ( ord_less_real @ one_one_real @ B )
% 15.55/8.52       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.52         => ( ( ord_less_eq_real @ ( log @ B @ X3 ) @ Y3 )
% 15.55/8.52            = ( ord_less_eq_real @ X3 @ ( powr_real @ B @ Y3 ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3243_le__powr__iff,axiom,
% 15.55/8.52      ! [B: real,X3: real,Y3: real] :
% 15.55/8.52        ( ( ord_less_real @ one_one_real @ B )
% 15.55/8.52       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.52         => ( ( ord_less_eq_real @ X3 @ ( powr_real @ B @ Y3 ) )
% 15.55/8.52            = ( ord_less_eq_real @ ( log @ B @ X3 ) @ Y3 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3244_powr__le__iff,axiom,
% 15.55/8.52      ! [B: real,X3: real,Y3: real] :
% 15.55/8.52        ( ( ord_less_real @ one_one_real @ B )
% 15.55/8.52       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.52         => ( ( ord_less_eq_real @ ( powr_real @ B @ Y3 ) @ X3 )
% 15.55/8.52            = ( ord_less_eq_real @ Y3 @ ( log @ B @ X3 ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3245_floor__eq2,axiom,
% 15.55/8.52      ! [N: int,X3: real] :
% 15.55/8.52        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X3 )
% 15.55/8.52       => ( ( ord_less_real @ X3 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 15.55/8.52         => ( ( archim6058952711729229775r_real @ X3 )
% 15.55/8.52            = N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3246_floor__divide__real__eq__div,axiom,
% 15.55/8.52      ! [B: int,A: real] :
% 15.55/8.52        ( ( ord_less_eq_int @ zero_zero_int @ B )
% 15.55/8.52       => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 15.55/8.52          = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3247_nat__approx__posE,axiom,
% 15.55/8.52      ! [E2: real] :
% 15.55/8.52        ( ( ord_less_real @ zero_zero_real @ E2 )
% 15.55/8.52       => ~ ! [N2: nat] :
% 15.55/8.52              ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ E2 ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3248_nat__approx__posE,axiom,
% 15.55/8.52      ! [E2: rat] :
% 15.55/8.52        ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 15.55/8.52       => ~ ! [N2: nat] :
% 15.55/8.52              ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N2 ) ) ) @ E2 ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3249_less__2__cases__iff,axiom,
% 15.55/8.52      ! [N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.52        = ( ( N = zero_zero_nat )
% 15.55/8.52          | ( N
% 15.55/8.52            = ( suc @ zero_zero_nat ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3250_less__2__cases,axiom,
% 15.55/8.52      ! [N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.52       => ( ( N = zero_zero_nat )
% 15.55/8.52          | ( N
% 15.55/8.52            = ( suc @ zero_zero_nat ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3251_nat__2,axiom,
% 15.55/8.52      ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.52      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3252_le__div__geq,axiom,
% 15.55/8.52      ! [N: nat,M: nat] :
% 15.55/8.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.52       => ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.52         => ( ( divide_divide_nat @ M @ N )
% 15.55/8.52            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3253_Suc__nat__eq__nat__zadd1,axiom,
% 15.55/8.52      ! [Z: int] :
% 15.55/8.52        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 15.55/8.52       => ( ( suc @ ( nat2 @ Z ) )
% 15.55/8.52          = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3254_ln__powr__bound,axiom,
% 15.55/8.52      ! [X3: real,A: real] :
% 15.55/8.52        ( ( ord_less_eq_real @ one_one_real @ X3 )
% 15.55/8.52       => ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.52         => ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ ( divide_divide_real @ ( powr_real @ X3 @ A ) @ A ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3255_minus__log__eq__powr,axiom,
% 15.55/8.52      ! [B: real,X3: real,Y3: real] :
% 15.55/8.52        ( ( ord_less_real @ zero_zero_real @ B )
% 15.55/8.52       => ( ( B != one_one_real )
% 15.55/8.52         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.52           => ( ( minus_minus_real @ Y3 @ ( log @ B @ X3 ) )
% 15.55/8.52              = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y3 ) @ X3 ) ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3256_Suc__n__div__2__gt__zero,axiom,
% 15.55/8.52      ! [N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.52       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3257_div__2__gt__zero,axiom,
% 15.55/8.52      ! [N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 15.55/8.52       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3258_powr__half__sqrt,axiom,
% 15.55/8.52      ! [X3: real] :
% 15.55/8.52        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.52       => ( ( powr_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.52          = ( sqrt @ X3 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3259_int__power__div__base,axiom,
% 15.55/8.52      ! [M: nat,K: int] :
% 15.55/8.52        ( ( ord_less_nat @ zero_zero_nat @ M )
% 15.55/8.52       => ( ( ord_less_int @ zero_zero_int @ K )
% 15.55/8.52         => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 15.55/8.52            = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3260_floor__log2__div2,axiom,
% 15.55/8.52      ! [N: nat] :
% 15.55/8.52        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.52       => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 15.55/8.52          = ( 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 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3261_floor__log__nat__eq__if,axiom,
% 15.55/8.52      ! [B: nat,N: nat,K: nat] :
% 15.55/8.52        ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 15.55/8.52       => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 15.55/8.52         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 15.55/8.52           => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 15.55/8.52              = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3262_of__int__round__le,axiom,
% 15.55/8.52      ! [X3: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X3 ) ) @ ( plus_plus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3263_of__int__round__le,axiom,
% 15.55/8.52      ! [X3: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X3 ) ) @ ( plus_plus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3264_of__int__round__ge,axiom,
% 15.55/8.52      ! [X3: real] : ( ord_less_eq_real @ ( minus_minus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X3 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3265_of__int__round__ge,axiom,
% 15.55/8.52      ! [X3: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X3 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3266_of__int__round__gt,axiom,
% 15.55/8.52      ! [X3: real] : ( ord_less_real @ ( minus_minus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X3 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3267_of__int__round__gt,axiom,
% 15.55/8.52      ! [X3: rat] : ( ord_less_rat @ ( minus_minus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X3 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3268_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 15.55/8.52      ! [X3: nat,N: nat,M: nat] :
% 15.55/8.52        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 15.55/8.52       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.52         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 15.55/8.52           => ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3269_high__inv,axiom,
% 15.55/8.52      ! [X3: nat,N: nat,Y3: nat] :
% 15.55/8.52        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.52       => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X3 ) @ N )
% 15.55/8.52          = Y3 ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3270_arcosh__def,axiom,
% 15.55/8.52      ( arcosh_real
% 15.55/8.52      = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( powr_real @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3271_round__altdef,axiom,
% 15.55/8.52      ( archim7778729529865785530nd_rat
% 15.55/8.52      = ( ^ [X: rat] : ( if_int @ ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( archimedean_frac_rat @ X ) ) @ ( archim2889992004027027881ng_rat @ X ) @ ( archim3151403230148437115or_rat @ X ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3272_round__altdef,axiom,
% 15.55/8.52      ( archim8280529875227126926d_real
% 15.55/8.52      = ( ^ [X: real] : ( if_int @ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( archim2898591450579166408c_real @ X ) ) @ ( archim7802044766580827645g_real @ X ) @ ( archim6058952711729229775r_real @ X ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3273_arsinh__def,axiom,
% 15.55/8.52      ( arsinh_real
% 15.55/8.52      = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( powr_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3274_mult__cancel__right,axiom,
% 15.55/8.52      ! [A: real,C: real,B: real] :
% 15.55/8.52        ( ( ( times_times_real @ A @ C )
% 15.55/8.52          = ( times_times_real @ B @ C ) )
% 15.55/8.52        = ( ( C = zero_zero_real )
% 15.55/8.52          | ( A = B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3275_mult__cancel__right,axiom,
% 15.55/8.52      ! [A: rat,C: rat,B: rat] :
% 15.55/8.52        ( ( ( times_times_rat @ A @ C )
% 15.55/8.52          = ( times_times_rat @ B @ C ) )
% 15.55/8.52        = ( ( C = zero_zero_rat )
% 15.55/8.52          | ( A = B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3276_mult__cancel__right,axiom,
% 15.55/8.52      ! [A: nat,C: nat,B: nat] :
% 15.55/8.52        ( ( ( times_times_nat @ A @ C )
% 15.55/8.52          = ( times_times_nat @ B @ C ) )
% 15.55/8.52        = ( ( C = zero_zero_nat )
% 15.55/8.52          | ( A = B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3277_mult__cancel__right,axiom,
% 15.55/8.52      ! [A: int,C: int,B: int] :
% 15.55/8.52        ( ( ( times_times_int @ A @ C )
% 15.55/8.52          = ( times_times_int @ B @ C ) )
% 15.55/8.52        = ( ( C = zero_zero_int )
% 15.55/8.52          | ( A = B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3278_mult__cancel__left,axiom,
% 15.55/8.52      ! [C: real,A: real,B: real] :
% 15.55/8.52        ( ( ( times_times_real @ C @ A )
% 15.55/8.52          = ( times_times_real @ C @ B ) )
% 15.55/8.52        = ( ( C = zero_zero_real )
% 15.55/8.52          | ( A = B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3279_mult__cancel__left,axiom,
% 15.55/8.52      ! [C: rat,A: rat,B: rat] :
% 15.55/8.52        ( ( ( times_times_rat @ C @ A )
% 15.55/8.52          = ( times_times_rat @ C @ B ) )
% 15.55/8.52        = ( ( C = zero_zero_rat )
% 15.55/8.52          | ( A = B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3280_mult__cancel__left,axiom,
% 15.55/8.52      ! [C: nat,A: nat,B: nat] :
% 15.55/8.52        ( ( ( times_times_nat @ C @ A )
% 15.55/8.52          = ( times_times_nat @ C @ B ) )
% 15.55/8.52        = ( ( C = zero_zero_nat )
% 15.55/8.52          | ( A = B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3281_mult__cancel__left,axiom,
% 15.55/8.52      ! [C: int,A: int,B: int] :
% 15.55/8.52        ( ( ( times_times_int @ C @ A )
% 15.55/8.52          = ( times_times_int @ C @ B ) )
% 15.55/8.52        = ( ( C = zero_zero_int )
% 15.55/8.52          | ( A = B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3282_mult__eq__0__iff,axiom,
% 15.55/8.52      ! [A: real,B: real] :
% 15.55/8.52        ( ( ( times_times_real @ A @ B )
% 15.55/8.52          = zero_zero_real )
% 15.55/8.52        = ( ( A = zero_zero_real )
% 15.55/8.52          | ( B = zero_zero_real ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3283_mult__eq__0__iff,axiom,
% 15.55/8.52      ! [A: rat,B: rat] :
% 15.55/8.52        ( ( ( times_times_rat @ A @ B )
% 15.55/8.52          = zero_zero_rat )
% 15.55/8.52        = ( ( A = zero_zero_rat )
% 15.55/8.52          | ( B = zero_zero_rat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3284_mult__eq__0__iff,axiom,
% 15.55/8.52      ! [A: nat,B: nat] :
% 15.55/8.52        ( ( ( times_times_nat @ A @ B )
% 15.55/8.52          = zero_zero_nat )
% 15.55/8.52        = ( ( A = zero_zero_nat )
% 15.55/8.52          | ( B = zero_zero_nat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3285_mult__eq__0__iff,axiom,
% 15.55/8.52      ! [A: int,B: int] :
% 15.55/8.52        ( ( ( times_times_int @ A @ B )
% 15.55/8.52          = zero_zero_int )
% 15.55/8.52        = ( ( A = zero_zero_int )
% 15.55/8.52          | ( B = zero_zero_int ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3286_mult__zero__right,axiom,
% 15.55/8.52      ! [A: real] :
% 15.55/8.52        ( ( times_times_real @ A @ zero_zero_real )
% 15.55/8.52        = zero_zero_real ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3287_mult__zero__right,axiom,
% 15.55/8.52      ! [A: rat] :
% 15.55/8.52        ( ( times_times_rat @ A @ zero_zero_rat )
% 15.55/8.52        = zero_zero_rat ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3288_mult__zero__right,axiom,
% 15.55/8.52      ! [A: nat] :
% 15.55/8.52        ( ( times_times_nat @ A @ zero_zero_nat )
% 15.55/8.52        = zero_zero_nat ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3289_mult__zero__right,axiom,
% 15.55/8.52      ! [A: int] :
% 15.55/8.52        ( ( times_times_int @ A @ zero_zero_int )
% 15.55/8.52        = zero_zero_int ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3290_mult__zero__left,axiom,
% 15.55/8.52      ! [A: real] :
% 15.55/8.52        ( ( times_times_real @ zero_zero_real @ A )
% 15.55/8.52        = zero_zero_real ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3291_mult__zero__left,axiom,
% 15.55/8.52      ! [A: rat] :
% 15.55/8.52        ( ( times_times_rat @ zero_zero_rat @ A )
% 15.55/8.52        = zero_zero_rat ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3292_mult__zero__left,axiom,
% 15.55/8.52      ! [A: nat] :
% 15.55/8.52        ( ( times_times_nat @ zero_zero_nat @ A )
% 15.55/8.52        = zero_zero_nat ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3293_mult__zero__left,axiom,
% 15.55/8.52      ! [A: int] :
% 15.55/8.52        ( ( times_times_int @ zero_zero_int @ A )
% 15.55/8.52        = zero_zero_int ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3294_numeral__times__numeral,axiom,
% 15.55/8.52      ! [M: num,N: num] :
% 15.55/8.52        ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 15.55/8.52        = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3295_numeral__times__numeral,axiom,
% 15.55/8.52      ! [M: num,N: num] :
% 15.55/8.52        ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 15.55/8.52        = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3296_numeral__times__numeral,axiom,
% 15.55/8.52      ! [M: num,N: num] :
% 15.55/8.52        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 15.55/8.52        = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3297_numeral__times__numeral,axiom,
% 15.55/8.52      ! [M: num,N: num] :
% 15.55/8.52        ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 15.55/8.52        = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3298_numeral__times__numeral,axiom,
% 15.55/8.52      ! [M: num,N: num] :
% 15.55/8.52        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 15.55/8.52        = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3299_mult__numeral__left__semiring__numeral,axiom,
% 15.55/8.52      ! [V: num,W: num,Z: complex] :
% 15.55/8.52        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 15.55/8.52        = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3300_mult__numeral__left__semiring__numeral,axiom,
% 15.55/8.52      ! [V: num,W: num,Z: real] :
% 15.55/8.52        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 15.55/8.52        = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3301_mult__numeral__left__semiring__numeral,axiom,
% 15.55/8.52      ! [V: num,W: num,Z: rat] :
% 15.55/8.52        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 15.55/8.52        = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3302_mult__numeral__left__semiring__numeral,axiom,
% 15.55/8.52      ! [V: num,W: num,Z: nat] :
% 15.55/8.52        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 15.55/8.52        = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3303_mult__numeral__left__semiring__numeral,axiom,
% 15.55/8.52      ! [V: num,W: num,Z: int] :
% 15.55/8.52        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 15.55/8.52        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3304_mult_Oright__neutral,axiom,
% 15.55/8.52      ! [A: complex] :
% 15.55/8.52        ( ( times_times_complex @ A @ one_one_complex )
% 15.55/8.52        = A ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3305_mult_Oright__neutral,axiom,
% 15.55/8.52      ! [A: real] :
% 15.55/8.52        ( ( times_times_real @ A @ one_one_real )
% 15.55/8.52        = A ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3306_mult_Oright__neutral,axiom,
% 15.55/8.52      ! [A: rat] :
% 15.55/8.52        ( ( times_times_rat @ A @ one_one_rat )
% 15.55/8.52        = A ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3307_mult_Oright__neutral,axiom,
% 15.55/8.52      ! [A: nat] :
% 15.55/8.52        ( ( times_times_nat @ A @ one_one_nat )
% 15.55/8.52        = A ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3308_mult_Oright__neutral,axiom,
% 15.55/8.52      ! [A: int] :
% 15.55/8.52        ( ( times_times_int @ A @ one_one_int )
% 15.55/8.52        = A ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3309_mult__1,axiom,
% 15.55/8.52      ! [A: complex] :
% 15.55/8.52        ( ( times_times_complex @ one_one_complex @ A )
% 15.55/8.52        = A ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3310_mult__1,axiom,
% 15.55/8.52      ! [A: real] :
% 15.55/8.52        ( ( times_times_real @ one_one_real @ A )
% 15.55/8.52        = A ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3311_mult__1,axiom,
% 15.55/8.52      ! [A: rat] :
% 15.55/8.52        ( ( times_times_rat @ one_one_rat @ A )
% 15.55/8.52        = A ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3312_mult__1,axiom,
% 15.55/8.52      ! [A: nat] :
% 15.55/8.52        ( ( times_times_nat @ one_one_nat @ A )
% 15.55/8.52        = A ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3313_mult__1,axiom,
% 15.55/8.52      ! [A: int] :
% 15.55/8.52        ( ( times_times_int @ one_one_int @ A )
% 15.55/8.52        = A ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3314_of__int__mult,axiom,
% 15.55/8.52      ! [W: int,Z: int] :
% 15.55/8.52        ( ( ring_17405671764205052669omplex @ ( times_times_int @ W @ Z ) )
% 15.55/8.52        = ( times_times_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3315_of__int__mult,axiom,
% 15.55/8.52      ! [W: int,Z: int] :
% 15.55/8.52        ( ( ring_1_of_int_real @ ( times_times_int @ W @ Z ) )
% 15.55/8.52        = ( times_times_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3316_of__int__mult,axiom,
% 15.55/8.52      ! [W: int,Z: int] :
% 15.55/8.52        ( ( ring_1_of_int_rat @ ( times_times_int @ W @ Z ) )
% 15.55/8.52        = ( times_times_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3317_of__int__mult,axiom,
% 15.55/8.52      ! [W: int,Z: int] :
% 15.55/8.52        ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z ) )
% 15.55/8.52        = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3318_mult__cancel2,axiom,
% 15.55/8.52      ! [M: nat,K: nat,N: nat] :
% 15.55/8.52        ( ( ( times_times_nat @ M @ K )
% 15.55/8.52          = ( times_times_nat @ N @ K ) )
% 15.55/8.52        = ( ( M = N )
% 15.55/8.52          | ( K = zero_zero_nat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3319_mult__cancel1,axiom,
% 15.55/8.52      ! [K: nat,M: nat,N: nat] :
% 15.55/8.52        ( ( ( times_times_nat @ K @ M )
% 15.55/8.52          = ( times_times_nat @ K @ N ) )
% 15.55/8.52        = ( ( M = N )
% 15.55/8.52          | ( K = zero_zero_nat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3320_mult__0__right,axiom,
% 15.55/8.52      ! [M: nat] :
% 15.55/8.52        ( ( times_times_nat @ M @ zero_zero_nat )
% 15.55/8.52        = zero_zero_nat ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3321_mult__is__0,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ( times_times_nat @ M @ N )
% 15.55/8.52          = zero_zero_nat )
% 15.55/8.52        = ( ( M = zero_zero_nat )
% 15.55/8.52          | ( N = zero_zero_nat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3322_nat__mult__eq__1__iff,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ( times_times_nat @ M @ N )
% 15.55/8.52          = one_one_nat )
% 15.55/8.52        = ( ( M = one_one_nat )
% 15.55/8.52          & ( N = one_one_nat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3323_nat__1__eq__mult__iff,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( one_one_nat
% 15.55/8.52          = ( times_times_nat @ M @ N ) )
% 15.55/8.52        = ( ( M = one_one_nat )
% 15.55/8.52          & ( N = one_one_nat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3324_bit__concat__def,axiom,
% 15.55/8.52      ( vEBT_VEBT_bit_concat
% 15.55/8.52      = ( ^ [H: nat,L2: nat,D4: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D4 ) ) @ L2 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3325_mult__cancel__right2,axiom,
% 15.55/8.52      ! [A: complex,C: complex] :
% 15.55/8.52        ( ( ( times_times_complex @ A @ C )
% 15.55/8.52          = C )
% 15.55/8.52        = ( ( C = zero_zero_complex )
% 15.55/8.52          | ( A = one_one_complex ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3326_mult__cancel__right2,axiom,
% 15.55/8.52      ! [A: real,C: real] :
% 15.55/8.52        ( ( ( times_times_real @ A @ C )
% 15.55/8.52          = C )
% 15.55/8.52        = ( ( C = zero_zero_real )
% 15.55/8.52          | ( A = one_one_real ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3327_mult__cancel__right2,axiom,
% 15.55/8.52      ! [A: rat,C: rat] :
% 15.55/8.52        ( ( ( times_times_rat @ A @ C )
% 15.55/8.52          = C )
% 15.55/8.52        = ( ( C = zero_zero_rat )
% 15.55/8.52          | ( A = one_one_rat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3328_mult__cancel__right2,axiom,
% 15.55/8.52      ! [A: int,C: int] :
% 15.55/8.52        ( ( ( times_times_int @ A @ C )
% 15.55/8.52          = C )
% 15.55/8.52        = ( ( C = zero_zero_int )
% 15.55/8.52          | ( A = one_one_int ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3329_mult__cancel__right1,axiom,
% 15.55/8.52      ! [C: complex,B: complex] :
% 15.55/8.52        ( ( C
% 15.55/8.52          = ( times_times_complex @ B @ C ) )
% 15.55/8.52        = ( ( C = zero_zero_complex )
% 15.55/8.52          | ( B = one_one_complex ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3330_mult__cancel__right1,axiom,
% 15.55/8.52      ! [C: real,B: real] :
% 15.55/8.52        ( ( C
% 15.55/8.52          = ( times_times_real @ B @ C ) )
% 15.55/8.52        = ( ( C = zero_zero_real )
% 15.55/8.52          | ( B = one_one_real ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3331_mult__cancel__right1,axiom,
% 15.55/8.52      ! [C: rat,B: rat] :
% 15.55/8.52        ( ( C
% 15.55/8.52          = ( times_times_rat @ B @ C ) )
% 15.55/8.52        = ( ( C = zero_zero_rat )
% 15.55/8.52          | ( B = one_one_rat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3332_mult__cancel__right1,axiom,
% 15.55/8.52      ! [C: int,B: int] :
% 15.55/8.52        ( ( C
% 15.55/8.52          = ( times_times_int @ B @ C ) )
% 15.55/8.52        = ( ( C = zero_zero_int )
% 15.55/8.52          | ( B = one_one_int ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3333_mult__cancel__left2,axiom,
% 15.55/8.52      ! [C: complex,A: complex] :
% 15.55/8.52        ( ( ( times_times_complex @ C @ A )
% 15.55/8.52          = C )
% 15.55/8.52        = ( ( C = zero_zero_complex )
% 15.55/8.52          | ( A = one_one_complex ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3334_mult__cancel__left2,axiom,
% 15.55/8.52      ! [C: real,A: real] :
% 15.55/8.52        ( ( ( times_times_real @ C @ A )
% 15.55/8.52          = C )
% 15.55/8.52        = ( ( C = zero_zero_real )
% 15.55/8.52          | ( A = one_one_real ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3335_mult__cancel__left2,axiom,
% 15.55/8.52      ! [C: rat,A: rat] :
% 15.55/8.52        ( ( ( times_times_rat @ C @ A )
% 15.55/8.52          = C )
% 15.55/8.52        = ( ( C = zero_zero_rat )
% 15.55/8.52          | ( A = one_one_rat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3336_mult__cancel__left2,axiom,
% 15.55/8.52      ! [C: int,A: int] :
% 15.55/8.52        ( ( ( times_times_int @ C @ A )
% 15.55/8.52          = C )
% 15.55/8.52        = ( ( C = zero_zero_int )
% 15.55/8.52          | ( A = one_one_int ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3337_mult__cancel__left1,axiom,
% 15.55/8.52      ! [C: complex,B: complex] :
% 15.55/8.52        ( ( C
% 15.55/8.52          = ( times_times_complex @ C @ B ) )
% 15.55/8.52        = ( ( C = zero_zero_complex )
% 15.55/8.52          | ( B = one_one_complex ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3338_mult__cancel__left1,axiom,
% 15.55/8.52      ! [C: real,B: real] :
% 15.55/8.52        ( ( C
% 15.55/8.52          = ( times_times_real @ C @ B ) )
% 15.55/8.52        = ( ( C = zero_zero_real )
% 15.55/8.52          | ( B = one_one_real ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3339_mult__cancel__left1,axiom,
% 15.55/8.52      ! [C: rat,B: rat] :
% 15.55/8.52        ( ( C
% 15.55/8.52          = ( times_times_rat @ C @ B ) )
% 15.55/8.52        = ( ( C = zero_zero_rat )
% 15.55/8.52          | ( B = one_one_rat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3340_mult__cancel__left1,axiom,
% 15.55/8.52      ! [C: int,B: int] :
% 15.55/8.52        ( ( C
% 15.55/8.52          = ( times_times_int @ C @ B ) )
% 15.55/8.52        = ( ( C = zero_zero_int )
% 15.55/8.52          | ( B = one_one_int ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3341_sum__squares__eq__zero__iff,axiom,
% 15.55/8.52      ! [X3: real,Y3: real] :
% 15.55/8.52        ( ( ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y3 @ Y3 ) )
% 15.55/8.52          = zero_zero_real )
% 15.55/8.52        = ( ( X3 = zero_zero_real )
% 15.55/8.52          & ( Y3 = zero_zero_real ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3342_sum__squares__eq__zero__iff,axiom,
% 15.55/8.52      ! [X3: rat,Y3: rat] :
% 15.55/8.52        ( ( ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y3 @ Y3 ) )
% 15.55/8.52          = zero_zero_rat )
% 15.55/8.52        = ( ( X3 = zero_zero_rat )
% 15.55/8.52          & ( Y3 = zero_zero_rat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3343_sum__squares__eq__zero__iff,axiom,
% 15.55/8.52      ! [X3: int,Y3: int] :
% 15.55/8.52        ( ( ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y3 @ Y3 ) )
% 15.55/8.52          = zero_zero_int )
% 15.55/8.52        = ( ( X3 = zero_zero_int )
% 15.55/8.52          & ( Y3 = zero_zero_int ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3344_div__mult__mult1__if,axiom,
% 15.55/8.52      ! [C: nat,A: nat,B: nat] :
% 15.55/8.52        ( ( ( C = zero_zero_nat )
% 15.55/8.52         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 15.55/8.52            = zero_zero_nat ) )
% 15.55/8.52        & ( ( C != zero_zero_nat )
% 15.55/8.52         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 15.55/8.52            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3345_div__mult__mult1__if,axiom,
% 15.55/8.52      ! [C: int,A: int,B: int] :
% 15.55/8.52        ( ( ( C = zero_zero_int )
% 15.55/8.52         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 15.55/8.52            = zero_zero_int ) )
% 15.55/8.52        & ( ( C != zero_zero_int )
% 15.55/8.52         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 15.55/8.52            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3346_div__mult__mult2,axiom,
% 15.55/8.52      ! [C: nat,A: nat,B: nat] :
% 15.55/8.52        ( ( C != zero_zero_nat )
% 15.55/8.52       => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 15.55/8.52          = ( divide_divide_nat @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3347_div__mult__mult2,axiom,
% 15.55/8.52      ! [C: int,A: int,B: int] :
% 15.55/8.52        ( ( C != zero_zero_int )
% 15.55/8.52       => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 15.55/8.52          = ( divide_divide_int @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3348_div__mult__mult1,axiom,
% 15.55/8.52      ! [C: nat,A: nat,B: nat] :
% 15.55/8.52        ( ( C != zero_zero_nat )
% 15.55/8.52       => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 15.55/8.52          = ( divide_divide_nat @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3349_div__mult__mult1,axiom,
% 15.55/8.52      ! [C: int,A: int,B: int] :
% 15.55/8.52        ( ( C != zero_zero_int )
% 15.55/8.52       => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 15.55/8.52          = ( divide_divide_int @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3350_nonzero__mult__div__cancel__right,axiom,
% 15.55/8.52      ! [B: complex,A: complex] :
% 15.55/8.52        ( ( B != zero_zero_complex )
% 15.55/8.52       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 15.55/8.52          = A ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3351_nonzero__mult__div__cancel__right,axiom,
% 15.55/8.52      ! [B: real,A: real] :
% 15.55/8.52        ( ( B != zero_zero_real )
% 15.55/8.52       => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 15.55/8.52          = A ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3352_nonzero__mult__div__cancel__right,axiom,
% 15.55/8.52      ! [B: rat,A: rat] :
% 15.55/8.52        ( ( B != zero_zero_rat )
% 15.55/8.52       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 15.55/8.52          = A ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3353_nonzero__mult__div__cancel__right,axiom,
% 15.55/8.52      ! [B: nat,A: nat] :
% 15.55/8.52        ( ( B != zero_zero_nat )
% 15.55/8.52       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 15.55/8.52          = A ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3354_nonzero__mult__div__cancel__right,axiom,
% 15.55/8.52      ! [B: int,A: int] :
% 15.55/8.52        ( ( B != zero_zero_int )
% 15.55/8.52       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 15.55/8.52          = A ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3355_nonzero__mult__div__cancel__left,axiom,
% 15.55/8.52      ! [A: complex,B: complex] :
% 15.55/8.52        ( ( A != zero_zero_complex )
% 15.55/8.52       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 15.55/8.52          = B ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3356_nonzero__mult__div__cancel__left,axiom,
% 15.55/8.52      ! [A: real,B: real] :
% 15.55/8.52        ( ( A != zero_zero_real )
% 15.55/8.52       => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 15.55/8.52          = B ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3357_nonzero__mult__div__cancel__left,axiom,
% 15.55/8.52      ! [A: rat,B: rat] :
% 15.55/8.52        ( ( A != zero_zero_rat )
% 15.55/8.52       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 15.55/8.52          = B ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3358_nonzero__mult__div__cancel__left,axiom,
% 15.55/8.52      ! [A: nat,B: nat] :
% 15.55/8.52        ( ( A != zero_zero_nat )
% 15.55/8.52       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 15.55/8.52          = B ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3359_nonzero__mult__div__cancel__left,axiom,
% 15.55/8.52      ! [A: int,B: int] :
% 15.55/8.52        ( ( A != zero_zero_int )
% 15.55/8.52       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 15.55/8.52          = B ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3360_nonzero__mult__divide__mult__cancel__right2,axiom,
% 15.55/8.52      ! [C: complex,A: complex,B: complex] :
% 15.55/8.52        ( ( C != zero_zero_complex )
% 15.55/8.52       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 15.55/8.52          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3361_nonzero__mult__divide__mult__cancel__right2,axiom,
% 15.55/8.52      ! [C: real,A: real,B: real] :
% 15.55/8.52        ( ( C != zero_zero_real )
% 15.55/8.52       => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 15.55/8.52          = ( divide_divide_real @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3362_nonzero__mult__divide__mult__cancel__right2,axiom,
% 15.55/8.52      ! [C: rat,A: rat,B: rat] :
% 15.55/8.52        ( ( C != zero_zero_rat )
% 15.55/8.52       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 15.55/8.52          = ( divide_divide_rat @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3363_nonzero__mult__divide__mult__cancel__right,axiom,
% 15.55/8.52      ! [C: complex,A: complex,B: complex] :
% 15.55/8.52        ( ( C != zero_zero_complex )
% 15.55/8.52       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 15.55/8.52          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3364_nonzero__mult__divide__mult__cancel__right,axiom,
% 15.55/8.52      ! [C: real,A: real,B: real] :
% 15.55/8.52        ( ( C != zero_zero_real )
% 15.55/8.52       => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 15.55/8.52          = ( divide_divide_real @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3365_nonzero__mult__divide__mult__cancel__right,axiom,
% 15.55/8.52      ! [C: rat,A: rat,B: rat] :
% 15.55/8.52        ( ( C != zero_zero_rat )
% 15.55/8.52       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 15.55/8.52          = ( divide_divide_rat @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3366_nonzero__mult__divide__mult__cancel__left2,axiom,
% 15.55/8.52      ! [C: complex,A: complex,B: complex] :
% 15.55/8.52        ( ( C != zero_zero_complex )
% 15.55/8.52       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 15.55/8.52          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3367_nonzero__mult__divide__mult__cancel__left2,axiom,
% 15.55/8.52      ! [C: real,A: real,B: real] :
% 15.55/8.52        ( ( C != zero_zero_real )
% 15.55/8.52       => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 15.55/8.52          = ( divide_divide_real @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3368_nonzero__mult__divide__mult__cancel__left2,axiom,
% 15.55/8.52      ! [C: rat,A: rat,B: rat] :
% 15.55/8.52        ( ( C != zero_zero_rat )
% 15.55/8.52       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 15.55/8.52          = ( divide_divide_rat @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3369_nonzero__mult__divide__mult__cancel__left,axiom,
% 15.55/8.52      ! [C: complex,A: complex,B: complex] :
% 15.55/8.52        ( ( C != zero_zero_complex )
% 15.55/8.52       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 15.55/8.52          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3370_nonzero__mult__divide__mult__cancel__left,axiom,
% 15.55/8.52      ! [C: real,A: real,B: real] :
% 15.55/8.52        ( ( C != zero_zero_real )
% 15.55/8.52       => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 15.55/8.52          = ( divide_divide_real @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3371_nonzero__mult__divide__mult__cancel__left,axiom,
% 15.55/8.52      ! [C: rat,A: rat,B: rat] :
% 15.55/8.52        ( ( C != zero_zero_rat )
% 15.55/8.52       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 15.55/8.52          = ( divide_divide_rat @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3372_mult__divide__mult__cancel__left__if,axiom,
% 15.55/8.52      ! [C: complex,A: complex,B: complex] :
% 15.55/8.52        ( ( ( C = zero_zero_complex )
% 15.55/8.52         => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 15.55/8.52            = zero_zero_complex ) )
% 15.55/8.52        & ( ( C != zero_zero_complex )
% 15.55/8.52         => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 15.55/8.52            = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3373_mult__divide__mult__cancel__left__if,axiom,
% 15.55/8.52      ! [C: real,A: real,B: real] :
% 15.55/8.52        ( ( ( C = zero_zero_real )
% 15.55/8.52         => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 15.55/8.52            = zero_zero_real ) )
% 15.55/8.52        & ( ( C != zero_zero_real )
% 15.55/8.52         => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 15.55/8.52            = ( divide_divide_real @ A @ B ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3374_mult__divide__mult__cancel__left__if,axiom,
% 15.55/8.52      ! [C: rat,A: rat,B: rat] :
% 15.55/8.52        ( ( ( C = zero_zero_rat )
% 15.55/8.52         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 15.55/8.52            = zero_zero_rat ) )
% 15.55/8.52        & ( ( C != zero_zero_rat )
% 15.55/8.52         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 15.55/8.52            = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3375_distrib__right__numeral,axiom,
% 15.55/8.52      ! [A: complex,B: complex,V: num] :
% 15.55/8.52        ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 15.55/8.52        = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3376_distrib__right__numeral,axiom,
% 15.55/8.52      ! [A: real,B: real,V: num] :
% 15.55/8.52        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 15.55/8.52        = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3377_distrib__right__numeral,axiom,
% 15.55/8.52      ! [A: rat,B: rat,V: num] :
% 15.55/8.52        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 15.55/8.52        = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3378_distrib__right__numeral,axiom,
% 15.55/8.52      ! [A: nat,B: nat,V: num] :
% 15.55/8.52        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 15.55/8.52        = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3379_distrib__right__numeral,axiom,
% 15.55/8.52      ! [A: int,B: int,V: num] :
% 15.55/8.52        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 15.55/8.52        = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3380_distrib__left__numeral,axiom,
% 15.55/8.52      ! [V: num,B: complex,C: complex] :
% 15.55/8.52        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 15.55/8.52        = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3381_distrib__left__numeral,axiom,
% 15.55/8.52      ! [V: num,B: real,C: real] :
% 15.55/8.52        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 15.55/8.52        = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3382_distrib__left__numeral,axiom,
% 15.55/8.52      ! [V: num,B: rat,C: rat] :
% 15.55/8.52        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 15.55/8.52        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3383_distrib__left__numeral,axiom,
% 15.55/8.52      ! [V: num,B: nat,C: nat] :
% 15.55/8.52        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 15.55/8.52        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3384_distrib__left__numeral,axiom,
% 15.55/8.52      ! [V: num,B: int,C: int] :
% 15.55/8.52        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 15.55/8.52        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3385_right__diff__distrib__numeral,axiom,
% 15.55/8.52      ! [V: num,B: complex,C: complex] :
% 15.55/8.52        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 15.55/8.52        = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3386_right__diff__distrib__numeral,axiom,
% 15.55/8.52      ! [V: num,B: real,C: real] :
% 15.55/8.52        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 15.55/8.52        = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3387_right__diff__distrib__numeral,axiom,
% 15.55/8.52      ! [V: num,B: rat,C: rat] :
% 15.55/8.52        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 15.55/8.52        = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3388_right__diff__distrib__numeral,axiom,
% 15.55/8.52      ! [V: num,B: int,C: int] :
% 15.55/8.52        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 15.55/8.52        = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3389_left__diff__distrib__numeral,axiom,
% 15.55/8.52      ! [A: complex,B: complex,V: num] :
% 15.55/8.52        ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 15.55/8.52        = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3390_left__diff__distrib__numeral,axiom,
% 15.55/8.52      ! [A: real,B: real,V: num] :
% 15.55/8.52        ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 15.55/8.52        = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3391_left__diff__distrib__numeral,axiom,
% 15.55/8.52      ! [A: rat,B: rat,V: num] :
% 15.55/8.52        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 15.55/8.52        = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3392_left__diff__distrib__numeral,axiom,
% 15.55/8.52      ! [A: int,B: int,V: num] :
% 15.55/8.52        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 15.55/8.52        = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3393_dvd__times__right__cancel__iff,axiom,
% 15.55/8.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 15.55/8.52        ( ( A != zero_z3403309356797280102nteger )
% 15.55/8.52       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 15.55/8.52          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3394_dvd__times__right__cancel__iff,axiom,
% 15.55/8.52      ! [A: nat,B: nat,C: nat] :
% 15.55/8.52        ( ( A != zero_zero_nat )
% 15.55/8.52       => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 15.55/8.52          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3395_dvd__times__right__cancel__iff,axiom,
% 15.55/8.52      ! [A: int,B: int,C: int] :
% 15.55/8.52        ( ( A != zero_zero_int )
% 15.55/8.52       => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 15.55/8.52          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3396_dvd__times__left__cancel__iff,axiom,
% 15.55/8.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 15.55/8.52        ( ( A != zero_z3403309356797280102nteger )
% 15.55/8.52       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 15.55/8.52          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3397_dvd__times__left__cancel__iff,axiom,
% 15.55/8.52      ! [A: nat,B: nat,C: nat] :
% 15.55/8.52        ( ( A != zero_zero_nat )
% 15.55/8.52       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 15.55/8.52          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3398_dvd__times__left__cancel__iff,axiom,
% 15.55/8.52      ! [A: int,B: int,C: int] :
% 15.55/8.52        ( ( A != zero_zero_int )
% 15.55/8.52       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 15.55/8.52          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3399_dvd__mult__cancel__right,axiom,
% 15.55/8.52      ! [A: code_integer,C: code_integer,B: code_integer] :
% 15.55/8.52        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 15.55/8.52        = ( ( C = zero_z3403309356797280102nteger )
% 15.55/8.52          | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3400_dvd__mult__cancel__right,axiom,
% 15.55/8.52      ! [A: real,C: real,B: real] :
% 15.55/8.52        ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 15.55/8.52        = ( ( C = zero_zero_real )
% 15.55/8.52          | ( dvd_dvd_real @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3401_dvd__mult__cancel__right,axiom,
% 15.55/8.52      ! [A: rat,C: rat,B: rat] :
% 15.55/8.52        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 15.55/8.52        = ( ( C = zero_zero_rat )
% 15.55/8.52          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3402_dvd__mult__cancel__right,axiom,
% 15.55/8.52      ! [A: int,C: int,B: int] :
% 15.55/8.52        ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 15.55/8.52        = ( ( C = zero_zero_int )
% 15.55/8.52          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3403_dvd__mult__cancel__left,axiom,
% 15.55/8.52      ! [C: code_integer,A: code_integer,B: code_integer] :
% 15.55/8.52        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 15.55/8.52        = ( ( C = zero_z3403309356797280102nteger )
% 15.55/8.52          | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3404_dvd__mult__cancel__left,axiom,
% 15.55/8.52      ! [C: real,A: real,B: real] :
% 15.55/8.52        ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 15.55/8.52        = ( ( C = zero_zero_real )
% 15.55/8.52          | ( dvd_dvd_real @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3405_dvd__mult__cancel__left,axiom,
% 15.55/8.52      ! [C: rat,A: rat,B: rat] :
% 15.55/8.52        ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 15.55/8.52        = ( ( C = zero_zero_rat )
% 15.55/8.52          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3406_dvd__mult__cancel__left,axiom,
% 15.55/8.52      ! [C: int,A: int,B: int] :
% 15.55/8.52        ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 15.55/8.52        = ( ( C = zero_zero_int )
% 15.55/8.52          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3407_mult__eq__1__iff,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ( times_times_nat @ M @ N )
% 15.55/8.52          = ( suc @ zero_zero_nat ) )
% 15.55/8.52        = ( ( M
% 15.55/8.52            = ( suc @ zero_zero_nat ) )
% 15.55/8.52          & ( N
% 15.55/8.52            = ( suc @ zero_zero_nat ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3408_one__eq__mult__iff,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ( suc @ zero_zero_nat )
% 15.55/8.52          = ( times_times_nat @ M @ N ) )
% 15.55/8.52        = ( ( M
% 15.55/8.52            = ( suc @ zero_zero_nat ) )
% 15.55/8.52          & ( N
% 15.55/8.52            = ( suc @ zero_zero_nat ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3409_of__nat__mult,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( semiri8010041392384452111omplex @ ( times_times_nat @ M @ N ) )
% 15.55/8.52        = ( times_times_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3410_of__nat__mult,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N ) )
% 15.55/8.52        = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3411_of__nat__mult,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N ) )
% 15.55/8.52        = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3412_of__nat__mult,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 15.55/8.52        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3413_of__nat__mult,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 15.55/8.52        = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3414_mult__less__cancel2,axiom,
% 15.55/8.52      ! [M: nat,K: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 15.55/8.52        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 15.55/8.52          & ( ord_less_nat @ M @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3415_nat__0__less__mult__iff,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 15.55/8.52        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 15.55/8.52          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3416_nat__mult__less__cancel__disj,axiom,
% 15.55/8.52      ! [K: nat,M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 15.55/8.52        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 15.55/8.52          & ( ord_less_nat @ M @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3417_mult__Suc__right,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( times_times_nat @ M @ ( suc @ N ) )
% 15.55/8.52        = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3418_nat__mult__div__cancel__disj,axiom,
% 15.55/8.52      ! [K: nat,M: nat,N: nat] :
% 15.55/8.52        ( ( ( K = zero_zero_nat )
% 15.55/8.52         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 15.55/8.52            = zero_zero_nat ) )
% 15.55/8.52        & ( ( K != zero_zero_nat )
% 15.55/8.52         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 15.55/8.52            = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3419_nat__mult__dvd__cancel__disj,axiom,
% 15.55/8.52      ! [K: nat,M: nat,N: nat] :
% 15.55/8.52        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 15.55/8.52        = ( ( K = zero_zero_nat )
% 15.55/8.52          | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3420_frac__of__int,axiom,
% 15.55/8.52      ! [Z: int] :
% 15.55/8.52        ( ( archim2898591450579166408c_real @ ( ring_1_of_int_real @ Z ) )
% 15.55/8.52        = zero_zero_real ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3421_frac__of__int,axiom,
% 15.55/8.52      ! [Z: int] :
% 15.55/8.52        ( ( archimedean_frac_rat @ ( ring_1_of_int_rat @ Z ) )
% 15.55/8.52        = zero_zero_rat ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3422_le__divide__eq__numeral1_I1_J,axiom,
% 15.55/8.52      ! [A: real,B: real,W: num] :
% 15.55/8.52        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 15.55/8.52        = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3423_le__divide__eq__numeral1_I1_J,axiom,
% 15.55/8.52      ! [A: rat,B: rat,W: num] :
% 15.55/8.52        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 15.55/8.52        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3424_divide__le__eq__numeral1_I1_J,axiom,
% 15.55/8.52      ! [B: real,W: num,A: real] :
% 15.55/8.52        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 15.55/8.52        = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3425_divide__le__eq__numeral1_I1_J,axiom,
% 15.55/8.52      ! [B: rat,W: num,A: rat] :
% 15.55/8.52        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 15.55/8.52        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3426_divide__eq__eq__numeral1_I1_J,axiom,
% 15.55/8.52      ! [B: complex,W: num,A: complex] :
% 15.55/8.52        ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 15.55/8.52          = A )
% 15.55/8.52        = ( ( ( ( numera6690914467698888265omplex @ W )
% 15.55/8.52             != zero_zero_complex )
% 15.55/8.52           => ( B
% 15.55/8.52              = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 15.55/8.52          & ( ( ( numera6690914467698888265omplex @ W )
% 15.55/8.52              = zero_zero_complex )
% 15.55/8.52           => ( A = zero_zero_complex ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3427_divide__eq__eq__numeral1_I1_J,axiom,
% 15.55/8.52      ! [B: real,W: num,A: real] :
% 15.55/8.52        ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 15.55/8.52          = A )
% 15.55/8.52        = ( ( ( ( numeral_numeral_real @ W )
% 15.55/8.52             != zero_zero_real )
% 15.55/8.52           => ( B
% 15.55/8.52              = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 15.55/8.52          & ( ( ( numeral_numeral_real @ W )
% 15.55/8.52              = zero_zero_real )
% 15.55/8.52           => ( A = zero_zero_real ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3428_divide__eq__eq__numeral1_I1_J,axiom,
% 15.55/8.52      ! [B: rat,W: num,A: rat] :
% 15.55/8.52        ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 15.55/8.52          = A )
% 15.55/8.52        = ( ( ( ( numeral_numeral_rat @ W )
% 15.55/8.52             != zero_zero_rat )
% 15.55/8.52           => ( B
% 15.55/8.52              = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 15.55/8.52          & ( ( ( numeral_numeral_rat @ W )
% 15.55/8.52              = zero_zero_rat )
% 15.55/8.52           => ( A = zero_zero_rat ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3429_eq__divide__eq__numeral1_I1_J,axiom,
% 15.55/8.52      ! [A: complex,B: complex,W: num] :
% 15.55/8.52        ( ( A
% 15.55/8.52          = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 15.55/8.52        = ( ( ( ( numera6690914467698888265omplex @ W )
% 15.55/8.52             != zero_zero_complex )
% 15.55/8.52           => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 15.55/8.52              = B ) )
% 15.55/8.52          & ( ( ( numera6690914467698888265omplex @ W )
% 15.55/8.52              = zero_zero_complex )
% 15.55/8.52           => ( A = zero_zero_complex ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3430_eq__divide__eq__numeral1_I1_J,axiom,
% 15.55/8.52      ! [A: real,B: real,W: num] :
% 15.55/8.52        ( ( A
% 15.55/8.52          = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 15.55/8.52        = ( ( ( ( numeral_numeral_real @ W )
% 15.55/8.52             != zero_zero_real )
% 15.55/8.52           => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 15.55/8.52              = B ) )
% 15.55/8.52          & ( ( ( numeral_numeral_real @ W )
% 15.55/8.52              = zero_zero_real )
% 15.55/8.52           => ( A = zero_zero_real ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3431_eq__divide__eq__numeral1_I1_J,axiom,
% 15.55/8.52      ! [A: rat,B: rat,W: num] :
% 15.55/8.52        ( ( A
% 15.55/8.52          = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 15.55/8.52        = ( ( ( ( numeral_numeral_rat @ W )
% 15.55/8.52             != zero_zero_rat )
% 15.55/8.52           => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 15.55/8.52              = B ) )
% 15.55/8.52          & ( ( ( numeral_numeral_rat @ W )
% 15.55/8.52              = zero_zero_rat )
% 15.55/8.52           => ( A = zero_zero_rat ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3432_divide__less__eq__numeral1_I1_J,axiom,
% 15.55/8.52      ! [B: real,W: num,A: real] :
% 15.55/8.52        ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 15.55/8.52        = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3433_divide__less__eq__numeral1_I1_J,axiom,
% 15.55/8.52      ! [B: rat,W: num,A: rat] :
% 15.55/8.52        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 15.55/8.52        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3434_less__divide__eq__numeral1_I1_J,axiom,
% 15.55/8.52      ! [A: real,B: real,W: num] :
% 15.55/8.52        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 15.55/8.52        = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3435_less__divide__eq__numeral1_I1_J,axiom,
% 15.55/8.52      ! [A: rat,B: rat,W: num] :
% 15.55/8.52        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 15.55/8.52        = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3436_nonzero__divide__mult__cancel__right,axiom,
% 15.55/8.52      ! [B: complex,A: complex] :
% 15.55/8.52        ( ( B != zero_zero_complex )
% 15.55/8.52       => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 15.55/8.52          = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3437_nonzero__divide__mult__cancel__right,axiom,
% 15.55/8.52      ! [B: real,A: real] :
% 15.55/8.52        ( ( B != zero_zero_real )
% 15.55/8.52       => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 15.55/8.52          = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3438_nonzero__divide__mult__cancel__right,axiom,
% 15.55/8.52      ! [B: rat,A: rat] :
% 15.55/8.52        ( ( B != zero_zero_rat )
% 15.55/8.52       => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 15.55/8.52          = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3439_nonzero__divide__mult__cancel__left,axiom,
% 15.55/8.52      ! [A: complex,B: complex] :
% 15.55/8.52        ( ( A != zero_zero_complex )
% 15.55/8.52       => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 15.55/8.52          = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3440_nonzero__divide__mult__cancel__left,axiom,
% 15.55/8.52      ! [A: real,B: real] :
% 15.55/8.52        ( ( A != zero_zero_real )
% 15.55/8.52       => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 15.55/8.52          = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3441_nonzero__divide__mult__cancel__left,axiom,
% 15.55/8.52      ! [A: rat,B: rat] :
% 15.55/8.52        ( ( A != zero_zero_rat )
% 15.55/8.52       => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 15.55/8.52          = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3442_div__mult__self1,axiom,
% 15.55/8.52      ! [B: nat,A: nat,C: nat] :
% 15.55/8.52        ( ( B != zero_zero_nat )
% 15.55/8.52       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 15.55/8.52          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3443_div__mult__self1,axiom,
% 15.55/8.52      ! [B: int,A: int,C: int] :
% 15.55/8.52        ( ( B != zero_zero_int )
% 15.55/8.52       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 15.55/8.52          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3444_div__mult__self2,axiom,
% 15.55/8.52      ! [B: nat,A: nat,C: nat] :
% 15.55/8.52        ( ( B != zero_zero_nat )
% 15.55/8.52       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 15.55/8.52          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3445_div__mult__self2,axiom,
% 15.55/8.52      ! [B: int,A: int,C: int] :
% 15.55/8.52        ( ( B != zero_zero_int )
% 15.55/8.52       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 15.55/8.52          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3446_div__mult__self3,axiom,
% 15.55/8.52      ! [B: nat,C: nat,A: nat] :
% 15.55/8.52        ( ( B != zero_zero_nat )
% 15.55/8.52       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 15.55/8.52          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3447_div__mult__self3,axiom,
% 15.55/8.52      ! [B: int,C: int,A: int] :
% 15.55/8.52        ( ( B != zero_zero_int )
% 15.55/8.52       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 15.55/8.52          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3448_div__mult__self4,axiom,
% 15.55/8.52      ! [B: nat,C: nat,A: nat] :
% 15.55/8.52        ( ( B != zero_zero_nat )
% 15.55/8.52       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 15.55/8.52          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3449_div__mult__self4,axiom,
% 15.55/8.52      ! [B: int,C: int,A: int] :
% 15.55/8.52        ( ( B != zero_zero_int )
% 15.55/8.52       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 15.55/8.52          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3450_one__le__mult__iff,axiom,
% 15.55/8.52      ! [M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 15.55/8.52        = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 15.55/8.52          & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3451_mult__le__cancel2,axiom,
% 15.55/8.52      ! [M: nat,K: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 15.55/8.52        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 15.55/8.52         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3452_nat__mult__le__cancel__disj,axiom,
% 15.55/8.52      ! [K: nat,M: nat,N: nat] :
% 15.55/8.52        ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 15.55/8.52        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 15.55/8.52         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3453_div__mult__self1__is__m,axiom,
% 15.55/8.52      ! [N: nat,M: nat] :
% 15.55/8.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.52       => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 15.55/8.52          = M ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3454_div__mult__self__is__m,axiom,
% 15.55/8.52      ! [N: nat,M: nat] :
% 15.55/8.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.52       => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 15.55/8.52          = M ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3455_power__add__numeral,axiom,
% 15.55/8.52      ! [A: complex,M: num,N: num] :
% 15.55/8.52        ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) )
% 15.55/8.52        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3456_power__add__numeral,axiom,
% 15.55/8.52      ! [A: real,M: num,N: num] :
% 15.55/8.52        ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) )
% 15.55/8.52        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3457_power__add__numeral,axiom,
% 15.55/8.52      ! [A: rat,M: num,N: num] :
% 15.55/8.52        ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) )
% 15.55/8.52        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3458_power__add__numeral,axiom,
% 15.55/8.52      ! [A: nat,M: num,N: num] :
% 15.55/8.52        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 15.55/8.52        = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3459_power__add__numeral,axiom,
% 15.55/8.52      ! [A: int,M: num,N: num] :
% 15.55/8.52        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 15.55/8.52        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3460_power__add__numeral2,axiom,
% 15.55/8.52      ! [A: complex,M: num,N: num,B: complex] :
% 15.55/8.52        ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 15.55/8.52        = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3461_power__add__numeral2,axiom,
% 15.55/8.52      ! [A: real,M: num,N: num,B: real] :
% 15.55/8.52        ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 15.55/8.52        = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3462_power__add__numeral2,axiom,
% 15.55/8.52      ! [A: rat,M: num,N: num,B: rat] :
% 15.55/8.52        ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 15.55/8.52        = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3463_power__add__numeral2,axiom,
% 15.55/8.52      ! [A: nat,M: num,N: num,B: nat] :
% 15.55/8.52        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 15.55/8.52        = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3464_power__add__numeral2,axiom,
% 15.55/8.52      ! [A: int,M: num,N: num,B: int] :
% 15.55/8.52        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 15.55/8.52        = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3465_even__mult__iff,axiom,
% 15.55/8.52      ! [A: code_integer,B: code_integer] :
% 15.55/8.52        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 15.55/8.52        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.55/8.52          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3466_even__mult__iff,axiom,
% 15.55/8.52      ! [A: nat,B: nat] :
% 15.55/8.52        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 15.55/8.52        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.55/8.52          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3467_even__mult__iff,axiom,
% 15.55/8.52      ! [A: int,B: int] :
% 15.55/8.52        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 15.55/8.52        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.55/8.52          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3468_or__numerals_I3_J,axiom,
% 15.55/8.52      ! [X3: num,Y3: num] :
% 15.55/8.52        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X3 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y3 ) ) )
% 15.55/8.52        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3469_or__numerals_I3_J,axiom,
% 15.55/8.52      ! [X3: num,Y3: num] :
% 15.55/8.52        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 15.55/8.52        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X3 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3470_xor__numerals_I3_J,axiom,
% 15.55/8.52      ! [X3: num,Y3: num] :
% 15.55/8.52        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X3 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y3 ) ) )
% 15.55/8.52        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3471_xor__numerals_I3_J,axiom,
% 15.55/8.52      ! [X3: num,Y3: num] :
% 15.55/8.52        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 15.55/8.52        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X3 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3472_unset__bit__0,axiom,
% 15.55/8.52      ! [A: int] :
% 15.55/8.52        ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 15.55/8.52        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3473_unset__bit__0,axiom,
% 15.55/8.52      ! [A: nat] :
% 15.55/8.52        ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 15.55/8.52        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3474_odd__two__times__div__two__succ,axiom,
% 15.55/8.52      ! [A: code_integer] :
% 15.55/8.52        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.55/8.52       => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 15.55/8.52          = A ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3475_odd__two__times__div__two__succ,axiom,
% 15.55/8.52      ! [A: nat] :
% 15.55/8.52        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.55/8.52       => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 15.55/8.52          = A ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3476_odd__two__times__div__two__succ,axiom,
% 15.55/8.52      ! [A: int] :
% 15.55/8.52        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.55/8.52       => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 15.55/8.52          = A ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3477_odd__two__times__div__two__nat,axiom,
% 15.55/8.52      ! [N: nat] :
% 15.55/8.52        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.52       => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.52          = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3478_set__bit__0,axiom,
% 15.55/8.52      ! [A: int] :
% 15.55/8.52        ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 15.55/8.52        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3479_set__bit__0,axiom,
% 15.55/8.52      ! [A: nat] :
% 15.55/8.52        ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 15.55/8.52        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3480_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 15.55/8.52      ! [A: real,B: real,C: real] :
% 15.55/8.52        ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 15.55/8.52        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3481_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 15.55/8.52      ! [A: rat,B: rat,C: rat] :
% 15.55/8.52        ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 15.55/8.52        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3482_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 15.55/8.52      ! [A: nat,B: nat,C: nat] :
% 15.55/8.52        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 15.55/8.52        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3483_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 15.55/8.52      ! [A: int,B: int,C: int] :
% 15.55/8.52        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 15.55/8.52        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3484_mult_Oassoc,axiom,
% 15.55/8.52      ! [A: real,B: real,C: real] :
% 15.55/8.52        ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 15.55/8.52        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3485_mult_Oassoc,axiom,
% 15.55/8.52      ! [A: rat,B: rat,C: rat] :
% 15.55/8.52        ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 15.55/8.52        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3486_mult_Oassoc,axiom,
% 15.55/8.52      ! [A: nat,B: nat,C: nat] :
% 15.55/8.52        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 15.55/8.52        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3487_mult_Oassoc,axiom,
% 15.55/8.52      ! [A: int,B: int,C: int] :
% 15.55/8.52        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 15.55/8.52        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3488_mult_Ocommute,axiom,
% 15.55/8.52      ( times_times_real
% 15.55/8.52      = ( ^ [A4: real,B3: real] : ( times_times_real @ B3 @ A4 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3489_mult_Ocommute,axiom,
% 15.55/8.52      ( times_times_rat
% 15.55/8.52      = ( ^ [A4: rat,B3: rat] : ( times_times_rat @ B3 @ A4 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3490_mult_Ocommute,axiom,
% 15.55/8.52      ( times_times_nat
% 15.55/8.52      = ( ^ [A4: nat,B3: nat] : ( times_times_nat @ B3 @ A4 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3491_mult_Ocommute,axiom,
% 15.55/8.52      ( times_times_int
% 15.55/8.52      = ( ^ [A4: int,B3: int] : ( times_times_int @ B3 @ A4 ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3492_mult_Oleft__commute,axiom,
% 15.55/8.52      ! [B: real,A: real,C: real] :
% 15.55/8.52        ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 15.55/8.52        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3493_mult_Oleft__commute,axiom,
% 15.55/8.52      ! [B: rat,A: rat,C: rat] :
% 15.55/8.52        ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 15.55/8.52        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3494_mult_Oleft__commute,axiom,
% 15.55/8.52      ! [B: nat,A: nat,C: nat] :
% 15.55/8.52        ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 15.55/8.52        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3495_mult_Oleft__commute,axiom,
% 15.55/8.52      ! [B: int,A: int,C: int] :
% 15.55/8.52        ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 15.55/8.52        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3496_mult__right__cancel,axiom,
% 15.55/8.52      ! [C: real,A: real,B: real] :
% 15.55/8.52        ( ( C != zero_zero_real )
% 15.55/8.52       => ( ( ( times_times_real @ A @ C )
% 15.55/8.52            = ( times_times_real @ B @ C ) )
% 15.55/8.52          = ( A = B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3497_mult__right__cancel,axiom,
% 15.55/8.52      ! [C: rat,A: rat,B: rat] :
% 15.55/8.52        ( ( C != zero_zero_rat )
% 15.55/8.52       => ( ( ( times_times_rat @ A @ C )
% 15.55/8.52            = ( times_times_rat @ B @ C ) )
% 15.55/8.52          = ( A = B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3498_mult__right__cancel,axiom,
% 15.55/8.52      ! [C: nat,A: nat,B: nat] :
% 15.55/8.52        ( ( C != zero_zero_nat )
% 15.55/8.52       => ( ( ( times_times_nat @ A @ C )
% 15.55/8.52            = ( times_times_nat @ B @ C ) )
% 15.55/8.52          = ( A = B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3499_mult__right__cancel,axiom,
% 15.55/8.52      ! [C: int,A: int,B: int] :
% 15.55/8.52        ( ( C != zero_zero_int )
% 15.55/8.52       => ( ( ( times_times_int @ A @ C )
% 15.55/8.52            = ( times_times_int @ B @ C ) )
% 15.55/8.52          = ( A = B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3500_mult__left__cancel,axiom,
% 15.55/8.52      ! [C: real,A: real,B: real] :
% 15.55/8.52        ( ( C != zero_zero_real )
% 15.55/8.52       => ( ( ( times_times_real @ C @ A )
% 15.55/8.52            = ( times_times_real @ C @ B ) )
% 15.55/8.52          = ( A = B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3501_mult__left__cancel,axiom,
% 15.55/8.52      ! [C: rat,A: rat,B: rat] :
% 15.55/8.52        ( ( C != zero_zero_rat )
% 15.55/8.52       => ( ( ( times_times_rat @ C @ A )
% 15.55/8.52            = ( times_times_rat @ C @ B ) )
% 15.55/8.52          = ( A = B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3502_mult__left__cancel,axiom,
% 15.55/8.52      ! [C: nat,A: nat,B: nat] :
% 15.55/8.52        ( ( C != zero_zero_nat )
% 15.55/8.52       => ( ( ( times_times_nat @ C @ A )
% 15.55/8.52            = ( times_times_nat @ C @ B ) )
% 15.55/8.52          = ( A = B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3503_mult__left__cancel,axiom,
% 15.55/8.52      ! [C: int,A: int,B: int] :
% 15.55/8.52        ( ( C != zero_zero_int )
% 15.55/8.52       => ( ( ( times_times_int @ C @ A )
% 15.55/8.52            = ( times_times_int @ C @ B ) )
% 15.55/8.52          = ( A = B ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3504_no__zero__divisors,axiom,
% 15.55/8.52      ! [A: real,B: real] :
% 15.55/8.52        ( ( A != zero_zero_real )
% 15.55/8.52       => ( ( B != zero_zero_real )
% 15.55/8.52         => ( ( times_times_real @ A @ B )
% 15.55/8.52           != zero_zero_real ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3505_no__zero__divisors,axiom,
% 15.55/8.52      ! [A: rat,B: rat] :
% 15.55/8.52        ( ( A != zero_zero_rat )
% 15.55/8.52       => ( ( B != zero_zero_rat )
% 15.55/8.52         => ( ( times_times_rat @ A @ B )
% 15.55/8.52           != zero_zero_rat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3506_no__zero__divisors,axiom,
% 15.55/8.52      ! [A: nat,B: nat] :
% 15.55/8.52        ( ( A != zero_zero_nat )
% 15.55/8.52       => ( ( B != zero_zero_nat )
% 15.55/8.52         => ( ( times_times_nat @ A @ B )
% 15.55/8.52           != zero_zero_nat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3507_no__zero__divisors,axiom,
% 15.55/8.52      ! [A: int,B: int] :
% 15.55/8.52        ( ( A != zero_zero_int )
% 15.55/8.52       => ( ( B != zero_zero_int )
% 15.55/8.52         => ( ( times_times_int @ A @ B )
% 15.55/8.52           != zero_zero_int ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3508_divisors__zero,axiom,
% 15.55/8.52      ! [A: real,B: real] :
% 15.55/8.52        ( ( ( times_times_real @ A @ B )
% 15.55/8.52          = zero_zero_real )
% 15.55/8.52       => ( ( A = zero_zero_real )
% 15.55/8.52          | ( B = zero_zero_real ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3509_divisors__zero,axiom,
% 15.55/8.52      ! [A: rat,B: rat] :
% 15.55/8.52        ( ( ( times_times_rat @ A @ B )
% 15.55/8.52          = zero_zero_rat )
% 15.55/8.52       => ( ( A = zero_zero_rat )
% 15.55/8.52          | ( B = zero_zero_rat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3510_divisors__zero,axiom,
% 15.55/8.52      ! [A: nat,B: nat] :
% 15.55/8.52        ( ( ( times_times_nat @ A @ B )
% 15.55/8.52          = zero_zero_nat )
% 15.55/8.52       => ( ( A = zero_zero_nat )
% 15.55/8.52          | ( B = zero_zero_nat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3511_divisors__zero,axiom,
% 15.55/8.52      ! [A: int,B: int] :
% 15.55/8.52        ( ( ( times_times_int @ A @ B )
% 15.55/8.52          = zero_zero_int )
% 15.55/8.52       => ( ( A = zero_zero_int )
% 15.55/8.52          | ( B = zero_zero_int ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3512_mult__not__zero,axiom,
% 15.55/8.52      ! [A: real,B: real] :
% 15.55/8.52        ( ( ( times_times_real @ A @ B )
% 15.55/8.52         != zero_zero_real )
% 15.55/8.52       => ( ( A != zero_zero_real )
% 15.55/8.52          & ( B != zero_zero_real ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3513_mult__not__zero,axiom,
% 15.55/8.52      ! [A: rat,B: rat] :
% 15.55/8.52        ( ( ( times_times_rat @ A @ B )
% 15.55/8.52         != zero_zero_rat )
% 15.55/8.52       => ( ( A != zero_zero_rat )
% 15.55/8.52          & ( B != zero_zero_rat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3514_mult__not__zero,axiom,
% 15.55/8.52      ! [A: nat,B: nat] :
% 15.55/8.52        ( ( ( times_times_nat @ A @ B )
% 15.55/8.52         != zero_zero_nat )
% 15.55/8.52       => ( ( A != zero_zero_nat )
% 15.55/8.52          & ( B != zero_zero_nat ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3515_mult__not__zero,axiom,
% 15.55/8.52      ! [A: int,B: int] :
% 15.55/8.52        ( ( ( times_times_int @ A @ B )
% 15.55/8.52         != zero_zero_int )
% 15.55/8.52       => ( ( A != zero_zero_int )
% 15.55/8.52          & ( B != zero_zero_int ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3516_comm__monoid__mult__class_Omult__1,axiom,
% 15.55/8.52      ! [A: complex] :
% 15.55/8.52        ( ( times_times_complex @ one_one_complex @ A )
% 15.55/8.52        = A ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3517_comm__monoid__mult__class_Omult__1,axiom,
% 15.55/8.52      ! [A: real] :
% 15.55/8.52        ( ( times_times_real @ one_one_real @ A )
% 15.55/8.52        = A ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3518_comm__monoid__mult__class_Omult__1,axiom,
% 15.55/8.52      ! [A: rat] :
% 15.55/8.52        ( ( times_times_rat @ one_one_rat @ A )
% 15.55/8.52        = A ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3519_comm__monoid__mult__class_Omult__1,axiom,
% 15.55/8.52      ! [A: nat] :
% 15.55/8.52        ( ( times_times_nat @ one_one_nat @ A )
% 15.55/8.52        = A ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3520_comm__monoid__mult__class_Omult__1,axiom,
% 15.55/8.52      ! [A: int] :
% 15.55/8.52        ( ( times_times_int @ one_one_int @ A )
% 15.55/8.52        = A ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3521_mult_Ocomm__neutral,axiom,
% 15.55/8.52      ! [A: complex] :
% 15.55/8.52        ( ( times_times_complex @ A @ one_one_complex )
% 15.55/8.52        = A ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3522_mult_Ocomm__neutral,axiom,
% 15.55/8.52      ! [A: real] :
% 15.55/8.52        ( ( times_times_real @ A @ one_one_real )
% 15.55/8.52        = A ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3523_mult_Ocomm__neutral,axiom,
% 15.55/8.52      ! [A: rat] :
% 15.55/8.52        ( ( times_times_rat @ A @ one_one_rat )
% 15.55/8.52        = A ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3524_mult_Ocomm__neutral,axiom,
% 15.55/8.52      ! [A: nat] :
% 15.55/8.52        ( ( times_times_nat @ A @ one_one_nat )
% 15.55/8.52        = A ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3525_mult_Ocomm__neutral,axiom,
% 15.55/8.52      ! [A: int] :
% 15.55/8.52        ( ( times_times_int @ A @ one_one_int )
% 15.55/8.52        = A ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3526_inf__period_I2_J,axiom,
% 15.55/8.52      ! [P: real > $o,D5: real,Q: real > $o] :
% 15.55/8.52        ( ! [X4: real,K2: real] :
% 15.55/8.52            ( ( P @ X4 )
% 15.55/8.52            = ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K2 @ D5 ) ) ) )
% 15.55/8.52       => ( ! [X4: real,K2: real] :
% 15.55/8.52              ( ( Q @ X4 )
% 15.55/8.52              = ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K2 @ D5 ) ) ) )
% 15.55/8.52         => ! [X6: real,K4: real] :
% 15.55/8.52              ( ( ( P @ X6 )
% 15.55/8.52                | ( Q @ X6 ) )
% 15.55/8.52              = ( ( P @ ( minus_minus_real @ X6 @ ( times_times_real @ K4 @ D5 ) ) )
% 15.55/8.52                | ( Q @ ( minus_minus_real @ X6 @ ( times_times_real @ K4 @ D5 ) ) ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3527_inf__period_I2_J,axiom,
% 15.55/8.52      ! [P: rat > $o,D5: rat,Q: rat > $o] :
% 15.55/8.52        ( ! [X4: rat,K2: rat] :
% 15.55/8.52            ( ( P @ X4 )
% 15.55/8.52            = ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K2 @ D5 ) ) ) )
% 15.55/8.52       => ( ! [X4: rat,K2: rat] :
% 15.55/8.52              ( ( Q @ X4 )
% 15.55/8.52              = ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K2 @ D5 ) ) ) )
% 15.55/8.52         => ! [X6: rat,K4: rat] :
% 15.55/8.52              ( ( ( P @ X6 )
% 15.55/8.52                | ( Q @ X6 ) )
% 15.55/8.52              = ( ( P @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D5 ) ) )
% 15.55/8.52                | ( Q @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D5 ) ) ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3528_inf__period_I2_J,axiom,
% 15.55/8.52      ! [P: int > $o,D5: int,Q: int > $o] :
% 15.55/8.52        ( ! [X4: int,K2: int] :
% 15.55/8.52            ( ( P @ X4 )
% 15.55/8.52            = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D5 ) ) ) )
% 15.55/8.52       => ( ! [X4: int,K2: int] :
% 15.55/8.52              ( ( Q @ X4 )
% 15.55/8.52              = ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D5 ) ) ) )
% 15.55/8.52         => ! [X6: int,K4: int] :
% 15.55/8.52              ( ( ( P @ X6 )
% 15.55/8.52                | ( Q @ X6 ) )
% 15.55/8.52              = ( ( P @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D5 ) ) )
% 15.55/8.52                | ( Q @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D5 ) ) ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3529_inf__period_I1_J,axiom,
% 15.55/8.52      ! [P: real > $o,D5: real,Q: real > $o] :
% 15.55/8.52        ( ! [X4: real,K2: real] :
% 15.55/8.52            ( ( P @ X4 )
% 15.55/8.52            = ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K2 @ D5 ) ) ) )
% 15.55/8.52       => ( ! [X4: real,K2: real] :
% 15.55/8.52              ( ( Q @ X4 )
% 15.55/8.52              = ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K2 @ D5 ) ) ) )
% 15.55/8.52         => ! [X6: real,K4: real] :
% 15.55/8.52              ( ( ( P @ X6 )
% 15.55/8.52                & ( Q @ X6 ) )
% 15.55/8.52              = ( ( P @ ( minus_minus_real @ X6 @ ( times_times_real @ K4 @ D5 ) ) )
% 15.55/8.52                & ( Q @ ( minus_minus_real @ X6 @ ( times_times_real @ K4 @ D5 ) ) ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3530_inf__period_I1_J,axiom,
% 15.55/8.52      ! [P: rat > $o,D5: rat,Q: rat > $o] :
% 15.55/8.52        ( ! [X4: rat,K2: rat] :
% 15.55/8.52            ( ( P @ X4 )
% 15.55/8.52            = ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K2 @ D5 ) ) ) )
% 15.55/8.52       => ( ! [X4: rat,K2: rat] :
% 15.55/8.52              ( ( Q @ X4 )
% 15.55/8.52              = ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K2 @ D5 ) ) ) )
% 15.55/8.52         => ! [X6: rat,K4: rat] :
% 15.55/8.52              ( ( ( P @ X6 )
% 15.55/8.52                & ( Q @ X6 ) )
% 15.55/8.52              = ( ( P @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D5 ) ) )
% 15.55/8.52                & ( Q @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D5 ) ) ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3531_inf__period_I1_J,axiom,
% 15.55/8.52      ! [P: int > $o,D5: int,Q: int > $o] :
% 15.55/8.52        ( ! [X4: int,K2: int] :
% 15.55/8.52            ( ( P @ X4 )
% 15.55/8.52            = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D5 ) ) ) )
% 15.55/8.52       => ( ! [X4: int,K2: int] :
% 15.55/8.52              ( ( Q @ X4 )
% 15.55/8.52              = ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D5 ) ) ) )
% 15.55/8.52         => ! [X6: int,K4: int] :
% 15.55/8.52              ( ( ( P @ X6 )
% 15.55/8.52                & ( Q @ X6 ) )
% 15.55/8.52              = ( ( P @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D5 ) ) )
% 15.55/8.52                & ( Q @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D5 ) ) ) ) ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3532_power__commutes,axiom,
% 15.55/8.52      ! [A: complex,N: nat] :
% 15.55/8.52        ( ( times_times_complex @ ( power_power_complex @ A @ N ) @ A )
% 15.55/8.52        = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3533_power__commutes,axiom,
% 15.55/8.52      ! [A: real,N: nat] :
% 15.55/8.52        ( ( times_times_real @ ( power_power_real @ A @ N ) @ A )
% 15.55/8.52        = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3534_power__commutes,axiom,
% 15.55/8.52      ! [A: rat,N: nat] :
% 15.55/8.52        ( ( times_times_rat @ ( power_power_rat @ A @ N ) @ A )
% 15.55/8.52        = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3535_power__commutes,axiom,
% 15.55/8.52      ! [A: nat,N: nat] :
% 15.55/8.52        ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 15.55/8.52        = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3536_power__commutes,axiom,
% 15.55/8.52      ! [A: int,N: nat] :
% 15.55/8.52        ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 15.55/8.52        = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3537_power__mult__distrib,axiom,
% 15.55/8.52      ! [A: complex,B: complex,N: nat] :
% 15.55/8.52        ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N )
% 15.55/8.52        = ( times_times_complex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.52  thf(fact_3538_power__mult__distrib,axiom,
% 15.55/8.52      ! [A: real,B: real,N: nat] :
% 15.55/8.52        ( ( power_power_real @ ( times_times_real @ A @ B ) @ N )
% 15.55/8.52        = ( times_times_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 15.55/8.52  
% 15.55/8.53  thf(fact_3539_power__mult__distrib,axiom,
% 15.55/8.53      ! [A: rat,B: rat,N: nat] :
% 15.55/8.53        ( ( power_power_rat @ ( times_times_rat @ A @ B ) @ N )
% 15.55/8.53        = ( times_times_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3540_power__mult__distrib,axiom,
% 15.55/8.53      ! [A: nat,B: nat,N: nat] :
% 15.55/8.53        ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 15.55/8.53        = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3541_power__mult__distrib,axiom,
% 15.55/8.53      ! [A: int,B: int,N: nat] :
% 15.55/8.53        ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 15.55/8.53        = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3542_power__commuting__commutes,axiom,
% 15.55/8.53      ! [X3: complex,Y3: complex,N: nat] :
% 15.55/8.53        ( ( ( times_times_complex @ X3 @ Y3 )
% 15.55/8.53          = ( times_times_complex @ Y3 @ X3 ) )
% 15.55/8.53       => ( ( times_times_complex @ ( power_power_complex @ X3 @ N ) @ Y3 )
% 15.55/8.53          = ( times_times_complex @ Y3 @ ( power_power_complex @ X3 @ N ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3543_power__commuting__commutes,axiom,
% 15.55/8.53      ! [X3: real,Y3: real,N: nat] :
% 15.55/8.53        ( ( ( times_times_real @ X3 @ Y3 )
% 15.55/8.53          = ( times_times_real @ Y3 @ X3 ) )
% 15.55/8.53       => ( ( times_times_real @ ( power_power_real @ X3 @ N ) @ Y3 )
% 15.55/8.53          = ( times_times_real @ Y3 @ ( power_power_real @ X3 @ N ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3544_power__commuting__commutes,axiom,
% 15.55/8.53      ! [X3: rat,Y3: rat,N: nat] :
% 15.55/8.53        ( ( ( times_times_rat @ X3 @ Y3 )
% 15.55/8.53          = ( times_times_rat @ Y3 @ X3 ) )
% 15.55/8.53       => ( ( times_times_rat @ ( power_power_rat @ X3 @ N ) @ Y3 )
% 15.55/8.53          = ( times_times_rat @ Y3 @ ( power_power_rat @ X3 @ N ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3545_power__commuting__commutes,axiom,
% 15.55/8.53      ! [X3: nat,Y3: nat,N: nat] :
% 15.55/8.53        ( ( ( times_times_nat @ X3 @ Y3 )
% 15.55/8.53          = ( times_times_nat @ Y3 @ X3 ) )
% 15.55/8.53       => ( ( times_times_nat @ ( power_power_nat @ X3 @ N ) @ Y3 )
% 15.55/8.53          = ( times_times_nat @ Y3 @ ( power_power_nat @ X3 @ N ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3546_power__commuting__commutes,axiom,
% 15.55/8.53      ! [X3: int,Y3: int,N: nat] :
% 15.55/8.53        ( ( ( times_times_int @ X3 @ Y3 )
% 15.55/8.53          = ( times_times_int @ Y3 @ X3 ) )
% 15.55/8.53       => ( ( times_times_int @ ( power_power_int @ X3 @ N ) @ Y3 )
% 15.55/8.53          = ( times_times_int @ Y3 @ ( power_power_int @ X3 @ N ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3547_Suc__mult__cancel1,axiom,
% 15.55/8.53      ! [K: nat,M: nat,N: nat] :
% 15.55/8.53        ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 15.55/8.53          = ( times_times_nat @ ( suc @ K ) @ N ) )
% 15.55/8.53        = ( M = N ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3548_mult__0,axiom,
% 15.55/8.53      ! [N: nat] :
% 15.55/8.53        ( ( times_times_nat @ zero_zero_nat @ N )
% 15.55/8.53        = zero_zero_nat ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3549_nat__mult__eq__cancel__disj,axiom,
% 15.55/8.53      ! [K: nat,M: nat,N: nat] :
% 15.55/8.53        ( ( ( times_times_nat @ K @ M )
% 15.55/8.53          = ( times_times_nat @ K @ N ) )
% 15.55/8.53        = ( ( K = zero_zero_nat )
% 15.55/8.53          | ( M = N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3550_power__mult,axiom,
% 15.55/8.53      ! [A: nat,M: nat,N: nat] :
% 15.55/8.53        ( ( power_power_nat @ A @ ( times_times_nat @ M @ N ) )
% 15.55/8.53        = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3551_power__mult,axiom,
% 15.55/8.53      ! [A: int,M: nat,N: nat] :
% 15.55/8.53        ( ( power_power_int @ A @ ( times_times_nat @ M @ N ) )
% 15.55/8.53        = ( power_power_int @ ( power_power_int @ A @ M ) @ N ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3552_power__mult,axiom,
% 15.55/8.53      ! [A: real,M: nat,N: nat] :
% 15.55/8.53        ( ( power_power_real @ A @ ( times_times_nat @ M @ N ) )
% 15.55/8.53        = ( power_power_real @ ( power_power_real @ A @ M ) @ N ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3553_power__mult,axiom,
% 15.55/8.53      ! [A: complex,M: nat,N: nat] :
% 15.55/8.53        ( ( power_power_complex @ A @ ( times_times_nat @ M @ N ) )
% 15.55/8.53        = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3554_mult__of__nat__commute,axiom,
% 15.55/8.53      ! [X3: nat,Y3: complex] :
% 15.55/8.53        ( ( times_times_complex @ ( semiri8010041392384452111omplex @ X3 ) @ Y3 )
% 15.55/8.53        = ( times_times_complex @ Y3 @ ( semiri8010041392384452111omplex @ X3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3555_mult__of__nat__commute,axiom,
% 15.55/8.53      ! [X3: nat,Y3: real] :
% 15.55/8.53        ( ( times_times_real @ ( semiri5074537144036343181t_real @ X3 ) @ Y3 )
% 15.55/8.53        = ( times_times_real @ Y3 @ ( semiri5074537144036343181t_real @ X3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3556_mult__of__nat__commute,axiom,
% 15.55/8.53      ! [X3: nat,Y3: rat] :
% 15.55/8.53        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X3 ) @ Y3 )
% 15.55/8.53        = ( times_times_rat @ Y3 @ ( semiri681578069525770553at_rat @ X3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3557_mult__of__nat__commute,axiom,
% 15.55/8.53      ! [X3: nat,Y3: nat] :
% 15.55/8.53        ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ Y3 )
% 15.55/8.53        = ( times_times_nat @ Y3 @ ( semiri1316708129612266289at_nat @ X3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3558_mult__of__nat__commute,axiom,
% 15.55/8.53      ! [X3: nat,Y3: int] :
% 15.55/8.53        ( ( times_times_int @ ( semiri1314217659103216013at_int @ X3 ) @ Y3 )
% 15.55/8.53        = ( times_times_int @ Y3 @ ( semiri1314217659103216013at_int @ X3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3559_add__mult__distrib2,axiom,
% 15.55/8.53      ! [K: nat,M: nat,N: nat] :
% 15.55/8.53        ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 15.55/8.53        = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3560_add__mult__distrib,axiom,
% 15.55/8.53      ! [M: nat,N: nat,K: nat] :
% 15.55/8.53        ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 15.55/8.53        = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3561_left__add__mult__distrib,axiom,
% 15.55/8.53      ! [I: nat,U: nat,J: nat,K: nat] :
% 15.55/8.53        ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 15.55/8.53        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3562_mult__le__mono2,axiom,
% 15.55/8.53      ! [I: nat,J: nat,K: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ I @ J )
% 15.55/8.53       => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3563_mult__le__mono1,axiom,
% 15.55/8.53      ! [I: nat,J: nat,K: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ I @ J )
% 15.55/8.53       => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3564_mult__le__mono,axiom,
% 15.55/8.53      ! [I: nat,J: nat,K: nat,L: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ I @ J )
% 15.55/8.53       => ( ( ord_less_eq_nat @ K @ L )
% 15.55/8.53         => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3565_le__square,axiom,
% 15.55/8.53      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3566_le__cube,axiom,
% 15.55/8.53      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3567_nat__mult__1__right,axiom,
% 15.55/8.53      ! [N: nat] :
% 15.55/8.53        ( ( times_times_nat @ N @ one_one_nat )
% 15.55/8.53        = N ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3568_nat__mult__1,axiom,
% 15.55/8.53      ! [N: nat] :
% 15.55/8.53        ( ( times_times_nat @ one_one_nat @ N )
% 15.55/8.53        = N ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3569_diff__mult__distrib2,axiom,
% 15.55/8.53      ! [K: nat,M: nat,N: nat] :
% 15.55/8.53        ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 15.55/8.53        = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3570_diff__mult__distrib,axiom,
% 15.55/8.53      ! [M: nat,N: nat,K: nat] :
% 15.55/8.53        ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 15.55/8.53        = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3571_mult__of__int__commute,axiom,
% 15.55/8.53      ! [X3: int,Y3: complex] :
% 15.55/8.53        ( ( times_times_complex @ ( ring_17405671764205052669omplex @ X3 ) @ Y3 )
% 15.55/8.53        = ( times_times_complex @ Y3 @ ( ring_17405671764205052669omplex @ X3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3572_mult__of__int__commute,axiom,
% 15.55/8.53      ! [X3: int,Y3: real] :
% 15.55/8.53        ( ( times_times_real @ ( ring_1_of_int_real @ X3 ) @ Y3 )
% 15.55/8.53        = ( times_times_real @ Y3 @ ( ring_1_of_int_real @ X3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3573_mult__of__int__commute,axiom,
% 15.55/8.53      ! [X3: int,Y3: rat] :
% 15.55/8.53        ( ( times_times_rat @ ( ring_1_of_int_rat @ X3 ) @ Y3 )
% 15.55/8.53        = ( times_times_rat @ Y3 @ ( ring_1_of_int_rat @ X3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3574_mult__of__int__commute,axiom,
% 15.55/8.53      ! [X3: int,Y3: int] :
% 15.55/8.53        ( ( times_times_int @ ( ring_1_of_int_int @ X3 ) @ Y3 )
% 15.55/8.53        = ( times_times_int @ Y3 @ ( ring_1_of_int_int @ X3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3575_le__mult__nat__floor,axiom,
% 15.55/8.53      ! [A: rat,B: rat] : ( ord_less_eq_nat @ ( times_times_nat @ ( nat2 @ ( archim3151403230148437115or_rat @ A ) ) @ ( nat2 @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( nat2 @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3576_le__mult__nat__floor,axiom,
% 15.55/8.53      ! [A: real,B: real] : ( ord_less_eq_nat @ ( times_times_nat @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) @ ( nat2 @ ( archim6058952711729229775r_real @ B ) ) ) @ ( nat2 @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3577_le__mult__floor,axiom,
% 15.55/8.53      ! [A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 15.55/8.53         => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3578_le__mult__floor,axiom,
% 15.55/8.53      ! [A: real,B: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.53       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 15.55/8.53         => ( ord_less_eq_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3579_mult__ceiling__le,axiom,
% 15.55/8.53      ! [A: real,B: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.53       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 15.55/8.53         => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3580_mult__ceiling__le,axiom,
% 15.55/8.53      ! [A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 15.55/8.53         => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3581_mult__mono,axiom,
% 15.55/8.53      ! [A: real,B: real,C: real,D3: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_real @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 15.55/8.53           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 15.55/8.53             => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3582_mult__mono,axiom,
% 15.55/8.53      ! [A: rat,B: rat,C: rat,D3: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_rat @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 15.55/8.53           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 15.55/8.53             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3583_mult__mono,axiom,
% 15.55/8.53      ! [A: nat,B: nat,C: nat,D3: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_nat @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 15.55/8.53           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 15.55/8.53             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3584_mult__mono,axiom,
% 15.55/8.53      ! [A: int,B: int,C: int,D3: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_int @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 15.55/8.53           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 15.55/8.53             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3585_mult__mono_H,axiom,
% 15.55/8.53      ! [A: real,B: real,C: real,D3: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_real @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.53           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 15.55/8.53             => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3586_mult__mono_H,axiom,
% 15.55/8.53      ! [A: rat,B: rat,C: rat,D3: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_rat @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.53           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 15.55/8.53             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3587_mult__mono_H,axiom,
% 15.55/8.53      ! [A: nat,B: nat,C: nat,D3: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_nat @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.55/8.53           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 15.55/8.53             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3588_mult__mono_H,axiom,
% 15.55/8.53      ! [A: int,B: int,C: int,D3: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_int @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.53           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 15.55/8.53             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3589_zero__le__square,axiom,
% 15.55/8.53      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3590_zero__le__square,axiom,
% 15.55/8.53      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3591_zero__le__square,axiom,
% 15.55/8.53      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3592_split__mult__pos__le,axiom,
% 15.55/8.53      ! [A: real,B: real] :
% 15.55/8.53        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.53            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 15.55/8.53          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 15.55/8.53            & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 15.55/8.53       => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3593_split__mult__pos__le,axiom,
% 15.55/8.53      ! [A: rat,B: rat] :
% 15.55/8.53        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.53            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 15.55/8.53          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 15.55/8.53            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 15.55/8.53       => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3594_split__mult__pos__le,axiom,
% 15.55/8.53      ! [A: int,B: int] :
% 15.55/8.53        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.53            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 15.55/8.53          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 15.55/8.53            & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 15.55/8.53       => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3595_mult__left__mono__neg,axiom,
% 15.55/8.53      ! [B: real,A: real,C: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ B @ A )
% 15.55/8.53       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 15.55/8.53         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3596_mult__left__mono__neg,axiom,
% 15.55/8.53      ! [B: rat,A: rat,C: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ B @ A )
% 15.55/8.53       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 15.55/8.53         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3597_mult__left__mono__neg,axiom,
% 15.55/8.53      ! [B: int,A: int,C: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ B @ A )
% 15.55/8.53       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 15.55/8.53         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3598_mult__nonpos__nonpos,axiom,
% 15.55/8.53      ! [A: real,B: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 15.55/8.53       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 15.55/8.53         => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3599_mult__nonpos__nonpos,axiom,
% 15.55/8.53      ! [A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 15.55/8.53       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 15.55/8.53         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3600_mult__nonpos__nonpos,axiom,
% 15.55/8.53      ! [A: int,B: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 15.55/8.53       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 15.55/8.53         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3601_mult__left__mono,axiom,
% 15.55/8.53      ! [A: real,B: real,C: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 15.55/8.53         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3602_mult__left__mono,axiom,
% 15.55/8.53      ! [A: rat,B: rat,C: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 15.55/8.53         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3603_mult__left__mono,axiom,
% 15.55/8.53      ! [A: nat,B: nat,C: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 15.55/8.53         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3604_mult__left__mono,axiom,
% 15.55/8.53      ! [A: int,B: int,C: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 15.55/8.53         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3605_mult__right__mono__neg,axiom,
% 15.55/8.53      ! [B: real,A: real,C: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ B @ A )
% 15.55/8.53       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 15.55/8.53         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3606_mult__right__mono__neg,axiom,
% 15.55/8.53      ! [B: rat,A: rat,C: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ B @ A )
% 15.55/8.53       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 15.55/8.53         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3607_mult__right__mono__neg,axiom,
% 15.55/8.53      ! [B: int,A: int,C: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ B @ A )
% 15.55/8.53       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 15.55/8.53         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3608_mult__right__mono,axiom,
% 15.55/8.53      ! [A: real,B: real,C: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 15.55/8.53         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3609_mult__right__mono,axiom,
% 15.55/8.53      ! [A: rat,B: rat,C: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 15.55/8.53         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3610_mult__right__mono,axiom,
% 15.55/8.53      ! [A: nat,B: nat,C: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 15.55/8.53         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3611_mult__right__mono,axiom,
% 15.55/8.53      ! [A: int,B: int,C: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 15.55/8.53         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3612_mult__le__0__iff,axiom,
% 15.55/8.53      ! [A: real,B: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 15.55/8.53        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.53            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 15.55/8.53          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 15.55/8.53            & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3613_mult__le__0__iff,axiom,
% 15.55/8.53      ! [A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 15.55/8.53        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.53            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 15.55/8.53          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 15.55/8.53            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3614_mult__le__0__iff,axiom,
% 15.55/8.53      ! [A: int,B: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 15.55/8.53        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.53            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 15.55/8.53          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 15.55/8.53            & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3615_split__mult__neg__le,axiom,
% 15.55/8.53      ! [A: real,B: real] :
% 15.55/8.53        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.53            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 15.55/8.53          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 15.55/8.53            & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 15.55/8.53       => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3616_split__mult__neg__le,axiom,
% 15.55/8.53      ! [A: rat,B: rat] :
% 15.55/8.53        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.53            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 15.55/8.53          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 15.55/8.53            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 15.55/8.53       => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3617_split__mult__neg__le,axiom,
% 15.55/8.53      ! [A: nat,B: nat] :
% 15.55/8.53        ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.55/8.53            & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 15.55/8.53          | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 15.55/8.53            & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 15.55/8.53       => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3618_split__mult__neg__le,axiom,
% 15.55/8.53      ! [A: int,B: int] :
% 15.55/8.53        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.53            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 15.55/8.53          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 15.55/8.53            & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 15.55/8.53       => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3619_mult__nonneg__nonneg,axiom,
% 15.55/8.53      ! [A: real,B: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.53       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 15.55/8.53         => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3620_mult__nonneg__nonneg,axiom,
% 15.55/8.53      ! [A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 15.55/8.53         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3621_mult__nonneg__nonneg,axiom,
% 15.55/8.53      ! [A: nat,B: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.55/8.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 15.55/8.53         => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3622_mult__nonneg__nonneg,axiom,
% 15.55/8.53      ! [A: int,B: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.53       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 15.55/8.53         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3623_mult__nonneg__nonpos,axiom,
% 15.55/8.53      ! [A: real,B: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.53       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 15.55/8.53         => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3624_mult__nonneg__nonpos,axiom,
% 15.55/8.53      ! [A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.53       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 15.55/8.53         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3625_mult__nonneg__nonpos,axiom,
% 15.55/8.53      ! [A: nat,B: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.55/8.53       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 15.55/8.53         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3626_mult__nonneg__nonpos,axiom,
% 15.55/8.53      ! [A: int,B: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.53       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 15.55/8.53         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3627_mult__nonpos__nonneg,axiom,
% 15.55/8.53      ! [A: real,B: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 15.55/8.53       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 15.55/8.53         => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3628_mult__nonpos__nonneg,axiom,
% 15.55/8.53      ! [A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 15.55/8.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 15.55/8.53         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3629_mult__nonpos__nonneg,axiom,
% 15.55/8.53      ! [A: nat,B: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 15.55/8.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 15.55/8.53         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3630_mult__nonpos__nonneg,axiom,
% 15.55/8.53      ! [A: int,B: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 15.55/8.53       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 15.55/8.53         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3631_mult__nonneg__nonpos2,axiom,
% 15.55/8.53      ! [A: real,B: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.53       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 15.55/8.53         => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3632_mult__nonneg__nonpos2,axiom,
% 15.55/8.53      ! [A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.53       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 15.55/8.53         => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3633_mult__nonneg__nonpos2,axiom,
% 15.55/8.53      ! [A: nat,B: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.55/8.53       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 15.55/8.53         => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3634_mult__nonneg__nonpos2,axiom,
% 15.55/8.53      ! [A: int,B: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.53       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 15.55/8.53         => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3635_zero__le__mult__iff,axiom,
% 15.55/8.53      ! [A: real,B: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 15.55/8.53        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.53            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 15.55/8.53          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 15.55/8.53            & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3636_zero__le__mult__iff,axiom,
% 15.55/8.53      ! [A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 15.55/8.53        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.53            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 15.55/8.53          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 15.55/8.53            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3637_zero__le__mult__iff,axiom,
% 15.55/8.53      ! [A: int,B: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 15.55/8.53        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.53            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 15.55/8.53          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 15.55/8.53            & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3638_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 15.55/8.53      ! [A: real,B: real,C: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 15.55/8.53         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3639_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 15.55/8.53      ! [A: rat,B: rat,C: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 15.55/8.53         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3640_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 15.55/8.53      ! [A: nat,B: nat,C: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 15.55/8.53         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3641_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 15.55/8.53      ! [A: int,B: int,C: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 15.55/8.53         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3642_mult__neg__neg,axiom,
% 15.55/8.53      ! [A: real,B: real] :
% 15.55/8.53        ( ( ord_less_real @ A @ zero_zero_real )
% 15.55/8.53       => ( ( ord_less_real @ B @ zero_zero_real )
% 15.55/8.53         => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3643_mult__neg__neg,axiom,
% 15.55/8.53      ! [A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_rat @ A @ zero_zero_rat )
% 15.55/8.53       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 15.55/8.53         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3644_mult__neg__neg,axiom,
% 15.55/8.53      ! [A: int,B: int] :
% 15.55/8.53        ( ( ord_less_int @ A @ zero_zero_int )
% 15.55/8.53       => ( ( ord_less_int @ B @ zero_zero_int )
% 15.55/8.53         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3645_not__square__less__zero,axiom,
% 15.55/8.53      ! [A: real] :
% 15.55/8.53        ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3646_not__square__less__zero,axiom,
% 15.55/8.53      ! [A: rat] :
% 15.55/8.53        ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3647_not__square__less__zero,axiom,
% 15.55/8.53      ! [A: int] :
% 15.55/8.53        ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3648_mult__less__0__iff,axiom,
% 15.55/8.53      ! [A: real,B: real] :
% 15.55/8.53        ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 15.55/8.53        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.53            & ( ord_less_real @ B @ zero_zero_real ) )
% 15.55/8.53          | ( ( ord_less_real @ A @ zero_zero_real )
% 15.55/8.53            & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3649_mult__less__0__iff,axiom,
% 15.55/8.53      ! [A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 15.55/8.53        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.53            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 15.55/8.53          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 15.55/8.53            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3650_mult__less__0__iff,axiom,
% 15.55/8.53      ! [A: int,B: int] :
% 15.55/8.53        ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 15.55/8.53        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 15.55/8.53            & ( ord_less_int @ B @ zero_zero_int ) )
% 15.55/8.53          | ( ( ord_less_int @ A @ zero_zero_int )
% 15.55/8.53            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3651_mult__neg__pos,axiom,
% 15.55/8.53      ! [A: real,B: real] :
% 15.55/8.53        ( ( ord_less_real @ A @ zero_zero_real )
% 15.55/8.53       => ( ( ord_less_real @ zero_zero_real @ B )
% 15.55/8.53         => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3652_mult__neg__pos,axiom,
% 15.55/8.53      ! [A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_rat @ A @ zero_zero_rat )
% 15.55/8.53       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 15.55/8.53         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3653_mult__neg__pos,axiom,
% 15.55/8.53      ! [A: nat,B: nat] :
% 15.55/8.53        ( ( ord_less_nat @ A @ zero_zero_nat )
% 15.55/8.53       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 15.55/8.53         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3654_mult__neg__pos,axiom,
% 15.55/8.53      ! [A: int,B: int] :
% 15.55/8.53        ( ( ord_less_int @ A @ zero_zero_int )
% 15.55/8.53       => ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.53         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3655_mult__pos__neg,axiom,
% 15.55/8.53      ! [A: real,B: real] :
% 15.55/8.53        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.53       => ( ( ord_less_real @ B @ zero_zero_real )
% 15.55/8.53         => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3656_mult__pos__neg,axiom,
% 15.55/8.53      ! [A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.53       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 15.55/8.53         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3657_mult__pos__neg,axiom,
% 15.55/8.53      ! [A: nat,B: nat] :
% 15.55/8.53        ( ( ord_less_nat @ zero_zero_nat @ A )
% 15.55/8.53       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 15.55/8.53         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3658_mult__pos__neg,axiom,
% 15.55/8.53      ! [A: int,B: int] :
% 15.55/8.53        ( ( ord_less_int @ zero_zero_int @ A )
% 15.55/8.53       => ( ( ord_less_int @ B @ zero_zero_int )
% 15.55/8.53         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3659_mult__pos__pos,axiom,
% 15.55/8.53      ! [A: real,B: real] :
% 15.55/8.53        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.53       => ( ( ord_less_real @ zero_zero_real @ B )
% 15.55/8.53         => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3660_mult__pos__pos,axiom,
% 15.55/8.53      ! [A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.53       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 15.55/8.53         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3661_mult__pos__pos,axiom,
% 15.55/8.53      ! [A: nat,B: nat] :
% 15.55/8.53        ( ( ord_less_nat @ zero_zero_nat @ A )
% 15.55/8.53       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 15.55/8.53         => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3662_mult__pos__pos,axiom,
% 15.55/8.53      ! [A: int,B: int] :
% 15.55/8.53        ( ( ord_less_int @ zero_zero_int @ A )
% 15.55/8.53       => ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.53         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3663_mult__pos__neg2,axiom,
% 15.55/8.53      ! [A: real,B: real] :
% 15.55/8.53        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.53       => ( ( ord_less_real @ B @ zero_zero_real )
% 15.55/8.53         => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3664_mult__pos__neg2,axiom,
% 15.55/8.53      ! [A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.53       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 15.55/8.53         => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3665_mult__pos__neg2,axiom,
% 15.55/8.53      ! [A: nat,B: nat] :
% 15.55/8.53        ( ( ord_less_nat @ zero_zero_nat @ A )
% 15.55/8.53       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 15.55/8.53         => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3666_mult__pos__neg2,axiom,
% 15.55/8.53      ! [A: int,B: int] :
% 15.55/8.53        ( ( ord_less_int @ zero_zero_int @ A )
% 15.55/8.53       => ( ( ord_less_int @ B @ zero_zero_int )
% 15.55/8.53         => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3667_zero__less__mult__iff,axiom,
% 15.55/8.53      ! [A: real,B: real] :
% 15.55/8.53        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 15.55/8.53        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.53            & ( ord_less_real @ zero_zero_real @ B ) )
% 15.55/8.53          | ( ( ord_less_real @ A @ zero_zero_real )
% 15.55/8.53            & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3668_zero__less__mult__iff,axiom,
% 15.55/8.53      ! [A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 15.55/8.53        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.53            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 15.55/8.53          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 15.55/8.53            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3669_zero__less__mult__iff,axiom,
% 15.55/8.53      ! [A: int,B: int] :
% 15.55/8.53        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 15.55/8.53        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 15.55/8.53            & ( ord_less_int @ zero_zero_int @ B ) )
% 15.55/8.53          | ( ( ord_less_int @ A @ zero_zero_int )
% 15.55/8.53            & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3670_zero__less__mult__pos,axiom,
% 15.55/8.53      ! [A: real,B: real] :
% 15.55/8.53        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 15.55/8.53       => ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.53         => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3671_zero__less__mult__pos,axiom,
% 15.55/8.53      ! [A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 15.55/8.53       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.53         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3672_zero__less__mult__pos,axiom,
% 15.55/8.53      ! [A: nat,B: nat] :
% 15.55/8.53        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 15.55/8.53       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 15.55/8.53         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3673_zero__less__mult__pos,axiom,
% 15.55/8.53      ! [A: int,B: int] :
% 15.55/8.53        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 15.55/8.53       => ( ( ord_less_int @ zero_zero_int @ A )
% 15.55/8.53         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3674_zero__less__mult__pos2,axiom,
% 15.55/8.53      ! [B: real,A: real] :
% 15.55/8.53        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 15.55/8.53       => ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.53         => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3675_zero__less__mult__pos2,axiom,
% 15.55/8.53      ! [B: rat,A: rat] :
% 15.55/8.53        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 15.55/8.53       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.53         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3676_zero__less__mult__pos2,axiom,
% 15.55/8.53      ! [B: nat,A: nat] :
% 15.55/8.53        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 15.55/8.53       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 15.55/8.53         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3677_zero__less__mult__pos2,axiom,
% 15.55/8.53      ! [B: int,A: int] :
% 15.55/8.53        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 15.55/8.53       => ( ( ord_less_int @ zero_zero_int @ A )
% 15.55/8.53         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3678_mult__less__cancel__left__neg,axiom,
% 15.55/8.53      ! [C: real,A: real,B: real] :
% 15.55/8.53        ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.53       => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 15.55/8.53          = ( ord_less_real @ B @ A ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3679_mult__less__cancel__left__neg,axiom,
% 15.55/8.53      ! [C: rat,A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.53       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 15.55/8.53          = ( ord_less_rat @ B @ A ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3680_mult__less__cancel__left__neg,axiom,
% 15.55/8.53      ! [C: int,A: int,B: int] :
% 15.55/8.53        ( ( ord_less_int @ C @ zero_zero_int )
% 15.55/8.53       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 15.55/8.53          = ( ord_less_int @ B @ A ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3681_mult__less__cancel__left__pos,axiom,
% 15.55/8.53      ! [C: real,A: real,B: real] :
% 15.55/8.53        ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53       => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 15.55/8.53          = ( ord_less_real @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3682_mult__less__cancel__left__pos,axiom,
% 15.55/8.53      ! [C: rat,A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 15.55/8.53          = ( ord_less_rat @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3683_mult__less__cancel__left__pos,axiom,
% 15.55/8.53      ! [C: int,A: int,B: int] :
% 15.55/8.53        ( ( ord_less_int @ zero_zero_int @ C )
% 15.55/8.53       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 15.55/8.53          = ( ord_less_int @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3684_mult__strict__left__mono__neg,axiom,
% 15.55/8.53      ! [B: real,A: real,C: real] :
% 15.55/8.53        ( ( ord_less_real @ B @ A )
% 15.55/8.53       => ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.53         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3685_mult__strict__left__mono__neg,axiom,
% 15.55/8.53      ! [B: rat,A: rat,C: rat] :
% 15.55/8.53        ( ( ord_less_rat @ B @ A )
% 15.55/8.53       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.53         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3686_mult__strict__left__mono__neg,axiom,
% 15.55/8.53      ! [B: int,A: int,C: int] :
% 15.55/8.53        ( ( ord_less_int @ B @ A )
% 15.55/8.53       => ( ( ord_less_int @ C @ zero_zero_int )
% 15.55/8.53         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3687_mult__strict__left__mono,axiom,
% 15.55/8.53      ! [A: real,B: real,C: real] :
% 15.55/8.53        ( ( ord_less_real @ A @ B )
% 15.55/8.53       => ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3688_mult__strict__left__mono,axiom,
% 15.55/8.53      ! [A: rat,B: rat,C: rat] :
% 15.55/8.53        ( ( ord_less_rat @ A @ B )
% 15.55/8.53       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3689_mult__strict__left__mono,axiom,
% 15.55/8.53      ! [A: nat,B: nat,C: nat] :
% 15.55/8.53        ( ( ord_less_nat @ A @ B )
% 15.55/8.53       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 15.55/8.53         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3690_mult__strict__left__mono,axiom,
% 15.55/8.53      ! [A: int,B: int,C: int] :
% 15.55/8.53        ( ( ord_less_int @ A @ B )
% 15.55/8.53       => ( ( ord_less_int @ zero_zero_int @ C )
% 15.55/8.53         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3691_mult__less__cancel__left__disj,axiom,
% 15.55/8.53      ! [C: real,A: real,B: real] :
% 15.55/8.53        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 15.55/8.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53            & ( ord_less_real @ A @ B ) )
% 15.55/8.53          | ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.53            & ( ord_less_real @ B @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3692_mult__less__cancel__left__disj,axiom,
% 15.55/8.53      ! [C: rat,A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 15.55/8.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53            & ( ord_less_rat @ A @ B ) )
% 15.55/8.53          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.53            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3693_mult__less__cancel__left__disj,axiom,
% 15.55/8.53      ! [C: int,A: int,B: int] :
% 15.55/8.53        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 15.55/8.53        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 15.55/8.53            & ( ord_less_int @ A @ B ) )
% 15.55/8.53          | ( ( ord_less_int @ C @ zero_zero_int )
% 15.55/8.53            & ( ord_less_int @ B @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3694_mult__strict__right__mono__neg,axiom,
% 15.55/8.53      ! [B: real,A: real,C: real] :
% 15.55/8.53        ( ( ord_less_real @ B @ A )
% 15.55/8.53       => ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.53         => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3695_mult__strict__right__mono__neg,axiom,
% 15.55/8.53      ! [B: rat,A: rat,C: rat] :
% 15.55/8.53        ( ( ord_less_rat @ B @ A )
% 15.55/8.53       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.53         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3696_mult__strict__right__mono__neg,axiom,
% 15.55/8.53      ! [B: int,A: int,C: int] :
% 15.55/8.53        ( ( ord_less_int @ B @ A )
% 15.55/8.53       => ( ( ord_less_int @ C @ zero_zero_int )
% 15.55/8.53         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3697_mult__strict__right__mono,axiom,
% 15.55/8.53      ! [A: real,B: real,C: real] :
% 15.55/8.53        ( ( ord_less_real @ A @ B )
% 15.55/8.53       => ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53         => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3698_mult__strict__right__mono,axiom,
% 15.55/8.53      ! [A: rat,B: rat,C: rat] :
% 15.55/8.53        ( ( ord_less_rat @ A @ B )
% 15.55/8.53       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3699_mult__strict__right__mono,axiom,
% 15.55/8.53      ! [A: nat,B: nat,C: nat] :
% 15.55/8.53        ( ( ord_less_nat @ A @ B )
% 15.55/8.53       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 15.55/8.53         => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3700_mult__strict__right__mono,axiom,
% 15.55/8.53      ! [A: int,B: int,C: int] :
% 15.55/8.53        ( ( ord_less_int @ A @ B )
% 15.55/8.53       => ( ( ord_less_int @ zero_zero_int @ C )
% 15.55/8.53         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3701_mult__less__cancel__right__disj,axiom,
% 15.55/8.53      ! [A: real,C: real,B: real] :
% 15.55/8.53        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 15.55/8.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53            & ( ord_less_real @ A @ B ) )
% 15.55/8.53          | ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.53            & ( ord_less_real @ B @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3702_mult__less__cancel__right__disj,axiom,
% 15.55/8.53      ! [A: rat,C: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 15.55/8.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53            & ( ord_less_rat @ A @ B ) )
% 15.55/8.53          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.53            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3703_mult__less__cancel__right__disj,axiom,
% 15.55/8.53      ! [A: int,C: int,B: int] :
% 15.55/8.53        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 15.55/8.53        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 15.55/8.53            & ( ord_less_int @ A @ B ) )
% 15.55/8.53          | ( ( ord_less_int @ C @ zero_zero_int )
% 15.55/8.53            & ( ord_less_int @ B @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3704_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 15.55/8.53      ! [A: real,B: real,C: real] :
% 15.55/8.53        ( ( ord_less_real @ A @ B )
% 15.55/8.53       => ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3705_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 15.55/8.53      ! [A: rat,B: rat,C: rat] :
% 15.55/8.53        ( ( ord_less_rat @ A @ B )
% 15.55/8.53       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3706_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 15.55/8.53      ! [A: nat,B: nat,C: nat] :
% 15.55/8.53        ( ( ord_less_nat @ A @ B )
% 15.55/8.53       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 15.55/8.53         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3707_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 15.55/8.53      ! [A: int,B: int,C: int] :
% 15.55/8.53        ( ( ord_less_int @ A @ B )
% 15.55/8.53       => ( ( ord_less_int @ zero_zero_int @ C )
% 15.55/8.53         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3708_less__1__mult,axiom,
% 15.55/8.53      ! [M: real,N: real] :
% 15.55/8.53        ( ( ord_less_real @ one_one_real @ M )
% 15.55/8.53       => ( ( ord_less_real @ one_one_real @ N )
% 15.55/8.53         => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3709_less__1__mult,axiom,
% 15.55/8.53      ! [M: rat,N: rat] :
% 15.55/8.53        ( ( ord_less_rat @ one_one_rat @ M )
% 15.55/8.53       => ( ( ord_less_rat @ one_one_rat @ N )
% 15.55/8.53         => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3710_less__1__mult,axiom,
% 15.55/8.53      ! [M: nat,N: nat] :
% 15.55/8.53        ( ( ord_less_nat @ one_one_nat @ M )
% 15.55/8.53       => ( ( ord_less_nat @ one_one_nat @ N )
% 15.55/8.53         => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3711_less__1__mult,axiom,
% 15.55/8.53      ! [M: int,N: int] :
% 15.55/8.53        ( ( ord_less_int @ one_one_int @ M )
% 15.55/8.53       => ( ( ord_less_int @ one_one_int @ N )
% 15.55/8.53         => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3712_nonzero__eq__divide__eq,axiom,
% 15.55/8.53      ! [C: complex,A: complex,B: complex] :
% 15.55/8.53        ( ( C != zero_zero_complex )
% 15.55/8.53       => ( ( A
% 15.55/8.53            = ( divide1717551699836669952omplex @ B @ C ) )
% 15.55/8.53          = ( ( times_times_complex @ A @ C )
% 15.55/8.53            = B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3713_nonzero__eq__divide__eq,axiom,
% 15.55/8.53      ! [C: real,A: real,B: real] :
% 15.55/8.53        ( ( C != zero_zero_real )
% 15.55/8.53       => ( ( A
% 15.55/8.53            = ( divide_divide_real @ B @ C ) )
% 15.55/8.53          = ( ( times_times_real @ A @ C )
% 15.55/8.53            = B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3714_nonzero__eq__divide__eq,axiom,
% 15.55/8.53      ! [C: rat,A: rat,B: rat] :
% 15.55/8.53        ( ( C != zero_zero_rat )
% 15.55/8.53       => ( ( A
% 15.55/8.53            = ( divide_divide_rat @ B @ C ) )
% 15.55/8.53          = ( ( times_times_rat @ A @ C )
% 15.55/8.53            = B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3715_nonzero__divide__eq__eq,axiom,
% 15.55/8.53      ! [C: complex,B: complex,A: complex] :
% 15.55/8.53        ( ( C != zero_zero_complex )
% 15.55/8.53       => ( ( ( divide1717551699836669952omplex @ B @ C )
% 15.55/8.53            = A )
% 15.55/8.53          = ( B
% 15.55/8.53            = ( times_times_complex @ A @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3716_nonzero__divide__eq__eq,axiom,
% 15.55/8.53      ! [C: real,B: real,A: real] :
% 15.55/8.53        ( ( C != zero_zero_real )
% 15.55/8.53       => ( ( ( divide_divide_real @ B @ C )
% 15.55/8.53            = A )
% 15.55/8.53          = ( B
% 15.55/8.53            = ( times_times_real @ A @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3717_nonzero__divide__eq__eq,axiom,
% 15.55/8.53      ! [C: rat,B: rat,A: rat] :
% 15.55/8.53        ( ( C != zero_zero_rat )
% 15.55/8.53       => ( ( ( divide_divide_rat @ B @ C )
% 15.55/8.53            = A )
% 15.55/8.53          = ( B
% 15.55/8.53            = ( times_times_rat @ A @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3718_eq__divide__imp,axiom,
% 15.55/8.53      ! [C: complex,A: complex,B: complex] :
% 15.55/8.53        ( ( C != zero_zero_complex )
% 15.55/8.53       => ( ( ( times_times_complex @ A @ C )
% 15.55/8.53            = B )
% 15.55/8.53         => ( A
% 15.55/8.53            = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3719_eq__divide__imp,axiom,
% 15.55/8.53      ! [C: real,A: real,B: real] :
% 15.55/8.53        ( ( C != zero_zero_real )
% 15.55/8.53       => ( ( ( times_times_real @ A @ C )
% 15.55/8.53            = B )
% 15.55/8.53         => ( A
% 15.55/8.53            = ( divide_divide_real @ B @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3720_eq__divide__imp,axiom,
% 15.55/8.53      ! [C: rat,A: rat,B: rat] :
% 15.55/8.53        ( ( C != zero_zero_rat )
% 15.55/8.53       => ( ( ( times_times_rat @ A @ C )
% 15.55/8.53            = B )
% 15.55/8.53         => ( A
% 15.55/8.53            = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3721_divide__eq__imp,axiom,
% 15.55/8.53      ! [C: complex,B: complex,A: complex] :
% 15.55/8.53        ( ( C != zero_zero_complex )
% 15.55/8.53       => ( ( B
% 15.55/8.53            = ( times_times_complex @ A @ C ) )
% 15.55/8.53         => ( ( divide1717551699836669952omplex @ B @ C )
% 15.55/8.53            = A ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3722_divide__eq__imp,axiom,
% 15.55/8.53      ! [C: real,B: real,A: real] :
% 15.55/8.53        ( ( C != zero_zero_real )
% 15.55/8.53       => ( ( B
% 15.55/8.53            = ( times_times_real @ A @ C ) )
% 15.55/8.53         => ( ( divide_divide_real @ B @ C )
% 15.55/8.53            = A ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3723_divide__eq__imp,axiom,
% 15.55/8.53      ! [C: rat,B: rat,A: rat] :
% 15.55/8.53        ( ( C != zero_zero_rat )
% 15.55/8.53       => ( ( B
% 15.55/8.53            = ( times_times_rat @ A @ C ) )
% 15.55/8.53         => ( ( divide_divide_rat @ B @ C )
% 15.55/8.53            = A ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3724_eq__divide__eq,axiom,
% 15.55/8.53      ! [A: complex,B: complex,C: complex] :
% 15.55/8.53        ( ( A
% 15.55/8.53          = ( divide1717551699836669952omplex @ B @ C ) )
% 15.55/8.53        = ( ( ( C != zero_zero_complex )
% 15.55/8.53           => ( ( times_times_complex @ A @ C )
% 15.55/8.53              = B ) )
% 15.55/8.53          & ( ( C = zero_zero_complex )
% 15.55/8.53           => ( A = zero_zero_complex ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3725_eq__divide__eq,axiom,
% 15.55/8.53      ! [A: real,B: real,C: real] :
% 15.55/8.53        ( ( A
% 15.55/8.53          = ( divide_divide_real @ B @ C ) )
% 15.55/8.53        = ( ( ( C != zero_zero_real )
% 15.55/8.53           => ( ( times_times_real @ A @ C )
% 15.55/8.53              = B ) )
% 15.55/8.53          & ( ( C = zero_zero_real )
% 15.55/8.53           => ( A = zero_zero_real ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3726_eq__divide__eq,axiom,
% 15.55/8.53      ! [A: rat,B: rat,C: rat] :
% 15.55/8.53        ( ( A
% 15.55/8.53          = ( divide_divide_rat @ B @ C ) )
% 15.55/8.53        = ( ( ( C != zero_zero_rat )
% 15.55/8.53           => ( ( times_times_rat @ A @ C )
% 15.55/8.53              = B ) )
% 15.55/8.53          & ( ( C = zero_zero_rat )
% 15.55/8.53           => ( A = zero_zero_rat ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3727_divide__eq__eq,axiom,
% 15.55/8.53      ! [B: complex,C: complex,A: complex] :
% 15.55/8.53        ( ( ( divide1717551699836669952omplex @ B @ C )
% 15.55/8.53          = A )
% 15.55/8.53        = ( ( ( C != zero_zero_complex )
% 15.55/8.53           => ( B
% 15.55/8.53              = ( times_times_complex @ A @ C ) ) )
% 15.55/8.53          & ( ( C = zero_zero_complex )
% 15.55/8.53           => ( A = zero_zero_complex ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3728_divide__eq__eq,axiom,
% 15.55/8.53      ! [B: real,C: real,A: real] :
% 15.55/8.53        ( ( ( divide_divide_real @ B @ C )
% 15.55/8.53          = A )
% 15.55/8.53        = ( ( ( C != zero_zero_real )
% 15.55/8.53           => ( B
% 15.55/8.53              = ( times_times_real @ A @ C ) ) )
% 15.55/8.53          & ( ( C = zero_zero_real )
% 15.55/8.53           => ( A = zero_zero_real ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3729_divide__eq__eq,axiom,
% 15.55/8.53      ! [B: rat,C: rat,A: rat] :
% 15.55/8.53        ( ( ( divide_divide_rat @ B @ C )
% 15.55/8.53          = A )
% 15.55/8.53        = ( ( ( C != zero_zero_rat )
% 15.55/8.53           => ( B
% 15.55/8.53              = ( times_times_rat @ A @ C ) ) )
% 15.55/8.53          & ( ( C = zero_zero_rat )
% 15.55/8.53           => ( A = zero_zero_rat ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3730_frac__eq__eq,axiom,
% 15.55/8.53      ! [Y3: complex,Z: complex,X3: complex,W: complex] :
% 15.55/8.53        ( ( Y3 != zero_zero_complex )
% 15.55/8.53       => ( ( Z != zero_zero_complex )
% 15.55/8.53         => ( ( ( divide1717551699836669952omplex @ X3 @ Y3 )
% 15.55/8.53              = ( divide1717551699836669952omplex @ W @ Z ) )
% 15.55/8.53            = ( ( times_times_complex @ X3 @ Z )
% 15.55/8.53              = ( times_times_complex @ W @ Y3 ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3731_frac__eq__eq,axiom,
% 15.55/8.53      ! [Y3: real,Z: real,X3: real,W: real] :
% 15.55/8.53        ( ( Y3 != zero_zero_real )
% 15.55/8.53       => ( ( Z != zero_zero_real )
% 15.55/8.53         => ( ( ( divide_divide_real @ X3 @ Y3 )
% 15.55/8.53              = ( divide_divide_real @ W @ Z ) )
% 15.55/8.53            = ( ( times_times_real @ X3 @ Z )
% 15.55/8.53              = ( times_times_real @ W @ Y3 ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3732_frac__eq__eq,axiom,
% 15.55/8.53      ! [Y3: rat,Z: rat,X3: rat,W: rat] :
% 15.55/8.53        ( ( Y3 != zero_zero_rat )
% 15.55/8.53       => ( ( Z != zero_zero_rat )
% 15.55/8.53         => ( ( ( divide_divide_rat @ X3 @ Y3 )
% 15.55/8.53              = ( divide_divide_rat @ W @ Z ) )
% 15.55/8.53            = ( ( times_times_rat @ X3 @ Z )
% 15.55/8.53              = ( times_times_rat @ W @ Y3 ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3733_mult__numeral__1,axiom,
% 15.55/8.53      ! [A: complex] :
% 15.55/8.53        ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 15.55/8.53        = A ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3734_mult__numeral__1,axiom,
% 15.55/8.53      ! [A: real] :
% 15.55/8.53        ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 15.55/8.53        = A ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3735_mult__numeral__1,axiom,
% 15.55/8.53      ! [A: rat] :
% 15.55/8.53        ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 15.55/8.53        = A ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3736_mult__numeral__1,axiom,
% 15.55/8.53      ! [A: nat] :
% 15.55/8.53        ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 15.55/8.53        = A ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3737_mult__numeral__1,axiom,
% 15.55/8.53      ! [A: int] :
% 15.55/8.53        ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 15.55/8.53        = A ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3738_mult__numeral__1__right,axiom,
% 15.55/8.53      ! [A: complex] :
% 15.55/8.53        ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 15.55/8.53        = A ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3739_mult__numeral__1__right,axiom,
% 15.55/8.53      ! [A: real] :
% 15.55/8.53        ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 15.55/8.53        = A ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3740_mult__numeral__1__right,axiom,
% 15.55/8.53      ! [A: rat] :
% 15.55/8.53        ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 15.55/8.53        = A ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3741_mult__numeral__1__right,axiom,
% 15.55/8.53      ! [A: nat] :
% 15.55/8.53        ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 15.55/8.53        = A ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3742_mult__numeral__1__right,axiom,
% 15.55/8.53      ! [A: int] :
% 15.55/8.53        ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 15.55/8.53        = A ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3743_mult__diff__mult,axiom,
% 15.55/8.53      ! [X3: real,Y3: real,A: real,B: real] :
% 15.55/8.53        ( ( minus_minus_real @ ( times_times_real @ X3 @ Y3 ) @ ( times_times_real @ A @ B ) )
% 15.55/8.53        = ( plus_plus_real @ ( times_times_real @ X3 @ ( minus_minus_real @ Y3 @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X3 @ A ) @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3744_mult__diff__mult,axiom,
% 15.55/8.53      ! [X3: rat,Y3: rat,A: rat,B: rat] :
% 15.55/8.53        ( ( minus_minus_rat @ ( times_times_rat @ X3 @ Y3 ) @ ( times_times_rat @ A @ B ) )
% 15.55/8.53        = ( plus_plus_rat @ ( times_times_rat @ X3 @ ( minus_minus_rat @ Y3 @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X3 @ A ) @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3745_mult__diff__mult,axiom,
% 15.55/8.53      ! [X3: int,Y3: int,A: int,B: int] :
% 15.55/8.53        ( ( minus_minus_int @ ( times_times_int @ X3 @ Y3 ) @ ( times_times_int @ A @ B ) )
% 15.55/8.53        = ( plus_plus_int @ ( times_times_int @ X3 @ ( minus_minus_int @ Y3 @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X3 @ A ) @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3746_left__right__inverse__power,axiom,
% 15.55/8.53      ! [X3: complex,Y3: complex,N: nat] :
% 15.55/8.53        ( ( ( times_times_complex @ X3 @ Y3 )
% 15.55/8.53          = one_one_complex )
% 15.55/8.53       => ( ( times_times_complex @ ( power_power_complex @ X3 @ N ) @ ( power_power_complex @ Y3 @ N ) )
% 15.55/8.53          = one_one_complex ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3747_left__right__inverse__power,axiom,
% 15.55/8.53      ! [X3: real,Y3: real,N: nat] :
% 15.55/8.53        ( ( ( times_times_real @ X3 @ Y3 )
% 15.55/8.53          = one_one_real )
% 15.55/8.53       => ( ( times_times_real @ ( power_power_real @ X3 @ N ) @ ( power_power_real @ Y3 @ N ) )
% 15.55/8.53          = one_one_real ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3748_left__right__inverse__power,axiom,
% 15.55/8.53      ! [X3: rat,Y3: rat,N: nat] :
% 15.55/8.53        ( ( ( times_times_rat @ X3 @ Y3 )
% 15.55/8.53          = one_one_rat )
% 15.55/8.53       => ( ( times_times_rat @ ( power_power_rat @ X3 @ N ) @ ( power_power_rat @ Y3 @ N ) )
% 15.55/8.53          = one_one_rat ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3749_left__right__inverse__power,axiom,
% 15.55/8.53      ! [X3: nat,Y3: nat,N: nat] :
% 15.55/8.53        ( ( ( times_times_nat @ X3 @ Y3 )
% 15.55/8.53          = one_one_nat )
% 15.55/8.53       => ( ( times_times_nat @ ( power_power_nat @ X3 @ N ) @ ( power_power_nat @ Y3 @ N ) )
% 15.55/8.53          = one_one_nat ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3750_left__right__inverse__power,axiom,
% 15.55/8.53      ! [X3: int,Y3: int,N: nat] :
% 15.55/8.53        ( ( ( times_times_int @ X3 @ Y3 )
% 15.55/8.53          = one_one_int )
% 15.55/8.53       => ( ( times_times_int @ ( power_power_int @ X3 @ N ) @ ( power_power_int @ Y3 @ N ) )
% 15.55/8.53          = one_one_int ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3751_power__Suc,axiom,
% 15.55/8.53      ! [A: complex,N: nat] :
% 15.55/8.53        ( ( power_power_complex @ A @ ( suc @ N ) )
% 15.55/8.53        = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3752_power__Suc,axiom,
% 15.55/8.53      ! [A: real,N: nat] :
% 15.55/8.53        ( ( power_power_real @ A @ ( suc @ N ) )
% 15.55/8.53        = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3753_power__Suc,axiom,
% 15.55/8.53      ! [A: rat,N: nat] :
% 15.55/8.53        ( ( power_power_rat @ A @ ( suc @ N ) )
% 15.55/8.53        = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3754_power__Suc,axiom,
% 15.55/8.53      ! [A: nat,N: nat] :
% 15.55/8.53        ( ( power_power_nat @ A @ ( suc @ N ) )
% 15.55/8.53        = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3755_power__Suc,axiom,
% 15.55/8.53      ! [A: int,N: nat] :
% 15.55/8.53        ( ( power_power_int @ A @ ( suc @ N ) )
% 15.55/8.53        = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3756_power__Suc2,axiom,
% 15.55/8.53      ! [A: complex,N: nat] :
% 15.55/8.53        ( ( power_power_complex @ A @ ( suc @ N ) )
% 15.55/8.53        = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3757_power__Suc2,axiom,
% 15.55/8.53      ! [A: real,N: nat] :
% 15.55/8.53        ( ( power_power_real @ A @ ( suc @ N ) )
% 15.55/8.53        = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3758_power__Suc2,axiom,
% 15.55/8.53      ! [A: rat,N: nat] :
% 15.55/8.53        ( ( power_power_rat @ A @ ( suc @ N ) )
% 15.55/8.53        = ( times_times_rat @ ( power_power_rat @ A @ N ) @ A ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3759_power__Suc2,axiom,
% 15.55/8.53      ! [A: nat,N: nat] :
% 15.55/8.53        ( ( power_power_nat @ A @ ( suc @ N ) )
% 15.55/8.53        = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3760_power__Suc2,axiom,
% 15.55/8.53      ! [A: int,N: nat] :
% 15.55/8.53        ( ( power_power_int @ A @ ( suc @ N ) )
% 15.55/8.53        = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3761_div__mult2__eq_H,axiom,
% 15.55/8.53      ! [A: nat,M: nat,N: nat] :
% 15.55/8.53        ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 15.55/8.53        = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3762_div__mult2__eq_H,axiom,
% 15.55/8.53      ! [A: int,M: nat,N: nat] :
% 15.55/8.53        ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 15.55/8.53        = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3763_Suc__mult__less__cancel1,axiom,
% 15.55/8.53      ! [K: nat,M: nat,N: nat] :
% 15.55/8.53        ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 15.55/8.53        = ( ord_less_nat @ M @ N ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3764_power__add,axiom,
% 15.55/8.53      ! [A: complex,M: nat,N: nat] :
% 15.55/8.53        ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N ) )
% 15.55/8.53        = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3765_power__add,axiom,
% 15.55/8.53      ! [A: real,M: nat,N: nat] :
% 15.55/8.53        ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N ) )
% 15.55/8.53        = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3766_power__add,axiom,
% 15.55/8.53      ! [A: rat,M: nat,N: nat] :
% 15.55/8.53        ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N ) )
% 15.55/8.53        = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3767_power__add,axiom,
% 15.55/8.53      ! [A: nat,M: nat,N: nat] :
% 15.55/8.53        ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 15.55/8.53        = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3768_power__add,axiom,
% 15.55/8.53      ! [A: int,M: nat,N: nat] :
% 15.55/8.53        ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 15.55/8.53        = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3769_mult__less__mono1,axiom,
% 15.55/8.53      ! [I: nat,J: nat,K: nat] :
% 15.55/8.53        ( ( ord_less_nat @ I @ J )
% 15.55/8.53       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 15.55/8.53         => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3770_mult__less__mono2,axiom,
% 15.55/8.53      ! [I: nat,J: nat,K: nat] :
% 15.55/8.53        ( ( ord_less_nat @ I @ J )
% 15.55/8.53       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 15.55/8.53         => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3771_nat__mult__less__cancel1,axiom,
% 15.55/8.53      ! [K: nat,M: nat,N: nat] :
% 15.55/8.53        ( ( ord_less_nat @ zero_zero_nat @ K )
% 15.55/8.53       => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 15.55/8.53          = ( ord_less_nat @ M @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3772_nat__mult__eq__cancel1,axiom,
% 15.55/8.53      ! [K: nat,M: nat,N: nat] :
% 15.55/8.53        ( ( ord_less_nat @ zero_zero_nat @ K )
% 15.55/8.53       => ( ( ( times_times_nat @ K @ M )
% 15.55/8.53            = ( times_times_nat @ K @ N ) )
% 15.55/8.53          = ( M = N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3773_mult__Suc,axiom,
% 15.55/8.53      ! [M: nat,N: nat] :
% 15.55/8.53        ( ( times_times_nat @ ( suc @ M ) @ N )
% 15.55/8.53        = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3774_Suc__mult__le__cancel1,axiom,
% 15.55/8.53      ! [K: nat,M: nat,N: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 15.55/8.53        = ( ord_less_eq_nat @ M @ N ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3775_mult__eq__self__implies__10,axiom,
% 15.55/8.53      ! [M: nat,N: nat] :
% 15.55/8.53        ( ( M
% 15.55/8.53          = ( times_times_nat @ M @ N ) )
% 15.55/8.53       => ( ( N = one_one_nat )
% 15.55/8.53          | ( M = zero_zero_nat ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3776_less__mult__imp__div__less,axiom,
% 15.55/8.53      ! [M: nat,I: nat,N: nat] :
% 15.55/8.53        ( ( ord_less_nat @ M @ ( times_times_nat @ I @ N ) )
% 15.55/8.53       => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ I ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3777_div__times__less__eq__dividend,axiom,
% 15.55/8.53      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3778_times__div__less__eq__dividend,axiom,
% 15.55/8.53      ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3779_power__odd__eq,axiom,
% 15.55/8.53      ! [A: complex,N: nat] :
% 15.55/8.53        ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 15.55/8.53        = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3780_power__odd__eq,axiom,
% 15.55/8.53      ! [A: real,N: nat] :
% 15.55/8.53        ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 15.55/8.53        = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3781_power__odd__eq,axiom,
% 15.55/8.53      ! [A: rat,N: nat] :
% 15.55/8.53        ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 15.55/8.53        = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3782_power__odd__eq,axiom,
% 15.55/8.53      ! [A: nat,N: nat] :
% 15.55/8.53        ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 15.55/8.53        = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3783_power__odd__eq,axiom,
% 15.55/8.53      ! [A: int,N: nat] :
% 15.55/8.53        ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 15.55/8.53        = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3784_frac__ge__0,axiom,
% 15.55/8.53      ! [X3: real] : ( ord_less_eq_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X3 ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3785_frac__ge__0,axiom,
% 15.55/8.53      ! [X3: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X3 ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3786_frac__lt__1,axiom,
% 15.55/8.53      ! [X3: real] : ( ord_less_real @ ( archim2898591450579166408c_real @ X3 ) @ one_one_real ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3787_frac__lt__1,axiom,
% 15.55/8.53      ! [X3: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X3 ) @ one_one_rat ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3788_frac__1__eq,axiom,
% 15.55/8.53      ! [X3: real] :
% 15.55/8.53        ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X3 @ one_one_real ) )
% 15.55/8.53        = ( archim2898591450579166408c_real @ X3 ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3789_frac__1__eq,axiom,
% 15.55/8.53      ! [X3: rat] :
% 15.55/8.53        ( ( archimedean_frac_rat @ ( plus_plus_rat @ X3 @ one_one_rat ) )
% 15.55/8.53        = ( archimedean_frac_rat @ X3 ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3790_mult__less__le__imp__less,axiom,
% 15.55/8.53      ! [A: real,B: real,C: real,D3: real] :
% 15.55/8.53        ( ( ord_less_real @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_real @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.53           => ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3791_mult__less__le__imp__less,axiom,
% 15.55/8.53      ! [A: rat,B: rat,C: rat,D3: rat] :
% 15.55/8.53        ( ( ord_less_rat @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_rat @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.53           => ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3792_mult__less__le__imp__less,axiom,
% 15.55/8.53      ! [A: nat,B: nat,C: nat,D3: nat] :
% 15.55/8.53        ( ( ord_less_nat @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_nat @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.55/8.53           => ( ( ord_less_nat @ zero_zero_nat @ C )
% 15.55/8.53             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3793_mult__less__le__imp__less,axiom,
% 15.55/8.53      ! [A: int,B: int,C: int,D3: int] :
% 15.55/8.53        ( ( ord_less_int @ A @ B )
% 15.55/8.53       => ( ( ord_less_eq_int @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.53           => ( ( ord_less_int @ zero_zero_int @ C )
% 15.55/8.53             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3794_mult__le__less__imp__less,axiom,
% 15.55/8.53      ! [A: real,B: real,C: real,D3: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.53       => ( ( ord_less_real @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.53           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 15.55/8.53             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3795_mult__le__less__imp__less,axiom,
% 15.55/8.53      ! [A: rat,B: rat,C: rat,D3: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ A @ B )
% 15.55/8.53       => ( ( ord_less_rat @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.53           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 15.55/8.53             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3796_mult__le__less__imp__less,axiom,
% 15.55/8.53      ! [A: nat,B: nat,C: nat,D3: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.53       => ( ( ord_less_nat @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_nat @ zero_zero_nat @ A )
% 15.55/8.53           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 15.55/8.53             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3797_mult__le__less__imp__less,axiom,
% 15.55/8.53      ! [A: int,B: int,C: int,D3: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ A @ B )
% 15.55/8.53       => ( ( ord_less_int @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_int @ zero_zero_int @ A )
% 15.55/8.53           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 15.55/8.53             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3798_mult__right__le__imp__le,axiom,
% 15.55/8.53      ! [A: real,C: real,B: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 15.55/8.53       => ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3799_mult__right__le__imp__le,axiom,
% 15.55/8.53      ! [A: rat,C: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 15.55/8.53       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3800_mult__right__le__imp__le,axiom,
% 15.55/8.53      ! [A: nat,C: nat,B: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 15.55/8.53       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 15.55/8.53         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3801_mult__right__le__imp__le,axiom,
% 15.55/8.53      ! [A: int,C: int,B: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 15.55/8.53       => ( ( ord_less_int @ zero_zero_int @ C )
% 15.55/8.53         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3802_mult__left__le__imp__le,axiom,
% 15.55/8.53      ! [C: real,A: real,B: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 15.55/8.53       => ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3803_mult__left__le__imp__le,axiom,
% 15.55/8.53      ! [C: rat,A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 15.55/8.53       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3804_mult__left__le__imp__le,axiom,
% 15.55/8.53      ! [C: nat,A: nat,B: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 15.55/8.53       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 15.55/8.53         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3805_mult__left__le__imp__le,axiom,
% 15.55/8.53      ! [C: int,A: int,B: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 15.55/8.53       => ( ( ord_less_int @ zero_zero_int @ C )
% 15.55/8.53         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3806_mult__le__cancel__left__pos,axiom,
% 15.55/8.53      ! [C: real,A: real,B: real] :
% 15.55/8.53        ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53       => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 15.55/8.53          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3807_mult__le__cancel__left__pos,axiom,
% 15.55/8.53      ! [C: rat,A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 15.55/8.53          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3808_mult__le__cancel__left__pos,axiom,
% 15.55/8.53      ! [C: int,A: int,B: int] :
% 15.55/8.53        ( ( ord_less_int @ zero_zero_int @ C )
% 15.55/8.53       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 15.55/8.53          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3809_mult__le__cancel__left__neg,axiom,
% 15.55/8.53      ! [C: real,A: real,B: real] :
% 15.55/8.53        ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.53       => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 15.55/8.53          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3810_mult__le__cancel__left__neg,axiom,
% 15.55/8.53      ! [C: rat,A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.53       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 15.55/8.53          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3811_mult__le__cancel__left__neg,axiom,
% 15.55/8.53      ! [C: int,A: int,B: int] :
% 15.55/8.53        ( ( ord_less_int @ C @ zero_zero_int )
% 15.55/8.53       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 15.55/8.53          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3812_mult__less__cancel__right,axiom,
% 15.55/8.53      ! [A: real,C: real,B: real] :
% 15.55/8.53        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 15.55/8.53        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 15.55/8.53           => ( ord_less_real @ A @ B ) )
% 15.55/8.53          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 15.55/8.53           => ( ord_less_real @ B @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3813_mult__less__cancel__right,axiom,
% 15.55/8.53      ! [A: rat,C: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 15.55/8.53        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 15.55/8.53           => ( ord_less_rat @ A @ B ) )
% 15.55/8.53          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 15.55/8.53           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3814_mult__less__cancel__right,axiom,
% 15.55/8.53      ! [A: int,C: int,B: int] :
% 15.55/8.53        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 15.55/8.53        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 15.55/8.53           => ( ord_less_int @ A @ B ) )
% 15.55/8.53          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 15.55/8.53           => ( ord_less_int @ B @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3815_mult__strict__mono_H,axiom,
% 15.55/8.53      ! [A: real,B: real,C: real,D3: real] :
% 15.55/8.53        ( ( ord_less_real @ A @ B )
% 15.55/8.53       => ( ( ord_less_real @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.53           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 15.55/8.53             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3816_mult__strict__mono_H,axiom,
% 15.55/8.53      ! [A: rat,B: rat,C: rat,D3: rat] :
% 15.55/8.53        ( ( ord_less_rat @ A @ B )
% 15.55/8.53       => ( ( ord_less_rat @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.53           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 15.55/8.53             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3817_mult__strict__mono_H,axiom,
% 15.55/8.53      ! [A: nat,B: nat,C: nat,D3: nat] :
% 15.55/8.53        ( ( ord_less_nat @ A @ B )
% 15.55/8.53       => ( ( ord_less_nat @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.55/8.53           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 15.55/8.53             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3818_mult__strict__mono_H,axiom,
% 15.55/8.53      ! [A: int,B: int,C: int,D3: int] :
% 15.55/8.53        ( ( ord_less_int @ A @ B )
% 15.55/8.53       => ( ( ord_less_int @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.53           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 15.55/8.53             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3819_mult__right__less__imp__less,axiom,
% 15.55/8.53      ! [A: real,C: real,B: real] :
% 15.55/8.53        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 15.55/8.53       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 15.55/8.53         => ( ord_less_real @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3820_mult__right__less__imp__less,axiom,
% 15.55/8.53      ! [A: rat,C: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 15.55/8.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 15.55/8.53         => ( ord_less_rat @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3821_mult__right__less__imp__less,axiom,
% 15.55/8.53      ! [A: nat,C: nat,B: nat] :
% 15.55/8.53        ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 15.55/8.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 15.55/8.53         => ( ord_less_nat @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3822_mult__right__less__imp__less,axiom,
% 15.55/8.53      ! [A: int,C: int,B: int] :
% 15.55/8.53        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 15.55/8.53       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 15.55/8.53         => ( ord_less_int @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3823_mult__less__cancel__left,axiom,
% 15.55/8.53      ! [C: real,A: real,B: real] :
% 15.55/8.53        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 15.55/8.53        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 15.55/8.53           => ( ord_less_real @ A @ B ) )
% 15.55/8.53          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 15.55/8.53           => ( ord_less_real @ B @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3824_mult__less__cancel__left,axiom,
% 15.55/8.53      ! [C: rat,A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 15.55/8.53        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 15.55/8.53           => ( ord_less_rat @ A @ B ) )
% 15.55/8.53          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 15.55/8.53           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3825_mult__less__cancel__left,axiom,
% 15.55/8.53      ! [C: int,A: int,B: int] :
% 15.55/8.53        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 15.55/8.53        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 15.55/8.53           => ( ord_less_int @ A @ B ) )
% 15.55/8.53          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 15.55/8.53           => ( ord_less_int @ B @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3826_mult__strict__mono,axiom,
% 15.55/8.53      ! [A: real,B: real,C: real,D3: real] :
% 15.55/8.53        ( ( ord_less_real @ A @ B )
% 15.55/8.53       => ( ( ord_less_real @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_real @ zero_zero_real @ B )
% 15.55/8.53           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 15.55/8.53             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3827_mult__strict__mono,axiom,
% 15.55/8.53      ! [A: rat,B: rat,C: rat,D3: rat] :
% 15.55/8.53        ( ( ord_less_rat @ A @ B )
% 15.55/8.53       => ( ( ord_less_rat @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_rat @ zero_zero_rat @ B )
% 15.55/8.53           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 15.55/8.53             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3828_mult__strict__mono,axiom,
% 15.55/8.53      ! [A: nat,B: nat,C: nat,D3: nat] :
% 15.55/8.53        ( ( ord_less_nat @ A @ B )
% 15.55/8.53       => ( ( ord_less_nat @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_nat @ zero_zero_nat @ B )
% 15.55/8.53           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 15.55/8.53             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3829_mult__strict__mono,axiom,
% 15.55/8.53      ! [A: int,B: int,C: int,D3: int] :
% 15.55/8.53        ( ( ord_less_int @ A @ B )
% 15.55/8.53       => ( ( ord_less_int @ C @ D3 )
% 15.55/8.53         => ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.53           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 15.55/8.53             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3830_mult__left__less__imp__less,axiom,
% 15.55/8.53      ! [C: real,A: real,B: real] :
% 15.55/8.53        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 15.55/8.53       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 15.55/8.53         => ( ord_less_real @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3831_mult__left__less__imp__less,axiom,
% 15.55/8.53      ! [C: rat,A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 15.55/8.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 15.55/8.53         => ( ord_less_rat @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3832_mult__left__less__imp__less,axiom,
% 15.55/8.53      ! [C: nat,A: nat,B: nat] :
% 15.55/8.53        ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 15.55/8.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 15.55/8.53         => ( ord_less_nat @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3833_mult__left__less__imp__less,axiom,
% 15.55/8.53      ! [C: int,A: int,B: int] :
% 15.55/8.53        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 15.55/8.53       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 15.55/8.53         => ( ord_less_int @ A @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3834_mult__le__cancel__right,axiom,
% 15.55/8.53      ! [A: real,C: real,B: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 15.55/8.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53           => ( ord_less_eq_real @ A @ B ) )
% 15.55/8.53          & ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.53           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3835_mult__le__cancel__right,axiom,
% 15.55/8.53      ! [A: rat,C: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 15.55/8.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53           => ( ord_less_eq_rat @ A @ B ) )
% 15.55/8.53          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.53           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3836_mult__le__cancel__right,axiom,
% 15.55/8.53      ! [A: int,C: int,B: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 15.55/8.53        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 15.55/8.53           => ( ord_less_eq_int @ A @ B ) )
% 15.55/8.53          & ( ( ord_less_int @ C @ zero_zero_int )
% 15.55/8.53           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3837_mult__le__cancel__left,axiom,
% 15.55/8.53      ! [C: real,A: real,B: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 15.55/8.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53           => ( ord_less_eq_real @ A @ B ) )
% 15.55/8.53          & ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.53           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3838_mult__le__cancel__left,axiom,
% 15.55/8.53      ! [C: rat,A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 15.55/8.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53           => ( ord_less_eq_rat @ A @ B ) )
% 15.55/8.53          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.53           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3839_mult__le__cancel__left,axiom,
% 15.55/8.53      ! [C: int,A: int,B: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 15.55/8.53        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 15.55/8.53           => ( ord_less_eq_int @ A @ B ) )
% 15.55/8.53          & ( ( ord_less_int @ C @ zero_zero_int )
% 15.55/8.53           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3840_mult__left__le__one__le,axiom,
% 15.55/8.53      ! [X3: real,Y3: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.53       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.53         => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 15.55/8.53           => ( ord_less_eq_real @ ( times_times_real @ Y3 @ X3 ) @ X3 ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3841_mult__left__le__one__le,axiom,
% 15.55/8.53      ! [X3: rat,Y3: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 15.55/8.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 15.55/8.53         => ( ( ord_less_eq_rat @ Y3 @ one_one_rat )
% 15.55/8.53           => ( ord_less_eq_rat @ ( times_times_rat @ Y3 @ X3 ) @ X3 ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3842_mult__left__le__one__le,axiom,
% 15.55/8.53      ! [X3: int,Y3: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 15.55/8.53       => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 15.55/8.53         => ( ( ord_less_eq_int @ Y3 @ one_one_int )
% 15.55/8.53           => ( ord_less_eq_int @ ( times_times_int @ Y3 @ X3 ) @ X3 ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3843_mult__right__le__one__le,axiom,
% 15.55/8.53      ! [X3: real,Y3: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.53       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.53         => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 15.55/8.53           => ( ord_less_eq_real @ ( times_times_real @ X3 @ Y3 ) @ X3 ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3844_mult__right__le__one__le,axiom,
% 15.55/8.53      ! [X3: rat,Y3: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 15.55/8.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 15.55/8.53         => ( ( ord_less_eq_rat @ Y3 @ one_one_rat )
% 15.55/8.53           => ( ord_less_eq_rat @ ( times_times_rat @ X3 @ Y3 ) @ X3 ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3845_mult__right__le__one__le,axiom,
% 15.55/8.53      ! [X3: int,Y3: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 15.55/8.53       => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 15.55/8.53         => ( ( ord_less_eq_int @ Y3 @ one_one_int )
% 15.55/8.53           => ( ord_less_eq_int @ ( times_times_int @ X3 @ Y3 ) @ X3 ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3846_mult__le__one,axiom,
% 15.55/8.53      ! [A: real,B: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ A @ one_one_real )
% 15.55/8.53       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 15.55/8.53         => ( ( ord_less_eq_real @ B @ one_one_real )
% 15.55/8.53           => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3847_mult__le__one,axiom,
% 15.55/8.53      ! [A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ A @ one_one_rat )
% 15.55/8.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 15.55/8.53         => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 15.55/8.53           => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3848_mult__le__one,axiom,
% 15.55/8.53      ! [A: nat,B: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ A @ one_one_nat )
% 15.55/8.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 15.55/8.53         => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 15.55/8.53           => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3849_mult__le__one,axiom,
% 15.55/8.53      ! [A: int,B: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ A @ one_one_int )
% 15.55/8.53       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 15.55/8.53         => ( ( ord_less_eq_int @ B @ one_one_int )
% 15.55/8.53           => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3850_mult__left__le,axiom,
% 15.55/8.53      ! [C: real,A: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ C @ one_one_real )
% 15.55/8.53       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.53         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3851_mult__left__le,axiom,
% 15.55/8.53      ! [C: rat,A: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ C @ one_one_rat )
% 15.55/8.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.53         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3852_mult__left__le,axiom,
% 15.55/8.53      ! [C: nat,A: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ C @ one_one_nat )
% 15.55/8.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.55/8.53         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3853_mult__left__le,axiom,
% 15.55/8.53      ! [C: int,A: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ C @ one_one_int )
% 15.55/8.53       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.53         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3854_sum__squares__le__zero__iff,axiom,
% 15.55/8.53      ! [X3: real,Y3: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y3 @ Y3 ) ) @ zero_zero_real )
% 15.55/8.53        = ( ( X3 = zero_zero_real )
% 15.55/8.53          & ( Y3 = zero_zero_real ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3855_sum__squares__le__zero__iff,axiom,
% 15.55/8.53      ! [X3: rat,Y3: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y3 @ Y3 ) ) @ zero_zero_rat )
% 15.55/8.53        = ( ( X3 = zero_zero_rat )
% 15.55/8.53          & ( Y3 = zero_zero_rat ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3856_sum__squares__le__zero__iff,axiom,
% 15.55/8.53      ! [X3: int,Y3: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y3 @ Y3 ) ) @ zero_zero_int )
% 15.55/8.53        = ( ( X3 = zero_zero_int )
% 15.55/8.53          & ( Y3 = zero_zero_int ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3857_sum__squares__ge__zero,axiom,
% 15.55/8.53      ! [X3: real,Y3: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y3 @ Y3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3858_sum__squares__ge__zero,axiom,
% 15.55/8.53      ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y3 @ Y3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3859_sum__squares__ge__zero,axiom,
% 15.55/8.53      ! [X3: int,Y3: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y3 @ Y3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3860_sum__squares__gt__zero__iff,axiom,
% 15.55/8.53      ! [X3: real,Y3: real] :
% 15.55/8.53        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y3 @ Y3 ) ) )
% 15.55/8.53        = ( ( X3 != zero_zero_real )
% 15.55/8.53          | ( Y3 != zero_zero_real ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3861_sum__squares__gt__zero__iff,axiom,
% 15.55/8.53      ! [X3: rat,Y3: rat] :
% 15.55/8.53        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y3 @ Y3 ) ) )
% 15.55/8.53        = ( ( X3 != zero_zero_rat )
% 15.55/8.53          | ( Y3 != zero_zero_rat ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3862_sum__squares__gt__zero__iff,axiom,
% 15.55/8.53      ! [X3: int,Y3: int] :
% 15.55/8.53        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y3 @ Y3 ) ) )
% 15.55/8.53        = ( ( X3 != zero_zero_int )
% 15.55/8.53          | ( Y3 != zero_zero_int ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3863_not__sum__squares__lt__zero,axiom,
% 15.55/8.53      ! [X3: real,Y3: real] :
% 15.55/8.53        ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y3 @ Y3 ) ) @ zero_zero_real ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3864_not__sum__squares__lt__zero,axiom,
% 15.55/8.53      ! [X3: rat,Y3: rat] :
% 15.55/8.53        ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y3 @ Y3 ) ) @ zero_zero_rat ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3865_not__sum__squares__lt__zero,axiom,
% 15.55/8.53      ! [X3: int,Y3: int] :
% 15.55/8.53        ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y3 @ Y3 ) ) @ zero_zero_int ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3866_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 15.55/8.53      ! [C: nat,A: nat,B: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 15.55/8.53       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 15.55/8.53          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3867_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 15.55/8.53      ! [C: int,A: int,B: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 15.55/8.53       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 15.55/8.53          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3868_divide__less__eq,axiom,
% 15.55/8.53      ! [B: real,C: real,A: real] :
% 15.55/8.53        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 15.55/8.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53           => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 15.55/8.53          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.53               => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 15.55/8.53              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.53               => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3869_divide__less__eq,axiom,
% 15.55/8.53      ! [B: rat,C: rat,A: rat] :
% 15.55/8.53        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 15.55/8.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53           => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 15.55/8.53          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.53               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 15.55/8.53              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.53               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3870_less__divide__eq,axiom,
% 15.55/8.53      ! [A: real,B: real,C: real] :
% 15.55/8.53        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 15.55/8.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53           => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 15.55/8.53          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.53               => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 15.55/8.53              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.53               => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3871_less__divide__eq,axiom,
% 15.55/8.53      ! [A: rat,B: rat,C: rat] :
% 15.55/8.53        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 15.55/8.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 15.55/8.53          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.53               => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 15.55/8.53              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.53               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3872_neg__divide__less__eq,axiom,
% 15.55/8.53      ! [C: real,B: real,A: real] :
% 15.55/8.53        ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.53       => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 15.55/8.53          = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3873_neg__divide__less__eq,axiom,
% 15.55/8.53      ! [C: rat,B: rat,A: rat] :
% 15.55/8.53        ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.53       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 15.55/8.53          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3874_neg__less__divide__eq,axiom,
% 15.55/8.53      ! [C: real,A: real,B: real] :
% 15.55/8.53        ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.53       => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 15.55/8.53          = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3875_neg__less__divide__eq,axiom,
% 15.55/8.53      ! [C: rat,A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.53       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 15.55/8.53          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3876_pos__divide__less__eq,axiom,
% 15.55/8.53      ! [C: real,B: real,A: real] :
% 15.55/8.53        ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53       => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 15.55/8.53          = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3877_pos__divide__less__eq,axiom,
% 15.55/8.53      ! [C: rat,B: rat,A: rat] :
% 15.55/8.53        ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 15.55/8.53          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3878_pos__less__divide__eq,axiom,
% 15.55/8.53      ! [C: real,A: real,B: real] :
% 15.55/8.53        ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53       => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 15.55/8.53          = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3879_pos__less__divide__eq,axiom,
% 15.55/8.53      ! [C: rat,A: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 15.55/8.53          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3880_mult__imp__div__pos__less,axiom,
% 15.55/8.53      ! [Y3: real,X3: real,Z: real] :
% 15.55/8.53        ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.55/8.53       => ( ( ord_less_real @ X3 @ ( times_times_real @ Z @ Y3 ) )
% 15.55/8.53         => ( ord_less_real @ ( divide_divide_real @ X3 @ Y3 ) @ Z ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3881_mult__imp__div__pos__less,axiom,
% 15.55/8.53      ! [Y3: rat,X3: rat,Z: rat] :
% 15.55/8.53        ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 15.55/8.53       => ( ( ord_less_rat @ X3 @ ( times_times_rat @ Z @ Y3 ) )
% 15.55/8.53         => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ Z ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3882_mult__imp__less__div__pos,axiom,
% 15.55/8.53      ! [Y3: real,Z: real,X3: real] :
% 15.55/8.53        ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.55/8.53       => ( ( ord_less_real @ ( times_times_real @ Z @ Y3 ) @ X3 )
% 15.55/8.53         => ( ord_less_real @ Z @ ( divide_divide_real @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3883_mult__imp__less__div__pos,axiom,
% 15.55/8.53      ! [Y3: rat,Z: rat,X3: rat] :
% 15.55/8.53        ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 15.55/8.53       => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y3 ) @ X3 )
% 15.55/8.53         => ( ord_less_rat @ Z @ ( divide_divide_rat @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3884_divide__strict__left__mono,axiom,
% 15.55/8.53      ! [B: real,A: real,C: real] :
% 15.55/8.53        ( ( ord_less_real @ B @ A )
% 15.55/8.53       => ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 15.55/8.53           => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3885_divide__strict__left__mono,axiom,
% 15.55/8.53      ! [B: rat,A: rat,C: rat] :
% 15.55/8.53        ( ( ord_less_rat @ B @ A )
% 15.55/8.53       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 15.55/8.53           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3886_divide__strict__left__mono__neg,axiom,
% 15.55/8.53      ! [A: real,B: real,C: real] :
% 15.55/8.53        ( ( ord_less_real @ A @ B )
% 15.55/8.53       => ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.53         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 15.55/8.53           => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3887_divide__strict__left__mono__neg,axiom,
% 15.55/8.53      ! [A: rat,B: rat,C: rat] :
% 15.55/8.53        ( ( ord_less_rat @ A @ B )
% 15.55/8.53       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.53         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 15.55/8.53           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3888_divide__eq__eq__numeral_I1_J,axiom,
% 15.55/8.53      ! [B: complex,C: complex,W: num] :
% 15.55/8.53        ( ( ( divide1717551699836669952omplex @ B @ C )
% 15.55/8.53          = ( numera6690914467698888265omplex @ W ) )
% 15.55/8.53        = ( ( ( C != zero_zero_complex )
% 15.55/8.53           => ( B
% 15.55/8.53              = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 15.55/8.53          & ( ( C = zero_zero_complex )
% 15.55/8.53           => ( ( numera6690914467698888265omplex @ W )
% 15.55/8.53              = zero_zero_complex ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3889_divide__eq__eq__numeral_I1_J,axiom,
% 15.55/8.53      ! [B: real,C: real,W: num] :
% 15.55/8.53        ( ( ( divide_divide_real @ B @ C )
% 15.55/8.53          = ( numeral_numeral_real @ W ) )
% 15.55/8.53        = ( ( ( C != zero_zero_real )
% 15.55/8.53           => ( B
% 15.55/8.53              = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 15.55/8.53          & ( ( C = zero_zero_real )
% 15.55/8.53           => ( ( numeral_numeral_real @ W )
% 15.55/8.53              = zero_zero_real ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3890_divide__eq__eq__numeral_I1_J,axiom,
% 15.55/8.53      ! [B: rat,C: rat,W: num] :
% 15.55/8.53        ( ( ( divide_divide_rat @ B @ C )
% 15.55/8.53          = ( numeral_numeral_rat @ W ) )
% 15.55/8.53        = ( ( ( C != zero_zero_rat )
% 15.55/8.53           => ( B
% 15.55/8.53              = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 15.55/8.53          & ( ( C = zero_zero_rat )
% 15.55/8.53           => ( ( numeral_numeral_rat @ W )
% 15.55/8.53              = zero_zero_rat ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3891_eq__divide__eq__numeral_I1_J,axiom,
% 15.55/8.53      ! [W: num,B: complex,C: complex] :
% 15.55/8.53        ( ( ( numera6690914467698888265omplex @ W )
% 15.55/8.53          = ( divide1717551699836669952omplex @ B @ C ) )
% 15.55/8.53        = ( ( ( C != zero_zero_complex )
% 15.55/8.53           => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 15.55/8.53              = B ) )
% 15.55/8.53          & ( ( C = zero_zero_complex )
% 15.55/8.53           => ( ( numera6690914467698888265omplex @ W )
% 15.55/8.53              = zero_zero_complex ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3892_eq__divide__eq__numeral_I1_J,axiom,
% 15.55/8.53      ! [W: num,B: real,C: real] :
% 15.55/8.53        ( ( ( numeral_numeral_real @ W )
% 15.55/8.53          = ( divide_divide_real @ B @ C ) )
% 15.55/8.53        = ( ( ( C != zero_zero_real )
% 15.55/8.53           => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 15.55/8.53              = B ) )
% 15.55/8.53          & ( ( C = zero_zero_real )
% 15.55/8.53           => ( ( numeral_numeral_real @ W )
% 15.55/8.53              = zero_zero_real ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3893_eq__divide__eq__numeral_I1_J,axiom,
% 15.55/8.53      ! [W: num,B: rat,C: rat] :
% 15.55/8.53        ( ( ( numeral_numeral_rat @ W )
% 15.55/8.53          = ( divide_divide_rat @ B @ C ) )
% 15.55/8.53        = ( ( ( C != zero_zero_rat )
% 15.55/8.53           => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 15.55/8.53              = B ) )
% 15.55/8.53          & ( ( C = zero_zero_rat )
% 15.55/8.53           => ( ( numeral_numeral_rat @ W )
% 15.55/8.53              = zero_zero_rat ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3894_ordered__ring__class_Ole__add__iff2,axiom,
% 15.55/8.53      ! [A: real,E2: real,C: real,B: real,D3: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D3 ) )
% 15.55/8.53        = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3895_ordered__ring__class_Ole__add__iff2,axiom,
% 15.55/8.53      ! [A: rat,E2: rat,C: rat,B: rat,D3: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D3 ) )
% 15.55/8.53        = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3896_ordered__ring__class_Ole__add__iff2,axiom,
% 15.55/8.53      ! [A: int,E2: int,C: int,B: int,D3: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D3 ) )
% 15.55/8.53        = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3897_ordered__ring__class_Ole__add__iff1,axiom,
% 15.55/8.53      ! [A: real,E2: real,C: real,B: real,D3: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D3 ) )
% 15.55/8.53        = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D3 ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3898_ordered__ring__class_Ole__add__iff1,axiom,
% 15.55/8.53      ! [A: rat,E2: rat,C: rat,B: rat,D3: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D3 ) )
% 15.55/8.53        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D3 ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3899_ordered__ring__class_Ole__add__iff1,axiom,
% 15.55/8.53      ! [A: int,E2: int,C: int,B: int,D3: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D3 ) )
% 15.55/8.53        = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D3 ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3900_divide__add__eq__iff,axiom,
% 15.55/8.53      ! [Z: complex,X3: complex,Y3: complex] :
% 15.55/8.53        ( ( Z != zero_zero_complex )
% 15.55/8.53       => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X3 @ Z ) @ Y3 )
% 15.55/8.53          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X3 @ ( times_times_complex @ Y3 @ Z ) ) @ Z ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3901_divide__add__eq__iff,axiom,
% 15.55/8.53      ! [Z: real,X3: real,Y3: real] :
% 15.55/8.53        ( ( Z != zero_zero_real )
% 15.55/8.53       => ( ( plus_plus_real @ ( divide_divide_real @ X3 @ Z ) @ Y3 )
% 15.55/8.53          = ( divide_divide_real @ ( plus_plus_real @ X3 @ ( times_times_real @ Y3 @ Z ) ) @ Z ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3902_divide__add__eq__iff,axiom,
% 15.55/8.53      ! [Z: rat,X3: rat,Y3: rat] :
% 15.55/8.53        ( ( Z != zero_zero_rat )
% 15.55/8.53       => ( ( plus_plus_rat @ ( divide_divide_rat @ X3 @ Z ) @ Y3 )
% 15.55/8.53          = ( divide_divide_rat @ ( plus_plus_rat @ X3 @ ( times_times_rat @ Y3 @ Z ) ) @ Z ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3903_add__divide__eq__iff,axiom,
% 15.55/8.53      ! [Z: complex,X3: complex,Y3: complex] :
% 15.55/8.53        ( ( Z != zero_zero_complex )
% 15.55/8.53       => ( ( plus_plus_complex @ X3 @ ( divide1717551699836669952omplex @ Y3 @ Z ) )
% 15.55/8.53          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X3 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3904_add__divide__eq__iff,axiom,
% 15.55/8.53      ! [Z: real,X3: real,Y3: real] :
% 15.55/8.53        ( ( Z != zero_zero_real )
% 15.55/8.53       => ( ( plus_plus_real @ X3 @ ( divide_divide_real @ Y3 @ Z ) )
% 15.55/8.53          = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X3 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3905_add__divide__eq__iff,axiom,
% 15.55/8.53      ! [Z: rat,X3: rat,Y3: rat] :
% 15.55/8.53        ( ( Z != zero_zero_rat )
% 15.55/8.53       => ( ( plus_plus_rat @ X3 @ ( divide_divide_rat @ Y3 @ Z ) )
% 15.55/8.53          = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3906_add__num__frac,axiom,
% 15.55/8.53      ! [Y3: complex,Z: complex,X3: complex] :
% 15.55/8.53        ( ( Y3 != zero_zero_complex )
% 15.55/8.53       => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X3 @ Y3 ) )
% 15.55/8.53          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X3 @ ( times_times_complex @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3907_add__num__frac,axiom,
% 15.55/8.53      ! [Y3: real,Z: real,X3: real] :
% 15.55/8.53        ( ( Y3 != zero_zero_real )
% 15.55/8.53       => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X3 @ Y3 ) )
% 15.55/8.53          = ( divide_divide_real @ ( plus_plus_real @ X3 @ ( times_times_real @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3908_add__num__frac,axiom,
% 15.55/8.53      ! [Y3: rat,Z: rat,X3: rat] :
% 15.55/8.53        ( ( Y3 != zero_zero_rat )
% 15.55/8.53       => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X3 @ Y3 ) )
% 15.55/8.53          = ( divide_divide_rat @ ( plus_plus_rat @ X3 @ ( times_times_rat @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3909_add__frac__num,axiom,
% 15.55/8.53      ! [Y3: complex,X3: complex,Z: complex] :
% 15.55/8.53        ( ( Y3 != zero_zero_complex )
% 15.55/8.53       => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X3 @ Y3 ) @ Z )
% 15.55/8.53          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X3 @ ( times_times_complex @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3910_add__frac__num,axiom,
% 15.55/8.53      ! [Y3: real,X3: real,Z: real] :
% 15.55/8.53        ( ( Y3 != zero_zero_real )
% 15.55/8.53       => ( ( plus_plus_real @ ( divide_divide_real @ X3 @ Y3 ) @ Z )
% 15.55/8.53          = ( divide_divide_real @ ( plus_plus_real @ X3 @ ( times_times_real @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3911_add__frac__num,axiom,
% 15.55/8.53      ! [Y3: rat,X3: rat,Z: rat] :
% 15.55/8.53        ( ( Y3 != zero_zero_rat )
% 15.55/8.53       => ( ( plus_plus_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ Z )
% 15.55/8.53          = ( divide_divide_rat @ ( plus_plus_rat @ X3 @ ( times_times_rat @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3912_add__frac__eq,axiom,
% 15.55/8.53      ! [Y3: complex,Z: complex,X3: complex,W: complex] :
% 15.55/8.53        ( ( Y3 != zero_zero_complex )
% 15.55/8.53       => ( ( Z != zero_zero_complex )
% 15.55/8.53         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X3 @ Y3 ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 15.55/8.53            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X3 @ Z ) @ ( times_times_complex @ W @ Y3 ) ) @ ( times_times_complex @ Y3 @ Z ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3913_add__frac__eq,axiom,
% 15.55/8.53      ! [Y3: real,Z: real,X3: real,W: real] :
% 15.55/8.53        ( ( Y3 != zero_zero_real )
% 15.55/8.53       => ( ( Z != zero_zero_real )
% 15.55/8.53         => ( ( plus_plus_real @ ( divide_divide_real @ X3 @ Y3 ) @ ( divide_divide_real @ W @ Z ) )
% 15.55/8.53            = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X3 @ Z ) @ ( times_times_real @ W @ Y3 ) ) @ ( times_times_real @ Y3 @ Z ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3914_add__frac__eq,axiom,
% 15.55/8.53      ! [Y3: rat,Z: rat,X3: rat,W: rat] :
% 15.55/8.53        ( ( Y3 != zero_zero_rat )
% 15.55/8.53       => ( ( Z != zero_zero_rat )
% 15.55/8.53         => ( ( plus_plus_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ ( divide_divide_rat @ W @ Z ) )
% 15.55/8.53            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ Z ) @ ( times_times_rat @ W @ Y3 ) ) @ ( times_times_rat @ Y3 @ Z ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3915_add__divide__eq__if__simps_I1_J,axiom,
% 15.55/8.53      ! [Z: complex,A: complex,B: complex] :
% 15.55/8.53        ( ( ( Z = zero_zero_complex )
% 15.55/8.53         => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 15.55/8.53            = A ) )
% 15.55/8.53        & ( ( Z != zero_zero_complex )
% 15.55/8.53         => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 15.55/8.53            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3916_add__divide__eq__if__simps_I1_J,axiom,
% 15.55/8.53      ! [Z: real,A: real,B: real] :
% 15.55/8.53        ( ( ( Z = zero_zero_real )
% 15.55/8.53         => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 15.55/8.53            = A ) )
% 15.55/8.53        & ( ( Z != zero_zero_real )
% 15.55/8.53         => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 15.55/8.53            = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3917_add__divide__eq__if__simps_I1_J,axiom,
% 15.55/8.53      ! [Z: rat,A: rat,B: rat] :
% 15.55/8.53        ( ( ( Z = zero_zero_rat )
% 15.55/8.53         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 15.55/8.53            = A ) )
% 15.55/8.53        & ( ( Z != zero_zero_rat )
% 15.55/8.53         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 15.55/8.53            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3918_add__divide__eq__if__simps_I2_J,axiom,
% 15.55/8.53      ! [Z: complex,A: complex,B: complex] :
% 15.55/8.53        ( ( ( Z = zero_zero_complex )
% 15.55/8.53         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 15.55/8.53            = B ) )
% 15.55/8.53        & ( ( Z != zero_zero_complex )
% 15.55/8.53         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 15.55/8.53            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3919_add__divide__eq__if__simps_I2_J,axiom,
% 15.55/8.53      ! [Z: real,A: real,B: real] :
% 15.55/8.53        ( ( ( Z = zero_zero_real )
% 15.55/8.53         => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 15.55/8.53            = B ) )
% 15.55/8.53        & ( ( Z != zero_zero_real )
% 15.55/8.53         => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 15.55/8.53            = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3920_add__divide__eq__if__simps_I2_J,axiom,
% 15.55/8.53      ! [Z: rat,A: rat,B: rat] :
% 15.55/8.53        ( ( ( Z = zero_zero_rat )
% 15.55/8.53         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 15.55/8.53            = B ) )
% 15.55/8.53        & ( ( Z != zero_zero_rat )
% 15.55/8.53         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 15.55/8.53            = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3921_less__add__iff1,axiom,
% 15.55/8.53      ! [A: real,E2: real,C: real,B: real,D3: real] :
% 15.55/8.53        ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D3 ) )
% 15.55/8.53        = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D3 ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3922_less__add__iff1,axiom,
% 15.55/8.53      ! [A: rat,E2: rat,C: rat,B: rat,D3: rat] :
% 15.55/8.53        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D3 ) )
% 15.55/8.53        = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D3 ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3923_less__add__iff1,axiom,
% 15.55/8.53      ! [A: int,E2: int,C: int,B: int,D3: int] :
% 15.55/8.53        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D3 ) )
% 15.55/8.53        = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D3 ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3924_less__add__iff2,axiom,
% 15.55/8.53      ! [A: real,E2: real,C: real,B: real,D3: real] :
% 15.55/8.53        ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D3 ) )
% 15.55/8.53        = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3925_less__add__iff2,axiom,
% 15.55/8.53      ! [A: rat,E2: rat,C: rat,B: rat,D3: rat] :
% 15.55/8.53        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D3 ) )
% 15.55/8.53        = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3926_less__add__iff2,axiom,
% 15.55/8.53      ! [A: int,E2: int,C: int,B: int,D3: int] :
% 15.55/8.53        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D3 ) )
% 15.55/8.53        = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3927_divide__diff__eq__iff,axiom,
% 15.55/8.53      ! [Z: complex,X3: complex,Y3: complex] :
% 15.55/8.53        ( ( Z != zero_zero_complex )
% 15.55/8.53       => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X3 @ Z ) @ Y3 )
% 15.55/8.53          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X3 @ ( times_times_complex @ Y3 @ Z ) ) @ Z ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3928_divide__diff__eq__iff,axiom,
% 15.55/8.53      ! [Z: real,X3: real,Y3: real] :
% 15.55/8.53        ( ( Z != zero_zero_real )
% 15.55/8.53       => ( ( minus_minus_real @ ( divide_divide_real @ X3 @ Z ) @ Y3 )
% 15.55/8.53          = ( divide_divide_real @ ( minus_minus_real @ X3 @ ( times_times_real @ Y3 @ Z ) ) @ Z ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3929_divide__diff__eq__iff,axiom,
% 15.55/8.53      ! [Z: rat,X3: rat,Y3: rat] :
% 15.55/8.53        ( ( Z != zero_zero_rat )
% 15.55/8.53       => ( ( minus_minus_rat @ ( divide_divide_rat @ X3 @ Z ) @ Y3 )
% 15.55/8.53          = ( divide_divide_rat @ ( minus_minus_rat @ X3 @ ( times_times_rat @ Y3 @ Z ) ) @ Z ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3930_diff__divide__eq__iff,axiom,
% 15.55/8.53      ! [Z: complex,X3: complex,Y3: complex] :
% 15.55/8.53        ( ( Z != zero_zero_complex )
% 15.55/8.53       => ( ( minus_minus_complex @ X3 @ ( divide1717551699836669952omplex @ Y3 @ Z ) )
% 15.55/8.53          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X3 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3931_diff__divide__eq__iff,axiom,
% 15.55/8.53      ! [Z: real,X3: real,Y3: real] :
% 15.55/8.53        ( ( Z != zero_zero_real )
% 15.55/8.53       => ( ( minus_minus_real @ X3 @ ( divide_divide_real @ Y3 @ Z ) )
% 15.55/8.53          = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X3 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3932_diff__divide__eq__iff,axiom,
% 15.55/8.53      ! [Z: rat,X3: rat,Y3: rat] :
% 15.55/8.53        ( ( Z != zero_zero_rat )
% 15.55/8.53       => ( ( minus_minus_rat @ X3 @ ( divide_divide_rat @ Y3 @ Z ) )
% 15.55/8.53          = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X3 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3933_diff__frac__eq,axiom,
% 15.55/8.53      ! [Y3: complex,Z: complex,X3: complex,W: complex] :
% 15.55/8.53        ( ( Y3 != zero_zero_complex )
% 15.55/8.53       => ( ( Z != zero_zero_complex )
% 15.55/8.53         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X3 @ Y3 ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 15.55/8.53            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X3 @ Z ) @ ( times_times_complex @ W @ Y3 ) ) @ ( times_times_complex @ Y3 @ Z ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3934_diff__frac__eq,axiom,
% 15.55/8.53      ! [Y3: real,Z: real,X3: real,W: real] :
% 15.55/8.53        ( ( Y3 != zero_zero_real )
% 15.55/8.53       => ( ( Z != zero_zero_real )
% 15.55/8.53         => ( ( minus_minus_real @ ( divide_divide_real @ X3 @ Y3 ) @ ( divide_divide_real @ W @ Z ) )
% 15.55/8.53            = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X3 @ Z ) @ ( times_times_real @ W @ Y3 ) ) @ ( times_times_real @ Y3 @ Z ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3935_diff__frac__eq,axiom,
% 15.55/8.53      ! [Y3: rat,Z: rat,X3: rat,W: rat] :
% 15.55/8.53        ( ( Y3 != zero_zero_rat )
% 15.55/8.53       => ( ( Z != zero_zero_rat )
% 15.55/8.53         => ( ( minus_minus_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ ( divide_divide_rat @ W @ Z ) )
% 15.55/8.53            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X3 @ Z ) @ ( times_times_rat @ W @ Y3 ) ) @ ( times_times_rat @ Y3 @ Z ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3936_add__divide__eq__if__simps_I4_J,axiom,
% 15.55/8.53      ! [Z: complex,A: complex,B: complex] :
% 15.55/8.53        ( ( ( Z = zero_zero_complex )
% 15.55/8.53         => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 15.55/8.53            = A ) )
% 15.55/8.53        & ( ( Z != zero_zero_complex )
% 15.55/8.53         => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 15.55/8.53            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3937_add__divide__eq__if__simps_I4_J,axiom,
% 15.55/8.53      ! [Z: real,A: real,B: real] :
% 15.55/8.53        ( ( ( Z = zero_zero_real )
% 15.55/8.53         => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 15.55/8.53            = A ) )
% 15.55/8.53        & ( ( Z != zero_zero_real )
% 15.55/8.53         => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 15.55/8.53            = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3938_add__divide__eq__if__simps_I4_J,axiom,
% 15.55/8.53      ! [Z: rat,A: rat,B: rat] :
% 15.55/8.53        ( ( ( Z = zero_zero_rat )
% 15.55/8.53         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 15.55/8.53            = A ) )
% 15.55/8.53        & ( ( Z != zero_zero_rat )
% 15.55/8.53         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 15.55/8.53            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3939_power__gt1__lemma,axiom,
% 15.55/8.53      ! [A: real,N: nat] :
% 15.55/8.53        ( ( ord_less_real @ one_one_real @ A )
% 15.55/8.53       => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3940_power__gt1__lemma,axiom,
% 15.55/8.53      ! [A: rat,N: nat] :
% 15.55/8.53        ( ( ord_less_rat @ one_one_rat @ A )
% 15.55/8.53       => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3941_power__gt1__lemma,axiom,
% 15.55/8.53      ! [A: nat,N: nat] :
% 15.55/8.53        ( ( ord_less_nat @ one_one_nat @ A )
% 15.55/8.53       => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3942_power__gt1__lemma,axiom,
% 15.55/8.53      ! [A: int,N: nat] :
% 15.55/8.53        ( ( ord_less_int @ one_one_int @ A )
% 15.55/8.53       => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3943_power__less__power__Suc,axiom,
% 15.55/8.53      ! [A: real,N: nat] :
% 15.55/8.53        ( ( ord_less_real @ one_one_real @ A )
% 15.55/8.53       => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3944_power__less__power__Suc,axiom,
% 15.55/8.53      ! [A: rat,N: nat] :
% 15.55/8.53        ( ( ord_less_rat @ one_one_rat @ A )
% 15.55/8.53       => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3945_power__less__power__Suc,axiom,
% 15.55/8.53      ! [A: nat,N: nat] :
% 15.55/8.53        ( ( ord_less_nat @ one_one_nat @ A )
% 15.55/8.53       => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3946_power__less__power__Suc,axiom,
% 15.55/8.53      ! [A: int,N: nat] :
% 15.55/8.53        ( ( ord_less_int @ one_one_int @ A )
% 15.55/8.53       => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3947_ex__less__of__nat__mult,axiom,
% 15.55/8.53      ! [X3: real,Y3: real] :
% 15.55/8.53        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.53       => ? [N2: nat] : ( ord_less_real @ Y3 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3948_ex__less__of__nat__mult,axiom,
% 15.55/8.53      ! [X3: rat,Y3: rat] :
% 15.55/8.53        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 15.55/8.53       => ? [N2: nat] : ( ord_less_rat @ Y3 @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ X3 ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3949_unit__dvdE,axiom,
% 15.55/8.53      ! [A: code_integer,B: code_integer] :
% 15.55/8.53        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 15.55/8.53       => ~ ( ( A != zero_z3403309356797280102nteger )
% 15.55/8.53           => ! [C2: code_integer] :
% 15.55/8.53                ( B
% 15.55/8.53               != ( times_3573771949741848930nteger @ A @ C2 ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3950_unit__dvdE,axiom,
% 15.55/8.53      ! [A: nat,B: nat] :
% 15.55/8.53        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 15.55/8.53       => ~ ( ( A != zero_zero_nat )
% 15.55/8.53           => ! [C2: nat] :
% 15.55/8.53                ( B
% 15.55/8.53               != ( times_times_nat @ A @ C2 ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3951_unit__dvdE,axiom,
% 15.55/8.53      ! [A: int,B: int] :
% 15.55/8.53        ( ( dvd_dvd_int @ A @ one_one_int )
% 15.55/8.53       => ~ ( ( A != zero_zero_int )
% 15.55/8.53           => ! [C2: int] :
% 15.55/8.53                ( B
% 15.55/8.53               != ( times_times_int @ A @ C2 ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3952_unity__coeff__ex,axiom,
% 15.55/8.53      ! [P: code_integer > $o,L: code_integer] :
% 15.55/8.53        ( ( ? [X: code_integer] : ( P @ ( times_3573771949741848930nteger @ L @ X ) ) )
% 15.55/8.53        = ( ? [X: code_integer] :
% 15.55/8.53              ( ( dvd_dvd_Code_integer @ L @ ( plus_p5714425477246183910nteger @ X @ zero_z3403309356797280102nteger ) )
% 15.55/8.53              & ( P @ X ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3953_unity__coeff__ex,axiom,
% 15.55/8.53      ! [P: real > $o,L: real] :
% 15.55/8.53        ( ( ? [X: real] : ( P @ ( times_times_real @ L @ X ) ) )
% 15.55/8.53        = ( ? [X: real] :
% 15.55/8.53              ( ( dvd_dvd_real @ L @ ( plus_plus_real @ X @ zero_zero_real ) )
% 15.55/8.53              & ( P @ X ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3954_unity__coeff__ex,axiom,
% 15.55/8.53      ! [P: rat > $o,L: rat] :
% 15.55/8.53        ( ( ? [X: rat] : ( P @ ( times_times_rat @ L @ X ) ) )
% 15.55/8.53        = ( ? [X: rat] :
% 15.55/8.53              ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X @ zero_zero_rat ) )
% 15.55/8.53              & ( P @ X ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3955_unity__coeff__ex,axiom,
% 15.55/8.53      ! [P: nat > $o,L: nat] :
% 15.55/8.53        ( ( ? [X: nat] : ( P @ ( times_times_nat @ L @ X ) ) )
% 15.55/8.53        = ( ? [X: nat] :
% 15.55/8.53              ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X @ zero_zero_nat ) )
% 15.55/8.53              & ( P @ X ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3956_unity__coeff__ex,axiom,
% 15.55/8.53      ! [P: int > $o,L: int] :
% 15.55/8.53        ( ( ? [X: int] : ( P @ ( times_times_int @ L @ X ) ) )
% 15.55/8.53        = ( ? [X: int] :
% 15.55/8.53              ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X @ zero_zero_int ) )
% 15.55/8.53              & ( P @ X ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3957_dvd__div__div__eq__mult,axiom,
% 15.55/8.53      ! [A: code_integer,C: code_integer,B: code_integer,D3: code_integer] :
% 15.55/8.53        ( ( A != zero_z3403309356797280102nteger )
% 15.55/8.53       => ( ( C != zero_z3403309356797280102nteger )
% 15.55/8.53         => ( ( dvd_dvd_Code_integer @ A @ B )
% 15.55/8.53           => ( ( dvd_dvd_Code_integer @ C @ D3 )
% 15.55/8.53             => ( ( ( divide6298287555418463151nteger @ B @ A )
% 15.55/8.53                  = ( divide6298287555418463151nteger @ D3 @ C ) )
% 15.55/8.53                = ( ( times_3573771949741848930nteger @ B @ C )
% 15.55/8.53                  = ( times_3573771949741848930nteger @ A @ D3 ) ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3958_dvd__div__div__eq__mult,axiom,
% 15.55/8.53      ! [A: nat,C: nat,B: nat,D3: nat] :
% 15.55/8.53        ( ( A != zero_zero_nat )
% 15.55/8.53       => ( ( C != zero_zero_nat )
% 15.55/8.53         => ( ( dvd_dvd_nat @ A @ B )
% 15.55/8.53           => ( ( dvd_dvd_nat @ C @ D3 )
% 15.55/8.53             => ( ( ( divide_divide_nat @ B @ A )
% 15.55/8.53                  = ( divide_divide_nat @ D3 @ C ) )
% 15.55/8.53                = ( ( times_times_nat @ B @ C )
% 15.55/8.53                  = ( times_times_nat @ A @ D3 ) ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3959_dvd__div__div__eq__mult,axiom,
% 15.55/8.53      ! [A: int,C: int,B: int,D3: int] :
% 15.55/8.53        ( ( A != zero_zero_int )
% 15.55/8.53       => ( ( C != zero_zero_int )
% 15.55/8.53         => ( ( dvd_dvd_int @ A @ B )
% 15.55/8.53           => ( ( dvd_dvd_int @ C @ D3 )
% 15.55/8.53             => ( ( ( divide_divide_int @ B @ A )
% 15.55/8.53                  = ( divide_divide_int @ D3 @ C ) )
% 15.55/8.53                = ( ( times_times_int @ B @ C )
% 15.55/8.53                  = ( times_times_int @ A @ D3 ) ) ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3960_dvd__div__iff__mult,axiom,
% 15.55/8.53      ! [C: code_integer,B: code_integer,A: code_integer] :
% 15.55/8.53        ( ( C != zero_z3403309356797280102nteger )
% 15.55/8.53       => ( ( dvd_dvd_Code_integer @ C @ B )
% 15.55/8.53         => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 15.55/8.53            = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3961_dvd__div__iff__mult,axiom,
% 15.55/8.53      ! [C: nat,B: nat,A: nat] :
% 15.55/8.53        ( ( C != zero_zero_nat )
% 15.55/8.53       => ( ( dvd_dvd_nat @ C @ B )
% 15.55/8.53         => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 15.55/8.53            = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3962_dvd__div__iff__mult,axiom,
% 15.55/8.53      ! [C: int,B: int,A: int] :
% 15.55/8.53        ( ( C != zero_zero_int )
% 15.55/8.53       => ( ( dvd_dvd_int @ C @ B )
% 15.55/8.53         => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 15.55/8.53            = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3963_div__dvd__iff__mult,axiom,
% 15.55/8.53      ! [B: code_integer,A: code_integer,C: code_integer] :
% 15.55/8.53        ( ( B != zero_z3403309356797280102nteger )
% 15.55/8.53       => ( ( dvd_dvd_Code_integer @ B @ A )
% 15.55/8.53         => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 15.55/8.53            = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3964_div__dvd__iff__mult,axiom,
% 15.55/8.53      ! [B: nat,A: nat,C: nat] :
% 15.55/8.53        ( ( B != zero_zero_nat )
% 15.55/8.53       => ( ( dvd_dvd_nat @ B @ A )
% 15.55/8.53         => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 15.55/8.53            = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3965_div__dvd__iff__mult,axiom,
% 15.55/8.53      ! [B: int,A: int,C: int] :
% 15.55/8.53        ( ( B != zero_zero_int )
% 15.55/8.53       => ( ( dvd_dvd_int @ B @ A )
% 15.55/8.53         => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 15.55/8.53            = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3966_dvd__div__eq__mult,axiom,
% 15.55/8.53      ! [A: code_integer,B: code_integer,C: code_integer] :
% 15.55/8.53        ( ( A != zero_z3403309356797280102nteger )
% 15.55/8.53       => ( ( dvd_dvd_Code_integer @ A @ B )
% 15.55/8.53         => ( ( ( divide6298287555418463151nteger @ B @ A )
% 15.55/8.53              = C )
% 15.55/8.53            = ( B
% 15.55/8.53              = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3967_dvd__div__eq__mult,axiom,
% 15.55/8.53      ! [A: nat,B: nat,C: nat] :
% 15.55/8.53        ( ( A != zero_zero_nat )
% 15.55/8.53       => ( ( dvd_dvd_nat @ A @ B )
% 15.55/8.53         => ( ( ( divide_divide_nat @ B @ A )
% 15.55/8.53              = C )
% 15.55/8.53            = ( B
% 15.55/8.53              = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3968_dvd__div__eq__mult,axiom,
% 15.55/8.53      ! [A: int,B: int,C: int] :
% 15.55/8.53        ( ( A != zero_zero_int )
% 15.55/8.53       => ( ( dvd_dvd_int @ A @ B )
% 15.55/8.53         => ( ( ( divide_divide_int @ B @ A )
% 15.55/8.53              = C )
% 15.55/8.53            = ( B
% 15.55/8.53              = ( times_times_int @ C @ A ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3969_inf__period_I4_J,axiom,
% 15.55/8.53      ! [D3: code_integer,D5: code_integer,T: code_integer] :
% 15.55/8.53        ( ( dvd_dvd_Code_integer @ D3 @ D5 )
% 15.55/8.53       => ! [X6: code_integer,K4: code_integer] :
% 15.55/8.53            ( ( ~ ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ X6 @ T ) ) )
% 15.55/8.53            = ( ~ ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X6 @ ( times_3573771949741848930nteger @ K4 @ D5 ) ) @ T ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3970_inf__period_I4_J,axiom,
% 15.55/8.53      ! [D3: real,D5: real,T: real] :
% 15.55/8.53        ( ( dvd_dvd_real @ D3 @ D5 )
% 15.55/8.53       => ! [X6: real,K4: real] :
% 15.55/8.53            ( ( ~ ( dvd_dvd_real @ D3 @ ( plus_plus_real @ X6 @ T ) ) )
% 15.55/8.53            = ( ~ ( dvd_dvd_real @ D3 @ ( plus_plus_real @ ( minus_minus_real @ X6 @ ( times_times_real @ K4 @ D5 ) ) @ T ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3971_inf__period_I4_J,axiom,
% 15.55/8.53      ! [D3: rat,D5: rat,T: rat] :
% 15.55/8.53        ( ( dvd_dvd_rat @ D3 @ D5 )
% 15.55/8.53       => ! [X6: rat,K4: rat] :
% 15.55/8.53            ( ( ~ ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ X6 @ T ) ) )
% 15.55/8.53            = ( ~ ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D5 ) ) @ T ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3972_inf__period_I4_J,axiom,
% 15.55/8.53      ! [D3: int,D5: int,T: int] :
% 15.55/8.53        ( ( dvd_dvd_int @ D3 @ D5 )
% 15.55/8.53       => ! [X6: int,K4: int] :
% 15.55/8.53            ( ( ~ ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ T ) ) )
% 15.55/8.53            = ( ~ ( dvd_dvd_int @ D3 @ ( plus_plus_int @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D5 ) ) @ T ) ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3973_inf__period_I3_J,axiom,
% 15.55/8.53      ! [D3: code_integer,D5: code_integer,T: code_integer] :
% 15.55/8.53        ( ( dvd_dvd_Code_integer @ D3 @ D5 )
% 15.55/8.53       => ! [X6: code_integer,K4: code_integer] :
% 15.55/8.53            ( ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ X6 @ T ) )
% 15.55/8.53            = ( dvd_dvd_Code_integer @ D3 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X6 @ ( times_3573771949741848930nteger @ K4 @ D5 ) ) @ T ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3974_inf__period_I3_J,axiom,
% 15.55/8.53      ! [D3: real,D5: real,T: real] :
% 15.55/8.53        ( ( dvd_dvd_real @ D3 @ D5 )
% 15.55/8.53       => ! [X6: real,K4: real] :
% 15.55/8.53            ( ( dvd_dvd_real @ D3 @ ( plus_plus_real @ X6 @ T ) )
% 15.55/8.53            = ( dvd_dvd_real @ D3 @ ( plus_plus_real @ ( minus_minus_real @ X6 @ ( times_times_real @ K4 @ D5 ) ) @ T ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3975_inf__period_I3_J,axiom,
% 15.55/8.53      ! [D3: rat,D5: rat,T: rat] :
% 15.55/8.53        ( ( dvd_dvd_rat @ D3 @ D5 )
% 15.55/8.53       => ! [X6: rat,K4: rat] :
% 15.55/8.53            ( ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ X6 @ T ) )
% 15.55/8.53            = ( dvd_dvd_rat @ D3 @ ( plus_plus_rat @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D5 ) ) @ T ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3976_inf__period_I3_J,axiom,
% 15.55/8.53      ! [D3: int,D5: int,T: int] :
% 15.55/8.53        ( ( dvd_dvd_int @ D3 @ D5 )
% 15.55/8.53       => ! [X6: int,K4: int] :
% 15.55/8.53            ( ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ T ) )
% 15.55/8.53            = ( dvd_dvd_int @ D3 @ ( plus_plus_int @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D5 ) ) @ T ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3977_one__less__mult,axiom,
% 15.55/8.53      ! [N: nat,M: nat] :
% 15.55/8.53        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 15.55/8.53       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 15.55/8.53         => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3978_n__less__m__mult__n,axiom,
% 15.55/8.53      ! [N: nat,M: nat] :
% 15.55/8.53        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.53       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 15.55/8.53         => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3979_n__less__n__mult__m,axiom,
% 15.55/8.53      ! [N: nat,M: nat] :
% 15.55/8.53        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.53       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 15.55/8.53         => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3980_nat__mult__le__cancel1,axiom,
% 15.55/8.53      ! [K: nat,M: nat,N: nat] :
% 15.55/8.53        ( ( ord_less_nat @ zero_zero_nat @ K )
% 15.55/8.53       => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 15.55/8.53          = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3981_nat__mult__div__cancel1,axiom,
% 15.55/8.53      ! [K: nat,M: nat,N: nat] :
% 15.55/8.53        ( ( ord_less_nat @ zero_zero_nat @ K )
% 15.55/8.53       => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 15.55/8.53          = ( divide_divide_nat @ M @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3982_div__less__iff__less__mult,axiom,
% 15.55/8.53      ! [Q3: nat,M: nat,N: nat] :
% 15.55/8.53        ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 15.55/8.53       => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q3 ) @ N )
% 15.55/8.53          = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q3 ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3983_dvd__mult__cancel,axiom,
% 15.55/8.53      ! [K: nat,M: nat,N: nat] :
% 15.55/8.53        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 15.55/8.53       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 15.55/8.53         => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3984_nat__mult__dvd__cancel1,axiom,
% 15.55/8.53      ! [K: nat,M: nat,N: nat] :
% 15.55/8.53        ( ( ord_less_nat @ zero_zero_nat @ K )
% 15.55/8.53       => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 15.55/8.53          = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3985_nat__eq__add__iff1,axiom,
% 15.55/8.53      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ J @ I )
% 15.55/8.53       => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 15.55/8.53            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 15.55/8.53          = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 15.55/8.53            = N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3986_nat__eq__add__iff2,axiom,
% 15.55/8.53      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ I @ J )
% 15.55/8.53       => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 15.55/8.53            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 15.55/8.53          = ( M
% 15.55/8.53            = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3987_nat__le__add__iff1,axiom,
% 15.55/8.53      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ J @ I )
% 15.55/8.53       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 15.55/8.53          = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3988_nat__le__add__iff2,axiom,
% 15.55/8.53      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ I @ J )
% 15.55/8.53       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 15.55/8.53          = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3989_nat__diff__add__eq1,axiom,
% 15.55/8.53      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ J @ I )
% 15.55/8.53       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 15.55/8.53          = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3990_nat__diff__add__eq2,axiom,
% 15.55/8.53      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 15.55/8.53        ( ( ord_less_eq_nat @ I @ J )
% 15.55/8.53       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 15.55/8.53          = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3991_bezout__add__strong__nat,axiom,
% 15.55/8.53      ! [A: nat,B: nat] :
% 15.55/8.53        ( ( A != zero_zero_nat )
% 15.55/8.53       => ? [D6: nat,X4: nat,Y4: nat] :
% 15.55/8.53            ( ( dvd_dvd_nat @ D6 @ A )
% 15.55/8.53            & ( dvd_dvd_nat @ D6 @ B )
% 15.55/8.53            & ( ( times_times_nat @ A @ X4 )
% 15.55/8.53              = ( plus_plus_nat @ ( times_times_nat @ B @ Y4 ) @ D6 ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3992_mult__le__cancel__left1,axiom,
% 15.55/8.53      ! [C: real,B: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 15.55/8.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53           => ( ord_less_eq_real @ one_one_real @ B ) )
% 15.55/8.53          & ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.53           => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3993_mult__le__cancel__left1,axiom,
% 15.55/8.53      ! [C: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 15.55/8.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 15.55/8.53          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.53           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3994_mult__le__cancel__left1,axiom,
% 15.55/8.53      ! [C: int,B: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 15.55/8.53        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 15.55/8.53           => ( ord_less_eq_int @ one_one_int @ B ) )
% 15.55/8.53          & ( ( ord_less_int @ C @ zero_zero_int )
% 15.55/8.53           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3995_mult__le__cancel__left2,axiom,
% 15.55/8.53      ! [C: real,A: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 15.55/8.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53           => ( ord_less_eq_real @ A @ one_one_real ) )
% 15.55/8.53          & ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.53           => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3996_mult__le__cancel__left2,axiom,
% 15.55/8.53      ! [C: rat,A: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 15.55/8.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 15.55/8.53          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.53           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3997_mult__le__cancel__left2,axiom,
% 15.55/8.53      ! [C: int,A: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 15.55/8.53        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 15.55/8.53           => ( ord_less_eq_int @ A @ one_one_int ) )
% 15.55/8.53          & ( ( ord_less_int @ C @ zero_zero_int )
% 15.55/8.53           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3998_mult__le__cancel__right1,axiom,
% 15.55/8.53      ! [C: real,B: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 15.55/8.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53           => ( ord_less_eq_real @ one_one_real @ B ) )
% 15.55/8.53          & ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.53           => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_3999_mult__le__cancel__right1,axiom,
% 15.55/8.53      ! [C: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 15.55/8.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 15.55/8.53          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.53           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_4000_mult__le__cancel__right1,axiom,
% 15.55/8.53      ! [C: int,B: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 15.55/8.53        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 15.55/8.53           => ( ord_less_eq_int @ one_one_int @ B ) )
% 15.55/8.53          & ( ( ord_less_int @ C @ zero_zero_int )
% 15.55/8.53           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_4001_mult__le__cancel__right2,axiom,
% 15.55/8.53      ! [A: real,C: real] :
% 15.55/8.53        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 15.55/8.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.53           => ( ord_less_eq_real @ A @ one_one_real ) )
% 15.55/8.53          & ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.53           => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_4002_mult__le__cancel__right2,axiom,
% 15.55/8.53      ! [A: rat,C: rat] :
% 15.55/8.53        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 15.55/8.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.53           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 15.55/8.53          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.53           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_4003_mult__le__cancel__right2,axiom,
% 15.55/8.53      ! [A: int,C: int] :
% 15.55/8.53        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 15.55/8.53        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 15.55/8.53           => ( ord_less_eq_int @ A @ one_one_int ) )
% 15.55/8.53          & ( ( ord_less_int @ C @ zero_zero_int )
% 15.55/8.53           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_4004_mult__less__cancel__left1,axiom,
% 15.55/8.53      ! [C: real,B: real] :
% 15.55/8.53        ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 15.55/8.53        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 15.55/8.53           => ( ord_less_real @ one_one_real @ B ) )
% 15.55/8.53          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 15.55/8.53           => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 15.55/8.53  
% 15.55/8.53  thf(fact_4005_mult__less__cancel__left1,axiom,
% 15.55/8.53      ! [C: rat,B: rat] :
% 15.55/8.53        ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 15.55/8.53        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 15.55/8.53           => ( ord_less_rat @ one_one_rat @ B ) )
% 15.55/8.53          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 15.55/8.54           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4006_mult__less__cancel__left1,axiom,
% 15.55/8.54      ! [C: int,B: int] :
% 15.55/8.54        ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 15.55/8.54        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 15.55/8.54           => ( ord_less_int @ one_one_int @ B ) )
% 15.55/8.54          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 15.55/8.54           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4007_mult__less__cancel__left2,axiom,
% 15.55/8.54      ! [C: real,A: real] :
% 15.55/8.54        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 15.55/8.54        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 15.55/8.54           => ( ord_less_real @ A @ one_one_real ) )
% 15.55/8.54          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 15.55/8.54           => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4008_mult__less__cancel__left2,axiom,
% 15.55/8.54      ! [C: rat,A: rat] :
% 15.55/8.54        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 15.55/8.54        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 15.55/8.54           => ( ord_less_rat @ A @ one_one_rat ) )
% 15.55/8.54          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 15.55/8.54           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4009_mult__less__cancel__left2,axiom,
% 15.55/8.54      ! [C: int,A: int] :
% 15.55/8.54        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 15.55/8.54        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 15.55/8.54           => ( ord_less_int @ A @ one_one_int ) )
% 15.55/8.54          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 15.55/8.54           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4010_mult__less__cancel__right1,axiom,
% 15.55/8.54      ! [C: real,B: real] :
% 15.55/8.54        ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 15.55/8.54        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 15.55/8.54           => ( ord_less_real @ one_one_real @ B ) )
% 15.55/8.54          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 15.55/8.54           => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4011_mult__less__cancel__right1,axiom,
% 15.55/8.54      ! [C: rat,B: rat] :
% 15.55/8.54        ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 15.55/8.54        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 15.55/8.54           => ( ord_less_rat @ one_one_rat @ B ) )
% 15.55/8.54          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 15.55/8.54           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4012_mult__less__cancel__right1,axiom,
% 15.55/8.54      ! [C: int,B: int] :
% 15.55/8.54        ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 15.55/8.54        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 15.55/8.54           => ( ord_less_int @ one_one_int @ B ) )
% 15.55/8.54          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 15.55/8.54           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4013_mult__less__cancel__right2,axiom,
% 15.55/8.54      ! [A: real,C: real] :
% 15.55/8.54        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 15.55/8.54        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 15.55/8.54           => ( ord_less_real @ A @ one_one_real ) )
% 15.55/8.54          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 15.55/8.54           => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4014_mult__less__cancel__right2,axiom,
% 15.55/8.54      ! [A: rat,C: rat] :
% 15.55/8.54        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 15.55/8.54        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 15.55/8.54           => ( ord_less_rat @ A @ one_one_rat ) )
% 15.55/8.54          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 15.55/8.54           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4015_mult__less__cancel__right2,axiom,
% 15.55/8.54      ! [A: int,C: int] :
% 15.55/8.54        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 15.55/8.54        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 15.55/8.54           => ( ord_less_int @ A @ one_one_int ) )
% 15.55/8.54          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 15.55/8.54           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4016_field__le__mult__one__interval,axiom,
% 15.55/8.54      ! [X3: real,Y3: real] :
% 15.55/8.54        ( ! [Z3: real] :
% 15.55/8.54            ( ( ord_less_real @ zero_zero_real @ Z3 )
% 15.55/8.54           => ( ( ord_less_real @ Z3 @ one_one_real )
% 15.55/8.54             => ( ord_less_eq_real @ ( times_times_real @ Z3 @ X3 ) @ Y3 ) ) )
% 15.55/8.54       => ( ord_less_eq_real @ X3 @ Y3 ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4017_field__le__mult__one__interval,axiom,
% 15.55/8.54      ! [X3: rat,Y3: rat] :
% 15.55/8.54        ( ! [Z3: rat] :
% 15.55/8.54            ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 15.55/8.54           => ( ( ord_less_rat @ Z3 @ one_one_rat )
% 15.55/8.54             => ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ X3 ) @ Y3 ) ) )
% 15.55/8.54       => ( ord_less_eq_rat @ X3 @ Y3 ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4018_divide__le__eq,axiom,
% 15.55/8.54      ! [B: real,C: real,A: real] :
% 15.55/8.54        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 15.55/8.54        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.54           => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 15.55/8.54          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.54           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.54               => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 15.55/8.54              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.54               => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4019_divide__le__eq,axiom,
% 15.55/8.54      ! [B: rat,C: rat,A: rat] :
% 15.55/8.54        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 15.55/8.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.54           => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 15.55/8.54          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.54           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.54               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 15.55/8.54              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.54               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4020_le__divide__eq,axiom,
% 15.55/8.54      ! [A: real,B: real,C: real] :
% 15.55/8.54        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 15.55/8.54        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.54           => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 15.55/8.54          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.54           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.54               => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 15.55/8.54              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.54               => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4021_le__divide__eq,axiom,
% 15.55/8.54      ! [A: rat,B: rat,C: rat] :
% 15.55/8.54        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 15.55/8.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.54           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 15.55/8.54          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.54           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.54               => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 15.55/8.54              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.54               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4022_divide__left__mono,axiom,
% 15.55/8.54      ! [B: real,A: real,C: real] :
% 15.55/8.54        ( ( ord_less_eq_real @ B @ A )
% 15.55/8.54       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 15.55/8.54         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 15.55/8.54           => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4023_divide__left__mono,axiom,
% 15.55/8.54      ! [B: rat,A: rat,C: rat] :
% 15.55/8.54        ( ( ord_less_eq_rat @ B @ A )
% 15.55/8.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 15.55/8.54         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 15.55/8.54           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4024_neg__divide__le__eq,axiom,
% 15.55/8.54      ! [C: real,B: real,A: real] :
% 15.55/8.54        ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.54       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 15.55/8.54          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4025_neg__divide__le__eq,axiom,
% 15.55/8.54      ! [C: rat,B: rat,A: rat] :
% 15.55/8.54        ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.54       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 15.55/8.54          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4026_neg__le__divide__eq,axiom,
% 15.55/8.54      ! [C: real,A: real,B: real] :
% 15.55/8.54        ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.54       => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 15.55/8.54          = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4027_neg__le__divide__eq,axiom,
% 15.55/8.54      ! [C: rat,A: rat,B: rat] :
% 15.55/8.54        ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.54       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 15.55/8.54          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4028_pos__divide__le__eq,axiom,
% 15.55/8.54      ! [C: real,B: real,A: real] :
% 15.55/8.54        ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.54       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 15.55/8.54          = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4029_pos__divide__le__eq,axiom,
% 15.55/8.54      ! [C: rat,B: rat,A: rat] :
% 15.55/8.54        ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.54       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 15.55/8.54          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4030_pos__le__divide__eq,axiom,
% 15.55/8.54      ! [C: real,A: real,B: real] :
% 15.55/8.54        ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.54       => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 15.55/8.54          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4031_pos__le__divide__eq,axiom,
% 15.55/8.54      ! [C: rat,A: rat,B: rat] :
% 15.55/8.54        ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.54       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 15.55/8.54          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4032_mult__imp__div__pos__le,axiom,
% 15.55/8.54      ! [Y3: real,X3: real,Z: real] :
% 15.55/8.54        ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.55/8.54       => ( ( ord_less_eq_real @ X3 @ ( times_times_real @ Z @ Y3 ) )
% 15.55/8.54         => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y3 ) @ Z ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4033_mult__imp__div__pos__le,axiom,
% 15.55/8.54      ! [Y3: rat,X3: rat,Z: rat] :
% 15.55/8.54        ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 15.55/8.54       => ( ( ord_less_eq_rat @ X3 @ ( times_times_rat @ Z @ Y3 ) )
% 15.55/8.54         => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ Z ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4034_mult__imp__le__div__pos,axiom,
% 15.55/8.54      ! [Y3: real,Z: real,X3: real] :
% 15.55/8.54        ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.55/8.54       => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y3 ) @ X3 )
% 15.55/8.54         => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4035_mult__imp__le__div__pos,axiom,
% 15.55/8.54      ! [Y3: rat,Z: rat,X3: rat] :
% 15.55/8.54        ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 15.55/8.54       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y3 ) @ X3 )
% 15.55/8.54         => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4036_divide__left__mono__neg,axiom,
% 15.55/8.54      ! [A: real,B: real,C: real] :
% 15.55/8.54        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.54       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 15.55/8.54         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 15.55/8.54           => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4037_divide__left__mono__neg,axiom,
% 15.55/8.54      ! [A: rat,B: rat,C: rat] :
% 15.55/8.54        ( ( ord_less_eq_rat @ A @ B )
% 15.55/8.54       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 15.55/8.54         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 15.55/8.54           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4038_convex__bound__le,axiom,
% 15.55/8.54      ! [X3: real,A: real,Y3: real,U: real,V: real] :
% 15.55/8.54        ( ( ord_less_eq_real @ X3 @ A )
% 15.55/8.54       => ( ( ord_less_eq_real @ Y3 @ A )
% 15.55/8.54         => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 15.55/8.54           => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 15.55/8.54             => ( ( ( plus_plus_real @ U @ V )
% 15.55/8.54                  = one_one_real )
% 15.55/8.54               => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X3 ) @ ( times_times_real @ V @ Y3 ) ) @ A ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4039_convex__bound__le,axiom,
% 15.55/8.54      ! [X3: rat,A: rat,Y3: rat,U: rat,V: rat] :
% 15.55/8.54        ( ( ord_less_eq_rat @ X3 @ A )
% 15.55/8.54       => ( ( ord_less_eq_rat @ Y3 @ A )
% 15.55/8.54         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 15.55/8.54           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 15.55/8.54             => ( ( ( plus_plus_rat @ U @ V )
% 15.55/8.54                  = one_one_rat )
% 15.55/8.54               => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X3 ) @ ( times_times_rat @ V @ Y3 ) ) @ A ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4040_convex__bound__le,axiom,
% 15.55/8.54      ! [X3: int,A: int,Y3: int,U: int,V: int] :
% 15.55/8.54        ( ( ord_less_eq_int @ X3 @ A )
% 15.55/8.54       => ( ( ord_less_eq_int @ Y3 @ A )
% 15.55/8.54         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 15.55/8.54           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 15.55/8.54             => ( ( ( plus_plus_int @ U @ V )
% 15.55/8.54                  = one_one_int )
% 15.55/8.54               => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X3 ) @ ( times_times_int @ V @ Y3 ) ) @ A ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4041_divide__less__eq__numeral_I1_J,axiom,
% 15.55/8.54      ! [B: real,C: real,W: num] :
% 15.55/8.54        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 15.55/8.54        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.54           => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 15.55/8.54          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.54           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.54               => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 15.55/8.54              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.54               => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4042_divide__less__eq__numeral_I1_J,axiom,
% 15.55/8.54      ! [B: rat,C: rat,W: num] :
% 15.55/8.54        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 15.55/8.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.54           => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 15.55/8.54          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.54           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.54               => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 15.55/8.54              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.54               => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4043_less__divide__eq__numeral_I1_J,axiom,
% 15.55/8.54      ! [W: num,B: real,C: real] :
% 15.55/8.54        ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 15.55/8.54        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.54           => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 15.55/8.54          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.54           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.54               => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 15.55/8.54              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.54               => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4044_less__divide__eq__numeral_I1_J,axiom,
% 15.55/8.54      ! [W: num,B: rat,C: rat] :
% 15.55/8.54        ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 15.55/8.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.54           => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 15.55/8.54          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.54           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.54               => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 15.55/8.54              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.54               => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4045_frac__le__eq,axiom,
% 15.55/8.54      ! [Y3: real,Z: real,X3: real,W: real] :
% 15.55/8.54        ( ( Y3 != zero_zero_real )
% 15.55/8.54       => ( ( Z != zero_zero_real )
% 15.55/8.54         => ( ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y3 ) @ ( divide_divide_real @ W @ Z ) )
% 15.55/8.54            = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X3 @ Z ) @ ( times_times_real @ W @ Y3 ) ) @ ( times_times_real @ Y3 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4046_frac__le__eq,axiom,
% 15.55/8.54      ! [Y3: rat,Z: rat,X3: rat,W: rat] :
% 15.55/8.54        ( ( Y3 != zero_zero_rat )
% 15.55/8.54       => ( ( Z != zero_zero_rat )
% 15.55/8.54         => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ ( divide_divide_rat @ W @ Z ) )
% 15.55/8.54            = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X3 @ Z ) @ ( times_times_rat @ W @ Y3 ) ) @ ( times_times_rat @ Y3 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4047_power__Suc__less,axiom,
% 15.55/8.54      ! [A: real,N: nat] :
% 15.55/8.54        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.54       => ( ( ord_less_real @ A @ one_one_real )
% 15.55/8.54         => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4048_power__Suc__less,axiom,
% 15.55/8.54      ! [A: rat,N: nat] :
% 15.55/8.54        ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.54       => ( ( ord_less_rat @ A @ one_one_rat )
% 15.55/8.54         => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4049_power__Suc__less,axiom,
% 15.55/8.54      ! [A: nat,N: nat] :
% 15.55/8.54        ( ( ord_less_nat @ zero_zero_nat @ A )
% 15.55/8.54       => ( ( ord_less_nat @ A @ one_one_nat )
% 15.55/8.54         => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4050_power__Suc__less,axiom,
% 15.55/8.54      ! [A: int,N: nat] :
% 15.55/8.54        ( ( ord_less_int @ zero_zero_int @ A )
% 15.55/8.54       => ( ( ord_less_int @ A @ one_one_int )
% 15.55/8.54         => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4051_frac__less__eq,axiom,
% 15.55/8.54      ! [Y3: real,Z: real,X3: real,W: real] :
% 15.55/8.54        ( ( Y3 != zero_zero_real )
% 15.55/8.54       => ( ( Z != zero_zero_real )
% 15.55/8.54         => ( ( ord_less_real @ ( divide_divide_real @ X3 @ Y3 ) @ ( divide_divide_real @ W @ Z ) )
% 15.55/8.54            = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X3 @ Z ) @ ( times_times_real @ W @ Y3 ) ) @ ( times_times_real @ Y3 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4052_frac__less__eq,axiom,
% 15.55/8.54      ! [Y3: rat,Z: rat,X3: rat,W: rat] :
% 15.55/8.54        ( ( Y3 != zero_zero_rat )
% 15.55/8.54       => ( ( Z != zero_zero_rat )
% 15.55/8.54         => ( ( ord_less_rat @ ( divide_divide_rat @ X3 @ Y3 ) @ ( divide_divide_rat @ W @ Z ) )
% 15.55/8.54            = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X3 @ Z ) @ ( times_times_rat @ W @ Y3 ) ) @ ( times_times_rat @ Y3 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4053_mult__2,axiom,
% 15.55/8.54      ! [Z: complex] :
% 15.55/8.54        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 15.55/8.54        = ( plus_plus_complex @ Z @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4054_mult__2,axiom,
% 15.55/8.54      ! [Z: real] :
% 15.55/8.54        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 15.55/8.54        = ( plus_plus_real @ Z @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4055_mult__2,axiom,
% 15.55/8.54      ! [Z: rat] :
% 15.55/8.54        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 15.55/8.54        = ( plus_plus_rat @ Z @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4056_mult__2,axiom,
% 15.55/8.54      ! [Z: nat] :
% 15.55/8.54        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 15.55/8.54        = ( plus_plus_nat @ Z @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4057_mult__2,axiom,
% 15.55/8.54      ! [Z: int] :
% 15.55/8.54        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 15.55/8.54        = ( plus_plus_int @ Z @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4058_mult__2__right,axiom,
% 15.55/8.54      ! [Z: complex] :
% 15.55/8.54        ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 15.55/8.54        = ( plus_plus_complex @ Z @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4059_mult__2__right,axiom,
% 15.55/8.54      ! [Z: real] :
% 15.55/8.54        ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 15.55/8.54        = ( plus_plus_real @ Z @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4060_mult__2__right,axiom,
% 15.55/8.54      ! [Z: rat] :
% 15.55/8.54        ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 15.55/8.54        = ( plus_plus_rat @ Z @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4061_mult__2__right,axiom,
% 15.55/8.54      ! [Z: nat] :
% 15.55/8.54        ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.54        = ( plus_plus_nat @ Z @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4062_mult__2__right,axiom,
% 15.55/8.54      ! [Z: int] :
% 15.55/8.54        ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.54        = ( plus_plus_int @ Z @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4063_left__add__twice,axiom,
% 15.55/8.54      ! [A: complex,B: complex] :
% 15.55/8.54        ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 15.55/8.54        = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4064_left__add__twice,axiom,
% 15.55/8.54      ! [A: real,B: real] :
% 15.55/8.54        ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 15.55/8.54        = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4065_left__add__twice,axiom,
% 15.55/8.54      ! [A: rat,B: rat] :
% 15.55/8.54        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 15.55/8.54        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4066_left__add__twice,axiom,
% 15.55/8.54      ! [A: nat,B: nat] :
% 15.55/8.54        ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 15.55/8.54        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4067_left__add__twice,axiom,
% 15.55/8.54      ! [A: int,B: int] :
% 15.55/8.54        ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 15.55/8.54        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4068_is__unit__div__mult__cancel__right,axiom,
% 15.55/8.54      ! [A: code_integer,B: code_integer] :
% 15.55/8.54        ( ( A != zero_z3403309356797280102nteger )
% 15.55/8.54       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 15.55/8.54         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 15.55/8.54            = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4069_is__unit__div__mult__cancel__right,axiom,
% 15.55/8.54      ! [A: nat,B: nat] :
% 15.55/8.54        ( ( A != zero_zero_nat )
% 15.55/8.54       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 15.55/8.54         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 15.55/8.54            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4070_is__unit__div__mult__cancel__right,axiom,
% 15.55/8.54      ! [A: int,B: int] :
% 15.55/8.54        ( ( A != zero_zero_int )
% 15.55/8.54       => ( ( dvd_dvd_int @ B @ one_one_int )
% 15.55/8.54         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 15.55/8.54            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4071_is__unit__div__mult__cancel__left,axiom,
% 15.55/8.54      ! [A: code_integer,B: code_integer] :
% 15.55/8.54        ( ( A != zero_z3403309356797280102nteger )
% 15.55/8.54       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 15.55/8.54         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 15.55/8.54            = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4072_is__unit__div__mult__cancel__left,axiom,
% 15.55/8.54      ! [A: nat,B: nat] :
% 15.55/8.54        ( ( A != zero_zero_nat )
% 15.55/8.54       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 15.55/8.54         => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 15.55/8.54            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4073_is__unit__div__mult__cancel__left,axiom,
% 15.55/8.54      ! [A: int,B: int] :
% 15.55/8.54        ( ( A != zero_zero_int )
% 15.55/8.54       => ( ( dvd_dvd_int @ B @ one_one_int )
% 15.55/8.54         => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 15.55/8.54            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4074_is__unitE,axiom,
% 15.55/8.54      ! [A: code_integer,C: code_integer] :
% 15.55/8.54        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 15.55/8.54       => ~ ( ( A != zero_z3403309356797280102nteger )
% 15.55/8.54           => ! [B4: code_integer] :
% 15.55/8.54                ( ( B4 != zero_z3403309356797280102nteger )
% 15.55/8.54               => ( ( dvd_dvd_Code_integer @ B4 @ one_one_Code_integer )
% 15.55/8.54                 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 15.55/8.54                      = B4 )
% 15.55/8.54                   => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B4 )
% 15.55/8.54                        = A )
% 15.55/8.54                     => ( ( ( times_3573771949741848930nteger @ A @ B4 )
% 15.55/8.54                          = one_one_Code_integer )
% 15.55/8.54                       => ( ( divide6298287555418463151nteger @ C @ A )
% 15.55/8.54                         != ( times_3573771949741848930nteger @ C @ B4 ) ) ) ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4075_is__unitE,axiom,
% 15.55/8.54      ! [A: nat,C: nat] :
% 15.55/8.54        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 15.55/8.54       => ~ ( ( A != zero_zero_nat )
% 15.55/8.54           => ! [B4: nat] :
% 15.55/8.54                ( ( B4 != zero_zero_nat )
% 15.55/8.54               => ( ( dvd_dvd_nat @ B4 @ one_one_nat )
% 15.55/8.54                 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 15.55/8.54                      = B4 )
% 15.55/8.54                   => ( ( ( divide_divide_nat @ one_one_nat @ B4 )
% 15.55/8.54                        = A )
% 15.55/8.54                     => ( ( ( times_times_nat @ A @ B4 )
% 15.55/8.54                          = one_one_nat )
% 15.55/8.54                       => ( ( divide_divide_nat @ C @ A )
% 15.55/8.54                         != ( times_times_nat @ C @ B4 ) ) ) ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4076_is__unitE,axiom,
% 15.55/8.54      ! [A: int,C: int] :
% 15.55/8.54        ( ( dvd_dvd_int @ A @ one_one_int )
% 15.55/8.54       => ~ ( ( A != zero_zero_int )
% 15.55/8.54           => ! [B4: int] :
% 15.55/8.54                ( ( B4 != zero_zero_int )
% 15.55/8.54               => ( ( dvd_dvd_int @ B4 @ one_one_int )
% 15.55/8.54                 => ( ( ( divide_divide_int @ one_one_int @ A )
% 15.55/8.54                      = B4 )
% 15.55/8.54                   => ( ( ( divide_divide_int @ one_one_int @ B4 )
% 15.55/8.54                        = A )
% 15.55/8.54                     => ( ( ( times_times_int @ A @ B4 )
% 15.55/8.54                          = one_one_int )
% 15.55/8.54                       => ( ( divide_divide_int @ C @ A )
% 15.55/8.54                         != ( times_times_int @ C @ B4 ) ) ) ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4077_evenE,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.55/8.54       => ~ ! [B4: code_integer] :
% 15.55/8.54              ( A
% 15.55/8.54             != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B4 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4078_evenE,axiom,
% 15.55/8.54      ! [A: nat] :
% 15.55/8.54        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.55/8.54       => ~ ! [B4: nat] :
% 15.55/8.54              ( A
% 15.55/8.54             != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B4 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4079_evenE,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.55/8.54       => ~ ! [B4: int] :
% 15.55/8.54              ( A
% 15.55/8.54             != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B4 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4080_power4__eq__xxxx,axiom,
% 15.55/8.54      ! [X3: complex] :
% 15.55/8.54        ( ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 15.55/8.54        = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X3 @ X3 ) @ X3 ) @ X3 ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4081_power4__eq__xxxx,axiom,
% 15.55/8.54      ! [X3: real] :
% 15.55/8.54        ( ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 15.55/8.54        = ( times_times_real @ ( times_times_real @ ( times_times_real @ X3 @ X3 ) @ X3 ) @ X3 ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4082_power4__eq__xxxx,axiom,
% 15.55/8.54      ! [X3: rat] :
% 15.55/8.54        ( ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 15.55/8.54        = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X3 @ X3 ) @ X3 ) @ X3 ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4083_power4__eq__xxxx,axiom,
% 15.55/8.54      ! [X3: nat] :
% 15.55/8.54        ( ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 15.55/8.54        = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X3 @ X3 ) @ X3 ) @ X3 ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4084_power4__eq__xxxx,axiom,
% 15.55/8.54      ! [X3: int] :
% 15.55/8.54        ( ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 15.55/8.54        = ( times_times_int @ ( times_times_int @ ( times_times_int @ X3 @ X3 ) @ X3 ) @ X3 ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4085_power2__eq__square,axiom,
% 15.55/8.54      ! [A: complex] :
% 15.55/8.54        ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.54        = ( times_times_complex @ A @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4086_power2__eq__square,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.54        = ( times_times_real @ A @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4087_power2__eq__square,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.54        = ( times_times_rat @ A @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4088_power2__eq__square,axiom,
% 15.55/8.54      ! [A: nat] :
% 15.55/8.54        ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.54        = ( times_times_nat @ A @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4089_power2__eq__square,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.54        = ( times_times_int @ A @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4090_Suc__double__not__eq__double,axiom,
% 15.55/8.54      ! [M: nat,N: nat] :
% 15.55/8.54        ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 15.55/8.54       != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4091_double__not__eq__Suc__double,axiom,
% 15.55/8.54      ! [M: nat,N: nat] :
% 15.55/8.54        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 15.55/8.54       != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4092_power__even__eq,axiom,
% 15.55/8.54      ! [A: nat,N: nat] :
% 15.55/8.54        ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.54        = ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4093_power__even__eq,axiom,
% 15.55/8.54      ! [A: int,N: nat] :
% 15.55/8.54        ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.54        = ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4094_power__even__eq,axiom,
% 15.55/8.54      ! [A: real,N: nat] :
% 15.55/8.54        ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.54        = ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4095_power__even__eq,axiom,
% 15.55/8.54      ! [A: complex,N: nat] :
% 15.55/8.54        ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.54        = ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4096_frac__def,axiom,
% 15.55/8.54      ( archimedean_frac_rat
% 15.55/8.54      = ( ^ [X: rat] : ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4097_frac__def,axiom,
% 15.55/8.54      ( archim2898591450579166408c_real
% 15.55/8.54      = ( ^ [X: real] : ( minus_minus_real @ X @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4098_num_Osize_I4_J,axiom,
% 15.55/8.54      ( ( size_size_num @ one )
% 15.55/8.54      = zero_zero_nat ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4099_div__nat__eqI,axiom,
% 15.55/8.54      ! [N: nat,Q3: nat,M: nat] :
% 15.55/8.54        ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q3 ) @ M )
% 15.55/8.54       => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q3 ) ) )
% 15.55/8.54         => ( ( divide_divide_nat @ M @ N )
% 15.55/8.54            = Q3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4100_split__div,axiom,
% 15.55/8.54      ! [P: nat > $o,M: nat,N: nat] :
% 15.55/8.54        ( ( P @ ( divide_divide_nat @ M @ N ) )
% 15.55/8.54        = ( ( ( N = zero_zero_nat )
% 15.55/8.54           => ( P @ zero_zero_nat ) )
% 15.55/8.54          & ( ( N != zero_zero_nat )
% 15.55/8.54           => ! [I4: nat,J3: nat] :
% 15.55/8.54                ( ( ord_less_nat @ J3 @ N )
% 15.55/8.54               => ( ( M
% 15.55/8.54                    = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J3 ) )
% 15.55/8.54                 => ( P @ I4 ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4101_dividend__less__div__times,axiom,
% 15.55/8.54      ! [N: nat,M: nat] :
% 15.55/8.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.54       => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4102_dividend__less__times__div,axiom,
% 15.55/8.54      ! [N: nat,M: nat] :
% 15.55/8.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.54       => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4103_less__eq__div__iff__mult__less__eq,axiom,
% 15.55/8.54      ! [Q3: nat,M: nat,N: nat] :
% 15.55/8.54        ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 15.55/8.54       => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q3 ) )
% 15.55/8.54          = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q3 ) @ N ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4104_nat__less__add__iff2,axiom,
% 15.55/8.54      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 15.55/8.54        ( ( ord_less_eq_nat @ I @ J )
% 15.55/8.54       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 15.55/8.54          = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4105_nat__less__add__iff1,axiom,
% 15.55/8.54      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 15.55/8.54        ( ( ord_less_eq_nat @ J @ I )
% 15.55/8.54       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 15.55/8.54          = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4106_mult__eq__if,axiom,
% 15.55/8.54      ( times_times_nat
% 15.55/8.54      = ( ^ [M3: nat,N3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N3 @ ( times_times_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N3 ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4107_dvd__mult__cancel2,axiom,
% 15.55/8.54      ! [M: nat,N: nat] :
% 15.55/8.54        ( ( ord_less_nat @ zero_zero_nat @ M )
% 15.55/8.54       => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 15.55/8.54          = ( N = one_one_nat ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4108_dvd__mult__cancel1,axiom,
% 15.55/8.54      ! [M: nat,N: nat] :
% 15.55/8.54        ( ( ord_less_nat @ zero_zero_nat @ M )
% 15.55/8.54       => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 15.55/8.54          = ( N = one_one_nat ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4109_dvd__minus__add,axiom,
% 15.55/8.54      ! [Q3: nat,N: nat,R2: nat,M: nat] :
% 15.55/8.54        ( ( ord_less_eq_nat @ Q3 @ N )
% 15.55/8.54       => ( ( ord_less_eq_nat @ Q3 @ ( times_times_nat @ R2 @ M ) )
% 15.55/8.54         => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q3 ) )
% 15.55/8.54            = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M ) @ Q3 ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4110_convex__bound__lt,axiom,
% 15.55/8.54      ! [X3: real,A: real,Y3: real,U: real,V: real] :
% 15.55/8.54        ( ( ord_less_real @ X3 @ A )
% 15.55/8.54       => ( ( ord_less_real @ Y3 @ A )
% 15.55/8.54         => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 15.55/8.54           => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 15.55/8.54             => ( ( ( plus_plus_real @ U @ V )
% 15.55/8.54                  = one_one_real )
% 15.55/8.54               => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X3 ) @ ( times_times_real @ V @ Y3 ) ) @ A ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4111_convex__bound__lt,axiom,
% 15.55/8.54      ! [X3: rat,A: rat,Y3: rat,U: rat,V: rat] :
% 15.55/8.54        ( ( ord_less_rat @ X3 @ A )
% 15.55/8.54       => ( ( ord_less_rat @ Y3 @ A )
% 15.55/8.54         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 15.55/8.54           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 15.55/8.54             => ( ( ( plus_plus_rat @ U @ V )
% 15.55/8.54                  = one_one_rat )
% 15.55/8.54               => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X3 ) @ ( times_times_rat @ V @ Y3 ) ) @ A ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4112_convex__bound__lt,axiom,
% 15.55/8.54      ! [X3: int,A: int,Y3: int,U: int,V: int] :
% 15.55/8.54        ( ( ord_less_int @ X3 @ A )
% 15.55/8.54       => ( ( ord_less_int @ Y3 @ A )
% 15.55/8.54         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 15.55/8.54           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 15.55/8.54             => ( ( ( plus_plus_int @ U @ V )
% 15.55/8.54                  = one_one_int )
% 15.55/8.54               => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X3 ) @ ( times_times_int @ V @ Y3 ) ) @ A ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4113_le__divide__eq__numeral_I1_J,axiom,
% 15.55/8.54      ! [W: num,B: real,C: real] :
% 15.55/8.54        ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 15.55/8.54        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.54           => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 15.55/8.54          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.54           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.54               => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 15.55/8.54              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.54               => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4114_le__divide__eq__numeral_I1_J,axiom,
% 15.55/8.54      ! [W: num,B: rat,C: rat] :
% 15.55/8.54        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 15.55/8.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.54           => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 15.55/8.54          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.54           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.54               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 15.55/8.54              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.54               => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4115_divide__le__eq__numeral_I1_J,axiom,
% 15.55/8.54      ! [B: real,C: real,W: num] :
% 15.55/8.54        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 15.55/8.54        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.54           => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 15.55/8.54          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.54           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.54               => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 15.55/8.54              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.54               => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4116_divide__le__eq__numeral_I1_J,axiom,
% 15.55/8.54      ! [B: rat,C: rat,W: num] :
% 15.55/8.54        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 15.55/8.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.54           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 15.55/8.54          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.54           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.54               => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 15.55/8.54              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.54               => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4117_scaling__mono,axiom,
% 15.55/8.54      ! [U: real,V: real,R2: real,S: real] :
% 15.55/8.54        ( ( ord_less_eq_real @ U @ V )
% 15.55/8.54       => ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 15.55/8.54         => ( ( ord_less_eq_real @ R2 @ S )
% 15.55/8.54           => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R2 @ ( minus_minus_real @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4118_scaling__mono,axiom,
% 15.55/8.54      ! [U: rat,V: rat,R2: rat,S: rat] :
% 15.55/8.54        ( ( ord_less_eq_rat @ U @ V )
% 15.55/8.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 15.55/8.54         => ( ( ord_less_eq_rat @ R2 @ S )
% 15.55/8.54           => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R2 @ ( minus_minus_rat @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4119_frac__eq,axiom,
% 15.55/8.54      ! [X3: real] :
% 15.55/8.54        ( ( ( archim2898591450579166408c_real @ X3 )
% 15.55/8.54          = X3 )
% 15.55/8.54        = ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.54          & ( ord_less_real @ X3 @ one_one_real ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4120_frac__eq,axiom,
% 15.55/8.54      ! [X3: rat] :
% 15.55/8.54        ( ( ( archimedean_frac_rat @ X3 )
% 15.55/8.54          = X3 )
% 15.55/8.54        = ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 15.55/8.54          & ( ord_less_rat @ X3 @ one_one_rat ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4121_even__two__times__div__two,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.55/8.54       => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 15.55/8.54          = A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4122_even__two__times__div__two,axiom,
% 15.55/8.54      ! [A: nat] :
% 15.55/8.54        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.55/8.54       => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.54          = A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4123_even__two__times__div__two,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.55/8.54       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 15.55/8.54          = A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4124_frac__add,axiom,
% 15.55/8.54      ! [X3: real,Y3: real] :
% 15.55/8.54        ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X3 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real )
% 15.55/8.54         => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X3 @ Y3 ) )
% 15.55/8.54            = ( plus_plus_real @ ( archim2898591450579166408c_real @ X3 ) @ ( archim2898591450579166408c_real @ Y3 ) ) ) )
% 15.55/8.54        & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X3 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real )
% 15.55/8.54         => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X3 @ Y3 ) )
% 15.55/8.54            = ( minus_minus_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X3 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4125_frac__add,axiom,
% 15.55/8.54      ! [X3: rat,Y3: rat] :
% 15.55/8.54        ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X3 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat )
% 15.55/8.54         => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X3 @ Y3 ) )
% 15.55/8.54            = ( plus_plus_rat @ ( archimedean_frac_rat @ X3 ) @ ( archimedean_frac_rat @ Y3 ) ) ) )
% 15.55/8.54        & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X3 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat )
% 15.55/8.54         => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X3 @ Y3 ) )
% 15.55/8.54            = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X3 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4126_take__bit__Suc__bit0,axiom,
% 15.55/8.54      ! [N: nat,K: num] :
% 15.55/8.54        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 15.55/8.54        = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4127_take__bit__Suc__bit0,axiom,
% 15.55/8.54      ! [N: nat,K: num] :
% 15.55/8.54        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 15.55/8.54        = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4128_power__eq__if,axiom,
% 15.55/8.54      ( power_power_complex
% 15.55/8.54      = ( ^ [P5: complex,M3: nat] : ( if_complex @ ( M3 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P5 @ ( power_power_complex @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4129_power__eq__if,axiom,
% 15.55/8.54      ( power_power_real
% 15.55/8.54      = ( ^ [P5: real,M3: nat] : ( if_real @ ( M3 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P5 @ ( power_power_real @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4130_power__eq__if,axiom,
% 15.55/8.54      ( power_power_rat
% 15.55/8.54      = ( ^ [P5: rat,M3: nat] : ( if_rat @ ( M3 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P5 @ ( power_power_rat @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4131_power__eq__if,axiom,
% 15.55/8.54      ( power_power_nat
% 15.55/8.54      = ( ^ [P5: nat,M3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P5 @ ( power_power_nat @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4132_power__eq__if,axiom,
% 15.55/8.54      ( power_power_int
% 15.55/8.54      = ( ^ [P5: int,M3: nat] : ( if_int @ ( M3 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P5 @ ( power_power_int @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4133_power__minus__mult,axiom,
% 15.55/8.54      ! [N: nat,A: complex] :
% 15.55/8.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.54       => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 15.55/8.54          = ( power_power_complex @ A @ N ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4134_power__minus__mult,axiom,
% 15.55/8.54      ! [N: nat,A: real] :
% 15.55/8.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.54       => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 15.55/8.54          = ( power_power_real @ A @ N ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4135_power__minus__mult,axiom,
% 15.55/8.54      ! [N: nat,A: rat] :
% 15.55/8.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.54       => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 15.55/8.54          = ( power_power_rat @ A @ N ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4136_power__minus__mult,axiom,
% 15.55/8.54      ! [N: nat,A: nat] :
% 15.55/8.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.54       => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 15.55/8.54          = ( power_power_nat @ A @ N ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4137_power__minus__mult,axiom,
% 15.55/8.54      ! [N: nat,A: int] :
% 15.55/8.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.54       => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 15.55/8.54          = ( power_power_int @ A @ N ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4138_split__div_H,axiom,
% 15.55/8.54      ! [P: nat > $o,M: nat,N: nat] :
% 15.55/8.54        ( ( P @ ( divide_divide_nat @ M @ N ) )
% 15.55/8.54        = ( ( ( N = zero_zero_nat )
% 15.55/8.54            & ( P @ zero_zero_nat ) )
% 15.55/8.54          | ? [Q5: nat] :
% 15.55/8.54              ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q5 ) @ M )
% 15.55/8.54              & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q5 ) ) )
% 15.55/8.54              & ( P @ Q5 ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4139_oddE,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.55/8.54       => ~ ! [B4: code_integer] :
% 15.55/8.54              ( A
% 15.55/8.54             != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B4 ) @ one_one_Code_integer ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4140_oddE,axiom,
% 15.55/8.54      ! [A: nat] :
% 15.55/8.54        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.55/8.54       => ~ ! [B4: nat] :
% 15.55/8.54              ( A
% 15.55/8.54             != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B4 ) @ one_one_nat ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4141_oddE,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.55/8.54       => ~ ! [B4: int] :
% 15.55/8.54              ( A
% 15.55/8.54             != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B4 ) @ one_one_int ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4142_power2__sum,axiom,
% 15.55/8.54      ! [X3: complex,Y3: complex] :
% 15.55/8.54        ( ( power_power_complex @ ( plus_plus_complex @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.54        = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) @ Y3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4143_power2__sum,axiom,
% 15.55/8.54      ! [X3: real,Y3: real] :
% 15.55/8.54        ( ( power_power_real @ ( plus_plus_real @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.54        = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) @ Y3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4144_power2__sum,axiom,
% 15.55/8.54      ! [X3: rat,Y3: rat] :
% 15.55/8.54        ( ( power_power_rat @ ( plus_plus_rat @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.54        = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X3 ) @ Y3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4145_power2__sum,axiom,
% 15.55/8.54      ! [X3: nat,Y3: nat] :
% 15.55/8.54        ( ( power_power_nat @ ( plus_plus_nat @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.54        = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X3 ) @ Y3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4146_power2__sum,axiom,
% 15.55/8.54      ! [X3: int,Y3: int] :
% 15.55/8.54        ( ( power_power_int @ ( plus_plus_int @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.54        = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 ) @ Y3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4147_zero__le__even__power_H,axiom,
% 15.55/8.54      ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4148_zero__le__even__power_H,axiom,
% 15.55/8.54      ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4149_zero__le__even__power_H,axiom,
% 15.55/8.54      ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4150_nat__bit__induct,axiom,
% 15.55/8.54      ! [P: nat > $o,N: nat] :
% 15.55/8.54        ( ( P @ zero_zero_nat )
% 15.55/8.54       => ( ! [N2: nat] :
% 15.55/8.54              ( ( P @ N2 )
% 15.55/8.54             => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 15.55/8.54               => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 15.55/8.54         => ( ! [N2: nat] :
% 15.55/8.54                ( ( P @ N2 )
% 15.55/8.54               => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 15.55/8.54           => ( P @ N ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4151_floor__divide__lower,axiom,
% 15.55/8.54      ! [Q3: rat,P6: rat] :
% 15.55/8.54        ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 15.55/8.54       => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P6 @ Q3 ) ) ) @ Q3 ) @ P6 ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4152_floor__divide__lower,axiom,
% 15.55/8.54      ! [Q3: real,P6: real] :
% 15.55/8.54        ( ( ord_less_real @ zero_zero_real @ Q3 )
% 15.55/8.54       => ( ord_less_eq_real @ ( times_times_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P6 @ Q3 ) ) ) @ Q3 ) @ P6 ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4153_ceiling__divide__upper,axiom,
% 15.55/8.54      ! [Q3: real,P6: real] :
% 15.55/8.54        ( ( ord_less_real @ zero_zero_real @ Q3 )
% 15.55/8.54       => ( ord_less_eq_real @ P6 @ ( times_times_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P6 @ Q3 ) ) ) @ Q3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4154_ceiling__divide__upper,axiom,
% 15.55/8.54      ! [Q3: rat,P6: rat] :
% 15.55/8.54        ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 15.55/8.54       => ( ord_less_eq_rat @ P6 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P6 @ Q3 ) ) ) @ Q3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4155_vebt__buildup_Ocases,axiom,
% 15.55/8.54      ! [X3: nat] :
% 15.55/8.54        ( ( X3 != zero_zero_nat )
% 15.55/8.54       => ( ( X3
% 15.55/8.54           != ( suc @ zero_zero_nat ) )
% 15.55/8.54         => ~ ! [Va: nat] :
% 15.55/8.54                ( X3
% 15.55/8.54               != ( suc @ ( suc @ Va ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4156_option_Osize_I4_J,axiom,
% 15.55/8.54      ! [X2: nat] :
% 15.55/8.54        ( ( size_size_option_nat @ ( some_nat @ X2 ) )
% 15.55/8.54        = ( suc @ zero_zero_nat ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4157_option_Osize_I4_J,axiom,
% 15.55/8.54      ! [X2: product_prod_nat_nat] :
% 15.55/8.54        ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X2 ) )
% 15.55/8.54        = ( suc @ zero_zero_nat ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4158_option_Osize_I4_J,axiom,
% 15.55/8.54      ! [X2: num] :
% 15.55/8.54        ( ( size_size_option_num @ ( some_num @ X2 ) )
% 15.55/8.54        = ( suc @ zero_zero_nat ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4159_sum__squares__bound,axiom,
% 15.55/8.54      ! [X3: real,Y3: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) @ Y3 ) @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4160_sum__squares__bound,axiom,
% 15.55/8.54      ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X3 ) @ Y3 ) @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4161_power2__diff,axiom,
% 15.55/8.54      ! [X3: complex,Y3: complex] :
% 15.55/8.54        ( ( power_power_complex @ ( minus_minus_complex @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.54        = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) @ Y3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4162_power2__diff,axiom,
% 15.55/8.54      ! [X3: real,Y3: real] :
% 15.55/8.54        ( ( power_power_real @ ( minus_minus_real @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.54        = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) @ Y3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4163_power2__diff,axiom,
% 15.55/8.54      ! [X3: rat,Y3: rat] :
% 15.55/8.54        ( ( power_power_rat @ ( minus_minus_rat @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.54        = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X3 ) @ Y3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4164_power2__diff,axiom,
% 15.55/8.54      ! [X3: int,Y3: int] :
% 15.55/8.54        ( ( power_power_int @ ( minus_minus_int @ X3 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.54        = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 ) @ Y3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4165_odd__0__le__power__imp__0__le,axiom,
% 15.55/8.54      ! [A: real,N: nat] :
% 15.55/8.54        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 15.55/8.54       => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4166_odd__0__le__power__imp__0__le,axiom,
% 15.55/8.54      ! [A: rat,N: nat] :
% 15.55/8.54        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 15.55/8.54       => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4167_odd__0__le__power__imp__0__le,axiom,
% 15.55/8.54      ! [A: int,N: nat] :
% 15.55/8.54        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 15.55/8.54       => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4168_odd__power__less__zero,axiom,
% 15.55/8.54      ! [A: real,N: nat] :
% 15.55/8.54        ( ( ord_less_real @ A @ zero_zero_real )
% 15.55/8.54       => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4169_odd__power__less__zero,axiom,
% 15.55/8.54      ! [A: rat,N: nat] :
% 15.55/8.54        ( ( ord_less_rat @ A @ zero_zero_rat )
% 15.55/8.54       => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4170_odd__power__less__zero,axiom,
% 15.55/8.54      ! [A: int,N: nat] :
% 15.55/8.54        ( ( ord_less_int @ A @ zero_zero_int )
% 15.55/8.54       => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4171_floor__divide__upper,axiom,
% 15.55/8.54      ! [Q3: rat,P6: rat] :
% 15.55/8.54        ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 15.55/8.54       => ( ord_less_rat @ P6 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P6 @ Q3 ) ) ) @ one_one_rat ) @ Q3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4172_floor__divide__upper,axiom,
% 15.55/8.54      ! [Q3: real,P6: real] :
% 15.55/8.54        ( ( ord_less_real @ zero_zero_real @ Q3 )
% 15.55/8.54       => ( ord_less_real @ P6 @ ( times_times_real @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P6 @ Q3 ) ) ) @ one_one_real ) @ Q3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4173_ceiling__divide__lower,axiom,
% 15.55/8.54      ! [Q3: real,P6: real] :
% 15.55/8.54        ( ( ord_less_real @ zero_zero_real @ Q3 )
% 15.55/8.54       => ( ord_less_real @ ( times_times_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P6 @ Q3 ) ) ) @ one_one_real ) @ Q3 ) @ P6 ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4174_ceiling__divide__lower,axiom,
% 15.55/8.54      ! [Q3: rat,P6: rat] :
% 15.55/8.54        ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 15.55/8.54       => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P6 @ Q3 ) ) ) @ one_one_rat ) @ Q3 ) @ P6 ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4175_floor__add,axiom,
% 15.55/8.54      ! [X3: rat,Y3: rat] :
% 15.55/8.54        ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X3 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat )
% 15.55/8.54         => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X3 @ Y3 ) )
% 15.55/8.54            = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X3 ) @ ( archim3151403230148437115or_rat @ Y3 ) ) ) )
% 15.55/8.54        & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X3 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat )
% 15.55/8.54         => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X3 @ Y3 ) )
% 15.55/8.54            = ( plus_plus_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X3 ) @ ( archim3151403230148437115or_rat @ Y3 ) ) @ one_one_int ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4176_floor__add,axiom,
% 15.55/8.54      ! [X3: real,Y3: real] :
% 15.55/8.54        ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X3 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real )
% 15.55/8.54         => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X3 @ Y3 ) )
% 15.55/8.54            = ( plus_plus_int @ ( archim6058952711729229775r_real @ X3 ) @ ( archim6058952711729229775r_real @ Y3 ) ) ) )
% 15.55/8.54        & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X3 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real )
% 15.55/8.54         => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X3 @ Y3 ) )
% 15.55/8.54            = ( plus_plus_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X3 ) @ ( archim6058952711729229775r_real @ Y3 ) ) @ one_one_int ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4177_num_Osize_I5_J,axiom,
% 15.55/8.54      ! [X2: num] :
% 15.55/8.54        ( ( size_size_num @ ( bit0 @ X2 ) )
% 15.55/8.54        = ( plus_plus_nat @ ( size_size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4178_arith__geo__mean,axiom,
% 15.55/8.54      ! [U: real,X3: real,Y3: real] :
% 15.55/8.54        ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.54          = ( times_times_real @ X3 @ Y3 ) )
% 15.55/8.54       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.54         => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.54           => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X3 @ Y3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4179_arith__geo__mean,axiom,
% 15.55/8.54      ! [U: rat,X3: rat,Y3: rat] :
% 15.55/8.54        ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.54          = ( times_times_rat @ X3 @ Y3 ) )
% 15.55/8.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 15.55/8.54         => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 15.55/8.54           => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X3 @ Y3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4180_even__mult__exp__div__exp__iff,axiom,
% 15.55/8.54      ! [A: code_integer,M: nat,N: nat] :
% 15.55/8.54        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 15.55/8.54        = ( ( ord_less_nat @ N @ M )
% 15.55/8.54          | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 15.55/8.54            = zero_z3403309356797280102nteger )
% 15.55/8.54          | ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.54            & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4181_even__mult__exp__div__exp__iff,axiom,
% 15.55/8.54      ! [A: nat,M: nat,N: nat] :
% 15.55/8.54        ( ( 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 ) ) )
% 15.55/8.54        = ( ( ord_less_nat @ N @ M )
% 15.55/8.54          | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.54            = zero_zero_nat )
% 15.55/8.54          | ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.54            & ( 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 ) ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4182_even__mult__exp__div__exp__iff,axiom,
% 15.55/8.54      ! [A: int,M: nat,N: nat] :
% 15.55/8.54        ( ( 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 ) ) )
% 15.55/8.54        = ( ( ord_less_nat @ N @ M )
% 15.55/8.54          | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 15.55/8.54            = zero_zero_int )
% 15.55/8.54          | ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.54            & ( 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 ) ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4183_of__real__of__int__eq,axiom,
% 15.55/8.54      ! [Z: int] :
% 15.55/8.54        ( ( real_V1803761363581548252l_real @ ( ring_1_of_int_real @ Z ) )
% 15.55/8.54        = ( ring_1_of_int_real @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4184_of__real__of__int__eq,axiom,
% 15.55/8.54      ! [Z: int] :
% 15.55/8.54        ( ( real_V4546457046886955230omplex @ ( ring_1_of_int_real @ Z ) )
% 15.55/8.54        = ( ring_17405671764205052669omplex @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4185_of__real__of__nat__eq,axiom,
% 15.55/8.54      ! [N: nat] :
% 15.55/8.54        ( ( real_V4546457046886955230omplex @ ( semiri5074537144036343181t_real @ N ) )
% 15.55/8.54        = ( semiri8010041392384452111omplex @ N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4186_of__real__of__nat__eq,axiom,
% 15.55/8.54      ! [N: nat] :
% 15.55/8.54        ( ( real_V1803761363581548252l_real @ ( semiri5074537144036343181t_real @ N ) )
% 15.55/8.54        = ( semiri5074537144036343181t_real @ N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4187_of__real__power,axiom,
% 15.55/8.54      ! [X3: real,N: nat] :
% 15.55/8.54        ( ( real_V1803761363581548252l_real @ ( power_power_real @ X3 @ N ) )
% 15.55/8.54        = ( power_power_real @ ( real_V1803761363581548252l_real @ X3 ) @ N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4188_of__real__power,axiom,
% 15.55/8.54      ! [X3: real,N: nat] :
% 15.55/8.54        ( ( real_V4546457046886955230omplex @ ( power_power_real @ X3 @ N ) )
% 15.55/8.54        = ( power_power_complex @ ( real_V4546457046886955230omplex @ X3 ) @ N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4189_of__real__numeral,axiom,
% 15.55/8.54      ! [W: num] :
% 15.55/8.54        ( ( real_V1803761363581548252l_real @ ( numeral_numeral_real @ W ) )
% 15.55/8.54        = ( numeral_numeral_real @ W ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4190_of__real__numeral,axiom,
% 15.55/8.54      ! [W: num] :
% 15.55/8.54        ( ( real_V4546457046886955230omplex @ ( numeral_numeral_real @ W ) )
% 15.55/8.54        = ( numera6690914467698888265omplex @ W ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4191_of__real__0,axiom,
% 15.55/8.54      ( ( real_V1803761363581548252l_real @ zero_zero_real )
% 15.55/8.54      = zero_zero_real ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4192_of__real__0,axiom,
% 15.55/8.54      ( ( real_V4546457046886955230omplex @ zero_zero_real )
% 15.55/8.54      = zero_zero_complex ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4193_of__real__eq__0__iff,axiom,
% 15.55/8.54      ! [X3: real] :
% 15.55/8.54        ( ( ( real_V1803761363581548252l_real @ X3 )
% 15.55/8.54          = zero_zero_real )
% 15.55/8.54        = ( X3 = zero_zero_real ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4194_of__real__eq__0__iff,axiom,
% 15.55/8.54      ! [X3: real] :
% 15.55/8.54        ( ( ( real_V4546457046886955230omplex @ X3 )
% 15.55/8.54          = zero_zero_complex )
% 15.55/8.54        = ( X3 = zero_zero_real ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4195_mul__def,axiom,
% 15.55/8.54      ( vEBT_VEBT_mul
% 15.55/8.54      = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4196_mul__shift,axiom,
% 15.55/8.54      ! [X3: nat,Y3: nat,Z: nat] :
% 15.55/8.54        ( ( ( times_times_nat @ X3 @ Y3 )
% 15.55/8.54          = Z )
% 15.55/8.54        = ( ( vEBT_VEBT_mul @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) )
% 15.55/8.54          = ( some_nat @ Z ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4197_real__divide__square__eq,axiom,
% 15.55/8.54      ! [R2: real,A: real] :
% 15.55/8.54        ( ( divide_divide_real @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ R2 ) )
% 15.55/8.54        = ( divide_divide_real @ A @ R2 ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4198_not__real__square__gt__zero,axiom,
% 15.55/8.54      ! [X3: real] :
% 15.55/8.54        ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X3 @ X3 ) ) )
% 15.55/8.54        = ( X3 = zero_zero_real ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4199_semiring__norm_I13_J,axiom,
% 15.55/8.54      ! [M: num,N: num] :
% 15.55/8.54        ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 15.55/8.54        = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4200_semiring__norm_I11_J,axiom,
% 15.55/8.54      ! [M: num] :
% 15.55/8.54        ( ( times_times_num @ M @ one )
% 15.55/8.54        = M ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4201_semiring__norm_I12_J,axiom,
% 15.55/8.54      ! [N: num] :
% 15.55/8.54        ( ( times_times_num @ one @ N )
% 15.55/8.54        = N ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4202_num__double,axiom,
% 15.55/8.54      ! [N: num] :
% 15.55/8.54        ( ( times_times_num @ ( bit0 @ one ) @ N )
% 15.55/8.54        = ( bit0 @ N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4203_power__mult__numeral,axiom,
% 15.55/8.54      ! [A: nat,M: num,N: num] :
% 15.55/8.54        ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 15.55/8.54        = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4204_power__mult__numeral,axiom,
% 15.55/8.54      ! [A: int,M: num,N: num] :
% 15.55/8.54        ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 15.55/8.54        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4205_power__mult__numeral,axiom,
% 15.55/8.54      ! [A: real,M: num,N: num] :
% 15.55/8.54        ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 15.55/8.54        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4206_power__mult__numeral,axiom,
% 15.55/8.54      ! [A: complex,M: num,N: num] :
% 15.55/8.54        ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 15.55/8.54        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4207_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 15.55/8.54      ! [X3: real,Y3: real,Xa: real,Ya: real] :
% 15.55/8.54        ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.54        = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4208_times__int__code_I2_J,axiom,
% 15.55/8.54      ! [L: int] :
% 15.55/8.54        ( ( times_times_int @ zero_zero_int @ L )
% 15.55/8.54        = zero_zero_int ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4209_times__int__code_I1_J,axiom,
% 15.55/8.54      ! [K: int] :
% 15.55/8.54        ( ( times_times_int @ K @ zero_zero_int )
% 15.55/8.54        = zero_zero_int ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4210_int__distrib_I1_J,axiom,
% 15.55/8.54      ! [Z1: int,Z22: int,W: int] :
% 15.55/8.54        ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W )
% 15.55/8.54        = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4211_int__distrib_I2_J,axiom,
% 15.55/8.54      ! [W: int,Z1: int,Z22: int] :
% 15.55/8.54        ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z22 ) )
% 15.55/8.54        = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4212_int__distrib_I3_J,axiom,
% 15.55/8.54      ! [Z1: int,Z22: int,W: int] :
% 15.55/8.54        ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W )
% 15.55/8.54        = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4213_int__distrib_I4_J,axiom,
% 15.55/8.54      ! [W: int,Z1: int,Z22: int] :
% 15.55/8.54        ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z22 ) )
% 15.55/8.54        = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4214_real__sqrt__mult,axiom,
% 15.55/8.54      ! [X3: real,Y3: real] :
% 15.55/8.54        ( ( sqrt @ ( times_times_real @ X3 @ Y3 ) )
% 15.55/8.54        = ( times_times_real @ ( sqrt @ X3 ) @ ( sqrt @ Y3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4215_take__bit__mult,axiom,
% 15.55/8.54      ! [N: nat,K: int,L: int] :
% 15.55/8.54        ( ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L ) ) )
% 15.55/8.54        = ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ K @ L ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4216_imult__is__0,axiom,
% 15.55/8.54      ! [M: extended_enat,N: extended_enat] :
% 15.55/8.54        ( ( ( times_7803423173614009249d_enat @ M @ N )
% 15.55/8.54          = zero_z5237406670263579293d_enat )
% 15.55/8.54        = ( ( M = zero_z5237406670263579293d_enat )
% 15.55/8.54          | ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4217_div__mult2__numeral__eq,axiom,
% 15.55/8.54      ! [A: nat,K: num,L: num] :
% 15.55/8.54        ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L ) )
% 15.55/8.54        = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4218_div__mult2__numeral__eq,axiom,
% 15.55/8.54      ! [A: int,K: num,L: num] :
% 15.55/8.54        ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L ) )
% 15.55/8.54        = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4219_zmult__zless__mono2,axiom,
% 15.55/8.54      ! [I: int,J: int,K: int] :
% 15.55/8.54        ( ( ord_less_int @ I @ J )
% 15.55/8.54       => ( ( ord_less_int @ zero_zero_int @ K )
% 15.55/8.54         => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4220_int__ops_I7_J,axiom,
% 15.55/8.54      ! [A: nat,B: nat] :
% 15.55/8.54        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 15.55/8.54        = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4221_zdvd__mult__cancel,axiom,
% 15.55/8.54      ! [K: int,M: int,N: int] :
% 15.55/8.54        ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) )
% 15.55/8.54       => ( ( K != zero_zero_int )
% 15.55/8.54         => ( dvd_dvd_int @ M @ N ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4222_zdvd__mono,axiom,
% 15.55/8.54      ! [K: int,M: int,T: int] :
% 15.55/8.54        ( ( K != zero_zero_int )
% 15.55/8.54       => ( ( dvd_dvd_int @ M @ T )
% 15.55/8.54          = ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ T ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4223_zdvd__period,axiom,
% 15.55/8.54      ! [A: int,D3: int,X3: int,T: int,C: int] :
% 15.55/8.54        ( ( dvd_dvd_int @ A @ D3 )
% 15.55/8.54       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X3 @ T ) )
% 15.55/8.54          = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X3 @ ( times_times_int @ C @ D3 ) ) @ T ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4224_zdvd__reduce,axiom,
% 15.55/8.54      ! [K: int,N: int,M: int] :
% 15.55/8.54        ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) )
% 15.55/8.54        = ( dvd_dvd_int @ K @ N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4225_enat__0__less__mult__iff,axiom,
% 15.55/8.54      ! [M: extended_enat,N: extended_enat] :
% 15.55/8.54        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N ) )
% 15.55/8.54        = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 15.55/8.54          & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4226_reals__Archimedean3,axiom,
% 15.55/8.54      ! [X3: real] :
% 15.55/8.54        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.54       => ! [Y6: real] :
% 15.55/8.54          ? [N2: nat] : ( ord_less_real @ Y6 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4227_pos__zmult__eq__1__iff,axiom,
% 15.55/8.54      ! [M: int,N: int] :
% 15.55/8.54        ( ( ord_less_int @ zero_zero_int @ M )
% 15.55/8.54       => ( ( ( times_times_int @ M @ N )
% 15.55/8.54            = one_one_int )
% 15.55/8.54          = ( ( M = one_one_int )
% 15.55/8.54            & ( N = one_one_int ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4228_powr__mult,axiom,
% 15.55/8.54      ! [X3: real,Y3: real,A: real] :
% 15.55/8.54        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.54       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.54         => ( ( powr_real @ ( times_times_real @ X3 @ Y3 ) @ A )
% 15.55/8.54            = ( times_times_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ Y3 @ A ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4229_minusinfinity,axiom,
% 15.55/8.54      ! [D3: int,P1: int > $o,P: int > $o] :
% 15.55/8.54        ( ( ord_less_int @ zero_zero_int @ D3 )
% 15.55/8.54       => ( ! [X4: int,K2: int] :
% 15.55/8.54              ( ( P1 @ X4 )
% 15.55/8.54              = ( P1 @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 15.55/8.54         => ( ? [Z4: int] :
% 15.55/8.54              ! [X4: int] :
% 15.55/8.54                ( ( ord_less_int @ X4 @ Z4 )
% 15.55/8.54               => ( ( P @ X4 )
% 15.55/8.54                  = ( P1 @ X4 ) ) )
% 15.55/8.54           => ( ? [X_12: int] : ( P1 @ X_12 )
% 15.55/8.54             => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4230_plusinfinity,axiom,
% 15.55/8.54      ! [D3: int,P4: int > $o,P: int > $o] :
% 15.55/8.54        ( ( ord_less_int @ zero_zero_int @ D3 )
% 15.55/8.54       => ( ! [X4: int,K2: int] :
% 15.55/8.54              ( ( P4 @ X4 )
% 15.55/8.54              = ( P4 @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 15.55/8.54         => ( ? [Z4: int] :
% 15.55/8.54              ! [X4: int] :
% 15.55/8.54                ( ( ord_less_int @ Z4 @ X4 )
% 15.55/8.54               => ( ( P @ X4 )
% 15.55/8.54                  = ( P4 @ X4 ) ) )
% 15.55/8.54           => ( ? [X_12: int] : ( P4 @ X_12 )
% 15.55/8.54             => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4231_zdiv__zmult2__eq,axiom,
% 15.55/8.54      ! [C: int,A: int,B: int] :
% 15.55/8.54        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 15.55/8.54       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 15.55/8.54          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4232_le__real__sqrt__sumsq,axiom,
% 15.55/8.54      ! [X3: real,Y3: real] : ( ord_less_eq_real @ X3 @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y3 @ Y3 ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4233_log__powr,axiom,
% 15.55/8.54      ! [X3: real,B: real,Y3: real] :
% 15.55/8.54        ( ( X3 != zero_zero_real )
% 15.55/8.54       => ( ( log @ B @ ( powr_real @ X3 @ Y3 ) )
% 15.55/8.54          = ( times_times_real @ Y3 @ ( log @ B @ X3 ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4234_ln__powr,axiom,
% 15.55/8.54      ! [X3: real,Y3: real] :
% 15.55/8.54        ( ( X3 != zero_zero_real )
% 15.55/8.54       => ( ( ln_ln_real @ ( powr_real @ X3 @ Y3 ) )
% 15.55/8.54          = ( times_times_real @ Y3 @ ( ln_ln_real @ X3 ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4235_zmult__zless__mono2__lemma,axiom,
% 15.55/8.54      ! [I: int,J: int,K: nat] :
% 15.55/8.54        ( ( ord_less_int @ I @ J )
% 15.55/8.54       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 15.55/8.54         => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4236_incr__mult__lemma,axiom,
% 15.55/8.54      ! [D3: int,P: int > $o,K: int] :
% 15.55/8.54        ( ( ord_less_int @ zero_zero_int @ D3 )
% 15.55/8.54       => ( ! [X4: int] :
% 15.55/8.54              ( ( P @ X4 )
% 15.55/8.54             => ( P @ ( plus_plus_int @ X4 @ D3 ) ) )
% 15.55/8.54         => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 15.55/8.54           => ! [X6: int] :
% 15.55/8.54                ( ( P @ X6 )
% 15.55/8.54               => ( P @ ( plus_plus_int @ X6 @ ( times_times_int @ K @ D3 ) ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4237_q__pos__lemma,axiom,
% 15.55/8.54      ! [B2: int,Q6: int,R4: int] :
% 15.55/8.54        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q6 ) @ R4 ) )
% 15.55/8.54       => ( ( ord_less_int @ R4 @ B2 )
% 15.55/8.54         => ( ( ord_less_int @ zero_zero_int @ B2 )
% 15.55/8.54           => ( ord_less_eq_int @ zero_zero_int @ Q6 ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4238_zdiv__mono2__lemma,axiom,
% 15.55/8.54      ! [B: int,Q3: int,R2: int,B2: int,Q6: int,R4: int] :
% 15.55/8.54        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 )
% 15.55/8.54          = ( plus_plus_int @ ( times_times_int @ B2 @ Q6 ) @ R4 ) )
% 15.55/8.54       => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q6 ) @ R4 ) )
% 15.55/8.54         => ( ( ord_less_int @ R4 @ B2 )
% 15.55/8.54           => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 15.55/8.54             => ( ( ord_less_int @ zero_zero_int @ B2 )
% 15.55/8.54               => ( ( ord_less_eq_int @ B2 @ B )
% 15.55/8.54                 => ( ord_less_eq_int @ Q3 @ Q6 ) ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4239_zdiv__mono2__neg__lemma,axiom,
% 15.55/8.54      ! [B: int,Q3: int,R2: int,B2: int,Q6: int,R4: int] :
% 15.55/8.54        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 )
% 15.55/8.54          = ( plus_plus_int @ ( times_times_int @ B2 @ Q6 ) @ R4 ) )
% 15.55/8.54       => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q6 ) @ R4 ) @ zero_zero_int )
% 15.55/8.54         => ( ( ord_less_int @ R2 @ B )
% 15.55/8.54           => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 15.55/8.54             => ( ( ord_less_int @ zero_zero_int @ B2 )
% 15.55/8.54               => ( ( ord_less_eq_int @ B2 @ B )
% 15.55/8.54                 => ( ord_less_eq_int @ Q6 @ Q3 ) ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4240_unique__quotient__lemma,axiom,
% 15.55/8.54      ! [B: int,Q6: int,R4: int,Q3: int,R2: int] :
% 15.55/8.54        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 15.55/8.54       => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 15.55/8.54         => ( ( ord_less_int @ R4 @ B )
% 15.55/8.54           => ( ( ord_less_int @ R2 @ B )
% 15.55/8.54             => ( ord_less_eq_int @ Q6 @ Q3 ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4241_unique__quotient__lemma__neg,axiom,
% 15.55/8.54      ! [B: int,Q6: int,R4: int,Q3: int,R2: int] :
% 15.55/8.54        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 15.55/8.54       => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 15.55/8.54         => ( ( ord_less_int @ B @ R2 )
% 15.55/8.54           => ( ( ord_less_int @ B @ R4 )
% 15.55/8.54             => ( ord_less_eq_int @ Q3 @ Q6 ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4242_nat__mult__distrib,axiom,
% 15.55/8.54      ! [Z: int,Z5: int] :
% 15.55/8.54        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 15.55/8.54       => ( ( nat2 @ ( times_times_int @ Z @ Z5 ) )
% 15.55/8.54          = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z5 ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4243_decr__mult__lemma,axiom,
% 15.55/8.54      ! [D3: int,P: int > $o,K: int] :
% 15.55/8.54        ( ( ord_less_int @ zero_zero_int @ D3 )
% 15.55/8.54       => ( ! [X4: int] :
% 15.55/8.54              ( ( P @ X4 )
% 15.55/8.54             => ( P @ ( minus_minus_int @ X4 @ D3 ) ) )
% 15.55/8.54         => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 15.55/8.54           => ! [X6: int] :
% 15.55/8.54                ( ( P @ X6 )
% 15.55/8.54               => ( P @ ( minus_minus_int @ X6 @ ( times_times_int @ K @ D3 ) ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4244_ln__mult,axiom,
% 15.55/8.54      ! [X3: real,Y3: real] :
% 15.55/8.54        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.54       => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.55/8.54         => ( ( ln_ln_real @ ( times_times_real @ X3 @ Y3 ) )
% 15.55/8.54            = ( plus_plus_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y3 ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4245_four__x__squared,axiom,
% 15.55/8.54      ! [X3: real] :
% 15.55/8.54        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.54        = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4246_real__archimedian__rdiv__eq__0,axiom,
% 15.55/8.54      ! [X3: real,C: real] :
% 15.55/8.54        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.54       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 15.55/8.54         => ( ! [M4: nat] :
% 15.55/8.54                ( ( ord_less_nat @ zero_zero_nat @ M4 )
% 15.55/8.54               => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M4 ) @ X3 ) @ C ) )
% 15.55/8.54           => ( X3 = zero_zero_real ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4247_log__mult,axiom,
% 15.55/8.54      ! [A: real,X3: real,Y3: real] :
% 15.55/8.54        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.54       => ( ( A != one_one_real )
% 15.55/8.54         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.54           => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.55/8.54             => ( ( log @ A @ ( times_times_real @ X3 @ Y3 ) )
% 15.55/8.54                = ( plus_plus_real @ ( log @ A @ X3 ) @ ( log @ A @ Y3 ) ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4248_powr__mult__base,axiom,
% 15.55/8.54      ! [X3: real,Y3: real] :
% 15.55/8.54        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.54       => ( ( times_times_real @ X3 @ ( powr_real @ X3 @ Y3 ) )
% 15.55/8.54          = ( powr_real @ X3 @ ( plus_plus_real @ one_one_real @ Y3 ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4249_log__nat__power,axiom,
% 15.55/8.54      ! [X3: real,B: real,N: nat] :
% 15.55/8.54        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.54       => ( ( log @ B @ ( power_power_real @ X3 @ N ) )
% 15.55/8.54          = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X3 ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4250_int__div__pos__eq,axiom,
% 15.55/8.54      ! [A: int,B: int,Q3: int,R2: int] :
% 15.55/8.54        ( ( A
% 15.55/8.54          = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 15.55/8.54       => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 15.55/8.54         => ( ( ord_less_int @ R2 @ B )
% 15.55/8.54           => ( ( divide_divide_int @ A @ B )
% 15.55/8.54              = Q3 ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4251_int__div__neg__eq,axiom,
% 15.55/8.54      ! [A: int,B: int,Q3: int,R2: int] :
% 15.55/8.54        ( ( A
% 15.55/8.54          = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 15.55/8.54       => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 15.55/8.54         => ( ( ord_less_int @ B @ R2 )
% 15.55/8.54           => ( ( divide_divide_int @ A @ B )
% 15.55/8.54              = Q3 ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4252_split__zdiv,axiom,
% 15.55/8.54      ! [P: int > $o,N: int,K: int] :
% 15.55/8.54        ( ( P @ ( divide_divide_int @ N @ K ) )
% 15.55/8.54        = ( ( ( K = zero_zero_int )
% 15.55/8.54           => ( P @ zero_zero_int ) )
% 15.55/8.54          & ( ( ord_less_int @ zero_zero_int @ K )
% 15.55/8.54           => ! [I4: int,J3: int] :
% 15.55/8.54                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 15.55/8.54                  & ( ord_less_int @ J3 @ K )
% 15.55/8.54                  & ( N
% 15.55/8.54                    = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 15.55/8.54               => ( P @ I4 ) ) )
% 15.55/8.54          & ( ( ord_less_int @ K @ zero_zero_int )
% 15.55/8.54           => ! [I4: int,J3: int] :
% 15.55/8.54                ( ( ( ord_less_int @ K @ J3 )
% 15.55/8.54                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 15.55/8.54                  & ( N
% 15.55/8.54                    = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 15.55/8.54               => ( P @ I4 ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4253_ln__realpow,axiom,
% 15.55/8.54      ! [X3: real,N: nat] :
% 15.55/8.54        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.54       => ( ( ln_ln_real @ ( power_power_real @ X3 @ N ) )
% 15.55/8.54          = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X3 ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4254_linear__plus__1__le__power,axiom,
% 15.55/8.54      ! [X3: real,N: nat] :
% 15.55/8.54        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.54       => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X3 ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X3 @ one_one_real ) @ N ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4255_ln__powr__bound2,axiom,
% 15.55/8.54      ! [X3: real,A: real] :
% 15.55/8.54        ( ( ord_less_real @ one_one_real @ X3 )
% 15.55/8.54       => ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.54         => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X3 ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X3 ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4256_log__eq__div__ln__mult__log,axiom,
% 15.55/8.54      ! [A: real,B: real,X3: real] :
% 15.55/8.54        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.54       => ( ( A != one_one_real )
% 15.55/8.54         => ( ( ord_less_real @ zero_zero_real @ B )
% 15.55/8.54           => ( ( B != one_one_real )
% 15.55/8.54             => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.54               => ( ( log @ A @ X3 )
% 15.55/8.54                  = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X3 ) ) ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4257_log__add__eq__powr,axiom,
% 15.55/8.54      ! [B: real,X3: real,Y3: real] :
% 15.55/8.54        ( ( ord_less_real @ zero_zero_real @ B )
% 15.55/8.54       => ( ( B != one_one_real )
% 15.55/8.54         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.54           => ( ( plus_plus_real @ ( log @ B @ X3 ) @ Y3 )
% 15.55/8.54              = ( log @ B @ ( times_times_real @ X3 @ ( powr_real @ B @ Y3 ) ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4258_add__log__eq__powr,axiom,
% 15.55/8.54      ! [B: real,X3: real,Y3: real] :
% 15.55/8.54        ( ( ord_less_real @ zero_zero_real @ B )
% 15.55/8.54       => ( ( B != one_one_real )
% 15.55/8.54         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.54           => ( ( plus_plus_real @ Y3 @ ( log @ B @ X3 ) )
% 15.55/8.54              = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y3 ) @ X3 ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4259_L2__set__mult__ineq__lemma,axiom,
% 15.55/8.54      ! [A: real,C: real,B: real,D3: 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 @ D3 ) ) @ ( plus_plus_real @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D3 @ ( 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 ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4260_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 15.55/8.54      ! [X3: real,Y3: real,Xa: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4261_arith__geo__mean__sqrt,axiom,
% 15.55/8.54      ! [X3: real,Y3: real] :
% 15.55/8.54        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.54       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.54         => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X3 @ Y3 ) ) @ ( divide_divide_real @ ( plus_plus_real @ X3 @ Y3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4262_neg__zdiv__mult__2,axiom,
% 15.55/8.54      ! [A: int,B: int] :
% 15.55/8.54        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 15.55/8.54       => ( ( 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 ) )
% 15.55/8.54          = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4263_pos__zdiv__mult__2,axiom,
% 15.55/8.54      ! [A: int,B: int] :
% 15.55/8.54        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.54       => ( ( 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 ) )
% 15.55/8.54          = ( divide_divide_int @ B @ A ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4264_Bernoulli__inequality__even,axiom,
% 15.55/8.54      ! [N: nat,X3: real] :
% 15.55/8.54        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.54       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X3 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X3 ) @ N ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4265_nonzero__of__real__divide,axiom,
% 15.55/8.54      ! [Y3: real,X3: real] :
% 15.55/8.54        ( ( Y3 != zero_zero_real )
% 15.55/8.54       => ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X3 @ Y3 ) )
% 15.55/8.54          = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X3 ) @ ( real_V1803761363581548252l_real @ Y3 ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4266_nonzero__of__real__divide,axiom,
% 15.55/8.54      ! [Y3: real,X3: real] :
% 15.55/8.54        ( ( Y3 != zero_zero_real )
% 15.55/8.54       => ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X3 @ Y3 ) )
% 15.55/8.54          = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X3 ) @ ( real_V4546457046886955230omplex @ Y3 ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4267_lemma__termdiff3,axiom,
% 15.55/8.54      ! [H2: real,Z: real,K5: real,N: nat] :
% 15.55/8.54        ( ( H2 != zero_zero_real )
% 15.55/8.54       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K5 )
% 15.55/8.54         => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H2 ) ) @ K5 )
% 15.55/8.54           => ( 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 ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4268_lemma__termdiff3,axiom,
% 15.55/8.54      ! [H2: complex,Z: complex,K5: real,N: nat] :
% 15.55/8.54        ( ( H2 != zero_zero_complex )
% 15.55/8.54       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K5 )
% 15.55/8.54         => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H2 ) ) @ K5 )
% 15.55/8.54           => ( 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 ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4269_low__inv,axiom,
% 15.55/8.54      ! [X3: nat,N: nat,Y3: nat] :
% 15.55/8.54        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.54       => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X3 ) @ N )
% 15.55/8.54          = X3 ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4270_mult__le__cancel__iff1,axiom,
% 15.55/8.54      ! [Z: real,X3: real,Y3: real] :
% 15.55/8.54        ( ( ord_less_real @ zero_zero_real @ Z )
% 15.55/8.54       => ( ( ord_less_eq_real @ ( times_times_real @ X3 @ Z ) @ ( times_times_real @ Y3 @ Z ) )
% 15.55/8.54          = ( ord_less_eq_real @ X3 @ Y3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4271_mult__le__cancel__iff1,axiom,
% 15.55/8.54      ! [Z: rat,X3: rat,Y3: rat] :
% 15.55/8.54        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 15.55/8.54       => ( ( ord_less_eq_rat @ ( times_times_rat @ X3 @ Z ) @ ( times_times_rat @ Y3 @ Z ) )
% 15.55/8.54          = ( ord_less_eq_rat @ X3 @ Y3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4272_mult__le__cancel__iff1,axiom,
% 15.55/8.54      ! [Z: int,X3: int,Y3: int] :
% 15.55/8.54        ( ( ord_less_int @ zero_zero_int @ Z )
% 15.55/8.54       => ( ( ord_less_eq_int @ ( times_times_int @ X3 @ Z ) @ ( times_times_int @ Y3 @ Z ) )
% 15.55/8.54          = ( ord_less_eq_int @ X3 @ Y3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4273_mult__le__cancel__iff2,axiom,
% 15.55/8.54      ! [Z: real,X3: real,Y3: real] :
% 15.55/8.54        ( ( ord_less_real @ zero_zero_real @ Z )
% 15.55/8.54       => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X3 ) @ ( times_times_real @ Z @ Y3 ) )
% 15.55/8.54          = ( ord_less_eq_real @ X3 @ Y3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4274_mult__le__cancel__iff2,axiom,
% 15.55/8.54      ! [Z: rat,X3: rat,Y3: rat] :
% 15.55/8.54        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 15.55/8.54       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X3 ) @ ( times_times_rat @ Z @ Y3 ) )
% 15.55/8.54          = ( ord_less_eq_rat @ X3 @ Y3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4275_mult__le__cancel__iff2,axiom,
% 15.55/8.54      ! [Z: int,X3: int,Y3: int] :
% 15.55/8.54        ( ( ord_less_int @ zero_zero_int @ Z )
% 15.55/8.54       => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X3 ) @ ( times_times_int @ Z @ Y3 ) )
% 15.55/8.54          = ( ord_less_eq_int @ X3 @ Y3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4276_triangle__def,axiom,
% 15.55/8.54      ( nat_triangle
% 15.55/8.54      = ( ^ [N3: nat] : ( divide_divide_nat @ ( times_times_nat @ N3 @ ( suc @ N3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4277_ln__one__minus__pos__lower__bound,axiom,
% 15.55/8.54      ! [X3: real] :
% 15.55/8.54        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.54       => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.54         => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X3 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4278_abs__ln__one__plus__x__minus__x__bound,axiom,
% 15.55/8.54      ! [X3: real] :
% 15.55/8.54        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.54       => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X3 ) ) @ X3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4279_bit__split__inv,axiom,
% 15.55/8.54      ! [X3: nat,D3: nat] :
% 15.55/8.54        ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X3 @ D3 ) @ ( vEBT_VEBT_low @ X3 @ D3 ) @ D3 )
% 15.55/8.54        = X3 ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4280_add_Oinverse__inverse,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 15.55/8.54        = A ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4281_add_Oinverse__inverse,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 15.55/8.54        = A ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4282_add_Oinverse__inverse,axiom,
% 15.55/8.54      ! [A: complex] :
% 15.55/8.54        ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 15.55/8.54        = A ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4283_add_Oinverse__inverse,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 15.55/8.54        = A ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4284_add_Oinverse__inverse,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 15.55/8.54        = A ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4285_neg__equal__iff__equal,axiom,
% 15.55/8.54      ! [A: real,B: real] :
% 15.55/8.54        ( ( ( uminus_uminus_real @ A )
% 15.55/8.54          = ( uminus_uminus_real @ B ) )
% 15.55/8.54        = ( A = B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4286_neg__equal__iff__equal,axiom,
% 15.55/8.54      ! [A: int,B: int] :
% 15.55/8.54        ( ( ( uminus_uminus_int @ A )
% 15.55/8.54          = ( uminus_uminus_int @ B ) )
% 15.55/8.54        = ( A = B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4287_neg__equal__iff__equal,axiom,
% 15.55/8.54      ! [A: complex,B: complex] :
% 15.55/8.54        ( ( ( uminus1482373934393186551omplex @ A )
% 15.55/8.54          = ( uminus1482373934393186551omplex @ B ) )
% 15.55/8.54        = ( A = B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4288_neg__equal__iff__equal,axiom,
% 15.55/8.54      ! [A: code_integer,B: code_integer] :
% 15.55/8.54        ( ( ( uminus1351360451143612070nteger @ A )
% 15.55/8.54          = ( uminus1351360451143612070nteger @ B ) )
% 15.55/8.54        = ( A = B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4289_neg__equal__iff__equal,axiom,
% 15.55/8.54      ! [A: rat,B: rat] :
% 15.55/8.54        ( ( ( uminus_uminus_rat @ A )
% 15.55/8.54          = ( uminus_uminus_rat @ B ) )
% 15.55/8.54        = ( A = B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4290_verit__minus__simplify_I4_J,axiom,
% 15.55/8.54      ! [B: real] :
% 15.55/8.54        ( ( uminus_uminus_real @ ( uminus_uminus_real @ B ) )
% 15.55/8.54        = B ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4291_verit__minus__simplify_I4_J,axiom,
% 15.55/8.54      ! [B: int] :
% 15.55/8.54        ( ( uminus_uminus_int @ ( uminus_uminus_int @ B ) )
% 15.55/8.54        = B ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4292_verit__minus__simplify_I4_J,axiom,
% 15.55/8.54      ! [B: complex] :
% 15.55/8.54        ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ B ) )
% 15.55/8.54        = B ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4293_verit__minus__simplify_I4_J,axiom,
% 15.55/8.54      ! [B: code_integer] :
% 15.55/8.54        ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ B ) )
% 15.55/8.54        = B ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4294_verit__minus__simplify_I4_J,axiom,
% 15.55/8.54      ! [B: rat] :
% 15.55/8.54        ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ B ) )
% 15.55/8.54        = B ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4295_abs__idempotent,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 15.55/8.54        = ( abs_abs_real @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4296_abs__idempotent,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 15.55/8.54        = ( abs_abs_int @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4297_abs__idempotent,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 15.55/8.54        = ( abs_abs_Code_integer @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4298_abs__idempotent,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 15.55/8.54        = ( abs_abs_rat @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4299_neg__le__iff__le,axiom,
% 15.55/8.54      ! [B: real,A: real] :
% 15.55/8.54        ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 15.55/8.54        = ( ord_less_eq_real @ A @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4300_neg__le__iff__le,axiom,
% 15.55/8.54      ! [B: code_integer,A: code_integer] :
% 15.55/8.54        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 15.55/8.54        = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4301_neg__le__iff__le,axiom,
% 15.55/8.54      ! [B: rat,A: rat] :
% 15.55/8.54        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 15.55/8.54        = ( ord_less_eq_rat @ A @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4302_neg__le__iff__le,axiom,
% 15.55/8.54      ! [B: int,A: int] :
% 15.55/8.54        ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 15.55/8.54        = ( ord_less_eq_int @ A @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4303_neg__equal__zero,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( ( uminus_uminus_real @ A )
% 15.55/8.54          = A )
% 15.55/8.54        = ( A = zero_zero_real ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4304_neg__equal__zero,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( ( uminus_uminus_int @ A )
% 15.55/8.54          = A )
% 15.55/8.54        = ( A = zero_zero_int ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4305_neg__equal__zero,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( ( uminus1351360451143612070nteger @ A )
% 15.55/8.54          = A )
% 15.55/8.54        = ( A = zero_z3403309356797280102nteger ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4306_neg__equal__zero,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( ( uminus_uminus_rat @ A )
% 15.55/8.54          = A )
% 15.55/8.54        = ( A = zero_zero_rat ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4307_equal__neg__zero,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( A
% 15.55/8.54          = ( uminus_uminus_real @ A ) )
% 15.55/8.54        = ( A = zero_zero_real ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4308_equal__neg__zero,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( A
% 15.55/8.54          = ( uminus_uminus_int @ A ) )
% 15.55/8.54        = ( A = zero_zero_int ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4309_equal__neg__zero,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( A
% 15.55/8.54          = ( uminus1351360451143612070nteger @ A ) )
% 15.55/8.54        = ( A = zero_z3403309356797280102nteger ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4310_equal__neg__zero,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( A
% 15.55/8.54          = ( uminus_uminus_rat @ A ) )
% 15.55/8.54        = ( A = zero_zero_rat ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4311_neg__equal__0__iff__equal,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( ( uminus_uminus_real @ A )
% 15.55/8.54          = zero_zero_real )
% 15.55/8.54        = ( A = zero_zero_real ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4312_neg__equal__0__iff__equal,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( ( uminus_uminus_int @ A )
% 15.55/8.54          = zero_zero_int )
% 15.55/8.54        = ( A = zero_zero_int ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4313_neg__equal__0__iff__equal,axiom,
% 15.55/8.54      ! [A: complex] :
% 15.55/8.54        ( ( ( uminus1482373934393186551omplex @ A )
% 15.55/8.54          = zero_zero_complex )
% 15.55/8.54        = ( A = zero_zero_complex ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4314_neg__equal__0__iff__equal,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( ( uminus1351360451143612070nteger @ A )
% 15.55/8.54          = zero_z3403309356797280102nteger )
% 15.55/8.54        = ( A = zero_z3403309356797280102nteger ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4315_neg__equal__0__iff__equal,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( ( uminus_uminus_rat @ A )
% 15.55/8.54          = zero_zero_rat )
% 15.55/8.54        = ( A = zero_zero_rat ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4316_neg__0__equal__iff__equal,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( zero_zero_real
% 15.55/8.54          = ( uminus_uminus_real @ A ) )
% 15.55/8.54        = ( zero_zero_real = A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4317_neg__0__equal__iff__equal,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( zero_zero_int
% 15.55/8.54          = ( uminus_uminus_int @ A ) )
% 15.55/8.54        = ( zero_zero_int = A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4318_neg__0__equal__iff__equal,axiom,
% 15.55/8.54      ! [A: complex] :
% 15.55/8.54        ( ( zero_zero_complex
% 15.55/8.54          = ( uminus1482373934393186551omplex @ A ) )
% 15.55/8.54        = ( zero_zero_complex = A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4319_neg__0__equal__iff__equal,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( zero_z3403309356797280102nteger
% 15.55/8.54          = ( uminus1351360451143612070nteger @ A ) )
% 15.55/8.54        = ( zero_z3403309356797280102nteger = A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4320_neg__0__equal__iff__equal,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( zero_zero_rat
% 15.55/8.54          = ( uminus_uminus_rat @ A ) )
% 15.55/8.54        = ( zero_zero_rat = A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4321_add_Oinverse__neutral,axiom,
% 15.55/8.54      ( ( uminus_uminus_real @ zero_zero_real )
% 15.55/8.54      = zero_zero_real ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4322_add_Oinverse__neutral,axiom,
% 15.55/8.54      ( ( uminus_uminus_int @ zero_zero_int )
% 15.55/8.54      = zero_zero_int ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4323_add_Oinverse__neutral,axiom,
% 15.55/8.54      ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 15.55/8.54      = zero_zero_complex ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4324_add_Oinverse__neutral,axiom,
% 15.55/8.54      ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 15.55/8.54      = zero_z3403309356797280102nteger ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4325_add_Oinverse__neutral,axiom,
% 15.55/8.54      ( ( uminus_uminus_rat @ zero_zero_rat )
% 15.55/8.54      = zero_zero_rat ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4326_neg__less__iff__less,axiom,
% 15.55/8.54      ! [B: real,A: real] :
% 15.55/8.54        ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 15.55/8.54        = ( ord_less_real @ A @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4327_neg__less__iff__less,axiom,
% 15.55/8.54      ! [B: int,A: int] :
% 15.55/8.54        ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 15.55/8.54        = ( ord_less_int @ A @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4328_neg__less__iff__less,axiom,
% 15.55/8.54      ! [B: code_integer,A: code_integer] :
% 15.55/8.54        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 15.55/8.54        = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4329_neg__less__iff__less,axiom,
% 15.55/8.54      ! [B: rat,A: rat] :
% 15.55/8.54        ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 15.55/8.54        = ( ord_less_rat @ A @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4330_neg__numeral__eq__iff,axiom,
% 15.55/8.54      ! [M: num,N: num] :
% 15.55/8.54        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 15.55/8.54          = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 15.55/8.54        = ( M = N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4331_neg__numeral__eq__iff,axiom,
% 15.55/8.54      ! [M: num,N: num] :
% 15.55/8.54        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 15.55/8.54          = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.54        = ( M = N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4332_neg__numeral__eq__iff,axiom,
% 15.55/8.54      ! [M: num,N: num] :
% 15.55/8.54        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 15.55/8.54          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 15.55/8.54        = ( M = N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4333_neg__numeral__eq__iff,axiom,
% 15.55/8.54      ! [M: num,N: num] :
% 15.55/8.54        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 15.55/8.54          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 15.55/8.54        = ( M = N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4334_neg__numeral__eq__iff,axiom,
% 15.55/8.54      ! [M: num,N: num] :
% 15.55/8.54        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 15.55/8.54          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 15.55/8.54        = ( M = N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4335_add__minus__cancel,axiom,
% 15.55/8.54      ! [A: real,B: real] :
% 15.55/8.54        ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 15.55/8.54        = B ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4336_add__minus__cancel,axiom,
% 15.55/8.54      ! [A: int,B: int] :
% 15.55/8.54        ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 15.55/8.54        = B ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4337_add__minus__cancel,axiom,
% 15.55/8.54      ! [A: complex,B: complex] :
% 15.55/8.54        ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 15.55/8.54        = B ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4338_add__minus__cancel,axiom,
% 15.55/8.54      ! [A: code_integer,B: code_integer] :
% 15.55/8.54        ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 15.55/8.54        = B ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4339_add__minus__cancel,axiom,
% 15.55/8.54      ! [A: rat,B: rat] :
% 15.55/8.54        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 15.55/8.54        = B ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4340_minus__add__cancel,axiom,
% 15.55/8.54      ! [A: real,B: real] :
% 15.55/8.54        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 15.55/8.54        = B ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4341_minus__add__cancel,axiom,
% 15.55/8.54      ! [A: int,B: int] :
% 15.55/8.54        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 15.55/8.54        = B ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4342_minus__add__cancel,axiom,
% 15.55/8.54      ! [A: complex,B: complex] :
% 15.55/8.54        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 15.55/8.54        = B ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4343_minus__add__cancel,axiom,
% 15.55/8.54      ! [A: code_integer,B: code_integer] :
% 15.55/8.54        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 15.55/8.54        = B ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4344_minus__add__cancel,axiom,
% 15.55/8.54      ! [A: rat,B: rat] :
% 15.55/8.54        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 15.55/8.54        = B ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4345_minus__add__distrib,axiom,
% 15.55/8.54      ! [A: real,B: real] :
% 15.55/8.54        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 15.55/8.54        = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4346_minus__add__distrib,axiom,
% 15.55/8.54      ! [A: int,B: int] :
% 15.55/8.54        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 15.55/8.54        = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4347_minus__add__distrib,axiom,
% 15.55/8.54      ! [A: complex,B: complex] :
% 15.55/8.54        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 15.55/8.54        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4348_minus__add__distrib,axiom,
% 15.55/8.54      ! [A: code_integer,B: code_integer] :
% 15.55/8.54        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 15.55/8.54        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4349_minus__add__distrib,axiom,
% 15.55/8.54      ! [A: rat,B: rat] :
% 15.55/8.54        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 15.55/8.54        = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4350_minus__diff__eq,axiom,
% 15.55/8.54      ! [A: real,B: real] :
% 15.55/8.54        ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 15.55/8.54        = ( minus_minus_real @ B @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4351_minus__diff__eq,axiom,
% 15.55/8.54      ! [A: int,B: int] :
% 15.55/8.54        ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 15.55/8.54        = ( minus_minus_int @ B @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4352_minus__diff__eq,axiom,
% 15.55/8.54      ! [A: complex,B: complex] :
% 15.55/8.54        ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 15.55/8.54        = ( minus_minus_complex @ B @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4353_minus__diff__eq,axiom,
% 15.55/8.54      ! [A: code_integer,B: code_integer] :
% 15.55/8.54        ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 15.55/8.54        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4354_minus__diff__eq,axiom,
% 15.55/8.54      ! [A: rat,B: rat] :
% 15.55/8.54        ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 15.55/8.54        = ( minus_minus_rat @ B @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4355_abs__zero,axiom,
% 15.55/8.54      ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 15.55/8.54      = zero_z3403309356797280102nteger ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4356_abs__zero,axiom,
% 15.55/8.54      ( ( abs_abs_real @ zero_zero_real )
% 15.55/8.54      = zero_zero_real ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4357_abs__zero,axiom,
% 15.55/8.54      ( ( abs_abs_rat @ zero_zero_rat )
% 15.55/8.54      = zero_zero_rat ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4358_abs__zero,axiom,
% 15.55/8.54      ( ( abs_abs_int @ zero_zero_int )
% 15.55/8.54      = zero_zero_int ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4359_abs__eq__0,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( ( abs_abs_Code_integer @ A )
% 15.55/8.54          = zero_z3403309356797280102nteger )
% 15.55/8.54        = ( A = zero_z3403309356797280102nteger ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4360_abs__eq__0,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( ( abs_abs_real @ A )
% 15.55/8.54          = zero_zero_real )
% 15.55/8.54        = ( A = zero_zero_real ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4361_abs__eq__0,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( ( abs_abs_rat @ A )
% 15.55/8.54          = zero_zero_rat )
% 15.55/8.54        = ( A = zero_zero_rat ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4362_abs__eq__0,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( ( abs_abs_int @ A )
% 15.55/8.54          = zero_zero_int )
% 15.55/8.54        = ( A = zero_zero_int ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4363_abs__0__eq,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( zero_z3403309356797280102nteger
% 15.55/8.54          = ( abs_abs_Code_integer @ A ) )
% 15.55/8.54        = ( A = zero_z3403309356797280102nteger ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4364_abs__0__eq,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( zero_zero_real
% 15.55/8.54          = ( abs_abs_real @ A ) )
% 15.55/8.54        = ( A = zero_zero_real ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4365_abs__0__eq,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( zero_zero_rat
% 15.55/8.54          = ( abs_abs_rat @ A ) )
% 15.55/8.54        = ( A = zero_zero_rat ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4366_abs__0__eq,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( zero_zero_int
% 15.55/8.54          = ( abs_abs_int @ A ) )
% 15.55/8.54        = ( A = zero_zero_int ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4367_abs__0,axiom,
% 15.55/8.54      ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 15.55/8.54      = zero_z3403309356797280102nteger ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4368_abs__0,axiom,
% 15.55/8.54      ( ( abs_abs_real @ zero_zero_real )
% 15.55/8.54      = zero_zero_real ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4369_abs__0,axiom,
% 15.55/8.54      ( ( abs_abs_rat @ zero_zero_rat )
% 15.55/8.54      = zero_zero_rat ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4370_abs__0,axiom,
% 15.55/8.54      ( ( abs_abs_int @ zero_zero_int )
% 15.55/8.54      = zero_zero_int ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4371_abs__numeral,axiom,
% 15.55/8.54      ! [N: num] :
% 15.55/8.54        ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 15.55/8.54        = ( numera6620942414471956472nteger @ N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4372_abs__numeral,axiom,
% 15.55/8.54      ! [N: num] :
% 15.55/8.54        ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 15.55/8.54        = ( numeral_numeral_real @ N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4373_abs__numeral,axiom,
% 15.55/8.54      ! [N: num] :
% 15.55/8.54        ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 15.55/8.54        = ( numeral_numeral_rat @ N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4374_abs__numeral,axiom,
% 15.55/8.54      ! [N: num] :
% 15.55/8.54        ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 15.55/8.54        = ( numeral_numeral_int @ N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4375_abs__add__abs,axiom,
% 15.55/8.54      ! [A: code_integer,B: code_integer] :
% 15.55/8.54        ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 15.55/8.54        = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4376_abs__add__abs,axiom,
% 15.55/8.54      ! [A: real,B: real] :
% 15.55/8.54        ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 15.55/8.54        = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4377_abs__add__abs,axiom,
% 15.55/8.54      ! [A: rat,B: rat] :
% 15.55/8.54        ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 15.55/8.54        = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4378_abs__add__abs,axiom,
% 15.55/8.54      ! [A: int,B: int] :
% 15.55/8.54        ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 15.55/8.54        = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4379_abs__minus__cancel,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 15.55/8.54        = ( abs_abs_real @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4380_abs__minus__cancel,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 15.55/8.54        = ( abs_abs_int @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4381_abs__minus__cancel,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 15.55/8.54        = ( abs_abs_Code_integer @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4382_abs__minus__cancel,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 15.55/8.54        = ( abs_abs_rat @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4383_of__int__minus,axiom,
% 15.55/8.54      ! [Z: int] :
% 15.55/8.54        ( ( ring_1_of_int_real @ ( uminus_uminus_int @ Z ) )
% 15.55/8.54        = ( uminus_uminus_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4384_of__int__minus,axiom,
% 15.55/8.54      ! [Z: int] :
% 15.55/8.54        ( ( ring_1_of_int_int @ ( uminus_uminus_int @ Z ) )
% 15.55/8.54        = ( uminus_uminus_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4385_of__int__minus,axiom,
% 15.55/8.54      ! [Z: int] :
% 15.55/8.54        ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ Z ) )
% 15.55/8.54        = ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4386_of__int__minus,axiom,
% 15.55/8.54      ! [Z: int] :
% 15.55/8.54        ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ Z ) )
% 15.55/8.54        = ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ Z ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4387_of__int__minus,axiom,
% 15.55/8.54      ! [Z: int] :
% 15.55/8.54        ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ Z ) )
% 15.55/8.54        = ( uminus_uminus_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4388_abs__of__nat,axiom,
% 15.55/8.54      ! [N: nat] :
% 15.55/8.54        ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 15.55/8.54        = ( semiri4939895301339042750nteger @ N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4389_abs__of__nat,axiom,
% 15.55/8.54      ! [N: nat] :
% 15.55/8.54        ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N ) )
% 15.55/8.54        = ( semiri5074537144036343181t_real @ N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4390_abs__of__nat,axiom,
% 15.55/8.54      ! [N: nat] :
% 15.55/8.54        ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N ) )
% 15.55/8.54        = ( semiri681578069525770553at_rat @ N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4391_abs__of__nat,axiom,
% 15.55/8.54      ! [N: nat] :
% 15.55/8.54        ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 15.55/8.54        = ( semiri1314217659103216013at_int @ N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4392_of__int__abs,axiom,
% 15.55/8.54      ! [X3: int] :
% 15.55/8.54        ( ( ring_1_of_int_int @ ( abs_abs_int @ X3 ) )
% 15.55/8.54        = ( abs_abs_int @ ( ring_1_of_int_int @ X3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4393_of__int__abs,axiom,
% 15.55/8.54      ! [X3: int] :
% 15.55/8.54        ( ( ring_18347121197199848620nteger @ ( abs_abs_int @ X3 ) )
% 15.55/8.54        = ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ X3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4394_of__int__abs,axiom,
% 15.55/8.54      ! [X3: int] :
% 15.55/8.54        ( ( ring_1_of_int_real @ ( abs_abs_int @ X3 ) )
% 15.55/8.54        = ( abs_abs_real @ ( ring_1_of_int_real @ X3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4395_of__int__abs,axiom,
% 15.55/8.54      ! [X3: int] :
% 15.55/8.54        ( ( ring_1_of_int_rat @ ( abs_abs_int @ X3 ) )
% 15.55/8.54        = ( abs_abs_rat @ ( ring_1_of_int_rat @ X3 ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4396_triangle__0,axiom,
% 15.55/8.54      ( ( nat_triangle @ zero_zero_nat )
% 15.55/8.54      = zero_zero_nat ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4397_neg__0__le__iff__le,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 15.55/8.54        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4398_neg__0__le__iff__le,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 15.55/8.54        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4399_neg__0__le__iff__le,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 15.55/8.54        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4400_neg__0__le__iff__le,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 15.55/8.54        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4401_neg__le__0__iff__le,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 15.55/8.54        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4402_neg__le__0__iff__le,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 15.55/8.54        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4403_neg__le__0__iff__le,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 15.55/8.54        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4404_neg__le__0__iff__le,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 15.55/8.54        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4405_less__eq__neg__nonpos,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 15.55/8.54        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4406_less__eq__neg__nonpos,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 15.55/8.54        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4407_less__eq__neg__nonpos,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 15.55/8.54        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4408_less__eq__neg__nonpos,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 15.55/8.54        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4409_neg__less__eq__nonneg,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 15.55/8.54        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4410_neg__less__eq__nonneg,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 15.55/8.54        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4411_neg__less__eq__nonneg,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 15.55/8.54        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4412_neg__less__eq__nonneg,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 15.55/8.54        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4413_less__neg__neg,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 15.55/8.54        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4414_less__neg__neg,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 15.55/8.54        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4415_less__neg__neg,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 15.55/8.54        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4416_less__neg__neg,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 15.55/8.54        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4417_neg__less__pos,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 15.55/8.54        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4418_neg__less__pos,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 15.55/8.54        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4419_neg__less__pos,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 15.55/8.54        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4420_neg__less__pos,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 15.55/8.54        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4421_neg__0__less__iff__less,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 15.55/8.54        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4422_neg__0__less__iff__less,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 15.55/8.54        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4423_neg__0__less__iff__less,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 15.55/8.54        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4424_neg__0__less__iff__less,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 15.55/8.54        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4425_neg__less__0__iff__less,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 15.55/8.54        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4426_neg__less__0__iff__less,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 15.55/8.54        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4427_neg__less__0__iff__less,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 15.55/8.54        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4428_neg__less__0__iff__less,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 15.55/8.54        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4429_add_Oright__inverse,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 15.55/8.54        = zero_zero_real ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4430_add_Oright__inverse,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 15.55/8.54        = zero_zero_int ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4431_add_Oright__inverse,axiom,
% 15.55/8.54      ! [A: complex] :
% 15.55/8.54        ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 15.55/8.54        = zero_zero_complex ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4432_add_Oright__inverse,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 15.55/8.54        = zero_z3403309356797280102nteger ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4433_add_Oright__inverse,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 15.55/8.54        = zero_zero_rat ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4434_ab__left__minus,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 15.55/8.54        = zero_zero_real ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4435_ab__left__minus,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 15.55/8.54        = zero_zero_int ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4436_ab__left__minus,axiom,
% 15.55/8.54      ! [A: complex] :
% 15.55/8.54        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 15.55/8.54        = zero_zero_complex ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4437_ab__left__minus,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 15.55/8.54        = zero_z3403309356797280102nteger ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4438_ab__left__minus,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 15.55/8.54        = zero_zero_rat ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4439_verit__minus__simplify_I3_J,axiom,
% 15.55/8.54      ! [B: real] :
% 15.55/8.54        ( ( minus_minus_real @ zero_zero_real @ B )
% 15.55/8.54        = ( uminus_uminus_real @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4440_verit__minus__simplify_I3_J,axiom,
% 15.55/8.54      ! [B: int] :
% 15.55/8.54        ( ( minus_minus_int @ zero_zero_int @ B )
% 15.55/8.54        = ( uminus_uminus_int @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4441_verit__minus__simplify_I3_J,axiom,
% 15.55/8.54      ! [B: complex] :
% 15.55/8.54        ( ( minus_minus_complex @ zero_zero_complex @ B )
% 15.55/8.54        = ( uminus1482373934393186551omplex @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4442_verit__minus__simplify_I3_J,axiom,
% 15.55/8.54      ! [B: code_integer] :
% 15.55/8.54        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 15.55/8.54        = ( uminus1351360451143612070nteger @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4443_verit__minus__simplify_I3_J,axiom,
% 15.55/8.54      ! [B: rat] :
% 15.55/8.54        ( ( minus_minus_rat @ zero_zero_rat @ B )
% 15.55/8.54        = ( uminus_uminus_rat @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4444_diff__0,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( minus_minus_real @ zero_zero_real @ A )
% 15.55/8.54        = ( uminus_uminus_real @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4445_diff__0,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( minus_minus_int @ zero_zero_int @ A )
% 15.55/8.54        = ( uminus_uminus_int @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4446_diff__0,axiom,
% 15.55/8.54      ! [A: complex] :
% 15.55/8.54        ( ( minus_minus_complex @ zero_zero_complex @ A )
% 15.55/8.54        = ( uminus1482373934393186551omplex @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4447_diff__0,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 15.55/8.54        = ( uminus1351360451143612070nteger @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4448_diff__0,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( minus_minus_rat @ zero_zero_rat @ A )
% 15.55/8.54        = ( uminus_uminus_rat @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4449_add__neg__numeral__simps_I3_J,axiom,
% 15.55/8.54      ! [M: num,N: num] :
% 15.55/8.54        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 15.55/8.54        = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4450_add__neg__numeral__simps_I3_J,axiom,
% 15.55/8.54      ! [M: num,N: num] :
% 15.55/8.54        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.54        = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4451_add__neg__numeral__simps_I3_J,axiom,
% 15.55/8.54      ! [M: num,N: num] :
% 15.55/8.54        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 15.55/8.54        = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4452_add__neg__numeral__simps_I3_J,axiom,
% 15.55/8.54      ! [M: num,N: num] :
% 15.55/8.54        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 15.55/8.54        = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4453_add__neg__numeral__simps_I3_J,axiom,
% 15.55/8.54      ! [M: num,N: num] :
% 15.55/8.54        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 15.55/8.54        = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4454_mult__minus1__right,axiom,
% 15.55/8.54      ! [Z: real] :
% 15.55/8.54        ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 15.55/8.54        = ( uminus_uminus_real @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4455_mult__minus1__right,axiom,
% 15.55/8.54      ! [Z: int] :
% 15.55/8.54        ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.54        = ( uminus_uminus_int @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4456_mult__minus1__right,axiom,
% 15.55/8.54      ! [Z: complex] :
% 15.55/8.54        ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 15.55/8.54        = ( uminus1482373934393186551omplex @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4457_mult__minus1__right,axiom,
% 15.55/8.54      ! [Z: code_integer] :
% 15.55/8.54        ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 15.55/8.54        = ( uminus1351360451143612070nteger @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4458_mult__minus1__right,axiom,
% 15.55/8.54      ! [Z: rat] :
% 15.55/8.54        ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 15.55/8.54        = ( uminus_uminus_rat @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4459_mult__minus1,axiom,
% 15.55/8.54      ! [Z: real] :
% 15.55/8.54        ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 15.55/8.54        = ( uminus_uminus_real @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4460_mult__minus1,axiom,
% 15.55/8.54      ! [Z: int] :
% 15.55/8.54        ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 15.55/8.54        = ( uminus_uminus_int @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4461_mult__minus1,axiom,
% 15.55/8.54      ! [Z: complex] :
% 15.55/8.54        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 15.55/8.54        = ( uminus1482373934393186551omplex @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4462_mult__minus1,axiom,
% 15.55/8.54      ! [Z: code_integer] :
% 15.55/8.54        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 15.55/8.54        = ( uminus1351360451143612070nteger @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4463_mult__minus1,axiom,
% 15.55/8.54      ! [Z: rat] :
% 15.55/8.54        ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 15.55/8.54        = ( uminus_uminus_rat @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4464_abs__of__nonneg,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 15.55/8.54       => ( ( abs_abs_Code_integer @ A )
% 15.55/8.54          = A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4465_abs__of__nonneg,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.54       => ( ( abs_abs_real @ A )
% 15.55/8.54          = A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4466_abs__of__nonneg,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.54       => ( ( abs_abs_rat @ A )
% 15.55/8.54          = A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4467_abs__of__nonneg,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.54       => ( ( abs_abs_int @ A )
% 15.55/8.54          = A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4468_abs__le__self__iff,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 15.55/8.54        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4469_abs__le__self__iff,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 15.55/8.54        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4470_abs__le__self__iff,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 15.55/8.54        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4471_abs__le__self__iff,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 15.55/8.54        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4472_abs__le__zero__iff,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 15.55/8.54        = ( A = zero_z3403309356797280102nteger ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4473_abs__le__zero__iff,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 15.55/8.54        = ( A = zero_zero_real ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4474_abs__le__zero__iff,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 15.55/8.54        = ( A = zero_zero_rat ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4475_abs__le__zero__iff,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 15.55/8.54        = ( A = zero_zero_int ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4476_diff__minus__eq__add,axiom,
% 15.55/8.54      ! [A: real,B: real] :
% 15.55/8.54        ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 15.55/8.54        = ( plus_plus_real @ A @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4477_diff__minus__eq__add,axiom,
% 15.55/8.54      ! [A: int,B: int] :
% 15.55/8.54        ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 15.55/8.54        = ( plus_plus_int @ A @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4478_diff__minus__eq__add,axiom,
% 15.55/8.54      ! [A: complex,B: complex] :
% 15.55/8.54        ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 15.55/8.54        = ( plus_plus_complex @ A @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4479_diff__minus__eq__add,axiom,
% 15.55/8.54      ! [A: code_integer,B: code_integer] :
% 15.55/8.54        ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 15.55/8.54        = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4480_diff__minus__eq__add,axiom,
% 15.55/8.54      ! [A: rat,B: rat] :
% 15.55/8.54        ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 15.55/8.54        = ( plus_plus_rat @ A @ B ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4481_uminus__add__conv__diff,axiom,
% 15.55/8.54      ! [A: real,B: real] :
% 15.55/8.54        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 15.55/8.54        = ( minus_minus_real @ B @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4482_uminus__add__conv__diff,axiom,
% 15.55/8.54      ! [A: int,B: int] :
% 15.55/8.54        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 15.55/8.54        = ( minus_minus_int @ B @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4483_uminus__add__conv__diff,axiom,
% 15.55/8.54      ! [A: complex,B: complex] :
% 15.55/8.54        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 15.55/8.54        = ( minus_minus_complex @ B @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4484_uminus__add__conv__diff,axiom,
% 15.55/8.54      ! [A: code_integer,B: code_integer] :
% 15.55/8.54        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 15.55/8.54        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4485_uminus__add__conv__diff,axiom,
% 15.55/8.54      ! [A: rat,B: rat] :
% 15.55/8.54        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 15.55/8.54        = ( minus_minus_rat @ B @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4486_zero__less__abs__iff,axiom,
% 15.55/8.54      ! [A: code_integer] :
% 15.55/8.54        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 15.55/8.54        = ( A != zero_z3403309356797280102nteger ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4487_zero__less__abs__iff,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 15.55/8.54        = ( A != zero_zero_real ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4488_zero__less__abs__iff,axiom,
% 15.55/8.54      ! [A: rat] :
% 15.55/8.54        ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 15.55/8.54        = ( A != zero_zero_rat ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4489_zero__less__abs__iff,axiom,
% 15.55/8.54      ! [A: int] :
% 15.55/8.54        ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 15.55/8.54        = ( A != zero_zero_int ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4490_abs__neg__numeral,axiom,
% 15.55/8.54      ! [N: num] :
% 15.55/8.54        ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 15.55/8.54        = ( numeral_numeral_real @ N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4491_abs__neg__numeral,axiom,
% 15.55/8.54      ! [N: num] :
% 15.55/8.54        ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.54        = ( numeral_numeral_int @ N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4492_abs__neg__numeral,axiom,
% 15.55/8.54      ! [N: num] :
% 15.55/8.54        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 15.55/8.54        = ( numera6620942414471956472nteger @ N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4493_abs__neg__numeral,axiom,
% 15.55/8.54      ! [N: num] :
% 15.55/8.54        ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 15.55/8.54        = ( numeral_numeral_rat @ N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4494_abs__neg__one,axiom,
% 15.55/8.54      ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 15.55/8.54      = one_one_real ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4495_abs__neg__one,axiom,
% 15.55/8.54      ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.54      = one_one_int ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4496_abs__neg__one,axiom,
% 15.55/8.54      ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 15.55/8.54      = one_one_Code_integer ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4497_abs__neg__one,axiom,
% 15.55/8.54      ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 15.55/8.54      = one_one_rat ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4498_norm__eq__zero,axiom,
% 15.55/8.54      ! [X3: real] :
% 15.55/8.54        ( ( ( real_V7735802525324610683m_real @ X3 )
% 15.55/8.54          = zero_zero_real )
% 15.55/8.54        = ( X3 = zero_zero_real ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4499_norm__eq__zero,axiom,
% 15.55/8.54      ! [X3: complex] :
% 15.55/8.54        ( ( ( real_V1022390504157884413omplex @ X3 )
% 15.55/8.54          = zero_zero_real )
% 15.55/8.54        = ( X3 = zero_zero_complex ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4500_norm__zero,axiom,
% 15.55/8.54      ( ( real_V7735802525324610683m_real @ zero_zero_real )
% 15.55/8.54      = zero_zero_real ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4501_norm__zero,axiom,
% 15.55/8.54      ( ( real_V1022390504157884413omplex @ zero_zero_complex )
% 15.55/8.54      = zero_zero_real ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4502_abs__power__minus,axiom,
% 15.55/8.54      ! [A: real,N: nat] :
% 15.55/8.54        ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 15.55/8.54        = ( abs_abs_real @ ( power_power_real @ A @ N ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4503_abs__power__minus,axiom,
% 15.55/8.54      ! [A: int,N: nat] :
% 15.55/8.54        ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 15.55/8.54        = ( abs_abs_int @ ( power_power_int @ A @ N ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4504_abs__power__minus,axiom,
% 15.55/8.54      ! [A: code_integer,N: nat] :
% 15.55/8.54        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 15.55/8.54        = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4505_abs__power__minus,axiom,
% 15.55/8.54      ! [A: rat,N: nat] :
% 15.55/8.54        ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 15.55/8.54        = ( abs_abs_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4506_norm__numeral,axiom,
% 15.55/8.54      ! [W: num] :
% 15.55/8.54        ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 15.55/8.54        = ( numeral_numeral_real @ W ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4507_norm__numeral,axiom,
% 15.55/8.54      ! [W: num] :
% 15.55/8.54        ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 15.55/8.54        = ( numeral_numeral_real @ W ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4508_bit_Odisj__one__left,axiom,
% 15.55/8.54      ! [X3: code_integer] :
% 15.55/8.54        ( ( bit_se1080825931792720795nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X3 )
% 15.55/8.54        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4509_bit_Odisj__one__left,axiom,
% 15.55/8.54      ! [X3: int] :
% 15.55/8.54        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ one_one_int ) @ X3 )
% 15.55/8.54        = ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4510_bit_Odisj__one__right,axiom,
% 15.55/8.54      ! [X3: code_integer] :
% 15.55/8.54        ( ( bit_se1080825931792720795nteger @ X3 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 15.55/8.54        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4511_bit_Odisj__one__right,axiom,
% 15.55/8.54      ! [X3: int] :
% 15.55/8.54        ( ( bit_se1409905431419307370or_int @ X3 @ ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.54        = ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4512_real__add__minus__iff,axiom,
% 15.55/8.54      ! [X3: real,A: real] :
% 15.55/8.54        ( ( ( plus_plus_real @ X3 @ ( uminus_uminus_real @ A ) )
% 15.55/8.54          = zero_zero_real )
% 15.55/8.54        = ( X3 = A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4513_norm__of__nat,axiom,
% 15.55/8.54      ! [N: nat] :
% 15.55/8.54        ( ( real_V7735802525324610683m_real @ ( semiri5074537144036343181t_real @ N ) )
% 15.55/8.54        = ( semiri5074537144036343181t_real @ N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4514_norm__of__nat,axiom,
% 15.55/8.54      ! [N: nat] :
% 15.55/8.54        ( ( real_V1022390504157884413omplex @ ( semiri8010041392384452111omplex @ N ) )
% 15.55/8.54        = ( semiri5074537144036343181t_real @ N ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4515_floor__uminus__of__int,axiom,
% 15.55/8.54      ! [Z: int] :
% 15.55/8.54        ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ Z ) ) )
% 15.55/8.54        = ( uminus_uminus_int @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4516_floor__uminus__of__int,axiom,
% 15.55/8.54      ! [Z: int] :
% 15.55/8.54        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( ring_1_of_int_real @ Z ) ) )
% 15.55/8.54        = ( uminus_uminus_int @ Z ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4517_real__sqrt__abs2,axiom,
% 15.55/8.54      ! [X3: real] :
% 15.55/8.54        ( ( sqrt @ ( times_times_real @ X3 @ X3 ) )
% 15.55/8.54        = ( abs_abs_real @ X3 ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4518_real__sqrt__mult__self,axiom,
% 15.55/8.54      ! [A: real] :
% 15.55/8.54        ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 15.55/8.54        = ( abs_abs_real @ A ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4519_dbl__simps_I1_J,axiom,
% 15.55/8.54      ! [K: num] :
% 15.55/8.54        ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 15.55/8.54        = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4520_dbl__simps_I1_J,axiom,
% 15.55/8.54      ! [K: num] :
% 15.55/8.54        ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 15.55/8.54        = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4521_dbl__simps_I1_J,axiom,
% 15.55/8.54      ! [K: num] :
% 15.55/8.54        ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 15.55/8.54        = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4522_dbl__simps_I1_J,axiom,
% 15.55/8.54      ! [K: num] :
% 15.55/8.54        ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 15.55/8.54        = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4523_dbl__simps_I1_J,axiom,
% 15.55/8.54      ! [K: num] :
% 15.55/8.54        ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 15.55/8.54        = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4524_add__neg__numeral__special_I8_J,axiom,
% 15.55/8.54      ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 15.55/8.54      = zero_zero_real ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4525_add__neg__numeral__special_I8_J,axiom,
% 15.55/8.54      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 15.55/8.54      = zero_zero_int ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4526_add__neg__numeral__special_I8_J,axiom,
% 15.55/8.54      ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 15.55/8.54      = zero_zero_complex ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4527_add__neg__numeral__special_I8_J,axiom,
% 15.55/8.54      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 15.55/8.54      = zero_z3403309356797280102nteger ) ).
% 15.55/8.54  
% 15.55/8.54  thf(fact_4528_add__neg__numeral__special_I8_J,axiom,
% 15.55/8.55      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 15.55/8.55      = zero_zero_rat ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4529_add__neg__numeral__special_I7_J,axiom,
% 15.55/8.55      ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 15.55/8.55      = zero_zero_real ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4530_add__neg__numeral__special_I7_J,axiom,
% 15.55/8.55      ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.55      = zero_zero_int ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4531_add__neg__numeral__special_I7_J,axiom,
% 15.55/8.55      ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 15.55/8.55      = zero_zero_complex ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4532_add__neg__numeral__special_I7_J,axiom,
% 15.55/8.55      ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 15.55/8.55      = zero_z3403309356797280102nteger ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4533_add__neg__numeral__special_I7_J,axiom,
% 15.55/8.55      ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 15.55/8.55      = zero_zero_rat ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4534_diff__numeral__special_I12_J,axiom,
% 15.55/8.55      ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 15.55/8.55      = zero_zero_real ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4535_diff__numeral__special_I12_J,axiom,
% 15.55/8.55      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.55      = zero_zero_int ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4536_diff__numeral__special_I12_J,axiom,
% 15.55/8.55      ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 15.55/8.55      = zero_zero_complex ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4537_diff__numeral__special_I12_J,axiom,
% 15.55/8.55      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 15.55/8.55      = zero_z3403309356797280102nteger ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4538_diff__numeral__special_I12_J,axiom,
% 15.55/8.55      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 15.55/8.55      = zero_zero_rat ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4539_neg__one__eq__numeral__iff,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( ( ( uminus_uminus_real @ one_one_real )
% 15.55/8.55          = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 15.55/8.55        = ( N = one ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4540_neg__one__eq__numeral__iff,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( ( ( uminus_uminus_int @ one_one_int )
% 15.55/8.55          = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.55        = ( N = one ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4541_neg__one__eq__numeral__iff,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 15.55/8.55          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 15.55/8.55        = ( N = one ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4542_neg__one__eq__numeral__iff,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 15.55/8.55          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 15.55/8.55        = ( N = one ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4543_neg__one__eq__numeral__iff,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( ( ( uminus_uminus_rat @ one_one_rat )
% 15.55/8.55          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 15.55/8.55        = ( N = one ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4544_numeral__eq__neg__one__iff,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N ) )
% 15.55/8.55          = ( uminus_uminus_real @ one_one_real ) )
% 15.55/8.55        = ( N = one ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4545_numeral__eq__neg__one__iff,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 15.55/8.55          = ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.55        = ( N = one ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4546_numeral__eq__neg__one__iff,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) )
% 15.55/8.55          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 15.55/8.55        = ( N = one ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4547_numeral__eq__neg__one__iff,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 15.55/8.55          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 15.55/8.55        = ( N = one ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4548_numeral__eq__neg__one__iff,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 15.55/8.55          = ( uminus_uminus_rat @ one_one_rat ) )
% 15.55/8.55        = ( N = one ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4549_divide__le__0__abs__iff,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 15.55/8.55        = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 15.55/8.55          | ( B = zero_zero_real ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4550_divide__le__0__abs__iff,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 15.55/8.55        = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 15.55/8.55          | ( B = zero_zero_rat ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4551_zero__le__divide__abs__iff,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 15.55/8.55        = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.55          | ( B = zero_zero_real ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4552_zero__le__divide__abs__iff,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 15.55/8.55        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.55          | ( B = zero_zero_rat ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4553_left__minus__one__mult__self,axiom,
% 15.55/8.55      ! [N: nat,A: real] :
% 15.55/8.55        ( ( 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 ) )
% 15.55/8.55        = A ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4554_left__minus__one__mult__self,axiom,
% 15.55/8.55      ! [N: nat,A: int] :
% 15.55/8.55        ( ( 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 ) )
% 15.55/8.55        = A ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4555_left__minus__one__mult__self,axiom,
% 15.55/8.55      ! [N: nat,A: complex] :
% 15.55/8.55        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ A ) )
% 15.55/8.55        = A ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4556_left__minus__one__mult__self,axiom,
% 15.55/8.55      ! [N: nat,A: code_integer] :
% 15.55/8.55        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 15.55/8.55        = A ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4557_left__minus__one__mult__self,axiom,
% 15.55/8.55      ! [N: nat,A: rat] :
% 15.55/8.55        ( ( 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 ) )
% 15.55/8.55        = A ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4558_minus__one__mult__self,axiom,
% 15.55/8.55      ! [N: nat] :
% 15.55/8.55        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) )
% 15.55/8.55        = one_one_real ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4559_minus__one__mult__self,axiom,
% 15.55/8.55      ! [N: nat] :
% 15.55/8.55        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 15.55/8.55        = one_one_int ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4560_minus__one__mult__self,axiom,
% 15.55/8.55      ! [N: nat] :
% 15.55/8.55        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) )
% 15.55/8.55        = one_one_complex ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4561_minus__one__mult__self,axiom,
% 15.55/8.55      ! [N: nat] :
% 15.55/8.55        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 15.55/8.55        = one_one_Code_integer ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4562_minus__one__mult__self,axiom,
% 15.55/8.55      ! [N: nat] :
% 15.55/8.55        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 15.55/8.55        = one_one_rat ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4563_abs__of__nonpos,axiom,
% 15.55/8.55      ! [A: real] :
% 15.55/8.55        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 15.55/8.55       => ( ( abs_abs_real @ A )
% 15.55/8.55          = ( uminus_uminus_real @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4564_abs__of__nonpos,axiom,
% 15.55/8.55      ! [A: code_integer] :
% 15.55/8.55        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 15.55/8.55       => ( ( abs_abs_Code_integer @ A )
% 15.55/8.55          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4565_abs__of__nonpos,axiom,
% 15.55/8.55      ! [A: rat] :
% 15.55/8.55        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 15.55/8.55       => ( ( abs_abs_rat @ A )
% 15.55/8.55          = ( uminus_uminus_rat @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4566_abs__of__nonpos,axiom,
% 15.55/8.55      ! [A: int] :
% 15.55/8.55        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 15.55/8.55       => ( ( abs_abs_int @ A )
% 15.55/8.55          = ( uminus_uminus_int @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4567_zero__less__norm__iff,axiom,
% 15.55/8.55      ! [X3: real] :
% 15.55/8.55        ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X3 ) )
% 15.55/8.55        = ( X3 != zero_zero_real ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4568_zero__less__norm__iff,axiom,
% 15.55/8.55      ! [X3: complex] :
% 15.55/8.55        ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X3 ) )
% 15.55/8.55        = ( X3 != zero_zero_complex ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4569_norm__le__zero__iff,axiom,
% 15.55/8.55      ! [X3: real] :
% 15.55/8.55        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X3 ) @ zero_zero_real )
% 15.55/8.55        = ( X3 = zero_zero_real ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4570_norm__le__zero__iff,axiom,
% 15.55/8.55      ! [X3: complex] :
% 15.55/8.55        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X3 ) @ zero_zero_real )
% 15.55/8.55        = ( X3 = zero_zero_complex ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4571_norm__neg__numeral,axiom,
% 15.55/8.55      ! [W: num] :
% 15.55/8.55        ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 15.55/8.55        = ( numeral_numeral_real @ W ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4572_norm__neg__numeral,axiom,
% 15.55/8.55      ! [W: num] :
% 15.55/8.55        ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 15.55/8.55        = ( numeral_numeral_real @ W ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4573_floor__neg__numeral,axiom,
% 15.55/8.55      ! [V: num] :
% 15.55/8.55        ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 15.55/8.55        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4574_floor__neg__numeral,axiom,
% 15.55/8.55      ! [V: num] :
% 15.55/8.55        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 15.55/8.55        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4575_semiring__norm_I168_J,axiom,
% 15.55/8.55      ! [V: num,W: num,Y3: real] :
% 15.55/8.55        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y3 ) )
% 15.55/8.55        = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4576_semiring__norm_I168_J,axiom,
% 15.55/8.55      ! [V: num,W: num,Y3: int] :
% 15.55/8.55        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y3 ) )
% 15.55/8.55        = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4577_semiring__norm_I168_J,axiom,
% 15.55/8.55      ! [V: num,W: num,Y3: complex] :
% 15.55/8.55        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y3 ) )
% 15.55/8.55        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4578_semiring__norm_I168_J,axiom,
% 15.55/8.55      ! [V: num,W: num,Y3: code_integer] :
% 15.55/8.55        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y3 ) )
% 15.55/8.55        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4579_semiring__norm_I168_J,axiom,
% 15.55/8.55      ! [V: num,W: num,Y3: rat] :
% 15.55/8.55        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y3 ) )
% 15.55/8.55        = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4580_diff__numeral__simps_I3_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 15.55/8.55        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4581_diff__numeral__simps_I3_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 15.55/8.55        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4582_diff__numeral__simps_I3_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 15.55/8.55        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4583_diff__numeral__simps_I3_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 15.55/8.55        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4584_diff__numeral__simps_I3_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 15.55/8.55        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4585_diff__numeral__simps_I2_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 15.55/8.55        = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4586_diff__numeral__simps_I2_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.55        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4587_diff__numeral__simps_I2_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 15.55/8.55        = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4588_diff__numeral__simps_I2_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 15.55/8.55        = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4589_diff__numeral__simps_I2_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 15.55/8.55        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4590_ceiling__neg__numeral,axiom,
% 15.55/8.55      ! [V: num] :
% 15.55/8.55        ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 15.55/8.55        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4591_ceiling__neg__numeral,axiom,
% 15.55/8.55      ! [V: num] :
% 15.55/8.55        ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 15.55/8.55        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4592_semiring__norm_I172_J,axiom,
% 15.55/8.55      ! [V: num,W: num,Y3: real] :
% 15.55/8.55        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y3 ) )
% 15.55/8.55        = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4593_semiring__norm_I172_J,axiom,
% 15.55/8.55      ! [V: num,W: num,Y3: int] :
% 15.55/8.55        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y3 ) )
% 15.55/8.55        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4594_semiring__norm_I172_J,axiom,
% 15.55/8.55      ! [V: num,W: num,Y3: complex] :
% 15.55/8.55        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y3 ) )
% 15.55/8.55        = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4595_semiring__norm_I172_J,axiom,
% 15.55/8.55      ! [V: num,W: num,Y3: code_integer] :
% 15.55/8.55        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y3 ) )
% 15.55/8.55        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4596_semiring__norm_I172_J,axiom,
% 15.55/8.55      ! [V: num,W: num,Y3: rat] :
% 15.55/8.55        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y3 ) )
% 15.55/8.55        = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4597_semiring__norm_I171_J,axiom,
% 15.55/8.55      ! [V: num,W: num,Y3: real] :
% 15.55/8.55        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y3 ) )
% 15.55/8.55        = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4598_semiring__norm_I171_J,axiom,
% 15.55/8.55      ! [V: num,W: num,Y3: int] :
% 15.55/8.55        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y3 ) )
% 15.55/8.55        = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4599_semiring__norm_I171_J,axiom,
% 15.55/8.55      ! [V: num,W: num,Y3: complex] :
% 15.55/8.55        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y3 ) )
% 15.55/8.55        = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4600_semiring__norm_I171_J,axiom,
% 15.55/8.55      ! [V: num,W: num,Y3: code_integer] :
% 15.55/8.55        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y3 ) )
% 15.55/8.55        = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4601_semiring__norm_I171_J,axiom,
% 15.55/8.55      ! [V: num,W: num,Y3: rat] :
% 15.55/8.55        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y3 ) )
% 15.55/8.55        = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4602_semiring__norm_I170_J,axiom,
% 15.55/8.55      ! [V: num,W: num,Y3: real] :
% 15.55/8.55        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y3 ) )
% 15.55/8.55        = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4603_semiring__norm_I170_J,axiom,
% 15.55/8.55      ! [V: num,W: num,Y3: int] :
% 15.55/8.55        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y3 ) )
% 15.55/8.55        = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4604_semiring__norm_I170_J,axiom,
% 15.55/8.55      ! [V: num,W: num,Y3: complex] :
% 15.55/8.55        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y3 ) )
% 15.55/8.55        = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4605_semiring__norm_I170_J,axiom,
% 15.55/8.55      ! [V: num,W: num,Y3: code_integer] :
% 15.55/8.55        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y3 ) )
% 15.55/8.55        = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4606_semiring__norm_I170_J,axiom,
% 15.55/8.55      ! [V: num,W: num,Y3: rat] :
% 15.55/8.55        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y3 ) )
% 15.55/8.55        = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4607_mult__neg__numeral__simps_I3_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 15.55/8.55        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4608_mult__neg__numeral__simps_I3_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.55        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4609_mult__neg__numeral__simps_I3_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 15.55/8.55        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4610_mult__neg__numeral__simps_I3_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 15.55/8.55        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4611_mult__neg__numeral__simps_I3_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 15.55/8.55        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4612_mult__neg__numeral__simps_I2_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 15.55/8.55        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4613_mult__neg__numeral__simps_I2_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 15.55/8.55        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4614_mult__neg__numeral__simps_I2_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 15.55/8.55        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4615_mult__neg__numeral__simps_I2_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 15.55/8.55        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4616_mult__neg__numeral__simps_I2_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 15.55/8.55        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4617_mult__neg__numeral__simps_I1_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 15.55/8.55        = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4618_mult__neg__numeral__simps_I1_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.55        = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4619_mult__neg__numeral__simps_I1_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 15.55/8.55        = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4620_mult__neg__numeral__simps_I1_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 15.55/8.55        = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4621_mult__neg__numeral__simps_I1_J,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 15.55/8.55        = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4622_artanh__minus__real,axiom,
% 15.55/8.55      ! [X3: real] :
% 15.55/8.55        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 15.55/8.55       => ( ( artanh_real @ ( uminus_uminus_real @ X3 ) )
% 15.55/8.55          = ( uminus_uminus_real @ ( artanh_real @ X3 ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4623_neg__numeral__le__iff,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 15.55/8.55        = ( ord_less_eq_num @ N @ M ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4624_neg__numeral__le__iff,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 15.55/8.55        = ( ord_less_eq_num @ N @ M ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4625_neg__numeral__le__iff,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 15.55/8.55        = ( ord_less_eq_num @ N @ M ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4626_neg__numeral__le__iff,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.55        = ( ord_less_eq_num @ N @ M ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4627_neg__numeral__less__iff,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 15.55/8.55        = ( ord_less_num @ N @ M ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4628_neg__numeral__less__iff,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.55        = ( ord_less_num @ N @ M ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4629_neg__numeral__less__iff,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 15.55/8.55        = ( ord_less_num @ N @ M ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4630_neg__numeral__less__iff,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 15.55/8.55        = ( ord_less_num @ N @ M ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4631_round__neg__numeral,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 15.55/8.55        = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4632_round__neg__numeral,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 15.55/8.55        = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4633_norm__of__int,axiom,
% 15.55/8.55      ! [Z: int] :
% 15.55/8.55        ( ( real_V7735802525324610683m_real @ ( ring_1_of_int_real @ Z ) )
% 15.55/8.55        = ( abs_abs_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4634_norm__of__int,axiom,
% 15.55/8.55      ! [Z: int] :
% 15.55/8.55        ( ( real_V1022390504157884413omplex @ ( ring_17405671764205052669omplex @ Z ) )
% 15.55/8.55        = ( abs_abs_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4635_not__neg__one__le__neg__numeral__iff,axiom,
% 15.55/8.55      ! [M: num] :
% 15.55/8.55        ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 15.55/8.55        = ( M != one ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4636_not__neg__one__le__neg__numeral__iff,axiom,
% 15.55/8.55      ! [M: num] :
% 15.55/8.55        ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 15.55/8.55        = ( M != one ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4637_not__neg__one__le__neg__numeral__iff,axiom,
% 15.55/8.55      ! [M: num] :
% 15.55/8.55        ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 15.55/8.55        = ( M != one ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4638_not__neg__one__le__neg__numeral__iff,axiom,
% 15.55/8.55      ! [M: num] :
% 15.55/8.55        ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 15.55/8.55        = ( M != one ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4639_neg__numeral__less__neg__one__iff,axiom,
% 15.55/8.55      ! [M: num] :
% 15.55/8.55        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 15.55/8.55        = ( M != one ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4640_neg__numeral__less__neg__one__iff,axiom,
% 15.55/8.55      ! [M: num] :
% 15.55/8.55        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.55        = ( M != one ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4641_neg__numeral__less__neg__one__iff,axiom,
% 15.55/8.55      ! [M: num] :
% 15.55/8.55        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 15.55/8.55        = ( M != one ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4642_neg__numeral__less__neg__one__iff,axiom,
% 15.55/8.55      ! [M: num] :
% 15.55/8.55        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 15.55/8.55        = ( M != one ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4643_le__divide__eq__numeral1_I2_J,axiom,
% 15.55/8.55      ! [A: real,B: real,W: num] :
% 15.55/8.55        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 15.55/8.55        = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4644_le__divide__eq__numeral1_I2_J,axiom,
% 15.55/8.55      ! [A: rat,B: rat,W: num] :
% 15.55/8.55        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 15.55/8.55        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4645_divide__le__eq__numeral1_I2_J,axiom,
% 15.55/8.55      ! [B: real,W: num,A: real] :
% 15.55/8.55        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 15.55/8.55        = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4646_divide__le__eq__numeral1_I2_J,axiom,
% 15.55/8.55      ! [B: rat,W: num,A: rat] :
% 15.55/8.55        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 15.55/8.55        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4647_divide__eq__eq__numeral1_I2_J,axiom,
% 15.55/8.55      ! [B: real,W: num,A: real] :
% 15.55/8.55        ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 15.55/8.55          = A )
% 15.55/8.55        = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 15.55/8.55             != zero_zero_real )
% 15.55/8.55           => ( B
% 15.55/8.55              = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 15.55/8.55          & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 15.55/8.55              = zero_zero_real )
% 15.55/8.55           => ( A = zero_zero_real ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4648_divide__eq__eq__numeral1_I2_J,axiom,
% 15.55/8.55      ! [B: complex,W: num,A: complex] :
% 15.55/8.55        ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 15.55/8.55          = A )
% 15.55/8.55        = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 15.55/8.55             != zero_zero_complex )
% 15.55/8.55           => ( B
% 15.55/8.55              = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 15.55/8.55          & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 15.55/8.55              = zero_zero_complex )
% 15.55/8.55           => ( A = zero_zero_complex ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4649_divide__eq__eq__numeral1_I2_J,axiom,
% 15.55/8.55      ! [B: rat,W: num,A: rat] :
% 15.55/8.55        ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 15.55/8.55          = A )
% 15.55/8.55        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 15.55/8.55             != zero_zero_rat )
% 15.55/8.55           => ( B
% 15.55/8.55              = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 15.55/8.55          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 15.55/8.55              = zero_zero_rat )
% 15.55/8.55           => ( A = zero_zero_rat ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4650_eq__divide__eq__numeral1_I2_J,axiom,
% 15.55/8.55      ! [A: real,B: real,W: num] :
% 15.55/8.55        ( ( A
% 15.55/8.55          = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 15.55/8.55        = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 15.55/8.55             != zero_zero_real )
% 15.55/8.55           => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 15.55/8.55              = B ) )
% 15.55/8.55          & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 15.55/8.55              = zero_zero_real )
% 15.55/8.55           => ( A = zero_zero_real ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4651_eq__divide__eq__numeral1_I2_J,axiom,
% 15.55/8.55      ! [A: complex,B: complex,W: num] :
% 15.55/8.55        ( ( A
% 15.55/8.55          = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 15.55/8.55        = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 15.55/8.55             != zero_zero_complex )
% 15.55/8.55           => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 15.55/8.55              = B ) )
% 15.55/8.55          & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 15.55/8.55              = zero_zero_complex )
% 15.55/8.55           => ( A = zero_zero_complex ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4652_eq__divide__eq__numeral1_I2_J,axiom,
% 15.55/8.55      ! [A: rat,B: rat,W: num] :
% 15.55/8.55        ( ( A
% 15.55/8.55          = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 15.55/8.55        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 15.55/8.55             != zero_zero_rat )
% 15.55/8.55           => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 15.55/8.55              = B ) )
% 15.55/8.55          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 15.55/8.55              = zero_zero_rat )
% 15.55/8.55           => ( A = zero_zero_rat ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4653_divide__less__eq__numeral1_I2_J,axiom,
% 15.55/8.55      ! [B: real,W: num,A: real] :
% 15.55/8.55        ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 15.55/8.55        = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4654_divide__less__eq__numeral1_I2_J,axiom,
% 15.55/8.55      ! [B: rat,W: num,A: rat] :
% 15.55/8.55        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 15.55/8.55        = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4655_less__divide__eq__numeral1_I2_J,axiom,
% 15.55/8.55      ! [A: real,B: real,W: num] :
% 15.55/8.55        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 15.55/8.55        = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4656_less__divide__eq__numeral1_I2_J,axiom,
% 15.55/8.55      ! [A: rat,B: rat,W: num] :
% 15.55/8.55        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 15.55/8.55        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4657_power2__minus,axiom,
% 15.55/8.55      ! [A: real] :
% 15.55/8.55        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.55        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4658_power2__minus,axiom,
% 15.55/8.55      ! [A: int] :
% 15.55/8.55        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.55        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4659_power2__minus,axiom,
% 15.55/8.55      ! [A: complex] :
% 15.55/8.55        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.55        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4660_power2__minus,axiom,
% 15.55/8.55      ! [A: code_integer] :
% 15.55/8.55        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.55        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4661_power2__minus,axiom,
% 15.55/8.55      ! [A: rat] :
% 15.55/8.55        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.55        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4662_zero__less__power__abs__iff,axiom,
% 15.55/8.55      ! [A: code_integer,N: nat] :
% 15.55/8.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 15.55/8.55        = ( ( A != zero_z3403309356797280102nteger )
% 15.55/8.55          | ( N = zero_zero_nat ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4663_zero__less__power__abs__iff,axiom,
% 15.55/8.55      ! [A: real,N: nat] :
% 15.55/8.55        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 15.55/8.55        = ( ( A != zero_zero_real )
% 15.55/8.55          | ( N = zero_zero_nat ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4664_zero__less__power__abs__iff,axiom,
% 15.55/8.55      ! [A: rat,N: nat] :
% 15.55/8.55        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 15.55/8.55        = ( ( A != zero_zero_rat )
% 15.55/8.55          | ( N = zero_zero_nat ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4665_zero__less__power__abs__iff,axiom,
% 15.55/8.55      ! [A: int,N: nat] :
% 15.55/8.55        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 15.55/8.55        = ( ( A != zero_zero_int )
% 15.55/8.55          | ( N = zero_zero_nat ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4666_abs__power2,axiom,
% 15.55/8.55      ! [A: code_integer] :
% 15.55/8.55        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.55        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4667_abs__power2,axiom,
% 15.55/8.55      ! [A: rat] :
% 15.55/8.55        ( ( abs_abs_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.55        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4668_abs__power2,axiom,
% 15.55/8.55      ! [A: int] :
% 15.55/8.55        ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.55        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4669_abs__power2,axiom,
% 15.55/8.55      ! [A: real] :
% 15.55/8.55        ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.55        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4670_power2__abs,axiom,
% 15.55/8.55      ! [A: code_integer] :
% 15.55/8.55        ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.55        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4671_power2__abs,axiom,
% 15.55/8.55      ! [A: rat] :
% 15.55/8.55        ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.55        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4672_power2__abs,axiom,
% 15.55/8.55      ! [A: int] :
% 15.55/8.55        ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.55        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4673_power2__abs,axiom,
% 15.55/8.55      ! [A: real] :
% 15.55/8.55        ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.55        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4674_norm__mult__numeral1,axiom,
% 15.55/8.55      ! [W: num,A: real] :
% 15.55/8.55        ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 15.55/8.55        = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4675_norm__mult__numeral1,axiom,
% 15.55/8.55      ! [W: num,A: complex] :
% 15.55/8.55        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 15.55/8.55        = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4676_norm__mult__numeral2,axiom,
% 15.55/8.55      ! [A: real,W: num] :
% 15.55/8.55        ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 15.55/8.55        = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4677_norm__mult__numeral2,axiom,
% 15.55/8.55      ! [A: complex,W: num] :
% 15.55/8.55        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 15.55/8.55        = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4678_norm__divide__numeral,axiom,
% 15.55/8.55      ! [A: real,W: num] :
% 15.55/8.55        ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 15.55/8.55        = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4679_norm__divide__numeral,axiom,
% 15.55/8.55      ! [A: complex,W: num] :
% 15.55/8.55        ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 15.55/8.55        = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4680_of__real__neg__numeral,axiom,
% 15.55/8.55      ! [W: num] :
% 15.55/8.55        ( ( real_V1803761363581548252l_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 15.55/8.55        = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4681_of__real__neg__numeral,axiom,
% 15.55/8.55      ! [W: num] :
% 15.55/8.55        ( ( real_V4546457046886955230omplex @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 15.55/8.55        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4682_add__neg__numeral__special_I9_J,axiom,
% 15.55/8.55      ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 15.55/8.55      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4683_add__neg__numeral__special_I9_J,axiom,
% 15.55/8.55      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.55      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4684_add__neg__numeral__special_I9_J,axiom,
% 15.55/8.55      ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 15.55/8.55      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4685_add__neg__numeral__special_I9_J,axiom,
% 15.55/8.55      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 15.55/8.55      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4686_add__neg__numeral__special_I9_J,axiom,
% 15.55/8.55      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 15.55/8.55      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4687_diff__numeral__special_I11_J,axiom,
% 15.55/8.55      ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 15.55/8.55      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4688_diff__numeral__special_I11_J,axiom,
% 15.55/8.55      ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.55      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4689_diff__numeral__special_I11_J,axiom,
% 15.55/8.55      ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 15.55/8.55      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4690_diff__numeral__special_I11_J,axiom,
% 15.55/8.55      ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 15.55/8.55      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4691_diff__numeral__special_I11_J,axiom,
% 15.55/8.55      ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 15.55/8.55      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4692_diff__numeral__special_I10_J,axiom,
% 15.55/8.55      ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 15.55/8.55      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4693_diff__numeral__special_I10_J,axiom,
% 15.55/8.55      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 15.55/8.55      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4694_diff__numeral__special_I10_J,axiom,
% 15.55/8.55      ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 15.55/8.55      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4695_diff__numeral__special_I10_J,axiom,
% 15.55/8.55      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 15.55/8.55      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4696_diff__numeral__special_I10_J,axiom,
% 15.55/8.55      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 15.55/8.55      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4697_minus__1__div__2__eq,axiom,
% 15.55/8.55      ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.55      = ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4698_minus__1__div__2__eq,axiom,
% 15.55/8.55      ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 15.55/8.55      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4699_Power_Oring__1__class_Opower__minus__even,axiom,
% 15.55/8.55      ! [A: real,N: nat] :
% 15.55/8.55        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.55        = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4700_Power_Oring__1__class_Opower__minus__even,axiom,
% 15.55/8.55      ! [A: int,N: nat] :
% 15.55/8.55        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.55        = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4701_Power_Oring__1__class_Opower__minus__even,axiom,
% 15.55/8.55      ! [A: complex,N: nat] :
% 15.55/8.55        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.55        = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4702_Power_Oring__1__class_Opower__minus__even,axiom,
% 15.55/8.55      ! [A: code_integer,N: nat] :
% 15.55/8.55        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.55        = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4703_Power_Oring__1__class_Opower__minus__even,axiom,
% 15.55/8.55      ! [A: rat,N: nat] :
% 15.55/8.55        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.55        = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4704_power__minus__odd,axiom,
% 15.55/8.55      ! [N: nat,A: real] :
% 15.55/8.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.55       => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 15.55/8.55          = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4705_power__minus__odd,axiom,
% 15.55/8.55      ! [N: nat,A: int] :
% 15.55/8.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.55       => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 15.55/8.55          = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4706_power__minus__odd,axiom,
% 15.55/8.55      ! [N: nat,A: complex] :
% 15.55/8.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.55       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 15.55/8.55          = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4707_power__minus__odd,axiom,
% 15.55/8.55      ! [N: nat,A: code_integer] :
% 15.55/8.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.55       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 15.55/8.55          = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4708_power__minus__odd,axiom,
% 15.55/8.55      ! [N: nat,A: rat] :
% 15.55/8.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.55       => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 15.55/8.55          = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4709_Parity_Oring__1__class_Opower__minus__even,axiom,
% 15.55/8.55      ! [N: nat,A: real] :
% 15.55/8.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.55       => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 15.55/8.55          = ( power_power_real @ A @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4710_Parity_Oring__1__class_Opower__minus__even,axiom,
% 15.55/8.55      ! [N: nat,A: int] :
% 15.55/8.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.55       => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 15.55/8.55          = ( power_power_int @ A @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4711_Parity_Oring__1__class_Opower__minus__even,axiom,
% 15.55/8.55      ! [N: nat,A: complex] :
% 15.55/8.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.55       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 15.55/8.55          = ( power_power_complex @ A @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4712_Parity_Oring__1__class_Opower__minus__even,axiom,
% 15.55/8.55      ! [N: nat,A: code_integer] :
% 15.55/8.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.55       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 15.55/8.55          = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4713_Parity_Oring__1__class_Opower__minus__even,axiom,
% 15.55/8.55      ! [N: nat,A: rat] :
% 15.55/8.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.55       => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 15.55/8.55          = ( power_power_rat @ A @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4714_power__even__abs__numeral,axiom,
% 15.55/8.55      ! [W: num,A: code_integer] :
% 15.55/8.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.55/8.55       => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W ) )
% 15.55/8.55          = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4715_power__even__abs__numeral,axiom,
% 15.55/8.55      ! [W: num,A: rat] :
% 15.55/8.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.55/8.55       => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ W ) )
% 15.55/8.55          = ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4716_power__even__abs__numeral,axiom,
% 15.55/8.55      ! [W: num,A: int] :
% 15.55/8.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.55/8.55       => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 15.55/8.55          = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4717_power__even__abs__numeral,axiom,
% 15.55/8.55      ! [W: num,A: real] :
% 15.55/8.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 15.55/8.55       => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 15.55/8.55          = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4718_diff__numeral__special_I4_J,axiom,
% 15.55/8.55      ! [M: num] :
% 15.55/8.55        ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 15.55/8.55        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4719_diff__numeral__special_I4_J,axiom,
% 15.55/8.55      ! [M: num] :
% 15.55/8.55        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 15.55/8.55        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4720_diff__numeral__special_I4_J,axiom,
% 15.55/8.55      ! [M: num] :
% 15.55/8.55        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 15.55/8.55        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4721_diff__numeral__special_I4_J,axiom,
% 15.55/8.55      ! [M: num] :
% 15.55/8.55        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 15.55/8.55        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4722_diff__numeral__special_I4_J,axiom,
% 15.55/8.55      ! [M: num] :
% 15.55/8.55        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 15.55/8.55        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4723_diff__numeral__special_I3_J,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 15.55/8.55        = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4724_diff__numeral__special_I3_J,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.55        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4725_diff__numeral__special_I3_J,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 15.55/8.55        = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4726_diff__numeral__special_I3_J,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 15.55/8.55        = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4727_diff__numeral__special_I3_J,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 15.55/8.55        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4728_neg__numeral__le__floor,axiom,
% 15.55/8.55      ! [V: num,X3: rat] :
% 15.55/8.55        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X3 ) )
% 15.55/8.55        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4729_neg__numeral__le__floor,axiom,
% 15.55/8.55      ! [V: num,X3: real] :
% 15.55/8.55        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X3 ) )
% 15.55/8.55        = ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4730_floor__less__neg__numeral,axiom,
% 15.55/8.55      ! [X3: rat,V: num] :
% 15.55/8.55        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X3 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 15.55/8.55        = ( ord_less_rat @ X3 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4731_floor__less__neg__numeral,axiom,
% 15.55/8.55      ! [X3: real,V: num] :
% 15.55/8.55        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X3 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 15.55/8.55        = ( ord_less_real @ X3 @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4732_ceiling__le__neg__numeral,axiom,
% 15.55/8.55      ! [X3: real,V: num] :
% 15.55/8.55        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X3 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 15.55/8.55        = ( ord_less_eq_real @ X3 @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4733_ceiling__le__neg__numeral,axiom,
% 15.55/8.55      ! [X3: rat,V: num] :
% 15.55/8.55        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X3 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 15.55/8.55        = ( ord_less_eq_rat @ X3 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4734_ceiling__less__zero,axiom,
% 15.55/8.55      ! [X3: real] :
% 15.55/8.55        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X3 ) @ zero_zero_int )
% 15.55/8.55        = ( ord_less_eq_real @ X3 @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4735_ceiling__less__zero,axiom,
% 15.55/8.55      ! [X3: rat] :
% 15.55/8.55        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X3 ) @ zero_zero_int )
% 15.55/8.55        = ( ord_less_eq_rat @ X3 @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4736_zero__le__ceiling,axiom,
% 15.55/8.55      ! [X3: real] :
% 15.55/8.55        ( ( ord_less_eq_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X3 ) )
% 15.55/8.55        = ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4737_zero__le__ceiling,axiom,
% 15.55/8.55      ! [X3: rat] :
% 15.55/8.55        ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X3 ) )
% 15.55/8.55        = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4738_neg__numeral__less__ceiling,axiom,
% 15.55/8.55      ! [V: num,X3: real] :
% 15.55/8.55        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X3 ) )
% 15.55/8.55        = ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4739_neg__numeral__less__ceiling,axiom,
% 15.55/8.55      ! [V: num,X3: rat] :
% 15.55/8.55        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X3 ) )
% 15.55/8.55        = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4740_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 15.55/8.55      ! [X3: num,N: nat,Y3: int] :
% 15.55/8.55        ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N )
% 15.55/8.55          = ( ring_1_of_int_real @ Y3 ) )
% 15.55/8.55        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N )
% 15.55/8.55          = Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4741_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 15.55/8.55      ! [X3: num,N: nat,Y3: int] :
% 15.55/8.55        ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N )
% 15.55/8.55          = ( ring_1_of_int_int @ Y3 ) )
% 15.55/8.55        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N )
% 15.55/8.55          = Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4742_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 15.55/8.55      ! [X3: num,N: nat,Y3: int] :
% 15.55/8.55        ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X3 ) ) @ N )
% 15.55/8.55          = ( ring_17405671764205052669omplex @ Y3 ) )
% 15.55/8.55        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N )
% 15.55/8.55          = Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4743_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 15.55/8.55      ! [X3: num,N: nat,Y3: int] :
% 15.55/8.55        ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N )
% 15.55/8.55          = ( ring_18347121197199848620nteger @ Y3 ) )
% 15.55/8.55        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N )
% 15.55/8.55          = Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4744_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 15.55/8.55      ! [X3: num,N: nat,Y3: int] :
% 15.55/8.55        ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N )
% 15.55/8.55          = ( ring_1_of_int_rat @ Y3 ) )
% 15.55/8.55        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N )
% 15.55/8.55          = Y3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4745_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 15.55/8.55      ! [Y3: int,X3: num,N: nat] :
% 15.55/8.55        ( ( ( ring_1_of_int_real @ Y3 )
% 15.55/8.55          = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N ) )
% 15.55/8.55        = ( Y3
% 15.55/8.55          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4746_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 15.55/8.55      ! [Y3: int,X3: num,N: nat] :
% 15.55/8.55        ( ( ( ring_1_of_int_int @ Y3 )
% 15.55/8.55          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) )
% 15.55/8.55        = ( Y3
% 15.55/8.55          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4747_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 15.55/8.55      ! [Y3: int,X3: num,N: nat] :
% 15.55/8.55        ( ( ( ring_17405671764205052669omplex @ Y3 )
% 15.55/8.55          = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X3 ) ) @ N ) )
% 15.55/8.55        = ( Y3
% 15.55/8.55          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4748_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 15.55/8.55      ! [Y3: int,X3: num,N: nat] :
% 15.55/8.55        ( ( ( ring_18347121197199848620nteger @ Y3 )
% 15.55/8.55          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N ) )
% 15.55/8.55        = ( Y3
% 15.55/8.55          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4749_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 15.55/8.55      ! [Y3: int,X3: num,N: nat] :
% 15.55/8.55        ( ( ( ring_1_of_int_rat @ Y3 )
% 15.55/8.55          = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N ) )
% 15.55/8.55        = ( Y3
% 15.55/8.55          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4750_real__sqrt__abs,axiom,
% 15.55/8.55      ! [X3: real] :
% 15.55/8.55        ( ( sqrt @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.55        = ( abs_abs_real @ X3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4751_dbl__simps_I4_J,axiom,
% 15.55/8.55      ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 15.55/8.55      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4752_dbl__simps_I4_J,axiom,
% 15.55/8.55      ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.55      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4753_dbl__simps_I4_J,axiom,
% 15.55/8.55      ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 15.55/8.55      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4754_dbl__simps_I4_J,axiom,
% 15.55/8.55      ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 15.55/8.55      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4755_dbl__simps_I4_J,axiom,
% 15.55/8.55      ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 15.55/8.55      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4756_power__minus1__even,axiom,
% 15.55/8.55      ! [N: nat] :
% 15.55/8.55        ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.55        = one_one_real ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4757_power__minus1__even,axiom,
% 15.55/8.55      ! [N: nat] :
% 15.55/8.55        ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.55        = one_one_int ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4758_power__minus1__even,axiom,
% 15.55/8.55      ! [N: nat] :
% 15.55/8.55        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.55        = one_one_complex ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4759_power__minus1__even,axiom,
% 15.55/8.55      ! [N: nat] :
% 15.55/8.55        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.55        = one_one_Code_integer ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4760_power__minus1__even,axiom,
% 15.55/8.55      ! [N: nat] :
% 15.55/8.55        ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.55        = one_one_rat ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4761_neg__one__odd__power,axiom,
% 15.55/8.55      ! [N: nat] :
% 15.55/8.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.55       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 15.55/8.55          = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4762_neg__one__odd__power,axiom,
% 15.55/8.55      ! [N: nat] :
% 15.55/8.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.55       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 15.55/8.55          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4763_neg__one__odd__power,axiom,
% 15.55/8.55      ! [N: nat] :
% 15.55/8.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.55       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 15.55/8.55          = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4764_neg__one__odd__power,axiom,
% 15.55/8.55      ! [N: nat] :
% 15.55/8.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.55       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 15.55/8.55          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4765_neg__one__odd__power,axiom,
% 15.55/8.55      ! [N: nat] :
% 15.55/8.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.55       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 15.55/8.55          = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4766_neg__one__even__power,axiom,
% 15.55/8.55      ! [N: nat] :
% 15.55/8.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.55       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 15.55/8.55          = one_one_real ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4767_neg__one__even__power,axiom,
% 15.55/8.55      ! [N: nat] :
% 15.55/8.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.55       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 15.55/8.55          = one_one_int ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4768_neg__one__even__power,axiom,
% 15.55/8.55      ! [N: nat] :
% 15.55/8.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.55       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 15.55/8.55          = one_one_complex ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4769_neg__one__even__power,axiom,
% 15.55/8.55      ! [N: nat] :
% 15.55/8.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.55       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 15.55/8.55          = one_one_Code_integer ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4770_neg__one__even__power,axiom,
% 15.55/8.55      ! [N: nat] :
% 15.55/8.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.55       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 15.55/8.55          = one_one_rat ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4771_norm__of__real__addn,axiom,
% 15.55/8.55      ! [X3: real,B: num] :
% 15.55/8.55        ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X3 ) @ ( numeral_numeral_real @ B ) ) )
% 15.55/8.55        = ( abs_abs_real @ ( plus_plus_real @ X3 @ ( numeral_numeral_real @ B ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4772_norm__of__real__addn,axiom,
% 15.55/8.55      ! [X3: real,B: num] :
% 15.55/8.55        ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X3 ) @ ( numera6690914467698888265omplex @ B ) ) )
% 15.55/8.55        = ( abs_abs_real @ ( plus_plus_real @ X3 @ ( numeral_numeral_real @ B ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4773_neg__numeral__less__floor,axiom,
% 15.55/8.55      ! [V: num,X3: rat] :
% 15.55/8.55        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X3 ) )
% 15.55/8.55        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4774_neg__numeral__less__floor,axiom,
% 15.55/8.55      ! [V: num,X3: real] :
% 15.55/8.55        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X3 ) )
% 15.55/8.55        = ( ord_less_eq_real @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4775_floor__le__neg__numeral,axiom,
% 15.55/8.55      ! [X3: rat,V: num] :
% 15.55/8.55        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X3 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 15.55/8.55        = ( ord_less_rat @ X3 @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4776_floor__le__neg__numeral,axiom,
% 15.55/8.55      ! [X3: real,V: num] :
% 15.55/8.55        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X3 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 15.55/8.55        = ( ord_less_real @ X3 @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4777_ceiling__less__neg__numeral,axiom,
% 15.55/8.55      ! [X3: real,V: num] :
% 15.55/8.55        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X3 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 15.55/8.55        = ( ord_less_eq_real @ X3 @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4778_ceiling__less__neg__numeral,axiom,
% 15.55/8.55      ! [X3: rat,V: num] :
% 15.55/8.55        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X3 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 15.55/8.55        = ( ord_less_eq_rat @ X3 @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4779_neg__numeral__le__ceiling,axiom,
% 15.55/8.55      ! [V: num,X3: real] :
% 15.55/8.55        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X3 ) )
% 15.55/8.55        = ( ord_less_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4780_neg__numeral__le__ceiling,axiom,
% 15.55/8.55      ! [V: num,X3: rat] :
% 15.55/8.55        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X3 ) )
% 15.55/8.55        = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4781_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 15.55/8.55      ! [A: int,X3: num,N: nat] :
% 15.55/8.55        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N ) )
% 15.55/8.55        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4782_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 15.55/8.55      ! [A: int,X3: num,N: nat] :
% 15.55/8.55        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N ) )
% 15.55/8.55        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4783_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 15.55/8.55      ! [A: int,X3: num,N: nat] :
% 15.55/8.55        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N ) )
% 15.55/8.55        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4784_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 15.55/8.55      ! [A: int,X3: num,N: nat] :
% 15.55/8.55        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) )
% 15.55/8.55        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4785_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 15.55/8.55      ! [X3: num,N: nat,A: int] :
% 15.55/8.55        ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 15.55/8.55        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4786_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 15.55/8.55      ! [X3: num,N: nat,A: int] :
% 15.55/8.55        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 15.55/8.55        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4787_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 15.55/8.55      ! [X3: num,N: nat,A: int] :
% 15.55/8.55        ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 15.55/8.55        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4788_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 15.55/8.55      ! [X3: num,N: nat,A: int] :
% 15.55/8.55        ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 15.55/8.55        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4789_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 15.55/8.55      ! [X3: num,N: nat,A: int] :
% 15.55/8.55        ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 15.55/8.55        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4790_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 15.55/8.55      ! [X3: num,N: nat,A: int] :
% 15.55/8.55        ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 15.55/8.55        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4791_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 15.55/8.55      ! [X3: num,N: nat,A: int] :
% 15.55/8.55        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 15.55/8.55        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4792_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 15.55/8.55      ! [X3: num,N: nat,A: int] :
% 15.55/8.55        ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 15.55/8.55        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4793_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 15.55/8.55      ! [A: int,X3: num,N: nat] :
% 15.55/8.55        ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N ) )
% 15.55/8.55        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4794_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 15.55/8.55      ! [A: int,X3: num,N: nat] :
% 15.55/8.55        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) )
% 15.55/8.55        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4795_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 15.55/8.55      ! [A: int,X3: num,N: nat] :
% 15.55/8.55        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N ) )
% 15.55/8.55        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4796_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 15.55/8.55      ! [A: int,X3: num,N: nat] :
% 15.55/8.55        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N ) )
% 15.55/8.55        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4797_square__powr__half,axiom,
% 15.55/8.55      ! [X3: real] :
% 15.55/8.55        ( ( powr_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.55        = ( abs_abs_real @ X3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4798_abs__less__iff,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 15.55/8.55        = ( ( ord_less_real @ A @ B )
% 15.55/8.55          & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4799_abs__less__iff,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 15.55/8.55        = ( ( ord_less_int @ A @ B )
% 15.55/8.55          & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4800_abs__less__iff,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 15.55/8.55        = ( ( ord_le6747313008572928689nteger @ A @ B )
% 15.55/8.55          & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4801_abs__less__iff,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 15.55/8.55        = ( ( ord_less_rat @ A @ B )
% 15.55/8.55          & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4802_equation__minus__iff,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( A
% 15.55/8.55          = ( uminus_uminus_real @ B ) )
% 15.55/8.55        = ( B
% 15.55/8.55          = ( uminus_uminus_real @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4803_equation__minus__iff,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( A
% 15.55/8.55          = ( uminus_uminus_int @ B ) )
% 15.55/8.55        = ( B
% 15.55/8.55          = ( uminus_uminus_int @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4804_equation__minus__iff,axiom,
% 15.55/8.55      ! [A: complex,B: complex] :
% 15.55/8.55        ( ( A
% 15.55/8.55          = ( uminus1482373934393186551omplex @ B ) )
% 15.55/8.55        = ( B
% 15.55/8.55          = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4805_equation__minus__iff,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( A
% 15.55/8.55          = ( uminus1351360451143612070nteger @ B ) )
% 15.55/8.55        = ( B
% 15.55/8.55          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4806_equation__minus__iff,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( A
% 15.55/8.55          = ( uminus_uminus_rat @ B ) )
% 15.55/8.55        = ( B
% 15.55/8.55          = ( uminus_uminus_rat @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4807_minus__equation__iff,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( ( uminus_uminus_real @ A )
% 15.55/8.55          = B )
% 15.55/8.55        = ( ( uminus_uminus_real @ B )
% 15.55/8.55          = A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4808_minus__equation__iff,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( ( uminus_uminus_int @ A )
% 15.55/8.55          = B )
% 15.55/8.55        = ( ( uminus_uminus_int @ B )
% 15.55/8.55          = A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4809_minus__equation__iff,axiom,
% 15.55/8.55      ! [A: complex,B: complex] :
% 15.55/8.55        ( ( ( uminus1482373934393186551omplex @ A )
% 15.55/8.55          = B )
% 15.55/8.55        = ( ( uminus1482373934393186551omplex @ B )
% 15.55/8.55          = A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4810_minus__equation__iff,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( ( uminus1351360451143612070nteger @ A )
% 15.55/8.55          = B )
% 15.55/8.55        = ( ( uminus1351360451143612070nteger @ B )
% 15.55/8.55          = A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4811_minus__equation__iff,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( ( uminus_uminus_rat @ A )
% 15.55/8.55          = B )
% 15.55/8.55        = ( ( uminus_uminus_rat @ B )
% 15.55/8.55          = A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4812_abs__ge__minus__self,axiom,
% 15.55/8.55      ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4813_abs__ge__minus__self,axiom,
% 15.55/8.55      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4814_abs__ge__minus__self,axiom,
% 15.55/8.55      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4815_abs__ge__minus__self,axiom,
% 15.55/8.55      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4816_abs__le__iff,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 15.55/8.55        = ( ( ord_less_eq_real @ A @ B )
% 15.55/8.55          & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4817_abs__le__iff,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 15.55/8.55        = ( ( ord_le3102999989581377725nteger @ A @ B )
% 15.55/8.55          & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4818_abs__le__iff,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 15.55/8.55        = ( ( ord_less_eq_rat @ A @ B )
% 15.55/8.55          & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4819_abs__le__iff,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 15.55/8.55        = ( ( ord_less_eq_int @ A @ B )
% 15.55/8.55          & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4820_abs__le__D2,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 15.55/8.55       => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4821_abs__le__D2,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 15.55/8.55       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4822_abs__le__D2,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 15.55/8.55       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4823_abs__le__D2,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 15.55/8.55       => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4824_abs__leI,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.55       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 15.55/8.55         => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4825_abs__leI,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( ord_le3102999989581377725nteger @ A @ B )
% 15.55/8.55       => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 15.55/8.55         => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4826_abs__leI,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( ord_less_eq_rat @ A @ B )
% 15.55/8.55       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 15.55/8.55         => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4827_abs__leI,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( ord_less_eq_int @ A @ B )
% 15.55/8.55       => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 15.55/8.55         => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4828_verit__negate__coefficient_I3_J,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( A = B )
% 15.55/8.55       => ( ( uminus_uminus_real @ A )
% 15.55/8.55          = ( uminus_uminus_real @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4829_verit__negate__coefficient_I3_J,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( A = B )
% 15.55/8.55       => ( ( uminus_uminus_int @ A )
% 15.55/8.55          = ( uminus_uminus_int @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4830_verit__negate__coefficient_I3_J,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( A = B )
% 15.55/8.55       => ( ( uminus1351360451143612070nteger @ A )
% 15.55/8.55          = ( uminus1351360451143612070nteger @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4831_verit__negate__coefficient_I3_J,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( A = B )
% 15.55/8.55       => ( ( uminus_uminus_rat @ A )
% 15.55/8.55          = ( uminus_uminus_rat @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4832_abs__minus__le__zero,axiom,
% 15.55/8.55      ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4833_abs__minus__le__zero,axiom,
% 15.55/8.55      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4834_abs__minus__le__zero,axiom,
% 15.55/8.55      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4835_abs__minus__le__zero,axiom,
% 15.55/8.55      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4836_abs__eq__iff_H,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( ( abs_abs_real @ A )
% 15.55/8.55          = B )
% 15.55/8.55        = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 15.55/8.55          & ( ( A = B )
% 15.55/8.55            | ( A
% 15.55/8.55              = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4837_abs__eq__iff_H,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( ( abs_abs_Code_integer @ A )
% 15.55/8.55          = B )
% 15.55/8.55        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 15.55/8.55          & ( ( A = B )
% 15.55/8.55            | ( A
% 15.55/8.55              = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4838_abs__eq__iff_H,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( ( abs_abs_rat @ A )
% 15.55/8.55          = B )
% 15.55/8.55        = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 15.55/8.55          & ( ( A = B )
% 15.55/8.55            | ( A
% 15.55/8.55              = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4839_abs__eq__iff_H,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( ( abs_abs_int @ A )
% 15.55/8.55          = B )
% 15.55/8.55        = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 15.55/8.55          & ( ( A = B )
% 15.55/8.55            | ( A
% 15.55/8.55              = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4840_eq__abs__iff_H,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( A
% 15.55/8.55          = ( abs_abs_real @ B ) )
% 15.55/8.55        = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.55          & ( ( B = A )
% 15.55/8.55            | ( B
% 15.55/8.55              = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4841_eq__abs__iff_H,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( A
% 15.55/8.55          = ( abs_abs_Code_integer @ B ) )
% 15.55/8.55        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 15.55/8.55          & ( ( B = A )
% 15.55/8.55            | ( B
% 15.55/8.55              = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4842_eq__abs__iff_H,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( A
% 15.55/8.55          = ( abs_abs_rat @ B ) )
% 15.55/8.55        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.55          & ( ( B = A )
% 15.55/8.55            | ( B
% 15.55/8.55              = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4843_eq__abs__iff_H,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( A
% 15.55/8.55          = ( abs_abs_int @ B ) )
% 15.55/8.55        = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.55          & ( ( B = A )
% 15.55/8.55            | ( B
% 15.55/8.55              = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4844_abs__if__raw,axiom,
% 15.55/8.55      ( abs_abs_real
% 15.55/8.55      = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4845_abs__if__raw,axiom,
% 15.55/8.55      ( abs_abs_int
% 15.55/8.55      = ( ^ [A4: int] : ( if_int @ ( ord_less_int @ A4 @ zero_zero_int ) @ ( uminus_uminus_int @ A4 ) @ A4 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4846_abs__if__raw,axiom,
% 15.55/8.55      ( abs_abs_Code_integer
% 15.55/8.55      = ( ^ [A4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A4 ) @ A4 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4847_abs__if__raw,axiom,
% 15.55/8.55      ( abs_abs_rat
% 15.55/8.55      = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4848_abs__of__neg,axiom,
% 15.55/8.55      ! [A: real] :
% 15.55/8.55        ( ( ord_less_real @ A @ zero_zero_real )
% 15.55/8.55       => ( ( abs_abs_real @ A )
% 15.55/8.55          = ( uminus_uminus_real @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4849_abs__of__neg,axiom,
% 15.55/8.55      ! [A: int] :
% 15.55/8.55        ( ( ord_less_int @ A @ zero_zero_int )
% 15.55/8.55       => ( ( abs_abs_int @ A )
% 15.55/8.55          = ( uminus_uminus_int @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4850_abs__of__neg,axiom,
% 15.55/8.55      ! [A: code_integer] :
% 15.55/8.55        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 15.55/8.55       => ( ( abs_abs_Code_integer @ A )
% 15.55/8.55          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4851_abs__of__neg,axiom,
% 15.55/8.55      ! [A: rat] :
% 15.55/8.55        ( ( ord_less_rat @ A @ zero_zero_rat )
% 15.55/8.55       => ( ( abs_abs_rat @ A )
% 15.55/8.55          = ( uminus_uminus_rat @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4852_abs__if,axiom,
% 15.55/8.55      ( abs_abs_real
% 15.55/8.55      = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4853_abs__if,axiom,
% 15.55/8.55      ( abs_abs_int
% 15.55/8.55      = ( ^ [A4: int] : ( if_int @ ( ord_less_int @ A4 @ zero_zero_int ) @ ( uminus_uminus_int @ A4 ) @ A4 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4854_abs__if,axiom,
% 15.55/8.55      ( abs_abs_Code_integer
% 15.55/8.55      = ( ^ [A4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A4 ) @ A4 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4855_abs__if,axiom,
% 15.55/8.55      ( abs_abs_rat
% 15.55/8.55      = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4856_abs__real__def,axiom,
% 15.55/8.55      ( abs_abs_real
% 15.55/8.55      = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4857_abs__ge__self,axiom,
% 15.55/8.55      ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4858_abs__ge__self,axiom,
% 15.55/8.55      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4859_abs__ge__self,axiom,
% 15.55/8.55      ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4860_abs__ge__self,axiom,
% 15.55/8.55      ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4861_abs__le__D1,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 15.55/8.55       => ( ord_less_eq_real @ A @ B ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4862_abs__le__D1,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 15.55/8.55       => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4863_abs__le__D1,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 15.55/8.55       => ( ord_less_eq_rat @ A @ B ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4864_abs__le__D1,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 15.55/8.55       => ( ord_less_eq_int @ A @ B ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4865_abs__eq__0__iff,axiom,
% 15.55/8.55      ! [A: code_integer] :
% 15.55/8.55        ( ( ( abs_abs_Code_integer @ A )
% 15.55/8.55          = zero_z3403309356797280102nteger )
% 15.55/8.55        = ( A = zero_z3403309356797280102nteger ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4866_abs__eq__0__iff,axiom,
% 15.55/8.55      ! [A: real] :
% 15.55/8.55        ( ( ( abs_abs_real @ A )
% 15.55/8.55          = zero_zero_real )
% 15.55/8.55        = ( A = zero_zero_real ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4867_abs__eq__0__iff,axiom,
% 15.55/8.55      ! [A: rat] :
% 15.55/8.55        ( ( ( abs_abs_rat @ A )
% 15.55/8.55          = zero_zero_rat )
% 15.55/8.55        = ( A = zero_zero_rat ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4868_abs__eq__0__iff,axiom,
% 15.55/8.55      ! [A: int] :
% 15.55/8.55        ( ( ( abs_abs_int @ A )
% 15.55/8.55          = zero_zero_int )
% 15.55/8.55        = ( A = zero_zero_int ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4869_abs__minus__commute,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 15.55/8.55        = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4870_abs__minus__commute,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 15.55/8.55        = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4871_abs__minus__commute,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 15.55/8.55        = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4872_abs__minus__commute,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 15.55/8.55        = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4873_power__abs,axiom,
% 15.55/8.55      ! [A: code_integer,N: nat] :
% 15.55/8.55        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) )
% 15.55/8.55        = ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4874_power__abs,axiom,
% 15.55/8.55      ! [A: rat,N: nat] :
% 15.55/8.55        ( ( abs_abs_rat @ ( power_power_rat @ A @ N ) )
% 15.55/8.55        = ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4875_power__abs,axiom,
% 15.55/8.55      ! [A: int,N: nat] :
% 15.55/8.55        ( ( abs_abs_int @ ( power_power_int @ A @ N ) )
% 15.55/8.55        = ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4876_power__abs,axiom,
% 15.55/8.55      ! [A: real,N: nat] :
% 15.55/8.55        ( ( abs_abs_real @ ( power_power_real @ A @ N ) )
% 15.55/8.55        = ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4877_ceiling__def,axiom,
% 15.55/8.55      ( archim2889992004027027881ng_rat
% 15.55/8.55      = ( ^ [X: rat] : ( uminus_uminus_int @ ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ X ) ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4878_ceiling__def,axiom,
% 15.55/8.55      ( archim7802044766580827645g_real
% 15.55/8.55      = ( ^ [X: real] : ( uminus_uminus_int @ ( archim6058952711729229775r_real @ ( uminus_uminus_real @ X ) ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4879_floor__minus,axiom,
% 15.55/8.55      ! [X3: rat] :
% 15.55/8.55        ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ X3 ) )
% 15.55/8.55        = ( uminus_uminus_int @ ( archim2889992004027027881ng_rat @ X3 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4880_floor__minus,axiom,
% 15.55/8.55      ! [X3: real] :
% 15.55/8.55        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ X3 ) )
% 15.55/8.55        = ( uminus_uminus_int @ ( archim7802044766580827645g_real @ X3 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4881_ceiling__minus,axiom,
% 15.55/8.55      ! [X3: rat] :
% 15.55/8.55        ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ X3 ) )
% 15.55/8.55        = ( uminus_uminus_int @ ( archim3151403230148437115or_rat @ X3 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4882_ceiling__minus,axiom,
% 15.55/8.55      ! [X3: real] :
% 15.55/8.55        ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ X3 ) )
% 15.55/8.55        = ( uminus_uminus_int @ ( archim6058952711729229775r_real @ X3 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4883_le__imp__neg__le,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.55       => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4884_le__imp__neg__le,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( ord_le3102999989581377725nteger @ A @ B )
% 15.55/8.55       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4885_le__imp__neg__le,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( ord_less_eq_rat @ A @ B )
% 15.55/8.55       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4886_le__imp__neg__le,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( ord_less_eq_int @ A @ B )
% 15.55/8.55       => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4887_minus__le__iff,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 15.55/8.55        = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4888_minus__le__iff,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 15.55/8.55        = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4889_minus__le__iff,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 15.55/8.55        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4890_minus__le__iff,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 15.55/8.55        = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4891_le__minus__iff,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 15.55/8.55        = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4892_le__minus__iff,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 15.55/8.55        = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4893_le__minus__iff,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 15.55/8.55        = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4894_le__minus__iff,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 15.55/8.55        = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4895_verit__negate__coefficient_I2_J,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( ord_less_real @ A @ B )
% 15.55/8.55       => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4896_verit__negate__coefficient_I2_J,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( ord_less_int @ A @ B )
% 15.55/8.55       => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4897_verit__negate__coefficient_I2_J,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( ord_le6747313008572928689nteger @ A @ B )
% 15.55/8.55       => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4898_verit__negate__coefficient_I2_J,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( ord_less_rat @ A @ B )
% 15.55/8.55       => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4899_less__minus__iff,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 15.55/8.55        = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4900_less__minus__iff,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 15.55/8.55        = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4901_less__minus__iff,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 15.55/8.55        = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4902_less__minus__iff,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 15.55/8.55        = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4903_minus__less__iff,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 15.55/8.55        = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4904_minus__less__iff,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 15.55/8.55        = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4905_minus__less__iff,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 15.55/8.55        = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4906_minus__less__iff,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 15.55/8.55        = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4907_neg__numeral__neq__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 15.55/8.55       != ( numeral_numeral_real @ N ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4908_neg__numeral__neq__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 15.55/8.55       != ( numeral_numeral_int @ N ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4909_neg__numeral__neq__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 15.55/8.55       != ( numera6690914467698888265omplex @ N ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4910_neg__numeral__neq__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 15.55/8.55       != ( numera6620942414471956472nteger @ N ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4911_neg__numeral__neq__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 15.55/8.55       != ( numeral_numeral_rat @ N ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4912_numeral__neq__neg__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( numeral_numeral_real @ M )
% 15.55/8.55       != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4913_numeral__neq__neg__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( numeral_numeral_int @ M )
% 15.55/8.55       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4914_numeral__neq__neg__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( numera6690914467698888265omplex @ M )
% 15.55/8.55       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4915_numeral__neq__neg__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( numera6620942414471956472nteger @ M )
% 15.55/8.55       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4916_numeral__neq__neg__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ( ( numeral_numeral_rat @ M )
% 15.55/8.55       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4917_one__neq__neg__one,axiom,
% 15.55/8.55      ( one_one_real
% 15.55/8.55     != ( uminus_uminus_real @ one_one_real ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4918_one__neq__neg__one,axiom,
% 15.55/8.55      ( one_one_int
% 15.55/8.55     != ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4919_one__neq__neg__one,axiom,
% 15.55/8.55      ( one_one_complex
% 15.55/8.55     != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4920_one__neq__neg__one,axiom,
% 15.55/8.55      ( one_one_Code_integer
% 15.55/8.55     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4921_one__neq__neg__one,axiom,
% 15.55/8.55      ( one_one_rat
% 15.55/8.55     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4922_group__cancel_Oneg1,axiom,
% 15.55/8.55      ! [A3: real,K: real,A: real] :
% 15.55/8.55        ( ( A3
% 15.55/8.55          = ( plus_plus_real @ K @ A ) )
% 15.55/8.55       => ( ( uminus_uminus_real @ A3 )
% 15.55/8.55          = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4923_group__cancel_Oneg1,axiom,
% 15.55/8.55      ! [A3: int,K: int,A: int] :
% 15.55/8.55        ( ( A3
% 15.55/8.55          = ( plus_plus_int @ K @ A ) )
% 15.55/8.55       => ( ( uminus_uminus_int @ A3 )
% 15.55/8.55          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4924_group__cancel_Oneg1,axiom,
% 15.55/8.55      ! [A3: complex,K: complex,A: complex] :
% 15.55/8.55        ( ( A3
% 15.55/8.55          = ( plus_plus_complex @ K @ A ) )
% 15.55/8.55       => ( ( uminus1482373934393186551omplex @ A3 )
% 15.55/8.55          = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4925_group__cancel_Oneg1,axiom,
% 15.55/8.55      ! [A3: code_integer,K: code_integer,A: code_integer] :
% 15.55/8.55        ( ( A3
% 15.55/8.55          = ( plus_p5714425477246183910nteger @ K @ A ) )
% 15.55/8.55       => ( ( uminus1351360451143612070nteger @ A3 )
% 15.55/8.55          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4926_group__cancel_Oneg1,axiom,
% 15.55/8.55      ! [A3: rat,K: rat,A: rat] :
% 15.55/8.55        ( ( A3
% 15.55/8.55          = ( plus_plus_rat @ K @ A ) )
% 15.55/8.55       => ( ( uminus_uminus_rat @ A3 )
% 15.55/8.55          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4927_add_Oinverse__distrib__swap,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 15.55/8.55        = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4928_add_Oinverse__distrib__swap,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 15.55/8.55        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4929_add_Oinverse__distrib__swap,axiom,
% 15.55/8.55      ! [A: complex,B: complex] :
% 15.55/8.55        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 15.55/8.55        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4930_add_Oinverse__distrib__swap,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 15.55/8.55        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4931_add_Oinverse__distrib__swap,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 15.55/8.55        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4932_is__num__normalize_I8_J,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 15.55/8.55        = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4933_is__num__normalize_I8_J,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 15.55/8.55        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4934_is__num__normalize_I8_J,axiom,
% 15.55/8.55      ! [A: complex,B: complex] :
% 15.55/8.55        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 15.55/8.55        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4935_is__num__normalize_I8_J,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 15.55/8.55        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4936_is__num__normalize_I8_J,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 15.55/8.55        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4937_minus__diff__commute,axiom,
% 15.55/8.55      ! [B: real,A: real] :
% 15.55/8.55        ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 15.55/8.55        = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4938_minus__diff__commute,axiom,
% 15.55/8.55      ! [B: int,A: int] :
% 15.55/8.55        ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 15.55/8.55        = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4939_minus__diff__commute,axiom,
% 15.55/8.55      ! [B: complex,A: complex] :
% 15.55/8.55        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 15.55/8.55        = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4940_minus__diff__commute,axiom,
% 15.55/8.55      ! [B: code_integer,A: code_integer] :
% 15.55/8.55        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 15.55/8.55        = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4941_minus__diff__commute,axiom,
% 15.55/8.55      ! [B: rat,A: rat] :
% 15.55/8.55        ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 15.55/8.55        = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4942_minus__diff__minus,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 15.55/8.55        = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4943_minus__diff__minus,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 15.55/8.55        = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4944_minus__diff__minus,axiom,
% 15.55/8.55      ! [A: complex,B: complex] :
% 15.55/8.55        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 15.55/8.55        = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4945_minus__diff__minus,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 15.55/8.55        = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4946_minus__diff__minus,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 15.55/8.55        = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4947_real__minus__mult__self__le,axiom,
% 15.55/8.55      ! [U: real,X3: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X3 @ X3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4948_real__sqrt__minus,axiom,
% 15.55/8.55      ! [X3: real] :
% 15.55/8.55        ( ( sqrt @ ( uminus_uminus_real @ X3 ) )
% 15.55/8.55        = ( uminus_uminus_real @ ( sqrt @ X3 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4949_norm__triangle__ineq3,axiom,
% 15.55/8.55      ! [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 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4950_norm__triangle__ineq3,axiom,
% 15.55/8.55      ! [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 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4951_of__int__neg__numeral,axiom,
% 15.55/8.55      ! [K: num] :
% 15.55/8.55        ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 15.55/8.55        = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4952_of__int__neg__numeral,axiom,
% 15.55/8.55      ! [K: num] :
% 15.55/8.55        ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 15.55/8.55        = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4953_of__int__neg__numeral,axiom,
% 15.55/8.55      ! [K: num] :
% 15.55/8.55        ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 15.55/8.55        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4954_of__int__neg__numeral,axiom,
% 15.55/8.55      ! [K: num] :
% 15.55/8.55        ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 15.55/8.55        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4955_of__int__neg__numeral,axiom,
% 15.55/8.55      ! [K: num] :
% 15.55/8.55        ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 15.55/8.55        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4956_abs__ge__zero,axiom,
% 15.55/8.55      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4957_abs__ge__zero,axiom,
% 15.55/8.55      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4958_abs__ge__zero,axiom,
% 15.55/8.55      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4959_abs__ge__zero,axiom,
% 15.55/8.55      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4960_abs__of__pos,axiom,
% 15.55/8.55      ! [A: code_integer] :
% 15.55/8.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 15.55/8.55       => ( ( abs_abs_Code_integer @ A )
% 15.55/8.55          = A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4961_abs__of__pos,axiom,
% 15.55/8.55      ! [A: real] :
% 15.55/8.55        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.55       => ( ( abs_abs_real @ A )
% 15.55/8.55          = A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4962_abs__of__pos,axiom,
% 15.55/8.55      ! [A: rat] :
% 15.55/8.55        ( ( ord_less_rat @ zero_zero_rat @ A )
% 15.55/8.55       => ( ( abs_abs_rat @ A )
% 15.55/8.55          = A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4963_abs__of__pos,axiom,
% 15.55/8.55      ! [A: int] :
% 15.55/8.55        ( ( ord_less_int @ zero_zero_int @ A )
% 15.55/8.55       => ( ( abs_abs_int @ A )
% 15.55/8.55          = A ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4964_abs__not__less__zero,axiom,
% 15.55/8.55      ! [A: code_integer] :
% 15.55/8.55        ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4965_abs__not__less__zero,axiom,
% 15.55/8.55      ! [A: real] :
% 15.55/8.55        ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4966_abs__not__less__zero,axiom,
% 15.55/8.55      ! [A: rat] :
% 15.55/8.55        ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4967_abs__not__less__zero,axiom,
% 15.55/8.55      ! [A: int] :
% 15.55/8.55        ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4968_abs__triangle__ineq,axiom,
% 15.55/8.55      ! [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 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4969_abs__triangle__ineq,axiom,
% 15.55/8.55      ! [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 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4970_abs__triangle__ineq,axiom,
% 15.55/8.55      ! [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 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4971_abs__triangle__ineq,axiom,
% 15.55/8.55      ! [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 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4972_abs__mult__less,axiom,
% 15.55/8.55      ! [A: code_integer,C: code_integer,B: code_integer,D3: code_integer] :
% 15.55/8.55        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 15.55/8.55       => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D3 )
% 15.55/8.55         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D3 ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4973_abs__mult__less,axiom,
% 15.55/8.55      ! [A: real,C: real,B: real,D3: real] :
% 15.55/8.55        ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 15.55/8.55       => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D3 )
% 15.55/8.55         => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D3 ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4974_abs__mult__less,axiom,
% 15.55/8.55      ! [A: rat,C: rat,B: rat,D3: rat] :
% 15.55/8.55        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 15.55/8.55       => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D3 )
% 15.55/8.55         => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D3 ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4975_abs__mult__less,axiom,
% 15.55/8.55      ! [A: int,C: int,B: int,D3: int] :
% 15.55/8.55        ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 15.55/8.55       => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D3 )
% 15.55/8.55         => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D3 ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4976_abs__triangle__ineq2__sym,axiom,
% 15.55/8.55      ! [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 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4977_abs__triangle__ineq2__sym,axiom,
% 15.55/8.55      ! [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 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4978_abs__triangle__ineq2__sym,axiom,
% 15.55/8.55      ! [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 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4979_abs__triangle__ineq2__sym,axiom,
% 15.55/8.55      ! [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 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4980_abs__triangle__ineq3,axiom,
% 15.55/8.55      ! [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 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4981_abs__triangle__ineq3,axiom,
% 15.55/8.55      ! [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 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4982_abs__triangle__ineq3,axiom,
% 15.55/8.55      ! [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 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4983_abs__triangle__ineq3,axiom,
% 15.55/8.55      ! [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 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4984_abs__triangle__ineq2,axiom,
% 15.55/8.55      ! [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 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4985_abs__triangle__ineq2,axiom,
% 15.55/8.55      ! [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 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4986_abs__triangle__ineq2,axiom,
% 15.55/8.55      ! [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 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4987_abs__triangle__ineq2,axiom,
% 15.55/8.55      ! [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 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4988_nonzero__abs__divide,axiom,
% 15.55/8.55      ! [B: real,A: real] :
% 15.55/8.55        ( ( B != zero_zero_real )
% 15.55/8.55       => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 15.55/8.55          = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4989_nonzero__abs__divide,axiom,
% 15.55/8.55      ! [B: rat,A: rat] :
% 15.55/8.55        ( ( B != zero_zero_rat )
% 15.55/8.55       => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 15.55/8.55          = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4990_norm__of__real__diff,axiom,
% 15.55/8.55      ! [B: real,A: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( real_V1803761363581548252l_real @ B ) @ ( real_V1803761363581548252l_real @ A ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4991_norm__of__real__diff,axiom,
% 15.55/8.55      ! [B: real,A: real] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( real_V4546457046886955230omplex @ B ) @ ( real_V4546457046886955230omplex @ A ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4992_norm__mult__less,axiom,
% 15.55/8.55      ! [X3: real,R2: real,Y3: real,S: real] :
% 15.55/8.55        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ R2 )
% 15.55/8.55       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y3 ) @ S )
% 15.55/8.55         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X3 @ Y3 ) ) @ ( times_times_real @ R2 @ S ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4993_norm__mult__less,axiom,
% 15.55/8.55      ! [X3: complex,R2: real,Y3: complex,S: real] :
% 15.55/8.55        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ R2 )
% 15.55/8.55       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y3 ) @ S )
% 15.55/8.55         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X3 @ Y3 ) ) @ ( times_times_real @ R2 @ S ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4994_norm__mult__ineq,axiom,
% 15.55/8.55      ! [X3: real,Y3: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X3 @ Y3 ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4995_norm__mult__ineq,axiom,
% 15.55/8.55      ! [X3: complex,Y3: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X3 @ Y3 ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4996_norm__not__less__zero,axiom,
% 15.55/8.55      ! [X3: complex] :
% 15.55/8.55        ~ ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ zero_zero_real ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4997_norm__ge__zero,axiom,
% 15.55/8.55      ! [X3: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X3 ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4998_not__numeral__le__neg__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_4999_not__numeral__le__neg__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5000_not__numeral__le__neg__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5001_not__numeral__le__neg__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5002_neg__numeral__le__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5003_neg__numeral__le__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5004_neg__numeral__le__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5005_neg__numeral__le__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5006_zero__neq__neg__numeral,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( zero_zero_real
% 15.55/8.55       != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5007_zero__neq__neg__numeral,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( zero_zero_int
% 15.55/8.55       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5008_zero__neq__neg__numeral,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( zero_zero_complex
% 15.55/8.55       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5009_zero__neq__neg__numeral,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( zero_z3403309356797280102nteger
% 15.55/8.55       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5010_zero__neq__neg__numeral,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( zero_zero_rat
% 15.55/8.55       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5011_neg__numeral__less__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5012_neg__numeral__less__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5013_neg__numeral__less__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5014_neg__numeral__less__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5015_not__numeral__less__neg__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5016_not__numeral__less__neg__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5017_not__numeral__less__neg__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5018_not__numeral__less__neg__numeral,axiom,
% 15.55/8.55      ! [M: num,N: num] :
% 15.55/8.55        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5019_le__minus__one__simps_I2_J,axiom,
% 15.55/8.55      ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5020_le__minus__one__simps_I2_J,axiom,
% 15.55/8.55      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5021_le__minus__one__simps_I2_J,axiom,
% 15.55/8.55      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5022_le__minus__one__simps_I2_J,axiom,
% 15.55/8.55      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5023_le__minus__one__simps_I4_J,axiom,
% 15.55/8.55      ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5024_le__minus__one__simps_I4_J,axiom,
% 15.55/8.55      ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5025_le__minus__one__simps_I4_J,axiom,
% 15.55/8.55      ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5026_le__minus__one__simps_I4_J,axiom,
% 15.55/8.55      ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5027_zero__neq__neg__one,axiom,
% 15.55/8.55      ( zero_zero_real
% 15.55/8.55     != ( uminus_uminus_real @ one_one_real ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5028_zero__neq__neg__one,axiom,
% 15.55/8.55      ( zero_zero_int
% 15.55/8.55     != ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5029_zero__neq__neg__one,axiom,
% 15.55/8.55      ( zero_zero_complex
% 15.55/8.55     != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5030_zero__neq__neg__one,axiom,
% 15.55/8.55      ( zero_z3403309356797280102nteger
% 15.55/8.55     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5031_zero__neq__neg__one,axiom,
% 15.55/8.55      ( zero_zero_rat
% 15.55/8.55     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5032_neg__eq__iff__add__eq__0,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( ( uminus_uminus_real @ A )
% 15.55/8.55          = B )
% 15.55/8.55        = ( ( plus_plus_real @ A @ B )
% 15.55/8.55          = zero_zero_real ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5033_neg__eq__iff__add__eq__0,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( ( uminus_uminus_int @ A )
% 15.55/8.55          = B )
% 15.55/8.55        = ( ( plus_plus_int @ A @ B )
% 15.55/8.55          = zero_zero_int ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5034_neg__eq__iff__add__eq__0,axiom,
% 15.55/8.55      ! [A: complex,B: complex] :
% 15.55/8.55        ( ( ( uminus1482373934393186551omplex @ A )
% 15.55/8.55          = B )
% 15.55/8.55        = ( ( plus_plus_complex @ A @ B )
% 15.55/8.55          = zero_zero_complex ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5035_neg__eq__iff__add__eq__0,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( ( uminus1351360451143612070nteger @ A )
% 15.55/8.55          = B )
% 15.55/8.55        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 15.55/8.55          = zero_z3403309356797280102nteger ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5036_neg__eq__iff__add__eq__0,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( ( uminus_uminus_rat @ A )
% 15.55/8.55          = B )
% 15.55/8.55        = ( ( plus_plus_rat @ A @ B )
% 15.55/8.55          = zero_zero_rat ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5037_eq__neg__iff__add__eq__0,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( A
% 15.55/8.55          = ( uminus_uminus_real @ B ) )
% 15.55/8.55        = ( ( plus_plus_real @ A @ B )
% 15.55/8.55          = zero_zero_real ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5038_eq__neg__iff__add__eq__0,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( A
% 15.55/8.55          = ( uminus_uminus_int @ B ) )
% 15.55/8.55        = ( ( plus_plus_int @ A @ B )
% 15.55/8.55          = zero_zero_int ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5039_eq__neg__iff__add__eq__0,axiom,
% 15.55/8.55      ! [A: complex,B: complex] :
% 15.55/8.55        ( ( A
% 15.55/8.55          = ( uminus1482373934393186551omplex @ B ) )
% 15.55/8.55        = ( ( plus_plus_complex @ A @ B )
% 15.55/8.55          = zero_zero_complex ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5040_eq__neg__iff__add__eq__0,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( A
% 15.55/8.55          = ( uminus1351360451143612070nteger @ B ) )
% 15.55/8.55        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 15.55/8.55          = zero_z3403309356797280102nteger ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5041_eq__neg__iff__add__eq__0,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( A
% 15.55/8.55          = ( uminus_uminus_rat @ B ) )
% 15.55/8.55        = ( ( plus_plus_rat @ A @ B )
% 15.55/8.55          = zero_zero_rat ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5042_add_Oinverse__unique,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( ( plus_plus_real @ A @ B )
% 15.55/8.55          = zero_zero_real )
% 15.55/8.55       => ( ( uminus_uminus_real @ A )
% 15.55/8.55          = B ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5043_add_Oinverse__unique,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( ( plus_plus_int @ A @ B )
% 15.55/8.55          = zero_zero_int )
% 15.55/8.55       => ( ( uminus_uminus_int @ A )
% 15.55/8.55          = B ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5044_add_Oinverse__unique,axiom,
% 15.55/8.55      ! [A: complex,B: complex] :
% 15.55/8.55        ( ( ( plus_plus_complex @ A @ B )
% 15.55/8.55          = zero_zero_complex )
% 15.55/8.55       => ( ( uminus1482373934393186551omplex @ A )
% 15.55/8.55          = B ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5045_add_Oinverse__unique,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 15.55/8.55          = zero_z3403309356797280102nteger )
% 15.55/8.55       => ( ( uminus1351360451143612070nteger @ A )
% 15.55/8.55          = B ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5046_add_Oinverse__unique,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( ( plus_plus_rat @ A @ B )
% 15.55/8.55          = zero_zero_rat )
% 15.55/8.55       => ( ( uminus_uminus_rat @ A )
% 15.55/8.55          = B ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5047_ab__group__add__class_Oab__left__minus,axiom,
% 15.55/8.55      ! [A: real] :
% 15.55/8.55        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 15.55/8.55        = zero_zero_real ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5048_ab__group__add__class_Oab__left__minus,axiom,
% 15.55/8.55      ! [A: int] :
% 15.55/8.55        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 15.55/8.55        = zero_zero_int ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5049_ab__group__add__class_Oab__left__minus,axiom,
% 15.55/8.55      ! [A: complex] :
% 15.55/8.55        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 15.55/8.55        = zero_zero_complex ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5050_ab__group__add__class_Oab__left__minus,axiom,
% 15.55/8.55      ! [A: code_integer] :
% 15.55/8.55        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 15.55/8.55        = zero_z3403309356797280102nteger ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5051_ab__group__add__class_Oab__left__minus,axiom,
% 15.55/8.55      ! [A: rat] :
% 15.55/8.55        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 15.55/8.55        = zero_zero_rat ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5052_add__eq__0__iff,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( ( plus_plus_real @ A @ B )
% 15.55/8.55          = zero_zero_real )
% 15.55/8.55        = ( B
% 15.55/8.55          = ( uminus_uminus_real @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5053_add__eq__0__iff,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( ( plus_plus_int @ A @ B )
% 15.55/8.55          = zero_zero_int )
% 15.55/8.55        = ( B
% 15.55/8.55          = ( uminus_uminus_int @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5054_add__eq__0__iff,axiom,
% 15.55/8.55      ! [A: complex,B: complex] :
% 15.55/8.55        ( ( ( plus_plus_complex @ A @ B )
% 15.55/8.55          = zero_zero_complex )
% 15.55/8.55        = ( B
% 15.55/8.55          = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5055_add__eq__0__iff,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 15.55/8.55          = zero_z3403309356797280102nteger )
% 15.55/8.55        = ( B
% 15.55/8.55          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5056_add__eq__0__iff,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( ( plus_plus_rat @ A @ B )
% 15.55/8.55          = zero_zero_rat )
% 15.55/8.55        = ( B
% 15.55/8.55          = ( uminus_uminus_rat @ A ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5057_less__minus__one__simps_I2_J,axiom,
% 15.55/8.55      ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5058_less__minus__one__simps_I2_J,axiom,
% 15.55/8.55      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5059_less__minus__one__simps_I2_J,axiom,
% 15.55/8.55      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5060_less__minus__one__simps_I2_J,axiom,
% 15.55/8.55      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5061_less__minus__one__simps_I4_J,axiom,
% 15.55/8.55      ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5062_less__minus__one__simps_I4_J,axiom,
% 15.55/8.55      ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5063_less__minus__one__simps_I4_J,axiom,
% 15.55/8.55      ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5064_less__minus__one__simps_I4_J,axiom,
% 15.55/8.55      ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5065_numeral__times__minus__swap,axiom,
% 15.55/8.55      ! [W: num,X3: real] :
% 15.55/8.55        ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X3 ) )
% 15.55/8.55        = ( times_times_real @ X3 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5066_numeral__times__minus__swap,axiom,
% 15.55/8.55      ! [W: num,X3: int] :
% 15.55/8.55        ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X3 ) )
% 15.55/8.55        = ( times_times_int @ X3 @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5067_numeral__times__minus__swap,axiom,
% 15.55/8.55      ! [W: num,X3: complex] :
% 15.55/8.55        ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X3 ) )
% 15.55/8.55        = ( times_times_complex @ X3 @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5068_numeral__times__minus__swap,axiom,
% 15.55/8.55      ! [W: num,X3: code_integer] :
% 15.55/8.55        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X3 ) )
% 15.55/8.55        = ( times_3573771949741848930nteger @ X3 @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5069_numeral__times__minus__swap,axiom,
% 15.55/8.55      ! [W: num,X3: rat] :
% 15.55/8.55        ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X3 ) )
% 15.55/8.55        = ( times_times_rat @ X3 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5070_one__neq__neg__numeral,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( one_one_real
% 15.55/8.55       != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5071_one__neq__neg__numeral,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( one_one_int
% 15.55/8.55       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5072_one__neq__neg__numeral,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( one_one_complex
% 15.55/8.55       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5073_one__neq__neg__numeral,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( one_one_Code_integer
% 15.55/8.55       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5074_one__neq__neg__numeral,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( one_one_rat
% 15.55/8.55       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5075_numeral__neq__neg__one,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( ( numeral_numeral_real @ N )
% 15.55/8.55       != ( uminus_uminus_real @ one_one_real ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5076_numeral__neq__neg__one,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( ( numeral_numeral_int @ N )
% 15.55/8.55       != ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5077_numeral__neq__neg__one,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( ( numera6690914467698888265omplex @ N )
% 15.55/8.55       != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5078_numeral__neq__neg__one,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( ( numera6620942414471956472nteger @ N )
% 15.55/8.55       != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5079_numeral__neq__neg__one,axiom,
% 15.55/8.55      ! [N: num] :
% 15.55/8.55        ( ( numeral_numeral_rat @ N )
% 15.55/8.55       != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5080_nonzero__minus__divide__divide,axiom,
% 15.55/8.55      ! [B: real,A: real] :
% 15.55/8.55        ( ( B != zero_zero_real )
% 15.55/8.55       => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 15.55/8.55          = ( divide_divide_real @ A @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5081_nonzero__minus__divide__divide,axiom,
% 15.55/8.55      ! [B: complex,A: complex] :
% 15.55/8.55        ( ( B != zero_zero_complex )
% 15.55/8.55       => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 15.55/8.55          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5082_nonzero__minus__divide__divide,axiom,
% 15.55/8.55      ! [B: rat,A: rat] :
% 15.55/8.55        ( ( B != zero_zero_rat )
% 15.55/8.55       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 15.55/8.55          = ( divide_divide_rat @ A @ B ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5083_nonzero__minus__divide__right,axiom,
% 15.55/8.55      ! [B: real,A: real] :
% 15.55/8.55        ( ( B != zero_zero_real )
% 15.55/8.55       => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 15.55/8.55          = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5084_nonzero__minus__divide__right,axiom,
% 15.55/8.55      ! [B: complex,A: complex] :
% 15.55/8.55        ( ( B != zero_zero_complex )
% 15.55/8.55       => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 15.55/8.55          = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5085_nonzero__minus__divide__right,axiom,
% 15.55/8.55      ! [B: rat,A: rat] :
% 15.55/8.55        ( ( B != zero_zero_rat )
% 15.55/8.55       => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 15.55/8.55          = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5086_norm__power,axiom,
% 15.55/8.55      ! [X3: real,N: nat] :
% 15.55/8.55        ( ( real_V7735802525324610683m_real @ ( power_power_real @ X3 @ N ) )
% 15.55/8.55        = ( power_power_real @ ( real_V7735802525324610683m_real @ X3 ) @ N ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5087_norm__power,axiom,
% 15.55/8.55      ! [X3: complex,N: nat] :
% 15.55/8.55        ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X3 @ N ) )
% 15.55/8.55        = ( power_power_real @ ( real_V1022390504157884413omplex @ X3 ) @ N ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5088_group__cancel_Osub2,axiom,
% 15.55/8.55      ! [B5: real,K: real,B: real,A: real] :
% 15.55/8.55        ( ( B5
% 15.55/8.55          = ( plus_plus_real @ K @ B ) )
% 15.55/8.55       => ( ( minus_minus_real @ A @ B5 )
% 15.55/8.55          = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5089_group__cancel_Osub2,axiom,
% 15.55/8.55      ! [B5: int,K: int,B: int,A: int] :
% 15.55/8.55        ( ( B5
% 15.55/8.55          = ( plus_plus_int @ K @ B ) )
% 15.55/8.55       => ( ( minus_minus_int @ A @ B5 )
% 15.55/8.55          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5090_group__cancel_Osub2,axiom,
% 15.55/8.55      ! [B5: complex,K: complex,B: complex,A: complex] :
% 15.55/8.55        ( ( B5
% 15.55/8.55          = ( plus_plus_complex @ K @ B ) )
% 15.55/8.55       => ( ( minus_minus_complex @ A @ B5 )
% 15.55/8.55          = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5091_group__cancel_Osub2,axiom,
% 15.55/8.55      ! [B5: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 15.55/8.55        ( ( B5
% 15.55/8.55          = ( plus_p5714425477246183910nteger @ K @ B ) )
% 15.55/8.55       => ( ( minus_8373710615458151222nteger @ A @ B5 )
% 15.55/8.55          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5092_group__cancel_Osub2,axiom,
% 15.55/8.55      ! [B5: rat,K: rat,B: rat,A: rat] :
% 15.55/8.55        ( ( B5
% 15.55/8.55          = ( plus_plus_rat @ K @ B ) )
% 15.55/8.55       => ( ( minus_minus_rat @ A @ B5 )
% 15.55/8.55          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5093_diff__conv__add__uminus,axiom,
% 15.55/8.55      ( minus_minus_real
% 15.55/8.55      = ( ^ [A4: real,B3: real] : ( plus_plus_real @ A4 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5094_diff__conv__add__uminus,axiom,
% 15.55/8.55      ( minus_minus_int
% 15.55/8.55      = ( ^ [A4: int,B3: int] : ( plus_plus_int @ A4 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5095_diff__conv__add__uminus,axiom,
% 15.55/8.55      ( minus_minus_complex
% 15.55/8.55      = ( ^ [A4: complex,B3: complex] : ( plus_plus_complex @ A4 @ ( uminus1482373934393186551omplex @ B3 ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5096_diff__conv__add__uminus,axiom,
% 15.55/8.55      ( minus_8373710615458151222nteger
% 15.55/8.55      = ( ^ [A4: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A4 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5097_diff__conv__add__uminus,axiom,
% 15.55/8.55      ( minus_minus_rat
% 15.55/8.55      = ( ^ [A4: rat,B3: rat] : ( plus_plus_rat @ A4 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5098_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 15.55/8.55      ( minus_minus_real
% 15.55/8.55      = ( ^ [A4: real,B3: real] : ( plus_plus_real @ A4 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5099_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 15.55/8.55      ( minus_minus_int
% 15.55/8.55      = ( ^ [A4: int,B3: int] : ( plus_plus_int @ A4 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5100_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 15.55/8.55      ( minus_minus_complex
% 15.55/8.55      = ( ^ [A4: complex,B3: complex] : ( plus_plus_complex @ A4 @ ( uminus1482373934393186551omplex @ B3 ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5101_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 15.55/8.55      ( minus_8373710615458151222nteger
% 15.55/8.55      = ( ^ [A4: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A4 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5102_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 15.55/8.55      ( minus_minus_rat
% 15.55/8.55      = ( ^ [A4: rat,B3: rat] : ( plus_plus_rat @ A4 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5103_minus__real__def,axiom,
% 15.55/8.55      ( minus_minus_real
% 15.55/8.55      = ( ^ [X: real,Y: real] : ( plus_plus_real @ X @ ( uminus_uminus_real @ Y ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5104_of__int__of__nat,axiom,
% 15.55/8.55      ( ring_18347121197199848620nteger
% 15.55/8.55      = ( ^ [K3: int] : ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri4939895301339042750nteger @ ( nat2 @ K3 ) ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5105_of__int__of__nat,axiom,
% 15.55/8.55      ( ring_17405671764205052669omplex
% 15.55/8.55      = ( ^ [K3: int] : ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri8010041392384452111omplex @ ( nat2 @ K3 ) ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5106_of__int__of__nat,axiom,
% 15.55/8.55      ( ring_1_of_int_real
% 15.55/8.55      = ( ^ [K3: int] : ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri5074537144036343181t_real @ ( nat2 @ K3 ) ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5107_of__int__of__nat,axiom,
% 15.55/8.55      ( ring_1_of_int_rat
% 15.55/8.55      = ( ^ [K3: int] : ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri681578069525770553at_rat @ ( nat2 @ K3 ) ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5108_of__int__of__nat,axiom,
% 15.55/8.55      ( ring_1_of_int_int
% 15.55/8.55      = ( ^ [K3: int] : ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri1314217659103216013at_int @ ( nat2 @ K3 ) ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5109_dense__eq0__I,axiom,
% 15.55/8.55      ! [X3: real] :
% 15.55/8.55        ( ! [E: real] :
% 15.55/8.55            ( ( ord_less_real @ zero_zero_real @ E )
% 15.55/8.55           => ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ E ) )
% 15.55/8.55       => ( X3 = zero_zero_real ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5110_dense__eq0__I,axiom,
% 15.55/8.55      ! [X3: rat] :
% 15.55/8.55        ( ! [E: rat] :
% 15.55/8.55            ( ( ord_less_rat @ zero_zero_rat @ E )
% 15.55/8.55           => ( ord_less_eq_rat @ ( abs_abs_rat @ X3 ) @ E ) )
% 15.55/8.55       => ( X3 = zero_zero_rat ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5111_abs__mult__pos,axiom,
% 15.55/8.55      ! [X3: code_integer,Y3: code_integer] :
% 15.55/8.55        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 15.55/8.55       => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y3 ) @ X3 )
% 15.55/8.55          = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y3 @ X3 ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5112_abs__mult__pos,axiom,
% 15.55/8.55      ! [X3: real,Y3: real] :
% 15.55/8.55        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.55       => ( ( times_times_real @ ( abs_abs_real @ Y3 ) @ X3 )
% 15.55/8.55          = ( abs_abs_real @ ( times_times_real @ Y3 @ X3 ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5113_abs__mult__pos,axiom,
% 15.55/8.55      ! [X3: rat,Y3: rat] :
% 15.55/8.55        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 15.55/8.55       => ( ( times_times_rat @ ( abs_abs_rat @ Y3 ) @ X3 )
% 15.55/8.55          = ( abs_abs_rat @ ( times_times_rat @ Y3 @ X3 ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5114_abs__mult__pos,axiom,
% 15.55/8.55      ! [X3: int,Y3: int] :
% 15.55/8.55        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 15.55/8.55       => ( ( times_times_int @ ( abs_abs_int @ Y3 ) @ X3 )
% 15.55/8.55          = ( abs_abs_int @ ( times_times_int @ Y3 @ X3 ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5115_abs__eq__mult,axiom,
% 15.55/8.55      ! [A: code_integer,B: code_integer] :
% 15.55/8.55        ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 15.55/8.55            | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 15.55/8.55          & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 15.55/8.55            | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 15.55/8.55       => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 15.55/8.55          = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5116_abs__eq__mult,axiom,
% 15.55/8.55      ! [A: real,B: real] :
% 15.55/8.55        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 15.55/8.55            | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 15.55/8.55          & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 15.55/8.55            | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 15.55/8.55       => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 15.55/8.55          = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5117_abs__eq__mult,axiom,
% 15.55/8.55      ! [A: rat,B: rat] :
% 15.55/8.55        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 15.55/8.55            | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 15.55/8.55          & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 15.55/8.55            | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 15.55/8.55       => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 15.55/8.55          = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5118_abs__eq__mult,axiom,
% 15.55/8.55      ! [A: int,B: int] :
% 15.55/8.55        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.55            | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 15.55/8.55          & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 15.55/8.55            | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 15.55/8.55       => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 15.55/8.55          = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5119_abs__div__pos,axiom,
% 15.55/8.55      ! [Y3: real,X3: real] :
% 15.55/8.55        ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.55/8.55       => ( ( divide_divide_real @ ( abs_abs_real @ X3 ) @ Y3 )
% 15.55/8.55          = ( abs_abs_real @ ( divide_divide_real @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.55  
% 15.55/8.55  thf(fact_5120_abs__div__pos,axiom,
% 15.55/8.55      ! [Y3: rat,X3: rat] :
% 15.55/8.55        ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 15.55/8.55       => ( ( divide_divide_rat @ ( abs_abs_rat @ X3 ) @ Y3 )
% 15.55/8.55          = ( abs_abs_rat @ ( divide_divide_rat @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5121_zero__le__power__abs,axiom,
% 15.55/8.56      ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5122_zero__le__power__abs,axiom,
% 15.55/8.56      ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5123_zero__le__power__abs,axiom,
% 15.55/8.56      ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5124_zero__le__power__abs,axiom,
% 15.55/8.56      ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5125_abs__diff__le__iff,axiom,
% 15.55/8.56      ! [X3: code_integer,A: code_integer,R2: code_integer] :
% 15.55/8.56        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X3 @ A ) ) @ R2 )
% 15.55/8.56        = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X3 )
% 15.55/8.56          & ( ord_le3102999989581377725nteger @ X3 @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5126_abs__diff__le__iff,axiom,
% 15.55/8.56      ! [X3: real,A: real,R2: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ A ) ) @ R2 )
% 15.55/8.56        = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R2 ) @ X3 )
% 15.55/8.56          & ( ord_less_eq_real @ X3 @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5127_abs__diff__le__iff,axiom,
% 15.55/8.56      ! [X3: rat,A: rat,R2: rat] :
% 15.55/8.56        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X3 @ A ) ) @ R2 )
% 15.55/8.56        = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R2 ) @ X3 )
% 15.55/8.56          & ( ord_less_eq_rat @ X3 @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5128_abs__diff__le__iff,axiom,
% 15.55/8.56      ! [X3: int,A: int,R2: int] :
% 15.55/8.56        ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X3 @ A ) ) @ R2 )
% 15.55/8.56        = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R2 ) @ X3 )
% 15.55/8.56          & ( ord_less_eq_int @ X3 @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5129_abs__diff__triangle__ineq,axiom,
% 15.55/8.56      ! [A: code_integer,B: code_integer,C: code_integer,D3: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D3 ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D3 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5130_abs__diff__triangle__ineq,axiom,
% 15.55/8.56      ! [A: real,B: real,C: real,D3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D3 ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D3 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5131_abs__diff__triangle__ineq,axiom,
% 15.55/8.56      ! [A: rat,B: rat,C: rat,D3: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D3 ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D3 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5132_abs__diff__triangle__ineq,axiom,
% 15.55/8.56      ! [A: int,B: int,C: int,D3: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D3 ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D3 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5133_abs__triangle__ineq4,axiom,
% 15.55/8.56      ! [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 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5134_abs__triangle__ineq4,axiom,
% 15.55/8.56      ! [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 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5135_abs__triangle__ineq4,axiom,
% 15.55/8.56      ! [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 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5136_abs__triangle__ineq4,axiom,
% 15.55/8.56      ! [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 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5137_abs__diff__less__iff,axiom,
% 15.55/8.56      ! [X3: code_integer,A: code_integer,R2: code_integer] :
% 15.55/8.56        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X3 @ A ) ) @ R2 )
% 15.55/8.56        = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X3 )
% 15.55/8.56          & ( ord_le6747313008572928689nteger @ X3 @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5138_abs__diff__less__iff,axiom,
% 15.55/8.56      ! [X3: real,A: real,R2: real] :
% 15.55/8.56        ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ A ) ) @ R2 )
% 15.55/8.56        = ( ( ord_less_real @ ( minus_minus_real @ A @ R2 ) @ X3 )
% 15.55/8.56          & ( ord_less_real @ X3 @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5139_abs__diff__less__iff,axiom,
% 15.55/8.56      ! [X3: rat,A: rat,R2: rat] :
% 15.55/8.56        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X3 @ A ) ) @ R2 )
% 15.55/8.56        = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R2 ) @ X3 )
% 15.55/8.56          & ( ord_less_rat @ X3 @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5140_abs__diff__less__iff,axiom,
% 15.55/8.56      ! [X3: int,A: int,R2: int] :
% 15.55/8.56        ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X3 @ A ) ) @ R2 )
% 15.55/8.56        = ( ( ord_less_int @ ( minus_minus_int @ A @ R2 ) @ X3 )
% 15.55/8.56          & ( ord_less_int @ X3 @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5141_nonzero__norm__divide,axiom,
% 15.55/8.56      ! [B: real,A: real] :
% 15.55/8.56        ( ( B != zero_zero_real )
% 15.55/8.56       => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 15.55/8.56          = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5142_nonzero__norm__divide,axiom,
% 15.55/8.56      ! [B: complex,A: complex] :
% 15.55/8.56        ( ( B != zero_zero_complex )
% 15.55/8.56       => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 15.55/8.56          = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5143_power__eq__imp__eq__norm,axiom,
% 15.55/8.56      ! [W: real,N: nat,Z: real] :
% 15.55/8.56        ( ( ( power_power_real @ W @ N )
% 15.55/8.56          = ( power_power_real @ Z @ N ) )
% 15.55/8.56       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.56         => ( ( real_V7735802525324610683m_real @ W )
% 15.55/8.56            = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5144_power__eq__imp__eq__norm,axiom,
% 15.55/8.56      ! [W: complex,N: nat,Z: complex] :
% 15.55/8.56        ( ( ( power_power_complex @ W @ N )
% 15.55/8.56          = ( power_power_complex @ Z @ N ) )
% 15.55/8.56       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.56         => ( ( real_V1022390504157884413omplex @ W )
% 15.55/8.56            = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5145_not__zero__le__neg__numeral,axiom,
% 15.55/8.56      ! [N: num] :
% 15.55/8.56        ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5146_not__zero__le__neg__numeral,axiom,
% 15.55/8.56      ! [N: num] :
% 15.55/8.56        ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5147_not__zero__le__neg__numeral,axiom,
% 15.55/8.56      ! [N: num] :
% 15.55/8.56        ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5148_not__zero__le__neg__numeral,axiom,
% 15.55/8.56      ! [N: num] :
% 15.55/8.56        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5149_neg__numeral__le__zero,axiom,
% 15.55/8.56      ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5150_neg__numeral__le__zero,axiom,
% 15.55/8.56      ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5151_neg__numeral__le__zero,axiom,
% 15.55/8.56      ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5152_neg__numeral__le__zero,axiom,
% 15.55/8.56      ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5153_neg__numeral__less__zero,axiom,
% 15.55/8.56      ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5154_neg__numeral__less__zero,axiom,
% 15.55/8.56      ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5155_neg__numeral__less__zero,axiom,
% 15.55/8.56      ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5156_neg__numeral__less__zero,axiom,
% 15.55/8.56      ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5157_not__zero__less__neg__numeral,axiom,
% 15.55/8.56      ! [N: num] :
% 15.55/8.56        ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5158_not__zero__less__neg__numeral,axiom,
% 15.55/8.56      ! [N: num] :
% 15.55/8.56        ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5159_not__zero__less__neg__numeral,axiom,
% 15.55/8.56      ! [N: num] :
% 15.55/8.56        ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5160_not__zero__less__neg__numeral,axiom,
% 15.55/8.56      ! [N: num] :
% 15.55/8.56        ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5161_le__minus__one__simps_I3_J,axiom,
% 15.55/8.56      ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5162_le__minus__one__simps_I3_J,axiom,
% 15.55/8.56      ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5163_le__minus__one__simps_I3_J,axiom,
% 15.55/8.56      ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5164_le__minus__one__simps_I3_J,axiom,
% 15.55/8.56      ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5165_le__minus__one__simps_I1_J,axiom,
% 15.55/8.56      ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5166_le__minus__one__simps_I1_J,axiom,
% 15.55/8.56      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5167_le__minus__one__simps_I1_J,axiom,
% 15.55/8.56      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5168_le__minus__one__simps_I1_J,axiom,
% 15.55/8.56      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5169_less__minus__one__simps_I3_J,axiom,
% 15.55/8.56      ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5170_less__minus__one__simps_I3_J,axiom,
% 15.55/8.56      ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5171_less__minus__one__simps_I3_J,axiom,
% 15.55/8.56      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5172_less__minus__one__simps_I3_J,axiom,
% 15.55/8.56      ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5173_less__minus__one__simps_I1_J,axiom,
% 15.55/8.56      ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5174_less__minus__one__simps_I1_J,axiom,
% 15.55/8.56      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5175_less__minus__one__simps_I1_J,axiom,
% 15.55/8.56      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5176_less__minus__one__simps_I1_J,axiom,
% 15.55/8.56      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5177_not__one__le__neg__numeral,axiom,
% 15.55/8.56      ! [M: num] :
% 15.55/8.56        ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5178_not__one__le__neg__numeral,axiom,
% 15.55/8.56      ! [M: num] :
% 15.55/8.56        ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5179_not__one__le__neg__numeral,axiom,
% 15.55/8.56      ! [M: num] :
% 15.55/8.56        ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5180_not__one__le__neg__numeral,axiom,
% 15.55/8.56      ! [M: num] :
% 15.55/8.56        ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5181_not__numeral__le__neg__one,axiom,
% 15.55/8.56      ! [M: num] :
% 15.55/8.56        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5182_not__numeral__le__neg__one,axiom,
% 15.55/8.56      ! [M: num] :
% 15.55/8.56        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5183_not__numeral__le__neg__one,axiom,
% 15.55/8.56      ! [M: num] :
% 15.55/8.56        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5184_not__numeral__le__neg__one,axiom,
% 15.55/8.56      ! [M: num] :
% 15.55/8.56        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5185_neg__numeral__le__neg__one,axiom,
% 15.55/8.56      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5186_neg__numeral__le__neg__one,axiom,
% 15.55/8.56      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5187_neg__numeral__le__neg__one,axiom,
% 15.55/8.56      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5188_neg__numeral__le__neg__one,axiom,
% 15.55/8.56      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5189_neg__one__le__numeral,axiom,
% 15.55/8.56      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5190_neg__one__le__numeral,axiom,
% 15.55/8.56      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5191_neg__one__le__numeral,axiom,
% 15.55/8.56      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5192_neg__one__le__numeral,axiom,
% 15.55/8.56      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5193_neg__numeral__le__one,axiom,
% 15.55/8.56      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5194_neg__numeral__le__one,axiom,
% 15.55/8.56      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5195_neg__numeral__le__one,axiom,
% 15.55/8.56      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5196_neg__numeral__le__one,axiom,
% 15.55/8.56      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5197_neg__numeral__less__one,axiom,
% 15.55/8.56      ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5198_neg__numeral__less__one,axiom,
% 15.55/8.56      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5199_neg__numeral__less__one,axiom,
% 15.55/8.56      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5200_neg__numeral__less__one,axiom,
% 15.55/8.56      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5201_neg__one__less__numeral,axiom,
% 15.55/8.56      ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5202_neg__one__less__numeral,axiom,
% 15.55/8.56      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5203_neg__one__less__numeral,axiom,
% 15.55/8.56      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5204_neg__one__less__numeral,axiom,
% 15.55/8.56      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5205_not__numeral__less__neg__one,axiom,
% 15.55/8.56      ! [M: num] :
% 15.55/8.56        ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5206_not__numeral__less__neg__one,axiom,
% 15.55/8.56      ! [M: num] :
% 15.55/8.56        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5207_not__numeral__less__neg__one,axiom,
% 15.55/8.56      ! [M: num] :
% 15.55/8.56        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5208_not__numeral__less__neg__one,axiom,
% 15.55/8.56      ! [M: num] :
% 15.55/8.56        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5209_not__one__less__neg__numeral,axiom,
% 15.55/8.56      ! [M: num] :
% 15.55/8.56        ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5210_not__one__less__neg__numeral,axiom,
% 15.55/8.56      ! [M: num] :
% 15.55/8.56        ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5211_not__one__less__neg__numeral,axiom,
% 15.55/8.56      ! [M: num] :
% 15.55/8.56        ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5212_not__one__less__neg__numeral,axiom,
% 15.55/8.56      ! [M: num] :
% 15.55/8.56        ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5213_not__neg__one__less__neg__numeral,axiom,
% 15.55/8.56      ! [M: num] :
% 15.55/8.56        ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5214_not__neg__one__less__neg__numeral,axiom,
% 15.55/8.56      ! [M: num] :
% 15.55/8.56        ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5215_not__neg__one__less__neg__numeral,axiom,
% 15.55/8.56      ! [M: num] :
% 15.55/8.56        ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5216_not__neg__one__less__neg__numeral,axiom,
% 15.55/8.56      ! [M: num] :
% 15.55/8.56        ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5217_nonzero__neg__divide__eq__eq2,axiom,
% 15.55/8.56      ! [B: real,C: real,A: real] :
% 15.55/8.56        ( ( B != zero_zero_real )
% 15.55/8.56       => ( ( C
% 15.55/8.56            = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 15.55/8.56          = ( ( times_times_real @ C @ B )
% 15.55/8.56            = ( uminus_uminus_real @ A ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5218_nonzero__neg__divide__eq__eq2,axiom,
% 15.55/8.56      ! [B: complex,C: complex,A: complex] :
% 15.55/8.56        ( ( B != zero_zero_complex )
% 15.55/8.56       => ( ( C
% 15.55/8.56            = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 15.55/8.56          = ( ( times_times_complex @ C @ B )
% 15.55/8.56            = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5219_nonzero__neg__divide__eq__eq2,axiom,
% 15.55/8.56      ! [B: rat,C: rat,A: rat] :
% 15.55/8.56        ( ( B != zero_zero_rat )
% 15.55/8.56       => ( ( C
% 15.55/8.56            = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 15.55/8.56          = ( ( times_times_rat @ C @ B )
% 15.55/8.56            = ( uminus_uminus_rat @ A ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5220_nonzero__neg__divide__eq__eq,axiom,
% 15.55/8.56      ! [B: real,A: real,C: real] :
% 15.55/8.56        ( ( B != zero_zero_real )
% 15.55/8.56       => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 15.55/8.56            = C )
% 15.55/8.56          = ( ( uminus_uminus_real @ A )
% 15.55/8.56            = ( times_times_real @ C @ B ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5221_nonzero__neg__divide__eq__eq,axiom,
% 15.55/8.56      ! [B: complex,A: complex,C: complex] :
% 15.55/8.56        ( ( B != zero_zero_complex )
% 15.55/8.56       => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 15.55/8.56            = C )
% 15.55/8.56          = ( ( uminus1482373934393186551omplex @ A )
% 15.55/8.56            = ( times_times_complex @ C @ B ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5222_nonzero__neg__divide__eq__eq,axiom,
% 15.55/8.56      ! [B: rat,A: rat,C: rat] :
% 15.55/8.56        ( ( B != zero_zero_rat )
% 15.55/8.56       => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 15.55/8.56            = C )
% 15.55/8.56          = ( ( uminus_uminus_rat @ A )
% 15.55/8.56            = ( times_times_rat @ C @ B ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5223_minus__divide__eq__eq,axiom,
% 15.55/8.56      ! [B: real,C: real,A: real] :
% 15.55/8.56        ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 15.55/8.56          = A )
% 15.55/8.56        = ( ( ( C != zero_zero_real )
% 15.55/8.56           => ( ( uminus_uminus_real @ B )
% 15.55/8.56              = ( times_times_real @ A @ C ) ) )
% 15.55/8.56          & ( ( C = zero_zero_real )
% 15.55/8.56           => ( A = zero_zero_real ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5224_minus__divide__eq__eq,axiom,
% 15.55/8.56      ! [B: complex,C: complex,A: complex] :
% 15.55/8.56        ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 15.55/8.56          = A )
% 15.55/8.56        = ( ( ( C != zero_zero_complex )
% 15.55/8.56           => ( ( uminus1482373934393186551omplex @ B )
% 15.55/8.56              = ( times_times_complex @ A @ C ) ) )
% 15.55/8.56          & ( ( C = zero_zero_complex )
% 15.55/8.56           => ( A = zero_zero_complex ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5225_minus__divide__eq__eq,axiom,
% 15.55/8.56      ! [B: rat,C: rat,A: rat] :
% 15.55/8.56        ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 15.55/8.56          = A )
% 15.55/8.56        = ( ( ( C != zero_zero_rat )
% 15.55/8.56           => ( ( uminus_uminus_rat @ B )
% 15.55/8.56              = ( times_times_rat @ A @ C ) ) )
% 15.55/8.56          & ( ( C = zero_zero_rat )
% 15.55/8.56           => ( A = zero_zero_rat ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5226_eq__minus__divide__eq,axiom,
% 15.55/8.56      ! [A: real,B: real,C: real] :
% 15.55/8.56        ( ( A
% 15.55/8.56          = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 15.55/8.56        = ( ( ( C != zero_zero_real )
% 15.55/8.56           => ( ( times_times_real @ A @ C )
% 15.55/8.56              = ( uminus_uminus_real @ B ) ) )
% 15.55/8.56          & ( ( C = zero_zero_real )
% 15.55/8.56           => ( A = zero_zero_real ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5227_eq__minus__divide__eq,axiom,
% 15.55/8.56      ! [A: complex,B: complex,C: complex] :
% 15.55/8.56        ( ( A
% 15.55/8.56          = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 15.55/8.56        = ( ( ( C != zero_zero_complex )
% 15.55/8.56           => ( ( times_times_complex @ A @ C )
% 15.55/8.56              = ( uminus1482373934393186551omplex @ B ) ) )
% 15.55/8.56          & ( ( C = zero_zero_complex )
% 15.55/8.56           => ( A = zero_zero_complex ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5228_eq__minus__divide__eq,axiom,
% 15.55/8.56      ! [A: rat,B: rat,C: rat] :
% 15.55/8.56        ( ( A
% 15.55/8.56          = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 15.55/8.56        = ( ( ( C != zero_zero_rat )
% 15.55/8.56           => ( ( times_times_rat @ A @ C )
% 15.55/8.56              = ( uminus_uminus_rat @ B ) ) )
% 15.55/8.56          & ( ( C = zero_zero_rat )
% 15.55/8.56           => ( A = zero_zero_rat ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5229_norm__triangle__lt,axiom,
% 15.55/8.56      ! [X3: real,Y3: real,E2: real] :
% 15.55/8.56        ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) @ E2 )
% 15.55/8.56       => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y3 ) ) @ E2 ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5230_norm__triangle__lt,axiom,
% 15.55/8.56      ! [X3: complex,Y3: complex,E2: real] :
% 15.55/8.56        ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) @ E2 )
% 15.55/8.56       => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y3 ) ) @ E2 ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5231_norm__add__less,axiom,
% 15.55/8.56      ! [X3: real,R2: real,Y3: real,S: real] :
% 15.55/8.56        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ R2 )
% 15.55/8.56       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y3 ) @ S )
% 15.55/8.56         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y3 ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5232_norm__add__less,axiom,
% 15.55/8.56      ! [X3: complex,R2: real,Y3: complex,S: real] :
% 15.55/8.56        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ R2 )
% 15.55/8.56       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y3 ) @ S )
% 15.55/8.56         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y3 ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5233_divide__eq__minus__1__iff,axiom,
% 15.55/8.56      ! [A: real,B: real] :
% 15.55/8.56        ( ( ( divide_divide_real @ A @ B )
% 15.55/8.56          = ( uminus_uminus_real @ one_one_real ) )
% 15.55/8.56        = ( ( B != zero_zero_real )
% 15.55/8.56          & ( A
% 15.55/8.56            = ( uminus_uminus_real @ B ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5234_divide__eq__minus__1__iff,axiom,
% 15.55/8.56      ! [A: complex,B: complex] :
% 15.55/8.56        ( ( ( divide1717551699836669952omplex @ A @ B )
% 15.55/8.56          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 15.55/8.56        = ( ( B != zero_zero_complex )
% 15.55/8.56          & ( A
% 15.55/8.56            = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5235_divide__eq__minus__1__iff,axiom,
% 15.55/8.56      ! [A: rat,B: rat] :
% 15.55/8.56        ( ( ( divide_divide_rat @ A @ B )
% 15.55/8.56          = ( uminus_uminus_rat @ one_one_rat ) )
% 15.55/8.56        = ( ( B != zero_zero_rat )
% 15.55/8.56          & ( A
% 15.55/8.56            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5236_mult__1s__ring__1_I2_J,axiom,
% 15.55/8.56      ! [B: real] :
% 15.55/8.56        ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 15.55/8.56        = ( uminus_uminus_real @ B ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5237_mult__1s__ring__1_I2_J,axiom,
% 15.55/8.56      ! [B: int] :
% 15.55/8.56        ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 15.55/8.56        = ( uminus_uminus_int @ B ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5238_mult__1s__ring__1_I2_J,axiom,
% 15.55/8.56      ! [B: complex] :
% 15.55/8.56        ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 15.55/8.56        = ( uminus1482373934393186551omplex @ B ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5239_mult__1s__ring__1_I2_J,axiom,
% 15.55/8.56      ! [B: code_integer] :
% 15.55/8.56        ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 15.55/8.56        = ( uminus1351360451143612070nteger @ B ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5240_mult__1s__ring__1_I2_J,axiom,
% 15.55/8.56      ! [B: rat] :
% 15.55/8.56        ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 15.55/8.56        = ( uminus_uminus_rat @ B ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5241_mult__1s__ring__1_I1_J,axiom,
% 15.55/8.56      ! [B: real] :
% 15.55/8.56        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 15.55/8.56        = ( uminus_uminus_real @ B ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5242_mult__1s__ring__1_I1_J,axiom,
% 15.55/8.56      ! [B: int] :
% 15.55/8.56        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 15.55/8.56        = ( uminus_uminus_int @ B ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5243_mult__1s__ring__1_I1_J,axiom,
% 15.55/8.56      ! [B: complex] :
% 15.55/8.56        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 15.55/8.56        = ( uminus1482373934393186551omplex @ B ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5244_mult__1s__ring__1_I1_J,axiom,
% 15.55/8.56      ! [B: code_integer] :
% 15.55/8.56        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 15.55/8.56        = ( uminus1351360451143612070nteger @ B ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5245_mult__1s__ring__1_I1_J,axiom,
% 15.55/8.56      ! [B: rat] :
% 15.55/8.56        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 15.55/8.56        = ( uminus_uminus_rat @ B ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5246_uminus__numeral__One,axiom,
% 15.55/8.56      ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 15.55/8.56      = ( uminus_uminus_real @ one_one_real ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5247_uminus__numeral__One,axiom,
% 15.55/8.56      ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 15.55/8.56      = ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5248_uminus__numeral__One,axiom,
% 15.55/8.56      ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 15.55/8.56      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5249_uminus__numeral__One,axiom,
% 15.55/8.56      ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 15.55/8.56      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5250_uminus__numeral__One,axiom,
% 15.55/8.56      ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 15.55/8.56      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5251_norm__add__leD,axiom,
% 15.55/8.56      ! [A: real,B: real,C: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 15.55/8.56       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5252_norm__add__leD,axiom,
% 15.55/8.56      ! [A: complex,B: complex,C: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 15.55/8.56       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5253_norm__triangle__le,axiom,
% 15.55/8.56      ! [X3: real,Y3: real,E2: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) @ E2 )
% 15.55/8.56       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y3 ) ) @ E2 ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5254_norm__triangle__le,axiom,
% 15.55/8.56      ! [X3: complex,Y3: complex,E2: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) @ E2 )
% 15.55/8.56       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y3 ) ) @ E2 ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5255_norm__triangle__ineq,axiom,
% 15.55/8.56      ! [X3: real,Y3: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y3 ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5256_norm__triangle__ineq,axiom,
% 15.55/8.56      ! [X3: complex,Y3: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y3 ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5257_norm__triangle__mono,axiom,
% 15.55/8.56      ! [A: real,R2: real,B: real,S: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R2 )
% 15.55/8.56       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S )
% 15.55/8.56         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5258_norm__triangle__mono,axiom,
% 15.55/8.56      ! [A: complex,R2: real,B: complex,S: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R2 )
% 15.55/8.56       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S )
% 15.55/8.56         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5259_norm__power__ineq,axiom,
% 15.55/8.56      ! [X3: real,N: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X3 @ N ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X3 ) @ N ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5260_norm__power__ineq,axiom,
% 15.55/8.56      ! [X3: complex,N: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X3 @ N ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X3 ) @ N ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5261_norm__diff__triangle__less,axiom,
% 15.55/8.56      ! [X3: real,Y3: real,E1: real,Z: real,E22: real] :
% 15.55/8.56        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X3 @ Y3 ) ) @ E1 )
% 15.55/8.56       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y3 @ Z ) ) @ E22 )
% 15.55/8.56         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X3 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5262_norm__diff__triangle__less,axiom,
% 15.55/8.56      ! [X3: complex,Y3: complex,E1: real,Z: complex,E22: real] :
% 15.55/8.56        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Y3 ) ) @ E1 )
% 15.55/8.56       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y3 @ Z ) ) @ E22 )
% 15.55/8.56         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5263_norm__triangle__sub,axiom,
% 15.55/8.56      ! [X3: real,Y3: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ Y3 ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5264_norm__triangle__sub,axiom,
% 15.55/8.56      ! [X3: complex,Y3: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y3 ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5265_norm__triangle__ineq4,axiom,
% 15.55/8.56      ! [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 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5266_norm__triangle__ineq4,axiom,
% 15.55/8.56      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5267_norm__diff__triangle__le,axiom,
% 15.55/8.56      ! [X3: real,Y3: real,E1: real,Z: real,E22: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X3 @ Y3 ) ) @ E1 )
% 15.55/8.56       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y3 @ Z ) ) @ E22 )
% 15.55/8.56         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X3 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5268_norm__diff__triangle__le,axiom,
% 15.55/8.56      ! [X3: complex,Y3: complex,E1: real,Z: complex,E22: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Y3 ) ) @ E1 )
% 15.55/8.56       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y3 @ Z ) ) @ E22 )
% 15.55/8.56         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5269_norm__triangle__le__diff,axiom,
% 15.55/8.56      ! [X3: real,Y3: real,E2: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) @ E2 )
% 15.55/8.56       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X3 @ Y3 ) ) @ E2 ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5270_norm__triangle__le__diff,axiom,
% 15.55/8.56      ! [X3: complex,Y3: complex,E2: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) @ E2 )
% 15.55/8.56       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Y3 ) ) @ E2 ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5271_power__minus,axiom,
% 15.55/8.56      ! [A: real,N: nat] :
% 15.55/8.56        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 15.55/8.56        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ A @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5272_power__minus,axiom,
% 15.55/8.56      ! [A: int,N: nat] :
% 15.55/8.56        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 15.55/8.56        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5273_power__minus,axiom,
% 15.55/8.56      ! [A: complex,N: nat] :
% 15.55/8.56        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 15.55/8.56        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ A @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5274_power__minus,axiom,
% 15.55/8.56      ! [A: code_integer,N: nat] :
% 15.55/8.56        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 15.55/8.56        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5275_power__minus,axiom,
% 15.55/8.56      ! [A: rat,N: nat] :
% 15.55/8.56        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 15.55/8.56        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5276_norm__diff__ineq,axiom,
% 15.55/8.56      ! [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 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5277_norm__diff__ineq,axiom,
% 15.55/8.56      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5278_norm__triangle__ineq2,axiom,
% 15.55/8.56      ! [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 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5279_norm__triangle__ineq2,axiom,
% 15.55/8.56      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5280_power__minus__Bit0,axiom,
% 15.55/8.56      ! [X3: real,K: num] :
% 15.55/8.56        ( ( power_power_real @ ( uminus_uminus_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 15.55/8.56        = ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5281_power__minus__Bit0,axiom,
% 15.55/8.56      ! [X3: int,K: num] :
% 15.55/8.56        ( ( power_power_int @ ( uminus_uminus_int @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 15.55/8.56        = ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5282_power__minus__Bit0,axiom,
% 15.55/8.56      ! [X3: complex,K: num] :
% 15.55/8.56        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 15.55/8.56        = ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5283_power__minus__Bit0,axiom,
% 15.55/8.56      ! [X3: code_integer,K: num] :
% 15.55/8.56        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 15.55/8.56        = ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5284_power__minus__Bit0,axiom,
% 15.55/8.56      ! [X3: rat,K: num] :
% 15.55/8.56        ( ( power_power_rat @ ( uminus_uminus_rat @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 15.55/8.56        = ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5285_lemma__interval__lt,axiom,
% 15.55/8.56      ! [A: real,X3: real,B: real] :
% 15.55/8.56        ( ( ord_less_real @ A @ X3 )
% 15.55/8.56       => ( ( ord_less_real @ X3 @ B )
% 15.55/8.56         => ? [D6: real] :
% 15.55/8.56              ( ( ord_less_real @ zero_zero_real @ D6 )
% 15.55/8.56              & ! [Y6: real] :
% 15.55/8.56                  ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y6 ) ) @ D6 )
% 15.55/8.56                 => ( ( ord_less_real @ A @ Y6 )
% 15.55/8.56                    & ( ord_less_real @ Y6 @ B ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5286_sin__bound__lemma,axiom,
% 15.55/8.56      ! [X3: real,Y3: real,U: real,V: real] :
% 15.55/8.56        ( ( X3 = Y3 )
% 15.55/8.56       => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 15.55/8.56         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X3 @ U ) @ Y3 ) ) @ V ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5287_real__0__less__add__iff,axiom,
% 15.55/8.56      ! [X3: real,Y3: real] :
% 15.55/8.56        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X3 @ Y3 ) )
% 15.55/8.56        = ( ord_less_real @ ( uminus_uminus_real @ X3 ) @ Y3 ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5288_real__add__less__0__iff,axiom,
% 15.55/8.56      ! [X3: real,Y3: real] :
% 15.55/8.56        ( ( ord_less_real @ ( plus_plus_real @ X3 @ Y3 ) @ zero_zero_real )
% 15.55/8.56        = ( ord_less_real @ Y3 @ ( uminus_uminus_real @ X3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5289_real__0__le__add__iff,axiom,
% 15.55/8.56      ! [X3: real,Y3: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X3 @ Y3 ) )
% 15.55/8.56        = ( ord_less_eq_real @ ( uminus_uminus_real @ X3 ) @ Y3 ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5290_real__add__le__0__iff,axiom,
% 15.55/8.56      ! [X3: real,Y3: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( plus_plus_real @ X3 @ Y3 ) @ zero_zero_real )
% 15.55/8.56        = ( ord_less_eq_real @ Y3 @ ( uminus_uminus_real @ X3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5291_tanh__real__gt__neg1,axiom,
% 15.55/8.56      ! [X3: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X3 ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5292_abs__add__one__gt__zero,axiom,
% 15.55/8.56      ! [X3: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5293_abs__add__one__gt__zero,axiom,
% 15.55/8.56      ! [X3: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5294_abs__add__one__gt__zero,axiom,
% 15.55/8.56      ! [X3: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5295_abs__add__one__gt__zero,axiom,
% 15.55/8.56      ! [X3: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5296_of__int__leD,axiom,
% 15.55/8.56      ! [N: int,X3: code_integer] :
% 15.55/8.56        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X3 )
% 15.55/8.56       => ( ( N = zero_zero_int )
% 15.55/8.56          | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5297_of__int__leD,axiom,
% 15.55/8.56      ! [N: int,X3: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X3 )
% 15.55/8.56       => ( ( N = zero_zero_int )
% 15.55/8.56          | ( ord_less_eq_real @ one_one_real @ X3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5298_of__int__leD,axiom,
% 15.55/8.56      ! [N: int,X3: rat] :
% 15.55/8.56        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X3 )
% 15.55/8.56       => ( ( N = zero_zero_int )
% 15.55/8.56          | ( ord_less_eq_rat @ one_one_rat @ X3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5299_of__int__leD,axiom,
% 15.55/8.56      ! [N: int,X3: int] :
% 15.55/8.56        ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X3 )
% 15.55/8.56       => ( ( N = zero_zero_int )
% 15.55/8.56          | ( ord_less_eq_int @ one_one_int @ X3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5300_of__int__lessD,axiom,
% 15.55/8.56      ! [N: int,X3: code_integer] :
% 15.55/8.56        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X3 )
% 15.55/8.56       => ( ( N = zero_zero_int )
% 15.55/8.56          | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5301_of__int__lessD,axiom,
% 15.55/8.56      ! [N: int,X3: real] :
% 15.55/8.56        ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X3 )
% 15.55/8.56       => ( ( N = zero_zero_int )
% 15.55/8.56          | ( ord_less_real @ one_one_real @ X3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5302_of__int__lessD,axiom,
% 15.55/8.56      ! [N: int,X3: rat] :
% 15.55/8.56        ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X3 )
% 15.55/8.56       => ( ( N = zero_zero_int )
% 15.55/8.56          | ( ord_less_rat @ one_one_rat @ X3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5303_of__int__lessD,axiom,
% 15.55/8.56      ! [N: int,X3: int] :
% 15.55/8.56        ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X3 )
% 15.55/8.56       => ( ( N = zero_zero_int )
% 15.55/8.56          | ( ord_less_int @ one_one_int @ X3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5304_power__eq__1__iff,axiom,
% 15.55/8.56      ! [W: real,N: nat] :
% 15.55/8.56        ( ( ( power_power_real @ W @ N )
% 15.55/8.56          = one_one_real )
% 15.55/8.56       => ( ( ( real_V7735802525324610683m_real @ W )
% 15.55/8.56            = one_one_real )
% 15.55/8.56          | ( N = zero_zero_nat ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5305_power__eq__1__iff,axiom,
% 15.55/8.56      ! [W: complex,N: nat] :
% 15.55/8.56        ( ( ( power_power_complex @ W @ N )
% 15.55/8.56          = one_one_complex )
% 15.55/8.56       => ( ( ( real_V1022390504157884413omplex @ W )
% 15.55/8.56            = one_one_real )
% 15.55/8.56          | ( N = zero_zero_nat ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5306_norm__diff__triangle__ineq,axiom,
% 15.55/8.56      ! [A: real,B: real,C: real,D3: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D3 ) ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ C ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ D3 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5307_norm__diff__triangle__ineq,axiom,
% 15.55/8.56      ! [A: complex,B: complex,C: complex,D3: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ ( plus_plus_complex @ C @ D3 ) ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ C ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ D3 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5308_norm__less__p1,axiom,
% 15.55/8.56      ! [X3: real] : ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ ( real_V7735802525324610683m_real @ X3 ) ) @ one_one_real ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5309_norm__less__p1,axiom,
% 15.55/8.56      ! [X3: complex] : ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( real_V1022390504157884413omplex @ X3 ) ) @ one_one_complex ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5310_less__minus__divide__eq,axiom,
% 15.55/8.56      ! [A: real,B: real,C: real] :
% 15.55/8.56        ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 15.55/8.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.56           => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 15.55/8.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.56               => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 15.55/8.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.56               => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5311_less__minus__divide__eq,axiom,
% 15.55/8.56      ! [A: rat,B: rat,C: rat] :
% 15.55/8.56        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 15.55/8.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.56           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 15.55/8.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.56               => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 15.55/8.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.56               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5312_minus__divide__less__eq,axiom,
% 15.55/8.56      ! [B: real,C: real,A: real] :
% 15.55/8.56        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 15.55/8.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.56           => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 15.55/8.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.56               => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 15.55/8.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.56               => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5313_minus__divide__less__eq,axiom,
% 15.55/8.56      ! [B: rat,C: rat,A: rat] :
% 15.55/8.56        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 15.55/8.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.56           => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 15.55/8.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.56               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 15.55/8.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.56               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5314_neg__less__minus__divide__eq,axiom,
% 15.55/8.56      ! [C: real,A: real,B: real] :
% 15.55/8.56        ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.56       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 15.55/8.56          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5315_neg__less__minus__divide__eq,axiom,
% 15.55/8.56      ! [C: rat,A: rat,B: rat] :
% 15.55/8.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.56       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 15.55/8.56          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5316_neg__minus__divide__less__eq,axiom,
% 15.55/8.56      ! [C: real,B: real,A: real] :
% 15.55/8.56        ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.56       => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 15.55/8.56          = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5317_neg__minus__divide__less__eq,axiom,
% 15.55/8.56      ! [C: rat,B: rat,A: rat] :
% 15.55/8.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.56       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 15.55/8.56          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5318_pos__less__minus__divide__eq,axiom,
% 15.55/8.56      ! [C: real,A: real,B: real] :
% 15.55/8.56        ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.56       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 15.55/8.56          = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5319_pos__less__minus__divide__eq,axiom,
% 15.55/8.56      ! [C: rat,A: rat,B: rat] :
% 15.55/8.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.56       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 15.55/8.56          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5320_pos__minus__divide__less__eq,axiom,
% 15.55/8.56      ! [C: real,B: real,A: real] :
% 15.55/8.56        ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.56       => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 15.55/8.56          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5321_pos__minus__divide__less__eq,axiom,
% 15.55/8.56      ! [C: rat,B: rat,A: rat] :
% 15.55/8.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.56       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 15.55/8.56          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5322_divide__eq__eq__numeral_I2_J,axiom,
% 15.55/8.56      ! [B: real,C: real,W: num] :
% 15.55/8.56        ( ( ( divide_divide_real @ B @ C )
% 15.55/8.56          = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 15.55/8.56        = ( ( ( C != zero_zero_real )
% 15.55/8.56           => ( B
% 15.55/8.56              = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 15.55/8.56          & ( ( C = zero_zero_real )
% 15.55/8.56           => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 15.55/8.56              = zero_zero_real ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5323_divide__eq__eq__numeral_I2_J,axiom,
% 15.55/8.56      ! [B: complex,C: complex,W: num] :
% 15.55/8.56        ( ( ( divide1717551699836669952omplex @ B @ C )
% 15.55/8.56          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 15.55/8.56        = ( ( ( C != zero_zero_complex )
% 15.55/8.56           => ( B
% 15.55/8.56              = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 15.55/8.56          & ( ( C = zero_zero_complex )
% 15.55/8.56           => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 15.55/8.56              = zero_zero_complex ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5324_divide__eq__eq__numeral_I2_J,axiom,
% 15.55/8.56      ! [B: rat,C: rat,W: num] :
% 15.55/8.56        ( ( ( divide_divide_rat @ B @ C )
% 15.55/8.56          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 15.55/8.56        = ( ( ( C != zero_zero_rat )
% 15.55/8.56           => ( B
% 15.55/8.56              = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 15.55/8.56          & ( ( C = zero_zero_rat )
% 15.55/8.56           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 15.55/8.56              = zero_zero_rat ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5325_eq__divide__eq__numeral_I2_J,axiom,
% 15.55/8.56      ! [W: num,B: real,C: real] :
% 15.55/8.56        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 15.55/8.56          = ( divide_divide_real @ B @ C ) )
% 15.55/8.56        = ( ( ( C != zero_zero_real )
% 15.55/8.56           => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 15.55/8.56              = B ) )
% 15.55/8.56          & ( ( C = zero_zero_real )
% 15.55/8.56           => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 15.55/8.56              = zero_zero_real ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5326_eq__divide__eq__numeral_I2_J,axiom,
% 15.55/8.56      ! [W: num,B: complex,C: complex] :
% 15.55/8.56        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 15.55/8.56          = ( divide1717551699836669952omplex @ B @ C ) )
% 15.55/8.56        = ( ( ( C != zero_zero_complex )
% 15.55/8.56           => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 15.55/8.56              = B ) )
% 15.55/8.56          & ( ( C = zero_zero_complex )
% 15.55/8.56           => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 15.55/8.56              = zero_zero_complex ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5327_eq__divide__eq__numeral_I2_J,axiom,
% 15.55/8.56      ! [W: num,B: rat,C: rat] :
% 15.55/8.56        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 15.55/8.56          = ( divide_divide_rat @ B @ C ) )
% 15.55/8.56        = ( ( ( C != zero_zero_rat )
% 15.55/8.56           => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 15.55/8.56              = B ) )
% 15.55/8.56          & ( ( C = zero_zero_rat )
% 15.55/8.56           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 15.55/8.56              = zero_zero_rat ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5328_minus__divide__add__eq__iff,axiom,
% 15.55/8.56      ! [Z: real,X3: real,Y3: real] :
% 15.55/8.56        ( ( Z != zero_zero_real )
% 15.55/8.56       => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X3 @ Z ) ) @ Y3 )
% 15.55/8.56          = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X3 ) @ ( times_times_real @ Y3 @ Z ) ) @ Z ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5329_minus__divide__add__eq__iff,axiom,
% 15.55/8.56      ! [Z: complex,X3: complex,Y3: complex] :
% 15.55/8.56        ( ( Z != zero_zero_complex )
% 15.55/8.56       => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X3 @ Z ) ) @ Y3 )
% 15.55/8.56          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X3 ) @ ( times_times_complex @ Y3 @ Z ) ) @ Z ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5330_minus__divide__add__eq__iff,axiom,
% 15.55/8.56      ! [Z: rat,X3: rat,Y3: rat] :
% 15.55/8.56        ( ( Z != zero_zero_rat )
% 15.55/8.56       => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X3 @ Z ) ) @ Y3 )
% 15.55/8.56          = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X3 ) @ ( times_times_rat @ Y3 @ Z ) ) @ Z ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5331_add__divide__eq__if__simps_I3_J,axiom,
% 15.55/8.56      ! [Z: real,A: real,B: real] :
% 15.55/8.56        ( ( ( Z = zero_zero_real )
% 15.55/8.56         => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 15.55/8.56            = B ) )
% 15.55/8.56        & ( ( Z != zero_zero_real )
% 15.55/8.56         => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 15.55/8.56            = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5332_add__divide__eq__if__simps_I3_J,axiom,
% 15.55/8.56      ! [Z: complex,A: complex,B: complex] :
% 15.55/8.56        ( ( ( Z = zero_zero_complex )
% 15.55/8.56         => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 15.55/8.56            = B ) )
% 15.55/8.56        & ( ( Z != zero_zero_complex )
% 15.55/8.56         => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 15.55/8.56            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5333_add__divide__eq__if__simps_I3_J,axiom,
% 15.55/8.56      ! [Z: rat,A: rat,B: rat] :
% 15.55/8.56        ( ( ( Z = zero_zero_rat )
% 15.55/8.56         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 15.55/8.56            = B ) )
% 15.55/8.56        & ( ( Z != zero_zero_rat )
% 15.55/8.56         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 15.55/8.56            = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5334_minus__divide__diff__eq__iff,axiom,
% 15.55/8.56      ! [Z: real,X3: real,Y3: real] :
% 15.55/8.56        ( ( Z != zero_zero_real )
% 15.55/8.56       => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X3 @ Z ) ) @ Y3 )
% 15.55/8.56          = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X3 ) @ ( times_times_real @ Y3 @ Z ) ) @ Z ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5335_minus__divide__diff__eq__iff,axiom,
% 15.55/8.56      ! [Z: complex,X3: complex,Y3: complex] :
% 15.55/8.56        ( ( Z != zero_zero_complex )
% 15.55/8.56       => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X3 @ Z ) ) @ Y3 )
% 15.55/8.56          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X3 ) @ ( times_times_complex @ Y3 @ Z ) ) @ Z ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5336_minus__divide__diff__eq__iff,axiom,
% 15.55/8.56      ! [Z: rat,X3: rat,Y3: rat] :
% 15.55/8.56        ( ( Z != zero_zero_rat )
% 15.55/8.56       => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X3 @ Z ) ) @ Y3 )
% 15.55/8.56          = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X3 ) @ ( times_times_rat @ Y3 @ Z ) ) @ Z ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5337_add__divide__eq__if__simps_I5_J,axiom,
% 15.55/8.56      ! [Z: real,A: real,B: real] :
% 15.55/8.56        ( ( ( Z = zero_zero_real )
% 15.55/8.56         => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 15.55/8.56            = ( uminus_uminus_real @ B ) ) )
% 15.55/8.56        & ( ( Z != zero_zero_real )
% 15.55/8.56         => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 15.55/8.56            = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5338_add__divide__eq__if__simps_I5_J,axiom,
% 15.55/8.56      ! [Z: complex,A: complex,B: complex] :
% 15.55/8.56        ( ( ( Z = zero_zero_complex )
% 15.55/8.56         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 15.55/8.56            = ( uminus1482373934393186551omplex @ B ) ) )
% 15.55/8.56        & ( ( Z != zero_zero_complex )
% 15.55/8.56         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 15.55/8.56            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5339_add__divide__eq__if__simps_I5_J,axiom,
% 15.55/8.56      ! [Z: rat,A: rat,B: rat] :
% 15.55/8.56        ( ( ( Z = zero_zero_rat )
% 15.55/8.56         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 15.55/8.56            = ( uminus_uminus_rat @ B ) ) )
% 15.55/8.56        & ( ( Z != zero_zero_rat )
% 15.55/8.56         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 15.55/8.56            = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5340_add__divide__eq__if__simps_I6_J,axiom,
% 15.55/8.56      ! [Z: real,A: real,B: real] :
% 15.55/8.56        ( ( ( Z = zero_zero_real )
% 15.55/8.56         => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 15.55/8.56            = ( uminus_uminus_real @ B ) ) )
% 15.55/8.56        & ( ( Z != zero_zero_real )
% 15.55/8.56         => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 15.55/8.56            = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5341_add__divide__eq__if__simps_I6_J,axiom,
% 15.55/8.56      ! [Z: complex,A: complex,B: complex] :
% 15.55/8.56        ( ( ( Z = zero_zero_complex )
% 15.55/8.56         => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 15.55/8.56            = ( uminus1482373934393186551omplex @ B ) ) )
% 15.55/8.56        & ( ( Z != zero_zero_complex )
% 15.55/8.56         => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 15.55/8.56            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5342_add__divide__eq__if__simps_I6_J,axiom,
% 15.55/8.56      ! [Z: rat,A: rat,B: rat] :
% 15.55/8.56        ( ( ( Z = zero_zero_rat )
% 15.55/8.56         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 15.55/8.56            = ( uminus_uminus_rat @ B ) ) )
% 15.55/8.56        & ( ( Z != zero_zero_rat )
% 15.55/8.56         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 15.55/8.56            = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5343_even__minus,axiom,
% 15.55/8.56      ! [A: int] :
% 15.55/8.56        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 15.55/8.56        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5344_even__minus,axiom,
% 15.55/8.56      ! [A: code_integer] :
% 15.55/8.56        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 15.55/8.56        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5345_power2__eq__iff,axiom,
% 15.55/8.56      ! [X3: real,Y3: real] :
% 15.55/8.56        ( ( ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56          = ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.56        = ( ( X3 = Y3 )
% 15.55/8.56          | ( X3
% 15.55/8.56            = ( uminus_uminus_real @ Y3 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5346_power2__eq__iff,axiom,
% 15.55/8.56      ! [X3: int,Y3: int] :
% 15.55/8.56        ( ( ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56          = ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.56        = ( ( X3 = Y3 )
% 15.55/8.56          | ( X3
% 15.55/8.56            = ( uminus_uminus_int @ Y3 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5347_power2__eq__iff,axiom,
% 15.55/8.56      ! [X3: complex,Y3: complex] :
% 15.55/8.56        ( ( ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56          = ( power_power_complex @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.56        = ( ( X3 = Y3 )
% 15.55/8.56          | ( X3
% 15.55/8.56            = ( uminus1482373934393186551omplex @ Y3 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5348_power2__eq__iff,axiom,
% 15.55/8.56      ! [X3: code_integer,Y3: code_integer] :
% 15.55/8.56        ( ( ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56          = ( power_8256067586552552935nteger @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.56        = ( ( X3 = Y3 )
% 15.55/8.56          | ( X3
% 15.55/8.56            = ( uminus1351360451143612070nteger @ Y3 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5349_power2__eq__iff,axiom,
% 15.55/8.56      ! [X3: rat,Y3: rat] :
% 15.55/8.56        ( ( ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56          = ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.56        = ( ( X3 = Y3 )
% 15.55/8.56          | ( X3
% 15.55/8.56            = ( uminus_uminus_rat @ Y3 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5350_lemma__interval,axiom,
% 15.55/8.56      ! [A: real,X3: real,B: real] :
% 15.55/8.56        ( ( ord_less_real @ A @ X3 )
% 15.55/8.56       => ( ( ord_less_real @ X3 @ B )
% 15.55/8.56         => ? [D6: real] :
% 15.55/8.56              ( ( ord_less_real @ zero_zero_real @ D6 )
% 15.55/8.56              & ! [Y6: real] :
% 15.55/8.56                  ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y6 ) ) @ D6 )
% 15.55/8.56                 => ( ( ord_less_eq_real @ A @ Y6 )
% 15.55/8.56                    & ( ord_less_eq_real @ Y6 @ B ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5351_round__diff__minimal,axiom,
% 15.55/8.56      ! [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 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5352_round__diff__minimal,axiom,
% 15.55/8.56      ! [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 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5353_abs__le__square__iff,axiom,
% 15.55/8.56      ! [X3: code_integer,Y3: code_integer] :
% 15.55/8.56        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X3 ) @ ( abs_abs_Code_integer @ Y3 ) )
% 15.55/8.56        = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5354_abs__le__square__iff,axiom,
% 15.55/8.56      ! [X3: real,Y3: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ ( abs_abs_real @ Y3 ) )
% 15.55/8.56        = ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5355_abs__le__square__iff,axiom,
% 15.55/8.56      ! [X3: rat,Y3: rat] :
% 15.55/8.56        ( ( ord_less_eq_rat @ ( abs_abs_rat @ X3 ) @ ( abs_abs_rat @ Y3 ) )
% 15.55/8.56        = ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5356_abs__le__square__iff,axiom,
% 15.55/8.56      ! [X3: int,Y3: int] :
% 15.55/8.56        ( ( ord_less_eq_int @ ( abs_abs_int @ X3 ) @ ( abs_abs_int @ Y3 ) )
% 15.55/8.56        = ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5357_abs__square__eq__1,axiom,
% 15.55/8.56      ! [X3: code_integer] :
% 15.55/8.56        ( ( ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56          = one_one_Code_integer )
% 15.55/8.56        = ( ( abs_abs_Code_integer @ X3 )
% 15.55/8.56          = one_one_Code_integer ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5358_abs__square__eq__1,axiom,
% 15.55/8.56      ! [X3: rat] :
% 15.55/8.56        ( ( ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56          = one_one_rat )
% 15.55/8.56        = ( ( abs_abs_rat @ X3 )
% 15.55/8.56          = one_one_rat ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5359_abs__square__eq__1,axiom,
% 15.55/8.56      ! [X3: int] :
% 15.55/8.56        ( ( ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56          = one_one_int )
% 15.55/8.56        = ( ( abs_abs_int @ X3 )
% 15.55/8.56          = one_one_int ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5360_abs__square__eq__1,axiom,
% 15.55/8.56      ! [X3: real] :
% 15.55/8.56        ( ( ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56          = one_one_real )
% 15.55/8.56        = ( ( abs_abs_real @ X3 )
% 15.55/8.56          = one_one_real ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5361_power__even__abs,axiom,
% 15.55/8.56      ! [N: nat,A: code_integer] :
% 15.55/8.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56       => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N )
% 15.55/8.56          = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5362_power__even__abs,axiom,
% 15.55/8.56      ! [N: nat,A: rat] :
% 15.55/8.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56       => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ N )
% 15.55/8.56          = ( power_power_rat @ A @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5363_power__even__abs,axiom,
% 15.55/8.56      ! [N: nat,A: int] :
% 15.55/8.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56       => ( ( power_power_int @ ( abs_abs_int @ A ) @ N )
% 15.55/8.56          = ( power_power_int @ A @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5364_power__even__abs,axiom,
% 15.55/8.56      ! [N: nat,A: real] :
% 15.55/8.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56       => ( ( power_power_real @ ( abs_abs_real @ A ) @ N )
% 15.55/8.56          = ( power_power_real @ A @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5365_le__minus__divide__eq,axiom,
% 15.55/8.56      ! [A: real,B: real,C: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 15.55/8.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.56           => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 15.55/8.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.56               => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 15.55/8.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.56               => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5366_le__minus__divide__eq,axiom,
% 15.55/8.56      ! [A: rat,B: rat,C: rat] :
% 15.55/8.56        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 15.55/8.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.56           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 15.55/8.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.56               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 15.55/8.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.56               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5367_minus__divide__le__eq,axiom,
% 15.55/8.56      ! [B: real,C: real,A: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 15.55/8.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.56           => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 15.55/8.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.56               => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 15.55/8.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.56               => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5368_minus__divide__le__eq,axiom,
% 15.55/8.56      ! [B: rat,C: rat,A: rat] :
% 15.55/8.56        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 15.55/8.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.56           => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 15.55/8.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.56               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 15.55/8.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.56               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5369_neg__le__minus__divide__eq,axiom,
% 15.55/8.56      ! [C: real,A: real,B: real] :
% 15.55/8.56        ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.56       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 15.55/8.56          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5370_neg__le__minus__divide__eq,axiom,
% 15.55/8.56      ! [C: rat,A: rat,B: rat] :
% 15.55/8.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.56       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 15.55/8.56          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5371_neg__minus__divide__le__eq,axiom,
% 15.55/8.56      ! [C: real,B: real,A: real] :
% 15.55/8.56        ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.56       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 15.55/8.56          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5372_neg__minus__divide__le__eq,axiom,
% 15.55/8.56      ! [C: rat,B: rat,A: rat] :
% 15.55/8.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.56       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 15.55/8.56          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5373_pos__le__minus__divide__eq,axiom,
% 15.55/8.56      ! [C: real,A: real,B: real] :
% 15.55/8.56        ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.56       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 15.55/8.56          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5374_pos__le__minus__divide__eq,axiom,
% 15.55/8.56      ! [C: rat,A: rat,B: rat] :
% 15.55/8.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.56       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 15.55/8.56          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5375_pos__minus__divide__le__eq,axiom,
% 15.55/8.56      ! [C: real,B: real,A: real] :
% 15.55/8.56        ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.56       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 15.55/8.56          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5376_pos__minus__divide__le__eq,axiom,
% 15.55/8.56      ! [C: rat,B: rat,A: rat] :
% 15.55/8.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.56       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 15.55/8.56          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5377_divide__less__eq__numeral_I2_J,axiom,
% 15.55/8.56      ! [B: real,C: real,W: num] :
% 15.55/8.56        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 15.55/8.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.56           => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 15.55/8.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.56               => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 15.55/8.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.56               => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5378_divide__less__eq__numeral_I2_J,axiom,
% 15.55/8.56      ! [B: rat,C: rat,W: num] :
% 15.55/8.56        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 15.55/8.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.56           => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 15.55/8.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.56               => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 15.55/8.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.56               => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5379_less__divide__eq__numeral_I2_J,axiom,
% 15.55/8.56      ! [W: num,B: real,C: real] :
% 15.55/8.56        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 15.55/8.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.56           => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 15.55/8.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.56               => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 15.55/8.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.56               => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5380_less__divide__eq__numeral_I2_J,axiom,
% 15.55/8.56      ! [W: num,B: rat,C: rat] :
% 15.55/8.56        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 15.55/8.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.56           => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 15.55/8.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.56               => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 15.55/8.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.56               => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5381_norm__power__diff,axiom,
% 15.55/8.56      ! [Z: real,W: real,M: nat] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 15.55/8.56       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W ) @ one_one_real )
% 15.55/8.56         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( power_power_real @ Z @ M ) @ ( power_power_real @ W @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Z @ W ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5382_norm__power__diff,axiom,
% 15.55/8.56      ! [Z: complex,W: complex,M: nat] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 15.55/8.56       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 15.55/8.56         => ( 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 ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5383_power2__eq__1__iff,axiom,
% 15.55/8.56      ! [A: real] :
% 15.55/8.56        ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56          = one_one_real )
% 15.55/8.56        = ( ( A = one_one_real )
% 15.55/8.56          | ( A
% 15.55/8.56            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5384_power2__eq__1__iff,axiom,
% 15.55/8.56      ! [A: int] :
% 15.55/8.56        ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56          = one_one_int )
% 15.55/8.56        = ( ( A = one_one_int )
% 15.55/8.56          | ( A
% 15.55/8.56            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5385_power2__eq__1__iff,axiom,
% 15.55/8.56      ! [A: complex] :
% 15.55/8.56        ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56          = one_one_complex )
% 15.55/8.56        = ( ( A = one_one_complex )
% 15.55/8.56          | ( A
% 15.55/8.56            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5386_power2__eq__1__iff,axiom,
% 15.55/8.56      ! [A: code_integer] :
% 15.55/8.56        ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56          = one_one_Code_integer )
% 15.55/8.56        = ( ( A = one_one_Code_integer )
% 15.55/8.56          | ( A
% 15.55/8.56            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5387_power2__eq__1__iff,axiom,
% 15.55/8.56      ! [A: rat] :
% 15.55/8.56        ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56          = one_one_rat )
% 15.55/8.56        = ( ( A = one_one_rat )
% 15.55/8.56          | ( A
% 15.55/8.56            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5388_uminus__power__if,axiom,
% 15.55/8.56      ! [N: nat,A: real] :
% 15.55/8.56        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56         => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 15.55/8.56            = ( power_power_real @ A @ N ) ) )
% 15.55/8.56        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56         => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 15.55/8.56            = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5389_uminus__power__if,axiom,
% 15.55/8.56      ! [N: nat,A: int] :
% 15.55/8.56        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56         => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 15.55/8.56            = ( power_power_int @ A @ N ) ) )
% 15.55/8.56        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56         => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 15.55/8.56            = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5390_uminus__power__if,axiom,
% 15.55/8.56      ! [N: nat,A: complex] :
% 15.55/8.56        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 15.55/8.56            = ( power_power_complex @ A @ N ) ) )
% 15.55/8.56        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 15.55/8.56            = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5391_uminus__power__if,axiom,
% 15.55/8.56      ! [N: nat,A: code_integer] :
% 15.55/8.56        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 15.55/8.56            = ( power_8256067586552552935nteger @ A @ N ) ) )
% 15.55/8.56        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 15.55/8.56            = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5392_uminus__power__if,axiom,
% 15.55/8.56      ! [N: nat,A: rat] :
% 15.55/8.56        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56         => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 15.55/8.56            = ( power_power_rat @ A @ N ) ) )
% 15.55/8.56        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56         => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 15.55/8.56            = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5393_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 15.55/8.56      ! [K: nat,N: nat] :
% 15.55/8.56        ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.56       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K ) )
% 15.55/8.56          = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5394_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 15.55/8.56      ! [K: nat,N: nat] :
% 15.55/8.56        ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.56       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 15.55/8.56          = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5395_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 15.55/8.56      ! [K: nat,N: nat] :
% 15.55/8.56        ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.56       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K ) )
% 15.55/8.56          = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5396_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 15.55/8.56      ! [K: nat,N: nat] :
% 15.55/8.56        ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.56       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 15.55/8.56          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5397_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 15.55/8.56      ! [K: nat,N: nat] :
% 15.55/8.56        ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.56       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 15.55/8.56          = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5398_realpow__square__minus__le,axiom,
% 15.55/8.56      ! [U: real,X3: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5399_powr__neg__one,axiom,
% 15.55/8.56      ! [X3: real] :
% 15.55/8.56        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.56       => ( ( powr_real @ X3 @ ( uminus_uminus_real @ one_one_real ) )
% 15.55/8.56          = ( divide_divide_real @ one_one_real @ X3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5400_Bernoulli__inequality,axiom,
% 15.55/8.56      ! [X3: real,N: nat] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 15.55/8.56       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X3 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X3 ) @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5401_ln__add__one__self__le__self2,axiom,
% 15.55/8.56      ! [X3: real] :
% 15.55/8.56        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 15.55/8.56       => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X3 ) ) @ X3 ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5402_power2__le__iff__abs__le,axiom,
% 15.55/8.56      ! [Y3: code_integer,X3: code_integer] :
% 15.55/8.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y3 )
% 15.55/8.56       => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.56          = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X3 ) @ Y3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5403_power2__le__iff__abs__le,axiom,
% 15.55/8.56      ! [Y3: real,X3: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.56       => ( ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.56          = ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ Y3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5404_power2__le__iff__abs__le,axiom,
% 15.55/8.56      ! [Y3: rat,X3: rat] :
% 15.55/8.56        ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 15.55/8.56       => ( ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.56          = ( ord_less_eq_rat @ ( abs_abs_rat @ X3 ) @ Y3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5405_power2__le__iff__abs__le,axiom,
% 15.55/8.56      ! [Y3: int,X3: int] :
% 15.55/8.56        ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 15.55/8.56       => ( ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.56          = ( ord_less_eq_int @ ( abs_abs_int @ X3 ) @ Y3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5406_abs__square__le__1,axiom,
% 15.55/8.56      ! [X3: code_integer] :
% 15.55/8.56        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 15.55/8.56        = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X3 ) @ one_one_Code_integer ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5407_abs__square__le__1,axiom,
% 15.55/8.56      ! [X3: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 15.55/8.56        = ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5408_abs__square__le__1,axiom,
% 15.55/8.56      ! [X3: rat] :
% 15.55/8.56        ( ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 15.55/8.56        = ( ord_less_eq_rat @ ( abs_abs_rat @ X3 ) @ one_one_rat ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5409_abs__square__le__1,axiom,
% 15.55/8.56      ! [X3: int] :
% 15.55/8.56        ( ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 15.55/8.56        = ( ord_less_eq_int @ ( abs_abs_int @ X3 ) @ one_one_int ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5410_abs__square__less__1,axiom,
% 15.55/8.56      ! [X3: code_integer] :
% 15.55/8.56        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 15.55/8.56        = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X3 ) @ one_one_Code_integer ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5411_abs__square__less__1,axiom,
% 15.55/8.56      ! [X3: real] :
% 15.55/8.56        ( ( ord_less_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 15.55/8.56        = ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5412_abs__square__less__1,axiom,
% 15.55/8.56      ! [X3: rat] :
% 15.55/8.56        ( ( ord_less_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 15.55/8.56        = ( ord_less_rat @ ( abs_abs_rat @ X3 ) @ one_one_rat ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5413_abs__square__less__1,axiom,
% 15.55/8.56      ! [X3: int] :
% 15.55/8.56        ( ( ord_less_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 15.55/8.56        = ( ord_less_int @ ( abs_abs_int @ X3 ) @ one_one_int ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5414_power__mono__even,axiom,
% 15.55/8.56      ! [N: nat,A: code_integer,B: code_integer] :
% 15.55/8.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56       => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 15.55/8.56         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5415_power__mono__even,axiom,
% 15.55/8.56      ! [N: nat,A: real,B: real] :
% 15.55/8.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56       => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 15.55/8.56         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5416_power__mono__even,axiom,
% 15.55/8.56      ! [N: nat,A: rat,B: rat] :
% 15.55/8.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56       => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 15.55/8.56         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5417_power__mono__even,axiom,
% 15.55/8.56      ! [N: nat,A: int,B: int] :
% 15.55/8.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56       => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 15.55/8.56         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5418_square__norm__one,axiom,
% 15.55/8.56      ! [X3: real] :
% 15.55/8.56        ( ( ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56          = one_one_real )
% 15.55/8.56       => ( ( real_V7735802525324610683m_real @ X3 )
% 15.55/8.56          = one_one_real ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5419_square__norm__one,axiom,
% 15.55/8.56      ! [X3: complex] :
% 15.55/8.56        ( ( ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56          = one_one_complex )
% 15.55/8.56       => ( ( real_V1022390504157884413omplex @ X3 )
% 15.55/8.56          = one_one_real ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5420_le__divide__eq__numeral_I2_J,axiom,
% 15.55/8.56      ! [W: num,B: real,C: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 15.55/8.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.56           => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 15.55/8.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.56               => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 15.55/8.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.56               => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5421_le__divide__eq__numeral_I2_J,axiom,
% 15.55/8.56      ! [W: num,B: rat,C: rat] :
% 15.55/8.56        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 15.55/8.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.56           => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 15.55/8.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.56               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 15.55/8.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.56               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5422_divide__le__eq__numeral_I2_J,axiom,
% 15.55/8.56      ! [B: real,C: real,W: num] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 15.55/8.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.56           => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 15.55/8.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.56               => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 15.55/8.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 15.55/8.56               => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5423_divide__le__eq__numeral_I2_J,axiom,
% 15.55/8.56      ! [B: rat,C: rat,W: num] :
% 15.55/8.56        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 15.55/8.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.56           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 15.55/8.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 15.55/8.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.56               => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 15.55/8.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 15.55/8.56               => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5424_sqrt__ge__absD,axiom,
% 15.55/8.56      ! [X3: real,Y3: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ ( sqrt @ Y3 ) )
% 15.55/8.56       => ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y3 ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5425_square__le__1,axiom,
% 15.55/8.56      ! [X3: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 15.55/8.56       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 15.55/8.56         => ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5426_square__le__1,axiom,
% 15.55/8.56      ! [X3: code_integer] :
% 15.55/8.56        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X3 )
% 15.55/8.56       => ( ( ord_le3102999989581377725nteger @ X3 @ one_one_Code_integer )
% 15.55/8.56         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5427_square__le__1,axiom,
% 15.55/8.56      ! [X3: rat] :
% 15.55/8.56        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X3 )
% 15.55/8.56       => ( ( ord_less_eq_rat @ X3 @ one_one_rat )
% 15.55/8.56         => ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5428_square__le__1,axiom,
% 15.55/8.56      ! [X3: int] :
% 15.55/8.56        ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X3 )
% 15.55/8.56       => ( ( ord_less_eq_int @ X3 @ one_one_int )
% 15.55/8.56         => ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5429_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 15.55/8.56      ! [X3: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 15.55/8.56       => ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 15.55/8.56         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X3 ) ) @ X3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5430_minus__power__mult__self,axiom,
% 15.55/8.56      ! [A: real,N: nat] :
% 15.55/8.56        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 15.55/8.56        = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5431_minus__power__mult__self,axiom,
% 15.55/8.56      ! [A: int,N: nat] :
% 15.55/8.56        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 15.55/8.56        = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5432_minus__power__mult__self,axiom,
% 15.55/8.56      ! [A: complex,N: nat] :
% 15.55/8.56        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) )
% 15.55/8.56        = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5433_minus__power__mult__self,axiom,
% 15.55/8.56      ! [A: code_integer,N: nat] :
% 15.55/8.56        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 15.55/8.56        = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5434_minus__power__mult__self,axiom,
% 15.55/8.56      ! [A: rat,N: nat] :
% 15.55/8.56        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 15.55/8.56        = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5435_minus__one__power__iff,axiom,
% 15.55/8.56      ! [N: nat] :
% 15.55/8.56        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56         => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 15.55/8.56            = one_one_real ) )
% 15.55/8.56        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56         => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 15.55/8.56            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5436_minus__one__power__iff,axiom,
% 15.55/8.56      ! [N: nat] :
% 15.55/8.56        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56         => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 15.55/8.56            = one_one_int ) )
% 15.55/8.56        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56         => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 15.55/8.56            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5437_minus__one__power__iff,axiom,
% 15.55/8.56      ! [N: nat] :
% 15.55/8.56        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 15.55/8.56            = one_one_complex ) )
% 15.55/8.56        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 15.55/8.56            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5438_minus__one__power__iff,axiom,
% 15.55/8.56      ! [N: nat] :
% 15.55/8.56        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 15.55/8.56            = one_one_Code_integer ) )
% 15.55/8.56        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 15.55/8.56            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5439_minus__one__power__iff,axiom,
% 15.55/8.56      ! [N: nat] :
% 15.55/8.56        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56         => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 15.55/8.56            = one_one_rat ) )
% 15.55/8.56        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.56         => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 15.55/8.56            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5440_ln__one__minus__pos__upper__bound,axiom,
% 15.55/8.56      ! [X3: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.56       => ( ( ord_less_real @ X3 @ one_one_real )
% 15.55/8.56         => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X3 ) ) @ ( uminus_uminus_real @ X3 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5441_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 15.55/8.56      ! [X3: nat,N: nat,M: nat] :
% 15.55/8.56        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 15.55/8.56       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.56         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 15.55/8.56           => ( ord_less_nat @ ( vEBT_VEBT_low @ X3 @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5442_log__minus__eq__powr,axiom,
% 15.55/8.56      ! [B: real,X3: real,Y3: real] :
% 15.55/8.56        ( ( ord_less_real @ zero_zero_real @ B )
% 15.55/8.56       => ( ( B != one_one_real )
% 15.55/8.56         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.56           => ( ( minus_minus_real @ ( log @ B @ X3 ) @ Y3 )
% 15.55/8.56              = ( log @ B @ ( times_times_real @ X3 @ ( powr_real @ B @ ( uminus_uminus_real @ Y3 ) ) ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5443_real__sqrt__ge__abs1,axiom,
% 15.55/8.56      ! [X3: real,Y3: real] : ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5444_real__sqrt__ge__abs2,axiom,
% 15.55/8.56      ! [Y3: real,X3: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5445_sqrt__sum__squares__le__sum__abs,axiom,
% 15.55/8.56      ! [X3: real,Y3: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X3 ) @ ( abs_abs_real @ Y3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5446_power__minus1__odd,axiom,
% 15.55/8.56      ! [N: nat] :
% 15.55/8.56        ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 15.55/8.56        = ( uminus_uminus_real @ one_one_real ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5447_power__minus1__odd,axiom,
% 15.55/8.56      ! [N: nat] :
% 15.55/8.56        ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 15.55/8.56        = ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5448_power__minus1__odd,axiom,
% 15.55/8.56      ! [N: nat] :
% 15.55/8.56        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 15.55/8.56        = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5449_power__minus1__odd,axiom,
% 15.55/8.56      ! [N: nat] :
% 15.55/8.56        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 15.55/8.56        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5450_power__minus1__odd,axiom,
% 15.55/8.56      ! [N: nat] :
% 15.55/8.56        ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 15.55/8.56        = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5451_take__bit__Suc__minus__1__eq,axiom,
% 15.55/8.56      ! [N: nat] :
% 15.55/8.56        ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 15.55/8.56        = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_Code_integer ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5452_take__bit__Suc__minus__1__eq,axiom,
% 15.55/8.56      ! [N: nat] :
% 15.55/8.56        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.56        = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_int ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5453_take__bit__numeral__minus__1__eq,axiom,
% 15.55/8.56      ! [K: num] :
% 15.55/8.56        ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 15.55/8.56        = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5454_take__bit__numeral__minus__1__eq,axiom,
% 15.55/8.56      ! [K: num] :
% 15.55/8.56        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.56        = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5455_powr__neg__numeral,axiom,
% 15.55/8.56      ! [X3: real,N: num] :
% 15.55/8.56        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.56       => ( ( powr_real @ X3 @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 15.55/8.56          = ( divide_divide_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5456_of__int__round__abs__le,axiom,
% 15.55/8.56      ! [X3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X3 ) ) @ X3 ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5457_of__int__round__abs__le,axiom,
% 15.55/8.56      ! [X3: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X3 ) ) @ X3 ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5458_round__unique_H,axiom,
% 15.55/8.56      ! [X3: real,N: int] :
% 15.55/8.56        ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ ( ring_1_of_int_real @ N ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.56       => ( ( archim8280529875227126926d_real @ X3 )
% 15.55/8.56          = N ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5459_round__unique_H,axiom,
% 15.55/8.56      ! [X3: rat,N: int] :
% 15.55/8.56        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X3 @ ( ring_1_of_int_rat @ N ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 15.55/8.56       => ( ( archim7778729529865785530nd_rat @ X3 )
% 15.55/8.56          = N ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5460_cos__x__y__le__one,axiom,
% 15.55/8.56      ! [X3: real,Y3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X3 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5461_real__sqrt__sum__squares__less,axiom,
% 15.55/8.56      ! [X3: real,U: real,Y3: real] :
% 15.55/8.56        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 15.55/8.56       => ( ( ord_less_real @ ( abs_abs_real @ Y3 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 15.55/8.56         => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5462_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 15.55/8.56      ! [X3: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.56       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 15.55/8.56         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X3 ) ) @ X3 ) ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5463_mult__less__iff1,axiom,
% 15.55/8.56      ! [Z: real,X3: real,Y3: real] :
% 15.55/8.56        ( ( ord_less_real @ zero_zero_real @ Z )
% 15.55/8.56       => ( ( ord_less_real @ ( times_times_real @ X3 @ Z ) @ ( times_times_real @ Y3 @ Z ) )
% 15.55/8.56          = ( ord_less_real @ X3 @ Y3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5464_mult__less__iff1,axiom,
% 15.55/8.56      ! [Z: rat,X3: rat,Y3: rat] :
% 15.55/8.56        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 15.55/8.56       => ( ( ord_less_rat @ ( times_times_rat @ X3 @ Z ) @ ( times_times_rat @ Y3 @ Z ) )
% 15.55/8.56          = ( ord_less_rat @ X3 @ Y3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5465_mult__less__iff1,axiom,
% 15.55/8.56      ! [Z: int,X3: int,Y3: int] :
% 15.55/8.56        ( ( ord_less_int @ zero_zero_int @ Z )
% 15.55/8.56       => ( ( ord_less_int @ ( times_times_int @ X3 @ Z ) @ ( times_times_int @ Y3 @ Z ) )
% 15.55/8.56          = ( ord_less_int @ X3 @ Y3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5466_abs__sqrt__wlog,axiom,
% 15.55/8.56      ! [P: code_integer > code_integer > $o,X3: code_integer] :
% 15.55/8.56        ( ! [X4: code_integer] :
% 15.55/8.56            ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X4 )
% 15.55/8.56           => ( P @ X4 @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.56       => ( P @ ( abs_abs_Code_integer @ X3 ) @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5467_abs__sqrt__wlog,axiom,
% 15.55/8.56      ! [P: real > real > $o,X3: real] :
% 15.55/8.56        ( ! [X4: real] :
% 15.55/8.56            ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 15.55/8.56           => ( P @ X4 @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.56       => ( P @ ( abs_abs_real @ X3 ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5468_abs__sqrt__wlog,axiom,
% 15.55/8.56      ! [P: rat > rat > $o,X3: rat] :
% 15.55/8.56        ( ! [X4: rat] :
% 15.55/8.56            ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 15.55/8.56           => ( P @ X4 @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.56       => ( P @ ( abs_abs_rat @ X3 ) @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5469_abs__sqrt__wlog,axiom,
% 15.55/8.56      ! [P: int > int > $o,X3: int] :
% 15.55/8.56        ( ! [X4: int] :
% 15.55/8.56            ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 15.55/8.56           => ( P @ X4 @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.56       => ( P @ ( abs_abs_int @ X3 ) @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5470__C5_Ohyps_C_I9_J,axiom,
% 15.55/8.56      ( ( mi != ma )
% 15.55/8.56     => ! [I2: nat] :
% 15.55/8.56          ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 15.55/8.56         => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 15.55/8.56                = I2 )
% 15.55/8.56             => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 15.55/8.56            & ! [X6: nat] :
% 15.55/8.56                ( ( ( ( vEBT_VEBT_high @ X6 @ na )
% 15.55/8.56                    = I2 )
% 15.55/8.56                  & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ ( vEBT_VEBT_low @ X6 @ na ) ) )
% 15.55/8.56               => ( ( ord_less_nat @ mi @ X6 )
% 15.55/8.56                  & ( ord_less_eq_nat @ X6 @ ma ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5471_compl__le__compl__iff,axiom,
% 15.55/8.56      ! [X3: set_nat,Y3: set_nat] :
% 15.55/8.56        ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X3 ) @ ( uminus5710092332889474511et_nat @ Y3 ) )
% 15.55/8.56        = ( ord_less_eq_set_nat @ Y3 @ X3 ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5472_low__def,axiom,
% 15.55/8.56      ( vEBT_VEBT_low
% 15.55/8.56      = ( ^ [X: nat,N3: nat] : ( modulo_modulo_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5473_arctan__double,axiom,
% 15.55/8.56      ! [X3: real] :
% 15.55/8.56        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 15.55/8.56       => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X3 ) )
% 15.55/8.56          = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5474_pochhammer__double,axiom,
% 15.55/8.56      ! [Z: complex,N: nat] :
% 15.55/8.56        ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.56        = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5475_pochhammer__double,axiom,
% 15.55/8.56      ! [Z: real,N: nat] :
% 15.55/8.56        ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.56        = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5476_pochhammer__double,axiom,
% 15.55/8.56      ! [Z: rat,N: nat] :
% 15.55/8.56        ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.56        = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5477_mod__0,axiom,
% 15.55/8.56      ! [A: nat] :
% 15.55/8.56        ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 15.55/8.56        = zero_zero_nat ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5478_mod__0,axiom,
% 15.55/8.56      ! [A: int] :
% 15.55/8.56        ( ( modulo_modulo_int @ zero_zero_int @ A )
% 15.55/8.56        = zero_zero_int ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5479_mod__0,axiom,
% 15.55/8.56      ! [A: code_integer] :
% 15.55/8.56        ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 15.55/8.56        = zero_z3403309356797280102nteger ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5480_mod__by__0,axiom,
% 15.55/8.56      ! [A: nat] :
% 15.55/8.56        ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 15.55/8.56        = A ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5481_mod__by__0,axiom,
% 15.55/8.56      ! [A: int] :
% 15.55/8.56        ( ( modulo_modulo_int @ A @ zero_zero_int )
% 15.55/8.56        = A ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5482_mod__by__0,axiom,
% 15.55/8.56      ! [A: code_integer] :
% 15.55/8.56        ( ( modulo364778990260209775nteger @ A @ zero_z3403309356797280102nteger )
% 15.55/8.56        = A ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5483_mod__self,axiom,
% 15.55/8.56      ! [A: nat] :
% 15.55/8.56        ( ( modulo_modulo_nat @ A @ A )
% 15.55/8.56        = zero_zero_nat ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5484_mod__self,axiom,
% 15.55/8.56      ! [A: int] :
% 15.55/8.56        ( ( modulo_modulo_int @ A @ A )
% 15.55/8.56        = zero_zero_int ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5485_mod__self,axiom,
% 15.55/8.56      ! [A: code_integer] :
% 15.55/8.56        ( ( modulo364778990260209775nteger @ A @ A )
% 15.55/8.56        = zero_z3403309356797280102nteger ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5486_bits__mod__0,axiom,
% 15.55/8.56      ! [A: nat] :
% 15.55/8.56        ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 15.55/8.56        = zero_zero_nat ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5487_bits__mod__0,axiom,
% 15.55/8.56      ! [A: int] :
% 15.55/8.56        ( ( modulo_modulo_int @ zero_zero_int @ A )
% 15.55/8.56        = zero_zero_int ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5488_bits__mod__0,axiom,
% 15.55/8.56      ! [A: code_integer] :
% 15.55/8.56        ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 15.55/8.56        = zero_z3403309356797280102nteger ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5489_mod__less,axiom,
% 15.55/8.56      ! [M: nat,N: nat] :
% 15.55/8.56        ( ( ord_less_nat @ M @ N )
% 15.55/8.56       => ( ( modulo_modulo_nat @ M @ N )
% 15.55/8.56          = M ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5490_arctan__eq__zero__iff,axiom,
% 15.55/8.56      ! [X3: real] :
% 15.55/8.56        ( ( ( arctan @ X3 )
% 15.55/8.56          = zero_zero_real )
% 15.55/8.56        = ( X3 = zero_zero_real ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5491_arctan__zero__zero,axiom,
% 15.55/8.56      ( ( arctan @ zero_zero_real )
% 15.55/8.56      = zero_zero_real ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5492_mod__mult__self2__is__0,axiom,
% 15.55/8.56      ! [A: nat,B: nat] :
% 15.55/8.56        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 15.55/8.56        = zero_zero_nat ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5493_mod__mult__self2__is__0,axiom,
% 15.55/8.56      ! [A: int,B: int] :
% 15.55/8.56        ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 15.55/8.56        = zero_zero_int ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5494_mod__mult__self2__is__0,axiom,
% 15.55/8.56      ! [A: code_integer,B: code_integer] :
% 15.55/8.56        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 15.55/8.56        = zero_z3403309356797280102nteger ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5495_mod__mult__self1__is__0,axiom,
% 15.55/8.56      ! [B: nat,A: nat] :
% 15.55/8.56        ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 15.55/8.56        = zero_zero_nat ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5496_mod__mult__self1__is__0,axiom,
% 15.55/8.56      ! [B: int,A: int] :
% 15.55/8.56        ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 15.55/8.56        = zero_zero_int ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5497_mod__mult__self1__is__0,axiom,
% 15.55/8.56      ! [B: code_integer,A: code_integer] :
% 15.55/8.56        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 15.55/8.56        = zero_z3403309356797280102nteger ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5498_mod__by__1,axiom,
% 15.55/8.56      ! [A: nat] :
% 15.55/8.56        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 15.55/8.56        = zero_zero_nat ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5499_mod__by__1,axiom,
% 15.55/8.56      ! [A: int] :
% 15.55/8.56        ( ( modulo_modulo_int @ A @ one_one_int )
% 15.55/8.56        = zero_zero_int ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5500_mod__by__1,axiom,
% 15.55/8.56      ! [A: code_integer] :
% 15.55/8.56        ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 15.55/8.56        = zero_z3403309356797280102nteger ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5501_bits__mod__by__1,axiom,
% 15.55/8.56      ! [A: nat] :
% 15.55/8.56        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 15.55/8.56        = zero_zero_nat ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5502_bits__mod__by__1,axiom,
% 15.55/8.56      ! [A: int] :
% 15.55/8.56        ( ( modulo_modulo_int @ A @ one_one_int )
% 15.55/8.56        = zero_zero_int ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5503_bits__mod__by__1,axiom,
% 15.55/8.56      ! [A: code_integer] :
% 15.55/8.56        ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 15.55/8.56        = zero_z3403309356797280102nteger ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5504_mod__div__trivial,axiom,
% 15.55/8.56      ! [A: nat,B: nat] :
% 15.55/8.56        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 15.55/8.56        = zero_zero_nat ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5505_mod__div__trivial,axiom,
% 15.55/8.56      ! [A: int,B: int] :
% 15.55/8.56        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 15.55/8.56        = zero_zero_int ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5506_mod__div__trivial,axiom,
% 15.55/8.56      ! [A: code_integer,B: code_integer] :
% 15.55/8.56        ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 15.55/8.56        = zero_z3403309356797280102nteger ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5507_bits__mod__div__trivial,axiom,
% 15.55/8.56      ! [A: nat,B: nat] :
% 15.55/8.56        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 15.55/8.56        = zero_zero_nat ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5508_bits__mod__div__trivial,axiom,
% 15.55/8.56      ! [A: int,B: int] :
% 15.55/8.56        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 15.55/8.56        = zero_zero_int ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5509_bits__mod__div__trivial,axiom,
% 15.55/8.56      ! [A: code_integer,B: code_integer] :
% 15.55/8.56        ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 15.55/8.56        = zero_z3403309356797280102nteger ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5510_dvd__imp__mod__0,axiom,
% 15.55/8.56      ! [A: nat,B: nat] :
% 15.55/8.56        ( ( dvd_dvd_nat @ A @ B )
% 15.55/8.56       => ( ( modulo_modulo_nat @ B @ A )
% 15.55/8.56          = zero_zero_nat ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5511_dvd__imp__mod__0,axiom,
% 15.55/8.56      ! [A: int,B: int] :
% 15.55/8.56        ( ( dvd_dvd_int @ A @ B )
% 15.55/8.56       => ( ( modulo_modulo_int @ B @ A )
% 15.55/8.56          = zero_zero_int ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5512_dvd__imp__mod__0,axiom,
% 15.55/8.56      ! [A: code_integer,B: code_integer] :
% 15.55/8.56        ( ( dvd_dvd_Code_integer @ A @ B )
% 15.55/8.56       => ( ( modulo364778990260209775nteger @ B @ A )
% 15.55/8.56          = zero_z3403309356797280102nteger ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5513_mod__by__Suc__0,axiom,
% 15.55/8.56      ! [M: nat] :
% 15.55/8.56        ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 15.55/8.56        = zero_zero_nat ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5514_negative__eq__positive,axiom,
% 15.55/8.56      ! [N: nat,M: nat] :
% 15.55/8.56        ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
% 15.55/8.56          = ( semiri1314217659103216013at_int @ M ) )
% 15.55/8.56        = ( ( N = zero_zero_nat )
% 15.55/8.56          & ( M = zero_zero_nat ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5515_pochhammer__0,axiom,
% 15.55/8.56      ! [A: complex] :
% 15.55/8.56        ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 15.55/8.56        = one_one_complex ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5516_pochhammer__0,axiom,
% 15.55/8.56      ! [A: real] :
% 15.55/8.56        ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 15.55/8.56        = one_one_real ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5517_pochhammer__0,axiom,
% 15.55/8.56      ! [A: rat] :
% 15.55/8.56        ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 15.55/8.56        = one_one_rat ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5518_pochhammer__0,axiom,
% 15.55/8.56      ! [A: nat] :
% 15.55/8.56        ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 15.55/8.56        = one_one_nat ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5519_pochhammer__0,axiom,
% 15.55/8.56      ! [A: int] :
% 15.55/8.56        ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 15.55/8.56        = one_one_int ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5520_negative__zle,axiom,
% 15.55/8.56      ! [N: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5521_zero__less__arctan__iff,axiom,
% 15.55/8.56      ! [X3: real] :
% 15.55/8.56        ( ( ord_less_real @ zero_zero_real @ ( arctan @ X3 ) )
% 15.55/8.56        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5522_arctan__less__zero__iff,axiom,
% 15.55/8.56      ! [X3: real] :
% 15.55/8.56        ( ( ord_less_real @ ( arctan @ X3 ) @ zero_zero_real )
% 15.55/8.56        = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5523_zero__le__arctan__iff,axiom,
% 15.55/8.56      ! [X3: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X3 ) )
% 15.55/8.56        = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5524_arctan__le__zero__iff,axiom,
% 15.55/8.56      ! [X3: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( arctan @ X3 ) @ zero_zero_real )
% 15.55/8.56        = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5525_zdvd1__eq,axiom,
% 15.55/8.56      ! [X3: int] :
% 15.55/8.56        ( ( dvd_dvd_int @ X3 @ one_one_int )
% 15.55/8.56        = ( ( abs_abs_int @ X3 )
% 15.55/8.56          = one_one_int ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5526__C5_Ohyps_C_I5_J,axiom,
% 15.55/8.56      ! [I2: nat] :
% 15.55/8.56        ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 15.55/8.56       => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ X8 ) )
% 15.55/8.56          = ( vEBT_V8194947554948674370ptions @ summary @ I2 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5527_mod__minus1__right,axiom,
% 15.55/8.56      ! [A: int] :
% 15.55/8.56        ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.56        = zero_zero_int ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5528_mod__minus1__right,axiom,
% 15.55/8.56      ! [A: code_integer] :
% 15.55/8.56        ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 15.55/8.56        = zero_z3403309356797280102nteger ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5529_negative__zless,axiom,
% 15.55/8.56      ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5530_nat__neg__numeral,axiom,
% 15.55/8.56      ! [K: num] :
% 15.55/8.56        ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 15.55/8.56        = zero_zero_nat ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5531_nat__zminus__int,axiom,
% 15.55/8.56      ! [N: nat] :
% 15.55/8.56        ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 15.55/8.56        = zero_zero_nat ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5532_zabs__less__one__iff,axiom,
% 15.55/8.56      ! [Z: int] :
% 15.55/8.56        ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 15.55/8.56        = ( Z = zero_zero_int ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5533_one__mod__two__eq__one,axiom,
% 15.55/8.56      ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56      = one_one_nat ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5534_one__mod__two__eq__one,axiom,
% 15.55/8.56      ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.56      = one_one_int ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5535_one__mod__two__eq__one,axiom,
% 15.55/8.56      ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 15.55/8.56      = one_one_Code_integer ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5536_bits__one__mod__two__eq__one,axiom,
% 15.55/8.56      ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56      = one_one_nat ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5537_bits__one__mod__two__eq__one,axiom,
% 15.55/8.56      ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.56      = one_one_int ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5538_bits__one__mod__two__eq__one,axiom,
% 15.55/8.56      ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 15.55/8.56      = one_one_Code_integer ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5539_even__mod__2__iff,axiom,
% 15.55/8.56      ! [A: nat] :
% 15.55/8.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.56        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5540_even__mod__2__iff,axiom,
% 15.55/8.56      ! [A: int] :
% 15.55/8.56        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 15.55/8.56        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5541_even__mod__2__iff,axiom,
% 15.55/8.56      ! [A: code_integer] :
% 15.55/8.56        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 15.55/8.56        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5542_mod2__Suc__Suc,axiom,
% 15.55/8.56      ! [M: nat] :
% 15.55/8.56        ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56        = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5543_Suc__times__numeral__mod__eq,axiom,
% 15.55/8.56      ! [K: num,N: nat] :
% 15.55/8.56        ( ( ( numeral_numeral_nat @ K )
% 15.55/8.56         != one_one_nat )
% 15.55/8.56       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 15.55/8.56          = one_one_nat ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5544_dvd__nat__abs__iff,axiom,
% 15.55/8.56      ! [N: nat,K: int] :
% 15.55/8.56        ( ( dvd_dvd_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 15.55/8.56        = ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5545_nat__abs__dvd__iff,axiom,
% 15.55/8.56      ! [K: int,N: nat] :
% 15.55/8.56        ( ( dvd_dvd_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 15.55/8.56        = ( dvd_dvd_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5546_not__mod__2__eq__1__eq__0,axiom,
% 15.55/8.56      ! [A: nat] :
% 15.55/8.56        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56         != one_one_nat )
% 15.55/8.56        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56          = zero_zero_nat ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5547_not__mod__2__eq__1__eq__0,axiom,
% 15.55/8.56      ! [A: int] :
% 15.55/8.56        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.56         != one_one_int )
% 15.55/8.56        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.56          = zero_zero_int ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5548_not__mod__2__eq__1__eq__0,axiom,
% 15.55/8.56      ! [A: code_integer] :
% 15.55/8.56        ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 15.55/8.56         != one_one_Code_integer )
% 15.55/8.56        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 15.55/8.56          = zero_z3403309356797280102nteger ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5549_not__mod__2__eq__0__eq__1,axiom,
% 15.55/8.56      ! [A: nat] :
% 15.55/8.56        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56         != zero_zero_nat )
% 15.55/8.56        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56          = one_one_nat ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5550_not__mod__2__eq__0__eq__1,axiom,
% 15.55/8.56      ! [A: int] :
% 15.55/8.56        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.56         != zero_zero_int )
% 15.55/8.56        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.56          = one_one_int ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5551_not__mod__2__eq__0__eq__1,axiom,
% 15.55/8.56      ! [A: code_integer] :
% 15.55/8.56        ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 15.55/8.56         != zero_z3403309356797280102nteger )
% 15.55/8.56        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 15.55/8.56          = one_one_Code_integer ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5552_bits__minus__1__mod__2__eq,axiom,
% 15.55/8.56      ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.56      = one_one_int ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5553_bits__minus__1__mod__2__eq,axiom,
% 15.55/8.56      ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 15.55/8.56      = one_one_Code_integer ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5554_minus__1__mod__2__eq,axiom,
% 15.55/8.56      ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.56      = one_one_int ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5555_minus__1__mod__2__eq,axiom,
% 15.55/8.56      ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 15.55/8.56      = one_one_Code_integer ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5556_not__mod2__eq__Suc__0__eq__0,axiom,
% 15.55/8.56      ! [N: nat] :
% 15.55/8.56        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56         != ( suc @ zero_zero_nat ) )
% 15.55/8.56        = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56          = zero_zero_nat ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5557_add__self__mod__2,axiom,
% 15.55/8.56      ! [M: nat] :
% 15.55/8.56        ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56        = zero_zero_nat ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5558_ceiling__divide__eq__div__numeral,axiom,
% 15.55/8.56      ! [A: num,B: num] :
% 15.55/8.56        ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 15.55/8.56        = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5559_take__bit__Suc__0,axiom,
% 15.55/8.56      ! [A: code_integer] :
% 15.55/8.56        ( ( bit_se1745604003318907178nteger @ ( suc @ zero_zero_nat ) @ A )
% 15.55/8.56        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5560_take__bit__Suc__0,axiom,
% 15.55/8.56      ! [A: int] :
% 15.55/8.56        ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 15.55/8.56        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5561_take__bit__Suc__0,axiom,
% 15.55/8.56      ! [A: nat] :
% 15.55/8.56        ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 15.55/8.56        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5562_mod2__gr__0,axiom,
% 15.55/8.56      ! [M: nat] :
% 15.55/8.56        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.56        = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.56          = one_one_nat ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5563_floor__minus__divide__eq__div__numeral,axiom,
% 15.55/8.56      ! [A: num,B: num] :
% 15.55/8.56        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 15.55/8.56        = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5564_ceiling__minus__divide__eq__div__numeral,axiom,
% 15.55/8.56      ! [A: num,B: num] :
% 15.55/8.56        ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 15.55/8.56        = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5565__C5_Ohyps_C_I6_J,axiom,
% 15.55/8.56      ( ( mi = ma )
% 15.55/8.56     => ! [X6: vEBT_VEBT] :
% 15.55/8.56          ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ treeList ) )
% 15.55/8.56         => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_12 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5566_floor__minus__one__divide__eq__div__numeral,axiom,
% 15.55/8.56      ! [B: num] :
% 15.55/8.56        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 15.55/8.56        = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5567_even__succ__mod__exp,axiom,
% 15.55/8.56      ! [A: nat,N: nat] :
% 15.55/8.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.55/8.56       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.56         => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.56            = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5568_even__succ__mod__exp,axiom,
% 15.55/8.56      ! [A: int,N: nat] :
% 15.55/8.56        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.55/8.56       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.56         => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.56            = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5569_even__succ__mod__exp,axiom,
% 15.55/8.56      ! [A: code_integer,N: nat] :
% 15.55/8.56        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.55/8.56       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.56         => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.56            = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5570_pochhammer__of__int,axiom,
% 15.55/8.56      ! [X3: int,N: nat] :
% 15.55/8.56        ( ( comm_s7457072308508201937r_real @ ( ring_1_of_int_real @ X3 ) @ N )
% 15.55/8.56        = ( ring_1_of_int_real @ ( comm_s4660882817536571857er_int @ X3 @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5571_pochhammer__of__int,axiom,
% 15.55/8.56      ! [X3: int,N: nat] :
% 15.55/8.56        ( ( comm_s2602460028002588243omplex @ ( ring_17405671764205052669omplex @ X3 ) @ N )
% 15.55/8.56        = ( ring_17405671764205052669omplex @ ( comm_s4660882817536571857er_int @ X3 @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5572_pochhammer__of__int,axiom,
% 15.55/8.56      ! [X3: int,N: nat] :
% 15.55/8.56        ( ( comm_s4028243227959126397er_rat @ ( ring_1_of_int_rat @ X3 ) @ N )
% 15.55/8.56        = ( ring_1_of_int_rat @ ( comm_s4660882817536571857er_int @ X3 @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5573_pochhammer__of__nat,axiom,
% 15.55/8.56      ! [X3: nat,N: nat] :
% 15.55/8.56        ( ( comm_s2602460028002588243omplex @ ( semiri8010041392384452111omplex @ X3 ) @ N )
% 15.55/8.56        = ( semiri8010041392384452111omplex @ ( comm_s4663373288045622133er_nat @ X3 @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5574_pochhammer__of__nat,axiom,
% 15.55/8.56      ! [X3: nat,N: nat] :
% 15.55/8.56        ( ( comm_s7457072308508201937r_real @ ( semiri5074537144036343181t_real @ X3 ) @ N )
% 15.55/8.56        = ( semiri5074537144036343181t_real @ ( comm_s4663373288045622133er_nat @ X3 @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5575_pochhammer__of__nat,axiom,
% 15.55/8.56      ! [X3: nat,N: nat] :
% 15.55/8.56        ( ( comm_s4028243227959126397er_rat @ ( semiri681578069525770553at_rat @ X3 ) @ N )
% 15.55/8.56        = ( semiri681578069525770553at_rat @ ( comm_s4663373288045622133er_nat @ X3 @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5576_pochhammer__of__nat,axiom,
% 15.55/8.56      ! [X3: nat,N: nat] :
% 15.55/8.56        ( ( comm_s4663373288045622133er_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ N )
% 15.55/8.56        = ( semiri1316708129612266289at_nat @ ( comm_s4663373288045622133er_nat @ X3 @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5577_pochhammer__of__nat,axiom,
% 15.55/8.56      ! [X3: nat,N: nat] :
% 15.55/8.56        ( ( comm_s4660882817536571857er_int @ ( semiri1314217659103216013at_int @ X3 ) @ N )
% 15.55/8.56        = ( semiri1314217659103216013at_int @ ( comm_s4663373288045622133er_nat @ X3 @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5578_of__nat__mod,axiom,
% 15.55/8.56      ! [M: nat,N: nat] :
% 15.55/8.56        ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M @ N ) )
% 15.55/8.56        = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5579_of__nat__mod,axiom,
% 15.55/8.56      ! [M: nat,N: nat] :
% 15.55/8.56        ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N ) )
% 15.55/8.56        = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5580_of__nat__mod,axiom,
% 15.55/8.56      ! [M: nat,N: nat] :
% 15.55/8.56        ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) )
% 15.55/8.56        = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5581_zabs__def,axiom,
% 15.55/8.56      ( abs_abs_int
% 15.55/8.56      = ( ^ [I4: int] : ( if_int @ ( ord_less_int @ I4 @ zero_zero_int ) @ ( uminus_uminus_int @ I4 ) @ I4 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5582_power__mod,axiom,
% 15.55/8.56      ! [A: nat,B: nat,N: nat] :
% 15.55/8.56        ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N ) @ B )
% 15.55/8.56        = ( modulo_modulo_nat @ ( power_power_nat @ A @ N ) @ B ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5583_power__mod,axiom,
% 15.55/8.56      ! [A: int,B: int,N: nat] :
% 15.55/8.56        ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N ) @ B )
% 15.55/8.56        = ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ B ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5584_power__mod,axiom,
% 15.55/8.56      ! [A: code_integer,B: code_integer,N: nat] :
% 15.55/8.56        ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( modulo364778990260209775nteger @ A @ B ) @ N ) @ B )
% 15.55/8.56        = ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ A @ N ) @ B ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5585_mod__less__eq__dividend,axiom,
% 15.55/8.56      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5586_uminus__int__code_I1_J,axiom,
% 15.55/8.56      ( ( uminus_uminus_int @ zero_zero_int )
% 15.55/8.56      = zero_zero_int ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5587_zdvd__antisym__abs,axiom,
% 15.55/8.56      ! [A: int,B: int] :
% 15.55/8.56        ( ( dvd_dvd_int @ A @ B )
% 15.55/8.56       => ( ( dvd_dvd_int @ B @ A )
% 15.55/8.56         => ( ( abs_abs_int @ A )
% 15.55/8.56            = ( abs_abs_int @ B ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5588_arctan__less__iff,axiom,
% 15.55/8.56      ! [X3: real,Y3: real] :
% 15.55/8.56        ( ( ord_less_real @ ( arctan @ X3 ) @ ( arctan @ Y3 ) )
% 15.55/8.56        = ( ord_less_real @ X3 @ Y3 ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5589_arctan__monotone,axiom,
% 15.55/8.56      ! [X3: real,Y3: real] :
% 15.55/8.56        ( ( ord_less_real @ X3 @ Y3 )
% 15.55/8.56       => ( ord_less_real @ ( arctan @ X3 ) @ ( arctan @ Y3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5590_arctan__le__iff,axiom,
% 15.55/8.56      ! [X3: real,Y3: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ ( arctan @ X3 ) @ ( arctan @ Y3 ) )
% 15.55/8.56        = ( ord_less_eq_real @ X3 @ Y3 ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5591_arctan__monotone_H,axiom,
% 15.55/8.56      ! [X3: real,Y3: real] :
% 15.55/8.56        ( ( ord_less_eq_real @ X3 @ Y3 )
% 15.55/8.56       => ( ord_less_eq_real @ ( arctan @ X3 ) @ ( arctan @ Y3 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5592_int__cases2,axiom,
% 15.55/8.56      ! [Z: int] :
% 15.55/8.56        ( ! [N2: nat] :
% 15.55/8.56            ( Z
% 15.55/8.56           != ( semiri1314217659103216013at_int @ N2 ) )
% 15.55/8.56       => ~ ! [N2: nat] :
% 15.55/8.56              ( Z
% 15.55/8.56             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5593_uminus__dvd__conv_I2_J,axiom,
% 15.55/8.56      ( dvd_dvd_int
% 15.55/8.56      = ( ^ [D4: int,T2: int] : ( dvd_dvd_int @ D4 @ ( uminus_uminus_int @ T2 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5594_uminus__dvd__conv_I1_J,axiom,
% 15.55/8.56      ( dvd_dvd_int
% 15.55/8.56      = ( ^ [D4: int] : ( dvd_dvd_int @ ( uminus_uminus_int @ D4 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5595_take__bit__minus,axiom,
% 15.55/8.56      ! [N: nat,K: int] :
% 15.55/8.56        ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 15.55/8.56        = ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5596_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 15.55/8.56      ! [A: code_integer,B: code_integer] :
% 15.55/8.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 15.55/8.56       => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B ) @ A ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5597_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 15.55/8.56      ! [A: nat,B: nat] :
% 15.55/8.56        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.55/8.56       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5598_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 15.55/8.56      ! [A: int,B: int] :
% 15.55/8.56        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.56       => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5599_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 15.55/8.56      ! [B: nat,A: nat] :
% 15.55/8.56        ( ( ord_less_nat @ zero_zero_nat @ B )
% 15.55/8.56       => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5600_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 15.55/8.56      ! [B: int,A: int] :
% 15.55/8.56        ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.56       => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5601_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 15.55/8.56      ! [B: code_integer,A: code_integer] :
% 15.55/8.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 15.55/8.56       => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5602_cong__exp__iff__simps_I9_J,axiom,
% 15.55/8.56      ! [M: num,Q3: num,N: num] :
% 15.55/8.56        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 15.55/8.56          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 15.55/8.56        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 15.55/8.56          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q3 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5603_cong__exp__iff__simps_I9_J,axiom,
% 15.55/8.56      ! [M: num,Q3: num,N: num] :
% 15.55/8.56        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 15.55/8.56          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 15.55/8.56        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 15.55/8.56          = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q3 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5604_cong__exp__iff__simps_I9_J,axiom,
% 15.55/8.56      ! [M: num,Q3: num,N: num] :
% 15.55/8.56        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 15.55/8.56          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 15.55/8.56        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 15.55/8.56          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q3 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5605_mod__eq__self__iff__div__eq__0,axiom,
% 15.55/8.56      ! [A: nat,B: nat] :
% 15.55/8.56        ( ( ( modulo_modulo_nat @ A @ B )
% 15.55/8.56          = A )
% 15.55/8.56        = ( ( divide_divide_nat @ A @ B )
% 15.55/8.56          = zero_zero_nat ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5606_mod__eq__self__iff__div__eq__0,axiom,
% 15.55/8.56      ! [A: int,B: int] :
% 15.55/8.56        ( ( ( modulo_modulo_int @ A @ B )
% 15.55/8.56          = A )
% 15.55/8.56        = ( ( divide_divide_int @ A @ B )
% 15.55/8.56          = zero_zero_int ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5607_mod__eq__self__iff__div__eq__0,axiom,
% 15.55/8.56      ! [A: code_integer,B: code_integer] :
% 15.55/8.56        ( ( ( modulo364778990260209775nteger @ A @ B )
% 15.55/8.56          = A )
% 15.55/8.56        = ( ( divide6298287555418463151nteger @ A @ B )
% 15.55/8.56          = zero_z3403309356797280102nteger ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5608_cong__exp__iff__simps_I4_J,axiom,
% 15.55/8.56      ! [M: num,N: num] :
% 15.55/8.56        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 15.55/8.56        = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5609_cong__exp__iff__simps_I4_J,axiom,
% 15.55/8.56      ! [M: num,N: num] :
% 15.55/8.56        ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 15.55/8.56        = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5610_cong__exp__iff__simps_I4_J,axiom,
% 15.55/8.56      ! [M: num,N: num] :
% 15.55/8.56        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ one ) )
% 15.55/8.56        = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5611_mod__0__imp__dvd,axiom,
% 15.55/8.56      ! [A: nat,B: nat] :
% 15.55/8.56        ( ( ( modulo_modulo_nat @ A @ B )
% 15.55/8.56          = zero_zero_nat )
% 15.55/8.56       => ( dvd_dvd_nat @ B @ A ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5612_mod__0__imp__dvd,axiom,
% 15.55/8.56      ! [A: int,B: int] :
% 15.55/8.56        ( ( ( modulo_modulo_int @ A @ B )
% 15.55/8.56          = zero_zero_int )
% 15.55/8.56       => ( dvd_dvd_int @ B @ A ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5613_mod__0__imp__dvd,axiom,
% 15.55/8.56      ! [A: code_integer,B: code_integer] :
% 15.55/8.56        ( ( ( modulo364778990260209775nteger @ A @ B )
% 15.55/8.56          = zero_z3403309356797280102nteger )
% 15.55/8.56       => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5614_dvd__eq__mod__eq__0,axiom,
% 15.55/8.56      ( dvd_dvd_nat
% 15.55/8.56      = ( ^ [A4: nat,B3: nat] :
% 15.55/8.56            ( ( modulo_modulo_nat @ B3 @ A4 )
% 15.55/8.56            = zero_zero_nat ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5615_dvd__eq__mod__eq__0,axiom,
% 15.55/8.56      ( dvd_dvd_int
% 15.55/8.56      = ( ^ [A4: int,B3: int] :
% 15.55/8.56            ( ( modulo_modulo_int @ B3 @ A4 )
% 15.55/8.56            = zero_zero_int ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5616_dvd__eq__mod__eq__0,axiom,
% 15.55/8.56      ( dvd_dvd_Code_integer
% 15.55/8.56      = ( ^ [A4: code_integer,B3: code_integer] :
% 15.55/8.56            ( ( modulo364778990260209775nteger @ B3 @ A4 )
% 15.55/8.56            = zero_z3403309356797280102nteger ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5617_mod__eq__0__iff__dvd,axiom,
% 15.55/8.56      ! [A: nat,B: nat] :
% 15.55/8.56        ( ( ( modulo_modulo_nat @ A @ B )
% 15.55/8.56          = zero_zero_nat )
% 15.55/8.56        = ( dvd_dvd_nat @ B @ A ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5618_mod__eq__0__iff__dvd,axiom,
% 15.55/8.56      ! [A: int,B: int] :
% 15.55/8.56        ( ( ( modulo_modulo_int @ A @ B )
% 15.55/8.56          = zero_zero_int )
% 15.55/8.56        = ( dvd_dvd_int @ B @ A ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5619_mod__eq__0__iff__dvd,axiom,
% 15.55/8.56      ! [A: code_integer,B: code_integer] :
% 15.55/8.56        ( ( ( modulo364778990260209775nteger @ A @ B )
% 15.55/8.56          = zero_z3403309356797280102nteger )
% 15.55/8.56        = ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5620_mod__Suc,axiom,
% 15.55/8.56      ! [M: nat,N: nat] :
% 15.55/8.56        ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 15.55/8.56            = N )
% 15.55/8.56         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 15.55/8.56            = zero_zero_nat ) )
% 15.55/8.56        & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 15.55/8.56           != N )
% 15.55/8.56         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 15.55/8.56            = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5621_mod__induct,axiom,
% 15.55/8.56      ! [P: nat > $o,N: nat,P6: nat,M: nat] :
% 15.55/8.56        ( ( P @ N )
% 15.55/8.56       => ( ( ord_less_nat @ N @ P6 )
% 15.55/8.56         => ( ( ord_less_nat @ M @ P6 )
% 15.55/8.56           => ( ! [N2: nat] :
% 15.55/8.56                  ( ( ord_less_nat @ N2 @ P6 )
% 15.55/8.56                 => ( ( P @ N2 )
% 15.55/8.56                   => ( P @ ( modulo_modulo_nat @ ( suc @ N2 ) @ P6 ) ) ) )
% 15.55/8.56             => ( P @ M ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5622_mod__less__divisor,axiom,
% 15.55/8.56      ! [N: nat,M: nat] :
% 15.55/8.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.56       => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5623_gcd__nat__induct,axiom,
% 15.55/8.56      ! [P: nat > nat > $o,M: nat,N: nat] :
% 15.55/8.56        ( ! [M4: nat] : ( P @ M4 @ zero_zero_nat )
% 15.55/8.56       => ( ! [M4: nat,N2: nat] :
% 15.55/8.56              ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 15.55/8.56             => ( ( P @ N2 @ ( modulo_modulo_nat @ M4 @ N2 ) )
% 15.55/8.56               => ( P @ M4 @ N2 ) ) )
% 15.55/8.56         => ( P @ M @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5624_mod__Suc__le__divisor,axiom,
% 15.55/8.56      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5625_mod__eq__0D,axiom,
% 15.55/8.56      ! [M: nat,D3: nat] :
% 15.55/8.56        ( ( ( modulo_modulo_nat @ M @ D3 )
% 15.55/8.56          = zero_zero_nat )
% 15.55/8.56       => ? [Q4: nat] :
% 15.55/8.56            ( M
% 15.55/8.56            = ( times_times_nat @ D3 @ Q4 ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5626_mod__if,axiom,
% 15.55/8.56      ( modulo_modulo_nat
% 15.55/8.56      = ( ^ [M3: nat,N3: nat] : ( if_nat @ ( ord_less_nat @ M3 @ N3 ) @ M3 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M3 @ N3 ) @ N3 ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5627_mod__geq,axiom,
% 15.55/8.56      ! [M: nat,N: nat] :
% 15.55/8.56        ( ~ ( ord_less_nat @ M @ N )
% 15.55/8.56       => ( ( modulo_modulo_nat @ M @ N )
% 15.55/8.56          = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5628_le__mod__geq,axiom,
% 15.55/8.56      ! [N: nat,M: nat] :
% 15.55/8.56        ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.56       => ( ( modulo_modulo_nat @ M @ N )
% 15.55/8.56          = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5629_pochhammer__pos,axiom,
% 15.55/8.56      ! [X3: real,N: nat] :
% 15.55/8.56        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.56       => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X3 @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5630_pochhammer__pos,axiom,
% 15.55/8.56      ! [X3: rat,N: nat] :
% 15.55/8.56        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 15.55/8.56       => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X3 @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5631_pochhammer__pos,axiom,
% 15.55/8.56      ! [X3: nat,N: nat] :
% 15.55/8.56        ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 15.55/8.56       => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X3 @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5632_pochhammer__pos,axiom,
% 15.55/8.56      ! [X3: int,N: nat] :
% 15.55/8.56        ( ( ord_less_int @ zero_zero_int @ X3 )
% 15.55/8.56       => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X3 @ N ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5633_abs__zmult__eq__1,axiom,
% 15.55/8.56      ! [M: int,N: int] :
% 15.55/8.56        ( ( ( abs_abs_int @ ( times_times_int @ M @ N ) )
% 15.55/8.56          = one_one_int )
% 15.55/8.56       => ( ( abs_abs_int @ M )
% 15.55/8.56          = one_one_int ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5634_pochhammer__neq__0__mono,axiom,
% 15.55/8.56      ! [A: real,M: nat,N: nat] :
% 15.55/8.56        ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 15.55/8.56         != zero_zero_real )
% 15.55/8.56       => ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.56         => ( ( comm_s7457072308508201937r_real @ A @ N )
% 15.55/8.56           != zero_zero_real ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5635_pochhammer__neq__0__mono,axiom,
% 15.55/8.56      ! [A: rat,M: nat,N: nat] :
% 15.55/8.56        ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 15.55/8.56         != zero_zero_rat )
% 15.55/8.56       => ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.56         => ( ( comm_s4028243227959126397er_rat @ A @ N )
% 15.55/8.56           != zero_zero_rat ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5636_pochhammer__eq__0__mono,axiom,
% 15.55/8.56      ! [A: real,N: nat,M: nat] :
% 15.55/8.56        ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 15.55/8.56          = zero_zero_real )
% 15.55/8.56       => ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.56         => ( ( comm_s7457072308508201937r_real @ A @ M )
% 15.55/8.56            = zero_zero_real ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5637_pochhammer__eq__0__mono,axiom,
% 15.55/8.56      ! [A: rat,N: nat,M: nat] :
% 15.55/8.56        ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 15.55/8.56          = zero_zero_rat )
% 15.55/8.56       => ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.56         => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 15.55/8.56            = zero_zero_rat ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5638_int__cases,axiom,
% 15.55/8.56      ! [Z: int] :
% 15.55/8.56        ( ! [N2: nat] :
% 15.55/8.56            ( Z
% 15.55/8.56           != ( semiri1314217659103216013at_int @ N2 ) )
% 15.55/8.56       => ~ ! [N2: nat] :
% 15.55/8.56              ( Z
% 15.55/8.56             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5639_int__of__nat__induct,axiom,
% 15.55/8.56      ! [P: int > $o,Z: int] :
% 15.55/8.56        ( ! [N2: nat] : ( P @ ( semiri1314217659103216013at_int @ N2 ) )
% 15.55/8.56       => ( ! [N2: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) )
% 15.55/8.56         => ( P @ Z ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5640_zmult__eq__1__iff,axiom,
% 15.55/8.56      ! [M: int,N: int] :
% 15.55/8.56        ( ( ( times_times_int @ M @ N )
% 15.55/8.56          = one_one_int )
% 15.55/8.56        = ( ( ( M = one_one_int )
% 15.55/8.56            & ( N = one_one_int ) )
% 15.55/8.56          | ( ( M
% 15.55/8.56              = ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.56            & ( N
% 15.55/8.56              = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5641_pos__zmult__eq__1__iff__lemma,axiom,
% 15.55/8.56      ! [M: int,N: int] :
% 15.55/8.56        ( ( ( times_times_int @ M @ N )
% 15.55/8.56          = one_one_int )
% 15.55/8.56       => ( ( M = one_one_int )
% 15.55/8.56          | ( M
% 15.55/8.56            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5642_minus__int__code_I2_J,axiom,
% 15.55/8.56      ! [L: int] :
% 15.55/8.56        ( ( minus_minus_int @ zero_zero_int @ L )
% 15.55/8.56        = ( uminus_uminus_int @ L ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5643_not__int__zless__negative,axiom,
% 15.55/8.56      ! [N: nat,M: nat] :
% 15.55/8.56        ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5644_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 15.55/8.56      ! [A: code_integer,B: code_integer] :
% 15.55/8.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 15.55/8.56       => ( ( ord_le6747313008572928689nteger @ A @ B )
% 15.55/8.56         => ( ( modulo364778990260209775nteger @ A @ B )
% 15.55/8.56            = A ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5645_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 15.55/8.56      ! [A: nat,B: nat] :
% 15.55/8.56        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.55/8.56       => ( ( ord_less_nat @ A @ B )
% 15.55/8.56         => ( ( modulo_modulo_nat @ A @ B )
% 15.55/8.56            = A ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5646_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 15.55/8.56      ! [A: int,B: int] :
% 15.55/8.56        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.56       => ( ( ord_less_int @ A @ B )
% 15.55/8.56         => ( ( modulo_modulo_int @ A @ B )
% 15.55/8.56            = A ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5647_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 15.55/8.56      ! [B: code_integer,A: code_integer] :
% 15.55/8.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 15.55/8.56       => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5648_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 15.55/8.56      ! [B: nat,A: nat] :
% 15.55/8.56        ( ( ord_less_nat @ zero_zero_nat @ B )
% 15.55/8.56       => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5649_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 15.55/8.56      ! [B: int,A: int] :
% 15.55/8.56        ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.56       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5650_cong__exp__iff__simps_I2_J,axiom,
% 15.55/8.56      ! [N: num,Q3: num] :
% 15.55/8.56        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 15.55/8.56          = zero_zero_nat )
% 15.55/8.56        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q3 ) )
% 15.55/8.56          = zero_zero_nat ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5651_cong__exp__iff__simps_I2_J,axiom,
% 15.55/8.56      ! [N: num,Q3: num] :
% 15.55/8.56        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 15.55/8.56          = zero_zero_int )
% 15.55/8.56        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q3 ) )
% 15.55/8.56          = zero_zero_int ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5652_cong__exp__iff__simps_I2_J,axiom,
% 15.55/8.56      ! [N: num,Q3: num] :
% 15.55/8.56        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 15.55/8.56          = zero_z3403309356797280102nteger )
% 15.55/8.56        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 15.55/8.56          = zero_z3403309356797280102nteger ) ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5653_cong__exp__iff__simps_I1_J,axiom,
% 15.55/8.56      ! [N: num] :
% 15.55/8.56        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 15.55/8.56        = zero_zero_nat ) ).
% 15.55/8.56  
% 15.55/8.56  thf(fact_5654_cong__exp__iff__simps_I1_J,axiom,
% 15.55/8.56      ! [N: num] :
% 15.55/8.56        ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 15.55/8.57        = zero_zero_int ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5655_cong__exp__iff__simps_I1_J,axiom,
% 15.55/8.57      ! [N: num] :
% 15.55/8.57        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) )
% 15.55/8.57        = zero_z3403309356797280102nteger ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5656_cong__exp__iff__simps_I6_J,axiom,
% 15.55/8.57      ! [Q3: num,N: num] :
% 15.55/8.57        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 15.55/8.57       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5657_cong__exp__iff__simps_I6_J,axiom,
% 15.55/8.57      ! [Q3: num,N: num] :
% 15.55/8.57        ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 15.55/8.57       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5658_cong__exp__iff__simps_I6_J,axiom,
% 15.55/8.57      ! [Q3: num,N: num] :
% 15.55/8.57        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 15.55/8.57       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5659_cong__exp__iff__simps_I8_J,axiom,
% 15.55/8.57      ! [M: num,Q3: num] :
% 15.55/8.57        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 15.55/8.57       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5660_cong__exp__iff__simps_I8_J,axiom,
% 15.55/8.57      ! [M: num,Q3: num] :
% 15.55/8.57        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 15.55/8.57       != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5661_cong__exp__iff__simps_I8_J,axiom,
% 15.55/8.57      ! [M: num,Q3: num] :
% 15.55/8.57        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 15.55/8.57       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5662_unit__imp__mod__eq__0,axiom,
% 15.55/8.57      ! [B: nat,A: nat] :
% 15.55/8.57        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 15.55/8.57       => ( ( modulo_modulo_nat @ A @ B )
% 15.55/8.57          = zero_zero_nat ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5663_unit__imp__mod__eq__0,axiom,
% 15.55/8.57      ! [B: int,A: int] :
% 15.55/8.57        ( ( dvd_dvd_int @ B @ one_one_int )
% 15.55/8.57       => ( ( modulo_modulo_int @ A @ B )
% 15.55/8.57          = zero_zero_int ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5664_unit__imp__mod__eq__0,axiom,
% 15.55/8.57      ! [B: code_integer,A: code_integer] :
% 15.55/8.57        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 15.55/8.57       => ( ( modulo364778990260209775nteger @ A @ B )
% 15.55/8.57          = zero_z3403309356797280102nteger ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5665_mod__le__divisor,axiom,
% 15.55/8.57      ! [N: nat,M: nat] :
% 15.55/8.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.57       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5666_div__less__mono,axiom,
% 15.55/8.57      ! [A3: nat,B5: nat,N: nat] :
% 15.55/8.57        ( ( ord_less_nat @ A3 @ B5 )
% 15.55/8.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.57         => ( ( ( modulo_modulo_nat @ A3 @ N )
% 15.55/8.57              = zero_zero_nat )
% 15.55/8.57           => ( ( ( modulo_modulo_nat @ B5 @ N )
% 15.55/8.57                = zero_zero_nat )
% 15.55/8.57             => ( ord_less_nat @ ( divide_divide_nat @ A3 @ N ) @ ( divide_divide_nat @ B5 @ N ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5667_mod__greater__zero__iff__not__dvd,axiom,
% 15.55/8.57      ! [M: nat,N: nat] :
% 15.55/8.57        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 15.55/8.57        = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5668_mod__eq__nat1E,axiom,
% 15.55/8.57      ! [M: nat,Q3: nat,N: nat] :
% 15.55/8.57        ( ( ( modulo_modulo_nat @ M @ Q3 )
% 15.55/8.57          = ( modulo_modulo_nat @ N @ Q3 ) )
% 15.55/8.57       => ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.57         => ~ ! [S3: nat] :
% 15.55/8.57                ( M
% 15.55/8.57               != ( plus_plus_nat @ N @ ( times_times_nat @ Q3 @ S3 ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5669_mod__eq__nat2E,axiom,
% 15.55/8.57      ! [M: nat,Q3: nat,N: nat] :
% 15.55/8.57        ( ( ( modulo_modulo_nat @ M @ Q3 )
% 15.55/8.57          = ( modulo_modulo_nat @ N @ Q3 ) )
% 15.55/8.57       => ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.57         => ~ ! [S3: nat] :
% 15.55/8.57                ( N
% 15.55/8.57               != ( plus_plus_nat @ M @ ( times_times_nat @ Q3 @ S3 ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5670_nat__mod__eq__lemma,axiom,
% 15.55/8.57      ! [X3: nat,N: nat,Y3: nat] :
% 15.55/8.57        ( ( ( modulo_modulo_nat @ X3 @ N )
% 15.55/8.57          = ( modulo_modulo_nat @ Y3 @ N ) )
% 15.55/8.57       => ( ( ord_less_eq_nat @ Y3 @ X3 )
% 15.55/8.57         => ? [Q4: nat] :
% 15.55/8.57              ( X3
% 15.55/8.57              = ( plus_plus_nat @ Y3 @ ( times_times_nat @ N @ Q4 ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5671_div__mod__decomp,axiom,
% 15.55/8.57      ! [A3: nat,N: nat] :
% 15.55/8.57        ( A3
% 15.55/8.57        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A3 @ N ) @ N ) @ ( modulo_modulo_nat @ A3 @ N ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5672_pochhammer__nonneg,axiom,
% 15.55/8.57      ! [X3: real,N: nat] :
% 15.55/8.57        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.57       => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X3 @ N ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5673_pochhammer__nonneg,axiom,
% 15.55/8.57      ! [X3: rat,N: nat] :
% 15.55/8.57        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 15.55/8.57       => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X3 @ N ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5674_pochhammer__nonneg,axiom,
% 15.55/8.57      ! [X3: nat,N: nat] :
% 15.55/8.57        ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 15.55/8.57       => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X3 @ N ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5675_pochhammer__nonneg,axiom,
% 15.55/8.57      ! [X3: int,N: nat] :
% 15.55/8.57        ( ( ord_less_int @ zero_zero_int @ X3 )
% 15.55/8.57       => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X3 @ N ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5676_mod__eq__dvd__iff__nat,axiom,
% 15.55/8.57      ! [N: nat,M: nat,Q3: nat] :
% 15.55/8.57        ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.57       => ( ( ( modulo_modulo_nat @ M @ Q3 )
% 15.55/8.57            = ( modulo_modulo_nat @ N @ Q3 ) )
% 15.55/8.57          = ( dvd_dvd_nat @ Q3 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5677_dvd__imp__le__int,axiom,
% 15.55/8.57      ! [I: int,D3: int] :
% 15.55/8.57        ( ( I != zero_zero_int )
% 15.55/8.57       => ( ( dvd_dvd_int @ D3 @ I )
% 15.55/8.57         => ( ord_less_eq_int @ ( abs_abs_int @ D3 ) @ ( abs_abs_int @ I ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5678_nat__abs__mult__distrib,axiom,
% 15.55/8.57      ! [W: int,Z: int] :
% 15.55/8.57        ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 15.55/8.57        = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5679_pochhammer__0__left,axiom,
% 15.55/8.57      ! [N: nat] :
% 15.55/8.57        ( ( ( N = zero_zero_nat )
% 15.55/8.57         => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 15.55/8.57            = one_one_complex ) )
% 15.55/8.57        & ( ( N != zero_zero_nat )
% 15.55/8.57         => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 15.55/8.57            = zero_zero_complex ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5680_pochhammer__0__left,axiom,
% 15.55/8.57      ! [N: nat] :
% 15.55/8.57        ( ( ( N = zero_zero_nat )
% 15.55/8.57         => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 15.55/8.57            = one_one_real ) )
% 15.55/8.57        & ( ( N != zero_zero_nat )
% 15.55/8.57         => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 15.55/8.57            = zero_zero_real ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5681_pochhammer__0__left,axiom,
% 15.55/8.57      ! [N: nat] :
% 15.55/8.57        ( ( ( N = zero_zero_nat )
% 15.55/8.57         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 15.55/8.57            = one_one_rat ) )
% 15.55/8.57        & ( ( N != zero_zero_nat )
% 15.55/8.57         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 15.55/8.57            = zero_zero_rat ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5682_pochhammer__0__left,axiom,
% 15.55/8.57      ! [N: nat] :
% 15.55/8.57        ( ( ( N = zero_zero_nat )
% 15.55/8.57         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 15.55/8.57            = one_one_nat ) )
% 15.55/8.57        & ( ( N != zero_zero_nat )
% 15.55/8.57         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 15.55/8.57            = zero_zero_nat ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5683_pochhammer__0__left,axiom,
% 15.55/8.57      ! [N: nat] :
% 15.55/8.57        ( ( ( N = zero_zero_nat )
% 15.55/8.57         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 15.55/8.57            = one_one_int ) )
% 15.55/8.57        & ( ( N != zero_zero_nat )
% 15.55/8.57         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 15.55/8.57            = zero_zero_int ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5684_int__cases4,axiom,
% 15.55/8.57      ! [M: int] :
% 15.55/8.57        ( ! [N2: nat] :
% 15.55/8.57            ( M
% 15.55/8.57           != ( semiri1314217659103216013at_int @ N2 ) )
% 15.55/8.57       => ~ ! [N2: nat] :
% 15.55/8.57              ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 15.55/8.57             => ( M
% 15.55/8.57               != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5685_int__zle__neg,axiom,
% 15.55/8.57      ! [N: nat,M: nat] :
% 15.55/8.57        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 15.55/8.57        = ( ( N = zero_zero_nat )
% 15.55/8.57          & ( M = zero_zero_nat ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5686_negative__zle__0,axiom,
% 15.55/8.57      ! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5687_nonpos__int__cases,axiom,
% 15.55/8.57      ! [K: int] :
% 15.55/8.57        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 15.55/8.57       => ~ ! [N2: nat] :
% 15.55/8.57              ( K
% 15.55/8.57             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5688_mod__mult2__eq_H,axiom,
% 15.55/8.57      ! [A: code_integer,M: nat,N: nat] :
% 15.55/8.57        ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 15.55/8.57        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5689_mod__mult2__eq_H,axiom,
% 15.55/8.57      ! [A: nat,M: nat,N: nat] :
% 15.55/8.57        ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 15.55/8.57        = ( 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 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5690_mod__mult2__eq_H,axiom,
% 15.55/8.57      ! [A: int,M: nat,N: nat] :
% 15.55/8.57        ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 15.55/8.57        = ( 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 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5691_even__even__mod__4__iff,axiom,
% 15.55/8.57      ! [N: nat] :
% 15.55/8.57        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.57        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5692_field__char__0__class_Oof__nat__div,axiom,
% 15.55/8.57      ! [M: nat,N: nat] :
% 15.55/8.57        ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N ) )
% 15.55/8.57        = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5693_field__char__0__class_Oof__nat__div,axiom,
% 15.55/8.57      ! [M: nat,N: nat] :
% 15.55/8.57        ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N ) )
% 15.55/8.57        = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5694_field__char__0__class_Oof__nat__div,axiom,
% 15.55/8.57      ! [M: nat,N: nat] :
% 15.55/8.57        ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N ) )
% 15.55/8.57        = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5695_split__mod,axiom,
% 15.55/8.57      ! [P: nat > $o,M: nat,N: nat] :
% 15.55/8.57        ( ( P @ ( modulo_modulo_nat @ M @ N ) )
% 15.55/8.57        = ( ( ( N = zero_zero_nat )
% 15.55/8.57           => ( P @ M ) )
% 15.55/8.57          & ( ( N != zero_zero_nat )
% 15.55/8.57           => ! [I4: nat,J3: nat] :
% 15.55/8.57                ( ( ord_less_nat @ J3 @ N )
% 15.55/8.57               => ( ( M
% 15.55/8.57                    = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J3 ) )
% 15.55/8.57                 => ( P @ J3 ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5696_mod__nat__eqI,axiom,
% 15.55/8.57      ! [R2: nat,N: nat,M: nat] :
% 15.55/8.57        ( ( ord_less_nat @ R2 @ N )
% 15.55/8.57       => ( ( ord_less_eq_nat @ R2 @ M )
% 15.55/8.57         => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R2 ) )
% 15.55/8.57           => ( ( modulo_modulo_nat @ M @ N )
% 15.55/8.57              = R2 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5697_nat__abs__triangle__ineq,axiom,
% 15.55/8.57      ! [K: int,L: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5698_zdvd__mult__cancel1,axiom,
% 15.55/8.57      ! [M: int,N: int] :
% 15.55/8.57        ( ( M != zero_zero_int )
% 15.55/8.57       => ( ( dvd_dvd_int @ ( times_times_int @ M @ N ) @ M )
% 15.55/8.57          = ( ( abs_abs_int @ N )
% 15.55/8.57            = one_one_int ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5699_real__of__nat__div__aux,axiom,
% 15.55/8.57      ! [X3: nat,D3: nat] :
% 15.55/8.57        ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( semiri5074537144036343181t_real @ D3 ) )
% 15.55/8.57        = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X3 @ D3 ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X3 @ D3 ) ) @ ( semiri5074537144036343181t_real @ D3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5700_div__abs__eq__div__nat,axiom,
% 15.55/8.57      ! [K: int,L: int] :
% 15.55/8.57        ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 15.55/8.57        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5701_pochhammer__rec_H,axiom,
% 15.55/8.57      ! [Z: complex,N: nat] :
% 15.55/8.57        ( ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) )
% 15.55/8.57        = ( times_times_complex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5702_pochhammer__rec_H,axiom,
% 15.55/8.57      ! [Z: real,N: nat] :
% 15.55/8.57        ( ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) )
% 15.55/8.57        = ( times_times_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5703_pochhammer__rec_H,axiom,
% 15.55/8.57      ! [Z: rat,N: nat] :
% 15.55/8.57        ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) )
% 15.55/8.57        = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5704_pochhammer__rec_H,axiom,
% 15.55/8.57      ! [Z: nat,N: nat] :
% 15.55/8.57        ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N ) )
% 15.55/8.57        = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5705_pochhammer__rec_H,axiom,
% 15.55/8.57      ! [Z: int,N: nat] :
% 15.55/8.57        ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N ) )
% 15.55/8.57        = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z @ N ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5706_pochhammer__Suc,axiom,
% 15.55/8.57      ! [A: complex,N: nat] :
% 15.55/8.57        ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 15.55/8.57        = ( times_times_complex @ ( comm_s2602460028002588243omplex @ A @ N ) @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5707_pochhammer__Suc,axiom,
% 15.55/8.57      ! [A: real,N: nat] :
% 15.55/8.57        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 15.55/8.57        = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5708_pochhammer__Suc,axiom,
% 15.55/8.57      ! [A: rat,N: nat] :
% 15.55/8.57        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 15.55/8.57        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5709_pochhammer__Suc,axiom,
% 15.55/8.57      ! [A: nat,N: nat] :
% 15.55/8.57        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 15.55/8.57        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5710_pochhammer__Suc,axiom,
% 15.55/8.57      ! [A: int,N: nat] :
% 15.55/8.57        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 15.55/8.57        = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5711_pochhammer__of__nat__eq__0__lemma,axiom,
% 15.55/8.57      ! [N: nat,K: nat] :
% 15.55/8.57        ( ( ord_less_nat @ N @ K )
% 15.55/8.57       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 15.55/8.57          = zero_z3403309356797280102nteger ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5712_pochhammer__of__nat__eq__0__lemma,axiom,
% 15.55/8.57      ! [N: nat,K: nat] :
% 15.55/8.57        ( ( ord_less_nat @ N @ K )
% 15.55/8.57       => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 15.55/8.57          = zero_zero_complex ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5713_pochhammer__of__nat__eq__0__lemma,axiom,
% 15.55/8.57      ! [N: nat,K: nat] :
% 15.55/8.57        ( ( ord_less_nat @ N @ K )
% 15.55/8.57       => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 15.55/8.57          = zero_zero_real ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5714_pochhammer__of__nat__eq__0__lemma,axiom,
% 15.55/8.57      ! [N: nat,K: nat] :
% 15.55/8.57        ( ( ord_less_nat @ N @ K )
% 15.55/8.57       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 15.55/8.57          = zero_zero_rat ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5715_pochhammer__of__nat__eq__0__lemma,axiom,
% 15.55/8.57      ! [N: nat,K: nat] :
% 15.55/8.57        ( ( ord_less_nat @ N @ K )
% 15.55/8.57       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 15.55/8.57          = zero_zero_int ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5716_pochhammer__of__nat__eq__0__iff,axiom,
% 15.55/8.57      ! [N: nat,K: nat] :
% 15.55/8.57        ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 15.55/8.57          = zero_z3403309356797280102nteger )
% 15.55/8.57        = ( ord_less_nat @ N @ K ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5717_pochhammer__of__nat__eq__0__iff,axiom,
% 15.55/8.57      ! [N: nat,K: nat] :
% 15.55/8.57        ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 15.55/8.57          = zero_zero_complex )
% 15.55/8.57        = ( ord_less_nat @ N @ K ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5718_pochhammer__of__nat__eq__0__iff,axiom,
% 15.55/8.57      ! [N: nat,K: nat] :
% 15.55/8.57        ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 15.55/8.57          = zero_zero_real )
% 15.55/8.57        = ( ord_less_nat @ N @ K ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5719_pochhammer__of__nat__eq__0__iff,axiom,
% 15.55/8.57      ! [N: nat,K: nat] :
% 15.55/8.57        ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 15.55/8.57          = zero_zero_rat )
% 15.55/8.57        = ( ord_less_nat @ N @ K ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5720_pochhammer__of__nat__eq__0__iff,axiom,
% 15.55/8.57      ! [N: nat,K: nat] :
% 15.55/8.57        ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 15.55/8.57          = zero_zero_int )
% 15.55/8.57        = ( ord_less_nat @ N @ K ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5721_pochhammer__eq__0__iff,axiom,
% 15.55/8.57      ! [A: complex,N: nat] :
% 15.55/8.57        ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 15.55/8.57          = zero_zero_complex )
% 15.55/8.57        = ( ? [K3: nat] :
% 15.55/8.57              ( ( ord_less_nat @ K3 @ N )
% 15.55/8.57              & ( A
% 15.55/8.57                = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K3 ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5722_pochhammer__eq__0__iff,axiom,
% 15.55/8.57      ! [A: real,N: nat] :
% 15.55/8.57        ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 15.55/8.57          = zero_zero_real )
% 15.55/8.57        = ( ? [K3: nat] :
% 15.55/8.57              ( ( ord_less_nat @ K3 @ N )
% 15.55/8.57              & ( A
% 15.55/8.57                = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K3 ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5723_pochhammer__eq__0__iff,axiom,
% 15.55/8.57      ! [A: rat,N: nat] :
% 15.55/8.57        ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 15.55/8.57          = zero_zero_rat )
% 15.55/8.57        = ( ? [K3: nat] :
% 15.55/8.57              ( ( ord_less_nat @ K3 @ N )
% 15.55/8.57              & ( A
% 15.55/8.57                = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5724_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 15.55/8.57      ! [K: nat,N: nat] :
% 15.55/8.57        ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.57       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 15.55/8.57         != zero_z3403309356797280102nteger ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5725_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 15.55/8.57      ! [K: nat,N: nat] :
% 15.55/8.57        ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.57       => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 15.55/8.57         != zero_zero_complex ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5726_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 15.55/8.57      ! [K: nat,N: nat] :
% 15.55/8.57        ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.57       => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 15.55/8.57         != zero_zero_real ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5727_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 15.55/8.57      ! [K: nat,N: nat] :
% 15.55/8.57        ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.57       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 15.55/8.57         != zero_zero_rat ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5728_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 15.55/8.57      ! [K: nat,N: nat] :
% 15.55/8.57        ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.57       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 15.55/8.57         != zero_zero_int ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5729_pochhammer__product_H,axiom,
% 15.55/8.57      ! [Z: complex,N: nat,M: nat] :
% 15.55/8.57        ( ( comm_s2602460028002588243omplex @ Z @ ( plus_plus_nat @ N @ M ) )
% 15.55/8.57        = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ N ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N ) ) @ M ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5730_pochhammer__product_H,axiom,
% 15.55/8.57      ! [Z: real,N: nat,M: nat] :
% 15.55/8.57        ( ( comm_s7457072308508201937r_real @ Z @ ( plus_plus_nat @ N @ M ) )
% 15.55/8.57        = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ N ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ M ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5731_pochhammer__product_H,axiom,
% 15.55/8.57      ! [Z: rat,N: nat,M: nat] :
% 15.55/8.57        ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N @ M ) )
% 15.55/8.57        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ M ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5732_pochhammer__product_H,axiom,
% 15.55/8.57      ! [Z: nat,N: nat,M: nat] :
% 15.55/8.57        ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N @ M ) )
% 15.55/8.57        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ M ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5733_pochhammer__product_H,axiom,
% 15.55/8.57      ! [Z: int,N: nat,M: nat] :
% 15.55/8.57        ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N @ M ) )
% 15.55/8.57        = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ M ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5734_int__cases3,axiom,
% 15.55/8.57      ! [K: int] :
% 15.55/8.57        ( ( K != zero_zero_int )
% 15.55/8.57       => ( ! [N2: nat] :
% 15.55/8.57              ( ( K
% 15.55/8.57                = ( semiri1314217659103216013at_int @ N2 ) )
% 15.55/8.57             => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 15.55/8.57         => ~ ! [N2: nat] :
% 15.55/8.57                ( ( K
% 15.55/8.57                  = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 15.55/8.57               => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5735_not__zle__0__negative,axiom,
% 15.55/8.57      ! [N: nat] :
% 15.55/8.57        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5736_negD,axiom,
% 15.55/8.57      ! [X3: int] :
% 15.55/8.57        ( ( ord_less_int @ X3 @ zero_zero_int )
% 15.55/8.57       => ? [N2: nat] :
% 15.55/8.57            ( X3
% 15.55/8.57            = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5737_negative__zless__0,axiom,
% 15.55/8.57      ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5738_verit__less__mono__div__int2,axiom,
% 15.55/8.57      ! [A3: int,B5: int,N: int] :
% 15.55/8.57        ( ( ord_less_eq_int @ A3 @ B5 )
% 15.55/8.57       => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 15.55/8.57         => ( ord_less_eq_int @ ( divide_divide_int @ B5 @ N ) @ ( divide_divide_int @ A3 @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5739_div__eq__minus1,axiom,
% 15.55/8.57      ! [B: int] :
% 15.55/8.57        ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.57       => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 15.55/8.57          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5740_ceiling__divide__eq__div,axiom,
% 15.55/8.57      ! [A: int,B: int] :
% 15.55/8.57        ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) )
% 15.55/8.57        = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5741_ceiling__divide__eq__div,axiom,
% 15.55/8.57      ! [A: int,B: int] :
% 15.55/8.57        ( ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B ) ) )
% 15.55/8.57        = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5742_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 15.55/8.57      ! [C: code_integer,A: code_integer,B: code_integer] :
% 15.55/8.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 15.55/8.57       => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 15.55/8.57          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5743_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 15.55/8.57      ! [C: nat,A: nat,B: nat] :
% 15.55/8.57        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 15.55/8.57       => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 15.55/8.57          = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5744_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 15.55/8.57      ! [C: int,A: int,B: int] :
% 15.55/8.57        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 15.55/8.57       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 15.55/8.57          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5745_even__iff__mod__2__eq__zero,axiom,
% 15.55/8.57      ! [A: nat] :
% 15.55/8.57        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.55/8.57        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.57          = zero_zero_nat ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5746_even__iff__mod__2__eq__zero,axiom,
% 15.55/8.57      ! [A: int] :
% 15.55/8.57        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.55/8.57        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.57          = zero_zero_int ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5747_even__iff__mod__2__eq__zero,axiom,
% 15.55/8.57      ! [A: code_integer] :
% 15.55/8.57        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.55/8.57        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 15.55/8.57          = zero_z3403309356797280102nteger ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5748_odd__iff__mod__2__eq__one,axiom,
% 15.55/8.57      ! [A: nat] :
% 15.55/8.57        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 15.55/8.57        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.57          = one_one_nat ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5749_odd__iff__mod__2__eq__one,axiom,
% 15.55/8.57      ! [A: int] :
% 15.55/8.57        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 15.55/8.57        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.57          = one_one_int ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5750_odd__iff__mod__2__eq__one,axiom,
% 15.55/8.57      ! [A: code_integer] :
% 15.55/8.57        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 15.55/8.57        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 15.55/8.57          = one_one_Code_integer ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5751_take__bit__eq__mod,axiom,
% 15.55/8.57      ( bit_se1745604003318907178nteger
% 15.55/8.57      = ( ^ [N3: nat,A4: code_integer] : ( modulo364778990260209775nteger @ A4 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5752_take__bit__eq__mod,axiom,
% 15.55/8.57      ( bit_se2923211474154528505it_int
% 15.55/8.57      = ( ^ [N3: nat,A4: int] : ( modulo_modulo_int @ A4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5753_take__bit__eq__mod,axiom,
% 15.55/8.57      ( bit_se2925701944663578781it_nat
% 15.55/8.57      = ( ^ [N3: nat,A4: nat] : ( modulo_modulo_nat @ A4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5754_Suc__times__mod__eq,axiom,
% 15.55/8.57      ! [M: nat,N: nat] :
% 15.55/8.57        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 15.55/8.57       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 15.55/8.57          = one_one_nat ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5755_even__abs__add__iff,axiom,
% 15.55/8.57      ! [K: int,L: int] :
% 15.55/8.57        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L ) )
% 15.55/8.57        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5756_even__add__abs__iff,axiom,
% 15.55/8.57      ! [K: int,L: int] :
% 15.55/8.57        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L ) ) )
% 15.55/8.57        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5757_nat__abs__int__diff,axiom,
% 15.55/8.57      ! [A: nat,B: nat] :
% 15.55/8.57        ( ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.57         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 15.55/8.57            = ( minus_minus_nat @ B @ A ) ) )
% 15.55/8.57        & ( ~ ( ord_less_eq_nat @ A @ B )
% 15.55/8.57         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 15.55/8.57            = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5758_take__bit__nat__def,axiom,
% 15.55/8.57      ( bit_se2925701944663578781it_nat
% 15.55/8.57      = ( ^ [N3: nat,M3: nat] : ( modulo_modulo_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5759_neg__int__cases,axiom,
% 15.55/8.57      ! [K: int] :
% 15.55/8.57        ( ( ord_less_int @ K @ zero_zero_int )
% 15.55/8.57       => ~ ! [N2: nat] :
% 15.55/8.57              ( ( K
% 15.55/8.57                = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 15.55/8.57             => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5760_pochhammer__product,axiom,
% 15.55/8.57      ! [M: nat,N: nat,Z: complex] :
% 15.55/8.57        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.57       => ( ( comm_s2602460028002588243omplex @ Z @ N )
% 15.55/8.57          = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ M ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5761_pochhammer__product,axiom,
% 15.55/8.57      ! [M: nat,N: nat,Z: real] :
% 15.55/8.57        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.57       => ( ( comm_s7457072308508201937r_real @ Z @ N )
% 15.55/8.57          = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5762_pochhammer__product,axiom,
% 15.55/8.57      ! [M: nat,N: nat,Z: rat] :
% 15.55/8.57        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.57       => ( ( comm_s4028243227959126397er_rat @ Z @ N )
% 15.55/8.57          = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5763_pochhammer__product,axiom,
% 15.55/8.57      ! [M: nat,N: nat,Z: nat] :
% 15.55/8.57        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.57       => ( ( comm_s4663373288045622133er_nat @ Z @ N )
% 15.55/8.57          = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5764_pochhammer__product,axiom,
% 15.55/8.57      ! [M: nat,N: nat,Z: int] :
% 15.55/8.57        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.57       => ( ( comm_s4660882817536571857er_int @ Z @ N )
% 15.55/8.57          = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5765_nat__mult__distrib__neg,axiom,
% 15.55/8.57      ! [Z: int,Z5: int] :
% 15.55/8.57        ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 15.55/8.57       => ( ( nat2 @ ( times_times_int @ Z @ Z5 ) )
% 15.55/8.57          = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z5 ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5766_divmod__digit__0_I2_J,axiom,
% 15.55/8.57      ! [B: nat,A: nat] :
% 15.55/8.57        ( ( ord_less_nat @ zero_zero_nat @ B )
% 15.55/8.57       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 15.55/8.57         => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 15.55/8.57            = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5767_divmod__digit__0_I2_J,axiom,
% 15.55/8.57      ! [B: int,A: int] :
% 15.55/8.57        ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.57       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 15.55/8.57         => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 15.55/8.57            = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5768_divmod__digit__0_I2_J,axiom,
% 15.55/8.57      ! [B: code_integer,A: code_integer] :
% 15.55/8.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 15.55/8.57       => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 15.55/8.57         => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 15.55/8.57            = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5769_bits__stable__imp__add__self,axiom,
% 15.55/8.57      ! [A: nat] :
% 15.55/8.57        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.57          = A )
% 15.55/8.57       => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.57          = zero_zero_nat ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5770_bits__stable__imp__add__self,axiom,
% 15.55/8.57      ! [A: int] :
% 15.55/8.57        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.57          = A )
% 15.55/8.57       => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 15.55/8.57          = zero_zero_int ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5771_bits__stable__imp__add__self,axiom,
% 15.55/8.57      ! [A: code_integer] :
% 15.55/8.57        ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 15.55/8.57          = A )
% 15.55/8.57       => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 15.55/8.57          = zero_z3403309356797280102nteger ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5772_parity__cases,axiom,
% 15.55/8.57      ! [A: nat] :
% 15.55/8.57        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.55/8.57         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.57           != zero_zero_nat ) )
% 15.55/8.57       => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.55/8.57           => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.57             != one_one_nat ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5773_parity__cases,axiom,
% 15.55/8.57      ! [A: int] :
% 15.55/8.57        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.55/8.57         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.57           != zero_zero_int ) )
% 15.55/8.57       => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.55/8.57           => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.57             != one_one_int ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5774_parity__cases,axiom,
% 15.55/8.57      ! [A: code_integer] :
% 15.55/8.57        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.55/8.57         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 15.55/8.57           != zero_z3403309356797280102nteger ) )
% 15.55/8.57       => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.55/8.57           => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 15.55/8.57             != one_one_Code_integer ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5775_mod2__eq__if,axiom,
% 15.55/8.57      ! [A: nat] :
% 15.55/8.57        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.55/8.57         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.57            = zero_zero_nat ) )
% 15.55/8.57        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 15.55/8.57         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.57            = one_one_nat ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5776_mod2__eq__if,axiom,
% 15.55/8.57      ! [A: int] :
% 15.55/8.57        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.55/8.57         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.57            = zero_zero_int ) )
% 15.55/8.57        & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 15.55/8.57         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.57            = one_one_int ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5777_mod2__eq__if,axiom,
% 15.55/8.57      ! [A: code_integer] :
% 15.55/8.57        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.55/8.57         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 15.55/8.57            = zero_z3403309356797280102nteger ) )
% 15.55/8.57        & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 15.55/8.57         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 15.55/8.57            = one_one_Code_integer ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5778_div__exp__mod__exp__eq,axiom,
% 15.55/8.57      ! [A: nat,N: nat,M: nat] :
% 15.55/8.57        ( ( 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 ) )
% 15.55/8.57        = ( 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 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5779_div__exp__mod__exp__eq,axiom,
% 15.55/8.57      ! [A: int,N: nat,M: nat] :
% 15.55/8.57        ( ( 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 ) )
% 15.55/8.57        = ( 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 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5780_div__exp__mod__exp__eq,axiom,
% 15.55/8.57      ! [A: code_integer,N: nat,M: nat] :
% 15.55/8.57        ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 15.55/8.57        = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5781_verit__le__mono__div,axiom,
% 15.55/8.57      ! [A3: nat,B5: nat,N: nat] :
% 15.55/8.57        ( ( ord_less_nat @ A3 @ B5 )
% 15.55/8.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.57         => ( ord_less_eq_nat
% 15.55/8.57            @ ( plus_plus_nat @ ( divide_divide_nat @ A3 @ N )
% 15.55/8.57              @ ( if_nat
% 15.55/8.57                @ ( ( modulo_modulo_nat @ B5 @ N )
% 15.55/8.57                  = zero_zero_nat )
% 15.55/8.57                @ one_one_nat
% 15.55/8.57                @ zero_zero_nat ) )
% 15.55/8.57            @ ( divide_divide_nat @ B5 @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5782_nat__intermed__int__val,axiom,
% 15.55/8.57      ! [M: nat,N: nat,F: nat > int,K: int] :
% 15.55/8.57        ( ! [I3: nat] :
% 15.55/8.57            ( ( ( ord_less_eq_nat @ M @ I3 )
% 15.55/8.57              & ( ord_less_nat @ I3 @ N ) )
% 15.55/8.57           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 15.55/8.57       => ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.57         => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 15.55/8.57           => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 15.55/8.57             => ? [I3: nat] :
% 15.55/8.57                  ( ( ord_less_eq_nat @ M @ I3 )
% 15.55/8.57                  & ( ord_less_eq_nat @ I3 @ N )
% 15.55/8.57                  & ( ( F @ I3 )
% 15.55/8.57                    = K ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5783_decr__lemma,axiom,
% 15.55/8.57      ! [D3: int,X3: int,Z: int] :
% 15.55/8.57        ( ( ord_less_int @ zero_zero_int @ D3 )
% 15.55/8.57       => ( ord_less_int @ ( minus_minus_int @ X3 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X3 @ Z ) ) @ one_one_int ) @ D3 ) ) @ Z ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5784_incr__lemma,axiom,
% 15.55/8.57      ! [D3: int,Z: int,X3: int] :
% 15.55/8.57        ( ( ord_less_int @ zero_zero_int @ D3 )
% 15.55/8.57       => ( ord_less_int @ Z @ ( plus_plus_int @ X3 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X3 @ Z ) ) @ one_one_int ) @ D3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5785_pochhammer__absorb__comp,axiom,
% 15.55/8.57      ! [R2: code_integer,K: nat] :
% 15.55/8.57        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R2 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R2 ) @ K ) )
% 15.55/8.57        = ( times_3573771949741848930nteger @ R2 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5786_pochhammer__absorb__comp,axiom,
% 15.55/8.57      ! [R2: complex,K: nat] :
% 15.55/8.57        ( ( times_times_complex @ ( minus_minus_complex @ R2 @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R2 ) @ K ) )
% 15.55/8.57        = ( times_times_complex @ R2 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R2 ) @ one_one_complex ) @ K ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5787_pochhammer__absorb__comp,axiom,
% 15.55/8.57      ! [R2: real,K: nat] :
% 15.55/8.57        ( ( times_times_real @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R2 ) @ K ) )
% 15.55/8.57        = ( times_times_real @ R2 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R2 ) @ one_one_real ) @ K ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5788_pochhammer__absorb__comp,axiom,
% 15.55/8.57      ! [R2: rat,K: nat] :
% 15.55/8.57        ( ( times_times_rat @ ( minus_minus_rat @ R2 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R2 ) @ K ) )
% 15.55/8.57        = ( times_times_rat @ R2 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R2 ) @ one_one_rat ) @ K ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5789_pochhammer__absorb__comp,axiom,
% 15.55/8.57      ! [R2: int,K: nat] :
% 15.55/8.57        ( ( times_times_int @ ( minus_minus_int @ R2 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R2 ) @ K ) )
% 15.55/8.57        = ( times_times_int @ R2 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R2 ) @ one_one_int ) @ K ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5790_take__bit__Suc__minus__bit0,axiom,
% 15.55/8.57      ! [N: nat,K: num] :
% 15.55/8.57        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 15.55/8.57        = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5791_minus__1__div__exp__eq__int,axiom,
% 15.55/8.57      ! [N: nat] :
% 15.55/8.57        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.57        = ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5792_div__pos__neg__trivial,axiom,
% 15.55/8.57      ! [K: int,L: int] :
% 15.55/8.57        ( ( ord_less_int @ zero_zero_int @ K )
% 15.55/8.57       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 15.55/8.57         => ( ( divide_divide_int @ K @ L )
% 15.55/8.57            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5793_divmod__digit__0_I1_J,axiom,
% 15.55/8.57      ! [B: nat,A: nat] :
% 15.55/8.57        ( ( ord_less_nat @ zero_zero_nat @ B )
% 15.55/8.57       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 15.55/8.57         => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 15.55/8.57            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5794_divmod__digit__0_I1_J,axiom,
% 15.55/8.57      ! [B: int,A: int] :
% 15.55/8.57        ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.57       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 15.55/8.57         => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 15.55/8.57            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5795_divmod__digit__0_I1_J,axiom,
% 15.55/8.57      ! [B: code_integer,A: code_integer] :
% 15.55/8.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 15.55/8.57       => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 15.55/8.57         => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 15.55/8.57            = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5796_mult__exp__mod__exp__eq,axiom,
% 15.55/8.57      ! [M: nat,N: nat,A: nat] :
% 15.55/8.57        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.57       => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.57          = ( 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 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5797_mult__exp__mod__exp__eq,axiom,
% 15.55/8.57      ! [M: nat,N: nat,A: int] :
% 15.55/8.57        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.57       => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.57          = ( 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 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5798_mult__exp__mod__exp__eq,axiom,
% 15.55/8.57      ! [M: nat,N: nat,A: code_integer] :
% 15.55/8.57        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.57       => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.57          = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5799_compl__le__swap2,axiom,
% 15.55/8.57      ! [Y3: set_nat,X3: set_nat] :
% 15.55/8.57        ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y3 ) @ X3 )
% 15.55/8.57       => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X3 ) @ Y3 ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5800_compl__le__swap1,axiom,
% 15.55/8.57      ! [Y3: set_nat,X3: set_nat] :
% 15.55/8.57        ( ( ord_less_eq_set_nat @ Y3 @ ( uminus5710092332889474511et_nat @ X3 ) )
% 15.55/8.57       => ( ord_less_eq_set_nat @ X3 @ ( uminus5710092332889474511et_nat @ Y3 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5801_compl__mono,axiom,
% 15.55/8.57      ! [X3: set_nat,Y3: set_nat] :
% 15.55/8.57        ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 15.55/8.57       => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y3 ) @ ( uminus5710092332889474511et_nat @ X3 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5802_nat__ivt__aux,axiom,
% 15.55/8.57      ! [N: nat,F: nat > int,K: int] :
% 15.55/8.57        ( ! [I3: nat] :
% 15.55/8.57            ( ( ord_less_nat @ I3 @ N )
% 15.55/8.57           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 15.55/8.57       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 15.55/8.57         => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 15.55/8.57           => ? [I3: nat] :
% 15.55/8.57                ( ( ord_less_eq_nat @ I3 @ N )
% 15.55/8.57                & ( ( F @ I3 )
% 15.55/8.57                  = K ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5803_complex__mod__minus__le__complex__mod,axiom,
% 15.55/8.57      ! [X3: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X3 ) ) @ ( real_V1022390504157884413omplex @ X3 ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5804_pochhammer__minus,axiom,
% 15.55/8.57      ! [B: code_integer,K: nat] :
% 15.55/8.57        ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 15.55/8.57        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5805_pochhammer__minus,axiom,
% 15.55/8.57      ! [B: complex,K: nat] :
% 15.55/8.57        ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 15.55/8.57        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5806_pochhammer__minus,axiom,
% 15.55/8.57      ! [B: real,K: nat] :
% 15.55/8.57        ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 15.55/8.57        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5807_pochhammer__minus,axiom,
% 15.55/8.57      ! [B: rat,K: nat] :
% 15.55/8.57        ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 15.55/8.57        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5808_pochhammer__minus,axiom,
% 15.55/8.57      ! [B: int,K: nat] :
% 15.55/8.57        ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 15.55/8.57        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5809_pochhammer__minus_H,axiom,
% 15.55/8.57      ! [B: code_integer,K: nat] :
% 15.55/8.57        ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 15.55/8.57        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5810_pochhammer__minus_H,axiom,
% 15.55/8.57      ! [B: complex,K: nat] :
% 15.55/8.57        ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 15.55/8.57        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5811_pochhammer__minus_H,axiom,
% 15.55/8.57      ! [B: real,K: nat] :
% 15.55/8.57        ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 15.55/8.57        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5812_pochhammer__minus_H,axiom,
% 15.55/8.57      ! [B: rat,K: nat] :
% 15.55/8.57        ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 15.55/8.57        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5813_pochhammer__minus_H,axiom,
% 15.55/8.57      ! [B: int,K: nat] :
% 15.55/8.57        ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 15.55/8.57        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5814_complex__mod__triangle__ineq2,axiom,
% 15.55/8.57      ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5815_int__bit__induct,axiom,
% 15.55/8.57      ! [P: int > $o,K: int] :
% 15.55/8.57        ( ( P @ zero_zero_int )
% 15.55/8.57       => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.57         => ( ! [K2: int] :
% 15.55/8.57                ( ( P @ K2 )
% 15.55/8.57               => ( ( K2 != zero_zero_int )
% 15.55/8.57                 => ( P @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.57           => ( ! [K2: int] :
% 15.55/8.57                  ( ( P @ K2 )
% 15.55/8.57                 => ( ( K2
% 15.55/8.57                     != ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.57                   => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 15.55/8.57             => ( P @ K ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5816_mod__double__modulus,axiom,
% 15.55/8.57      ! [M: code_integer,X3: code_integer] :
% 15.55/8.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 15.55/8.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 15.55/8.57         => ( ( ( modulo364778990260209775nteger @ X3 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 15.55/8.57              = ( modulo364778990260209775nteger @ X3 @ M ) )
% 15.55/8.57            | ( ( modulo364778990260209775nteger @ X3 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 15.55/8.57              = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X3 @ M ) @ M ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5817_mod__double__modulus,axiom,
% 15.55/8.57      ! [M: nat,X3: nat] :
% 15.55/8.57        ( ( ord_less_nat @ zero_zero_nat @ M )
% 15.55/8.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ X3 )
% 15.55/8.57         => ( ( ( modulo_modulo_nat @ X3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 15.55/8.57              = ( modulo_modulo_nat @ X3 @ M ) )
% 15.55/8.57            | ( ( modulo_modulo_nat @ X3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 15.55/8.57              = ( plus_plus_nat @ ( modulo_modulo_nat @ X3 @ M ) @ M ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5818_mod__double__modulus,axiom,
% 15.55/8.57      ! [M: int,X3: int] :
% 15.55/8.57        ( ( ord_less_int @ zero_zero_int @ M )
% 15.55/8.57       => ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 15.55/8.57         => ( ( ( modulo_modulo_int @ X3 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 15.55/8.57              = ( modulo_modulo_int @ X3 @ M ) )
% 15.55/8.57            | ( ( modulo_modulo_int @ X3 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 15.55/8.57              = ( plus_plus_int @ ( modulo_modulo_int @ X3 @ M ) @ M ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5819_divmod__digit__1_I2_J,axiom,
% 15.55/8.57      ! [A: code_integer,B: code_integer] :
% 15.55/8.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 15.55/8.57       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 15.55/8.57         => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 15.55/8.57           => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 15.55/8.57              = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5820_divmod__digit__1_I2_J,axiom,
% 15.55/8.57      ! [A: nat,B: nat] :
% 15.55/8.57        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.55/8.57       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 15.55/8.57         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 15.55/8.57           => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 15.55/8.57              = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5821_divmod__digit__1_I2_J,axiom,
% 15.55/8.57      ! [A: int,B: int] :
% 15.55/8.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.57       => ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.57         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 15.55/8.57           => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 15.55/8.57              = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5822_take__bit__Suc,axiom,
% 15.55/8.57      ! [N: nat,A: code_integer] :
% 15.55/8.57        ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A )
% 15.55/8.57        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5823_take__bit__Suc,axiom,
% 15.55/8.57      ! [N: nat,A: int] :
% 15.55/8.57        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 15.55/8.57        = ( 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 ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5824_take__bit__Suc,axiom,
% 15.55/8.57      ! [N: nat,A: nat] :
% 15.55/8.57        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ A )
% 15.55/8.57        = ( 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 ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5825_unset__bit__Suc,axiom,
% 15.55/8.57      ! [N: nat,A: code_integer] :
% 15.55/8.57        ( ( bit_se8260200283734997820nteger @ ( suc @ N ) @ A )
% 15.55/8.57        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5826_unset__bit__Suc,axiom,
% 15.55/8.57      ! [N: nat,A: int] :
% 15.55/8.57        ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 15.55/8.57        = ( 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 ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5827_unset__bit__Suc,axiom,
% 15.55/8.57      ! [N: nat,A: nat] :
% 15.55/8.57        ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 15.55/8.57        = ( 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 ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5828_set__bit__Suc,axiom,
% 15.55/8.57      ! [N: nat,A: code_integer] :
% 15.55/8.57        ( ( bit_se2793503036327961859nteger @ ( suc @ N ) @ A )
% 15.55/8.57        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5829_set__bit__Suc,axiom,
% 15.55/8.57      ! [N: nat,A: int] :
% 15.55/8.57        ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 15.55/8.57        = ( 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 ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5830_set__bit__Suc,axiom,
% 15.55/8.57      ! [N: nat,A: nat] :
% 15.55/8.57        ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 15.55/8.57        = ( 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 ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5831_flip__bit__Suc,axiom,
% 15.55/8.57      ! [N: nat,A: code_integer] :
% 15.55/8.57        ( ( bit_se1345352211410354436nteger @ ( suc @ N ) @ A )
% 15.55/8.57        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5832_flip__bit__Suc,axiom,
% 15.55/8.57      ! [N: nat,A: int] :
% 15.55/8.57        ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 15.55/8.57        = ( 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 ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5833_flip__bit__Suc,axiom,
% 15.55/8.57      ! [N: nat,A: nat] :
% 15.55/8.57        ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 15.55/8.57        = ( 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 ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5834_even__mod__4__div__2,axiom,
% 15.55/8.57      ! [N: nat] :
% 15.55/8.57        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 15.55/8.57          = ( suc @ zero_zero_nat ) )
% 15.55/8.57       => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5835_nat0__intermed__int__val,axiom,
% 15.55/8.57      ! [N: nat,F: nat > int,K: int] :
% 15.55/8.57        ( ! [I3: nat] :
% 15.55/8.57            ( ( ord_less_nat @ I3 @ N )
% 15.55/8.57           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 15.55/8.57       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 15.55/8.57         => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 15.55/8.57           => ? [I3: nat] :
% 15.55/8.57                ( ( ord_less_eq_nat @ I3 @ N )
% 15.55/8.57                & ( ( F @ I3 )
% 15.55/8.57                  = K ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5836_xor__nat__unfold,axiom,
% 15.55/8.57      ( bit_se6528837805403552850or_nat
% 15.55/8.57      = ( ^ [M3: nat,N3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N3 @ ( if_nat @ ( N3 = 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 @ N3 @ ( 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 @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5837_arctan__add,axiom,
% 15.55/8.57      ! [X3: real,Y3: real] :
% 15.55/8.57        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 15.55/8.57       => ( ( ord_less_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 15.55/8.57         => ( ( plus_plus_real @ ( arctan @ X3 ) @ ( arctan @ Y3 ) )
% 15.55/8.57            = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X3 @ Y3 ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X3 @ Y3 ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5838_divmod__digit__1_I1_J,axiom,
% 15.55/8.57      ! [A: code_integer,B: code_integer] :
% 15.55/8.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 15.55/8.57       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 15.55/8.57         => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 15.55/8.57           => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 15.55/8.57              = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5839_divmod__digit__1_I1_J,axiom,
% 15.55/8.57      ! [A: nat,B: nat] :
% 15.55/8.57        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 15.55/8.57       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 15.55/8.57         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 15.55/8.57           => ( ( 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 )
% 15.55/8.57              = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5840_divmod__digit__1_I1_J,axiom,
% 15.55/8.57      ! [A: int,B: int] :
% 15.55/8.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.57       => ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.57         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 15.55/8.57           => ( ( 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 )
% 15.55/8.57              = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5841_take__bit__minus__small__eq,axiom,
% 15.55/8.57      ! [K: int,N: nat] :
% 15.55/8.57        ( ( ord_less_int @ zero_zero_int @ K )
% 15.55/8.57       => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.57         => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 15.55/8.57            = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5842_take__bit__rec,axiom,
% 15.55/8.57      ( bit_se1745604003318907178nteger
% 15.55/8.57      = ( ^ [N3: nat,A4: code_integer] : ( if_Code_integer @ ( N3 = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5843_take__bit__rec,axiom,
% 15.55/8.57      ( bit_se2923211474154528505it_int
% 15.55/8.57      = ( ^ [N3: nat,A4: int] : ( if_int @ ( N3 = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5844_take__bit__rec,axiom,
% 15.55/8.57      ( bit_se2925701944663578781it_nat
% 15.55/8.57      = ( ^ [N3: nat,A4: nat] : ( if_nat @ ( N3 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5845_powr__int,axiom,
% 15.55/8.57      ! [X3: real,I: int] :
% 15.55/8.57        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.57       => ( ( ( ord_less_eq_int @ zero_zero_int @ I )
% 15.55/8.57           => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ I ) )
% 15.55/8.57              = ( power_power_real @ X3 @ ( nat2 @ I ) ) ) )
% 15.55/8.57          & ( ~ ( ord_less_eq_int @ zero_zero_int @ I )
% 15.55/8.57           => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ I ) )
% 15.55/8.57              = ( divide_divide_real @ one_one_real @ ( power_power_real @ X3 @ ( nat2 @ ( uminus_uminus_int @ I ) ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5846_arctan__half,axiom,
% 15.55/8.57      ( arctan
% 15.55/8.57      = ( ^ [X: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5847_in__children__def,axiom,
% 15.55/8.57      ( vEBT_V5917875025757280293ildren
% 15.55/8.57      = ( ^ [N3: nat,TreeList: list_VEBT_VEBT,X: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ N3 ) ) @ ( vEBT_VEBT_low @ X @ N3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5848_signed__take__bit__rec,axiom,
% 15.55/8.57      ( bit_ri6519982836138164636nteger
% 15.55/8.57      = ( ^ [N3: nat,A4: code_integer] : ( if_Code_integer @ ( N3 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5849_signed__take__bit__rec,axiom,
% 15.55/8.57      ( bit_ri631733984087533419it_int
% 15.55/8.57      = ( ^ [N3: nat,A4: int] : ( if_int @ ( N3 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5850_central__binomial__lower__bound,axiom,
% 15.55/8.57      ! [N: nat] :
% 15.55/8.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.57       => ( 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 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5851_nth__equalityI,axiom,
% 15.55/8.57      ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 15.55/8.57        ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 15.55/8.57          = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 15.55/8.57       => ( ! [I3: nat] :
% 15.55/8.57              ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 15.55/8.57             => ( ( nth_VEBT_VEBT @ Xs2 @ I3 )
% 15.55/8.57                = ( nth_VEBT_VEBT @ Ys @ I3 ) ) )
% 15.55/8.57         => ( Xs2 = Ys ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5852_nth__equalityI,axiom,
% 15.55/8.57      ! [Xs2: list_o,Ys: list_o] :
% 15.55/8.57        ( ( ( size_size_list_o @ Xs2 )
% 15.55/8.57          = ( size_size_list_o @ Ys ) )
% 15.55/8.57       => ( ! [I3: nat] :
% 15.55/8.57              ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 15.55/8.57             => ( ( nth_o @ Xs2 @ I3 )
% 15.55/8.57                = ( nth_o @ Ys @ I3 ) ) )
% 15.55/8.57         => ( Xs2 = Ys ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5853_nth__equalityI,axiom,
% 15.55/8.57      ! [Xs2: list_nat,Ys: list_nat] :
% 15.55/8.57        ( ( ( size_size_list_nat @ Xs2 )
% 15.55/8.57          = ( size_size_list_nat @ Ys ) )
% 15.55/8.57       => ( ! [I3: nat] :
% 15.55/8.57              ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 15.55/8.57             => ( ( nth_nat @ Xs2 @ I3 )
% 15.55/8.57                = ( nth_nat @ Ys @ I3 ) ) )
% 15.55/8.57         => ( Xs2 = Ys ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5854_nth__equalityI,axiom,
% 15.55/8.57      ! [Xs2: list_int,Ys: list_int] :
% 15.55/8.57        ( ( ( size_size_list_int @ Xs2 )
% 15.55/8.57          = ( size_size_list_int @ Ys ) )
% 15.55/8.57       => ( ! [I3: nat] :
% 15.55/8.57              ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 15.55/8.57             => ( ( nth_int @ Xs2 @ I3 )
% 15.55/8.57                = ( nth_int @ Ys @ I3 ) ) )
% 15.55/8.57         => ( Xs2 = Ys ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5855_inthall,axiom,
% 15.55/8.57      ! [Xs2: list_option_nat,P: option_nat > $o,N: nat] :
% 15.55/8.57        ( ! [X4: option_nat] :
% 15.55/8.57            ( ( member_option_nat @ X4 @ ( set_option_nat2 @ Xs2 ) )
% 15.55/8.57           => ( P @ X4 ) )
% 15.55/8.57       => ( ( ord_less_nat @ N @ ( size_s6086282163384603972on_nat @ Xs2 ) )
% 15.55/8.57         => ( P @ ( nth_option_nat @ Xs2 @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5856_inthall,axiom,
% 15.55/8.57      ! [Xs2: list_real,P: real > $o,N: nat] :
% 15.55/8.57        ( ! [X4: real] :
% 15.55/8.57            ( ( member_real @ X4 @ ( set_real2 @ Xs2 ) )
% 15.55/8.57           => ( P @ X4 ) )
% 15.55/8.57       => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 15.55/8.57         => ( P @ ( nth_real @ Xs2 @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5857_inthall,axiom,
% 15.55/8.57      ! [Xs2: list_set_nat,P: set_nat > $o,N: nat] :
% 15.55/8.57        ( ! [X4: set_nat] :
% 15.55/8.57            ( ( member_set_nat @ X4 @ ( set_set_nat2 @ Xs2 ) )
% 15.55/8.57           => ( P @ X4 ) )
% 15.55/8.57       => ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 15.55/8.57         => ( P @ ( nth_set_nat @ Xs2 @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5858_inthall,axiom,
% 15.55/8.57      ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,N: nat] :
% 15.55/8.57        ( ! [X4: vEBT_VEBT] :
% 15.55/8.57            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 15.55/8.57           => ( P @ X4 ) )
% 15.55/8.57       => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 15.55/8.57         => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5859_inthall,axiom,
% 15.55/8.57      ! [Xs2: list_o,P: $o > $o,N: nat] :
% 15.55/8.57        ( ! [X4: $o] :
% 15.55/8.57            ( ( member_o @ X4 @ ( set_o2 @ Xs2 ) )
% 15.55/8.57           => ( P @ X4 ) )
% 15.55/8.57       => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 15.55/8.57         => ( P @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5860_inthall,axiom,
% 15.55/8.57      ! [Xs2: list_nat,P: nat > $o,N: nat] :
% 15.55/8.57        ( ! [X4: nat] :
% 15.55/8.57            ( ( member_nat @ X4 @ ( set_nat2 @ Xs2 ) )
% 15.55/8.57           => ( P @ X4 ) )
% 15.55/8.57       => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 15.55/8.57         => ( P @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5861_inthall,axiom,
% 15.55/8.57      ! [Xs2: list_int,P: int > $o,N: nat] :
% 15.55/8.57        ( ! [X4: int] :
% 15.55/8.57            ( ( member_int @ X4 @ ( set_int2 @ Xs2 ) )
% 15.55/8.57           => ( P @ X4 ) )
% 15.55/8.57       => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 15.55/8.57         => ( P @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5862_signed__take__bit__of__0,axiom,
% 15.55/8.57      ! [N: nat] :
% 15.55/8.57        ( ( bit_ri631733984087533419it_int @ N @ zero_zero_int )
% 15.55/8.57        = zero_zero_int ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5863_mod__pos__pos__trivial,axiom,
% 15.55/8.57      ! [K: int,L: int] :
% 15.55/8.57        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 15.55/8.57       => ( ( ord_less_int @ K @ L )
% 15.55/8.57         => ( ( modulo_modulo_int @ K @ L )
% 15.55/8.57            = K ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5864_mod__neg__neg__trivial,axiom,
% 15.55/8.57      ! [K: int,L: int] :
% 15.55/8.57        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 15.55/8.57       => ( ( ord_less_int @ L @ K )
% 15.55/8.57         => ( ( modulo_modulo_int @ K @ L )
% 15.55/8.57            = K ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5865_signed__take__bit__Suc__1,axiom,
% 15.55/8.57      ! [N: nat] :
% 15.55/8.57        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 15.55/8.57        = one_one_int ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5866_signed__take__bit__of__minus__1,axiom,
% 15.55/8.57      ! [N: nat] :
% 15.55/8.57        ( ( bit_ri6519982836138164636nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 15.55/8.57        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5867_signed__take__bit__of__minus__1,axiom,
% 15.55/8.57      ! [N: nat] :
% 15.55/8.57        ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.57        = ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5868_signed__take__bit__numeral__of__1,axiom,
% 15.55/8.57      ! [K: num] :
% 15.55/8.57        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 15.55/8.57        = one_one_int ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5869_zmod__numeral__Bit0,axiom,
% 15.55/8.57      ! [V: num,W: num] :
% 15.55/8.57        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 15.55/8.57        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5870_signed__take__bit__Suc__bit0,axiom,
% 15.55/8.57      ! [N: nat,K: num] :
% 15.55/8.57        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 15.55/8.57        = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5871_signed__take__bit__Suc__minus__bit0,axiom,
% 15.55/8.57      ! [N: nat,K: num] :
% 15.55/8.57        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 15.55/8.57        = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5872_signed__take__bit__0,axiom,
% 15.55/8.57      ! [A: code_integer] :
% 15.55/8.57        ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 15.55/8.57        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5873_signed__take__bit__0,axiom,
% 15.55/8.57      ! [A: int] :
% 15.55/8.57        ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 15.55/8.57        = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5874__C5_Ohyps_C_I1_J,axiom,
% 15.55/8.57      vEBT_invar_vebt @ summary @ m ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5875_signed__take__bit__minus,axiom,
% 15.55/8.57      ! [N: nat,K: int] :
% 15.55/8.57        ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N @ K ) ) )
% 15.55/8.57        = ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5876_signed__take__bit__mult,axiom,
% 15.55/8.57      ! [N: nat,K: int,L: int] :
% 15.55/8.57        ( ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 15.55/8.57        = ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ K @ L ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5877_signed__take__bit__add,axiom,
% 15.55/8.57      ! [N: nat,K: int,L: int] :
% 15.55/8.57        ( ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 15.55/8.57        = ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ K @ L ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5878_signed__take__bit__diff,axiom,
% 15.55/8.57      ! [N: nat,K: int,L: int] :
% 15.55/8.57        ( ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 15.55/8.57        = ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ K @ L ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5879_length__pos__if__in__set,axiom,
% 15.55/8.57      ! [X3: option_nat,Xs2: list_option_nat] :
% 15.55/8.57        ( ( member_option_nat @ X3 @ ( set_option_nat2 @ Xs2 ) )
% 15.55/8.57       => ( ord_less_nat @ zero_zero_nat @ ( size_s6086282163384603972on_nat @ Xs2 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5880_length__pos__if__in__set,axiom,
% 15.55/8.57      ! [X3: real,Xs2: list_real] :
% 15.55/8.57        ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 15.55/8.57       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs2 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5881_length__pos__if__in__set,axiom,
% 15.55/8.57      ! [X3: set_nat,Xs2: list_set_nat] :
% 15.55/8.57        ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs2 ) )
% 15.55/8.57       => ( ord_less_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ Xs2 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5882_length__pos__if__in__set,axiom,
% 15.55/8.57      ! [X3: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 15.55/8.57        ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 15.55/8.57       => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5883_length__pos__if__in__set,axiom,
% 15.55/8.57      ! [X3: $o,Xs2: list_o] :
% 15.55/8.57        ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 15.55/8.57       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs2 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5884_length__pos__if__in__set,axiom,
% 15.55/8.57      ! [X3: nat,Xs2: list_nat] :
% 15.55/8.57        ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 15.55/8.57       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs2 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5885_length__pos__if__in__set,axiom,
% 15.55/8.57      ! [X3: int,Xs2: list_int] :
% 15.55/8.57        ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 15.55/8.57       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs2 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5886_all__set__conv__all__nth,axiom,
% 15.55/8.57      ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 15.55/8.57        ( ( ! [X: vEBT_VEBT] :
% 15.55/8.57              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 15.55/8.57             => ( P @ X ) ) )
% 15.55/8.57        = ( ! [I4: nat] :
% 15.55/8.57              ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 15.55/8.57             => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I4 ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5887_all__set__conv__all__nth,axiom,
% 15.55/8.57      ! [Xs2: list_o,P: $o > $o] :
% 15.55/8.57        ( ( ! [X: $o] :
% 15.55/8.57              ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 15.55/8.57             => ( P @ X ) ) )
% 15.55/8.57        = ( ! [I4: nat] :
% 15.55/8.57              ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs2 ) )
% 15.55/8.57             => ( P @ ( nth_o @ Xs2 @ I4 ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5888_all__set__conv__all__nth,axiom,
% 15.55/8.57      ! [Xs2: list_nat,P: nat > $o] :
% 15.55/8.57        ( ( ! [X: nat] :
% 15.55/8.57              ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 15.55/8.57             => ( P @ X ) ) )
% 15.55/8.57        = ( ! [I4: nat] :
% 15.55/8.57              ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 15.55/8.57             => ( P @ ( nth_nat @ Xs2 @ I4 ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5889_all__set__conv__all__nth,axiom,
% 15.55/8.57      ! [Xs2: list_int,P: int > $o] :
% 15.55/8.57        ( ( ! [X: int] :
% 15.55/8.57              ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 15.55/8.57             => ( P @ X ) ) )
% 15.55/8.57        = ( ! [I4: nat] :
% 15.55/8.57              ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs2 ) )
% 15.55/8.57             => ( P @ ( nth_int @ Xs2 @ I4 ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5890_all__nth__imp__all__set,axiom,
% 15.55/8.57      ! [Xs2: list_option_nat,P: option_nat > $o,X3: option_nat] :
% 15.55/8.57        ( ! [I3: nat] :
% 15.55/8.57            ( ( ord_less_nat @ I3 @ ( size_s6086282163384603972on_nat @ Xs2 ) )
% 15.55/8.57           => ( P @ ( nth_option_nat @ Xs2 @ I3 ) ) )
% 15.55/8.57       => ( ( member_option_nat @ X3 @ ( set_option_nat2 @ Xs2 ) )
% 15.55/8.57         => ( P @ X3 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5891_all__nth__imp__all__set,axiom,
% 15.55/8.57      ! [Xs2: list_real,P: real > $o,X3: real] :
% 15.55/8.57        ( ! [I3: nat] :
% 15.55/8.57            ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs2 ) )
% 15.55/8.57           => ( P @ ( nth_real @ Xs2 @ I3 ) ) )
% 15.55/8.57       => ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 15.55/8.57         => ( P @ X3 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5892_all__nth__imp__all__set,axiom,
% 15.55/8.57      ! [Xs2: list_set_nat,P: set_nat > $o,X3: set_nat] :
% 15.55/8.57        ( ! [I3: nat] :
% 15.55/8.57            ( ( ord_less_nat @ I3 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 15.55/8.57           => ( P @ ( nth_set_nat @ Xs2 @ I3 ) ) )
% 15.55/8.57       => ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs2 ) )
% 15.55/8.57         => ( P @ X3 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5893_all__nth__imp__all__set,axiom,
% 15.55/8.57      ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,X3: vEBT_VEBT] :
% 15.55/8.57        ( ! [I3: nat] :
% 15.55/8.57            ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 15.55/8.57           => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I3 ) ) )
% 15.55/8.57       => ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 15.55/8.57         => ( P @ X3 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5894_all__nth__imp__all__set,axiom,
% 15.55/8.57      ! [Xs2: list_o,P: $o > $o,X3: $o] :
% 15.55/8.57        ( ! [I3: nat] :
% 15.55/8.57            ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 15.55/8.57           => ( P @ ( nth_o @ Xs2 @ I3 ) ) )
% 15.55/8.57       => ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 15.55/8.57         => ( P @ X3 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5895_all__nth__imp__all__set,axiom,
% 15.55/8.57      ! [Xs2: list_nat,P: nat > $o,X3: nat] :
% 15.55/8.57        ( ! [I3: nat] :
% 15.55/8.57            ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 15.55/8.57           => ( P @ ( nth_nat @ Xs2 @ I3 ) ) )
% 15.55/8.57       => ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 15.55/8.57         => ( P @ X3 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5896_all__nth__imp__all__set,axiom,
% 15.55/8.57      ! [Xs2: list_int,P: int > $o,X3: int] :
% 15.55/8.57        ( ! [I3: nat] :
% 15.55/8.57            ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 15.55/8.57           => ( P @ ( nth_int @ Xs2 @ I3 ) ) )
% 15.55/8.57       => ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 15.55/8.57         => ( P @ X3 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5897_in__set__conv__nth,axiom,
% 15.55/8.57      ! [X3: option_nat,Xs2: list_option_nat] :
% 15.55/8.57        ( ( member_option_nat @ X3 @ ( set_option_nat2 @ Xs2 ) )
% 15.55/8.57        = ( ? [I4: nat] :
% 15.55/8.57              ( ( ord_less_nat @ I4 @ ( size_s6086282163384603972on_nat @ Xs2 ) )
% 15.55/8.57              & ( ( nth_option_nat @ Xs2 @ I4 )
% 15.55/8.57                = X3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5898_in__set__conv__nth,axiom,
% 15.55/8.57      ! [X3: real,Xs2: list_real] :
% 15.55/8.57        ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 15.55/8.57        = ( ? [I4: nat] :
% 15.55/8.57              ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs2 ) )
% 15.55/8.57              & ( ( nth_real @ Xs2 @ I4 )
% 15.55/8.57                = X3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5899_in__set__conv__nth,axiom,
% 15.55/8.57      ! [X3: set_nat,Xs2: list_set_nat] :
% 15.55/8.57        ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs2 ) )
% 15.55/8.57        = ( ? [I4: nat] :
% 15.55/8.57              ( ( ord_less_nat @ I4 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 15.55/8.57              & ( ( nth_set_nat @ Xs2 @ I4 )
% 15.55/8.57                = X3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5900_in__set__conv__nth,axiom,
% 15.55/8.57      ! [X3: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 15.55/8.57        ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 15.55/8.57        = ( ? [I4: nat] :
% 15.55/8.57              ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 15.55/8.57              & ( ( nth_VEBT_VEBT @ Xs2 @ I4 )
% 15.55/8.57                = X3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5901_in__set__conv__nth,axiom,
% 15.55/8.57      ! [X3: $o,Xs2: list_o] :
% 15.55/8.57        ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 15.55/8.57        = ( ? [I4: nat] :
% 15.55/8.57              ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs2 ) )
% 15.55/8.57              & ( ( nth_o @ Xs2 @ I4 )
% 15.55/8.57                = X3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5902_in__set__conv__nth,axiom,
% 15.55/8.57      ! [X3: nat,Xs2: list_nat] :
% 15.55/8.57        ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 15.55/8.57        = ( ? [I4: nat] :
% 15.55/8.57              ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 15.55/8.57              & ( ( nth_nat @ Xs2 @ I4 )
% 15.55/8.57                = X3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5903_in__set__conv__nth,axiom,
% 15.55/8.57      ! [X3: int,Xs2: list_int] :
% 15.55/8.57        ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 15.55/8.57        = ( ? [I4: nat] :
% 15.55/8.57              ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs2 ) )
% 15.55/8.57              & ( ( nth_int @ Xs2 @ I4 )
% 15.55/8.57                = X3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5904_list__ball__nth,axiom,
% 15.55/8.57      ! [N: nat,Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 15.55/8.57        ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 15.55/8.57       => ( ! [X4: vEBT_VEBT] :
% 15.55/8.57              ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 15.55/8.57             => ( P @ X4 ) )
% 15.55/8.57         => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5905_list__ball__nth,axiom,
% 15.55/8.57      ! [N: nat,Xs2: list_o,P: $o > $o] :
% 15.55/8.57        ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 15.55/8.57       => ( ! [X4: $o] :
% 15.55/8.57              ( ( member_o @ X4 @ ( set_o2 @ Xs2 ) )
% 15.55/8.57             => ( P @ X4 ) )
% 15.55/8.57         => ( P @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5906_list__ball__nth,axiom,
% 15.55/8.57      ! [N: nat,Xs2: list_nat,P: nat > $o] :
% 15.55/8.57        ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 15.55/8.57       => ( ! [X4: nat] :
% 15.55/8.57              ( ( member_nat @ X4 @ ( set_nat2 @ Xs2 ) )
% 15.55/8.57             => ( P @ X4 ) )
% 15.55/8.57         => ( P @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5907_list__ball__nth,axiom,
% 15.55/8.57      ! [N: nat,Xs2: list_int,P: int > $o] :
% 15.55/8.57        ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 15.55/8.57       => ( ! [X4: int] :
% 15.55/8.57              ( ( member_int @ X4 @ ( set_int2 @ Xs2 ) )
% 15.55/8.57             => ( P @ X4 ) )
% 15.55/8.57         => ( P @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5908_nth__mem,axiom,
% 15.55/8.57      ! [N: nat,Xs2: list_option_nat] :
% 15.55/8.57        ( ( ord_less_nat @ N @ ( size_s6086282163384603972on_nat @ Xs2 ) )
% 15.55/8.57       => ( member_option_nat @ ( nth_option_nat @ Xs2 @ N ) @ ( set_option_nat2 @ Xs2 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5909_nth__mem,axiom,
% 15.55/8.57      ! [N: nat,Xs2: list_real] :
% 15.55/8.57        ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 15.55/8.57       => ( member_real @ ( nth_real @ Xs2 @ N ) @ ( set_real2 @ Xs2 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5910_nth__mem,axiom,
% 15.55/8.57      ! [N: nat,Xs2: list_set_nat] :
% 15.55/8.57        ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 15.55/8.57       => ( member_set_nat @ ( nth_set_nat @ Xs2 @ N ) @ ( set_set_nat2 @ Xs2 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5911_nth__mem,axiom,
% 15.55/8.57      ! [N: nat,Xs2: list_VEBT_VEBT] :
% 15.55/8.57        ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 15.55/8.57       => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N ) @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5912_nth__mem,axiom,
% 15.55/8.57      ! [N: nat,Xs2: list_o] :
% 15.55/8.57        ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 15.55/8.57       => ( member_o @ ( nth_o @ Xs2 @ N ) @ ( set_o2 @ Xs2 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5913_nth__mem,axiom,
% 15.55/8.57      ! [N: nat,Xs2: list_nat] :
% 15.55/8.57        ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 15.55/8.57       => ( member_nat @ ( nth_nat @ Xs2 @ N ) @ ( set_nat2 @ Xs2 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5914_nth__mem,axiom,
% 15.55/8.57      ! [N: nat,Xs2: list_int] :
% 15.55/8.57        ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 15.55/8.57       => ( member_int @ ( nth_int @ Xs2 @ N ) @ ( set_int2 @ Xs2 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5915_zmod__le__nonneg__dividend,axiom,
% 15.55/8.57      ! [M: int,K: int] :
% 15.55/8.57        ( ( ord_less_eq_int @ zero_zero_int @ M )
% 15.55/8.57       => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5916_neg__mod__bound,axiom,
% 15.55/8.57      ! [L: int,K: int] :
% 15.55/8.57        ( ( ord_less_int @ L @ zero_zero_int )
% 15.55/8.57       => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5917_Euclidean__Division_Opos__mod__bound,axiom,
% 15.55/8.57      ! [L: int,K: int] :
% 15.55/8.57        ( ( ord_less_int @ zero_zero_int @ L )
% 15.55/8.57       => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5918_zmod__zminus2__not__zero,axiom,
% 15.55/8.57      ! [K: int,L: int] :
% 15.55/8.57        ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L ) )
% 15.55/8.57         != zero_zero_int )
% 15.55/8.57       => ( ( modulo_modulo_int @ K @ L )
% 15.55/8.57         != zero_zero_int ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5919_zmod__zminus1__not__zero,axiom,
% 15.55/8.57      ! [K: int,L: int] :
% 15.55/8.57        ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 15.55/8.57         != zero_zero_int )
% 15.55/8.57       => ( ( modulo_modulo_int @ K @ L )
% 15.55/8.57         != zero_zero_int ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5920_zmod__eq__0__iff,axiom,
% 15.55/8.57      ! [M: int,D3: int] :
% 15.55/8.57        ( ( ( modulo_modulo_int @ M @ D3 )
% 15.55/8.57          = zero_zero_int )
% 15.55/8.57        = ( ? [Q5: int] :
% 15.55/8.57              ( M
% 15.55/8.57              = ( times_times_int @ D3 @ Q5 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5921_zmod__eq__0D,axiom,
% 15.55/8.57      ! [M: int,D3: int] :
% 15.55/8.57        ( ( ( modulo_modulo_int @ M @ D3 )
% 15.55/8.57          = zero_zero_int )
% 15.55/8.57       => ? [Q4: int] :
% 15.55/8.57            ( M
% 15.55/8.57            = ( times_times_int @ D3 @ Q4 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5922_zmod__int,axiom,
% 15.55/8.57      ! [A: nat,B: nat] :
% 15.55/8.57        ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 15.55/8.57        = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5923_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 15.55/8.57      ! [N: nat,A: int,B: int] :
% 15.55/8.57        ( ( ( bit_ri631733984087533419it_int @ N @ A )
% 15.55/8.57          = ( bit_ri631733984087533419it_int @ N @ B ) )
% 15.55/8.57        = ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 15.55/8.57          = ( bit_se2923211474154528505it_int @ ( suc @ N ) @ B ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5924_signed__take__bit__take__bit,axiom,
% 15.55/8.57      ! [M: nat,N: nat,A: int] :
% 15.55/8.57        ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 15.55/8.57        = ( if_int_int @ ( ord_less_eq_nat @ N @ M ) @ ( bit_se2923211474154528505it_int @ N ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5925_zmod__trivial__iff,axiom,
% 15.55/8.57      ! [I: int,K: int] :
% 15.55/8.57        ( ( ( modulo_modulo_int @ I @ K )
% 15.55/8.57          = I )
% 15.55/8.57        = ( ( K = zero_zero_int )
% 15.55/8.57          | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 15.55/8.57            & ( ord_less_int @ I @ K ) )
% 15.55/8.57          | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 15.55/8.57            & ( ord_less_int @ K @ I ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5926_pos__mod__conj,axiom,
% 15.55/8.57      ! [B: int,A: int] :
% 15.55/8.57        ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.57       => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 15.55/8.57          & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5927_neg__mod__conj,axiom,
% 15.55/8.57      ! [B: int,A: int] :
% 15.55/8.57        ( ( ord_less_int @ B @ zero_zero_int )
% 15.55/8.57       => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 15.55/8.57          & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5928_Euclidean__Division_Opos__mod__sign,axiom,
% 15.55/8.57      ! [L: int,K: int] :
% 15.55/8.57        ( ( ord_less_int @ zero_zero_int @ L )
% 15.55/8.57       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5929_neg__mod__sign,axiom,
% 15.55/8.57      ! [L: int,K: int] :
% 15.55/8.57        ( ( ord_less_int @ L @ zero_zero_int )
% 15.55/8.57       => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5930_zdiv__mono__strict,axiom,
% 15.55/8.57      ! [A3: int,B5: int,N: int] :
% 15.55/8.57        ( ( ord_less_int @ A3 @ B5 )
% 15.55/8.57       => ( ( ord_less_int @ zero_zero_int @ N )
% 15.55/8.57         => ( ( ( modulo_modulo_int @ A3 @ N )
% 15.55/8.57              = zero_zero_int )
% 15.55/8.57           => ( ( ( modulo_modulo_int @ B5 @ N )
% 15.55/8.57                = zero_zero_int )
% 15.55/8.57             => ( ord_less_int @ ( divide_divide_int @ A3 @ N ) @ ( divide_divide_int @ B5 @ N ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5931_zmod__zminus2__eq__if,axiom,
% 15.55/8.57      ! [A: int,B: int] :
% 15.55/8.57        ( ( ( ( modulo_modulo_int @ A @ B )
% 15.55/8.57            = zero_zero_int )
% 15.55/8.57         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 15.55/8.57            = zero_zero_int ) )
% 15.55/8.57        & ( ( ( modulo_modulo_int @ A @ B )
% 15.55/8.57           != zero_zero_int )
% 15.55/8.57         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 15.55/8.57            = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5932_zmod__zminus1__eq__if,axiom,
% 15.55/8.57      ! [A: int,B: int] :
% 15.55/8.57        ( ( ( ( modulo_modulo_int @ A @ B )
% 15.55/8.57            = zero_zero_int )
% 15.55/8.57         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 15.55/8.57            = zero_zero_int ) )
% 15.55/8.57        & ( ( ( modulo_modulo_int @ A @ B )
% 15.55/8.57           != zero_zero_int )
% 15.55/8.57         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 15.55/8.57            = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5933_abs__mod__less,axiom,
% 15.55/8.57      ! [L: int,K: int] :
% 15.55/8.57        ( ( L != zero_zero_int )
% 15.55/8.57       => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5934_div__mod__decomp__int,axiom,
% 15.55/8.57      ! [A3: int,N: int] :
% 15.55/8.57        ( A3
% 15.55/8.57        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A3 @ N ) @ N ) @ ( modulo_modulo_int @ A3 @ N ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5935_mod__pos__neg__trivial,axiom,
% 15.55/8.57      ! [K: int,L: int] :
% 15.55/8.57        ( ( ord_less_int @ zero_zero_int @ K )
% 15.55/8.57       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 15.55/8.57         => ( ( modulo_modulo_int @ K @ L )
% 15.55/8.57            = ( plus_plus_int @ K @ L ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5936_mod__pos__geq,axiom,
% 15.55/8.57      ! [L: int,K: int] :
% 15.55/8.57        ( ( ord_less_int @ zero_zero_int @ L )
% 15.55/8.57       => ( ( ord_less_eq_int @ L @ K )
% 15.55/8.57         => ( ( modulo_modulo_int @ K @ L )
% 15.55/8.57            = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5937_mod__int__pos__iff,axiom,
% 15.55/8.57      ! [K: int,L: int] :
% 15.55/8.57        ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 15.55/8.57        = ( ( dvd_dvd_int @ L @ K )
% 15.55/8.57          | ( ( L = zero_zero_int )
% 15.55/8.57            & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 15.55/8.57          | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5938_nat__mod__distrib,axiom,
% 15.55/8.57      ! [X3: int,Y3: int] :
% 15.55/8.57        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 15.55/8.57       => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 15.55/8.57         => ( ( nat2 @ ( modulo_modulo_int @ X3 @ Y3 ) )
% 15.55/8.57            = ( modulo_modulo_nat @ ( nat2 @ X3 ) @ ( nat2 @ Y3 ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5939_take__bit__signed__take__bit,axiom,
% 15.55/8.57      ! [M: nat,N: nat,A: int] :
% 15.55/8.57        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 15.55/8.57       => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N @ A ) )
% 15.55/8.57          = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5940_mod__abs__eq__div__nat,axiom,
% 15.55/8.57      ! [K: int,L: int] :
% 15.55/8.57        ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 15.55/8.57        = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5941_real__of__int__div__aux,axiom,
% 15.55/8.57      ! [X3: int,D3: int] :
% 15.55/8.57        ( ( divide_divide_real @ ( ring_1_of_int_real @ X3 ) @ ( ring_1_of_int_real @ D3 ) )
% 15.55/8.57        = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X3 @ D3 ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X3 @ D3 ) ) @ ( ring_1_of_int_real @ D3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5942_binomial__maximum,axiom,
% 15.55/8.57      ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5943_binomial__antimono,axiom,
% 15.55/8.57      ! [K: nat,K6: nat,N: nat] :
% 15.55/8.57        ( ( ord_less_eq_nat @ K @ K6 )
% 15.55/8.57       => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 15.55/8.57         => ( ( ord_less_eq_nat @ K6 @ N )
% 15.55/8.57           => ( ord_less_eq_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5944_binomial__mono,axiom,
% 15.55/8.57      ! [K: nat,K6: nat,N: nat] :
% 15.55/8.57        ( ( ord_less_eq_nat @ K @ K6 )
% 15.55/8.57       => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 15.55/8.57         => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5945_binomial__maximum_H,axiom,
% 15.55/8.57      ! [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 ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5946_split__zmod,axiom,
% 15.55/8.57      ! [P: int > $o,N: int,K: int] :
% 15.55/8.57        ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 15.55/8.57        = ( ( ( K = zero_zero_int )
% 15.55/8.57           => ( P @ N ) )
% 15.55/8.57          & ( ( ord_less_int @ zero_zero_int @ K )
% 15.55/8.57           => ! [I4: int,J3: int] :
% 15.55/8.57                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 15.55/8.57                  & ( ord_less_int @ J3 @ K )
% 15.55/8.57                  & ( N
% 15.55/8.57                    = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 15.55/8.57               => ( P @ J3 ) ) )
% 15.55/8.57          & ( ( ord_less_int @ K @ zero_zero_int )
% 15.55/8.57           => ! [I4: int,J3: int] :
% 15.55/8.57                ( ( ( ord_less_int @ K @ J3 )
% 15.55/8.57                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 15.55/8.57                  & ( N
% 15.55/8.57                    = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 15.55/8.57               => ( P @ J3 ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5947_int__mod__neg__eq,axiom,
% 15.55/8.57      ! [A: int,B: int,Q3: int,R2: int] :
% 15.55/8.57        ( ( A
% 15.55/8.57          = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 15.55/8.57       => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 15.55/8.57         => ( ( ord_less_int @ B @ R2 )
% 15.55/8.57           => ( ( modulo_modulo_int @ A @ B )
% 15.55/8.57              = R2 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5948_int__mod__pos__eq,axiom,
% 15.55/8.57      ! [A: int,B: int,Q3: int,R2: int] :
% 15.55/8.57        ( ( A
% 15.55/8.57          = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 15.55/8.57       => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 15.55/8.57         => ( ( ord_less_int @ R2 @ B )
% 15.55/8.57           => ( ( modulo_modulo_int @ A @ B )
% 15.55/8.57              = R2 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5949_minus__mod__int__eq,axiom,
% 15.55/8.57      ! [L: int,K: int] :
% 15.55/8.57        ( ( ord_less_eq_int @ zero_zero_int @ L )
% 15.55/8.57       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 15.55/8.57          = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5950_zmod__minus1,axiom,
% 15.55/8.57      ! [B: int] :
% 15.55/8.57        ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.57       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 15.55/8.57          = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5951_signed__take__bit__int__less__exp,axiom,
% 15.55/8.57      ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5952_take__bit__int__def,axiom,
% 15.55/8.57      ( bit_se2923211474154528505it_int
% 15.55/8.57      = ( ^ [N3: nat,K3: int] : ( modulo_modulo_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5953_zmod__zmult2__eq,axiom,
% 15.55/8.57      ! [C: int,A: int,B: int] :
% 15.55/8.57        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 15.55/8.57       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 15.55/8.57          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5954_zdiv__zminus2__eq__if,axiom,
% 15.55/8.57      ! [B: int,A: int] :
% 15.55/8.57        ( ( B != zero_zero_int )
% 15.55/8.57       => ( ( ( ( modulo_modulo_int @ A @ B )
% 15.55/8.57              = zero_zero_int )
% 15.55/8.57           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 15.55/8.57              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 15.55/8.57          & ( ( ( modulo_modulo_int @ A @ B )
% 15.55/8.57             != zero_zero_int )
% 15.55/8.57           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 15.55/8.57              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5955_zdiv__zminus1__eq__if,axiom,
% 15.55/8.57      ! [B: int,A: int] :
% 15.55/8.57        ( ( B != zero_zero_int )
% 15.55/8.57       => ( ( ( ( modulo_modulo_int @ A @ B )
% 15.55/8.57              = zero_zero_int )
% 15.55/8.57           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 15.55/8.57              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 15.55/8.57          & ( ( ( modulo_modulo_int @ A @ B )
% 15.55/8.57             != zero_zero_int )
% 15.55/8.57           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 15.55/8.57              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5956_even__signed__take__bit__iff,axiom,
% 15.55/8.57      ! [M: nat,A: code_integer] :
% 15.55/8.57        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 15.55/8.57        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5957_even__signed__take__bit__iff,axiom,
% 15.55/8.57      ! [M: nat,A: int] :
% 15.55/8.57        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 15.55/8.57        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5958_binomial__less__binomial__Suc,axiom,
% 15.55/8.57      ! [K: nat,N: nat] :
% 15.55/8.57        ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.57       => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5959_binomial__strict__mono,axiom,
% 15.55/8.57      ! [K: nat,K6: nat,N: nat] :
% 15.55/8.57        ( ( ord_less_nat @ K @ K6 )
% 15.55/8.57       => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 15.55/8.57         => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5960_binomial__strict__antimono,axiom,
% 15.55/8.57      ! [K: nat,K6: nat,N: nat] :
% 15.55/8.57        ( ( ord_less_nat @ K @ K6 )
% 15.55/8.57       => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 15.55/8.57         => ( ( ord_less_eq_nat @ K6 @ N )
% 15.55/8.57           => ( ord_less_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5961_central__binomial__odd,axiom,
% 15.55/8.57      ! [N: nat] :
% 15.55/8.57        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.57       => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.57          = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5962_verit__le__mono__div__int,axiom,
% 15.55/8.57      ! [A3: int,B5: int,N: int] :
% 15.55/8.57        ( ( ord_less_int @ A3 @ B5 )
% 15.55/8.57       => ( ( ord_less_int @ zero_zero_int @ N )
% 15.55/8.57         => ( ord_less_eq_int
% 15.55/8.57            @ ( plus_plus_int @ ( divide_divide_int @ A3 @ N )
% 15.55/8.57              @ ( if_int
% 15.55/8.57                @ ( ( modulo_modulo_int @ B5 @ N )
% 15.55/8.57                  = zero_zero_int )
% 15.55/8.57                @ one_one_int
% 15.55/8.57                @ zero_zero_int ) )
% 15.55/8.57            @ ( divide_divide_int @ B5 @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5963_signed__take__bit__int__greater__eq__self__iff,axiom,
% 15.55/8.57      ! [K: int,N: nat] :
% 15.55/8.57        ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 15.55/8.57        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5964_signed__take__bit__int__less__self__iff,axiom,
% 15.55/8.57      ! [N: nat,K: int] :
% 15.55/8.57        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 15.55/8.57        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5965_split__pos__lemma,axiom,
% 15.55/8.57      ! [K: int,P: int > int > $o,N: int] :
% 15.55/8.57        ( ( ord_less_int @ zero_zero_int @ K )
% 15.55/8.57       => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 15.55/8.57          = ( ! [I4: int,J3: int] :
% 15.55/8.57                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 15.55/8.57                  & ( ord_less_int @ J3 @ K )
% 15.55/8.57                  & ( N
% 15.55/8.57                    = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 15.55/8.57               => ( P @ I4 @ J3 ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5966_split__neg__lemma,axiom,
% 15.55/8.57      ! [K: int,P: int > int > $o,N: int] :
% 15.55/8.57        ( ( ord_less_int @ K @ zero_zero_int )
% 15.55/8.57       => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 15.55/8.57          = ( ! [I4: int,J3: int] :
% 15.55/8.57                ( ( ( ord_less_int @ K @ J3 )
% 15.55/8.57                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 15.55/8.57                  & ( N
% 15.55/8.57                    = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 15.55/8.57               => ( P @ I4 @ J3 ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5967_signed__take__bit__int__less__eq__self__iff,axiom,
% 15.55/8.57      ! [N: nat,K: int] :
% 15.55/8.57        ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 15.55/8.57        = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5968_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 15.55/8.57      ! [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 ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5969_signed__take__bit__int__greater__self__iff,axiom,
% 15.55/8.57      ! [K: int,N: nat] :
% 15.55/8.57        ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 15.55/8.57        = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5970_length__induct,axiom,
% 15.55/8.57      ! [P: list_VEBT_VEBT > $o,Xs2: list_VEBT_VEBT] :
% 15.55/8.57        ( ! [Xs3: list_VEBT_VEBT] :
% 15.55/8.57            ( ! [Ys2: list_VEBT_VEBT] :
% 15.55/8.57                ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 15.55/8.57               => ( P @ Ys2 ) )
% 15.55/8.57           => ( P @ Xs3 ) )
% 15.55/8.57       => ( P @ Xs2 ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5971_length__induct,axiom,
% 15.55/8.57      ! [P: list_o > $o,Xs2: list_o] :
% 15.55/8.57        ( ! [Xs3: list_o] :
% 15.55/8.57            ( ! [Ys2: list_o] :
% 15.55/8.57                ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs3 ) )
% 15.55/8.57               => ( P @ Ys2 ) )
% 15.55/8.57           => ( P @ Xs3 ) )
% 15.55/8.57       => ( P @ Xs2 ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5972_length__induct,axiom,
% 15.55/8.57      ! [P: list_nat > $o,Xs2: list_nat] :
% 15.55/8.57        ( ! [Xs3: list_nat] :
% 15.55/8.57            ( ! [Ys2: list_nat] :
% 15.55/8.57                ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs3 ) )
% 15.55/8.57               => ( P @ Ys2 ) )
% 15.55/8.57           => ( P @ Xs3 ) )
% 15.55/8.57       => ( P @ Xs2 ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5973_length__induct,axiom,
% 15.55/8.57      ! [P: list_int > $o,Xs2: list_int] :
% 15.55/8.57        ( ! [Xs3: list_int] :
% 15.55/8.57            ( ! [Ys2: list_int] :
% 15.55/8.57                ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs3 ) )
% 15.55/8.57               => ( P @ Ys2 ) )
% 15.55/8.57           => ( P @ Xs3 ) )
% 15.55/8.57       => ( P @ Xs2 ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5974_signed__take__bit__int__less__eq,axiom,
% 15.55/8.57      ! [N: nat,K: int] :
% 15.55/8.57        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 15.55/8.57       => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5975_signed__take__bit__int__eq__self,axiom,
% 15.55/8.57      ! [N: nat,K: int] :
% 15.55/8.57        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 15.55/8.57       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.57         => ( ( bit_ri631733984087533419it_int @ N @ K )
% 15.55/8.57            = K ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5976_signed__take__bit__int__eq__self__iff,axiom,
% 15.55/8.57      ! [N: nat,K: int] :
% 15.55/8.57        ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 15.55/8.57          = K )
% 15.55/8.57        = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 15.55/8.57          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5977_pos__zmod__mult__2,axiom,
% 15.55/8.57      ! [A: int,B: int] :
% 15.55/8.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 15.55/8.57       => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 15.55/8.57          = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5978_signed__take__bit__eq__take__bit__shift,axiom,
% 15.55/8.57      ( bit_ri631733984087533419it_int
% 15.55/8.57      = ( ^ [N3: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N3 ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5979_neg__zmod__mult__2,axiom,
% 15.55/8.57      ! [A: int,B: int] :
% 15.55/8.57        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 15.55/8.57       => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 15.55/8.57          = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) @ one_one_int ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5980_signed__take__bit__int__greater__eq,axiom,
% 15.55/8.57      ! [K: int,N: nat] :
% 15.55/8.57        ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 15.55/8.57       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5981_signed__take__bit__Suc,axiom,
% 15.55/8.57      ! [N: nat,A: code_integer] :
% 15.55/8.57        ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ A )
% 15.55/8.57        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5982_signed__take__bit__Suc,axiom,
% 15.55/8.57      ! [N: nat,A: int] :
% 15.55/8.57        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 15.55/8.57        = ( 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 ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5983_list__eq__iff__nth__eq,axiom,
% 15.55/8.57      ( ( ^ [Y5: list_VEBT_VEBT,Z2: list_VEBT_VEBT] : ( Y5 = Z2 ) )
% 15.55/8.57      = ( ^ [Xs: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 15.55/8.57            ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 15.55/8.57              = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 15.55/8.57            & ! [I4: nat] :
% 15.55/8.57                ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 15.55/8.57               => ( ( nth_VEBT_VEBT @ Xs @ I4 )
% 15.55/8.57                  = ( nth_VEBT_VEBT @ Ys3 @ I4 ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5984_list__eq__iff__nth__eq,axiom,
% 15.55/8.57      ( ( ^ [Y5: list_o,Z2: list_o] : ( Y5 = Z2 ) )
% 15.55/8.57      = ( ^ [Xs: list_o,Ys3: list_o] :
% 15.55/8.57            ( ( ( size_size_list_o @ Xs )
% 15.55/8.57              = ( size_size_list_o @ Ys3 ) )
% 15.55/8.57            & ! [I4: nat] :
% 15.55/8.57                ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 15.55/8.57               => ( ( nth_o @ Xs @ I4 )
% 15.55/8.57                  = ( nth_o @ Ys3 @ I4 ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5985_list__eq__iff__nth__eq,axiom,
% 15.55/8.57      ( ( ^ [Y5: list_nat,Z2: list_nat] : ( Y5 = Z2 ) )
% 15.55/8.57      = ( ^ [Xs: list_nat,Ys3: list_nat] :
% 15.55/8.57            ( ( ( size_size_list_nat @ Xs )
% 15.55/8.57              = ( size_size_list_nat @ Ys3 ) )
% 15.55/8.57            & ! [I4: nat] :
% 15.55/8.57                ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 15.55/8.57               => ( ( nth_nat @ Xs @ I4 )
% 15.55/8.57                  = ( nth_nat @ Ys3 @ I4 ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5986_list__eq__iff__nth__eq,axiom,
% 15.55/8.57      ( ( ^ [Y5: list_int,Z2: list_int] : ( Y5 = Z2 ) )
% 15.55/8.57      = ( ^ [Xs: list_int,Ys3: list_int] :
% 15.55/8.57            ( ( ( size_size_list_int @ Xs )
% 15.55/8.57              = ( size_size_list_int @ Ys3 ) )
% 15.55/8.57            & ! [I4: nat] :
% 15.55/8.57                ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 15.55/8.57               => ( ( nth_int @ Xs @ I4 )
% 15.55/8.57                  = ( nth_int @ Ys3 @ I4 ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5987_Skolem__list__nth,axiom,
% 15.55/8.57      ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 15.55/8.57        ( ( ! [I4: nat] :
% 15.55/8.57              ( ( ord_less_nat @ I4 @ K )
% 15.55/8.57             => ? [X8: vEBT_VEBT] : ( P @ I4 @ X8 ) ) )
% 15.55/8.57        = ( ? [Xs: list_VEBT_VEBT] :
% 15.55/8.57              ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 15.55/8.57                = K )
% 15.55/8.57              & ! [I4: nat] :
% 15.55/8.57                  ( ( ord_less_nat @ I4 @ K )
% 15.55/8.57                 => ( P @ I4 @ ( nth_VEBT_VEBT @ Xs @ I4 ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5988_Skolem__list__nth,axiom,
% 15.55/8.57      ! [K: nat,P: nat > $o > $o] :
% 15.55/8.57        ( ( ! [I4: nat] :
% 15.55/8.57              ( ( ord_less_nat @ I4 @ K )
% 15.55/8.57             => ? [X8: $o] : ( P @ I4 @ X8 ) ) )
% 15.55/8.57        = ( ? [Xs: list_o] :
% 15.55/8.57              ( ( ( size_size_list_o @ Xs )
% 15.55/8.57                = K )
% 15.55/8.57              & ! [I4: nat] :
% 15.55/8.57                  ( ( ord_less_nat @ I4 @ K )
% 15.55/8.57                 => ( P @ I4 @ ( nth_o @ Xs @ I4 ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5989_Skolem__list__nth,axiom,
% 15.55/8.57      ! [K: nat,P: nat > nat > $o] :
% 15.55/8.57        ( ( ! [I4: nat] :
% 15.55/8.57              ( ( ord_less_nat @ I4 @ K )
% 15.55/8.57             => ? [X8: nat] : ( P @ I4 @ X8 ) ) )
% 15.55/8.57        = ( ? [Xs: list_nat] :
% 15.55/8.57              ( ( ( size_size_list_nat @ Xs )
% 15.55/8.57                = K )
% 15.55/8.57              & ! [I4: nat] :
% 15.55/8.57                  ( ( ord_less_nat @ I4 @ K )
% 15.55/8.57                 => ( P @ I4 @ ( nth_nat @ Xs @ I4 ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5990_Skolem__list__nth,axiom,
% 15.55/8.57      ! [K: nat,P: nat > int > $o] :
% 15.55/8.57        ( ( ! [I4: nat] :
% 15.55/8.57              ( ( ord_less_nat @ I4 @ K )
% 15.55/8.57             => ? [X8: int] : ( P @ I4 @ X8 ) ) )
% 15.55/8.57        = ( ? [Xs: list_int] :
% 15.55/8.57              ( ( ( size_size_list_int @ Xs )
% 15.55/8.57                = K )
% 15.55/8.57              & ! [I4: nat] :
% 15.55/8.57                  ( ( ord_less_nat @ I4 @ K )
% 15.55/8.57                 => ( P @ I4 @ ( nth_int @ Xs @ I4 ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5991_zero__less__binomial__iff,axiom,
% 15.55/8.57      ! [N: nat,K: nat] :
% 15.55/8.57        ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 15.55/8.57        = ( ord_less_eq_nat @ K @ N ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5992_choose__two,axiom,
% 15.55/8.57      ! [N: nat] :
% 15.55/8.57        ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.57        = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5993_binomial__n__0,axiom,
% 15.55/8.57      ! [N: nat] :
% 15.55/8.57        ( ( binomial @ N @ zero_zero_nat )
% 15.55/8.57        = one_one_nat ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5994_binomial__eq__0__iff,axiom,
% 15.55/8.57      ! [N: nat,K: nat] :
% 15.55/8.57        ( ( ( binomial @ N @ K )
% 15.55/8.57          = zero_zero_nat )
% 15.55/8.57        = ( ord_less_nat @ N @ K ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5995_binomial__0__Suc,axiom,
% 15.55/8.57      ! [K: nat] :
% 15.55/8.57        ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 15.55/8.57        = zero_zero_nat ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5996_binomial__1,axiom,
% 15.55/8.57      ! [N: nat] :
% 15.55/8.57        ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 15.55/8.57        = N ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5997_valid__0__not,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT] :
% 15.55/8.57        ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5998_valid__tree__deg__neq__0,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT] :
% 15.55/8.57        ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_5999_deg__not__0,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,N: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.57       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6000_set__n__deg__not__0,axiom,
% 15.55/8.57      ! [TreeList2: list_VEBT_VEBT,N: nat,M: nat] :
% 15.55/8.57        ( ! [X4: vEBT_VEBT] :
% 15.55/8.57            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 15.55/8.57           => ( vEBT_invar_vebt @ X4 @ N ) )
% 15.55/8.57       => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 15.55/8.57            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 15.55/8.57         => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6001_binomial__eq__0,axiom,
% 15.55/8.57      ! [N: nat,K: nat] :
% 15.55/8.57        ( ( ord_less_nat @ N @ K )
% 15.55/8.57       => ( ( binomial @ N @ K )
% 15.55/8.57          = zero_zero_nat ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6002_binomial__symmetric,axiom,
% 15.55/8.57      ! [K: nat,N: nat] :
% 15.55/8.57        ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.57       => ( ( binomial @ N @ K )
% 15.55/8.57          = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6003_binomial__le__pow,axiom,
% 15.55/8.57      ! [R2: nat,N: nat] :
% 15.55/8.57        ( ( ord_less_eq_nat @ R2 @ N )
% 15.55/8.57       => ( ord_less_eq_nat @ ( binomial @ N @ R2 ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6004_zero__less__binomial,axiom,
% 15.55/8.57      ! [K: nat,N: nat] :
% 15.55/8.57        ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.57       => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6005_choose__mult,axiom,
% 15.55/8.57      ! [K: nat,M: nat,N: nat] :
% 15.55/8.57        ( ( ord_less_eq_nat @ K @ M )
% 15.55/8.57       => ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.57         => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 15.55/8.57            = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6006_binomial__ge__n__over__k__pow__k,axiom,
% 15.55/8.57      ! [K: nat,N: nat] :
% 15.55/8.57        ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.57       => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6007_binomial__ge__n__over__k__pow__k,axiom,
% 15.55/8.57      ! [K: nat,N: nat] :
% 15.55/8.57        ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.57       => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6008_binomial__le__pow2,axiom,
% 15.55/8.57      ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6009_choose__reduce__nat,axiom,
% 15.55/8.57      ! [N: nat,K: nat] :
% 15.55/8.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.57       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 15.55/8.57         => ( ( binomial @ N @ K )
% 15.55/8.57            = ( 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 ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6010_times__binomial__minus1__eq,axiom,
% 15.55/8.57      ! [K: nat,N: nat] :
% 15.55/8.57        ( ( ord_less_nat @ zero_zero_nat @ K )
% 15.55/8.57       => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 15.55/8.57          = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6011_binomial__addition__formula,axiom,
% 15.55/8.57      ! [N: nat,K: nat] :
% 15.55/8.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.57       => ( ( binomial @ N @ ( suc @ K ) )
% 15.55/8.57          = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6012_valid__insert__both__member__options__pres,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,N: nat,X3: nat,Y3: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.57       => ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.57         => ( ( ord_less_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.57           => ( ( vEBT_V8194947554948674370ptions @ T @ X3 )
% 15.55/8.57             => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y3 ) @ X3 ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6013_valid__insert__both__member__options__add,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.57       => ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.57         => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X3 ) @ X3 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6014_height__double__log__univ__size,axiom,
% 15.55/8.57      ! [U: real,Deg: nat,T: vEBT_VEBT] :
% 15.55/8.57        ( ( U
% 15.55/8.57          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Deg ) )
% 15.55/8.57       => ( ( vEBT_invar_vebt @ T @ Deg )
% 15.55/8.57         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_VEBT_height @ T ) ) @ ( plus_plus_real @ one_one_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6015_heigt__uplog__rel,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,N: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.57       => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ T ) )
% 15.55/8.57          = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6016_helpypredd,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,N: nat,X3: nat,Y3: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.57       => ( ( ( vEBT_vebt_pred @ T @ X3 )
% 15.55/8.57            = ( some_nat @ Y3 ) )
% 15.55/8.57         => ( ord_less_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6017_helpyd,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,N: nat,X3: nat,Y3: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.57       => ( ( ( vEBT_vebt_succ @ T @ X3 )
% 15.55/8.57            = ( some_nat @ Y3 ) )
% 15.55/8.57         => ( ord_less_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6018_two__powr__height__bound__deg,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,N: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.57       => ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_VEBT_height @ T ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6019_both__member__options__ding,axiom,
% 15.55/8.57      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 15.55/8.57       => ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 15.55/8.57         => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.57           => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ X3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6020_post__member__pre__member,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,N: nat,X3: nat,Y3: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.57       => ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.57         => ( ( ord_less_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.57           => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X3 ) @ Y3 )
% 15.55/8.57             => ( ( vEBT_vebt_member @ T @ Y3 )
% 15.55/8.57                | ( X3 = Y3 ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6021_buildup__gives__valid,axiom,
% 15.55/8.57      ! [N: nat] :
% 15.55/8.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.57       => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6022_member__bound,axiom,
% 15.55/8.57      ! [Tree: vEBT_VEBT,X3: nat,N: nat] :
% 15.55/8.57        ( ( vEBT_vebt_member @ Tree @ X3 )
% 15.55/8.57       => ( ( vEBT_invar_vebt @ Tree @ N )
% 15.55/8.57         => ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6023_misiz,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,N: nat,M: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.57       => ( ( ( some_nat @ M )
% 15.55/8.57            = ( vEBT_vebt_mint @ T ) )
% 15.55/8.57         => ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6024_height__compose__child,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,Summary: vEBT_VEBT] :
% 15.55/8.57        ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 15.55/8.57       => ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6025_deg__deg__n,axiom,
% 15.55/8.57      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 15.55/8.57       => ( Deg = N ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6026_deg__SUcn__Node,axiom,
% 15.55/8.57      ! [Tree: vEBT_VEBT,N: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 15.55/8.57       => ? [Info2: option4927543243414619207at_nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 15.55/8.57            ( Tree
% 15.55/8.57            = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N ) ) @ TreeList3 @ S3 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6027_valid__member__both__member__options,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.57       => ( ( vEBT_V8194947554948674370ptions @ T @ X3 )
% 15.55/8.57         => ( vEBT_vebt_member @ T @ X3 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6028_both__member__options__equiv__member,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.57       => ( ( vEBT_V8194947554948674370ptions @ T @ X3 )
% 15.55/8.57          = ( vEBT_vebt_member @ T @ X3 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6029_mint__member,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.57       => ( ( ( vEBT_vebt_mint @ T )
% 15.55/8.57            = ( some_nat @ Maxi ) )
% 15.55/8.57         => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6030_height__compose__summary,axiom,
% 15.55/8.57      ! [Summary: vEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ Summary ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6031_mint__corr__help,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,N: nat,Mini: nat,X3: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.57       => ( ( ( vEBT_vebt_mint @ T )
% 15.55/8.57            = ( some_nat @ Mini ) )
% 15.55/8.57         => ( ( vEBT_vebt_member @ T @ X3 )
% 15.55/8.57           => ( ord_less_eq_nat @ Mini @ X3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6032_member__correct,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.57       => ( ( vEBT_vebt_member @ T @ X3 )
% 15.55/8.57          = ( member_nat @ X3 @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6033_mint__corr,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.57       => ( ( ( vEBT_vebt_mint @ T )
% 15.55/8.57            = ( some_nat @ X3 ) )
% 15.55/8.57         => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X3 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6034_mint__sound,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.57       => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X3 )
% 15.55/8.57         => ( ( vEBT_vebt_mint @ T )
% 15.55/8.57            = ( some_nat @ X3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6035_both__member__options__from__chilf__to__complete__tree,axiom,
% 15.55/8.57      ! [X3: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 15.55/8.57        ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.57       => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 15.55/8.57         => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.57           => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6036_member__inv,axiom,
% 15.55/8.57      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 15.55/8.57        ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.57       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.57          & ( ( X3 = Mi )
% 15.55/8.57            | ( X3 = Ma )
% 15.55/8.57            | ( ( ord_less_nat @ X3 @ Ma )
% 15.55/8.57              & ( ord_less_nat @ Mi @ X3 )
% 15.55/8.57              & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.57              & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6037_mintlistlength,axiom,
% 15.55/8.57      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 15.55/8.57       => ( ( Mi != Ma )
% 15.55/8.57         => ( ( ord_less_nat @ Mi @ Ma )
% 15.55/8.57            & ? [M4: nat] :
% 15.55/8.57                ( ( ( some_nat @ M4 )
% 15.55/8.57                  = ( vEBT_vebt_mint @ Summary ) )
% 15.55/8.57                & ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6038_both__member__options__from__complete__tree__to__child,axiom,
% 15.55/8.57      ! [Deg: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 15.55/8.57        ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 15.55/8.57       => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.57         => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.57            | ( X3 = Mi )
% 15.55/8.57            | ( X3 = Ma ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6039_set__vebt__set__vebt_H__valid,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,N: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.57       => ( ( vEBT_set_vebt @ T )
% 15.55/8.57          = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6040_mi__eq__ma__no__ch,axiom,
% 15.55/8.57      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 15.55/8.57       => ( ( Mi = Ma )
% 15.55/8.57         => ( ! [X6: vEBT_VEBT] :
% 15.55/8.57                ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 15.55/8.57               => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_12 ) )
% 15.55/8.57            & ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6041_insert__simp__mima,axiom,
% 15.55/8.57      ! [X3: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 15.55/8.57        ( ( ( X3 = Mi )
% 15.55/8.57          | ( X3 = Ma ) )
% 15.55/8.57       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.57         => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.57            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6042_mi__ma__2__deg,axiom,
% 15.55/8.57      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 15.55/8.57       => ( ( ord_less_eq_nat @ Mi @ Ma )
% 15.55/8.57          & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6043_pred__max,axiom,
% 15.55/8.57      ! [Deg: nat,Ma: nat,X3: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 15.55/8.57        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.57       => ( ( ord_less_nat @ Ma @ X3 )
% 15.55/8.57         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.57            = ( some_nat @ Ma ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6044_succ__min,axiom,
% 15.55/8.57      ! [Deg: nat,X3: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 15.55/8.57        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.57       => ( ( ord_less_nat @ X3 @ Mi )
% 15.55/8.57         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.57            = ( some_nat @ Mi ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6045_succ__member,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,X3: nat,Y3: nat] :
% 15.55/8.57        ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X3 @ Y3 )
% 15.55/8.57        = ( ( vEBT_vebt_member @ T @ Y3 )
% 15.55/8.57          & ( ord_less_nat @ X3 @ Y3 )
% 15.55/8.57          & ! [Z6: nat] :
% 15.55/8.57              ( ( ( vEBT_vebt_member @ T @ Z6 )
% 15.55/8.57                & ( ord_less_nat @ X3 @ Z6 ) )
% 15.55/8.57             => ( ord_less_eq_nat @ Y3 @ Z6 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6046_pred__member,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,X3: nat,Y3: nat] :
% 15.55/8.57        ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X3 @ Y3 )
% 15.55/8.57        = ( ( vEBT_vebt_member @ T @ Y3 )
% 15.55/8.57          & ( ord_less_nat @ Y3 @ X3 )
% 15.55/8.57          & ! [Z6: nat] :
% 15.55/8.57              ( ( ( vEBT_vebt_member @ T @ Z6 )
% 15.55/8.57                & ( ord_less_nat @ Z6 @ X3 ) )
% 15.55/8.57             => ( ord_less_eq_nat @ Z6 @ Y3 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6047_pred__corr,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,N: nat,X3: nat,Px: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.57       => ( ( ( vEBT_vebt_pred @ T @ X3 )
% 15.55/8.57            = ( some_nat @ Px ) )
% 15.55/8.57          = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X3 @ Px ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6048_succ__corr,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,N: nat,X3: nat,Sx: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.57       => ( ( ( vEBT_vebt_succ @ T @ X3 )
% 15.55/8.57            = ( some_nat @ Sx ) )
% 15.55/8.57          = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X3 @ Sx ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6049_pred__correct,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,N: nat,X3: nat,Sx: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.57       => ( ( ( vEBT_vebt_pred @ T @ X3 )
% 15.55/8.57            = ( some_nat @ Sx ) )
% 15.55/8.57          = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X3 @ Sx ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6050_succ__correct,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,N: nat,X3: nat,Sx: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.57       => ( ( ( vEBT_vebt_succ @ T @ X3 )
% 15.55/8.57            = ( some_nat @ Sx ) )
% 15.55/8.57          = ( vEBT_is_succ_in_set @ ( vEBT_set_vebt @ T ) @ X3 @ Sx ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6051_vebt__mint_Osimps_I3_J,axiom,
% 15.55/8.57      ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 15.55/8.57        ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 15.55/8.57        = ( some_nat @ Mi ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6052_invar__vebt_Ointros_I4_J,axiom,
% 15.55/8.57      ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 15.55/8.57        ( ! [X4: vEBT_VEBT] :
% 15.55/8.57            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 15.55/8.57           => ( vEBT_invar_vebt @ X4 @ N ) )
% 15.55/8.57       => ( ( vEBT_invar_vebt @ Summary @ M )
% 15.55/8.57         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 15.55/8.57              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 15.55/8.57           => ( ( M = N )
% 15.55/8.57             => ( ( Deg
% 15.55/8.57                  = ( plus_plus_nat @ N @ M ) )
% 15.55/8.57               => ( ! [I3: nat] :
% 15.55/8.57                      ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 15.55/8.57                     => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X8 ) )
% 15.55/8.57                        = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 15.55/8.57                 => ( ( ( Mi = Ma )
% 15.55/8.57                     => ! [X4: vEBT_VEBT] :
% 15.55/8.57                          ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 15.55/8.57                         => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) ) )
% 15.55/8.57                   => ( ( ord_less_eq_nat @ Mi @ Ma )
% 15.55/8.57                     => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 15.55/8.57                       => ( ( ( Mi != Ma )
% 15.55/8.57                           => ! [I3: nat] :
% 15.55/8.57                                ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 15.55/8.57                               => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 15.55/8.57                                      = I3 )
% 15.55/8.57                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 15.55/8.57                                  & ! [X4: nat] :
% 15.55/8.57                                      ( ( ( ( vEBT_VEBT_high @ X4 @ N )
% 15.55/8.57                                          = I3 )
% 15.55/8.57                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N ) ) )
% 15.55/8.57                                     => ( ( ord_less_nat @ Mi @ X4 )
% 15.55/8.57                                        & ( ord_less_eq_nat @ X4 @ Ma ) ) ) ) ) )
% 15.55/8.57                         => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6053_invar__vebt_Ointros_I5_J,axiom,
% 15.55/8.57      ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 15.55/8.57        ( ! [X4: vEBT_VEBT] :
% 15.55/8.57            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 15.55/8.57           => ( vEBT_invar_vebt @ X4 @ N ) )
% 15.55/8.57       => ( ( vEBT_invar_vebt @ Summary @ M )
% 15.55/8.57         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 15.55/8.57              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 15.55/8.57           => ( ( M
% 15.55/8.57                = ( suc @ N ) )
% 15.55/8.57             => ( ( Deg
% 15.55/8.57                  = ( plus_plus_nat @ N @ M ) )
% 15.55/8.57               => ( ! [I3: nat] :
% 15.55/8.57                      ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 15.55/8.57                     => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X8 ) )
% 15.55/8.57                        = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 15.55/8.57                 => ( ( ( Mi = Ma )
% 15.55/8.57                     => ! [X4: vEBT_VEBT] :
% 15.55/8.57                          ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 15.55/8.57                         => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) ) )
% 15.55/8.57                   => ( ( ord_less_eq_nat @ Mi @ Ma )
% 15.55/8.57                     => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 15.55/8.57                       => ( ( ( Mi != Ma )
% 15.55/8.57                           => ! [I3: nat] :
% 15.55/8.57                                ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 15.55/8.57                               => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 15.55/8.57                                      = I3 )
% 15.55/8.57                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 15.55/8.57                                  & ! [X4: nat] :
% 15.55/8.57                                      ( ( ( ( vEBT_VEBT_high @ X4 @ N )
% 15.55/8.57                                          = I3 )
% 15.55/8.57                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N ) ) )
% 15.55/8.57                                     => ( ( ord_less_nat @ Mi @ X4 )
% 15.55/8.57                                        & ( ord_less_eq_nat @ X4 @ Ma ) ) ) ) ) )
% 15.55/8.57                         => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6054_nested__mint,axiom,
% 15.55/8.57      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,Va2: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 15.55/8.57       => ( ( N
% 15.55/8.57            = ( suc @ ( suc @ Va2 ) ) )
% 15.55/8.57         => ( ~ ( ord_less_nat @ Ma @ Mi )
% 15.55/8.57           => ( ( Ma != Mi )
% 15.55/8.57             => ( 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 @ Va2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6055_divmod__step__eq,axiom,
% 15.55/8.57      ! [L: num,R2: nat,Q3: nat] :
% 15.55/8.57        ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 15.55/8.57         => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 15.55/8.57            = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ one_one_nat ) @ ( minus_minus_nat @ R2 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 15.55/8.57        & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 15.55/8.57         => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 15.55/8.57            = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6056_divmod__step__eq,axiom,
% 15.55/8.57      ! [L: num,R2: int,Q3: int] :
% 15.55/8.57        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 15.55/8.57         => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 15.55/8.57            = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ one_one_int ) @ ( minus_minus_int @ R2 @ ( numeral_numeral_int @ L ) ) ) ) )
% 15.55/8.57        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 15.55/8.57         => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 15.55/8.57            = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6057_divmod__step__eq,axiom,
% 15.55/8.57      ! [L: num,R2: code_integer,Q3: code_integer] :
% 15.55/8.57        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 15.55/8.57         => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R2 ) )
% 15.55/8.57            = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R2 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 15.55/8.57        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 15.55/8.57         => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R2 ) )
% 15.55/8.57            = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6058_pred__list__to__short,axiom,
% 15.55/8.57      ! [Deg: nat,X3: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 15.55/8.57        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.57       => ( ( ord_less_eq_nat @ X3 @ Ma )
% 15.55/8.57         => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.57           => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.57              = none_nat ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6059_succ__list__to__short,axiom,
% 15.55/8.57      ! [Deg: nat,Mi: nat,X3: nat,TreeList2: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 15.55/8.57        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.57       => ( ( ord_less_eq_nat @ Mi @ X3 )
% 15.55/8.57         => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.57           => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.57              = none_nat ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6060_height__node,axiom,
% 15.55/8.57      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 15.55/8.57       => ( ord_less_eq_nat @ one_one_nat @ ( vEBT_VEBT_height @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6061_inrange,axiom,
% 15.55/8.57      ! [T: vEBT_VEBT,N: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.57       => ( ord_less_eq_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6062_geqmaxNone,axiom,
% 15.55/8.57      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.57        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 15.55/8.57       => ( ( ord_less_eq_nat @ Ma @ X3 )
% 15.55/8.57         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.57            = none_nat ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6063_not__None__eq,axiom,
% 15.55/8.57      ! [X3: option_nat] :
% 15.55/8.57        ( ( X3 != none_nat )
% 15.55/8.57        = ( ? [Y: nat] :
% 15.55/8.57              ( X3
% 15.55/8.57              = ( some_nat @ Y ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6064_not__None__eq,axiom,
% 15.55/8.57      ! [X3: option4927543243414619207at_nat] :
% 15.55/8.57        ( ( X3 != none_P5556105721700978146at_nat )
% 15.55/8.57        = ( ? [Y: product_prod_nat_nat] :
% 15.55/8.57              ( X3
% 15.55/8.57              = ( some_P7363390416028606310at_nat @ Y ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6065_not__None__eq,axiom,
% 15.55/8.57      ! [X3: option_num] :
% 15.55/8.57        ( ( X3 != none_num )
% 15.55/8.57        = ( ? [Y: num] :
% 15.55/8.57              ( X3
% 15.55/8.57              = ( some_num @ Y ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6066_not__Some__eq,axiom,
% 15.55/8.57      ! [X3: option_nat] :
% 15.55/8.57        ( ( ! [Y: nat] :
% 15.55/8.57              ( X3
% 15.55/8.57             != ( some_nat @ Y ) ) )
% 15.55/8.57        = ( X3 = none_nat ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6067_not__Some__eq,axiom,
% 15.55/8.57      ! [X3: option4927543243414619207at_nat] :
% 15.55/8.57        ( ( ! [Y: product_prod_nat_nat] :
% 15.55/8.57              ( X3
% 15.55/8.57             != ( some_P7363390416028606310at_nat @ Y ) ) )
% 15.55/8.57        = ( X3 = none_P5556105721700978146at_nat ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6068_not__Some__eq,axiom,
% 15.55/8.57      ! [X3: option_num] :
% 15.55/8.57        ( ( ! [Y: num] :
% 15.55/8.57              ( X3
% 15.55/8.57             != ( some_num @ Y ) ) )
% 15.55/8.57        = ( X3 = none_num ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6069_option_Ocollapse,axiom,
% 15.55/8.57      ! [Option: option_nat] :
% 15.55/8.57        ( ( Option != none_nat )
% 15.55/8.57       => ( ( some_nat @ ( the_nat @ Option ) )
% 15.55/8.57          = Option ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6070_option_Ocollapse,axiom,
% 15.55/8.57      ! [Option: option4927543243414619207at_nat] :
% 15.55/8.57        ( ( Option != none_P5556105721700978146at_nat )
% 15.55/8.57       => ( ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) )
% 15.55/8.57          = Option ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6071_option_Ocollapse,axiom,
% 15.55/8.57      ! [Option: option_num] :
% 15.55/8.57        ( ( Option != none_num )
% 15.55/8.57       => ( ( some_num @ ( the_num @ Option ) )
% 15.55/8.57          = Option ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6072_option_Oexhaust__sel,axiom,
% 15.55/8.57      ! [Option: option_nat] :
% 15.55/8.57        ( ( Option != none_nat )
% 15.55/8.57       => ( Option
% 15.55/8.57          = ( some_nat @ ( the_nat @ Option ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6073_option_Oexhaust__sel,axiom,
% 15.55/8.57      ! [Option: option4927543243414619207at_nat] :
% 15.55/8.57        ( ( Option != none_P5556105721700978146at_nat )
% 15.55/8.57       => ( Option
% 15.55/8.57          = ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6074_option_Oexhaust__sel,axiom,
% 15.55/8.57      ! [Option: option_num] :
% 15.55/8.57        ( ( Option != none_num )
% 15.55/8.57       => ( Option
% 15.55/8.57          = ( some_num @ ( the_num @ Option ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6075_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 15.55/8.57      ! [X3: produc2233624965454879586on_nat] :
% 15.55/8.57        ( ! [Uu: nat > nat > $o,Uv: option_nat] :
% 15.55/8.57            ( X3
% 15.55/8.57           != ( produc4035269172776083154on_nat @ Uu @ ( produc5098337634421038937on_nat @ none_nat @ Uv ) ) )
% 15.55/8.57       => ( ! [Uw: nat > nat > $o,V3: nat] :
% 15.55/8.57              ( X3
% 15.55/8.57             != ( produc4035269172776083154on_nat @ Uw @ ( produc5098337634421038937on_nat @ ( some_nat @ V3 ) @ none_nat ) ) )
% 15.55/8.57         => ~ ! [F2: nat > nat > $o,X4: nat,Y4: nat] :
% 15.55/8.57                ( X3
% 15.55/8.57               != ( produc4035269172776083154on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ X4 ) @ ( some_nat @ Y4 ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6076_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 15.55/8.57      ! [X3: produc5491161045314408544at_nat] :
% 15.55/8.57        ( ! [Uu: product_prod_nat_nat > product_prod_nat_nat > $o,Uv: option4927543243414619207at_nat] :
% 15.55/8.57            ( X3
% 15.55/8.57           != ( produc3994169339658061776at_nat @ Uu @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv ) ) )
% 15.55/8.57       => ( ! [Uw: product_prod_nat_nat > product_prod_nat_nat > $o,V3: product_prod_nat_nat] :
% 15.55/8.57              ( X3
% 15.55/8.57             != ( produc3994169339658061776at_nat @ Uw @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V3 ) @ none_P5556105721700978146at_nat ) ) )
% 15.55/8.57         => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > $o,X4: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 15.55/8.57                ( X3
% 15.55/8.57               != ( produc3994169339658061776at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ X4 ) @ ( some_P7363390416028606310at_nat @ Y4 ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6077_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 15.55/8.57      ! [X3: produc7036089656553540234on_num] :
% 15.55/8.57        ( ! [Uu: num > num > $o,Uv: option_num] :
% 15.55/8.57            ( X3
% 15.55/8.57           != ( produc3576312749637752826on_num @ Uu @ ( produc8585076106096196333on_num @ none_num @ Uv ) ) )
% 15.55/8.57       => ( ! [Uw: num > num > $o,V3: num] :
% 15.55/8.57              ( X3
% 15.55/8.57             != ( produc3576312749637752826on_num @ Uw @ ( produc8585076106096196333on_num @ ( some_num @ V3 ) @ none_num ) ) )
% 15.55/8.57         => ~ ! [F2: num > num > $o,X4: num,Y4: num] :
% 15.55/8.57                ( X3
% 15.55/8.57               != ( produc3576312749637752826on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ X4 ) @ ( some_num @ Y4 ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6078_VEBT__internal_Ooption__shift_Ocases,axiom,
% 15.55/8.57      ! [X3: produc8306885398267862888on_nat] :
% 15.55/8.57        ( ! [Uu: nat > nat > nat,Uv: option_nat] :
% 15.55/8.57            ( X3
% 15.55/8.57           != ( produc8929957630744042906on_nat @ Uu @ ( produc5098337634421038937on_nat @ none_nat @ Uv ) ) )
% 15.55/8.57       => ( ! [Uw: nat > nat > nat,V3: nat] :
% 15.55/8.57              ( X3
% 15.55/8.57             != ( produc8929957630744042906on_nat @ Uw @ ( produc5098337634421038937on_nat @ ( some_nat @ V3 ) @ none_nat ) ) )
% 15.55/8.57         => ~ ! [F2: nat > nat > nat,A5: nat,B4: nat] :
% 15.55/8.57                ( X3
% 15.55/8.57               != ( produc8929957630744042906on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ A5 ) @ ( some_nat @ B4 ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6079_VEBT__internal_Ooption__shift_Ocases,axiom,
% 15.55/8.57      ! [X3: produc5542196010084753463at_nat] :
% 15.55/8.57        ( ! [Uu: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv: option4927543243414619207at_nat] :
% 15.55/8.57            ( X3
% 15.55/8.57           != ( produc2899441246263362727at_nat @ Uu @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv ) ) )
% 15.55/8.57       => ( ! [Uw: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V3: product_prod_nat_nat] :
% 15.55/8.57              ( X3
% 15.55/8.57             != ( produc2899441246263362727at_nat @ Uw @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V3 ) @ none_P5556105721700978146at_nat ) ) )
% 15.55/8.57         => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A5: product_prod_nat_nat,B4: product_prod_nat_nat] :
% 15.55/8.57                ( X3
% 15.55/8.57               != ( produc2899441246263362727at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A5 ) @ ( some_P7363390416028606310at_nat @ B4 ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6080_VEBT__internal_Ooption__shift_Ocases,axiom,
% 15.55/8.57      ! [X3: produc1193250871479095198on_num] :
% 15.55/8.57        ( ! [Uu: num > num > num,Uv: option_num] :
% 15.55/8.57            ( X3
% 15.55/8.57           != ( produc5778274026573060048on_num @ Uu @ ( produc8585076106096196333on_num @ none_num @ Uv ) ) )
% 15.55/8.57       => ( ! [Uw: num > num > num,V3: num] :
% 15.55/8.57              ( X3
% 15.55/8.57             != ( produc5778274026573060048on_num @ Uw @ ( produc8585076106096196333on_num @ ( some_num @ V3 ) @ none_num ) ) )
% 15.55/8.57         => ~ ! [F2: num > num > num,A5: num,B4: num] :
% 15.55/8.57                ( X3
% 15.55/8.57               != ( produc5778274026573060048on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ A5 ) @ ( some_num @ B4 ) ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6081_option_Oexpand,axiom,
% 15.55/8.57      ! [Option: option_nat,Option2: option_nat] :
% 15.55/8.57        ( ( ( Option = none_nat )
% 15.55/8.57          = ( Option2 = none_nat ) )
% 15.55/8.57       => ( ( ( Option != none_nat )
% 15.55/8.57           => ( ( Option2 != none_nat )
% 15.55/8.57             => ( ( the_nat @ Option )
% 15.55/8.57                = ( the_nat @ Option2 ) ) ) )
% 15.55/8.57         => ( Option = Option2 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6082_option_Oexpand,axiom,
% 15.55/8.57      ! [Option: option4927543243414619207at_nat,Option2: option4927543243414619207at_nat] :
% 15.55/8.57        ( ( ( Option = none_P5556105721700978146at_nat )
% 15.55/8.57          = ( Option2 = none_P5556105721700978146at_nat ) )
% 15.55/8.57       => ( ( ( Option != none_P5556105721700978146at_nat )
% 15.55/8.57           => ( ( Option2 != none_P5556105721700978146at_nat )
% 15.55/8.57             => ( ( the_Pr8591224930841456533at_nat @ Option )
% 15.55/8.57                = ( the_Pr8591224930841456533at_nat @ Option2 ) ) ) )
% 15.55/8.57         => ( Option = Option2 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6083_option_Oexpand,axiom,
% 15.55/8.57      ! [Option: option_num,Option2: option_num] :
% 15.55/8.57        ( ( ( Option = none_num )
% 15.55/8.57          = ( Option2 = none_num ) )
% 15.55/8.57       => ( ( ( Option != none_num )
% 15.55/8.57           => ( ( Option2 != none_num )
% 15.55/8.57             => ( ( the_num @ Option )
% 15.55/8.57                = ( the_num @ Option2 ) ) ) )
% 15.55/8.57         => ( Option = Option2 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6084_option_Odistinct_I1_J,axiom,
% 15.55/8.57      ! [X2: nat] :
% 15.55/8.57        ( none_nat
% 15.55/8.57       != ( some_nat @ X2 ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6085_option_Odistinct_I1_J,axiom,
% 15.55/8.57      ! [X2: product_prod_nat_nat] :
% 15.55/8.57        ( none_P5556105721700978146at_nat
% 15.55/8.57       != ( some_P7363390416028606310at_nat @ X2 ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6086_option_Odistinct_I1_J,axiom,
% 15.55/8.57      ! [X2: num] :
% 15.55/8.57        ( none_num
% 15.55/8.57       != ( some_num @ X2 ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6087_option_OdiscI,axiom,
% 15.55/8.57      ! [Option: option_nat,X2: nat] :
% 15.55/8.57        ( ( Option
% 15.55/8.57          = ( some_nat @ X2 ) )
% 15.55/8.57       => ( Option != none_nat ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6088_option_OdiscI,axiom,
% 15.55/8.57      ! [Option: option4927543243414619207at_nat,X2: product_prod_nat_nat] :
% 15.55/8.57        ( ( Option
% 15.55/8.57          = ( some_P7363390416028606310at_nat @ X2 ) )
% 15.55/8.57       => ( Option != none_P5556105721700978146at_nat ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6089_option_OdiscI,axiom,
% 15.55/8.57      ! [Option: option_num,X2: num] :
% 15.55/8.57        ( ( Option
% 15.55/8.57          = ( some_num @ X2 ) )
% 15.55/8.57       => ( Option != none_num ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6090_option_Oexhaust,axiom,
% 15.55/8.57      ! [Y3: option_nat] :
% 15.55/8.57        ( ( Y3 != none_nat )
% 15.55/8.57       => ~ ! [X22: nat] :
% 15.55/8.57              ( Y3
% 15.55/8.57             != ( some_nat @ X22 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6091_option_Oexhaust,axiom,
% 15.55/8.57      ! [Y3: option4927543243414619207at_nat] :
% 15.55/8.57        ( ( Y3 != none_P5556105721700978146at_nat )
% 15.55/8.57       => ~ ! [X22: product_prod_nat_nat] :
% 15.55/8.57              ( Y3
% 15.55/8.57             != ( some_P7363390416028606310at_nat @ X22 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6092_option_Oexhaust,axiom,
% 15.55/8.57      ! [Y3: option_num] :
% 15.55/8.57        ( ( Y3 != none_num )
% 15.55/8.57       => ~ ! [X22: num] :
% 15.55/8.57              ( Y3
% 15.55/8.57             != ( some_num @ X22 ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6093_split__option__ex,axiom,
% 15.55/8.57      ( ( ^ [P2: option_nat > $o] :
% 15.55/8.57          ? [X5: option_nat] : ( P2 @ X5 ) )
% 15.55/8.57      = ( ^ [P3: option_nat > $o] :
% 15.55/8.57            ( ( P3 @ none_nat )
% 15.55/8.57            | ? [X: nat] : ( P3 @ ( some_nat @ X ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6094_split__option__ex,axiom,
% 15.55/8.57      ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 15.55/8.57          ? [X5: option4927543243414619207at_nat] : ( P2 @ X5 ) )
% 15.55/8.57      = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 15.55/8.57            ( ( P3 @ none_P5556105721700978146at_nat )
% 15.55/8.57            | ? [X: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6095_split__option__ex,axiom,
% 15.55/8.57      ( ( ^ [P2: option_num > $o] :
% 15.55/8.57          ? [X5: option_num] : ( P2 @ X5 ) )
% 15.55/8.57      = ( ^ [P3: option_num > $o] :
% 15.55/8.57            ( ( P3 @ none_num )
% 15.55/8.57            | ? [X: num] : ( P3 @ ( some_num @ X ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6096_split__option__all,axiom,
% 15.55/8.57      ( ( ^ [P2: option_nat > $o] :
% 15.55/8.57          ! [X5: option_nat] : ( P2 @ X5 ) )
% 15.55/8.57      = ( ^ [P3: option_nat > $o] :
% 15.55/8.57            ( ( P3 @ none_nat )
% 15.55/8.57            & ! [X: nat] : ( P3 @ ( some_nat @ X ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6097_split__option__all,axiom,
% 15.55/8.57      ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 15.55/8.57          ! [X5: option4927543243414619207at_nat] : ( P2 @ X5 ) )
% 15.55/8.57      = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 15.55/8.57            ( ( P3 @ none_P5556105721700978146at_nat )
% 15.55/8.57            & ! [X: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X ) ) ) ) ) ).
% 15.55/8.57  
% 15.55/8.57  thf(fact_6098_split__option__all,axiom,
% 15.55/8.57      ( ( ^ [P2: option_num > $o] :
% 15.55/8.57          ! [X5: option_num] : ( P2 @ X5 ) )
% 15.55/8.57      = ( ^ [P3: option_num > $o] :
% 15.55/8.57            ( ( P3 @ none_num )
% 15.55/8.57            & ! [X: num] : ( P3 @ ( some_num @ X ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6099_combine__options__cases,axiom,
% 15.55/8.58      ! [X3: option_nat,P: option_nat > option_nat > $o,Y3: option_nat] :
% 15.55/8.58        ( ( ( X3 = none_nat )
% 15.55/8.58         => ( P @ X3 @ Y3 ) )
% 15.55/8.58       => ( ( ( Y3 = none_nat )
% 15.55/8.58           => ( P @ X3 @ Y3 ) )
% 15.55/8.58         => ( ! [A5: nat,B4: nat] :
% 15.55/8.58                ( ( X3
% 15.55/8.58                  = ( some_nat @ A5 ) )
% 15.55/8.58               => ( ( Y3
% 15.55/8.58                    = ( some_nat @ B4 ) )
% 15.55/8.58                 => ( P @ X3 @ Y3 ) ) )
% 15.55/8.58           => ( P @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6100_combine__options__cases,axiom,
% 15.55/8.58      ! [X3: option_nat,P: option_nat > option4927543243414619207at_nat > $o,Y3: option4927543243414619207at_nat] :
% 15.55/8.58        ( ( ( X3 = none_nat )
% 15.55/8.58         => ( P @ X3 @ Y3 ) )
% 15.55/8.58       => ( ( ( Y3 = none_P5556105721700978146at_nat )
% 15.55/8.58           => ( P @ X3 @ Y3 ) )
% 15.55/8.58         => ( ! [A5: nat,B4: product_prod_nat_nat] :
% 15.55/8.58                ( ( X3
% 15.55/8.58                  = ( some_nat @ A5 ) )
% 15.55/8.58               => ( ( Y3
% 15.55/8.58                    = ( some_P7363390416028606310at_nat @ B4 ) )
% 15.55/8.58                 => ( P @ X3 @ Y3 ) ) )
% 15.55/8.58           => ( P @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6101_combine__options__cases,axiom,
% 15.55/8.58      ! [X3: option_nat,P: option_nat > option_num > $o,Y3: option_num] :
% 15.55/8.58        ( ( ( X3 = none_nat )
% 15.55/8.58         => ( P @ X3 @ Y3 ) )
% 15.55/8.58       => ( ( ( Y3 = none_num )
% 15.55/8.58           => ( P @ X3 @ Y3 ) )
% 15.55/8.58         => ( ! [A5: nat,B4: num] :
% 15.55/8.58                ( ( X3
% 15.55/8.58                  = ( some_nat @ A5 ) )
% 15.55/8.58               => ( ( Y3
% 15.55/8.58                    = ( some_num @ B4 ) )
% 15.55/8.58                 => ( P @ X3 @ Y3 ) ) )
% 15.55/8.58           => ( P @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6102_combine__options__cases,axiom,
% 15.55/8.58      ! [X3: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_nat > $o,Y3: option_nat] :
% 15.55/8.58        ( ( ( X3 = none_P5556105721700978146at_nat )
% 15.55/8.58         => ( P @ X3 @ Y3 ) )
% 15.55/8.58       => ( ( ( Y3 = none_nat )
% 15.55/8.58           => ( P @ X3 @ Y3 ) )
% 15.55/8.58         => ( ! [A5: product_prod_nat_nat,B4: nat] :
% 15.55/8.58                ( ( X3
% 15.55/8.58                  = ( some_P7363390416028606310at_nat @ A5 ) )
% 15.55/8.58               => ( ( Y3
% 15.55/8.58                    = ( some_nat @ B4 ) )
% 15.55/8.58                 => ( P @ X3 @ Y3 ) ) )
% 15.55/8.58           => ( P @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6103_combine__options__cases,axiom,
% 15.55/8.58      ! [X3: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y3: option4927543243414619207at_nat] :
% 15.55/8.58        ( ( ( X3 = none_P5556105721700978146at_nat )
% 15.55/8.58         => ( P @ X3 @ Y3 ) )
% 15.55/8.58       => ( ( ( Y3 = none_P5556105721700978146at_nat )
% 15.55/8.58           => ( P @ X3 @ Y3 ) )
% 15.55/8.58         => ( ! [A5: product_prod_nat_nat,B4: product_prod_nat_nat] :
% 15.55/8.58                ( ( X3
% 15.55/8.58                  = ( some_P7363390416028606310at_nat @ A5 ) )
% 15.55/8.58               => ( ( Y3
% 15.55/8.58                    = ( some_P7363390416028606310at_nat @ B4 ) )
% 15.55/8.58                 => ( P @ X3 @ Y3 ) ) )
% 15.55/8.58           => ( P @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6104_combine__options__cases,axiom,
% 15.55/8.58      ! [X3: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y3: option_num] :
% 15.55/8.58        ( ( ( X3 = none_P5556105721700978146at_nat )
% 15.55/8.58         => ( P @ X3 @ Y3 ) )
% 15.55/8.58       => ( ( ( Y3 = none_num )
% 15.55/8.58           => ( P @ X3 @ Y3 ) )
% 15.55/8.58         => ( ! [A5: product_prod_nat_nat,B4: num] :
% 15.55/8.58                ( ( X3
% 15.55/8.58                  = ( some_P7363390416028606310at_nat @ A5 ) )
% 15.55/8.58               => ( ( Y3
% 15.55/8.58                    = ( some_num @ B4 ) )
% 15.55/8.58                 => ( P @ X3 @ Y3 ) ) )
% 15.55/8.58           => ( P @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6105_combine__options__cases,axiom,
% 15.55/8.58      ! [X3: option_num,P: option_num > option_nat > $o,Y3: option_nat] :
% 15.55/8.58        ( ( ( X3 = none_num )
% 15.55/8.58         => ( P @ X3 @ Y3 ) )
% 15.55/8.58       => ( ( ( Y3 = none_nat )
% 15.55/8.58           => ( P @ X3 @ Y3 ) )
% 15.55/8.58         => ( ! [A5: num,B4: nat] :
% 15.55/8.58                ( ( X3
% 15.55/8.58                  = ( some_num @ A5 ) )
% 15.55/8.58               => ( ( Y3
% 15.55/8.58                    = ( some_nat @ B4 ) )
% 15.55/8.58                 => ( P @ X3 @ Y3 ) ) )
% 15.55/8.58           => ( P @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6106_combine__options__cases,axiom,
% 15.55/8.58      ! [X3: option_num,P: option_num > option4927543243414619207at_nat > $o,Y3: option4927543243414619207at_nat] :
% 15.55/8.58        ( ( ( X3 = none_num )
% 15.55/8.58         => ( P @ X3 @ Y3 ) )
% 15.55/8.58       => ( ( ( Y3 = none_P5556105721700978146at_nat )
% 15.55/8.58           => ( P @ X3 @ Y3 ) )
% 15.55/8.58         => ( ! [A5: num,B4: product_prod_nat_nat] :
% 15.55/8.58                ( ( X3
% 15.55/8.58                  = ( some_num @ A5 ) )
% 15.55/8.58               => ( ( Y3
% 15.55/8.58                    = ( some_P7363390416028606310at_nat @ B4 ) )
% 15.55/8.58                 => ( P @ X3 @ Y3 ) ) )
% 15.55/8.58           => ( P @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6107_combine__options__cases,axiom,
% 15.55/8.58      ! [X3: option_num,P: option_num > option_num > $o,Y3: option_num] :
% 15.55/8.58        ( ( ( X3 = none_num )
% 15.55/8.58         => ( P @ X3 @ Y3 ) )
% 15.55/8.58       => ( ( ( Y3 = none_num )
% 15.55/8.58           => ( P @ X3 @ Y3 ) )
% 15.55/8.58         => ( ! [A5: num,B4: num] :
% 15.55/8.58                ( ( X3
% 15.55/8.58                  = ( some_num @ A5 ) )
% 15.55/8.58               => ( ( Y3
% 15.55/8.58                    = ( some_num @ B4 ) )
% 15.55/8.58                 => ( P @ X3 @ Y3 ) ) )
% 15.55/8.58           => ( P @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6108_option_Osel,axiom,
% 15.55/8.58      ! [X2: nat] :
% 15.55/8.58        ( ( the_nat @ ( some_nat @ X2 ) )
% 15.55/8.58        = X2 ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6109_option_Osel,axiom,
% 15.55/8.58      ! [X2: product_prod_nat_nat] :
% 15.55/8.58        ( ( the_Pr8591224930841456533at_nat @ ( some_P7363390416028606310at_nat @ X2 ) )
% 15.55/8.58        = X2 ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6110_option_Osel,axiom,
% 15.55/8.58      ! [X2: num] :
% 15.55/8.58        ( ( the_num @ ( some_num @ X2 ) )
% 15.55/8.58        = X2 ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6111_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 15.55/8.58      ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv2: option4927543243414619207at_nat] :
% 15.55/8.58        ( ( vEBT_V1502963449132264192at_nat @ Uu2 @ none_P5556105721700978146at_nat @ Uv2 )
% 15.55/8.58        = none_P5556105721700978146at_nat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6112_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 15.55/8.58      ! [Uu2: num > num > num,Uv2: option_num] :
% 15.55/8.58        ( ( vEBT_V819420779217536731ft_num @ Uu2 @ none_num @ Uv2 )
% 15.55/8.58        = none_num ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6113_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 15.55/8.58      ! [Uu2: nat > nat > nat,Uv2: option_nat] :
% 15.55/8.58        ( ( vEBT_V4262088993061758097ft_nat @ Uu2 @ none_nat @ Uv2 )
% 15.55/8.58        = none_nat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6114_all__nat__less,axiom,
% 15.55/8.58      ! [N: nat,P: nat > $o] :
% 15.55/8.58        ( ( ! [M3: nat] :
% 15.55/8.58              ( ( ord_less_eq_nat @ M3 @ N )
% 15.55/8.58             => ( P @ M3 ) ) )
% 15.55/8.58        = ( ! [X: nat] :
% 15.55/8.58              ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 15.55/8.58             => ( P @ X ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6115_ex__nat__less,axiom,
% 15.55/8.58      ! [N: nat,P: nat > $o] :
% 15.55/8.58        ( ( ? [M3: nat] :
% 15.55/8.58              ( ( ord_less_eq_nat @ M3 @ N )
% 15.55/8.58              & ( P @ M3 ) ) )
% 15.55/8.58        = ( ? [X: nat] :
% 15.55/8.58              ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 15.55/8.58              & ( P @ X ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6116_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 15.55/8.58      ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V: product_prod_nat_nat] :
% 15.55/8.58        ( ( vEBT_V1502963449132264192at_nat @ Uw2 @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat )
% 15.55/8.58        = none_P5556105721700978146at_nat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6117_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 15.55/8.58      ! [Uw2: num > num > num,V: num] :
% 15.55/8.58        ( ( vEBT_V819420779217536731ft_num @ Uw2 @ ( some_num @ V ) @ none_num )
% 15.55/8.58        = none_num ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6118_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 15.55/8.58      ! [Uw2: nat > nat > nat,V: nat] :
% 15.55/8.58        ( ( vEBT_V4262088993061758097ft_nat @ Uw2 @ ( some_nat @ V ) @ none_nat )
% 15.55/8.58        = none_nat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6119_VEBT__internal_Ooption__shift_Oelims,axiom,
% 15.55/8.58      ! [X3: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa: option4927543243414619207at_nat,Xb: option4927543243414619207at_nat,Y3: option4927543243414619207at_nat] :
% 15.55/8.58        ( ( ( vEBT_V1502963449132264192at_nat @ X3 @ Xa @ Xb )
% 15.55/8.58          = Y3 )
% 15.55/8.58       => ( ( ( Xa = none_P5556105721700978146at_nat )
% 15.55/8.58           => ( Y3 != none_P5556105721700978146at_nat ) )
% 15.55/8.58         => ( ( ? [V3: product_prod_nat_nat] :
% 15.55/8.58                  ( Xa
% 15.55/8.58                  = ( some_P7363390416028606310at_nat @ V3 ) )
% 15.55/8.58             => ( ( Xb = none_P5556105721700978146at_nat )
% 15.55/8.58               => ( Y3 != none_P5556105721700978146at_nat ) ) )
% 15.55/8.58           => ~ ! [A5: product_prod_nat_nat] :
% 15.55/8.58                  ( ( Xa
% 15.55/8.58                    = ( some_P7363390416028606310at_nat @ A5 ) )
% 15.55/8.58                 => ! [B4: product_prod_nat_nat] :
% 15.55/8.58                      ( ( Xb
% 15.55/8.58                        = ( some_P7363390416028606310at_nat @ B4 ) )
% 15.55/8.58                     => ( Y3
% 15.55/8.58                       != ( some_P7363390416028606310at_nat @ ( X3 @ A5 @ B4 ) ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6120_VEBT__internal_Ooption__shift_Oelims,axiom,
% 15.55/8.58      ! [X3: num > num > num,Xa: option_num,Xb: option_num,Y3: option_num] :
% 15.55/8.58        ( ( ( vEBT_V819420779217536731ft_num @ X3 @ Xa @ Xb )
% 15.55/8.58          = Y3 )
% 15.55/8.58       => ( ( ( Xa = none_num )
% 15.55/8.58           => ( Y3 != none_num ) )
% 15.55/8.58         => ( ( ? [V3: num] :
% 15.55/8.58                  ( Xa
% 15.55/8.58                  = ( some_num @ V3 ) )
% 15.55/8.58             => ( ( Xb = none_num )
% 15.55/8.58               => ( Y3 != none_num ) ) )
% 15.55/8.58           => ~ ! [A5: num] :
% 15.55/8.58                  ( ( Xa
% 15.55/8.58                    = ( some_num @ A5 ) )
% 15.55/8.58                 => ! [B4: num] :
% 15.55/8.58                      ( ( Xb
% 15.55/8.58                        = ( some_num @ B4 ) )
% 15.55/8.58                     => ( Y3
% 15.55/8.58                       != ( some_num @ ( X3 @ A5 @ B4 ) ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6121_VEBT__internal_Ooption__shift_Oelims,axiom,
% 15.55/8.58      ! [X3: nat > nat > nat,Xa: option_nat,Xb: option_nat,Y3: option_nat] :
% 15.55/8.58        ( ( ( vEBT_V4262088993061758097ft_nat @ X3 @ Xa @ Xb )
% 15.55/8.58          = Y3 )
% 15.55/8.58       => ( ( ( Xa = none_nat )
% 15.55/8.58           => ( Y3 != none_nat ) )
% 15.55/8.58         => ( ( ? [V3: nat] :
% 15.55/8.58                  ( Xa
% 15.55/8.58                  = ( some_nat @ V3 ) )
% 15.55/8.58             => ( ( Xb = none_nat )
% 15.55/8.58               => ( Y3 != none_nat ) ) )
% 15.55/8.58           => ~ ! [A5: nat] :
% 15.55/8.58                  ( ( Xa
% 15.55/8.58                    = ( some_nat @ A5 ) )
% 15.55/8.58                 => ! [B4: nat] :
% 15.55/8.58                      ( ( Xb
% 15.55/8.58                        = ( some_nat @ B4 ) )
% 15.55/8.58                     => ( Y3
% 15.55/8.58                       != ( some_nat @ ( X3 @ A5 @ B4 ) ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6122_option_Osize_I3_J,axiom,
% 15.55/8.58      ( ( size_size_option_nat @ none_nat )
% 15.55/8.58      = ( suc @ zero_zero_nat ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6123_option_Osize_I3_J,axiom,
% 15.55/8.58      ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 15.55/8.58      = ( suc @ zero_zero_nat ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6124_option_Osize_I3_J,axiom,
% 15.55/8.58      ( ( size_size_option_num @ none_num )
% 15.55/8.58      = ( suc @ zero_zero_nat ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6125_atLeastatMost__subset__iff,axiom,
% 15.55/8.58      ! [A: set_nat,B: set_nat,C: set_nat,D3: set_nat] :
% 15.55/8.58        ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D3 ) )
% 15.55/8.58        = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 15.55/8.58          | ( ( ord_less_eq_set_nat @ C @ A )
% 15.55/8.58            & ( ord_less_eq_set_nat @ B @ D3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6126_atLeastatMost__subset__iff,axiom,
% 15.55/8.58      ! [A: rat,B: rat,C: rat,D3: rat] :
% 15.55/8.58        ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D3 ) )
% 15.55/8.58        = ( ~ ( ord_less_eq_rat @ A @ B )
% 15.55/8.58          | ( ( ord_less_eq_rat @ C @ A )
% 15.55/8.58            & ( ord_less_eq_rat @ B @ D3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6127_atLeastatMost__subset__iff,axiom,
% 15.55/8.58      ! [A: num,B: num,C: num,D3: num] :
% 15.55/8.58        ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D3 ) )
% 15.55/8.58        = ( ~ ( ord_less_eq_num @ A @ B )
% 15.55/8.58          | ( ( ord_less_eq_num @ C @ A )
% 15.55/8.58            & ( ord_less_eq_num @ B @ D3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6128_atLeastatMost__subset__iff,axiom,
% 15.55/8.58      ! [A: nat,B: nat,C: nat,D3: nat] :
% 15.55/8.58        ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D3 ) )
% 15.55/8.58        = ( ~ ( ord_less_eq_nat @ A @ B )
% 15.55/8.58          | ( ( ord_less_eq_nat @ C @ A )
% 15.55/8.58            & ( ord_less_eq_nat @ B @ D3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6129_atLeastatMost__subset__iff,axiom,
% 15.55/8.58      ! [A: int,B: int,C: int,D3: int] :
% 15.55/8.58        ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D3 ) )
% 15.55/8.58        = ( ~ ( ord_less_eq_int @ A @ B )
% 15.55/8.58          | ( ( ord_less_eq_int @ C @ A )
% 15.55/8.58            & ( ord_less_eq_int @ B @ D3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6130_atLeastatMost__subset__iff,axiom,
% 15.55/8.58      ! [A: real,B: real,C: real,D3: real] :
% 15.55/8.58        ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D3 ) )
% 15.55/8.58        = ( ~ ( ord_less_eq_real @ A @ B )
% 15.55/8.58          | ( ( ord_less_eq_real @ C @ A )
% 15.55/8.58            & ( ord_less_eq_real @ B @ D3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6131_summaxma,axiom,
% 15.55/8.58      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 15.55/8.58        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 15.55/8.58       => ( ( Mi != Ma )
% 15.55/8.58         => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 15.55/8.58            = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6132_vebt__succ_Osimps_I5_J,axiom,
% 15.55/8.58      ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 15.55/8.58        ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi )
% 15.55/8.58        = none_nat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6133_vebt__pred_Osimps_I6_J,axiom,
% 15.55/8.58      ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 15.55/8.58        ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj )
% 15.55/8.58        = none_nat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6134__C5_Oprems_C,axiom,
% 15.55/8.58      vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ x ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6135_delt__out__of__range,axiom,
% 15.55/8.58      ! [X3: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 15.55/8.58        ( ( ( ord_less_nat @ X3 @ Mi )
% 15.55/8.58          | ( ord_less_nat @ Ma @ X3 ) )
% 15.55/8.58       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.58         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.58            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6136_delete__pres__valid,axiom,
% 15.55/8.58      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.58        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.58       => ( vEBT_invar_vebt @ ( vEBT_vebt_delete @ T @ X3 ) @ N ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6137_not__min__Null__member,axiom,
% 15.55/8.58      ! [T: vEBT_VEBT] :
% 15.55/8.58        ( ~ ( vEBT_VEBT_minNull @ T )
% 15.55/8.58       => ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6138_min__Null__member,axiom,
% 15.55/8.58      ! [T: vEBT_VEBT,X3: nat] :
% 15.55/8.58        ( ( vEBT_VEBT_minNull @ T )
% 15.55/8.58       => ~ ( vEBT_vebt_member @ T @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6139_maxbmo,axiom,
% 15.55/8.58      ! [T: vEBT_VEBT,X3: nat] :
% 15.55/8.58        ( ( ( vEBT_vebt_maxt @ T )
% 15.55/8.58          = ( some_nat @ X3 ) )
% 15.55/8.58       => ( vEBT_V8194947554948674370ptions @ T @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6140_dele__bmo__cont__corr,axiom,
% 15.55/8.58      ! [T: vEBT_VEBT,N: nat,X3: nat,Y3: nat] :
% 15.55/8.58        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.58       => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ T @ X3 ) @ Y3 )
% 15.55/8.58          = ( ( X3 != Y3 )
% 15.55/8.58            & ( vEBT_V8194947554948674370ptions @ T @ Y3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6141_minNullmin,axiom,
% 15.55/8.58      ! [T: vEBT_VEBT] :
% 15.55/8.58        ( ( vEBT_VEBT_minNull @ T )
% 15.55/8.58       => ( ( vEBT_vebt_mint @ T )
% 15.55/8.58          = none_nat ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6142_minminNull,axiom,
% 15.55/8.58      ! [T: vEBT_VEBT] :
% 15.55/8.58        ( ( ( vEBT_vebt_mint @ T )
% 15.55/8.58          = none_nat )
% 15.55/8.58       => ( vEBT_VEBT_minNull @ T ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6143_dele__member__cont__corr,axiom,
% 15.55/8.58      ! [T: vEBT_VEBT,N: nat,X3: nat,Y3: nat] :
% 15.55/8.58        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.58       => ( ( vEBT_vebt_member @ ( vEBT_vebt_delete @ T @ X3 ) @ Y3 )
% 15.55/8.58          = ( ( X3 != Y3 )
% 15.55/8.58            & ( vEBT_vebt_member @ T @ Y3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6144_maxt__member,axiom,
% 15.55/8.58      ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 15.55/8.58        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.58       => ( ( ( vEBT_vebt_maxt @ T )
% 15.55/8.58            = ( some_nat @ Maxi ) )
% 15.55/8.58         => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6145_maxt__corr__help,axiom,
% 15.55/8.58      ! [T: vEBT_VEBT,N: nat,Maxi: nat,X3: nat] :
% 15.55/8.58        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.58       => ( ( ( vEBT_vebt_maxt @ T )
% 15.55/8.58            = ( some_nat @ Maxi ) )
% 15.55/8.58         => ( ( vEBT_vebt_member @ T @ X3 )
% 15.55/8.58           => ( ord_less_eq_nat @ X3 @ Maxi ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6146_maxt__sound,axiom,
% 15.55/8.58      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.58        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.58       => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X3 )
% 15.55/8.58         => ( ( vEBT_vebt_maxt @ T )
% 15.55/8.58            = ( some_nat @ X3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6147_maxt__corr,axiom,
% 15.55/8.58      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.58        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.58       => ( ( ( vEBT_vebt_maxt @ T )
% 15.55/8.58            = ( some_nat @ X3 ) )
% 15.55/8.58         => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6148_del__single__cont,axiom,
% 15.55/8.58      ! [X3: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 15.55/8.58        ( ( ( X3 = Mi )
% 15.55/8.58          & ( X3 = Ma ) )
% 15.55/8.58       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.58         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.58            = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6149_Icc__eq__Icc,axiom,
% 15.55/8.58      ! [L: set_nat,H2: set_nat,L3: set_nat,H3: set_nat] :
% 15.55/8.58        ( ( ( set_or4548717258645045905et_nat @ L @ H2 )
% 15.55/8.58          = ( set_or4548717258645045905et_nat @ L3 @ H3 ) )
% 15.55/8.58        = ( ( ( L = L3 )
% 15.55/8.58            & ( H2 = H3 ) )
% 15.55/8.58          | ( ~ ( ord_less_eq_set_nat @ L @ H2 )
% 15.55/8.58            & ~ ( ord_less_eq_set_nat @ L3 @ H3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6150_Icc__eq__Icc,axiom,
% 15.55/8.58      ! [L: rat,H2: rat,L3: rat,H3: rat] :
% 15.55/8.58        ( ( ( set_or633870826150836451st_rat @ L @ H2 )
% 15.55/8.58          = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 15.55/8.58        = ( ( ( L = L3 )
% 15.55/8.58            & ( H2 = H3 ) )
% 15.55/8.58          | ( ~ ( ord_less_eq_rat @ L @ H2 )
% 15.55/8.58            & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6151_Icc__eq__Icc,axiom,
% 15.55/8.58      ! [L: num,H2: num,L3: num,H3: num] :
% 15.55/8.58        ( ( ( set_or7049704709247886629st_num @ L @ H2 )
% 15.55/8.58          = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 15.55/8.58        = ( ( ( L = L3 )
% 15.55/8.58            & ( H2 = H3 ) )
% 15.55/8.58          | ( ~ ( ord_less_eq_num @ L @ H2 )
% 15.55/8.58            & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6152_Icc__eq__Icc,axiom,
% 15.55/8.58      ! [L: nat,H2: nat,L3: nat,H3: nat] :
% 15.55/8.58        ( ( ( set_or1269000886237332187st_nat @ L @ H2 )
% 15.55/8.58          = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 15.55/8.58        = ( ( ( L = L3 )
% 15.55/8.58            & ( H2 = H3 ) )
% 15.55/8.58          | ( ~ ( ord_less_eq_nat @ L @ H2 )
% 15.55/8.58            & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6153_Icc__eq__Icc,axiom,
% 15.55/8.58      ! [L: int,H2: int,L3: int,H3: int] :
% 15.55/8.58        ( ( ( set_or1266510415728281911st_int @ L @ H2 )
% 15.55/8.58          = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 15.55/8.58        = ( ( ( L = L3 )
% 15.55/8.58            & ( H2 = H3 ) )
% 15.55/8.58          | ( ~ ( ord_less_eq_int @ L @ H2 )
% 15.55/8.58            & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6154_Icc__eq__Icc,axiom,
% 15.55/8.58      ! [L: real,H2: real,L3: real,H3: real] :
% 15.55/8.58        ( ( ( set_or1222579329274155063t_real @ L @ H2 )
% 15.55/8.58          = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 15.55/8.58        = ( ( ( L = L3 )
% 15.55/8.58            & ( H2 = H3 ) )
% 15.55/8.58          | ( ~ ( ord_less_eq_real @ L @ H2 )
% 15.55/8.58            & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6155_atLeastAtMost__iff,axiom,
% 15.55/8.58      ! [I: set_nat,L: set_nat,U: set_nat] :
% 15.55/8.58        ( ( member_set_nat @ I @ ( set_or4548717258645045905et_nat @ L @ U ) )
% 15.55/8.58        = ( ( ord_less_eq_set_nat @ L @ I )
% 15.55/8.58          & ( ord_less_eq_set_nat @ I @ U ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6156_atLeastAtMost__iff,axiom,
% 15.55/8.58      ! [I: rat,L: rat,U: rat] :
% 15.55/8.58        ( ( member_rat @ I @ ( set_or633870826150836451st_rat @ L @ U ) )
% 15.55/8.58        = ( ( ord_less_eq_rat @ L @ I )
% 15.55/8.58          & ( ord_less_eq_rat @ I @ U ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6157_atLeastAtMost__iff,axiom,
% 15.55/8.58      ! [I: num,L: num,U: num] :
% 15.55/8.58        ( ( member_num @ I @ ( set_or7049704709247886629st_num @ L @ U ) )
% 15.55/8.58        = ( ( ord_less_eq_num @ L @ I )
% 15.55/8.58          & ( ord_less_eq_num @ I @ U ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6158_atLeastAtMost__iff,axiom,
% 15.55/8.58      ! [I: nat,L: nat,U: nat] :
% 15.55/8.58        ( ( member_nat @ I @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 15.55/8.58        = ( ( ord_less_eq_nat @ L @ I )
% 15.55/8.58          & ( ord_less_eq_nat @ I @ U ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6159_atLeastAtMost__iff,axiom,
% 15.55/8.58      ! [I: int,L: int,U: int] :
% 15.55/8.58        ( ( member_int @ I @ ( set_or1266510415728281911st_int @ L @ U ) )
% 15.55/8.58        = ( ( ord_less_eq_int @ L @ I )
% 15.55/8.58          & ( ord_less_eq_int @ I @ U ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6160_atLeastAtMost__iff,axiom,
% 15.55/8.58      ! [I: real,L: real,U: real] :
% 15.55/8.58        ( ( member_real @ I @ ( set_or1222579329274155063t_real @ L @ U ) )
% 15.55/8.58        = ( ( ord_less_eq_real @ L @ I )
% 15.55/8.58          & ( ord_less_eq_real @ I @ U ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6161_vebt__maxt_Osimps_I2_J,axiom,
% 15.55/8.58      ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 15.55/8.58        ( ( vEBT_vebt_maxt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 15.55/8.58        = none_nat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6162_aset_I2_J,axiom,
% 15.55/8.58      ! [D5: int,A3: set_int,P: int > $o,Q: int > $o] :
% 15.55/8.58        ( ! [X4: int] :
% 15.55/8.58            ( ! [Xa2: int] :
% 15.55/8.58                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58               => ! [Xb2: int] :
% 15.55/8.58                    ( ( member_int @ Xb2 @ A3 )
% 15.55/8.58                   => ( X4
% 15.55/8.58                     != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 15.55/8.58           => ( ( P @ X4 )
% 15.55/8.58             => ( P @ ( plus_plus_int @ X4 @ D5 ) ) ) )
% 15.55/8.58       => ( ! [X4: int] :
% 15.55/8.58              ( ! [Xa2: int] :
% 15.55/8.58                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58                 => ! [Xb2: int] :
% 15.55/8.58                      ( ( member_int @ Xb2 @ A3 )
% 15.55/8.58                     => ( X4
% 15.55/8.58                       != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 15.55/8.58             => ( ( Q @ X4 )
% 15.55/8.58               => ( Q @ ( plus_plus_int @ X4 @ D5 ) ) ) )
% 15.55/8.58         => ! [X6: int] :
% 15.55/8.58              ( ! [Xa3: int] :
% 15.55/8.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58                 => ! [Xb3: int] :
% 15.55/8.58                      ( ( member_int @ Xb3 @ A3 )
% 15.55/8.58                     => ( X6
% 15.55/8.58                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 15.55/8.58             => ( ( ( P @ X6 )
% 15.55/8.58                  | ( Q @ X6 ) )
% 15.55/8.58               => ( ( P @ ( plus_plus_int @ X6 @ D5 ) )
% 15.55/8.58                  | ( Q @ ( plus_plus_int @ X6 @ D5 ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6163_aset_I1_J,axiom,
% 15.55/8.58      ! [D5: int,A3: set_int,P: int > $o,Q: int > $o] :
% 15.55/8.58        ( ! [X4: int] :
% 15.55/8.58            ( ! [Xa2: int] :
% 15.55/8.58                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58               => ! [Xb2: int] :
% 15.55/8.58                    ( ( member_int @ Xb2 @ A3 )
% 15.55/8.58                   => ( X4
% 15.55/8.58                     != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 15.55/8.58           => ( ( P @ X4 )
% 15.55/8.58             => ( P @ ( plus_plus_int @ X4 @ D5 ) ) ) )
% 15.55/8.58       => ( ! [X4: int] :
% 15.55/8.58              ( ! [Xa2: int] :
% 15.55/8.58                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58                 => ! [Xb2: int] :
% 15.55/8.58                      ( ( member_int @ Xb2 @ A3 )
% 15.55/8.58                     => ( X4
% 15.55/8.58                       != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 15.55/8.58             => ( ( Q @ X4 )
% 15.55/8.58               => ( Q @ ( plus_plus_int @ X4 @ D5 ) ) ) )
% 15.55/8.58         => ! [X6: int] :
% 15.55/8.58              ( ! [Xa3: int] :
% 15.55/8.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58                 => ! [Xb3: int] :
% 15.55/8.58                      ( ( member_int @ Xb3 @ A3 )
% 15.55/8.58                     => ( X6
% 15.55/8.58                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 15.55/8.58             => ( ( ( P @ X6 )
% 15.55/8.58                  & ( Q @ X6 ) )
% 15.55/8.58               => ( ( P @ ( plus_plus_int @ X6 @ D5 ) )
% 15.55/8.58                  & ( Q @ ( plus_plus_int @ X6 @ D5 ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6164_bset_I2_J,axiom,
% 15.55/8.58      ! [D5: int,B5: set_int,P: int > $o,Q: int > $o] :
% 15.55/8.58        ( ! [X4: int] :
% 15.55/8.58            ( ! [Xa2: int] :
% 15.55/8.58                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58               => ! [Xb2: int] :
% 15.55/8.58                    ( ( member_int @ Xb2 @ B5 )
% 15.55/8.58                   => ( X4
% 15.55/8.58                     != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 15.55/8.58           => ( ( P @ X4 )
% 15.55/8.58             => ( P @ ( minus_minus_int @ X4 @ D5 ) ) ) )
% 15.55/8.58       => ( ! [X4: int] :
% 15.55/8.58              ( ! [Xa2: int] :
% 15.55/8.58                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58                 => ! [Xb2: int] :
% 15.55/8.58                      ( ( member_int @ Xb2 @ B5 )
% 15.55/8.58                     => ( X4
% 15.55/8.58                       != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 15.55/8.58             => ( ( Q @ X4 )
% 15.55/8.58               => ( Q @ ( minus_minus_int @ X4 @ D5 ) ) ) )
% 15.55/8.58         => ! [X6: int] :
% 15.55/8.58              ( ! [Xa3: int] :
% 15.55/8.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58                 => ! [Xb3: int] :
% 15.55/8.58                      ( ( member_int @ Xb3 @ B5 )
% 15.55/8.58                     => ( X6
% 15.55/8.58                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 15.55/8.58             => ( ( ( P @ X6 )
% 15.55/8.58                  | ( Q @ X6 ) )
% 15.55/8.58               => ( ( P @ ( minus_minus_int @ X6 @ D5 ) )
% 15.55/8.58                  | ( Q @ ( minus_minus_int @ X6 @ D5 ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6165_bset_I1_J,axiom,
% 15.55/8.58      ! [D5: int,B5: set_int,P: int > $o,Q: int > $o] :
% 15.55/8.58        ( ! [X4: int] :
% 15.55/8.58            ( ! [Xa2: int] :
% 15.55/8.58                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58               => ! [Xb2: int] :
% 15.55/8.58                    ( ( member_int @ Xb2 @ B5 )
% 15.55/8.58                   => ( X4
% 15.55/8.58                     != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 15.55/8.58           => ( ( P @ X4 )
% 15.55/8.58             => ( P @ ( minus_minus_int @ X4 @ D5 ) ) ) )
% 15.55/8.58       => ( ! [X4: int] :
% 15.55/8.58              ( ! [Xa2: int] :
% 15.55/8.58                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58                 => ! [Xb2: int] :
% 15.55/8.58                      ( ( member_int @ Xb2 @ B5 )
% 15.55/8.58                     => ( X4
% 15.55/8.58                       != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 15.55/8.58             => ( ( Q @ X4 )
% 15.55/8.58               => ( Q @ ( minus_minus_int @ X4 @ D5 ) ) ) )
% 15.55/8.58         => ! [X6: int] :
% 15.55/8.58              ( ! [Xa3: int] :
% 15.55/8.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58                 => ! [Xb3: int] :
% 15.55/8.58                      ( ( member_int @ Xb3 @ B5 )
% 15.55/8.58                     => ( X6
% 15.55/8.58                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 15.55/8.58             => ( ( ( P @ X6 )
% 15.55/8.58                  & ( Q @ X6 ) )
% 15.55/8.58               => ( ( P @ ( minus_minus_int @ X6 @ D5 ) )
% 15.55/8.58                  & ( Q @ ( minus_minus_int @ X6 @ D5 ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6166_bounded__Max__nat,axiom,
% 15.55/8.58      ! [P: nat > $o,X3: nat,M7: nat] :
% 15.55/8.58        ( ( P @ X3 )
% 15.55/8.58       => ( ! [X4: nat] :
% 15.55/8.58              ( ( P @ X4 )
% 15.55/8.58             => ( ord_less_eq_nat @ X4 @ M7 ) )
% 15.55/8.58         => ~ ! [M4: nat] :
% 15.55/8.58                ( ( P @ M4 )
% 15.55/8.58               => ~ ! [X6: nat] :
% 15.55/8.58                      ( ( P @ X6 )
% 15.55/8.58                     => ( ord_less_eq_nat @ X6 @ M4 ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6167_vebt__mint_Osimps_I2_J,axiom,
% 15.55/8.58      ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 15.55/8.58        ( ( vEBT_vebt_mint @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 15.55/8.58        = none_nat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6168_bset_I9_J,axiom,
% 15.55/8.58      ! [D3: int,D5: int,B5: set_int,T: int] :
% 15.55/8.58        ( ( dvd_dvd_int @ D3 @ D5 )
% 15.55/8.58       => ! [X6: int] :
% 15.55/8.58            ( ! [Xa3: int] :
% 15.55/8.58                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58               => ! [Xb3: int] :
% 15.55/8.58                    ( ( member_int @ Xb3 @ B5 )
% 15.55/8.58                   => ( X6
% 15.55/8.58                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 15.55/8.58           => ( ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ T ) )
% 15.55/8.58             => ( dvd_dvd_int @ D3 @ ( plus_plus_int @ ( minus_minus_int @ X6 @ D5 ) @ T ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6169_bset_I10_J,axiom,
% 15.55/8.58      ! [D3: int,D5: int,B5: set_int,T: int] :
% 15.55/8.58        ( ( dvd_dvd_int @ D3 @ D5 )
% 15.55/8.58       => ! [X6: int] :
% 15.55/8.58            ( ! [Xa3: int] :
% 15.55/8.58                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58               => ! [Xb3: int] :
% 15.55/8.58                    ( ( member_int @ Xb3 @ B5 )
% 15.55/8.58                   => ( X6
% 15.55/8.58                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 15.55/8.58           => ( ~ ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ T ) )
% 15.55/8.58             => ~ ( dvd_dvd_int @ D3 @ ( plus_plus_int @ ( minus_minus_int @ X6 @ D5 ) @ T ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6170_aset_I9_J,axiom,
% 15.55/8.58      ! [D3: int,D5: int,A3: set_int,T: int] :
% 15.55/8.58        ( ( dvd_dvd_int @ D3 @ D5 )
% 15.55/8.58       => ! [X6: int] :
% 15.55/8.58            ( ! [Xa3: int] :
% 15.55/8.58                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58               => ! [Xb3: int] :
% 15.55/8.58                    ( ( member_int @ Xb3 @ A3 )
% 15.55/8.58                   => ( X6
% 15.55/8.58                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 15.55/8.58           => ( ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ T ) )
% 15.55/8.58             => ( dvd_dvd_int @ D3 @ ( plus_plus_int @ ( plus_plus_int @ X6 @ D5 ) @ T ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6171_aset_I10_J,axiom,
% 15.55/8.58      ! [D3: int,D5: int,A3: set_int,T: int] :
% 15.55/8.58        ( ( dvd_dvd_int @ D3 @ D5 )
% 15.55/8.58       => ! [X6: int] :
% 15.55/8.58            ( ! [Xa3: int] :
% 15.55/8.58                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58               => ! [Xb3: int] :
% 15.55/8.58                    ( ( member_int @ Xb3 @ A3 )
% 15.55/8.58                   => ( X6
% 15.55/8.58                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 15.55/8.58           => ( ~ ( dvd_dvd_int @ D3 @ ( plus_plus_int @ X6 @ T ) )
% 15.55/8.58             => ~ ( dvd_dvd_int @ D3 @ ( plus_plus_int @ ( plus_plus_int @ X6 @ D5 ) @ T ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6172_vebt__maxt_Osimps_I3_J,axiom,
% 15.55/8.58      ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 15.55/8.58        ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 15.55/8.58        = ( some_nat @ Ma ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6173_periodic__finite__ex,axiom,
% 15.55/8.58      ! [D3: int,P: int > $o] :
% 15.55/8.58        ( ( ord_less_int @ zero_zero_int @ D3 )
% 15.55/8.58       => ( ! [X4: int,K2: int] :
% 15.55/8.58              ( ( P @ X4 )
% 15.55/8.58              = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 15.55/8.58         => ( ( ? [X8: int] : ( P @ X8 ) )
% 15.55/8.58            = ( ? [X: int] :
% 15.55/8.58                  ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 15.55/8.58                  & ( P @ X ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6174_aset_I7_J,axiom,
% 15.55/8.58      ! [D5: int,A3: set_int,T: int] :
% 15.55/8.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 15.55/8.58       => ! [X6: int] :
% 15.55/8.58            ( ! [Xa3: int] :
% 15.55/8.58                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58               => ! [Xb3: int] :
% 15.55/8.58                    ( ( member_int @ Xb3 @ A3 )
% 15.55/8.58                   => ( X6
% 15.55/8.58                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 15.55/8.58           => ( ( ord_less_int @ T @ X6 )
% 15.55/8.58             => ( ord_less_int @ T @ ( plus_plus_int @ X6 @ D5 ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6175_aset_I5_J,axiom,
% 15.55/8.58      ! [D5: int,T: int,A3: set_int] :
% 15.55/8.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 15.55/8.58       => ( ( member_int @ T @ A3 )
% 15.55/8.58         => ! [X6: int] :
% 15.55/8.58              ( ! [Xa3: int] :
% 15.55/8.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58                 => ! [Xb3: int] :
% 15.55/8.58                      ( ( member_int @ Xb3 @ A3 )
% 15.55/8.58                     => ( X6
% 15.55/8.58                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 15.55/8.58             => ( ( ord_less_int @ X6 @ T )
% 15.55/8.58               => ( ord_less_int @ ( plus_plus_int @ X6 @ D5 ) @ T ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6176_aset_I4_J,axiom,
% 15.55/8.58      ! [D5: int,T: int,A3: set_int] :
% 15.55/8.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 15.55/8.58       => ( ( member_int @ T @ A3 )
% 15.55/8.58         => ! [X6: int] :
% 15.55/8.58              ( ! [Xa3: int] :
% 15.55/8.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58                 => ! [Xb3: int] :
% 15.55/8.58                      ( ( member_int @ Xb3 @ A3 )
% 15.55/8.58                     => ( X6
% 15.55/8.58                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 15.55/8.58             => ( ( X6 != T )
% 15.55/8.58               => ( ( plus_plus_int @ X6 @ D5 )
% 15.55/8.58                 != T ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6177_aset_I3_J,axiom,
% 15.55/8.58      ! [D5: int,T: int,A3: set_int] :
% 15.55/8.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 15.55/8.58       => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A3 )
% 15.55/8.58         => ! [X6: int] :
% 15.55/8.58              ( ! [Xa3: int] :
% 15.55/8.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58                 => ! [Xb3: int] :
% 15.55/8.58                      ( ( member_int @ Xb3 @ A3 )
% 15.55/8.58                     => ( X6
% 15.55/8.58                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 15.55/8.58             => ( ( X6 = T )
% 15.55/8.58               => ( ( plus_plus_int @ X6 @ D5 )
% 15.55/8.58                  = T ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6178_bset_I7_J,axiom,
% 15.55/8.58      ! [D5: int,T: int,B5: set_int] :
% 15.55/8.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 15.55/8.58       => ( ( member_int @ T @ B5 )
% 15.55/8.58         => ! [X6: int] :
% 15.55/8.58              ( ! [Xa3: int] :
% 15.55/8.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58                 => ! [Xb3: int] :
% 15.55/8.58                      ( ( member_int @ Xb3 @ B5 )
% 15.55/8.58                     => ( X6
% 15.55/8.58                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 15.55/8.58             => ( ( ord_less_int @ T @ X6 )
% 15.55/8.58               => ( ord_less_int @ T @ ( minus_minus_int @ X6 @ D5 ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6179_bset_I5_J,axiom,
% 15.55/8.58      ! [D5: int,B5: set_int,T: int] :
% 15.55/8.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 15.55/8.58       => ! [X6: int] :
% 15.55/8.58            ( ! [Xa3: int] :
% 15.55/8.58                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58               => ! [Xb3: int] :
% 15.55/8.58                    ( ( member_int @ Xb3 @ B5 )
% 15.55/8.58                   => ( X6
% 15.55/8.58                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 15.55/8.58           => ( ( ord_less_int @ X6 @ T )
% 15.55/8.58             => ( ord_less_int @ ( minus_minus_int @ X6 @ D5 ) @ T ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6180_bset_I4_J,axiom,
% 15.55/8.58      ! [D5: int,T: int,B5: set_int] :
% 15.55/8.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 15.55/8.58       => ( ( member_int @ T @ B5 )
% 15.55/8.58         => ! [X6: int] :
% 15.55/8.58              ( ! [Xa3: int] :
% 15.55/8.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58                 => ! [Xb3: int] :
% 15.55/8.58                      ( ( member_int @ Xb3 @ B5 )
% 15.55/8.58                     => ( X6
% 15.55/8.58                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 15.55/8.58             => ( ( X6 != T )
% 15.55/8.58               => ( ( minus_minus_int @ X6 @ D5 )
% 15.55/8.58                 != T ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6181_bset_I3_J,axiom,
% 15.55/8.58      ! [D5: int,T: int,B5: set_int] :
% 15.55/8.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 15.55/8.58       => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B5 )
% 15.55/8.58         => ! [X6: int] :
% 15.55/8.58              ( ! [Xa3: int] :
% 15.55/8.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58                 => ! [Xb3: int] :
% 15.55/8.58                      ( ( member_int @ Xb3 @ B5 )
% 15.55/8.58                     => ( X6
% 15.55/8.58                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 15.55/8.58             => ( ( X6 = T )
% 15.55/8.58               => ( ( minus_minus_int @ X6 @ D5 )
% 15.55/8.58                  = T ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6182_bset_I6_J,axiom,
% 15.55/8.58      ! [D5: int,B5: set_int,T: int] :
% 15.55/8.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 15.55/8.58       => ! [X6: int] :
% 15.55/8.58            ( ! [Xa3: int] :
% 15.55/8.58                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58               => ! [Xb3: int] :
% 15.55/8.58                    ( ( member_int @ Xb3 @ B5 )
% 15.55/8.58                   => ( X6
% 15.55/8.58                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 15.55/8.58           => ( ( ord_less_eq_int @ X6 @ T )
% 15.55/8.58             => ( ord_less_eq_int @ ( minus_minus_int @ X6 @ D5 ) @ T ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6183_bset_I8_J,axiom,
% 15.55/8.58      ! [D5: int,T: int,B5: set_int] :
% 15.55/8.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 15.55/8.58       => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B5 )
% 15.55/8.58         => ! [X6: int] :
% 15.55/8.58              ( ! [Xa3: int] :
% 15.55/8.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58                 => ! [Xb3: int] :
% 15.55/8.58                      ( ( member_int @ Xb3 @ B5 )
% 15.55/8.58                     => ( X6
% 15.55/8.58                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 15.55/8.58             => ( ( ord_less_eq_int @ T @ X6 )
% 15.55/8.58               => ( ord_less_eq_int @ T @ ( minus_minus_int @ X6 @ D5 ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6184_aset_I6_J,axiom,
% 15.55/8.58      ! [D5: int,T: int,A3: set_int] :
% 15.55/8.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 15.55/8.58       => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A3 )
% 15.55/8.58         => ! [X6: int] :
% 15.55/8.58              ( ! [Xa3: int] :
% 15.55/8.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58                 => ! [Xb3: int] :
% 15.55/8.58                      ( ( member_int @ Xb3 @ A3 )
% 15.55/8.58                     => ( X6
% 15.55/8.58                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 15.55/8.58             => ( ( ord_less_eq_int @ X6 @ T )
% 15.55/8.58               => ( ord_less_eq_int @ ( plus_plus_int @ X6 @ D5 ) @ T ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6185_aset_I8_J,axiom,
% 15.55/8.58      ! [D5: int,A3: set_int,T: int] :
% 15.55/8.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 15.55/8.58       => ! [X6: int] :
% 15.55/8.58            ( ! [Xa3: int] :
% 15.55/8.58                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58               => ! [Xb3: int] :
% 15.55/8.58                    ( ( member_int @ Xb3 @ A3 )
% 15.55/8.58                   => ( X6
% 15.55/8.58                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 15.55/8.58           => ( ( ord_less_eq_int @ T @ X6 )
% 15.55/8.58             => ( ord_less_eq_int @ T @ ( plus_plus_int @ X6 @ D5 ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6186_cppi,axiom,
% 15.55/8.58      ! [D5: int,P: int > $o,P4: int > $o,A3: set_int] :
% 15.55/8.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 15.55/8.58       => ( ? [Z4: int] :
% 15.55/8.58            ! [X4: int] :
% 15.55/8.58              ( ( ord_less_int @ Z4 @ X4 )
% 15.55/8.58             => ( ( P @ X4 )
% 15.55/8.58                = ( P4 @ X4 ) ) )
% 15.55/8.58         => ( ! [X4: int] :
% 15.55/8.58                ( ! [Xa2: int] :
% 15.55/8.58                    ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58                   => ! [Xb2: int] :
% 15.55/8.58                        ( ( member_int @ Xb2 @ A3 )
% 15.55/8.58                       => ( X4
% 15.55/8.58                         != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 15.55/8.58               => ( ( P @ X4 )
% 15.55/8.58                 => ( P @ ( plus_plus_int @ X4 @ D5 ) ) ) )
% 15.55/8.58           => ( ! [X4: int,K2: int] :
% 15.55/8.58                  ( ( P4 @ X4 )
% 15.55/8.58                  = ( P4 @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D5 ) ) ) )
% 15.55/8.58             => ( ( ? [X8: int] : ( P @ X8 ) )
% 15.55/8.58                = ( ? [X: int] :
% 15.55/8.58                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58                      & ( P4 @ X ) )
% 15.55/8.58                  | ? [X: int] :
% 15.55/8.58                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58                      & ? [Y: int] :
% 15.55/8.58                          ( ( member_int @ Y @ A3 )
% 15.55/8.58                          & ( P @ ( minus_minus_int @ Y @ X ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6187_cpmi,axiom,
% 15.55/8.58      ! [D5: int,P: int > $o,P4: int > $o,B5: set_int] :
% 15.55/8.58        ( ( ord_less_int @ zero_zero_int @ D5 )
% 15.55/8.58       => ( ? [Z4: int] :
% 15.55/8.58            ! [X4: int] :
% 15.55/8.58              ( ( ord_less_int @ X4 @ Z4 )
% 15.55/8.58             => ( ( P @ X4 )
% 15.55/8.58                = ( P4 @ X4 ) ) )
% 15.55/8.58         => ( ! [X4: int] :
% 15.55/8.58                ( ! [Xa2: int] :
% 15.55/8.58                    ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58                   => ! [Xb2: int] :
% 15.55/8.58                        ( ( member_int @ Xb2 @ B5 )
% 15.55/8.58                       => ( X4
% 15.55/8.58                         != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 15.55/8.58               => ( ( P @ X4 )
% 15.55/8.58                 => ( P @ ( minus_minus_int @ X4 @ D5 ) ) ) )
% 15.55/8.58           => ( ! [X4: int,K2: int] :
% 15.55/8.58                  ( ( P4 @ X4 )
% 15.55/8.58                  = ( P4 @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D5 ) ) ) )
% 15.55/8.58             => ( ( ? [X8: int] : ( P @ X8 ) )
% 15.55/8.58                = ( ? [X: int] :
% 15.55/8.58                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58                      & ( P4 @ X ) )
% 15.55/8.58                  | ? [X: int] :
% 15.55/8.58                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 15.55/8.58                      & ? [Y: int] :
% 15.55/8.58                          ( ( member_int @ Y @ B5 )
% 15.55/8.58                          & ( P @ ( plus_plus_int @ Y @ X ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6188_atLeastatMost__psubset__iff,axiom,
% 15.55/8.58      ! [A: set_nat,B: set_nat,C: set_nat,D3: set_nat] :
% 15.55/8.58        ( ( ord_less_set_set_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D3 ) )
% 15.55/8.58        = ( ( ~ ( ord_less_eq_set_nat @ A @ B )
% 15.55/8.58            | ( ( ord_less_eq_set_nat @ C @ A )
% 15.55/8.58              & ( ord_less_eq_set_nat @ B @ D3 )
% 15.55/8.58              & ( ( ord_less_set_nat @ C @ A )
% 15.55/8.58                | ( ord_less_set_nat @ B @ D3 ) ) ) )
% 15.55/8.58          & ( ord_less_eq_set_nat @ C @ D3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6189_atLeastatMost__psubset__iff,axiom,
% 15.55/8.58      ! [A: rat,B: rat,C: rat,D3: rat] :
% 15.55/8.58        ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D3 ) )
% 15.55/8.58        = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 15.55/8.58            | ( ( ord_less_eq_rat @ C @ A )
% 15.55/8.58              & ( ord_less_eq_rat @ B @ D3 )
% 15.55/8.58              & ( ( ord_less_rat @ C @ A )
% 15.55/8.58                | ( ord_less_rat @ B @ D3 ) ) ) )
% 15.55/8.58          & ( ord_less_eq_rat @ C @ D3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6190_atLeastatMost__psubset__iff,axiom,
% 15.55/8.58      ! [A: num,B: num,C: num,D3: num] :
% 15.55/8.58        ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D3 ) )
% 15.55/8.58        = ( ( ~ ( ord_less_eq_num @ A @ B )
% 15.55/8.58            | ( ( ord_less_eq_num @ C @ A )
% 15.55/8.58              & ( ord_less_eq_num @ B @ D3 )
% 15.55/8.58              & ( ( ord_less_num @ C @ A )
% 15.55/8.58                | ( ord_less_num @ B @ D3 ) ) ) )
% 15.55/8.58          & ( ord_less_eq_num @ C @ D3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6191_atLeastatMost__psubset__iff,axiom,
% 15.55/8.58      ! [A: nat,B: nat,C: nat,D3: nat] :
% 15.55/8.58        ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D3 ) )
% 15.55/8.58        = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 15.55/8.58            | ( ( ord_less_eq_nat @ C @ A )
% 15.55/8.58              & ( ord_less_eq_nat @ B @ D3 )
% 15.55/8.58              & ( ( ord_less_nat @ C @ A )
% 15.55/8.58                | ( ord_less_nat @ B @ D3 ) ) ) )
% 15.55/8.58          & ( ord_less_eq_nat @ C @ D3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6192_atLeastatMost__psubset__iff,axiom,
% 15.55/8.58      ! [A: int,B: int,C: int,D3: int] :
% 15.55/8.58        ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D3 ) )
% 15.55/8.58        = ( ( ~ ( ord_less_eq_int @ A @ B )
% 15.55/8.58            | ( ( ord_less_eq_int @ C @ A )
% 15.55/8.58              & ( ord_less_eq_int @ B @ D3 )
% 15.55/8.58              & ( ( ord_less_int @ C @ A )
% 15.55/8.58                | ( ord_less_int @ B @ D3 ) ) ) )
% 15.55/8.58          & ( ord_less_eq_int @ C @ D3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6193_atLeastatMost__psubset__iff,axiom,
% 15.55/8.58      ! [A: real,B: real,C: real,D3: real] :
% 15.55/8.58        ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D3 ) )
% 15.55/8.58        = ( ( ~ ( ord_less_eq_real @ A @ B )
% 15.55/8.58            | ( ( ord_less_eq_real @ C @ A )
% 15.55/8.58              & ( ord_less_eq_real @ B @ D3 )
% 15.55/8.58              & ( ( ord_less_real @ C @ A )
% 15.55/8.58                | ( ord_less_real @ B @ D3 ) ) ) )
% 15.55/8.58          & ( ord_less_eq_real @ C @ D3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6194_invar__vebt_Ointros_I2_J,axiom,
% 15.55/8.58      ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 15.55/8.58        ( ! [X4: vEBT_VEBT] :
% 15.55/8.58            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 15.55/8.58           => ( vEBT_invar_vebt @ X4 @ N ) )
% 15.55/8.58       => ( ( vEBT_invar_vebt @ Summary @ M )
% 15.55/8.58         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 15.55/8.58              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 15.55/8.58           => ( ( M = N )
% 15.55/8.58             => ( ( Deg
% 15.55/8.58                  = ( plus_plus_nat @ N @ M ) )
% 15.55/8.58               => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 15.55/8.58                 => ( ! [X4: vEBT_VEBT] :
% 15.55/8.58                        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 15.55/8.58                       => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) )
% 15.55/8.58                   => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6195_invar__vebt_Ointros_I3_J,axiom,
% 15.55/8.58      ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 15.55/8.58        ( ! [X4: vEBT_VEBT] :
% 15.55/8.58            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 15.55/8.58           => ( vEBT_invar_vebt @ X4 @ N ) )
% 15.55/8.58       => ( ( vEBT_invar_vebt @ Summary @ M )
% 15.55/8.58         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 15.55/8.58              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 15.55/8.58           => ( ( M
% 15.55/8.58                = ( suc @ N ) )
% 15.55/8.58             => ( ( Deg
% 15.55/8.58                  = ( plus_plus_nat @ N @ M ) )
% 15.55/8.58               => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 15.55/8.58                 => ( ! [X4: vEBT_VEBT] :
% 15.55/8.58                        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 15.55/8.58                       => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) )
% 15.55/8.58                   => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6196_is__pred__in__set__def,axiom,
% 15.55/8.58      ( vEBT_is_pred_in_set
% 15.55/8.58      = ( ^ [Xs: set_nat,X: nat,Y: nat] :
% 15.55/8.58            ( ( member_nat @ Y @ Xs )
% 15.55/8.58            & ( ord_less_nat @ Y @ X )
% 15.55/8.58            & ! [Z6: nat] :
% 15.55/8.58                ( ( member_nat @ Z6 @ Xs )
% 15.55/8.58               => ( ( ord_less_nat @ Z6 @ X )
% 15.55/8.58                 => ( ord_less_eq_nat @ Z6 @ Y ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6197_is__succ__in__set__def,axiom,
% 15.55/8.58      ( vEBT_is_succ_in_set
% 15.55/8.58      = ( ^ [Xs: set_nat,X: nat,Y: nat] :
% 15.55/8.58            ( ( member_nat @ Y @ Xs )
% 15.55/8.58            & ( ord_less_nat @ X @ Y )
% 15.55/8.58            & ! [Z6: nat] :
% 15.55/8.58                ( ( member_nat @ Z6 @ Xs )
% 15.55/8.58               => ( ( ord_less_nat @ X @ Z6 )
% 15.55/8.58                 => ( ord_less_eq_nat @ Y @ Z6 ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6198_vebt__pred_Osimps_I5_J,axiom,
% 15.55/8.58      ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 15.55/8.58        ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf )
% 15.55/8.58        = none_nat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6199_vebt__succ_Osimps_I4_J,axiom,
% 15.55/8.58      ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 15.55/8.58        ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve )
% 15.55/8.58        = none_nat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6200_del__x__mi__lets__in__not__minNull,axiom,
% 15.55/8.58      ! [X3: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 15.55/8.58        ( ( ( X3 = Mi )
% 15.55/8.58          & ( ord_less_nat @ X3 @ Ma ) )
% 15.55/8.58       => ( ( Mi != Ma )
% 15.55/8.58         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.58           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.58                = H2 )
% 15.55/8.58             => ( ( Xn
% 15.55/8.58                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_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 ) ) ) ) ) ) )
% 15.55/8.58               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.58                    = L )
% 15.55/8.58                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.58                   => ( ( Newnode
% 15.55/8.58                        = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 15.55/8.58                     => ( ( Newlist
% 15.55/8.58                          = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 15.55/8.58                       => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 15.55/8.58                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.58                            = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6201_del__x__not__mi__newnode__not__nil,axiom,
% 15.55/8.58      ! [Mi: nat,X3: nat,Ma: nat,Deg: nat,H2: nat,L: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 15.55/8.58        ( ( ( ord_less_nat @ Mi @ X3 )
% 15.55/8.58          & ( ord_less_eq_nat @ X3 @ Ma ) )
% 15.55/8.58       => ( ( Mi != Ma )
% 15.55/8.58         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.58           => ( ( ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.58                = H2 )
% 15.55/8.58             => ( ( ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.58                  = L )
% 15.55/8.58               => ( ( Newnode
% 15.55/8.58                    = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 15.55/8.58                 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 15.55/8.58                   => ( ( Newlist
% 15.55/8.58                        = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 15.55/8.58                     => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.58                       => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.58                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6202__C5_OIH_C_I1_J,axiom,
% 15.55/8.58      ! [X6: vEBT_VEBT] :
% 15.55/8.58        ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ treeList ) )
% 15.55/8.58       => ( ( vEBT_invar_vebt @ X6 @ na )
% 15.55/8.58          & ( ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ X6 @ x ) )
% 15.55/8.58           => ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ X6 @ x ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6203_vebt__delete_Osimps_I6_J,axiom,
% 15.55/8.58      ! [Mi: nat,Ma: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT,X3: nat] :
% 15.55/8.58        ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ X3 )
% 15.55/8.58        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6204__C5_OIH_C_I2_J,axiom,
% 15.55/8.58      ( ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ summary @ x ) )
% 15.55/8.58     => ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ summary @ x ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6205_Leaf__0__not,axiom,
% 15.55/8.58      ! [A: $o,B: $o] :
% 15.55/8.58        ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6206_deg1Leaf,axiom,
% 15.55/8.58      ! [T: vEBT_VEBT] :
% 15.55/8.58        ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 15.55/8.58        = ( ? [A4: $o,B3: $o] :
% 15.55/8.58              ( T
% 15.55/8.58              = ( vEBT_Leaf @ A4 @ B3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6207_deg__1__Leaf,axiom,
% 15.55/8.58      ! [T: vEBT_VEBT] :
% 15.55/8.58        ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 15.55/8.58       => ? [A5: $o,B4: $o] :
% 15.55/8.58            ( T
% 15.55/8.58            = ( vEBT_Leaf @ A5 @ B4 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6208_deg__1__Leafy,axiom,
% 15.55/8.58      ! [T: vEBT_VEBT,N: nat] :
% 15.55/8.58        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.58       => ( ( N = one_one_nat )
% 15.55/8.58         => ? [A5: $o,B4: $o] :
% 15.55/8.58              ( T
% 15.55/8.58              = ( vEBT_Leaf @ A5 @ B4 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6209_semiring__norm_I90_J,axiom,
% 15.55/8.58      ! [M: num,N: num] :
% 15.55/8.58        ( ( ( bit1 @ M )
% 15.55/8.58          = ( bit1 @ N ) )
% 15.55/8.58        = ( M = N ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6210_verit__eq__simplify_I9_J,axiom,
% 15.55/8.58      ! [X32: num,Y32: num] :
% 15.55/8.58        ( ( ( bit1 @ X32 )
% 15.55/8.58          = ( bit1 @ Y32 ) )
% 15.55/8.58        = ( X32 = Y32 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6211_semiring__norm_I88_J,axiom,
% 15.55/8.58      ! [M: num,N: num] :
% 15.55/8.58        ( ( bit0 @ M )
% 15.55/8.58       != ( bit1 @ N ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6212_semiring__norm_I89_J,axiom,
% 15.55/8.58      ! [M: num,N: num] :
% 15.55/8.58        ( ( bit1 @ M )
% 15.55/8.58       != ( bit0 @ N ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6213_semiring__norm_I84_J,axiom,
% 15.55/8.58      ! [N: num] :
% 15.55/8.58        ( one
% 15.55/8.58       != ( bit1 @ N ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6214_semiring__norm_I86_J,axiom,
% 15.55/8.58      ! [M: num] :
% 15.55/8.58        ( ( bit1 @ M )
% 15.55/8.58       != one ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6215_tdeletemimi,axiom,
% 15.55/8.58      ! [Deg: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 15.55/8.58        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.58       => ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Mi ) ) @ Deg @ TreeList2 @ Summary ) @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6216_semiring__norm_I80_J,axiom,
% 15.55/8.58      ! [M: num,N: num] :
% 15.55/8.58        ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 15.55/8.58        = ( ord_less_num @ M @ N ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6217_semiring__norm_I73_J,axiom,
% 15.55/8.58      ! [M: num,N: num] :
% 15.55/8.58        ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 15.55/8.58        = ( ord_less_eq_num @ M @ N ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6218_semiring__norm_I9_J,axiom,
% 15.55/8.58      ! [M: num,N: num] :
% 15.55/8.58        ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 15.55/8.58        = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6219_semiring__norm_I7_J,axiom,
% 15.55/8.58      ! [M: num,N: num] :
% 15.55/8.58        ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 15.55/8.58        = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6220_list__update__beyond,axiom,
% 15.55/8.58      ! [Xs2: list_VEBT_VEBT,I: nat,X3: vEBT_VEBT] :
% 15.55/8.58        ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ I )
% 15.55/8.58       => ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X3 )
% 15.55/8.58          = Xs2 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6221_list__update__beyond,axiom,
% 15.55/8.58      ! [Xs2: list_o,I: nat,X3: $o] :
% 15.55/8.58        ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ I )
% 15.55/8.58       => ( ( list_update_o @ Xs2 @ I @ X3 )
% 15.55/8.58          = Xs2 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6222_list__update__beyond,axiom,
% 15.55/8.58      ! [Xs2: list_nat,I: nat,X3: nat] :
% 15.55/8.58        ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ I )
% 15.55/8.58       => ( ( list_update_nat @ Xs2 @ I @ X3 )
% 15.55/8.58          = Xs2 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6223_list__update__beyond,axiom,
% 15.55/8.58      ! [Xs2: list_int,I: nat,X3: int] :
% 15.55/8.58        ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ I )
% 15.55/8.58       => ( ( list_update_int @ Xs2 @ I @ X3 )
% 15.55/8.58          = Xs2 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6224_semiring__norm_I15_J,axiom,
% 15.55/8.58      ! [M: num,N: num] :
% 15.55/8.58        ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 15.55/8.58        = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6225_semiring__norm_I14_J,axiom,
% 15.55/8.58      ! [M: num,N: num] :
% 15.55/8.58        ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 15.55/8.58        = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6226_semiring__norm_I81_J,axiom,
% 15.55/8.58      ! [M: num,N: num] :
% 15.55/8.58        ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 15.55/8.58        = ( ord_less_num @ M @ N ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6227_semiring__norm_I72_J,axiom,
% 15.55/8.58      ! [M: num,N: num] :
% 15.55/8.58        ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 15.55/8.58        = ( ord_less_eq_num @ M @ N ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6228_semiring__norm_I77_J,axiom,
% 15.55/8.58      ! [N: num] : ( ord_less_num @ one @ ( bit1 @ N ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6229_semiring__norm_I70_J,axiom,
% 15.55/8.58      ! [M: num] :
% 15.55/8.58        ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6230_or__numerals_I8_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X3 ) ) @ one_one_int )
% 15.55/8.58        = ( numeral_numeral_int @ ( bit1 @ X3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6231_or__numerals_I8_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ one_one_nat )
% 15.55/8.58        = ( numeral_numeral_nat @ ( bit1 @ X3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6232_or__numerals_I2_J,axiom,
% 15.55/8.58      ! [Y3: num] :
% 15.55/8.58        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y3 ) ) )
% 15.55/8.58        = ( numeral_numeral_int @ ( bit1 @ Y3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6233_or__numerals_I2_J,axiom,
% 15.55/8.58      ! [Y3: num] :
% 15.55/8.58        ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 15.55/8.58        = ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6234_zdiv__numeral__Bit1,axiom,
% 15.55/8.58      ! [V: num,W: num] :
% 15.55/8.58        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 15.55/8.58        = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6235_semiring__norm_I3_J,axiom,
% 15.55/8.58      ! [N: num] :
% 15.55/8.58        ( ( plus_plus_num @ one @ ( bit0 @ N ) )
% 15.55/8.58        = ( bit1 @ N ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6236_semiring__norm_I4_J,axiom,
% 15.55/8.58      ! [N: num] :
% 15.55/8.58        ( ( plus_plus_num @ one @ ( bit1 @ N ) )
% 15.55/8.58        = ( bit0 @ ( plus_plus_num @ N @ one ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6237_semiring__norm_I5_J,axiom,
% 15.55/8.58      ! [M: num] :
% 15.55/8.58        ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 15.55/8.58        = ( bit1 @ M ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6238_semiring__norm_I8_J,axiom,
% 15.55/8.58      ! [M: num] :
% 15.55/8.58        ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 15.55/8.58        = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6239_semiring__norm_I10_J,axiom,
% 15.55/8.58      ! [M: num,N: num] :
% 15.55/8.58        ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 15.55/8.58        = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ one ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6240_nth__list__update__eq,axiom,
% 15.55/8.58      ! [I: nat,Xs2: list_VEBT_VEBT,X3: vEBT_VEBT] :
% 15.55/8.58        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 15.55/8.58       => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X3 ) @ I )
% 15.55/8.58          = X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6241_nth__list__update__eq,axiom,
% 15.55/8.58      ! [I: nat,Xs2: list_o,X3: $o] :
% 15.55/8.58        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 15.55/8.58       => ( ( nth_o @ ( list_update_o @ Xs2 @ I @ X3 ) @ I )
% 15.55/8.58          = X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6242_nth__list__update__eq,axiom,
% 15.55/8.58      ! [I: nat,Xs2: list_nat,X3: nat] :
% 15.55/8.58        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 15.55/8.58       => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X3 ) @ I )
% 15.55/8.58          = X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6243_nth__list__update__eq,axiom,
% 15.55/8.58      ! [I: nat,Xs2: list_int,X3: int] :
% 15.55/8.58        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 15.55/8.58       => ( ( nth_int @ ( list_update_int @ Xs2 @ I @ X3 ) @ I )
% 15.55/8.58          = X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6244_semiring__norm_I16_J,axiom,
% 15.55/8.58      ! [M: num,N: num] :
% 15.55/8.58        ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 15.55/8.58        = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6245_semiring__norm_I79_J,axiom,
% 15.55/8.58      ! [M: num,N: num] :
% 15.55/8.58        ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 15.55/8.58        = ( ord_less_eq_num @ M @ N ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6246_semiring__norm_I74_J,axiom,
% 15.55/8.58      ! [M: num,N: num] :
% 15.55/8.58        ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 15.55/8.58        = ( ord_less_num @ M @ N ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6247_or__numerals_I5_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X3 ) ) @ one_one_int )
% 15.55/8.58        = ( numeral_numeral_int @ ( bit1 @ X3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6248_or__numerals_I5_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ one_one_nat )
% 15.55/8.58        = ( numeral_numeral_nat @ ( bit1 @ X3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6249_or__numerals_I1_J,axiom,
% 15.55/8.58      ! [Y3: num] :
% 15.55/8.58        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y3 ) ) )
% 15.55/8.58        = ( numeral_numeral_int @ ( bit1 @ Y3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6250_or__numerals_I1_J,axiom,
% 15.55/8.58      ! [Y3: num] :
% 15.55/8.58        ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 15.55/8.58        = ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6251_xor__numerals_I1_J,axiom,
% 15.55/8.58      ! [Y3: num] :
% 15.55/8.58        ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y3 ) ) )
% 15.55/8.58        = ( numeral_numeral_int @ ( bit1 @ Y3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6252_xor__numerals_I1_J,axiom,
% 15.55/8.58      ! [Y3: num] :
% 15.55/8.58        ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 15.55/8.58        = ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6253_xor__numerals_I2_J,axiom,
% 15.55/8.58      ! [Y3: num] :
% 15.55/8.58        ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y3 ) ) )
% 15.55/8.58        = ( numeral_numeral_int @ ( bit0 @ Y3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6254_xor__numerals_I2_J,axiom,
% 15.55/8.58      ! [Y3: num] :
% 15.55/8.58        ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 15.55/8.58        = ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6255_xor__numerals_I5_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X3 ) ) @ one_one_int )
% 15.55/8.58        = ( numeral_numeral_int @ ( bit1 @ X3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6256_xor__numerals_I5_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ one_one_nat )
% 15.55/8.58        = ( numeral_numeral_nat @ ( bit1 @ X3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6257_xor__numerals_I8_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X3 ) ) @ one_one_int )
% 15.55/8.58        = ( numeral_numeral_int @ ( bit0 @ X3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6258_xor__numerals_I8_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ one_one_nat )
% 15.55/8.58        = ( numeral_numeral_nat @ ( bit0 @ X3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6259_set__swap,axiom,
% 15.55/8.58      ! [I: nat,Xs2: list_VEBT_VEBT,J: nat] :
% 15.55/8.58        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 15.55/8.58       => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 15.55/8.58         => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ ( nth_VEBT_VEBT @ Xs2 @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs2 @ I ) ) )
% 15.55/8.58            = ( set_VEBT_VEBT2 @ Xs2 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6260_set__swap,axiom,
% 15.55/8.58      ! [I: nat,Xs2: list_o,J: nat] :
% 15.55/8.58        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 15.55/8.58       => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs2 ) )
% 15.55/8.58         => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs2 @ I @ ( nth_o @ Xs2 @ J ) ) @ J @ ( nth_o @ Xs2 @ I ) ) )
% 15.55/8.58            = ( set_o2 @ Xs2 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6261_set__swap,axiom,
% 15.55/8.58      ! [I: nat,Xs2: list_nat,J: nat] :
% 15.55/8.58        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 15.55/8.58       => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 15.55/8.58         => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs2 @ I @ ( nth_nat @ Xs2 @ J ) ) @ J @ ( nth_nat @ Xs2 @ I ) ) )
% 15.55/8.58            = ( set_nat2 @ Xs2 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6262_set__swap,axiom,
% 15.55/8.58      ! [I: nat,Xs2: list_int,J: nat] :
% 15.55/8.58        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 15.55/8.58       => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs2 ) )
% 15.55/8.58         => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs2 @ I @ ( nth_int @ Xs2 @ J ) ) @ J @ ( nth_int @ Xs2 @ I ) ) )
% 15.55/8.58            = ( set_int2 @ Xs2 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6263_or__nat__numerals_I4_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 15.55/8.58        = ( numeral_numeral_nat @ ( bit1 @ X3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6264_or__nat__numerals_I2_J,axiom,
% 15.55/8.58      ! [Y3: num] :
% 15.55/8.58        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 15.55/8.58        = ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6265_or__minus__numerals_I6_J,axiom,
% 15.55/8.58      ! [N: num] :
% 15.55/8.58        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 15.55/8.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6266_or__minus__numerals_I2_J,axiom,
% 15.55/8.58      ! [N: num] :
% 15.55/8.58        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 15.55/8.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6267_div__Suc__eq__div__add3,axiom,
% 15.55/8.58      ! [M: nat,N: nat] :
% 15.55/8.58        ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 15.55/8.58        = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6268_Suc__div__eq__add3__div__numeral,axiom,
% 15.55/8.58      ! [M: nat,V: num] :
% 15.55/8.58        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 15.55/8.58        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6269_xor__numerals_I7_J,axiom,
% 15.55/8.58      ! [X3: num,Y3: num] :
% 15.55/8.58        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X3 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y3 ) ) )
% 15.55/8.58        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6270_xor__numerals_I7_J,axiom,
% 15.55/8.58      ! [X3: num,Y3: num] :
% 15.55/8.58        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 15.55/8.58        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X3 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6271_Suc__mod__eq__add3__mod__numeral,axiom,
% 15.55/8.58      ! [M: nat,V: num] :
% 15.55/8.58        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 15.55/8.58        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6272_mod__Suc__eq__mod__add3,axiom,
% 15.55/8.58      ! [M: nat,N: nat] :
% 15.55/8.58        ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 15.55/8.58        = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6273_or__nat__numerals_I3_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 15.55/8.58        = ( numeral_numeral_nat @ ( bit1 @ X3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6274_or__nat__numerals_I1_J,axiom,
% 15.55/8.58      ! [Y3: num] :
% 15.55/8.58        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 15.55/8.58        = ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6275_xor__nat__numerals_I4_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 15.55/8.58        = ( numeral_numeral_nat @ ( bit0 @ X3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6276_xor__nat__numerals_I3_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 15.55/8.58        = ( numeral_numeral_nat @ ( bit1 @ X3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6277_xor__nat__numerals_I2_J,axiom,
% 15.55/8.58      ! [Y3: num] :
% 15.55/8.58        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 15.55/8.58        = ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6278_xor__nat__numerals_I1_J,axiom,
% 15.55/8.58      ! [Y3: num] :
% 15.55/8.58        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 15.55/8.58        = ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6279_or__numerals_I4_J,axiom,
% 15.55/8.58      ! [X3: num,Y3: num] :
% 15.55/8.58        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X3 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y3 ) ) )
% 15.55/8.58        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6280_or__numerals_I4_J,axiom,
% 15.55/8.58      ! [X3: num,Y3: num] :
% 15.55/8.58        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 15.55/8.58        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X3 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6281_or__numerals_I6_J,axiom,
% 15.55/8.58      ! [X3: num,Y3: num] :
% 15.55/8.58        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X3 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y3 ) ) )
% 15.55/8.58        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6282_or__numerals_I6_J,axiom,
% 15.55/8.58      ! [X3: num,Y3: num] :
% 15.55/8.58        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 15.55/8.58        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X3 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6283_or__numerals_I7_J,axiom,
% 15.55/8.58      ! [X3: num,Y3: num] :
% 15.55/8.58        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X3 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y3 ) ) )
% 15.55/8.58        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6284_or__numerals_I7_J,axiom,
% 15.55/8.58      ! [X3: num,Y3: num] :
% 15.55/8.58        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 15.55/8.58        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X3 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6285_xor__numerals_I4_J,axiom,
% 15.55/8.58      ! [X3: num,Y3: num] :
% 15.55/8.58        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X3 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y3 ) ) )
% 15.55/8.58        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6286_xor__numerals_I4_J,axiom,
% 15.55/8.58      ! [X3: num,Y3: num] :
% 15.55/8.58        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 15.55/8.58        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X3 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6287_xor__numerals_I6_J,axiom,
% 15.55/8.58      ! [X3: num,Y3: num] :
% 15.55/8.58        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X3 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y3 ) ) )
% 15.55/8.58        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6288_xor__numerals_I6_J,axiom,
% 15.55/8.58      ! [X3: num,Y3: num] :
% 15.55/8.58        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 15.55/8.58        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X3 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6289_zmod__numeral__Bit1,axiom,
% 15.55/8.58      ! [V: num,W: num] :
% 15.55/8.58        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 15.55/8.58        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) @ one_one_int ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6290_signed__take__bit__Suc__bit1,axiom,
% 15.55/8.58      ! [N: nat,K: num] :
% 15.55/8.58        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 15.55/8.58        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6291_signed__take__bit__Suc__minus__bit1,axiom,
% 15.55/8.58      ! [N: nat,K: num] :
% 15.55/8.58        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 15.55/8.58        = ( 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 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6292_VEBT_Osize_I4_J,axiom,
% 15.55/8.58      ! [X21: $o,X222: $o] :
% 15.55/8.58        ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 15.55/8.58        = zero_zero_nat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6293_verit__eq__simplify_I14_J,axiom,
% 15.55/8.58      ! [X2: num,X32: num] :
% 15.55/8.58        ( ( bit0 @ X2 )
% 15.55/8.58       != ( bit1 @ X32 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6294_verit__eq__simplify_I12_J,axiom,
% 15.55/8.58      ! [X32: num] :
% 15.55/8.58        ( one
% 15.55/8.58       != ( bit1 @ X32 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6295_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I3_J,axiom,
% 15.55/8.58      ! [A: $o,B: $o,N: nat] :
% 15.55/8.58        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N ) ) )
% 15.55/8.58        = one_one_nat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6296_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I1_J,axiom,
% 15.55/8.58      ! [A: $o,B: $o] :
% 15.55/8.58        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 15.55/8.58        = one_one_nat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6297_vebt__delete_Osimps_I1_J,axiom,
% 15.55/8.58      ! [A: $o,B: $o] :
% 15.55/8.58        ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 15.55/8.58        = ( vEBT_Leaf @ $false @ B ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6298_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I2_J,axiom,
% 15.55/8.58      ! [A: $o,B: $o] :
% 15.55/8.58        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 15.55/8.58        = one_one_nat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6299_xor__num_Ocases,axiom,
% 15.55/8.58      ! [X3: product_prod_num_num] :
% 15.55/8.58        ( ( X3
% 15.55/8.58         != ( product_Pair_num_num @ one @ one ) )
% 15.55/8.58       => ( ! [N2: num] :
% 15.55/8.58              ( X3
% 15.55/8.58             != ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) )
% 15.55/8.58         => ( ! [N2: num] :
% 15.55/8.58                ( X3
% 15.55/8.58               != ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) )
% 15.55/8.58           => ( ! [M4: num] :
% 15.55/8.58                  ( X3
% 15.55/8.58                 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) )
% 15.55/8.58             => ( ! [M4: num,N2: num] :
% 15.55/8.58                    ( X3
% 15.55/8.58                   != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) ) )
% 15.55/8.58               => ( ! [M4: num,N2: num] :
% 15.55/8.58                      ( X3
% 15.55/8.58                     != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) ) )
% 15.55/8.58                 => ( ! [M4: num] :
% 15.55/8.58                        ( X3
% 15.55/8.58                       != ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) )
% 15.55/8.58                   => ( ! [M4: num,N2: num] :
% 15.55/8.58                          ( X3
% 15.55/8.58                         != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) ) )
% 15.55/8.58                     => ~ ! [M4: num,N2: num] :
% 15.55/8.58                            ( X3
% 15.55/8.58                           != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6300_num_Oexhaust,axiom,
% 15.55/8.58      ! [Y3: num] :
% 15.55/8.58        ( ( Y3 != one )
% 15.55/8.58       => ( ! [X22: num] :
% 15.55/8.58              ( Y3
% 15.55/8.58             != ( bit0 @ X22 ) )
% 15.55/8.58         => ~ ! [X33: num] :
% 15.55/8.58                ( Y3
% 15.55/8.58               != ( bit1 @ X33 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6301_vebt__delete_Osimps_I2_J,axiom,
% 15.55/8.58      ! [A: $o,B: $o] :
% 15.55/8.58        ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 15.55/8.58        = ( vEBT_Leaf @ A @ $false ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6302_vebt__buildup_Osimps_I1_J,axiom,
% 15.55/8.58      ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 15.55/8.58      = ( vEBT_Leaf @ $false @ $false ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6303_VEBT__internal_Onaive__member_Ocases,axiom,
% 15.55/8.58      ! [X3: produc9072475918466114483BT_nat] :
% 15.55/8.58        ( ! [A5: $o,B4: $o,X4: nat] :
% 15.55/8.58            ( X3
% 15.55/8.58           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ X4 ) )
% 15.55/8.58       => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux2: nat] :
% 15.55/8.58              ( X3
% 15.55/8.58             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux2 ) )
% 15.55/8.58         => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT,X4: nat] :
% 15.55/8.58                ( X3
% 15.55/8.58               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) @ X4 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6304_numeral__Bit1,axiom,
% 15.55/8.58      ! [N: num] :
% 15.55/8.58        ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 15.55/8.58        = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6305_numeral__Bit1,axiom,
% 15.55/8.58      ! [N: num] :
% 15.55/8.58        ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 15.55/8.58        = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6306_numeral__Bit1,axiom,
% 15.55/8.58      ! [N: num] :
% 15.55/8.58        ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 15.55/8.58        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6307_numeral__Bit1,axiom,
% 15.55/8.58      ! [N: num] :
% 15.55/8.58        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 15.55/8.58        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6308_numeral__Bit1,axiom,
% 15.55/8.58      ! [N: num] :
% 15.55/8.58        ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 15.55/8.58        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6309_invar__vebt_Ointros_I1_J,axiom,
% 15.55/8.58      ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6310_eval__nat__numeral_I3_J,axiom,
% 15.55/8.58      ! [N: num] :
% 15.55/8.58        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 15.55/8.58        = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6311_cong__exp__iff__simps_I10_J,axiom,
% 15.55/8.58      ! [M: num,Q3: num,N: num] :
% 15.55/8.58        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 15.55/8.58       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6312_cong__exp__iff__simps_I10_J,axiom,
% 15.55/8.58      ! [M: num,Q3: num,N: num] :
% 15.55/8.58        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 15.55/8.58       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6313_cong__exp__iff__simps_I10_J,axiom,
% 15.55/8.58      ! [M: num,Q3: num,N: num] :
% 15.55/8.58        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 15.55/8.58       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6314_cong__exp__iff__simps_I12_J,axiom,
% 15.55/8.58      ! [M: num,Q3: num,N: num] :
% 15.55/8.58        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 15.55/8.58       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6315_cong__exp__iff__simps_I12_J,axiom,
% 15.55/8.58      ! [M: num,Q3: num,N: num] :
% 15.55/8.58        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 15.55/8.58       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6316_cong__exp__iff__simps_I12_J,axiom,
% 15.55/8.58      ! [M: num,Q3: num,N: num] :
% 15.55/8.58        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 15.55/8.58       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6317_cong__exp__iff__simps_I13_J,axiom,
% 15.55/8.58      ! [M: num,Q3: num,N: num] :
% 15.55/8.58        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 15.55/8.58          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 15.55/8.58        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 15.55/8.58          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6318_cong__exp__iff__simps_I13_J,axiom,
% 15.55/8.58      ! [M: num,Q3: num,N: num] :
% 15.55/8.58        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 15.55/8.58          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 15.55/8.58        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 15.55/8.58          = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6319_cong__exp__iff__simps_I13_J,axiom,
% 15.55/8.58      ! [M: num,Q3: num,N: num] :
% 15.55/8.58        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 15.55/8.58          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 15.55/8.58        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 15.55/8.58          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6320_power__minus__Bit1,axiom,
% 15.55/8.58      ! [X3: real,K: num] :
% 15.55/8.58        ( ( power_power_real @ ( uminus_uminus_real @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 15.55/8.58        = ( uminus_uminus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6321_power__minus__Bit1,axiom,
% 15.55/8.58      ! [X3: int,K: num] :
% 15.55/8.58        ( ( power_power_int @ ( uminus_uminus_int @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 15.55/8.58        = ( uminus_uminus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6322_power__minus__Bit1,axiom,
% 15.55/8.58      ! [X3: complex,K: num] :
% 15.55/8.58        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 15.55/8.58        = ( uminus1482373934393186551omplex @ ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6323_power__minus__Bit1,axiom,
% 15.55/8.58      ! [X3: code_integer,K: num] :
% 15.55/8.58        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 15.55/8.58        = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6324_power__minus__Bit1,axiom,
% 15.55/8.58      ! [X3: rat,K: num] :
% 15.55/8.58        ( ( power_power_rat @ ( uminus_uminus_rat @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 15.55/8.58        = ( uminus_uminus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6325_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I4_J,axiom,
% 15.55/8.58      ! [Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu2: nat] :
% 15.55/8.58        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Uu2 )
% 15.55/8.58        = one_one_nat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6326_set__update__memI,axiom,
% 15.55/8.58      ! [N: nat,Xs2: list_option_nat,X3: option_nat] :
% 15.55/8.58        ( ( ord_less_nat @ N @ ( size_s6086282163384603972on_nat @ Xs2 ) )
% 15.55/8.58       => ( member_option_nat @ X3 @ ( set_option_nat2 @ ( list_u3411377215356412978on_nat @ Xs2 @ N @ X3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6327_set__update__memI,axiom,
% 15.55/8.58      ! [N: nat,Xs2: list_real,X3: real] :
% 15.55/8.58        ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 15.55/8.58       => ( member_real @ X3 @ ( set_real2 @ ( list_update_real @ Xs2 @ N @ X3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6328_set__update__memI,axiom,
% 15.55/8.58      ! [N: nat,Xs2: list_set_nat,X3: set_nat] :
% 15.55/8.58        ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 15.55/8.58       => ( member_set_nat @ X3 @ ( set_set_nat2 @ ( list_update_set_nat @ Xs2 @ N @ X3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6329_set__update__memI,axiom,
% 15.55/8.58      ! [N: nat,Xs2: list_VEBT_VEBT,X3: vEBT_VEBT] :
% 15.55/8.58        ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 15.55/8.58       => ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ N @ X3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6330_set__update__memI,axiom,
% 15.55/8.58      ! [N: nat,Xs2: list_o,X3: $o] :
% 15.55/8.58        ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 15.55/8.58       => ( member_o @ X3 @ ( set_o2 @ ( list_update_o @ Xs2 @ N @ X3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6331_set__update__memI,axiom,
% 15.55/8.58      ! [N: nat,Xs2: list_nat,X3: nat] :
% 15.55/8.58        ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 15.55/8.58       => ( member_nat @ X3 @ ( set_nat2 @ ( list_update_nat @ Xs2 @ N @ X3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6332_set__update__memI,axiom,
% 15.55/8.58      ! [N: nat,Xs2: list_int,X3: int] :
% 15.55/8.58        ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 15.55/8.58       => ( member_int @ X3 @ ( set_int2 @ ( list_update_int @ Xs2 @ N @ X3 ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6333_nth__list__update,axiom,
% 15.55/8.58      ! [I: nat,Xs2: list_VEBT_VEBT,J: nat,X3: vEBT_VEBT] :
% 15.55/8.58        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 15.55/8.58       => ( ( ( I = J )
% 15.55/8.58           => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X3 ) @ J )
% 15.55/8.58              = X3 ) )
% 15.55/8.58          & ( ( I != J )
% 15.55/8.58           => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X3 ) @ J )
% 15.55/8.58              = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6334_nth__list__update,axiom,
% 15.55/8.58      ! [I: nat,Xs2: list_o,X3: $o,J: nat] :
% 15.55/8.58        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 15.55/8.58       => ( ( nth_o @ ( list_update_o @ Xs2 @ I @ X3 ) @ J )
% 15.55/8.58          = ( ( ( I = J )
% 15.55/8.58             => X3 )
% 15.55/8.58            & ( ( I != J )
% 15.55/8.58             => ( nth_o @ Xs2 @ J ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6335_nth__list__update,axiom,
% 15.55/8.58      ! [I: nat,Xs2: list_nat,J: nat,X3: nat] :
% 15.55/8.58        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 15.55/8.58       => ( ( ( I = J )
% 15.55/8.58           => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X3 ) @ J )
% 15.55/8.58              = X3 ) )
% 15.55/8.58          & ( ( I != J )
% 15.55/8.58           => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X3 ) @ J )
% 15.55/8.58              = ( nth_nat @ Xs2 @ J ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6336_nth__list__update,axiom,
% 15.55/8.58      ! [I: nat,Xs2: list_int,J: nat,X3: int] :
% 15.55/8.58        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 15.55/8.58       => ( ( ( I = J )
% 15.55/8.58           => ( ( nth_int @ ( list_update_int @ Xs2 @ I @ X3 ) @ J )
% 15.55/8.58              = X3 ) )
% 15.55/8.58          & ( ( I != J )
% 15.55/8.58           => ( ( nth_int @ ( list_update_int @ Xs2 @ I @ X3 ) @ J )
% 15.55/8.58              = ( nth_int @ Xs2 @ J ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6337_list__update__same__conv,axiom,
% 15.55/8.58      ! [I: nat,Xs2: list_VEBT_VEBT,X3: vEBT_VEBT] :
% 15.55/8.58        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 15.55/8.58       => ( ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X3 )
% 15.55/8.58            = Xs2 )
% 15.55/8.58          = ( ( nth_VEBT_VEBT @ Xs2 @ I )
% 15.55/8.58            = X3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6338_list__update__same__conv,axiom,
% 15.55/8.58      ! [I: nat,Xs2: list_o,X3: $o] :
% 15.55/8.58        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 15.55/8.58       => ( ( ( list_update_o @ Xs2 @ I @ X3 )
% 15.55/8.58            = Xs2 )
% 15.55/8.58          = ( ( nth_o @ Xs2 @ I )
% 15.55/8.58            = X3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6339_list__update__same__conv,axiom,
% 15.55/8.58      ! [I: nat,Xs2: list_nat,X3: nat] :
% 15.55/8.58        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 15.55/8.58       => ( ( ( list_update_nat @ Xs2 @ I @ X3 )
% 15.55/8.58            = Xs2 )
% 15.55/8.58          = ( ( nth_nat @ Xs2 @ I )
% 15.55/8.58            = X3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6340_list__update__same__conv,axiom,
% 15.55/8.58      ! [I: nat,Xs2: list_int,X3: int] :
% 15.55/8.58        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 15.55/8.58       => ( ( ( list_update_int @ Xs2 @ I @ X3 )
% 15.55/8.58            = Xs2 )
% 15.55/8.58          = ( ( nth_int @ Xs2 @ I )
% 15.55/8.58            = X3 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6341_vebt__buildup_Osimps_I2_J,axiom,
% 15.55/8.58      ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 15.55/8.58      = ( vEBT_Leaf @ $false @ $false ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6342_vebt__pred_Osimps_I1_J,axiom,
% 15.55/8.58      ! [Uu2: $o,Uv2: $o] :
% 15.55/8.58        ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat )
% 15.55/8.58        = none_nat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6343_numeral__Bit1__div__2,axiom,
% 15.55/8.58      ! [N: num] :
% 15.55/8.58        ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.58        = ( numeral_numeral_nat @ N ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6344_numeral__Bit1__div__2,axiom,
% 15.55/8.58      ! [N: num] :
% 15.55/8.58        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.58        = ( numeral_numeral_int @ N ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6345_odd__numeral,axiom,
% 15.55/8.58      ! [N: num] :
% 15.55/8.58        ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6346_odd__numeral,axiom,
% 15.55/8.58      ! [N: num] :
% 15.55/8.58        ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6347_odd__numeral,axiom,
% 15.55/8.58      ! [N: num] :
% 15.55/8.58        ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6348_cong__exp__iff__simps_I3_J,axiom,
% 15.55/8.58      ! [N: num,Q3: num] :
% 15.55/8.58        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 15.55/8.58       != zero_zero_nat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6349_cong__exp__iff__simps_I3_J,axiom,
% 15.55/8.58      ! [N: num,Q3: num] :
% 15.55/8.58        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 15.55/8.58       != zero_zero_int ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6350_cong__exp__iff__simps_I3_J,axiom,
% 15.55/8.58      ! [N: num,Q3: num] :
% 15.55/8.58        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 15.55/8.58       != zero_z3403309356797280102nteger ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6351_power3__eq__cube,axiom,
% 15.55/8.58      ! [A: complex] :
% 15.55/8.58        ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 15.55/8.58        = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6352_power3__eq__cube,axiom,
% 15.55/8.58      ! [A: real] :
% 15.55/8.58        ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 15.55/8.58        = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6353_power3__eq__cube,axiom,
% 15.55/8.58      ! [A: rat] :
% 15.55/8.58        ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 15.55/8.58        = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6354_power3__eq__cube,axiom,
% 15.55/8.58      ! [A: nat] :
% 15.55/8.58        ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 15.55/8.58        = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6355_power3__eq__cube,axiom,
% 15.55/8.58      ! [A: int] :
% 15.55/8.58        ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 15.55/8.58        = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6356_numeral__3__eq__3,axiom,
% 15.55/8.58      ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 15.55/8.58      = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6357_Suc3__eq__add__3,axiom,
% 15.55/8.58      ! [N: nat] :
% 15.55/8.58        ( ( suc @ ( suc @ ( suc @ N ) ) )
% 15.55/8.58        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6358_num_Osize_I6_J,axiom,
% 15.55/8.58      ! [X32: num] :
% 15.55/8.58        ( ( size_size_num @ ( bit1 @ X32 ) )
% 15.55/8.58        = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6359_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Ocases,axiom,
% 15.55/8.58      ! [X3: produc9072475918466114483BT_nat] :
% 15.55/8.58        ( ! [Uu: $o,Uv: $o] :
% 15.55/8.58            ( X3
% 15.55/8.58           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat ) )
% 15.55/8.58       => ( ! [A5: $o,Uw: $o] :
% 15.55/8.58              ( X3
% 15.55/8.58             != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw ) @ ( suc @ zero_zero_nat ) ) )
% 15.55/8.58         => ( ! [A5: $o,B4: $o,Va: nat] :
% 15.55/8.58                ( X3
% 15.55/8.58               != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ ( suc @ ( suc @ Va ) ) ) )
% 15.55/8.58           => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT,Vb: nat] :
% 15.55/8.58                  ( X3
% 15.55/8.58                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Vb ) )
% 15.55/8.58             => ( ! [V3: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 15.55/8.58                    ( X3
% 15.55/8.58                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Vf2 ) )
% 15.55/8.58               => ( ! [V3: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 15.55/8.58                      ( X3
% 15.55/8.58                     != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 ) )
% 15.55/8.58                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 15.55/8.58                        ( X3
% 15.55/8.58                       != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ X4 ) ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6360_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Ocases,axiom,
% 15.55/8.58      ! [X3: produc9072475918466114483BT_nat] :
% 15.55/8.58        ( ! [Uu: $o,B4: $o] :
% 15.55/8.58            ( X3
% 15.55/8.58           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ B4 ) @ zero_zero_nat ) )
% 15.55/8.58       => ( ! [Uv: $o,Uw: $o,N2: nat] :
% 15.55/8.58              ( X3
% 15.55/8.58             != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N2 ) ) )
% 15.55/8.58         => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va3: nat] :
% 15.55/8.58                ( X3
% 15.55/8.58               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Va3 ) )
% 15.55/8.58           => ( ! [V3: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve2: nat] :
% 15.55/8.58                  ( X3
% 15.55/8.58                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Ve2 ) )
% 15.55/8.58             => ( ! [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 15.55/8.58                    ( X3
% 15.55/8.58                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 ) )
% 15.55/8.58               => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 15.55/8.58                      ( X3
% 15.55/8.58                     != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ X4 ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6361_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Ocases,axiom,
% 15.55/8.58      ! [X3: produc9072475918466114483BT_nat] :
% 15.55/8.58        ( ! [A5: $o,B4: $o,X4: nat] :
% 15.55/8.58            ( X3
% 15.55/8.58           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ X4 ) )
% 15.55/8.58       => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT,X4: nat] :
% 15.55/8.58              ( X3
% 15.55/8.58             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) @ X4 ) )
% 15.55/8.58         => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT,X4: nat] :
% 15.55/8.58                ( X3
% 15.55/8.58               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) @ X4 ) )
% 15.55/8.58           => ( ! [V3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 15.55/8.58                  ( X3
% 15.55/8.58                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) @ X4 ) )
% 15.55/8.58             => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 15.55/8.58                    ( X3
% 15.55/8.58                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ X4 ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6362_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Ocases,axiom,
% 15.55/8.58      ! [X3: produc9072475918466114483BT_nat] :
% 15.55/8.58        ( ! [A5: $o,B4: $o,X4: nat] :
% 15.55/8.58            ( X3
% 15.55/8.58           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ X4 ) )
% 15.55/8.58       => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X4: nat] :
% 15.55/8.58              ( X3
% 15.55/8.58             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X4 ) )
% 15.55/8.58         => ( ! [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X4: nat] :
% 15.55/8.58                ( X3
% 15.55/8.58               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X4 ) )
% 15.55/8.58           => ( ! [V3: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT,X4: nat] :
% 15.55/8.58                  ( X3
% 15.55/8.58                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) @ X4 ) )
% 15.55/8.58             => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 15.55/8.58                    ( X3
% 15.55/8.58                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ X4 ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6363_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Ocases,axiom,
% 15.55/8.58      ! [X3: produc9072475918466114483BT_nat] :
% 15.55/8.58        ( ! [A5: $o,B4: $o] :
% 15.55/8.58            ( X3
% 15.55/8.58           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ zero_zero_nat ) )
% 15.55/8.58       => ( ! [A5: $o,B4: $o] :
% 15.55/8.58              ( X3
% 15.55/8.58             != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ ( suc @ zero_zero_nat ) ) )
% 15.55/8.58         => ( ! [A5: $o,B4: $o,N2: nat] :
% 15.55/8.58                ( X3
% 15.55/8.58               != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ ( suc @ ( suc @ N2 ) ) ) )
% 15.55/8.58           => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,Uu: nat] :
% 15.55/8.58                  ( X3
% 15.55/8.58                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) @ Uu ) )
% 15.55/8.58             => ( ! [Mi2: nat,Ma2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 15.55/8.58                    ( X3
% 15.55/8.58                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList3 @ Summary2 ) @ X4 ) )
% 15.55/8.58               => ( ! [Mi2: nat,Ma2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 15.55/8.58                      ( X3
% 15.55/8.58                     != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList3 @ Summary2 ) @ X4 ) )
% 15.55/8.58                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 15.55/8.58                        ( X3
% 15.55/8.58                       != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ X4 ) ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6364_VEBT__internal_Omembermima_Ocases,axiom,
% 15.55/8.58      ! [X3: produc9072475918466114483BT_nat] :
% 15.55/8.58        ( ! [Uu: $o,Uv: $o,Uw: nat] :
% 15.55/8.58            ( X3
% 15.55/8.58           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) )
% 15.55/8.58       => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 15.55/8.58              ( X3
% 15.55/8.58             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 15.55/8.58         => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb: vEBT_VEBT,X4: nat] :
% 15.55/8.58                ( X3
% 15.55/8.58               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb ) @ X4 ) )
% 15.55/8.58           => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT,X4: nat] :
% 15.55/8.58                  ( X3
% 15.55/8.58                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) @ X4 ) )
% 15.55/8.58             => ~ ! [V3: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT,X4: nat] :
% 15.55/8.58                    ( X3
% 15.55/8.58                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) @ X4 ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6365_cong__exp__iff__simps_I7_J,axiom,
% 15.55/8.58      ! [Q3: num,N: num] :
% 15.55/8.58        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 15.55/8.58          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 15.55/8.58        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q3 ) )
% 15.55/8.58          = zero_zero_nat ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6366_cong__exp__iff__simps_I7_J,axiom,
% 15.55/8.58      ! [Q3: num,N: num] :
% 15.55/8.58        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 15.55/8.58          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 15.55/8.58        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q3 ) )
% 15.55/8.58          = zero_zero_int ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6367_cong__exp__iff__simps_I7_J,axiom,
% 15.55/8.58      ! [Q3: num,N: num] :
% 15.55/8.58        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 15.55/8.58          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 15.55/8.58        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 15.55/8.58          = zero_z3403309356797280102nteger ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6368_cong__exp__iff__simps_I11_J,axiom,
% 15.55/8.58      ! [M: num,Q3: num] :
% 15.55/8.58        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 15.55/8.58          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 15.55/8.58        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 15.55/8.58          = zero_zero_nat ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6369_cong__exp__iff__simps_I11_J,axiom,
% 15.55/8.58      ! [M: num,Q3: num] :
% 15.55/8.58        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 15.55/8.58          = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 15.55/8.58        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 15.55/8.58          = zero_zero_int ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6370_cong__exp__iff__simps_I11_J,axiom,
% 15.55/8.58      ! [M: num,Q3: num] :
% 15.55/8.58        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 15.55/8.58          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 15.55/8.58        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 15.55/8.58          = zero_z3403309356797280102nteger ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6371_Suc__div__eq__add3__div,axiom,
% 15.55/8.58      ! [M: nat,N: nat] :
% 15.55/8.58        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 15.55/8.58        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6372_Suc__mod__eq__add3__mod,axiom,
% 15.55/8.58      ! [M: nat,N: nat] :
% 15.55/8.58        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 15.55/8.58        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6373_vebt__mint_Osimps_I1_J,axiom,
% 15.55/8.58      ! [A: $o,B: $o] :
% 15.55/8.58        ( ( A
% 15.55/8.58         => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 15.55/8.58            = ( some_nat @ zero_zero_nat ) ) )
% 15.55/8.58        & ( ~ A
% 15.55/8.58         => ( ( B
% 15.55/8.58             => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 15.55/8.58                = ( some_nat @ one_one_nat ) ) )
% 15.55/8.58            & ( ~ B
% 15.55/8.58             => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 15.55/8.58                = none_nat ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6374_vebt__maxt_Osimps_I1_J,axiom,
% 15.55/8.58      ! [B: $o,A: $o] :
% 15.55/8.58        ( ( B
% 15.55/8.58         => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 15.55/8.58            = ( some_nat @ one_one_nat ) ) )
% 15.55/8.58        & ( ~ B
% 15.55/8.58         => ( ( A
% 15.55/8.58             => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 15.55/8.58                = ( some_nat @ zero_zero_nat ) ) )
% 15.55/8.58            & ( ~ A
% 15.55/8.58             => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 15.55/8.58                = none_nat ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6375_vebt__pred_Osimps_I2_J,axiom,
% 15.55/8.58      ! [A: $o,Uw2: $o] :
% 15.55/8.58        ( ( A
% 15.55/8.58         => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 15.55/8.58            = ( some_nat @ zero_zero_nat ) ) )
% 15.55/8.58        & ( ~ A
% 15.55/8.58         => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 15.55/8.58            = none_nat ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6376_vebt__succ_Osimps_I1_J,axiom,
% 15.55/8.58      ! [B: $o,Uu2: $o] :
% 15.55/8.58        ( ( B
% 15.55/8.58         => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu2 @ B ) @ zero_zero_nat )
% 15.55/8.58            = ( some_nat @ one_one_nat ) ) )
% 15.55/8.58        & ( ~ B
% 15.55/8.58         => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu2 @ B ) @ zero_zero_nat )
% 15.55/8.58            = none_nat ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6377_mod__exhaust__less__4,axiom,
% 15.55/8.58      ! [M: nat] :
% 15.55/8.58        ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 15.55/8.58          = zero_zero_nat )
% 15.55/8.58        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 15.55/8.58          = one_one_nat )
% 15.55/8.58        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 15.55/8.58          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.58        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 15.55/8.58          = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6378_vebt__pred_Osimps_I3_J,axiom,
% 15.55/8.58      ! [B: $o,A: $o,Va2: nat] :
% 15.55/8.58        ( ( B
% 15.55/8.58         => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 15.55/8.58            = ( some_nat @ one_one_nat ) ) )
% 15.55/8.58        & ( ~ B
% 15.55/8.58         => ( ( A
% 15.55/8.58             => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 15.55/8.58                = ( some_nat @ zero_zero_nat ) ) )
% 15.55/8.58            & ( ~ A
% 15.55/8.58             => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 15.55/8.58                = none_nat ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6379_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I5_J,axiom,
% 15.55/8.58      ! [Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 15.55/8.58        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.58        = one_one_nat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6380_take__bit__Suc__bit1,axiom,
% 15.55/8.58      ! [N: nat,K: num] :
% 15.55/8.58        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 15.55/8.58        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6381_take__bit__Suc__bit1,axiom,
% 15.55/8.58      ! [N: nat,K: num] :
% 15.55/8.58        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 15.55/8.58        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6382_vebt__mint_Oelims,axiom,
% 15.55/8.58      ! [X3: vEBT_VEBT,Y3: option_nat] :
% 15.55/8.58        ( ( ( vEBT_vebt_mint @ X3 )
% 15.55/8.58          = Y3 )
% 15.55/8.58       => ( ! [A5: $o,B4: $o] :
% 15.55/8.58              ( ( X3
% 15.55/8.58                = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.58             => ~ ( ( A5
% 15.55/8.58                   => ( Y3
% 15.55/8.58                      = ( some_nat @ zero_zero_nat ) ) )
% 15.55/8.58                  & ( ~ A5
% 15.55/8.58                   => ( ( B4
% 15.55/8.58                       => ( Y3
% 15.55/8.58                          = ( some_nat @ one_one_nat ) ) )
% 15.55/8.58                      & ( ~ B4
% 15.55/8.58                       => ( Y3 = none_nat ) ) ) ) ) )
% 15.55/8.58         => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 15.55/8.58                  ( X3
% 15.55/8.58                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 15.55/8.58             => ( Y3 != none_nat ) )
% 15.55/8.58           => ~ ! [Mi2: nat] :
% 15.55/8.58                  ( ? [Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 15.55/8.58                      ( X3
% 15.55/8.58                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 15.55/8.58                 => ( Y3
% 15.55/8.58                   != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6383_vebt__maxt_Oelims,axiom,
% 15.55/8.58      ! [X3: vEBT_VEBT,Y3: option_nat] :
% 15.55/8.58        ( ( ( vEBT_vebt_maxt @ X3 )
% 15.55/8.58          = Y3 )
% 15.55/8.58       => ( ! [A5: $o,B4: $o] :
% 15.55/8.58              ( ( X3
% 15.55/8.58                = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.58             => ~ ( ( B4
% 15.55/8.58                   => ( Y3
% 15.55/8.58                      = ( some_nat @ one_one_nat ) ) )
% 15.55/8.58                  & ( ~ B4
% 15.55/8.58                   => ( ( A5
% 15.55/8.58                       => ( Y3
% 15.55/8.58                          = ( some_nat @ zero_zero_nat ) ) )
% 15.55/8.58                      & ( ~ A5
% 15.55/8.58                       => ( Y3 = none_nat ) ) ) ) ) )
% 15.55/8.58         => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 15.55/8.58                  ( X3
% 15.55/8.58                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 15.55/8.58             => ( Y3 != none_nat ) )
% 15.55/8.58           => ~ ! [Mi2: nat,Ma2: nat] :
% 15.55/8.58                  ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 15.55/8.58                      ( X3
% 15.55/8.58                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 15.55/8.58                 => ( Y3
% 15.55/8.58                   != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6384_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I6_J,axiom,
% 15.55/8.58      ! [Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 15.55/8.58        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.58        = one_one_nat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6385_odd__mod__4__div__2,axiom,
% 15.55/8.58      ! [N: nat] :
% 15.55/8.58        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 15.55/8.58          = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 15.55/8.58       => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6386_vebt__delete_Osimps_I5_J,axiom,
% 15.55/8.58      ! [Mi: nat,Ma: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT,X3: nat] :
% 15.55/8.58        ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) @ X3 )
% 15.55/8.58        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6387_invar__vebt_Ocases,axiom,
% 15.55/8.58      ! [A1: vEBT_VEBT,A22: nat] :
% 15.55/8.58        ( ( vEBT_invar_vebt @ A1 @ A22 )
% 15.55/8.58       => ( ( ? [A5: $o,B4: $o] :
% 15.55/8.58                ( A1
% 15.55/8.58                = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.58           => ( A22
% 15.55/8.58             != ( suc @ zero_zero_nat ) ) )
% 15.55/8.58         => ( ! [TreeList3: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 15.55/8.58                ( ( A1
% 15.55/8.58                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 15.55/8.58               => ( ( A22 = Deg2 )
% 15.55/8.58                 => ( ! [X6: vEBT_VEBT] :
% 15.55/8.58                        ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.58                       => ( vEBT_invar_vebt @ X6 @ N2 ) )
% 15.55/8.58                   => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 15.55/8.58                     => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 15.55/8.58                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 15.55/8.58                       => ( ( M4 = N2 )
% 15.55/8.58                         => ( ( Deg2
% 15.55/8.58                              = ( plus_plus_nat @ N2 @ M4 ) )
% 15.55/8.58                           => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 15.55/8.58                             => ~ ! [X6: vEBT_VEBT] :
% 15.55/8.58                                    ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.58                                   => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_12 ) ) ) ) ) ) ) ) ) )
% 15.55/8.58           => ( ! [TreeList3: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 15.55/8.58                  ( ( A1
% 15.55/8.58                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 15.55/8.58                 => ( ( A22 = Deg2 )
% 15.55/8.58                   => ( ! [X6: vEBT_VEBT] :
% 15.55/8.58                          ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.58                         => ( vEBT_invar_vebt @ X6 @ N2 ) )
% 15.55/8.58                     => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 15.55/8.58                       => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 15.55/8.58                            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 15.55/8.58                         => ( ( M4
% 15.55/8.58                              = ( suc @ N2 ) )
% 15.55/8.58                           => ( ( Deg2
% 15.55/8.58                                = ( plus_plus_nat @ N2 @ M4 ) )
% 15.55/8.58                             => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 15.55/8.58                               => ~ ! [X6: vEBT_VEBT] :
% 15.55/8.58                                      ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.58                                     => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_12 ) ) ) ) ) ) ) ) ) )
% 15.55/8.58             => ( ! [TreeList3: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 15.55/8.58                    ( ( A1
% 15.55/8.58                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 15.55/8.58                   => ( ( A22 = Deg2 )
% 15.55/8.58                     => ( ! [X6: vEBT_VEBT] :
% 15.55/8.58                            ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.58                           => ( vEBT_invar_vebt @ X6 @ N2 ) )
% 15.55/8.58                       => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 15.55/8.58                         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 15.55/8.58                              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 15.55/8.58                           => ( ( M4 = N2 )
% 15.55/8.58                             => ( ( Deg2
% 15.55/8.58                                  = ( plus_plus_nat @ N2 @ M4 ) )
% 15.55/8.58                               => ( ! [I2: nat] :
% 15.55/8.58                                      ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 15.55/8.58                                     => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X8 ) )
% 15.55/8.58                                        = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 15.55/8.58                                 => ( ( ( Mi2 = Ma2 )
% 15.55/8.58                                     => ! [X6: vEBT_VEBT] :
% 15.55/8.58                                          ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.58                                         => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_12 ) ) )
% 15.55/8.58                                   => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 15.55/8.58                                     => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 15.55/8.58                                       => ~ ( ( Mi2 != Ma2 )
% 15.55/8.58                                           => ! [I2: nat] :
% 15.55/8.58                                                ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 15.55/8.58                                               => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N2 )
% 15.55/8.58                                                      = I2 )
% 15.55/8.58                                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ Ma2 @ N2 ) ) )
% 15.55/8.58                                                  & ! [X6: nat] :
% 15.55/8.58                                                      ( ( ( ( vEBT_VEBT_high @ X6 @ N2 )
% 15.55/8.58                                                          = I2 )
% 15.55/8.58                                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ X6 @ N2 ) ) )
% 15.55/8.58                                                     => ( ( ord_less_nat @ Mi2 @ X6 )
% 15.55/8.58                                                        & ( ord_less_eq_nat @ X6 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.58               => ~ ! [TreeList3: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 15.55/8.58                      ( ( A1
% 15.55/8.58                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 15.55/8.58                     => ( ( A22 = Deg2 )
% 15.55/8.58                       => ( ! [X6: vEBT_VEBT] :
% 15.55/8.58                              ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.58                             => ( vEBT_invar_vebt @ X6 @ N2 ) )
% 15.55/8.58                         => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 15.55/8.58                           => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 15.55/8.58                                = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 15.55/8.58                             => ( ( M4
% 15.55/8.58                                  = ( suc @ N2 ) )
% 15.55/8.58                               => ( ( Deg2
% 15.55/8.58                                    = ( plus_plus_nat @ N2 @ M4 ) )
% 15.55/8.58                                 => ( ! [I2: nat] :
% 15.55/8.58                                        ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 15.55/8.58                                       => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X8 ) )
% 15.55/8.58                                          = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 15.55/8.58                                   => ( ( ( Mi2 = Ma2 )
% 15.55/8.58                                       => ! [X6: vEBT_VEBT] :
% 15.55/8.58                                            ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.58                                           => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_12 ) ) )
% 15.55/8.58                                     => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 15.55/8.58                                       => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 15.55/8.58                                         => ~ ( ( Mi2 != Ma2 )
% 15.55/8.58                                             => ! [I2: nat] :
% 15.55/8.58                                                  ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 15.55/8.58                                                 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N2 )
% 15.55/8.58                                                        = I2 )
% 15.55/8.58                                                     => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ Ma2 @ N2 ) ) )
% 15.55/8.58                                                    & ! [X6: nat] :
% 15.55/8.58                                                        ( ( ( ( vEBT_VEBT_high @ X6 @ N2 )
% 15.55/8.58                                                            = I2 )
% 15.55/8.58                                                          & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ X6 @ N2 ) ) )
% 15.55/8.58                                                       => ( ( ord_less_nat @ Mi2 @ X6 )
% 15.55/8.58                                                          & ( ord_less_eq_nat @ X6 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6388_invar__vebt_Osimps,axiom,
% 15.55/8.58      ( vEBT_invar_vebt
% 15.55/8.58      = ( ^ [A12: vEBT_VEBT,A23: nat] :
% 15.55/8.58            ( ( ? [A4: $o,B3: $o] :
% 15.55/8.58                  ( A12
% 15.55/8.58                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 15.55/8.58              & ( A23
% 15.55/8.58                = ( suc @ zero_zero_nat ) ) )
% 15.55/8.58            | ? [TreeList: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT] :
% 15.55/8.58                ( ( A12
% 15.55/8.58                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList @ Summary3 ) )
% 15.55/8.58                & ! [X: vEBT_VEBT] :
% 15.55/8.58                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 15.55/8.58                   => ( vEBT_invar_vebt @ X @ N3 ) )
% 15.55/8.58                & ( vEBT_invar_vebt @ Summary3 @ N3 )
% 15.55/8.58                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 15.55/8.58                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 15.55/8.58                & ( A23
% 15.55/8.58                  = ( plus_plus_nat @ N3 @ N3 ) )
% 15.55/8.58                & ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X8 )
% 15.55/8.58                & ! [X: vEBT_VEBT] :
% 15.55/8.58                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 15.55/8.58                   => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 15.55/8.58            | ? [TreeList: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT] :
% 15.55/8.58                ( ( A12
% 15.55/8.58                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList @ Summary3 ) )
% 15.55/8.58                & ! [X: vEBT_VEBT] :
% 15.55/8.58                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 15.55/8.58                   => ( vEBT_invar_vebt @ X @ N3 ) )
% 15.55/8.58                & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N3 ) )
% 15.55/8.58                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 15.55/8.58                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 15.55/8.58                & ( A23
% 15.55/8.58                  = ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) )
% 15.55/8.58                & ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X8 )
% 15.55/8.58                & ! [X: vEBT_VEBT] :
% 15.55/8.58                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 15.55/8.58                   => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 15.55/8.58            | ? [TreeList: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 15.55/8.58                ( ( A12
% 15.55/8.58                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList @ Summary3 ) )
% 15.55/8.58                & ! [X: vEBT_VEBT] :
% 15.55/8.58                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 15.55/8.58                   => ( vEBT_invar_vebt @ X @ N3 ) )
% 15.55/8.58                & ( vEBT_invar_vebt @ Summary3 @ N3 )
% 15.55/8.58                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 15.55/8.58                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 15.55/8.58                & ( A23
% 15.55/8.58                  = ( plus_plus_nat @ N3 @ N3 ) )
% 15.55/8.58                & ! [I4: nat] :
% 15.55/8.58                    ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 15.55/8.58                   => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X8 ) )
% 15.55/8.58                      = ( vEBT_V8194947554948674370ptions @ Summary3 @ I4 ) ) )
% 15.55/8.58                & ( ( Mi3 = Ma3 )
% 15.55/8.58                 => ! [X: vEBT_VEBT] :
% 15.55/8.58                      ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 15.55/8.58                     => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 15.55/8.58                & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 15.55/8.58                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 15.55/8.58                & ( ( Mi3 != Ma3 )
% 15.55/8.58                 => ! [I4: nat] :
% 15.55/8.58                      ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 15.55/8.58                     => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N3 )
% 15.55/8.58                            = I4 )
% 15.55/8.58                         => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ Ma3 @ N3 ) ) )
% 15.55/8.58                        & ! [X: nat] :
% 15.55/8.58                            ( ( ( ( vEBT_VEBT_high @ X @ N3 )
% 15.55/8.58                                = I4 )
% 15.55/8.58                              & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ X @ N3 ) ) )
% 15.55/8.58                           => ( ( ord_less_nat @ Mi3 @ X )
% 15.55/8.58                              & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) )
% 15.55/8.58            | ? [TreeList: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 15.55/8.58                ( ( A12
% 15.55/8.58                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList @ Summary3 ) )
% 15.55/8.58                & ! [X: vEBT_VEBT] :
% 15.55/8.58                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 15.55/8.58                   => ( vEBT_invar_vebt @ X @ N3 ) )
% 15.55/8.58                & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N3 ) )
% 15.55/8.58                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 15.55/8.58                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 15.55/8.58                & ( A23
% 15.55/8.58                  = ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) )
% 15.55/8.58                & ! [I4: nat] :
% 15.55/8.58                    ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 15.55/8.58                   => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X8 ) )
% 15.55/8.58                      = ( vEBT_V8194947554948674370ptions @ Summary3 @ I4 ) ) )
% 15.55/8.58                & ( ( Mi3 = Ma3 )
% 15.55/8.58                 => ! [X: vEBT_VEBT] :
% 15.55/8.58                      ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 15.55/8.58                     => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 15.55/8.58                & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 15.55/8.58                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 15.55/8.58                & ( ( Mi3 != Ma3 )
% 15.55/8.58                 => ! [I4: nat] :
% 15.55/8.58                      ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 15.55/8.58                     => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N3 )
% 15.55/8.58                            = I4 )
% 15.55/8.58                         => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ Ma3 @ N3 ) ) )
% 15.55/8.58                        & ! [X: nat] :
% 15.55/8.58                            ( ( ( ( vEBT_VEBT_high @ X @ N3 )
% 15.55/8.58                                = I4 )
% 15.55/8.58                              & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ X @ N3 ) ) )
% 15.55/8.58                           => ( ( ord_less_nat @ Mi3 @ X )
% 15.55/8.58                              & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6389_insert__simp__norm,axiom,
% 15.55/8.58      ! [X3: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 15.55/8.58        ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.58       => ( ( ord_less_nat @ Mi @ X3 )
% 15.55/8.58         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.58           => ( ( X3 != Ma )
% 15.55/8.58             => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.58                = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X3 @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6390_insert__simp__excp,axiom,
% 15.55/8.58      ! [Mi: nat,Deg: nat,TreeList2: list_VEBT_VEBT,X3: nat,Ma: nat,Summary: vEBT_VEBT] :
% 15.55/8.58        ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.58       => ( ( ord_less_nat @ X3 @ Mi )
% 15.55/8.58         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.58           => ( ( X3 != Ma )
% 15.55/8.58             => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.58                = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X3 @ ( 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 ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6391_member__bound__size__univ,axiom,
% 15.55/8.58      ! [T: vEBT_VEBT,N: nat,U: real,X3: nat] :
% 15.55/8.58        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.58       => ( ( U
% 15.55/8.58            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.58         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_m_e_m_b_e_r @ T @ X3 ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6392_vebt__member_Osimps_I4_J,axiom,
% 15.55/8.58      ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc: vEBT_VEBT,X3: nat] :
% 15.55/8.58        ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc ) @ X3 ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6393_succ__bound__size__univ,axiom,
% 15.55/8.58      ! [T: vEBT_VEBT,N: nat,U: real,X3: nat] :
% 15.55/8.58        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.58       => ( ( U
% 15.55/8.58            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.58         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_s_u_c_c @ T @ X3 ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6394_pred__bound__size__univ,axiom,
% 15.55/8.58      ! [T: vEBT_VEBT,N: nat,U: real,X3: nat] :
% 15.55/8.58        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.58       => ( ( U
% 15.55/8.58            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.58         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_p_r_e_d @ T @ X3 ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6395_max__Suc__Suc,axiom,
% 15.55/8.58      ! [M: nat,N: nat] :
% 15.55/8.58        ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 15.55/8.58        = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6396_max__0R,axiom,
% 15.55/8.58      ! [N: nat] :
% 15.55/8.58        ( ( ord_max_nat @ N @ zero_zero_nat )
% 15.55/8.58        = N ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6397_max__0L,axiom,
% 15.55/8.58      ! [N: nat] :
% 15.55/8.58        ( ( ord_max_nat @ zero_zero_nat @ N )
% 15.55/8.58        = N ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6398_max__nat_Oright__neutral,axiom,
% 15.55/8.58      ! [A: nat] :
% 15.55/8.58        ( ( ord_max_nat @ A @ zero_zero_nat )
% 15.55/8.58        = A ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6399_max__nat_Oneutr__eq__iff,axiom,
% 15.55/8.58      ! [A: nat,B: nat] :
% 15.55/8.58        ( ( zero_zero_nat
% 15.55/8.58          = ( ord_max_nat @ A @ B ) )
% 15.55/8.58        = ( ( A = zero_zero_nat )
% 15.55/8.58          & ( B = zero_zero_nat ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6400_max__nat_Oleft__neutral,axiom,
% 15.55/8.58      ! [A: nat] :
% 15.55/8.58        ( ( ord_max_nat @ zero_zero_nat @ A )
% 15.55/8.58        = A ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6401_max__nat_Oeq__neutr__iff,axiom,
% 15.55/8.58      ! [A: nat,B: nat] :
% 15.55/8.58        ( ( ( ord_max_nat @ A @ B )
% 15.55/8.58          = zero_zero_nat )
% 15.55/8.58        = ( ( A = zero_zero_nat )
% 15.55/8.58          & ( B = zero_zero_nat ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6402_max__number__of_I1_J,axiom,
% 15.55/8.58      ! [U: num,V: num] :
% 15.55/8.58        ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 15.55/8.58         => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 15.55/8.58            = ( numera1916890842035813515d_enat @ V ) ) )
% 15.55/8.58        & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 15.55/8.58         => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 15.55/8.58            = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6403_max__number__of_I1_J,axiom,
% 15.55/8.58      ! [U: num,V: num] :
% 15.55/8.58        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 15.55/8.58         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 15.55/8.58            = ( numera6620942414471956472nteger @ V ) ) )
% 15.55/8.58        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 15.55/8.58         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 15.55/8.58            = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6404_max__number__of_I1_J,axiom,
% 15.55/8.58      ! [U: num,V: num] :
% 15.55/8.58        ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 15.55/8.58         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 15.55/8.58            = ( numeral_numeral_real @ V ) ) )
% 15.55/8.58        & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 15.55/8.58         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 15.55/8.58            = ( numeral_numeral_real @ U ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6405_max__number__of_I1_J,axiom,
% 15.55/8.58      ! [U: num,V: num] :
% 15.55/8.58        ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 15.55/8.58         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 15.55/8.58            = ( numeral_numeral_rat @ V ) ) )
% 15.55/8.58        & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 15.55/8.58         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 15.55/8.58            = ( numeral_numeral_rat @ U ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6406_max__number__of_I1_J,axiom,
% 15.55/8.58      ! [U: num,V: num] :
% 15.55/8.58        ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 15.55/8.58         => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 15.55/8.58            = ( numeral_numeral_nat @ V ) ) )
% 15.55/8.58        & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 15.55/8.58         => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 15.55/8.58            = ( numeral_numeral_nat @ U ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6407_max__number__of_I1_J,axiom,
% 15.55/8.58      ! [U: num,V: num] :
% 15.55/8.58        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 15.55/8.58         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 15.55/8.58            = ( numeral_numeral_int @ V ) ) )
% 15.55/8.58        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 15.55/8.58         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 15.55/8.58            = ( numeral_numeral_int @ U ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6408_max__0__1_I3_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X3 ) )
% 15.55/8.58        = ( numera1916890842035813515d_enat @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6409_max__0__1_I3_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ X3 ) )
% 15.55/8.58        = ( numera6620942414471956472nteger @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6410_max__0__1_I3_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X3 ) )
% 15.55/8.58        = ( numeral_numeral_real @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6411_max__0__1_I3_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X3 ) )
% 15.55/8.58        = ( numeral_numeral_rat @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6412_max__0__1_I3_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X3 ) )
% 15.55/8.58        = ( numeral_numeral_nat @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6413_max__0__1_I3_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X3 ) )
% 15.55/8.58        = ( numeral_numeral_int @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6414_max__0__1_I4_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X3 ) @ zero_z5237406670263579293d_enat )
% 15.55/8.58        = ( numera1916890842035813515d_enat @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6415_max__0__1_I4_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X3 ) @ zero_z3403309356797280102nteger )
% 15.55/8.58        = ( numera6620942414471956472nteger @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6416_max__0__1_I4_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_max_real @ ( numeral_numeral_real @ X3 ) @ zero_zero_real )
% 15.55/8.58        = ( numeral_numeral_real @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6417_max__0__1_I4_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_max_rat @ ( numeral_numeral_rat @ X3 ) @ zero_zero_rat )
% 15.55/8.58        = ( numeral_numeral_rat @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6418_max__0__1_I4_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_max_nat @ ( numeral_numeral_nat @ X3 ) @ zero_zero_nat )
% 15.55/8.58        = ( numeral_numeral_nat @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6419_max__0__1_I4_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_max_int @ ( numeral_numeral_int @ X3 ) @ zero_zero_int )
% 15.55/8.58        = ( numeral_numeral_int @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6420_max__0__1_I2_J,axiom,
% 15.55/8.58      ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 15.55/8.58      = one_one_real ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6421_max__0__1_I2_J,axiom,
% 15.55/8.58      ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 15.55/8.58      = one_one_rat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6422_max__0__1_I2_J,axiom,
% 15.55/8.58      ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 15.55/8.58      = one_one_nat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6423_max__0__1_I2_J,axiom,
% 15.55/8.58      ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat )
% 15.55/8.58      = one_on7984719198319812577d_enat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6424_max__0__1_I2_J,axiom,
% 15.55/8.58      ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 15.55/8.58      = one_one_int ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6425_max__0__1_I2_J,axiom,
% 15.55/8.58      ( ( ord_max_Code_integer @ one_one_Code_integer @ zero_z3403309356797280102nteger )
% 15.55/8.58      = one_one_Code_integer ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6426_max__0__1_I1_J,axiom,
% 15.55/8.58      ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 15.55/8.58      = one_one_real ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6427_max__0__1_I1_J,axiom,
% 15.55/8.58      ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 15.55/8.58      = one_one_rat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6428_max__0__1_I1_J,axiom,
% 15.55/8.58      ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 15.55/8.58      = one_one_nat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6429_max__0__1_I1_J,axiom,
% 15.55/8.58      ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat )
% 15.55/8.58      = one_on7984719198319812577d_enat ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6430_max__0__1_I1_J,axiom,
% 15.55/8.58      ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 15.55/8.58      = one_one_int ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6431_max__0__1_I1_J,axiom,
% 15.55/8.58      ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer )
% 15.55/8.58      = one_one_Code_integer ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6432_max__0__1_I5_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X3 ) )
% 15.55/8.58        = ( numera1916890842035813515d_enat @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6433_max__0__1_I5_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_max_Code_integer @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X3 ) )
% 15.55/8.58        = ( numera6620942414471956472nteger @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6434_max__0__1_I5_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X3 ) )
% 15.55/8.58        = ( numeral_numeral_real @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6435_max__0__1_I5_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X3 ) )
% 15.55/8.58        = ( numeral_numeral_rat @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6436_max__0__1_I5_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X3 ) )
% 15.55/8.58        = ( numeral_numeral_nat @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6437_max__0__1_I5_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X3 ) )
% 15.55/8.58        = ( numeral_numeral_int @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6438_max__0__1_I6_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X3 ) @ one_on7984719198319812577d_enat )
% 15.55/8.58        = ( numera1916890842035813515d_enat @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6439_max__0__1_I6_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X3 ) @ one_one_Code_integer )
% 15.55/8.58        = ( numera6620942414471956472nteger @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6440_max__0__1_I6_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_max_real @ ( numeral_numeral_real @ X3 ) @ one_one_real )
% 15.55/8.58        = ( numeral_numeral_real @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6441_max__0__1_I6_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_max_rat @ ( numeral_numeral_rat @ X3 ) @ one_one_rat )
% 15.55/8.58        = ( numeral_numeral_rat @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6442_max__0__1_I6_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_max_nat @ ( numeral_numeral_nat @ X3 ) @ one_one_nat )
% 15.55/8.58        = ( numeral_numeral_nat @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6443_max__0__1_I6_J,axiom,
% 15.55/8.58      ! [X3: num] :
% 15.55/8.58        ( ( ord_max_int @ ( numeral_numeral_int @ X3 ) @ one_one_int )
% 15.55/8.58        = ( numeral_numeral_int @ X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6444_max__number__of_I2_J,axiom,
% 15.55/8.58      ! [U: num,V: num] :
% 15.55/8.58        ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 15.55/8.58         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 15.55/8.58            = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 15.55/8.58        & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 15.55/8.58         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 15.55/8.58            = ( numeral_numeral_real @ U ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6445_max__number__of_I2_J,axiom,
% 15.55/8.58      ! [U: num,V: num] :
% 15.55/8.58        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 15.55/8.58         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 15.55/8.58            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 15.55/8.58        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 15.55/8.58         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 15.55/8.58            = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6446_max__number__of_I2_J,axiom,
% 15.55/8.58      ! [U: num,V: num] :
% 15.55/8.58        ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 15.55/8.58         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 15.55/8.58            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 15.55/8.58        & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 15.55/8.58         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 15.55/8.58            = ( numeral_numeral_rat @ U ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6447_max__number__of_I2_J,axiom,
% 15.55/8.58      ! [U: num,V: num] :
% 15.55/8.58        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 15.55/8.58         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 15.55/8.58            = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 15.55/8.58        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 15.55/8.58         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 15.55/8.58            = ( numeral_numeral_int @ U ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6448_max__number__of_I3_J,axiom,
% 15.55/8.58      ! [U: num,V: num] :
% 15.55/8.58        ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 15.55/8.58         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 15.55/8.58            = ( numeral_numeral_real @ V ) ) )
% 15.55/8.58        & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 15.55/8.58         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 15.55/8.58            = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6449_max__number__of_I3_J,axiom,
% 15.55/8.58      ! [U: num,V: num] :
% 15.55/8.58        ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 15.55/8.58         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 15.55/8.58            = ( numera6620942414471956472nteger @ V ) ) )
% 15.55/8.58        & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 15.55/8.58         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 15.55/8.58            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6450_max__number__of_I3_J,axiom,
% 15.55/8.58      ! [U: num,V: num] :
% 15.55/8.58        ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 15.55/8.58         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 15.55/8.58            = ( numeral_numeral_rat @ V ) ) )
% 15.55/8.58        & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 15.55/8.58         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 15.55/8.58            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6451_max__number__of_I3_J,axiom,
% 15.55/8.58      ! [U: num,V: num] :
% 15.55/8.58        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 15.55/8.58         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 15.55/8.58            = ( numeral_numeral_int @ V ) ) )
% 15.55/8.58        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 15.55/8.58         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 15.55/8.58            = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6452_max__number__of_I4_J,axiom,
% 15.55/8.58      ! [U: num,V: num] :
% 15.55/8.58        ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 15.55/8.58         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 15.55/8.58            = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 15.55/8.58        & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 15.55/8.58         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 15.55/8.58            = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6453_max__number__of_I4_J,axiom,
% 15.55/8.58      ! [U: num,V: num] :
% 15.55/8.58        ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 15.55/8.58         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 15.55/8.58            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 15.55/8.58        & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 15.55/8.58         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 15.55/8.58            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6454_max__number__of_I4_J,axiom,
% 15.55/8.58      ! [U: num,V: num] :
% 15.55/8.58        ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 15.55/8.58         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 15.55/8.58            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 15.55/8.58        & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 15.55/8.58         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 15.55/8.58            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6455_max__number__of_I4_J,axiom,
% 15.55/8.58      ! [U: num,V: num] :
% 15.55/8.58        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 15.55/8.58         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 15.55/8.58            = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 15.55/8.58        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 15.55/8.58         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 15.55/8.58            = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6456_max__def,axiom,
% 15.55/8.58      ( ord_ma741700101516333627d_enat
% 15.55/8.58      = ( ^ [A4: extended_enat,B3: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6457_max__def,axiom,
% 15.55/8.58      ( ord_max_Code_integer
% 15.55/8.58      = ( ^ [A4: code_integer,B3: code_integer] : ( if_Code_integer @ ( ord_le3102999989581377725nteger @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6458_max__def,axiom,
% 15.55/8.58      ( ord_max_set_nat
% 15.55/8.58      = ( ^ [A4: set_nat,B3: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6459_max__def,axiom,
% 15.55/8.58      ( ord_max_rat
% 15.55/8.58      = ( ^ [A4: rat,B3: rat] : ( if_rat @ ( ord_less_eq_rat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6460_max__def,axiom,
% 15.55/8.58      ( ord_max_num
% 15.55/8.58      = ( ^ [A4: num,B3: num] : ( if_num @ ( ord_less_eq_num @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6461_max__def,axiom,
% 15.55/8.58      ( ord_max_nat
% 15.55/8.58      = ( ^ [A4: nat,B3: nat] : ( if_nat @ ( ord_less_eq_nat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6462_max__def,axiom,
% 15.55/8.58      ( ord_max_int
% 15.55/8.58      = ( ^ [A4: int,B3: int] : ( if_int @ ( ord_less_eq_int @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6463_max__absorb1,axiom,
% 15.55/8.58      ! [Y3: extended_enat,X3: extended_enat] :
% 15.55/8.58        ( ( ord_le2932123472753598470d_enat @ Y3 @ X3 )
% 15.55/8.58       => ( ( ord_ma741700101516333627d_enat @ X3 @ Y3 )
% 15.55/8.58          = X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6464_max__absorb1,axiom,
% 15.55/8.58      ! [Y3: code_integer,X3: code_integer] :
% 15.55/8.58        ( ( ord_le3102999989581377725nteger @ Y3 @ X3 )
% 15.55/8.58       => ( ( ord_max_Code_integer @ X3 @ Y3 )
% 15.55/8.58          = X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6465_max__absorb1,axiom,
% 15.55/8.58      ! [Y3: set_nat,X3: set_nat] :
% 15.55/8.58        ( ( ord_less_eq_set_nat @ Y3 @ X3 )
% 15.55/8.58       => ( ( ord_max_set_nat @ X3 @ Y3 )
% 15.55/8.58          = X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6466_max__absorb1,axiom,
% 15.55/8.58      ! [Y3: rat,X3: rat] :
% 15.55/8.58        ( ( ord_less_eq_rat @ Y3 @ X3 )
% 15.55/8.58       => ( ( ord_max_rat @ X3 @ Y3 )
% 15.55/8.58          = X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6467_max__absorb1,axiom,
% 15.55/8.58      ! [Y3: num,X3: num] :
% 15.55/8.58        ( ( ord_less_eq_num @ Y3 @ X3 )
% 15.55/8.58       => ( ( ord_max_num @ X3 @ Y3 )
% 15.55/8.58          = X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6468_max__absorb1,axiom,
% 15.55/8.58      ! [Y3: nat,X3: nat] :
% 15.55/8.58        ( ( ord_less_eq_nat @ Y3 @ X3 )
% 15.55/8.58       => ( ( ord_max_nat @ X3 @ Y3 )
% 15.55/8.58          = X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6469_max__absorb1,axiom,
% 15.55/8.58      ! [Y3: int,X3: int] :
% 15.55/8.58        ( ( ord_less_eq_int @ Y3 @ X3 )
% 15.55/8.58       => ( ( ord_max_int @ X3 @ Y3 )
% 15.55/8.58          = X3 ) ) ).
% 15.55/8.58  
% 15.55/8.58  thf(fact_6470_max__absorb2,axiom,
% 15.55/8.59      ! [X3: extended_enat,Y3: extended_enat] :
% 15.55/8.59        ( ( ord_le2932123472753598470d_enat @ X3 @ Y3 )
% 15.55/8.59       => ( ( ord_ma741700101516333627d_enat @ X3 @ Y3 )
% 15.55/8.59          = Y3 ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6471_max__absorb2,axiom,
% 15.55/8.59      ! [X3: code_integer,Y3: code_integer] :
% 15.55/8.59        ( ( ord_le3102999989581377725nteger @ X3 @ Y3 )
% 15.55/8.59       => ( ( ord_max_Code_integer @ X3 @ Y3 )
% 15.55/8.59          = Y3 ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6472_max__absorb2,axiom,
% 15.55/8.59      ! [X3: set_nat,Y3: set_nat] :
% 15.55/8.59        ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 15.55/8.59       => ( ( ord_max_set_nat @ X3 @ Y3 )
% 15.55/8.59          = Y3 ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6473_max__absorb2,axiom,
% 15.55/8.59      ! [X3: rat,Y3: rat] :
% 15.55/8.59        ( ( ord_less_eq_rat @ X3 @ Y3 )
% 15.55/8.59       => ( ( ord_max_rat @ X3 @ Y3 )
% 15.55/8.59          = Y3 ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6474_max__absorb2,axiom,
% 15.55/8.59      ! [X3: num,Y3: num] :
% 15.55/8.59        ( ( ord_less_eq_num @ X3 @ Y3 )
% 15.55/8.59       => ( ( ord_max_num @ X3 @ Y3 )
% 15.55/8.59          = Y3 ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6475_max__absorb2,axiom,
% 15.55/8.59      ! [X3: nat,Y3: nat] :
% 15.55/8.59        ( ( ord_less_eq_nat @ X3 @ Y3 )
% 15.55/8.59       => ( ( ord_max_nat @ X3 @ Y3 )
% 15.55/8.59          = Y3 ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6476_max__absorb2,axiom,
% 15.55/8.59      ! [X3: int,Y3: int] :
% 15.55/8.59        ( ( ord_less_eq_int @ X3 @ Y3 )
% 15.55/8.59       => ( ( ord_max_int @ X3 @ Y3 )
% 15.55/8.59          = Y3 ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6477_of__int__max,axiom,
% 15.55/8.59      ! [X3: int,Y3: int] :
% 15.55/8.59        ( ( ring_1_of_int_real @ ( ord_max_int @ X3 @ Y3 ) )
% 15.55/8.59        = ( ord_max_real @ ( ring_1_of_int_real @ X3 ) @ ( ring_1_of_int_real @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6478_of__int__max,axiom,
% 15.55/8.59      ! [X3: int,Y3: int] :
% 15.55/8.59        ( ( ring_1_of_int_rat @ ( ord_max_int @ X3 @ Y3 ) )
% 15.55/8.59        = ( ord_max_rat @ ( ring_1_of_int_rat @ X3 ) @ ( ring_1_of_int_rat @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6479_of__int__max,axiom,
% 15.55/8.59      ! [X3: int,Y3: int] :
% 15.55/8.59        ( ( ring_1_of_int_int @ ( ord_max_int @ X3 @ Y3 ) )
% 15.55/8.59        = ( ord_max_int @ ( ring_1_of_int_int @ X3 ) @ ( ring_1_of_int_int @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6480_of__int__max,axiom,
% 15.55/8.59      ! [X3: int,Y3: int] :
% 15.55/8.59        ( ( ring_18347121197199848620nteger @ ( ord_max_int @ X3 @ Y3 ) )
% 15.55/8.59        = ( ord_max_Code_integer @ ( ring_18347121197199848620nteger @ X3 ) @ ( ring_18347121197199848620nteger @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6481_of__nat__max,axiom,
% 15.55/8.59      ! [X3: nat,Y3: nat] :
% 15.55/8.59        ( ( semiri4216267220026989637d_enat @ ( ord_max_nat @ X3 @ Y3 ) )
% 15.55/8.59        = ( ord_ma741700101516333627d_enat @ ( semiri4216267220026989637d_enat @ X3 ) @ ( semiri4216267220026989637d_enat @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6482_of__nat__max,axiom,
% 15.55/8.59      ! [X3: nat,Y3: nat] :
% 15.55/8.59        ( ( semiri4939895301339042750nteger @ ( ord_max_nat @ X3 @ Y3 ) )
% 15.55/8.59        = ( ord_max_Code_integer @ ( semiri4939895301339042750nteger @ X3 ) @ ( semiri4939895301339042750nteger @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6483_of__nat__max,axiom,
% 15.55/8.59      ! [X3: nat,Y3: nat] :
% 15.55/8.59        ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X3 @ Y3 ) )
% 15.55/8.59        = ( ord_max_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( semiri5074537144036343181t_real @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6484_of__nat__max,axiom,
% 15.55/8.59      ! [X3: nat,Y3: nat] :
% 15.55/8.59        ( ( semiri681578069525770553at_rat @ ( ord_max_nat @ X3 @ Y3 ) )
% 15.55/8.59        = ( ord_max_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( semiri681578069525770553at_rat @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6485_of__nat__max,axiom,
% 15.55/8.59      ! [X3: nat,Y3: nat] :
% 15.55/8.59        ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X3 @ Y3 ) )
% 15.55/8.59        = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( semiri1316708129612266289at_nat @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6486_of__nat__max,axiom,
% 15.55/8.59      ! [X3: nat,Y3: nat] :
% 15.55/8.59        ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X3 @ Y3 ) )
% 15.55/8.59        = ( ord_max_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( semiri1314217659103216013at_int @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6487_max__add__distrib__left,axiom,
% 15.55/8.59      ! [X3: real,Y3: real,Z: real] :
% 15.55/8.59        ( ( plus_plus_real @ ( ord_max_real @ X3 @ Y3 ) @ Z )
% 15.55/8.59        = ( ord_max_real @ ( plus_plus_real @ X3 @ Z ) @ ( plus_plus_real @ Y3 @ Z ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6488_max__add__distrib__left,axiom,
% 15.55/8.59      ! [X3: rat,Y3: rat,Z: rat] :
% 15.55/8.59        ( ( plus_plus_rat @ ( ord_max_rat @ X3 @ Y3 ) @ Z )
% 15.55/8.59        = ( ord_max_rat @ ( plus_plus_rat @ X3 @ Z ) @ ( plus_plus_rat @ Y3 @ Z ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6489_max__add__distrib__left,axiom,
% 15.55/8.59      ! [X3: nat,Y3: nat,Z: nat] :
% 15.55/8.59        ( ( plus_plus_nat @ ( ord_max_nat @ X3 @ Y3 ) @ Z )
% 15.55/8.59        = ( ord_max_nat @ ( plus_plus_nat @ X3 @ Z ) @ ( plus_plus_nat @ Y3 @ Z ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6490_max__add__distrib__left,axiom,
% 15.55/8.59      ! [X3: int,Y3: int,Z: int] :
% 15.55/8.59        ( ( plus_plus_int @ ( ord_max_int @ X3 @ Y3 ) @ Z )
% 15.55/8.59        = ( ord_max_int @ ( plus_plus_int @ X3 @ Z ) @ ( plus_plus_int @ Y3 @ Z ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6491_max__add__distrib__left,axiom,
% 15.55/8.59      ! [X3: code_integer,Y3: code_integer,Z: code_integer] :
% 15.55/8.59        ( ( plus_p5714425477246183910nteger @ ( ord_max_Code_integer @ X3 @ Y3 ) @ Z )
% 15.55/8.59        = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X3 @ Z ) @ ( plus_p5714425477246183910nteger @ Y3 @ Z ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6492_max__add__distrib__right,axiom,
% 15.55/8.59      ! [X3: real,Y3: real,Z: real] :
% 15.55/8.59        ( ( plus_plus_real @ X3 @ ( ord_max_real @ Y3 @ Z ) )
% 15.55/8.59        = ( ord_max_real @ ( plus_plus_real @ X3 @ Y3 ) @ ( plus_plus_real @ X3 @ Z ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6493_max__add__distrib__right,axiom,
% 15.55/8.59      ! [X3: rat,Y3: rat,Z: rat] :
% 15.55/8.59        ( ( plus_plus_rat @ X3 @ ( ord_max_rat @ Y3 @ Z ) )
% 15.55/8.59        = ( ord_max_rat @ ( plus_plus_rat @ X3 @ Y3 ) @ ( plus_plus_rat @ X3 @ Z ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6494_max__add__distrib__right,axiom,
% 15.55/8.59      ! [X3: nat,Y3: nat,Z: nat] :
% 15.55/8.59        ( ( plus_plus_nat @ X3 @ ( ord_max_nat @ Y3 @ Z ) )
% 15.55/8.59        = ( ord_max_nat @ ( plus_plus_nat @ X3 @ Y3 ) @ ( plus_plus_nat @ X3 @ Z ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6495_max__add__distrib__right,axiom,
% 15.55/8.59      ! [X3: int,Y3: int,Z: int] :
% 15.55/8.59        ( ( plus_plus_int @ X3 @ ( ord_max_int @ Y3 @ Z ) )
% 15.55/8.59        = ( ord_max_int @ ( plus_plus_int @ X3 @ Y3 ) @ ( plus_plus_int @ X3 @ Z ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6496_max__add__distrib__right,axiom,
% 15.55/8.59      ! [X3: code_integer,Y3: code_integer,Z: code_integer] :
% 15.55/8.59        ( ( plus_p5714425477246183910nteger @ X3 @ ( ord_max_Code_integer @ Y3 @ Z ) )
% 15.55/8.59        = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X3 @ Y3 ) @ ( plus_p5714425477246183910nteger @ X3 @ Z ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6497_max__diff__distrib__left,axiom,
% 15.55/8.59      ! [X3: code_integer,Y3: code_integer,Z: code_integer] :
% 15.55/8.59        ( ( minus_8373710615458151222nteger @ ( ord_max_Code_integer @ X3 @ Y3 ) @ Z )
% 15.55/8.59        = ( ord_max_Code_integer @ ( minus_8373710615458151222nteger @ X3 @ Z ) @ ( minus_8373710615458151222nteger @ Y3 @ Z ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6498_max__diff__distrib__left,axiom,
% 15.55/8.59      ! [X3: real,Y3: real,Z: real] :
% 15.55/8.59        ( ( minus_minus_real @ ( ord_max_real @ X3 @ Y3 ) @ Z )
% 15.55/8.59        = ( ord_max_real @ ( minus_minus_real @ X3 @ Z ) @ ( minus_minus_real @ Y3 @ Z ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6499_max__diff__distrib__left,axiom,
% 15.55/8.59      ! [X3: rat,Y3: rat,Z: rat] :
% 15.55/8.59        ( ( minus_minus_rat @ ( ord_max_rat @ X3 @ Y3 ) @ Z )
% 15.55/8.59        = ( ord_max_rat @ ( minus_minus_rat @ X3 @ Z ) @ ( minus_minus_rat @ Y3 @ Z ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6500_max__diff__distrib__left,axiom,
% 15.55/8.59      ! [X3: int,Y3: int,Z: int] :
% 15.55/8.59        ( ( minus_minus_int @ ( ord_max_int @ X3 @ Y3 ) @ Z )
% 15.55/8.59        = ( ord_max_int @ ( minus_minus_int @ X3 @ Z ) @ ( minus_minus_int @ Y3 @ Z ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6501_nat__add__max__right,axiom,
% 15.55/8.59      ! [M: nat,N: nat,Q3: nat] :
% 15.55/8.59        ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q3 ) )
% 15.55/8.59        = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6502_nat__add__max__left,axiom,
% 15.55/8.59      ! [M: nat,N: nat,Q3: nat] :
% 15.55/8.59        ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q3 )
% 15.55/8.59        = ( ord_max_nat @ ( plus_plus_nat @ M @ Q3 ) @ ( plus_plus_nat @ N @ Q3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6503_nat__mult__max__left,axiom,
% 15.55/8.59      ! [M: nat,N: nat,Q3: nat] :
% 15.55/8.59        ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q3 )
% 15.55/8.59        = ( ord_max_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N @ Q3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6504_nat__mult__max__right,axiom,
% 15.55/8.59      ! [M: nat,N: nat,Q3: nat] :
% 15.55/8.59        ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q3 ) )
% 15.55/8.59        = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6505_nat__minus__add__max,axiom,
% 15.55/8.59      ! [N: nat,M: nat] :
% 15.55/8.59        ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 15.55/8.59        = ( ord_max_nat @ N @ M ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6506_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I1_J,axiom,
% 15.55/8.59      ! [Uu2: $o,Uv2: $o] :
% 15.55/8.59        ( ( vEBT_T_p_r_e_d @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat )
% 15.55/8.59        = one_one_nat ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6507_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I5_J,axiom,
% 15.55/8.59      ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 15.55/8.59        ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf )
% 15.55/8.59        = one_one_nat ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6508_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I1_J,axiom,
% 15.55/8.59      ! [Uu2: $o,B: $o] :
% 15.55/8.59        ( ( vEBT_T_s_u_c_c @ ( vEBT_Leaf @ Uu2 @ B ) @ zero_zero_nat )
% 15.55/8.59        = ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6509_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I4_J,axiom,
% 15.55/8.59      ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 15.55/8.59        ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve )
% 15.55/8.59        = one_one_nat ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6510_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I2_J,axiom,
% 15.55/8.59      ! [A: $o,Uw2: $o] :
% 15.55/8.59        ( ( vEBT_T_p_r_e_d @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 15.55/8.59        = ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6511_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I6_J,axiom,
% 15.55/8.59      ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 15.55/8.59        ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj )
% 15.55/8.59        = one_one_nat ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6512_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I5_J,axiom,
% 15.55/8.59      ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 15.55/8.59        ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi )
% 15.55/8.59        = one_one_nat ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6513_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I2_J,axiom,
% 15.55/8.59      ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X3: nat] :
% 15.55/8.59        ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X3 )
% 15.55/8.59        = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6514_or__nat__unfold,axiom,
% 15.55/8.59      ( bit_se1412395901928357646or_nat
% 15.55/8.59      = ( ^ [M3: nat,N3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N3 @ ( if_nat @ ( N3 = zero_zero_nat ) @ M3 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N3 @ ( 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 @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6515_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I3_J,axiom,
% 15.55/8.59      ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X3: nat] :
% 15.55/8.59        ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X3 )
% 15.55/8.59        = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6516_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I4_J,axiom,
% 15.55/8.59      ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc: vEBT_VEBT,X3: nat] :
% 15.55/8.59        ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc ) @ X3 )
% 15.55/8.59        = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6517_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I1_J,axiom,
% 15.55/8.59      ! [A: $o,B: $o,X3: nat] :
% 15.55/8.59        ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 15.55/8.59        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X3 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6518_vebt__member_Osimps_I3_J,axiom,
% 15.55/8.59      ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X3: nat] :
% 15.55/8.59        ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X3 ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6519_vebt__member_Osimps_I1_J,axiom,
% 15.55/8.59      ! [A: $o,B: $o,X3: nat] :
% 15.55/8.59        ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 15.55/8.59        = ( ( ( X3 = zero_zero_nat )
% 15.55/8.59           => A )
% 15.55/8.59          & ( ( X3 != zero_zero_nat )
% 15.55/8.59           => ( ( ( X3 = one_one_nat )
% 15.55/8.59               => B )
% 15.55/8.59              & ( X3 = one_one_nat ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6520_pred__bound__height,axiom,
% 15.55/8.59      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.59        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.59       => ( ord_less_eq_nat @ ( vEBT_T_p_r_e_d @ T @ X3 ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6521_succ__bound__height,axiom,
% 15.55/8.59      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.59        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.59       => ( ord_less_eq_nat @ ( vEBT_T_s_u_c_c @ T @ X3 ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6522_member__bound__height,axiom,
% 15.55/8.59      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.59        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.59       => ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r @ T @ X3 ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6523_max_Oabsorb3,axiom,
% 15.55/8.59      ! [B: extended_enat,A: extended_enat] :
% 15.55/8.59        ( ( ord_le72135733267957522d_enat @ B @ A )
% 15.55/8.59       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 15.55/8.59          = A ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6524_max_Oabsorb3,axiom,
% 15.55/8.59      ! [B: code_integer,A: code_integer] :
% 15.55/8.59        ( ( ord_le6747313008572928689nteger @ B @ A )
% 15.55/8.59       => ( ( ord_max_Code_integer @ A @ B )
% 15.55/8.59          = A ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6525_max_Oabsorb3,axiom,
% 15.55/8.59      ! [B: real,A: real] :
% 15.55/8.59        ( ( ord_less_real @ B @ A )
% 15.55/8.59       => ( ( ord_max_real @ A @ B )
% 15.55/8.59          = A ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6526_max_Oabsorb3,axiom,
% 15.55/8.59      ! [B: rat,A: rat] :
% 15.55/8.59        ( ( ord_less_rat @ B @ A )
% 15.55/8.59       => ( ( ord_max_rat @ A @ B )
% 15.55/8.59          = A ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6527_max_Oabsorb3,axiom,
% 15.55/8.59      ! [B: num,A: num] :
% 15.55/8.59        ( ( ord_less_num @ B @ A )
% 15.55/8.59       => ( ( ord_max_num @ A @ B )
% 15.55/8.59          = A ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6528_max_Oabsorb3,axiom,
% 15.55/8.59      ! [B: nat,A: nat] :
% 15.55/8.59        ( ( ord_less_nat @ B @ A )
% 15.55/8.59       => ( ( ord_max_nat @ A @ B )
% 15.55/8.59          = A ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6529_max_Oabsorb3,axiom,
% 15.55/8.59      ! [B: int,A: int] :
% 15.55/8.59        ( ( ord_less_int @ B @ A )
% 15.55/8.59       => ( ( ord_max_int @ A @ B )
% 15.55/8.59          = A ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6530_max_Oabsorb4,axiom,
% 15.55/8.59      ! [A: extended_enat,B: extended_enat] :
% 15.55/8.59        ( ( ord_le72135733267957522d_enat @ A @ B )
% 15.55/8.59       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 15.55/8.59          = B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6531_max_Oabsorb4,axiom,
% 15.55/8.59      ! [A: code_integer,B: code_integer] :
% 15.55/8.59        ( ( ord_le6747313008572928689nteger @ A @ B )
% 15.55/8.59       => ( ( ord_max_Code_integer @ A @ B )
% 15.55/8.59          = B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6532_max_Oabsorb4,axiom,
% 15.55/8.59      ! [A: real,B: real] :
% 15.55/8.59        ( ( ord_less_real @ A @ B )
% 15.55/8.59       => ( ( ord_max_real @ A @ B )
% 15.55/8.59          = B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6533_max_Oabsorb4,axiom,
% 15.55/8.59      ! [A: rat,B: rat] :
% 15.55/8.59        ( ( ord_less_rat @ A @ B )
% 15.55/8.59       => ( ( ord_max_rat @ A @ B )
% 15.55/8.59          = B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6534_max_Oabsorb4,axiom,
% 15.55/8.59      ! [A: num,B: num] :
% 15.55/8.59        ( ( ord_less_num @ A @ B )
% 15.55/8.59       => ( ( ord_max_num @ A @ B )
% 15.55/8.59          = B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6535_max_Oabsorb4,axiom,
% 15.55/8.59      ! [A: nat,B: nat] :
% 15.55/8.59        ( ( ord_less_nat @ A @ B )
% 15.55/8.59       => ( ( ord_max_nat @ A @ B )
% 15.55/8.59          = B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6536_max_Oabsorb4,axiom,
% 15.55/8.59      ! [A: int,B: int] :
% 15.55/8.59        ( ( ord_less_int @ A @ B )
% 15.55/8.59       => ( ( ord_max_int @ A @ B )
% 15.55/8.59          = B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6537_max__less__iff__conj,axiom,
% 15.55/8.59      ! [X3: extended_enat,Y3: extended_enat,Z: extended_enat] :
% 15.55/8.59        ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ X3 @ Y3 ) @ Z )
% 15.55/8.59        = ( ( ord_le72135733267957522d_enat @ X3 @ Z )
% 15.55/8.59          & ( ord_le72135733267957522d_enat @ Y3 @ Z ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6538_max__less__iff__conj,axiom,
% 15.55/8.59      ! [X3: code_integer,Y3: code_integer,Z: code_integer] :
% 15.55/8.59        ( ( ord_le6747313008572928689nteger @ ( ord_max_Code_integer @ X3 @ Y3 ) @ Z )
% 15.55/8.59        = ( ( ord_le6747313008572928689nteger @ X3 @ Z )
% 15.55/8.59          & ( ord_le6747313008572928689nteger @ Y3 @ Z ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6539_max__less__iff__conj,axiom,
% 15.55/8.59      ! [X3: real,Y3: real,Z: real] :
% 15.55/8.59        ( ( ord_less_real @ ( ord_max_real @ X3 @ Y3 ) @ Z )
% 15.55/8.59        = ( ( ord_less_real @ X3 @ Z )
% 15.55/8.59          & ( ord_less_real @ Y3 @ Z ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6540_max__less__iff__conj,axiom,
% 15.55/8.59      ! [X3: rat,Y3: rat,Z: rat] :
% 15.55/8.59        ( ( ord_less_rat @ ( ord_max_rat @ X3 @ Y3 ) @ Z )
% 15.55/8.59        = ( ( ord_less_rat @ X3 @ Z )
% 15.55/8.59          & ( ord_less_rat @ Y3 @ Z ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6541_max__less__iff__conj,axiom,
% 15.55/8.59      ! [X3: num,Y3: num,Z: num] :
% 15.55/8.59        ( ( ord_less_num @ ( ord_max_num @ X3 @ Y3 ) @ Z )
% 15.55/8.59        = ( ( ord_less_num @ X3 @ Z )
% 15.55/8.59          & ( ord_less_num @ Y3 @ Z ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6542_max__less__iff__conj,axiom,
% 15.55/8.59      ! [X3: nat,Y3: nat,Z: nat] :
% 15.55/8.59        ( ( ord_less_nat @ ( ord_max_nat @ X3 @ Y3 ) @ Z )
% 15.55/8.59        = ( ( ord_less_nat @ X3 @ Z )
% 15.55/8.59          & ( ord_less_nat @ Y3 @ Z ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6543_max__less__iff__conj,axiom,
% 15.55/8.59      ! [X3: int,Y3: int,Z: int] :
% 15.55/8.59        ( ( ord_less_int @ ( ord_max_int @ X3 @ Y3 ) @ Z )
% 15.55/8.59        = ( ( ord_less_int @ X3 @ Z )
% 15.55/8.59          & ( ord_less_int @ Y3 @ Z ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6544_max_Oabsorb1,axiom,
% 15.55/8.59      ! [B: extended_enat,A: extended_enat] :
% 15.55/8.59        ( ( ord_le2932123472753598470d_enat @ B @ A )
% 15.55/8.59       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 15.55/8.59          = A ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6545_max_Oabsorb1,axiom,
% 15.55/8.59      ! [B: code_integer,A: code_integer] :
% 15.55/8.59        ( ( ord_le3102999989581377725nteger @ B @ A )
% 15.55/8.59       => ( ( ord_max_Code_integer @ A @ B )
% 15.55/8.59          = A ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6546_max_Oabsorb1,axiom,
% 15.55/8.59      ! [B: rat,A: rat] :
% 15.55/8.59        ( ( ord_less_eq_rat @ B @ A )
% 15.55/8.59       => ( ( ord_max_rat @ A @ B )
% 15.55/8.59          = A ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6547_max_Oabsorb1,axiom,
% 15.55/8.59      ! [B: num,A: num] :
% 15.55/8.59        ( ( ord_less_eq_num @ B @ A )
% 15.55/8.59       => ( ( ord_max_num @ A @ B )
% 15.55/8.59          = A ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6548_max_Oabsorb1,axiom,
% 15.55/8.59      ! [B: nat,A: nat] :
% 15.55/8.59        ( ( ord_less_eq_nat @ B @ A )
% 15.55/8.59       => ( ( ord_max_nat @ A @ B )
% 15.55/8.59          = A ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6549_max_Oabsorb1,axiom,
% 15.55/8.59      ! [B: int,A: int] :
% 15.55/8.59        ( ( ord_less_eq_int @ B @ A )
% 15.55/8.59       => ( ( ord_max_int @ A @ B )
% 15.55/8.59          = A ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6550_max_Oabsorb2,axiom,
% 15.55/8.59      ! [A: extended_enat,B: extended_enat] :
% 15.55/8.59        ( ( ord_le2932123472753598470d_enat @ A @ B )
% 15.55/8.59       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 15.55/8.59          = B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6551_max_Oabsorb2,axiom,
% 15.55/8.59      ! [A: code_integer,B: code_integer] :
% 15.55/8.59        ( ( ord_le3102999989581377725nteger @ A @ B )
% 15.55/8.59       => ( ( ord_max_Code_integer @ A @ B )
% 15.55/8.59          = B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6552_max_Oabsorb2,axiom,
% 15.55/8.59      ! [A: rat,B: rat] :
% 15.55/8.59        ( ( ord_less_eq_rat @ A @ B )
% 15.55/8.59       => ( ( ord_max_rat @ A @ B )
% 15.55/8.59          = B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6553_max_Oabsorb2,axiom,
% 15.55/8.59      ! [A: num,B: num] :
% 15.55/8.59        ( ( ord_less_eq_num @ A @ B )
% 15.55/8.59       => ( ( ord_max_num @ A @ B )
% 15.55/8.59          = B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6554_max_Oabsorb2,axiom,
% 15.55/8.59      ! [A: nat,B: nat] :
% 15.55/8.59        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.59       => ( ( ord_max_nat @ A @ B )
% 15.55/8.59          = B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6555_max_Oabsorb2,axiom,
% 15.55/8.59      ! [A: int,B: int] :
% 15.55/8.59        ( ( ord_less_eq_int @ A @ B )
% 15.55/8.59       => ( ( ord_max_int @ A @ B )
% 15.55/8.59          = B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6556_max_Obounded__iff,axiom,
% 15.55/8.59      ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 15.55/8.59        ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 15.55/8.59        = ( ( ord_le2932123472753598470d_enat @ B @ A )
% 15.55/8.59          & ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6557_max_Obounded__iff,axiom,
% 15.55/8.59      ! [B: code_integer,C: code_integer,A: code_integer] :
% 15.55/8.59        ( ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 15.55/8.59        = ( ( ord_le3102999989581377725nteger @ B @ A )
% 15.55/8.59          & ( ord_le3102999989581377725nteger @ C @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6558_max_Obounded__iff,axiom,
% 15.55/8.59      ! [B: rat,C: rat,A: rat] :
% 15.55/8.59        ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 15.55/8.59        = ( ( ord_less_eq_rat @ B @ A )
% 15.55/8.59          & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6559_max_Obounded__iff,axiom,
% 15.55/8.59      ! [B: num,C: num,A: num] :
% 15.55/8.59        ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 15.55/8.59        = ( ( ord_less_eq_num @ B @ A )
% 15.55/8.59          & ( ord_less_eq_num @ C @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6560_max_Obounded__iff,axiom,
% 15.55/8.59      ! [B: nat,C: nat,A: nat] :
% 15.55/8.59        ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 15.55/8.59        = ( ( ord_less_eq_nat @ B @ A )
% 15.55/8.59          & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6561_max_Obounded__iff,axiom,
% 15.55/8.59      ! [B: int,C: int,A: int] :
% 15.55/8.59        ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 15.55/8.59        = ( ( ord_less_eq_int @ B @ A )
% 15.55/8.59          & ( ord_less_eq_int @ C @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6562_max__enat__simps_I3_J,axiom,
% 15.55/8.59      ! [Q3: extended_enat] :
% 15.55/8.59        ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q3 )
% 15.55/8.59        = Q3 ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6563_max__enat__simps_I2_J,axiom,
% 15.55/8.59      ! [Q3: extended_enat] :
% 15.55/8.59        ( ( ord_ma741700101516333627d_enat @ Q3 @ zero_z5237406670263579293d_enat )
% 15.55/8.59        = Q3 ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6564_max_OcoboundedI2,axiom,
% 15.55/8.59      ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 15.55/8.59        ( ( ord_le2932123472753598470d_enat @ C @ B )
% 15.55/8.59       => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6565_max_OcoboundedI2,axiom,
% 15.55/8.59      ! [C: code_integer,B: code_integer,A: code_integer] :
% 15.55/8.59        ( ( ord_le3102999989581377725nteger @ C @ B )
% 15.55/8.59       => ( ord_le3102999989581377725nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6566_max_OcoboundedI2,axiom,
% 15.55/8.59      ! [C: rat,B: rat,A: rat] :
% 15.55/8.59        ( ( ord_less_eq_rat @ C @ B )
% 15.55/8.59       => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6567_max_OcoboundedI2,axiom,
% 15.55/8.59      ! [C: num,B: num,A: num] :
% 15.55/8.59        ( ( ord_less_eq_num @ C @ B )
% 15.55/8.59       => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6568_max_OcoboundedI2,axiom,
% 15.55/8.59      ! [C: nat,B: nat,A: nat] :
% 15.55/8.59        ( ( ord_less_eq_nat @ C @ B )
% 15.55/8.59       => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6569_max_OcoboundedI2,axiom,
% 15.55/8.59      ! [C: int,B: int,A: int] :
% 15.55/8.59        ( ( ord_less_eq_int @ C @ B )
% 15.55/8.59       => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6570_max_OcoboundedI1,axiom,
% 15.55/8.59      ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 15.55/8.59        ( ( ord_le2932123472753598470d_enat @ C @ A )
% 15.55/8.59       => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6571_max_OcoboundedI1,axiom,
% 15.55/8.59      ! [C: code_integer,A: code_integer,B: code_integer] :
% 15.55/8.59        ( ( ord_le3102999989581377725nteger @ C @ A )
% 15.55/8.59       => ( ord_le3102999989581377725nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6572_max_OcoboundedI1,axiom,
% 15.55/8.59      ! [C: rat,A: rat,B: rat] :
% 15.55/8.59        ( ( ord_less_eq_rat @ C @ A )
% 15.55/8.59       => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6573_max_OcoboundedI1,axiom,
% 15.55/8.59      ! [C: num,A: num,B: num] :
% 15.55/8.59        ( ( ord_less_eq_num @ C @ A )
% 15.55/8.59       => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6574_max_OcoboundedI1,axiom,
% 15.55/8.59      ! [C: nat,A: nat,B: nat] :
% 15.55/8.59        ( ( ord_less_eq_nat @ C @ A )
% 15.55/8.59       => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6575_max_OcoboundedI1,axiom,
% 15.55/8.59      ! [C: int,A: int,B: int] :
% 15.55/8.59        ( ( ord_less_eq_int @ C @ A )
% 15.55/8.59       => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6576_max_Oabsorb__iff2,axiom,
% 15.55/8.59      ( ord_le2932123472753598470d_enat
% 15.55/8.59      = ( ^ [A4: extended_enat,B3: extended_enat] :
% 15.55/8.59            ( ( ord_ma741700101516333627d_enat @ A4 @ B3 )
% 15.55/8.59            = B3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6577_max_Oabsorb__iff2,axiom,
% 15.55/8.59      ( ord_le3102999989581377725nteger
% 15.55/8.59      = ( ^ [A4: code_integer,B3: code_integer] :
% 15.55/8.59            ( ( ord_max_Code_integer @ A4 @ B3 )
% 15.55/8.59            = B3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6578_max_Oabsorb__iff2,axiom,
% 15.55/8.59      ( ord_less_eq_rat
% 15.55/8.59      = ( ^ [A4: rat,B3: rat] :
% 15.55/8.59            ( ( ord_max_rat @ A4 @ B3 )
% 15.55/8.59            = B3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6579_max_Oabsorb__iff2,axiom,
% 15.55/8.59      ( ord_less_eq_num
% 15.55/8.59      = ( ^ [A4: num,B3: num] :
% 15.55/8.59            ( ( ord_max_num @ A4 @ B3 )
% 15.55/8.59            = B3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6580_max_Oabsorb__iff2,axiom,
% 15.55/8.59      ( ord_less_eq_nat
% 15.55/8.59      = ( ^ [A4: nat,B3: nat] :
% 15.55/8.59            ( ( ord_max_nat @ A4 @ B3 )
% 15.55/8.59            = B3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6581_max_Oabsorb__iff2,axiom,
% 15.55/8.59      ( ord_less_eq_int
% 15.55/8.59      = ( ^ [A4: int,B3: int] :
% 15.55/8.59            ( ( ord_max_int @ A4 @ B3 )
% 15.55/8.59            = B3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6582_max_Oabsorb__iff1,axiom,
% 15.55/8.59      ( ord_le2932123472753598470d_enat
% 15.55/8.59      = ( ^ [B3: extended_enat,A4: extended_enat] :
% 15.55/8.59            ( ( ord_ma741700101516333627d_enat @ A4 @ B3 )
% 15.55/8.59            = A4 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6583_max_Oabsorb__iff1,axiom,
% 15.55/8.59      ( ord_le3102999989581377725nteger
% 15.55/8.59      = ( ^ [B3: code_integer,A4: code_integer] :
% 15.55/8.59            ( ( ord_max_Code_integer @ A4 @ B3 )
% 15.55/8.59            = A4 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6584_max_Oabsorb__iff1,axiom,
% 15.55/8.59      ( ord_less_eq_rat
% 15.55/8.59      = ( ^ [B3: rat,A4: rat] :
% 15.55/8.59            ( ( ord_max_rat @ A4 @ B3 )
% 15.55/8.59            = A4 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6585_max_Oabsorb__iff1,axiom,
% 15.55/8.59      ( ord_less_eq_num
% 15.55/8.59      = ( ^ [B3: num,A4: num] :
% 15.55/8.59            ( ( ord_max_num @ A4 @ B3 )
% 15.55/8.59            = A4 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6586_max_Oabsorb__iff1,axiom,
% 15.55/8.59      ( ord_less_eq_nat
% 15.55/8.59      = ( ^ [B3: nat,A4: nat] :
% 15.55/8.59            ( ( ord_max_nat @ A4 @ B3 )
% 15.55/8.59            = A4 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6587_max_Oabsorb__iff1,axiom,
% 15.55/8.59      ( ord_less_eq_int
% 15.55/8.59      = ( ^ [B3: int,A4: int] :
% 15.55/8.59            ( ( ord_max_int @ A4 @ B3 )
% 15.55/8.59            = A4 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6588_le__max__iff__disj,axiom,
% 15.55/8.59      ! [Z: extended_enat,X3: extended_enat,Y3: extended_enat] :
% 15.55/8.59        ( ( ord_le2932123472753598470d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X3 @ Y3 ) )
% 15.55/8.59        = ( ( ord_le2932123472753598470d_enat @ Z @ X3 )
% 15.55/8.59          | ( ord_le2932123472753598470d_enat @ Z @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6589_le__max__iff__disj,axiom,
% 15.55/8.59      ! [Z: code_integer,X3: code_integer,Y3: code_integer] :
% 15.55/8.59        ( ( ord_le3102999989581377725nteger @ Z @ ( ord_max_Code_integer @ X3 @ Y3 ) )
% 15.55/8.59        = ( ( ord_le3102999989581377725nteger @ Z @ X3 )
% 15.55/8.59          | ( ord_le3102999989581377725nteger @ Z @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6590_le__max__iff__disj,axiom,
% 15.55/8.59      ! [Z: rat,X3: rat,Y3: rat] :
% 15.55/8.59        ( ( ord_less_eq_rat @ Z @ ( ord_max_rat @ X3 @ Y3 ) )
% 15.55/8.59        = ( ( ord_less_eq_rat @ Z @ X3 )
% 15.55/8.59          | ( ord_less_eq_rat @ Z @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6591_le__max__iff__disj,axiom,
% 15.55/8.59      ! [Z: num,X3: num,Y3: num] :
% 15.55/8.59        ( ( ord_less_eq_num @ Z @ ( ord_max_num @ X3 @ Y3 ) )
% 15.55/8.59        = ( ( ord_less_eq_num @ Z @ X3 )
% 15.55/8.59          | ( ord_less_eq_num @ Z @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6592_le__max__iff__disj,axiom,
% 15.55/8.59      ! [Z: nat,X3: nat,Y3: nat] :
% 15.55/8.59        ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X3 @ Y3 ) )
% 15.55/8.59        = ( ( ord_less_eq_nat @ Z @ X3 )
% 15.55/8.59          | ( ord_less_eq_nat @ Z @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6593_le__max__iff__disj,axiom,
% 15.55/8.59      ! [Z: int,X3: int,Y3: int] :
% 15.55/8.59        ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X3 @ Y3 ) )
% 15.55/8.59        = ( ( ord_less_eq_int @ Z @ X3 )
% 15.55/8.59          | ( ord_less_eq_int @ Z @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6594_max_Ocobounded2,axiom,
% 15.55/8.59      ! [B: extended_enat,A: extended_enat] : ( ord_le2932123472753598470d_enat @ B @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6595_max_Ocobounded2,axiom,
% 15.55/8.59      ! [B: code_integer,A: code_integer] : ( ord_le3102999989581377725nteger @ B @ ( ord_max_Code_integer @ A @ B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6596_max_Ocobounded2,axiom,
% 15.55/8.59      ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6597_max_Ocobounded2,axiom,
% 15.55/8.59      ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6598_max_Ocobounded2,axiom,
% 15.55/8.59      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6599_max_Ocobounded2,axiom,
% 15.55/8.59      ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6600_max_Ocobounded1,axiom,
% 15.55/8.59      ! [A: extended_enat,B: extended_enat] : ( ord_le2932123472753598470d_enat @ A @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6601_max_Ocobounded1,axiom,
% 15.55/8.59      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( ord_max_Code_integer @ A @ B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6602_max_Ocobounded1,axiom,
% 15.55/8.59      ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6603_max_Ocobounded1,axiom,
% 15.55/8.59      ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6604_max_Ocobounded1,axiom,
% 15.55/8.59      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6605_max_Ocobounded1,axiom,
% 15.55/8.59      ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6606_max_Oorder__iff,axiom,
% 15.55/8.59      ( ord_le2932123472753598470d_enat
% 15.55/8.59      = ( ^ [B3: extended_enat,A4: extended_enat] :
% 15.55/8.59            ( A4
% 15.55/8.59            = ( ord_ma741700101516333627d_enat @ A4 @ B3 ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6607_max_Oorder__iff,axiom,
% 15.55/8.59      ( ord_le3102999989581377725nteger
% 15.55/8.59      = ( ^ [B3: code_integer,A4: code_integer] :
% 15.55/8.59            ( A4
% 15.55/8.59            = ( ord_max_Code_integer @ A4 @ B3 ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6608_max_Oorder__iff,axiom,
% 15.55/8.59      ( ord_less_eq_rat
% 15.55/8.59      = ( ^ [B3: rat,A4: rat] :
% 15.55/8.59            ( A4
% 15.55/8.59            = ( ord_max_rat @ A4 @ B3 ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6609_max_Oorder__iff,axiom,
% 15.55/8.59      ( ord_less_eq_num
% 15.55/8.59      = ( ^ [B3: num,A4: num] :
% 15.55/8.59            ( A4
% 15.55/8.59            = ( ord_max_num @ A4 @ B3 ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6610_max_Oorder__iff,axiom,
% 15.55/8.59      ( ord_less_eq_nat
% 15.55/8.59      = ( ^ [B3: nat,A4: nat] :
% 15.55/8.59            ( A4
% 15.55/8.59            = ( ord_max_nat @ A4 @ B3 ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6611_max_Oorder__iff,axiom,
% 15.55/8.59      ( ord_less_eq_int
% 15.55/8.59      = ( ^ [B3: int,A4: int] :
% 15.55/8.59            ( A4
% 15.55/8.59            = ( ord_max_int @ A4 @ B3 ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6612_max_OboundedI,axiom,
% 15.55/8.59      ! [B: extended_enat,A: extended_enat,C: extended_enat] :
% 15.55/8.59        ( ( ord_le2932123472753598470d_enat @ B @ A )
% 15.55/8.59       => ( ( ord_le2932123472753598470d_enat @ C @ A )
% 15.55/8.59         => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6613_max_OboundedI,axiom,
% 15.55/8.59      ! [B: code_integer,A: code_integer,C: code_integer] :
% 15.55/8.59        ( ( ord_le3102999989581377725nteger @ B @ A )
% 15.55/8.59       => ( ( ord_le3102999989581377725nteger @ C @ A )
% 15.55/8.59         => ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C ) @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6614_max_OboundedI,axiom,
% 15.55/8.59      ! [B: rat,A: rat,C: rat] :
% 15.55/8.59        ( ( ord_less_eq_rat @ B @ A )
% 15.55/8.59       => ( ( ord_less_eq_rat @ C @ A )
% 15.55/8.59         => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6615_max_OboundedI,axiom,
% 15.55/8.59      ! [B: num,A: num,C: num] :
% 15.55/8.59        ( ( ord_less_eq_num @ B @ A )
% 15.55/8.59       => ( ( ord_less_eq_num @ C @ A )
% 15.55/8.59         => ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6616_max_OboundedI,axiom,
% 15.55/8.59      ! [B: nat,A: nat,C: nat] :
% 15.55/8.59        ( ( ord_less_eq_nat @ B @ A )
% 15.55/8.59       => ( ( ord_less_eq_nat @ C @ A )
% 15.55/8.59         => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6617_max_OboundedI,axiom,
% 15.55/8.59      ! [B: int,A: int,C: int] :
% 15.55/8.59        ( ( ord_less_eq_int @ B @ A )
% 15.55/8.59       => ( ( ord_less_eq_int @ C @ A )
% 15.55/8.59         => ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6618_max_OboundedE,axiom,
% 15.55/8.59      ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 15.55/8.59        ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 15.55/8.59       => ~ ( ( ord_le2932123472753598470d_enat @ B @ A )
% 15.55/8.59           => ~ ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6619_max_OboundedE,axiom,
% 15.55/8.59      ! [B: code_integer,C: code_integer,A: code_integer] :
% 15.55/8.59        ( ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 15.55/8.59       => ~ ( ( ord_le3102999989581377725nteger @ B @ A )
% 15.55/8.59           => ~ ( ord_le3102999989581377725nteger @ C @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6620_max_OboundedE,axiom,
% 15.55/8.59      ! [B: rat,C: rat,A: rat] :
% 15.55/8.59        ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 15.55/8.59       => ~ ( ( ord_less_eq_rat @ B @ A )
% 15.55/8.59           => ~ ( ord_less_eq_rat @ C @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6621_max_OboundedE,axiom,
% 15.55/8.59      ! [B: num,C: num,A: num] :
% 15.55/8.59        ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 15.55/8.59       => ~ ( ( ord_less_eq_num @ B @ A )
% 15.55/8.59           => ~ ( ord_less_eq_num @ C @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6622_max_OboundedE,axiom,
% 15.55/8.59      ! [B: nat,C: nat,A: nat] :
% 15.55/8.59        ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 15.55/8.59       => ~ ( ( ord_less_eq_nat @ B @ A )
% 15.55/8.59           => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6623_max_OboundedE,axiom,
% 15.55/8.59      ! [B: int,C: int,A: int] :
% 15.55/8.59        ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 15.55/8.59       => ~ ( ( ord_less_eq_int @ B @ A )
% 15.55/8.59           => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6624_max_OorderI,axiom,
% 15.55/8.59      ! [A: extended_enat,B: extended_enat] :
% 15.55/8.59        ( ( A
% 15.55/8.59          = ( ord_ma741700101516333627d_enat @ A @ B ) )
% 15.55/8.59       => ( ord_le2932123472753598470d_enat @ B @ A ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6625_max_OorderI,axiom,
% 15.55/8.59      ! [A: code_integer,B: code_integer] :
% 15.55/8.59        ( ( A
% 15.55/8.59          = ( ord_max_Code_integer @ A @ B ) )
% 15.55/8.59       => ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6626_max_OorderI,axiom,
% 15.55/8.59      ! [A: rat,B: rat] :
% 15.55/8.59        ( ( A
% 15.55/8.59          = ( ord_max_rat @ A @ B ) )
% 15.55/8.59       => ( ord_less_eq_rat @ B @ A ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6627_max_OorderI,axiom,
% 15.55/8.59      ! [A: num,B: num] :
% 15.55/8.59        ( ( A
% 15.55/8.59          = ( ord_max_num @ A @ B ) )
% 15.55/8.59       => ( ord_less_eq_num @ B @ A ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6628_max_OorderI,axiom,
% 15.55/8.59      ! [A: nat,B: nat] :
% 15.55/8.59        ( ( A
% 15.55/8.59          = ( ord_max_nat @ A @ B ) )
% 15.55/8.59       => ( ord_less_eq_nat @ B @ A ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6629_max_OorderI,axiom,
% 15.55/8.59      ! [A: int,B: int] :
% 15.55/8.59        ( ( A
% 15.55/8.59          = ( ord_max_int @ A @ B ) )
% 15.55/8.59       => ( ord_less_eq_int @ B @ A ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6630_max_OorderE,axiom,
% 15.55/8.59      ! [B: extended_enat,A: extended_enat] :
% 15.55/8.59        ( ( ord_le2932123472753598470d_enat @ B @ A )
% 15.55/8.59       => ( A
% 15.55/8.59          = ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6631_max_OorderE,axiom,
% 15.55/8.59      ! [B: code_integer,A: code_integer] :
% 15.55/8.59        ( ( ord_le3102999989581377725nteger @ B @ A )
% 15.55/8.59       => ( A
% 15.55/8.59          = ( ord_max_Code_integer @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6632_max_OorderE,axiom,
% 15.55/8.59      ! [B: rat,A: rat] :
% 15.55/8.59        ( ( ord_less_eq_rat @ B @ A )
% 15.55/8.59       => ( A
% 15.55/8.59          = ( ord_max_rat @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6633_max_OorderE,axiom,
% 15.55/8.59      ! [B: num,A: num] :
% 15.55/8.59        ( ( ord_less_eq_num @ B @ A )
% 15.55/8.59       => ( A
% 15.55/8.59          = ( ord_max_num @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6634_max_OorderE,axiom,
% 15.55/8.59      ! [B: nat,A: nat] :
% 15.55/8.59        ( ( ord_less_eq_nat @ B @ A )
% 15.55/8.59       => ( A
% 15.55/8.59          = ( ord_max_nat @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6635_max_OorderE,axiom,
% 15.55/8.59      ! [B: int,A: int] :
% 15.55/8.59        ( ( ord_less_eq_int @ B @ A )
% 15.55/8.59       => ( A
% 15.55/8.59          = ( ord_max_int @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6636_max_Omono,axiom,
% 15.55/8.59      ! [C: extended_enat,A: extended_enat,D3: extended_enat,B: extended_enat] :
% 15.55/8.59        ( ( ord_le2932123472753598470d_enat @ C @ A )
% 15.55/8.59       => ( ( ord_le2932123472753598470d_enat @ D3 @ B )
% 15.55/8.59         => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ C @ D3 ) @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6637_max_Omono,axiom,
% 15.55/8.59      ! [C: code_integer,A: code_integer,D3: code_integer,B: code_integer] :
% 15.55/8.59        ( ( ord_le3102999989581377725nteger @ C @ A )
% 15.55/8.59       => ( ( ord_le3102999989581377725nteger @ D3 @ B )
% 15.55/8.59         => ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ C @ D3 ) @ ( ord_max_Code_integer @ A @ B ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6638_max_Omono,axiom,
% 15.55/8.59      ! [C: rat,A: rat,D3: rat,B: rat] :
% 15.55/8.59        ( ( ord_less_eq_rat @ C @ A )
% 15.55/8.59       => ( ( ord_less_eq_rat @ D3 @ B )
% 15.55/8.59         => ( ord_less_eq_rat @ ( ord_max_rat @ C @ D3 ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6639_max_Omono,axiom,
% 15.55/8.59      ! [C: num,A: num,D3: num,B: num] :
% 15.55/8.59        ( ( ord_less_eq_num @ C @ A )
% 15.55/8.59       => ( ( ord_less_eq_num @ D3 @ B )
% 15.55/8.59         => ( ord_less_eq_num @ ( ord_max_num @ C @ D3 ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6640_max_Omono,axiom,
% 15.55/8.59      ! [C: nat,A: nat,D3: nat,B: nat] :
% 15.55/8.59        ( ( ord_less_eq_nat @ C @ A )
% 15.55/8.59       => ( ( ord_less_eq_nat @ D3 @ B )
% 15.55/8.59         => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D3 ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6641_max_Omono,axiom,
% 15.55/8.59      ! [C: int,A: int,D3: int,B: int] :
% 15.55/8.59        ( ( ord_less_eq_int @ C @ A )
% 15.55/8.59       => ( ( ord_less_eq_int @ D3 @ B )
% 15.55/8.59         => ( ord_less_eq_int @ ( ord_max_int @ C @ D3 ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6642_max_Ostrict__coboundedI2,axiom,
% 15.55/8.59      ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 15.55/8.59        ( ( ord_le72135733267957522d_enat @ C @ B )
% 15.55/8.59       => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6643_max_Ostrict__coboundedI2,axiom,
% 15.55/8.59      ! [C: code_integer,B: code_integer,A: code_integer] :
% 15.55/8.59        ( ( ord_le6747313008572928689nteger @ C @ B )
% 15.55/8.59       => ( ord_le6747313008572928689nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6644_max_Ostrict__coboundedI2,axiom,
% 15.55/8.59      ! [C: real,B: real,A: real] :
% 15.55/8.59        ( ( ord_less_real @ C @ B )
% 15.55/8.59       => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6645_max_Ostrict__coboundedI2,axiom,
% 15.55/8.59      ! [C: rat,B: rat,A: rat] :
% 15.55/8.59        ( ( ord_less_rat @ C @ B )
% 15.55/8.59       => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6646_max_Ostrict__coboundedI2,axiom,
% 15.55/8.59      ! [C: num,B: num,A: num] :
% 15.55/8.59        ( ( ord_less_num @ C @ B )
% 15.55/8.59       => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6647_max_Ostrict__coboundedI2,axiom,
% 15.55/8.59      ! [C: nat,B: nat,A: nat] :
% 15.55/8.59        ( ( ord_less_nat @ C @ B )
% 15.55/8.59       => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6648_max_Ostrict__coboundedI2,axiom,
% 15.55/8.59      ! [C: int,B: int,A: int] :
% 15.55/8.59        ( ( ord_less_int @ C @ B )
% 15.55/8.59       => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6649_max_Ostrict__coboundedI1,axiom,
% 15.55/8.59      ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 15.55/8.59        ( ( ord_le72135733267957522d_enat @ C @ A )
% 15.55/8.59       => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6650_max_Ostrict__coboundedI1,axiom,
% 15.55/8.59      ! [C: code_integer,A: code_integer,B: code_integer] :
% 15.55/8.59        ( ( ord_le6747313008572928689nteger @ C @ A )
% 15.55/8.59       => ( ord_le6747313008572928689nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6651_max_Ostrict__coboundedI1,axiom,
% 15.55/8.59      ! [C: real,A: real,B: real] :
% 15.55/8.59        ( ( ord_less_real @ C @ A )
% 15.55/8.59       => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6652_max_Ostrict__coboundedI1,axiom,
% 15.55/8.59      ! [C: rat,A: rat,B: rat] :
% 15.55/8.59        ( ( ord_less_rat @ C @ A )
% 15.55/8.59       => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6653_max_Ostrict__coboundedI1,axiom,
% 15.55/8.59      ! [C: num,A: num,B: num] :
% 15.55/8.59        ( ( ord_less_num @ C @ A )
% 15.55/8.59       => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6654_max_Ostrict__coboundedI1,axiom,
% 15.55/8.59      ! [C: nat,A: nat,B: nat] :
% 15.55/8.59        ( ( ord_less_nat @ C @ A )
% 15.55/8.59       => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6655_max_Ostrict__coboundedI1,axiom,
% 15.55/8.59      ! [C: int,A: int,B: int] :
% 15.55/8.59        ( ( ord_less_int @ C @ A )
% 15.55/8.59       => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6656_max_Ostrict__order__iff,axiom,
% 15.55/8.59      ( ord_le72135733267957522d_enat
% 15.55/8.59      = ( ^ [B3: extended_enat,A4: extended_enat] :
% 15.55/8.59            ( ( A4
% 15.55/8.59              = ( ord_ma741700101516333627d_enat @ A4 @ B3 ) )
% 15.55/8.59            & ( A4 != B3 ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6657_max_Ostrict__order__iff,axiom,
% 15.55/8.59      ( ord_le6747313008572928689nteger
% 15.55/8.59      = ( ^ [B3: code_integer,A4: code_integer] :
% 15.55/8.59            ( ( A4
% 15.55/8.59              = ( ord_max_Code_integer @ A4 @ B3 ) )
% 15.55/8.59            & ( A4 != B3 ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6658_max_Ostrict__order__iff,axiom,
% 15.55/8.59      ( ord_less_real
% 15.55/8.59      = ( ^ [B3: real,A4: real] :
% 15.55/8.59            ( ( A4
% 15.55/8.59              = ( ord_max_real @ A4 @ B3 ) )
% 15.55/8.59            & ( A4 != B3 ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6659_max_Ostrict__order__iff,axiom,
% 15.55/8.59      ( ord_less_rat
% 15.55/8.59      = ( ^ [B3: rat,A4: rat] :
% 15.55/8.59            ( ( A4
% 15.55/8.59              = ( ord_max_rat @ A4 @ B3 ) )
% 15.55/8.59            & ( A4 != B3 ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6660_max_Ostrict__order__iff,axiom,
% 15.55/8.59      ( ord_less_num
% 15.55/8.59      = ( ^ [B3: num,A4: num] :
% 15.55/8.59            ( ( A4
% 15.55/8.59              = ( ord_max_num @ A4 @ B3 ) )
% 15.55/8.59            & ( A4 != B3 ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6661_max_Ostrict__order__iff,axiom,
% 15.55/8.59      ( ord_less_nat
% 15.55/8.59      = ( ^ [B3: nat,A4: nat] :
% 15.55/8.59            ( ( A4
% 15.55/8.59              = ( ord_max_nat @ A4 @ B3 ) )
% 15.55/8.59            & ( A4 != B3 ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6662_max_Ostrict__order__iff,axiom,
% 15.55/8.59      ( ord_less_int
% 15.55/8.59      = ( ^ [B3: int,A4: int] :
% 15.55/8.59            ( ( A4
% 15.55/8.59              = ( ord_max_int @ A4 @ B3 ) )
% 15.55/8.59            & ( A4 != B3 ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6663_max_Ostrict__boundedE,axiom,
% 15.55/8.59      ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 15.55/8.59        ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 15.55/8.59       => ~ ( ( ord_le72135733267957522d_enat @ B @ A )
% 15.55/8.59           => ~ ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6664_max_Ostrict__boundedE,axiom,
% 15.55/8.59      ! [B: code_integer,C: code_integer,A: code_integer] :
% 15.55/8.59        ( ( ord_le6747313008572928689nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 15.55/8.59       => ~ ( ( ord_le6747313008572928689nteger @ B @ A )
% 15.55/8.59           => ~ ( ord_le6747313008572928689nteger @ C @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6665_max_Ostrict__boundedE,axiom,
% 15.55/8.59      ! [B: real,C: real,A: real] :
% 15.55/8.59        ( ( ord_less_real @ ( ord_max_real @ B @ C ) @ A )
% 15.55/8.59       => ~ ( ( ord_less_real @ B @ A )
% 15.55/8.59           => ~ ( ord_less_real @ C @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6666_max_Ostrict__boundedE,axiom,
% 15.55/8.59      ! [B: rat,C: rat,A: rat] :
% 15.55/8.59        ( ( ord_less_rat @ ( ord_max_rat @ B @ C ) @ A )
% 15.55/8.59       => ~ ( ( ord_less_rat @ B @ A )
% 15.55/8.59           => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6667_max_Ostrict__boundedE,axiom,
% 15.55/8.59      ! [B: num,C: num,A: num] :
% 15.55/8.59        ( ( ord_less_num @ ( ord_max_num @ B @ C ) @ A )
% 15.55/8.59       => ~ ( ( ord_less_num @ B @ A )
% 15.55/8.59           => ~ ( ord_less_num @ C @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6668_max_Ostrict__boundedE,axiom,
% 15.55/8.59      ! [B: nat,C: nat,A: nat] :
% 15.55/8.59        ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
% 15.55/8.59       => ~ ( ( ord_less_nat @ B @ A )
% 15.55/8.59           => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6669_max_Ostrict__boundedE,axiom,
% 15.55/8.59      ! [B: int,C: int,A: int] :
% 15.55/8.59        ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
% 15.55/8.59       => ~ ( ( ord_less_int @ B @ A )
% 15.55/8.59           => ~ ( ord_less_int @ C @ A ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6670_less__max__iff__disj,axiom,
% 15.55/8.59      ! [Z: extended_enat,X3: extended_enat,Y3: extended_enat] :
% 15.55/8.59        ( ( ord_le72135733267957522d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X3 @ Y3 ) )
% 15.55/8.59        = ( ( ord_le72135733267957522d_enat @ Z @ X3 )
% 15.55/8.59          | ( ord_le72135733267957522d_enat @ Z @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6671_less__max__iff__disj,axiom,
% 15.55/8.59      ! [Z: code_integer,X3: code_integer,Y3: code_integer] :
% 15.55/8.59        ( ( ord_le6747313008572928689nteger @ Z @ ( ord_max_Code_integer @ X3 @ Y3 ) )
% 15.55/8.59        = ( ( ord_le6747313008572928689nteger @ Z @ X3 )
% 15.55/8.59          | ( ord_le6747313008572928689nteger @ Z @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6672_less__max__iff__disj,axiom,
% 15.55/8.59      ! [Z: real,X3: real,Y3: real] :
% 15.55/8.59        ( ( ord_less_real @ Z @ ( ord_max_real @ X3 @ Y3 ) )
% 15.55/8.59        = ( ( ord_less_real @ Z @ X3 )
% 15.55/8.59          | ( ord_less_real @ Z @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6673_less__max__iff__disj,axiom,
% 15.55/8.59      ! [Z: rat,X3: rat,Y3: rat] :
% 15.55/8.59        ( ( ord_less_rat @ Z @ ( ord_max_rat @ X3 @ Y3 ) )
% 15.55/8.59        = ( ( ord_less_rat @ Z @ X3 )
% 15.55/8.59          | ( ord_less_rat @ Z @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6674_less__max__iff__disj,axiom,
% 15.55/8.59      ! [Z: num,X3: num,Y3: num] :
% 15.55/8.59        ( ( ord_less_num @ Z @ ( ord_max_num @ X3 @ Y3 ) )
% 15.55/8.59        = ( ( ord_less_num @ Z @ X3 )
% 15.55/8.59          | ( ord_less_num @ Z @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6675_less__max__iff__disj,axiom,
% 15.55/8.59      ! [Z: nat,X3: nat,Y3: nat] :
% 15.55/8.59        ( ( ord_less_nat @ Z @ ( ord_max_nat @ X3 @ Y3 ) )
% 15.55/8.59        = ( ( ord_less_nat @ Z @ X3 )
% 15.55/8.59          | ( ord_less_nat @ Z @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6676_less__max__iff__disj,axiom,
% 15.55/8.59      ! [Z: int,X3: int,Y3: int] :
% 15.55/8.59        ( ( ord_less_int @ Z @ ( ord_max_int @ X3 @ Y3 ) )
% 15.55/8.59        = ( ( ord_less_int @ Z @ X3 )
% 15.55/8.59          | ( ord_less_int @ Z @ Y3 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6677_or__int__unfold,axiom,
% 15.55/8.59      ( bit_se1409905431419307370or_int
% 15.55/8.59      = ( ^ [K3: int,L2: int] :
% 15.55/8.59            ( if_int
% 15.55/8.59            @ ( ( K3
% 15.55/8.59                = ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.59              | ( L2
% 15.55/8.59                = ( uminus_uminus_int @ one_one_int ) ) )
% 15.55/8.59            @ ( uminus_uminus_int @ one_one_int )
% 15.55/8.59            @ ( if_int @ ( K3 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6678_insert__bound__size__univ,axiom,
% 15.55/8.59      ! [T: vEBT_VEBT,N: nat,U: real,X3: nat] :
% 15.55/8.59        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.59       => ( ( U
% 15.55/8.59            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.59         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_i_n_s_e_r_t @ T @ X3 ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6679_pred__less__length__list,axiom,
% 15.55/8.59      ! [Deg: nat,X3: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 15.55/8.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.59       => ( ( ord_less_eq_nat @ X3 @ Ma )
% 15.55/8.59         => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.59           => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59              = ( if_option_nat
% 15.55/8.59                @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                   != none_nat )
% 15.55/8.59                  & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.59                @ ( 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 @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                @ ( if_option_nat
% 15.55/8.59                  @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.59                    = none_nat )
% 15.55/8.59                  @ ( if_option_nat @ ( ord_less_nat @ Mi @ X3 ) @ ( some_nat @ Mi ) @ none_nat )
% 15.55/8.59                  @ ( 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 @ X3 @ ( 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 @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6680_pred__lesseq__max,axiom,
% 15.55/8.59      ! [Deg: nat,X3: nat,Ma: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 15.55/8.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.59       => ( ( ord_less_eq_nat @ X3 @ Ma )
% 15.55/8.59         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.59              @ ( if_option_nat
% 15.55/8.59                @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                   != none_nat )
% 15.55/8.59                  & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.59                @ ( 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 @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                @ ( if_option_nat
% 15.55/8.59                  @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.59                    = none_nat )
% 15.55/8.59                  @ ( if_option_nat @ ( ord_less_nat @ Mi @ X3 ) @ ( some_nat @ Mi ) @ none_nat )
% 15.55/8.59                  @ ( 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 @ X3 @ ( 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 @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.59              @ none_nat ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6681_succ__greatereq__min,axiom,
% 15.55/8.59      ! [Deg: nat,Mi: nat,X3: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 15.55/8.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.59       => ( ( ord_less_eq_nat @ Mi @ X3 )
% 15.55/8.59         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.59              @ ( if_option_nat
% 15.55/8.59                @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                   != none_nat )
% 15.55/8.59                  & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.59                @ ( 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 @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                @ ( if_option_nat
% 15.55/8.59                  @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.59                    = none_nat )
% 15.55/8.59                  @ none_nat
% 15.55/8.59                  @ ( 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 @ X3 @ ( 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 @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.59              @ none_nat ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6682_succ__less__length__list,axiom,
% 15.55/8.59      ! [Deg: nat,Mi: nat,X3: nat,TreeList2: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 15.55/8.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.59       => ( ( ord_less_eq_nat @ Mi @ X3 )
% 15.55/8.59         => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.59           => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59              = ( if_option_nat
% 15.55/8.59                @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                   != none_nat )
% 15.55/8.59                  & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.59                @ ( 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 @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                @ ( if_option_nat
% 15.55/8.59                  @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.59                    = none_nat )
% 15.55/8.59                  @ none_nat
% 15.55/8.59                  @ ( 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 @ X3 @ ( 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 @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6683_set__vebt_H__def,axiom,
% 15.55/8.59      ( vEBT_VEBT_set_vebt
% 15.55/8.59      = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6684_del__x__not__mia,axiom,
% 15.55/8.59      ! [Mi: nat,X3: nat,Ma: nat,Deg: nat,H2: nat,L: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 15.55/8.59        ( ( ( ord_less_nat @ Mi @ X3 )
% 15.55/8.59          & ( ord_less_eq_nat @ X3 @ Ma ) )
% 15.55/8.59       => ( ( Mi != Ma )
% 15.55/8.59         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.59           => ( ( ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.59                = H2 )
% 15.55/8.59             => ( ( ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.59                  = L )
% 15.55/8.59               => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.59                 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59                    = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 15.55/8.59                      @ ( vEBT_Node
% 15.55/8.59                        @ ( some_P7363390416028606310at_nat
% 15.55/8.59                          @ ( product_Pair_nat_nat @ Mi
% 15.55/8.59                            @ ( if_nat @ ( X3 = Ma )
% 15.55/8.59                              @ ( if_nat
% 15.55/8.59                                @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 15.55/8.59                                  = none_nat )
% 15.55/8.59                                @ Mi
% 15.55/8.59                                @ ( 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 ) @ L ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 15.55/8.59                              @ Ma ) ) )
% 15.55/8.59                        @ Deg
% 15.55/8.59                        @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 15.55/8.59                        @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 15.55/8.59                      @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X3 = 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 ) @ L ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) ) @ Summary ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6685_del__x__not__mi__new__node__nil,axiom,
% 15.55/8.59      ! [Mi: nat,X3: nat,Ma: nat,Deg: nat,H2: nat,L: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Sn: vEBT_VEBT,Summary: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 15.55/8.59        ( ( ( ord_less_nat @ Mi @ X3 )
% 15.55/8.59          & ( ord_less_eq_nat @ X3 @ Ma ) )
% 15.55/8.59       => ( ( Mi != Ma )
% 15.55/8.59         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.59           => ( ( ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.59                = H2 )
% 15.55/8.59             => ( ( ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.59                  = L )
% 15.55/8.59               => ( ( Newnode
% 15.55/8.59                    = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 15.55/8.59                 => ( ( vEBT_VEBT_minNull @ Newnode )
% 15.55/8.59                   => ( ( Sn
% 15.55/8.59                        = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 15.55/8.59                     => ( ( Newlist
% 15.55/8.59                          = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 15.55/8.59                       => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.59                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59                            = ( vEBT_Node
% 15.55/8.59                              @ ( some_P7363390416028606310at_nat
% 15.55/8.59                                @ ( product_Pair_nat_nat @ Mi
% 15.55/8.59                                  @ ( if_nat @ ( X3 = Ma )
% 15.55/8.59                                    @ ( if_nat
% 15.55/8.59                                      @ ( ( vEBT_vebt_maxt @ Sn )
% 15.55/8.59                                        = none_nat )
% 15.55/8.59                                      @ Mi
% 15.55/8.59                                      @ ( 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 ) ) ) ) ) ) )
% 15.55/8.59                                    @ Ma ) ) )
% 15.55/8.59                              @ Deg
% 15.55/8.59                              @ Newlist
% 15.55/8.59                              @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6686_del__x__not__mi,axiom,
% 15.55/8.59      ! [Mi: nat,X3: nat,Ma: nat,Deg: nat,H2: nat,L: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 15.55/8.59        ( ( ( ord_less_nat @ Mi @ X3 )
% 15.55/8.59          & ( ord_less_eq_nat @ X3 @ Ma ) )
% 15.55/8.59       => ( ( Mi != Ma )
% 15.55/8.59         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.59           => ( ( ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.59                = H2 )
% 15.55/8.59             => ( ( ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.59                  = L )
% 15.55/8.59               => ( ( Newnode
% 15.55/8.59                    = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 15.55/8.59                 => ( ( Newlist
% 15.55/8.59                      = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 15.55/8.59                   => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.59                     => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 15.55/8.59                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59                            = ( vEBT_Node
% 15.55/8.59                              @ ( some_P7363390416028606310at_nat
% 15.55/8.59                                @ ( product_Pair_nat_nat @ Mi
% 15.55/8.59                                  @ ( if_nat @ ( X3 = Ma )
% 15.55/8.59                                    @ ( if_nat
% 15.55/8.59                                      @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 15.55/8.59                                        = none_nat )
% 15.55/8.59                                      @ Mi
% 15.55/8.59                                      @ ( 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 ) ) ) ) ) ) ) )
% 15.55/8.59                                    @ Ma ) ) )
% 15.55/8.59                              @ Deg
% 15.55/8.59                              @ Newlist
% 15.55/8.59                              @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 15.55/8.59                        & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 15.55/8.59                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6687_del__x__mia,axiom,
% 15.55/8.59      ! [X3: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 15.55/8.59        ( ( ( X3 = Mi )
% 15.55/8.59          & ( ord_less_nat @ X3 @ Ma ) )
% 15.55/8.59       => ( ( Mi != Ma )
% 15.55/8.59         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.59           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59              = ( 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 ) )
% 15.55/8.59                @ ( 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 ) ) ) ) ) )
% 15.55/8.59                  @ ( vEBT_Node
% 15.55/8.59                    @ ( some_P7363390416028606310at_nat
% 15.55/8.59                      @ ( 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 ) ) ) ) ) )
% 15.55/8.59                        @ ( if_nat
% 15.55/8.59                          @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_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 ) ) ) ) ) )
% 15.55/8.59                            = Ma )
% 15.55/8.59                          @ ( if_nat
% 15.55/8.59                            @ ( ( 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 ) ) ) ) ) )
% 15.55/8.59                              = none_nat )
% 15.55/8.59                            @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_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 ) ) ) ) ) )
% 15.55/8.59                            @ ( 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 ) ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.59                          @ Ma ) ) )
% 15.55/8.59                    @ Deg
% 15.55/8.59                    @ ( 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 ) ) ) ) ) )
% 15.55/8.59                    @ ( 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 ) ) ) ) ) )
% 15.55/8.59                  @ ( vEBT_Node
% 15.55/8.59                    @ ( some_P7363390416028606310at_nat
% 15.55/8.59                      @ ( 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 ) ) ) ) ) )
% 15.55/8.59                        @ ( if_nat
% 15.55/8.59                          @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_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 ) ) ) ) ) )
% 15.55/8.59                            = Ma )
% 15.55/8.59                          @ ( 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 ) ) ) ) ) ) ) )
% 15.55/8.59                          @ Ma ) ) )
% 15.55/8.59                    @ Deg
% 15.55/8.59                    @ ( 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 ) ) ) ) ) )
% 15.55/8.59                    @ Summary ) )
% 15.55/8.59                @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6688_del__x__mi__lets__in__minNull,axiom,
% 15.55/8.59      ! [X3: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT,Sn: vEBT_VEBT] :
% 15.55/8.59        ( ( ( X3 = Mi )
% 15.55/8.59          & ( ord_less_nat @ X3 @ Ma ) )
% 15.55/8.59       => ( ( Mi != Ma )
% 15.55/8.59         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.59           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.59                = H2 )
% 15.55/8.59             => ( ( Xn
% 15.55/8.59                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_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 ) ) ) ) ) ) )
% 15.55/8.59               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.59                    = L )
% 15.55/8.59                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.59                   => ( ( Newnode
% 15.55/8.59                        = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 15.55/8.59                     => ( ( Newlist
% 15.55/8.59                          = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 15.55/8.59                       => ( ( vEBT_VEBT_minNull @ Newnode )
% 15.55/8.59                         => ( ( Sn
% 15.55/8.59                              = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 15.55/8.59                           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59                              = ( vEBT_Node
% 15.55/8.59                                @ ( some_P7363390416028606310at_nat
% 15.55/8.59                                  @ ( product_Pair_nat_nat @ Xn
% 15.55/8.59                                    @ ( if_nat @ ( Xn = Ma )
% 15.55/8.59                                      @ ( if_nat
% 15.55/8.59                                        @ ( ( vEBT_vebt_maxt @ Sn )
% 15.55/8.59                                          = none_nat )
% 15.55/8.59                                        @ Xn
% 15.55/8.59                                        @ ( 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 ) ) ) ) ) ) )
% 15.55/8.59                                      @ Ma ) ) )
% 15.55/8.59                                @ Deg
% 15.55/8.59                                @ Newlist
% 15.55/8.59                                @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6689_del__x__mi__lets__in,axiom,
% 15.55/8.59      ! [X3: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 15.55/8.59        ( ( ( X3 = Mi )
% 15.55/8.59          & ( ord_less_nat @ X3 @ Ma ) )
% 15.55/8.59       => ( ( Mi != Ma )
% 15.55/8.59         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.59           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.59                = H2 )
% 15.55/8.59             => ( ( Xn
% 15.55/8.59                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_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 ) ) ) ) ) ) )
% 15.55/8.59               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.59                    = L )
% 15.55/8.59                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.59                   => ( ( Newnode
% 15.55/8.59                        = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 15.55/8.59                     => ( ( Newlist
% 15.55/8.59                          = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 15.55/8.59                       => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 15.55/8.59                           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59                              = ( vEBT_Node
% 15.55/8.59                                @ ( some_P7363390416028606310at_nat
% 15.55/8.59                                  @ ( product_Pair_nat_nat @ Xn
% 15.55/8.59                                    @ ( if_nat @ ( Xn = Ma )
% 15.55/8.59                                      @ ( if_nat
% 15.55/8.59                                        @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 15.55/8.59                                          = none_nat )
% 15.55/8.59                                        @ Xn
% 15.55/8.59                                        @ ( 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 ) ) ) ) ) ) ) )
% 15.55/8.59                                      @ Ma ) ) )
% 15.55/8.59                                @ Deg
% 15.55/8.59                                @ Newlist
% 15.55/8.59                                @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 15.55/8.59                          & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 15.55/8.59                           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59                              = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6690_del__x__mi,axiom,
% 15.55/8.59      ! [X3: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat] :
% 15.55/8.59        ( ( ( X3 = Mi )
% 15.55/8.59          & ( ord_less_nat @ X3 @ Ma ) )
% 15.55/8.59       => ( ( Mi != Ma )
% 15.55/8.59         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.59           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.59                = H2 )
% 15.55/8.59             => ( ( Xn
% 15.55/8.59                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_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 ) ) ) ) ) ) )
% 15.55/8.59               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.59                    = L )
% 15.55/8.59                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.59                   => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59                      = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 15.55/8.59                        @ ( vEBT_Node
% 15.55/8.59                          @ ( some_P7363390416028606310at_nat
% 15.55/8.59                            @ ( product_Pair_nat_nat @ Xn
% 15.55/8.59                              @ ( if_nat @ ( Xn = Ma )
% 15.55/8.59                                @ ( if_nat
% 15.55/8.59                                  @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 15.55/8.59                                    = none_nat )
% 15.55/8.59                                  @ Xn
% 15.55/8.59                                  @ ( 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 ) @ L ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 15.55/8.59                                @ Ma ) ) )
% 15.55/8.59                          @ Deg
% 15.55/8.59                          @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 15.55/8.59                          @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 15.55/8.59                        @ ( 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 ) @ L ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) ) @ Summary ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6691_del__in__range,axiom,
% 15.55/8.59      ! [Mi: nat,X3: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 15.55/8.59        ( ( ( ord_less_eq_nat @ Mi @ X3 )
% 15.55/8.59          & ( ord_less_eq_nat @ X3 @ Ma ) )
% 15.55/8.59       => ( ( Mi != Ma )
% 15.55/8.59         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 15.55/8.59           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59              = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.59                @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                  @ ( vEBT_Node
% 15.55/8.59                    @ ( some_P7363390416028606310at_nat
% 15.55/8.59                      @ ( product_Pair_nat_nat @ ( if_nat @ ( X3 = Mi ) @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ Mi )
% 15.55/8.59                        @ ( if_nat
% 15.55/8.59                          @ ( ( ( X3 = Mi )
% 15.55/8.59                             => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_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 ) ) ) ) ) )
% 15.55/8.59                                = Ma ) )
% 15.55/8.59                            & ( ( X3 != Mi )
% 15.55/8.59                             => ( X3 = Ma ) ) )
% 15.55/8.59                          @ ( if_nat
% 15.55/8.59                            @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                              = none_nat )
% 15.55/8.59                            @ ( if_nat @ ( X3 = Mi ) @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ Mi )
% 15.55/8.59                            @ ( 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 @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( 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 @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.59                          @ Ma ) ) )
% 15.55/8.59                    @ Deg
% 15.55/8.59                    @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                    @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                  @ ( vEBT_Node
% 15.55/8.59                    @ ( some_P7363390416028606310at_nat
% 15.55/8.59                      @ ( product_Pair_nat_nat @ ( if_nat @ ( X3 = Mi ) @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ Mi )
% 15.55/8.59                        @ ( if_nat
% 15.55/8.59                          @ ( ( ( X3 = Mi )
% 15.55/8.59                             => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_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 ) ) ) ) ) )
% 15.55/8.59                                = Ma ) )
% 15.55/8.59                            & ( ( X3 != Mi )
% 15.55/8.59                             => ( X3 = Ma ) ) )
% 15.55/8.59                          @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( 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 @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.59                          @ Ma ) ) )
% 15.55/8.59                    @ Deg
% 15.55/8.59                    @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                    @ Summary ) )
% 15.55/8.59                @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6692_max__def__raw,axiom,
% 15.55/8.59      ( ord_ma741700101516333627d_enat
% 15.55/8.59      = ( ^ [A4: extended_enat,B3: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6693_max__def__raw,axiom,
% 15.55/8.59      ( ord_max_Code_integer
% 15.55/8.59      = ( ^ [A4: code_integer,B3: code_integer] : ( if_Code_integer @ ( ord_le3102999989581377725nteger @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6694_max__def__raw,axiom,
% 15.55/8.59      ( ord_max_set_nat
% 15.55/8.59      = ( ^ [A4: set_nat,B3: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6695_max__def__raw,axiom,
% 15.55/8.59      ( ord_max_rat
% 15.55/8.59      = ( ^ [A4: rat,B3: rat] : ( if_rat @ ( ord_less_eq_rat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6696_max__def__raw,axiom,
% 15.55/8.59      ( ord_max_num
% 15.55/8.59      = ( ^ [A4: num,B3: num] : ( if_num @ ( ord_less_eq_num @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6697_max__def__raw,axiom,
% 15.55/8.59      ( ord_max_nat
% 15.55/8.59      = ( ^ [A4: nat,B3: nat] : ( if_nat @ ( ord_less_eq_nat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6698_max__def__raw,axiom,
% 15.55/8.59      ( ord_max_int
% 15.55/8.59      = ( ^ [A4: int,B3: int] : ( if_int @ ( ord_less_eq_int @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6699_lambda__zero,axiom,
% 15.55/8.59      ( ( ^ [H: real] : zero_zero_real )
% 15.55/8.59      = ( times_times_real @ zero_zero_real ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6700_lambda__zero,axiom,
% 15.55/8.59      ( ( ^ [H: rat] : zero_zero_rat )
% 15.55/8.59      = ( times_times_rat @ zero_zero_rat ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6701_lambda__zero,axiom,
% 15.55/8.59      ( ( ^ [H: nat] : zero_zero_nat )
% 15.55/8.59      = ( times_times_nat @ zero_zero_nat ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6702_lambda__zero,axiom,
% 15.55/8.59      ( ( ^ [H: int] : zero_zero_int )
% 15.55/8.59      = ( times_times_int @ zero_zero_int ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6703_numeral__code_I2_J,axiom,
% 15.55/8.59      ! [N: num] :
% 15.55/8.59        ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 15.55/8.59        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6704_numeral__code_I2_J,axiom,
% 15.55/8.59      ! [N: num] :
% 15.55/8.59        ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 15.55/8.59        = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6705_numeral__code_I2_J,axiom,
% 15.55/8.59      ! [N: num] :
% 15.55/8.59        ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 15.55/8.59        = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6706_numeral__code_I2_J,axiom,
% 15.55/8.59      ! [N: num] :
% 15.55/8.59        ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 15.55/8.59        = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6707_numeral__code_I2_J,axiom,
% 15.55/8.59      ! [N: num] :
% 15.55/8.59        ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 15.55/8.59        = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6708_nat__less__as__int,axiom,
% 15.55/8.59      ( ord_less_nat
% 15.55/8.59      = ( ^ [A4: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6709_nat__leq__as__int,axiom,
% 15.55/8.59      ( ord_less_eq_nat
% 15.55/8.59      = ( ^ [A4: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6710_numeral__code_I3_J,axiom,
% 15.55/8.59      ! [N: num] :
% 15.55/8.59        ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 15.55/8.59        = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6711_numeral__code_I3_J,axiom,
% 15.55/8.59      ! [N: num] :
% 15.55/8.59        ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 15.55/8.59        = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6712_numeral__code_I3_J,axiom,
% 15.55/8.59      ! [N: num] :
% 15.55/8.59        ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 15.55/8.59        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6713_numeral__code_I3_J,axiom,
% 15.55/8.59      ! [N: num] :
% 15.55/8.59        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 15.55/8.59        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6714_numeral__code_I3_J,axiom,
% 15.55/8.59      ! [N: num] :
% 15.55/8.59        ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 15.55/8.59        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6715_power__numeral__even,axiom,
% 15.55/8.59      ! [Z: complex,W: num] :
% 15.55/8.59        ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 15.55/8.59        = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6716_power__numeral__even,axiom,
% 15.55/8.59      ! [Z: real,W: num] :
% 15.55/8.59        ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 15.55/8.59        = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6717_power__numeral__even,axiom,
% 15.55/8.59      ! [Z: rat,W: num] :
% 15.55/8.59        ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 15.55/8.59        = ( times_times_rat @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6718_power__numeral__even,axiom,
% 15.55/8.59      ! [Z: nat,W: num] :
% 15.55/8.59        ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 15.55/8.59        = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6719_power__numeral__even,axiom,
% 15.55/8.59      ! [Z: int,W: num] :
% 15.55/8.59        ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 15.55/8.59        = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6720_power__numeral__odd,axiom,
% 15.55/8.59      ! [Z: complex,W: num] :
% 15.55/8.59        ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 15.55/8.59        = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6721_power__numeral__odd,axiom,
% 15.55/8.59      ! [Z: real,W: num] :
% 15.55/8.59        ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 15.55/8.59        = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6722_power__numeral__odd,axiom,
% 15.55/8.59      ! [Z: rat,W: num] :
% 15.55/8.59        ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 15.55/8.59        = ( times_times_rat @ ( times_times_rat @ Z @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6723_power__numeral__odd,axiom,
% 15.55/8.59      ! [Z: nat,W: num] :
% 15.55/8.59        ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 15.55/8.59        = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6724_power__numeral__odd,axiom,
% 15.55/8.59      ! [Z: int,W: num] :
% 15.55/8.59        ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 15.55/8.59        = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6725_nat__plus__as__int,axiom,
% 15.55/8.59      ( plus_plus_nat
% 15.55/8.59      = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6726_nat__times__as__int,axiom,
% 15.55/8.59      ( times_times_nat
% 15.55/8.59      = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6727_nat__minus__as__int,axiom,
% 15.55/8.59      ( minus_minus_nat
% 15.55/8.59      = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6728_nat__div__as__int,axiom,
% 15.55/8.59      ( divide_divide_nat
% 15.55/8.59      = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6729_nat__mod__as__int,axiom,
% 15.55/8.59      ( modulo_modulo_nat
% 15.55/8.59      = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6730_diff__nat__eq__if,axiom,
% 15.55/8.59      ! [Z5: int,Z: int] :
% 15.55/8.59        ( ( ( ord_less_int @ Z5 @ zero_zero_int )
% 15.55/8.59         => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z5 ) )
% 15.55/8.59            = ( nat2 @ Z ) ) )
% 15.55/8.59        & ( ~ ( ord_less_int @ Z5 @ zero_zero_int )
% 15.55/8.59         => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z5 ) )
% 15.55/8.59            = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z5 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z5 ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6731_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I2_J,axiom,
% 15.55/8.59      ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 15.55/8.59        ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S ) @ X3 )
% 15.55/8.59        = one_one_nat ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6732_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I3_J,axiom,
% 15.55/8.59      ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 15.55/8.59        ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ X3 )
% 15.55/8.59        = one_one_nat ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6733_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I1_J,axiom,
% 15.55/8.59      ! [A: $o,B: $o,X3: nat] :
% 15.55/8.59        ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 15.55/8.59        = ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( X3 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6734_vebt__member_Osimps_I5_J,axiom,
% 15.55/8.59      ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 15.55/8.59        ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59        = ( ( X3 != Mi )
% 15.55/8.59         => ( ( X3 != Ma )
% 15.55/8.59           => ( ~ ( ord_less_nat @ X3 @ Mi )
% 15.55/8.59              & ( ~ ( ord_less_nat @ X3 @ Mi )
% 15.55/8.59               => ( ~ ( ord_less_nat @ Ma @ X3 )
% 15.55/8.59                  & ( ~ ( ord_less_nat @ Ma @ X3 )
% 15.55/8.59                   => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.59                       => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                      & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6735_vebt__member_Oelims_I2_J,axiom,
% 15.55/8.59      ! [X3: vEBT_VEBT,Xa: nat] :
% 15.55/8.59        ( ( vEBT_vebt_member @ X3 @ Xa )
% 15.55/8.59       => ( ! [A5: $o,B4: $o] :
% 15.55/8.59              ( ( X3
% 15.55/8.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.59             => ~ ( ( ( Xa = zero_zero_nat )
% 15.55/8.59                   => A5 )
% 15.55/8.59                  & ( ( Xa != zero_zero_nat )
% 15.55/8.59                   => ( ( ( Xa = one_one_nat )
% 15.55/8.59                       => B4 )
% 15.55/8.59                      & ( Xa = one_one_nat ) ) ) ) )
% 15.55/8.59         => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT] :
% 15.55/8.59                ( ? [Summary2: vEBT_VEBT] :
% 15.55/8.59                    ( X3
% 15.55/8.59                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.59               => ~ ( ( Xa != Mi2 )
% 15.55/8.59                   => ( ( Xa != Ma2 )
% 15.55/8.59                     => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.59                        & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.59                         => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 15.55/8.59                            & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 15.55/8.59                             => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.59                                 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                                & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6736_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I5_J,axiom,
% 15.55/8.59      ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 15.55/8.59        ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X3 = Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( X3 = Ma ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma @ X3 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6737_vebt__member_Oelims_I1_J,axiom,
% 15.55/8.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: $o] :
% 15.55/8.59        ( ( ( vEBT_vebt_member @ X3 @ Xa )
% 15.55/8.59          = Y3 )
% 15.55/8.59       => ( ! [A5: $o,B4: $o] :
% 15.55/8.59              ( ( X3
% 15.55/8.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.59             => ( Y3
% 15.55/8.59                = ( ~ ( ( ( Xa = zero_zero_nat )
% 15.55/8.59                       => A5 )
% 15.55/8.59                      & ( ( Xa != zero_zero_nat )
% 15.55/8.59                       => ( ( ( Xa = one_one_nat )
% 15.55/8.59                           => B4 )
% 15.55/8.59                          & ( Xa = one_one_nat ) ) ) ) ) ) )
% 15.55/8.59         => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 15.55/8.59                  ( X3
% 15.55/8.59                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 15.55/8.59             => Y3 )
% 15.55/8.59           => ( ( ? [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 15.55/8.59                    ( X3
% 15.55/8.59                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 15.55/8.59               => Y3 )
% 15.55/8.59             => ( ( ? [V3: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 15.55/8.59                      ( X3
% 15.55/8.59                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) )
% 15.55/8.59                 => Y3 )
% 15.55/8.59               => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT] :
% 15.55/8.59                      ( ? [Summary2: vEBT_VEBT] :
% 15.55/8.59                          ( X3
% 15.55/8.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.59                     => ( Y3
% 15.55/8.59                        = ( ~ ( ( Xa != Mi2 )
% 15.55/8.59                             => ( ( Xa != Ma2 )
% 15.55/8.59                               => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.59                                  & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.59                                   => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 15.55/8.59                                      & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 15.55/8.59                                       => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.59                                           => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6738_vebt__member_Oelims_I3_J,axiom,
% 15.55/8.59      ! [X3: vEBT_VEBT,Xa: nat] :
% 15.55/8.59        ( ~ ( vEBT_vebt_member @ X3 @ Xa )
% 15.55/8.59       => ( ! [A5: $o,B4: $o] :
% 15.55/8.59              ( ( X3
% 15.55/8.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.59             => ( ( ( Xa = zero_zero_nat )
% 15.55/8.59                 => A5 )
% 15.55/8.59                & ( ( Xa != zero_zero_nat )
% 15.55/8.59                 => ( ( ( Xa = one_one_nat )
% 15.55/8.59                     => B4 )
% 15.55/8.59                    & ( Xa = one_one_nat ) ) ) ) )
% 15.55/8.59         => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 15.55/8.59                ( X3
% 15.55/8.59               != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 15.55/8.59           => ( ! [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 15.55/8.59                  ( X3
% 15.55/8.59                 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 15.55/8.59             => ( ! [V3: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 15.55/8.59                    ( X3
% 15.55/8.59                   != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) )
% 15.55/8.59               => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT] :
% 15.55/8.59                      ( ? [Summary2: vEBT_VEBT] :
% 15.55/8.59                          ( X3
% 15.55/8.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.59                     => ( ( Xa != Mi2 )
% 15.55/8.59                       => ( ( Xa != Ma2 )
% 15.55/8.59                         => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.59                            & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.59                             => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 15.55/8.59                                & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 15.55/8.59                                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.59                                     => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6739_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I4_J,axiom,
% 15.55/8.59      ! [V: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 15.55/8.59        ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59        = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6740_insersimp,axiom,
% 15.55/8.59      ! [T: vEBT_VEBT,N: nat,Y3: nat] :
% 15.55/8.59        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.59       => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 )
% 15.55/8.59         => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ Y3 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6741_insertsimp,axiom,
% 15.55/8.59      ! [T: vEBT_VEBT,N: nat,L: nat] :
% 15.55/8.59        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.59       => ( ( vEBT_VEBT_minNull @ T )
% 15.55/8.59         => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ L ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6742_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Oelims,axiom,
% 15.55/8.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 15.55/8.59        ( ( ( vEBT_T_m_e_m_b_e_r @ X3 @ Xa )
% 15.55/8.59          = Y3 )
% 15.55/8.59       => ( ( ? [A5: $o,B4: $o] :
% 15.55/8.59                ( X3
% 15.55/8.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.59           => ( Y3
% 15.55/8.59             != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 15.55/8.59         => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 15.55/8.59                  ( X3
% 15.55/8.59                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 15.55/8.59             => ( Y3
% 15.55/8.59               != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.59           => ( ( ? [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 15.55/8.59                    ( X3
% 15.55/8.59                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 15.55/8.59               => ( Y3
% 15.55/8.59                 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.59             => ( ( ? [V3: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 15.55/8.59                      ( X3
% 15.55/8.59                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) )
% 15.55/8.59                 => ( Y3
% 15.55/8.59                   != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.59               => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT] :
% 15.55/8.59                      ( ? [Summary2: vEBT_VEBT] :
% 15.55/8.59                          ( X3
% 15.55/8.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.59                     => ( Y3
% 15.55/8.59                       != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa = Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6743_vebt__succ_Osimps_I6_J,axiom,
% 15.55/8.59      ! [X3: nat,Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 15.55/8.59        ( ( ( ord_less_nat @ X3 @ Mi )
% 15.55/8.59         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59            = ( some_nat @ Mi ) ) )
% 15.55/8.59        & ( ~ ( ord_less_nat @ X3 @ Mi )
% 15.55/8.59         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.59              @ ( if_option_nat
% 15.55/8.59                @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                   != none_nat )
% 15.55/8.59                  & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.59                @ ( 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 @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                @ ( if_option_nat
% 15.55/8.59                  @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.59                    = none_nat )
% 15.55/8.59                  @ none_nat
% 15.55/8.59                  @ ( 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 @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.59              @ none_nat ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6744_vebt__pred_Osimps_I7_J,axiom,
% 15.55/8.59      ! [Ma: nat,X3: nat,Mi: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 15.55/8.59        ( ( ( ord_less_nat @ Ma @ X3 )
% 15.55/8.59         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59            = ( some_nat @ Ma ) ) )
% 15.55/8.59        & ( ~ ( ord_less_nat @ Ma @ X3 )
% 15.55/8.59         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.59              @ ( if_option_nat
% 15.55/8.59                @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                   != none_nat )
% 15.55/8.59                  & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.59                @ ( 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 @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                @ ( if_option_nat
% 15.55/8.59                  @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.59                    = none_nat )
% 15.55/8.59                  @ ( if_option_nat @ ( ord_less_nat @ Mi @ X3 ) @ ( some_nat @ Mi ) @ none_nat )
% 15.55/8.59                  @ ( 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 @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.59              @ none_nat ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6745_vebt__delete_Osimps_I7_J,axiom,
% 15.55/8.59      ! [X3: nat,Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 15.55/8.59        ( ( ( ( ord_less_nat @ X3 @ Mi )
% 15.55/8.59            | ( ord_less_nat @ Ma @ X3 ) )
% 15.55/8.59         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) ) )
% 15.55/8.59        & ( ~ ( ( ord_less_nat @ X3 @ Mi )
% 15.55/8.59              | ( ord_less_nat @ Ma @ X3 ) )
% 15.55/8.59         => ( ( ( ( X3 = Mi )
% 15.55/8.59                & ( X3 = Ma ) )
% 15.55/8.59             => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59                = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) ) )
% 15.55/8.59            & ( ~ ( ( X3 = Mi )
% 15.55/8.59                  & ( X3 = Ma ) )
% 15.55/8.59             => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59                = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.59                  @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                    @ ( vEBT_Node
% 15.55/8.59                      @ ( some_P7363390416028606310at_nat
% 15.55/8.59                        @ ( product_Pair_nat_nat @ ( if_nat @ ( X3 = Mi ) @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ Mi )
% 15.55/8.59                          @ ( if_nat
% 15.55/8.59                            @ ( ( ( X3 = Mi )
% 15.55/8.59                               => ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 15.55/8.59                                  = Ma ) )
% 15.55/8.59                              & ( ( X3 != Mi )
% 15.55/8.59                               => ( X3 = Ma ) ) )
% 15.55/8.59                            @ ( if_nat
% 15.55/8.59                              @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                                = none_nat )
% 15.55/8.59                              @ ( if_nat @ ( X3 = Mi ) @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ Mi )
% 15.55/8.59                              @ ( 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 @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.59                            @ Ma ) ) )
% 15.55/8.59                      @ ( suc @ ( suc @ Va2 ) )
% 15.55/8.59                      @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                      @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                    @ ( vEBT_Node
% 15.55/8.59                      @ ( some_P7363390416028606310at_nat
% 15.55/8.59                        @ ( product_Pair_nat_nat @ ( if_nat @ ( X3 = Mi ) @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ Mi )
% 15.55/8.59                          @ ( if_nat
% 15.55/8.59                            @ ( ( ( X3 = Mi )
% 15.55/8.59                               => ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 15.55/8.59                                  = Ma ) )
% 15.55/8.59                              & ( ( X3 != Mi )
% 15.55/8.59                               => ( X3 = Ma ) ) )
% 15.55/8.59                            @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.59                            @ Ma ) ) )
% 15.55/8.59                      @ ( suc @ ( suc @ Va2 ) )
% 15.55/8.59                      @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                      @ Summary ) )
% 15.55/8.59                  @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6746_vebt__delete_Oelims,axiom,
% 15.55/8.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: vEBT_VEBT] :
% 15.55/8.59        ( ( ( vEBT_vebt_delete @ X3 @ Xa )
% 15.55/8.59          = Y3 )
% 15.55/8.59       => ( ! [A5: $o,B4: $o] :
% 15.55/8.59              ( ( X3
% 15.55/8.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.59             => ( ( Xa = zero_zero_nat )
% 15.55/8.59               => ( Y3
% 15.55/8.59                 != ( vEBT_Leaf @ $false @ B4 ) ) ) )
% 15.55/8.59         => ( ! [A5: $o] :
% 15.55/8.59                ( ? [B4: $o] :
% 15.55/8.59                    ( X3
% 15.55/8.59                    = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.59               => ( ( Xa
% 15.55/8.59                    = ( suc @ zero_zero_nat ) )
% 15.55/8.59                 => ( Y3
% 15.55/8.59                   != ( vEBT_Leaf @ A5 @ $false ) ) ) )
% 15.55/8.59           => ( ! [A5: $o,B4: $o] :
% 15.55/8.59                  ( ( X3
% 15.55/8.59                    = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.59                 => ( ? [N2: nat] :
% 15.55/8.59                        ( Xa
% 15.55/8.59                        = ( suc @ ( suc @ N2 ) ) )
% 15.55/8.59                   => ( Y3
% 15.55/8.59                     != ( vEBT_Leaf @ A5 @ B4 ) ) ) )
% 15.55/8.59             => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.59                    ( ( X3
% 15.55/8.59                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 15.55/8.59                   => ( Y3
% 15.55/8.59                     != ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) ) )
% 15.55/8.59               => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 15.55/8.59                      ( ( X3
% 15.55/8.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 15.55/8.59                     => ( Y3
% 15.55/8.59                       != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) ) )
% 15.55/8.59                 => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 15.55/8.59                        ( ( X3
% 15.55/8.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 15.55/8.59                       => ( Y3
% 15.55/8.59                         != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) ) )
% 15.55/8.59                   => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.59                          ( ( X3
% 15.55/8.59                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.59                         => ~ ( ( ( ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.59                                  | ( ord_less_nat @ Ma2 @ Xa ) )
% 15.55/8.59                               => ( Y3
% 15.55/8.59                                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) )
% 15.55/8.59                              & ( ~ ( ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.59                                    | ( ord_less_nat @ Ma2 @ Xa ) )
% 15.55/8.59                               => ( ( ( ( Xa = Mi2 )
% 15.55/8.59                                      & ( Xa = Ma2 ) )
% 15.55/8.59                                   => ( Y3
% 15.55/8.59                                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) )
% 15.55/8.59                                  & ( ~ ( ( Xa = Mi2 )
% 15.55/8.59                                        & ( Xa = Ma2 ) )
% 15.55/8.59                                   => ( Y3
% 15.55/8.59                                      = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.59                                        @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                                          @ ( vEBT_Node
% 15.55/8.59                                            @ ( some_P7363390416028606310at_nat
% 15.55/8.59                                              @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa = Mi2 ) @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ Mi2 )
% 15.55/8.59                                                @ ( if_nat
% 15.55/8.59                                                  @ ( ( ( Xa = Mi2 )
% 15.55/8.59                                                     => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 15.55/8.59                                                        = Ma2 ) )
% 15.55/8.59                                                    & ( ( Xa != Mi2 )
% 15.55/8.59                                                     => ( Xa = Ma2 ) ) )
% 15.55/8.59                                                  @ ( if_nat
% 15.55/8.59                                                    @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                                                      = none_nat )
% 15.55/8.59                                                    @ ( if_nat @ ( Xa = Mi2 ) @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ Mi2 )
% 15.55/8.59                                                    @ ( 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 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.59                                                  @ Ma2 ) ) )
% 15.55/8.59                                            @ ( suc @ ( suc @ Va ) )
% 15.55/8.59                                            @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                                            @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                                          @ ( vEBT_Node
% 15.55/8.59                                            @ ( some_P7363390416028606310at_nat
% 15.55/8.59                                              @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa = Mi2 ) @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ Mi2 )
% 15.55/8.59                                                @ ( if_nat
% 15.55/8.59                                                  @ ( ( ( Xa = Mi2 )
% 15.55/8.59                                                     => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 15.55/8.59                                                        = Ma2 ) )
% 15.55/8.59                                                    & ( ( Xa != Mi2 )
% 15.55/8.59                                                     => ( Xa = Ma2 ) ) )
% 15.55/8.59                                                  @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( 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 @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.59                                                  @ Ma2 ) ) )
% 15.55/8.59                                            @ ( suc @ ( suc @ Va ) )
% 15.55/8.59                                            @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                                            @ Summary2 ) )
% 15.55/8.59                                        @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6747_vebt__succ_Oelims,axiom,
% 15.55/8.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: option_nat] :
% 15.55/8.59        ( ( ( vEBT_vebt_succ @ X3 @ Xa )
% 15.55/8.59          = Y3 )
% 15.55/8.59       => ( ! [Uu: $o,B4: $o] :
% 15.55/8.59              ( ( X3
% 15.55/8.59                = ( vEBT_Leaf @ Uu @ B4 ) )
% 15.55/8.59             => ( ( Xa = zero_zero_nat )
% 15.55/8.59               => ~ ( ( B4
% 15.55/8.59                     => ( Y3
% 15.55/8.59                        = ( some_nat @ one_one_nat ) ) )
% 15.55/8.59                    & ( ~ B4
% 15.55/8.59                     => ( Y3 = none_nat ) ) ) ) )
% 15.55/8.59         => ( ( ? [Uv: $o,Uw: $o] :
% 15.55/8.59                  ( X3
% 15.55/8.59                  = ( vEBT_Leaf @ Uv @ Uw ) )
% 15.55/8.59             => ( ? [N2: nat] :
% 15.55/8.59                    ( Xa
% 15.55/8.59                    = ( suc @ N2 ) )
% 15.55/8.59               => ( Y3 != none_nat ) ) )
% 15.55/8.59           => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 15.55/8.59                    ( X3
% 15.55/8.59                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 15.55/8.59               => ( Y3 != none_nat ) )
% 15.55/8.59             => ( ( ? [V3: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 15.55/8.59                      ( X3
% 15.55/8.59                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 15.55/8.59                 => ( Y3 != none_nat ) )
% 15.55/8.59               => ( ( ? [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 15.55/8.59                        ( X3
% 15.55/8.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 15.55/8.59                   => ( Y3 != none_nat ) )
% 15.55/8.59                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.59                        ( ( X3
% 15.55/8.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.59                       => ~ ( ( ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.59                             => ( Y3
% 15.55/8.59                                = ( some_nat @ Mi2 ) ) )
% 15.55/8.59                            & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.59                             => ( Y3
% 15.55/8.59                                = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.59                                  @ ( if_option_nat
% 15.55/8.59                                    @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                                       != none_nat )
% 15.55/8.59                                      & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.59                                    @ ( 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 @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                                    @ ( if_option_nat
% 15.55/8.59                                      @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.59                                        = none_nat )
% 15.55/8.59                                      @ none_nat
% 15.55/8.59                                      @ ( 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 @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.59                                  @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6748_vebt__pred_Oelims,axiom,
% 15.55/8.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: option_nat] :
% 15.55/8.59        ( ( ( vEBT_vebt_pred @ X3 @ Xa )
% 15.55/8.59          = Y3 )
% 15.55/8.59       => ( ( ? [Uu: $o,Uv: $o] :
% 15.55/8.59                ( X3
% 15.55/8.59                = ( vEBT_Leaf @ Uu @ Uv ) )
% 15.55/8.59           => ( ( Xa = zero_zero_nat )
% 15.55/8.59             => ( Y3 != none_nat ) ) )
% 15.55/8.59         => ( ! [A5: $o] :
% 15.55/8.59                ( ? [Uw: $o] :
% 15.55/8.59                    ( X3
% 15.55/8.59                    = ( vEBT_Leaf @ A5 @ Uw ) )
% 15.55/8.59               => ( ( Xa
% 15.55/8.59                    = ( suc @ zero_zero_nat ) )
% 15.55/8.59                 => ~ ( ( A5
% 15.55/8.59                       => ( Y3
% 15.55/8.59                          = ( some_nat @ zero_zero_nat ) ) )
% 15.55/8.59                      & ( ~ A5
% 15.55/8.59                       => ( Y3 = none_nat ) ) ) ) )
% 15.55/8.59           => ( ! [A5: $o,B4: $o] :
% 15.55/8.59                  ( ( X3
% 15.55/8.59                    = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.59                 => ( ? [Va: nat] :
% 15.55/8.59                        ( Xa
% 15.55/8.59                        = ( suc @ ( suc @ Va ) ) )
% 15.55/8.59                   => ~ ( ( B4
% 15.55/8.59                         => ( Y3
% 15.55/8.59                            = ( some_nat @ one_one_nat ) ) )
% 15.55/8.59                        & ( ~ B4
% 15.55/8.59                         => ( ( A5
% 15.55/8.59                             => ( Y3
% 15.55/8.59                                = ( some_nat @ zero_zero_nat ) ) )
% 15.55/8.59                            & ( ~ A5
% 15.55/8.59                             => ( Y3 = none_nat ) ) ) ) ) ) )
% 15.55/8.59             => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 15.55/8.59                      ( X3
% 15.55/8.59                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 15.55/8.59                 => ( Y3 != none_nat ) )
% 15.55/8.59               => ( ( ? [V3: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 15.55/8.59                        ( X3
% 15.55/8.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 15.55/8.59                   => ( Y3 != none_nat ) )
% 15.55/8.59                 => ( ( ? [V3: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 15.55/8.59                          ( X3
% 15.55/8.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 15.55/8.59                     => ( Y3 != none_nat ) )
% 15.55/8.59                   => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.59                          ( ( X3
% 15.55/8.59                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.59                         => ~ ( ( ( ord_less_nat @ Ma2 @ Xa )
% 15.55/8.59                               => ( Y3
% 15.55/8.59                                  = ( some_nat @ Ma2 ) ) )
% 15.55/8.59                              & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 15.55/8.59                               => ( Y3
% 15.55/8.59                                  = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.59                                    @ ( if_option_nat
% 15.55/8.59                                      @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                                         != none_nat )
% 15.55/8.59                                        & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.59                                      @ ( 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 @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                                      @ ( if_option_nat
% 15.55/8.59                                        @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.59                                          = none_nat )
% 15.55/8.59                                        @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa ) @ ( some_nat @ Mi2 ) @ none_nat )
% 15.55/8.59                                        @ ( 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 @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.59                                    @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6749_insert__bound__height,axiom,
% 15.55/8.59      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.59        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.59       => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ X3 ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6750_vebt__insert_Oelims,axiom,
% 15.55/8.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: vEBT_VEBT] :
% 15.55/8.59        ( ( ( vEBT_vebt_insert @ X3 @ Xa )
% 15.55/8.59          = Y3 )
% 15.55/8.59       => ( ! [A5: $o,B4: $o] :
% 15.55/8.59              ( ( X3
% 15.55/8.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.59             => ~ ( ( ( Xa = zero_zero_nat )
% 15.55/8.59                   => ( Y3
% 15.55/8.59                      = ( vEBT_Leaf @ $true @ B4 ) ) )
% 15.55/8.59                  & ( ( Xa != zero_zero_nat )
% 15.55/8.59                   => ( ( ( Xa = one_one_nat )
% 15.55/8.59                       => ( Y3
% 15.55/8.59                          = ( vEBT_Leaf @ A5 @ $true ) ) )
% 15.55/8.59                      & ( ( Xa != one_one_nat )
% 15.55/8.59                       => ( Y3
% 15.55/8.59                          = ( vEBT_Leaf @ A5 @ B4 ) ) ) ) ) ) )
% 15.55/8.59         => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 15.55/8.59                ( ( X3
% 15.55/8.59                  = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 15.55/8.59               => ( Y3
% 15.55/8.59                 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) ) )
% 15.55/8.59           => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 15.55/8.59                  ( ( X3
% 15.55/8.59                    = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 15.55/8.59                 => ( Y3
% 15.55/8.59                   != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) ) )
% 15.55/8.59             => ( ! [V3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.59                    ( ( X3
% 15.55/8.59                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.59                   => ( Y3
% 15.55/8.59                     != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa @ Xa ) ) @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) ) )
% 15.55/8.59               => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.59                      ( ( X3
% 15.55/8.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.59                     => ( Y3
% 15.55/8.59                       != ( if_VEBT_VEBT
% 15.55/8.59                          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.59                            & ~ ( ( Xa = Mi2 )
% 15.55/8.59                                | ( Xa = Ma2 ) ) )
% 15.55/8.59                          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Xa @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 15.55/8.59                          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6751_vebt__insert_Osimps_I5_J,axiom,
% 15.55/8.59      ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 15.55/8.59        ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59        = ( if_VEBT_VEBT
% 15.55/8.59          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.59            & ~ ( ( X3 = Mi )
% 15.55/8.59                | ( X3 = Ma ) ) )
% 15.55/8.59          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ X3 @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ Ma ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 15.55/8.59          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6752_of__int__code__if,axiom,
% 15.55/8.59      ( ring_1_of_int_real
% 15.55/8.59      = ( ^ [K3: int] :
% 15.55/8.59            ( if_real @ ( K3 = zero_zero_int ) @ zero_zero_real
% 15.55/8.59            @ ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K3 ) ) )
% 15.55/8.59              @ ( if_real
% 15.55/8.59                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.59                  = zero_zero_int )
% 15.55/8.59                @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 15.55/8.59                @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6753_of__int__code__if,axiom,
% 15.55/8.59      ( ring_1_of_int_int
% 15.55/8.59      = ( ^ [K3: int] :
% 15.55/8.59            ( if_int @ ( K3 = zero_zero_int ) @ zero_zero_int
% 15.55/8.59            @ ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K3 ) ) )
% 15.55/8.59              @ ( if_int
% 15.55/8.59                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.59                  = zero_zero_int )
% 15.55/8.59                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 15.55/8.59                @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_int ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6754_of__int__code__if,axiom,
% 15.55/8.59      ( ring_17405671764205052669omplex
% 15.55/8.59      = ( ^ [K3: int] :
% 15.55/8.59            ( if_complex @ ( K3 = zero_zero_int ) @ zero_zero_complex
% 15.55/8.59            @ ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K3 ) ) )
% 15.55/8.59              @ ( if_complex
% 15.55/8.59                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.59                  = zero_zero_int )
% 15.55/8.59                @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 15.55/8.59                @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6755_of__int__code__if,axiom,
% 15.55/8.59      ( ring_18347121197199848620nteger
% 15.55/8.59      = ( ^ [K3: int] :
% 15.55/8.59            ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 15.55/8.59            @ ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K3 ) ) )
% 15.55/8.59              @ ( if_Code_integer
% 15.55/8.59                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.59                  = zero_zero_int )
% 15.55/8.59                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 15.55/8.59                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6756_of__int__code__if,axiom,
% 15.55/8.59      ( ring_1_of_int_rat
% 15.55/8.59      = ( ^ [K3: int] :
% 15.55/8.59            ( if_rat @ ( K3 = zero_zero_int ) @ zero_zero_rat
% 15.55/8.59            @ ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K3 ) ) )
% 15.55/8.59              @ ( if_rat
% 15.55/8.59                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.59                  = zero_zero_int )
% 15.55/8.59                @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 15.55/8.59                @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_rat ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6757_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Oelims,axiom,
% 15.55/8.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 15.55/8.59        ( ( ( vEBT_T_s_u_c_c2 @ X3 @ Xa )
% 15.55/8.59          = Y3 )
% 15.55/8.59       => ( ( ? [Uu: $o,B4: $o] :
% 15.55/8.59                ( X3
% 15.55/8.59                = ( vEBT_Leaf @ Uu @ B4 ) )
% 15.55/8.59           => ( ( Xa = zero_zero_nat )
% 15.55/8.59             => ( Y3 != one_one_nat ) ) )
% 15.55/8.59         => ( ( ? [Uv: $o,Uw: $o] :
% 15.55/8.59                  ( X3
% 15.55/8.59                  = ( vEBT_Leaf @ Uv @ Uw ) )
% 15.55/8.59             => ( ? [N2: nat] :
% 15.55/8.59                    ( Xa
% 15.55/8.59                    = ( suc @ N2 ) )
% 15.55/8.59               => ( Y3 != one_one_nat ) ) )
% 15.55/8.59           => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 15.55/8.59                    ( X3
% 15.55/8.59                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 15.55/8.59               => ( Y3 != one_one_nat ) )
% 15.55/8.59             => ( ( ? [V3: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 15.55/8.59                      ( X3
% 15.55/8.59                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 15.55/8.59                 => ( Y3 != one_one_nat ) )
% 15.55/8.59               => ( ( ? [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 15.55/8.59                        ( X3
% 15.55/8.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 15.55/8.59                   => ( Y3 != one_one_nat ) )
% 15.55/8.59                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.59                        ( ( X3
% 15.55/8.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.59                       => ~ ( ( ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.59                             => ( Y3 = one_one_nat ) )
% 15.55/8.59                            & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.59                             => ( Y3
% 15.55/8.59                                = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.59                                  @ ( if_nat
% 15.55/8.59                                    @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                                       != none_nat )
% 15.55/8.59                                      & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.59                                    @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                                    @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 15.55/8.59                                  @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6758_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Oelims,axiom,
% 15.55/8.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 15.55/8.59        ( ( ( vEBT_T_p_r_e_d2 @ X3 @ Xa )
% 15.55/8.59          = Y3 )
% 15.55/8.59       => ( ( ? [Uu: $o,Uv: $o] :
% 15.55/8.59                ( X3
% 15.55/8.59                = ( vEBT_Leaf @ Uu @ Uv ) )
% 15.55/8.59           => ( ( Xa = zero_zero_nat )
% 15.55/8.59             => ( Y3 != one_one_nat ) ) )
% 15.55/8.59         => ( ( ? [A5: $o,Uw: $o] :
% 15.55/8.59                  ( X3
% 15.55/8.59                  = ( vEBT_Leaf @ A5 @ Uw ) )
% 15.55/8.59             => ( ( Xa
% 15.55/8.59                  = ( suc @ zero_zero_nat ) )
% 15.55/8.59               => ( Y3 != one_one_nat ) ) )
% 15.55/8.59           => ( ( ? [A5: $o,B4: $o] :
% 15.55/8.59                    ( X3
% 15.55/8.59                    = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.59               => ( ? [Va: nat] :
% 15.55/8.59                      ( Xa
% 15.55/8.59                      = ( suc @ ( suc @ Va ) ) )
% 15.55/8.59                 => ( Y3 != one_one_nat ) ) )
% 15.55/8.59             => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 15.55/8.59                      ( X3
% 15.55/8.59                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 15.55/8.59                 => ( Y3 != one_one_nat ) )
% 15.55/8.59               => ( ( ? [V3: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 15.55/8.59                        ( X3
% 15.55/8.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 15.55/8.59                   => ( Y3 != one_one_nat ) )
% 15.55/8.59                 => ( ( ? [V3: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 15.55/8.59                          ( X3
% 15.55/8.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 15.55/8.59                     => ( Y3 != one_one_nat ) )
% 15.55/8.59                   => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.59                          ( ( X3
% 15.55/8.59                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.59                         => ~ ( ( ( ord_less_nat @ Ma2 @ Xa )
% 15.55/8.59                               => ( Y3 = one_one_nat ) )
% 15.55/8.59                              & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 15.55/8.59                               => ( Y3
% 15.55/8.59                                  = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.59                                    @ ( if_nat
% 15.55/8.59                                      @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                                         != none_nat )
% 15.55/8.59                                        & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.59                                      @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                                      @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 15.55/8.59                                    @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6759_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I1_J,axiom,
% 15.55/8.59      ! [Uu2: $o,Uv2: $o] :
% 15.55/8.59        ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat )
% 15.55/8.59        = one_one_nat ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6760_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I1_J,axiom,
% 15.55/8.59      ! [Uu2: $o,B: $o] :
% 15.55/8.59        ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Leaf @ Uu2 @ B ) @ zero_zero_nat )
% 15.55/8.59        = one_one_nat ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6761_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I2_J,axiom,
% 15.55/8.59      ! [A: $o,Uw2: $o] :
% 15.55/8.59        ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 15.55/8.59        = one_one_nat ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6762_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I5_J,axiom,
% 15.55/8.59      ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 15.55/8.59        ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf )
% 15.55/8.59        = one_one_nat ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6763_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I4_J,axiom,
% 15.55/8.59      ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 15.55/8.59        ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve )
% 15.55/8.59        = one_one_nat ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6764_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I6_J,axiom,
% 15.55/8.59      ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 15.55/8.59        ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj )
% 15.55/8.59        = one_one_nat ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6765_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I5_J,axiom,
% 15.55/8.59      ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 15.55/8.59        ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi )
% 15.55/8.59        = one_one_nat ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6766_pred__bound__height_H,axiom,
% 15.55/8.59      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.59        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.59       => ( ord_less_eq_nat @ ( vEBT_T_p_r_e_d2 @ T @ X3 ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6767_succ_H__bound__height,axiom,
% 15.55/8.59      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.59        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.59       => ( ord_less_eq_nat @ ( vEBT_T_s_u_c_c2 @ T @ X3 ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6768_vebt__insert_Osimps_I2_J,axiom,
% 15.55/8.59      ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 15.55/8.59        ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S ) @ X3 )
% 15.55/8.59        = ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6769_pred__bound__size__univ_H,axiom,
% 15.55/8.59      ! [T: vEBT_VEBT,N: nat,U: real,X3: nat] :
% 15.55/8.59        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.59       => ( ( U
% 15.55/8.59            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.59         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_p_r_e_d2 @ T @ X3 ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6770_succ__bound__size__univ_H,axiom,
% 15.55/8.59      ! [T: vEBT_VEBT,N: nat,U: real,X3: nat] :
% 15.55/8.59        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.59       => ( ( U
% 15.55/8.59            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 15.55/8.59         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_s_u_c_c2 @ T @ X3 ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6771_vebt__insert_Osimps_I3_J,axiom,
% 15.55/8.59      ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 15.55/8.59        ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ X3 )
% 15.55/8.59        = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6772_vebt__insert_Osimps_I1_J,axiom,
% 15.55/8.59      ! [X3: nat,A: $o,B: $o] :
% 15.55/8.59        ( ( ( X3 = zero_zero_nat )
% 15.55/8.59         => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 15.55/8.59            = ( vEBT_Leaf @ $true @ B ) ) )
% 15.55/8.59        & ( ( X3 != zero_zero_nat )
% 15.55/8.59         => ( ( ( X3 = one_one_nat )
% 15.55/8.59             => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 15.55/8.59                = ( vEBT_Leaf @ A @ $true ) ) )
% 15.55/8.59            & ( ( X3 != one_one_nat )
% 15.55/8.59             => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 15.55/8.59                = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6773_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I7_J,axiom,
% 15.55/8.59      ! [Ma: nat,X3: nat,Mi: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 15.55/8.59        ( ( ( ord_less_nat @ Ma @ X3 )
% 15.55/8.59         => ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59            = one_one_nat ) )
% 15.55/8.59        & ( ~ ( ord_less_nat @ Ma @ X3 )
% 15.55/8.59         => ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59            = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.59              @ ( if_nat
% 15.55/8.59                @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                   != none_nat )
% 15.55/8.59                  & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.59                @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 15.55/8.59              @ one_one_nat ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6774_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I6_J,axiom,
% 15.55/8.59      ! [X3: nat,Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 15.55/8.59        ( ( ( ord_less_nat @ X3 @ Mi )
% 15.55/8.59         => ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59            = one_one_nat ) )
% 15.55/8.59        & ( ~ ( ord_less_nat @ X3 @ Mi )
% 15.55/8.59         => ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59            = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.59              @ ( if_nat
% 15.55/8.59                @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                   != none_nat )
% 15.55/8.59                  & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.59                @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 15.55/8.59              @ one_one_nat ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6775_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Oelims,axiom,
% 15.55/8.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 15.55/8.59        ( ( ( vEBT_T_i_n_s_e_r_t @ X3 @ Xa )
% 15.55/8.59          = Y3 )
% 15.55/8.59       => ( ( ? [A5: $o,B4: $o] :
% 15.55/8.59                ( X3
% 15.55/8.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.59           => ( Y3
% 15.55/8.59             != ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 15.55/8.59         => ( ( ? [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 15.55/8.59                  ( X3
% 15.55/8.59                  = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 15.55/8.59             => ( Y3 != one_one_nat ) )
% 15.55/8.59           => ( ( ? [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 15.55/8.59                    ( X3
% 15.55/8.59                    = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 15.55/8.59               => ( Y3 != one_one_nat ) )
% 15.55/8.59             => ( ( ? [V3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.59                      ( X3
% 15.55/8.59                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.59                 => ( Y3
% 15.55/8.59                   != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.59               => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.59                      ( ( X3
% 15.55/8.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.59                     => ( Y3
% 15.55/8.59                       != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 15.55/8.59                          @ ( if_nat
% 15.55/8.59                            @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.59                              & ~ ( ( Xa = Mi2 )
% 15.55/8.59                                  | ( Xa = Ma2 ) ) )
% 15.55/8.59                            @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 15.55/8.59                            @ one_one_nat ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6776_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Oelims,axiom,
% 15.55/8.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 15.55/8.59        ( ( ( vEBT_T_m_e_m_b_e_r2 @ X3 @ Xa )
% 15.55/8.59          = Y3 )
% 15.55/8.59       => ( ( ? [A5: $o,B4: $o] :
% 15.55/8.59                ( X3
% 15.55/8.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.59           => ( Y3 != one_one_nat ) )
% 15.55/8.59         => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 15.55/8.59                  ( X3
% 15.55/8.59                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 15.55/8.59             => ( Y3 != one_one_nat ) )
% 15.55/8.59           => ( ( ? [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 15.55/8.59                    ( X3
% 15.55/8.59                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 15.55/8.59               => ( Y3 != one_one_nat ) )
% 15.55/8.59             => ( ( ? [V3: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 15.55/8.59                      ( X3
% 15.55/8.59                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) )
% 15.55/8.59                 => ( Y3 != one_one_nat ) )
% 15.55/8.59               => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT] :
% 15.55/8.59                      ( ? [Summary2: vEBT_VEBT] :
% 15.55/8.59                          ( X3
% 15.55/8.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.59                     => ( Y3
% 15.55/8.59                       != ( plus_plus_nat @ one_one_nat
% 15.55/8.59                          @ ( if_nat @ ( Xa = Mi2 ) @ zero_zero_nat
% 15.55/8.59                            @ ( if_nat @ ( Xa = Ma2 ) @ zero_zero_nat
% 15.55/8.59                              @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ zero_zero_nat
% 15.55/8.59                                @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa ) @ zero_zero_nat
% 15.55/8.59                                  @ ( if_nat
% 15.55/8.59                                    @ ( ( ord_less_nat @ Mi2 @ Xa )
% 15.55/8.59                                      & ( ord_less_nat @ Xa @ Ma2 ) )
% 15.55/8.59                                    @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 15.55/8.59                                    @ zero_zero_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6777_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I5_J,axiom,
% 15.55/8.59      ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 15.55/8.59        ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 15.55/8.59          @ ( if_nat
% 15.55/8.59            @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.59              & ~ ( ( X3 = Mi )
% 15.55/8.59                  | ( X3 = Ma ) ) )
% 15.55/8.59            @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 15.55/8.59            @ one_one_nat ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6778_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Oelims,axiom,
% 15.55/8.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 15.55/8.59        ( ( ( vEBT_T_i_n_s_e_r_t2 @ X3 @ Xa )
% 15.55/8.59          = Y3 )
% 15.55/8.59       => ( ( ? [A5: $o,B4: $o] :
% 15.55/8.59                ( X3
% 15.55/8.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.59           => ( Y3 != one_one_nat ) )
% 15.55/8.59         => ( ( ? [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 15.55/8.59                  ( X3
% 15.55/8.59                  = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 15.55/8.59             => ( Y3 != one_one_nat ) )
% 15.55/8.59           => ( ( ? [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 15.55/8.59                    ( X3
% 15.55/8.59                    = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 15.55/8.59               => ( Y3 != one_one_nat ) )
% 15.55/8.59             => ( ( ? [V3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.59                      ( X3
% 15.55/8.59                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.59                 => ( Y3 != one_one_nat ) )
% 15.55/8.59               => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.59                      ( ( X3
% 15.55/8.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.59                     => ( Y3
% 15.55/8.59                       != ( if_nat
% 15.55/8.59                          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.59                            & ~ ( ( Xa = Mi2 )
% 15.55/8.59                                | ( Xa = Ma2 ) ) )
% 15.55/8.59                          @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 15.55/8.59                          @ one_one_nat ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6779_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I5_J,axiom,
% 15.55/8.59      ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 15.55/8.59        ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59        = ( plus_plus_nat @ one_one_nat
% 15.55/8.59          @ ( if_nat @ ( X3 = Mi ) @ zero_zero_nat
% 15.55/8.59            @ ( if_nat @ ( X3 = Ma ) @ zero_zero_nat
% 15.55/8.59              @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ zero_zero_nat
% 15.55/8.59                @ ( if_nat @ ( ord_less_nat @ Ma @ X3 ) @ zero_zero_nat
% 15.55/8.59                  @ ( if_nat
% 15.55/8.59                    @ ( ( ord_less_nat @ Mi @ X3 )
% 15.55/8.59                      & ( ord_less_nat @ X3 @ Ma ) )
% 15.55/8.59                    @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 15.55/8.59                    @ zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6780_minNull__bound,axiom,
% 15.55/8.59      ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_i_n_N_u_l_l @ T ) @ one_one_nat ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6781_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I2_J,axiom,
% 15.55/8.59      ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 15.55/8.59        ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S ) @ X3 )
% 15.55/8.59        = one_one_nat ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6782_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I3_J,axiom,
% 15.55/8.59      ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 15.55/8.59        ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ X3 )
% 15.55/8.59        = one_one_nat ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6783_insersimp_H,axiom,
% 15.55/8.59      ! [T: vEBT_VEBT,N: nat,Y3: nat] :
% 15.55/8.59        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.59       => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 )
% 15.55/8.59         => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ Y3 ) @ one_one_nat ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6784_insertsimp_H,axiom,
% 15.55/8.59      ! [T: vEBT_VEBT,N: nat,L: nat] :
% 15.55/8.59        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.59       => ( ( vEBT_VEBT_minNull @ T )
% 15.55/8.59         => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ L ) @ one_one_nat ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6785_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I3_J,axiom,
% 15.55/8.59      ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X3: nat] :
% 15.55/8.59        ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X3 )
% 15.55/8.59        = one_one_nat ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6786_insert_H__bound__height,axiom,
% 15.55/8.59      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.59        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.59       => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ X3 ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6787_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I4_J,axiom,
% 15.55/8.59      ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc: vEBT_VEBT,X3: nat] :
% 15.55/8.59        ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc ) @ X3 )
% 15.55/8.59        = one_one_nat ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6788_member__bound__height_H,axiom,
% 15.55/8.59      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.59        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.59       => ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r2 @ T @ X3 ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6789_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I5_J,axiom,
% 15.55/8.59      ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 15.55/8.59        ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.59        = ( if_nat
% 15.55/8.59          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.59            & ~ ( ( X3 = Mi )
% 15.55/8.59                | ( X3 = Ma ) ) )
% 15.55/8.59          @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 15.55/8.59          @ one_one_nat ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6790_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Oelims,axiom,
% 15.55/8.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 15.55/8.59        ( ( ( vEBT_T_d_e_l_e_t_e @ X3 @ Xa )
% 15.55/8.59          = Y3 )
% 15.55/8.59       => ( ( ? [A5: $o,B4: $o] :
% 15.55/8.59                ( X3
% 15.55/8.59                = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.59           => ( ( Xa = zero_zero_nat )
% 15.55/8.59             => ( Y3 != one_one_nat ) ) )
% 15.55/8.59         => ( ( ? [A5: $o,B4: $o] :
% 15.55/8.59                  ( X3
% 15.55/8.59                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.59             => ( ( Xa
% 15.55/8.59                  = ( suc @ zero_zero_nat ) )
% 15.55/8.59               => ( Y3 != one_one_nat ) ) )
% 15.55/8.59           => ( ( ? [A5: $o,B4: $o] :
% 15.55/8.59                    ( X3
% 15.55/8.59                    = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.59               => ( ? [N2: nat] :
% 15.55/8.59                      ( Xa
% 15.55/8.59                      = ( suc @ ( suc @ N2 ) ) )
% 15.55/8.59                 => ( Y3 != one_one_nat ) ) )
% 15.55/8.59             => ( ( ? [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.59                      ( X3
% 15.55/8.59                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 15.55/8.59                 => ( Y3 != one_one_nat ) )
% 15.55/8.59               => ( ( ? [Mi2: nat,Ma2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.59                        ( X3
% 15.55/8.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList3 @ Summary2 ) )
% 15.55/8.59                   => ( Y3 != one_one_nat ) )
% 15.55/8.59                 => ( ( ? [Mi2: nat,Ma2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.59                          ( X3
% 15.55/8.59                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList3 @ Summary2 ) )
% 15.55/8.59                     => ( Y3 != one_one_nat ) )
% 15.55/8.59                   => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.59                          ( ( X3
% 15.55/8.59                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.59                         => ( Y3
% 15.55/8.59                           != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 15.55/8.59                              @ ( if_nat
% 15.55/8.59                                @ ( ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.59                                  | ( ord_less_nat @ Ma2 @ Xa ) )
% 15.55/8.59                                @ one_one_nat
% 15.55/8.59                                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 15.55/8.59                                  @ ( if_nat
% 15.55/8.59                                    @ ( ( Xa = Mi2 )
% 15.55/8.59                                      & ( Xa = Ma2 ) )
% 15.55/8.59                                    @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 15.55/8.59                                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ Summary2 ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 15.55/8.59                                      @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.59                                        @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                                          @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 15.55/8.59                                            @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                                              @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                                                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 15.55/8.59                                                  @ ( if_nat
% 15.55/8.59                                                    @ ( ( ( Xa = Mi2 )
% 15.55/8.59                                                       => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 15.55/8.59                                                          = Ma2 ) )
% 15.55/8.59                                                      & ( ( Xa != Mi2 )
% 15.55/8.59                                                       => ( Xa = Ma2 ) ) )
% 15.55/8.59                                                    @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 15.55/8.59                                                      @ ( plus_plus_nat @ one_one_nat
% 15.55/8.59                                                        @ ( if_nat
% 15.55/8.59                                                          @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                                                            = none_nat )
% 15.55/8.59                                                          @ one_one_nat
% 15.55/8.59                                                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.59                                                    @ one_one_nat ) ) )
% 15.55/8.59                                              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 15.55/8.59                                                @ ( if_nat
% 15.55/8.59                                                  @ ( ( ( Xa = Mi2 )
% 15.55/8.59                                                     => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 15.55/8.59                                                        = Ma2 ) )
% 15.55/8.59                                                    & ( ( Xa != Mi2 )
% 15.55/8.59                                                     => ( Xa = Ma2 ) ) )
% 15.55/8.59                                                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 15.55/8.59                                                  @ one_one_nat ) ) ) ) )
% 15.55/8.59                                        @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6791_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 15.55/8.59      ! [X3: vEBT_VEBT,Xa: nat,Y3: $o] :
% 15.55/8.59        ( ( ( vEBT_VEBT_membermima @ X3 @ Xa )
% 15.55/8.59          = Y3 )
% 15.55/8.59       => ( ( ? [Uu: $o,Uv: $o] :
% 15.55/8.59                ( X3
% 15.55/8.59                = ( vEBT_Leaf @ Uu @ Uv ) )
% 15.55/8.59           => Y3 )
% 15.55/8.59         => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 15.55/8.59                  ( X3
% 15.55/8.59                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 15.55/8.59             => Y3 )
% 15.55/8.59           => ( ! [Mi2: nat,Ma2: nat] :
% 15.55/8.59                  ( ? [Va3: list_VEBT_VEBT,Vb: vEBT_VEBT] :
% 15.55/8.59                      ( X3
% 15.55/8.59                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb ) )
% 15.55/8.59                 => ( Y3
% 15.55/8.59                    = ( ~ ( ( Xa = Mi2 )
% 15.55/8.59                          | ( Xa = Ma2 ) ) ) ) )
% 15.55/8.59             => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList3: list_VEBT_VEBT] :
% 15.55/8.59                    ( ? [Vc2: vEBT_VEBT] :
% 15.55/8.59                        ( X3
% 15.55/8.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) )
% 15.55/8.59                   => ( Y3
% 15.55/8.59                      = ( ~ ( ( Xa = Mi2 )
% 15.55/8.59                            | ( Xa = Ma2 )
% 15.55/8.59                            | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.59                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) )
% 15.55/8.59               => ~ ! [V3: nat,TreeList3: list_VEBT_VEBT] :
% 15.55/8.59                      ( ? [Vd2: vEBT_VEBT] :
% 15.55/8.59                          ( X3
% 15.55/8.59                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) )
% 15.55/8.59                     => ( Y3
% 15.55/8.59                        = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.59                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.59  
% 15.55/8.59  thf(fact_6792_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 15.55/8.59      ! [X3: vEBT_VEBT,Xa: nat] :
% 15.55/8.59        ( ~ ( vEBT_VEBT_membermima @ X3 @ Xa )
% 15.55/8.59       => ( ! [Uu: $o,Uv: $o] :
% 15.55/8.59              ( X3
% 15.55/8.59             != ( vEBT_Leaf @ Uu @ Uv ) )
% 15.55/8.59         => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 15.55/8.59                ( X3
% 15.55/8.59               != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 15.55/8.59           => ( ! [Mi2: nat,Ma2: nat] :
% 15.55/8.59                  ( ? [Va3: list_VEBT_VEBT,Vb: vEBT_VEBT] :
% 15.55/8.59                      ( X3
% 15.55/8.59                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb ) )
% 15.55/8.59                 => ( ( Xa = Mi2 )
% 15.55/8.59                    | ( Xa = Ma2 ) ) )
% 15.55/8.59             => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList3: list_VEBT_VEBT] :
% 15.55/8.59                    ( ? [Vc2: vEBT_VEBT] :
% 15.55/8.59                        ( X3
% 15.55/8.59                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) )
% 15.55/8.59                   => ( ( Xa = Mi2 )
% 15.55/8.59                      | ( Xa = Ma2 )
% 15.55/8.59                      | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.59                         => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.59                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 15.55/8.59               => ~ ! [V3: nat,TreeList3: list_VEBT_VEBT] :
% 15.55/8.59                      ( ? [Vd2: vEBT_VEBT] :
% 15.55/8.59                          ( X3
% 15.55/8.59                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) )
% 15.55/8.59                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.59                         => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6793_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: $o] :
% 15.55/8.60        ( ( ( vEBT_V5719532721284313246member @ X3 @ Xa )
% 15.55/8.60          = Y3 )
% 15.55/8.60       => ( ! [A5: $o,B4: $o] :
% 15.55/8.60              ( ( X3
% 15.55/8.60                = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60             => ( Y3
% 15.55/8.60                = ( ~ ( ( ( Xa = zero_zero_nat )
% 15.55/8.60                       => A5 )
% 15.55/8.60                      & ( ( Xa != zero_zero_nat )
% 15.55/8.60                       => ( ( ( Xa = one_one_nat )
% 15.55/8.60                           => B4 )
% 15.55/8.60                          & ( Xa = one_one_nat ) ) ) ) ) ) )
% 15.55/8.60         => ( ( ? [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 15.55/8.60                  ( X3
% 15.55/8.60                  = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 15.55/8.60             => Y3 )
% 15.55/8.60           => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList3: list_VEBT_VEBT] :
% 15.55/8.60                  ( ? [S3: vEBT_VEBT] :
% 15.55/8.60                      ( X3
% 15.55/8.60                      = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) )
% 15.55/8.60                 => ( Y3
% 15.55/8.60                    = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6794_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat] :
% 15.55/8.60        ( ( vEBT_V5719532721284313246member @ X3 @ Xa )
% 15.55/8.60       => ( ! [A5: $o,B4: $o] :
% 15.55/8.60              ( ( X3
% 15.55/8.60                = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60             => ~ ( ( ( Xa = zero_zero_nat )
% 15.55/8.60                   => A5 )
% 15.55/8.60                  & ( ( Xa != zero_zero_nat )
% 15.55/8.60                   => ( ( ( Xa = one_one_nat )
% 15.55/8.60                       => B4 )
% 15.55/8.60                      & ( Xa = one_one_nat ) ) ) ) )
% 15.55/8.60         => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList3: list_VEBT_VEBT] :
% 15.55/8.60                ( ? [S3: vEBT_VEBT] :
% 15.55/8.60                    ( X3
% 15.55/8.60                    = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) )
% 15.55/8.60               => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                     => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6795_buildup__nothing__in__min__max,axiom,
% 15.55/8.60      ! [N: nat,X3: nat] :
% 15.55/8.60        ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X3 ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6796_buildup__nothing__in__leaf,axiom,
% 15.55/8.60      ! [N: nat,X3: nat] :
% 15.55/8.60        ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X3 ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6797_both__member__options__def,axiom,
% 15.55/8.60      ( vEBT_V8194947554948674370ptions
% 15.55/8.60      = ( ^ [T2: vEBT_VEBT,X: nat] :
% 15.55/8.60            ( ( vEBT_V5719532721284313246member @ T2 @ X )
% 15.55/8.60            | ( vEBT_VEBT_membermima @ T2 @ X ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6798_member__valid__both__member__options,axiom,
% 15.55/8.60      ! [Tree: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.60        ( ( vEBT_invar_vebt @ Tree @ N )
% 15.55/8.60       => ( ( vEBT_vebt_member @ Tree @ X3 )
% 15.55/8.60         => ( ( vEBT_V5719532721284313246member @ Tree @ X3 )
% 15.55/8.60            | ( vEBT_VEBT_membermima @ Tree @ X3 ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6799_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 15.55/8.60      ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux: nat] :
% 15.55/8.60        ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6800_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 15.55/8.60      ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 15.55/8.60        ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6801_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 15.55/8.60      ! [A: $o,B: $o,X3: nat] :
% 15.55/8.60        ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 15.55/8.60        = ( ( ( X3 = zero_zero_nat )
% 15.55/8.60           => A )
% 15.55/8.60          & ( ( X3 != zero_zero_nat )
% 15.55/8.60           => ( ( ( X3 = one_one_nat )
% 15.55/8.60               => B )
% 15.55/8.60              & ( X3 = one_one_nat ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6802_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 15.55/8.60      ! [Mi: nat,Ma: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT,X3: nat] :
% 15.55/8.60        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ X3 )
% 15.55/8.60        = ( ( X3 = Mi )
% 15.55/8.60          | ( X3 = Ma ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6803_maxt__bound,axiom,
% 15.55/8.60      ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_a_x_t @ T ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6804_mint__bound,axiom,
% 15.55/8.60      ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_i_n_t @ T ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6805_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I1_J,axiom,
% 15.55/8.60      ! [A: $o,B: $o] :
% 15.55/8.60        ( ( vEBT_T_m_i_n_t @ ( vEBT_Leaf @ A @ B ) )
% 15.55/8.60        = ( plus_plus_nat @ one_one_nat @ ( if_nat @ A @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6806_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Oelims,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Y3: nat] :
% 15.55/8.60        ( ( ( vEBT_T_m_i_n_t @ X3 )
% 15.55/8.60          = Y3 )
% 15.55/8.60       => ( ! [A5: $o] :
% 15.55/8.60              ( ? [B4: $o] :
% 15.55/8.60                  ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60             => ( Y3
% 15.55/8.60               != ( plus_plus_nat @ one_one_nat @ ( if_nat @ A5 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 15.55/8.60         => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 15.55/8.60                  ( X3
% 15.55/8.60                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 15.55/8.60             => ( Y3 != one_one_nat ) )
% 15.55/8.60           => ~ ( ? [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 15.55/8.60                    ( X3
% 15.55/8.60                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 15.55/8.60               => ( Y3 != one_one_nat ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6807_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 15.55/8.60      ! [V: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT,X3: nat] :
% 15.55/8.60        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) @ X3 )
% 15.55/8.60        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.60           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60          & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6808_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 15.55/8.60      ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 15.55/8.60        ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S ) @ X3 )
% 15.55/8.60        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.60           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60          & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6809_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 15.55/8.60      ! [Mi: nat,Ma: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT,X3: nat] :
% 15.55/8.60        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList2 @ Vc ) @ X3 )
% 15.55/8.60        = ( ( X3 = Mi )
% 15.55/8.60          | ( X3 = Ma )
% 15.55/8.60          | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.60             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60            & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6810_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I7_J,axiom,
% 15.55/8.60      ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 15.55/8.60        ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.60        = ( plus_plus_nat @ one_one_nat
% 15.55/8.60          @ ( if_nat @ ( ord_less_nat @ Ma @ X3 ) @ one_one_nat
% 15.55/8.60            @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 15.55/8.60              @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.60                @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 15.55/8.60                  @ ( if_nat
% 15.55/8.60                    @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                       != none_nat )
% 15.55/8.60                      & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.60                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 15.55/8.60                      @ ( if_nat
% 15.55/8.60                        @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.60                          = none_nat )
% 15.55/8.60                        @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 15.55/8.60                        @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.60                @ one_one_nat ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6811_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I6_J,axiom,
% 15.55/8.60      ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 15.55/8.60        ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.60        = ( plus_plus_nat @ one_one_nat
% 15.55/8.60          @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ one_one_nat
% 15.55/8.60            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 15.55/8.60              @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.60                @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 15.55/8.60                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 15.55/8.60                    @ ( if_nat
% 15.55/8.60                      @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                         != none_nat )
% 15.55/8.60                        & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.60                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                      @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 15.55/8.60                        @ ( if_nat
% 15.55/8.60                          @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.60                            = none_nat )
% 15.55/8.60                          @ one_one_nat
% 15.55/8.60                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.60                @ one_one_nat ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6812_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Oelims,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 15.55/8.60        ( ( ( vEBT_T_p_r_e_d @ X3 @ Xa )
% 15.55/8.60          = Y3 )
% 15.55/8.60       => ( ( ? [Uu: $o,Uv: $o] :
% 15.55/8.60                ( X3
% 15.55/8.60                = ( vEBT_Leaf @ Uu @ Uv ) )
% 15.55/8.60           => ( ( Xa = zero_zero_nat )
% 15.55/8.60             => ( Y3 != one_one_nat ) ) )
% 15.55/8.60         => ( ( ? [A5: $o,Uw: $o] :
% 15.55/8.60                  ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ A5 @ Uw ) )
% 15.55/8.60             => ( ( Xa
% 15.55/8.60                  = ( suc @ zero_zero_nat ) )
% 15.55/8.60               => ( Y3
% 15.55/8.60                 != ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 15.55/8.60           => ( ! [A5: $o,B4: $o] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60                 => ( ? [Va: nat] :
% 15.55/8.60                        ( Xa
% 15.55/8.60                        = ( suc @ ( suc @ Va ) ) )
% 15.55/8.60                   => ( Y3
% 15.55/8.60                     != ( plus_plus_nat @ one_one_nat @ ( if_nat @ B4 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ) )
% 15.55/8.60             => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 15.55/8.60                      ( X3
% 15.55/8.60                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 15.55/8.60                 => ( Y3 != one_one_nat ) )
% 15.55/8.60               => ( ( ? [V3: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 15.55/8.60                        ( X3
% 15.55/8.60                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 15.55/8.60                   => ( Y3 != one_one_nat ) )
% 15.55/8.60                 => ( ( ? [V3: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 15.55/8.60                          ( X3
% 15.55/8.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 15.55/8.60                     => ( Y3 != one_one_nat ) )
% 15.55/8.60                   => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                          ( ( X3
% 15.55/8.60                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                         => ( Y3
% 15.55/8.60                           != ( plus_plus_nat @ one_one_nat
% 15.55/8.60                              @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa ) @ one_one_nat
% 15.55/8.60                                @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 15.55/8.60                                  @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 15.55/8.60                                      @ ( if_nat
% 15.55/8.60                                        @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                           != none_nat )
% 15.55/8.60                                          & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.60                                        @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                        @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 15.55/8.60                                          @ ( if_nat
% 15.55/8.60                                            @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.60                                              = none_nat )
% 15.55/8.60                                            @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 15.55/8.60                                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.60                                    @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6813_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Oelims,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 15.55/8.60        ( ( ( vEBT_T_s_u_c_c @ X3 @ Xa )
% 15.55/8.60          = Y3 )
% 15.55/8.60       => ( ( ? [Uu: $o,B4: $o] :
% 15.55/8.60                ( X3
% 15.55/8.60                = ( vEBT_Leaf @ Uu @ B4 ) )
% 15.55/8.60           => ( ( Xa = zero_zero_nat )
% 15.55/8.60             => ( Y3
% 15.55/8.60               != ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 15.55/8.60         => ( ( ? [Uv: $o,Uw: $o] :
% 15.55/8.60                  ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ Uv @ Uw ) )
% 15.55/8.60             => ( ? [N2: nat] :
% 15.55/8.60                    ( Xa
% 15.55/8.60                    = ( suc @ N2 ) )
% 15.55/8.60               => ( Y3 != one_one_nat ) ) )
% 15.55/8.60           => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 15.55/8.60                    ( X3
% 15.55/8.60                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 15.55/8.60               => ( Y3 != one_one_nat ) )
% 15.55/8.60             => ( ( ? [V3: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 15.55/8.60                      ( X3
% 15.55/8.60                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 15.55/8.60                 => ( Y3 != one_one_nat ) )
% 15.55/8.60               => ( ( ? [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 15.55/8.60                        ( X3
% 15.55/8.60                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 15.55/8.60                   => ( Y3 != one_one_nat ) )
% 15.55/8.60                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                        ( ( X3
% 15.55/8.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                       => ( Y3
% 15.55/8.60                         != ( plus_plus_nat @ one_one_nat
% 15.55/8.60                            @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ one_one_nat
% 15.55/8.60                              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 15.55/8.60                                @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                                  @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 15.55/8.60                                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 15.55/8.60                                      @ ( if_nat
% 15.55/8.60                                        @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                           != none_nat )
% 15.55/8.60                                          & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.60                                        @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                        @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 15.55/8.60                                          @ ( if_nat
% 15.55/8.60                                            @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.60                                              = none_nat )
% 15.55/8.60                                            @ one_one_nat
% 15.55/8.60                                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.60                                  @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6814_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat] :
% 15.55/8.60        ( ( vEBT_VEBT_membermima @ X3 @ Xa )
% 15.55/8.60       => ( ! [Mi2: nat,Ma2: nat] :
% 15.55/8.60              ( ? [Va3: list_VEBT_VEBT,Vb: vEBT_VEBT] :
% 15.55/8.60                  ( X3
% 15.55/8.60                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb ) )
% 15.55/8.60             => ~ ( ( Xa = Mi2 )
% 15.55/8.60                  | ( Xa = Ma2 ) ) )
% 15.55/8.60         => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList3: list_VEBT_VEBT] :
% 15.55/8.60                ( ? [Vc2: vEBT_VEBT] :
% 15.55/8.60                    ( X3
% 15.55/8.60                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) )
% 15.55/8.60               => ~ ( ( Xa = Mi2 )
% 15.55/8.60                    | ( Xa = Ma2 )
% 15.55/8.60                    | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                       => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                      & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 15.55/8.60           => ~ ! [V3: nat,TreeList3: list_VEBT_VEBT] :
% 15.55/8.60                  ( ? [Vd2: vEBT_VEBT] :
% 15.55/8.60                      ( X3
% 15.55/8.60                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) )
% 15.55/8.60                 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                       => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                      & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6815_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I7_J,axiom,
% 15.55/8.60      ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 15.55/8.60        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X3 )
% 15.55/8.60        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 15.55/8.60          @ ( if_nat
% 15.55/8.60            @ ( ( ord_less_nat @ X3 @ Mi )
% 15.55/8.60              | ( ord_less_nat @ Ma @ X3 ) )
% 15.55/8.60            @ one_one_nat
% 15.55/8.60            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 15.55/8.60              @ ( if_nat
% 15.55/8.60                @ ( ( X3 = Mi )
% 15.55/8.60                  & ( X3 = Ma ) )
% 15.55/8.60                @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 15.55/8.60                @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( X3 = Mi ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ Summary ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 15.55/8.60                  @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 15.55/8.60                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                      @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 15.55/8.60                        @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                          @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 15.55/8.60                              @ ( if_nat
% 15.55/8.60                                @ ( ( ( X3 = Mi )
% 15.55/8.60                                   => ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 15.55/8.60                                      = Ma ) )
% 15.55/8.60                                  & ( ( X3 != Mi )
% 15.55/8.60                                   => ( X3 = Ma ) ) )
% 15.55/8.60                                @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 15.55/8.60                                  @ ( plus_plus_nat @ one_one_nat
% 15.55/8.60                                    @ ( if_nat
% 15.55/8.60                                      @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                        = none_nat )
% 15.55/8.60                                      @ one_one_nat
% 15.55/8.60                                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.60                                @ one_one_nat ) ) )
% 15.55/8.60                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 15.55/8.60                            @ ( if_nat
% 15.55/8.60                              @ ( ( ( X3 = Mi )
% 15.55/8.60                                 => ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 15.55/8.60                                    = Ma ) )
% 15.55/8.60                                & ( ( X3 != Mi )
% 15.55/8.60                                 => ( X3 = Ma ) ) )
% 15.55/8.60                              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X3 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 15.55/8.60                              @ one_one_nat ) ) ) ) )
% 15.55/8.60                    @ one_one_nat ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6816_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat] :
% 15.55/8.60        ( ~ ( vEBT_V5719532721284313246member @ X3 @ Xa )
% 15.55/8.60       => ( ! [A5: $o,B4: $o] :
% 15.55/8.60              ( ( X3
% 15.55/8.60                = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60             => ( ( ( Xa = zero_zero_nat )
% 15.55/8.60                 => A5 )
% 15.55/8.60                & ( ( Xa != zero_zero_nat )
% 15.55/8.60                 => ( ( ( Xa = one_one_nat )
% 15.55/8.60                     => B4 )
% 15.55/8.60                    & ( Xa = one_one_nat ) ) ) ) )
% 15.55/8.60         => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 15.55/8.60                ( X3
% 15.55/8.60               != ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 15.55/8.60           => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList3: list_VEBT_VEBT] :
% 15.55/8.60                  ( ? [S3: vEBT_VEBT] :
% 15.55/8.60                      ( X3
% 15.55/8.60                      = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) )
% 15.55/8.60                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                     => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6817_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Opelims,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 15.55/8.60        ( ( ( vEBT_T_d_e_l_e_t_e @ X3 @ Xa )
% 15.55/8.60          = Y3 )
% 15.55/8.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.60         => ( ! [A5: $o,B4: $o] :
% 15.55/8.60                ( ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60               => ( ( Xa = zero_zero_nat )
% 15.55/8.60                 => ( ( Y3 = one_one_nat )
% 15.55/8.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ zero_zero_nat ) ) ) ) )
% 15.55/8.60           => ( ! [A5: $o,B4: $o] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60                 => ( ( Xa
% 15.55/8.60                      = ( suc @ zero_zero_nat ) )
% 15.55/8.60                   => ( ( Y3 = one_one_nat )
% 15.55/8.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 15.55/8.60             => ( ! [A5: $o,B4: $o] :
% 15.55/8.60                    ( ( X3
% 15.55/8.60                      = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60                   => ! [N2: nat] :
% 15.55/8.60                        ( ( Xa
% 15.55/8.60                          = ( suc @ ( suc @ N2 ) ) )
% 15.55/8.60                       => ( ( Y3 = one_one_nat )
% 15.55/8.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ ( suc @ ( suc @ N2 ) ) ) ) ) ) )
% 15.55/8.60               => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                      ( ( X3
% 15.55/8.60                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 15.55/8.60                     => ( ( Y3 = one_one_nat )
% 15.55/8.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) @ Xa ) ) ) )
% 15.55/8.60                 => ( ! [Mi2: nat,Ma2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                        ( ( X3
% 15.55/8.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList3 @ Summary2 ) )
% 15.55/8.60                       => ( ( Y3 = one_one_nat )
% 15.55/8.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList3 @ Summary2 ) @ Xa ) ) ) )
% 15.55/8.60                   => ( ! [Mi2: nat,Ma2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                          ( ( X3
% 15.55/8.60                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                         => ( ( Y3 = one_one_nat )
% 15.55/8.60                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) )
% 15.55/8.60                     => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                            ( ( X3
% 15.55/8.60                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                           => ( ( Y3
% 15.55/8.60                                = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 15.55/8.60                                  @ ( if_nat
% 15.55/8.60                                    @ ( ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.60                                      | ( ord_less_nat @ Ma2 @ Xa ) )
% 15.55/8.60                                    @ one_one_nat
% 15.55/8.60                                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 15.55/8.60                                      @ ( if_nat
% 15.55/8.60                                        @ ( ( Xa = Mi2 )
% 15.55/8.60                                          & ( Xa = Ma2 ) )
% 15.55/8.60                                        @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 15.55/8.60                                        @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ Summary2 ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 15.55/8.60                                          @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                                            @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                              @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 15.55/8.60                                                @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                                  @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 15.55/8.60                                                      @ ( if_nat
% 15.55/8.60                                                        @ ( ( ( Xa = Mi2 )
% 15.55/8.60                                                           => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 15.55/8.60                                                              = Ma2 ) )
% 15.55/8.60                                                          & ( ( Xa != Mi2 )
% 15.55/8.60                                                           => ( Xa = Ma2 ) ) )
% 15.55/8.60                                                        @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 15.55/8.60                                                          @ ( plus_plus_nat @ one_one_nat
% 15.55/8.60                                                            @ ( if_nat
% 15.55/8.60                                                              @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                                                = none_nat )
% 15.55/8.60                                                              @ one_one_nat
% 15.55/8.60                                                              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.60                                                        @ one_one_nat ) ) )
% 15.55/8.60                                                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 15.55/8.60                                                    @ ( if_nat
% 15.55/8.60                                                      @ ( ( ( Xa = Mi2 )
% 15.55/8.60                                                         => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 15.55/8.60                                                            = Ma2 ) )
% 15.55/8.60                                                        & ( ( Xa != Mi2 )
% 15.55/8.60                                                         => ( Xa = Ma2 ) ) )
% 15.55/8.60                                                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 15.55/8.60                                                      @ one_one_nat ) ) ) ) )
% 15.55/8.60                                            @ one_one_nat ) ) ) ) ) ) )
% 15.55/8.60                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6818_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Opelims,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 15.55/8.60        ( ( ( vEBT_T_s_u_c_c @ X3 @ Xa )
% 15.55/8.60          = Y3 )
% 15.55/8.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.60         => ( ! [Uu: $o,B4: $o] :
% 15.55/8.60                ( ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ Uu @ B4 ) )
% 15.55/8.60               => ( ( Xa = zero_zero_nat )
% 15.55/8.60                 => ( ( Y3
% 15.55/8.60                      = ( plus_plus_nat @ one_one_nat @ one_one_nat ) )
% 15.55/8.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ B4 ) @ zero_zero_nat ) ) ) ) )
% 15.55/8.60           => ( ! [Uv: $o,Uw: $o] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Leaf @ Uv @ Uw ) )
% 15.55/8.60                 => ! [N2: nat] :
% 15.55/8.60                      ( ( Xa
% 15.55/8.60                        = ( suc @ N2 ) )
% 15.55/8.60                     => ( ( Y3 = one_one_nat )
% 15.55/8.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N2 ) ) ) ) ) )
% 15.55/8.60             => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 15.55/8.60                    ( ( X3
% 15.55/8.60                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 15.55/8.60                   => ( ( Y3 = one_one_nat )
% 15.55/8.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa ) ) ) )
% 15.55/8.60               => ( ! [V3: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 15.55/8.60                      ( ( X3
% 15.55/8.60                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 15.55/8.60                     => ( ( Y3 = one_one_nat )
% 15.55/8.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa ) ) ) )
% 15.55/8.60                 => ( ! [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 15.55/8.60                        ( ( X3
% 15.55/8.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 15.55/8.60                       => ( ( Y3 = one_one_nat )
% 15.55/8.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Xa ) ) ) )
% 15.55/8.60                   => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                          ( ( X3
% 15.55/8.60                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                         => ( ( Y3
% 15.55/8.60                              = ( plus_plus_nat @ one_one_nat
% 15.55/8.60                                @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ one_one_nat
% 15.55/8.60                                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 15.55/8.60                                    @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                                      @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 15.55/8.60                                        @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 15.55/8.60                                          @ ( if_nat
% 15.55/8.60                                            @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                               != none_nat )
% 15.55/8.60                                              & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.60                                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                            @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 15.55/8.60                                              @ ( if_nat
% 15.55/8.60                                                @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.60                                                  = none_nat )
% 15.55/8.60                                                @ one_one_nat
% 15.55/8.60                                                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.60                                      @ one_one_nat ) ) ) ) )
% 15.55/8.60                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6819_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Opelims,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 15.55/8.60        ( ( ( vEBT_T_p_r_e_d @ X3 @ Xa )
% 15.55/8.60          = Y3 )
% 15.55/8.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.60         => ( ! [Uu: $o,Uv: $o] :
% 15.55/8.60                ( ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ Uu @ Uv ) )
% 15.55/8.60               => ( ( Xa = zero_zero_nat )
% 15.55/8.60                 => ( ( Y3 = one_one_nat )
% 15.55/8.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat ) ) ) ) )
% 15.55/8.60           => ( ! [A5: $o,Uw: $o] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Leaf @ A5 @ Uw ) )
% 15.55/8.60                 => ( ( Xa
% 15.55/8.60                      = ( suc @ zero_zero_nat ) )
% 15.55/8.60                   => ( ( Y3
% 15.55/8.60                        = ( plus_plus_nat @ one_one_nat @ one_one_nat ) )
% 15.55/8.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 15.55/8.60             => ( ! [A5: $o,B4: $o] :
% 15.55/8.60                    ( ( X3
% 15.55/8.60                      = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60                   => ! [Va: nat] :
% 15.55/8.60                        ( ( Xa
% 15.55/8.60                          = ( suc @ ( suc @ Va ) ) )
% 15.55/8.60                       => ( ( Y3
% 15.55/8.60                            = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B4 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 15.55/8.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ ( suc @ ( suc @ Va ) ) ) ) ) ) )
% 15.55/8.60               => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 15.55/8.60                      ( ( X3
% 15.55/8.60                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 15.55/8.60                     => ( ( Y3 = one_one_nat )
% 15.55/8.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa ) ) ) )
% 15.55/8.60                 => ( ! [V3: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 15.55/8.60                        ( ( X3
% 15.55/8.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 15.55/8.60                       => ( ( Y3 = one_one_nat )
% 15.55/8.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa ) ) ) )
% 15.55/8.60                   => ( ! [V3: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 15.55/8.60                          ( ( X3
% 15.55/8.60                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 15.55/8.60                         => ( ( Y3 = one_one_nat )
% 15.55/8.60                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Xa ) ) ) )
% 15.55/8.60                     => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                            ( ( X3
% 15.55/8.60                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                           => ( ( Y3
% 15.55/8.60                                = ( plus_plus_nat @ one_one_nat
% 15.55/8.60                                  @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa ) @ one_one_nat
% 15.55/8.60                                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 15.55/8.60                                      @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                                        @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 15.55/8.60                                          @ ( if_nat
% 15.55/8.60                                            @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                               != none_nat )
% 15.55/8.60                                              & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.60                                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                            @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 15.55/8.60                                              @ ( if_nat
% 15.55/8.60                                                @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.60                                                  = none_nat )
% 15.55/8.60                                                @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 15.55/8.60                                                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.60                                        @ one_one_nat ) ) ) ) )
% 15.55/8.60                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6820_pred__empty,axiom,
% 15.55/8.60      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.60        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.60       => ( ( ( vEBT_vebt_pred @ T @ X3 )
% 15.55/8.60            = none_nat )
% 15.55/8.60          = ( ( collect_nat
% 15.55/8.60              @ ^ [Y: nat] :
% 15.55/8.60                  ( ( vEBT_vebt_member @ T @ Y )
% 15.55/8.60                  & ( ord_less_nat @ Y @ X3 ) ) )
% 15.55/8.60            = bot_bot_set_nat ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6821_succ__empty,axiom,
% 15.55/8.60      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.60        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.60       => ( ( ( vEBT_vebt_succ @ T @ X3 )
% 15.55/8.60            = none_nat )
% 15.55/8.60          = ( ( collect_nat
% 15.55/8.60              @ ^ [Y: nat] :
% 15.55/8.60                  ( ( vEBT_vebt_member @ T @ Y )
% 15.55/8.60                  & ( ord_less_nat @ X3 @ Y ) ) )
% 15.55/8.60            = bot_bot_set_nat ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6822_buildup__gives__empty,axiom,
% 15.55/8.60      ! [N: nat] :
% 15.55/8.60        ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 15.55/8.60        = bot_bot_set_nat ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6823_mint__corr__help__empty,axiom,
% 15.55/8.60      ! [T: vEBT_VEBT,N: nat] :
% 15.55/8.60        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.60       => ( ( ( vEBT_vebt_mint @ T )
% 15.55/8.60            = none_nat )
% 15.55/8.60         => ( ( vEBT_VEBT_set_vebt @ T )
% 15.55/8.60            = bot_bot_set_nat ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6824_maxt__corr__help__empty,axiom,
% 15.55/8.60      ! [T: vEBT_VEBT,N: nat] :
% 15.55/8.60        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.60       => ( ( ( vEBT_vebt_maxt @ T )
% 15.55/8.60            = none_nat )
% 15.55/8.60         => ( ( vEBT_VEBT_set_vebt @ T )
% 15.55/8.60            = bot_bot_set_nat ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6825_max__bot,axiom,
% 15.55/8.60      ! [X3: set_Extended_enat] :
% 15.55/8.60        ( ( ord_ma4205026669011143323d_enat @ bot_bo7653980558646680370d_enat @ X3 )
% 15.55/8.60        = X3 ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6826_max__bot,axiom,
% 15.55/8.60      ! [X3: set_real] :
% 15.55/8.60        ( ( ord_max_set_real @ bot_bot_set_real @ X3 )
% 15.55/8.60        = X3 ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6827_max__bot,axiom,
% 15.55/8.60      ! [X3: set_nat] :
% 15.55/8.60        ( ( ord_max_set_nat @ bot_bot_set_nat @ X3 )
% 15.55/8.60        = X3 ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6828_max__bot,axiom,
% 15.55/8.60      ! [X3: set_int] :
% 15.55/8.60        ( ( ord_max_set_int @ bot_bot_set_int @ X3 )
% 15.55/8.60        = X3 ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6829_max__bot,axiom,
% 15.55/8.60      ! [X3: nat] :
% 15.55/8.60        ( ( ord_max_nat @ bot_bot_nat @ X3 )
% 15.55/8.60        = X3 ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6830_max__bot,axiom,
% 15.55/8.60      ! [X3: extended_enat] :
% 15.55/8.60        ( ( ord_ma741700101516333627d_enat @ bot_bo4199563552545308370d_enat @ X3 )
% 15.55/8.60        = X3 ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6831_max__bot2,axiom,
% 15.55/8.60      ! [X3: set_Extended_enat] :
% 15.55/8.60        ( ( ord_ma4205026669011143323d_enat @ X3 @ bot_bo7653980558646680370d_enat )
% 15.55/8.60        = X3 ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6832_max__bot2,axiom,
% 15.55/8.60      ! [X3: set_real] :
% 15.55/8.60        ( ( ord_max_set_real @ X3 @ bot_bot_set_real )
% 15.55/8.60        = X3 ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6833_max__bot2,axiom,
% 15.55/8.60      ! [X3: set_nat] :
% 15.55/8.60        ( ( ord_max_set_nat @ X3 @ bot_bot_set_nat )
% 15.55/8.60        = X3 ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6834_max__bot2,axiom,
% 15.55/8.60      ! [X3: set_int] :
% 15.55/8.60        ( ( ord_max_set_int @ X3 @ bot_bot_set_int )
% 15.55/8.60        = X3 ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6835_max__bot2,axiom,
% 15.55/8.60      ! [X3: nat] :
% 15.55/8.60        ( ( ord_max_nat @ X3 @ bot_bot_nat )
% 15.55/8.60        = X3 ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6836_max__bot2,axiom,
% 15.55/8.60      ! [X3: extended_enat] :
% 15.55/8.60        ( ( ord_ma741700101516333627d_enat @ X3 @ bot_bo4199563552545308370d_enat )
% 15.55/8.60        = X3 ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6837_atLeastatMost__empty__iff,axiom,
% 15.55/8.60      ! [A: extended_enat,B: extended_enat] :
% 15.55/8.60        ( ( ( set_or5403411693681687835d_enat @ A @ B )
% 15.55/8.60          = bot_bo7653980558646680370d_enat )
% 15.55/8.60        = ( ~ ( ord_le2932123472753598470d_enat @ A @ B ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6838_atLeastatMost__empty__iff,axiom,
% 15.55/8.60      ! [A: set_nat,B: set_nat] :
% 15.55/8.60        ( ( ( set_or4548717258645045905et_nat @ A @ B )
% 15.55/8.60          = bot_bot_set_set_nat )
% 15.55/8.60        = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6839_atLeastatMost__empty__iff,axiom,
% 15.55/8.60      ! [A: rat,B: rat] :
% 15.55/8.60        ( ( ( set_or633870826150836451st_rat @ A @ B )
% 15.55/8.60          = bot_bot_set_rat )
% 15.55/8.60        = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6840_atLeastatMost__empty__iff,axiom,
% 15.55/8.60      ! [A: num,B: num] :
% 15.55/8.60        ( ( ( set_or7049704709247886629st_num @ A @ B )
% 15.55/8.60          = bot_bot_set_num )
% 15.55/8.60        = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6841_atLeastatMost__empty__iff,axiom,
% 15.55/8.60      ! [A: nat,B: nat] :
% 15.55/8.60        ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 15.55/8.60          = bot_bot_set_nat )
% 15.55/8.60        = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6842_atLeastatMost__empty__iff,axiom,
% 15.55/8.60      ! [A: int,B: int] :
% 15.55/8.60        ( ( ( set_or1266510415728281911st_int @ A @ B )
% 15.55/8.60          = bot_bot_set_int )
% 15.55/8.60        = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6843_atLeastatMost__empty__iff,axiom,
% 15.55/8.60      ! [A: real,B: real] :
% 15.55/8.60        ( ( ( set_or1222579329274155063t_real @ A @ B )
% 15.55/8.60          = bot_bot_set_real )
% 15.55/8.60        = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6844_atLeastatMost__empty__iff2,axiom,
% 15.55/8.60      ! [A: extended_enat,B: extended_enat] :
% 15.55/8.60        ( ( bot_bo7653980558646680370d_enat
% 15.55/8.60          = ( set_or5403411693681687835d_enat @ A @ B ) )
% 15.55/8.60        = ( ~ ( ord_le2932123472753598470d_enat @ A @ B ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6845_atLeastatMost__empty__iff2,axiom,
% 15.55/8.60      ! [A: set_nat,B: set_nat] :
% 15.55/8.60        ( ( bot_bot_set_set_nat
% 15.55/8.60          = ( set_or4548717258645045905et_nat @ A @ B ) )
% 15.55/8.60        = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6846_atLeastatMost__empty__iff2,axiom,
% 15.55/8.60      ! [A: rat,B: rat] :
% 15.55/8.60        ( ( bot_bot_set_rat
% 15.55/8.60          = ( set_or633870826150836451st_rat @ A @ B ) )
% 15.55/8.60        = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6847_atLeastatMost__empty__iff2,axiom,
% 15.55/8.60      ! [A: num,B: num] :
% 15.55/8.60        ( ( bot_bot_set_num
% 15.55/8.60          = ( set_or7049704709247886629st_num @ A @ B ) )
% 15.55/8.60        = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6848_atLeastatMost__empty__iff2,axiom,
% 15.55/8.60      ! [A: nat,B: nat] :
% 15.55/8.60        ( ( bot_bot_set_nat
% 15.55/8.60          = ( set_or1269000886237332187st_nat @ A @ B ) )
% 15.55/8.60        = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6849_atLeastatMost__empty__iff2,axiom,
% 15.55/8.60      ! [A: int,B: int] :
% 15.55/8.60        ( ( bot_bot_set_int
% 15.55/8.60          = ( set_or1266510415728281911st_int @ A @ B ) )
% 15.55/8.60        = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6850_atLeastatMost__empty__iff2,axiom,
% 15.55/8.60      ! [A: real,B: real] :
% 15.55/8.60        ( ( bot_bot_set_real
% 15.55/8.60          = ( set_or1222579329274155063t_real @ A @ B ) )
% 15.55/8.60        = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6851_atLeastatMost__empty,axiom,
% 15.55/8.60      ! [B: extended_enat,A: extended_enat] :
% 15.55/8.60        ( ( ord_le72135733267957522d_enat @ B @ A )
% 15.55/8.60       => ( ( set_or5403411693681687835d_enat @ A @ B )
% 15.55/8.60          = bot_bo7653980558646680370d_enat ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6852_atLeastatMost__empty,axiom,
% 15.55/8.60      ! [B: rat,A: rat] :
% 15.55/8.60        ( ( ord_less_rat @ B @ A )
% 15.55/8.60       => ( ( set_or633870826150836451st_rat @ A @ B )
% 15.55/8.60          = bot_bot_set_rat ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6853_atLeastatMost__empty,axiom,
% 15.55/8.60      ! [B: num,A: num] :
% 15.55/8.60        ( ( ord_less_num @ B @ A )
% 15.55/8.60       => ( ( set_or7049704709247886629st_num @ A @ B )
% 15.55/8.60          = bot_bot_set_num ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6854_atLeastatMost__empty,axiom,
% 15.55/8.60      ! [B: nat,A: nat] :
% 15.55/8.60        ( ( ord_less_nat @ B @ A )
% 15.55/8.60       => ( ( set_or1269000886237332187st_nat @ A @ B )
% 15.55/8.60          = bot_bot_set_nat ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6855_atLeastatMost__empty,axiom,
% 15.55/8.60      ! [B: int,A: int] :
% 15.55/8.60        ( ( ord_less_int @ B @ A )
% 15.55/8.60       => ( ( set_or1266510415728281911st_int @ A @ B )
% 15.55/8.60          = bot_bot_set_int ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6856_atLeastatMost__empty,axiom,
% 15.55/8.60      ! [B: real,A: real] :
% 15.55/8.60        ( ( ord_less_real @ B @ A )
% 15.55/8.60       => ( ( set_or1222579329274155063t_real @ A @ B )
% 15.55/8.60          = bot_bot_set_real ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6857_bot_Oextremum,axiom,
% 15.55/8.60      ! [A: set_Extended_enat] : ( ord_le7203529160286727270d_enat @ bot_bo7653980558646680370d_enat @ A ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6858_bot_Oextremum,axiom,
% 15.55/8.60      ! [A: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6859_bot_Oextremum,axiom,
% 15.55/8.60      ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6860_bot_Oextremum,axiom,
% 15.55/8.60      ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6861_bot_Oextremum,axiom,
% 15.55/8.60      ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6862_bot_Oextremum__unique,axiom,
% 15.55/8.60      ! [A: set_Extended_enat] :
% 15.55/8.60        ( ( ord_le7203529160286727270d_enat @ A @ bot_bo7653980558646680370d_enat )
% 15.55/8.60        = ( A = bot_bo7653980558646680370d_enat ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6863_bot_Oextremum__unique,axiom,
% 15.55/8.60      ! [A: set_real] :
% 15.55/8.60        ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 15.55/8.60        = ( A = bot_bot_set_real ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6864_bot_Oextremum__unique,axiom,
% 15.55/8.60      ! [A: set_int] :
% 15.55/8.60        ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 15.55/8.60        = ( A = bot_bot_set_int ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6865_bot_Oextremum__unique,axiom,
% 15.55/8.60      ! [A: set_nat] :
% 15.55/8.60        ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 15.55/8.60        = ( A = bot_bot_set_nat ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6866_bot_Oextremum__unique,axiom,
% 15.55/8.60      ! [A: nat] :
% 15.55/8.60        ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 15.55/8.60        = ( A = bot_bot_nat ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6867_bot_Oextremum__uniqueI,axiom,
% 15.55/8.60      ! [A: set_Extended_enat] :
% 15.55/8.60        ( ( ord_le7203529160286727270d_enat @ A @ bot_bo7653980558646680370d_enat )
% 15.55/8.60       => ( A = bot_bo7653980558646680370d_enat ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6868_bot_Oextremum__uniqueI,axiom,
% 15.55/8.60      ! [A: set_real] :
% 15.55/8.60        ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 15.55/8.60       => ( A = bot_bot_set_real ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6869_bot_Oextremum__uniqueI,axiom,
% 15.55/8.60      ! [A: set_int] :
% 15.55/8.60        ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 15.55/8.60       => ( A = bot_bot_set_int ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6870_bot_Oextremum__uniqueI,axiom,
% 15.55/8.60      ! [A: set_nat] :
% 15.55/8.60        ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 15.55/8.60       => ( A = bot_bot_set_nat ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6871_bot_Oextremum__uniqueI,axiom,
% 15.55/8.60      ! [A: nat] :
% 15.55/8.60        ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 15.55/8.60       => ( A = bot_bot_nat ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6872_bot_Onot__eq__extremum,axiom,
% 15.55/8.60      ! [A: set_Extended_enat] :
% 15.55/8.60        ( ( A != bot_bo7653980558646680370d_enat )
% 15.55/8.60        = ( ord_le2529575680413868914d_enat @ bot_bo7653980558646680370d_enat @ A ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6873_bot_Onot__eq__extremum,axiom,
% 15.55/8.60      ! [A: set_real] :
% 15.55/8.60        ( ( A != bot_bot_set_real )
% 15.55/8.60        = ( ord_less_set_real @ bot_bot_set_real @ A ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6874_bot_Onot__eq__extremum,axiom,
% 15.55/8.60      ! [A: set_nat] :
% 15.55/8.60        ( ( A != bot_bot_set_nat )
% 15.55/8.60        = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6875_bot_Onot__eq__extremum,axiom,
% 15.55/8.60      ! [A: set_int] :
% 15.55/8.60        ( ( A != bot_bot_set_int )
% 15.55/8.60        = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6876_bot_Onot__eq__extremum,axiom,
% 15.55/8.60      ! [A: nat] :
% 15.55/8.60        ( ( A != bot_bot_nat )
% 15.55/8.60        = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6877_bot_Oextremum__strict,axiom,
% 15.55/8.60      ! [A: set_Extended_enat] :
% 15.55/8.60        ~ ( ord_le2529575680413868914d_enat @ A @ bot_bo7653980558646680370d_enat ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6878_bot_Oextremum__strict,axiom,
% 15.55/8.60      ! [A: set_real] :
% 15.55/8.60        ~ ( ord_less_set_real @ A @ bot_bot_set_real ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6879_bot_Oextremum__strict,axiom,
% 15.55/8.60      ! [A: set_nat] :
% 15.55/8.60        ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6880_bot_Oextremum__strict,axiom,
% 15.55/8.60      ! [A: set_int] :
% 15.55/8.60        ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6881_bot_Oextremum__strict,axiom,
% 15.55/8.60      ! [A: nat] :
% 15.55/8.60        ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6882_diff__shunt__var,axiom,
% 15.55/8.60      ! [X3: set_Extended_enat,Y3: set_Extended_enat] :
% 15.55/8.60        ( ( ( minus_925952699566721837d_enat @ X3 @ Y3 )
% 15.55/8.60          = bot_bo7653980558646680370d_enat )
% 15.55/8.60        = ( ord_le7203529160286727270d_enat @ X3 @ Y3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6883_diff__shunt__var,axiom,
% 15.55/8.60      ! [X3: set_real,Y3: set_real] :
% 15.55/8.60        ( ( ( minus_minus_set_real @ X3 @ Y3 )
% 15.55/8.60          = bot_bot_set_real )
% 15.55/8.60        = ( ord_less_eq_set_real @ X3 @ Y3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6884_diff__shunt__var,axiom,
% 15.55/8.60      ! [X3: set_int,Y3: set_int] :
% 15.55/8.60        ( ( ( minus_minus_set_int @ X3 @ Y3 )
% 15.55/8.60          = bot_bot_set_int )
% 15.55/8.60        = ( ord_less_eq_set_int @ X3 @ Y3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6885_diff__shunt__var,axiom,
% 15.55/8.60      ! [X3: set_nat,Y3: set_nat] :
% 15.55/8.60        ( ( ( minus_minus_set_nat @ X3 @ Y3 )
% 15.55/8.60          = bot_bot_set_nat )
% 15.55/8.60        = ( ord_less_eq_set_nat @ X3 @ Y3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6886_vebt__succ_Opelims,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: option_nat] :
% 15.55/8.60        ( ( ( vEBT_vebt_succ @ X3 @ Xa )
% 15.55/8.60          = Y3 )
% 15.55/8.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.60         => ( ! [Uu: $o,B4: $o] :
% 15.55/8.60                ( ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ Uu @ B4 ) )
% 15.55/8.60               => ( ( Xa = zero_zero_nat )
% 15.55/8.60                 => ( ( ( B4
% 15.55/8.60                       => ( Y3
% 15.55/8.60                          = ( some_nat @ one_one_nat ) ) )
% 15.55/8.60                      & ( ~ B4
% 15.55/8.60                       => ( Y3 = none_nat ) ) )
% 15.55/8.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ B4 ) @ zero_zero_nat ) ) ) ) )
% 15.55/8.60           => ( ! [Uv: $o,Uw: $o] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Leaf @ Uv @ Uw ) )
% 15.55/8.60                 => ! [N2: nat] :
% 15.55/8.60                      ( ( Xa
% 15.55/8.60                        = ( suc @ N2 ) )
% 15.55/8.60                     => ( ( Y3 = none_nat )
% 15.55/8.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N2 ) ) ) ) ) )
% 15.55/8.60             => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 15.55/8.60                    ( ( X3
% 15.55/8.60                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 15.55/8.60                   => ( ( Y3 = none_nat )
% 15.55/8.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa ) ) ) )
% 15.55/8.60               => ( ! [V3: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 15.55/8.60                      ( ( X3
% 15.55/8.60                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 15.55/8.60                     => ( ( Y3 = none_nat )
% 15.55/8.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa ) ) ) )
% 15.55/8.60                 => ( ! [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 15.55/8.60                        ( ( X3
% 15.55/8.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 15.55/8.60                       => ( ( Y3 = none_nat )
% 15.55/8.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Xa ) ) ) )
% 15.55/8.60                   => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                          ( ( X3
% 15.55/8.60                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                         => ( ( ( ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.60                               => ( Y3
% 15.55/8.60                                  = ( some_nat @ Mi2 ) ) )
% 15.55/8.60                              & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.60                               => ( Y3
% 15.55/8.60                                  = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                                    @ ( if_option_nat
% 15.55/8.60                                      @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                         != none_nat )
% 15.55/8.60                                        & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.60                                      @ ( 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 @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                      @ ( if_option_nat
% 15.55/8.60                                        @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.60                                          = none_nat )
% 15.55/8.60                                        @ none_nat
% 15.55/8.60                                        @ ( 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 @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.60                                    @ none_nat ) ) ) )
% 15.55/8.60                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6887_vebt__pred_Opelims,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: option_nat] :
% 15.55/8.60        ( ( ( vEBT_vebt_pred @ X3 @ Xa )
% 15.55/8.60          = Y3 )
% 15.55/8.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.60         => ( ! [Uu: $o,Uv: $o] :
% 15.55/8.60                ( ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ Uu @ Uv ) )
% 15.55/8.60               => ( ( Xa = zero_zero_nat )
% 15.55/8.60                 => ( ( Y3 = none_nat )
% 15.55/8.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat ) ) ) ) )
% 15.55/8.60           => ( ! [A5: $o,Uw: $o] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Leaf @ A5 @ Uw ) )
% 15.55/8.60                 => ( ( Xa
% 15.55/8.60                      = ( suc @ zero_zero_nat ) )
% 15.55/8.60                   => ( ( ( A5
% 15.55/8.60                         => ( Y3
% 15.55/8.60                            = ( some_nat @ zero_zero_nat ) ) )
% 15.55/8.60                        & ( ~ A5
% 15.55/8.60                         => ( Y3 = none_nat ) ) )
% 15.55/8.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 15.55/8.60             => ( ! [A5: $o,B4: $o] :
% 15.55/8.60                    ( ( X3
% 15.55/8.60                      = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60                   => ! [Va: nat] :
% 15.55/8.60                        ( ( Xa
% 15.55/8.60                          = ( suc @ ( suc @ Va ) ) )
% 15.55/8.60                       => ( ( ( B4
% 15.55/8.60                             => ( Y3
% 15.55/8.60                                = ( some_nat @ one_one_nat ) ) )
% 15.55/8.60                            & ( ~ B4
% 15.55/8.60                             => ( ( A5
% 15.55/8.60                                 => ( Y3
% 15.55/8.60                                    = ( some_nat @ zero_zero_nat ) ) )
% 15.55/8.60                                & ( ~ A5
% 15.55/8.60                                 => ( Y3 = none_nat ) ) ) ) )
% 15.55/8.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ ( suc @ ( suc @ Va ) ) ) ) ) ) )
% 15.55/8.60               => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 15.55/8.60                      ( ( X3
% 15.55/8.60                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 15.55/8.60                     => ( ( Y3 = none_nat )
% 15.55/8.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa ) ) ) )
% 15.55/8.60                 => ( ! [V3: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 15.55/8.60                        ( ( X3
% 15.55/8.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 15.55/8.60                       => ( ( Y3 = none_nat )
% 15.55/8.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa ) ) ) )
% 15.55/8.60                   => ( ! [V3: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 15.55/8.60                          ( ( X3
% 15.55/8.60                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 15.55/8.60                         => ( ( Y3 = none_nat )
% 15.55/8.60                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Xa ) ) ) )
% 15.55/8.60                     => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                            ( ( X3
% 15.55/8.60                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                           => ( ( ( ( ord_less_nat @ Ma2 @ Xa )
% 15.55/8.60                                 => ( Y3
% 15.55/8.60                                    = ( some_nat @ Ma2 ) ) )
% 15.55/8.60                                & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 15.55/8.60                                 => ( Y3
% 15.55/8.60                                    = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                                      @ ( if_option_nat
% 15.55/8.60                                        @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                           != none_nat )
% 15.55/8.60                                          & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.60                                        @ ( 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 @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                        @ ( if_option_nat
% 15.55/8.60                                          @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.60                                            = none_nat )
% 15.55/8.60                                          @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa ) @ ( some_nat @ Mi2 ) @ none_nat )
% 15.55/8.60                                          @ ( 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 @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.60                                      @ none_nat ) ) ) )
% 15.55/8.60                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6888_vebt__delete_Opelims,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: vEBT_VEBT] :
% 15.55/8.60        ( ( ( vEBT_vebt_delete @ X3 @ Xa )
% 15.55/8.60          = Y3 )
% 15.55/8.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.60         => ( ! [A5: $o,B4: $o] :
% 15.55/8.60                ( ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60               => ( ( Xa = zero_zero_nat )
% 15.55/8.60                 => ( ( Y3
% 15.55/8.60                      = ( vEBT_Leaf @ $false @ B4 ) )
% 15.55/8.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ zero_zero_nat ) ) ) ) )
% 15.55/8.60           => ( ! [A5: $o,B4: $o] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60                 => ( ( Xa
% 15.55/8.60                      = ( suc @ zero_zero_nat ) )
% 15.55/8.60                   => ( ( Y3
% 15.55/8.60                        = ( vEBT_Leaf @ A5 @ $false ) )
% 15.55/8.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 15.55/8.60             => ( ! [A5: $o,B4: $o] :
% 15.55/8.60                    ( ( X3
% 15.55/8.60                      = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60                   => ! [N2: nat] :
% 15.55/8.60                        ( ( Xa
% 15.55/8.60                          = ( suc @ ( suc @ N2 ) ) )
% 15.55/8.60                       => ( ( Y3
% 15.55/8.60                            = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ ( suc @ ( suc @ N2 ) ) ) ) ) ) )
% 15.55/8.60               => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                      ( ( X3
% 15.55/8.60                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 15.55/8.60                     => ( ( Y3
% 15.55/8.60                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 15.55/8.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) @ Xa ) ) ) )
% 15.55/8.60                 => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 15.55/8.60                        ( ( X3
% 15.55/8.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 15.55/8.60                       => ( ( Y3
% 15.55/8.60                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 15.55/8.60                         => ~ ( 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 ) @ Xa ) ) ) )
% 15.55/8.60                   => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 15.55/8.60                          ( ( X3
% 15.55/8.60                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 15.55/8.60                         => ( ( Y3
% 15.55/8.60                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 15.55/8.60                           => ~ ( 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 ) @ Xa ) ) ) )
% 15.55/8.60                     => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                            ( ( X3
% 15.55/8.60                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                           => ( ( ( ( ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.60                                    | ( ord_less_nat @ Ma2 @ Xa ) )
% 15.55/8.60                                 => ( Y3
% 15.55/8.60                                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) )
% 15.55/8.60                                & ( ~ ( ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.60                                      | ( ord_less_nat @ Ma2 @ Xa ) )
% 15.55/8.60                                 => ( ( ( ( Xa = Mi2 )
% 15.55/8.60                                        & ( Xa = Ma2 ) )
% 15.55/8.60                                     => ( Y3
% 15.55/8.60                                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) )
% 15.55/8.60                                    & ( ~ ( ( Xa = Mi2 )
% 15.55/8.60                                          & ( Xa = Ma2 ) )
% 15.55/8.60                                     => ( Y3
% 15.55/8.60                                        = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                                          @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                            @ ( vEBT_Node
% 15.55/8.60                                              @ ( some_P7363390416028606310at_nat
% 15.55/8.60                                                @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa = Mi2 ) @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ Mi2 )
% 15.55/8.60                                                  @ ( if_nat
% 15.55/8.60                                                    @ ( ( ( Xa = Mi2 )
% 15.55/8.60                                                       => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 15.55/8.60                                                          = Ma2 ) )
% 15.55/8.60                                                      & ( ( Xa != Mi2 )
% 15.55/8.60                                                       => ( Xa = Ma2 ) ) )
% 15.55/8.60                                                    @ ( if_nat
% 15.55/8.60                                                      @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                                        = none_nat )
% 15.55/8.60                                                      @ ( if_nat @ ( Xa = Mi2 ) @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ Mi2 )
% 15.55/8.60                                                      @ ( 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 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.60                                                    @ Ma2 ) ) )
% 15.55/8.60                                              @ ( suc @ ( suc @ Va ) )
% 15.55/8.60                                              @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                              @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                            @ ( vEBT_Node
% 15.55/8.60                                              @ ( some_P7363390416028606310at_nat
% 15.55/8.60                                                @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa = Mi2 ) @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ Mi2 )
% 15.55/8.60                                                  @ ( if_nat
% 15.55/8.60                                                    @ ( ( ( Xa = Mi2 )
% 15.55/8.60                                                       => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 15.55/8.60                                                          = Ma2 ) )
% 15.55/8.60                                                      & ( ( Xa != Mi2 )
% 15.55/8.60                                                       => ( Xa = Ma2 ) ) )
% 15.55/8.60                                                    @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( 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 @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.60                                                    @ Ma2 ) ) )
% 15.55/8.60                                              @ ( suc @ ( suc @ Va ) )
% 15.55/8.60                                              @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                              @ Summary2 ) )
% 15.55/8.60                                          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) )
% 15.55/8.60                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6889_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Opelims,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 15.55/8.60        ( ( ( vEBT_T_s_u_c_c2 @ X3 @ Xa )
% 15.55/8.60          = Y3 )
% 15.55/8.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.60         => ( ! [Uu: $o,B4: $o] :
% 15.55/8.60                ( ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ Uu @ B4 ) )
% 15.55/8.60               => ( ( Xa = zero_zero_nat )
% 15.55/8.60                 => ( ( Y3 = one_one_nat )
% 15.55/8.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ B4 ) @ zero_zero_nat ) ) ) ) )
% 15.55/8.60           => ( ! [Uv: $o,Uw: $o] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Leaf @ Uv @ Uw ) )
% 15.55/8.60                 => ! [N2: nat] :
% 15.55/8.60                      ( ( Xa
% 15.55/8.60                        = ( suc @ N2 ) )
% 15.55/8.60                     => ( ( Y3 = one_one_nat )
% 15.55/8.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N2 ) ) ) ) ) )
% 15.55/8.60             => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 15.55/8.60                    ( ( X3
% 15.55/8.60                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 15.55/8.60                   => ( ( Y3 = one_one_nat )
% 15.55/8.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa ) ) ) )
% 15.55/8.60               => ( ! [V3: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 15.55/8.60                      ( ( X3
% 15.55/8.60                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 15.55/8.60                     => ( ( Y3 = one_one_nat )
% 15.55/8.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa ) ) ) )
% 15.55/8.60                 => ( ! [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 15.55/8.60                        ( ( X3
% 15.55/8.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 15.55/8.60                       => ( ( Y3 = one_one_nat )
% 15.55/8.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Xa ) ) ) )
% 15.55/8.60                   => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                          ( ( X3
% 15.55/8.60                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                         => ( ( ( ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.60                               => ( Y3 = one_one_nat ) )
% 15.55/8.60                              & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.60                               => ( Y3
% 15.55/8.60                                  = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                                    @ ( if_nat
% 15.55/8.60                                      @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                         != none_nat )
% 15.55/8.60                                        & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.60                                      @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                      @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 15.55/8.60                                    @ one_one_nat ) ) ) )
% 15.55/8.60                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6890_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Opelims,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 15.55/8.60        ( ( ( vEBT_T_i_n_s_e_r_t @ X3 @ Xa )
% 15.55/8.60          = Y3 )
% 15.55/8.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.60         => ( ! [A5: $o,B4: $o] :
% 15.55/8.60                ( ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60               => ( ( Y3
% 15.55/8.60                    = ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 15.55/8.60                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) ) ) )
% 15.55/8.60           => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 15.55/8.60                 => ( ( Y3 = one_one_nat )
% 15.55/8.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) @ Xa ) ) ) )
% 15.55/8.60             => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 15.55/8.60                    ( ( X3
% 15.55/8.60                      = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 15.55/8.60                   => ( ( Y3 = one_one_nat )
% 15.55/8.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) @ Xa ) ) ) )
% 15.55/8.60               => ( ! [V3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                      ( ( X3
% 15.55/8.60                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                     => ( ( Y3
% 15.55/8.60                          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) )
% 15.55/8.60                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                        ( ( X3
% 15.55/8.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                       => ( ( Y3
% 15.55/8.60                            = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 15.55/8.60                              @ ( if_nat
% 15.55/8.60                                @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                                  & ~ ( ( Xa = Mi2 )
% 15.55/8.60                                      | ( Xa = Ma2 ) ) )
% 15.55/8.60                                @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 15.55/8.60                                @ one_one_nat ) ) )
% 15.55/8.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6891_bot__nat__def,axiom,
% 15.55/8.60      bot_bot_nat = zero_zero_nat ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6892_bot__enat__def,axiom,
% 15.55/8.60      bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6893_vebt__insert_Opelims,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: vEBT_VEBT] :
% 15.55/8.60        ( ( ( vEBT_vebt_insert @ X3 @ Xa )
% 15.55/8.60          = Y3 )
% 15.55/8.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.60         => ( ! [A5: $o,B4: $o] :
% 15.55/8.60                ( ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60               => ( ( ( ( Xa = zero_zero_nat )
% 15.55/8.60                     => ( Y3
% 15.55/8.60                        = ( vEBT_Leaf @ $true @ B4 ) ) )
% 15.55/8.60                    & ( ( Xa != zero_zero_nat )
% 15.55/8.60                     => ( ( ( Xa = one_one_nat )
% 15.55/8.60                         => ( Y3
% 15.55/8.60                            = ( vEBT_Leaf @ A5 @ $true ) ) )
% 15.55/8.60                        & ( ( Xa != one_one_nat )
% 15.55/8.60                         => ( Y3
% 15.55/8.60                            = ( vEBT_Leaf @ A5 @ B4 ) ) ) ) ) )
% 15.55/8.60                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) ) ) )
% 15.55/8.60           => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 15.55/8.60                 => ( ( Y3
% 15.55/8.60                      = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 15.55/8.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) @ Xa ) ) ) )
% 15.55/8.60             => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 15.55/8.60                    ( ( X3
% 15.55/8.60                      = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 15.55/8.60                   => ( ( Y3
% 15.55/8.60                        = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 15.55/8.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) @ Xa ) ) ) )
% 15.55/8.60               => ( ! [V3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                      ( ( X3
% 15.55/8.60                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                     => ( ( Y3
% 15.55/8.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa @ Xa ) ) @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) )
% 15.55/8.60                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                        ( ( X3
% 15.55/8.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                       => ( ( Y3
% 15.55/8.60                            = ( if_VEBT_VEBT
% 15.55/8.60                              @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                                & ~ ( ( Xa = Mi2 )
% 15.55/8.60                                    | ( Xa = Ma2 ) ) )
% 15.55/8.60                              @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Xa @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 15.55/8.60                              @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) )
% 15.55/8.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6894_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Opelims,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 15.55/8.60        ( ( ( vEBT_T_p_r_e_d2 @ X3 @ Xa )
% 15.55/8.60          = Y3 )
% 15.55/8.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.60         => ( ! [Uu: $o,Uv: $o] :
% 15.55/8.60                ( ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ Uu @ Uv ) )
% 15.55/8.60               => ( ( Xa = zero_zero_nat )
% 15.55/8.60                 => ( ( Y3 = one_one_nat )
% 15.55/8.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat ) ) ) ) )
% 15.55/8.60           => ( ! [A5: $o,Uw: $o] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Leaf @ A5 @ Uw ) )
% 15.55/8.60                 => ( ( Xa
% 15.55/8.60                      = ( suc @ zero_zero_nat ) )
% 15.55/8.60                   => ( ( Y3 = one_one_nat )
% 15.55/8.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 15.55/8.60             => ( ! [A5: $o,B4: $o] :
% 15.55/8.60                    ( ( X3
% 15.55/8.60                      = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60                   => ! [Va: nat] :
% 15.55/8.60                        ( ( Xa
% 15.55/8.60                          = ( suc @ ( suc @ Va ) ) )
% 15.55/8.60                       => ( ( Y3 = one_one_nat )
% 15.55/8.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ ( suc @ ( suc @ Va ) ) ) ) ) ) )
% 15.55/8.60               => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 15.55/8.60                      ( ( X3
% 15.55/8.60                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 15.55/8.60                     => ( ( Y3 = one_one_nat )
% 15.55/8.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa ) ) ) )
% 15.55/8.60                 => ( ! [V3: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 15.55/8.60                        ( ( X3
% 15.55/8.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 15.55/8.60                       => ( ( Y3 = one_one_nat )
% 15.55/8.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa ) ) ) )
% 15.55/8.60                   => ( ! [V3: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 15.55/8.60                          ( ( X3
% 15.55/8.60                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 15.55/8.60                         => ( ( Y3 = one_one_nat )
% 15.55/8.60                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Xa ) ) ) )
% 15.55/8.60                     => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                            ( ( X3
% 15.55/8.60                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                           => ( ( ( ( ord_less_nat @ Ma2 @ Xa )
% 15.55/8.60                                 => ( Y3 = one_one_nat ) )
% 15.55/8.60                                & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 15.55/8.60                                 => ( Y3
% 15.55/8.60                                    = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                                      @ ( if_nat
% 15.55/8.60                                        @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                           != none_nat )
% 15.55/8.60                                          & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 15.55/8.60                                        @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                        @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 15.55/8.60                                      @ one_one_nat ) ) ) )
% 15.55/8.60                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6895_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Opelims,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 15.55/8.60        ( ( ( vEBT_T_i_n_s_e_r_t2 @ X3 @ Xa )
% 15.55/8.60          = Y3 )
% 15.55/8.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.60         => ( ! [A5: $o,B4: $o] :
% 15.55/8.60                ( ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60               => ( ( Y3 = one_one_nat )
% 15.55/8.60                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) ) ) )
% 15.55/8.60           => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 15.55/8.60                 => ( ( Y3 = one_one_nat )
% 15.55/8.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) @ Xa ) ) ) )
% 15.55/8.60             => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 15.55/8.60                    ( ( X3
% 15.55/8.60                      = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 15.55/8.60                   => ( ( Y3 = one_one_nat )
% 15.55/8.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) @ Xa ) ) ) )
% 15.55/8.60               => ( ! [V3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                      ( ( X3
% 15.55/8.60                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                     => ( ( Y3 = one_one_nat )
% 15.55/8.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) )
% 15.55/8.60                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                        ( ( X3
% 15.55/8.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                       => ( ( Y3
% 15.55/8.60                            = ( if_nat
% 15.55/8.60                              @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                                & ~ ( ( Xa = Mi2 )
% 15.55/8.60                                    | ( Xa = Ma2 ) ) )
% 15.55/8.60                              @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 15.55/8.60                              @ one_one_nat ) )
% 15.55/8.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6896_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Opelims,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 15.55/8.60        ( ( ( vEBT_T_m_e_m_b_e_r @ X3 @ Xa )
% 15.55/8.60          = Y3 )
% 15.55/8.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.60         => ( ! [A5: $o,B4: $o] :
% 15.55/8.60                ( ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60               => ( ( Y3
% 15.55/8.60                    = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 15.55/8.60                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) ) ) )
% 15.55/8.60           => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 15.55/8.60                 => ( ( Y3
% 15.55/8.60                      = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa ) ) ) )
% 15.55/8.60             => ( ! [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 15.55/8.60                    ( ( X3
% 15.55/8.60                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 15.55/8.60                   => ( ( Y3
% 15.55/8.60                        = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa ) ) ) )
% 15.55/8.60               => ( ! [V3: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 15.55/8.60                      ( ( X3
% 15.55/8.60                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) )
% 15.55/8.60                     => ( ( Y3
% 15.55/8.60                          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) @ Xa ) ) ) )
% 15.55/8.60                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                        ( ( X3
% 15.55/8.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                       => ( ( Y3
% 15.55/8.60                            = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa = Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6897_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Opelims,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: nat] :
% 15.55/8.60        ( ( ( vEBT_T_m_e_m_b_e_r2 @ X3 @ Xa )
% 15.55/8.60          = Y3 )
% 15.55/8.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.60         => ( ! [A5: $o,B4: $o] :
% 15.55/8.60                ( ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60               => ( ( Y3 = one_one_nat )
% 15.55/8.60                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) ) ) )
% 15.55/8.60           => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 15.55/8.60                 => ( ( Y3 = one_one_nat )
% 15.55/8.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa ) ) ) )
% 15.55/8.60             => ( ! [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 15.55/8.60                    ( ( X3
% 15.55/8.60                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 15.55/8.60                   => ( ( Y3 = one_one_nat )
% 15.55/8.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa ) ) ) )
% 15.55/8.60               => ( ! [V3: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 15.55/8.60                      ( ( X3
% 15.55/8.60                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) )
% 15.55/8.60                     => ( ( Y3 = one_one_nat )
% 15.55/8.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) @ Xa ) ) ) )
% 15.55/8.60                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                        ( ( X3
% 15.55/8.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                       => ( ( Y3
% 15.55/8.60                            = ( plus_plus_nat @ one_one_nat
% 15.55/8.60                              @ ( if_nat @ ( Xa = Mi2 ) @ zero_zero_nat
% 15.55/8.60                                @ ( if_nat @ ( Xa = Ma2 ) @ zero_zero_nat
% 15.55/8.60                                  @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ zero_zero_nat
% 15.55/8.60                                    @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa ) @ zero_zero_nat
% 15.55/8.60                                      @ ( if_nat
% 15.55/8.60                                        @ ( ( ord_less_nat @ Mi2 @ Xa )
% 15.55/8.60                                          & ( ord_less_nat @ Xa @ Ma2 ) )
% 15.55/8.60                                        @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 15.55/8.60                                        @ zero_zero_nat ) ) ) ) ) ) )
% 15.55/8.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6898_vebt__member_Opelims_I1_J,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: $o] :
% 15.55/8.60        ( ( ( vEBT_vebt_member @ X3 @ Xa )
% 15.55/8.60          = Y3 )
% 15.55/8.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.60         => ( ! [A5: $o,B4: $o] :
% 15.55/8.60                ( ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60               => ( ( Y3
% 15.55/8.60                    = ( ( ( Xa = zero_zero_nat )
% 15.55/8.60                       => A5 )
% 15.55/8.60                      & ( ( Xa != zero_zero_nat )
% 15.55/8.60                       => ( ( ( Xa = one_one_nat )
% 15.55/8.60                           => B4 )
% 15.55/8.60                          & ( Xa = one_one_nat ) ) ) ) )
% 15.55/8.60                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) ) ) )
% 15.55/8.60           => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 15.55/8.60                 => ( ~ Y3
% 15.55/8.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa ) ) ) )
% 15.55/8.60             => ( ! [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 15.55/8.60                    ( ( X3
% 15.55/8.60                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 15.55/8.60                   => ( ~ Y3
% 15.55/8.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa ) ) ) )
% 15.55/8.60               => ( ! [V3: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 15.55/8.60                      ( ( X3
% 15.55/8.60                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) )
% 15.55/8.60                     => ( ~ Y3
% 15.55/8.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) @ Xa ) ) ) )
% 15.55/8.60                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                        ( ( X3
% 15.55/8.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                       => ( ( Y3
% 15.55/8.60                            = ( ( Xa != Mi2 )
% 15.55/8.60                             => ( ( Xa != Ma2 )
% 15.55/8.60                               => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.60                                  & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.60                                   => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 15.55/8.60                                      & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 15.55/8.60                                       => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                                           => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) )
% 15.55/8.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6899_vebt__member_Opelims_I3_J,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat] :
% 15.55/8.60        ( ~ ( vEBT_vebt_member @ X3 @ Xa )
% 15.55/8.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.60         => ( ! [A5: $o,B4: $o] :
% 15.55/8.60                ( ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60               => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) )
% 15.55/8.60                 => ( ( ( Xa = zero_zero_nat )
% 15.55/8.60                     => A5 )
% 15.55/8.60                    & ( ( Xa != zero_zero_nat )
% 15.55/8.60                     => ( ( ( Xa = one_one_nat )
% 15.55/8.60                         => B4 )
% 15.55/8.60                        & ( Xa = one_one_nat ) ) ) ) ) )
% 15.55/8.60           => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 15.55/8.60                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa ) ) )
% 15.55/8.60             => ( ! [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 15.55/8.60                    ( ( X3
% 15.55/8.60                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 15.55/8.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa ) ) )
% 15.55/8.60               => ( ! [V3: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 15.55/8.60                      ( ( X3
% 15.55/8.60                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) )
% 15.55/8.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) @ Xa ) ) )
% 15.55/8.60                 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                        ( ( X3
% 15.55/8.60                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) )
% 15.55/8.60                         => ( ( Xa != Mi2 )
% 15.55/8.60                           => ( ( Xa != Ma2 )
% 15.55/8.60                             => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.60                                & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.60                                 => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 15.55/8.60                                    & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 15.55/8.60                                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                                         => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6900_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: $o] :
% 15.55/8.60        ( ( ( vEBT_V5719532721284313246member @ X3 @ Xa )
% 15.55/8.60          = Y3 )
% 15.55/8.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.60         => ( ! [A5: $o,B4: $o] :
% 15.55/8.60                ( ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60               => ( ( Y3
% 15.55/8.60                    = ( ( ( Xa = zero_zero_nat )
% 15.55/8.60                       => A5 )
% 15.55/8.60                      & ( ( Xa != zero_zero_nat )
% 15.55/8.60                       => ( ( ( Xa = one_one_nat )
% 15.55/8.60                           => B4 )
% 15.55/8.60                          & ( Xa = one_one_nat ) ) ) ) )
% 15.55/8.60                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) ) ) )
% 15.55/8.60           => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 15.55/8.60                 => ( ~ Y3
% 15.55/8.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Xa ) ) ) )
% 15.55/8.60             => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 15.55/8.60                    ( ( X3
% 15.55/8.60                      = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) )
% 15.55/8.60                   => ( ( Y3
% 15.55/8.60                        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 15.55/8.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) @ Xa ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6901_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat] :
% 15.55/8.60        ( ( vEBT_V5719532721284313246member @ X3 @ Xa )
% 15.55/8.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.60         => ( ! [A5: $o,B4: $o] :
% 15.55/8.60                ( ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) )
% 15.55/8.60                 => ~ ( ( ( Xa = zero_zero_nat )
% 15.55/8.60                       => A5 )
% 15.55/8.60                      & ( ( Xa != zero_zero_nat )
% 15.55/8.60                       => ( ( ( Xa = one_one_nat )
% 15.55/8.60                           => B4 )
% 15.55/8.60                          & ( Xa = one_one_nat ) ) ) ) ) )
% 15.55/8.60           => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) )
% 15.55/8.60                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) @ Xa ) )
% 15.55/8.60                   => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                         => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6902_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat] :
% 15.55/8.60        ( ~ ( vEBT_V5719532721284313246member @ X3 @ Xa )
% 15.55/8.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.60         => ( ! [A5: $o,B4: $o] :
% 15.55/8.60                ( ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) )
% 15.55/8.60                 => ( ( ( Xa = zero_zero_nat )
% 15.55/8.60                     => A5 )
% 15.55/8.60                    & ( ( Xa != zero_zero_nat )
% 15.55/8.60                     => ( ( ( Xa = one_one_nat )
% 15.55/8.60                         => B4 )
% 15.55/8.60                        & ( Xa = one_one_nat ) ) ) ) ) )
% 15.55/8.60           => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 15.55/8.60                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Xa ) ) )
% 15.55/8.60             => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 15.55/8.60                    ( ( X3
% 15.55/8.60                      = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) )
% 15.55/8.60                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) @ Xa ) )
% 15.55/8.60                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                         => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6903_vebt__member_Opelims_I2_J,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat] :
% 15.55/8.60        ( ( vEBT_vebt_member @ X3 @ Xa )
% 15.55/8.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.60         => ( ! [A5: $o,B4: $o] :
% 15.55/8.60                ( ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.60               => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) )
% 15.55/8.60                 => ~ ( ( ( Xa = zero_zero_nat )
% 15.55/8.60                       => A5 )
% 15.55/8.60                      & ( ( Xa != zero_zero_nat )
% 15.55/8.60                       => ( ( ( Xa = one_one_nat )
% 15.55/8.60                           => B4 )
% 15.55/8.60                          & ( Xa = one_one_nat ) ) ) ) ) )
% 15.55/8.60           => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 15.55/8.60                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) )
% 15.55/8.60                   => ~ ( ( Xa != Mi2 )
% 15.55/8.60                       => ( ( Xa != Ma2 )
% 15.55/8.60                         => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.60                            & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 15.55/8.60                             => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 15.55/8.60                                & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 15.55/8.60                                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                                     => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6904_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat,Y3: $o] :
% 15.55/8.60        ( ( ( vEBT_VEBT_membermima @ X3 @ Xa )
% 15.55/8.60          = Y3 )
% 15.55/8.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.60         => ( ! [Uu: $o,Uv: $o] :
% 15.55/8.60                ( ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ Uu @ Uv ) )
% 15.55/8.60               => ( ~ Y3
% 15.55/8.60                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa ) ) ) )
% 15.55/8.60           => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 15.55/8.60                 => ( ~ Y3
% 15.55/8.60                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa ) ) ) )
% 15.55/8.60             => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb: vEBT_VEBT] :
% 15.55/8.60                    ( ( X3
% 15.55/8.60                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb ) )
% 15.55/8.60                   => ( ( Y3
% 15.55/8.60                        = ( ( Xa = Mi2 )
% 15.55/8.60                          | ( Xa = Ma2 ) ) )
% 15.55/8.60                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb ) @ Xa ) ) ) )
% 15.55/8.60               => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 15.55/8.60                      ( ( X3
% 15.55/8.60                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) )
% 15.55/8.60                     => ( ( Y3
% 15.55/8.60                          = ( ( Xa = Mi2 )
% 15.55/8.60                            | ( Xa = Ma2 )
% 15.55/8.60                            | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 15.55/8.60                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) @ Xa ) ) ) )
% 15.55/8.60                 => ~ ! [V3: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 15.55/8.60                        ( ( X3
% 15.55/8.60                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) )
% 15.55/8.60                       => ( ( Y3
% 15.55/8.60                            = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 15.55/8.60                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6905_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat] :
% 15.55/8.60        ( ~ ( vEBT_VEBT_membermima @ X3 @ Xa )
% 15.55/8.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.60         => ( ! [Uu: $o,Uv: $o] :
% 15.55/8.60                ( ( X3
% 15.55/8.60                  = ( vEBT_Leaf @ Uu @ Uv ) )
% 15.55/8.60               => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa ) ) )
% 15.55/8.60           => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 15.55/8.60                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa ) ) )
% 15.55/8.60             => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb: vEBT_VEBT] :
% 15.55/8.60                    ( ( X3
% 15.55/8.60                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb ) )
% 15.55/8.60                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb ) @ Xa ) )
% 15.55/8.60                     => ( ( Xa = Mi2 )
% 15.55/8.60                        | ( Xa = Ma2 ) ) ) )
% 15.55/8.60               => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 15.55/8.60                      ( ( X3
% 15.55/8.60                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) )
% 15.55/8.60                     => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) @ Xa ) )
% 15.55/8.60                       => ( ( Xa = Mi2 )
% 15.55/8.60                          | ( Xa = Ma2 )
% 15.55/8.60                          | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                            & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 15.55/8.60                 => ~ ! [V3: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 15.55/8.60                        ( ( X3
% 15.55/8.60                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) )
% 15.55/8.60                       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) @ Xa ) )
% 15.55/8.60                         => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                            & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6906_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 15.55/8.60      ! [X3: vEBT_VEBT,Xa: nat] :
% 15.55/8.60        ( ( vEBT_VEBT_membermima @ X3 @ Xa )
% 15.55/8.60       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.60         => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb: vEBT_VEBT] :
% 15.55/8.60                ( ( X3
% 15.55/8.60                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb ) )
% 15.55/8.60               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb ) @ Xa ) )
% 15.55/8.60                 => ~ ( ( Xa = Mi2 )
% 15.55/8.60                      | ( Xa = Ma2 ) ) ) )
% 15.55/8.60           => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 15.55/8.60                  ( ( X3
% 15.55/8.60                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) )
% 15.55/8.60                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) @ Xa ) )
% 15.55/8.60                   => ~ ( ( Xa = Mi2 )
% 15.55/8.60                        | ( Xa = Ma2 )
% 15.55/8.60                        | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 15.55/8.60             => ~ ! [V3: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 15.55/8.60                    ( ( X3
% 15.55/8.60                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) )
% 15.55/8.60                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) @ Xa ) )
% 15.55/8.60                     => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 15.55/8.60                           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.60                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6907_monoseq__arctan__series,axiom,
% 15.55/8.60      ! [X3: real] :
% 15.55/8.60        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 15.55/8.60       => ( topolo6980174941875973593q_real
% 15.55/8.60          @ ^ [N3: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6908_delete__correct,axiom,
% 15.55/8.60      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.60        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.60       => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X3 ) )
% 15.55/8.60          = ( minus_minus_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6909_delete__correct_H,axiom,
% 15.55/8.60      ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 15.55/8.60        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.60       => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X3 ) )
% 15.55/8.60          = ( minus_minus_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6910_atLeast0__atMost__Suc,axiom,
% 15.55/8.60      ! [N: nat] :
% 15.55/8.60        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 15.55/8.60        = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6911_atLeastAtMost__insertL,axiom,
% 15.55/8.60      ! [M: nat,N: nat] :
% 15.55/8.60        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.60       => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 15.55/8.60          = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6912_atLeastAtMostSuc__conv,axiom,
% 15.55/8.60      ! [M: nat,N: nat] :
% 15.55/8.60        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 15.55/8.60       => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 15.55/8.60          = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6913_Icc__eq__insert__lb__nat,axiom,
% 15.55/8.60      ! [M: nat,N: nat] :
% 15.55/8.60        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.60       => ( ( set_or1269000886237332187st_nat @ M @ N )
% 15.55/8.60          = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6914_monoseq__realpow,axiom,
% 15.55/8.60      ! [X3: real] :
% 15.55/8.60        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.60       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 15.55/8.60         => ( topolo6980174941875973593q_real @ ( power_power_real @ X3 ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6915_pochhammer__times__pochhammer__half,axiom,
% 15.55/8.60      ! [Z: complex,N: nat] :
% 15.55/8.60        ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 15.55/8.60        = ( groups6464643781859351333omplex
% 15.55/8.60          @ ^ [K3: nat] : ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 15.55/8.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6916_pochhammer__times__pochhammer__half,axiom,
% 15.55/8.60      ! [Z: real,N: nat] :
% 15.55/8.60        ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 15.55/8.60        = ( groups129246275422532515t_real
% 15.55/8.60          @ ^ [K3: nat] : ( plus_plus_real @ Z @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6917_pochhammer__times__pochhammer__half,axiom,
% 15.55/8.60      ! [Z: rat,N: nat] :
% 15.55/8.60        ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 15.55/8.60        = ( groups73079841787564623at_rat
% 15.55/8.60          @ ^ [K3: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 15.55/8.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6918_signed__take__bit__numeral__minus__bit1,axiom,
% 15.55/8.60      ! [L: num,K: num] :
% 15.55/8.60        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 15.55/8.60        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6919_ln__series,axiom,
% 15.55/8.60      ! [X3: real] :
% 15.55/8.60        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.60       => ( ( ord_less_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 15.55/8.60         => ( ( ln_ln_real @ X3 )
% 15.55/8.60            = ( suminf_real
% 15.55/8.60              @ ^ [N3: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X3 @ one_one_real ) @ ( suc @ N3 ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6920_dbl__dec__simps_I4_J,axiom,
% 15.55/8.60      ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 15.55/8.60      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6921_dbl__dec__simps_I4_J,axiom,
% 15.55/8.60      ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.60      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6922_dbl__dec__simps_I4_J,axiom,
% 15.55/8.60      ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 15.55/8.60      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6923_dbl__dec__simps_I4_J,axiom,
% 15.55/8.60      ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 15.55/8.60      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6924_dbl__dec__simps_I4_J,axiom,
% 15.55/8.60      ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 15.55/8.60      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6925_arctan__series,axiom,
% 15.55/8.60      ! [X3: real] :
% 15.55/8.60        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 15.55/8.60       => ( ( arctan @ X3 )
% 15.55/8.60          = ( suminf_real
% 15.55/8.60            @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6926_of__nat__prod,axiom,
% 15.55/8.60      ! [F: int > nat,A3: set_int] :
% 15.55/8.60        ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F @ A3 ) )
% 15.55/8.60        = ( groups1705073143266064639nt_int
% 15.55/8.60          @ ^ [X: int] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 15.55/8.60          @ A3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6927_of__nat__prod,axiom,
% 15.55/8.60      ! [F: nat > nat,A3: set_nat] :
% 15.55/8.60        ( ( semiri8010041392384452111omplex @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 15.55/8.60        = ( groups6464643781859351333omplex
% 15.55/8.60          @ ^ [X: nat] : ( semiri8010041392384452111omplex @ ( F @ X ) )
% 15.55/8.60          @ A3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6928_of__nat__prod,axiom,
% 15.55/8.60      ! [F: nat > nat,A3: set_nat] :
% 15.55/8.60        ( ( semiri5074537144036343181t_real @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 15.55/8.60        = ( groups129246275422532515t_real
% 15.55/8.60          @ ^ [X: nat] : ( semiri5074537144036343181t_real @ ( F @ X ) )
% 15.55/8.60          @ A3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6929_of__nat__prod,axiom,
% 15.55/8.60      ! [F: nat > nat,A3: set_nat] :
% 15.55/8.60        ( ( semiri681578069525770553at_rat @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 15.55/8.60        = ( groups73079841787564623at_rat
% 15.55/8.60          @ ^ [X: nat] : ( semiri681578069525770553at_rat @ ( F @ X ) )
% 15.55/8.60          @ A3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6930_of__nat__prod,axiom,
% 15.55/8.60      ! [F: nat > nat,A3: set_nat] :
% 15.55/8.60        ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 15.55/8.60        = ( groups705719431365010083at_int
% 15.55/8.60          @ ^ [X: nat] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 15.55/8.60          @ A3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6931_of__nat__prod,axiom,
% 15.55/8.60      ! [F: nat > nat,A3: set_nat] :
% 15.55/8.60        ( ( semiri1316708129612266289at_nat @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 15.55/8.60        = ( groups708209901874060359at_nat
% 15.55/8.60          @ ^ [X: nat] : ( semiri1316708129612266289at_nat @ ( F @ X ) )
% 15.55/8.60          @ A3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6932_dbl__dec__simps_I3_J,axiom,
% 15.55/8.60      ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 15.55/8.60      = one_one_complex ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6933_dbl__dec__simps_I3_J,axiom,
% 15.55/8.60      ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 15.55/8.60      = one_one_real ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6934_dbl__dec__simps_I3_J,axiom,
% 15.55/8.60      ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 15.55/8.60      = one_one_rat ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6935_dbl__dec__simps_I3_J,axiom,
% 15.55/8.60      ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 15.55/8.60      = one_one_int ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6936_of__int__prod,axiom,
% 15.55/8.60      ! [F: nat > int,A3: set_nat] :
% 15.55/8.60        ( ( ring_1_of_int_real @ ( groups705719431365010083at_int @ F @ A3 ) )
% 15.55/8.60        = ( groups129246275422532515t_real
% 15.55/8.60          @ ^ [X: nat] : ( ring_1_of_int_real @ ( F @ X ) )
% 15.55/8.60          @ A3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6937_of__int__prod,axiom,
% 15.55/8.60      ! [F: nat > int,A3: set_nat] :
% 15.55/8.60        ( ( ring_17405671764205052669omplex @ ( groups705719431365010083at_int @ F @ A3 ) )
% 15.55/8.60        = ( groups6464643781859351333omplex
% 15.55/8.60          @ ^ [X: nat] : ( ring_17405671764205052669omplex @ ( F @ X ) )
% 15.55/8.60          @ A3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6938_of__int__prod,axiom,
% 15.55/8.60      ! [F: nat > int,A3: set_nat] :
% 15.55/8.60        ( ( ring_1_of_int_rat @ ( groups705719431365010083at_int @ F @ A3 ) )
% 15.55/8.60        = ( groups73079841787564623at_rat
% 15.55/8.60          @ ^ [X: nat] : ( ring_1_of_int_rat @ ( F @ X ) )
% 15.55/8.60          @ A3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6939_of__int__prod,axiom,
% 15.55/8.60      ! [F: nat > int,A3: set_nat] :
% 15.55/8.60        ( ( ring_1_of_int_int @ ( groups705719431365010083at_int @ F @ A3 ) )
% 15.55/8.60        = ( groups705719431365010083at_int
% 15.55/8.60          @ ^ [X: nat] : ( ring_1_of_int_int @ ( F @ X ) )
% 15.55/8.60          @ A3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6940_of__int__prod,axiom,
% 15.55/8.60      ! [F: int > int,A3: set_int] :
% 15.55/8.60        ( ( ring_1_of_int_real @ ( groups1705073143266064639nt_int @ F @ A3 ) )
% 15.55/8.60        = ( groups2316167850115554303t_real
% 15.55/8.60          @ ^ [X: int] : ( ring_1_of_int_real @ ( F @ X ) )
% 15.55/8.60          @ A3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6941_of__int__prod,axiom,
% 15.55/8.60      ! [F: int > int,A3: set_int] :
% 15.55/8.60        ( ( ring_17405671764205052669omplex @ ( groups1705073143266064639nt_int @ F @ A3 ) )
% 15.55/8.60        = ( groups7440179247065528705omplex
% 15.55/8.60          @ ^ [X: int] : ( ring_17405671764205052669omplex @ ( F @ X ) )
% 15.55/8.60          @ A3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6942_of__int__prod,axiom,
% 15.55/8.60      ! [F: int > int,A3: set_int] :
% 15.55/8.60        ( ( ring_1_of_int_rat @ ( groups1705073143266064639nt_int @ F @ A3 ) )
% 15.55/8.60        = ( groups1072433553688619179nt_rat
% 15.55/8.60          @ ^ [X: int] : ( ring_1_of_int_rat @ ( F @ X ) )
% 15.55/8.60          @ A3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6943_of__int__prod,axiom,
% 15.55/8.60      ! [F: int > int,A3: set_int] :
% 15.55/8.60        ( ( ring_1_of_int_int @ ( groups1705073143266064639nt_int @ F @ A3 ) )
% 15.55/8.60        = ( groups1705073143266064639nt_int
% 15.55/8.60          @ ^ [X: int] : ( ring_1_of_int_int @ ( F @ X ) )
% 15.55/8.60          @ A3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6944_pred__numeral__simps_I1_J,axiom,
% 15.55/8.60      ( ( pred_numeral @ one )
% 15.55/8.60      = zero_zero_nat ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6945_eq__numeral__Suc,axiom,
% 15.55/8.60      ! [K: num,N: nat] :
% 15.55/8.60        ( ( ( numeral_numeral_nat @ K )
% 15.55/8.60          = ( suc @ N ) )
% 15.55/8.60        = ( ( pred_numeral @ K )
% 15.55/8.60          = N ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6946_Suc__eq__numeral,axiom,
% 15.55/8.60      ! [N: nat,K: num] :
% 15.55/8.60        ( ( ( suc @ N )
% 15.55/8.60          = ( numeral_numeral_nat @ K ) )
% 15.55/8.60        = ( N
% 15.55/8.60          = ( pred_numeral @ K ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6947_less__numeral__Suc,axiom,
% 15.55/8.60      ! [K: num,N: nat] :
% 15.55/8.60        ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 15.55/8.60        = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6948_less__Suc__numeral,axiom,
% 15.55/8.60      ! [N: nat,K: num] :
% 15.55/8.60        ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 15.55/8.60        = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6949_pred__numeral__simps_I3_J,axiom,
% 15.55/8.60      ! [K: num] :
% 15.55/8.60        ( ( pred_numeral @ ( bit1 @ K ) )
% 15.55/8.60        = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6950_le__Suc__numeral,axiom,
% 15.55/8.60      ! [N: nat,K: num] :
% 15.55/8.60        ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 15.55/8.60        = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6951_le__numeral__Suc,axiom,
% 15.55/8.60      ! [K: num,N: nat] :
% 15.55/8.60        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 15.55/8.60        = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6952_diff__numeral__Suc,axiom,
% 15.55/8.60      ! [K: num,N: nat] :
% 15.55/8.60        ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 15.55/8.60        = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6953_diff__Suc__numeral,axiom,
% 15.55/8.60      ! [N: nat,K: num] :
% 15.55/8.60        ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 15.55/8.60        = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6954_max__numeral__Suc,axiom,
% 15.55/8.60      ! [K: num,N: nat] :
% 15.55/8.60        ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 15.55/8.60        = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6955_max__Suc__numeral,axiom,
% 15.55/8.60      ! [N: nat,K: num] :
% 15.55/8.60        ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 15.55/8.60        = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6956_dbl__dec__simps_I2_J,axiom,
% 15.55/8.60      ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 15.55/8.60      = ( uminus_uminus_real @ one_one_real ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6957_dbl__dec__simps_I2_J,axiom,
% 15.55/8.60      ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 15.55/8.60      = ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6958_dbl__dec__simps_I2_J,axiom,
% 15.55/8.60      ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 15.55/8.60      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6959_dbl__dec__simps_I2_J,axiom,
% 15.55/8.60      ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 15.55/8.60      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6960_dbl__dec__simps_I2_J,axiom,
% 15.55/8.60      ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 15.55/8.60      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6961_powser__zero,axiom,
% 15.55/8.60      ! [F: nat > complex] :
% 15.55/8.60        ( ( suminf_complex
% 15.55/8.60          @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ zero_zero_complex @ N3 ) ) )
% 15.55/8.60        = ( F @ zero_zero_nat ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6962_powser__zero,axiom,
% 15.55/8.60      ! [F: nat > real] :
% 15.55/8.60        ( ( suminf_real
% 15.55/8.60          @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ zero_zero_real @ N3 ) ) )
% 15.55/8.60        = ( F @ zero_zero_nat ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6963_prod_Ocl__ivl__Suc,axiom,
% 15.55/8.60      ! [N: nat,M: nat,G: nat > complex] :
% 15.55/8.60        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 15.55/8.60         => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.60            = one_one_complex ) )
% 15.55/8.60        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 15.55/8.60         => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.60            = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6964_prod_Ocl__ivl__Suc,axiom,
% 15.55/8.60      ! [N: nat,M: nat,G: nat > real] :
% 15.55/8.60        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 15.55/8.60         => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.60            = one_one_real ) )
% 15.55/8.60        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 15.55/8.60         => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.60            = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6965_prod_Ocl__ivl__Suc,axiom,
% 15.55/8.60      ! [N: nat,M: nat,G: nat > rat] :
% 15.55/8.60        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 15.55/8.60         => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.60            = one_one_rat ) )
% 15.55/8.60        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 15.55/8.60         => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.60            = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6966_prod_Ocl__ivl__Suc,axiom,
% 15.55/8.60      ! [N: nat,M: nat,G: nat > int] :
% 15.55/8.60        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 15.55/8.60         => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.60            = one_one_int ) )
% 15.55/8.60        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 15.55/8.60         => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.60            = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6967_prod_Ocl__ivl__Suc,axiom,
% 15.55/8.60      ! [N: nat,M: nat,G: nat > nat] :
% 15.55/8.60        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 15.55/8.60         => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.60            = one_one_nat ) )
% 15.55/8.60        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 15.55/8.60         => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.60            = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6968_signed__take__bit__numeral__bit0,axiom,
% 15.55/8.60      ! [L: num,K: num] :
% 15.55/8.60        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 15.55/8.60        = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6969_signed__take__bit__numeral__minus__bit0,axiom,
% 15.55/8.60      ! [L: num,K: num] :
% 15.55/8.60        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 15.55/8.60        = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6970_signed__take__bit__numeral__bit1,axiom,
% 15.55/8.60      ! [L: num,K: num] :
% 15.55/8.60        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 15.55/8.60        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6971_numeral__eq__Suc,axiom,
% 15.55/8.60      ( numeral_numeral_nat
% 15.55/8.60      = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6972_pred__numeral__def,axiom,
% 15.55/8.60      ( pred_numeral
% 15.55/8.60      = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6973_prod_OatLeast0__atMost__Suc,axiom,
% 15.55/8.60      ! [G: nat > real,N: nat] :
% 15.55/8.60        ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 15.55/8.60        = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6974_prod_OatLeast0__atMost__Suc,axiom,
% 15.55/8.60      ! [G: nat > rat,N: nat] :
% 15.55/8.60        ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 15.55/8.60        = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6975_prod_OatLeast0__atMost__Suc,axiom,
% 15.55/8.60      ! [G: nat > int,N: nat] :
% 15.55/8.60        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 15.55/8.60        = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6976_prod_OatLeast0__atMost__Suc,axiom,
% 15.55/8.60      ! [G: nat > nat,N: nat] :
% 15.55/8.60        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 15.55/8.60        = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6977_prod_Onat__ivl__Suc_H,axiom,
% 15.55/8.60      ! [M: nat,N: nat,G: nat > real] :
% 15.55/8.60        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 15.55/8.60       => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.60          = ( times_times_real @ ( G @ ( suc @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6978_prod_Onat__ivl__Suc_H,axiom,
% 15.55/8.60      ! [M: nat,N: nat,G: nat > rat] :
% 15.55/8.60        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 15.55/8.60       => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.60          = ( times_times_rat @ ( G @ ( suc @ N ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6979_prod_Onat__ivl__Suc_H,axiom,
% 15.55/8.60      ! [M: nat,N: nat,G: nat > int] :
% 15.55/8.60        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 15.55/8.60       => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.60          = ( times_times_int @ ( G @ ( suc @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6980_prod_Onat__ivl__Suc_H,axiom,
% 15.55/8.60      ! [M: nat,N: nat,G: nat > nat] :
% 15.55/8.60        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 15.55/8.60       => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.60          = ( times_times_nat @ ( G @ ( suc @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6981_prod_OatLeast__Suc__atMost,axiom,
% 15.55/8.60      ! [M: nat,N: nat,G: nat > real] :
% 15.55/8.60        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.60       => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.60          = ( times_times_real @ ( G @ M ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6982_prod_OatLeast__Suc__atMost,axiom,
% 15.55/8.60      ! [M: nat,N: nat,G: nat > rat] :
% 15.55/8.60        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.60       => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.60          = ( times_times_rat @ ( G @ M ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6983_prod_OatLeast__Suc__atMost,axiom,
% 15.55/8.60      ! [M: nat,N: nat,G: nat > int] :
% 15.55/8.60        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.60       => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.60          = ( times_times_int @ ( G @ M ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6984_prod_OatLeast__Suc__atMost,axiom,
% 15.55/8.60      ! [M: nat,N: nat,G: nat > nat] :
% 15.55/8.60        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.60       => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.60          = ( times_times_nat @ ( G @ M ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6985_prod_OSuc__reindex__ivl,axiom,
% 15.55/8.60      ! [M: nat,N: nat,G: nat > real] :
% 15.55/8.60        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.60       => ( ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 15.55/8.60          = ( times_times_real @ ( G @ M )
% 15.55/8.60            @ ( groups129246275422532515t_real
% 15.55/8.60              @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.60              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6986_prod_OSuc__reindex__ivl,axiom,
% 15.55/8.60      ! [M: nat,N: nat,G: nat > rat] :
% 15.55/8.60        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.60       => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 15.55/8.60          = ( times_times_rat @ ( G @ M )
% 15.55/8.60            @ ( groups73079841787564623at_rat
% 15.55/8.60              @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.60              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6987_prod_OSuc__reindex__ivl,axiom,
% 15.55/8.60      ! [M: nat,N: nat,G: nat > int] :
% 15.55/8.60        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.60       => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 15.55/8.60          = ( times_times_int @ ( G @ M )
% 15.55/8.60            @ ( groups705719431365010083at_int
% 15.55/8.60              @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.60              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6988_prod_OSuc__reindex__ivl,axiom,
% 15.55/8.60      ! [M: nat,N: nat,G: nat > nat] :
% 15.55/8.60        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.60       => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 15.55/8.60          = ( times_times_nat @ ( G @ M )
% 15.55/8.60            @ ( groups708209901874060359at_nat
% 15.55/8.60              @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.60              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6989_prod_Oub__add__nat,axiom,
% 15.55/8.60      ! [M: nat,N: nat,G: nat > real,P6: nat] :
% 15.55/8.60        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 15.55/8.60       => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 15.55/8.60          = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6990_prod_Oub__add__nat,axiom,
% 15.55/8.60      ! [M: nat,N: nat,G: nat > rat,P6: nat] :
% 15.55/8.60        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 15.55/8.60       => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 15.55/8.60          = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6991_prod_Oub__add__nat,axiom,
% 15.55/8.60      ! [M: nat,N: nat,G: nat > int,P6: nat] :
% 15.55/8.60        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 15.55/8.60       => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 15.55/8.60          = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6992_prod_Oub__add__nat,axiom,
% 15.55/8.60      ! [M: nat,N: nat,G: nat > nat,P6: nat] :
% 15.55/8.60        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 15.55/8.60       => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 15.55/8.60          = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6993_dbl__dec__def,axiom,
% 15.55/8.60      ( neg_nu6511756317524482435omplex
% 15.55/8.60      = ( ^ [X: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X @ X ) @ one_one_complex ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6994_dbl__dec__def,axiom,
% 15.55/8.60      ( neg_nu6075765906172075777c_real
% 15.55/8.60      = ( ^ [X: real] : ( minus_minus_real @ ( plus_plus_real @ X @ X ) @ one_one_real ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6995_dbl__dec__def,axiom,
% 15.55/8.60      ( neg_nu3179335615603231917ec_rat
% 15.55/8.60      = ( ^ [X: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6996_dbl__dec__def,axiom,
% 15.55/8.60      ( neg_nu3811975205180677377ec_int
% 15.55/8.60      = ( ^ [X: int] : ( minus_minus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6997_pochhammer__Suc__prod,axiom,
% 15.55/8.60      ! [A: complex,N: nat] :
% 15.55/8.60        ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 15.55/8.60        = ( groups6464643781859351333omplex
% 15.55/8.60          @ ^ [I4: nat] : ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ I4 ) )
% 15.55/8.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6998_pochhammer__Suc__prod,axiom,
% 15.55/8.60      ! [A: real,N: nat] :
% 15.55/8.60        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 15.55/8.60        = ( groups129246275422532515t_real
% 15.55/8.60          @ ^ [I4: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ I4 ) )
% 15.55/8.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_6999_pochhammer__Suc__prod,axiom,
% 15.55/8.60      ! [A: rat,N: nat] :
% 15.55/8.60        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 15.55/8.60        = ( groups73079841787564623at_rat
% 15.55/8.60          @ ^ [I4: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I4 ) )
% 15.55/8.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7000_pochhammer__Suc__prod,axiom,
% 15.55/8.60      ! [A: int,N: nat] :
% 15.55/8.60        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 15.55/8.60        = ( groups705719431365010083at_int
% 15.55/8.60          @ ^ [I4: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I4 ) )
% 15.55/8.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7001_pochhammer__Suc__prod,axiom,
% 15.55/8.60      ! [A: nat,N: nat] :
% 15.55/8.60        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 15.55/8.60        = ( groups708209901874060359at_nat
% 15.55/8.60          @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I4 ) )
% 15.55/8.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7002_pochhammer__prod__rev,axiom,
% 15.55/8.60      ( comm_s2602460028002588243omplex
% 15.55/8.60      = ( ^ [A4: complex,N3: nat] :
% 15.55/8.60            ( groups6464643781859351333omplex
% 15.55/8.60            @ ^ [I4: nat] : ( plus_plus_complex @ A4 @ ( semiri8010041392384452111omplex @ ( minus_minus_nat @ N3 @ I4 ) ) )
% 15.55/8.60            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7003_pochhammer__prod__rev,axiom,
% 15.55/8.60      ( comm_s7457072308508201937r_real
% 15.55/8.60      = ( ^ [A4: real,N3: nat] :
% 15.55/8.60            ( groups129246275422532515t_real
% 15.55/8.60            @ ^ [I4: nat] : ( plus_plus_real @ A4 @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N3 @ I4 ) ) )
% 15.55/8.60            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7004_pochhammer__prod__rev,axiom,
% 15.55/8.60      ( comm_s4028243227959126397er_rat
% 15.55/8.60      = ( ^ [A4: rat,N3: nat] :
% 15.55/8.60            ( groups73079841787564623at_rat
% 15.55/8.60            @ ^ [I4: nat] : ( plus_plus_rat @ A4 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N3 @ I4 ) ) )
% 15.55/8.60            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7005_pochhammer__prod__rev,axiom,
% 15.55/8.60      ( comm_s4660882817536571857er_int
% 15.55/8.60      = ( ^ [A4: int,N3: nat] :
% 15.55/8.60            ( groups705719431365010083at_int
% 15.55/8.60            @ ^ [I4: nat] : ( plus_plus_int @ A4 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N3 @ I4 ) ) )
% 15.55/8.60            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7006_pochhammer__prod__rev,axiom,
% 15.55/8.60      ( comm_s4663373288045622133er_nat
% 15.55/8.60      = ( ^ [A4: nat,N3: nat] :
% 15.55/8.60            ( groups708209901874060359at_nat
% 15.55/8.60            @ ^ [I4: nat] : ( plus_plus_nat @ A4 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N3 @ I4 ) ) )
% 15.55/8.60            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7007_take__bit__numeral__bit0,axiom,
% 15.55/8.60      ! [L: num,K: num] :
% 15.55/8.60        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 15.55/8.60        = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7008_take__bit__numeral__bit0,axiom,
% 15.55/8.60      ! [L: num,K: num] :
% 15.55/8.60        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 15.55/8.60        = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7009_prod_Oin__pairs,axiom,
% 15.55/8.60      ! [G: nat > real,M: nat,N: nat] :
% 15.55/8.60        ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 15.55/8.60        = ( groups129246275422532515t_real
% 15.55/8.60          @ ^ [I4: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 15.55/8.60          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7010_prod_Oin__pairs,axiom,
% 15.55/8.60      ! [G: nat > rat,M: nat,N: nat] :
% 15.55/8.60        ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 15.55/8.60        = ( groups73079841787564623at_rat
% 15.55/8.60          @ ^ [I4: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 15.55/8.60          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7011_prod_Oin__pairs,axiom,
% 15.55/8.60      ! [G: nat > int,M: nat,N: nat] :
% 15.55/8.60        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 15.55/8.60        = ( groups705719431365010083at_int
% 15.55/8.60          @ ^ [I4: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 15.55/8.60          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7012_prod_Oin__pairs,axiom,
% 15.55/8.60      ! [G: nat > nat,M: nat,N: nat] :
% 15.55/8.60        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 15.55/8.60        = ( groups708209901874060359at_nat
% 15.55/8.60          @ ^ [I4: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 15.55/8.60          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7013_pochhammer__Suc__prod__rev,axiom,
% 15.55/8.60      ! [A: complex,N: nat] :
% 15.55/8.60        ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 15.55/8.60        = ( groups6464643781859351333omplex
% 15.55/8.60          @ ^ [I4: nat] : ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ ( minus_minus_nat @ N @ I4 ) ) )
% 15.55/8.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7014_pochhammer__Suc__prod__rev,axiom,
% 15.55/8.60      ! [A: real,N: nat] :
% 15.55/8.60        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 15.55/8.60        = ( groups129246275422532515t_real
% 15.55/8.60          @ ^ [I4: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ I4 ) ) )
% 15.55/8.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7015_pochhammer__Suc__prod__rev,axiom,
% 15.55/8.60      ! [A: rat,N: nat] :
% 15.55/8.60        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 15.55/8.60        = ( groups73079841787564623at_rat
% 15.55/8.60          @ ^ [I4: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I4 ) ) )
% 15.55/8.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7016_pochhammer__Suc__prod__rev,axiom,
% 15.55/8.60      ! [A: int,N: nat] :
% 15.55/8.60        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 15.55/8.60        = ( groups705719431365010083at_int
% 15.55/8.60          @ ^ [I4: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I4 ) ) )
% 15.55/8.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7017_pochhammer__Suc__prod__rev,axiom,
% 15.55/8.60      ! [A: nat,N: nat] :
% 15.55/8.60        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 15.55/8.60        = ( groups708209901874060359at_nat
% 15.55/8.60          @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I4 ) ) )
% 15.55/8.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7018_take__bit__numeral__minus__bit0,axiom,
% 15.55/8.60      ! [L: num,K: num] :
% 15.55/8.60        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 15.55/8.60        = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7019_take__bit__numeral__bit1,axiom,
% 15.55/8.60      ! [L: num,K: num] :
% 15.55/8.60        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 15.55/8.60        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7020_take__bit__numeral__bit1,axiom,
% 15.55/8.60      ! [L: num,K: num] :
% 15.55/8.60        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 15.55/8.60        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7021_suminf__geometric,axiom,
% 15.55/8.60      ! [C: real] :
% 15.55/8.60        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 15.55/8.60       => ( ( suminf_real @ ( power_power_real @ C ) )
% 15.55/8.60          = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7022_suminf__geometric,axiom,
% 15.55/8.60      ! [C: complex] :
% 15.55/8.60        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 15.55/8.60       => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 15.55/8.60          = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7023_suminf__zero,axiom,
% 15.55/8.60      ( ( suminf_real
% 15.55/8.60        @ ^ [N3: nat] : zero_zero_real )
% 15.55/8.60      = zero_zero_real ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7024_suminf__zero,axiom,
% 15.55/8.60      ( ( suminf_nat
% 15.55/8.60        @ ^ [N3: nat] : zero_zero_nat )
% 15.55/8.60      = zero_zero_nat ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7025_suminf__zero,axiom,
% 15.55/8.60      ( ( suminf_int
% 15.55/8.60        @ ^ [N3: nat] : zero_zero_int )
% 15.55/8.60      = zero_zero_int ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7026_pi__series,axiom,
% 15.55/8.60      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 15.55/8.60      = ( suminf_real
% 15.55/8.60        @ ^ [K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7027_take__bit__numeral__minus__bit1,axiom,
% 15.55/8.60      ! [L: num,K: num] :
% 15.55/8.60        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 15.55/8.60        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7028_prod__le__1,axiom,
% 15.55/8.60      ! [A3: set_real,F: real > real] :
% 15.55/8.60        ( ! [X4: real] :
% 15.55/8.60            ( ( member_real @ X4 @ A3 )
% 15.55/8.60           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 15.55/8.60              & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 15.55/8.60       => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A3 ) @ one_one_real ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7029_prod__le__1,axiom,
% 15.55/8.60      ! [A3: set_nat,F: nat > real] :
% 15.55/8.60        ( ! [X4: nat] :
% 15.55/8.60            ( ( member_nat @ X4 @ A3 )
% 15.55/8.60           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 15.55/8.60              & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 15.55/8.60       => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A3 ) @ one_one_real ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7030_prod__le__1,axiom,
% 15.55/8.60      ! [A3: set_int,F: int > real] :
% 15.55/8.60        ( ! [X4: int] :
% 15.55/8.60            ( ( member_int @ X4 @ A3 )
% 15.55/8.60           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 15.55/8.60              & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 15.55/8.60       => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A3 ) @ one_one_real ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7031_prod__le__1,axiom,
% 15.55/8.60      ! [A3: set_real,F: real > rat] :
% 15.55/8.60        ( ! [X4: real] :
% 15.55/8.60            ( ( member_real @ X4 @ A3 )
% 15.55/8.60           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 15.55/8.60              & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 15.55/8.60       => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A3 ) @ one_one_rat ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7032_prod__le__1,axiom,
% 15.55/8.60      ! [A3: set_nat,F: nat > rat] :
% 15.55/8.60        ( ! [X4: nat] :
% 15.55/8.60            ( ( member_nat @ X4 @ A3 )
% 15.55/8.60           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 15.55/8.60              & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 15.55/8.60       => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A3 ) @ one_one_rat ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7033_prod__le__1,axiom,
% 15.55/8.60      ! [A3: set_int,F: int > rat] :
% 15.55/8.60        ( ! [X4: int] :
% 15.55/8.60            ( ( member_int @ X4 @ A3 )
% 15.55/8.60           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 15.55/8.60              & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 15.55/8.60       => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A3 ) @ one_one_rat ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7034_prod__le__1,axiom,
% 15.55/8.60      ! [A3: set_real,F: real > nat] :
% 15.55/8.60        ( ! [X4: real] :
% 15.55/8.60            ( ( member_real @ X4 @ A3 )
% 15.55/8.60           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 15.55/8.60              & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 15.55/8.60       => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A3 ) @ one_one_nat ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7035_prod__le__1,axiom,
% 15.55/8.60      ! [A3: set_int,F: int > nat] :
% 15.55/8.60        ( ! [X4: int] :
% 15.55/8.60            ( ( member_int @ X4 @ A3 )
% 15.55/8.60           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 15.55/8.60              & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 15.55/8.60       => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A3 ) @ one_one_nat ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7036_prod__le__1,axiom,
% 15.55/8.60      ! [A3: set_real,F: real > int] :
% 15.55/8.60        ( ! [X4: real] :
% 15.55/8.60            ( ( member_real @ X4 @ A3 )
% 15.55/8.60           => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) )
% 15.55/8.60              & ( ord_less_eq_int @ ( F @ X4 ) @ one_one_int ) ) )
% 15.55/8.60       => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F @ A3 ) @ one_one_int ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7037_prod__le__1,axiom,
% 15.55/8.60      ! [A3: set_nat,F: nat > int] :
% 15.55/8.60        ( ! [X4: nat] :
% 15.55/8.60            ( ( member_nat @ X4 @ A3 )
% 15.55/8.60           => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) )
% 15.55/8.60              & ( ord_less_eq_int @ ( F @ X4 ) @ one_one_int ) ) )
% 15.55/8.60       => ( ord_less_eq_int @ ( groups705719431365010083at_int @ F @ A3 ) @ one_one_int ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7038_pred__numeral__inc,axiom,
% 15.55/8.60      ! [K: num] :
% 15.55/8.60        ( ( pred_numeral @ ( inc @ K ) )
% 15.55/8.60        = ( numeral_numeral_nat @ K ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7039_add__neg__numeral__special_I6_J,axiom,
% 15.55/8.60      ! [M: num] :
% 15.55/8.60        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 15.55/8.60        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7040_add__neg__numeral__special_I6_J,axiom,
% 15.55/8.60      ! [M: num] :
% 15.55/8.60        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.60        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7041_add__neg__numeral__special_I6_J,axiom,
% 15.55/8.60      ! [M: num] :
% 15.55/8.60        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 15.55/8.60        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7042_add__neg__numeral__special_I6_J,axiom,
% 15.55/8.60      ! [M: num] :
% 15.55/8.60        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 15.55/8.60        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7043_add__neg__numeral__special_I6_J,axiom,
% 15.55/8.60      ! [M: num] :
% 15.55/8.60        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 15.55/8.60        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7044_add__neg__numeral__special_I5_J,axiom,
% 15.55/8.60      ! [N: num] :
% 15.55/8.60        ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 15.55/8.60        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7045_add__neg__numeral__special_I5_J,axiom,
% 15.55/8.60      ! [N: num] :
% 15.55/8.60        ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.60        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7046_add__neg__numeral__special_I5_J,axiom,
% 15.55/8.60      ! [N: num] :
% 15.55/8.60        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 15.55/8.60        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7047_add__neg__numeral__special_I5_J,axiom,
% 15.55/8.60      ! [N: num] :
% 15.55/8.60        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 15.55/8.60        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7048_add__neg__numeral__special_I5_J,axiom,
% 15.55/8.60      ! [N: num] :
% 15.55/8.60        ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 15.55/8.60        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7049_diff__numeral__special_I6_J,axiom,
% 15.55/8.60      ! [M: num] :
% 15.55/8.60        ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) )
% 15.55/8.60        = ( numeral_numeral_real @ ( inc @ M ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7050_diff__numeral__special_I6_J,axiom,
% 15.55/8.60      ! [M: num] :
% 15.55/8.60        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.60        = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7051_diff__numeral__special_I6_J,axiom,
% 15.55/8.60      ! [M: num] :
% 15.55/8.60        ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 15.55/8.60        = ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7052_diff__numeral__special_I6_J,axiom,
% 15.55/8.60      ! [M: num] :
% 15.55/8.60        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 15.55/8.60        = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7053_diff__numeral__special_I6_J,axiom,
% 15.55/8.60      ! [M: num] :
% 15.55/8.60        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 15.55/8.60        = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7054_diff__numeral__special_I5_J,axiom,
% 15.55/8.60      ! [N: num] :
% 15.55/8.60        ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ N ) )
% 15.55/8.60        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7055_diff__numeral__special_I5_J,axiom,
% 15.55/8.60      ! [N: num] :
% 15.55/8.60        ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 15.55/8.60        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7056_diff__numeral__special_I5_J,axiom,
% 15.55/8.60      ! [N: num] :
% 15.55/8.60        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( numera6690914467698888265omplex @ N ) )
% 15.55/8.60        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7057_diff__numeral__special_I5_J,axiom,
% 15.55/8.60      ! [N: num] :
% 15.55/8.60        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 15.55/8.60        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7058_diff__numeral__special_I5_J,axiom,
% 15.55/8.60      ! [N: num] :
% 15.55/8.60        ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 15.55/8.60        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7059_int__prod,axiom,
% 15.55/8.60      ! [F: int > nat,A3: set_int] :
% 15.55/8.60        ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F @ A3 ) )
% 15.55/8.60        = ( groups1705073143266064639nt_int
% 15.55/8.60          @ ^ [X: int] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 15.55/8.60          @ A3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7060_int__prod,axiom,
% 15.55/8.60      ! [F: nat > nat,A3: set_nat] :
% 15.55/8.60        ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 15.55/8.60        = ( groups705719431365010083at_int
% 15.55/8.60          @ ^ [X: nat] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 15.55/8.60          @ A3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7061_pi__neq__zero,axiom,
% 15.55/8.60      pi != zero_zero_real ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7062_num__induct,axiom,
% 15.55/8.60      ! [P: num > $o,X3: num] :
% 15.55/8.60        ( ( P @ one )
% 15.55/8.60       => ( ! [X4: num] :
% 15.55/8.60              ( ( P @ X4 )
% 15.55/8.60             => ( P @ ( inc @ X4 ) ) )
% 15.55/8.60         => ( P @ X3 ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7063_add__inc,axiom,
% 15.55/8.60      ! [X3: num,Y3: num] :
% 15.55/8.60        ( ( plus_plus_num @ X3 @ ( inc @ Y3 ) )
% 15.55/8.60        = ( inc @ ( plus_plus_num @ X3 @ Y3 ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7064_pi__gt__zero,axiom,
% 15.55/8.60      ord_less_real @ zero_zero_real @ pi ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7065_pi__not__less__zero,axiom,
% 15.55/8.60      ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7066_pi__ge__zero,axiom,
% 15.55/8.60      ord_less_eq_real @ zero_zero_real @ pi ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7067_inc_Osimps_I1_J,axiom,
% 15.55/8.60      ( ( inc @ one )
% 15.55/8.60      = ( bit0 @ one ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7068_inc_Osimps_I3_J,axiom,
% 15.55/8.60      ! [X3: num] :
% 15.55/8.60        ( ( inc @ ( bit1 @ X3 ) )
% 15.55/8.60        = ( bit0 @ ( inc @ X3 ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7069_inc_Osimps_I2_J,axiom,
% 15.55/8.60      ! [X3: num] :
% 15.55/8.60        ( ( inc @ ( bit0 @ X3 ) )
% 15.55/8.60        = ( bit1 @ X3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7070_add__One,axiom,
% 15.55/8.60      ! [X3: num] :
% 15.55/8.60        ( ( plus_plus_num @ X3 @ one )
% 15.55/8.60        = ( inc @ X3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7071_mult__inc,axiom,
% 15.55/8.60      ! [X3: num,Y3: num] :
% 15.55/8.60        ( ( times_times_num @ X3 @ ( inc @ Y3 ) )
% 15.55/8.60        = ( plus_plus_num @ ( times_times_num @ X3 @ Y3 ) @ X3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7072_prod__int__eq,axiom,
% 15.55/8.60      ! [I: nat,J: nat] :
% 15.55/8.60        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 15.55/8.60        = ( groups1705073143266064639nt_int
% 15.55/8.60          @ ^ [X: int] : X
% 15.55/8.60          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7073_numeral__inc,axiom,
% 15.55/8.60      ! [X3: num] :
% 15.55/8.60        ( ( numera6690914467698888265omplex @ ( inc @ X3 ) )
% 15.55/8.60        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X3 ) @ one_one_complex ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7074_numeral__inc,axiom,
% 15.55/8.60      ! [X3: num] :
% 15.55/8.60        ( ( numeral_numeral_real @ ( inc @ X3 ) )
% 15.55/8.60        = ( plus_plus_real @ ( numeral_numeral_real @ X3 ) @ one_one_real ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7075_numeral__inc,axiom,
% 15.55/8.60      ! [X3: num] :
% 15.55/8.60        ( ( numeral_numeral_rat @ ( inc @ X3 ) )
% 15.55/8.60        = ( plus_plus_rat @ ( numeral_numeral_rat @ X3 ) @ one_one_rat ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7076_numeral__inc,axiom,
% 15.55/8.60      ! [X3: num] :
% 15.55/8.60        ( ( numeral_numeral_nat @ ( inc @ X3 ) )
% 15.55/8.60        = ( plus_plus_nat @ ( numeral_numeral_nat @ X3 ) @ one_one_nat ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7077_numeral__inc,axiom,
% 15.55/8.60      ! [X3: num] :
% 15.55/8.60        ( ( numeral_numeral_int @ ( inc @ X3 ) )
% 15.55/8.60        = ( plus_plus_int @ ( numeral_numeral_int @ X3 ) @ one_one_int ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7078_pi__less__4,axiom,
% 15.55/8.60      ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7079_pi__ge__two,axiom,
% 15.55/8.60      ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7080_pi__half__neq__two,axiom,
% 15.55/8.60      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 15.55/8.60     != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7081_prod__int__plus__eq,axiom,
% 15.55/8.60      ! [I: nat,J: nat] :
% 15.55/8.60        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 15.55/8.60        = ( groups1705073143266064639nt_int
% 15.55/8.60          @ ^ [X: int] : X
% 15.55/8.60          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7082_pi__half__neq__zero,axiom,
% 15.55/8.60      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 15.55/8.60     != zero_zero_real ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7083_pi__half__less__two,axiom,
% 15.55/8.60      ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7084_pi__half__le__two,axiom,
% 15.55/8.60      ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7085_pi__half__gt__zero,axiom,
% 15.55/8.60      ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7086_pi__half__ge__zero,axiom,
% 15.55/8.60      ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7087_m2pi__less__pi,axiom,
% 15.55/8.60      ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7088_arctan__ubound,axiom,
% 15.55/8.60      ! [Y3: real] : ( ord_less_real @ ( arctan @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7089_arctan__one,axiom,
% 15.55/8.60      ( ( arctan @ one_one_real )
% 15.55/8.60      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7090_minus__pi__half__less__zero,axiom,
% 15.55/8.60      ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7091_arctan__bounded,axiom,
% 15.55/8.60      ! [Y3: real] :
% 15.55/8.60        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y3 ) )
% 15.55/8.60        & ( ord_less_real @ ( arctan @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7092_arctan__lbound,axiom,
% 15.55/8.60      ! [Y3: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y3 ) ) ).
% 15.55/8.60  
% 15.55/8.60  thf(fact_7093_prod__power__distrib,axiom,
% 15.55/8.60      ! [F: nat > int,A3: set_nat,N: nat] :
% 15.55/8.61        ( ( power_power_int @ ( groups705719431365010083at_int @ F @ A3 ) @ N )
% 15.55/8.61        = ( groups705719431365010083at_int
% 15.55/8.61          @ ^ [X: nat] : ( power_power_int @ ( F @ X ) @ N )
% 15.55/8.61          @ A3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7094_prod__power__distrib,axiom,
% 15.55/8.61      ! [F: int > int,A3: set_int,N: nat] :
% 15.55/8.61        ( ( power_power_int @ ( groups1705073143266064639nt_int @ F @ A3 ) @ N )
% 15.55/8.61        = ( groups1705073143266064639nt_int
% 15.55/8.61          @ ^ [X: int] : ( power_power_int @ ( F @ X ) @ N )
% 15.55/8.61          @ A3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7095_prod__power__distrib,axiom,
% 15.55/8.61      ! [F: nat > nat,A3: set_nat,N: nat] :
% 15.55/8.61        ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A3 ) @ N )
% 15.55/8.61        = ( groups708209901874060359at_nat
% 15.55/8.61          @ ^ [X: nat] : ( power_power_nat @ ( F @ X ) @ N )
% 15.55/8.61          @ A3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7096_machin__Euler,axiom,
% 15.55/8.61      ( ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.61      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7097_machin,axiom,
% 15.55/8.61      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 15.55/8.61      = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7098_prod__mono,axiom,
% 15.55/8.61      ! [A3: set_real,F: real > real,G: real > real] :
% 15.55/8.61        ( ! [I3: real] :
% 15.55/8.61            ( ( member_real @ I3 @ A3 )
% 15.55/8.61           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 15.55/8.61              & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 15.55/8.61       => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A3 ) @ ( groups1681761925125756287l_real @ G @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7099_prod__mono,axiom,
% 15.55/8.61      ! [A3: set_nat,F: nat > real,G: nat > real] :
% 15.55/8.61        ( ! [I3: nat] :
% 15.55/8.61            ( ( member_nat @ I3 @ A3 )
% 15.55/8.61           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 15.55/8.61              & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 15.55/8.61       => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A3 ) @ ( groups129246275422532515t_real @ G @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7100_prod__mono,axiom,
% 15.55/8.61      ! [A3: set_int,F: int > real,G: int > real] :
% 15.55/8.61        ( ! [I3: int] :
% 15.55/8.61            ( ( member_int @ I3 @ A3 )
% 15.55/8.61           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 15.55/8.61              & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 15.55/8.61       => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A3 ) @ ( groups2316167850115554303t_real @ G @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7101_prod__mono,axiom,
% 15.55/8.61      ! [A3: set_real,F: real > rat,G: real > rat] :
% 15.55/8.61        ( ! [I3: real] :
% 15.55/8.61            ( ( member_real @ I3 @ A3 )
% 15.55/8.61           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 15.55/8.61              & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 15.55/8.61       => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A3 ) @ ( groups4061424788464935467al_rat @ G @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7102_prod__mono,axiom,
% 15.55/8.61      ! [A3: set_nat,F: nat > rat,G: nat > rat] :
% 15.55/8.61        ( ! [I3: nat] :
% 15.55/8.61            ( ( member_nat @ I3 @ A3 )
% 15.55/8.61           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 15.55/8.61              & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 15.55/8.61       => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A3 ) @ ( groups73079841787564623at_rat @ G @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7103_prod__mono,axiom,
% 15.55/8.61      ! [A3: set_int,F: int > rat,G: int > rat] :
% 15.55/8.61        ( ! [I3: int] :
% 15.55/8.61            ( ( member_int @ I3 @ A3 )
% 15.55/8.61           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 15.55/8.61              & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 15.55/8.61       => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A3 ) @ ( groups1072433553688619179nt_rat @ G @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7104_prod__mono,axiom,
% 15.55/8.61      ! [A3: set_real,F: real > nat,G: real > nat] :
% 15.55/8.61        ( ! [I3: real] :
% 15.55/8.61            ( ( member_real @ I3 @ A3 )
% 15.55/8.61           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 15.55/8.61              & ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 15.55/8.61       => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A3 ) @ ( groups4696554848551431203al_nat @ G @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7105_prod__mono,axiom,
% 15.55/8.61      ! [A3: set_int,F: int > nat,G: int > nat] :
% 15.55/8.61        ( ! [I3: int] :
% 15.55/8.61            ( ( member_int @ I3 @ A3 )
% 15.55/8.61           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 15.55/8.61              & ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 15.55/8.61       => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A3 ) @ ( groups1707563613775114915nt_nat @ G @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7106_prod__mono,axiom,
% 15.55/8.61      ! [A3: set_real,F: real > int,G: real > int] :
% 15.55/8.61        ( ! [I3: real] :
% 15.55/8.61            ( ( member_real @ I3 @ A3 )
% 15.55/8.61           => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I3 ) )
% 15.55/8.61              & ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 15.55/8.61       => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F @ A3 ) @ ( groups4694064378042380927al_int @ G @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7107_prod__mono,axiom,
% 15.55/8.61      ! [A3: set_nat,F: nat > int,G: nat > int] :
% 15.55/8.61        ( ! [I3: nat] :
% 15.55/8.61            ( ( member_nat @ I3 @ A3 )
% 15.55/8.61           => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I3 ) )
% 15.55/8.61              & ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 15.55/8.61       => ( ord_less_eq_int @ ( groups705719431365010083at_int @ F @ A3 ) @ ( groups705719431365010083at_int @ G @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7108_prod__nonneg,axiom,
% 15.55/8.61      ! [A3: set_nat,F: nat > int] :
% 15.55/8.61        ( ! [X4: nat] :
% 15.55/8.61            ( ( member_nat @ X4 @ A3 )
% 15.55/8.61           => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 15.55/8.61       => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7109_prod__nonneg,axiom,
% 15.55/8.61      ! [A3: set_int,F: int > int] :
% 15.55/8.61        ( ! [X4: int] :
% 15.55/8.61            ( ( member_int @ X4 @ A3 )
% 15.55/8.61           => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 15.55/8.61       => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7110_prod__nonneg,axiom,
% 15.55/8.61      ! [A3: set_nat,F: nat > nat] :
% 15.55/8.61        ( ! [X4: nat] :
% 15.55/8.61            ( ( member_nat @ X4 @ A3 )
% 15.55/8.61           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 15.55/8.61       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7111_prod__pos,axiom,
% 15.55/8.61      ! [A3: set_nat,F: nat > int] :
% 15.55/8.61        ( ! [X4: nat] :
% 15.55/8.61            ( ( member_nat @ X4 @ A3 )
% 15.55/8.61           => ( ord_less_int @ zero_zero_int @ ( F @ X4 ) ) )
% 15.55/8.61       => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7112_prod__pos,axiom,
% 15.55/8.61      ! [A3: set_int,F: int > int] :
% 15.55/8.61        ( ! [X4: int] :
% 15.55/8.61            ( ( member_int @ X4 @ A3 )
% 15.55/8.61           => ( ord_less_int @ zero_zero_int @ ( F @ X4 ) ) )
% 15.55/8.61       => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7113_prod__pos,axiom,
% 15.55/8.61      ! [A3: set_nat,F: nat > nat] :
% 15.55/8.61        ( ! [X4: nat] :
% 15.55/8.61            ( ( member_nat @ X4 @ A3 )
% 15.55/8.61           => ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 15.55/8.61       => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7114_prod__ge__1,axiom,
% 15.55/8.61      ! [A3: set_real,F: real > real] :
% 15.55/8.61        ( ! [X4: real] :
% 15.55/8.61            ( ( member_real @ X4 @ A3 )
% 15.55/8.61           => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 15.55/8.61       => ( ord_less_eq_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7115_prod__ge__1,axiom,
% 15.55/8.61      ! [A3: set_nat,F: nat > real] :
% 15.55/8.61        ( ! [X4: nat] :
% 15.55/8.61            ( ( member_nat @ X4 @ A3 )
% 15.55/8.61           => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 15.55/8.61       => ( ord_less_eq_real @ one_one_real @ ( groups129246275422532515t_real @ F @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7116_prod__ge__1,axiom,
% 15.55/8.61      ! [A3: set_int,F: int > real] :
% 15.55/8.61        ( ! [X4: int] :
% 15.55/8.61            ( ( member_int @ X4 @ A3 )
% 15.55/8.61           => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 15.55/8.61       => ( ord_less_eq_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7117_prod__ge__1,axiom,
% 15.55/8.61      ! [A3: set_real,F: real > rat] :
% 15.55/8.61        ( ! [X4: real] :
% 15.55/8.61            ( ( member_real @ X4 @ A3 )
% 15.55/8.61           => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 15.55/8.61       => ( ord_less_eq_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7118_prod__ge__1,axiom,
% 15.55/8.61      ! [A3: set_nat,F: nat > rat] :
% 15.55/8.61        ( ! [X4: nat] :
% 15.55/8.61            ( ( member_nat @ X4 @ A3 )
% 15.55/8.61           => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 15.55/8.61       => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7119_prod__ge__1,axiom,
% 15.55/8.61      ! [A3: set_int,F: int > rat] :
% 15.55/8.61        ( ! [X4: int] :
% 15.55/8.61            ( ( member_int @ X4 @ A3 )
% 15.55/8.61           => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 15.55/8.61       => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7120_prod__ge__1,axiom,
% 15.55/8.61      ! [A3: set_real,F: real > nat] :
% 15.55/8.61        ( ! [X4: real] :
% 15.55/8.61            ( ( member_real @ X4 @ A3 )
% 15.55/8.61           => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 15.55/8.61       => ( ord_less_eq_nat @ one_one_nat @ ( groups4696554848551431203al_nat @ F @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7121_prod__ge__1,axiom,
% 15.55/8.61      ! [A3: set_int,F: int > nat] :
% 15.55/8.61        ( ! [X4: int] :
% 15.55/8.61            ( ( member_int @ X4 @ A3 )
% 15.55/8.61           => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 15.55/8.61       => ( ord_less_eq_nat @ one_one_nat @ ( groups1707563613775114915nt_nat @ F @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7122_prod__ge__1,axiom,
% 15.55/8.61      ! [A3: set_real,F: real > int] :
% 15.55/8.61        ( ! [X4: real] :
% 15.55/8.61            ( ( member_real @ X4 @ A3 )
% 15.55/8.61           => ( ord_less_eq_int @ one_one_int @ ( F @ X4 ) ) )
% 15.55/8.61       => ( ord_less_eq_int @ one_one_int @ ( groups4694064378042380927al_int @ F @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7123_prod__ge__1,axiom,
% 15.55/8.61      ! [A3: set_nat,F: nat > int] :
% 15.55/8.61        ( ! [X4: nat] :
% 15.55/8.61            ( ( member_nat @ X4 @ A3 )
% 15.55/8.61           => ( ord_less_eq_int @ one_one_int @ ( F @ X4 ) ) )
% 15.55/8.61       => ( ord_less_eq_int @ one_one_int @ ( groups705719431365010083at_int @ F @ A3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7124_take__bit__Suc__minus__bit1,axiom,
% 15.55/8.61      ! [N: nat,K: num] :
% 15.55/8.61        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 15.55/8.61        = ( 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 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7125_sin__cos__npi,axiom,
% 15.55/8.61      ! [N: nat] :
% 15.55/8.61        ( ( 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 ) ) ) )
% 15.55/8.61        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7126_divmod__algorithm__code_I7_J,axiom,
% 15.55/8.61      ! [M: num,N: num] :
% 15.55/8.61        ( ( ( ord_less_eq_num @ M @ N )
% 15.55/8.61         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 15.55/8.61            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 15.55/8.61        & ( ~ ( ord_less_eq_num @ M @ N )
% 15.55/8.61         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 15.55/8.61            = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7127_divmod__algorithm__code_I7_J,axiom,
% 15.55/8.61      ! [M: num,N: num] :
% 15.55/8.61        ( ( ( ord_less_eq_num @ M @ N )
% 15.55/8.61         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 15.55/8.61            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 15.55/8.61        & ( ~ ( ord_less_eq_num @ M @ N )
% 15.55/8.61         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 15.55/8.61            = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7128_divmod__algorithm__code_I7_J,axiom,
% 15.55/8.61      ! [M: num,N: num] :
% 15.55/8.61        ( ( ( ord_less_eq_num @ M @ N )
% 15.55/8.61         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 15.55/8.61            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 15.55/8.61        & ( ~ ( ord_less_eq_num @ M @ N )
% 15.55/8.61         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 15.55/8.61            = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7129_divmod__algorithm__code_I8_J,axiom,
% 15.55/8.61      ! [M: num,N: num] :
% 15.55/8.61        ( ( ( ord_less_num @ M @ N )
% 15.55/8.61         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 15.55/8.61            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 15.55/8.61        & ( ~ ( ord_less_num @ M @ N )
% 15.55/8.61         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 15.55/8.61            = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7130_divmod__algorithm__code_I8_J,axiom,
% 15.55/8.61      ! [M: num,N: num] :
% 15.55/8.61        ( ( ( ord_less_num @ M @ N )
% 15.55/8.61         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 15.55/8.61            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 15.55/8.61        & ( ~ ( ord_less_num @ M @ N )
% 15.55/8.61         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 15.55/8.61            = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7131_divmod__algorithm__code_I8_J,axiom,
% 15.55/8.61      ! [M: num,N: num] :
% 15.55/8.61        ( ( ( ord_less_num @ M @ N )
% 15.55/8.61         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 15.55/8.61            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 15.55/8.61        & ( ~ ( ord_less_num @ M @ N )
% 15.55/8.61         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 15.55/8.61            = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7132_divides__aux__eq,axiom,
% 15.55/8.61      ! [Q3: nat,R2: nat] :
% 15.55/8.61        ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 15.55/8.61        = ( R2 = zero_zero_nat ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7133_divides__aux__eq,axiom,
% 15.55/8.61      ! [Q3: int,R2: int] :
% 15.55/8.61        ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 15.55/8.61        = ( R2 = zero_zero_int ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7134_summable__arctan__series,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 15.55/8.61       => ( summable_real
% 15.55/8.61          @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7135_sin__zero,axiom,
% 15.55/8.61      ( ( sin_real @ zero_zero_real )
% 15.55/8.61      = zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7136_summable__single,axiom,
% 15.55/8.61      ! [I: nat,F: nat > real] :
% 15.55/8.61        ( summable_real
% 15.55/8.61        @ ^ [R5: nat] : ( if_real @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_real ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7137_summable__single,axiom,
% 15.55/8.61      ! [I: nat,F: nat > nat] :
% 15.55/8.61        ( summable_nat
% 15.55/8.61        @ ^ [R5: nat] : ( if_nat @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_nat ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7138_summable__single,axiom,
% 15.55/8.61      ! [I: nat,F: nat > int] :
% 15.55/8.61        ( summable_int
% 15.55/8.61        @ ^ [R5: nat] : ( if_int @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_int ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7139_summable__zero,axiom,
% 15.55/8.61      ( summable_real
% 15.55/8.61      @ ^ [N3: nat] : zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7140_summable__zero,axiom,
% 15.55/8.61      ( summable_nat
% 15.55/8.61      @ ^ [N3: nat] : zero_zero_nat ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7141_summable__zero,axiom,
% 15.55/8.61      ( summable_int
% 15.55/8.61      @ ^ [N3: nat] : zero_zero_int ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7142_sin__pi,axiom,
% 15.55/8.61      ( ( sin_real @ pi )
% 15.55/8.61      = zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7143_summable__cmult__iff,axiom,
% 15.55/8.61      ! [C: real,F: nat > real] :
% 15.55/8.61        ( ( summable_real
% 15.55/8.61          @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) ) )
% 15.55/8.61        = ( ( C = zero_zero_real )
% 15.55/8.61          | ( summable_real @ F ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7144_summable__divide__iff,axiom,
% 15.55/8.61      ! [F: nat > complex,C: complex] :
% 15.55/8.61        ( ( summable_complex
% 15.55/8.61          @ ^ [N3: nat] : ( divide1717551699836669952omplex @ ( F @ N3 ) @ C ) )
% 15.55/8.61        = ( ( C = zero_zero_complex )
% 15.55/8.61          | ( summable_complex @ F ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7145_summable__divide__iff,axiom,
% 15.55/8.61      ! [F: nat > real,C: real] :
% 15.55/8.61        ( ( summable_real
% 15.55/8.61          @ ^ [N3: nat] : ( divide_divide_real @ ( F @ N3 ) @ C ) )
% 15.55/8.61        = ( ( C = zero_zero_real )
% 15.55/8.61          | ( summable_real @ F ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7146_sin__of__real__pi,axiom,
% 15.55/8.61      ( ( sin_real @ ( real_V1803761363581548252l_real @ pi ) )
% 15.55/8.61      = zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7147_sin__of__real__pi,axiom,
% 15.55/8.61      ( ( sin_complex @ ( real_V4546457046886955230omplex @ pi ) )
% 15.55/8.61      = zero_zero_complex ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7148_dvd__numeral__simp,axiom,
% 15.55/8.61      ! [M: num,N: num] :
% 15.55/8.61        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 15.55/8.61        = ( unique5706413561485394159nteger @ ( unique3479559517661332726nteger @ N @ M ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7149_dvd__numeral__simp,axiom,
% 15.55/8.61      ! [M: num,N: num] :
% 15.55/8.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 15.55/8.61        = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N @ M ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7150_dvd__numeral__simp,axiom,
% 15.55/8.61      ! [M: num,N: num] :
% 15.55/8.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 15.55/8.61        = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N @ M ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7151_divmod__algorithm__code_I2_J,axiom,
% 15.55/8.61      ! [M: num] :
% 15.55/8.61        ( ( unique5052692396658037445od_int @ M @ one )
% 15.55/8.61        = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7152_divmod__algorithm__code_I2_J,axiom,
% 15.55/8.61      ! [M: num] :
% 15.55/8.61        ( ( unique5055182867167087721od_nat @ M @ one )
% 15.55/8.61        = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7153_sin__npi,axiom,
% 15.55/8.61      ! [N: nat] :
% 15.55/8.61        ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 15.55/8.61        = zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7154_sin__npi2,axiom,
% 15.55/8.61      ! [N: nat] :
% 15.55/8.61        ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 15.55/8.61        = zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7155_sin__npi__int,axiom,
% 15.55/8.61      ! [N: int] :
% 15.55/8.61        ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 15.55/8.61        = zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7156_summable__geometric__iff,axiom,
% 15.55/8.61      ! [C: real] :
% 15.55/8.61        ( ( summable_real @ ( power_power_real @ C ) )
% 15.55/8.61        = ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7157_summable__geometric__iff,axiom,
% 15.55/8.61      ! [C: complex] :
% 15.55/8.61        ( ( summable_complex @ ( power_power_complex @ C ) )
% 15.55/8.61        = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7158_divmod__algorithm__code_I3_J,axiom,
% 15.55/8.61      ! [N: num] :
% 15.55/8.61        ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 15.55/8.61        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7159_divmod__algorithm__code_I3_J,axiom,
% 15.55/8.61      ! [N: num] :
% 15.55/8.61        ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 15.55/8.61        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7160_divmod__algorithm__code_I4_J,axiom,
% 15.55/8.61      ! [N: num] :
% 15.55/8.61        ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 15.55/8.61        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7161_divmod__algorithm__code_I4_J,axiom,
% 15.55/8.61      ! [N: num] :
% 15.55/8.61        ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 15.55/8.61        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7162_sin__two__pi,axiom,
% 15.55/8.61      ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 15.55/8.61      = zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7163_sin__pi__half,axiom,
% 15.55/8.61      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61      = one_one_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7164_sin__periodic,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( sin_real @ ( plus_plus_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 15.55/8.61        = ( sin_real @ X3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7165_sin__of__real__pi__half,axiom,
% 15.55/8.61      ( ( sin_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61      = one_one_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7166_sin__of__real__pi__half,axiom,
% 15.55/8.61      ( ( sin_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 15.55/8.61      = one_one_complex ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7167_sin__2npi,axiom,
% 15.55/8.61      ! [N: nat] :
% 15.55/8.61        ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 15.55/8.61        = zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7168_sin__2pi__minus,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X3 ) )
% 15.55/8.61        = ( uminus_uminus_real @ ( sin_real @ X3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7169_sin__int__2pin,axiom,
% 15.55/8.61      ! [N: int] :
% 15.55/8.61        ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 15.55/8.61        = zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7170_sin__3over2__pi,axiom,
% 15.55/8.61      ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 15.55/8.61      = ( uminus_uminus_real @ one_one_real ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7171_summable__comparison__test,axiom,
% 15.55/8.61      ! [F: nat > real,G: nat > real] :
% 15.55/8.61        ( ? [N6: nat] :
% 15.55/8.61          ! [N2: nat] :
% 15.55/8.61            ( ( ord_less_eq_nat @ N6 @ N2 )
% 15.55/8.61           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N2 ) ) @ ( G @ N2 ) ) )
% 15.55/8.61       => ( ( summable_real @ G )
% 15.55/8.61         => ( summable_real @ F ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7172_summable__comparison__test,axiom,
% 15.55/8.61      ! [F: nat > complex,G: nat > real] :
% 15.55/8.61        ( ? [N6: nat] :
% 15.55/8.61          ! [N2: nat] :
% 15.55/8.61            ( ( ord_less_eq_nat @ N6 @ N2 )
% 15.55/8.61           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N2 ) ) @ ( G @ N2 ) ) )
% 15.55/8.61       => ( ( summable_real @ G )
% 15.55/8.61         => ( summable_complex @ F ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7173_summable__comparison__test_H,axiom,
% 15.55/8.61      ! [G: nat > real,N4: nat,F: nat > real] :
% 15.55/8.61        ( ( summable_real @ G )
% 15.55/8.61       => ( ! [N2: nat] :
% 15.55/8.61              ( ( ord_less_eq_nat @ N4 @ N2 )
% 15.55/8.61             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N2 ) ) @ ( G @ N2 ) ) )
% 15.55/8.61         => ( summable_real @ F ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7174_summable__comparison__test_H,axiom,
% 15.55/8.61      ! [G: nat > real,N4: nat,F: nat > complex] :
% 15.55/8.61        ( ( summable_real @ G )
% 15.55/8.61       => ( ! [N2: nat] :
% 15.55/8.61              ( ( ord_less_eq_nat @ N4 @ N2 )
% 15.55/8.61             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N2 ) ) @ ( G @ N2 ) ) )
% 15.55/8.61         => ( summable_complex @ F ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7175_summable__const__iff,axiom,
% 15.55/8.61      ! [C: real] :
% 15.55/8.61        ( ( summable_real
% 15.55/8.61          @ ^ [Uu3: nat] : C )
% 15.55/8.61        = ( C = zero_zero_real ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7176_powser__insidea,axiom,
% 15.55/8.61      ! [F: nat > real,X3: real,Z: real] :
% 15.55/8.61        ( ( summable_real
% 15.55/8.61          @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ X3 @ N3 ) ) )
% 15.55/8.61       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X3 ) )
% 15.55/8.61         => ( summable_real
% 15.55/8.61            @ ^ [N3: nat] : ( real_V7735802525324610683m_real @ ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7177_powser__insidea,axiom,
% 15.55/8.61      ! [F: nat > complex,X3: complex,Z: complex] :
% 15.55/8.61        ( ( summable_complex
% 15.55/8.61          @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ X3 @ N3 ) ) )
% 15.55/8.61       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X3 ) )
% 15.55/8.61         => ( summable_real
% 15.55/8.61            @ ^ [N3: nat] : ( real_V1022390504157884413omplex @ ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7178_suminf__le,axiom,
% 15.55/8.61      ! [F: nat > real,G: nat > real] :
% 15.55/8.61        ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 15.55/8.61       => ( ( summable_real @ F )
% 15.55/8.61         => ( ( summable_real @ G )
% 15.55/8.61           => ( ord_less_eq_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7179_suminf__le,axiom,
% 15.55/8.61      ! [F: nat > nat,G: nat > nat] :
% 15.55/8.61        ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( G @ N2 ) )
% 15.55/8.61       => ( ( summable_nat @ F )
% 15.55/8.61         => ( ( summable_nat @ G )
% 15.55/8.61           => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7180_suminf__le,axiom,
% 15.55/8.61      ! [F: nat > int,G: nat > int] :
% 15.55/8.61        ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ N2 ) @ ( G @ N2 ) )
% 15.55/8.61       => ( ( summable_int @ F )
% 15.55/8.61         => ( ( summable_int @ G )
% 15.55/8.61           => ( ord_less_eq_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7181_sin__x__le__x,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.61       => ( ord_less_eq_real @ ( sin_real @ X3 ) @ X3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7182_sin__le__one,axiom,
% 15.55/8.61      ! [X3: real] : ( ord_less_eq_real @ ( sin_real @ X3 ) @ one_one_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7183_abs__sin__x__le__abs__x,axiom,
% 15.55/8.61      ! [X3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X3 ) ) @ ( abs_abs_real @ X3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7184_summable__mult__D,axiom,
% 15.55/8.61      ! [C: real,F: nat > real] :
% 15.55/8.61        ( ( summable_real
% 15.55/8.61          @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) ) )
% 15.55/8.61       => ( ( C != zero_zero_real )
% 15.55/8.61         => ( summable_real @ F ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7185_summable__zero__power,axiom,
% 15.55/8.61      summable_int @ ( power_power_int @ zero_zero_int ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7186_summable__zero__power,axiom,
% 15.55/8.61      summable_real @ ( power_power_real @ zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7187_summable__zero__power,axiom,
% 15.55/8.61      summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7188_sin__int__times__real,axiom,
% 15.55/8.61      ! [M: int,X3: real] :
% 15.55/8.61        ( ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X3 ) ) )
% 15.55/8.61        = ( real_V1803761363581548252l_real @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7189_sin__int__times__real,axiom,
% 15.55/8.61      ! [M: int,X3: real] :
% 15.55/8.61        ( ( sin_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X3 ) ) )
% 15.55/8.61        = ( real_V4546457046886955230omplex @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7190_suminf__nonneg,axiom,
% 15.55/8.61      ! [F: nat > real] :
% 15.55/8.61        ( ( summable_real @ F )
% 15.55/8.61       => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 15.55/8.61         => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7191_suminf__nonneg,axiom,
% 15.55/8.61      ! [F: nat > nat] :
% 15.55/8.61        ( ( summable_nat @ F )
% 15.55/8.61       => ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 15.55/8.61         => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7192_suminf__nonneg,axiom,
% 15.55/8.61      ! [F: nat > int] :
% 15.55/8.61        ( ( summable_int @ F )
% 15.55/8.61       => ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 15.55/8.61         => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7193_suminf__eq__zero__iff,axiom,
% 15.55/8.61      ! [F: nat > real] :
% 15.55/8.61        ( ( summable_real @ F )
% 15.55/8.61       => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 15.55/8.61         => ( ( ( suminf_real @ F )
% 15.55/8.61              = zero_zero_real )
% 15.55/8.61            = ( ! [N3: nat] :
% 15.55/8.61                  ( ( F @ N3 )
% 15.55/8.61                  = zero_zero_real ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7194_suminf__eq__zero__iff,axiom,
% 15.55/8.61      ! [F: nat > nat] :
% 15.55/8.61        ( ( summable_nat @ F )
% 15.55/8.61       => ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 15.55/8.61         => ( ( ( suminf_nat @ F )
% 15.55/8.61              = zero_zero_nat )
% 15.55/8.61            = ( ! [N3: nat] :
% 15.55/8.61                  ( ( F @ N3 )
% 15.55/8.61                  = zero_zero_nat ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7195_suminf__eq__zero__iff,axiom,
% 15.55/8.61      ! [F: nat > int] :
% 15.55/8.61        ( ( summable_int @ F )
% 15.55/8.61       => ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 15.55/8.61         => ( ( ( suminf_int @ F )
% 15.55/8.61              = zero_zero_int )
% 15.55/8.61            = ( ! [N3: nat] :
% 15.55/8.61                  ( ( F @ N3 )
% 15.55/8.61                  = zero_zero_int ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7196_suminf__pos,axiom,
% 15.55/8.61      ! [F: nat > real] :
% 15.55/8.61        ( ( summable_real @ F )
% 15.55/8.61       => ( ! [N2: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N2 ) )
% 15.55/8.61         => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7197_suminf__pos,axiom,
% 15.55/8.61      ! [F: nat > nat] :
% 15.55/8.61        ( ( summable_nat @ F )
% 15.55/8.61       => ( ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N2 ) )
% 15.55/8.61         => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7198_suminf__pos,axiom,
% 15.55/8.61      ! [F: nat > int] :
% 15.55/8.61        ( ( summable_int @ F )
% 15.55/8.61       => ( ! [N2: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N2 ) )
% 15.55/8.61         => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7199_sin__gt__zero,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.61       => ( ( ord_less_real @ X3 @ pi )
% 15.55/8.61         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7200_sin__x__ge__neg__x,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.61       => ( ord_less_eq_real @ ( uminus_uminus_real @ X3 ) @ ( sin_real @ X3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7201_sin__ge__zero,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.61       => ( ( ord_less_eq_real @ X3 @ pi )
% 15.55/8.61         => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7202_summable__0__powser,axiom,
% 15.55/8.61      ! [F: nat > complex] :
% 15.55/8.61        ( summable_complex
% 15.55/8.61        @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ zero_zero_complex @ N3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7203_summable__0__powser,axiom,
% 15.55/8.61      ! [F: nat > real] :
% 15.55/8.61        ( summable_real
% 15.55/8.61        @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ zero_zero_real @ N3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7204_summable__zero__power_H,axiom,
% 15.55/8.61      ! [F: nat > complex] :
% 15.55/8.61        ( summable_complex
% 15.55/8.61        @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ zero_zero_complex @ N3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7205_summable__zero__power_H,axiom,
% 15.55/8.61      ! [F: nat > real] :
% 15.55/8.61        ( summable_real
% 15.55/8.61        @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ zero_zero_real @ N3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7206_summable__zero__power_H,axiom,
% 15.55/8.61      ! [F: nat > int] :
% 15.55/8.61        ( summable_int
% 15.55/8.61        @ ^ [N3: nat] : ( times_times_int @ ( F @ N3 ) @ ( power_power_int @ zero_zero_int @ N3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7207_sin__ge__minus__one,axiom,
% 15.55/8.61      ! [X3: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7208_summable__powser__split__head,axiom,
% 15.55/8.61      ! [F: nat > complex,Z: complex] :
% 15.55/8.61        ( ( summable_complex
% 15.55/8.61          @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) ) )
% 15.55/8.61        = ( summable_complex
% 15.55/8.61          @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7209_summable__powser__split__head,axiom,
% 15.55/8.61      ! [F: nat > real,Z: real] :
% 15.55/8.61        ( ( summable_real
% 15.55/8.61          @ ^ [N3: nat] : ( times_times_real @ ( F @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) ) )
% 15.55/8.61        = ( summable_real
% 15.55/8.61          @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7210_powser__split__head_I3_J,axiom,
% 15.55/8.61      ! [F: nat > complex,Z: complex] :
% 15.55/8.61        ( ( summable_complex
% 15.55/8.61          @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 15.55/8.61       => ( summable_complex
% 15.55/8.61          @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7211_powser__split__head_I3_J,axiom,
% 15.55/8.61      ! [F: nat > real,Z: real] :
% 15.55/8.61        ( ( summable_real
% 15.55/8.61          @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 15.55/8.61       => ( summable_real
% 15.55/8.61          @ ^ [N3: nat] : ( times_times_real @ ( F @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7212_abs__sin__le__one,axiom,
% 15.55/8.61      ! [X3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X3 ) ) @ one_one_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7213_summable__powser__ignore__initial__segment,axiom,
% 15.55/8.61      ! [F: nat > complex,M: nat,Z: complex] :
% 15.55/8.61        ( ( summable_complex
% 15.55/8.61          @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( plus_plus_nat @ N3 @ M ) ) @ ( power_power_complex @ Z @ N3 ) ) )
% 15.55/8.61        = ( summable_complex
% 15.55/8.61          @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7214_summable__powser__ignore__initial__segment,axiom,
% 15.55/8.61      ! [F: nat > real,M: nat,Z: real] :
% 15.55/8.61        ( ( summable_real
% 15.55/8.61          @ ^ [N3: nat] : ( times_times_real @ ( F @ ( plus_plus_nat @ N3 @ M ) ) @ ( power_power_real @ Z @ N3 ) ) )
% 15.55/8.61        = ( summable_real
% 15.55/8.61          @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7215_summable__norm__comparison__test,axiom,
% 15.55/8.61      ! [F: nat > complex,G: nat > real] :
% 15.55/8.61        ( ? [N6: nat] :
% 15.55/8.61          ! [N2: nat] :
% 15.55/8.61            ( ( ord_less_eq_nat @ N6 @ N2 )
% 15.55/8.61           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N2 ) ) @ ( G @ N2 ) ) )
% 15.55/8.61       => ( ( summable_real @ G )
% 15.55/8.61         => ( summable_real
% 15.55/8.61            @ ^ [N3: nat] : ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7216_summable__rabs__comparison__test,axiom,
% 15.55/8.61      ! [F: nat > real,G: nat > real] :
% 15.55/8.61        ( ? [N6: nat] :
% 15.55/8.61          ! [N2: nat] :
% 15.55/8.61            ( ( ord_less_eq_nat @ N6 @ N2 )
% 15.55/8.61           => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N2 ) ) @ ( G @ N2 ) ) )
% 15.55/8.61       => ( ( summable_real @ G )
% 15.55/8.61         => ( summable_real
% 15.55/8.61            @ ^ [N3: nat] : ( abs_abs_real @ ( F @ N3 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7217_summable__rabs,axiom,
% 15.55/8.61      ! [F: nat > real] :
% 15.55/8.61        ( ( summable_real
% 15.55/8.61          @ ^ [N3: nat] : ( abs_abs_real @ ( F @ N3 ) ) )
% 15.55/8.61       => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 15.55/8.61          @ ( suminf_real
% 15.55/8.61            @ ^ [N3: nat] : ( abs_abs_real @ ( F @ N3 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7218_suminf__pos__iff,axiom,
% 15.55/8.61      ! [F: nat > real] :
% 15.55/8.61        ( ( summable_real @ F )
% 15.55/8.61       => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 15.55/8.61         => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 15.55/8.61            = ( ? [I4: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7219_suminf__pos__iff,axiom,
% 15.55/8.61      ! [F: nat > nat] :
% 15.55/8.61        ( ( summable_nat @ F )
% 15.55/8.61       => ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 15.55/8.61         => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 15.55/8.61            = ( ? [I4: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7220_suminf__pos__iff,axiom,
% 15.55/8.61      ! [F: nat > int] :
% 15.55/8.61        ( ( summable_int @ F )
% 15.55/8.61       => ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 15.55/8.61         => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 15.55/8.61            = ( ? [I4: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I4 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7221_suminf__pos2,axiom,
% 15.55/8.61      ! [F: nat > real,I: nat] :
% 15.55/8.61        ( ( summable_real @ F )
% 15.55/8.61       => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 15.55/8.61         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 15.55/8.61           => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7222_suminf__pos2,axiom,
% 15.55/8.61      ! [F: nat > nat,I: nat] :
% 15.55/8.61        ( ( summable_nat @ F )
% 15.55/8.61       => ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 15.55/8.61         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 15.55/8.61           => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7223_suminf__pos2,axiom,
% 15.55/8.61      ! [F: nat > int,I: nat] :
% 15.55/8.61        ( ( summable_int @ F )
% 15.55/8.61       => ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 15.55/8.61         => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 15.55/8.61           => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7224_powser__inside,axiom,
% 15.55/8.61      ! [F: nat > real,X3: real,Z: real] :
% 15.55/8.61        ( ( summable_real
% 15.55/8.61          @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ X3 @ N3 ) ) )
% 15.55/8.61       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X3 ) )
% 15.55/8.61         => ( summable_real
% 15.55/8.61            @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7225_powser__inside,axiom,
% 15.55/8.61      ! [F: nat > complex,X3: complex,Z: complex] :
% 15.55/8.61        ( ( summable_complex
% 15.55/8.61          @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ X3 @ N3 ) ) )
% 15.55/8.61       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X3 ) )
% 15.55/8.61         => ( summable_complex
% 15.55/8.61            @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7226_sin__eq__0__pi,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X3 )
% 15.55/8.61       => ( ( ord_less_real @ X3 @ pi )
% 15.55/8.61         => ( ( ( sin_real @ X3 )
% 15.55/8.61              = zero_zero_real )
% 15.55/8.61           => ( X3 = zero_zero_real ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7227_complete__algebra__summable__geometric,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ one_one_real )
% 15.55/8.61       => ( summable_real @ ( power_power_real @ X3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7228_complete__algebra__summable__geometric,axiom,
% 15.55/8.61      ! [X3: complex] :
% 15.55/8.61        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ one_one_real )
% 15.55/8.61       => ( summable_complex @ ( power_power_complex @ X3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7229_summable__geometric,axiom,
% 15.55/8.61      ! [C: real] :
% 15.55/8.61        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 15.55/8.61       => ( summable_real @ ( power_power_real @ C ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7230_summable__geometric,axiom,
% 15.55/8.61      ! [C: complex] :
% 15.55/8.61        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 15.55/8.61       => ( summable_complex @ ( power_power_complex @ C ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7231_suminf__split__head,axiom,
% 15.55/8.61      ! [F: nat > real] :
% 15.55/8.61        ( ( summable_real @ F )
% 15.55/8.61       => ( ( suminf_real
% 15.55/8.61            @ ^ [N3: nat] : ( F @ ( suc @ N3 ) ) )
% 15.55/8.61          = ( minus_minus_real @ ( suminf_real @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7232_sin__zero__pi__iff,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ pi )
% 15.55/8.61       => ( ( ( sin_real @ X3 )
% 15.55/8.61            = zero_zero_real )
% 15.55/8.61          = ( X3 = zero_zero_real ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7233_sin__zero__iff__int2,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ( sin_real @ X3 )
% 15.55/8.61          = zero_zero_real )
% 15.55/8.61        = ( ? [I4: int] :
% 15.55/8.61              ( X3
% 15.55/8.61              = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ pi ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7234_divmod__int__def,axiom,
% 15.55/8.61      ( unique5052692396658037445od_int
% 15.55/8.61      = ( ^ [M3: num,N3: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N3 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N3 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7235_summable__norm,axiom,
% 15.55/8.61      ! [F: nat > real] :
% 15.55/8.61        ( ( summable_real
% 15.55/8.61          @ ^ [N3: nat] : ( real_V7735802525324610683m_real @ ( F @ N3 ) ) )
% 15.55/8.61       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( suminf_real @ F ) )
% 15.55/8.61          @ ( suminf_real
% 15.55/8.61            @ ^ [N3: nat] : ( real_V7735802525324610683m_real @ ( F @ N3 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7236_summable__norm,axiom,
% 15.55/8.61      ! [F: nat > complex] :
% 15.55/8.61        ( ( summable_real
% 15.55/8.61          @ ^ [N3: nat] : ( real_V1022390504157884413omplex @ ( F @ N3 ) ) )
% 15.55/8.61       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( suminf_complex @ F ) )
% 15.55/8.61          @ ( suminf_real
% 15.55/8.61            @ ^ [N3: nat] : ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7237_sin__gt__zero__02,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.61       => ( ( ord_less_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 15.55/8.61         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7238_divmod__def,axiom,
% 15.55/8.61      ( unique3479559517661332726nteger
% 15.55/8.61      = ( ^ [M3: num,N3: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N3 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N3 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7239_divmod__def,axiom,
% 15.55/8.61      ( unique5052692396658037445od_int
% 15.55/8.61      = ( ^ [M3: num,N3: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N3 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N3 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7240_divmod__def,axiom,
% 15.55/8.61      ( unique5055182867167087721od_nat
% 15.55/8.61      = ( ^ [M3: num,N3: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N3 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N3 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7241_divmod_H__nat__def,axiom,
% 15.55/8.61      ( unique5055182867167087721od_nat
% 15.55/8.61      = ( ^ [M3: num,N3: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N3 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N3 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7242_powser__split__head_I1_J,axiom,
% 15.55/8.61      ! [F: nat > complex,Z: complex] :
% 15.55/8.61        ( ( summable_complex
% 15.55/8.61          @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 15.55/8.61       => ( ( suminf_complex
% 15.55/8.61            @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 15.55/8.61          = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 15.55/8.61            @ ( times_times_complex
% 15.55/8.61              @ ( suminf_complex
% 15.55/8.61                @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) ) )
% 15.55/8.61              @ Z ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7243_powser__split__head_I1_J,axiom,
% 15.55/8.61      ! [F: nat > real,Z: real] :
% 15.55/8.61        ( ( summable_real
% 15.55/8.61          @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 15.55/8.61       => ( ( suminf_real
% 15.55/8.61            @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 15.55/8.61          = ( plus_plus_real @ ( F @ zero_zero_nat )
% 15.55/8.61            @ ( times_times_real
% 15.55/8.61              @ ( suminf_real
% 15.55/8.61                @ ^ [N3: nat] : ( times_times_real @ ( F @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) ) )
% 15.55/8.61              @ Z ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7244_powser__split__head_I2_J,axiom,
% 15.55/8.61      ! [F: nat > complex,Z: complex] :
% 15.55/8.61        ( ( summable_complex
% 15.55/8.61          @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 15.55/8.61       => ( ( times_times_complex
% 15.55/8.61            @ ( suminf_complex
% 15.55/8.61              @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) ) )
% 15.55/8.61            @ Z )
% 15.55/8.61          = ( minus_minus_complex
% 15.55/8.61            @ ( suminf_complex
% 15.55/8.61              @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 15.55/8.61            @ ( F @ zero_zero_nat ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7245_powser__split__head_I2_J,axiom,
% 15.55/8.61      ! [F: nat > real,Z: real] :
% 15.55/8.61        ( ( summable_real
% 15.55/8.61          @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 15.55/8.61       => ( ( times_times_real
% 15.55/8.61            @ ( suminf_real
% 15.55/8.61              @ ^ [N3: nat] : ( times_times_real @ ( F @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) ) )
% 15.55/8.61            @ Z )
% 15.55/8.61          = ( minus_minus_real
% 15.55/8.61            @ ( suminf_real
% 15.55/8.61              @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 15.55/8.61            @ ( F @ zero_zero_nat ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7246_suminf__exist__split,axiom,
% 15.55/8.61      ! [R2: real,F: nat > real] :
% 15.55/8.61        ( ( ord_less_real @ zero_zero_real @ R2 )
% 15.55/8.61       => ( ( summable_real @ F )
% 15.55/8.61         => ? [N7: nat] :
% 15.55/8.61            ! [N8: nat] :
% 15.55/8.61              ( ( ord_less_eq_nat @ N7 @ N8 )
% 15.55/8.61             => ( ord_less_real
% 15.55/8.61                @ ( real_V7735802525324610683m_real
% 15.55/8.61                  @ ( suminf_real
% 15.55/8.61                    @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N8 ) ) ) )
% 15.55/8.61                @ R2 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7247_suminf__exist__split,axiom,
% 15.55/8.61      ! [R2: real,F: nat > complex] :
% 15.55/8.61        ( ( ord_less_real @ zero_zero_real @ R2 )
% 15.55/8.61       => ( ( summable_complex @ F )
% 15.55/8.61         => ? [N7: nat] :
% 15.55/8.61            ! [N8: nat] :
% 15.55/8.61              ( ( ord_less_eq_nat @ N7 @ N8 )
% 15.55/8.61             => ( ord_less_real
% 15.55/8.61                @ ( real_V1022390504157884413omplex
% 15.55/8.61                  @ ( suminf_complex
% 15.55/8.61                    @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N8 ) ) ) )
% 15.55/8.61                @ R2 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7248_sin__pi__divide__n__ge__0,axiom,
% 15.55/8.61      ! [N: nat] :
% 15.55/8.61        ( ( N != zero_zero_nat )
% 15.55/8.61       => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7249_summable__power__series,axiom,
% 15.55/8.61      ! [F: nat > real,Z: real] :
% 15.55/8.61        ( ! [I3: nat] : ( ord_less_eq_real @ ( F @ I3 ) @ one_one_real )
% 15.55/8.61       => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 15.55/8.61         => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 15.55/8.61           => ( ( ord_less_real @ Z @ one_one_real )
% 15.55/8.61             => ( summable_real
% 15.55/8.61                @ ^ [I4: nat] : ( times_times_real @ ( F @ I4 ) @ ( power_power_real @ Z @ I4 ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7250_sin__45,axiom,
% 15.55/8.61      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 15.55/8.61      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7251_Abel__lemma,axiom,
% 15.55/8.61      ! [R2: real,R0: real,A: nat > complex,M7: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 15.55/8.61       => ( ( ord_less_real @ R2 @ R0 )
% 15.55/8.61         => ( ! [N2: nat] : ( ord_less_eq_real @ ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N2 ) ) @ ( power_power_real @ R0 @ N2 ) ) @ M7 )
% 15.55/8.61           => ( summable_real
% 15.55/8.61              @ ^ [N3: nat] : ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N3 ) ) @ ( power_power_real @ R2 @ N3 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7252_summable__ratio__test,axiom,
% 15.55/8.61      ! [C: real,N4: nat,F: nat > real] :
% 15.55/8.61        ( ( ord_less_real @ C @ one_one_real )
% 15.55/8.61       => ( ! [N2: nat] :
% 15.55/8.61              ( ( ord_less_eq_nat @ N4 @ N2 )
% 15.55/8.61             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N2 ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N2 ) ) ) ) )
% 15.55/8.61         => ( summable_real @ F ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7253_summable__ratio__test,axiom,
% 15.55/8.61      ! [C: real,N4: nat,F: nat > complex] :
% 15.55/8.61        ( ( ord_less_real @ C @ one_one_real )
% 15.55/8.61       => ( ! [N2: nat] :
% 15.55/8.61              ( ( ord_less_eq_nat @ N4 @ N2 )
% 15.55/8.61             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N2 ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N2 ) ) ) ) )
% 15.55/8.61         => ( summable_complex @ F ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7254_sin__gt__zero2,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7255_sin__lt__zero,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_real @ pi @ X3 )
% 15.55/8.61       => ( ( ord_less_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 15.55/8.61         => ( ord_less_real @ ( sin_real @ X3 ) @ zero_zero_real ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7256_sin__30,axiom,
% 15.55/8.61      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 15.55/8.61      = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7257_sin__inj__pi,axiom,
% 15.55/8.61      ! [X3: real,Y3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 15.55/8.61       => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 15.55/8.61           => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61             => ( ( ( sin_real @ X3 )
% 15.55/8.61                  = ( sin_real @ Y3 ) )
% 15.55/8.61               => ( X3 = Y3 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7258_sin__mono__le__eq,axiom,
% 15.55/8.61      ! [X3: real,Y3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 15.55/8.61       => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 15.55/8.61           => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61             => ( ( ord_less_eq_real @ ( sin_real @ X3 ) @ ( sin_real @ Y3 ) )
% 15.55/8.61                = ( ord_less_eq_real @ X3 @ Y3 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7259_sin__monotone__2pi__le,axiom,
% 15.55/8.61      ! [Y3: real,X3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 15.55/8.61       => ( ( ord_less_eq_real @ Y3 @ X3 )
% 15.55/8.61         => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61           => ( ord_less_eq_real @ ( sin_real @ Y3 ) @ ( sin_real @ X3 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7260_sin__60,axiom,
% 15.55/8.61      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 15.55/8.61      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7261_sin__le__zero,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ pi @ X3 )
% 15.55/8.61       => ( ( ord_less_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 15.55/8.61         => ( ord_less_eq_real @ ( sin_real @ X3 ) @ zero_zero_real ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7262_sin__less__zero,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 )
% 15.55/8.61       => ( ( ord_less_real @ X3 @ zero_zero_real )
% 15.55/8.61         => ( ord_less_real @ ( sin_real @ X3 ) @ zero_zero_real ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7263_sin__mono__less__eq,axiom,
% 15.55/8.61      ! [X3: real,Y3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 15.55/8.61       => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 15.55/8.61           => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61             => ( ( ord_less_real @ ( sin_real @ X3 ) @ ( sin_real @ Y3 ) )
% 15.55/8.61                = ( ord_less_real @ X3 @ Y3 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7264_sin__monotone__2pi,axiom,
% 15.55/8.61      ! [Y3: real,X3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 15.55/8.61       => ( ( ord_less_real @ Y3 @ X3 )
% 15.55/8.61         => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61           => ( ord_less_real @ ( sin_real @ Y3 ) @ ( sin_real @ X3 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7265_sin__total,axiom,
% 15.55/8.61      ! [Y3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 15.55/8.61       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 15.55/8.61         => ? [X4: real] :
% 15.55/8.61              ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 15.55/8.61              & ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61              & ( ( sin_real @ X4 )
% 15.55/8.61                = Y3 )
% 15.55/8.61              & ! [Y6: real] :
% 15.55/8.61                  ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y6 )
% 15.55/8.61                    & ( ord_less_eq_real @ Y6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61                    & ( ( sin_real @ Y6 )
% 15.55/8.61                      = Y3 ) )
% 15.55/8.61                 => ( Y6 = X4 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7266_sin__pi__divide__n__gt__0,axiom,
% 15.55/8.61      ! [N: nat] :
% 15.55/8.61        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.61       => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7267_sin__arctan,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( sin_real @ ( arctan @ X3 ) )
% 15.55/8.61        = ( divide_divide_real @ X3 @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7268_divmod__divmod__step,axiom,
% 15.55/8.61      ( unique5055182867167087721od_nat
% 15.55/8.61      = ( ^ [M3: num,N3: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M3 @ N3 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M3 ) ) @ ( unique5026877609467782581ep_nat @ N3 @ ( unique5055182867167087721od_nat @ M3 @ ( bit0 @ N3 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7269_divmod__divmod__step,axiom,
% 15.55/8.61      ( unique5052692396658037445od_int
% 15.55/8.61      = ( ^ [M3: num,N3: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M3 @ N3 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M3 ) ) @ ( unique5024387138958732305ep_int @ N3 @ ( unique5052692396658037445od_int @ M3 @ ( bit0 @ N3 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7270_divmod__divmod__step,axiom,
% 15.55/8.61      ( unique3479559517661332726nteger
% 15.55/8.61      = ( ^ [M3: num,N3: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M3 @ N3 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M3 ) ) @ ( unique4921790084139445826nteger @ N3 @ ( unique3479559517661332726nteger @ M3 @ ( bit0 @ N3 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7271_sin__zero__iff__int,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ( sin_real @ X3 )
% 15.55/8.61          = zero_zero_real )
% 15.55/8.61        = ( ? [I4: int] :
% 15.55/8.61              ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I4 )
% 15.55/8.61              & ( X3
% 15.55/8.61                = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7272_sin__zero__lemma,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.61       => ( ( ( sin_real @ X3 )
% 15.55/8.61            = zero_zero_real )
% 15.55/8.61         => ? [N2: nat] :
% 15.55/8.61              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 15.55/8.61              & ( X3
% 15.55/8.61                = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7273_sin__zero__iff,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ( sin_real @ X3 )
% 15.55/8.61          = zero_zero_real )
% 15.55/8.61        = ( ? [N3: nat] :
% 15.55/8.61              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 15.55/8.61              & ( X3
% 15.55/8.61                = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.61          | ? [N3: nat] :
% 15.55/8.61              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 15.55/8.61              & ( X3
% 15.55/8.61                = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7274_minus__one__div__numeral,axiom,
% 15.55/8.61      ! [N: num] :
% 15.55/8.61        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 15.55/8.61        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7275_one__div__minus__numeral,axiom,
% 15.55/8.61      ! [N: num] :
% 15.55/8.61        ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.61        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7276_pochhammer__code,axiom,
% 15.55/8.61      ( comm_s2602460028002588243omplex
% 15.55/8.61      = ( ^ [A4: complex,N3: nat] :
% 15.55/8.61            ( if_complex @ ( N3 = zero_zero_nat ) @ one_one_complex
% 15.55/8.61            @ ( set_fo1517530859248394432omplex
% 15.55/8.61              @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A4 @ ( semiri8010041392384452111omplex @ O ) ) )
% 15.55/8.61              @ zero_zero_nat
% 15.55/8.61              @ ( minus_minus_nat @ N3 @ one_one_nat )
% 15.55/8.61              @ one_one_complex ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7277_pochhammer__code,axiom,
% 15.55/8.61      ( comm_s7457072308508201937r_real
% 15.55/8.61      = ( ^ [A4: real,N3: nat] :
% 15.55/8.61            ( if_real @ ( N3 = zero_zero_nat ) @ one_one_real
% 15.55/8.61            @ ( set_fo3111899725591712190t_real
% 15.55/8.61              @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A4 @ ( semiri5074537144036343181t_real @ O ) ) )
% 15.55/8.61              @ zero_zero_nat
% 15.55/8.61              @ ( minus_minus_nat @ N3 @ one_one_nat )
% 15.55/8.61              @ one_one_real ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7278_pochhammer__code,axiom,
% 15.55/8.61      ( comm_s4028243227959126397er_rat
% 15.55/8.61      = ( ^ [A4: rat,N3: nat] :
% 15.55/8.61            ( if_rat @ ( N3 = zero_zero_nat ) @ one_one_rat
% 15.55/8.61            @ ( set_fo1949268297981939178at_rat
% 15.55/8.61              @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A4 @ ( semiri681578069525770553at_rat @ O ) ) )
% 15.55/8.61              @ zero_zero_nat
% 15.55/8.61              @ ( minus_minus_nat @ N3 @ one_one_nat )
% 15.55/8.61              @ one_one_rat ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7279_pochhammer__code,axiom,
% 15.55/8.61      ( comm_s4660882817536571857er_int
% 15.55/8.61      = ( ^ [A4: int,N3: nat] :
% 15.55/8.61            ( if_int @ ( N3 = zero_zero_nat ) @ one_one_int
% 15.55/8.61            @ ( set_fo2581907887559384638at_int
% 15.55/8.61              @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A4 @ ( semiri1314217659103216013at_int @ O ) ) )
% 15.55/8.61              @ zero_zero_nat
% 15.55/8.61              @ ( minus_minus_nat @ N3 @ one_one_nat )
% 15.55/8.61              @ one_one_int ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7280_pochhammer__code,axiom,
% 15.55/8.61      ( comm_s4663373288045622133er_nat
% 15.55/8.61      = ( ^ [A4: nat,N3: nat] :
% 15.55/8.61            ( if_nat @ ( N3 = zero_zero_nat ) @ one_one_nat
% 15.55/8.61            @ ( set_fo2584398358068434914at_nat
% 15.55/8.61              @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A4 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 15.55/8.61              @ zero_zero_nat
% 15.55/8.61              @ ( minus_minus_nat @ N3 @ one_one_nat )
% 15.55/8.61              @ one_one_nat ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7281_neg__eucl__rel__int__mult__2,axiom,
% 15.55/8.61      ! [B: int,A: int,Q3: int,R2: int] :
% 15.55/8.61        ( ( ord_less_eq_int @ B @ zero_zero_int )
% 15.55/8.61       => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 15.55/8.61         => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q3 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) @ one_one_int ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7282_product__nth,axiom,
% 15.55/8.61      ! [N: nat,Xs2: list_num,Ys: list_num] :
% 15.55/8.61        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_num @ Xs2 ) @ ( size_size_list_num @ Ys ) ) )
% 15.55/8.61       => ( ( nth_Pr6456567536196504476um_num @ ( product_num_num @ Xs2 @ Ys ) @ N )
% 15.55/8.61          = ( product_Pair_num_num @ ( nth_num @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_num @ Ys ) ) ) @ ( nth_num @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_num @ Ys ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7283_product__nth,axiom,
% 15.55/8.61      ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 15.55/8.61        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 15.55/8.61       => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) @ N )
% 15.55/8.61          = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7284_product__nth,axiom,
% 15.55/8.61      ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_o] :
% 15.55/8.61        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 15.55/8.61       => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) @ N )
% 15.55/8.61          = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7285_product__nth,axiom,
% 15.55/8.61      ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 15.55/8.61        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 15.55/8.61       => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) @ N )
% 15.55/8.61          = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7286_product__nth,axiom,
% 15.55/8.61      ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_int] :
% 15.55/8.61        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 15.55/8.61       => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) @ N )
% 15.55/8.61          = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7287_product__nth,axiom,
% 15.55/8.61      ! [N: nat,Xs2: list_o,Ys: list_VEBT_VEBT] :
% 15.55/8.61        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 15.55/8.61       => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) @ N )
% 15.55/8.61          = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7288_product__nth,axiom,
% 15.55/8.61      ! [N: nat,Xs2: list_o,Ys: list_o] :
% 15.55/8.61        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 15.55/8.61       => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs2 @ Ys ) @ N )
% 15.55/8.61          = ( product_Pair_o_o @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7289_product__nth,axiom,
% 15.55/8.61      ! [N: nat,Xs2: list_o,Ys: list_nat] :
% 15.55/8.61        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 15.55/8.61       => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs2 @ Ys ) @ N )
% 15.55/8.61          = ( product_Pair_o_nat @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7290_product__nth,axiom,
% 15.55/8.61      ! [N: nat,Xs2: list_o,Ys: list_int] :
% 15.55/8.61        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 15.55/8.61       => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs2 @ Ys ) @ N )
% 15.55/8.61          = ( product_Pair_o_int @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7291_product__nth,axiom,
% 15.55/8.61      ! [N: nat,Xs2: list_nat,Ys: list_num] :
% 15.55/8.61        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_num @ Ys ) ) )
% 15.55/8.61       => ( ( nth_Pr8326237132889035090at_num @ ( product_nat_num @ Xs2 @ Ys ) @ N )
% 15.55/8.61          = ( product_Pair_nat_num @ ( nth_nat @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_num @ Ys ) ) ) @ ( nth_num @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_num @ Ys ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7292_minus__numeral__div__numeral,axiom,
% 15.55/8.61      ! [M: num,N: num] :
% 15.55/8.61        ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 15.55/8.61        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7293_numeral__div__minus__numeral,axiom,
% 15.55/8.61      ! [M: num,N: num] :
% 15.55/8.61        ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.61        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7294_eucl__rel__int__by0,axiom,
% 15.55/8.61      ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7295_eucl__rel__int__dividesI,axiom,
% 15.55/8.61      ! [L: int,K: int,Q3: int] :
% 15.55/8.61        ( ( L != zero_zero_int )
% 15.55/8.61       => ( ( K
% 15.55/8.61            = ( times_times_int @ Q3 @ L ) )
% 15.55/8.61         => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ zero_zero_int ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7296_fold__atLeastAtMost__nat_Oelims,axiom,
% 15.55/8.61      ! [X3: nat > nat > nat,Xa: nat,Xb: nat,Xc: nat,Y3: nat] :
% 15.55/8.61        ( ( ( set_fo2584398358068434914at_nat @ X3 @ Xa @ Xb @ Xc )
% 15.55/8.61          = Y3 )
% 15.55/8.61       => ( ( ( ord_less_nat @ Xb @ Xa )
% 15.55/8.61           => ( Y3 = Xc ) )
% 15.55/8.61          & ( ~ ( ord_less_nat @ Xb @ Xa )
% 15.55/8.61           => ( Y3
% 15.55/8.61              = ( set_fo2584398358068434914at_nat @ X3 @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb @ ( X3 @ Xa @ Xc ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7297_fold__atLeastAtMost__nat_Osimps,axiom,
% 15.55/8.61      ( set_fo2584398358068434914at_nat
% 15.55/8.61      = ( ^ [F3: nat > nat > nat,A4: nat,B3: nat,Acc: nat] : ( if_nat @ ( ord_less_nat @ B3 @ A4 ) @ Acc @ ( set_fo2584398358068434914at_nat @ F3 @ ( plus_plus_nat @ A4 @ one_one_nat ) @ B3 @ ( F3 @ A4 @ Acc ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7298_zminus1__lemma,axiom,
% 15.55/8.61      ! [A: int,B: int,Q3: int,R2: int] :
% 15.55/8.61        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 15.55/8.61       => ( ( B != zero_zero_int )
% 15.55/8.61         => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R2 = zero_zero_int ) @ ( uminus_uminus_int @ Q3 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q3 ) @ one_one_int ) ) @ ( if_int @ ( R2 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R2 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7299_eucl__rel__int__iff,axiom,
% 15.55/8.61      ! [K: int,L: int,Q3: int,R2: int] :
% 15.55/8.61        ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 15.55/8.61        = ( ( K
% 15.55/8.61            = ( plus_plus_int @ ( times_times_int @ L @ Q3 ) @ R2 ) )
% 15.55/8.61          & ( ( ord_less_int @ zero_zero_int @ L )
% 15.55/8.61           => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 15.55/8.61              & ( ord_less_int @ R2 @ L ) ) )
% 15.55/8.61          & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 15.55/8.61           => ( ( ( ord_less_int @ L @ zero_zero_int )
% 15.55/8.61               => ( ( ord_less_int @ L @ R2 )
% 15.55/8.61                  & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 15.55/8.61              & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 15.55/8.61               => ( Q3 = zero_zero_int ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7300_pos__eucl__rel__int__mult__2,axiom,
% 15.55/8.61      ! [B: int,A: int,Q3: int,R2: int] :
% 15.55/8.61        ( ( ord_less_eq_int @ zero_zero_int @ B )
% 15.55/8.61       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 15.55/8.61         => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q3 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7301_xor__int__unfold,axiom,
% 15.55/8.61      ( bit_se6526347334894502574or_int
% 15.55/8.61      = ( ^ [K3: int,L2: int] :
% 15.55/8.61            ( if_int
% 15.55/8.61            @ ( K3
% 15.55/8.61              = ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.61            @ ( bit_ri7919022796975470100ot_int @ L2 )
% 15.55/8.61            @ ( if_int
% 15.55/8.61              @ ( L2
% 15.55/8.61                = ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.61              @ ( bit_ri7919022796975470100ot_int @ K3 )
% 15.55/8.61              @ ( if_int @ ( K3 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7302_cos__pi__eq__zero,axiom,
% 15.55/8.61      ! [M: nat] :
% 15.55/8.61        ( ( cos_real @ ( divide_divide_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61        = zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7303_sincos__total__2pi,axiom,
% 15.55/8.61      ! [X3: real,Y3: real] :
% 15.55/8.61        ( ( ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.61          = one_one_real )
% 15.55/8.61       => ~ ! [T3: real] :
% 15.55/8.61              ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 15.55/8.61             => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 15.55/8.61               => ( ( X3
% 15.55/8.61                    = ( cos_real @ T3 ) )
% 15.55/8.61                 => ( Y3
% 15.55/8.61                   != ( sin_real @ T3 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7304_sin__tan,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61       => ( ( sin_real @ X3 )
% 15.55/8.61          = ( divide_divide_real @ ( tan_real @ X3 ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7305_vebt__buildup_Oelims,axiom,
% 15.55/8.61      ! [X3: nat,Y3: vEBT_VEBT] :
% 15.55/8.61        ( ( ( vEBT_vebt_buildup @ X3 )
% 15.55/8.61          = Y3 )
% 15.55/8.61       => ( ( ( X3 = zero_zero_nat )
% 15.55/8.61           => ( Y3
% 15.55/8.61             != ( vEBT_Leaf @ $false @ $false ) ) )
% 15.55/8.61         => ( ( ( X3
% 15.55/8.61                = ( suc @ zero_zero_nat ) )
% 15.55/8.61             => ( Y3
% 15.55/8.61               != ( vEBT_Leaf @ $false @ $false ) ) )
% 15.55/8.61           => ~ ! [Va: nat] :
% 15.55/8.61                  ( ( X3
% 15.55/8.61                    = ( suc @ ( suc @ Va ) ) )
% 15.55/8.61                 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 15.55/8.61                       => ( Y3
% 15.55/8.61                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 15.55/8.61                      & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 15.55/8.61                       => ( Y3
% 15.55/8.61                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7306_intind,axiom,
% 15.55/8.61      ! [I: nat,N: nat,P: nat > $o,X3: nat] :
% 15.55/8.61        ( ( ord_less_nat @ I @ N )
% 15.55/8.61       => ( ( P @ X3 )
% 15.55/8.61         => ( P @ ( nth_nat @ ( replicate_nat @ N @ X3 ) @ I ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7307_intind,axiom,
% 15.55/8.61      ! [I: nat,N: nat,P: int > $o,X3: int] :
% 15.55/8.61        ( ( ord_less_nat @ I @ N )
% 15.55/8.61       => ( ( P @ X3 )
% 15.55/8.61         => ( P @ ( nth_int @ ( replicate_int @ N @ X3 ) @ I ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7308_intind,axiom,
% 15.55/8.61      ! [I: nat,N: nat,P: vEBT_VEBT > $o,X3: vEBT_VEBT] :
% 15.55/8.61        ( ( ord_less_nat @ I @ N )
% 15.55/8.61       => ( ( P @ X3 )
% 15.55/8.61         => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X3 ) @ I ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7309_bit_Ocompl__eq__compl__iff,axiom,
% 15.55/8.61      ! [X3: int,Y3: int] :
% 15.55/8.61        ( ( ( bit_ri7919022796975470100ot_int @ X3 )
% 15.55/8.61          = ( bit_ri7919022796975470100ot_int @ Y3 ) )
% 15.55/8.61        = ( X3 = Y3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7310_bit_Odouble__compl,axiom,
% 15.55/8.61      ! [X3: int] :
% 15.55/8.61        ( ( bit_ri7919022796975470100ot_int @ ( bit_ri7919022796975470100ot_int @ X3 ) )
% 15.55/8.61        = X3 ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7311_tan__zero,axiom,
% 15.55/8.61      ( ( tan_real @ zero_zero_real )
% 15.55/8.61      = zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7312_replicate__eq__replicate,axiom,
% 15.55/8.61      ! [M: nat,X3: vEBT_VEBT,N: nat,Y3: vEBT_VEBT] :
% 15.55/8.61        ( ( ( replicate_VEBT_VEBT @ M @ X3 )
% 15.55/8.61          = ( replicate_VEBT_VEBT @ N @ Y3 ) )
% 15.55/8.61        = ( ( M = N )
% 15.55/8.61          & ( ( M != zero_zero_nat )
% 15.55/8.61           => ( X3 = Y3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7313_bit_Oxor__compl__right,axiom,
% 15.55/8.61      ! [X3: int,Y3: int] :
% 15.55/8.61        ( ( bit_se6526347334894502574or_int @ X3 @ ( bit_ri7919022796975470100ot_int @ Y3 ) )
% 15.55/8.61        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ X3 @ Y3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7314_bit_Oxor__compl__left,axiom,
% 15.55/8.61      ! [X3: int,Y3: int] :
% 15.55/8.61        ( ( bit_se6526347334894502574or_int @ ( bit_ri7919022796975470100ot_int @ X3 ) @ Y3 )
% 15.55/8.61        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ X3 @ Y3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7315_cos__zero,axiom,
% 15.55/8.61      ( ( cos_complex @ zero_zero_complex )
% 15.55/8.61      = one_one_complex ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7316_cos__zero,axiom,
% 15.55/8.61      ( ( cos_real @ zero_zero_real )
% 15.55/8.61      = one_one_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7317_in__set__replicate,axiom,
% 15.55/8.61      ! [X3: option_nat,N: nat,Y3: option_nat] :
% 15.55/8.61        ( ( member_option_nat @ X3 @ ( set_option_nat2 @ ( replicate_option_nat @ N @ Y3 ) ) )
% 15.55/8.61        = ( ( X3 = Y3 )
% 15.55/8.61          & ( N != zero_zero_nat ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7318_in__set__replicate,axiom,
% 15.55/8.61      ! [X3: real,N: nat,Y3: real] :
% 15.55/8.61        ( ( member_real @ X3 @ ( set_real2 @ ( replicate_real @ N @ Y3 ) ) )
% 15.55/8.61        = ( ( X3 = Y3 )
% 15.55/8.61          & ( N != zero_zero_nat ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7319_in__set__replicate,axiom,
% 15.55/8.61      ! [X3: set_nat,N: nat,Y3: set_nat] :
% 15.55/8.61        ( ( member_set_nat @ X3 @ ( set_set_nat2 @ ( replicate_set_nat @ N @ Y3 ) ) )
% 15.55/8.61        = ( ( X3 = Y3 )
% 15.55/8.61          & ( N != zero_zero_nat ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7320_in__set__replicate,axiom,
% 15.55/8.61      ! [X3: nat,N: nat,Y3: nat] :
% 15.55/8.61        ( ( member_nat @ X3 @ ( set_nat2 @ ( replicate_nat @ N @ Y3 ) ) )
% 15.55/8.61        = ( ( X3 = Y3 )
% 15.55/8.61          & ( N != zero_zero_nat ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7321_in__set__replicate,axiom,
% 15.55/8.61      ! [X3: int,N: nat,Y3: int] :
% 15.55/8.61        ( ( member_int @ X3 @ ( set_int2 @ ( replicate_int @ N @ Y3 ) ) )
% 15.55/8.61        = ( ( X3 = Y3 )
% 15.55/8.61          & ( N != zero_zero_nat ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7322_in__set__replicate,axiom,
% 15.55/8.61      ! [X3: vEBT_VEBT,N: nat,Y3: vEBT_VEBT] :
% 15.55/8.61        ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ Y3 ) ) )
% 15.55/8.61        = ( ( X3 = Y3 )
% 15.55/8.61          & ( N != zero_zero_nat ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7323_Bex__set__replicate,axiom,
% 15.55/8.61      ! [N: nat,A: nat,P: nat > $o] :
% 15.55/8.61        ( ( ? [X: nat] :
% 15.55/8.61              ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 15.55/8.61              & ( P @ X ) ) )
% 15.55/8.61        = ( ( P @ A )
% 15.55/8.61          & ( N != zero_zero_nat ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7324_Bex__set__replicate,axiom,
% 15.55/8.61      ! [N: nat,A: int,P: int > $o] :
% 15.55/8.61        ( ( ? [X: int] :
% 15.55/8.61              ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 15.55/8.61              & ( P @ X ) ) )
% 15.55/8.61        = ( ( P @ A )
% 15.55/8.61          & ( N != zero_zero_nat ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7325_Bex__set__replicate,axiom,
% 15.55/8.61      ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 15.55/8.61        ( ( ? [X: vEBT_VEBT] :
% 15.55/8.61              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 15.55/8.61              & ( P @ X ) ) )
% 15.55/8.61        = ( ( P @ A )
% 15.55/8.61          & ( N != zero_zero_nat ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7326_Ball__set__replicate,axiom,
% 15.55/8.61      ! [N: nat,A: nat,P: nat > $o] :
% 15.55/8.61        ( ( ! [X: nat] :
% 15.55/8.61              ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 15.55/8.61             => ( P @ X ) ) )
% 15.55/8.61        = ( ( P @ A )
% 15.55/8.61          | ( N = zero_zero_nat ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7327_Ball__set__replicate,axiom,
% 15.55/8.61      ! [N: nat,A: int,P: int > $o] :
% 15.55/8.61        ( ( ! [X: int] :
% 15.55/8.61              ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 15.55/8.61             => ( P @ X ) ) )
% 15.55/8.61        = ( ( P @ A )
% 15.55/8.61          | ( N = zero_zero_nat ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7328_Ball__set__replicate,axiom,
% 15.55/8.61      ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 15.55/8.61        ( ( ! [X: vEBT_VEBT] :
% 15.55/8.61              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 15.55/8.61             => ( P @ X ) ) )
% 15.55/8.61        = ( ( P @ A )
% 15.55/8.61          | ( N = zero_zero_nat ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7329_nth__replicate,axiom,
% 15.55/8.61      ! [I: nat,N: nat,X3: nat] :
% 15.55/8.61        ( ( ord_less_nat @ I @ N )
% 15.55/8.61       => ( ( nth_nat @ ( replicate_nat @ N @ X3 ) @ I )
% 15.55/8.61          = X3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7330_nth__replicate,axiom,
% 15.55/8.61      ! [I: nat,N: nat,X3: int] :
% 15.55/8.61        ( ( ord_less_nat @ I @ N )
% 15.55/8.61       => ( ( nth_int @ ( replicate_int @ N @ X3 ) @ I )
% 15.55/8.61          = X3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7331_nth__replicate,axiom,
% 15.55/8.61      ! [I: nat,N: nat,X3: vEBT_VEBT] :
% 15.55/8.61        ( ( ord_less_nat @ I @ N )
% 15.55/8.61       => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X3 ) @ I )
% 15.55/8.61          = X3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7332_tan__pi,axiom,
% 15.55/8.61      ( ( tan_real @ pi )
% 15.55/8.61      = zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7333_bit_Ocompl__one,axiom,
% 15.55/8.61      ( ( bit_ri7632146776885996613nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 15.55/8.61      = zero_z3403309356797280102nteger ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7334_bit_Ocompl__one,axiom,
% 15.55/8.61      ( ( bit_ri7919022796975470100ot_int @ ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.61      = zero_zero_int ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7335_bit_Ocompl__zero,axiom,
% 15.55/8.61      ( ( bit_ri7632146776885996613nteger @ zero_z3403309356797280102nteger )
% 15.55/8.61      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7336_bit_Ocompl__zero,axiom,
% 15.55/8.61      ( ( bit_ri7919022796975470100ot_int @ zero_zero_int )
% 15.55/8.61      = ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7337_bit_Odisj__cancel__right,axiom,
% 15.55/8.61      ! [X3: code_integer] :
% 15.55/8.61        ( ( bit_se1080825931792720795nteger @ X3 @ ( bit_ri7632146776885996613nteger @ X3 ) )
% 15.55/8.61        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7338_bit_Odisj__cancel__right,axiom,
% 15.55/8.61      ! [X3: int] :
% 15.55/8.61        ( ( bit_se1409905431419307370or_int @ X3 @ ( bit_ri7919022796975470100ot_int @ X3 ) )
% 15.55/8.61        = ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7339_bit_Odisj__cancel__left,axiom,
% 15.55/8.61      ! [X3: code_integer] :
% 15.55/8.61        ( ( bit_se1080825931792720795nteger @ ( bit_ri7632146776885996613nteger @ X3 ) @ X3 )
% 15.55/8.61        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7340_bit_Odisj__cancel__left,axiom,
% 15.55/8.61      ! [X3: int] :
% 15.55/8.61        ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ X3 ) @ X3 )
% 15.55/8.61        = ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7341_bit_Oxor__cancel__right,axiom,
% 15.55/8.61      ! [X3: code_integer] :
% 15.55/8.61        ( ( bit_se3222712562003087583nteger @ X3 @ ( bit_ri7632146776885996613nteger @ X3 ) )
% 15.55/8.61        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7342_bit_Oxor__cancel__right,axiom,
% 15.55/8.61      ! [X3: int] :
% 15.55/8.61        ( ( bit_se6526347334894502574or_int @ X3 @ ( bit_ri7919022796975470100ot_int @ X3 ) )
% 15.55/8.61        = ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7343_bit_Oxor__cancel__left,axiom,
% 15.55/8.61      ! [X3: code_integer] :
% 15.55/8.61        ( ( bit_se3222712562003087583nteger @ ( bit_ri7632146776885996613nteger @ X3 ) @ X3 )
% 15.55/8.61        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7344_bit_Oxor__cancel__left,axiom,
% 15.55/8.61      ! [X3: int] :
% 15.55/8.61        ( ( bit_se6526347334894502574or_int @ ( bit_ri7919022796975470100ot_int @ X3 ) @ X3 )
% 15.55/8.61        = ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7345_bit_Oxor__one__right,axiom,
% 15.55/8.61      ! [X3: code_integer] :
% 15.55/8.61        ( ( bit_se3222712562003087583nteger @ X3 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 15.55/8.61        = ( bit_ri7632146776885996613nteger @ X3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7346_bit_Oxor__one__right,axiom,
% 15.55/8.61      ! [X3: int] :
% 15.55/8.61        ( ( bit_se6526347334894502574or_int @ X3 @ ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.61        = ( bit_ri7919022796975470100ot_int @ X3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7347_bit_Oxor__one__left,axiom,
% 15.55/8.61      ! [X3: code_integer] :
% 15.55/8.61        ( ( bit_se3222712562003087583nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X3 )
% 15.55/8.61        = ( bit_ri7632146776885996613nteger @ X3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7348_bit_Oxor__one__left,axiom,
% 15.55/8.61      ! [X3: int] :
% 15.55/8.61        ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ one_one_int ) @ X3 )
% 15.55/8.61        = ( bit_ri7919022796975470100ot_int @ X3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7349_not__negative__int__iff,axiom,
% 15.55/8.61      ! [K: int] :
% 15.55/8.61        ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 15.55/8.61        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7350_not__nonnegative__int__iff,axiom,
% 15.55/8.61      ! [K: int] :
% 15.55/8.61        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 15.55/8.61        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7351_minus__not__numeral__eq,axiom,
% 15.55/8.61      ! [N: num] :
% 15.55/8.61        ( ( uminus1351360451143612070nteger @ ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 15.55/8.61        = ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7352_minus__not__numeral__eq,axiom,
% 15.55/8.61      ! [N: num] :
% 15.55/8.61        ( ( uminus_uminus_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.61        = ( numeral_numeral_int @ ( inc @ N ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7353_even__not__iff,axiom,
% 15.55/8.61      ! [A: code_integer] :
% 15.55/8.61        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri7632146776885996613nteger @ A ) )
% 15.55/8.61        = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7354_even__not__iff,axiom,
% 15.55/8.61      ! [A: int] :
% 15.55/8.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ A ) )
% 15.55/8.61        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7355_set__replicate,axiom,
% 15.55/8.61      ! [N: nat,X3: produc3843707927480180839at_nat] :
% 15.55/8.61        ( ( N != zero_zero_nat )
% 15.55/8.61       => ( ( set_Pr3765526544606949372at_nat @ ( replic2264142908078655527at_nat @ N @ X3 ) )
% 15.55/8.61          = ( insert9069300056098147895at_nat @ X3 @ bot_bo228742789529271731at_nat ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7356_set__replicate,axiom,
% 15.55/8.61      ! [N: nat,X3: product_prod_nat_nat] :
% 15.55/8.61        ( ( N != zero_zero_nat )
% 15.55/8.61       => ( ( set_Pr5648618587558075414at_nat @ ( replic4235873036481779905at_nat @ N @ X3 ) )
% 15.55/8.61          = ( insert8211810215607154385at_nat @ X3 @ bot_bo2099793752762293965at_nat ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7357_set__replicate,axiom,
% 15.55/8.61      ! [N: nat,X3: vEBT_VEBT] :
% 15.55/8.61        ( ( N != zero_zero_nat )
% 15.55/8.61       => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X3 ) )
% 15.55/8.61          = ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7358_set__replicate,axiom,
% 15.55/8.61      ! [N: nat,X3: extended_enat] :
% 15.55/8.61        ( ( N != zero_zero_nat )
% 15.55/8.61       => ( ( set_Extended_enat2 @ ( replic7216382294607269926d_enat @ N @ X3 ) )
% 15.55/8.61          = ( insert_Extended_enat @ X3 @ bot_bo7653980558646680370d_enat ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7359_set__replicate,axiom,
% 15.55/8.61      ! [N: nat,X3: real] :
% 15.55/8.61        ( ( N != zero_zero_nat )
% 15.55/8.61       => ( ( set_real2 @ ( replicate_real @ N @ X3 ) )
% 15.55/8.61          = ( insert_real @ X3 @ bot_bot_set_real ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7360_set__replicate,axiom,
% 15.55/8.61      ! [N: nat,X3: nat] :
% 15.55/8.61        ( ( N != zero_zero_nat )
% 15.55/8.61       => ( ( set_nat2 @ ( replicate_nat @ N @ X3 ) )
% 15.55/8.61          = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7361_set__replicate,axiom,
% 15.55/8.61      ! [N: nat,X3: int] :
% 15.55/8.61        ( ( N != zero_zero_nat )
% 15.55/8.61       => ( ( set_int2 @ ( replicate_int @ N @ X3 ) )
% 15.55/8.61          = ( insert_int @ X3 @ bot_bot_set_int ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7362_tan__npi,axiom,
% 15.55/8.61      ! [N: nat] :
% 15.55/8.61        ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 15.55/8.61        = zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7363_tan__periodic__n,axiom,
% 15.55/8.61      ! [X3: real,N: num] :
% 15.55/8.61        ( ( tan_real @ ( plus_plus_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ N ) @ pi ) ) )
% 15.55/8.61        = ( tan_real @ X3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7364_tan__periodic__nat,axiom,
% 15.55/8.61      ! [X3: real,N: nat] :
% 15.55/8.61        ( ( tan_real @ ( plus_plus_real @ X3 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) ) )
% 15.55/8.61        = ( tan_real @ X3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7365_not__one__eq,axiom,
% 15.55/8.61      ( ( bit_ri7632146776885996613nteger @ one_one_Code_integer )
% 15.55/8.61      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7366_not__one__eq,axiom,
% 15.55/8.61      ( ( bit_ri7919022796975470100ot_int @ one_one_int )
% 15.55/8.61      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7367_cos__pi__half,axiom,
% 15.55/8.61      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61      = zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7368_cos__two__pi,axiom,
% 15.55/8.61      ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 15.55/8.61      = one_one_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7369_cos__periodic,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( cos_real @ ( plus_plus_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 15.55/8.61        = ( cos_real @ X3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7370_cos__2pi__minus,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X3 ) )
% 15.55/8.61        = ( cos_real @ X3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7371_tan__periodic,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( tan_real @ ( plus_plus_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 15.55/8.61        = ( tan_real @ X3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7372_cos__npi2,axiom,
% 15.55/8.61      ! [N: nat] :
% 15.55/8.61        ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 15.55/8.61        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7373_cos__npi,axiom,
% 15.55/8.61      ! [N: nat] :
% 15.55/8.61        ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 15.55/8.61        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7374_sin__cos__squared__add2,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( plus_plus_real @ ( power_power_real @ ( cos_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.61        = one_one_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7375_sin__cos__squared__add2,axiom,
% 15.55/8.61      ! [X3: complex] :
% 15.55/8.61        ( ( plus_plus_complex @ ( power_power_complex @ ( cos_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.61        = one_one_complex ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7376_sin__cos__squared__add,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( plus_plus_real @ ( power_power_real @ ( sin_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.61        = one_one_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7377_sin__cos__squared__add,axiom,
% 15.55/8.61      ! [X3: complex] :
% 15.55/8.61        ( ( plus_plus_complex @ ( power_power_complex @ ( sin_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.61        = one_one_complex ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7378_cos__of__real__pi__half,axiom,
% 15.55/8.61      ( ( cos_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61      = zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7379_cos__of__real__pi__half,axiom,
% 15.55/8.61      ( ( cos_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 15.55/8.61      = zero_zero_complex ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7380_cos__2npi,axiom,
% 15.55/8.61      ! [N: nat] :
% 15.55/8.61        ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 15.55/8.61        = one_one_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7381_cos__int__2pin,axiom,
% 15.55/8.61      ! [N: int] :
% 15.55/8.61        ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 15.55/8.61        = one_one_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7382_cos__3over2__pi,axiom,
% 15.55/8.61      ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 15.55/8.61      = zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7383_cos__npi__int,axiom,
% 15.55/8.61      ! [N: int] :
% 15.55/8.61        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 15.55/8.61         => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 15.55/8.61            = one_one_real ) )
% 15.55/8.61        & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 15.55/8.61         => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 15.55/8.61            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7384_of__int__not__eq,axiom,
% 15.55/8.61      ! [K: int] :
% 15.55/8.61        ( ( ring_1_of_int_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 15.55/8.61        = ( bit_ri7919022796975470100ot_int @ ( ring_1_of_int_int @ K ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7385_take__bit__not__take__bit,axiom,
% 15.55/8.61      ! [N: nat,A: int] :
% 15.55/8.61        ( ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 15.55/8.61        = ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ A ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7386_take__bit__not__iff,axiom,
% 15.55/8.61      ! [N: nat,A: int,B: int] :
% 15.55/8.61        ( ( ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ A ) )
% 15.55/8.61          = ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ B ) ) )
% 15.55/8.61        = ( ( bit_se2923211474154528505it_int @ N @ A )
% 15.55/8.61          = ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7387_of__int__not__numeral,axiom,
% 15.55/8.61      ! [K: num] :
% 15.55/8.61        ( ( ring_1_of_int_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ K ) ) )
% 15.55/8.61        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ K ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7388_not__diff__distrib,axiom,
% 15.55/8.61      ! [A: int,B: int] :
% 15.55/8.61        ( ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A @ B ) )
% 15.55/8.61        = ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7389_not__add__distrib,axiom,
% 15.55/8.61      ! [A: int,B: int] :
% 15.55/8.61        ( ( bit_ri7919022796975470100ot_int @ ( plus_plus_int @ A @ B ) )
% 15.55/8.61        = ( minus_minus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7390_cos__le__one,axiom,
% 15.55/8.61      ! [X3: real] : ( ord_less_eq_real @ ( cos_real @ X3 ) @ one_one_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7391_cos__arctan__not__zero,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( cos_real @ ( arctan @ X3 ) )
% 15.55/8.61       != zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7392_cos__int__times__real,axiom,
% 15.55/8.61      ! [M: int,X3: real] :
% 15.55/8.61        ( ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X3 ) ) )
% 15.55/8.61        = ( real_V1803761363581548252l_real @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7393_cos__int__times__real,axiom,
% 15.55/8.61      ! [M: int,X3: real] :
% 15.55/8.61        ( ( cos_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X3 ) ) )
% 15.55/8.61        = ( real_V4546457046886955230omplex @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7394_add__tan__eq,axiom,
% 15.55/8.61      ! [X3: complex,Y3: complex] :
% 15.55/8.61        ( ( ( cos_complex @ X3 )
% 15.55/8.61         != zero_zero_complex )
% 15.55/8.61       => ( ( ( cos_complex @ Y3 )
% 15.55/8.61           != zero_zero_complex )
% 15.55/8.61         => ( ( plus_plus_complex @ ( tan_complex @ X3 ) @ ( tan_complex @ Y3 ) )
% 15.55/8.61            = ( divide1717551699836669952omplex @ ( sin_complex @ ( plus_plus_complex @ X3 @ Y3 ) ) @ ( times_times_complex @ ( cos_complex @ X3 ) @ ( cos_complex @ Y3 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7395_add__tan__eq,axiom,
% 15.55/8.61      ! [X3: real,Y3: real] :
% 15.55/8.61        ( ( ( cos_real @ X3 )
% 15.55/8.61         != zero_zero_real )
% 15.55/8.61       => ( ( ( cos_real @ Y3 )
% 15.55/8.61           != zero_zero_real )
% 15.55/8.61         => ( ( plus_plus_real @ ( tan_real @ X3 ) @ ( tan_real @ Y3 ) )
% 15.55/8.61            = ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ X3 @ Y3 ) ) @ ( times_times_real @ ( cos_real @ X3 ) @ ( cos_real @ Y3 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7396_cos__one__sin__zero,axiom,
% 15.55/8.61      ! [X3: complex] :
% 15.55/8.61        ( ( ( cos_complex @ X3 )
% 15.55/8.61          = one_one_complex )
% 15.55/8.61       => ( ( sin_complex @ X3 )
% 15.55/8.61          = zero_zero_complex ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7397_cos__one__sin__zero,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ( cos_real @ X3 )
% 15.55/8.61          = one_one_real )
% 15.55/8.61       => ( ( sin_real @ X3 )
% 15.55/8.61          = zero_zero_real ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7398_tan__add,axiom,
% 15.55/8.61      ! [X3: complex,Y3: complex] :
% 15.55/8.61        ( ( ( cos_complex @ X3 )
% 15.55/8.61         != zero_zero_complex )
% 15.55/8.61       => ( ( ( cos_complex @ Y3 )
% 15.55/8.61           != zero_zero_complex )
% 15.55/8.61         => ( ( ( cos_complex @ ( plus_plus_complex @ X3 @ Y3 ) )
% 15.55/8.61             != zero_zero_complex )
% 15.55/8.61           => ( ( tan_complex @ ( plus_plus_complex @ X3 @ Y3 ) )
% 15.55/8.61              = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tan_complex @ X3 ) @ ( tan_complex @ Y3 ) ) @ ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X3 ) @ ( tan_complex @ Y3 ) ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7399_tan__add,axiom,
% 15.55/8.61      ! [X3: real,Y3: real] :
% 15.55/8.61        ( ( ( cos_real @ X3 )
% 15.55/8.61         != zero_zero_real )
% 15.55/8.61       => ( ( ( cos_real @ Y3 )
% 15.55/8.61           != zero_zero_real )
% 15.55/8.61         => ( ( ( cos_real @ ( plus_plus_real @ X3 @ Y3 ) )
% 15.55/8.61             != zero_zero_real )
% 15.55/8.61           => ( ( tan_real @ ( plus_plus_real @ X3 @ Y3 ) )
% 15.55/8.61              = ( divide_divide_real @ ( plus_plus_real @ ( tan_real @ X3 ) @ ( tan_real @ Y3 ) ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X3 ) @ ( tan_real @ Y3 ) ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7400_tan__diff,axiom,
% 15.55/8.61      ! [X3: complex,Y3: complex] :
% 15.55/8.61        ( ( ( cos_complex @ X3 )
% 15.55/8.61         != zero_zero_complex )
% 15.55/8.61       => ( ( ( cos_complex @ Y3 )
% 15.55/8.61           != zero_zero_complex )
% 15.55/8.61         => ( ( ( cos_complex @ ( minus_minus_complex @ X3 @ Y3 ) )
% 15.55/8.61             != zero_zero_complex )
% 15.55/8.61           => ( ( tan_complex @ ( minus_minus_complex @ X3 @ Y3 ) )
% 15.55/8.61              = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( tan_complex @ X3 ) @ ( tan_complex @ Y3 ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X3 ) @ ( tan_complex @ Y3 ) ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7401_tan__diff,axiom,
% 15.55/8.61      ! [X3: real,Y3: real] :
% 15.55/8.61        ( ( ( cos_real @ X3 )
% 15.55/8.61         != zero_zero_real )
% 15.55/8.61       => ( ( ( cos_real @ Y3 )
% 15.55/8.61           != zero_zero_real )
% 15.55/8.61         => ( ( ( cos_real @ ( minus_minus_real @ X3 @ Y3 ) )
% 15.55/8.61             != zero_zero_real )
% 15.55/8.61           => ( ( tan_real @ ( minus_minus_real @ X3 @ Y3 ) )
% 15.55/8.61              = ( divide_divide_real @ ( minus_minus_real @ ( tan_real @ X3 ) @ ( tan_real @ Y3 ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X3 ) @ ( tan_real @ Y3 ) ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7402_lemma__tan__add1,axiom,
% 15.55/8.61      ! [X3: complex,Y3: complex] :
% 15.55/8.61        ( ( ( cos_complex @ X3 )
% 15.55/8.61         != zero_zero_complex )
% 15.55/8.61       => ( ( ( cos_complex @ Y3 )
% 15.55/8.61           != zero_zero_complex )
% 15.55/8.61         => ( ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X3 ) @ ( tan_complex @ Y3 ) ) )
% 15.55/8.61            = ( divide1717551699836669952omplex @ ( cos_complex @ ( plus_plus_complex @ X3 @ Y3 ) ) @ ( times_times_complex @ ( cos_complex @ X3 ) @ ( cos_complex @ Y3 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7403_lemma__tan__add1,axiom,
% 15.55/8.61      ! [X3: real,Y3: real] :
% 15.55/8.61        ( ( ( cos_real @ X3 )
% 15.55/8.61         != zero_zero_real )
% 15.55/8.61       => ( ( ( cos_real @ Y3 )
% 15.55/8.61           != zero_zero_real )
% 15.55/8.61         => ( ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X3 ) @ ( tan_real @ Y3 ) ) )
% 15.55/8.61            = ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ X3 @ Y3 ) ) @ ( times_times_real @ ( cos_real @ X3 ) @ ( cos_real @ Y3 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7404_minus__eq__not__plus__1,axiom,
% 15.55/8.61      ( uminus1351360451143612070nteger
% 15.55/8.61      = ( ^ [A4: code_integer] : ( plus_p5714425477246183910nteger @ ( bit_ri7632146776885996613nteger @ A4 ) @ one_one_Code_integer ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7405_minus__eq__not__plus__1,axiom,
% 15.55/8.61      ( uminus_uminus_int
% 15.55/8.61      = ( ^ [A4: int] : ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A4 ) @ one_one_int ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7406_minus__eq__not__minus__1,axiom,
% 15.55/8.61      ( uminus1351360451143612070nteger
% 15.55/8.61      = ( ^ [A4: code_integer] : ( bit_ri7632146776885996613nteger @ ( minus_8373710615458151222nteger @ A4 @ one_one_Code_integer ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7407_minus__eq__not__minus__1,axiom,
% 15.55/8.61      ( uminus_uminus_int
% 15.55/8.61      = ( ^ [A4: int] : ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A4 @ one_one_int ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7408_not__eq__complement,axiom,
% 15.55/8.61      ( bit_ri7632146776885996613nteger
% 15.55/8.61      = ( ^ [A4: code_integer] : ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A4 ) @ one_one_Code_integer ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7409_not__eq__complement,axiom,
% 15.55/8.61      ( bit_ri7919022796975470100ot_int
% 15.55/8.61      = ( ^ [A4: int] : ( minus_minus_int @ ( uminus_uminus_int @ A4 ) @ one_one_int ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7410_cos__monotone__0__pi__le,axiom,
% 15.55/8.61      ! [Y3: real,X3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.61       => ( ( ord_less_eq_real @ Y3 @ X3 )
% 15.55/8.61         => ( ( ord_less_eq_real @ X3 @ pi )
% 15.55/8.61           => ( ord_less_eq_real @ ( cos_real @ X3 ) @ ( cos_real @ Y3 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7411_cos__mono__le__eq,axiom,
% 15.55/8.61      ! [X3: real,Y3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.61       => ( ( ord_less_eq_real @ X3 @ pi )
% 15.55/8.61         => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.61           => ( ( ord_less_eq_real @ Y3 @ pi )
% 15.55/8.61             => ( ( ord_less_eq_real @ ( cos_real @ X3 ) @ ( cos_real @ Y3 ) )
% 15.55/8.61                = ( ord_less_eq_real @ Y3 @ X3 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7412_cos__inj__pi,axiom,
% 15.55/8.61      ! [X3: real,Y3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.61       => ( ( ord_less_eq_real @ X3 @ pi )
% 15.55/8.61         => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.61           => ( ( ord_less_eq_real @ Y3 @ pi )
% 15.55/8.61             => ( ( ( cos_real @ X3 )
% 15.55/8.61                  = ( cos_real @ Y3 ) )
% 15.55/8.61               => ( X3 = Y3 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7413_cos__ge__minus__one,axiom,
% 15.55/8.61      ! [X3: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7414_not__int__def,axiom,
% 15.55/8.61      ( bit_ri7919022796975470100ot_int
% 15.55/8.61      = ( ^ [K3: int] : ( minus_minus_int @ ( uminus_uminus_int @ K3 ) @ one_one_int ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7415_abs__cos__le__one,axiom,
% 15.55/8.61      ! [X3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X3 ) ) @ one_one_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7416_or__not__numerals_I1_J,axiom,
% 15.55/8.61      ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 15.55/8.61      = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7417_minus__numeral__inc__eq,axiom,
% 15.55/8.61      ! [N: num] :
% 15.55/8.61        ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) )
% 15.55/8.61        = ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7418_minus__numeral__inc__eq,axiom,
% 15.55/8.61      ! [N: num] :
% 15.55/8.61        ( ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) )
% 15.55/8.61        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7419_sin__zero__norm__cos__one,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ( sin_real @ X3 )
% 15.55/8.61          = zero_zero_real )
% 15.55/8.61       => ( ( real_V7735802525324610683m_real @ ( cos_real @ X3 ) )
% 15.55/8.61          = one_one_real ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7420_sin__zero__norm__cos__one,axiom,
% 15.55/8.61      ! [X3: complex] :
% 15.55/8.61        ( ( ( sin_complex @ X3 )
% 15.55/8.61          = zero_zero_complex )
% 15.55/8.61       => ( ( real_V1022390504157884413omplex @ ( cos_complex @ X3 ) )
% 15.55/8.61          = one_one_real ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7421_not__int__div__2,axiom,
% 15.55/8.61      ! [K: int] :
% 15.55/8.61        ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.61        = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7422_even__not__iff__int,axiom,
% 15.55/8.61      ! [K: int] :
% 15.55/8.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 15.55/8.61        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7423_cos__two__neq__zero,axiom,
% 15.55/8.61      ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 15.55/8.61     != zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7424_cos__mono__less__eq,axiom,
% 15.55/8.61      ! [X3: real,Y3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.61       => ( ( ord_less_eq_real @ X3 @ pi )
% 15.55/8.61         => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.61           => ( ( ord_less_eq_real @ Y3 @ pi )
% 15.55/8.61             => ( ( ord_less_real @ ( cos_real @ X3 ) @ ( cos_real @ Y3 ) )
% 15.55/8.61                = ( ord_less_real @ Y3 @ X3 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7425_cos__monotone__0__pi,axiom,
% 15.55/8.61      ! [Y3: real,X3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.61       => ( ( ord_less_real @ Y3 @ X3 )
% 15.55/8.61         => ( ( ord_less_eq_real @ X3 @ pi )
% 15.55/8.61           => ( ord_less_real @ ( cos_real @ X3 ) @ ( cos_real @ Y3 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7426_tan__half,axiom,
% 15.55/8.61      ( tan_complex
% 15.55/8.61      = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) ) @ ( plus_plus_complex @ ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) ) @ one_one_complex ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7427_tan__half,axiom,
% 15.55/8.61      ( tan_real
% 15.55/8.61      = ( ^ [X: real] : ( divide_divide_real @ ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ ( plus_plus_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7428_not__numeral__Bit0__eq,axiom,
% 15.55/8.61      ! [N: num] :
% 15.55/8.61        ( ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) )
% 15.55/8.61        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7429_not__numeral__Bit0__eq,axiom,
% 15.55/8.61      ! [N: num] :
% 15.55/8.61        ( ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) )
% 15.55/8.61        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7430_or__not__numerals_I2_J,axiom,
% 15.55/8.61      ! [N: num] :
% 15.55/8.61        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 15.55/8.61        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7431_or__not__numerals_I4_J,axiom,
% 15.55/8.61      ! [M: num] :
% 15.55/8.61        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 15.55/8.61        = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7432_cos__monotone__minus__pi__0_H,axiom,
% 15.55/8.61      ! [Y3: real,X3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 15.55/8.61       => ( ( ord_less_eq_real @ Y3 @ X3 )
% 15.55/8.61         => ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 15.55/8.61           => ( ord_less_eq_real @ ( cos_real @ Y3 ) @ ( cos_real @ X3 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7433_set__replicate__conv__if,axiom,
% 15.55/8.61      ! [N: nat,X3: produc3843707927480180839at_nat] :
% 15.55/8.61        ( ( ( N = zero_zero_nat )
% 15.55/8.61         => ( ( set_Pr3765526544606949372at_nat @ ( replic2264142908078655527at_nat @ N @ X3 ) )
% 15.55/8.61            = bot_bo228742789529271731at_nat ) )
% 15.55/8.61        & ( ( N != zero_zero_nat )
% 15.55/8.61         => ( ( set_Pr3765526544606949372at_nat @ ( replic2264142908078655527at_nat @ N @ X3 ) )
% 15.55/8.61            = ( insert9069300056098147895at_nat @ X3 @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7434_set__replicate__conv__if,axiom,
% 15.55/8.61      ! [N: nat,X3: product_prod_nat_nat] :
% 15.55/8.61        ( ( ( N = zero_zero_nat )
% 15.55/8.61         => ( ( set_Pr5648618587558075414at_nat @ ( replic4235873036481779905at_nat @ N @ X3 ) )
% 15.55/8.61            = bot_bo2099793752762293965at_nat ) )
% 15.55/8.61        & ( ( N != zero_zero_nat )
% 15.55/8.61         => ( ( set_Pr5648618587558075414at_nat @ ( replic4235873036481779905at_nat @ N @ X3 ) )
% 15.55/8.61            = ( insert8211810215607154385at_nat @ X3 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7435_set__replicate__conv__if,axiom,
% 15.55/8.61      ! [N: nat,X3: vEBT_VEBT] :
% 15.55/8.61        ( ( ( N = zero_zero_nat )
% 15.55/8.61         => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X3 ) )
% 15.55/8.61            = bot_bo8194388402131092736T_VEBT ) )
% 15.55/8.61        & ( ( N != zero_zero_nat )
% 15.55/8.61         => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X3 ) )
% 15.55/8.61            = ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7436_set__replicate__conv__if,axiom,
% 15.55/8.61      ! [N: nat,X3: extended_enat] :
% 15.55/8.61        ( ( ( N = zero_zero_nat )
% 15.55/8.61         => ( ( set_Extended_enat2 @ ( replic7216382294607269926d_enat @ N @ X3 ) )
% 15.55/8.61            = bot_bo7653980558646680370d_enat ) )
% 15.55/8.61        & ( ( N != zero_zero_nat )
% 15.55/8.61         => ( ( set_Extended_enat2 @ ( replic7216382294607269926d_enat @ N @ X3 ) )
% 15.55/8.61            = ( insert_Extended_enat @ X3 @ bot_bo7653980558646680370d_enat ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7437_set__replicate__conv__if,axiom,
% 15.55/8.61      ! [N: nat,X3: real] :
% 15.55/8.61        ( ( ( N = zero_zero_nat )
% 15.55/8.61         => ( ( set_real2 @ ( replicate_real @ N @ X3 ) )
% 15.55/8.61            = bot_bot_set_real ) )
% 15.55/8.61        & ( ( N != zero_zero_nat )
% 15.55/8.61         => ( ( set_real2 @ ( replicate_real @ N @ X3 ) )
% 15.55/8.61            = ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7438_set__replicate__conv__if,axiom,
% 15.55/8.61      ! [N: nat,X3: nat] :
% 15.55/8.61        ( ( ( N = zero_zero_nat )
% 15.55/8.61         => ( ( set_nat2 @ ( replicate_nat @ N @ X3 ) )
% 15.55/8.61            = bot_bot_set_nat ) )
% 15.55/8.61        & ( ( N != zero_zero_nat )
% 15.55/8.61         => ( ( set_nat2 @ ( replicate_nat @ N @ X3 ) )
% 15.55/8.61            = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7439_set__replicate__conv__if,axiom,
% 15.55/8.61      ! [N: nat,X3: int] :
% 15.55/8.61        ( ( ( N = zero_zero_nat )
% 15.55/8.61         => ( ( set_int2 @ ( replicate_int @ N @ X3 ) )
% 15.55/8.61            = bot_bot_set_int ) )
% 15.55/8.61        & ( ( N != zero_zero_nat )
% 15.55/8.61         => ( ( set_int2 @ ( replicate_int @ N @ X3 ) )
% 15.55/8.61            = ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7440_sin__zero__abs__cos__one,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ( sin_real @ X3 )
% 15.55/8.61          = zero_zero_real )
% 15.55/8.61       => ( ( abs_abs_real @ ( cos_real @ X3 ) )
% 15.55/8.61          = one_one_real ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7441_sin__double,axiom,
% 15.55/8.61      ! [X3: complex] :
% 15.55/8.61        ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) )
% 15.55/8.61        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X3 ) ) @ ( cos_complex @ X3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7442_sin__double,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) )
% 15.55/8.61        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X3 ) ) @ ( cos_real @ X3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7443_cos__two__less__zero,axiom,
% 15.55/8.61      ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7444_cos__is__zero,axiom,
% 15.55/8.61      ? [X4: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 15.55/8.61        & ( ord_less_eq_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 15.55/8.61        & ( ( cos_real @ X4 )
% 15.55/8.61          = zero_zero_real )
% 15.55/8.61        & ! [Y6: real] :
% 15.55/8.61            ( ( ( ord_less_eq_real @ zero_zero_real @ Y6 )
% 15.55/8.61              & ( ord_less_eq_real @ Y6 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 15.55/8.61              & ( ( cos_real @ Y6 )
% 15.55/8.61                = zero_zero_real ) )
% 15.55/8.61           => ( Y6 = X4 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7445_cos__two__le__zero,axiom,
% 15.55/8.61      ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7446_tan__double,axiom,
% 15.55/8.61      ! [X3: complex] :
% 15.55/8.61        ( ( ( cos_complex @ X3 )
% 15.55/8.61         != zero_zero_complex )
% 15.55/8.61       => ( ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) )
% 15.55/8.61           != zero_zero_complex )
% 15.55/8.61         => ( ( tan_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) )
% 15.55/8.61            = ( divide1717551699836669952omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( tan_complex @ X3 ) ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7447_tan__double,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ( cos_real @ X3 )
% 15.55/8.61         != zero_zero_real )
% 15.55/8.61       => ( ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) )
% 15.55/8.61           != zero_zero_real )
% 15.55/8.61         => ( ( tan_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) )
% 15.55/8.61            = ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( tan_real @ X3 ) ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7448_or__not__numerals_I3_J,axiom,
% 15.55/8.61      ! [N: num] :
% 15.55/8.61        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 15.55/8.61        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7449_cos__monotone__minus__pi__0,axiom,
% 15.55/8.61      ! [Y3: real,X3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 15.55/8.61       => ( ( ord_less_real @ Y3 @ X3 )
% 15.55/8.61         => ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 15.55/8.61           => ( ord_less_real @ ( cos_real @ Y3 ) @ ( cos_real @ X3 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7450_or__not__numerals_I7_J,axiom,
% 15.55/8.61      ! [M: num] :
% 15.55/8.61        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 15.55/8.61        = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7451_cos__total,axiom,
% 15.55/8.61      ! [Y3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 15.55/8.61       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 15.55/8.61         => ? [X4: real] :
% 15.55/8.61              ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 15.55/8.61              & ( ord_less_eq_real @ X4 @ pi )
% 15.55/8.61              & ( ( cos_real @ X4 )
% 15.55/8.61                = Y3 )
% 15.55/8.61              & ! [Y6: real] :
% 15.55/8.61                  ( ( ( ord_less_eq_real @ zero_zero_real @ Y6 )
% 15.55/8.61                    & ( ord_less_eq_real @ Y6 @ pi )
% 15.55/8.61                    & ( ( cos_real @ Y6 )
% 15.55/8.61                      = Y3 ) )
% 15.55/8.61                 => ( Y6 = X4 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7452_sincos__principal__value,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61      ? [Y4: real] :
% 15.55/8.61        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y4 )
% 15.55/8.61        & ( ord_less_eq_real @ Y4 @ pi )
% 15.55/8.61        & ( ( sin_real @ Y4 )
% 15.55/8.61          = ( sin_real @ X3 ) )
% 15.55/8.61        & ( ( cos_real @ Y4 )
% 15.55/8.61          = ( cos_real @ X3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7453_cos__tan,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61       => ( ( cos_real @ X3 )
% 15.55/8.61          = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7454_tan__45,axiom,
% 15.55/8.61      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 15.55/8.61      = one_one_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7455_or__not__numerals_I6_J,axiom,
% 15.55/8.61      ! [M: num,N: num] :
% 15.55/8.61        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 15.55/8.61        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7456_tan__60,axiom,
% 15.55/8.61      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 15.55/8.61      = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7457_cos__45,axiom,
% 15.55/8.61      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 15.55/8.61      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7458_sin__cos__le1,axiom,
% 15.55/8.61      ! [X3: real,Y3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X3 ) @ ( sin_real @ Y3 ) ) @ ( times_times_real @ ( cos_real @ X3 ) @ ( cos_real @ Y3 ) ) ) ) @ one_one_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7459_cos__plus__cos,axiom,
% 15.55/8.61      ! [W: complex,Z: complex] :
% 15.55/8.61        ( ( plus_plus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 15.55/8.61        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7460_cos__plus__cos,axiom,
% 15.55/8.61      ! [W: real,Z: real] :
% 15.55/8.61        ( ( plus_plus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 15.55/8.61        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7461_cos__times__cos,axiom,
% 15.55/8.61      ! [W: complex,Z: complex] :
% 15.55/8.61        ( ( times_times_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 15.55/8.61        = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7462_cos__times__cos,axiom,
% 15.55/8.61      ! [W: real,Z: real] :
% 15.55/8.61        ( ( times_times_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 15.55/8.61        = ( divide_divide_real @ ( plus_plus_real @ ( cos_real @ ( minus_minus_real @ W @ Z ) ) @ ( cos_real @ ( plus_plus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7463_sin__squared__eq,axiom,
% 15.55/8.61      ! [X3: complex] :
% 15.55/8.61        ( ( power_power_complex @ ( sin_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.61        = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( cos_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7464_sin__squared__eq,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( power_power_real @ ( sin_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.61        = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7465_cos__squared__eq,axiom,
% 15.55/8.61      ! [X3: complex] :
% 15.55/8.61        ( ( power_power_complex @ ( cos_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.61        = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( sin_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7466_cos__squared__eq,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( power_power_real @ ( cos_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.61        = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( sin_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7467_tan__gt__zero,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61         => ( ord_less_real @ zero_zero_real @ ( tan_real @ X3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7468_lemma__tan__total,axiom,
% 15.55/8.61      ! [Y3: real] :
% 15.55/8.61        ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.55/8.61       => ? [X4: real] :
% 15.55/8.61            ( ( ord_less_real @ zero_zero_real @ X4 )
% 15.55/8.61            & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61            & ( ord_less_real @ Y3 @ ( tan_real @ X4 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7469_tan__total,axiom,
% 15.55/8.61      ! [Y3: real] :
% 15.55/8.61      ? [X4: real] :
% 15.55/8.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 15.55/8.61        & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61        & ( ( tan_real @ X4 )
% 15.55/8.61          = Y3 )
% 15.55/8.61        & ! [Y6: real] :
% 15.55/8.61            ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y6 )
% 15.55/8.61              & ( ord_less_real @ Y6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61              & ( ( tan_real @ Y6 )
% 15.55/8.61                = Y3 ) )
% 15.55/8.61           => ( Y6 = X4 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7470_tan__monotone,axiom,
% 15.55/8.61      ! [Y3: real,X3: real] :
% 15.55/8.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 15.55/8.61       => ( ( ord_less_real @ Y3 @ X3 )
% 15.55/8.61         => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61           => ( ord_less_real @ ( tan_real @ Y3 ) @ ( tan_real @ X3 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7471_tan__monotone_H,axiom,
% 15.55/8.61      ! [Y3: real,X3: real] :
% 15.55/8.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 15.55/8.61       => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 15.55/8.61           => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61             => ( ( ord_less_real @ Y3 @ X3 )
% 15.55/8.61                = ( ord_less_real @ ( tan_real @ Y3 ) @ ( tan_real @ X3 ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7472_tan__mono__lt__eq,axiom,
% 15.55/8.61      ! [X3: real,Y3: real] :
% 15.55/8.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 15.55/8.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 15.55/8.61           => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61             => ( ( ord_less_real @ ( tan_real @ X3 ) @ ( tan_real @ Y3 ) )
% 15.55/8.61                = ( ord_less_real @ X3 @ Y3 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7473_lemma__tan__total1,axiom,
% 15.55/8.61      ! [Y3: real] :
% 15.55/8.61      ? [X4: real] :
% 15.55/8.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 15.55/8.61        & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61        & ( ( tan_real @ X4 )
% 15.55/8.61          = Y3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7474_tan__minus__45,axiom,
% 15.55/8.61      ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.61      = ( uminus_uminus_real @ one_one_real ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7475_cos__double__less__one,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.61       => ( ( ord_less_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 15.55/8.61         => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) ) @ one_one_real ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7476_tan__inverse,axiom,
% 15.55/8.61      ! [Y3: real] :
% 15.55/8.61        ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y3 ) )
% 15.55/8.61        = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7477_cos__gt__zero,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61         => ( ord_less_real @ zero_zero_real @ ( cos_real @ X3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7478_cos__60,axiom,
% 15.55/8.61      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 15.55/8.61      = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7479_or__not__numerals_I5_J,axiom,
% 15.55/8.61      ! [M: num,N: num] :
% 15.55/8.61        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 15.55/8.61        = ( 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 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7480_cos__30,axiom,
% 15.55/8.61      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 15.55/8.61      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7481_cos__one__2pi__int,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ( cos_real @ X3 )
% 15.55/8.61          = one_one_real )
% 15.55/8.61        = ( ? [X: int] :
% 15.55/8.61              ( X3
% 15.55/8.61              = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7482_cos__double__cos,axiom,
% 15.55/8.61      ! [W: complex] :
% 15.55/8.61        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 15.55/8.61        = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7483_cos__double__cos,axiom,
% 15.55/8.61      ! [W: real] :
% 15.55/8.61        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 15.55/8.61        = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( cos_real @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_real ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7484_cos__treble__cos,axiom,
% 15.55/8.61      ! [X3: complex] :
% 15.55/8.61        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X3 ) )
% 15.55/8.61        = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ ( cos_complex @ X3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7485_cos__treble__cos,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X3 ) )
% 15.55/8.61        = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( cos_real @ X3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7486_cos__diff__cos,axiom,
% 15.55/8.61      ! [W: complex,Z: complex] :
% 15.55/8.61        ( ( minus_minus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 15.55/8.61        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ Z @ W ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7487_cos__diff__cos,axiom,
% 15.55/8.61      ! [W: real,Z: real] :
% 15.55/8.61        ( ( minus_minus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 15.55/8.61        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ Z @ W ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7488_sin__diff__sin,axiom,
% 15.55/8.61      ! [W: complex,Z: complex] :
% 15.55/8.61        ( ( minus_minus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 15.55/8.61        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7489_sin__diff__sin,axiom,
% 15.55/8.61      ! [W: real,Z: real] :
% 15.55/8.61        ( ( minus_minus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 15.55/8.61        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7490_sin__plus__sin,axiom,
% 15.55/8.61      ! [W: complex,Z: complex] :
% 15.55/8.61        ( ( plus_plus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 15.55/8.61        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7491_sin__plus__sin,axiom,
% 15.55/8.61      ! [W: real,Z: real] :
% 15.55/8.61        ( ( plus_plus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 15.55/8.61        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7492_cos__times__sin,axiom,
% 15.55/8.61      ! [W: complex,Z: complex] :
% 15.55/8.61        ( ( times_times_complex @ ( cos_complex @ W ) @ ( sin_complex @ Z ) )
% 15.55/8.61        = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7493_cos__times__sin,axiom,
% 15.55/8.61      ! [W: real,Z: real] :
% 15.55/8.61        ( ( times_times_real @ ( cos_real @ W ) @ ( sin_real @ Z ) )
% 15.55/8.61        = ( divide_divide_real @ ( minus_minus_real @ ( sin_real @ ( plus_plus_real @ W @ Z ) ) @ ( sin_real @ ( minus_minus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7494_sin__times__cos,axiom,
% 15.55/8.61      ! [W: complex,Z: complex] :
% 15.55/8.61        ( ( times_times_complex @ ( sin_complex @ W ) @ ( cos_complex @ Z ) )
% 15.55/8.61        = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7495_sin__times__cos,axiom,
% 15.55/8.61      ! [W: real,Z: real] :
% 15.55/8.61        ( ( times_times_real @ ( sin_real @ W ) @ ( cos_real @ Z ) )
% 15.55/8.61        = ( divide_divide_real @ ( plus_plus_real @ ( sin_real @ ( plus_plus_real @ W @ Z ) ) @ ( sin_real @ ( minus_minus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7496_sin__times__sin,axiom,
% 15.55/8.61      ! [W: complex,Z: complex] :
% 15.55/8.61        ( ( times_times_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 15.55/8.61        = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7497_sin__times__sin,axiom,
% 15.55/8.61      ! [W: real,Z: real] :
% 15.55/8.61        ( ( times_times_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 15.55/8.61        = ( divide_divide_real @ ( minus_minus_real @ ( cos_real @ ( minus_minus_real @ W @ Z ) ) @ ( cos_real @ ( plus_plus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7498_cos__double,axiom,
% 15.55/8.61      ! [X3: complex] :
% 15.55/8.61        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) )
% 15.55/8.61        = ( minus_minus_complex @ ( power_power_complex @ ( cos_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7499_cos__double,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) )
% 15.55/8.61        = ( minus_minus_real @ ( power_power_real @ ( cos_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7500_cos__sin__eq,axiom,
% 15.55/8.61      ( cos_real
% 15.55/8.61      = ( ^ [X: real] : ( sin_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7501_cos__sin__eq,axiom,
% 15.55/8.61      ( cos_complex
% 15.55/8.61      = ( ^ [X: complex] : ( sin_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7502_sin__cos__eq,axiom,
% 15.55/8.61      ( sin_real
% 15.55/8.61      = ( ^ [X: real] : ( cos_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7503_sin__cos__eq,axiom,
% 15.55/8.61      ( sin_complex
% 15.55/8.61      = ( ^ [X: complex] : ( cos_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7504_tan__total__pos,axiom,
% 15.55/8.61      ! [Y3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.61       => ? [X4: real] :
% 15.55/8.61            ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 15.55/8.61            & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61            & ( ( tan_real @ X4 )
% 15.55/8.61              = Y3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7505_tan__pos__pi2__le,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61         => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7506_tan__less__zero,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 )
% 15.55/8.61       => ( ( ord_less_real @ X3 @ zero_zero_real )
% 15.55/8.61         => ( ord_less_real @ ( tan_real @ X3 ) @ zero_zero_real ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7507_tan__mono__le,axiom,
% 15.55/8.61      ! [X3: real,Y3: real] :
% 15.55/8.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 15.55/8.61       => ( ( ord_less_eq_real @ X3 @ Y3 )
% 15.55/8.61         => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61           => ( ord_less_eq_real @ ( tan_real @ X3 ) @ ( tan_real @ Y3 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7508_tan__mono__le__eq,axiom,
% 15.55/8.61      ! [X3: real,Y3: real] :
% 15.55/8.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 15.55/8.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 15.55/8.61           => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61             => ( ( ord_less_eq_real @ ( tan_real @ X3 ) @ ( tan_real @ Y3 ) )
% 15.55/8.61                = ( ord_less_eq_real @ X3 @ Y3 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7509_tan__bound__pi2,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 15.55/8.61       => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X3 ) ) @ one_one_real ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7510_tan__30,axiom,
% 15.55/8.61      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 15.55/8.61      = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7511_or__not__numerals_I9_J,axiom,
% 15.55/8.61      ! [M: num,N: num] :
% 15.55/8.61        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 15.55/8.61        = ( 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 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7512_or__not__numerals_I8_J,axiom,
% 15.55/8.61      ! [M: num,N: num] :
% 15.55/8.61        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 15.55/8.61        = ( 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 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7513_cos__gt__zero__pi,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 15.55/8.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61         => ( ord_less_real @ zero_zero_real @ ( cos_real @ X3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7514_cos__ge__zero,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 15.55/8.61       => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61         => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7515_arctan,axiom,
% 15.55/8.61      ! [Y3: real] :
% 15.55/8.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y3 ) )
% 15.55/8.61        & ( ord_less_real @ ( arctan @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61        & ( ( tan_real @ ( arctan @ Y3 ) )
% 15.55/8.61          = Y3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7516_arctan__tan,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 15.55/8.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61         => ( ( arctan @ ( tan_real @ X3 ) )
% 15.55/8.61            = X3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7517_arctan__unique,axiom,
% 15.55/8.61      ! [X3: real,Y3: real] :
% 15.55/8.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 15.55/8.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61         => ( ( ( tan_real @ X3 )
% 15.55/8.61              = Y3 )
% 15.55/8.61           => ( ( arctan @ Y3 )
% 15.55/8.61              = X3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7518_cos__one__2pi,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ( cos_real @ X3 )
% 15.55/8.61          = one_one_real )
% 15.55/8.61        = ( ? [X: nat] :
% 15.55/8.61              ( X3
% 15.55/8.61              = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 15.55/8.61          | ? [X: nat] :
% 15.55/8.61              ( X3
% 15.55/8.61              = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7519_cos__double__sin,axiom,
% 15.55/8.61      ! [W: complex] :
% 15.55/8.61        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 15.55/8.61        = ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( sin_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7520_cos__double__sin,axiom,
% 15.55/8.61      ! [W: real] :
% 15.55/8.61        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 15.55/8.61        = ( minus_minus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( sin_real @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7521_minus__sin__cos__eq,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( uminus_uminus_real @ ( sin_real @ X3 ) )
% 15.55/8.61        = ( cos_real @ ( plus_plus_real @ X3 @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7522_minus__sin__cos__eq,axiom,
% 15.55/8.61      ! [X3: complex] :
% 15.55/8.61        ( ( uminus1482373934393186551omplex @ ( sin_complex @ X3 ) )
% 15.55/8.61        = ( cos_complex @ ( plus_plus_complex @ X3 @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7523_tan__total__pi4,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 15.55/8.61       => ? [Z3: real] :
% 15.55/8.61            ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z3 )
% 15.55/8.61            & ( ord_less_real @ Z3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 15.55/8.61            & ( ( tan_real @ Z3 )
% 15.55/8.61              = X3 ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7524_cos__arctan,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( cos_real @ ( arctan @ X3 ) )
% 15.55/8.61        = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7525_sincos__total__pi,axiom,
% 15.55/8.61      ! [Y3: real,X3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.61       => ( ( ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.61            = one_one_real )
% 15.55/8.61         => ? [T3: real] :
% 15.55/8.61              ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 15.55/8.61              & ( ord_less_eq_real @ T3 @ pi )
% 15.55/8.61              & ( X3
% 15.55/8.61                = ( cos_real @ T3 ) )
% 15.55/8.61              & ( Y3
% 15.55/8.61                = ( sin_real @ T3 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7526_sin__cos__sqrt,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X3 ) )
% 15.55/8.61       => ( ( sin_real @ X3 )
% 15.55/8.61          = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7527_sin__expansion__lemma,axiom,
% 15.55/8.61      ! [X3: real,M: nat] :
% 15.55/8.61        ( ( sin_real @ ( plus_plus_real @ X3 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 15.55/8.61        = ( cos_real @ ( plus_plus_real @ X3 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7528_cos__zero__iff__int,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ( cos_real @ X3 )
% 15.55/8.61          = zero_zero_real )
% 15.55/8.61        = ( ? [I4: int] :
% 15.55/8.61              ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I4 )
% 15.55/8.61              & ( X3
% 15.55/8.61                = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7529_vebt__buildup_Osimps_I3_J,axiom,
% 15.55/8.61      ! [Va2: nat] :
% 15.55/8.61        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 15.55/8.61         => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 15.55/8.61            = ( 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 ) ) ) ) ) ) )
% 15.55/8.61        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 15.55/8.61         => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 15.55/8.61            = ( 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 ) ) ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7530_cos__zero__lemma,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.61       => ( ( ( cos_real @ X3 )
% 15.55/8.61            = zero_zero_real )
% 15.55/8.61         => ? [N2: nat] :
% 15.55/8.61              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 15.55/8.61              & ( X3
% 15.55/8.61                = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7531_cos__zero__iff,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ( cos_real @ X3 )
% 15.55/8.61          = zero_zero_real )
% 15.55/8.61        = ( ? [N3: nat] :
% 15.55/8.61              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 15.55/8.61              & ( X3
% 15.55/8.61                = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.61          | ? [N3: nat] :
% 15.55/8.61              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 15.55/8.61              & ( X3
% 15.55/8.61                = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7532_cos__expansion__lemma,axiom,
% 15.55/8.61      ! [X3: real,M: nat] :
% 15.55/8.61        ( ( cos_real @ ( plus_plus_real @ X3 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 15.55/8.61        = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X3 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7533_sincos__total__pi__half,axiom,
% 15.55/8.61      ! [X3: real,Y3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.61       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.61         => ( ( ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.61              = one_one_real )
% 15.55/8.61           => ? [T3: real] :
% 15.55/8.61                ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 15.55/8.61                & ( ord_less_eq_real @ T3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.61                & ( X3
% 15.55/8.61                  = ( cos_real @ T3 ) )
% 15.55/8.61                & ( Y3
% 15.55/8.61                  = ( sin_real @ T3 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7534_sincos__total__2pi__le,axiom,
% 15.55/8.61      ! [X3: real,Y3: real] :
% 15.55/8.61        ( ( ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.61          = one_one_real )
% 15.55/8.61       => ? [T3: real] :
% 15.55/8.61            ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 15.55/8.61            & ( ord_less_eq_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 15.55/8.61            & ( X3
% 15.55/8.61              = ( cos_real @ T3 ) )
% 15.55/8.61            & ( Y3
% 15.55/8.61              = ( sin_real @ T3 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7535_complex__unimodular__polar,axiom,
% 15.55/8.61      ! [Z: complex] :
% 15.55/8.61        ( ( ( real_V1022390504157884413omplex @ Z )
% 15.55/8.61          = one_one_real )
% 15.55/8.61       => ~ ! [T3: real] :
% 15.55/8.61              ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 15.55/8.61             => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 15.55/8.61               => ( Z
% 15.55/8.61                 != ( complex2 @ ( cos_real @ T3 ) @ ( sin_real @ T3 ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7536_obtain__set__succ,axiom,
% 15.55/8.61      ! [X3: nat,Z: nat,A3: set_nat,B5: set_nat] :
% 15.55/8.61        ( ( ord_less_nat @ X3 @ Z )
% 15.55/8.61       => ( ( vEBT_VEBT_max_in_set @ A3 @ Z )
% 15.55/8.61         => ( ( finite_finite_nat @ B5 )
% 15.55/8.61           => ( ( A3 = B5 )
% 15.55/8.61             => ? [X_1: nat] : ( vEBT_is_succ_in_set @ A3 @ X3 @ X_1 ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7537_obtain__set__pred,axiom,
% 15.55/8.61      ! [Z: nat,X3: nat,A3: set_nat] :
% 15.55/8.61        ( ( ord_less_nat @ Z @ X3 )
% 15.55/8.61       => ( ( vEBT_VEBT_min_in_set @ A3 @ Z )
% 15.55/8.61         => ( ( finite_finite_nat @ A3 )
% 15.55/8.61           => ? [X_1: nat] : ( vEBT_is_pred_in_set @ A3 @ X3 @ X_1 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7538_cos__arcsin,axiom,
% 15.55/8.61      ! [X3: real] :
% 15.55/8.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 15.55/8.61       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 15.55/8.61         => ( ( cos_real @ ( arcsin @ X3 ) )
% 15.55/8.61            = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7539_sum__gp,axiom,
% 15.55/8.61      ! [N: nat,M: nat,X3: complex] :
% 15.55/8.61        ( ( ( ord_less_nat @ N @ M )
% 15.55/8.61         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.61            = zero_zero_complex ) )
% 15.55/8.61        & ( ~ ( ord_less_nat @ N @ M )
% 15.55/8.61         => ( ( ( X3 = one_one_complex )
% 15.55/8.61             => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.61                = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 15.55/8.61            & ( ( X3 != one_one_complex )
% 15.55/8.61             => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.61                = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X3 @ M ) @ ( power_power_complex @ X3 @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X3 ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7540_sum__gp,axiom,
% 15.55/8.61      ! [N: nat,M: nat,X3: rat] :
% 15.55/8.61        ( ( ( ord_less_nat @ N @ M )
% 15.55/8.61         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.61            = zero_zero_rat ) )
% 15.55/8.61        & ( ~ ( ord_less_nat @ N @ M )
% 15.55/8.61         => ( ( ( X3 = one_one_rat )
% 15.55/8.61             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.61                = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 15.55/8.61            & ( ( X3 != one_one_rat )
% 15.55/8.61             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.61                = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X3 @ M ) @ ( power_power_rat @ X3 @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X3 ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7541_sum__gp,axiom,
% 15.55/8.61      ! [N: nat,M: nat,X3: real] :
% 15.55/8.61        ( ( ( ord_less_nat @ N @ M )
% 15.55/8.61         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.61            = zero_zero_real ) )
% 15.55/8.61        & ( ~ ( ord_less_nat @ N @ M )
% 15.55/8.61         => ( ( ( X3 = one_one_real )
% 15.55/8.61             => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.61                = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 15.55/8.61            & ( ( X3 != one_one_real )
% 15.55/8.61             => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.61                = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X3 @ M ) @ ( power_power_real @ X3 @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7542_set__vebt__finite,axiom,
% 15.55/8.61      ! [T: vEBT_VEBT,N: nat] :
% 15.55/8.61        ( ( vEBT_invar_vebt @ T @ N )
% 15.55/8.61       => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7543_pred__none__empty,axiom,
% 15.55/8.61      ! [Xs2: set_nat,A: nat] :
% 15.55/8.61        ( ~ ? [X_1: nat] : ( vEBT_is_pred_in_set @ Xs2 @ A @ X_1 )
% 15.55/8.61       => ( ( finite_finite_nat @ Xs2 )
% 15.55/8.61         => ~ ? [X6: nat] :
% 15.55/8.61                ( ( member_nat @ X6 @ Xs2 )
% 15.55/8.61                & ( ord_less_nat @ X6 @ A ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7544_succ__none__empty,axiom,
% 15.55/8.61      ! [Xs2: set_nat,A: nat] :
% 15.55/8.61        ( ~ ? [X_1: nat] : ( vEBT_is_succ_in_set @ Xs2 @ A @ X_1 )
% 15.55/8.61       => ( ( finite_finite_nat @ Xs2 )
% 15.55/8.61         => ~ ? [X6: nat] :
% 15.55/8.61                ( ( member_nat @ X6 @ Xs2 )
% 15.55/8.61                & ( ord_less_nat @ A @ X6 ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7545_arcsin__0,axiom,
% 15.55/8.61      ( ( arcsin @ zero_zero_real )
% 15.55/8.61      = zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7546_sum_Oneutral__const,axiom,
% 15.55/8.61      ! [A3: set_nat] :
% 15.55/8.61        ( ( groups3542108847815614940at_nat
% 15.55/8.61          @ ^ [Uu3: nat] : zero_zero_nat
% 15.55/8.61          @ A3 )
% 15.55/8.61        = zero_zero_nat ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7547_sum_Oneutral__const,axiom,
% 15.55/8.61      ! [A3: set_complex] :
% 15.55/8.61        ( ( groups7754918857620584856omplex
% 15.55/8.61          @ ^ [Uu3: complex] : zero_zero_complex
% 15.55/8.61          @ A3 )
% 15.55/8.61        = zero_zero_complex ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7548_sum_Oneutral__const,axiom,
% 15.55/8.61      ! [A3: set_nat] :
% 15.55/8.61        ( ( groups6591440286371151544t_real
% 15.55/8.61          @ ^ [Uu3: nat] : zero_zero_real
% 15.55/8.61          @ A3 )
% 15.55/8.61        = zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7549_sum_Oneutral__const,axiom,
% 15.55/8.61      ! [A3: set_int] :
% 15.55/8.61        ( ( groups4538972089207619220nt_int
% 15.55/8.61          @ ^ [Uu3: int] : zero_zero_int
% 15.55/8.61          @ A3 )
% 15.55/8.61        = zero_zero_int ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7550_of__nat__sum,axiom,
% 15.55/8.61      ! [F: complex > nat,A3: set_complex] :
% 15.55/8.61        ( ( semiri8010041392384452111omplex @ ( groups5693394587270226106ex_nat @ F @ A3 ) )
% 15.55/8.61        = ( groups7754918857620584856omplex
% 15.55/8.61          @ ^ [X: complex] : ( semiri8010041392384452111omplex @ ( F @ X ) )
% 15.55/8.61          @ A3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7551_of__nat__sum,axiom,
% 15.55/8.61      ! [F: int > nat,A3: set_int] :
% 15.55/8.61        ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A3 ) )
% 15.55/8.61        = ( groups4538972089207619220nt_int
% 15.55/8.61          @ ^ [X: int] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 15.55/8.61          @ A3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7552_of__nat__sum,axiom,
% 15.55/8.61      ! [F: nat > nat,A3: set_nat] :
% 15.55/8.61        ( ( semiri8010041392384452111omplex @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 15.55/8.61        = ( groups2073611262835488442omplex
% 15.55/8.61          @ ^ [X: nat] : ( semiri8010041392384452111omplex @ ( F @ X ) )
% 15.55/8.61          @ A3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7553_of__nat__sum,axiom,
% 15.55/8.61      ! [F: nat > nat,A3: set_nat] :
% 15.55/8.61        ( ( semiri681578069525770553at_rat @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 15.55/8.61        = ( groups2906978787729119204at_rat
% 15.55/8.61          @ ^ [X: nat] : ( semiri681578069525770553at_rat @ ( F @ X ) )
% 15.55/8.61          @ A3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7554_of__nat__sum,axiom,
% 15.55/8.61      ! [F: nat > nat,A3: set_nat] :
% 15.55/8.61        ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 15.55/8.61        = ( groups3539618377306564664at_int
% 15.55/8.61          @ ^ [X: nat] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 15.55/8.61          @ A3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7555_of__nat__sum,axiom,
% 15.55/8.61      ! [F: nat > nat,A3: set_nat] :
% 15.55/8.61        ( ( semiri1316708129612266289at_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 15.55/8.61        = ( groups3542108847815614940at_nat
% 15.55/8.61          @ ^ [X: nat] : ( semiri1316708129612266289at_nat @ ( F @ X ) )
% 15.55/8.61          @ A3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7556_of__nat__sum,axiom,
% 15.55/8.61      ! [F: nat > nat,A3: set_nat] :
% 15.55/8.61        ( ( semiri5074537144036343181t_real @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 15.55/8.61        = ( groups6591440286371151544t_real
% 15.55/8.61          @ ^ [X: nat] : ( semiri5074537144036343181t_real @ ( F @ X ) )
% 15.55/8.61          @ A3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7557_of__int__sum,axiom,
% 15.55/8.61      ! [F: complex > int,A3: set_complex] :
% 15.55/8.61        ( ( ring_17405671764205052669omplex @ ( groups5690904116761175830ex_int @ F @ A3 ) )
% 15.55/8.61        = ( groups7754918857620584856omplex
% 15.55/8.61          @ ^ [X: complex] : ( ring_17405671764205052669omplex @ ( F @ X ) )
% 15.55/8.61          @ A3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7558_of__int__sum,axiom,
% 15.55/8.61      ! [F: nat > int,A3: set_nat] :
% 15.55/8.61        ( ( ring_1_of_int_real @ ( groups3539618377306564664at_int @ F @ A3 ) )
% 15.55/8.61        = ( groups6591440286371151544t_real
% 15.55/8.61          @ ^ [X: nat] : ( ring_1_of_int_real @ ( F @ X ) )
% 15.55/8.61          @ A3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7559_of__int__sum,axiom,
% 15.55/8.61      ! [F: int > int,A3: set_int] :
% 15.55/8.61        ( ( ring_1_of_int_real @ ( groups4538972089207619220nt_int @ F @ A3 ) )
% 15.55/8.61        = ( groups8778361861064173332t_real
% 15.55/8.61          @ ^ [X: int] : ( ring_1_of_int_real @ ( F @ X ) )
% 15.55/8.61          @ A3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7560_of__int__sum,axiom,
% 15.55/8.61      ! [F: int > int,A3: set_int] :
% 15.55/8.61        ( ( ring_17405671764205052669omplex @ ( groups4538972089207619220nt_int @ F @ A3 ) )
% 15.55/8.61        = ( groups3049146728041665814omplex
% 15.55/8.61          @ ^ [X: int] : ( ring_17405671764205052669omplex @ ( F @ X ) )
% 15.55/8.61          @ A3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7561_of__int__sum,axiom,
% 15.55/8.61      ! [F: int > int,A3: set_int] :
% 15.55/8.61        ( ( ring_1_of_int_rat @ ( groups4538972089207619220nt_int @ F @ A3 ) )
% 15.55/8.61        = ( groups3906332499630173760nt_rat
% 15.55/8.61          @ ^ [X: int] : ( ring_1_of_int_rat @ ( F @ X ) )
% 15.55/8.61          @ A3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7562_of__int__sum,axiom,
% 15.55/8.61      ! [F: int > int,A3: set_int] :
% 15.55/8.61        ( ( ring_1_of_int_int @ ( groups4538972089207619220nt_int @ F @ A3 ) )
% 15.55/8.61        = ( groups4538972089207619220nt_int
% 15.55/8.61          @ ^ [X: int] : ( ring_1_of_int_int @ ( F @ X ) )
% 15.55/8.61          @ A3 ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7563_sum_Oempty,axiom,
% 15.55/8.61      ! [G: extended_enat > real] :
% 15.55/8.61        ( ( groups4148127829035722712t_real @ G @ bot_bo7653980558646680370d_enat )
% 15.55/8.61        = zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7564_sum_Oempty,axiom,
% 15.55/8.61      ! [G: extended_enat > rat] :
% 15.55/8.61        ( ( groups1392844769737527556at_rat @ G @ bot_bo7653980558646680370d_enat )
% 15.55/8.61        = zero_zero_rat ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7565_sum_Oempty,axiom,
% 15.55/8.61      ! [G: extended_enat > nat] :
% 15.55/8.61        ( ( groups2027974829824023292at_nat @ G @ bot_bo7653980558646680370d_enat )
% 15.55/8.61        = zero_zero_nat ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7566_sum_Oempty,axiom,
% 15.55/8.61      ! [G: extended_enat > int] :
% 15.55/8.61        ( ( groups2025484359314973016at_int @ G @ bot_bo7653980558646680370d_enat )
% 15.55/8.61        = zero_zero_int ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7567_sum_Oempty,axiom,
% 15.55/8.61      ! [G: real > real] :
% 15.55/8.61        ( ( groups8097168146408367636l_real @ G @ bot_bot_set_real )
% 15.55/8.61        = zero_zero_real ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7568_sum_Oempty,axiom,
% 15.55/8.61      ! [G: real > rat] :
% 15.55/8.61        ( ( groups1300246762558778688al_rat @ G @ bot_bot_set_real )
% 15.55/8.61        = zero_zero_rat ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7569_sum_Oempty,axiom,
% 15.55/8.61      ! [G: real > nat] :
% 15.55/8.61        ( ( groups1935376822645274424al_nat @ G @ bot_bot_set_real )
% 15.55/8.61        = zero_zero_nat ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7570_sum_Oempty,axiom,
% 15.55/8.61      ! [G: real > int] :
% 15.55/8.61        ( ( groups1932886352136224148al_int @ G @ bot_bot_set_real )
% 15.55/8.61        = zero_zero_int ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7571_sum_Oempty,axiom,
% 15.55/8.61      ! [G: nat > rat] :
% 15.55/8.61        ( ( groups2906978787729119204at_rat @ G @ bot_bot_set_nat )
% 15.55/8.61        = zero_zero_rat ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7572_sum_Oempty,axiom,
% 15.55/8.61      ! [G: nat > int] :
% 15.55/8.61        ( ( groups3539618377306564664at_int @ G @ bot_bot_set_nat )
% 15.55/8.61        = zero_zero_int ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7573_sum_Oinfinite,axiom,
% 15.55/8.61      ! [A3: set_int,G: int > real] :
% 15.55/8.61        ( ~ ( finite_finite_int @ A3 )
% 15.55/8.61       => ( ( groups8778361861064173332t_real @ G @ A3 )
% 15.55/8.61          = zero_zero_real ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7574_sum_Oinfinite,axiom,
% 15.55/8.61      ! [A3: set_complex,G: complex > real] :
% 15.55/8.61        ( ~ ( finite3207457112153483333omplex @ A3 )
% 15.55/8.61       => ( ( groups5808333547571424918x_real @ G @ A3 )
% 15.55/8.61          = zero_zero_real ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7575_sum_Oinfinite,axiom,
% 15.55/8.61      ! [A3: set_Extended_enat,G: extended_enat > real] :
% 15.55/8.61        ( ~ ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.61       => ( ( groups4148127829035722712t_real @ G @ A3 )
% 15.55/8.61          = zero_zero_real ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7576_sum_Oinfinite,axiom,
% 15.55/8.61      ! [A3: set_nat,G: nat > rat] :
% 15.55/8.61        ( ~ ( finite_finite_nat @ A3 )
% 15.55/8.61       => ( ( groups2906978787729119204at_rat @ G @ A3 )
% 15.55/8.61          = zero_zero_rat ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7577_sum_Oinfinite,axiom,
% 15.55/8.61      ! [A3: set_int,G: int > rat] :
% 15.55/8.61        ( ~ ( finite_finite_int @ A3 )
% 15.55/8.61       => ( ( groups3906332499630173760nt_rat @ G @ A3 )
% 15.55/8.61          = zero_zero_rat ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7578_sum_Oinfinite,axiom,
% 15.55/8.61      ! [A3: set_complex,G: complex > rat] :
% 15.55/8.61        ( ~ ( finite3207457112153483333omplex @ A3 )
% 15.55/8.61       => ( ( groups5058264527183730370ex_rat @ G @ A3 )
% 15.55/8.61          = zero_zero_rat ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7579_sum_Oinfinite,axiom,
% 15.55/8.61      ! [A3: set_Extended_enat,G: extended_enat > rat] :
% 15.55/8.61        ( ~ ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.61       => ( ( groups1392844769737527556at_rat @ G @ A3 )
% 15.55/8.61          = zero_zero_rat ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7580_sum_Oinfinite,axiom,
% 15.55/8.61      ! [A3: set_int,G: int > nat] :
% 15.55/8.61        ( ~ ( finite_finite_int @ A3 )
% 15.55/8.61       => ( ( groups4541462559716669496nt_nat @ G @ A3 )
% 15.55/8.61          = zero_zero_nat ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7581_sum_Oinfinite,axiom,
% 15.55/8.61      ! [A3: set_complex,G: complex > nat] :
% 15.55/8.61        ( ~ ( finite3207457112153483333omplex @ A3 )
% 15.55/8.61       => ( ( groups5693394587270226106ex_nat @ G @ A3 )
% 15.55/8.61          = zero_zero_nat ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7582_sum_Oinfinite,axiom,
% 15.55/8.61      ! [A3: set_Extended_enat,G: extended_enat > nat] :
% 15.55/8.61        ( ~ ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.61       => ( ( groups2027974829824023292at_nat @ G @ A3 )
% 15.55/8.61          = zero_zero_nat ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7583_sum__eq__0__iff,axiom,
% 15.55/8.61      ! [F4: set_int,F: int > nat] :
% 15.55/8.61        ( ( finite_finite_int @ F4 )
% 15.55/8.61       => ( ( ( groups4541462559716669496nt_nat @ F @ F4 )
% 15.55/8.61            = zero_zero_nat )
% 15.55/8.61          = ( ! [X: int] :
% 15.55/8.61                ( ( member_int @ X @ F4 )
% 15.55/8.61               => ( ( F @ X )
% 15.55/8.61                  = zero_zero_nat ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7584_sum__eq__0__iff,axiom,
% 15.55/8.61      ! [F4: set_complex,F: complex > nat] :
% 15.55/8.61        ( ( finite3207457112153483333omplex @ F4 )
% 15.55/8.61       => ( ( ( groups5693394587270226106ex_nat @ F @ F4 )
% 15.55/8.61            = zero_zero_nat )
% 15.55/8.61          = ( ! [X: complex] :
% 15.55/8.61                ( ( member_complex @ X @ F4 )
% 15.55/8.61               => ( ( F @ X )
% 15.55/8.61                  = zero_zero_nat ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7585_sum__eq__0__iff,axiom,
% 15.55/8.61      ! [F4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 15.55/8.61        ( ( finite6177210948735845034at_nat @ F4 )
% 15.55/8.61       => ( ( ( groups977919841031483927at_nat @ F @ F4 )
% 15.55/8.61            = zero_zero_nat )
% 15.55/8.61          = ( ! [X: product_prod_nat_nat] :
% 15.55/8.61                ( ( member8440522571783428010at_nat @ X @ F4 )
% 15.55/8.61               => ( ( F @ X )
% 15.55/8.61                  = zero_zero_nat ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7586_sum__eq__0__iff,axiom,
% 15.55/8.61      ! [F4: set_Extended_enat,F: extended_enat > nat] :
% 15.55/8.61        ( ( finite4001608067531595151d_enat @ F4 )
% 15.55/8.61       => ( ( ( groups2027974829824023292at_nat @ F @ F4 )
% 15.55/8.61            = zero_zero_nat )
% 15.55/8.61          = ( ! [X: extended_enat] :
% 15.55/8.61                ( ( member_Extended_enat @ X @ F4 )
% 15.55/8.61               => ( ( F @ X )
% 15.55/8.61                  = zero_zero_nat ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7587_sum__eq__0__iff,axiom,
% 15.55/8.61      ! [F4: set_nat,F: nat > nat] :
% 15.55/8.61        ( ( finite_finite_nat @ F4 )
% 15.55/8.61       => ( ( ( groups3542108847815614940at_nat @ F @ F4 )
% 15.55/8.61            = zero_zero_nat )
% 15.55/8.61          = ( ! [X: nat] :
% 15.55/8.61                ( ( member_nat @ X @ F4 )
% 15.55/8.61               => ( ( F @ X )
% 15.55/8.61                  = zero_zero_nat ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7588_prod__zero__iff,axiom,
% 15.55/8.61      ! [A3: set_nat,F: nat > real] :
% 15.55/8.61        ( ( finite_finite_nat @ A3 )
% 15.55/8.61       => ( ( ( groups129246275422532515t_real @ F @ A3 )
% 15.55/8.61            = zero_zero_real )
% 15.55/8.61          = ( ? [X: nat] :
% 15.55/8.61                ( ( member_nat @ X @ A3 )
% 15.55/8.61                & ( ( F @ X )
% 15.55/8.61                  = zero_zero_real ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7589_prod__zero__iff,axiom,
% 15.55/8.61      ! [A3: set_int,F: int > real] :
% 15.55/8.61        ( ( finite_finite_int @ A3 )
% 15.55/8.61       => ( ( ( groups2316167850115554303t_real @ F @ A3 )
% 15.55/8.61            = zero_zero_real )
% 15.55/8.61          = ( ? [X: int] :
% 15.55/8.61                ( ( member_int @ X @ A3 )
% 15.55/8.61                & ( ( F @ X )
% 15.55/8.61                  = zero_zero_real ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7590_prod__zero__iff,axiom,
% 15.55/8.61      ! [A3: set_complex,F: complex > real] :
% 15.55/8.61        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.61       => ( ( ( groups766887009212190081x_real @ F @ A3 )
% 15.55/8.61            = zero_zero_real )
% 15.55/8.61          = ( ? [X: complex] :
% 15.55/8.61                ( ( member_complex @ X @ A3 )
% 15.55/8.61                & ( ( F @ X )
% 15.55/8.61                  = zero_zero_real ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7591_prod__zero__iff,axiom,
% 15.55/8.61      ! [A3: set_Extended_enat,F: extended_enat > real] :
% 15.55/8.61        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.61       => ( ( ( groups97031904164794029t_real @ F @ A3 )
% 15.55/8.61            = zero_zero_real )
% 15.55/8.61          = ( ? [X: extended_enat] :
% 15.55/8.61                ( ( member_Extended_enat @ X @ A3 )
% 15.55/8.61                & ( ( F @ X )
% 15.55/8.61                  = zero_zero_real ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7592_prod__zero__iff,axiom,
% 15.55/8.61      ! [A3: set_nat,F: nat > rat] :
% 15.55/8.61        ( ( finite_finite_nat @ A3 )
% 15.55/8.61       => ( ( ( groups73079841787564623at_rat @ F @ A3 )
% 15.55/8.61            = zero_zero_rat )
% 15.55/8.61          = ( ? [X: nat] :
% 15.55/8.61                ( ( member_nat @ X @ A3 )
% 15.55/8.61                & ( ( F @ X )
% 15.55/8.61                  = zero_zero_rat ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7593_prod__zero__iff,axiom,
% 15.55/8.61      ! [A3: set_int,F: int > rat] :
% 15.55/8.61        ( ( finite_finite_int @ A3 )
% 15.55/8.61       => ( ( ( groups1072433553688619179nt_rat @ F @ A3 )
% 15.55/8.61            = zero_zero_rat )
% 15.55/8.61          = ( ? [X: int] :
% 15.55/8.61                ( ( member_int @ X @ A3 )
% 15.55/8.61                & ( ( F @ X )
% 15.55/8.61                  = zero_zero_rat ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7594_prod__zero__iff,axiom,
% 15.55/8.61      ! [A3: set_complex,F: complex > rat] :
% 15.55/8.61        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.61       => ( ( ( groups225925009352817453ex_rat @ F @ A3 )
% 15.55/8.61            = zero_zero_rat )
% 15.55/8.61          = ( ? [X: complex] :
% 15.55/8.61                ( ( member_complex @ X @ A3 )
% 15.55/8.61                & ( ( F @ X )
% 15.55/8.61                  = zero_zero_rat ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7595_prod__zero__iff,axiom,
% 15.55/8.61      ! [A3: set_Extended_enat,F: extended_enat > rat] :
% 15.55/8.61        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.61       => ( ( ( groups2245840878043517529at_rat @ F @ A3 )
% 15.55/8.61            = zero_zero_rat )
% 15.55/8.61          = ( ? [X: extended_enat] :
% 15.55/8.61                ( ( member_Extended_enat @ X @ A3 )
% 15.55/8.61                & ( ( F @ X )
% 15.55/8.61                  = zero_zero_rat ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7596_prod__zero__iff,axiom,
% 15.55/8.61      ! [A3: set_int,F: int > nat] :
% 15.55/8.61        ( ( finite_finite_int @ A3 )
% 15.55/8.61       => ( ( ( groups1707563613775114915nt_nat @ F @ A3 )
% 15.55/8.61            = zero_zero_nat )
% 15.55/8.61          = ( ? [X: int] :
% 15.55/8.61                ( ( member_int @ X @ A3 )
% 15.55/8.61                & ( ( F @ X )
% 15.55/8.61                  = zero_zero_nat ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7597_prod__zero__iff,axiom,
% 15.55/8.61      ! [A3: set_complex,F: complex > nat] :
% 15.55/8.61        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.61       => ( ( ( groups861055069439313189ex_nat @ F @ A3 )
% 15.55/8.61            = zero_zero_nat )
% 15.55/8.61          = ( ? [X: complex] :
% 15.55/8.61                ( ( member_complex @ X @ A3 )
% 15.55/8.61                & ( ( F @ X )
% 15.55/8.61                  = zero_zero_nat ) ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7598_infinite__Icc__iff,axiom,
% 15.55/8.61      ! [A: rat,B: rat] :
% 15.55/8.61        ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 15.55/8.61        = ( ord_less_rat @ A @ B ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7599_infinite__Icc__iff,axiom,
% 15.55/8.61      ! [A: real,B: real] :
% 15.55/8.61        ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) )
% 15.55/8.61        = ( ord_less_real @ A @ B ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7600_sum_Odelta_H,axiom,
% 15.55/8.61      ! [S2: set_real,A: real,B: real > real] :
% 15.55/8.61        ( ( finite_finite_real @ S2 )
% 15.55/8.61       => ( ( ( member_real @ A @ S2 )
% 15.55/8.61           => ( ( groups8097168146408367636l_real
% 15.55/8.61                @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 15.55/8.61                @ S2 )
% 15.55/8.61              = ( B @ A ) ) )
% 15.55/8.61          & ( ~ ( member_real @ A @ S2 )
% 15.55/8.61           => ( ( groups8097168146408367636l_real
% 15.55/8.61                @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 15.55/8.61                @ S2 )
% 15.55/8.61              = zero_zero_real ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7601_sum_Odelta_H,axiom,
% 15.55/8.61      ! [S2: set_int,A: int,B: int > real] :
% 15.55/8.61        ( ( finite_finite_int @ S2 )
% 15.55/8.61       => ( ( ( member_int @ A @ S2 )
% 15.55/8.61           => ( ( groups8778361861064173332t_real
% 15.55/8.61                @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 15.55/8.61                @ S2 )
% 15.55/8.61              = ( B @ A ) ) )
% 15.55/8.61          & ( ~ ( member_int @ A @ S2 )
% 15.55/8.61           => ( ( groups8778361861064173332t_real
% 15.55/8.61                @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 15.55/8.61                @ S2 )
% 15.55/8.61              = zero_zero_real ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7602_sum_Odelta_H,axiom,
% 15.55/8.61      ! [S2: set_complex,A: complex,B: complex > real] :
% 15.55/8.61        ( ( finite3207457112153483333omplex @ S2 )
% 15.55/8.61       => ( ( ( member_complex @ A @ S2 )
% 15.55/8.61           => ( ( groups5808333547571424918x_real
% 15.55/8.61                @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 15.55/8.61                @ S2 )
% 15.55/8.61              = ( B @ A ) ) )
% 15.55/8.61          & ( ~ ( member_complex @ A @ S2 )
% 15.55/8.61           => ( ( groups5808333547571424918x_real
% 15.55/8.61                @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 15.55/8.61                @ S2 )
% 15.55/8.61              = zero_zero_real ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7603_sum_Odelta_H,axiom,
% 15.55/8.61      ! [S2: set_Extended_enat,A: extended_enat,B: extended_enat > real] :
% 15.55/8.61        ( ( finite4001608067531595151d_enat @ S2 )
% 15.55/8.61       => ( ( ( member_Extended_enat @ A @ S2 )
% 15.55/8.61           => ( ( groups4148127829035722712t_real
% 15.55/8.61                @ ^ [K3: extended_enat] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 15.55/8.61                @ S2 )
% 15.55/8.61              = ( B @ A ) ) )
% 15.55/8.61          & ( ~ ( member_Extended_enat @ A @ S2 )
% 15.55/8.61           => ( ( groups4148127829035722712t_real
% 15.55/8.61                @ ^ [K3: extended_enat] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 15.55/8.61                @ S2 )
% 15.55/8.61              = zero_zero_real ) ) ) ) ).
% 15.55/8.61  
% 15.55/8.61  thf(fact_7604_sum_Odelta_H,axiom,
% 15.55/8.61      ! [S2: set_real,A: real,B: real > rat] :
% 15.55/8.61        ( ( finite_finite_real @ S2 )
% 15.55/8.61       => ( ( ( member_real @ A @ S2 )
% 15.55/8.61           => ( ( groups1300246762558778688al_rat
% 15.55/8.61                @ ^ [K3: real] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 15.55/8.61                @ S2 )
% 15.55/8.61              = ( B @ A ) ) )
% 15.55/8.61          & ( ~ ( member_real @ A @ S2 )
% 15.55/8.61           => ( ( groups1300246762558778688al_rat
% 15.55/8.61                @ ^ [K3: real] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 15.55/8.61                @ S2 )
% 15.55/8.61              = zero_zero_rat ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7605_sum_Odelta_H,axiom,
% 15.55/8.62      ! [S2: set_nat,A: nat,B: nat > rat] :
% 15.55/8.62        ( ( finite_finite_nat @ S2 )
% 15.55/8.62       => ( ( ( member_nat @ A @ S2 )
% 15.55/8.62           => ( ( groups2906978787729119204at_rat
% 15.55/8.62                @ ^ [K3: nat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = ( B @ A ) ) )
% 15.55/8.62          & ( ~ ( member_nat @ A @ S2 )
% 15.55/8.62           => ( ( groups2906978787729119204at_rat
% 15.55/8.62                @ ^ [K3: nat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = zero_zero_rat ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7606_sum_Odelta_H,axiom,
% 15.55/8.62      ! [S2: set_int,A: int,B: int > rat] :
% 15.55/8.62        ( ( finite_finite_int @ S2 )
% 15.55/8.62       => ( ( ( member_int @ A @ S2 )
% 15.55/8.62           => ( ( groups3906332499630173760nt_rat
% 15.55/8.62                @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = ( B @ A ) ) )
% 15.55/8.62          & ( ~ ( member_int @ A @ S2 )
% 15.55/8.62           => ( ( groups3906332499630173760nt_rat
% 15.55/8.62                @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = zero_zero_rat ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7607_sum_Odelta_H,axiom,
% 15.55/8.62      ! [S2: set_complex,A: complex,B: complex > rat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ S2 )
% 15.55/8.62       => ( ( ( member_complex @ A @ S2 )
% 15.55/8.62           => ( ( groups5058264527183730370ex_rat
% 15.55/8.62                @ ^ [K3: complex] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = ( B @ A ) ) )
% 15.55/8.62          & ( ~ ( member_complex @ A @ S2 )
% 15.55/8.62           => ( ( groups5058264527183730370ex_rat
% 15.55/8.62                @ ^ [K3: complex] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = zero_zero_rat ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7608_sum_Odelta_H,axiom,
% 15.55/8.62      ! [S2: set_Extended_enat,A: extended_enat,B: extended_enat > rat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ S2 )
% 15.55/8.62       => ( ( ( member_Extended_enat @ A @ S2 )
% 15.55/8.62           => ( ( groups1392844769737527556at_rat
% 15.55/8.62                @ ^ [K3: extended_enat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = ( B @ A ) ) )
% 15.55/8.62          & ( ~ ( member_Extended_enat @ A @ S2 )
% 15.55/8.62           => ( ( groups1392844769737527556at_rat
% 15.55/8.62                @ ^ [K3: extended_enat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = zero_zero_rat ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7609_sum_Odelta_H,axiom,
% 15.55/8.62      ! [S2: set_real,A: real,B: real > nat] :
% 15.55/8.62        ( ( finite_finite_real @ S2 )
% 15.55/8.62       => ( ( ( member_real @ A @ S2 )
% 15.55/8.62           => ( ( groups1935376822645274424al_nat
% 15.55/8.62                @ ^ [K3: real] : ( if_nat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_nat )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = ( B @ A ) ) )
% 15.55/8.62          & ( ~ ( member_real @ A @ S2 )
% 15.55/8.62           => ( ( groups1935376822645274424al_nat
% 15.55/8.62                @ ^ [K3: real] : ( if_nat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_nat )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = zero_zero_nat ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7610_sum_Odelta,axiom,
% 15.55/8.62      ! [S2: set_real,A: real,B: real > real] :
% 15.55/8.62        ( ( finite_finite_real @ S2 )
% 15.55/8.62       => ( ( ( member_real @ A @ S2 )
% 15.55/8.62           => ( ( groups8097168146408367636l_real
% 15.55/8.62                @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = ( B @ A ) ) )
% 15.55/8.62          & ( ~ ( member_real @ A @ S2 )
% 15.55/8.62           => ( ( groups8097168146408367636l_real
% 15.55/8.62                @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = zero_zero_real ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7611_sum_Odelta,axiom,
% 15.55/8.62      ! [S2: set_int,A: int,B: int > real] :
% 15.55/8.62        ( ( finite_finite_int @ S2 )
% 15.55/8.62       => ( ( ( member_int @ A @ S2 )
% 15.55/8.62           => ( ( groups8778361861064173332t_real
% 15.55/8.62                @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = ( B @ A ) ) )
% 15.55/8.62          & ( ~ ( member_int @ A @ S2 )
% 15.55/8.62           => ( ( groups8778361861064173332t_real
% 15.55/8.62                @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = zero_zero_real ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7612_sum_Odelta,axiom,
% 15.55/8.62      ! [S2: set_complex,A: complex,B: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ S2 )
% 15.55/8.62       => ( ( ( member_complex @ A @ S2 )
% 15.55/8.62           => ( ( groups5808333547571424918x_real
% 15.55/8.62                @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = ( B @ A ) ) )
% 15.55/8.62          & ( ~ ( member_complex @ A @ S2 )
% 15.55/8.62           => ( ( groups5808333547571424918x_real
% 15.55/8.62                @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = zero_zero_real ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7613_sum_Odelta,axiom,
% 15.55/8.62      ! [S2: set_Extended_enat,A: extended_enat,B: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ S2 )
% 15.55/8.62       => ( ( ( member_Extended_enat @ A @ S2 )
% 15.55/8.62           => ( ( groups4148127829035722712t_real
% 15.55/8.62                @ ^ [K3: extended_enat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = ( B @ A ) ) )
% 15.55/8.62          & ( ~ ( member_Extended_enat @ A @ S2 )
% 15.55/8.62           => ( ( groups4148127829035722712t_real
% 15.55/8.62                @ ^ [K3: extended_enat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = zero_zero_real ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7614_sum_Odelta,axiom,
% 15.55/8.62      ! [S2: set_real,A: real,B: real > rat] :
% 15.55/8.62        ( ( finite_finite_real @ S2 )
% 15.55/8.62       => ( ( ( member_real @ A @ S2 )
% 15.55/8.62           => ( ( groups1300246762558778688al_rat
% 15.55/8.62                @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = ( B @ A ) ) )
% 15.55/8.62          & ( ~ ( member_real @ A @ S2 )
% 15.55/8.62           => ( ( groups1300246762558778688al_rat
% 15.55/8.62                @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = zero_zero_rat ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7615_sum_Odelta,axiom,
% 15.55/8.62      ! [S2: set_nat,A: nat,B: nat > rat] :
% 15.55/8.62        ( ( finite_finite_nat @ S2 )
% 15.55/8.62       => ( ( ( member_nat @ A @ S2 )
% 15.55/8.62           => ( ( groups2906978787729119204at_rat
% 15.55/8.62                @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = ( B @ A ) ) )
% 15.55/8.62          & ( ~ ( member_nat @ A @ S2 )
% 15.55/8.62           => ( ( groups2906978787729119204at_rat
% 15.55/8.62                @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = zero_zero_rat ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7616_sum_Odelta,axiom,
% 15.55/8.62      ! [S2: set_int,A: int,B: int > rat] :
% 15.55/8.62        ( ( finite_finite_int @ S2 )
% 15.55/8.62       => ( ( ( member_int @ A @ S2 )
% 15.55/8.62           => ( ( groups3906332499630173760nt_rat
% 15.55/8.62                @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = ( B @ A ) ) )
% 15.55/8.62          & ( ~ ( member_int @ A @ S2 )
% 15.55/8.62           => ( ( groups3906332499630173760nt_rat
% 15.55/8.62                @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = zero_zero_rat ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7617_sum_Odelta,axiom,
% 15.55/8.62      ! [S2: set_complex,A: complex,B: complex > rat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ S2 )
% 15.55/8.62       => ( ( ( member_complex @ A @ S2 )
% 15.55/8.62           => ( ( groups5058264527183730370ex_rat
% 15.55/8.62                @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = ( B @ A ) ) )
% 15.55/8.62          & ( ~ ( member_complex @ A @ S2 )
% 15.55/8.62           => ( ( groups5058264527183730370ex_rat
% 15.55/8.62                @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = zero_zero_rat ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7618_sum_Odelta,axiom,
% 15.55/8.62      ! [S2: set_Extended_enat,A: extended_enat,B: extended_enat > rat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ S2 )
% 15.55/8.62       => ( ( ( member_Extended_enat @ A @ S2 )
% 15.55/8.62           => ( ( groups1392844769737527556at_rat
% 15.55/8.62                @ ^ [K3: extended_enat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = ( B @ A ) ) )
% 15.55/8.62          & ( ~ ( member_Extended_enat @ A @ S2 )
% 15.55/8.62           => ( ( groups1392844769737527556at_rat
% 15.55/8.62                @ ^ [K3: extended_enat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = zero_zero_rat ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7619_sum_Odelta,axiom,
% 15.55/8.62      ! [S2: set_real,A: real,B: real > nat] :
% 15.55/8.62        ( ( finite_finite_real @ S2 )
% 15.55/8.62       => ( ( ( member_real @ A @ S2 )
% 15.55/8.62           => ( ( groups1935376822645274424al_nat
% 15.55/8.62                @ ^ [K3: real] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_nat )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = ( B @ A ) ) )
% 15.55/8.62          & ( ~ ( member_real @ A @ S2 )
% 15.55/8.62           => ( ( groups1935376822645274424al_nat
% 15.55/8.62                @ ^ [K3: real] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_nat )
% 15.55/8.62                @ S2 )
% 15.55/8.62              = zero_zero_nat ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7620_sum__abs,axiom,
% 15.55/8.62      ! [F: nat > real,A3: set_nat] :
% 15.55/8.62        ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A3 ) )
% 15.55/8.62        @ ( groups6591440286371151544t_real
% 15.55/8.62          @ ^ [I4: nat] : ( abs_abs_real @ ( F @ I4 ) )
% 15.55/8.62          @ A3 ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7621_sum__abs,axiom,
% 15.55/8.62      ! [F: int > int,A3: set_int] :
% 15.55/8.62        ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A3 ) )
% 15.55/8.62        @ ( groups4538972089207619220nt_int
% 15.55/8.62          @ ^ [I4: int] : ( abs_abs_int @ ( F @ I4 ) )
% 15.55/8.62          @ A3 ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7622_summable__If__finite__set,axiom,
% 15.55/8.62      ! [A3: set_nat,F: nat > real] :
% 15.55/8.62        ( ( finite_finite_nat @ A3 )
% 15.55/8.62       => ( summable_real
% 15.55/8.62          @ ^ [R5: nat] : ( if_real @ ( member_nat @ R5 @ A3 ) @ ( F @ R5 ) @ zero_zero_real ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7623_summable__If__finite__set,axiom,
% 15.55/8.62      ! [A3: set_nat,F: nat > nat] :
% 15.55/8.62        ( ( finite_finite_nat @ A3 )
% 15.55/8.62       => ( summable_nat
% 15.55/8.62          @ ^ [R5: nat] : ( if_nat @ ( member_nat @ R5 @ A3 ) @ ( F @ R5 ) @ zero_zero_nat ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7624_summable__If__finite__set,axiom,
% 15.55/8.62      ! [A3: set_nat,F: nat > int] :
% 15.55/8.62        ( ( finite_finite_nat @ A3 )
% 15.55/8.62       => ( summable_int
% 15.55/8.62          @ ^ [R5: nat] : ( if_int @ ( member_nat @ R5 @ A3 ) @ ( F @ R5 ) @ zero_zero_int ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7625_summable__If__finite,axiom,
% 15.55/8.62      ! [P: nat > $o,F: nat > real] :
% 15.55/8.62        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 15.55/8.62       => ( summable_real
% 15.55/8.62          @ ^ [R5: nat] : ( if_real @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_real ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7626_summable__If__finite,axiom,
% 15.55/8.62      ! [P: nat > $o,F: nat > nat] :
% 15.55/8.62        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 15.55/8.62       => ( summable_nat
% 15.55/8.62          @ ^ [R5: nat] : ( if_nat @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_nat ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7627_summable__If__finite,axiom,
% 15.55/8.62      ! [P: nat > $o,F: nat > int] :
% 15.55/8.62        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 15.55/8.62       => ( summable_int
% 15.55/8.62          @ ^ [R5: nat] : ( if_int @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_int ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7628_prod__pos__nat__iff,axiom,
% 15.55/8.62      ! [A3: set_int,F: int > nat] :
% 15.55/8.62        ( ( finite_finite_int @ A3 )
% 15.55/8.62       => ( ( ord_less_nat @ zero_zero_nat @ ( groups1707563613775114915nt_nat @ F @ A3 ) )
% 15.55/8.62          = ( ! [X: int] :
% 15.55/8.62                ( ( member_int @ X @ A3 )
% 15.55/8.62               => ( ord_less_nat @ zero_zero_nat @ ( F @ X ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7629_prod__pos__nat__iff,axiom,
% 15.55/8.62      ! [A3: set_complex,F: complex > nat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.62       => ( ( ord_less_nat @ zero_zero_nat @ ( groups861055069439313189ex_nat @ F @ A3 ) )
% 15.55/8.62          = ( ! [X: complex] :
% 15.55/8.62                ( ( member_complex @ X @ A3 )
% 15.55/8.62               => ( ord_less_nat @ zero_zero_nat @ ( F @ X ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7630_prod__pos__nat__iff,axiom,
% 15.55/8.62      ! [A3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 15.55/8.62        ( ( finite6177210948735845034at_nat @ A3 )
% 15.55/8.62       => ( ( ord_less_nat @ zero_zero_nat @ ( groups4077766827762148844at_nat @ F @ A3 ) )
% 15.55/8.62          = ( ! [X: product_prod_nat_nat] :
% 15.55/8.62                ( ( member8440522571783428010at_nat @ X @ A3 )
% 15.55/8.62               => ( ord_less_nat @ zero_zero_nat @ ( F @ X ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7631_prod__pos__nat__iff,axiom,
% 15.55/8.62      ! [A3: set_Extended_enat,F: extended_enat > nat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.62       => ( ( ord_less_nat @ zero_zero_nat @ ( groups2880970938130013265at_nat @ F @ A3 ) )
% 15.55/8.62          = ( ! [X: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ X @ A3 )
% 15.55/8.62               => ( ord_less_nat @ zero_zero_nat @ ( F @ X ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7632_prod__pos__nat__iff,axiom,
% 15.55/8.62      ! [A3: set_nat,F: nat > nat] :
% 15.55/8.62        ( ( finite_finite_nat @ A3 )
% 15.55/8.62       => ( ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 15.55/8.62          = ( ! [X: nat] :
% 15.55/8.62                ( ( member_nat @ X @ A3 )
% 15.55/8.62               => ( ord_less_nat @ zero_zero_nat @ ( F @ X ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7633_sum__abs__ge__zero,axiom,
% 15.55/8.62      ! [F: nat > real,A3: set_nat] :
% 15.55/8.62        ( ord_less_eq_real @ zero_zero_real
% 15.55/8.62        @ ( groups6591440286371151544t_real
% 15.55/8.62          @ ^ [I4: nat] : ( abs_abs_real @ ( F @ I4 ) )
% 15.55/8.62          @ A3 ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7634_sum__abs__ge__zero,axiom,
% 15.55/8.62      ! [F: int > int,A3: set_int] :
% 15.55/8.62        ( ord_less_eq_int @ zero_zero_int
% 15.55/8.62        @ ( groups4538972089207619220nt_int
% 15.55/8.62          @ ^ [I4: int] : ( abs_abs_int @ ( F @ I4 ) )
% 15.55/8.62          @ A3 ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7635_sin__arcsin,axiom,
% 15.55/8.62      ! [Y3: real] :
% 15.55/8.62        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 15.55/8.62       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 15.55/8.62         => ( ( sin_real @ ( arcsin @ Y3 ) )
% 15.55/8.62            = Y3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7636_sum_Ocl__ivl__Suc,axiom,
% 15.55/8.62      ! [N: nat,M: nat,G: nat > rat] :
% 15.55/8.62        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 15.55/8.62         => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.62            = zero_zero_rat ) )
% 15.55/8.62        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 15.55/8.62         => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.62            = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7637_sum_Ocl__ivl__Suc,axiom,
% 15.55/8.62      ! [N: nat,M: nat,G: nat > int] :
% 15.55/8.62        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 15.55/8.62         => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.62            = zero_zero_int ) )
% 15.55/8.62        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 15.55/8.62         => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.62            = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7638_sum_Ocl__ivl__Suc,axiom,
% 15.55/8.62      ! [N: nat,M: nat,G: nat > nat] :
% 15.55/8.62        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 15.55/8.62         => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.62            = zero_zero_nat ) )
% 15.55/8.62        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 15.55/8.62         => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.62            = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7639_sum_Ocl__ivl__Suc,axiom,
% 15.55/8.62      ! [N: nat,M: nat,G: nat > real] :
% 15.55/8.62        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 15.55/8.62         => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.62            = zero_zero_real ) )
% 15.55/8.62        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 15.55/8.62         => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.62            = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7640_sum__zero__power,axiom,
% 15.55/8.62      ! [A3: set_nat,C: nat > complex] :
% 15.55/8.62        ( ( ( ( finite_finite_nat @ A3 )
% 15.55/8.62            & ( member_nat @ zero_zero_nat @ A3 ) )
% 15.55/8.62         => ( ( groups2073611262835488442omplex
% 15.55/8.62              @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) )
% 15.55/8.62              @ A3 )
% 15.55/8.62            = ( C @ zero_zero_nat ) ) )
% 15.55/8.62        & ( ~ ( ( finite_finite_nat @ A3 )
% 15.55/8.62              & ( member_nat @ zero_zero_nat @ A3 ) )
% 15.55/8.62         => ( ( groups2073611262835488442omplex
% 15.55/8.62              @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) )
% 15.55/8.62              @ A3 )
% 15.55/8.62            = zero_zero_complex ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7641_sum__zero__power,axiom,
% 15.55/8.62      ! [A3: set_nat,C: nat > rat] :
% 15.55/8.62        ( ( ( ( finite_finite_nat @ A3 )
% 15.55/8.62            & ( member_nat @ zero_zero_nat @ A3 ) )
% 15.55/8.62         => ( ( groups2906978787729119204at_rat
% 15.55/8.62              @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) )
% 15.55/8.62              @ A3 )
% 15.55/8.62            = ( C @ zero_zero_nat ) ) )
% 15.55/8.62        & ( ~ ( ( finite_finite_nat @ A3 )
% 15.55/8.62              & ( member_nat @ zero_zero_nat @ A3 ) )
% 15.55/8.62         => ( ( groups2906978787729119204at_rat
% 15.55/8.62              @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) )
% 15.55/8.62              @ A3 )
% 15.55/8.62            = zero_zero_rat ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7642_sum__zero__power,axiom,
% 15.55/8.62      ! [A3: set_nat,C: nat > real] :
% 15.55/8.62        ( ( ( ( finite_finite_nat @ A3 )
% 15.55/8.62            & ( member_nat @ zero_zero_nat @ A3 ) )
% 15.55/8.62         => ( ( groups6591440286371151544t_real
% 15.55/8.62              @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) )
% 15.55/8.62              @ A3 )
% 15.55/8.62            = ( C @ zero_zero_nat ) ) )
% 15.55/8.62        & ( ~ ( ( finite_finite_nat @ A3 )
% 15.55/8.62              & ( member_nat @ zero_zero_nat @ A3 ) )
% 15.55/8.62         => ( ( groups6591440286371151544t_real
% 15.55/8.62              @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) )
% 15.55/8.62              @ A3 )
% 15.55/8.62            = zero_zero_real ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7643_arcsin__1,axiom,
% 15.55/8.62      ( ( arcsin @ one_one_real )
% 15.55/8.62      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7644_sum__zero__power_H,axiom,
% 15.55/8.62      ! [A3: set_nat,C: nat > complex,D3: nat > complex] :
% 15.55/8.62        ( ( ( ( finite_finite_nat @ A3 )
% 15.55/8.62            & ( member_nat @ zero_zero_nat @ A3 ) )
% 15.55/8.62         => ( ( groups2073611262835488442omplex
% 15.55/8.62              @ ^ [I4: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) ) @ ( D3 @ I4 ) )
% 15.55/8.62              @ A3 )
% 15.55/8.62            = ( divide1717551699836669952omplex @ ( C @ zero_zero_nat ) @ ( D3 @ zero_zero_nat ) ) ) )
% 15.55/8.62        & ( ~ ( ( finite_finite_nat @ A3 )
% 15.55/8.62              & ( member_nat @ zero_zero_nat @ A3 ) )
% 15.55/8.62         => ( ( groups2073611262835488442omplex
% 15.55/8.62              @ ^ [I4: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) ) @ ( D3 @ I4 ) )
% 15.55/8.62              @ A3 )
% 15.55/8.62            = zero_zero_complex ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7645_sum__zero__power_H,axiom,
% 15.55/8.62      ! [A3: set_nat,C: nat > rat,D3: nat > rat] :
% 15.55/8.62        ( ( ( ( finite_finite_nat @ A3 )
% 15.55/8.62            & ( member_nat @ zero_zero_nat @ A3 ) )
% 15.55/8.62         => ( ( groups2906978787729119204at_rat
% 15.55/8.62              @ ^ [I4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) ) @ ( D3 @ I4 ) )
% 15.55/8.62              @ A3 )
% 15.55/8.62            = ( divide_divide_rat @ ( C @ zero_zero_nat ) @ ( D3 @ zero_zero_nat ) ) ) )
% 15.55/8.62        & ( ~ ( ( finite_finite_nat @ A3 )
% 15.55/8.62              & ( member_nat @ zero_zero_nat @ A3 ) )
% 15.55/8.62         => ( ( groups2906978787729119204at_rat
% 15.55/8.62              @ ^ [I4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) ) @ ( D3 @ I4 ) )
% 15.55/8.62              @ A3 )
% 15.55/8.62            = zero_zero_rat ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7646_sum__zero__power_H,axiom,
% 15.55/8.62      ! [A3: set_nat,C: nat > real,D3: nat > real] :
% 15.55/8.62        ( ( ( ( finite_finite_nat @ A3 )
% 15.55/8.62            & ( member_nat @ zero_zero_nat @ A3 ) )
% 15.55/8.62         => ( ( groups6591440286371151544t_real
% 15.55/8.62              @ ^ [I4: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) ) @ ( D3 @ I4 ) )
% 15.55/8.62              @ A3 )
% 15.55/8.62            = ( divide_divide_real @ ( C @ zero_zero_nat ) @ ( D3 @ zero_zero_nat ) ) ) )
% 15.55/8.62        & ( ~ ( ( finite_finite_nat @ A3 )
% 15.55/8.62              & ( member_nat @ zero_zero_nat @ A3 ) )
% 15.55/8.62         => ( ( groups6591440286371151544t_real
% 15.55/8.62              @ ^ [I4: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) ) @ ( D3 @ I4 ) )
% 15.55/8.62              @ A3 )
% 15.55/8.62            = zero_zero_real ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7647_arcsin__minus__1,axiom,
% 15.55/8.62      ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 15.55/8.62      = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7648_suminf__finite,axiom,
% 15.55/8.62      ! [N4: set_nat,F: nat > int] :
% 15.55/8.62        ( ( finite_finite_nat @ N4 )
% 15.55/8.62       => ( ! [N2: nat] :
% 15.55/8.62              ( ~ ( member_nat @ N2 @ N4 )
% 15.55/8.62             => ( ( F @ N2 )
% 15.55/8.62                = zero_zero_int ) )
% 15.55/8.62         => ( ( suminf_int @ F )
% 15.55/8.62            = ( groups3539618377306564664at_int @ F @ N4 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7649_suminf__finite,axiom,
% 15.55/8.62      ! [N4: set_nat,F: nat > nat] :
% 15.55/8.62        ( ( finite_finite_nat @ N4 )
% 15.55/8.62       => ( ! [N2: nat] :
% 15.55/8.62              ( ~ ( member_nat @ N2 @ N4 )
% 15.55/8.62             => ( ( F @ N2 )
% 15.55/8.62                = zero_zero_nat ) )
% 15.55/8.62         => ( ( suminf_nat @ F )
% 15.55/8.62            = ( groups3542108847815614940at_nat @ F @ N4 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7650_suminf__finite,axiom,
% 15.55/8.62      ! [N4: set_nat,F: nat > real] :
% 15.55/8.62        ( ( finite_finite_nat @ N4 )
% 15.55/8.62       => ( ! [N2: nat] :
% 15.55/8.62              ( ~ ( member_nat @ N2 @ N4 )
% 15.55/8.62             => ( ( F @ N2 )
% 15.55/8.62                = zero_zero_real ) )
% 15.55/8.62         => ( ( suminf_real @ F )
% 15.55/8.62            = ( groups6591440286371151544t_real @ F @ N4 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7651_sum__norm__le,axiom,
% 15.55/8.62      ! [S2: set_option_nat,F: option_nat > complex,G: option_nat > real] :
% 15.55/8.62        ( ! [X4: option_nat] :
% 15.55/8.62            ( ( member_option_nat @ X4 @ S2 )
% 15.55/8.62           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G @ X4 ) ) )
% 15.55/8.62       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3209896439523537802omplex @ F @ S2 ) ) @ ( groups4518532050878116744t_real @ G @ S2 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7652_sum__norm__le,axiom,
% 15.55/8.62      ! [S2: set_real,F: real > complex,G: real > real] :
% 15.55/8.62        ( ! [X4: real] :
% 15.55/8.62            ( ( member_real @ X4 @ S2 )
% 15.55/8.62           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G @ X4 ) ) )
% 15.55/8.62       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5754745047067104278omplex @ F @ S2 ) ) @ ( groups8097168146408367636l_real @ G @ S2 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7653_sum__norm__le,axiom,
% 15.55/8.62      ! [S2: set_set_nat,F: set_nat > complex,G: set_nat > real] :
% 15.55/8.62        ( ! [X4: set_nat] :
% 15.55/8.62            ( ( member_set_nat @ X4 @ S2 )
% 15.55/8.62           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G @ X4 ) ) )
% 15.55/8.62       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups8255218700646806128omplex @ F @ S2 ) ) @ ( groups5107569545109728110t_real @ G @ S2 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7654_sum__norm__le,axiom,
% 15.55/8.62      ! [S2: set_int,F: int > complex,G: int > real] :
% 15.55/8.62        ( ! [X4: int] :
% 15.55/8.62            ( ( member_int @ X4 @ S2 )
% 15.55/8.62           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G @ X4 ) ) )
% 15.55/8.62       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F @ S2 ) ) @ ( groups8778361861064173332t_real @ G @ S2 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7655_sum__norm__le,axiom,
% 15.55/8.62      ! [S2: set_nat,F: nat > complex,G: nat > real] :
% 15.55/8.62        ( ! [X4: nat] :
% 15.55/8.62            ( ( member_nat @ X4 @ S2 )
% 15.55/8.62           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G @ X4 ) ) )
% 15.55/8.62       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G @ S2 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7656_sum__norm__le,axiom,
% 15.55/8.62      ! [S2: set_complex,F: complex > complex,G: complex > real] :
% 15.55/8.62        ( ! [X4: complex] :
% 15.55/8.62            ( ( member_complex @ X4 @ S2 )
% 15.55/8.62           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G @ X4 ) ) )
% 15.55/8.62       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ S2 ) ) @ ( groups5808333547571424918x_real @ G @ S2 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7657_sum__norm__le,axiom,
% 15.55/8.62      ! [S2: set_nat,F: nat > real,G: nat > real] :
% 15.55/8.62        ( ! [X4: nat] :
% 15.55/8.62            ( ( member_nat @ X4 @ S2 )
% 15.55/8.62           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ X4 ) ) @ ( G @ X4 ) ) )
% 15.55/8.62       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G @ S2 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7658_norm__sum,axiom,
% 15.55/8.62      ! [F: nat > complex,A3: set_nat] :
% 15.55/8.62        ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ A3 ) )
% 15.55/8.62        @ ( groups6591440286371151544t_real
% 15.55/8.62          @ ^ [I4: nat] : ( real_V1022390504157884413omplex @ ( F @ I4 ) )
% 15.55/8.62          @ A3 ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7659_norm__sum,axiom,
% 15.55/8.62      ! [F: complex > complex,A3: set_complex] :
% 15.55/8.62        ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ A3 ) )
% 15.55/8.62        @ ( groups5808333547571424918x_real
% 15.55/8.62          @ ^ [I4: complex] : ( real_V1022390504157884413omplex @ ( F @ I4 ) )
% 15.55/8.62          @ A3 ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7660_norm__sum,axiom,
% 15.55/8.62      ! [F: nat > real,A3: set_nat] :
% 15.55/8.62        ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ A3 ) )
% 15.55/8.62        @ ( groups6591440286371151544t_real
% 15.55/8.62          @ ^ [I4: nat] : ( real_V7735802525324610683m_real @ ( F @ I4 ) )
% 15.55/8.62          @ A3 ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7661_complex__eq__cancel__iff2,axiom,
% 15.55/8.62      ! [X3: real,Y3: real,Xa: real] :
% 15.55/8.62        ( ( ( complex2 @ X3 @ Y3 )
% 15.55/8.62          = ( real_V4546457046886955230omplex @ Xa ) )
% 15.55/8.62        = ( ( X3 = Xa )
% 15.55/8.62          & ( Y3 = zero_zero_real ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7662_complex__of__real__code,axiom,
% 15.55/8.62      ( real_V4546457046886955230omplex
% 15.55/8.62      = ( ^ [X: real] : ( complex2 @ X @ zero_zero_real ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7663_complex__of__real__def,axiom,
% 15.55/8.62      ( real_V4546457046886955230omplex
% 15.55/8.62      = ( ^ [R5: real] : ( complex2 @ R5 @ zero_zero_real ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7664_zero__complex_Ocode,axiom,
% 15.55/8.62      ( zero_zero_complex
% 15.55/8.62      = ( complex2 @ zero_zero_real @ zero_zero_real ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7665_Complex__eq__0,axiom,
% 15.55/8.62      ! [A: real,B: real] :
% 15.55/8.62        ( ( ( complex2 @ A @ B )
% 15.55/8.62          = zero_zero_complex )
% 15.55/8.62        = ( ( A = zero_zero_real )
% 15.55/8.62          & ( B = zero_zero_real ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7666_sum_Oreindex__bij__witness__not__neutral,axiom,
% 15.55/8.62      ! [S4: set_real,T4: set_real,S2: set_real,I: real > real,J: real > real,T5: set_real,G: real > real,H2: real > real] :
% 15.55/8.62        ( ( finite_finite_real @ S4 )
% 15.55/8.62       => ( ( finite_finite_real @ T4 )
% 15.55/8.62         => ( ! [A5: real] :
% 15.55/8.62                ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 15.55/8.62               => ( ( I @ ( J @ A5 ) )
% 15.55/8.62                  = A5 ) )
% 15.55/8.62           => ( ! [A5: real] :
% 15.55/8.62                  ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 15.55/8.62                 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 15.55/8.62             => ( ! [B4: real] :
% 15.55/8.62                    ( ( member_real @ B4 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 15.55/8.62                   => ( ( J @ ( I @ B4 ) )
% 15.55/8.62                      = B4 ) )
% 15.55/8.62               => ( ! [B4: real] :
% 15.55/8.62                      ( ( member_real @ B4 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 15.55/8.62                     => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 15.55/8.62                 => ( ! [A5: real] :
% 15.55/8.62                        ( ( member_real @ A5 @ S4 )
% 15.55/8.62                       => ( ( G @ A5 )
% 15.55/8.62                          = zero_zero_real ) )
% 15.55/8.62                   => ( ! [B4: real] :
% 15.55/8.62                          ( ( member_real @ B4 @ T4 )
% 15.55/8.62                         => ( ( H2 @ B4 )
% 15.55/8.62                            = zero_zero_real ) )
% 15.55/8.62                     => ( ! [A5: real] :
% 15.55/8.62                            ( ( member_real @ A5 @ S2 )
% 15.55/8.62                           => ( ( H2 @ ( J @ A5 ) )
% 15.55/8.62                              = ( G @ A5 ) ) )
% 15.55/8.62                       => ( ( groups8097168146408367636l_real @ G @ S2 )
% 15.55/8.62                          = ( groups8097168146408367636l_real @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7667_sum_Oreindex__bij__witness__not__neutral,axiom,
% 15.55/8.62      ! [S4: set_real,T4: set_int,S2: set_real,I: int > real,J: real > int,T5: set_int,G: real > real,H2: int > real] :
% 15.55/8.62        ( ( finite_finite_real @ S4 )
% 15.55/8.62       => ( ( finite_finite_int @ T4 )
% 15.55/8.62         => ( ! [A5: real] :
% 15.55/8.62                ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 15.55/8.62               => ( ( I @ ( J @ A5 ) )
% 15.55/8.62                  = A5 ) )
% 15.55/8.62           => ( ! [A5: real] :
% 15.55/8.62                  ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 15.55/8.62                 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 15.55/8.62             => ( ! [B4: int] :
% 15.55/8.62                    ( ( member_int @ B4 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 15.55/8.62                   => ( ( J @ ( I @ B4 ) )
% 15.55/8.62                      = B4 ) )
% 15.55/8.62               => ( ! [B4: int] :
% 15.55/8.62                      ( ( member_int @ B4 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 15.55/8.62                     => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 15.55/8.62                 => ( ! [A5: real] :
% 15.55/8.62                        ( ( member_real @ A5 @ S4 )
% 15.55/8.62                       => ( ( G @ A5 )
% 15.55/8.62                          = zero_zero_real ) )
% 15.55/8.62                   => ( ! [B4: int] :
% 15.55/8.62                          ( ( member_int @ B4 @ T4 )
% 15.55/8.62                         => ( ( H2 @ B4 )
% 15.55/8.62                            = zero_zero_real ) )
% 15.55/8.62                     => ( ! [A5: real] :
% 15.55/8.62                            ( ( member_real @ A5 @ S2 )
% 15.55/8.62                           => ( ( H2 @ ( J @ A5 ) )
% 15.55/8.62                              = ( G @ A5 ) ) )
% 15.55/8.62                       => ( ( groups8097168146408367636l_real @ G @ S2 )
% 15.55/8.62                          = ( groups8778361861064173332t_real @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7668_sum_Oreindex__bij__witness__not__neutral,axiom,
% 15.55/8.62      ! [S4: set_real,T4: set_complex,S2: set_real,I: complex > real,J: real > complex,T5: set_complex,G: real > real,H2: complex > real] :
% 15.55/8.62        ( ( finite_finite_real @ S4 )
% 15.55/8.62       => ( ( finite3207457112153483333omplex @ T4 )
% 15.55/8.62         => ( ! [A5: real] :
% 15.55/8.62                ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 15.55/8.62               => ( ( I @ ( J @ A5 ) )
% 15.55/8.62                  = A5 ) )
% 15.55/8.62           => ( ! [A5: real] :
% 15.55/8.62                  ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 15.55/8.62                 => ( member_complex @ ( J @ A5 ) @ ( minus_811609699411566653omplex @ T5 @ T4 ) ) )
% 15.55/8.62             => ( ! [B4: complex] :
% 15.55/8.62                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 15.55/8.62                   => ( ( J @ ( I @ B4 ) )
% 15.55/8.62                      = B4 ) )
% 15.55/8.62               => ( ! [B4: complex] :
% 15.55/8.62                      ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 15.55/8.62                     => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 15.55/8.62                 => ( ! [A5: real] :
% 15.55/8.62                        ( ( member_real @ A5 @ S4 )
% 15.55/8.62                       => ( ( G @ A5 )
% 15.55/8.62                          = zero_zero_real ) )
% 15.55/8.62                   => ( ! [B4: complex] :
% 15.55/8.62                          ( ( member_complex @ B4 @ T4 )
% 15.55/8.62                         => ( ( H2 @ B4 )
% 15.55/8.62                            = zero_zero_real ) )
% 15.55/8.62                     => ( ! [A5: real] :
% 15.55/8.62                            ( ( member_real @ A5 @ S2 )
% 15.55/8.62                           => ( ( H2 @ ( J @ A5 ) )
% 15.55/8.62                              = ( G @ A5 ) ) )
% 15.55/8.62                       => ( ( groups8097168146408367636l_real @ G @ S2 )
% 15.55/8.62                          = ( groups5808333547571424918x_real @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7669_sum_Oreindex__bij__witness__not__neutral,axiom,
% 15.55/8.62      ! [S4: set_real,T4: set_Extended_enat,S2: set_real,I: extended_enat > real,J: real > extended_enat,T5: set_Extended_enat,G: real > real,H2: extended_enat > real] :
% 15.55/8.62        ( ( finite_finite_real @ S4 )
% 15.55/8.62       => ( ( finite4001608067531595151d_enat @ T4 )
% 15.55/8.62         => ( ! [A5: real] :
% 15.55/8.62                ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 15.55/8.62               => ( ( I @ ( J @ A5 ) )
% 15.55/8.62                  = A5 ) )
% 15.55/8.62           => ( ! [A5: real] :
% 15.55/8.62                  ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 15.55/8.62                 => ( member_Extended_enat @ ( J @ A5 ) @ ( minus_925952699566721837d_enat @ T5 @ T4 ) ) )
% 15.55/8.62             => ( ! [B4: extended_enat] :
% 15.55/8.62                    ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ T5 @ T4 ) )
% 15.55/8.62                   => ( ( J @ ( I @ B4 ) )
% 15.55/8.62                      = B4 ) )
% 15.55/8.62               => ( ! [B4: extended_enat] :
% 15.55/8.62                      ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ T5 @ T4 ) )
% 15.55/8.62                     => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 15.55/8.62                 => ( ! [A5: real] :
% 15.55/8.62                        ( ( member_real @ A5 @ S4 )
% 15.55/8.62                       => ( ( G @ A5 )
% 15.55/8.62                          = zero_zero_real ) )
% 15.55/8.62                   => ( ! [B4: extended_enat] :
% 15.55/8.62                          ( ( member_Extended_enat @ B4 @ T4 )
% 15.55/8.62                         => ( ( H2 @ B4 )
% 15.55/8.62                            = zero_zero_real ) )
% 15.55/8.62                     => ( ! [A5: real] :
% 15.55/8.62                            ( ( member_real @ A5 @ S2 )
% 15.55/8.62                           => ( ( H2 @ ( J @ A5 ) )
% 15.55/8.62                              = ( G @ A5 ) ) )
% 15.55/8.62                       => ( ( groups8097168146408367636l_real @ G @ S2 )
% 15.55/8.62                          = ( groups4148127829035722712t_real @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7670_sum_Oreindex__bij__witness__not__neutral,axiom,
% 15.55/8.62      ! [S4: set_int,T4: set_real,S2: set_int,I: real > int,J: int > real,T5: set_real,G: int > real,H2: real > real] :
% 15.55/8.62        ( ( finite_finite_int @ S4 )
% 15.55/8.62       => ( ( finite_finite_real @ T4 )
% 15.55/8.62         => ( ! [A5: int] :
% 15.55/8.62                ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 15.55/8.62               => ( ( I @ ( J @ A5 ) )
% 15.55/8.62                  = A5 ) )
% 15.55/8.62           => ( ! [A5: int] :
% 15.55/8.62                  ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 15.55/8.62                 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 15.55/8.62             => ( ! [B4: real] :
% 15.55/8.62                    ( ( member_real @ B4 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 15.55/8.62                   => ( ( J @ ( I @ B4 ) )
% 15.55/8.62                      = B4 ) )
% 15.55/8.62               => ( ! [B4: real] :
% 15.55/8.62                      ( ( member_real @ B4 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 15.55/8.62                     => ( member_int @ ( I @ B4 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 15.55/8.62                 => ( ! [A5: int] :
% 15.55/8.62                        ( ( member_int @ A5 @ S4 )
% 15.55/8.62                       => ( ( G @ A5 )
% 15.55/8.62                          = zero_zero_real ) )
% 15.55/8.62                   => ( ! [B4: real] :
% 15.55/8.62                          ( ( member_real @ B4 @ T4 )
% 15.55/8.62                         => ( ( H2 @ B4 )
% 15.55/8.62                            = zero_zero_real ) )
% 15.55/8.62                     => ( ! [A5: int] :
% 15.55/8.62                            ( ( member_int @ A5 @ S2 )
% 15.55/8.62                           => ( ( H2 @ ( J @ A5 ) )
% 15.55/8.62                              = ( G @ A5 ) ) )
% 15.55/8.62                       => ( ( groups8778361861064173332t_real @ G @ S2 )
% 15.55/8.62                          = ( groups8097168146408367636l_real @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7671_sum_Oreindex__bij__witness__not__neutral,axiom,
% 15.55/8.62      ! [S4: set_int,T4: set_int,S2: set_int,I: int > int,J: int > int,T5: set_int,G: int > real,H2: int > real] :
% 15.55/8.62        ( ( finite_finite_int @ S4 )
% 15.55/8.62       => ( ( finite_finite_int @ T4 )
% 15.55/8.62         => ( ! [A5: int] :
% 15.55/8.62                ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 15.55/8.62               => ( ( I @ ( J @ A5 ) )
% 15.55/8.62                  = A5 ) )
% 15.55/8.62           => ( ! [A5: int] :
% 15.55/8.62                  ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 15.55/8.62                 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 15.55/8.62             => ( ! [B4: int] :
% 15.55/8.62                    ( ( member_int @ B4 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 15.55/8.62                   => ( ( J @ ( I @ B4 ) )
% 15.55/8.62                      = B4 ) )
% 15.55/8.62               => ( ! [B4: int] :
% 15.55/8.62                      ( ( member_int @ B4 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 15.55/8.62                     => ( member_int @ ( I @ B4 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 15.55/8.62                 => ( ! [A5: int] :
% 15.55/8.62                        ( ( member_int @ A5 @ S4 )
% 15.55/8.62                       => ( ( G @ A5 )
% 15.55/8.62                          = zero_zero_real ) )
% 15.55/8.62                   => ( ! [B4: int] :
% 15.55/8.62                          ( ( member_int @ B4 @ T4 )
% 15.55/8.62                         => ( ( H2 @ B4 )
% 15.55/8.62                            = zero_zero_real ) )
% 15.55/8.62                     => ( ! [A5: int] :
% 15.55/8.62                            ( ( member_int @ A5 @ S2 )
% 15.55/8.62                           => ( ( H2 @ ( J @ A5 ) )
% 15.55/8.62                              = ( G @ A5 ) ) )
% 15.55/8.62                       => ( ( groups8778361861064173332t_real @ G @ S2 )
% 15.55/8.62                          = ( groups8778361861064173332t_real @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7672_sum_Oreindex__bij__witness__not__neutral,axiom,
% 15.55/8.62      ! [S4: set_int,T4: set_complex,S2: set_int,I: complex > int,J: int > complex,T5: set_complex,G: int > real,H2: complex > real] :
% 15.55/8.62        ( ( finite_finite_int @ S4 )
% 15.55/8.62       => ( ( finite3207457112153483333omplex @ T4 )
% 15.55/8.62         => ( ! [A5: int] :
% 15.55/8.62                ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 15.55/8.62               => ( ( I @ ( J @ A5 ) )
% 15.55/8.62                  = A5 ) )
% 15.55/8.62           => ( ! [A5: int] :
% 15.55/8.62                  ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 15.55/8.62                 => ( member_complex @ ( J @ A5 ) @ ( minus_811609699411566653omplex @ T5 @ T4 ) ) )
% 15.55/8.62             => ( ! [B4: complex] :
% 15.55/8.62                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 15.55/8.62                   => ( ( J @ ( I @ B4 ) )
% 15.55/8.62                      = B4 ) )
% 15.55/8.62               => ( ! [B4: complex] :
% 15.55/8.62                      ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 15.55/8.62                     => ( member_int @ ( I @ B4 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 15.55/8.62                 => ( ! [A5: int] :
% 15.55/8.62                        ( ( member_int @ A5 @ S4 )
% 15.55/8.62                       => ( ( G @ A5 )
% 15.55/8.62                          = zero_zero_real ) )
% 15.55/8.62                   => ( ! [B4: complex] :
% 15.55/8.62                          ( ( member_complex @ B4 @ T4 )
% 15.55/8.62                         => ( ( H2 @ B4 )
% 15.55/8.62                            = zero_zero_real ) )
% 15.55/8.62                     => ( ! [A5: int] :
% 15.55/8.62                            ( ( member_int @ A5 @ S2 )
% 15.55/8.62                           => ( ( H2 @ ( J @ A5 ) )
% 15.55/8.62                              = ( G @ A5 ) ) )
% 15.55/8.62                       => ( ( groups8778361861064173332t_real @ G @ S2 )
% 15.55/8.62                          = ( groups5808333547571424918x_real @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7673_sum_Oreindex__bij__witness__not__neutral,axiom,
% 15.55/8.62      ! [S4: set_int,T4: set_Extended_enat,S2: set_int,I: extended_enat > int,J: int > extended_enat,T5: set_Extended_enat,G: int > real,H2: extended_enat > real] :
% 15.55/8.62        ( ( finite_finite_int @ S4 )
% 15.55/8.62       => ( ( finite4001608067531595151d_enat @ T4 )
% 15.55/8.62         => ( ! [A5: int] :
% 15.55/8.62                ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 15.55/8.62               => ( ( I @ ( J @ A5 ) )
% 15.55/8.62                  = A5 ) )
% 15.55/8.62           => ( ! [A5: int] :
% 15.55/8.62                  ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 15.55/8.62                 => ( member_Extended_enat @ ( J @ A5 ) @ ( minus_925952699566721837d_enat @ T5 @ T4 ) ) )
% 15.55/8.62             => ( ! [B4: extended_enat] :
% 15.55/8.62                    ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ T5 @ T4 ) )
% 15.55/8.62                   => ( ( J @ ( I @ B4 ) )
% 15.55/8.62                      = B4 ) )
% 15.55/8.62               => ( ! [B4: extended_enat] :
% 15.55/8.62                      ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ T5 @ T4 ) )
% 15.55/8.62                     => ( member_int @ ( I @ B4 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 15.55/8.62                 => ( ! [A5: int] :
% 15.55/8.62                        ( ( member_int @ A5 @ S4 )
% 15.55/8.62                       => ( ( G @ A5 )
% 15.55/8.62                          = zero_zero_real ) )
% 15.55/8.62                   => ( ! [B4: extended_enat] :
% 15.55/8.62                          ( ( member_Extended_enat @ B4 @ T4 )
% 15.55/8.62                         => ( ( H2 @ B4 )
% 15.55/8.62                            = zero_zero_real ) )
% 15.55/8.62                     => ( ! [A5: int] :
% 15.55/8.62                            ( ( member_int @ A5 @ S2 )
% 15.55/8.62                           => ( ( H2 @ ( J @ A5 ) )
% 15.55/8.62                              = ( G @ A5 ) ) )
% 15.55/8.62                       => ( ( groups8778361861064173332t_real @ G @ S2 )
% 15.55/8.62                          = ( groups4148127829035722712t_real @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7674_sum_Oreindex__bij__witness__not__neutral,axiom,
% 15.55/8.62      ! [S4: set_complex,T4: set_real,S2: set_complex,I: real > complex,J: complex > real,T5: set_real,G: complex > real,H2: real > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ S4 )
% 15.55/8.62       => ( ( finite_finite_real @ T4 )
% 15.55/8.62         => ( ! [A5: complex] :
% 15.55/8.62                ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ S2 @ S4 ) )
% 15.55/8.62               => ( ( I @ ( J @ A5 ) )
% 15.55/8.62                  = A5 ) )
% 15.55/8.62           => ( ! [A5: complex] :
% 15.55/8.62                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ S2 @ S4 ) )
% 15.55/8.62                 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 15.55/8.62             => ( ! [B4: real] :
% 15.55/8.62                    ( ( member_real @ B4 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 15.55/8.62                   => ( ( J @ ( I @ B4 ) )
% 15.55/8.62                      = B4 ) )
% 15.55/8.62               => ( ! [B4: real] :
% 15.55/8.62                      ( ( member_real @ B4 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 15.55/8.62                     => ( member_complex @ ( I @ B4 ) @ ( minus_811609699411566653omplex @ S2 @ S4 ) ) )
% 15.55/8.62                 => ( ! [A5: complex] :
% 15.55/8.62                        ( ( member_complex @ A5 @ S4 )
% 15.55/8.62                       => ( ( G @ A5 )
% 15.55/8.62                          = zero_zero_real ) )
% 15.55/8.62                   => ( ! [B4: real] :
% 15.55/8.62                          ( ( member_real @ B4 @ T4 )
% 15.55/8.62                         => ( ( H2 @ B4 )
% 15.55/8.62                            = zero_zero_real ) )
% 15.55/8.62                     => ( ! [A5: complex] :
% 15.55/8.62                            ( ( member_complex @ A5 @ S2 )
% 15.55/8.62                           => ( ( H2 @ ( J @ A5 ) )
% 15.55/8.62                              = ( G @ A5 ) ) )
% 15.55/8.62                       => ( ( groups5808333547571424918x_real @ G @ S2 )
% 15.55/8.62                          = ( groups8097168146408367636l_real @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7675_sum_Oreindex__bij__witness__not__neutral,axiom,
% 15.55/8.62      ! [S4: set_complex,T4: set_int,S2: set_complex,I: int > complex,J: complex > int,T5: set_int,G: complex > real,H2: int > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ S4 )
% 15.55/8.62       => ( ( finite_finite_int @ T4 )
% 15.55/8.62         => ( ! [A5: complex] :
% 15.55/8.62                ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ S2 @ S4 ) )
% 15.55/8.62               => ( ( I @ ( J @ A5 ) )
% 15.55/8.62                  = A5 ) )
% 15.55/8.62           => ( ! [A5: complex] :
% 15.55/8.62                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ S2 @ S4 ) )
% 15.55/8.62                 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 15.55/8.62             => ( ! [B4: int] :
% 15.55/8.62                    ( ( member_int @ B4 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 15.55/8.62                   => ( ( J @ ( I @ B4 ) )
% 15.55/8.62                      = B4 ) )
% 15.55/8.62               => ( ! [B4: int] :
% 15.55/8.62                      ( ( member_int @ B4 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 15.55/8.62                     => ( member_complex @ ( I @ B4 ) @ ( minus_811609699411566653omplex @ S2 @ S4 ) ) )
% 15.55/8.62                 => ( ! [A5: complex] :
% 15.55/8.62                        ( ( member_complex @ A5 @ S4 )
% 15.55/8.62                       => ( ( G @ A5 )
% 15.55/8.62                          = zero_zero_real ) )
% 15.55/8.62                   => ( ! [B4: int] :
% 15.55/8.62                          ( ( member_int @ B4 @ T4 )
% 15.55/8.62                         => ( ( H2 @ B4 )
% 15.55/8.62                            = zero_zero_real ) )
% 15.55/8.62                     => ( ! [A5: complex] :
% 15.55/8.62                            ( ( member_complex @ A5 @ S2 )
% 15.55/8.62                           => ( ( H2 @ ( J @ A5 ) )
% 15.55/8.62                              = ( G @ A5 ) ) )
% 15.55/8.62                       => ( ( groups5808333547571424918x_real @ G @ S2 )
% 15.55/8.62                          = ( groups8778361861064173332t_real @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7676_sum_Osetdiff__irrelevant,axiom,
% 15.55/8.62      ! [A3: set_real,G: real > real] :
% 15.55/8.62        ( ( finite_finite_real @ A3 )
% 15.55/8.62       => ( ( groups8097168146408367636l_real @ G
% 15.55/8.62            @ ( minus_minus_set_real @ A3
% 15.55/8.62              @ ( collect_real
% 15.55/8.62                @ ^ [X: real] :
% 15.55/8.62                    ( ( G @ X )
% 15.55/8.62                    = zero_zero_real ) ) ) )
% 15.55/8.62          = ( groups8097168146408367636l_real @ G @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7677_sum_Osetdiff__irrelevant,axiom,
% 15.55/8.62      ! [A3: set_int,G: int > real] :
% 15.55/8.62        ( ( finite_finite_int @ A3 )
% 15.55/8.62       => ( ( groups8778361861064173332t_real @ G
% 15.55/8.62            @ ( minus_minus_set_int @ A3
% 15.55/8.62              @ ( collect_int
% 15.55/8.62                @ ^ [X: int] :
% 15.55/8.62                    ( ( G @ X )
% 15.55/8.62                    = zero_zero_real ) ) ) )
% 15.55/8.62          = ( groups8778361861064173332t_real @ G @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7678_sum_Osetdiff__irrelevant,axiom,
% 15.55/8.62      ! [A3: set_complex,G: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.62       => ( ( groups5808333547571424918x_real @ G
% 15.55/8.62            @ ( minus_811609699411566653omplex @ A3
% 15.55/8.62              @ ( collect_complex
% 15.55/8.62                @ ^ [X: complex] :
% 15.55/8.62                    ( ( G @ X )
% 15.55/8.62                    = zero_zero_real ) ) ) )
% 15.55/8.62          = ( groups5808333547571424918x_real @ G @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7679_sum_Osetdiff__irrelevant,axiom,
% 15.55/8.62      ! [A3: set_Extended_enat,G: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.62       => ( ( groups4148127829035722712t_real @ G
% 15.55/8.62            @ ( minus_925952699566721837d_enat @ A3
% 15.55/8.62              @ ( collec4429806609662206161d_enat
% 15.55/8.62                @ ^ [X: extended_enat] :
% 15.55/8.62                    ( ( G @ X )
% 15.55/8.62                    = zero_zero_real ) ) ) )
% 15.55/8.62          = ( groups4148127829035722712t_real @ G @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7680_sum_Osetdiff__irrelevant,axiom,
% 15.55/8.62      ! [A3: set_real,G: real > rat] :
% 15.55/8.62        ( ( finite_finite_real @ A3 )
% 15.55/8.62       => ( ( groups1300246762558778688al_rat @ G
% 15.55/8.62            @ ( minus_minus_set_real @ A3
% 15.55/8.62              @ ( collect_real
% 15.55/8.62                @ ^ [X: real] :
% 15.55/8.62                    ( ( G @ X )
% 15.55/8.62                    = zero_zero_rat ) ) ) )
% 15.55/8.62          = ( groups1300246762558778688al_rat @ G @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7681_sum_Osetdiff__irrelevant,axiom,
% 15.55/8.62      ! [A3: set_int,G: int > rat] :
% 15.55/8.62        ( ( finite_finite_int @ A3 )
% 15.55/8.62       => ( ( groups3906332499630173760nt_rat @ G
% 15.55/8.62            @ ( minus_minus_set_int @ A3
% 15.55/8.62              @ ( collect_int
% 15.55/8.62                @ ^ [X: int] :
% 15.55/8.62                    ( ( G @ X )
% 15.55/8.62                    = zero_zero_rat ) ) ) )
% 15.55/8.62          = ( groups3906332499630173760nt_rat @ G @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7682_sum_Osetdiff__irrelevant,axiom,
% 15.55/8.62      ! [A3: set_complex,G: complex > rat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.62       => ( ( groups5058264527183730370ex_rat @ G
% 15.55/8.62            @ ( minus_811609699411566653omplex @ A3
% 15.55/8.62              @ ( collect_complex
% 15.55/8.62                @ ^ [X: complex] :
% 15.55/8.62                    ( ( G @ X )
% 15.55/8.62                    = zero_zero_rat ) ) ) )
% 15.55/8.62          = ( groups5058264527183730370ex_rat @ G @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7683_sum_Osetdiff__irrelevant,axiom,
% 15.55/8.62      ! [A3: set_Extended_enat,G: extended_enat > rat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.62       => ( ( groups1392844769737527556at_rat @ G
% 15.55/8.62            @ ( minus_925952699566721837d_enat @ A3
% 15.55/8.62              @ ( collec4429806609662206161d_enat
% 15.55/8.62                @ ^ [X: extended_enat] :
% 15.55/8.62                    ( ( G @ X )
% 15.55/8.62                    = zero_zero_rat ) ) ) )
% 15.55/8.62          = ( groups1392844769737527556at_rat @ G @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7684_sum_Osetdiff__irrelevant,axiom,
% 15.55/8.62      ! [A3: set_real,G: real > nat] :
% 15.55/8.62        ( ( finite_finite_real @ A3 )
% 15.55/8.62       => ( ( groups1935376822645274424al_nat @ G
% 15.55/8.62            @ ( minus_minus_set_real @ A3
% 15.55/8.62              @ ( collect_real
% 15.55/8.62                @ ^ [X: real] :
% 15.55/8.62                    ( ( G @ X )
% 15.55/8.62                    = zero_zero_nat ) ) ) )
% 15.55/8.62          = ( groups1935376822645274424al_nat @ G @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7685_sum_Osetdiff__irrelevant,axiom,
% 15.55/8.62      ! [A3: set_int,G: int > nat] :
% 15.55/8.62        ( ( finite_finite_int @ A3 )
% 15.55/8.62       => ( ( groups4541462559716669496nt_nat @ G
% 15.55/8.62            @ ( minus_minus_set_int @ A3
% 15.55/8.62              @ ( collect_int
% 15.55/8.62                @ ^ [X: int] :
% 15.55/8.62                    ( ( G @ X )
% 15.55/8.62                    = zero_zero_nat ) ) ) )
% 15.55/8.62          = ( groups4541462559716669496nt_nat @ G @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7686_sum__strict__mono,axiom,
% 15.55/8.62      ! [A3: set_complex,F: complex > real,G: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.62       => ( ( A3 != bot_bot_set_complex )
% 15.55/8.62         => ( ! [X4: complex] :
% 15.55/8.62                ( ( member_complex @ X4 @ A3 )
% 15.55/8.62               => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62           => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A3 ) @ ( groups5808333547571424918x_real @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7687_sum__strict__mono,axiom,
% 15.55/8.62      ! [A3: set_Extended_enat,F: extended_enat > real,G: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.62       => ( ( A3 != bot_bo7653980558646680370d_enat )
% 15.55/8.62         => ( ! [X4: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ X4 @ A3 )
% 15.55/8.62               => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62           => ( ord_less_real @ ( groups4148127829035722712t_real @ F @ A3 ) @ ( groups4148127829035722712t_real @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7688_sum__strict__mono,axiom,
% 15.55/8.62      ! [A3: set_real,F: real > real,G: real > real] :
% 15.55/8.62        ( ( finite_finite_real @ A3 )
% 15.55/8.62       => ( ( A3 != bot_bot_set_real )
% 15.55/8.62         => ( ! [X4: real] :
% 15.55/8.62                ( ( member_real @ X4 @ A3 )
% 15.55/8.62               => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62           => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A3 ) @ ( groups8097168146408367636l_real @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7689_sum__strict__mono,axiom,
% 15.55/8.62      ! [A3: set_int,F: int > real,G: int > real] :
% 15.55/8.62        ( ( finite_finite_int @ A3 )
% 15.55/8.62       => ( ( A3 != bot_bot_set_int )
% 15.55/8.62         => ( ! [X4: int] :
% 15.55/8.62                ( ( member_int @ X4 @ A3 )
% 15.55/8.62               => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62           => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A3 ) @ ( groups8778361861064173332t_real @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7690_sum__strict__mono,axiom,
% 15.55/8.62      ! [A3: set_complex,F: complex > rat,G: complex > rat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.62       => ( ( A3 != bot_bot_set_complex )
% 15.55/8.62         => ( ! [X4: complex] :
% 15.55/8.62                ( ( member_complex @ X4 @ A3 )
% 15.55/8.62               => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62           => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A3 ) @ ( groups5058264527183730370ex_rat @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7691_sum__strict__mono,axiom,
% 15.55/8.62      ! [A3: set_Extended_enat,F: extended_enat > rat,G: extended_enat > rat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.62       => ( ( A3 != bot_bo7653980558646680370d_enat )
% 15.55/8.62         => ( ! [X4: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ X4 @ A3 )
% 15.55/8.62               => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62           => ( ord_less_rat @ ( groups1392844769737527556at_rat @ F @ A3 ) @ ( groups1392844769737527556at_rat @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7692_sum__strict__mono,axiom,
% 15.55/8.62      ! [A3: set_real,F: real > rat,G: real > rat] :
% 15.55/8.62        ( ( finite_finite_real @ A3 )
% 15.55/8.62       => ( ( A3 != bot_bot_set_real )
% 15.55/8.62         => ( ! [X4: real] :
% 15.55/8.62                ( ( member_real @ X4 @ A3 )
% 15.55/8.62               => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62           => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A3 ) @ ( groups1300246762558778688al_rat @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7693_sum__strict__mono,axiom,
% 15.55/8.62      ! [A3: set_nat,F: nat > rat,G: nat > rat] :
% 15.55/8.62        ( ( finite_finite_nat @ A3 )
% 15.55/8.62       => ( ( A3 != bot_bot_set_nat )
% 15.55/8.62         => ( ! [X4: nat] :
% 15.55/8.62                ( ( member_nat @ X4 @ A3 )
% 15.55/8.62               => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62           => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ ( groups2906978787729119204at_rat @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7694_sum__strict__mono,axiom,
% 15.55/8.62      ! [A3: set_int,F: int > rat,G: int > rat] :
% 15.55/8.62        ( ( finite_finite_int @ A3 )
% 15.55/8.62       => ( ( A3 != bot_bot_set_int )
% 15.55/8.62         => ( ! [X4: int] :
% 15.55/8.62                ( ( member_int @ X4 @ A3 )
% 15.55/8.62               => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62           => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ ( groups3906332499630173760nt_rat @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7695_sum__strict__mono,axiom,
% 15.55/8.62      ! [A3: set_complex,F: complex > nat,G: complex > nat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.62       => ( ( A3 != bot_bot_set_complex )
% 15.55/8.62         => ( ! [X4: complex] :
% 15.55/8.62                ( ( member_complex @ X4 @ A3 )
% 15.55/8.62               => ( ord_less_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62           => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A3 ) @ ( groups5693394587270226106ex_nat @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7696_sum_Ointer__filter,axiom,
% 15.55/8.62      ! [A3: set_real,G: real > real,P: real > $o] :
% 15.55/8.62        ( ( finite_finite_real @ A3 )
% 15.55/8.62       => ( ( groups8097168146408367636l_real @ G
% 15.55/8.62            @ ( collect_real
% 15.55/8.62              @ ^ [X: real] :
% 15.55/8.62                  ( ( member_real @ X @ A3 )
% 15.55/8.62                  & ( P @ X ) ) ) )
% 15.55/8.62          = ( groups8097168146408367636l_real
% 15.55/8.62            @ ^ [X: real] : ( if_real @ ( P @ X ) @ ( G @ X ) @ zero_zero_real )
% 15.55/8.62            @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7697_sum_Ointer__filter,axiom,
% 15.55/8.62      ! [A3: set_int,G: int > real,P: int > $o] :
% 15.55/8.62        ( ( finite_finite_int @ A3 )
% 15.55/8.62       => ( ( groups8778361861064173332t_real @ G
% 15.55/8.62            @ ( collect_int
% 15.55/8.62              @ ^ [X: int] :
% 15.55/8.62                  ( ( member_int @ X @ A3 )
% 15.55/8.62                  & ( P @ X ) ) ) )
% 15.55/8.62          = ( groups8778361861064173332t_real
% 15.55/8.62            @ ^ [X: int] : ( if_real @ ( P @ X ) @ ( G @ X ) @ zero_zero_real )
% 15.55/8.62            @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7698_sum_Ointer__filter,axiom,
% 15.55/8.62      ! [A3: set_complex,G: complex > real,P: complex > $o] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.62       => ( ( groups5808333547571424918x_real @ G
% 15.55/8.62            @ ( collect_complex
% 15.55/8.62              @ ^ [X: complex] :
% 15.55/8.62                  ( ( member_complex @ X @ A3 )
% 15.55/8.62                  & ( P @ X ) ) ) )
% 15.55/8.62          = ( groups5808333547571424918x_real
% 15.55/8.62            @ ^ [X: complex] : ( if_real @ ( P @ X ) @ ( G @ X ) @ zero_zero_real )
% 15.55/8.62            @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7699_sum_Ointer__filter,axiom,
% 15.55/8.62      ! [A3: set_Extended_enat,G: extended_enat > real,P: extended_enat > $o] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.62       => ( ( groups4148127829035722712t_real @ G
% 15.55/8.62            @ ( collec4429806609662206161d_enat
% 15.55/8.62              @ ^ [X: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ X @ A3 )
% 15.55/8.62                  & ( P @ X ) ) ) )
% 15.55/8.62          = ( groups4148127829035722712t_real
% 15.55/8.62            @ ^ [X: extended_enat] : ( if_real @ ( P @ X ) @ ( G @ X ) @ zero_zero_real )
% 15.55/8.62            @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7700_sum_Ointer__filter,axiom,
% 15.55/8.62      ! [A3: set_real,G: real > rat,P: real > $o] :
% 15.55/8.62        ( ( finite_finite_real @ A3 )
% 15.55/8.62       => ( ( groups1300246762558778688al_rat @ G
% 15.55/8.62            @ ( collect_real
% 15.55/8.62              @ ^ [X: real] :
% 15.55/8.62                  ( ( member_real @ X @ A3 )
% 15.55/8.62                  & ( P @ X ) ) ) )
% 15.55/8.62          = ( groups1300246762558778688al_rat
% 15.55/8.62            @ ^ [X: real] : ( if_rat @ ( P @ X ) @ ( G @ X ) @ zero_zero_rat )
% 15.55/8.62            @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7701_sum_Ointer__filter,axiom,
% 15.55/8.62      ! [A3: set_nat,G: nat > rat,P: nat > $o] :
% 15.55/8.62        ( ( finite_finite_nat @ A3 )
% 15.55/8.62       => ( ( groups2906978787729119204at_rat @ G
% 15.55/8.62            @ ( collect_nat
% 15.55/8.62              @ ^ [X: nat] :
% 15.55/8.62                  ( ( member_nat @ X @ A3 )
% 15.55/8.62                  & ( P @ X ) ) ) )
% 15.55/8.62          = ( groups2906978787729119204at_rat
% 15.55/8.62            @ ^ [X: nat] : ( if_rat @ ( P @ X ) @ ( G @ X ) @ zero_zero_rat )
% 15.55/8.62            @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7702_sum_Ointer__filter,axiom,
% 15.55/8.62      ! [A3: set_int,G: int > rat,P: int > $o] :
% 15.55/8.62        ( ( finite_finite_int @ A3 )
% 15.55/8.62       => ( ( groups3906332499630173760nt_rat @ G
% 15.55/8.62            @ ( collect_int
% 15.55/8.62              @ ^ [X: int] :
% 15.55/8.62                  ( ( member_int @ X @ A3 )
% 15.55/8.62                  & ( P @ X ) ) ) )
% 15.55/8.62          = ( groups3906332499630173760nt_rat
% 15.55/8.62            @ ^ [X: int] : ( if_rat @ ( P @ X ) @ ( G @ X ) @ zero_zero_rat )
% 15.55/8.62            @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7703_sum_Ointer__filter,axiom,
% 15.55/8.62      ! [A3: set_complex,G: complex > rat,P: complex > $o] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.62       => ( ( groups5058264527183730370ex_rat @ G
% 15.55/8.62            @ ( collect_complex
% 15.55/8.62              @ ^ [X: complex] :
% 15.55/8.62                  ( ( member_complex @ X @ A3 )
% 15.55/8.62                  & ( P @ X ) ) ) )
% 15.55/8.62          = ( groups5058264527183730370ex_rat
% 15.55/8.62            @ ^ [X: complex] : ( if_rat @ ( P @ X ) @ ( G @ X ) @ zero_zero_rat )
% 15.55/8.62            @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7704_sum_Ointer__filter,axiom,
% 15.55/8.62      ! [A3: set_Extended_enat,G: extended_enat > rat,P: extended_enat > $o] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.62       => ( ( groups1392844769737527556at_rat @ G
% 15.55/8.62            @ ( collec4429806609662206161d_enat
% 15.55/8.62              @ ^ [X: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ X @ A3 )
% 15.55/8.62                  & ( P @ X ) ) ) )
% 15.55/8.62          = ( groups1392844769737527556at_rat
% 15.55/8.62            @ ^ [X: extended_enat] : ( if_rat @ ( P @ X ) @ ( G @ X ) @ zero_zero_rat )
% 15.55/8.62            @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7705_sum_Ointer__filter,axiom,
% 15.55/8.62      ! [A3: set_real,G: real > nat,P: real > $o] :
% 15.55/8.62        ( ( finite_finite_real @ A3 )
% 15.55/8.62       => ( ( groups1935376822645274424al_nat @ G
% 15.55/8.62            @ ( collect_real
% 15.55/8.62              @ ^ [X: real] :
% 15.55/8.62                  ( ( member_real @ X @ A3 )
% 15.55/8.62                  & ( P @ X ) ) ) )
% 15.55/8.62          = ( groups1935376822645274424al_nat
% 15.55/8.62            @ ^ [X: real] : ( if_nat @ ( P @ X ) @ ( G @ X ) @ zero_zero_nat )
% 15.55/8.62            @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7706_sum__nonneg__0,axiom,
% 15.55/8.62      ! [S: set_real,F: real > real,I: real] :
% 15.55/8.62        ( ( finite_finite_real @ S )
% 15.55/8.62       => ( ! [I3: real] :
% 15.55/8.62              ( ( member_real @ I3 @ S )
% 15.55/8.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.62         => ( ( ( groups8097168146408367636l_real @ F @ S )
% 15.55/8.62              = zero_zero_real )
% 15.55/8.62           => ( ( member_real @ I @ S )
% 15.55/8.62             => ( ( F @ I )
% 15.55/8.62                = zero_zero_real ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7707_sum__nonneg__0,axiom,
% 15.55/8.62      ! [S: set_int,F: int > real,I: int] :
% 15.55/8.62        ( ( finite_finite_int @ S )
% 15.55/8.62       => ( ! [I3: int] :
% 15.55/8.62              ( ( member_int @ I3 @ S )
% 15.55/8.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.62         => ( ( ( groups8778361861064173332t_real @ F @ S )
% 15.55/8.62              = zero_zero_real )
% 15.55/8.62           => ( ( member_int @ I @ S )
% 15.55/8.62             => ( ( F @ I )
% 15.55/8.62                = zero_zero_real ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7708_sum__nonneg__0,axiom,
% 15.55/8.62      ! [S: set_complex,F: complex > real,I: complex] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ S )
% 15.55/8.62       => ( ! [I3: complex] :
% 15.55/8.62              ( ( member_complex @ I3 @ S )
% 15.55/8.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.62         => ( ( ( groups5808333547571424918x_real @ F @ S )
% 15.55/8.62              = zero_zero_real )
% 15.55/8.62           => ( ( member_complex @ I @ S )
% 15.55/8.62             => ( ( F @ I )
% 15.55/8.62                = zero_zero_real ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7709_sum__nonneg__0,axiom,
% 15.55/8.62      ! [S: set_Extended_enat,F: extended_enat > real,I: extended_enat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ S )
% 15.55/8.62       => ( ! [I3: extended_enat] :
% 15.55/8.62              ( ( member_Extended_enat @ I3 @ S )
% 15.55/8.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.62         => ( ( ( groups4148127829035722712t_real @ F @ S )
% 15.55/8.62              = zero_zero_real )
% 15.55/8.62           => ( ( member_Extended_enat @ I @ S )
% 15.55/8.62             => ( ( F @ I )
% 15.55/8.62                = zero_zero_real ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7710_sum__nonneg__0,axiom,
% 15.55/8.62      ! [S: set_real,F: real > rat,I: real] :
% 15.55/8.62        ( ( finite_finite_real @ S )
% 15.55/8.62       => ( ! [I3: real] :
% 15.55/8.62              ( ( member_real @ I3 @ S )
% 15.55/8.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 15.55/8.62         => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 15.55/8.62              = zero_zero_rat )
% 15.55/8.62           => ( ( member_real @ I @ S )
% 15.55/8.62             => ( ( F @ I )
% 15.55/8.62                = zero_zero_rat ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7711_sum__nonneg__0,axiom,
% 15.55/8.62      ! [S: set_nat,F: nat > rat,I: nat] :
% 15.55/8.62        ( ( finite_finite_nat @ S )
% 15.55/8.62       => ( ! [I3: nat] :
% 15.55/8.62              ( ( member_nat @ I3 @ S )
% 15.55/8.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 15.55/8.62         => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 15.55/8.62              = zero_zero_rat )
% 15.55/8.62           => ( ( member_nat @ I @ S )
% 15.55/8.62             => ( ( F @ I )
% 15.55/8.62                = zero_zero_rat ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7712_sum__nonneg__0,axiom,
% 15.55/8.62      ! [S: set_int,F: int > rat,I: int] :
% 15.55/8.62        ( ( finite_finite_int @ S )
% 15.55/8.62       => ( ! [I3: int] :
% 15.55/8.62              ( ( member_int @ I3 @ S )
% 15.55/8.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 15.55/8.62         => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 15.55/8.62              = zero_zero_rat )
% 15.55/8.62           => ( ( member_int @ I @ S )
% 15.55/8.62             => ( ( F @ I )
% 15.55/8.62                = zero_zero_rat ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7713_sum__nonneg__0,axiom,
% 15.55/8.62      ! [S: set_complex,F: complex > rat,I: complex] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ S )
% 15.55/8.62       => ( ! [I3: complex] :
% 15.55/8.62              ( ( member_complex @ I3 @ S )
% 15.55/8.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 15.55/8.62         => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 15.55/8.62              = zero_zero_rat )
% 15.55/8.62           => ( ( member_complex @ I @ S )
% 15.55/8.62             => ( ( F @ I )
% 15.55/8.62                = zero_zero_rat ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7714_sum__nonneg__0,axiom,
% 15.55/8.62      ! [S: set_Extended_enat,F: extended_enat > rat,I: extended_enat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ S )
% 15.55/8.62       => ( ! [I3: extended_enat] :
% 15.55/8.62              ( ( member_Extended_enat @ I3 @ S )
% 15.55/8.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 15.55/8.62         => ( ( ( groups1392844769737527556at_rat @ F @ S )
% 15.55/8.62              = zero_zero_rat )
% 15.55/8.62           => ( ( member_Extended_enat @ I @ S )
% 15.55/8.62             => ( ( F @ I )
% 15.55/8.62                = zero_zero_rat ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7715_sum__nonneg__0,axiom,
% 15.55/8.62      ! [S: set_real,F: real > nat,I: real] :
% 15.55/8.62        ( ( finite_finite_real @ S )
% 15.55/8.62       => ( ! [I3: real] :
% 15.55/8.62              ( ( member_real @ I3 @ S )
% 15.55/8.62             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 15.55/8.62         => ( ( ( groups1935376822645274424al_nat @ F @ S )
% 15.55/8.62              = zero_zero_nat )
% 15.55/8.62           => ( ( member_real @ I @ S )
% 15.55/8.62             => ( ( F @ I )
% 15.55/8.62                = zero_zero_nat ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7716_sum__nonneg__leq__bound,axiom,
% 15.55/8.62      ! [S: set_real,F: real > real,B5: real,I: real] :
% 15.55/8.62        ( ( finite_finite_real @ S )
% 15.55/8.62       => ( ! [I3: real] :
% 15.55/8.62              ( ( member_real @ I3 @ S )
% 15.55/8.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.62         => ( ( ( groups8097168146408367636l_real @ F @ S )
% 15.55/8.62              = B5 )
% 15.55/8.62           => ( ( member_real @ I @ S )
% 15.55/8.62             => ( ord_less_eq_real @ ( F @ I ) @ B5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7717_sum__nonneg__leq__bound,axiom,
% 15.55/8.62      ! [S: set_int,F: int > real,B5: real,I: int] :
% 15.55/8.62        ( ( finite_finite_int @ S )
% 15.55/8.62       => ( ! [I3: int] :
% 15.55/8.62              ( ( member_int @ I3 @ S )
% 15.55/8.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.62         => ( ( ( groups8778361861064173332t_real @ F @ S )
% 15.55/8.62              = B5 )
% 15.55/8.62           => ( ( member_int @ I @ S )
% 15.55/8.62             => ( ord_less_eq_real @ ( F @ I ) @ B5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7718_sum__nonneg__leq__bound,axiom,
% 15.55/8.62      ! [S: set_complex,F: complex > real,B5: real,I: complex] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ S )
% 15.55/8.62       => ( ! [I3: complex] :
% 15.55/8.62              ( ( member_complex @ I3 @ S )
% 15.55/8.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.62         => ( ( ( groups5808333547571424918x_real @ F @ S )
% 15.55/8.62              = B5 )
% 15.55/8.62           => ( ( member_complex @ I @ S )
% 15.55/8.62             => ( ord_less_eq_real @ ( F @ I ) @ B5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7719_sum__nonneg__leq__bound,axiom,
% 15.55/8.62      ! [S: set_Extended_enat,F: extended_enat > real,B5: real,I: extended_enat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ S )
% 15.55/8.62       => ( ! [I3: extended_enat] :
% 15.55/8.62              ( ( member_Extended_enat @ I3 @ S )
% 15.55/8.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.62         => ( ( ( groups4148127829035722712t_real @ F @ S )
% 15.55/8.62              = B5 )
% 15.55/8.62           => ( ( member_Extended_enat @ I @ S )
% 15.55/8.62             => ( ord_less_eq_real @ ( F @ I ) @ B5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7720_sum__nonneg__leq__bound,axiom,
% 15.55/8.62      ! [S: set_real,F: real > rat,B5: rat,I: real] :
% 15.55/8.62        ( ( finite_finite_real @ S )
% 15.55/8.62       => ( ! [I3: real] :
% 15.55/8.62              ( ( member_real @ I3 @ S )
% 15.55/8.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 15.55/8.62         => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 15.55/8.62              = B5 )
% 15.55/8.62           => ( ( member_real @ I @ S )
% 15.55/8.62             => ( ord_less_eq_rat @ ( F @ I ) @ B5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7721_sum__nonneg__leq__bound,axiom,
% 15.55/8.62      ! [S: set_nat,F: nat > rat,B5: rat,I: nat] :
% 15.55/8.62        ( ( finite_finite_nat @ S )
% 15.55/8.62       => ( ! [I3: nat] :
% 15.55/8.62              ( ( member_nat @ I3 @ S )
% 15.55/8.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 15.55/8.62         => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 15.55/8.62              = B5 )
% 15.55/8.62           => ( ( member_nat @ I @ S )
% 15.55/8.62             => ( ord_less_eq_rat @ ( F @ I ) @ B5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7722_sum__nonneg__leq__bound,axiom,
% 15.55/8.62      ! [S: set_int,F: int > rat,B5: rat,I: int] :
% 15.55/8.62        ( ( finite_finite_int @ S )
% 15.55/8.62       => ( ! [I3: int] :
% 15.55/8.62              ( ( member_int @ I3 @ S )
% 15.55/8.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 15.55/8.62         => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 15.55/8.62              = B5 )
% 15.55/8.62           => ( ( member_int @ I @ S )
% 15.55/8.62             => ( ord_less_eq_rat @ ( F @ I ) @ B5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7723_sum__nonneg__leq__bound,axiom,
% 15.55/8.62      ! [S: set_complex,F: complex > rat,B5: rat,I: complex] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ S )
% 15.55/8.62       => ( ! [I3: complex] :
% 15.55/8.62              ( ( member_complex @ I3 @ S )
% 15.55/8.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 15.55/8.62         => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 15.55/8.62              = B5 )
% 15.55/8.62           => ( ( member_complex @ I @ S )
% 15.55/8.62             => ( ord_less_eq_rat @ ( F @ I ) @ B5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7724_sum__nonneg__leq__bound,axiom,
% 15.55/8.62      ! [S: set_Extended_enat,F: extended_enat > rat,B5: rat,I: extended_enat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ S )
% 15.55/8.62       => ( ! [I3: extended_enat] :
% 15.55/8.62              ( ( member_Extended_enat @ I3 @ S )
% 15.55/8.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 15.55/8.62         => ( ( ( groups1392844769737527556at_rat @ F @ S )
% 15.55/8.62              = B5 )
% 15.55/8.62           => ( ( member_Extended_enat @ I @ S )
% 15.55/8.62             => ( ord_less_eq_rat @ ( F @ I ) @ B5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7725_sum__nonneg__leq__bound,axiom,
% 15.55/8.62      ! [S: set_real,F: real > nat,B5: nat,I: real] :
% 15.55/8.62        ( ( finite_finite_real @ S )
% 15.55/8.62       => ( ! [I3: real] :
% 15.55/8.62              ( ( member_real @ I3 @ S )
% 15.55/8.62             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 15.55/8.62         => ( ( ( groups1935376822645274424al_nat @ F @ S )
% 15.55/8.62              = B5 )
% 15.55/8.62           => ( ( member_real @ I @ S )
% 15.55/8.62             => ( ord_less_eq_nat @ ( F @ I ) @ B5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7726_sum__le__included,axiom,
% 15.55/8.62      ! [S: set_int,T: set_int,G: int > real,I: int > int,F: int > real] :
% 15.55/8.62        ( ( finite_finite_int @ S )
% 15.55/8.62       => ( ( finite_finite_int @ T )
% 15.55/8.62         => ( ! [X4: int] :
% 15.55/8.62                ( ( member_int @ X4 @ T )
% 15.55/8.62               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 15.55/8.62           => ( ! [X4: int] :
% 15.55/8.62                  ( ( member_int @ X4 @ S )
% 15.55/8.62                 => ? [Xa2: int] :
% 15.55/8.62                      ( ( member_int @ Xa2 @ T )
% 15.55/8.62                      & ( ( I @ Xa2 )
% 15.55/8.62                        = X4 )
% 15.55/8.62                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 15.55/8.62             => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7727_sum__le__included,axiom,
% 15.55/8.62      ! [S: set_int,T: set_complex,G: complex > real,I: complex > int,F: int > real] :
% 15.55/8.62        ( ( finite_finite_int @ S )
% 15.55/8.62       => ( ( finite3207457112153483333omplex @ T )
% 15.55/8.62         => ( ! [X4: complex] :
% 15.55/8.62                ( ( member_complex @ X4 @ T )
% 15.55/8.62               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 15.55/8.62           => ( ! [X4: int] :
% 15.55/8.62                  ( ( member_int @ X4 @ S )
% 15.55/8.62                 => ? [Xa2: complex] :
% 15.55/8.62                      ( ( member_complex @ Xa2 @ T )
% 15.55/8.62                      & ( ( I @ Xa2 )
% 15.55/8.62                        = X4 )
% 15.55/8.62                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 15.55/8.62             => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7728_sum__le__included,axiom,
% 15.55/8.62      ! [S: set_int,T: set_Extended_enat,G: extended_enat > real,I: extended_enat > int,F: int > real] :
% 15.55/8.62        ( ( finite_finite_int @ S )
% 15.55/8.62       => ( ( finite4001608067531595151d_enat @ T )
% 15.55/8.62         => ( ! [X4: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ X4 @ T )
% 15.55/8.62               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 15.55/8.62           => ( ! [X4: int] :
% 15.55/8.62                  ( ( member_int @ X4 @ S )
% 15.55/8.62                 => ? [Xa2: extended_enat] :
% 15.55/8.62                      ( ( member_Extended_enat @ Xa2 @ T )
% 15.55/8.62                      & ( ( I @ Xa2 )
% 15.55/8.62                        = X4 )
% 15.55/8.62                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 15.55/8.62             => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups4148127829035722712t_real @ G @ T ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7729_sum__le__included,axiom,
% 15.55/8.62      ! [S: set_complex,T: set_int,G: int > real,I: int > complex,F: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ S )
% 15.55/8.62       => ( ( finite_finite_int @ T )
% 15.55/8.62         => ( ! [X4: int] :
% 15.55/8.62                ( ( member_int @ X4 @ T )
% 15.55/8.62               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 15.55/8.62           => ( ! [X4: complex] :
% 15.55/8.62                  ( ( member_complex @ X4 @ S )
% 15.55/8.62                 => ? [Xa2: int] :
% 15.55/8.62                      ( ( member_int @ Xa2 @ T )
% 15.55/8.62                      & ( ( I @ Xa2 )
% 15.55/8.62                        = X4 )
% 15.55/8.62                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 15.55/8.62             => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7730_sum__le__included,axiom,
% 15.55/8.62      ! [S: set_complex,T: set_complex,G: complex > real,I: complex > complex,F: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ S )
% 15.55/8.62       => ( ( finite3207457112153483333omplex @ T )
% 15.55/8.62         => ( ! [X4: complex] :
% 15.55/8.62                ( ( member_complex @ X4 @ T )
% 15.55/8.62               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 15.55/8.62           => ( ! [X4: complex] :
% 15.55/8.62                  ( ( member_complex @ X4 @ S )
% 15.55/8.62                 => ? [Xa2: complex] :
% 15.55/8.62                      ( ( member_complex @ Xa2 @ T )
% 15.55/8.62                      & ( ( I @ Xa2 )
% 15.55/8.62                        = X4 )
% 15.55/8.62                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 15.55/8.62             => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7731_sum__le__included,axiom,
% 15.55/8.62      ! [S: set_complex,T: set_Extended_enat,G: extended_enat > real,I: extended_enat > complex,F: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ S )
% 15.55/8.62       => ( ( finite4001608067531595151d_enat @ T )
% 15.55/8.62         => ( ! [X4: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ X4 @ T )
% 15.55/8.62               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 15.55/8.62           => ( ! [X4: complex] :
% 15.55/8.62                  ( ( member_complex @ X4 @ S )
% 15.55/8.62                 => ? [Xa2: extended_enat] :
% 15.55/8.62                      ( ( member_Extended_enat @ Xa2 @ T )
% 15.55/8.62                      & ( ( I @ Xa2 )
% 15.55/8.62                        = X4 )
% 15.55/8.62                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 15.55/8.62             => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups4148127829035722712t_real @ G @ T ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7732_sum__le__included,axiom,
% 15.55/8.62      ! [S: set_Extended_enat,T: set_int,G: int > real,I: int > extended_enat,F: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ S )
% 15.55/8.62       => ( ( finite_finite_int @ T )
% 15.55/8.62         => ( ! [X4: int] :
% 15.55/8.62                ( ( member_int @ X4 @ T )
% 15.55/8.62               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 15.55/8.62           => ( ! [X4: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ X4 @ S )
% 15.55/8.62                 => ? [Xa2: int] :
% 15.55/8.62                      ( ( member_int @ Xa2 @ T )
% 15.55/8.62                      & ( ( I @ Xa2 )
% 15.55/8.62                        = X4 )
% 15.55/8.62                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 15.55/8.62             => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7733_sum__le__included,axiom,
% 15.55/8.62      ! [S: set_Extended_enat,T: set_complex,G: complex > real,I: complex > extended_enat,F: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ S )
% 15.55/8.62       => ( ( finite3207457112153483333omplex @ T )
% 15.55/8.62         => ( ! [X4: complex] :
% 15.55/8.62                ( ( member_complex @ X4 @ T )
% 15.55/8.62               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 15.55/8.62           => ( ! [X4: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ X4 @ S )
% 15.55/8.62                 => ? [Xa2: complex] :
% 15.55/8.62                      ( ( member_complex @ Xa2 @ T )
% 15.55/8.62                      & ( ( I @ Xa2 )
% 15.55/8.62                        = X4 )
% 15.55/8.62                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 15.55/8.62             => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7734_sum__le__included,axiom,
% 15.55/8.62      ! [S: set_Extended_enat,T: set_Extended_enat,G: extended_enat > real,I: extended_enat > extended_enat,F: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ S )
% 15.55/8.62       => ( ( finite4001608067531595151d_enat @ T )
% 15.55/8.62         => ( ! [X4: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ X4 @ T )
% 15.55/8.62               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 15.55/8.62           => ( ! [X4: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ X4 @ S )
% 15.55/8.62                 => ? [Xa2: extended_enat] :
% 15.55/8.62                      ( ( member_Extended_enat @ Xa2 @ T )
% 15.55/8.62                      & ( ( I @ Xa2 )
% 15.55/8.62                        = X4 )
% 15.55/8.62                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 15.55/8.62             => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ S ) @ ( groups4148127829035722712t_real @ G @ T ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7735_sum__le__included,axiom,
% 15.55/8.62      ! [S: set_nat,T: set_nat,G: nat > rat,I: nat > nat,F: nat > rat] :
% 15.55/8.62        ( ( finite_finite_nat @ S )
% 15.55/8.62       => ( ( finite_finite_nat @ T )
% 15.55/8.62         => ( ! [X4: nat] :
% 15.55/8.62                ( ( member_nat @ X4 @ T )
% 15.55/8.62               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 15.55/8.62           => ( ! [X4: nat] :
% 15.55/8.62                  ( ( member_nat @ X4 @ S )
% 15.55/8.62                 => ? [Xa2: nat] :
% 15.55/8.62                      ( ( member_nat @ Xa2 @ T )
% 15.55/8.62                      & ( ( I @ Xa2 )
% 15.55/8.62                        = X4 )
% 15.55/8.62                      & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 15.55/8.62             => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7736_sum__nonneg__eq__0__iff,axiom,
% 15.55/8.62      ! [A3: set_real,F: real > real] :
% 15.55/8.62        ( ( finite_finite_real @ A3 )
% 15.55/8.62       => ( ! [X4: real] :
% 15.55/8.62              ( ( member_real @ X4 @ A3 )
% 15.55/8.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 15.55/8.62         => ( ( ( groups8097168146408367636l_real @ F @ A3 )
% 15.55/8.62              = zero_zero_real )
% 15.55/8.62            = ( ! [X: real] :
% 15.55/8.62                  ( ( member_real @ X @ A3 )
% 15.55/8.62                 => ( ( F @ X )
% 15.55/8.62                    = zero_zero_real ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7737_sum__nonneg__eq__0__iff,axiom,
% 15.55/8.62      ! [A3: set_int,F: int > real] :
% 15.55/8.62        ( ( finite_finite_int @ A3 )
% 15.55/8.62       => ( ! [X4: int] :
% 15.55/8.62              ( ( member_int @ X4 @ A3 )
% 15.55/8.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 15.55/8.62         => ( ( ( groups8778361861064173332t_real @ F @ A3 )
% 15.55/8.62              = zero_zero_real )
% 15.55/8.62            = ( ! [X: int] :
% 15.55/8.62                  ( ( member_int @ X @ A3 )
% 15.55/8.62                 => ( ( F @ X )
% 15.55/8.62                    = zero_zero_real ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7738_sum__nonneg__eq__0__iff,axiom,
% 15.55/8.62      ! [A3: set_complex,F: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.62       => ( ! [X4: complex] :
% 15.55/8.62              ( ( member_complex @ X4 @ A3 )
% 15.55/8.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 15.55/8.62         => ( ( ( groups5808333547571424918x_real @ F @ A3 )
% 15.55/8.62              = zero_zero_real )
% 15.55/8.62            = ( ! [X: complex] :
% 15.55/8.62                  ( ( member_complex @ X @ A3 )
% 15.55/8.62                 => ( ( F @ X )
% 15.55/8.62                    = zero_zero_real ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7739_sum__nonneg__eq__0__iff,axiom,
% 15.55/8.62      ! [A3: set_Extended_enat,F: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.62       => ( ! [X4: extended_enat] :
% 15.55/8.62              ( ( member_Extended_enat @ X4 @ A3 )
% 15.55/8.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 15.55/8.62         => ( ( ( groups4148127829035722712t_real @ F @ A3 )
% 15.55/8.62              = zero_zero_real )
% 15.55/8.62            = ( ! [X: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ X @ A3 )
% 15.55/8.62                 => ( ( F @ X )
% 15.55/8.62                    = zero_zero_real ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7740_sum__nonneg__eq__0__iff,axiom,
% 15.55/8.62      ! [A3: set_real,F: real > rat] :
% 15.55/8.62        ( ( finite_finite_real @ A3 )
% 15.55/8.62       => ( ! [X4: real] :
% 15.55/8.62              ( ( member_real @ X4 @ A3 )
% 15.55/8.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 15.55/8.62         => ( ( ( groups1300246762558778688al_rat @ F @ A3 )
% 15.55/8.62              = zero_zero_rat )
% 15.55/8.62            = ( ! [X: real] :
% 15.55/8.62                  ( ( member_real @ X @ A3 )
% 15.55/8.62                 => ( ( F @ X )
% 15.55/8.62                    = zero_zero_rat ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7741_sum__nonneg__eq__0__iff,axiom,
% 15.55/8.62      ! [A3: set_nat,F: nat > rat] :
% 15.55/8.62        ( ( finite_finite_nat @ A3 )
% 15.55/8.62       => ( ! [X4: nat] :
% 15.55/8.62              ( ( member_nat @ X4 @ A3 )
% 15.55/8.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 15.55/8.62         => ( ( ( groups2906978787729119204at_rat @ F @ A3 )
% 15.55/8.62              = zero_zero_rat )
% 15.55/8.62            = ( ! [X: nat] :
% 15.55/8.62                  ( ( member_nat @ X @ A3 )
% 15.55/8.62                 => ( ( F @ X )
% 15.55/8.62                    = zero_zero_rat ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7742_sum__nonneg__eq__0__iff,axiom,
% 15.55/8.62      ! [A3: set_int,F: int > rat] :
% 15.55/8.62        ( ( finite_finite_int @ A3 )
% 15.55/8.62       => ( ! [X4: int] :
% 15.55/8.62              ( ( member_int @ X4 @ A3 )
% 15.55/8.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 15.55/8.62         => ( ( ( groups3906332499630173760nt_rat @ F @ A3 )
% 15.55/8.62              = zero_zero_rat )
% 15.55/8.62            = ( ! [X: int] :
% 15.55/8.62                  ( ( member_int @ X @ A3 )
% 15.55/8.62                 => ( ( F @ X )
% 15.55/8.62                    = zero_zero_rat ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7743_sum__nonneg__eq__0__iff,axiom,
% 15.55/8.62      ! [A3: set_complex,F: complex > rat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.62       => ( ! [X4: complex] :
% 15.55/8.62              ( ( member_complex @ X4 @ A3 )
% 15.55/8.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 15.55/8.62         => ( ( ( groups5058264527183730370ex_rat @ F @ A3 )
% 15.55/8.62              = zero_zero_rat )
% 15.55/8.62            = ( ! [X: complex] :
% 15.55/8.62                  ( ( member_complex @ X @ A3 )
% 15.55/8.62                 => ( ( F @ X )
% 15.55/8.62                    = zero_zero_rat ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7744_sum__nonneg__eq__0__iff,axiom,
% 15.55/8.62      ! [A3: set_Extended_enat,F: extended_enat > rat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.62       => ( ! [X4: extended_enat] :
% 15.55/8.62              ( ( member_Extended_enat @ X4 @ A3 )
% 15.55/8.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 15.55/8.62         => ( ( ( groups1392844769737527556at_rat @ F @ A3 )
% 15.55/8.62              = zero_zero_rat )
% 15.55/8.62            = ( ! [X: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ X @ A3 )
% 15.55/8.62                 => ( ( F @ X )
% 15.55/8.62                    = zero_zero_rat ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7745_sum__nonneg__eq__0__iff,axiom,
% 15.55/8.62      ! [A3: set_real,F: real > nat] :
% 15.55/8.62        ( ( finite_finite_real @ A3 )
% 15.55/8.62       => ( ! [X4: real] :
% 15.55/8.62              ( ( member_real @ X4 @ A3 )
% 15.55/8.62             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 15.55/8.62         => ( ( ( groups1935376822645274424al_nat @ F @ A3 )
% 15.55/8.62              = zero_zero_nat )
% 15.55/8.62            = ( ! [X: real] :
% 15.55/8.62                  ( ( member_real @ X @ A3 )
% 15.55/8.62                 => ( ( F @ X )
% 15.55/8.62                    = zero_zero_nat ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7746_sum__mono__inv,axiom,
% 15.55/8.62      ! [F: real > rat,I5: set_real,G: real > rat,I: real] :
% 15.55/8.62        ( ( ( groups1300246762558778688al_rat @ F @ I5 )
% 15.55/8.62          = ( groups1300246762558778688al_rat @ G @ I5 ) )
% 15.55/8.62       => ( ! [I3: real] :
% 15.55/8.62              ( ( member_real @ I3 @ I5 )
% 15.55/8.62             => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 15.55/8.62         => ( ( member_real @ I @ I5 )
% 15.55/8.62           => ( ( finite_finite_real @ I5 )
% 15.55/8.62             => ( ( F @ I )
% 15.55/8.62                = ( G @ I ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7747_sum__mono__inv,axiom,
% 15.55/8.62      ! [F: nat > rat,I5: set_nat,G: nat > rat,I: nat] :
% 15.55/8.62        ( ( ( groups2906978787729119204at_rat @ F @ I5 )
% 15.55/8.62          = ( groups2906978787729119204at_rat @ G @ I5 ) )
% 15.55/8.62       => ( ! [I3: nat] :
% 15.55/8.62              ( ( member_nat @ I3 @ I5 )
% 15.55/8.62             => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 15.55/8.62         => ( ( member_nat @ I @ I5 )
% 15.55/8.62           => ( ( finite_finite_nat @ I5 )
% 15.55/8.62             => ( ( F @ I )
% 15.55/8.62                = ( G @ I ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7748_sum__mono__inv,axiom,
% 15.55/8.62      ! [F: int > rat,I5: set_int,G: int > rat,I: int] :
% 15.55/8.62        ( ( ( groups3906332499630173760nt_rat @ F @ I5 )
% 15.55/8.62          = ( groups3906332499630173760nt_rat @ G @ I5 ) )
% 15.55/8.62       => ( ! [I3: int] :
% 15.55/8.62              ( ( member_int @ I3 @ I5 )
% 15.55/8.62             => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 15.55/8.62         => ( ( member_int @ I @ I5 )
% 15.55/8.62           => ( ( finite_finite_int @ I5 )
% 15.55/8.62             => ( ( F @ I )
% 15.55/8.62                = ( G @ I ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7749_sum__mono__inv,axiom,
% 15.55/8.62      ! [F: complex > rat,I5: set_complex,G: complex > rat,I: complex] :
% 15.55/8.62        ( ( ( groups5058264527183730370ex_rat @ F @ I5 )
% 15.55/8.62          = ( groups5058264527183730370ex_rat @ G @ I5 ) )
% 15.55/8.62       => ( ! [I3: complex] :
% 15.55/8.62              ( ( member_complex @ I3 @ I5 )
% 15.55/8.62             => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 15.55/8.62         => ( ( member_complex @ I @ I5 )
% 15.55/8.62           => ( ( finite3207457112153483333omplex @ I5 )
% 15.55/8.62             => ( ( F @ I )
% 15.55/8.62                = ( G @ I ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7750_sum__mono__inv,axiom,
% 15.55/8.62      ! [F: extended_enat > rat,I5: set_Extended_enat,G: extended_enat > rat,I: extended_enat] :
% 15.55/8.62        ( ( ( groups1392844769737527556at_rat @ F @ I5 )
% 15.55/8.62          = ( groups1392844769737527556at_rat @ G @ I5 ) )
% 15.55/8.62       => ( ! [I3: extended_enat] :
% 15.55/8.62              ( ( member_Extended_enat @ I3 @ I5 )
% 15.55/8.62             => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 15.55/8.62         => ( ( member_Extended_enat @ I @ I5 )
% 15.55/8.62           => ( ( finite4001608067531595151d_enat @ I5 )
% 15.55/8.62             => ( ( F @ I )
% 15.55/8.62                = ( G @ I ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7751_sum__mono__inv,axiom,
% 15.55/8.62      ! [F: real > nat,I5: set_real,G: real > nat,I: real] :
% 15.55/8.62        ( ( ( groups1935376822645274424al_nat @ F @ I5 )
% 15.55/8.62          = ( groups1935376822645274424al_nat @ G @ I5 ) )
% 15.55/8.62       => ( ! [I3: real] :
% 15.55/8.62              ( ( member_real @ I3 @ I5 )
% 15.55/8.62             => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 15.55/8.62         => ( ( member_real @ I @ I5 )
% 15.55/8.62           => ( ( finite_finite_real @ I5 )
% 15.55/8.62             => ( ( F @ I )
% 15.55/8.62                = ( G @ I ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7752_sum__mono__inv,axiom,
% 15.55/8.62      ! [F: int > nat,I5: set_int,G: int > nat,I: int] :
% 15.55/8.62        ( ( ( groups4541462559716669496nt_nat @ F @ I5 )
% 15.55/8.62          = ( groups4541462559716669496nt_nat @ G @ I5 ) )
% 15.55/8.62       => ( ! [I3: int] :
% 15.55/8.62              ( ( member_int @ I3 @ I5 )
% 15.55/8.62             => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 15.55/8.62         => ( ( member_int @ I @ I5 )
% 15.55/8.62           => ( ( finite_finite_int @ I5 )
% 15.55/8.62             => ( ( F @ I )
% 15.55/8.62                = ( G @ I ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7753_sum__mono__inv,axiom,
% 15.55/8.62      ! [F: complex > nat,I5: set_complex,G: complex > nat,I: complex] :
% 15.55/8.62        ( ( ( groups5693394587270226106ex_nat @ F @ I5 )
% 15.55/8.62          = ( groups5693394587270226106ex_nat @ G @ I5 ) )
% 15.55/8.62       => ( ! [I3: complex] :
% 15.55/8.62              ( ( member_complex @ I3 @ I5 )
% 15.55/8.62             => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 15.55/8.62         => ( ( member_complex @ I @ I5 )
% 15.55/8.62           => ( ( finite3207457112153483333omplex @ I5 )
% 15.55/8.62             => ( ( F @ I )
% 15.55/8.62                = ( G @ I ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7754_sum__mono__inv,axiom,
% 15.55/8.62      ! [F: extended_enat > nat,I5: set_Extended_enat,G: extended_enat > nat,I: extended_enat] :
% 15.55/8.62        ( ( ( groups2027974829824023292at_nat @ F @ I5 )
% 15.55/8.62          = ( groups2027974829824023292at_nat @ G @ I5 ) )
% 15.55/8.62       => ( ! [I3: extended_enat] :
% 15.55/8.62              ( ( member_Extended_enat @ I3 @ I5 )
% 15.55/8.62             => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 15.55/8.62         => ( ( member_Extended_enat @ I @ I5 )
% 15.55/8.62           => ( ( finite4001608067531595151d_enat @ I5 )
% 15.55/8.62             => ( ( F @ I )
% 15.55/8.62                = ( G @ I ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7755_sum__mono__inv,axiom,
% 15.55/8.62      ! [F: real > int,I5: set_real,G: real > int,I: real] :
% 15.55/8.62        ( ( ( groups1932886352136224148al_int @ F @ I5 )
% 15.55/8.62          = ( groups1932886352136224148al_int @ G @ I5 ) )
% 15.55/8.62       => ( ! [I3: real] :
% 15.55/8.62              ( ( member_real @ I3 @ I5 )
% 15.55/8.62             => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 15.55/8.62         => ( ( member_real @ I @ I5 )
% 15.55/8.62           => ( ( finite_finite_real @ I5 )
% 15.55/8.62             => ( ( F @ I )
% 15.55/8.62                = ( G @ I ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7756_sum_Orelated,axiom,
% 15.55/8.62      ! [R3: real > real > $o,S2: set_int,H2: int > real,G: int > real] :
% 15.55/8.62        ( ( R3 @ zero_zero_real @ zero_zero_real )
% 15.55/8.62       => ( ! [X1: real,Y1: real,X22: real,Y22: real] :
% 15.55/8.62              ( ( ( R3 @ X1 @ X22 )
% 15.55/8.62                & ( R3 @ Y1 @ Y22 ) )
% 15.55/8.62             => ( R3 @ ( plus_plus_real @ X1 @ Y1 ) @ ( plus_plus_real @ X22 @ Y22 ) ) )
% 15.55/8.62         => ( ( finite_finite_int @ S2 )
% 15.55/8.62           => ( ! [X4: int] :
% 15.55/8.62                  ( ( member_int @ X4 @ S2 )
% 15.55/8.62                 => ( R3 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62             => ( R3 @ ( groups8778361861064173332t_real @ H2 @ S2 ) @ ( groups8778361861064173332t_real @ G @ S2 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7757_sum_Orelated,axiom,
% 15.55/8.62      ! [R3: real > real > $o,S2: set_complex,H2: complex > real,G: complex > real] :
% 15.55/8.62        ( ( R3 @ zero_zero_real @ zero_zero_real )
% 15.55/8.62       => ( ! [X1: real,Y1: real,X22: real,Y22: real] :
% 15.55/8.62              ( ( ( R3 @ X1 @ X22 )
% 15.55/8.62                & ( R3 @ Y1 @ Y22 ) )
% 15.55/8.62             => ( R3 @ ( plus_plus_real @ X1 @ Y1 ) @ ( plus_plus_real @ X22 @ Y22 ) ) )
% 15.55/8.62         => ( ( finite3207457112153483333omplex @ S2 )
% 15.55/8.62           => ( ! [X4: complex] :
% 15.55/8.62                  ( ( member_complex @ X4 @ S2 )
% 15.55/8.62                 => ( R3 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62             => ( R3 @ ( groups5808333547571424918x_real @ H2 @ S2 ) @ ( groups5808333547571424918x_real @ G @ S2 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7758_sum_Orelated,axiom,
% 15.55/8.62      ! [R3: real > real > $o,S2: set_Extended_enat,H2: extended_enat > real,G: extended_enat > real] :
% 15.55/8.62        ( ( R3 @ zero_zero_real @ zero_zero_real )
% 15.55/8.62       => ( ! [X1: real,Y1: real,X22: real,Y22: real] :
% 15.55/8.62              ( ( ( R3 @ X1 @ X22 )
% 15.55/8.62                & ( R3 @ Y1 @ Y22 ) )
% 15.55/8.62             => ( R3 @ ( plus_plus_real @ X1 @ Y1 ) @ ( plus_plus_real @ X22 @ Y22 ) ) )
% 15.55/8.62         => ( ( finite4001608067531595151d_enat @ S2 )
% 15.55/8.62           => ( ! [X4: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ X4 @ S2 )
% 15.55/8.62                 => ( R3 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62             => ( R3 @ ( groups4148127829035722712t_real @ H2 @ S2 ) @ ( groups4148127829035722712t_real @ G @ S2 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7759_sum_Orelated,axiom,
% 15.55/8.62      ! [R3: rat > rat > $o,S2: set_nat,H2: nat > rat,G: nat > rat] :
% 15.55/8.62        ( ( R3 @ zero_zero_rat @ zero_zero_rat )
% 15.55/8.62       => ( ! [X1: rat,Y1: rat,X22: rat,Y22: rat] :
% 15.55/8.62              ( ( ( R3 @ X1 @ X22 )
% 15.55/8.62                & ( R3 @ Y1 @ Y22 ) )
% 15.55/8.62             => ( R3 @ ( plus_plus_rat @ X1 @ Y1 ) @ ( plus_plus_rat @ X22 @ Y22 ) ) )
% 15.55/8.62         => ( ( finite_finite_nat @ S2 )
% 15.55/8.62           => ( ! [X4: nat] :
% 15.55/8.62                  ( ( member_nat @ X4 @ S2 )
% 15.55/8.62                 => ( R3 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62             => ( R3 @ ( groups2906978787729119204at_rat @ H2 @ S2 ) @ ( groups2906978787729119204at_rat @ G @ S2 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7760_sum_Orelated,axiom,
% 15.55/8.62      ! [R3: rat > rat > $o,S2: set_int,H2: int > rat,G: int > rat] :
% 15.55/8.62        ( ( R3 @ zero_zero_rat @ zero_zero_rat )
% 15.55/8.62       => ( ! [X1: rat,Y1: rat,X22: rat,Y22: rat] :
% 15.55/8.62              ( ( ( R3 @ X1 @ X22 )
% 15.55/8.62                & ( R3 @ Y1 @ Y22 ) )
% 15.55/8.62             => ( R3 @ ( plus_plus_rat @ X1 @ Y1 ) @ ( plus_plus_rat @ X22 @ Y22 ) ) )
% 15.55/8.62         => ( ( finite_finite_int @ S2 )
% 15.55/8.62           => ( ! [X4: int] :
% 15.55/8.62                  ( ( member_int @ X4 @ S2 )
% 15.55/8.62                 => ( R3 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62             => ( R3 @ ( groups3906332499630173760nt_rat @ H2 @ S2 ) @ ( groups3906332499630173760nt_rat @ G @ S2 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7761_sum_Orelated,axiom,
% 15.55/8.62      ! [R3: rat > rat > $o,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 15.55/8.62        ( ( R3 @ zero_zero_rat @ zero_zero_rat )
% 15.55/8.62       => ( ! [X1: rat,Y1: rat,X22: rat,Y22: rat] :
% 15.55/8.62              ( ( ( R3 @ X1 @ X22 )
% 15.55/8.62                & ( R3 @ Y1 @ Y22 ) )
% 15.55/8.62             => ( R3 @ ( plus_plus_rat @ X1 @ Y1 ) @ ( plus_plus_rat @ X22 @ Y22 ) ) )
% 15.55/8.62         => ( ( finite3207457112153483333omplex @ S2 )
% 15.55/8.62           => ( ! [X4: complex] :
% 15.55/8.62                  ( ( member_complex @ X4 @ S2 )
% 15.55/8.62                 => ( R3 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62             => ( R3 @ ( groups5058264527183730370ex_rat @ H2 @ S2 ) @ ( groups5058264527183730370ex_rat @ G @ S2 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7762_sum_Orelated,axiom,
% 15.55/8.62      ! [R3: rat > rat > $o,S2: set_Extended_enat,H2: extended_enat > rat,G: extended_enat > rat] :
% 15.55/8.62        ( ( R3 @ zero_zero_rat @ zero_zero_rat )
% 15.55/8.62       => ( ! [X1: rat,Y1: rat,X22: rat,Y22: rat] :
% 15.55/8.62              ( ( ( R3 @ X1 @ X22 )
% 15.55/8.62                & ( R3 @ Y1 @ Y22 ) )
% 15.55/8.62             => ( R3 @ ( plus_plus_rat @ X1 @ Y1 ) @ ( plus_plus_rat @ X22 @ Y22 ) ) )
% 15.55/8.62         => ( ( finite4001608067531595151d_enat @ S2 )
% 15.55/8.62           => ( ! [X4: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ X4 @ S2 )
% 15.55/8.62                 => ( R3 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62             => ( R3 @ ( groups1392844769737527556at_rat @ H2 @ S2 ) @ ( groups1392844769737527556at_rat @ G @ S2 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7763_sum_Orelated,axiom,
% 15.55/8.62      ! [R3: nat > nat > $o,S2: set_int,H2: int > nat,G: int > nat] :
% 15.55/8.62        ( ( R3 @ zero_zero_nat @ zero_zero_nat )
% 15.55/8.62       => ( ! [X1: nat,Y1: nat,X22: nat,Y22: nat] :
% 15.55/8.62              ( ( ( R3 @ X1 @ X22 )
% 15.55/8.62                & ( R3 @ Y1 @ Y22 ) )
% 15.55/8.62             => ( R3 @ ( plus_plus_nat @ X1 @ Y1 ) @ ( plus_plus_nat @ X22 @ Y22 ) ) )
% 15.55/8.62         => ( ( finite_finite_int @ S2 )
% 15.55/8.62           => ( ! [X4: int] :
% 15.55/8.62                  ( ( member_int @ X4 @ S2 )
% 15.55/8.62                 => ( R3 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62             => ( R3 @ ( groups4541462559716669496nt_nat @ H2 @ S2 ) @ ( groups4541462559716669496nt_nat @ G @ S2 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7764_sum_Orelated,axiom,
% 15.55/8.62      ! [R3: nat > nat > $o,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 15.55/8.62        ( ( R3 @ zero_zero_nat @ zero_zero_nat )
% 15.55/8.62       => ( ! [X1: nat,Y1: nat,X22: nat,Y22: nat] :
% 15.55/8.62              ( ( ( R3 @ X1 @ X22 )
% 15.55/8.62                & ( R3 @ Y1 @ Y22 ) )
% 15.55/8.62             => ( R3 @ ( plus_plus_nat @ X1 @ Y1 ) @ ( plus_plus_nat @ X22 @ Y22 ) ) )
% 15.55/8.62         => ( ( finite3207457112153483333omplex @ S2 )
% 15.55/8.62           => ( ! [X4: complex] :
% 15.55/8.62                  ( ( member_complex @ X4 @ S2 )
% 15.55/8.62                 => ( R3 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62             => ( R3 @ ( groups5693394587270226106ex_nat @ H2 @ S2 ) @ ( groups5693394587270226106ex_nat @ G @ S2 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7765_sum_Orelated,axiom,
% 15.55/8.62      ! [R3: nat > nat > $o,S2: set_Extended_enat,H2: extended_enat > nat,G: extended_enat > nat] :
% 15.55/8.62        ( ( R3 @ zero_zero_nat @ zero_zero_nat )
% 15.55/8.62       => ( ! [X1: nat,Y1: nat,X22: nat,Y22: nat] :
% 15.55/8.62              ( ( ( R3 @ X1 @ X22 )
% 15.55/8.62                & ( R3 @ Y1 @ Y22 ) )
% 15.55/8.62             => ( R3 @ ( plus_plus_nat @ X1 @ Y1 ) @ ( plus_plus_nat @ X22 @ Y22 ) ) )
% 15.55/8.62         => ( ( finite4001608067531595151d_enat @ S2 )
% 15.55/8.62           => ( ! [X4: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ X4 @ S2 )
% 15.55/8.62                 => ( R3 @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62             => ( R3 @ ( groups2027974829824023292at_nat @ H2 @ S2 ) @ ( groups2027974829824023292at_nat @ G @ S2 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7766_sum_Onot__neutral__contains__not__neutral,axiom,
% 15.55/8.62      ! [G: real > real,A3: set_real] :
% 15.55/8.62        ( ( ( groups8097168146408367636l_real @ G @ A3 )
% 15.55/8.62         != zero_zero_real )
% 15.55/8.62       => ~ ! [A5: real] :
% 15.55/8.62              ( ( member_real @ A5 @ A3 )
% 15.55/8.62             => ( ( G @ A5 )
% 15.55/8.62                = zero_zero_real ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7767_sum_Onot__neutral__contains__not__neutral,axiom,
% 15.55/8.62      ! [G: int > real,A3: set_int] :
% 15.55/8.62        ( ( ( groups8778361861064173332t_real @ G @ A3 )
% 15.55/8.62         != zero_zero_real )
% 15.55/8.62       => ~ ! [A5: int] :
% 15.55/8.62              ( ( member_int @ A5 @ A3 )
% 15.55/8.62             => ( ( G @ A5 )
% 15.55/8.62                = zero_zero_real ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7768_sum_Onot__neutral__contains__not__neutral,axiom,
% 15.55/8.62      ! [G: real > rat,A3: set_real] :
% 15.55/8.62        ( ( ( groups1300246762558778688al_rat @ G @ A3 )
% 15.55/8.62         != zero_zero_rat )
% 15.55/8.62       => ~ ! [A5: real] :
% 15.55/8.62              ( ( member_real @ A5 @ A3 )
% 15.55/8.62             => ( ( G @ A5 )
% 15.55/8.62                = zero_zero_rat ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7769_sum_Onot__neutral__contains__not__neutral,axiom,
% 15.55/8.62      ! [G: nat > rat,A3: set_nat] :
% 15.55/8.62        ( ( ( groups2906978787729119204at_rat @ G @ A3 )
% 15.55/8.62         != zero_zero_rat )
% 15.55/8.62       => ~ ! [A5: nat] :
% 15.55/8.62              ( ( member_nat @ A5 @ A3 )
% 15.55/8.62             => ( ( G @ A5 )
% 15.55/8.62                = zero_zero_rat ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7770_sum_Onot__neutral__contains__not__neutral,axiom,
% 15.55/8.62      ! [G: int > rat,A3: set_int] :
% 15.55/8.62        ( ( ( groups3906332499630173760nt_rat @ G @ A3 )
% 15.55/8.62         != zero_zero_rat )
% 15.55/8.62       => ~ ! [A5: int] :
% 15.55/8.62              ( ( member_int @ A5 @ A3 )
% 15.55/8.62             => ( ( G @ A5 )
% 15.55/8.62                = zero_zero_rat ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7771_sum_Onot__neutral__contains__not__neutral,axiom,
% 15.55/8.62      ! [G: real > nat,A3: set_real] :
% 15.55/8.62        ( ( ( groups1935376822645274424al_nat @ G @ A3 )
% 15.55/8.62         != zero_zero_nat )
% 15.55/8.62       => ~ ! [A5: real] :
% 15.55/8.62              ( ( member_real @ A5 @ A3 )
% 15.55/8.62             => ( ( G @ A5 )
% 15.55/8.62                = zero_zero_nat ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7772_sum_Onot__neutral__contains__not__neutral,axiom,
% 15.55/8.62      ! [G: int > nat,A3: set_int] :
% 15.55/8.62        ( ( ( groups4541462559716669496nt_nat @ G @ A3 )
% 15.55/8.62         != zero_zero_nat )
% 15.55/8.62       => ~ ! [A5: int] :
% 15.55/8.62              ( ( member_int @ A5 @ A3 )
% 15.55/8.62             => ( ( G @ A5 )
% 15.55/8.62                = zero_zero_nat ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7773_sum_Onot__neutral__contains__not__neutral,axiom,
% 15.55/8.62      ! [G: real > int,A3: set_real] :
% 15.55/8.62        ( ( ( groups1932886352136224148al_int @ G @ A3 )
% 15.55/8.62         != zero_zero_int )
% 15.55/8.62       => ~ ! [A5: real] :
% 15.55/8.62              ( ( member_real @ A5 @ A3 )
% 15.55/8.62             => ( ( G @ A5 )
% 15.55/8.62                = zero_zero_int ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7774_sum_Onot__neutral__contains__not__neutral,axiom,
% 15.55/8.62      ! [G: nat > int,A3: set_nat] :
% 15.55/8.62        ( ( ( groups3539618377306564664at_int @ G @ A3 )
% 15.55/8.62         != zero_zero_int )
% 15.55/8.62       => ~ ! [A5: nat] :
% 15.55/8.62              ( ( member_nat @ A5 @ A3 )
% 15.55/8.62             => ( ( G @ A5 )
% 15.55/8.62                = zero_zero_int ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7775_sum_Onot__neutral__contains__not__neutral,axiom,
% 15.55/8.62      ! [G: nat > nat,A3: set_nat] :
% 15.55/8.62        ( ( ( groups3542108847815614940at_nat @ G @ A3 )
% 15.55/8.62         != zero_zero_nat )
% 15.55/8.62       => ~ ! [A5: nat] :
% 15.55/8.62              ( ( member_nat @ A5 @ A3 )
% 15.55/8.62             => ( ( G @ A5 )
% 15.55/8.62                = zero_zero_nat ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7776_sum_Oneutral,axiom,
% 15.55/8.62      ! [A3: set_nat,G: nat > nat] :
% 15.55/8.62        ( ! [X4: nat] :
% 15.55/8.62            ( ( member_nat @ X4 @ A3 )
% 15.55/8.62           => ( ( G @ X4 )
% 15.55/8.62              = zero_zero_nat ) )
% 15.55/8.62       => ( ( groups3542108847815614940at_nat @ G @ A3 )
% 15.55/8.62          = zero_zero_nat ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7777_sum_Oneutral,axiom,
% 15.55/8.62      ! [A3: set_complex,G: complex > complex] :
% 15.55/8.62        ( ! [X4: complex] :
% 15.55/8.62            ( ( member_complex @ X4 @ A3 )
% 15.55/8.62           => ( ( G @ X4 )
% 15.55/8.62              = zero_zero_complex ) )
% 15.55/8.62       => ( ( groups7754918857620584856omplex @ G @ A3 )
% 15.55/8.62          = zero_zero_complex ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7778_sum_Oneutral,axiom,
% 15.55/8.62      ! [A3: set_nat,G: nat > real] :
% 15.55/8.62        ( ! [X4: nat] :
% 15.55/8.62            ( ( member_nat @ X4 @ A3 )
% 15.55/8.62           => ( ( G @ X4 )
% 15.55/8.62              = zero_zero_real ) )
% 15.55/8.62       => ( ( groups6591440286371151544t_real @ G @ A3 )
% 15.55/8.62          = zero_zero_real ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7779_sum_Oneutral,axiom,
% 15.55/8.62      ! [A3: set_int,G: int > int] :
% 15.55/8.62        ( ! [X4: int] :
% 15.55/8.62            ( ( member_int @ X4 @ A3 )
% 15.55/8.62           => ( ( G @ X4 )
% 15.55/8.62              = zero_zero_int ) )
% 15.55/8.62       => ( ( groups4538972089207619220nt_int @ G @ A3 )
% 15.55/8.62          = zero_zero_int ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7780_sum__strict__mono__ex1,axiom,
% 15.55/8.62      ! [A3: set_int,F: int > real,G: int > real] :
% 15.55/8.62        ( ( finite_finite_int @ A3 )
% 15.55/8.62       => ( ! [X4: int] :
% 15.55/8.62              ( ( member_int @ X4 @ A3 )
% 15.55/8.62             => ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62         => ( ? [X6: int] :
% 15.55/8.62                ( ( member_int @ X6 @ A3 )
% 15.55/8.62                & ( ord_less_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 15.55/8.62           => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A3 ) @ ( groups8778361861064173332t_real @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7781_sum__strict__mono__ex1,axiom,
% 15.55/8.62      ! [A3: set_complex,F: complex > real,G: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.62       => ( ! [X4: complex] :
% 15.55/8.62              ( ( member_complex @ X4 @ A3 )
% 15.55/8.62             => ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62         => ( ? [X6: complex] :
% 15.55/8.62                ( ( member_complex @ X6 @ A3 )
% 15.55/8.62                & ( ord_less_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 15.55/8.62           => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A3 ) @ ( groups5808333547571424918x_real @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7782_sum__strict__mono__ex1,axiom,
% 15.55/8.62      ! [A3: set_Extended_enat,F: extended_enat > real,G: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.62       => ( ! [X4: extended_enat] :
% 15.55/8.62              ( ( member_Extended_enat @ X4 @ A3 )
% 15.55/8.62             => ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62         => ( ? [X6: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ X6 @ A3 )
% 15.55/8.62                & ( ord_less_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 15.55/8.62           => ( ord_less_real @ ( groups4148127829035722712t_real @ F @ A3 ) @ ( groups4148127829035722712t_real @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7783_sum__strict__mono__ex1,axiom,
% 15.55/8.62      ! [A3: set_nat,F: nat > rat,G: nat > rat] :
% 15.55/8.62        ( ( finite_finite_nat @ A3 )
% 15.55/8.62       => ( ! [X4: nat] :
% 15.55/8.62              ( ( member_nat @ X4 @ A3 )
% 15.55/8.62             => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62         => ( ? [X6: nat] :
% 15.55/8.62                ( ( member_nat @ X6 @ A3 )
% 15.55/8.62                & ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 15.55/8.62           => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ ( groups2906978787729119204at_rat @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7784_sum__strict__mono__ex1,axiom,
% 15.55/8.62      ! [A3: set_int,F: int > rat,G: int > rat] :
% 15.55/8.62        ( ( finite_finite_int @ A3 )
% 15.55/8.62       => ( ! [X4: int] :
% 15.55/8.62              ( ( member_int @ X4 @ A3 )
% 15.55/8.62             => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62         => ( ? [X6: int] :
% 15.55/8.62                ( ( member_int @ X6 @ A3 )
% 15.55/8.62                & ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 15.55/8.62           => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ ( groups3906332499630173760nt_rat @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7785_sum__strict__mono__ex1,axiom,
% 15.55/8.62      ! [A3: set_complex,F: complex > rat,G: complex > rat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.62       => ( ! [X4: complex] :
% 15.55/8.62              ( ( member_complex @ X4 @ A3 )
% 15.55/8.62             => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62         => ( ? [X6: complex] :
% 15.55/8.62                ( ( member_complex @ X6 @ A3 )
% 15.55/8.62                & ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 15.55/8.62           => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A3 ) @ ( groups5058264527183730370ex_rat @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7786_sum__strict__mono__ex1,axiom,
% 15.55/8.62      ! [A3: set_Extended_enat,F: extended_enat > rat,G: extended_enat > rat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.62       => ( ! [X4: extended_enat] :
% 15.55/8.62              ( ( member_Extended_enat @ X4 @ A3 )
% 15.55/8.62             => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62         => ( ? [X6: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ X6 @ A3 )
% 15.55/8.62                & ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 15.55/8.62           => ( ord_less_rat @ ( groups1392844769737527556at_rat @ F @ A3 ) @ ( groups1392844769737527556at_rat @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7787_sum__strict__mono__ex1,axiom,
% 15.55/8.62      ! [A3: set_int,F: int > nat,G: int > nat] :
% 15.55/8.62        ( ( finite_finite_int @ A3 )
% 15.55/8.62       => ( ! [X4: int] :
% 15.55/8.62              ( ( member_int @ X4 @ A3 )
% 15.55/8.62             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62         => ( ? [X6: int] :
% 15.55/8.62                ( ( member_int @ X6 @ A3 )
% 15.55/8.62                & ( ord_less_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 15.55/8.62           => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ ( groups4541462559716669496nt_nat @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7788_sum__strict__mono__ex1,axiom,
% 15.55/8.62      ! [A3: set_complex,F: complex > nat,G: complex > nat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.62       => ( ! [X4: complex] :
% 15.55/8.62              ( ( member_complex @ X4 @ A3 )
% 15.55/8.62             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62         => ( ? [X6: complex] :
% 15.55/8.62                ( ( member_complex @ X6 @ A3 )
% 15.55/8.62                & ( ord_less_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 15.55/8.62           => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A3 ) @ ( groups5693394587270226106ex_nat @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7789_sum__strict__mono__ex1,axiom,
% 15.55/8.62      ! [A3: set_Extended_enat,F: extended_enat > nat,G: extended_enat > nat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.62       => ( ! [X4: extended_enat] :
% 15.55/8.62              ( ( member_Extended_enat @ X4 @ A3 )
% 15.55/8.62             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 15.55/8.62         => ( ? [X6: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ X6 @ A3 )
% 15.55/8.62                & ( ord_less_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 15.55/8.62           => ( ord_less_nat @ ( groups2027974829824023292at_nat @ F @ A3 ) @ ( groups2027974829824023292at_nat @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7790_finite__nat__set__iff__bounded__le,axiom,
% 15.55/8.62      ( finite_finite_nat
% 15.55/8.62      = ( ^ [N9: set_nat] :
% 15.55/8.62          ? [M3: nat] :
% 15.55/8.62          ! [X: nat] :
% 15.55/8.62            ( ( member_nat @ X @ N9 )
% 15.55/8.62           => ( ord_less_eq_nat @ X @ M3 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7791_bounded__nat__set__is__finite,axiom,
% 15.55/8.62      ! [N4: set_nat,N: nat] :
% 15.55/8.62        ( ! [X4: nat] :
% 15.55/8.62            ( ( member_nat @ X4 @ N4 )
% 15.55/8.62           => ( ord_less_nat @ X4 @ N ) )
% 15.55/8.62       => ( finite_finite_nat @ N4 ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7792_finite__nat__set__iff__bounded,axiom,
% 15.55/8.62      ( finite_finite_nat
% 15.55/8.62      = ( ^ [N9: set_nat] :
% 15.55/8.62          ? [M3: nat] :
% 15.55/8.62          ! [X: nat] :
% 15.55/8.62            ( ( member_nat @ X @ N9 )
% 15.55/8.62           => ( ord_less_nat @ X @ M3 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7793_sum__pos2,axiom,
% 15.55/8.62      ! [I5: set_real,I: real,F: real > real] :
% 15.55/8.62        ( ( finite_finite_real @ I5 )
% 15.55/8.62       => ( ( member_real @ I @ I5 )
% 15.55/8.62         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 15.55/8.62           => ( ! [I3: real] :
% 15.55/8.62                  ( ( member_real @ I3 @ I5 )
% 15.55/8.62                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.62             => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7794_sum__pos2,axiom,
% 15.55/8.62      ! [I5: set_int,I: int,F: int > real] :
% 15.55/8.62        ( ( finite_finite_int @ I5 )
% 15.55/8.62       => ( ( member_int @ I @ I5 )
% 15.55/8.62         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 15.55/8.62           => ( ! [I3: int] :
% 15.55/8.62                  ( ( member_int @ I3 @ I5 )
% 15.55/8.62                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.62             => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7795_sum__pos2,axiom,
% 15.55/8.62      ! [I5: set_complex,I: complex,F: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ I5 )
% 15.55/8.62       => ( ( member_complex @ I @ I5 )
% 15.55/8.62         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 15.55/8.62           => ( ! [I3: complex] :
% 15.55/8.62                  ( ( member_complex @ I3 @ I5 )
% 15.55/8.62                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.62             => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7796_sum__pos2,axiom,
% 15.55/8.62      ! [I5: set_Extended_enat,I: extended_enat,F: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ I5 )
% 15.55/8.62       => ( ( member_Extended_enat @ I @ I5 )
% 15.55/8.62         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 15.55/8.62           => ( ! [I3: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ I3 @ I5 )
% 15.55/8.62                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.62             => ( ord_less_real @ zero_zero_real @ ( groups4148127829035722712t_real @ F @ I5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7797_sum__pos2,axiom,
% 15.55/8.62      ! [I5: set_real,I: real,F: real > rat] :
% 15.55/8.62        ( ( finite_finite_real @ I5 )
% 15.55/8.62       => ( ( member_real @ I @ I5 )
% 15.55/8.62         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 15.55/8.62           => ( ! [I3: real] :
% 15.55/8.62                  ( ( member_real @ I3 @ I5 )
% 15.55/8.62                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 15.55/8.62             => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7798_sum__pos2,axiom,
% 15.55/8.62      ! [I5: set_nat,I: nat,F: nat > rat] :
% 15.55/8.62        ( ( finite_finite_nat @ I5 )
% 15.55/8.62       => ( ( member_nat @ I @ I5 )
% 15.55/8.62         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 15.55/8.62           => ( ! [I3: nat] :
% 15.55/8.62                  ( ( member_nat @ I3 @ I5 )
% 15.55/8.62                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 15.55/8.62             => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7799_sum__pos2,axiom,
% 15.55/8.62      ! [I5: set_int,I: int,F: int > rat] :
% 15.55/8.62        ( ( finite_finite_int @ I5 )
% 15.55/8.62       => ( ( member_int @ I @ I5 )
% 15.55/8.62         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 15.55/8.62           => ( ! [I3: int] :
% 15.55/8.62                  ( ( member_int @ I3 @ I5 )
% 15.55/8.62                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 15.55/8.62             => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7800_sum__pos2,axiom,
% 15.55/8.62      ! [I5: set_complex,I: complex,F: complex > rat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ I5 )
% 15.55/8.62       => ( ( member_complex @ I @ I5 )
% 15.55/8.62         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 15.55/8.62           => ( ! [I3: complex] :
% 15.55/8.62                  ( ( member_complex @ I3 @ I5 )
% 15.55/8.62                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 15.55/8.62             => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7801_sum__pos2,axiom,
% 15.55/8.62      ! [I5: set_Extended_enat,I: extended_enat,F: extended_enat > rat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ I5 )
% 15.55/8.62       => ( ( member_Extended_enat @ I @ I5 )
% 15.55/8.62         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 15.55/8.62           => ( ! [I3: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ I3 @ I5 )
% 15.55/8.62                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 15.55/8.62             => ( ord_less_rat @ zero_zero_rat @ ( groups1392844769737527556at_rat @ F @ I5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7802_sum__pos2,axiom,
% 15.55/8.62      ! [I5: set_real,I: real,F: real > nat] :
% 15.55/8.62        ( ( finite_finite_real @ I5 )
% 15.55/8.62       => ( ( member_real @ I @ I5 )
% 15.55/8.62         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 15.55/8.62           => ( ! [I3: real] :
% 15.55/8.62                  ( ( member_real @ I3 @ I5 )
% 15.55/8.62                 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 15.55/8.62             => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7803_sum__pos,axiom,
% 15.55/8.62      ! [I5: set_complex,F: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ I5 )
% 15.55/8.62       => ( ( I5 != bot_bot_set_complex )
% 15.55/8.62         => ( ! [I3: complex] :
% 15.55/8.62                ( ( member_complex @ I3 @ I5 )
% 15.55/8.62               => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.62           => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7804_sum__pos,axiom,
% 15.55/8.62      ! [I5: set_Extended_enat,F: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ I5 )
% 15.55/8.62       => ( ( I5 != bot_bo7653980558646680370d_enat )
% 15.55/8.62         => ( ! [I3: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ I3 @ I5 )
% 15.55/8.62               => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.62           => ( ord_less_real @ zero_zero_real @ ( groups4148127829035722712t_real @ F @ I5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7805_sum__pos,axiom,
% 15.55/8.62      ! [I5: set_real,F: real > real] :
% 15.55/8.62        ( ( finite_finite_real @ I5 )
% 15.55/8.62       => ( ( I5 != bot_bot_set_real )
% 15.55/8.62         => ( ! [I3: real] :
% 15.55/8.62                ( ( member_real @ I3 @ I5 )
% 15.55/8.62               => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.62           => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7806_sum__pos,axiom,
% 15.55/8.62      ! [I5: set_int,F: int > real] :
% 15.55/8.62        ( ( finite_finite_int @ I5 )
% 15.55/8.62       => ( ( I5 != bot_bot_set_int )
% 15.55/8.62         => ( ! [I3: int] :
% 15.55/8.62                ( ( member_int @ I3 @ I5 )
% 15.55/8.62               => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.62           => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7807_sum__pos,axiom,
% 15.55/8.62      ! [I5: set_complex,F: complex > rat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ I5 )
% 15.55/8.62       => ( ( I5 != bot_bot_set_complex )
% 15.55/8.62         => ( ! [I3: complex] :
% 15.55/8.62                ( ( member_complex @ I3 @ I5 )
% 15.55/8.62               => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 15.55/8.62           => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7808_sum__pos,axiom,
% 15.55/8.62      ! [I5: set_Extended_enat,F: extended_enat > rat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ I5 )
% 15.55/8.62       => ( ( I5 != bot_bo7653980558646680370d_enat )
% 15.55/8.62         => ( ! [I3: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ I3 @ I5 )
% 15.55/8.62               => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 15.55/8.62           => ( ord_less_rat @ zero_zero_rat @ ( groups1392844769737527556at_rat @ F @ I5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7809_sum__pos,axiom,
% 15.55/8.62      ! [I5: set_real,F: real > rat] :
% 15.55/8.62        ( ( finite_finite_real @ I5 )
% 15.55/8.62       => ( ( I5 != bot_bot_set_real )
% 15.55/8.62         => ( ! [I3: real] :
% 15.55/8.62                ( ( member_real @ I3 @ I5 )
% 15.55/8.62               => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 15.55/8.62           => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7810_sum__pos,axiom,
% 15.55/8.62      ! [I5: set_nat,F: nat > rat] :
% 15.55/8.62        ( ( finite_finite_nat @ I5 )
% 15.55/8.62       => ( ( I5 != bot_bot_set_nat )
% 15.55/8.62         => ( ! [I3: nat] :
% 15.55/8.62                ( ( member_nat @ I3 @ I5 )
% 15.55/8.62               => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 15.55/8.62           => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7811_sum__pos,axiom,
% 15.55/8.62      ! [I5: set_int,F: int > rat] :
% 15.55/8.62        ( ( finite_finite_int @ I5 )
% 15.55/8.62       => ( ( I5 != bot_bot_set_int )
% 15.55/8.62         => ( ! [I3: int] :
% 15.55/8.62                ( ( member_int @ I3 @ I5 )
% 15.55/8.62               => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 15.55/8.62           => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7812_sum__pos,axiom,
% 15.55/8.62      ! [I5: set_complex,F: complex > nat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ I5 )
% 15.55/8.62       => ( ( I5 != bot_bot_set_complex )
% 15.55/8.62         => ( ! [I3: complex] :
% 15.55/8.62                ( ( member_complex @ I3 @ I5 )
% 15.55/8.62               => ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 15.55/8.62           => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7813_sum__mono,axiom,
% 15.55/8.62      ! [K5: set_real,F: real > rat,G: real > rat] :
% 15.55/8.62        ( ! [I3: real] :
% 15.55/8.62            ( ( member_real @ I3 @ K5 )
% 15.55/8.62           => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 15.55/8.62       => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K5 ) @ ( groups1300246762558778688al_rat @ G @ K5 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7814_sum__mono,axiom,
% 15.55/8.62      ! [K5: set_nat,F: nat > rat,G: nat > rat] :
% 15.55/8.62        ( ! [I3: nat] :
% 15.55/8.62            ( ( member_nat @ I3 @ K5 )
% 15.55/8.62           => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 15.55/8.62       => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K5 ) @ ( groups2906978787729119204at_rat @ G @ K5 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7815_sum__mono,axiom,
% 15.55/8.62      ! [K5: set_int,F: int > rat,G: int > rat] :
% 15.55/8.62        ( ! [I3: int] :
% 15.55/8.62            ( ( member_int @ I3 @ K5 )
% 15.55/8.62           => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 15.55/8.62       => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K5 ) @ ( groups3906332499630173760nt_rat @ G @ K5 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7816_sum__mono,axiom,
% 15.55/8.62      ! [K5: set_real,F: real > nat,G: real > nat] :
% 15.55/8.62        ( ! [I3: real] :
% 15.55/8.62            ( ( member_real @ I3 @ K5 )
% 15.55/8.62           => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 15.55/8.62       => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7817_sum__mono,axiom,
% 15.55/8.62      ! [K5: set_int,F: int > nat,G: int > nat] :
% 15.55/8.62        ( ! [I3: int] :
% 15.55/8.62            ( ( member_int @ I3 @ K5 )
% 15.55/8.62           => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 15.55/8.62       => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7818_sum__mono,axiom,
% 15.55/8.62      ! [K5: set_real,F: real > int,G: real > int] :
% 15.55/8.62        ( ! [I3: real] :
% 15.55/8.62            ( ( member_real @ I3 @ K5 )
% 15.55/8.62           => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 15.55/8.62       => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7819_sum__mono,axiom,
% 15.55/8.62      ! [K5: set_nat,F: nat > int,G: nat > int] :
% 15.55/8.62        ( ! [I3: nat] :
% 15.55/8.62            ( ( member_nat @ I3 @ K5 )
% 15.55/8.62           => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 15.55/8.62       => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7820_sum__mono,axiom,
% 15.55/8.62      ! [K5: set_nat,F: nat > nat,G: nat > nat] :
% 15.55/8.62        ( ! [I3: nat] :
% 15.55/8.62            ( ( member_nat @ I3 @ K5 )
% 15.55/8.62           => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 15.55/8.62       => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ K5 ) @ ( groups3542108847815614940at_nat @ G @ K5 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7821_sum__mono,axiom,
% 15.55/8.62      ! [K5: set_nat,F: nat > real,G: nat > real] :
% 15.55/8.62        ( ! [I3: nat] :
% 15.55/8.62            ( ( member_nat @ I3 @ K5 )
% 15.55/8.62           => ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 15.55/8.62       => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ K5 ) @ ( groups6591440286371151544t_real @ G @ K5 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7822_sum__mono,axiom,
% 15.55/8.62      ! [K5: set_int,F: int > int,G: int > int] :
% 15.55/8.62        ( ! [I3: int] :
% 15.55/8.62            ( ( member_int @ I3 @ K5 )
% 15.55/8.62           => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 15.55/8.62       => ( ord_less_eq_int @ ( groups4538972089207619220nt_int @ F @ K5 ) @ ( groups4538972089207619220nt_int @ G @ K5 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7823_sum_Omono__neutral__cong__right,axiom,
% 15.55/8.62      ! [T5: set_real,S2: set_real,G: real > real,H2: real > real] :
% 15.55/8.62        ( ( finite_finite_real @ T5 )
% 15.55/8.62       => ( ( ord_less_eq_set_real @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: real] :
% 15.55/8.62                ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_real ) )
% 15.55/8.62           => ( ! [X4: real] :
% 15.55/8.62                  ( ( member_real @ X4 @ S2 )
% 15.55/8.62                 => ( ( G @ X4 )
% 15.55/8.62                    = ( H2 @ X4 ) ) )
% 15.55/8.62             => ( ( groups8097168146408367636l_real @ G @ T5 )
% 15.55/8.62                = ( groups8097168146408367636l_real @ H2 @ S2 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7824_sum_Omono__neutral__cong__right,axiom,
% 15.55/8.62      ! [T5: set_int,S2: set_int,G: int > real,H2: int > real] :
% 15.55/8.62        ( ( finite_finite_int @ T5 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: int] :
% 15.55/8.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_real ) )
% 15.55/8.62           => ( ! [X4: int] :
% 15.55/8.62                  ( ( member_int @ X4 @ S2 )
% 15.55/8.62                 => ( ( G @ X4 )
% 15.55/8.62                    = ( H2 @ X4 ) ) )
% 15.55/8.62             => ( ( groups8778361861064173332t_real @ G @ T5 )
% 15.55/8.62                = ( groups8778361861064173332t_real @ H2 @ S2 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7825_sum_Omono__neutral__cong__right,axiom,
% 15.55/8.62      ! [T5: set_complex,S2: set_complex,G: complex > real,H2: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ T5 )
% 15.55/8.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: complex] :
% 15.55/8.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_real ) )
% 15.55/8.62           => ( ! [X4: complex] :
% 15.55/8.62                  ( ( member_complex @ X4 @ S2 )
% 15.55/8.62                 => ( ( G @ X4 )
% 15.55/8.62                    = ( H2 @ X4 ) ) )
% 15.55/8.62             => ( ( groups5808333547571424918x_real @ G @ T5 )
% 15.55/8.62                = ( groups5808333547571424918x_real @ H2 @ S2 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7826_sum_Omono__neutral__cong__right,axiom,
% 15.55/8.62      ! [T5: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > real,H2: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ T5 )
% 15.55/8.62       => ( ( ord_le7203529160286727270d_enat @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_real ) )
% 15.55/8.62           => ( ! [X4: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ X4 @ S2 )
% 15.55/8.62                 => ( ( G @ X4 )
% 15.55/8.62                    = ( H2 @ X4 ) ) )
% 15.55/8.62             => ( ( groups4148127829035722712t_real @ G @ T5 )
% 15.55/8.62                = ( groups4148127829035722712t_real @ H2 @ S2 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7827_sum_Omono__neutral__cong__right,axiom,
% 15.55/8.62      ! [T5: set_real,S2: set_real,G: real > rat,H2: real > rat] :
% 15.55/8.62        ( ( finite_finite_real @ T5 )
% 15.55/8.62       => ( ( ord_less_eq_set_real @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: real] :
% 15.55/8.62                ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_rat ) )
% 15.55/8.62           => ( ! [X4: real] :
% 15.55/8.62                  ( ( member_real @ X4 @ S2 )
% 15.55/8.62                 => ( ( G @ X4 )
% 15.55/8.62                    = ( H2 @ X4 ) ) )
% 15.55/8.62             => ( ( groups1300246762558778688al_rat @ G @ T5 )
% 15.55/8.62                = ( groups1300246762558778688al_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7828_sum_Omono__neutral__cong__right,axiom,
% 15.55/8.62      ! [T5: set_int,S2: set_int,G: int > rat,H2: int > rat] :
% 15.55/8.62        ( ( finite_finite_int @ T5 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: int] :
% 15.55/8.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_rat ) )
% 15.55/8.62           => ( ! [X4: int] :
% 15.55/8.62                  ( ( member_int @ X4 @ S2 )
% 15.55/8.62                 => ( ( G @ X4 )
% 15.55/8.62                    = ( H2 @ X4 ) ) )
% 15.55/8.62             => ( ( groups3906332499630173760nt_rat @ G @ T5 )
% 15.55/8.62                = ( groups3906332499630173760nt_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7829_sum_Omono__neutral__cong__right,axiom,
% 15.55/8.62      ! [T5: set_complex,S2: set_complex,G: complex > rat,H2: complex > rat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ T5 )
% 15.55/8.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: complex] :
% 15.55/8.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_rat ) )
% 15.55/8.62           => ( ! [X4: complex] :
% 15.55/8.62                  ( ( member_complex @ X4 @ S2 )
% 15.55/8.62                 => ( ( G @ X4 )
% 15.55/8.62                    = ( H2 @ X4 ) ) )
% 15.55/8.62             => ( ( groups5058264527183730370ex_rat @ G @ T5 )
% 15.55/8.62                = ( groups5058264527183730370ex_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7830_sum_Omono__neutral__cong__right,axiom,
% 15.55/8.62      ! [T5: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > rat,H2: extended_enat > rat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ T5 )
% 15.55/8.62       => ( ( ord_le7203529160286727270d_enat @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_rat ) )
% 15.55/8.62           => ( ! [X4: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ X4 @ S2 )
% 15.55/8.62                 => ( ( G @ X4 )
% 15.55/8.62                    = ( H2 @ X4 ) ) )
% 15.55/8.62             => ( ( groups1392844769737527556at_rat @ G @ T5 )
% 15.55/8.62                = ( groups1392844769737527556at_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7831_sum_Omono__neutral__cong__right,axiom,
% 15.55/8.62      ! [T5: set_real,S2: set_real,G: real > nat,H2: real > nat] :
% 15.55/8.62        ( ( finite_finite_real @ T5 )
% 15.55/8.62       => ( ( ord_less_eq_set_real @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: real] :
% 15.55/8.62                ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_nat ) )
% 15.55/8.62           => ( ! [X4: real] :
% 15.55/8.62                  ( ( member_real @ X4 @ S2 )
% 15.55/8.62                 => ( ( G @ X4 )
% 15.55/8.62                    = ( H2 @ X4 ) ) )
% 15.55/8.62             => ( ( groups1935376822645274424al_nat @ G @ T5 )
% 15.55/8.62                = ( groups1935376822645274424al_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7832_sum_Omono__neutral__cong__right,axiom,
% 15.55/8.62      ! [T5: set_int,S2: set_int,G: int > nat,H2: int > nat] :
% 15.55/8.62        ( ( finite_finite_int @ T5 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: int] :
% 15.55/8.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_nat ) )
% 15.55/8.62           => ( ! [X4: int] :
% 15.55/8.62                  ( ( member_int @ X4 @ S2 )
% 15.55/8.62                 => ( ( G @ X4 )
% 15.55/8.62                    = ( H2 @ X4 ) ) )
% 15.55/8.62             => ( ( groups4541462559716669496nt_nat @ G @ T5 )
% 15.55/8.62                = ( groups4541462559716669496nt_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7833_sum_Omono__neutral__cong__left,axiom,
% 15.55/8.62      ! [T5: set_real,S2: set_real,H2: real > real,G: real > real] :
% 15.55/8.62        ( ( finite_finite_real @ T5 )
% 15.55/8.62       => ( ( ord_less_eq_set_real @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: real] :
% 15.55/8.62                ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S2 ) )
% 15.55/8.62               => ( ( H2 @ X4 )
% 15.55/8.62                  = zero_zero_real ) )
% 15.55/8.62           => ( ! [X4: real] :
% 15.55/8.62                  ( ( member_real @ X4 @ S2 )
% 15.55/8.62                 => ( ( G @ X4 )
% 15.55/8.62                    = ( H2 @ X4 ) ) )
% 15.55/8.62             => ( ( groups8097168146408367636l_real @ G @ S2 )
% 15.55/8.62                = ( groups8097168146408367636l_real @ H2 @ T5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7834_sum_Omono__neutral__cong__left,axiom,
% 15.55/8.62      ! [T5: set_int,S2: set_int,H2: int > real,G: int > real] :
% 15.55/8.62        ( ( finite_finite_int @ T5 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: int] :
% 15.55/8.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 15.55/8.62               => ( ( H2 @ X4 )
% 15.55/8.62                  = zero_zero_real ) )
% 15.55/8.62           => ( ! [X4: int] :
% 15.55/8.62                  ( ( member_int @ X4 @ S2 )
% 15.55/8.62                 => ( ( G @ X4 )
% 15.55/8.62                    = ( H2 @ X4 ) ) )
% 15.55/8.62             => ( ( groups8778361861064173332t_real @ G @ S2 )
% 15.55/8.62                = ( groups8778361861064173332t_real @ H2 @ T5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7835_sum_Omono__neutral__cong__left,axiom,
% 15.55/8.62      ! [T5: set_complex,S2: set_complex,H2: complex > real,G: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ T5 )
% 15.55/8.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: complex] :
% 15.55/8.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 15.55/8.62               => ( ( H2 @ X4 )
% 15.55/8.62                  = zero_zero_real ) )
% 15.55/8.62           => ( ! [X4: complex] :
% 15.55/8.62                  ( ( member_complex @ X4 @ S2 )
% 15.55/8.62                 => ( ( G @ X4 )
% 15.55/8.62                    = ( H2 @ X4 ) ) )
% 15.55/8.62             => ( ( groups5808333547571424918x_real @ G @ S2 )
% 15.55/8.62                = ( groups5808333547571424918x_real @ H2 @ T5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7836_sum_Omono__neutral__cong__left,axiom,
% 15.55/8.62      ! [T5: set_Extended_enat,S2: set_Extended_enat,H2: extended_enat > real,G: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ T5 )
% 15.55/8.62       => ( ( ord_le7203529160286727270d_enat @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T5 @ S2 ) )
% 15.55/8.62               => ( ( H2 @ X4 )
% 15.55/8.62                  = zero_zero_real ) )
% 15.55/8.62           => ( ! [X4: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ X4 @ S2 )
% 15.55/8.62                 => ( ( G @ X4 )
% 15.55/8.62                    = ( H2 @ X4 ) ) )
% 15.55/8.62             => ( ( groups4148127829035722712t_real @ G @ S2 )
% 15.55/8.62                = ( groups4148127829035722712t_real @ H2 @ T5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7837_sum_Omono__neutral__cong__left,axiom,
% 15.55/8.62      ! [T5: set_real,S2: set_real,H2: real > rat,G: real > rat] :
% 15.55/8.62        ( ( finite_finite_real @ T5 )
% 15.55/8.62       => ( ( ord_less_eq_set_real @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: real] :
% 15.55/8.62                ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S2 ) )
% 15.55/8.62               => ( ( H2 @ X4 )
% 15.55/8.62                  = zero_zero_rat ) )
% 15.55/8.62           => ( ! [X4: real] :
% 15.55/8.62                  ( ( member_real @ X4 @ S2 )
% 15.55/8.62                 => ( ( G @ X4 )
% 15.55/8.62                    = ( H2 @ X4 ) ) )
% 15.55/8.62             => ( ( groups1300246762558778688al_rat @ G @ S2 )
% 15.55/8.62                = ( groups1300246762558778688al_rat @ H2 @ T5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7838_sum_Omono__neutral__cong__left,axiom,
% 15.55/8.62      ! [T5: set_int,S2: set_int,H2: int > rat,G: int > rat] :
% 15.55/8.62        ( ( finite_finite_int @ T5 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: int] :
% 15.55/8.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 15.55/8.62               => ( ( H2 @ X4 )
% 15.55/8.62                  = zero_zero_rat ) )
% 15.55/8.62           => ( ! [X4: int] :
% 15.55/8.62                  ( ( member_int @ X4 @ S2 )
% 15.55/8.62                 => ( ( G @ X4 )
% 15.55/8.62                    = ( H2 @ X4 ) ) )
% 15.55/8.62             => ( ( groups3906332499630173760nt_rat @ G @ S2 )
% 15.55/8.62                = ( groups3906332499630173760nt_rat @ H2 @ T5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7839_sum_Omono__neutral__cong__left,axiom,
% 15.55/8.62      ! [T5: set_complex,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ T5 )
% 15.55/8.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: complex] :
% 15.55/8.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 15.55/8.62               => ( ( H2 @ X4 )
% 15.55/8.62                  = zero_zero_rat ) )
% 15.55/8.62           => ( ! [X4: complex] :
% 15.55/8.62                  ( ( member_complex @ X4 @ S2 )
% 15.55/8.62                 => ( ( G @ X4 )
% 15.55/8.62                    = ( H2 @ X4 ) ) )
% 15.55/8.62             => ( ( groups5058264527183730370ex_rat @ G @ S2 )
% 15.55/8.62                = ( groups5058264527183730370ex_rat @ H2 @ T5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7840_sum_Omono__neutral__cong__left,axiom,
% 15.55/8.62      ! [T5: set_Extended_enat,S2: set_Extended_enat,H2: extended_enat > rat,G: extended_enat > rat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ T5 )
% 15.55/8.62       => ( ( ord_le7203529160286727270d_enat @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T5 @ S2 ) )
% 15.55/8.62               => ( ( H2 @ X4 )
% 15.55/8.62                  = zero_zero_rat ) )
% 15.55/8.62           => ( ! [X4: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ X4 @ S2 )
% 15.55/8.62                 => ( ( G @ X4 )
% 15.55/8.62                    = ( H2 @ X4 ) ) )
% 15.55/8.62             => ( ( groups1392844769737527556at_rat @ G @ S2 )
% 15.55/8.62                = ( groups1392844769737527556at_rat @ H2 @ T5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7841_sum_Omono__neutral__cong__left,axiom,
% 15.55/8.62      ! [T5: set_real,S2: set_real,H2: real > nat,G: real > nat] :
% 15.55/8.62        ( ( finite_finite_real @ T5 )
% 15.55/8.62       => ( ( ord_less_eq_set_real @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: real] :
% 15.55/8.62                ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S2 ) )
% 15.55/8.62               => ( ( H2 @ X4 )
% 15.55/8.62                  = zero_zero_nat ) )
% 15.55/8.62           => ( ! [X4: real] :
% 15.55/8.62                  ( ( member_real @ X4 @ S2 )
% 15.55/8.62                 => ( ( G @ X4 )
% 15.55/8.62                    = ( H2 @ X4 ) ) )
% 15.55/8.62             => ( ( groups1935376822645274424al_nat @ G @ S2 )
% 15.55/8.62                = ( groups1935376822645274424al_nat @ H2 @ T5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7842_sum_Omono__neutral__cong__left,axiom,
% 15.55/8.62      ! [T5: set_int,S2: set_int,H2: int > nat,G: int > nat] :
% 15.55/8.62        ( ( finite_finite_int @ T5 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: int] :
% 15.55/8.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 15.55/8.62               => ( ( H2 @ X4 )
% 15.55/8.62                  = zero_zero_nat ) )
% 15.55/8.62           => ( ! [X4: int] :
% 15.55/8.62                  ( ( member_int @ X4 @ S2 )
% 15.55/8.62                 => ( ( G @ X4 )
% 15.55/8.62                    = ( H2 @ X4 ) ) )
% 15.55/8.62             => ( ( groups4541462559716669496nt_nat @ G @ S2 )
% 15.55/8.62                = ( groups4541462559716669496nt_nat @ H2 @ T5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7843_sum_Omono__neutral__right,axiom,
% 15.55/8.62      ! [T5: set_int,S2: set_int,G: int > real] :
% 15.55/8.62        ( ( finite_finite_int @ T5 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: int] :
% 15.55/8.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_real ) )
% 15.55/8.62           => ( ( groups8778361861064173332t_real @ G @ T5 )
% 15.55/8.62              = ( groups8778361861064173332t_real @ G @ S2 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7844_sum_Omono__neutral__right,axiom,
% 15.55/8.62      ! [T5: set_complex,S2: set_complex,G: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ T5 )
% 15.55/8.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: complex] :
% 15.55/8.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_real ) )
% 15.55/8.62           => ( ( groups5808333547571424918x_real @ G @ T5 )
% 15.55/8.62              = ( groups5808333547571424918x_real @ G @ S2 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7845_sum_Omono__neutral__right,axiom,
% 15.55/8.62      ! [T5: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ T5 )
% 15.55/8.62       => ( ( ord_le7203529160286727270d_enat @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_real ) )
% 15.55/8.62           => ( ( groups4148127829035722712t_real @ G @ T5 )
% 15.55/8.62              = ( groups4148127829035722712t_real @ G @ S2 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7846_sum_Omono__neutral__right,axiom,
% 15.55/8.62      ! [T5: set_int,S2: set_int,G: int > rat] :
% 15.55/8.62        ( ( finite_finite_int @ T5 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: int] :
% 15.55/8.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_rat ) )
% 15.55/8.62           => ( ( groups3906332499630173760nt_rat @ G @ T5 )
% 15.55/8.62              = ( groups3906332499630173760nt_rat @ G @ S2 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7847_sum_Omono__neutral__right,axiom,
% 15.55/8.62      ! [T5: set_complex,S2: set_complex,G: complex > rat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ T5 )
% 15.55/8.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: complex] :
% 15.55/8.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_rat ) )
% 15.55/8.62           => ( ( groups5058264527183730370ex_rat @ G @ T5 )
% 15.55/8.62              = ( groups5058264527183730370ex_rat @ G @ S2 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7848_sum_Omono__neutral__right,axiom,
% 15.55/8.62      ! [T5: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > rat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ T5 )
% 15.55/8.62       => ( ( ord_le7203529160286727270d_enat @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_rat ) )
% 15.55/8.62           => ( ( groups1392844769737527556at_rat @ G @ T5 )
% 15.55/8.62              = ( groups1392844769737527556at_rat @ G @ S2 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7849_sum_Omono__neutral__right,axiom,
% 15.55/8.62      ! [T5: set_int,S2: set_int,G: int > nat] :
% 15.55/8.62        ( ( finite_finite_int @ T5 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: int] :
% 15.55/8.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_nat ) )
% 15.55/8.62           => ( ( groups4541462559716669496nt_nat @ G @ T5 )
% 15.55/8.62              = ( groups4541462559716669496nt_nat @ G @ S2 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7850_sum_Omono__neutral__right,axiom,
% 15.55/8.62      ! [T5: set_complex,S2: set_complex,G: complex > nat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ T5 )
% 15.55/8.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: complex] :
% 15.55/8.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_nat ) )
% 15.55/8.62           => ( ( groups5693394587270226106ex_nat @ G @ T5 )
% 15.55/8.62              = ( groups5693394587270226106ex_nat @ G @ S2 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7851_sum_Omono__neutral__right,axiom,
% 15.55/8.62      ! [T5: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > nat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ T5 )
% 15.55/8.62       => ( ( ord_le7203529160286727270d_enat @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_nat ) )
% 15.55/8.62           => ( ( groups2027974829824023292at_nat @ G @ T5 )
% 15.55/8.62              = ( groups2027974829824023292at_nat @ G @ S2 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7852_sum_Omono__neutral__right,axiom,
% 15.55/8.62      ! [T5: set_complex,S2: set_complex,G: complex > int] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ T5 )
% 15.55/8.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: complex] :
% 15.55/8.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_int ) )
% 15.55/8.62           => ( ( groups5690904116761175830ex_int @ G @ T5 )
% 15.55/8.62              = ( groups5690904116761175830ex_int @ G @ S2 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7853_sum_Omono__neutral__left,axiom,
% 15.55/8.62      ! [T5: set_int,S2: set_int,G: int > real] :
% 15.55/8.62        ( ( finite_finite_int @ T5 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: int] :
% 15.55/8.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_real ) )
% 15.55/8.62           => ( ( groups8778361861064173332t_real @ G @ S2 )
% 15.55/8.62              = ( groups8778361861064173332t_real @ G @ T5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7854_sum_Omono__neutral__left,axiom,
% 15.55/8.62      ! [T5: set_complex,S2: set_complex,G: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ T5 )
% 15.55/8.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: complex] :
% 15.55/8.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_real ) )
% 15.55/8.62           => ( ( groups5808333547571424918x_real @ G @ S2 )
% 15.55/8.62              = ( groups5808333547571424918x_real @ G @ T5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7855_sum_Omono__neutral__left,axiom,
% 15.55/8.62      ! [T5: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ T5 )
% 15.55/8.62       => ( ( ord_le7203529160286727270d_enat @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_real ) )
% 15.55/8.62           => ( ( groups4148127829035722712t_real @ G @ S2 )
% 15.55/8.62              = ( groups4148127829035722712t_real @ G @ T5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7856_sum_Omono__neutral__left,axiom,
% 15.55/8.62      ! [T5: set_int,S2: set_int,G: int > rat] :
% 15.55/8.62        ( ( finite_finite_int @ T5 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: int] :
% 15.55/8.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_rat ) )
% 15.55/8.62           => ( ( groups3906332499630173760nt_rat @ G @ S2 )
% 15.55/8.62              = ( groups3906332499630173760nt_rat @ G @ T5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7857_sum_Omono__neutral__left,axiom,
% 15.55/8.62      ! [T5: set_complex,S2: set_complex,G: complex > rat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ T5 )
% 15.55/8.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: complex] :
% 15.55/8.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_rat ) )
% 15.55/8.62           => ( ( groups5058264527183730370ex_rat @ G @ S2 )
% 15.55/8.62              = ( groups5058264527183730370ex_rat @ G @ T5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7858_sum_Omono__neutral__left,axiom,
% 15.55/8.62      ! [T5: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > rat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ T5 )
% 15.55/8.62       => ( ( ord_le7203529160286727270d_enat @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_rat ) )
% 15.55/8.62           => ( ( groups1392844769737527556at_rat @ G @ S2 )
% 15.55/8.62              = ( groups1392844769737527556at_rat @ G @ T5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7859_sum_Omono__neutral__left,axiom,
% 15.55/8.62      ! [T5: set_int,S2: set_int,G: int > nat] :
% 15.55/8.62        ( ( finite_finite_int @ T5 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: int] :
% 15.55/8.62                ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_nat ) )
% 15.55/8.62           => ( ( groups4541462559716669496nt_nat @ G @ S2 )
% 15.55/8.62              = ( groups4541462559716669496nt_nat @ G @ T5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7860_sum_Omono__neutral__left,axiom,
% 15.55/8.62      ! [T5: set_complex,S2: set_complex,G: complex > nat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ T5 )
% 15.55/8.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: complex] :
% 15.55/8.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_nat ) )
% 15.55/8.62           => ( ( groups5693394587270226106ex_nat @ G @ S2 )
% 15.55/8.62              = ( groups5693394587270226106ex_nat @ G @ T5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7861_sum_Omono__neutral__left,axiom,
% 15.55/8.62      ! [T5: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > nat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ T5 )
% 15.55/8.62       => ( ( ord_le7203529160286727270d_enat @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_nat ) )
% 15.55/8.62           => ( ( groups2027974829824023292at_nat @ G @ S2 )
% 15.55/8.62              = ( groups2027974829824023292at_nat @ G @ T5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7862_sum_Omono__neutral__left,axiom,
% 15.55/8.62      ! [T5: set_complex,S2: set_complex,G: complex > int] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ T5 )
% 15.55/8.62       => ( ( ord_le211207098394363844omplex @ S2 @ T5 )
% 15.55/8.62         => ( ! [X4: complex] :
% 15.55/8.62                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S2 ) )
% 15.55/8.62               => ( ( G @ X4 )
% 15.55/8.62                  = zero_zero_int ) )
% 15.55/8.62           => ( ( groups5690904116761175830ex_int @ G @ S2 )
% 15.55/8.62              = ( groups5690904116761175830ex_int @ G @ T5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7863_sum_Osame__carrierI,axiom,
% 15.55/8.62      ! [C4: set_real,A3: set_real,B5: set_real,G: real > real,H2: real > real] :
% 15.55/8.62        ( ( finite_finite_real @ C4 )
% 15.55/8.62       => ( ( ord_less_eq_set_real @ A3 @ C4 )
% 15.55/8.62         => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 15.55/8.62           => ( ! [A5: real] :
% 15.55/8.62                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A3 ) )
% 15.55/8.62                 => ( ( G @ A5 )
% 15.55/8.62                    = zero_zero_real ) )
% 15.55/8.62             => ( ! [B4: real] :
% 15.55/8.62                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 15.55/8.62                   => ( ( H2 @ B4 )
% 15.55/8.62                      = zero_zero_real ) )
% 15.55/8.62               => ( ( ( groups8097168146408367636l_real @ G @ C4 )
% 15.55/8.62                    = ( groups8097168146408367636l_real @ H2 @ C4 ) )
% 15.55/8.62                 => ( ( groups8097168146408367636l_real @ G @ A3 )
% 15.55/8.62                    = ( groups8097168146408367636l_real @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7864_sum_Osame__carrierI,axiom,
% 15.55/8.62      ! [C4: set_int,A3: set_int,B5: set_int,G: int > real,H2: int > real] :
% 15.55/8.62        ( ( finite_finite_int @ C4 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ A3 @ C4 )
% 15.55/8.62         => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 15.55/8.62           => ( ! [A5: int] :
% 15.55/8.62                  ( ( member_int @ A5 @ ( minus_minus_set_int @ C4 @ A3 ) )
% 15.55/8.62                 => ( ( G @ A5 )
% 15.55/8.62                    = zero_zero_real ) )
% 15.55/8.62             => ( ! [B4: int] :
% 15.55/8.62                    ( ( member_int @ B4 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 15.55/8.62                   => ( ( H2 @ B4 )
% 15.55/8.62                      = zero_zero_real ) )
% 15.55/8.62               => ( ( ( groups8778361861064173332t_real @ G @ C4 )
% 15.55/8.62                    = ( groups8778361861064173332t_real @ H2 @ C4 ) )
% 15.55/8.62                 => ( ( groups8778361861064173332t_real @ G @ A3 )
% 15.55/8.62                    = ( groups8778361861064173332t_real @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7865_sum_Osame__carrierI,axiom,
% 15.55/8.62      ! [C4: set_complex,A3: set_complex,B5: set_complex,G: complex > real,H2: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ C4 )
% 15.55/8.62       => ( ( ord_le211207098394363844omplex @ A3 @ C4 )
% 15.55/8.62         => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 15.55/8.62           => ( ! [A5: complex] :
% 15.55/8.62                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A3 ) )
% 15.55/8.62                 => ( ( G @ A5 )
% 15.55/8.62                    = zero_zero_real ) )
% 15.55/8.62             => ( ! [B4: complex] :
% 15.55/8.62                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 15.55/8.62                   => ( ( H2 @ B4 )
% 15.55/8.62                      = zero_zero_real ) )
% 15.55/8.62               => ( ( ( groups5808333547571424918x_real @ G @ C4 )
% 15.55/8.62                    = ( groups5808333547571424918x_real @ H2 @ C4 ) )
% 15.55/8.62                 => ( ( groups5808333547571424918x_real @ G @ A3 )
% 15.55/8.62                    = ( groups5808333547571424918x_real @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7866_sum_Osame__carrierI,axiom,
% 15.55/8.62      ! [C4: set_Extended_enat,A3: set_Extended_enat,B5: set_Extended_enat,G: extended_enat > real,H2: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ C4 )
% 15.55/8.62       => ( ( ord_le7203529160286727270d_enat @ A3 @ C4 )
% 15.55/8.62         => ( ( ord_le7203529160286727270d_enat @ B5 @ C4 )
% 15.55/8.62           => ( ! [A5: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ A5 @ ( minus_925952699566721837d_enat @ C4 @ A3 ) )
% 15.55/8.62                 => ( ( G @ A5 )
% 15.55/8.62                    = zero_zero_real ) )
% 15.55/8.62             => ( ! [B4: extended_enat] :
% 15.55/8.62                    ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ C4 @ B5 ) )
% 15.55/8.62                   => ( ( H2 @ B4 )
% 15.55/8.62                      = zero_zero_real ) )
% 15.55/8.62               => ( ( ( groups4148127829035722712t_real @ G @ C4 )
% 15.55/8.62                    = ( groups4148127829035722712t_real @ H2 @ C4 ) )
% 15.55/8.62                 => ( ( groups4148127829035722712t_real @ G @ A3 )
% 15.55/8.62                    = ( groups4148127829035722712t_real @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7867_sum_Osame__carrierI,axiom,
% 15.55/8.62      ! [C4: set_real,A3: set_real,B5: set_real,G: real > rat,H2: real > rat] :
% 15.55/8.62        ( ( finite_finite_real @ C4 )
% 15.55/8.62       => ( ( ord_less_eq_set_real @ A3 @ C4 )
% 15.55/8.62         => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 15.55/8.62           => ( ! [A5: real] :
% 15.55/8.62                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A3 ) )
% 15.55/8.62                 => ( ( G @ A5 )
% 15.55/8.62                    = zero_zero_rat ) )
% 15.55/8.62             => ( ! [B4: real] :
% 15.55/8.62                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 15.55/8.62                   => ( ( H2 @ B4 )
% 15.55/8.62                      = zero_zero_rat ) )
% 15.55/8.62               => ( ( ( groups1300246762558778688al_rat @ G @ C4 )
% 15.55/8.62                    = ( groups1300246762558778688al_rat @ H2 @ C4 ) )
% 15.55/8.62                 => ( ( groups1300246762558778688al_rat @ G @ A3 )
% 15.55/8.62                    = ( groups1300246762558778688al_rat @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7868_sum_Osame__carrierI,axiom,
% 15.55/8.62      ! [C4: set_int,A3: set_int,B5: set_int,G: int > rat,H2: int > rat] :
% 15.55/8.62        ( ( finite_finite_int @ C4 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ A3 @ C4 )
% 15.55/8.62         => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 15.55/8.62           => ( ! [A5: int] :
% 15.55/8.62                  ( ( member_int @ A5 @ ( minus_minus_set_int @ C4 @ A3 ) )
% 15.55/8.62                 => ( ( G @ A5 )
% 15.55/8.62                    = zero_zero_rat ) )
% 15.55/8.62             => ( ! [B4: int] :
% 15.55/8.62                    ( ( member_int @ B4 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 15.55/8.62                   => ( ( H2 @ B4 )
% 15.55/8.62                      = zero_zero_rat ) )
% 15.55/8.62               => ( ( ( groups3906332499630173760nt_rat @ G @ C4 )
% 15.55/8.62                    = ( groups3906332499630173760nt_rat @ H2 @ C4 ) )
% 15.55/8.62                 => ( ( groups3906332499630173760nt_rat @ G @ A3 )
% 15.55/8.62                    = ( groups3906332499630173760nt_rat @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7869_sum_Osame__carrierI,axiom,
% 15.55/8.62      ! [C4: set_complex,A3: set_complex,B5: set_complex,G: complex > rat,H2: complex > rat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ C4 )
% 15.55/8.62       => ( ( ord_le211207098394363844omplex @ A3 @ C4 )
% 15.55/8.62         => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 15.55/8.62           => ( ! [A5: complex] :
% 15.55/8.62                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A3 ) )
% 15.55/8.62                 => ( ( G @ A5 )
% 15.55/8.62                    = zero_zero_rat ) )
% 15.55/8.62             => ( ! [B4: complex] :
% 15.55/8.62                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 15.55/8.62                   => ( ( H2 @ B4 )
% 15.55/8.62                      = zero_zero_rat ) )
% 15.55/8.62               => ( ( ( groups5058264527183730370ex_rat @ G @ C4 )
% 15.55/8.62                    = ( groups5058264527183730370ex_rat @ H2 @ C4 ) )
% 15.55/8.62                 => ( ( groups5058264527183730370ex_rat @ G @ A3 )
% 15.55/8.62                    = ( groups5058264527183730370ex_rat @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7870_sum_Osame__carrierI,axiom,
% 15.55/8.62      ! [C4: set_Extended_enat,A3: set_Extended_enat,B5: set_Extended_enat,G: extended_enat > rat,H2: extended_enat > rat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ C4 )
% 15.55/8.62       => ( ( ord_le7203529160286727270d_enat @ A3 @ C4 )
% 15.55/8.62         => ( ( ord_le7203529160286727270d_enat @ B5 @ C4 )
% 15.55/8.62           => ( ! [A5: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ A5 @ ( minus_925952699566721837d_enat @ C4 @ A3 ) )
% 15.55/8.62                 => ( ( G @ A5 )
% 15.55/8.62                    = zero_zero_rat ) )
% 15.55/8.62             => ( ! [B4: extended_enat] :
% 15.55/8.62                    ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ C4 @ B5 ) )
% 15.55/8.62                   => ( ( H2 @ B4 )
% 15.55/8.62                      = zero_zero_rat ) )
% 15.55/8.62               => ( ( ( groups1392844769737527556at_rat @ G @ C4 )
% 15.55/8.62                    = ( groups1392844769737527556at_rat @ H2 @ C4 ) )
% 15.55/8.62                 => ( ( groups1392844769737527556at_rat @ G @ A3 )
% 15.55/8.62                    = ( groups1392844769737527556at_rat @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7871_sum_Osame__carrierI,axiom,
% 15.55/8.62      ! [C4: set_real,A3: set_real,B5: set_real,G: real > nat,H2: real > nat] :
% 15.55/8.62        ( ( finite_finite_real @ C4 )
% 15.55/8.62       => ( ( ord_less_eq_set_real @ A3 @ C4 )
% 15.55/8.62         => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 15.55/8.62           => ( ! [A5: real] :
% 15.55/8.62                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A3 ) )
% 15.55/8.62                 => ( ( G @ A5 )
% 15.55/8.62                    = zero_zero_nat ) )
% 15.55/8.62             => ( ! [B4: real] :
% 15.55/8.62                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 15.55/8.62                   => ( ( H2 @ B4 )
% 15.55/8.62                      = zero_zero_nat ) )
% 15.55/8.62               => ( ( ( groups1935376822645274424al_nat @ G @ C4 )
% 15.55/8.62                    = ( groups1935376822645274424al_nat @ H2 @ C4 ) )
% 15.55/8.62                 => ( ( groups1935376822645274424al_nat @ G @ A3 )
% 15.55/8.62                    = ( groups1935376822645274424al_nat @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7872_sum_Osame__carrierI,axiom,
% 15.55/8.62      ! [C4: set_int,A3: set_int,B5: set_int,G: int > nat,H2: int > nat] :
% 15.55/8.62        ( ( finite_finite_int @ C4 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ A3 @ C4 )
% 15.55/8.62         => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 15.55/8.62           => ( ! [A5: int] :
% 15.55/8.62                  ( ( member_int @ A5 @ ( minus_minus_set_int @ C4 @ A3 ) )
% 15.55/8.62                 => ( ( G @ A5 )
% 15.55/8.62                    = zero_zero_nat ) )
% 15.55/8.62             => ( ! [B4: int] :
% 15.55/8.62                    ( ( member_int @ B4 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 15.55/8.62                   => ( ( H2 @ B4 )
% 15.55/8.62                      = zero_zero_nat ) )
% 15.55/8.62               => ( ( ( groups4541462559716669496nt_nat @ G @ C4 )
% 15.55/8.62                    = ( groups4541462559716669496nt_nat @ H2 @ C4 ) )
% 15.55/8.62                 => ( ( groups4541462559716669496nt_nat @ G @ A3 )
% 15.55/8.62                    = ( groups4541462559716669496nt_nat @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7873_sum_Osame__carrier,axiom,
% 15.55/8.62      ! [C4: set_real,A3: set_real,B5: set_real,G: real > real,H2: real > real] :
% 15.55/8.62        ( ( finite_finite_real @ C4 )
% 15.55/8.62       => ( ( ord_less_eq_set_real @ A3 @ C4 )
% 15.55/8.62         => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 15.55/8.62           => ( ! [A5: real] :
% 15.55/8.62                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A3 ) )
% 15.55/8.62                 => ( ( G @ A5 )
% 15.55/8.62                    = zero_zero_real ) )
% 15.55/8.62             => ( ! [B4: real] :
% 15.55/8.62                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 15.55/8.62                   => ( ( H2 @ B4 )
% 15.55/8.62                      = zero_zero_real ) )
% 15.55/8.62               => ( ( ( groups8097168146408367636l_real @ G @ A3 )
% 15.55/8.62                    = ( groups8097168146408367636l_real @ H2 @ B5 ) )
% 15.55/8.62                  = ( ( groups8097168146408367636l_real @ G @ C4 )
% 15.55/8.62                    = ( groups8097168146408367636l_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7874_sum_Osame__carrier,axiom,
% 15.55/8.62      ! [C4: set_int,A3: set_int,B5: set_int,G: int > real,H2: int > real] :
% 15.55/8.62        ( ( finite_finite_int @ C4 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ A3 @ C4 )
% 15.55/8.62         => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 15.55/8.62           => ( ! [A5: int] :
% 15.55/8.62                  ( ( member_int @ A5 @ ( minus_minus_set_int @ C4 @ A3 ) )
% 15.55/8.62                 => ( ( G @ A5 )
% 15.55/8.62                    = zero_zero_real ) )
% 15.55/8.62             => ( ! [B4: int] :
% 15.55/8.62                    ( ( member_int @ B4 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 15.55/8.62                   => ( ( H2 @ B4 )
% 15.55/8.62                      = zero_zero_real ) )
% 15.55/8.62               => ( ( ( groups8778361861064173332t_real @ G @ A3 )
% 15.55/8.62                    = ( groups8778361861064173332t_real @ H2 @ B5 ) )
% 15.55/8.62                  = ( ( groups8778361861064173332t_real @ G @ C4 )
% 15.55/8.62                    = ( groups8778361861064173332t_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7875_sum_Osame__carrier,axiom,
% 15.55/8.62      ! [C4: set_complex,A3: set_complex,B5: set_complex,G: complex > real,H2: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ C4 )
% 15.55/8.62       => ( ( ord_le211207098394363844omplex @ A3 @ C4 )
% 15.55/8.62         => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 15.55/8.62           => ( ! [A5: complex] :
% 15.55/8.62                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A3 ) )
% 15.55/8.62                 => ( ( G @ A5 )
% 15.55/8.62                    = zero_zero_real ) )
% 15.55/8.62             => ( ! [B4: complex] :
% 15.55/8.62                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 15.55/8.62                   => ( ( H2 @ B4 )
% 15.55/8.62                      = zero_zero_real ) )
% 15.55/8.62               => ( ( ( groups5808333547571424918x_real @ G @ A3 )
% 15.55/8.62                    = ( groups5808333547571424918x_real @ H2 @ B5 ) )
% 15.55/8.62                  = ( ( groups5808333547571424918x_real @ G @ C4 )
% 15.55/8.62                    = ( groups5808333547571424918x_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7876_sum_Osame__carrier,axiom,
% 15.55/8.62      ! [C4: set_Extended_enat,A3: set_Extended_enat,B5: set_Extended_enat,G: extended_enat > real,H2: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ C4 )
% 15.55/8.62       => ( ( ord_le7203529160286727270d_enat @ A3 @ C4 )
% 15.55/8.62         => ( ( ord_le7203529160286727270d_enat @ B5 @ C4 )
% 15.55/8.62           => ( ! [A5: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ A5 @ ( minus_925952699566721837d_enat @ C4 @ A3 ) )
% 15.55/8.62                 => ( ( G @ A5 )
% 15.55/8.62                    = zero_zero_real ) )
% 15.55/8.62             => ( ! [B4: extended_enat] :
% 15.55/8.62                    ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ C4 @ B5 ) )
% 15.55/8.62                   => ( ( H2 @ B4 )
% 15.55/8.62                      = zero_zero_real ) )
% 15.55/8.62               => ( ( ( groups4148127829035722712t_real @ G @ A3 )
% 15.55/8.62                    = ( groups4148127829035722712t_real @ H2 @ B5 ) )
% 15.55/8.62                  = ( ( groups4148127829035722712t_real @ G @ C4 )
% 15.55/8.62                    = ( groups4148127829035722712t_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7877_sum_Osame__carrier,axiom,
% 15.55/8.62      ! [C4: set_real,A3: set_real,B5: set_real,G: real > rat,H2: real > rat] :
% 15.55/8.62        ( ( finite_finite_real @ C4 )
% 15.55/8.62       => ( ( ord_less_eq_set_real @ A3 @ C4 )
% 15.55/8.62         => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 15.55/8.62           => ( ! [A5: real] :
% 15.55/8.62                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A3 ) )
% 15.55/8.62                 => ( ( G @ A5 )
% 15.55/8.62                    = zero_zero_rat ) )
% 15.55/8.62             => ( ! [B4: real] :
% 15.55/8.62                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 15.55/8.62                   => ( ( H2 @ B4 )
% 15.55/8.62                      = zero_zero_rat ) )
% 15.55/8.62               => ( ( ( groups1300246762558778688al_rat @ G @ A3 )
% 15.55/8.62                    = ( groups1300246762558778688al_rat @ H2 @ B5 ) )
% 15.55/8.62                  = ( ( groups1300246762558778688al_rat @ G @ C4 )
% 15.55/8.62                    = ( groups1300246762558778688al_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7878_sum_Osame__carrier,axiom,
% 15.55/8.62      ! [C4: set_int,A3: set_int,B5: set_int,G: int > rat,H2: int > rat] :
% 15.55/8.62        ( ( finite_finite_int @ C4 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ A3 @ C4 )
% 15.55/8.62         => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 15.55/8.62           => ( ! [A5: int] :
% 15.55/8.62                  ( ( member_int @ A5 @ ( minus_minus_set_int @ C4 @ A3 ) )
% 15.55/8.62                 => ( ( G @ A5 )
% 15.55/8.62                    = zero_zero_rat ) )
% 15.55/8.62             => ( ! [B4: int] :
% 15.55/8.62                    ( ( member_int @ B4 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 15.55/8.62                   => ( ( H2 @ B4 )
% 15.55/8.62                      = zero_zero_rat ) )
% 15.55/8.62               => ( ( ( groups3906332499630173760nt_rat @ G @ A3 )
% 15.55/8.62                    = ( groups3906332499630173760nt_rat @ H2 @ B5 ) )
% 15.55/8.62                  = ( ( groups3906332499630173760nt_rat @ G @ C4 )
% 15.55/8.62                    = ( groups3906332499630173760nt_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7879_sum_Osame__carrier,axiom,
% 15.55/8.62      ! [C4: set_complex,A3: set_complex,B5: set_complex,G: complex > rat,H2: complex > rat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ C4 )
% 15.55/8.62       => ( ( ord_le211207098394363844omplex @ A3 @ C4 )
% 15.55/8.62         => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 15.55/8.62           => ( ! [A5: complex] :
% 15.55/8.62                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A3 ) )
% 15.55/8.62                 => ( ( G @ A5 )
% 15.55/8.62                    = zero_zero_rat ) )
% 15.55/8.62             => ( ! [B4: complex] :
% 15.55/8.62                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 15.55/8.62                   => ( ( H2 @ B4 )
% 15.55/8.62                      = zero_zero_rat ) )
% 15.55/8.62               => ( ( ( groups5058264527183730370ex_rat @ G @ A3 )
% 15.55/8.62                    = ( groups5058264527183730370ex_rat @ H2 @ B5 ) )
% 15.55/8.62                  = ( ( groups5058264527183730370ex_rat @ G @ C4 )
% 15.55/8.62                    = ( groups5058264527183730370ex_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7880_sum_Osame__carrier,axiom,
% 15.55/8.62      ! [C4: set_Extended_enat,A3: set_Extended_enat,B5: set_Extended_enat,G: extended_enat > rat,H2: extended_enat > rat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ C4 )
% 15.55/8.62       => ( ( ord_le7203529160286727270d_enat @ A3 @ C4 )
% 15.55/8.62         => ( ( ord_le7203529160286727270d_enat @ B5 @ C4 )
% 15.55/8.62           => ( ! [A5: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ A5 @ ( minus_925952699566721837d_enat @ C4 @ A3 ) )
% 15.55/8.62                 => ( ( G @ A5 )
% 15.55/8.62                    = zero_zero_rat ) )
% 15.55/8.62             => ( ! [B4: extended_enat] :
% 15.55/8.62                    ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ C4 @ B5 ) )
% 15.55/8.62                   => ( ( H2 @ B4 )
% 15.55/8.62                      = zero_zero_rat ) )
% 15.55/8.62               => ( ( ( groups1392844769737527556at_rat @ G @ A3 )
% 15.55/8.62                    = ( groups1392844769737527556at_rat @ H2 @ B5 ) )
% 15.55/8.62                  = ( ( groups1392844769737527556at_rat @ G @ C4 )
% 15.55/8.62                    = ( groups1392844769737527556at_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7881_sum_Osame__carrier,axiom,
% 15.55/8.62      ! [C4: set_real,A3: set_real,B5: set_real,G: real > nat,H2: real > nat] :
% 15.55/8.62        ( ( finite_finite_real @ C4 )
% 15.55/8.62       => ( ( ord_less_eq_set_real @ A3 @ C4 )
% 15.55/8.62         => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 15.55/8.62           => ( ! [A5: real] :
% 15.55/8.62                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A3 ) )
% 15.55/8.62                 => ( ( G @ A5 )
% 15.55/8.62                    = zero_zero_nat ) )
% 15.55/8.62             => ( ! [B4: real] :
% 15.55/8.62                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 15.55/8.62                   => ( ( H2 @ B4 )
% 15.55/8.62                      = zero_zero_nat ) )
% 15.55/8.62               => ( ( ( groups1935376822645274424al_nat @ G @ A3 )
% 15.55/8.62                    = ( groups1935376822645274424al_nat @ H2 @ B5 ) )
% 15.55/8.62                  = ( ( groups1935376822645274424al_nat @ G @ C4 )
% 15.55/8.62                    = ( groups1935376822645274424al_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7882_sum_Osame__carrier,axiom,
% 15.55/8.62      ! [C4: set_int,A3: set_int,B5: set_int,G: int > nat,H2: int > nat] :
% 15.55/8.62        ( ( finite_finite_int @ C4 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ A3 @ C4 )
% 15.55/8.62         => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 15.55/8.62           => ( ! [A5: int] :
% 15.55/8.62                  ( ( member_int @ A5 @ ( minus_minus_set_int @ C4 @ A3 ) )
% 15.55/8.62                 => ( ( G @ A5 )
% 15.55/8.62                    = zero_zero_nat ) )
% 15.55/8.62             => ( ! [B4: int] :
% 15.55/8.62                    ( ( member_int @ B4 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 15.55/8.62                   => ( ( H2 @ B4 )
% 15.55/8.62                      = zero_zero_nat ) )
% 15.55/8.62               => ( ( ( groups4541462559716669496nt_nat @ G @ A3 )
% 15.55/8.62                    = ( groups4541462559716669496nt_nat @ H2 @ B5 ) )
% 15.55/8.62                  = ( ( groups4541462559716669496nt_nat @ G @ C4 )
% 15.55/8.62                    = ( groups4541462559716669496nt_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7883_finite__M__bounded__by__nat,axiom,
% 15.55/8.62      ! [P: nat > $o,I: nat] :
% 15.55/8.62        ( finite_finite_nat
% 15.55/8.62        @ ( collect_nat
% 15.55/8.62          @ ^ [K3: nat] :
% 15.55/8.62              ( ( P @ K3 )
% 15.55/8.62              & ( ord_less_nat @ K3 @ I ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7884_finite__less__ub,axiom,
% 15.55/8.62      ! [F: nat > nat,U: nat] :
% 15.55/8.62        ( ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( F @ N2 ) )
% 15.55/8.62       => ( finite_finite_nat
% 15.55/8.62          @ ( collect_nat
% 15.55/8.62            @ ^ [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ U ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7885_sum__mono2,axiom,
% 15.55/8.62      ! [B5: set_real,A3: set_real,F: real > real] :
% 15.55/8.62        ( ( finite_finite_real @ B5 )
% 15.55/8.62       => ( ( ord_less_eq_set_real @ A3 @ B5 )
% 15.55/8.62         => ( ! [B4: real] :
% 15.55/8.62                ( ( member_real @ B4 @ ( minus_minus_set_real @ B5 @ A3 ) )
% 15.55/8.62               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B4 ) ) )
% 15.55/8.62           => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A3 ) @ ( groups8097168146408367636l_real @ F @ B5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7886_sum__mono2,axiom,
% 15.55/8.62      ! [B5: set_int,A3: set_int,F: int > real] :
% 15.55/8.62        ( ( finite_finite_int @ B5 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ A3 @ B5 )
% 15.55/8.62         => ( ! [B4: int] :
% 15.55/8.62                ( ( member_int @ B4 @ ( minus_minus_set_int @ B5 @ A3 ) )
% 15.55/8.62               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B4 ) ) )
% 15.55/8.62           => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A3 ) @ ( groups8778361861064173332t_real @ F @ B5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7887_sum__mono2,axiom,
% 15.55/8.62      ! [B5: set_complex,A3: set_complex,F: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ B5 )
% 15.55/8.62       => ( ( ord_le211207098394363844omplex @ A3 @ B5 )
% 15.55/8.62         => ( ! [B4: complex] :
% 15.55/8.62                ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B5 @ A3 ) )
% 15.55/8.62               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B4 ) ) )
% 15.55/8.62           => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A3 ) @ ( groups5808333547571424918x_real @ F @ B5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7888_sum__mono2,axiom,
% 15.55/8.62      ! [B5: set_Extended_enat,A3: set_Extended_enat,F: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ B5 )
% 15.55/8.62       => ( ( ord_le7203529160286727270d_enat @ A3 @ B5 )
% 15.55/8.62         => ( ! [B4: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ B5 @ A3 ) )
% 15.55/8.62               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B4 ) ) )
% 15.55/8.62           => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ A3 ) @ ( groups4148127829035722712t_real @ F @ B5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7889_sum__mono2,axiom,
% 15.55/8.62      ! [B5: set_real,A3: set_real,F: real > rat] :
% 15.55/8.62        ( ( finite_finite_real @ B5 )
% 15.55/8.62       => ( ( ord_less_eq_set_real @ A3 @ B5 )
% 15.55/8.62         => ( ! [B4: real] :
% 15.55/8.62                ( ( member_real @ B4 @ ( minus_minus_set_real @ B5 @ A3 ) )
% 15.55/8.62               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B4 ) ) )
% 15.55/8.62           => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A3 ) @ ( groups1300246762558778688al_rat @ F @ B5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7890_sum__mono2,axiom,
% 15.55/8.62      ! [B5: set_int,A3: set_int,F: int > rat] :
% 15.55/8.62        ( ( finite_finite_int @ B5 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ A3 @ B5 )
% 15.55/8.62         => ( ! [B4: int] :
% 15.55/8.62                ( ( member_int @ B4 @ ( minus_minus_set_int @ B5 @ A3 ) )
% 15.55/8.62               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B4 ) ) )
% 15.55/8.62           => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ ( groups3906332499630173760nt_rat @ F @ B5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7891_sum__mono2,axiom,
% 15.55/8.62      ! [B5: set_complex,A3: set_complex,F: complex > rat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ B5 )
% 15.55/8.62       => ( ( ord_le211207098394363844omplex @ A3 @ B5 )
% 15.55/8.62         => ( ! [B4: complex] :
% 15.55/8.62                ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B5 @ A3 ) )
% 15.55/8.62               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B4 ) ) )
% 15.55/8.62           => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A3 ) @ ( groups5058264527183730370ex_rat @ F @ B5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7892_sum__mono2,axiom,
% 15.55/8.62      ! [B5: set_Extended_enat,A3: set_Extended_enat,F: extended_enat > rat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ B5 )
% 15.55/8.62       => ( ( ord_le7203529160286727270d_enat @ A3 @ B5 )
% 15.55/8.62         => ( ! [B4: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ B5 @ A3 ) )
% 15.55/8.62               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B4 ) ) )
% 15.55/8.62           => ( ord_less_eq_rat @ ( groups1392844769737527556at_rat @ F @ A3 ) @ ( groups1392844769737527556at_rat @ F @ B5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7893_sum__mono2,axiom,
% 15.55/8.62      ! [B5: set_real,A3: set_real,F: real > nat] :
% 15.55/8.62        ( ( finite_finite_real @ B5 )
% 15.55/8.62       => ( ( ord_less_eq_set_real @ A3 @ B5 )
% 15.55/8.62         => ( ! [B4: real] :
% 15.55/8.62                ( ( member_real @ B4 @ ( minus_minus_set_real @ B5 @ A3 ) )
% 15.55/8.62               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B4 ) ) )
% 15.55/8.62           => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A3 ) @ ( groups1935376822645274424al_nat @ F @ B5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7894_sum__mono2,axiom,
% 15.55/8.62      ! [B5: set_int,A3: set_int,F: int > nat] :
% 15.55/8.62        ( ( finite_finite_int @ B5 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ A3 @ B5 )
% 15.55/8.62         => ( ! [B4: int] :
% 15.55/8.62                ( ( member_int @ B4 @ ( minus_minus_set_int @ B5 @ A3 ) )
% 15.55/8.62               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B4 ) ) )
% 15.55/8.62           => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ ( groups4541462559716669496nt_nat @ F @ B5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7895_sum__nonneg,axiom,
% 15.55/8.62      ! [A3: set_real,F: real > real] :
% 15.55/8.62        ( ! [X4: real] :
% 15.55/8.62            ( ( member_real @ X4 @ A3 )
% 15.55/8.62           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 15.55/8.62       => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7896_sum__nonneg,axiom,
% 15.55/8.62      ! [A3: set_int,F: int > real] :
% 15.55/8.62        ( ! [X4: int] :
% 15.55/8.62            ( ( member_int @ X4 @ A3 )
% 15.55/8.62           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 15.55/8.62       => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7897_sum__nonneg,axiom,
% 15.55/8.62      ! [A3: set_real,F: real > rat] :
% 15.55/8.62        ( ! [X4: real] :
% 15.55/8.62            ( ( member_real @ X4 @ A3 )
% 15.55/8.62           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 15.55/8.62       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7898_sum__nonneg,axiom,
% 15.55/8.62      ! [A3: set_nat,F: nat > rat] :
% 15.55/8.62        ( ! [X4: nat] :
% 15.55/8.62            ( ( member_nat @ X4 @ A3 )
% 15.55/8.62           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 15.55/8.62       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7899_sum__nonneg,axiom,
% 15.55/8.62      ! [A3: set_int,F: int > rat] :
% 15.55/8.62        ( ! [X4: int] :
% 15.55/8.62            ( ( member_int @ X4 @ A3 )
% 15.55/8.62           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 15.55/8.62       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7900_sum__nonneg,axiom,
% 15.55/8.62      ! [A3: set_real,F: real > nat] :
% 15.55/8.62        ( ! [X4: real] :
% 15.55/8.62            ( ( member_real @ X4 @ A3 )
% 15.55/8.62           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 15.55/8.62       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7901_sum__nonneg,axiom,
% 15.55/8.62      ! [A3: set_int,F: int > nat] :
% 15.55/8.62        ( ! [X4: int] :
% 15.55/8.62            ( ( member_int @ X4 @ A3 )
% 15.55/8.62           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 15.55/8.62       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7902_sum__nonneg,axiom,
% 15.55/8.62      ! [A3: set_real,F: real > int] :
% 15.55/8.62        ( ! [X4: real] :
% 15.55/8.62            ( ( member_real @ X4 @ A3 )
% 15.55/8.62           => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 15.55/8.62       => ( ord_less_eq_int @ zero_zero_int @ ( groups1932886352136224148al_int @ F @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7903_sum__nonneg,axiom,
% 15.55/8.62      ! [A3: set_nat,F: nat > int] :
% 15.55/8.62        ( ! [X4: nat] :
% 15.55/8.62            ( ( member_nat @ X4 @ A3 )
% 15.55/8.62           => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 15.55/8.62       => ( ord_less_eq_int @ zero_zero_int @ ( groups3539618377306564664at_int @ F @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7904_sum__nonneg,axiom,
% 15.55/8.62      ! [A3: set_nat,F: nat > nat] :
% 15.55/8.62        ( ! [X4: nat] :
% 15.55/8.62            ( ( member_nat @ X4 @ A3 )
% 15.55/8.62           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 15.55/8.62       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7905_sum__nonpos,axiom,
% 15.55/8.62      ! [A3: set_real,F: real > real] :
% 15.55/8.62        ( ! [X4: real] :
% 15.55/8.62            ( ( member_real @ X4 @ A3 )
% 15.55/8.62           => ( ord_less_eq_real @ ( F @ X4 ) @ zero_zero_real ) )
% 15.55/8.62       => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A3 ) @ zero_zero_real ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7906_sum__nonpos,axiom,
% 15.55/8.62      ! [A3: set_int,F: int > real] :
% 15.55/8.62        ( ! [X4: int] :
% 15.55/8.62            ( ( member_int @ X4 @ A3 )
% 15.55/8.62           => ( ord_less_eq_real @ ( F @ X4 ) @ zero_zero_real ) )
% 15.55/8.62       => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A3 ) @ zero_zero_real ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7907_sum__nonpos,axiom,
% 15.55/8.62      ! [A3: set_real,F: real > rat] :
% 15.55/8.62        ( ! [X4: real] :
% 15.55/8.62            ( ( member_real @ X4 @ A3 )
% 15.55/8.62           => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 15.55/8.62       => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A3 ) @ zero_zero_rat ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7908_sum__nonpos,axiom,
% 15.55/8.62      ! [A3: set_nat,F: nat > rat] :
% 15.55/8.62        ( ! [X4: nat] :
% 15.55/8.62            ( ( member_nat @ X4 @ A3 )
% 15.55/8.62           => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 15.55/8.62       => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ zero_zero_rat ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7909_sum__nonpos,axiom,
% 15.55/8.62      ! [A3: set_int,F: int > rat] :
% 15.55/8.62        ( ! [X4: int] :
% 15.55/8.62            ( ( member_int @ X4 @ A3 )
% 15.55/8.62           => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 15.55/8.62       => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ zero_zero_rat ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7910_sum__nonpos,axiom,
% 15.55/8.62      ! [A3: set_real,F: real > nat] :
% 15.55/8.62        ( ! [X4: real] :
% 15.55/8.62            ( ( member_real @ X4 @ A3 )
% 15.55/8.62           => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 15.55/8.62       => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A3 ) @ zero_zero_nat ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7911_sum__nonpos,axiom,
% 15.55/8.62      ! [A3: set_int,F: int > nat] :
% 15.55/8.62        ( ! [X4: int] :
% 15.55/8.62            ( ( member_int @ X4 @ A3 )
% 15.55/8.62           => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 15.55/8.62       => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ zero_zero_nat ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7912_sum__nonpos,axiom,
% 15.55/8.62      ! [A3: set_real,F: real > int] :
% 15.55/8.62        ( ! [X4: real] :
% 15.55/8.62            ( ( member_real @ X4 @ A3 )
% 15.55/8.62           => ( ord_less_eq_int @ ( F @ X4 ) @ zero_zero_int ) )
% 15.55/8.62       => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ A3 ) @ zero_zero_int ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7913_sum__nonpos,axiom,
% 15.55/8.62      ! [A3: set_nat,F: nat > int] :
% 15.55/8.62        ( ! [X4: nat] :
% 15.55/8.62            ( ( member_nat @ X4 @ A3 )
% 15.55/8.62           => ( ord_less_eq_int @ ( F @ X4 ) @ zero_zero_int ) )
% 15.55/8.62       => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ A3 ) @ zero_zero_int ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7914_sum__nonpos,axiom,
% 15.55/8.62      ! [A3: set_nat,F: nat > nat] :
% 15.55/8.62        ( ! [X4: nat] :
% 15.55/8.62            ( ( member_nat @ X4 @ A3 )
% 15.55/8.62           => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 15.55/8.62       => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) @ zero_zero_nat ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7915_sum__le__suminf,axiom,
% 15.55/8.62      ! [F: nat > int,I5: set_nat] :
% 15.55/8.62        ( ( summable_int @ F )
% 15.55/8.62       => ( ( finite_finite_nat @ I5 )
% 15.55/8.62         => ( ! [N2: nat] :
% 15.55/8.62                ( ( member_nat @ N2 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 15.55/8.62               => ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) ) )
% 15.55/8.62           => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ I5 ) @ ( suminf_int @ F ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7916_sum__le__suminf,axiom,
% 15.55/8.62      ! [F: nat > nat,I5: set_nat] :
% 15.55/8.62        ( ( summable_nat @ F )
% 15.55/8.62       => ( ( finite_finite_nat @ I5 )
% 15.55/8.62         => ( ! [N2: nat] :
% 15.55/8.62                ( ( member_nat @ N2 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 15.55/8.62               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) ) )
% 15.55/8.62           => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ I5 ) @ ( suminf_nat @ F ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7917_sum__le__suminf,axiom,
% 15.55/8.62      ! [F: nat > real,I5: set_nat] :
% 15.55/8.62        ( ( summable_real @ F )
% 15.55/8.62       => ( ( finite_finite_nat @ I5 )
% 15.55/8.62         => ( ! [N2: nat] :
% 15.55/8.62                ( ( member_nat @ N2 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 15.55/8.62               => ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) ) )
% 15.55/8.62           => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ I5 ) @ ( suminf_real @ F ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7918_sum__cong__Suc,axiom,
% 15.55/8.62      ! [A3: set_nat,F: nat > nat,G: nat > nat] :
% 15.55/8.62        ( ~ ( member_nat @ zero_zero_nat @ A3 )
% 15.55/8.62       => ( ! [X4: nat] :
% 15.55/8.62              ( ( member_nat @ ( suc @ X4 ) @ A3 )
% 15.55/8.62             => ( ( F @ ( suc @ X4 ) )
% 15.55/8.62                = ( G @ ( suc @ X4 ) ) ) )
% 15.55/8.62         => ( ( groups3542108847815614940at_nat @ F @ A3 )
% 15.55/8.62            = ( groups3542108847815614940at_nat @ G @ A3 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7919_sum__cong__Suc,axiom,
% 15.55/8.62      ! [A3: set_nat,F: nat > real,G: nat > real] :
% 15.55/8.62        ( ~ ( member_nat @ zero_zero_nat @ A3 )
% 15.55/8.62       => ( ! [X4: nat] :
% 15.55/8.62              ( ( member_nat @ ( suc @ X4 ) @ A3 )
% 15.55/8.62             => ( ( F @ ( suc @ X4 ) )
% 15.55/8.62                = ( G @ ( suc @ X4 ) ) ) )
% 15.55/8.62         => ( ( groups6591440286371151544t_real @ F @ A3 )
% 15.55/8.62            = ( groups6591440286371151544t_real @ G @ A3 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7920_Complex__eq__1,axiom,
% 15.55/8.62      ! [A: real,B: real] :
% 15.55/8.62        ( ( ( complex2 @ A @ B )
% 15.55/8.62          = one_one_complex )
% 15.55/8.62        = ( ( A = one_one_real )
% 15.55/8.62          & ( B = zero_zero_real ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7921_one__complex_Ocode,axiom,
% 15.55/8.62      ( one_one_complex
% 15.55/8.62      = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7922_Complex__eq__numeral,axiom,
% 15.55/8.62      ! [A: real,B: real,W: num] :
% 15.55/8.62        ( ( ( complex2 @ A @ B )
% 15.55/8.62          = ( numera6690914467698888265omplex @ W ) )
% 15.55/8.62        = ( ( A
% 15.55/8.62            = ( numeral_numeral_real @ W ) )
% 15.55/8.62          & ( B = zero_zero_real ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7923_infinite__growing,axiom,
% 15.55/8.62      ! [X9: set_Extended_enat] :
% 15.55/8.62        ( ( X9 != bot_bo7653980558646680370d_enat )
% 15.55/8.62       => ( ! [X4: extended_enat] :
% 15.55/8.62              ( ( member_Extended_enat @ X4 @ X9 )
% 15.55/8.62             => ? [Xa2: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ Xa2 @ X9 )
% 15.55/8.62                  & ( ord_le72135733267957522d_enat @ X4 @ Xa2 ) ) )
% 15.55/8.62         => ~ ( finite4001608067531595151d_enat @ X9 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7924_infinite__growing,axiom,
% 15.55/8.62      ! [X9: set_real] :
% 15.55/8.62        ( ( X9 != bot_bot_set_real )
% 15.55/8.62       => ( ! [X4: real] :
% 15.55/8.62              ( ( member_real @ X4 @ X9 )
% 15.55/8.62             => ? [Xa2: real] :
% 15.55/8.62                  ( ( member_real @ Xa2 @ X9 )
% 15.55/8.62                  & ( ord_less_real @ X4 @ Xa2 ) ) )
% 15.55/8.62         => ~ ( finite_finite_real @ X9 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7925_infinite__growing,axiom,
% 15.55/8.62      ! [X9: set_rat] :
% 15.55/8.62        ( ( X9 != bot_bot_set_rat )
% 15.55/8.62       => ( ! [X4: rat] :
% 15.55/8.62              ( ( member_rat @ X4 @ X9 )
% 15.55/8.62             => ? [Xa2: rat] :
% 15.55/8.62                  ( ( member_rat @ Xa2 @ X9 )
% 15.55/8.62                  & ( ord_less_rat @ X4 @ Xa2 ) ) )
% 15.55/8.62         => ~ ( finite_finite_rat @ X9 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7926_infinite__growing,axiom,
% 15.55/8.62      ! [X9: set_num] :
% 15.55/8.62        ( ( X9 != bot_bot_set_num )
% 15.55/8.62       => ( ! [X4: num] :
% 15.55/8.62              ( ( member_num @ X4 @ X9 )
% 15.55/8.62             => ? [Xa2: num] :
% 15.55/8.62                  ( ( member_num @ Xa2 @ X9 )
% 15.55/8.62                  & ( ord_less_num @ X4 @ Xa2 ) ) )
% 15.55/8.62         => ~ ( finite_finite_num @ X9 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7927_infinite__growing,axiom,
% 15.55/8.62      ! [X9: set_nat] :
% 15.55/8.62        ( ( X9 != bot_bot_set_nat )
% 15.55/8.62       => ( ! [X4: nat] :
% 15.55/8.62              ( ( member_nat @ X4 @ X9 )
% 15.55/8.62             => ? [Xa2: nat] :
% 15.55/8.62                  ( ( member_nat @ Xa2 @ X9 )
% 15.55/8.62                  & ( ord_less_nat @ X4 @ Xa2 ) ) )
% 15.55/8.62         => ~ ( finite_finite_nat @ X9 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7928_infinite__growing,axiom,
% 15.55/8.62      ! [X9: set_int] :
% 15.55/8.62        ( ( X9 != bot_bot_set_int )
% 15.55/8.62       => ( ! [X4: int] :
% 15.55/8.62              ( ( member_int @ X4 @ X9 )
% 15.55/8.62             => ? [Xa2: int] :
% 15.55/8.62                  ( ( member_int @ Xa2 @ X9 )
% 15.55/8.62                  & ( ord_less_int @ X4 @ Xa2 ) ) )
% 15.55/8.62         => ~ ( finite_finite_int @ X9 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7929_ex__min__if__finite,axiom,
% 15.55/8.62      ! [S2: set_Extended_enat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ S2 )
% 15.55/8.62       => ( ( S2 != bot_bo7653980558646680370d_enat )
% 15.55/8.62         => ? [X4: extended_enat] :
% 15.55/8.62              ( ( member_Extended_enat @ X4 @ S2 )
% 15.55/8.62              & ~ ? [Xa2: extended_enat] :
% 15.55/8.62                    ( ( member_Extended_enat @ Xa2 @ S2 )
% 15.55/8.62                    & ( ord_le72135733267957522d_enat @ Xa2 @ X4 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7930_ex__min__if__finite,axiom,
% 15.55/8.62      ! [S2: set_real] :
% 15.55/8.62        ( ( finite_finite_real @ S2 )
% 15.55/8.62       => ( ( S2 != bot_bot_set_real )
% 15.55/8.62         => ? [X4: real] :
% 15.55/8.62              ( ( member_real @ X4 @ S2 )
% 15.55/8.62              & ~ ? [Xa2: real] :
% 15.55/8.62                    ( ( member_real @ Xa2 @ S2 )
% 15.55/8.62                    & ( ord_less_real @ Xa2 @ X4 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7931_ex__min__if__finite,axiom,
% 15.55/8.62      ! [S2: set_rat] :
% 15.55/8.62        ( ( finite_finite_rat @ S2 )
% 15.55/8.62       => ( ( S2 != bot_bot_set_rat )
% 15.55/8.62         => ? [X4: rat] :
% 15.55/8.62              ( ( member_rat @ X4 @ S2 )
% 15.55/8.62              & ~ ? [Xa2: rat] :
% 15.55/8.62                    ( ( member_rat @ Xa2 @ S2 )
% 15.55/8.62                    & ( ord_less_rat @ Xa2 @ X4 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7932_ex__min__if__finite,axiom,
% 15.55/8.62      ! [S2: set_num] :
% 15.55/8.62        ( ( finite_finite_num @ S2 )
% 15.55/8.62       => ( ( S2 != bot_bot_set_num )
% 15.55/8.62         => ? [X4: num] :
% 15.55/8.62              ( ( member_num @ X4 @ S2 )
% 15.55/8.62              & ~ ? [Xa2: num] :
% 15.55/8.62                    ( ( member_num @ Xa2 @ S2 )
% 15.55/8.62                    & ( ord_less_num @ Xa2 @ X4 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7933_ex__min__if__finite,axiom,
% 15.55/8.62      ! [S2: set_nat] :
% 15.55/8.62        ( ( finite_finite_nat @ S2 )
% 15.55/8.62       => ( ( S2 != bot_bot_set_nat )
% 15.55/8.62         => ? [X4: nat] :
% 15.55/8.62              ( ( member_nat @ X4 @ S2 )
% 15.55/8.62              & ~ ? [Xa2: nat] :
% 15.55/8.62                    ( ( member_nat @ Xa2 @ S2 )
% 15.55/8.62                    & ( ord_less_nat @ Xa2 @ X4 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7934_ex__min__if__finite,axiom,
% 15.55/8.62      ! [S2: set_int] :
% 15.55/8.62        ( ( finite_finite_int @ S2 )
% 15.55/8.62       => ( ( S2 != bot_bot_set_int )
% 15.55/8.62         => ? [X4: int] :
% 15.55/8.62              ( ( member_int @ X4 @ S2 )
% 15.55/8.62              & ~ ? [Xa2: int] :
% 15.55/8.62                    ( ( member_int @ Xa2 @ S2 )
% 15.55/8.62                    & ( ord_less_int @ Xa2 @ X4 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7935_prod__zero,axiom,
% 15.55/8.62      ! [A3: set_nat,F: nat > real] :
% 15.55/8.62        ( ( finite_finite_nat @ A3 )
% 15.55/8.62       => ( ? [X6: nat] :
% 15.55/8.62              ( ( member_nat @ X6 @ A3 )
% 15.55/8.62              & ( ( F @ X6 )
% 15.55/8.62                = zero_zero_real ) )
% 15.55/8.62         => ( ( groups129246275422532515t_real @ F @ A3 )
% 15.55/8.62            = zero_zero_real ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7936_prod__zero,axiom,
% 15.55/8.62      ! [A3: set_int,F: int > real] :
% 15.55/8.62        ( ( finite_finite_int @ A3 )
% 15.55/8.62       => ( ? [X6: int] :
% 15.55/8.62              ( ( member_int @ X6 @ A3 )
% 15.55/8.62              & ( ( F @ X6 )
% 15.55/8.62                = zero_zero_real ) )
% 15.55/8.62         => ( ( groups2316167850115554303t_real @ F @ A3 )
% 15.55/8.62            = zero_zero_real ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7937_prod__zero,axiom,
% 15.55/8.62      ! [A3: set_complex,F: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.62       => ( ? [X6: complex] :
% 15.55/8.62              ( ( member_complex @ X6 @ A3 )
% 15.55/8.62              & ( ( F @ X6 )
% 15.55/8.62                = zero_zero_real ) )
% 15.55/8.62         => ( ( groups766887009212190081x_real @ F @ A3 )
% 15.55/8.62            = zero_zero_real ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7938_prod__zero,axiom,
% 15.55/8.62      ! [A3: set_Extended_enat,F: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.62       => ( ? [X6: extended_enat] :
% 15.55/8.62              ( ( member_Extended_enat @ X6 @ A3 )
% 15.55/8.62              & ( ( F @ X6 )
% 15.55/8.62                = zero_zero_real ) )
% 15.55/8.62         => ( ( groups97031904164794029t_real @ F @ A3 )
% 15.55/8.62            = zero_zero_real ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7939_prod__zero,axiom,
% 15.55/8.62      ! [A3: set_nat,F: nat > rat] :
% 15.55/8.62        ( ( finite_finite_nat @ A3 )
% 15.55/8.62       => ( ? [X6: nat] :
% 15.55/8.62              ( ( member_nat @ X6 @ A3 )
% 15.55/8.62              & ( ( F @ X6 )
% 15.55/8.62                = zero_zero_rat ) )
% 15.55/8.62         => ( ( groups73079841787564623at_rat @ F @ A3 )
% 15.55/8.62            = zero_zero_rat ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7940_prod__zero,axiom,
% 15.55/8.62      ! [A3: set_int,F: int > rat] :
% 15.55/8.62        ( ( finite_finite_int @ A3 )
% 15.55/8.62       => ( ? [X6: int] :
% 15.55/8.62              ( ( member_int @ X6 @ A3 )
% 15.55/8.62              & ( ( F @ X6 )
% 15.55/8.62                = zero_zero_rat ) )
% 15.55/8.62         => ( ( groups1072433553688619179nt_rat @ F @ A3 )
% 15.55/8.62            = zero_zero_rat ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7941_prod__zero,axiom,
% 15.55/8.62      ! [A3: set_complex,F: complex > rat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.62       => ( ? [X6: complex] :
% 15.55/8.62              ( ( member_complex @ X6 @ A3 )
% 15.55/8.62              & ( ( F @ X6 )
% 15.55/8.62                = zero_zero_rat ) )
% 15.55/8.62         => ( ( groups225925009352817453ex_rat @ F @ A3 )
% 15.55/8.62            = zero_zero_rat ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7942_prod__zero,axiom,
% 15.55/8.62      ! [A3: set_Extended_enat,F: extended_enat > rat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.62       => ( ? [X6: extended_enat] :
% 15.55/8.62              ( ( member_Extended_enat @ X6 @ A3 )
% 15.55/8.62              & ( ( F @ X6 )
% 15.55/8.62                = zero_zero_rat ) )
% 15.55/8.62         => ( ( groups2245840878043517529at_rat @ F @ A3 )
% 15.55/8.62            = zero_zero_rat ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7943_prod__zero,axiom,
% 15.55/8.62      ! [A3: set_int,F: int > nat] :
% 15.55/8.62        ( ( finite_finite_int @ A3 )
% 15.55/8.62       => ( ? [X6: int] :
% 15.55/8.62              ( ( member_int @ X6 @ A3 )
% 15.55/8.62              & ( ( F @ X6 )
% 15.55/8.62                = zero_zero_nat ) )
% 15.55/8.62         => ( ( groups1707563613775114915nt_nat @ F @ A3 )
% 15.55/8.62            = zero_zero_nat ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7944_prod__zero,axiom,
% 15.55/8.62      ! [A3: set_complex,F: complex > nat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.62       => ( ? [X6: complex] :
% 15.55/8.62              ( ( member_complex @ X6 @ A3 )
% 15.55/8.62              & ( ( F @ X6 )
% 15.55/8.62                = zero_zero_nat ) )
% 15.55/8.62         => ( ( groups861055069439313189ex_nat @ F @ A3 )
% 15.55/8.62            = zero_zero_nat ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7945_infinite__Icc,axiom,
% 15.55/8.62      ! [A: rat,B: rat] :
% 15.55/8.62        ( ( ord_less_rat @ A @ B )
% 15.55/8.62       => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7946_infinite__Icc,axiom,
% 15.55/8.62      ! [A: real,B: real] :
% 15.55/8.62        ( ( ord_less_real @ A @ B )
% 15.55/8.62       => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7947_finite__lists__length__le,axiom,
% 15.55/8.62      ! [A3: set_complex,N: nat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.62       => ( finite8712137658972009173omplex
% 15.55/8.62          @ ( collect_list_complex
% 15.55/8.62            @ ^ [Xs: list_complex] :
% 15.55/8.62                ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A3 )
% 15.55/8.62                & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs ) @ N ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7948_finite__lists__length__le,axiom,
% 15.55/8.62      ! [A3: set_Pr1261947904930325089at_nat,N: nat] :
% 15.55/8.62        ( ( finite6177210948735845034at_nat @ A3 )
% 15.55/8.62       => ( finite500796754983035824at_nat
% 15.55/8.62          @ ( collec3343600615725829874at_nat
% 15.55/8.62            @ ^ [Xs: list_P6011104703257516679at_nat] :
% 15.55/8.62                ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs ) @ A3 )
% 15.55/8.62                & ( ord_less_eq_nat @ ( size_s5460976970255530739at_nat @ Xs ) @ N ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7949_finite__lists__length__le,axiom,
% 15.55/8.62      ! [A3: set_Extended_enat,N: nat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.62       => ( finite1862508098717546133d_enat
% 15.55/8.62          @ ( collec8433460942617342167d_enat
% 15.55/8.62            @ ^ [Xs: list_Extended_enat] :
% 15.55/8.62                ( ( ord_le7203529160286727270d_enat @ ( set_Extended_enat2 @ Xs ) @ A3 )
% 15.55/8.62                & ( ord_less_eq_nat @ ( size_s3941691890525107288d_enat @ Xs ) @ N ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7950_finite__lists__length__le,axiom,
% 15.55/8.62      ! [A3: set_VEBT_VEBT,N: nat] :
% 15.55/8.62        ( ( finite5795047828879050333T_VEBT @ A3 )
% 15.55/8.62       => ( finite3004134309566078307T_VEBT
% 15.55/8.62          @ ( collec5608196760682091941T_VEBT
% 15.55/8.62            @ ^ [Xs: list_VEBT_VEBT] :
% 15.55/8.62                ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A3 )
% 15.55/8.62                & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7951_finite__lists__length__le,axiom,
% 15.55/8.62      ! [A3: set_o,N: nat] :
% 15.55/8.62        ( ( finite_finite_o @ A3 )
% 15.55/8.62       => ( finite_finite_list_o
% 15.55/8.62          @ ( collect_list_o
% 15.55/8.62            @ ^ [Xs: list_o] :
% 15.55/8.62                ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A3 )
% 15.55/8.62                & ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7952_finite__lists__length__le,axiom,
% 15.55/8.62      ! [A3: set_int,N: nat] :
% 15.55/8.62        ( ( finite_finite_int @ A3 )
% 15.55/8.62       => ( finite3922522038869484883st_int
% 15.55/8.62          @ ( collect_list_int
% 15.55/8.62            @ ^ [Xs: list_int] :
% 15.55/8.62                ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A3 )
% 15.55/8.62                & ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7953_finite__lists__length__le,axiom,
% 15.55/8.62      ! [A3: set_nat,N: nat] :
% 15.55/8.62        ( ( finite_finite_nat @ A3 )
% 15.55/8.62       => ( finite8100373058378681591st_nat
% 15.55/8.62          @ ( collect_list_nat
% 15.55/8.62            @ ^ [Xs: list_nat] :
% 15.55/8.62                ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A3 )
% 15.55/8.62                & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7954_summable__finite,axiom,
% 15.55/8.62      ! [N4: set_nat,F: nat > real] :
% 15.55/8.62        ( ( finite_finite_nat @ N4 )
% 15.55/8.62       => ( ! [N2: nat] :
% 15.55/8.62              ( ~ ( member_nat @ N2 @ N4 )
% 15.55/8.62             => ( ( F @ N2 )
% 15.55/8.62                = zero_zero_real ) )
% 15.55/8.62         => ( summable_real @ F ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7955_summable__finite,axiom,
% 15.55/8.62      ! [N4: set_nat,F: nat > nat] :
% 15.55/8.62        ( ( finite_finite_nat @ N4 )
% 15.55/8.62       => ( ! [N2: nat] :
% 15.55/8.62              ( ~ ( member_nat @ N2 @ N4 )
% 15.55/8.62             => ( ( F @ N2 )
% 15.55/8.62                = zero_zero_nat ) )
% 15.55/8.62         => ( summable_nat @ F ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7956_summable__finite,axiom,
% 15.55/8.62      ! [N4: set_nat,F: nat > int] :
% 15.55/8.62        ( ( finite_finite_nat @ N4 )
% 15.55/8.62       => ( ! [N2: nat] :
% 15.55/8.62              ( ~ ( member_nat @ N2 @ N4 )
% 15.55/8.62             => ( ( F @ N2 )
% 15.55/8.62                = zero_zero_int ) )
% 15.55/8.62         => ( summable_int @ F ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7957_sum__strict__mono2,axiom,
% 15.55/8.62      ! [B5: set_real,A3: set_real,B: real,F: real > real] :
% 15.55/8.62        ( ( finite_finite_real @ B5 )
% 15.55/8.62       => ( ( ord_less_eq_set_real @ A3 @ B5 )
% 15.55/8.62         => ( ( member_real @ B @ ( minus_minus_set_real @ B5 @ A3 ) )
% 15.55/8.62           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 15.55/8.62             => ( ! [X4: real] :
% 15.55/8.62                    ( ( member_real @ X4 @ B5 )
% 15.55/8.62                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 15.55/8.62               => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A3 ) @ ( groups8097168146408367636l_real @ F @ B5 ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7958_sum__strict__mono2,axiom,
% 15.55/8.62      ! [B5: set_int,A3: set_int,B: int,F: int > real] :
% 15.55/8.62        ( ( finite_finite_int @ B5 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ A3 @ B5 )
% 15.55/8.62         => ( ( member_int @ B @ ( minus_minus_set_int @ B5 @ A3 ) )
% 15.55/8.62           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 15.55/8.62             => ( ! [X4: int] :
% 15.55/8.62                    ( ( member_int @ X4 @ B5 )
% 15.55/8.62                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 15.55/8.62               => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A3 ) @ ( groups8778361861064173332t_real @ F @ B5 ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7959_sum__strict__mono2,axiom,
% 15.55/8.62      ! [B5: set_complex,A3: set_complex,B: complex,F: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ B5 )
% 15.55/8.62       => ( ( ord_le211207098394363844omplex @ A3 @ B5 )
% 15.55/8.62         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B5 @ A3 ) )
% 15.55/8.62           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 15.55/8.62             => ( ! [X4: complex] :
% 15.55/8.62                    ( ( member_complex @ X4 @ B5 )
% 15.55/8.62                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 15.55/8.62               => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A3 ) @ ( groups5808333547571424918x_real @ F @ B5 ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7960_sum__strict__mono2,axiom,
% 15.55/8.62      ! [B5: set_Extended_enat,A3: set_Extended_enat,B: extended_enat,F: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ B5 )
% 15.55/8.62       => ( ( ord_le7203529160286727270d_enat @ A3 @ B5 )
% 15.55/8.62         => ( ( member_Extended_enat @ B @ ( minus_925952699566721837d_enat @ B5 @ A3 ) )
% 15.55/8.62           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 15.55/8.62             => ( ! [X4: extended_enat] :
% 15.55/8.62                    ( ( member_Extended_enat @ X4 @ B5 )
% 15.55/8.62                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 15.55/8.62               => ( ord_less_real @ ( groups4148127829035722712t_real @ F @ A3 ) @ ( groups4148127829035722712t_real @ F @ B5 ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7961_sum__strict__mono2,axiom,
% 15.55/8.62      ! [B5: set_real,A3: set_real,B: real,F: real > rat] :
% 15.55/8.62        ( ( finite_finite_real @ B5 )
% 15.55/8.62       => ( ( ord_less_eq_set_real @ A3 @ B5 )
% 15.55/8.62         => ( ( member_real @ B @ ( minus_minus_set_real @ B5 @ A3 ) )
% 15.55/8.62           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 15.55/8.62             => ( ! [X4: real] :
% 15.55/8.62                    ( ( member_real @ X4 @ B5 )
% 15.55/8.62                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 15.55/8.62               => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A3 ) @ ( groups1300246762558778688al_rat @ F @ B5 ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7962_sum__strict__mono2,axiom,
% 15.55/8.62      ! [B5: set_int,A3: set_int,B: int,F: int > rat] :
% 15.55/8.62        ( ( finite_finite_int @ B5 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ A3 @ B5 )
% 15.55/8.62         => ( ( member_int @ B @ ( minus_minus_set_int @ B5 @ A3 ) )
% 15.55/8.62           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 15.55/8.62             => ( ! [X4: int] :
% 15.55/8.62                    ( ( member_int @ X4 @ B5 )
% 15.55/8.62                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 15.55/8.62               => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ ( groups3906332499630173760nt_rat @ F @ B5 ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7963_sum__strict__mono2,axiom,
% 15.55/8.62      ! [B5: set_complex,A3: set_complex,B: complex,F: complex > rat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ B5 )
% 15.55/8.62       => ( ( ord_le211207098394363844omplex @ A3 @ B5 )
% 15.55/8.62         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B5 @ A3 ) )
% 15.55/8.62           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 15.55/8.62             => ( ! [X4: complex] :
% 15.55/8.62                    ( ( member_complex @ X4 @ B5 )
% 15.55/8.62                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 15.55/8.62               => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A3 ) @ ( groups5058264527183730370ex_rat @ F @ B5 ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7964_sum__strict__mono2,axiom,
% 15.55/8.62      ! [B5: set_Extended_enat,A3: set_Extended_enat,B: extended_enat,F: extended_enat > rat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ B5 )
% 15.55/8.62       => ( ( ord_le7203529160286727270d_enat @ A3 @ B5 )
% 15.55/8.62         => ( ( member_Extended_enat @ B @ ( minus_925952699566721837d_enat @ B5 @ A3 ) )
% 15.55/8.62           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 15.55/8.62             => ( ! [X4: extended_enat] :
% 15.55/8.62                    ( ( member_Extended_enat @ X4 @ B5 )
% 15.55/8.62                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 15.55/8.62               => ( ord_less_rat @ ( groups1392844769737527556at_rat @ F @ A3 ) @ ( groups1392844769737527556at_rat @ F @ B5 ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7965_sum__strict__mono2,axiom,
% 15.55/8.62      ! [B5: set_real,A3: set_real,B: real,F: real > nat] :
% 15.55/8.62        ( ( finite_finite_real @ B5 )
% 15.55/8.62       => ( ( ord_less_eq_set_real @ A3 @ B5 )
% 15.55/8.62         => ( ( member_real @ B @ ( minus_minus_set_real @ B5 @ A3 ) )
% 15.55/8.62           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 15.55/8.62             => ( ! [X4: real] :
% 15.55/8.62                    ( ( member_real @ X4 @ B5 )
% 15.55/8.62                   => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 15.55/8.62               => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A3 ) @ ( groups1935376822645274424al_nat @ F @ B5 ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7966_sum__strict__mono2,axiom,
% 15.55/8.62      ! [B5: set_int,A3: set_int,B: int,F: int > nat] :
% 15.55/8.62        ( ( finite_finite_int @ B5 )
% 15.55/8.62       => ( ( ord_less_eq_set_int @ A3 @ B5 )
% 15.55/8.62         => ( ( member_int @ B @ ( minus_minus_set_int @ B5 @ A3 ) )
% 15.55/8.62           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 15.55/8.62             => ( ! [X4: int] :
% 15.55/8.62                    ( ( member_int @ X4 @ B5 )
% 15.55/8.62                   => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 15.55/8.62               => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ ( groups4541462559716669496nt_nat @ F @ B5 ) ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7967_member__le__sum,axiom,
% 15.55/8.62      ! [I: complex,A3: set_complex,F: complex > real] :
% 15.55/8.62        ( ( member_complex @ I @ A3 )
% 15.55/8.62       => ( ! [X4: complex] :
% 15.55/8.62              ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 15.55/8.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 15.55/8.62         => ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.62           => ( ord_less_eq_real @ ( F @ I ) @ ( groups5808333547571424918x_real @ F @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7968_member__le__sum,axiom,
% 15.55/8.62      ! [I: extended_enat,A3: set_Extended_enat,F: extended_enat > real] :
% 15.55/8.62        ( ( member_Extended_enat @ I @ A3 )
% 15.55/8.62       => ( ! [X4: extended_enat] :
% 15.55/8.62              ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ I @ bot_bo7653980558646680370d_enat ) ) )
% 15.55/8.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 15.55/8.62         => ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.62           => ( ord_less_eq_real @ ( F @ I ) @ ( groups4148127829035722712t_real @ F @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7969_member__le__sum,axiom,
% 15.55/8.62      ! [I: real,A3: set_real,F: real > real] :
% 15.55/8.62        ( ( member_real @ I @ A3 )
% 15.55/8.62       => ( ! [X4: real] :
% 15.55/8.62              ( ( member_real @ X4 @ ( minus_minus_set_real @ A3 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 15.55/8.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 15.55/8.62         => ( ( finite_finite_real @ A3 )
% 15.55/8.62           => ( ord_less_eq_real @ ( F @ I ) @ ( groups8097168146408367636l_real @ F @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7970_member__le__sum,axiom,
% 15.55/8.62      ! [I: int,A3: set_int,F: int > real] :
% 15.55/8.62        ( ( member_int @ I @ A3 )
% 15.55/8.62       => ( ! [X4: int] :
% 15.55/8.62              ( ( member_int @ X4 @ ( minus_minus_set_int @ A3 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 15.55/8.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 15.55/8.62         => ( ( finite_finite_int @ A3 )
% 15.55/8.62           => ( ord_less_eq_real @ ( F @ I ) @ ( groups8778361861064173332t_real @ F @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7971_member__le__sum,axiom,
% 15.55/8.62      ! [I: complex,A3: set_complex,F: complex > rat] :
% 15.55/8.62        ( ( member_complex @ I @ A3 )
% 15.55/8.62       => ( ! [X4: complex] :
% 15.55/8.62              ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 15.55/8.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 15.55/8.62         => ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.62           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups5058264527183730370ex_rat @ F @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7972_member__le__sum,axiom,
% 15.55/8.62      ! [I: extended_enat,A3: set_Extended_enat,F: extended_enat > rat] :
% 15.55/8.62        ( ( member_Extended_enat @ I @ A3 )
% 15.55/8.62       => ( ! [X4: extended_enat] :
% 15.55/8.62              ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ I @ bot_bo7653980558646680370d_enat ) ) )
% 15.55/8.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 15.55/8.62         => ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.62           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups1392844769737527556at_rat @ F @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7973_member__le__sum,axiom,
% 15.55/8.62      ! [I: real,A3: set_real,F: real > rat] :
% 15.55/8.62        ( ( member_real @ I @ A3 )
% 15.55/8.62       => ( ! [X4: real] :
% 15.55/8.62              ( ( member_real @ X4 @ ( minus_minus_set_real @ A3 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 15.55/8.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 15.55/8.62         => ( ( finite_finite_real @ A3 )
% 15.55/8.62           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups1300246762558778688al_rat @ F @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7974_member__le__sum,axiom,
% 15.55/8.62      ! [I: int,A3: set_int,F: int > rat] :
% 15.55/8.62        ( ( member_int @ I @ A3 )
% 15.55/8.62       => ( ! [X4: int] :
% 15.55/8.62              ( ( member_int @ X4 @ ( minus_minus_set_int @ A3 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 15.55/8.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 15.55/8.62         => ( ( finite_finite_int @ A3 )
% 15.55/8.62           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups3906332499630173760nt_rat @ F @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7975_member__le__sum,axiom,
% 15.55/8.62      ! [I: nat,A3: set_nat,F: nat > rat] :
% 15.55/8.62        ( ( member_nat @ I @ A3 )
% 15.55/8.62       => ( ! [X4: nat] :
% 15.55/8.62              ( ( member_nat @ X4 @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 15.55/8.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 15.55/8.62         => ( ( finite_finite_nat @ A3 )
% 15.55/8.62           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups2906978787729119204at_rat @ F @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7976_member__le__sum,axiom,
% 15.55/8.62      ! [I: complex,A3: set_complex,F: complex > nat] :
% 15.55/8.62        ( ( member_complex @ I @ A3 )
% 15.55/8.62       => ( ! [X4: complex] :
% 15.55/8.62              ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 15.55/8.62             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 15.55/8.62         => ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.62           => ( ord_less_eq_nat @ ( F @ I ) @ ( groups5693394587270226106ex_nat @ F @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7977_sum_Ofinite__Collect__op,axiom,
% 15.55/8.62      ! [I5: set_real,X3: real > real,Y3: real > real] :
% 15.55/8.62        ( ( finite_finite_real
% 15.55/8.62          @ ( collect_real
% 15.55/8.62            @ ^ [I4: real] :
% 15.55/8.62                ( ( member_real @ I4 @ I5 )
% 15.55/8.62                & ( ( X3 @ I4 )
% 15.55/8.62                 != zero_zero_real ) ) ) )
% 15.55/8.62       => ( ( finite_finite_real
% 15.55/8.62            @ ( collect_real
% 15.55/8.62              @ ^ [I4: real] :
% 15.55/8.62                  ( ( member_real @ I4 @ I5 )
% 15.55/8.62                  & ( ( Y3 @ I4 )
% 15.55/8.62                   != zero_zero_real ) ) ) )
% 15.55/8.62         => ( finite_finite_real
% 15.55/8.62            @ ( collect_real
% 15.55/8.62              @ ^ [I4: real] :
% 15.55/8.62                  ( ( member_real @ I4 @ I5 )
% 15.55/8.62                  & ( ( plus_plus_real @ ( X3 @ I4 ) @ ( Y3 @ I4 ) )
% 15.55/8.62                   != zero_zero_real ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7978_sum_Ofinite__Collect__op,axiom,
% 15.55/8.62      ! [I5: set_nat,X3: nat > real,Y3: nat > real] :
% 15.55/8.62        ( ( finite_finite_nat
% 15.55/8.62          @ ( collect_nat
% 15.55/8.62            @ ^ [I4: nat] :
% 15.55/8.62                ( ( member_nat @ I4 @ I5 )
% 15.55/8.62                & ( ( X3 @ I4 )
% 15.55/8.62                 != zero_zero_real ) ) ) )
% 15.55/8.62       => ( ( finite_finite_nat
% 15.55/8.62            @ ( collect_nat
% 15.55/8.62              @ ^ [I4: nat] :
% 15.55/8.62                  ( ( member_nat @ I4 @ I5 )
% 15.55/8.62                  & ( ( Y3 @ I4 )
% 15.55/8.62                   != zero_zero_real ) ) ) )
% 15.55/8.62         => ( finite_finite_nat
% 15.55/8.62            @ ( collect_nat
% 15.55/8.62              @ ^ [I4: nat] :
% 15.55/8.62                  ( ( member_nat @ I4 @ I5 )
% 15.55/8.62                  & ( ( plus_plus_real @ ( X3 @ I4 ) @ ( Y3 @ I4 ) )
% 15.55/8.62                   != zero_zero_real ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7979_sum_Ofinite__Collect__op,axiom,
% 15.55/8.62      ! [I5: set_int,X3: int > real,Y3: int > real] :
% 15.55/8.62        ( ( finite_finite_int
% 15.55/8.62          @ ( collect_int
% 15.55/8.62            @ ^ [I4: int] :
% 15.55/8.62                ( ( member_int @ I4 @ I5 )
% 15.55/8.62                & ( ( X3 @ I4 )
% 15.55/8.62                 != zero_zero_real ) ) ) )
% 15.55/8.62       => ( ( finite_finite_int
% 15.55/8.62            @ ( collect_int
% 15.55/8.62              @ ^ [I4: int] :
% 15.55/8.62                  ( ( member_int @ I4 @ I5 )
% 15.55/8.62                  & ( ( Y3 @ I4 )
% 15.55/8.62                   != zero_zero_real ) ) ) )
% 15.55/8.62         => ( finite_finite_int
% 15.55/8.62            @ ( collect_int
% 15.55/8.62              @ ^ [I4: int] :
% 15.55/8.62                  ( ( member_int @ I4 @ I5 )
% 15.55/8.62                  & ( ( plus_plus_real @ ( X3 @ I4 ) @ ( Y3 @ I4 ) )
% 15.55/8.62                   != zero_zero_real ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7980_sum_Ofinite__Collect__op,axiom,
% 15.55/8.62      ! [I5: set_complex,X3: complex > real,Y3: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex
% 15.55/8.62          @ ( collect_complex
% 15.55/8.62            @ ^ [I4: complex] :
% 15.55/8.62                ( ( member_complex @ I4 @ I5 )
% 15.55/8.62                & ( ( X3 @ I4 )
% 15.55/8.62                 != zero_zero_real ) ) ) )
% 15.55/8.62       => ( ( finite3207457112153483333omplex
% 15.55/8.62            @ ( collect_complex
% 15.55/8.62              @ ^ [I4: complex] :
% 15.55/8.62                  ( ( member_complex @ I4 @ I5 )
% 15.55/8.62                  & ( ( Y3 @ I4 )
% 15.55/8.62                   != zero_zero_real ) ) ) )
% 15.55/8.62         => ( finite3207457112153483333omplex
% 15.55/8.62            @ ( collect_complex
% 15.55/8.62              @ ^ [I4: complex] :
% 15.55/8.62                  ( ( member_complex @ I4 @ I5 )
% 15.55/8.62                  & ( ( plus_plus_real @ ( X3 @ I4 ) @ ( Y3 @ I4 ) )
% 15.55/8.62                   != zero_zero_real ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7981_sum_Ofinite__Collect__op,axiom,
% 15.55/8.62      ! [I5: set_Extended_enat,X3: extended_enat > real,Y3: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat
% 15.55/8.62          @ ( collec4429806609662206161d_enat
% 15.55/8.62            @ ^ [I4: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ I4 @ I5 )
% 15.55/8.62                & ( ( X3 @ I4 )
% 15.55/8.62                 != zero_zero_real ) ) ) )
% 15.55/8.62       => ( ( finite4001608067531595151d_enat
% 15.55/8.62            @ ( collec4429806609662206161d_enat
% 15.55/8.62              @ ^ [I4: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ I4 @ I5 )
% 15.55/8.62                  & ( ( Y3 @ I4 )
% 15.55/8.62                   != zero_zero_real ) ) ) )
% 15.55/8.62         => ( finite4001608067531595151d_enat
% 15.55/8.62            @ ( collec4429806609662206161d_enat
% 15.55/8.62              @ ^ [I4: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ I4 @ I5 )
% 15.55/8.62                  & ( ( plus_plus_real @ ( X3 @ I4 ) @ ( Y3 @ I4 ) )
% 15.55/8.62                   != zero_zero_real ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7982_sum_Ofinite__Collect__op,axiom,
% 15.55/8.62      ! [I5: set_real,X3: real > rat,Y3: real > rat] :
% 15.55/8.62        ( ( finite_finite_real
% 15.55/8.62          @ ( collect_real
% 15.55/8.62            @ ^ [I4: real] :
% 15.55/8.62                ( ( member_real @ I4 @ I5 )
% 15.55/8.62                & ( ( X3 @ I4 )
% 15.55/8.62                 != zero_zero_rat ) ) ) )
% 15.55/8.62       => ( ( finite_finite_real
% 15.55/8.62            @ ( collect_real
% 15.55/8.62              @ ^ [I4: real] :
% 15.55/8.62                  ( ( member_real @ I4 @ I5 )
% 15.55/8.62                  & ( ( Y3 @ I4 )
% 15.55/8.62                   != zero_zero_rat ) ) ) )
% 15.55/8.62         => ( finite_finite_real
% 15.55/8.62            @ ( collect_real
% 15.55/8.62              @ ^ [I4: real] :
% 15.55/8.62                  ( ( member_real @ I4 @ I5 )
% 15.55/8.62                  & ( ( plus_plus_rat @ ( X3 @ I4 ) @ ( Y3 @ I4 ) )
% 15.55/8.62                   != zero_zero_rat ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7983_sum_Ofinite__Collect__op,axiom,
% 15.55/8.62      ! [I5: set_nat,X3: nat > rat,Y3: nat > rat] :
% 15.55/8.62        ( ( finite_finite_nat
% 15.55/8.62          @ ( collect_nat
% 15.55/8.62            @ ^ [I4: nat] :
% 15.55/8.62                ( ( member_nat @ I4 @ I5 )
% 15.55/8.62                & ( ( X3 @ I4 )
% 15.55/8.62                 != zero_zero_rat ) ) ) )
% 15.55/8.62       => ( ( finite_finite_nat
% 15.55/8.62            @ ( collect_nat
% 15.55/8.62              @ ^ [I4: nat] :
% 15.55/8.62                  ( ( member_nat @ I4 @ I5 )
% 15.55/8.62                  & ( ( Y3 @ I4 )
% 15.55/8.62                   != zero_zero_rat ) ) ) )
% 15.55/8.62         => ( finite_finite_nat
% 15.55/8.62            @ ( collect_nat
% 15.55/8.62              @ ^ [I4: nat] :
% 15.55/8.62                  ( ( member_nat @ I4 @ I5 )
% 15.55/8.62                  & ( ( plus_plus_rat @ ( X3 @ I4 ) @ ( Y3 @ I4 ) )
% 15.55/8.62                   != zero_zero_rat ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7984_sum_Ofinite__Collect__op,axiom,
% 15.55/8.62      ! [I5: set_int,X3: int > rat,Y3: int > rat] :
% 15.55/8.62        ( ( finite_finite_int
% 15.55/8.62          @ ( collect_int
% 15.55/8.62            @ ^ [I4: int] :
% 15.55/8.62                ( ( member_int @ I4 @ I5 )
% 15.55/8.62                & ( ( X3 @ I4 )
% 15.55/8.62                 != zero_zero_rat ) ) ) )
% 15.55/8.62       => ( ( finite_finite_int
% 15.55/8.62            @ ( collect_int
% 15.55/8.62              @ ^ [I4: int] :
% 15.55/8.62                  ( ( member_int @ I4 @ I5 )
% 15.55/8.62                  & ( ( Y3 @ I4 )
% 15.55/8.62                   != zero_zero_rat ) ) ) )
% 15.55/8.62         => ( finite_finite_int
% 15.55/8.62            @ ( collect_int
% 15.55/8.62              @ ^ [I4: int] :
% 15.55/8.62                  ( ( member_int @ I4 @ I5 )
% 15.55/8.62                  & ( ( plus_plus_rat @ ( X3 @ I4 ) @ ( Y3 @ I4 ) )
% 15.55/8.62                   != zero_zero_rat ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7985_sum_Ofinite__Collect__op,axiom,
% 15.55/8.62      ! [I5: set_complex,X3: complex > rat,Y3: complex > rat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex
% 15.55/8.62          @ ( collect_complex
% 15.55/8.62            @ ^ [I4: complex] :
% 15.55/8.62                ( ( member_complex @ I4 @ I5 )
% 15.55/8.62                & ( ( X3 @ I4 )
% 15.55/8.62                 != zero_zero_rat ) ) ) )
% 15.55/8.62       => ( ( finite3207457112153483333omplex
% 15.55/8.62            @ ( collect_complex
% 15.55/8.62              @ ^ [I4: complex] :
% 15.55/8.62                  ( ( member_complex @ I4 @ I5 )
% 15.55/8.62                  & ( ( Y3 @ I4 )
% 15.55/8.62                   != zero_zero_rat ) ) ) )
% 15.55/8.62         => ( finite3207457112153483333omplex
% 15.55/8.62            @ ( collect_complex
% 15.55/8.62              @ ^ [I4: complex] :
% 15.55/8.62                  ( ( member_complex @ I4 @ I5 )
% 15.55/8.62                  & ( ( plus_plus_rat @ ( X3 @ I4 ) @ ( Y3 @ I4 ) )
% 15.55/8.62                   != zero_zero_rat ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7986_sum_Ofinite__Collect__op,axiom,
% 15.55/8.62      ! [I5: set_Extended_enat,X3: extended_enat > rat,Y3: extended_enat > rat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat
% 15.55/8.62          @ ( collec4429806609662206161d_enat
% 15.55/8.62            @ ^ [I4: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ I4 @ I5 )
% 15.55/8.62                & ( ( X3 @ I4 )
% 15.55/8.62                 != zero_zero_rat ) ) ) )
% 15.55/8.62       => ( ( finite4001608067531595151d_enat
% 15.55/8.62            @ ( collec4429806609662206161d_enat
% 15.55/8.62              @ ^ [I4: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ I4 @ I5 )
% 15.55/8.62                  & ( ( Y3 @ I4 )
% 15.55/8.62                   != zero_zero_rat ) ) ) )
% 15.55/8.62         => ( finite4001608067531595151d_enat
% 15.55/8.62            @ ( collec4429806609662206161d_enat
% 15.55/8.62              @ ^ [I4: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ I4 @ I5 )
% 15.55/8.62                  & ( ( plus_plus_rat @ ( X3 @ I4 ) @ ( Y3 @ I4 ) )
% 15.55/8.62                   != zero_zero_rat ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7987_Complex__eq__neg__1,axiom,
% 15.55/8.62      ! [A: real,B: real] :
% 15.55/8.62        ( ( ( complex2 @ A @ B )
% 15.55/8.62          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 15.55/8.62        = ( ( A
% 15.55/8.62            = ( uminus_uminus_real @ one_one_real ) )
% 15.55/8.62          & ( B = zero_zero_real ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7988_Complex__eq__neg__numeral,axiom,
% 15.55/8.62      ! [A: real,B: real,W: num] :
% 15.55/8.62        ( ( ( complex2 @ A @ B )
% 15.55/8.62          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 15.55/8.62        = ( ( A
% 15.55/8.62            = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 15.55/8.62          & ( B = zero_zero_real ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7989_finite__ranking__induct,axiom,
% 15.55/8.62      ! [S2: set_complex,P: set_complex > $o,F: complex > rat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ S2 )
% 15.55/8.62       => ( ( P @ bot_bot_set_complex )
% 15.55/8.62         => ( ! [X4: complex,S5: set_complex] :
% 15.55/8.62                ( ( finite3207457112153483333omplex @ S5 )
% 15.55/8.62               => ( ! [Y6: complex] :
% 15.55/8.62                      ( ( member_complex @ Y6 @ S5 )
% 15.55/8.62                     => ( ord_less_eq_rat @ ( F @ Y6 ) @ ( F @ X4 ) ) )
% 15.55/8.62                 => ( ( P @ S5 )
% 15.55/8.62                   => ( P @ ( insert_complex @ X4 @ S5 ) ) ) ) )
% 15.55/8.62           => ( P @ S2 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7990_finite__ranking__induct,axiom,
% 15.55/8.62      ! [S2: set_Extended_enat,P: set_Extended_enat > $o,F: extended_enat > rat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ S2 )
% 15.55/8.62       => ( ( P @ bot_bo7653980558646680370d_enat )
% 15.55/8.62         => ( ! [X4: extended_enat,S5: set_Extended_enat] :
% 15.55/8.62                ( ( finite4001608067531595151d_enat @ S5 )
% 15.55/8.62               => ( ! [Y6: extended_enat] :
% 15.55/8.62                      ( ( member_Extended_enat @ Y6 @ S5 )
% 15.55/8.62                     => ( ord_less_eq_rat @ ( F @ Y6 ) @ ( F @ X4 ) ) )
% 15.55/8.62                 => ( ( P @ S5 )
% 15.55/8.62                   => ( P @ ( insert_Extended_enat @ X4 @ S5 ) ) ) ) )
% 15.55/8.62           => ( P @ S2 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7991_finite__ranking__induct,axiom,
% 15.55/8.62      ! [S2: set_real,P: set_real > $o,F: real > rat] :
% 15.55/8.62        ( ( finite_finite_real @ S2 )
% 15.55/8.62       => ( ( P @ bot_bot_set_real )
% 15.55/8.62         => ( ! [X4: real,S5: set_real] :
% 15.55/8.62                ( ( finite_finite_real @ S5 )
% 15.55/8.62               => ( ! [Y6: real] :
% 15.55/8.62                      ( ( member_real @ Y6 @ S5 )
% 15.55/8.62                     => ( ord_less_eq_rat @ ( F @ Y6 ) @ ( F @ X4 ) ) )
% 15.55/8.62                 => ( ( P @ S5 )
% 15.55/8.62                   => ( P @ ( insert_real @ X4 @ S5 ) ) ) ) )
% 15.55/8.62           => ( P @ S2 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7992_finite__ranking__induct,axiom,
% 15.55/8.62      ! [S2: set_nat,P: set_nat > $o,F: nat > rat] :
% 15.55/8.62        ( ( finite_finite_nat @ S2 )
% 15.55/8.62       => ( ( P @ bot_bot_set_nat )
% 15.55/8.62         => ( ! [X4: nat,S5: set_nat] :
% 15.55/8.62                ( ( finite_finite_nat @ S5 )
% 15.55/8.62               => ( ! [Y6: nat] :
% 15.55/8.62                      ( ( member_nat @ Y6 @ S5 )
% 15.55/8.62                     => ( ord_less_eq_rat @ ( F @ Y6 ) @ ( F @ X4 ) ) )
% 15.55/8.62                 => ( ( P @ S5 )
% 15.55/8.62                   => ( P @ ( insert_nat @ X4 @ S5 ) ) ) ) )
% 15.55/8.62           => ( P @ S2 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7993_finite__ranking__induct,axiom,
% 15.55/8.62      ! [S2: set_int,P: set_int > $o,F: int > rat] :
% 15.55/8.62        ( ( finite_finite_int @ S2 )
% 15.55/8.62       => ( ( P @ bot_bot_set_int )
% 15.55/8.62         => ( ! [X4: int,S5: set_int] :
% 15.55/8.62                ( ( finite_finite_int @ S5 )
% 15.55/8.62               => ( ! [Y6: int] :
% 15.55/8.62                      ( ( member_int @ Y6 @ S5 )
% 15.55/8.62                     => ( ord_less_eq_rat @ ( F @ Y6 ) @ ( F @ X4 ) ) )
% 15.55/8.62                 => ( ( P @ S5 )
% 15.55/8.62                   => ( P @ ( insert_int @ X4 @ S5 ) ) ) ) )
% 15.55/8.62           => ( P @ S2 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7994_finite__ranking__induct,axiom,
% 15.55/8.62      ! [S2: set_complex,P: set_complex > $o,F: complex > num] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ S2 )
% 15.55/8.62       => ( ( P @ bot_bot_set_complex )
% 15.55/8.62         => ( ! [X4: complex,S5: set_complex] :
% 15.55/8.62                ( ( finite3207457112153483333omplex @ S5 )
% 15.55/8.62               => ( ! [Y6: complex] :
% 15.55/8.62                      ( ( member_complex @ Y6 @ S5 )
% 15.55/8.62                     => ( ord_less_eq_num @ ( F @ Y6 ) @ ( F @ X4 ) ) )
% 15.55/8.62                 => ( ( P @ S5 )
% 15.55/8.62                   => ( P @ ( insert_complex @ X4 @ S5 ) ) ) ) )
% 15.55/8.62           => ( P @ S2 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7995_finite__ranking__induct,axiom,
% 15.55/8.62      ! [S2: set_Extended_enat,P: set_Extended_enat > $o,F: extended_enat > num] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ S2 )
% 15.55/8.62       => ( ( P @ bot_bo7653980558646680370d_enat )
% 15.55/8.62         => ( ! [X4: extended_enat,S5: set_Extended_enat] :
% 15.55/8.62                ( ( finite4001608067531595151d_enat @ S5 )
% 15.55/8.62               => ( ! [Y6: extended_enat] :
% 15.55/8.62                      ( ( member_Extended_enat @ Y6 @ S5 )
% 15.55/8.62                     => ( ord_less_eq_num @ ( F @ Y6 ) @ ( F @ X4 ) ) )
% 15.55/8.62                 => ( ( P @ S5 )
% 15.55/8.62                   => ( P @ ( insert_Extended_enat @ X4 @ S5 ) ) ) ) )
% 15.55/8.62           => ( P @ S2 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7996_finite__ranking__induct,axiom,
% 15.55/8.62      ! [S2: set_real,P: set_real > $o,F: real > num] :
% 15.55/8.62        ( ( finite_finite_real @ S2 )
% 15.55/8.62       => ( ( P @ bot_bot_set_real )
% 15.55/8.62         => ( ! [X4: real,S5: set_real] :
% 15.55/8.62                ( ( finite_finite_real @ S5 )
% 15.55/8.62               => ( ! [Y6: real] :
% 15.55/8.62                      ( ( member_real @ Y6 @ S5 )
% 15.55/8.62                     => ( ord_less_eq_num @ ( F @ Y6 ) @ ( F @ X4 ) ) )
% 15.55/8.62                 => ( ( P @ S5 )
% 15.55/8.62                   => ( P @ ( insert_real @ X4 @ S5 ) ) ) ) )
% 15.55/8.62           => ( P @ S2 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7997_finite__ranking__induct,axiom,
% 15.55/8.62      ! [S2: set_nat,P: set_nat > $o,F: nat > num] :
% 15.55/8.62        ( ( finite_finite_nat @ S2 )
% 15.55/8.62       => ( ( P @ bot_bot_set_nat )
% 15.55/8.62         => ( ! [X4: nat,S5: set_nat] :
% 15.55/8.62                ( ( finite_finite_nat @ S5 )
% 15.55/8.62               => ( ! [Y6: nat] :
% 15.55/8.62                      ( ( member_nat @ Y6 @ S5 )
% 15.55/8.62                     => ( ord_less_eq_num @ ( F @ Y6 ) @ ( F @ X4 ) ) )
% 15.55/8.62                 => ( ( P @ S5 )
% 15.55/8.62                   => ( P @ ( insert_nat @ X4 @ S5 ) ) ) ) )
% 15.55/8.62           => ( P @ S2 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7998_finite__ranking__induct,axiom,
% 15.55/8.62      ! [S2: set_int,P: set_int > $o,F: int > num] :
% 15.55/8.62        ( ( finite_finite_int @ S2 )
% 15.55/8.62       => ( ( P @ bot_bot_set_int )
% 15.55/8.62         => ( ! [X4: int,S5: set_int] :
% 15.55/8.62                ( ( finite_finite_int @ S5 )
% 15.55/8.62               => ( ! [Y6: int] :
% 15.55/8.62                      ( ( member_int @ Y6 @ S5 )
% 15.55/8.62                     => ( ord_less_eq_num @ ( F @ Y6 ) @ ( F @ X4 ) ) )
% 15.55/8.62                 => ( ( P @ S5 )
% 15.55/8.62                   => ( P @ ( insert_int @ X4 @ S5 ) ) ) ) )
% 15.55/8.62           => ( P @ S2 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_7999_finite__linorder__min__induct,axiom,
% 15.55/8.62      ! [A3: set_Extended_enat,P: set_Extended_enat > $o] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.62       => ( ( P @ bot_bo7653980558646680370d_enat )
% 15.55/8.62         => ( ! [B4: extended_enat,A6: set_Extended_enat] :
% 15.55/8.62                ( ( finite4001608067531595151d_enat @ A6 )
% 15.55/8.62               => ( ! [X6: extended_enat] :
% 15.55/8.62                      ( ( member_Extended_enat @ X6 @ A6 )
% 15.55/8.62                     => ( ord_le72135733267957522d_enat @ B4 @ X6 ) )
% 15.55/8.62                 => ( ( P @ A6 )
% 15.55/8.62                   => ( P @ ( insert_Extended_enat @ B4 @ A6 ) ) ) ) )
% 15.55/8.62           => ( P @ A3 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8000_finite__linorder__min__induct,axiom,
% 15.55/8.62      ! [A3: set_real,P: set_real > $o] :
% 15.55/8.62        ( ( finite_finite_real @ A3 )
% 15.55/8.62       => ( ( P @ bot_bot_set_real )
% 15.55/8.62         => ( ! [B4: real,A6: set_real] :
% 15.55/8.62                ( ( finite_finite_real @ A6 )
% 15.55/8.62               => ( ! [X6: real] :
% 15.55/8.62                      ( ( member_real @ X6 @ A6 )
% 15.55/8.62                     => ( ord_less_real @ B4 @ X6 ) )
% 15.55/8.62                 => ( ( P @ A6 )
% 15.55/8.62                   => ( P @ ( insert_real @ B4 @ A6 ) ) ) ) )
% 15.55/8.62           => ( P @ A3 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8001_finite__linorder__min__induct,axiom,
% 15.55/8.62      ! [A3: set_rat,P: set_rat > $o] :
% 15.55/8.62        ( ( finite_finite_rat @ A3 )
% 15.55/8.62       => ( ( P @ bot_bot_set_rat )
% 15.55/8.62         => ( ! [B4: rat,A6: set_rat] :
% 15.55/8.62                ( ( finite_finite_rat @ A6 )
% 15.55/8.62               => ( ! [X6: rat] :
% 15.55/8.62                      ( ( member_rat @ X6 @ A6 )
% 15.55/8.62                     => ( ord_less_rat @ B4 @ X6 ) )
% 15.55/8.62                 => ( ( P @ A6 )
% 15.55/8.62                   => ( P @ ( insert_rat @ B4 @ A6 ) ) ) ) )
% 15.55/8.62           => ( P @ A3 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8002_finite__linorder__min__induct,axiom,
% 15.55/8.62      ! [A3: set_num,P: set_num > $o] :
% 15.55/8.62        ( ( finite_finite_num @ A3 )
% 15.55/8.62       => ( ( P @ bot_bot_set_num )
% 15.55/8.62         => ( ! [B4: num,A6: set_num] :
% 15.55/8.62                ( ( finite_finite_num @ A6 )
% 15.55/8.62               => ( ! [X6: num] :
% 15.55/8.62                      ( ( member_num @ X6 @ A6 )
% 15.55/8.62                     => ( ord_less_num @ B4 @ X6 ) )
% 15.55/8.62                 => ( ( P @ A6 )
% 15.55/8.62                   => ( P @ ( insert_num @ B4 @ A6 ) ) ) ) )
% 15.55/8.62           => ( P @ A3 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8003_finite__linorder__min__induct,axiom,
% 15.55/8.62      ! [A3: set_nat,P: set_nat > $o] :
% 15.55/8.62        ( ( finite_finite_nat @ A3 )
% 15.55/8.62       => ( ( P @ bot_bot_set_nat )
% 15.55/8.62         => ( ! [B4: nat,A6: set_nat] :
% 15.55/8.62                ( ( finite_finite_nat @ A6 )
% 15.55/8.62               => ( ! [X6: nat] :
% 15.55/8.62                      ( ( member_nat @ X6 @ A6 )
% 15.55/8.62                     => ( ord_less_nat @ B4 @ X6 ) )
% 15.55/8.62                 => ( ( P @ A6 )
% 15.55/8.62                   => ( P @ ( insert_nat @ B4 @ A6 ) ) ) ) )
% 15.55/8.62           => ( P @ A3 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8004_finite__linorder__min__induct,axiom,
% 15.55/8.62      ! [A3: set_int,P: set_int > $o] :
% 15.55/8.62        ( ( finite_finite_int @ A3 )
% 15.55/8.62       => ( ( P @ bot_bot_set_int )
% 15.55/8.62         => ( ! [B4: int,A6: set_int] :
% 15.55/8.62                ( ( finite_finite_int @ A6 )
% 15.55/8.62               => ( ! [X6: int] :
% 15.55/8.62                      ( ( member_int @ X6 @ A6 )
% 15.55/8.62                     => ( ord_less_int @ B4 @ X6 ) )
% 15.55/8.62                 => ( ( P @ A6 )
% 15.55/8.62                   => ( P @ ( insert_int @ B4 @ A6 ) ) ) ) )
% 15.55/8.62           => ( P @ A3 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8005_finite__linorder__max__induct,axiom,
% 15.55/8.62      ! [A3: set_Extended_enat,P: set_Extended_enat > $o] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.62       => ( ( P @ bot_bo7653980558646680370d_enat )
% 15.55/8.62         => ( ! [B4: extended_enat,A6: set_Extended_enat] :
% 15.55/8.62                ( ( finite4001608067531595151d_enat @ A6 )
% 15.55/8.62               => ( ! [X6: extended_enat] :
% 15.55/8.62                      ( ( member_Extended_enat @ X6 @ A6 )
% 15.55/8.62                     => ( ord_le72135733267957522d_enat @ X6 @ B4 ) )
% 15.55/8.62                 => ( ( P @ A6 )
% 15.55/8.62                   => ( P @ ( insert_Extended_enat @ B4 @ A6 ) ) ) ) )
% 15.55/8.62           => ( P @ A3 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8006_finite__linorder__max__induct,axiom,
% 15.55/8.62      ! [A3: set_real,P: set_real > $o] :
% 15.55/8.62        ( ( finite_finite_real @ A3 )
% 15.55/8.62       => ( ( P @ bot_bot_set_real )
% 15.55/8.62         => ( ! [B4: real,A6: set_real] :
% 15.55/8.62                ( ( finite_finite_real @ A6 )
% 15.55/8.62               => ( ! [X6: real] :
% 15.55/8.62                      ( ( member_real @ X6 @ A6 )
% 15.55/8.62                     => ( ord_less_real @ X6 @ B4 ) )
% 15.55/8.62                 => ( ( P @ A6 )
% 15.55/8.62                   => ( P @ ( insert_real @ B4 @ A6 ) ) ) ) )
% 15.55/8.62           => ( P @ A3 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8007_finite__linorder__max__induct,axiom,
% 15.55/8.62      ! [A3: set_rat,P: set_rat > $o] :
% 15.55/8.62        ( ( finite_finite_rat @ A3 )
% 15.55/8.62       => ( ( P @ bot_bot_set_rat )
% 15.55/8.62         => ( ! [B4: rat,A6: set_rat] :
% 15.55/8.62                ( ( finite_finite_rat @ A6 )
% 15.55/8.62               => ( ! [X6: rat] :
% 15.55/8.62                      ( ( member_rat @ X6 @ A6 )
% 15.55/8.62                     => ( ord_less_rat @ X6 @ B4 ) )
% 15.55/8.62                 => ( ( P @ A6 )
% 15.55/8.62                   => ( P @ ( insert_rat @ B4 @ A6 ) ) ) ) )
% 15.55/8.62           => ( P @ A3 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8008_finite__linorder__max__induct,axiom,
% 15.55/8.62      ! [A3: set_num,P: set_num > $o] :
% 15.55/8.62        ( ( finite_finite_num @ A3 )
% 15.55/8.62       => ( ( P @ bot_bot_set_num )
% 15.55/8.62         => ( ! [B4: num,A6: set_num] :
% 15.55/8.62                ( ( finite_finite_num @ A6 )
% 15.55/8.62               => ( ! [X6: num] :
% 15.55/8.62                      ( ( member_num @ X6 @ A6 )
% 15.55/8.62                     => ( ord_less_num @ X6 @ B4 ) )
% 15.55/8.62                 => ( ( P @ A6 )
% 15.55/8.62                   => ( P @ ( insert_num @ B4 @ A6 ) ) ) ) )
% 15.55/8.62           => ( P @ A3 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8009_finite__linorder__max__induct,axiom,
% 15.55/8.62      ! [A3: set_nat,P: set_nat > $o] :
% 15.55/8.62        ( ( finite_finite_nat @ A3 )
% 15.55/8.62       => ( ( P @ bot_bot_set_nat )
% 15.55/8.62         => ( ! [B4: nat,A6: set_nat] :
% 15.55/8.62                ( ( finite_finite_nat @ A6 )
% 15.55/8.62               => ( ! [X6: nat] :
% 15.55/8.62                      ( ( member_nat @ X6 @ A6 )
% 15.55/8.62                     => ( ord_less_nat @ X6 @ B4 ) )
% 15.55/8.62                 => ( ( P @ A6 )
% 15.55/8.62                   => ( P @ ( insert_nat @ B4 @ A6 ) ) ) ) )
% 15.55/8.62           => ( P @ A3 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8010_finite__linorder__max__induct,axiom,
% 15.55/8.62      ! [A3: set_int,P: set_int > $o] :
% 15.55/8.62        ( ( finite_finite_int @ A3 )
% 15.55/8.62       => ( ( P @ bot_bot_set_int )
% 15.55/8.62         => ( ! [B4: int,A6: set_int] :
% 15.55/8.62                ( ( finite_finite_int @ A6 )
% 15.55/8.62               => ( ! [X6: int] :
% 15.55/8.62                      ( ( member_int @ X6 @ A6 )
% 15.55/8.62                     => ( ord_less_int @ X6 @ B4 ) )
% 15.55/8.62                 => ( ( P @ A6 )
% 15.55/8.62                   => ( P @ ( insert_int @ B4 @ A6 ) ) ) ) )
% 15.55/8.62           => ( P @ A3 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8011_sum__power__add,axiom,
% 15.55/8.62      ! [X3: complex,M: nat,I5: set_nat] :
% 15.55/8.62        ( ( groups2073611262835488442omplex
% 15.55/8.62          @ ^ [I4: nat] : ( power_power_complex @ X3 @ ( plus_plus_nat @ M @ I4 ) )
% 15.55/8.62          @ I5 )
% 15.55/8.62        = ( times_times_complex @ ( power_power_complex @ X3 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ I5 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8012_sum__power__add,axiom,
% 15.55/8.62      ! [X3: rat,M: nat,I5: set_nat] :
% 15.55/8.62        ( ( groups2906978787729119204at_rat
% 15.55/8.62          @ ^ [I4: nat] : ( power_power_rat @ X3 @ ( plus_plus_nat @ M @ I4 ) )
% 15.55/8.62          @ I5 )
% 15.55/8.62        = ( times_times_rat @ ( power_power_rat @ X3 @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ I5 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8013_sum__power__add,axiom,
% 15.55/8.62      ! [X3: int,M: nat,I5: set_nat] :
% 15.55/8.62        ( ( groups3539618377306564664at_int
% 15.55/8.62          @ ^ [I4: nat] : ( power_power_int @ X3 @ ( plus_plus_nat @ M @ I4 ) )
% 15.55/8.62          @ I5 )
% 15.55/8.62        = ( times_times_int @ ( power_power_int @ X3 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ I5 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8014_sum__power__add,axiom,
% 15.55/8.62      ! [X3: real,M: nat,I5: set_nat] :
% 15.55/8.62        ( ( groups6591440286371151544t_real
% 15.55/8.62          @ ^ [I4: nat] : ( power_power_real @ X3 @ ( plus_plus_nat @ M @ I4 ) )
% 15.55/8.62          @ I5 )
% 15.55/8.62        = ( times_times_real @ ( power_power_real @ X3 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ I5 ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8015_finite__divisors__nat,axiom,
% 15.55/8.62      ! [M: nat] :
% 15.55/8.62        ( ( ord_less_nat @ zero_zero_nat @ M )
% 15.55/8.62       => ( finite_finite_nat
% 15.55/8.62          @ ( collect_nat
% 15.55/8.62            @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8016_arcsin__minus,axiom,
% 15.55/8.62      ! [X3: real] :
% 15.55/8.62        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 15.55/8.62       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 15.55/8.62         => ( ( arcsin @ ( uminus_uminus_real @ X3 ) )
% 15.55/8.62            = ( uminus_uminus_real @ ( arcsin @ X3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8017_arcsin__le__arcsin,axiom,
% 15.55/8.62      ! [X3: real,Y3: real] :
% 15.55/8.62        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 15.55/8.62       => ( ( ord_less_eq_real @ X3 @ Y3 )
% 15.55/8.62         => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 15.55/8.62           => ( ord_less_eq_real @ ( arcsin @ X3 ) @ ( arcsin @ Y3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8018_subset__eq__atLeast0__atMost__finite,axiom,
% 15.55/8.62      ! [N4: set_nat,N: nat] :
% 15.55/8.62        ( ( ord_less_eq_set_nat @ N4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 15.55/8.62       => ( finite_finite_nat @ N4 ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8019_arcsin__eq__iff,axiom,
% 15.55/8.62      ! [X3: real,Y3: real] :
% 15.55/8.62        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 15.55/8.62       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 15.55/8.62         => ( ( ( arcsin @ X3 )
% 15.55/8.62              = ( arcsin @ Y3 ) )
% 15.55/8.62            = ( X3 = Y3 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8020_arcsin__le__mono,axiom,
% 15.55/8.62      ! [X3: real,Y3: real] :
% 15.55/8.62        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 15.55/8.62       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 15.55/8.62         => ( ( ord_less_eq_real @ ( arcsin @ X3 ) @ ( arcsin @ Y3 ) )
% 15.55/8.62            = ( ord_less_eq_real @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8021_sum__shift__lb__Suc0__0,axiom,
% 15.55/8.62      ! [F: nat > rat,K: nat] :
% 15.55/8.62        ( ( ( F @ zero_zero_nat )
% 15.55/8.62          = zero_zero_rat )
% 15.55/8.62       => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 15.55/8.62          = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8022_sum__shift__lb__Suc0__0,axiom,
% 15.55/8.62      ! [F: nat > int,K: nat] :
% 15.55/8.62        ( ( ( F @ zero_zero_nat )
% 15.55/8.62          = zero_zero_int )
% 15.55/8.62       => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 15.55/8.62          = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8023_sum__shift__lb__Suc0__0,axiom,
% 15.55/8.62      ! [F: nat > nat,K: nat] :
% 15.55/8.62        ( ( ( F @ zero_zero_nat )
% 15.55/8.62          = zero_zero_nat )
% 15.55/8.62       => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 15.55/8.62          = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8024_sum__shift__lb__Suc0__0,axiom,
% 15.55/8.62      ! [F: nat > real,K: nat] :
% 15.55/8.62        ( ( ( F @ zero_zero_nat )
% 15.55/8.62          = zero_zero_real )
% 15.55/8.62       => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 15.55/8.62          = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8025_sum_OatLeast0__atMost__Suc,axiom,
% 15.55/8.62      ! [G: nat > rat,N: nat] :
% 15.55/8.62        ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 15.55/8.62        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8026_sum_OatLeast0__atMost__Suc,axiom,
% 15.55/8.62      ! [G: nat > int,N: nat] :
% 15.55/8.62        ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 15.55/8.62        = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8027_sum_OatLeast0__atMost__Suc,axiom,
% 15.55/8.62      ! [G: nat > nat,N: nat] :
% 15.55/8.62        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 15.55/8.62        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8028_sum_OatLeast0__atMost__Suc,axiom,
% 15.55/8.62      ! [G: nat > real,N: nat] :
% 15.55/8.62        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 15.55/8.62        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8029_sum_OatLeast__Suc__atMost,axiom,
% 15.55/8.62      ! [M: nat,N: nat,G: nat > rat] :
% 15.55/8.62        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.62       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.62          = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8030_sum_OatLeast__Suc__atMost,axiom,
% 15.55/8.62      ! [M: nat,N: nat,G: nat > int] :
% 15.55/8.62        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.62       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.62          = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8031_sum_OatLeast__Suc__atMost,axiom,
% 15.55/8.62      ! [M: nat,N: nat,G: nat > nat] :
% 15.55/8.62        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.62       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.62          = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8032_sum_OatLeast__Suc__atMost,axiom,
% 15.55/8.62      ! [M: nat,N: nat,G: nat > real] :
% 15.55/8.62        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.62       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.62          = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8033_sum_Onat__ivl__Suc_H,axiom,
% 15.55/8.62      ! [M: nat,N: nat,G: nat > rat] :
% 15.55/8.62        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 15.55/8.62       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.62          = ( plus_plus_rat @ ( G @ ( suc @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8034_sum_Onat__ivl__Suc_H,axiom,
% 15.55/8.62      ! [M: nat,N: nat,G: nat > int] :
% 15.55/8.62        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 15.55/8.62       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.62          = ( plus_plus_int @ ( G @ ( suc @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8035_sum_Onat__ivl__Suc_H,axiom,
% 15.55/8.62      ! [M: nat,N: nat,G: nat > nat] :
% 15.55/8.62        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 15.55/8.62       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.62          = ( plus_plus_nat @ ( G @ ( suc @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8036_sum_Onat__ivl__Suc_H,axiom,
% 15.55/8.62      ! [M: nat,N: nat,G: nat > real] :
% 15.55/8.62        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 15.55/8.62       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 15.55/8.62          = ( plus_plus_real @ ( G @ ( suc @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8037_less__1__prod2,axiom,
% 15.55/8.62      ! [I5: set_real,I: real,F: real > real] :
% 15.55/8.62        ( ( finite_finite_real @ I5 )
% 15.55/8.62       => ( ( member_real @ I @ I5 )
% 15.55/8.62         => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 15.55/8.62           => ( ! [I3: real] :
% 15.55/8.62                  ( ( member_real @ I3 @ I5 )
% 15.55/8.62                 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 15.55/8.62             => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8038_less__1__prod2,axiom,
% 15.55/8.62      ! [I5: set_nat,I: nat,F: nat > real] :
% 15.55/8.62        ( ( finite_finite_nat @ I5 )
% 15.55/8.62       => ( ( member_nat @ I @ I5 )
% 15.55/8.62         => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 15.55/8.62           => ( ! [I3: nat] :
% 15.55/8.62                  ( ( member_nat @ I3 @ I5 )
% 15.55/8.62                 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 15.55/8.62             => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8039_less__1__prod2,axiom,
% 15.55/8.62      ! [I5: set_int,I: int,F: int > real] :
% 15.55/8.62        ( ( finite_finite_int @ I5 )
% 15.55/8.62       => ( ( member_int @ I @ I5 )
% 15.55/8.62         => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 15.55/8.62           => ( ! [I3: int] :
% 15.55/8.62                  ( ( member_int @ I3 @ I5 )
% 15.55/8.62                 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 15.55/8.62             => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8040_less__1__prod2,axiom,
% 15.55/8.62      ! [I5: set_complex,I: complex,F: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ I5 )
% 15.55/8.62       => ( ( member_complex @ I @ I5 )
% 15.55/8.62         => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 15.55/8.62           => ( ! [I3: complex] :
% 15.55/8.62                  ( ( member_complex @ I3 @ I5 )
% 15.55/8.62                 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 15.55/8.62             => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8041_less__1__prod2,axiom,
% 15.55/8.62      ! [I5: set_Extended_enat,I: extended_enat,F: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ I5 )
% 15.55/8.62       => ( ( member_Extended_enat @ I @ I5 )
% 15.55/8.62         => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 15.55/8.62           => ( ! [I3: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ I3 @ I5 )
% 15.55/8.62                 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 15.55/8.62             => ( ord_less_real @ one_one_real @ ( groups97031904164794029t_real @ F @ I5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8042_less__1__prod2,axiom,
% 15.55/8.62      ! [I5: set_real,I: real,F: real > rat] :
% 15.55/8.62        ( ( finite_finite_real @ I5 )
% 15.55/8.62       => ( ( member_real @ I @ I5 )
% 15.55/8.62         => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 15.55/8.62           => ( ! [I3: real] :
% 15.55/8.62                  ( ( member_real @ I3 @ I5 )
% 15.55/8.62                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 15.55/8.62             => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8043_less__1__prod2,axiom,
% 15.55/8.62      ! [I5: set_nat,I: nat,F: nat > rat] :
% 15.55/8.62        ( ( finite_finite_nat @ I5 )
% 15.55/8.62       => ( ( member_nat @ I @ I5 )
% 15.55/8.62         => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 15.55/8.62           => ( ! [I3: nat] :
% 15.55/8.62                  ( ( member_nat @ I3 @ I5 )
% 15.55/8.62                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 15.55/8.62             => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8044_less__1__prod2,axiom,
% 15.55/8.62      ! [I5: set_int,I: int,F: int > rat] :
% 15.55/8.62        ( ( finite_finite_int @ I5 )
% 15.55/8.62       => ( ( member_int @ I @ I5 )
% 15.55/8.62         => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 15.55/8.62           => ( ! [I3: int] :
% 15.55/8.62                  ( ( member_int @ I3 @ I5 )
% 15.55/8.62                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 15.55/8.62             => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8045_less__1__prod2,axiom,
% 15.55/8.62      ! [I5: set_complex,I: complex,F: complex > rat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ I5 )
% 15.55/8.62       => ( ( member_complex @ I @ I5 )
% 15.55/8.62         => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 15.55/8.62           => ( ! [I3: complex] :
% 15.55/8.62                  ( ( member_complex @ I3 @ I5 )
% 15.55/8.62                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 15.55/8.62             => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8046_less__1__prod2,axiom,
% 15.55/8.62      ! [I5: set_Extended_enat,I: extended_enat,F: extended_enat > rat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ I5 )
% 15.55/8.62       => ( ( member_Extended_enat @ I @ I5 )
% 15.55/8.62         => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 15.55/8.62           => ( ! [I3: extended_enat] :
% 15.55/8.62                  ( ( member_Extended_enat @ I3 @ I5 )
% 15.55/8.62                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 15.55/8.62             => ( ord_less_rat @ one_one_rat @ ( groups2245840878043517529at_rat @ F @ I5 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8047_less__1__prod,axiom,
% 15.55/8.62      ! [I5: set_complex,F: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ I5 )
% 15.55/8.62       => ( ( I5 != bot_bot_set_complex )
% 15.55/8.62         => ( ! [I3: complex] :
% 15.55/8.62                ( ( member_complex @ I3 @ I5 )
% 15.55/8.62               => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 15.55/8.62           => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8048_less__1__prod,axiom,
% 15.55/8.62      ! [I5: set_Extended_enat,F: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ I5 )
% 15.55/8.62       => ( ( I5 != bot_bo7653980558646680370d_enat )
% 15.55/8.62         => ( ! [I3: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ I3 @ I5 )
% 15.55/8.62               => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 15.55/8.62           => ( ord_less_real @ one_one_real @ ( groups97031904164794029t_real @ F @ I5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8049_less__1__prod,axiom,
% 15.55/8.62      ! [I5: set_real,F: real > real] :
% 15.55/8.62        ( ( finite_finite_real @ I5 )
% 15.55/8.62       => ( ( I5 != bot_bot_set_real )
% 15.55/8.62         => ( ! [I3: real] :
% 15.55/8.62                ( ( member_real @ I3 @ I5 )
% 15.55/8.62               => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 15.55/8.62           => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8050_less__1__prod,axiom,
% 15.55/8.62      ! [I5: set_nat,F: nat > real] :
% 15.55/8.62        ( ( finite_finite_nat @ I5 )
% 15.55/8.62       => ( ( I5 != bot_bot_set_nat )
% 15.55/8.62         => ( ! [I3: nat] :
% 15.55/8.62                ( ( member_nat @ I3 @ I5 )
% 15.55/8.62               => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 15.55/8.62           => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8051_less__1__prod,axiom,
% 15.55/8.62      ! [I5: set_int,F: int > real] :
% 15.55/8.62        ( ( finite_finite_int @ I5 )
% 15.55/8.62       => ( ( I5 != bot_bot_set_int )
% 15.55/8.62         => ( ! [I3: int] :
% 15.55/8.62                ( ( member_int @ I3 @ I5 )
% 15.55/8.62               => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 15.55/8.62           => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8052_less__1__prod,axiom,
% 15.55/8.62      ! [I5: set_complex,F: complex > rat] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ I5 )
% 15.55/8.62       => ( ( I5 != bot_bot_set_complex )
% 15.55/8.62         => ( ! [I3: complex] :
% 15.55/8.62                ( ( member_complex @ I3 @ I5 )
% 15.55/8.62               => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 15.55/8.62           => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8053_less__1__prod,axiom,
% 15.55/8.62      ! [I5: set_Extended_enat,F: extended_enat > rat] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ I5 )
% 15.55/8.62       => ( ( I5 != bot_bo7653980558646680370d_enat )
% 15.55/8.62         => ( ! [I3: extended_enat] :
% 15.55/8.62                ( ( member_Extended_enat @ I3 @ I5 )
% 15.55/8.62               => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 15.55/8.62           => ( ord_less_rat @ one_one_rat @ ( groups2245840878043517529at_rat @ F @ I5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8054_less__1__prod,axiom,
% 15.55/8.62      ! [I5: set_real,F: real > rat] :
% 15.55/8.62        ( ( finite_finite_real @ I5 )
% 15.55/8.62       => ( ( I5 != bot_bot_set_real )
% 15.55/8.62         => ( ! [I3: real] :
% 15.55/8.62                ( ( member_real @ I3 @ I5 )
% 15.55/8.62               => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 15.55/8.62           => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8055_less__1__prod,axiom,
% 15.55/8.62      ! [I5: set_nat,F: nat > rat] :
% 15.55/8.62        ( ( finite_finite_nat @ I5 )
% 15.55/8.62       => ( ( I5 != bot_bot_set_nat )
% 15.55/8.62         => ( ! [I3: nat] :
% 15.55/8.62                ( ( member_nat @ I3 @ I5 )
% 15.55/8.62               => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 15.55/8.62           => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8056_less__1__prod,axiom,
% 15.55/8.62      ! [I5: set_int,F: int > rat] :
% 15.55/8.62        ( ( finite_finite_int @ I5 )
% 15.55/8.62       => ( ( I5 != bot_bot_set_int )
% 15.55/8.62         => ( ! [I3: int] :
% 15.55/8.62                ( ( member_int @ I3 @ I5 )
% 15.55/8.62               => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 15.55/8.62           => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I5 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8057_sum_OSuc__reindex__ivl,axiom,
% 15.55/8.62      ! [M: nat,N: nat,G: nat > rat] :
% 15.55/8.62        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.62       => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 15.55/8.62          = ( plus_plus_rat @ ( G @ M )
% 15.55/8.62            @ ( groups2906978787729119204at_rat
% 15.55/8.62              @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.62              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8058_sum_OSuc__reindex__ivl,axiom,
% 15.55/8.62      ! [M: nat,N: nat,G: nat > int] :
% 15.55/8.62        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.62       => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 15.55/8.62          = ( plus_plus_int @ ( G @ M )
% 15.55/8.62            @ ( groups3539618377306564664at_int
% 15.55/8.62              @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.62              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8059_sum_OSuc__reindex__ivl,axiom,
% 15.55/8.62      ! [M: nat,N: nat,G: nat > nat] :
% 15.55/8.62        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.62       => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 15.55/8.62          = ( plus_plus_nat @ ( G @ M )
% 15.55/8.62            @ ( groups3542108847815614940at_nat
% 15.55/8.62              @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.62              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8060_sum_OSuc__reindex__ivl,axiom,
% 15.55/8.62      ! [M: nat,N: nat,G: nat > real] :
% 15.55/8.62        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.62       => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 15.55/8.62          = ( plus_plus_real @ ( G @ M )
% 15.55/8.62            @ ( groups6591440286371151544t_real
% 15.55/8.62              @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.62              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8061_sum__Suc__diff,axiom,
% 15.55/8.62      ! [M: nat,N: nat,F: nat > rat] :
% 15.55/8.62        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 15.55/8.62       => ( ( groups2906978787729119204at_rat
% 15.55/8.62            @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 15.55/8.62            @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.62          = ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8062_sum__Suc__diff,axiom,
% 15.55/8.62      ! [M: nat,N: nat,F: nat > int] :
% 15.55/8.62        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 15.55/8.62       => ( ( groups3539618377306564664at_int
% 15.55/8.62            @ ^ [I4: nat] : ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 15.55/8.62            @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.62          = ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8063_sum__Suc__diff,axiom,
% 15.55/8.62      ! [M: nat,N: nat,F: nat > real] :
% 15.55/8.62        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 15.55/8.62       => ( ( groups6591440286371151544t_real
% 15.55/8.62            @ ^ [I4: nat] : ( minus_minus_real @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 15.55/8.62            @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.62          = ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8064_atLeastAtMostPlus1__int__conv,axiom,
% 15.55/8.62      ! [M: int,N: int] :
% 15.55/8.62        ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 15.55/8.62       => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 15.55/8.62          = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M @ N ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8065_simp__from__to,axiom,
% 15.55/8.62      ( set_or1266510415728281911st_int
% 15.55/8.62      = ( ^ [I4: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I4 ) @ bot_bot_set_int @ ( insert_int @ I4 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8066_finite__roots__unity,axiom,
% 15.55/8.62      ! [N: nat] :
% 15.55/8.62        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 15.55/8.62       => ( finite_finite_real
% 15.55/8.62          @ ( collect_real
% 15.55/8.62            @ ^ [Z6: real] :
% 15.55/8.62                ( ( power_power_real @ Z6 @ N )
% 15.55/8.62                = one_one_real ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8067_finite__roots__unity,axiom,
% 15.55/8.62      ! [N: nat] :
% 15.55/8.62        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 15.55/8.62       => ( finite3207457112153483333omplex
% 15.55/8.62          @ ( collect_complex
% 15.55/8.62            @ ^ [Z6: complex] :
% 15.55/8.62                ( ( power_power_complex @ Z6 @ N )
% 15.55/8.62                = one_one_complex ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8068_sum__atLeastAtMost__code,axiom,
% 15.55/8.62      ! [F: nat > rat,A: nat,B: nat] :
% 15.55/8.62        ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 15.55/8.62        = ( set_fo1949268297981939178at_rat
% 15.55/8.62          @ ^ [A4: nat] : ( plus_plus_rat @ ( F @ A4 ) )
% 15.55/8.62          @ A
% 15.55/8.62          @ B
% 15.55/8.62          @ zero_zero_rat ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8069_sum__atLeastAtMost__code,axiom,
% 15.55/8.62      ! [F: nat > int,A: nat,B: nat] :
% 15.55/8.62        ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 15.55/8.62        = ( set_fo2581907887559384638at_int
% 15.55/8.62          @ ^ [A4: nat] : ( plus_plus_int @ ( F @ A4 ) )
% 15.55/8.62          @ A
% 15.55/8.62          @ B
% 15.55/8.62          @ zero_zero_int ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8070_sum__atLeastAtMost__code,axiom,
% 15.55/8.62      ! [F: nat > nat,A: nat,B: nat] :
% 15.55/8.62        ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 15.55/8.62        = ( set_fo2584398358068434914at_nat
% 15.55/8.62          @ ^ [A4: nat] : ( plus_plus_nat @ ( F @ A4 ) )
% 15.55/8.62          @ A
% 15.55/8.62          @ B
% 15.55/8.62          @ zero_zero_nat ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8071_sum__atLeastAtMost__code,axiom,
% 15.55/8.62      ! [F: nat > real,A: nat,B: nat] :
% 15.55/8.62        ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 15.55/8.62        = ( set_fo3111899725591712190t_real
% 15.55/8.62          @ ^ [A4: nat] : ( plus_plus_real @ ( F @ A4 ) )
% 15.55/8.62          @ A
% 15.55/8.62          @ B
% 15.55/8.62          @ zero_zero_real ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8072_arcsin__less__arcsin,axiom,
% 15.55/8.62      ! [X3: real,Y3: real] :
% 15.55/8.62        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 15.55/8.62       => ( ( ord_less_real @ X3 @ Y3 )
% 15.55/8.62         => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 15.55/8.62           => ( ord_less_real @ ( arcsin @ X3 ) @ ( arcsin @ Y3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8073_arcsin__less__mono,axiom,
% 15.55/8.62      ! [X3: real,Y3: real] :
% 15.55/8.62        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 15.55/8.62       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 15.55/8.62         => ( ( ord_less_real @ ( arcsin @ X3 ) @ ( arcsin @ Y3 ) )
% 15.55/8.62            = ( ord_less_real @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8074_sum_Oub__add__nat,axiom,
% 15.55/8.62      ! [M: nat,N: nat,G: nat > rat,P6: nat] :
% 15.55/8.62        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 15.55/8.62       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 15.55/8.62          = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8075_sum_Oub__add__nat,axiom,
% 15.55/8.62      ! [M: nat,N: nat,G: nat > int,P6: nat] :
% 15.55/8.62        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 15.55/8.62       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 15.55/8.62          = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8076_sum_Oub__add__nat,axiom,
% 15.55/8.62      ! [M: nat,N: nat,G: nat > nat,P6: nat] :
% 15.55/8.62        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 15.55/8.62       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 15.55/8.62          = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8077_sum_Oub__add__nat,axiom,
% 15.55/8.62      ! [M: nat,N: nat,G: nat > real,P6: nat] :
% 15.55/8.62        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 15.55/8.62       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 15.55/8.62          = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8078_prod__mono__strict,axiom,
% 15.55/8.62      ! [A3: set_complex,F: complex > real,G: complex > real] :
% 15.55/8.62        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.62       => ( ! [I3: complex] :
% 15.55/8.62              ( ( member_complex @ I3 @ A3 )
% 15.55/8.62             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 15.55/8.62                & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 15.55/8.62         => ( ( A3 != bot_bot_set_complex )
% 15.55/8.62           => ( ord_less_real @ ( groups766887009212190081x_real @ F @ A3 ) @ ( groups766887009212190081x_real @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8079_prod__mono__strict,axiom,
% 15.55/8.62      ! [A3: set_Extended_enat,F: extended_enat > real,G: extended_enat > real] :
% 15.55/8.62        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.62       => ( ! [I3: extended_enat] :
% 15.55/8.62              ( ( member_Extended_enat @ I3 @ A3 )
% 15.55/8.62             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 15.55/8.62                & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 15.55/8.62         => ( ( A3 != bot_bo7653980558646680370d_enat )
% 15.55/8.62           => ( ord_less_real @ ( groups97031904164794029t_real @ F @ A3 ) @ ( groups97031904164794029t_real @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8080_prod__mono__strict,axiom,
% 15.55/8.62      ! [A3: set_real,F: real > real,G: real > real] :
% 15.55/8.62        ( ( finite_finite_real @ A3 )
% 15.55/8.62       => ( ! [I3: real] :
% 15.55/8.62              ( ( member_real @ I3 @ A3 )
% 15.55/8.62             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 15.55/8.62                & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 15.55/8.62         => ( ( A3 != bot_bot_set_real )
% 15.55/8.62           => ( ord_less_real @ ( groups1681761925125756287l_real @ F @ A3 ) @ ( groups1681761925125756287l_real @ G @ A3 ) ) ) ) ) ).
% 15.55/8.62  
% 15.55/8.62  thf(fact_8081_prod__mono__strict,axiom,
% 15.55/8.62      ! [A3: set_nat,F: nat > real,G: nat > real] :
% 15.55/8.62        ( ( finite_finite_nat @ A3 )
% 15.55/8.62       => ( ! [I3: nat] :
% 15.55/8.62              ( ( member_nat @ I3 @ A3 )
% 15.55/8.62             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 15.55/8.62                & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 15.55/8.62         => ( ( A3 != bot_bot_set_nat )
% 15.55/8.62           => ( ord_less_real @ ( groups129246275422532515t_real @ F @ A3 ) @ ( groups129246275422532515t_real @ G @ A3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8082_prod__mono__strict,axiom,
% 15.55/8.63      ! [A3: set_int,F: int > real,G: int > real] :
% 15.55/8.63        ( ( finite_finite_int @ A3 )
% 15.55/8.63       => ( ! [I3: int] :
% 15.55/8.63              ( ( member_int @ I3 @ A3 )
% 15.55/8.63             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 15.55/8.63                & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 15.55/8.63         => ( ( A3 != bot_bot_set_int )
% 15.55/8.63           => ( ord_less_real @ ( groups2316167850115554303t_real @ F @ A3 ) @ ( groups2316167850115554303t_real @ G @ A3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8083_prod__mono__strict,axiom,
% 15.55/8.63      ! [A3: set_complex,F: complex > rat,G: complex > rat] :
% 15.55/8.63        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.63       => ( ! [I3: complex] :
% 15.55/8.63              ( ( member_complex @ I3 @ A3 )
% 15.55/8.63             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 15.55/8.63                & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 15.55/8.63         => ( ( A3 != bot_bot_set_complex )
% 15.55/8.63           => ( ord_less_rat @ ( groups225925009352817453ex_rat @ F @ A3 ) @ ( groups225925009352817453ex_rat @ G @ A3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8084_prod__mono__strict,axiom,
% 15.55/8.63      ! [A3: set_Extended_enat,F: extended_enat > rat,G: extended_enat > rat] :
% 15.55/8.63        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.63       => ( ! [I3: extended_enat] :
% 15.55/8.63              ( ( member_Extended_enat @ I3 @ A3 )
% 15.55/8.63             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 15.55/8.63                & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 15.55/8.63         => ( ( A3 != bot_bo7653980558646680370d_enat )
% 15.55/8.63           => ( ord_less_rat @ ( groups2245840878043517529at_rat @ F @ A3 ) @ ( groups2245840878043517529at_rat @ G @ A3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8085_prod__mono__strict,axiom,
% 15.55/8.63      ! [A3: set_real,F: real > rat,G: real > rat] :
% 15.55/8.63        ( ( finite_finite_real @ A3 )
% 15.55/8.63       => ( ! [I3: real] :
% 15.55/8.63              ( ( member_real @ I3 @ A3 )
% 15.55/8.63             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 15.55/8.63                & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 15.55/8.63         => ( ( A3 != bot_bot_set_real )
% 15.55/8.63           => ( ord_less_rat @ ( groups4061424788464935467al_rat @ F @ A3 ) @ ( groups4061424788464935467al_rat @ G @ A3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8086_prod__mono__strict,axiom,
% 15.55/8.63      ! [A3: set_nat,F: nat > rat,G: nat > rat] :
% 15.55/8.63        ( ( finite_finite_nat @ A3 )
% 15.55/8.63       => ( ! [I3: nat] :
% 15.55/8.63              ( ( member_nat @ I3 @ A3 )
% 15.55/8.63             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 15.55/8.63                & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 15.55/8.63         => ( ( A3 != bot_bot_set_nat )
% 15.55/8.63           => ( ord_less_rat @ ( groups73079841787564623at_rat @ F @ A3 ) @ ( groups73079841787564623at_rat @ G @ A3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8087_prod__mono__strict,axiom,
% 15.55/8.63      ! [A3: set_int,F: int > rat,G: int > rat] :
% 15.55/8.63        ( ( finite_finite_int @ A3 )
% 15.55/8.63       => ( ! [I3: int] :
% 15.55/8.63              ( ( member_int @ I3 @ A3 )
% 15.55/8.63             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 15.55/8.63                & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 15.55/8.63         => ( ( A3 != bot_bot_set_int )
% 15.55/8.63           => ( ord_less_rat @ ( groups1072433553688619179nt_rat @ F @ A3 ) @ ( groups1072433553688619179nt_rat @ G @ A3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8088_even__prod__iff,axiom,
% 15.55/8.63      ! [A3: set_nat,F: nat > code_integer] :
% 15.55/8.63        ( ( finite_finite_nat @ A3 )
% 15.55/8.63       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups3455450783089532116nteger @ F @ A3 ) )
% 15.55/8.63          = ( ? [X: nat] :
% 15.55/8.63                ( ( member_nat @ X @ A3 )
% 15.55/8.63                & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8089_even__prod__iff,axiom,
% 15.55/8.63      ! [A3: set_int,F: int > code_integer] :
% 15.55/8.63        ( ( finite_finite_int @ A3 )
% 15.55/8.63       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups3827104343326376752nteger @ F @ A3 ) )
% 15.55/8.63          = ( ? [X: int] :
% 15.55/8.63                ( ( member_int @ X @ A3 )
% 15.55/8.63                & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8090_even__prod__iff,axiom,
% 15.55/8.63      ! [A3: set_complex,F: complex > code_integer] :
% 15.55/8.63        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.63       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups8682486955453173170nteger @ F @ A3 ) )
% 15.55/8.63          = ( ? [X: complex] :
% 15.55/8.63                ( ( member_complex @ X @ A3 )
% 15.55/8.63                & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8091_even__prod__iff,axiom,
% 15.55/8.63      ! [A3: set_Extended_enat,F: extended_enat > code_integer] :
% 15.55/8.63        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.63       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups845124408420398302nteger @ F @ A3 ) )
% 15.55/8.63          = ( ? [X: extended_enat] :
% 15.55/8.63                ( ( member_Extended_enat @ X @ A3 )
% 15.55/8.63                & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8092_even__prod__iff,axiom,
% 15.55/8.63      ! [A3: set_int,F: int > nat] :
% 15.55/8.63        ( ( finite_finite_int @ A3 )
% 15.55/8.63       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups1707563613775114915nt_nat @ F @ A3 ) )
% 15.55/8.63          = ( ? [X: int] :
% 15.55/8.63                ( ( member_int @ X @ A3 )
% 15.55/8.63                & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8093_even__prod__iff,axiom,
% 15.55/8.63      ! [A3: set_complex,F: complex > nat] :
% 15.55/8.63        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.63       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups861055069439313189ex_nat @ F @ A3 ) )
% 15.55/8.63          = ( ? [X: complex] :
% 15.55/8.63                ( ( member_complex @ X @ A3 )
% 15.55/8.63                & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8094_even__prod__iff,axiom,
% 15.55/8.63      ! [A3: set_Extended_enat,F: extended_enat > nat] :
% 15.55/8.63        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.63       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups2880970938130013265at_nat @ F @ A3 ) )
% 15.55/8.63          = ( ? [X: extended_enat] :
% 15.55/8.63                ( ( member_Extended_enat @ X @ A3 )
% 15.55/8.63                & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8095_even__prod__iff,axiom,
% 15.55/8.63      ! [A3: set_complex,F: complex > int] :
% 15.55/8.63        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.63       => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups858564598930262913ex_int @ F @ A3 ) )
% 15.55/8.63          = ( ? [X: complex] :
% 15.55/8.63                ( ( member_complex @ X @ A3 )
% 15.55/8.63                & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8096_even__prod__iff,axiom,
% 15.55/8.63      ! [A3: set_Extended_enat,F: extended_enat > int] :
% 15.55/8.63        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.63       => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups2878480467620962989at_int @ F @ A3 ) )
% 15.55/8.63          = ( ? [X: extended_enat] :
% 15.55/8.63                ( ( member_Extended_enat @ X @ A3 )
% 15.55/8.63                & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8097_even__prod__iff,axiom,
% 15.55/8.63      ! [A3: set_nat,F: nat > int] :
% 15.55/8.63        ( ( finite_finite_nat @ A3 )
% 15.55/8.63       => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups705719431365010083at_int @ F @ A3 ) )
% 15.55/8.63          = ( ? [X: nat] :
% 15.55/8.63                ( ( member_nat @ X @ A3 )
% 15.55/8.63                & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8098_convex__sum__bound__le,axiom,
% 15.55/8.63      ! [I5: set_real,X3: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 15.55/8.63        ( ! [I3: real] :
% 15.55/8.63            ( ( member_real @ I3 @ I5 )
% 15.55/8.63           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X3 @ I3 ) ) )
% 15.55/8.63       => ( ( ( groups7713935264441627589nteger @ X3 @ I5 )
% 15.55/8.63            = one_one_Code_integer )
% 15.55/8.63         => ( ! [I3: real] :
% 15.55/8.63                ( ( member_real @ I3 @ I5 )
% 15.55/8.63               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 15.55/8.63           => ( ord_le3102999989581377725nteger
% 15.55/8.63              @ ( abs_abs_Code_integer
% 15.55/8.63                @ ( minus_8373710615458151222nteger
% 15.55/8.63                  @ ( groups7713935264441627589nteger
% 15.55/8.63                    @ ^ [I4: real] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X3 @ I4 ) )
% 15.55/8.63                    @ I5 )
% 15.55/8.63                  @ B ) )
% 15.55/8.63              @ Delta ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8099_convex__sum__bound__le,axiom,
% 15.55/8.63      ! [I5: set_nat,X3: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 15.55/8.63        ( ! [I3: nat] :
% 15.55/8.63            ( ( member_nat @ I3 @ I5 )
% 15.55/8.63           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X3 @ I3 ) ) )
% 15.55/8.63       => ( ( ( groups7501900531339628137nteger @ X3 @ I5 )
% 15.55/8.63            = one_one_Code_integer )
% 15.55/8.63         => ( ! [I3: nat] :
% 15.55/8.63                ( ( member_nat @ I3 @ I5 )
% 15.55/8.63               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 15.55/8.63           => ( ord_le3102999989581377725nteger
% 15.55/8.63              @ ( abs_abs_Code_integer
% 15.55/8.63                @ ( minus_8373710615458151222nteger
% 15.55/8.63                  @ ( groups7501900531339628137nteger
% 15.55/8.63                    @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X3 @ I4 ) )
% 15.55/8.63                    @ I5 )
% 15.55/8.63                  @ B ) )
% 15.55/8.63              @ Delta ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8100_convex__sum__bound__le,axiom,
% 15.55/8.63      ! [I5: set_int,X3: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 15.55/8.63        ( ! [I3: int] :
% 15.55/8.63            ( ( member_int @ I3 @ I5 )
% 15.55/8.63           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X3 @ I3 ) ) )
% 15.55/8.63       => ( ( ( groups7873554091576472773nteger @ X3 @ I5 )
% 15.55/8.63            = one_one_Code_integer )
% 15.55/8.63         => ( ! [I3: int] :
% 15.55/8.63                ( ( member_int @ I3 @ I5 )
% 15.55/8.63               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 15.55/8.63           => ( ord_le3102999989581377725nteger
% 15.55/8.63              @ ( abs_abs_Code_integer
% 15.55/8.63                @ ( minus_8373710615458151222nteger
% 15.55/8.63                  @ ( groups7873554091576472773nteger
% 15.55/8.63                    @ ^ [I4: int] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X3 @ I4 ) )
% 15.55/8.63                    @ I5 )
% 15.55/8.63                  @ B ) )
% 15.55/8.63              @ Delta ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8101_convex__sum__bound__le,axiom,
% 15.55/8.63      ! [I5: set_real,X3: real > real,A: real > real,B: real,Delta: real] :
% 15.55/8.63        ( ! [I3: real] :
% 15.55/8.63            ( ( member_real @ I3 @ I5 )
% 15.55/8.63           => ( ord_less_eq_real @ zero_zero_real @ ( X3 @ I3 ) ) )
% 15.55/8.63       => ( ( ( groups8097168146408367636l_real @ X3 @ I5 )
% 15.55/8.63            = one_one_real )
% 15.55/8.63         => ( ! [I3: real] :
% 15.55/8.63                ( ( member_real @ I3 @ I5 )
% 15.55/8.63               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 15.55/8.63           => ( ord_less_eq_real
% 15.55/8.63              @ ( abs_abs_real
% 15.55/8.63                @ ( minus_minus_real
% 15.55/8.63                  @ ( groups8097168146408367636l_real
% 15.55/8.63                    @ ^ [I4: real] : ( times_times_real @ ( A @ I4 ) @ ( X3 @ I4 ) )
% 15.55/8.63                    @ I5 )
% 15.55/8.63                  @ B ) )
% 15.55/8.63              @ Delta ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8102_convex__sum__bound__le,axiom,
% 15.55/8.63      ! [I5: set_int,X3: int > real,A: int > real,B: real,Delta: real] :
% 15.55/8.63        ( ! [I3: int] :
% 15.55/8.63            ( ( member_int @ I3 @ I5 )
% 15.55/8.63           => ( ord_less_eq_real @ zero_zero_real @ ( X3 @ I3 ) ) )
% 15.55/8.63       => ( ( ( groups8778361861064173332t_real @ X3 @ I5 )
% 15.55/8.63            = one_one_real )
% 15.55/8.63         => ( ! [I3: int] :
% 15.55/8.63                ( ( member_int @ I3 @ I5 )
% 15.55/8.63               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 15.55/8.63           => ( ord_less_eq_real
% 15.55/8.63              @ ( abs_abs_real
% 15.55/8.63                @ ( minus_minus_real
% 15.55/8.63                  @ ( groups8778361861064173332t_real
% 15.55/8.63                    @ ^ [I4: int] : ( times_times_real @ ( A @ I4 ) @ ( X3 @ I4 ) )
% 15.55/8.63                    @ I5 )
% 15.55/8.63                  @ B ) )
% 15.55/8.63              @ Delta ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8103_convex__sum__bound__le,axiom,
% 15.55/8.63      ! [I5: set_real,X3: real > rat,A: real > rat,B: rat,Delta: rat] :
% 15.55/8.63        ( ! [I3: real] :
% 15.55/8.63            ( ( member_real @ I3 @ I5 )
% 15.55/8.63           => ( ord_less_eq_rat @ zero_zero_rat @ ( X3 @ I3 ) ) )
% 15.55/8.63       => ( ( ( groups1300246762558778688al_rat @ X3 @ I5 )
% 15.55/8.63            = one_one_rat )
% 15.55/8.63         => ( ! [I3: real] :
% 15.55/8.63                ( ( member_real @ I3 @ I5 )
% 15.55/8.63               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 15.55/8.63           => ( ord_less_eq_rat
% 15.55/8.63              @ ( abs_abs_rat
% 15.55/8.63                @ ( minus_minus_rat
% 15.55/8.63                  @ ( groups1300246762558778688al_rat
% 15.55/8.63                    @ ^ [I4: real] : ( times_times_rat @ ( A @ I4 ) @ ( X3 @ I4 ) )
% 15.55/8.63                    @ I5 )
% 15.55/8.63                  @ B ) )
% 15.55/8.63              @ Delta ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8104_convex__sum__bound__le,axiom,
% 15.55/8.63      ! [I5: set_nat,X3: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 15.55/8.63        ( ! [I3: nat] :
% 15.55/8.63            ( ( member_nat @ I3 @ I5 )
% 15.55/8.63           => ( ord_less_eq_rat @ zero_zero_rat @ ( X3 @ I3 ) ) )
% 15.55/8.63       => ( ( ( groups2906978787729119204at_rat @ X3 @ I5 )
% 15.55/8.63            = one_one_rat )
% 15.55/8.63         => ( ! [I3: nat] :
% 15.55/8.63                ( ( member_nat @ I3 @ I5 )
% 15.55/8.63               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 15.55/8.63           => ( ord_less_eq_rat
% 15.55/8.63              @ ( abs_abs_rat
% 15.55/8.63                @ ( minus_minus_rat
% 15.55/8.63                  @ ( groups2906978787729119204at_rat
% 15.55/8.63                    @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( X3 @ I4 ) )
% 15.55/8.63                    @ I5 )
% 15.55/8.63                  @ B ) )
% 15.55/8.63              @ Delta ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8105_convex__sum__bound__le,axiom,
% 15.55/8.63      ! [I5: set_int,X3: int > rat,A: int > rat,B: rat,Delta: rat] :
% 15.55/8.63        ( ! [I3: int] :
% 15.55/8.63            ( ( member_int @ I3 @ I5 )
% 15.55/8.63           => ( ord_less_eq_rat @ zero_zero_rat @ ( X3 @ I3 ) ) )
% 15.55/8.63       => ( ( ( groups3906332499630173760nt_rat @ X3 @ I5 )
% 15.55/8.63            = one_one_rat )
% 15.55/8.63         => ( ! [I3: int] :
% 15.55/8.63                ( ( member_int @ I3 @ I5 )
% 15.55/8.63               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 15.55/8.63           => ( ord_less_eq_rat
% 15.55/8.63              @ ( abs_abs_rat
% 15.55/8.63                @ ( minus_minus_rat
% 15.55/8.63                  @ ( groups3906332499630173760nt_rat
% 15.55/8.63                    @ ^ [I4: int] : ( times_times_rat @ ( A @ I4 ) @ ( X3 @ I4 ) )
% 15.55/8.63                    @ I5 )
% 15.55/8.63                  @ B ) )
% 15.55/8.63              @ Delta ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8106_convex__sum__bound__le,axiom,
% 15.55/8.63      ! [I5: set_real,X3: real > int,A: real > int,B: int,Delta: int] :
% 15.55/8.63        ( ! [I3: real] :
% 15.55/8.63            ( ( member_real @ I3 @ I5 )
% 15.55/8.63           => ( ord_less_eq_int @ zero_zero_int @ ( X3 @ I3 ) ) )
% 15.55/8.63       => ( ( ( groups1932886352136224148al_int @ X3 @ I5 )
% 15.55/8.63            = one_one_int )
% 15.55/8.63         => ( ! [I3: real] :
% 15.55/8.63                ( ( member_real @ I3 @ I5 )
% 15.55/8.63               => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 15.55/8.63           => ( ord_less_eq_int
% 15.55/8.63              @ ( abs_abs_int
% 15.55/8.63                @ ( minus_minus_int
% 15.55/8.63                  @ ( groups1932886352136224148al_int
% 15.55/8.63                    @ ^ [I4: real] : ( times_times_int @ ( A @ I4 ) @ ( X3 @ I4 ) )
% 15.55/8.63                    @ I5 )
% 15.55/8.63                  @ B ) )
% 15.55/8.63              @ Delta ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8107_convex__sum__bound__le,axiom,
% 15.55/8.63      ! [I5: set_nat,X3: nat > int,A: nat > int,B: int,Delta: int] :
% 15.55/8.63        ( ! [I3: nat] :
% 15.55/8.63            ( ( member_nat @ I3 @ I5 )
% 15.55/8.63           => ( ord_less_eq_int @ zero_zero_int @ ( X3 @ I3 ) ) )
% 15.55/8.63       => ( ( ( groups3539618377306564664at_int @ X3 @ I5 )
% 15.55/8.63            = one_one_int )
% 15.55/8.63         => ( ! [I3: nat] :
% 15.55/8.63                ( ( member_nat @ I3 @ I5 )
% 15.55/8.63               => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 15.55/8.63           => ( ord_less_eq_int
% 15.55/8.63              @ ( abs_abs_int
% 15.55/8.63                @ ( minus_minus_int
% 15.55/8.63                  @ ( groups3539618377306564664at_int
% 15.55/8.63                    @ ^ [I4: nat] : ( times_times_int @ ( A @ I4 ) @ ( X3 @ I4 ) )
% 15.55/8.63                    @ I5 )
% 15.55/8.63                  @ B ) )
% 15.55/8.63              @ Delta ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8108_cos__arcsin__nonzero,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 15.55/8.63       => ( ( ord_less_real @ X3 @ one_one_real )
% 15.55/8.63         => ( ( cos_real @ ( arcsin @ X3 ) )
% 15.55/8.63           != zero_zero_real ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8109_prod__mono2,axiom,
% 15.55/8.63      ! [B5: set_real,A3: set_real,F: real > real] :
% 15.55/8.63        ( ( finite_finite_real @ B5 )
% 15.55/8.63       => ( ( ord_less_eq_set_real @ A3 @ B5 )
% 15.55/8.63         => ( ! [B4: real] :
% 15.55/8.63                ( ( member_real @ B4 @ ( minus_minus_set_real @ B5 @ A3 ) )
% 15.55/8.63               => ( ord_less_eq_real @ one_one_real @ ( F @ B4 ) ) )
% 15.55/8.63           => ( ! [A5: real] :
% 15.55/8.63                  ( ( member_real @ A5 @ A3 )
% 15.55/8.63                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A5 ) ) )
% 15.55/8.63             => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A3 ) @ ( groups1681761925125756287l_real @ F @ B5 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8110_prod__mono2,axiom,
% 15.55/8.63      ! [B5: set_int,A3: set_int,F: int > real] :
% 15.55/8.63        ( ( finite_finite_int @ B5 )
% 15.55/8.63       => ( ( ord_less_eq_set_int @ A3 @ B5 )
% 15.55/8.63         => ( ! [B4: int] :
% 15.55/8.63                ( ( member_int @ B4 @ ( minus_minus_set_int @ B5 @ A3 ) )
% 15.55/8.63               => ( ord_less_eq_real @ one_one_real @ ( F @ B4 ) ) )
% 15.55/8.63           => ( ! [A5: int] :
% 15.55/8.63                  ( ( member_int @ A5 @ A3 )
% 15.55/8.63                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A5 ) ) )
% 15.55/8.63             => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A3 ) @ ( groups2316167850115554303t_real @ F @ B5 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8111_prod__mono2,axiom,
% 15.55/8.63      ! [B5: set_complex,A3: set_complex,F: complex > real] :
% 15.55/8.63        ( ( finite3207457112153483333omplex @ B5 )
% 15.55/8.63       => ( ( ord_le211207098394363844omplex @ A3 @ B5 )
% 15.55/8.63         => ( ! [B4: complex] :
% 15.55/8.63                ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B5 @ A3 ) )
% 15.55/8.63               => ( ord_less_eq_real @ one_one_real @ ( F @ B4 ) ) )
% 15.55/8.63           => ( ! [A5: complex] :
% 15.55/8.63                  ( ( member_complex @ A5 @ A3 )
% 15.55/8.63                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A5 ) ) )
% 15.55/8.63             => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A3 ) @ ( groups766887009212190081x_real @ F @ B5 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8112_prod__mono2,axiom,
% 15.55/8.63      ! [B5: set_Extended_enat,A3: set_Extended_enat,F: extended_enat > real] :
% 15.55/8.63        ( ( finite4001608067531595151d_enat @ B5 )
% 15.55/8.63       => ( ( ord_le7203529160286727270d_enat @ A3 @ B5 )
% 15.55/8.63         => ( ! [B4: extended_enat] :
% 15.55/8.63                ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ B5 @ A3 ) )
% 15.55/8.63               => ( ord_less_eq_real @ one_one_real @ ( F @ B4 ) ) )
% 15.55/8.63           => ( ! [A5: extended_enat] :
% 15.55/8.63                  ( ( member_Extended_enat @ A5 @ A3 )
% 15.55/8.63                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A5 ) ) )
% 15.55/8.63             => ( ord_less_eq_real @ ( groups97031904164794029t_real @ F @ A3 ) @ ( groups97031904164794029t_real @ F @ B5 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8113_prod__mono2,axiom,
% 15.55/8.63      ! [B5: set_real,A3: set_real,F: real > rat] :
% 15.55/8.63        ( ( finite_finite_real @ B5 )
% 15.55/8.63       => ( ( ord_less_eq_set_real @ A3 @ B5 )
% 15.55/8.63         => ( ! [B4: real] :
% 15.55/8.63                ( ( member_real @ B4 @ ( minus_minus_set_real @ B5 @ A3 ) )
% 15.55/8.63               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B4 ) ) )
% 15.55/8.63           => ( ! [A5: real] :
% 15.55/8.63                  ( ( member_real @ A5 @ A3 )
% 15.55/8.63                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A5 ) ) )
% 15.55/8.63             => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A3 ) @ ( groups4061424788464935467al_rat @ F @ B5 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8114_prod__mono2,axiom,
% 15.55/8.63      ! [B5: set_int,A3: set_int,F: int > rat] :
% 15.55/8.63        ( ( finite_finite_int @ B5 )
% 15.55/8.63       => ( ( ord_less_eq_set_int @ A3 @ B5 )
% 15.55/8.63         => ( ! [B4: int] :
% 15.55/8.63                ( ( member_int @ B4 @ ( minus_minus_set_int @ B5 @ A3 ) )
% 15.55/8.63               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B4 ) ) )
% 15.55/8.63           => ( ! [A5: int] :
% 15.55/8.63                  ( ( member_int @ A5 @ A3 )
% 15.55/8.63                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A5 ) ) )
% 15.55/8.63             => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A3 ) @ ( groups1072433553688619179nt_rat @ F @ B5 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8115_prod__mono2,axiom,
% 15.55/8.63      ! [B5: set_complex,A3: set_complex,F: complex > rat] :
% 15.55/8.63        ( ( finite3207457112153483333omplex @ B5 )
% 15.55/8.63       => ( ( ord_le211207098394363844omplex @ A3 @ B5 )
% 15.55/8.63         => ( ! [B4: complex] :
% 15.55/8.63                ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B5 @ A3 ) )
% 15.55/8.63               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B4 ) ) )
% 15.55/8.63           => ( ! [A5: complex] :
% 15.55/8.63                  ( ( member_complex @ A5 @ A3 )
% 15.55/8.63                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A5 ) ) )
% 15.55/8.63             => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A3 ) @ ( groups225925009352817453ex_rat @ F @ B5 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8116_prod__mono2,axiom,
% 15.55/8.63      ! [B5: set_Extended_enat,A3: set_Extended_enat,F: extended_enat > rat] :
% 15.55/8.63        ( ( finite4001608067531595151d_enat @ B5 )
% 15.55/8.63       => ( ( ord_le7203529160286727270d_enat @ A3 @ B5 )
% 15.55/8.63         => ( ! [B4: extended_enat] :
% 15.55/8.63                ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ B5 @ A3 ) )
% 15.55/8.63               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B4 ) ) )
% 15.55/8.63           => ( ! [A5: extended_enat] :
% 15.55/8.63                  ( ( member_Extended_enat @ A5 @ A3 )
% 15.55/8.63                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A5 ) ) )
% 15.55/8.63             => ( ord_less_eq_rat @ ( groups2245840878043517529at_rat @ F @ A3 ) @ ( groups2245840878043517529at_rat @ F @ B5 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8117_prod__mono2,axiom,
% 15.55/8.63      ! [B5: set_real,A3: set_real,F: real > int] :
% 15.55/8.63        ( ( finite_finite_real @ B5 )
% 15.55/8.63       => ( ( ord_less_eq_set_real @ A3 @ B5 )
% 15.55/8.63         => ( ! [B4: real] :
% 15.55/8.63                ( ( member_real @ B4 @ ( minus_minus_set_real @ B5 @ A3 ) )
% 15.55/8.63               => ( ord_less_eq_int @ one_one_int @ ( F @ B4 ) ) )
% 15.55/8.63           => ( ! [A5: real] :
% 15.55/8.63                  ( ( member_real @ A5 @ A3 )
% 15.55/8.63                 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A5 ) ) )
% 15.55/8.63             => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F @ A3 ) @ ( groups4694064378042380927al_int @ F @ B5 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8118_prod__mono2,axiom,
% 15.55/8.63      ! [B5: set_complex,A3: set_complex,F: complex > int] :
% 15.55/8.63        ( ( finite3207457112153483333omplex @ B5 )
% 15.55/8.63       => ( ( ord_le211207098394363844omplex @ A3 @ B5 )
% 15.55/8.63         => ( ! [B4: complex] :
% 15.55/8.63                ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B5 @ A3 ) )
% 15.55/8.63               => ( ord_less_eq_int @ one_one_int @ ( F @ B4 ) ) )
% 15.55/8.63           => ( ! [A5: complex] :
% 15.55/8.63                  ( ( member_complex @ A5 @ A3 )
% 15.55/8.63                 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A5 ) ) )
% 15.55/8.63             => ( ord_less_eq_int @ ( groups858564598930262913ex_int @ F @ A3 ) @ ( groups858564598930262913ex_int @ F @ B5 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8119_sum__natinterval__diff,axiom,
% 15.55/8.63      ! [M: nat,N: nat,F: nat > rat] :
% 15.55/8.63        ( ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.63         => ( ( groups2906978787729119204at_rat
% 15.55/8.63              @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 15.55/8.63              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.63            = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 15.55/8.63        & ( ~ ( ord_less_eq_nat @ M @ N )
% 15.55/8.63         => ( ( groups2906978787729119204at_rat
% 15.55/8.63              @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 15.55/8.63              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.63            = zero_zero_rat ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8120_sum__natinterval__diff,axiom,
% 15.55/8.63      ! [M: nat,N: nat,F: nat > int] :
% 15.55/8.63        ( ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.63         => ( ( groups3539618377306564664at_int
% 15.55/8.63              @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 15.55/8.63              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.63            = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 15.55/8.63        & ( ~ ( ord_less_eq_nat @ M @ N )
% 15.55/8.63         => ( ( groups3539618377306564664at_int
% 15.55/8.63              @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 15.55/8.63              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.63            = zero_zero_int ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8121_sum__natinterval__diff,axiom,
% 15.55/8.63      ! [M: nat,N: nat,F: nat > real] :
% 15.55/8.63        ( ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.63         => ( ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 15.55/8.63              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.63            = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 15.55/8.63        & ( ~ ( ord_less_eq_nat @ M @ N )
% 15.55/8.63         => ( ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 15.55/8.63              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.63            = zero_zero_real ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8122_sum__telescope_H_H,axiom,
% 15.55/8.63      ! [M: nat,N: nat,F: nat > rat] :
% 15.55/8.63        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.63       => ( ( groups2906978787729119204at_rat
% 15.55/8.63            @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 15.55/8.63            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 15.55/8.63          = ( minus_minus_rat @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8123_sum__telescope_H_H,axiom,
% 15.55/8.63      ! [M: nat,N: nat,F: nat > int] :
% 15.55/8.63        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.63       => ( ( groups3539618377306564664at_int
% 15.55/8.63            @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 15.55/8.63            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 15.55/8.63          = ( minus_minus_int @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8124_sum__telescope_H_H,axiom,
% 15.55/8.63      ! [M: nat,N: nat,F: nat > real] :
% 15.55/8.63        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.63       => ( ( groups6591440286371151544t_real
% 15.55/8.63            @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 15.55/8.63            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 15.55/8.63          = ( minus_minus_real @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8125_prod__diff1,axiom,
% 15.55/8.63      ! [A3: set_complex,F: complex > complex,A: complex] :
% 15.55/8.63        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.63       => ( ( ( F @ A )
% 15.55/8.63           != zero_zero_complex )
% 15.55/8.63         => ( ( ( member_complex @ A @ A3 )
% 15.55/8.63             => ( ( groups3708469109370488835omplex @ F @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 15.55/8.63                = ( divide1717551699836669952omplex @ ( groups3708469109370488835omplex @ F @ A3 ) @ ( F @ A ) ) ) )
% 15.55/8.63            & ( ~ ( member_complex @ A @ A3 )
% 15.55/8.63             => ( ( groups3708469109370488835omplex @ F @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 15.55/8.63                = ( groups3708469109370488835omplex @ F @ A3 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8126_prod__diff1,axiom,
% 15.55/8.63      ! [A3: set_Extended_enat,F: extended_enat > complex,A: extended_enat] :
% 15.55/8.63        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.63       => ( ( ( F @ A )
% 15.55/8.63           != zero_zero_complex )
% 15.55/8.63         => ( ( ( member_Extended_enat @ A @ A3 )
% 15.55/8.63             => ( ( groups4622424608036095791omplex @ F @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 15.55/8.63                = ( divide1717551699836669952omplex @ ( groups4622424608036095791omplex @ F @ A3 ) @ ( F @ A ) ) ) )
% 15.55/8.63            & ( ~ ( member_Extended_enat @ A @ A3 )
% 15.55/8.63             => ( ( groups4622424608036095791omplex @ F @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 15.55/8.63                = ( groups4622424608036095791omplex @ F @ A3 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8127_prod__diff1,axiom,
% 15.55/8.63      ! [A3: set_real,F: real > complex,A: real] :
% 15.55/8.63        ( ( finite_finite_real @ A3 )
% 15.55/8.63       => ( ( ( F @ A )
% 15.55/8.63           != zero_zero_complex )
% 15.55/8.63         => ( ( ( member_real @ A @ A3 )
% 15.55/8.63             => ( ( groups713298508707869441omplex @ F @ ( minus_minus_set_real @ A3 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 15.55/8.63                = ( divide1717551699836669952omplex @ ( groups713298508707869441omplex @ F @ A3 ) @ ( F @ A ) ) ) )
% 15.55/8.63            & ( ~ ( member_real @ A @ A3 )
% 15.55/8.63             => ( ( groups713298508707869441omplex @ F @ ( minus_minus_set_real @ A3 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 15.55/8.63                = ( groups713298508707869441omplex @ F @ A3 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8128_prod__diff1,axiom,
% 15.55/8.63      ! [A3: set_int,F: int > complex,A: int] :
% 15.55/8.63        ( ( finite_finite_int @ A3 )
% 15.55/8.63       => ( ( ( F @ A )
% 15.55/8.63           != zero_zero_complex )
% 15.55/8.63         => ( ( ( member_int @ A @ A3 )
% 15.55/8.63             => ( ( groups7440179247065528705omplex @ F @ ( minus_minus_set_int @ A3 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 15.55/8.63                = ( divide1717551699836669952omplex @ ( groups7440179247065528705omplex @ F @ A3 ) @ ( F @ A ) ) ) )
% 15.55/8.63            & ( ~ ( member_int @ A @ A3 )
% 15.55/8.63             => ( ( groups7440179247065528705omplex @ F @ ( minus_minus_set_int @ A3 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 15.55/8.63                = ( groups7440179247065528705omplex @ F @ A3 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8129_prod__diff1,axiom,
% 15.55/8.63      ! [A3: set_nat,F: nat > complex,A: nat] :
% 15.55/8.63        ( ( finite_finite_nat @ A3 )
% 15.55/8.63       => ( ( ( F @ A )
% 15.55/8.63           != zero_zero_complex )
% 15.55/8.63         => ( ( ( member_nat @ A @ A3 )
% 15.55/8.63             => ( ( groups6464643781859351333omplex @ F @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 15.55/8.63                = ( divide1717551699836669952omplex @ ( groups6464643781859351333omplex @ F @ A3 ) @ ( F @ A ) ) ) )
% 15.55/8.63            & ( ~ ( member_nat @ A @ A3 )
% 15.55/8.63             => ( ( groups6464643781859351333omplex @ F @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 15.55/8.63                = ( groups6464643781859351333omplex @ F @ A3 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8130_prod__diff1,axiom,
% 15.55/8.63      ! [A3: set_complex,F: complex > real,A: complex] :
% 15.55/8.63        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.63       => ( ( ( F @ A )
% 15.55/8.63           != zero_zero_real )
% 15.55/8.63         => ( ( ( member_complex @ A @ A3 )
% 15.55/8.63             => ( ( groups766887009212190081x_real @ F @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 15.55/8.63                = ( divide_divide_real @ ( groups766887009212190081x_real @ F @ A3 ) @ ( F @ A ) ) ) )
% 15.55/8.63            & ( ~ ( member_complex @ A @ A3 )
% 15.55/8.63             => ( ( groups766887009212190081x_real @ F @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 15.55/8.63                = ( groups766887009212190081x_real @ F @ A3 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8131_prod__diff1,axiom,
% 15.55/8.63      ! [A3: set_Extended_enat,F: extended_enat > real,A: extended_enat] :
% 15.55/8.63        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.63       => ( ( ( F @ A )
% 15.55/8.63           != zero_zero_real )
% 15.55/8.63         => ( ( ( member_Extended_enat @ A @ A3 )
% 15.55/8.63             => ( ( groups97031904164794029t_real @ F @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 15.55/8.63                = ( divide_divide_real @ ( groups97031904164794029t_real @ F @ A3 ) @ ( F @ A ) ) ) )
% 15.55/8.63            & ( ~ ( member_Extended_enat @ A @ A3 )
% 15.55/8.63             => ( ( groups97031904164794029t_real @ F @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 15.55/8.63                = ( groups97031904164794029t_real @ F @ A3 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8132_prod__diff1,axiom,
% 15.55/8.63      ! [A3: set_real,F: real > real,A: real] :
% 15.55/8.63        ( ( finite_finite_real @ A3 )
% 15.55/8.63       => ( ( ( F @ A )
% 15.55/8.63           != zero_zero_real )
% 15.55/8.63         => ( ( ( member_real @ A @ A3 )
% 15.55/8.63             => ( ( groups1681761925125756287l_real @ F @ ( minus_minus_set_real @ A3 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 15.55/8.63                = ( divide_divide_real @ ( groups1681761925125756287l_real @ F @ A3 ) @ ( F @ A ) ) ) )
% 15.55/8.63            & ( ~ ( member_real @ A @ A3 )
% 15.55/8.63             => ( ( groups1681761925125756287l_real @ F @ ( minus_minus_set_real @ A3 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 15.55/8.63                = ( groups1681761925125756287l_real @ F @ A3 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8133_prod__diff1,axiom,
% 15.55/8.63      ! [A3: set_int,F: int > real,A: int] :
% 15.55/8.63        ( ( finite_finite_int @ A3 )
% 15.55/8.63       => ( ( ( F @ A )
% 15.55/8.63           != zero_zero_real )
% 15.55/8.63         => ( ( ( member_int @ A @ A3 )
% 15.55/8.63             => ( ( groups2316167850115554303t_real @ F @ ( minus_minus_set_int @ A3 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 15.55/8.63                = ( divide_divide_real @ ( groups2316167850115554303t_real @ F @ A3 ) @ ( F @ A ) ) ) )
% 15.55/8.63            & ( ~ ( member_int @ A @ A3 )
% 15.55/8.63             => ( ( groups2316167850115554303t_real @ F @ ( minus_minus_set_int @ A3 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 15.55/8.63                = ( groups2316167850115554303t_real @ F @ A3 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8134_prod__diff1,axiom,
% 15.55/8.63      ! [A3: set_nat,F: nat > real,A: nat] :
% 15.55/8.63        ( ( finite_finite_nat @ A3 )
% 15.55/8.63       => ( ( ( F @ A )
% 15.55/8.63           != zero_zero_real )
% 15.55/8.63         => ( ( ( member_nat @ A @ A3 )
% 15.55/8.63             => ( ( groups129246275422532515t_real @ F @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 15.55/8.63                = ( divide_divide_real @ ( groups129246275422532515t_real @ F @ A3 ) @ ( F @ A ) ) ) )
% 15.55/8.63            & ( ~ ( member_nat @ A @ A3 )
% 15.55/8.63             => ( ( groups129246275422532515t_real @ F @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 15.55/8.63                = ( groups129246275422532515t_real @ F @ A3 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8135_summable__partial__sum__bound,axiom,
% 15.55/8.63      ! [F: nat > complex,E2: real] :
% 15.55/8.63        ( ( summable_complex @ F )
% 15.55/8.63       => ( ( ord_less_real @ zero_zero_real @ E2 )
% 15.55/8.63         => ~ ! [N7: nat] :
% 15.55/8.63                ~ ! [M2: nat] :
% 15.55/8.63                    ( ( ord_less_eq_nat @ N7 @ M2 )
% 15.55/8.63                   => ! [N8: nat] : ( ord_less_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ M2 @ N8 ) ) ) @ E2 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8136_summable__partial__sum__bound,axiom,
% 15.55/8.63      ! [F: nat > real,E2: real] :
% 15.55/8.63        ( ( summable_real @ F )
% 15.55/8.63       => ( ( ord_less_real @ zero_zero_real @ E2 )
% 15.55/8.63         => ~ ! [N7: nat] :
% 15.55/8.63                ~ ! [M2: nat] :
% 15.55/8.63                    ( ( ord_less_eq_nat @ N7 @ M2 )
% 15.55/8.63                   => ! [N8: nat] : ( ord_less_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ M2 @ N8 ) ) ) @ E2 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8137_mask__eq__sum__exp,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int )
% 15.55/8.63        = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.63          @ ( collect_nat
% 15.55/8.63            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8138_mask__eq__sum__exp,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat )
% 15.55/8.63        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.63          @ ( collect_nat
% 15.55/8.63            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8139_sum__gp__multiplied,axiom,
% 15.55/8.63      ! [M: nat,N: nat,X3: complex] :
% 15.55/8.63        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.63       => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X3 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 15.55/8.63          = ( minus_minus_complex @ ( power_power_complex @ X3 @ M ) @ ( power_power_complex @ X3 @ ( suc @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8140_sum__gp__multiplied,axiom,
% 15.55/8.63      ! [M: nat,N: nat,X3: rat] :
% 15.55/8.63        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.63       => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X3 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 15.55/8.63          = ( minus_minus_rat @ ( power_power_rat @ X3 @ M ) @ ( power_power_rat @ X3 @ ( suc @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8141_sum__gp__multiplied,axiom,
% 15.55/8.63      ! [M: nat,N: nat,X3: int] :
% 15.55/8.63        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.63       => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X3 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 15.55/8.63          = ( minus_minus_int @ ( power_power_int @ X3 @ M ) @ ( power_power_int @ X3 @ ( suc @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8142_sum__gp__multiplied,axiom,
% 15.55/8.63      ! [M: nat,N: nat,X3: real] :
% 15.55/8.63        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.63       => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X3 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 15.55/8.63          = ( minus_minus_real @ ( power_power_real @ X3 @ M ) @ ( power_power_real @ X3 @ ( suc @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8143_sum_Oin__pairs,axiom,
% 15.55/8.63      ! [G: nat > rat,M: nat,N: nat] :
% 15.55/8.63        ( ( 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 ) ) ) )
% 15.55/8.63        = ( groups2906978787729119204at_rat
% 15.55/8.63          @ ^ [I4: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 15.55/8.63          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8144_sum_Oin__pairs,axiom,
% 15.55/8.63      ! [G: nat > int,M: nat,N: nat] :
% 15.55/8.63        ( ( 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 ) ) ) )
% 15.55/8.63        = ( groups3539618377306564664at_int
% 15.55/8.63          @ ^ [I4: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 15.55/8.63          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8145_sum_Oin__pairs,axiom,
% 15.55/8.63      ! [G: nat > nat,M: nat,N: nat] :
% 15.55/8.63        ( ( 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 ) ) ) )
% 15.55/8.63        = ( groups3542108847815614940at_nat
% 15.55/8.63          @ ^ [I4: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 15.55/8.63          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8146_sum_Oin__pairs,axiom,
% 15.55/8.63      ! [G: nat > real,M: nat,N: nat] :
% 15.55/8.63        ( ( 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 ) ) ) )
% 15.55/8.63        = ( groups6591440286371151544t_real
% 15.55/8.63          @ ^ [I4: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 15.55/8.63          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8147_complex__norm,axiom,
% 15.55/8.63      ! [X3: real,Y3: real] :
% 15.55/8.63        ( ( real_V1022390504157884413omplex @ ( complex2 @ X3 @ Y3 ) )
% 15.55/8.63        = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8148_mask__eq__sum__exp__nat,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 15.55/8.63        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.63          @ ( collect_nat
% 15.55/8.63            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8149_gauss__sum__nat,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( groups3542108847815614940at_nat
% 15.55/8.63          @ ^ [X: nat] : X
% 15.55/8.63          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 15.55/8.63        = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8150_double__arith__series,axiom,
% 15.55/8.63      ! [A: complex,D3: complex,N: nat] :
% 15.55/8.63        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 15.55/8.63          @ ( groups2073611262835488442omplex
% 15.55/8.63            @ ^ [I4: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I4 ) @ D3 ) )
% 15.55/8.63            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 15.55/8.63        = ( 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 ) @ D3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8151_double__arith__series,axiom,
% 15.55/8.63      ! [A: rat,D3: rat,N: nat] :
% 15.55/8.63        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 15.55/8.63          @ ( groups2906978787729119204at_rat
% 15.55/8.63            @ ^ [I4: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I4 ) @ D3 ) )
% 15.55/8.63            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 15.55/8.63        = ( 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 ) @ D3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8152_double__arith__series,axiom,
% 15.55/8.63      ! [A: int,D3: int,N: nat] :
% 15.55/8.63        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 15.55/8.63          @ ( groups3539618377306564664at_int
% 15.55/8.63            @ ^ [I4: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I4 ) @ D3 ) )
% 15.55/8.63            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 15.55/8.63        = ( 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 ) @ D3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8153_double__arith__series,axiom,
% 15.55/8.63      ! [A: nat,D3: nat,N: nat] :
% 15.55/8.63        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 15.55/8.63          @ ( groups3542108847815614940at_nat
% 15.55/8.63            @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I4 ) @ D3 ) )
% 15.55/8.63            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 15.55/8.63        = ( 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 ) @ D3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8154_double__arith__series,axiom,
% 15.55/8.63      ! [A: real,D3: real,N: nat] :
% 15.55/8.63        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 15.55/8.63          @ ( groups6591440286371151544t_real
% 15.55/8.63            @ ^ [I4: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I4 ) @ D3 ) )
% 15.55/8.63            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 15.55/8.63        = ( 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 ) @ D3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8155_double__gauss__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 15.55/8.63        = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8156_double__gauss__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 15.55/8.63        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8157_double__gauss__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 15.55/8.63        = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8158_double__gauss__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 15.55/8.63        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8159_double__gauss__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 15.55/8.63        = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8160_arith__series__nat,axiom,
% 15.55/8.63      ! [A: nat,D3: nat,N: nat] :
% 15.55/8.63        ( ( groups3542108847815614940at_nat
% 15.55/8.63          @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I4 @ D3 ) )
% 15.55/8.63          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 15.55/8.63        = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N @ D3 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8161_Sum__Icc__nat,axiom,
% 15.55/8.63      ! [M: nat,N: nat] :
% 15.55/8.63        ( ( groups3542108847815614940at_nat
% 15.55/8.63          @ ^ [X: nat] : X
% 15.55/8.63          @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.63        = ( 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 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8162_arcsin__lt__bounded,axiom,
% 15.55/8.63      ! [Y3: real] :
% 15.55/8.63        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 15.55/8.63       => ( ( ord_less_real @ Y3 @ one_one_real )
% 15.55/8.63         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) )
% 15.55/8.63            & ( ord_less_real @ ( arcsin @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8163_arcsin__bounded,axiom,
% 15.55/8.63      ! [Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 15.55/8.63       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 15.55/8.63         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) )
% 15.55/8.63            & ( ord_less_eq_real @ ( arcsin @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8164_arcsin__ubound,axiom,
% 15.55/8.63      ! [Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 15.55/8.63       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 15.55/8.63         => ( ord_less_eq_real @ ( arcsin @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8165_arcsin__lbound,axiom,
% 15.55/8.63      ! [Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 15.55/8.63       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 15.55/8.63         => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8166_arcsin__sin,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 15.55/8.63       => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.63         => ( ( arcsin @ ( sin_real @ X3 ) )
% 15.55/8.63            = X3 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8167_double__gauss__sum__from__Suc__0,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 15.55/8.63        = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8168_double__gauss__sum__from__Suc__0,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 15.55/8.63        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8169_double__gauss__sum__from__Suc__0,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 15.55/8.63        = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8170_double__gauss__sum__from__Suc__0,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 15.55/8.63        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8171_double__gauss__sum__from__Suc__0,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 15.55/8.63        = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8172_gauss__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 15.55/8.63        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8173_gauss__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 15.55/8.63        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8174_arith__series,axiom,
% 15.55/8.63      ! [A: int,D3: int,N: nat] :
% 15.55/8.63        ( ( groups3539618377306564664at_int
% 15.55/8.63          @ ^ [I4: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I4 ) @ D3 ) )
% 15.55/8.63          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 15.55/8.63        = ( 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 ) @ D3 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8175_arith__series,axiom,
% 15.55/8.63      ! [A: nat,D3: nat,N: nat] :
% 15.55/8.63        ( ( groups3542108847815614940at_nat
% 15.55/8.63          @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I4 ) @ D3 ) )
% 15.55/8.63          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 15.55/8.63        = ( 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 ) @ D3 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8176_sum__gp__offset,axiom,
% 15.55/8.63      ! [X3: complex,M: nat,N: nat] :
% 15.55/8.63        ( ( ( X3 = one_one_complex )
% 15.55/8.63         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 15.55/8.63            = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) )
% 15.55/8.63        & ( ( X3 != one_one_complex )
% 15.55/8.63         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 15.55/8.63            = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X3 @ M ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ ( suc @ N ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8177_sum__gp__offset,axiom,
% 15.55/8.63      ! [X3: rat,M: nat,N: nat] :
% 15.55/8.63        ( ( ( X3 = one_one_rat )
% 15.55/8.63         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 15.55/8.63            = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) )
% 15.55/8.63        & ( ( X3 != one_one_rat )
% 15.55/8.63         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 15.55/8.63            = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X3 @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ ( suc @ N ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8178_sum__gp__offset,axiom,
% 15.55/8.63      ! [X3: real,M: nat,N: nat] :
% 15.55/8.63        ( ( ( X3 = one_one_real )
% 15.55/8.63         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 15.55/8.63            = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) )
% 15.55/8.63        & ( ( X3 != one_one_real )
% 15.55/8.63         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 15.55/8.63            = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X3 @ M ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( suc @ N ) ) ) ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8179_arcsin,axiom,
% 15.55/8.63      ! [Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 15.55/8.63       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 15.55/8.63         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) )
% 15.55/8.63            & ( ord_less_eq_real @ ( arcsin @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.63            & ( ( sin_real @ ( arcsin @ Y3 ) )
% 15.55/8.63              = Y3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8180_arcsin__pi,axiom,
% 15.55/8.63      ! [Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 15.55/8.63       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 15.55/8.63         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) )
% 15.55/8.63            & ( ord_less_eq_real @ ( arcsin @ Y3 ) @ pi )
% 15.55/8.63            & ( ( sin_real @ ( arcsin @ Y3 ) )
% 15.55/8.63              = Y3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8181_arcsin__le__iff,axiom,
% 15.55/8.63      ! [X3: real,Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 15.55/8.63       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 15.55/8.63         => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y3 )
% 15.55/8.63           => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.63             => ( ( ord_less_eq_real @ ( arcsin @ X3 ) @ Y3 )
% 15.55/8.63                = ( ord_less_eq_real @ X3 @ ( sin_real @ Y3 ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8182_le__arcsin__iff,axiom,
% 15.55/8.63      ! [X3: real,Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 15.55/8.63       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 15.55/8.63         => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y3 )
% 15.55/8.63           => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.63             => ( ( ord_less_eq_real @ Y3 @ ( arcsin @ X3 ) )
% 15.55/8.63                = ( ord_less_eq_real @ ( sin_real @ Y3 ) @ X3 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8183_gauss__sum__from__Suc__0,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 15.55/8.63        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8184_gauss__sum__from__Suc__0,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 15.55/8.63        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8185_finite__Collect__le__nat,axiom,
% 15.55/8.63      ! [K: nat] :
% 15.55/8.63        ( finite_finite_nat
% 15.55/8.63        @ ( collect_nat
% 15.55/8.63          @ ^ [N3: nat] : ( ord_less_eq_nat @ N3 @ K ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8186_finite__Collect__less__nat,axiom,
% 15.55/8.63      ! [K: nat] :
% 15.55/8.63        ( finite_finite_nat
% 15.55/8.63        @ ( collect_nat
% 15.55/8.63          @ ^ [N3: nat] : ( ord_less_nat @ N3 @ K ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8187_set__encode__insert,axiom,
% 15.55/8.63      ! [A3: set_nat,N: nat] :
% 15.55/8.63        ( ( finite_finite_nat @ A3 )
% 15.55/8.63       => ( ~ ( member_nat @ N @ A3 )
% 15.55/8.63         => ( ( nat_set_encode @ ( insert_nat @ N @ A3 ) )
% 15.55/8.63            = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8188_lemma__termdiff2,axiom,
% 15.55/8.63      ! [H2: complex,Z: complex,N: nat] :
% 15.55/8.63        ( ( H2 != zero_zero_complex )
% 15.55/8.63       => ( ( 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 ) ) ) ) )
% 15.55/8.63          = ( times_times_complex @ H2
% 15.55/8.63            @ ( groups2073611262835488442omplex
% 15.55/8.63              @ ^ [P5: nat] :
% 15.55/8.63                  ( groups2073611262835488442omplex
% 15.55/8.63                  @ ^ [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 ) ) )
% 15.55/8.63                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 15.55/8.63              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8189_lemma__termdiff2,axiom,
% 15.55/8.63      ! [H2: rat,Z: rat,N: nat] :
% 15.55/8.63        ( ( H2 != zero_zero_rat )
% 15.55/8.63       => ( ( 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 ) ) ) ) )
% 15.55/8.63          = ( times_times_rat @ H2
% 15.55/8.63            @ ( groups2906978787729119204at_rat
% 15.55/8.63              @ ^ [P5: nat] :
% 15.55/8.63                  ( groups2906978787729119204at_rat
% 15.55/8.63                  @ ^ [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 ) ) )
% 15.55/8.63                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 15.55/8.63              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8190_lemma__termdiff2,axiom,
% 15.55/8.63      ! [H2: real,Z: real,N: nat] :
% 15.55/8.63        ( ( H2 != zero_zero_real )
% 15.55/8.63       => ( ( 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 ) ) ) ) )
% 15.55/8.63          = ( times_times_real @ H2
% 15.55/8.63            @ ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [P5: nat] :
% 15.55/8.63                  ( groups6591440286371151544t_real
% 15.55/8.63                  @ ^ [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 ) ) )
% 15.55/8.63                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 15.55/8.63              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8191_choose__odd__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.63       => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 15.55/8.63            @ ( groups2073611262835488442omplex
% 15.55/8.63              @ ^ [I4: nat] :
% 15.55/8.63                  ( if_complex
% 15.55/8.63                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 15.55/8.63                  @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I4 ) )
% 15.55/8.63                  @ zero_zero_complex )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63          = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8192_choose__odd__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.63       => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 15.55/8.63            @ ( groups2906978787729119204at_rat
% 15.55/8.63              @ ^ [I4: nat] :
% 15.55/8.63                  ( if_rat
% 15.55/8.63                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 15.55/8.63                  @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I4 ) )
% 15.55/8.63                  @ zero_zero_rat )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63          = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8193_choose__odd__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.63       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 15.55/8.63            @ ( groups3539618377306564664at_int
% 15.55/8.63              @ ^ [I4: nat] :
% 15.55/8.63                  ( if_int
% 15.55/8.63                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 15.55/8.63                  @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I4 ) )
% 15.55/8.63                  @ zero_zero_int )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63          = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8194_choose__odd__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.63       => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 15.55/8.63            @ ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [I4: nat] :
% 15.55/8.63                  ( if_real
% 15.55/8.63                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 15.55/8.63                  @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I4 ) )
% 15.55/8.63                  @ zero_zero_real )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8195_finite__interval__int1,axiom,
% 15.55/8.63      ! [A: int,B: int] :
% 15.55/8.63        ( finite_finite_int
% 15.55/8.63        @ ( collect_int
% 15.55/8.63          @ ^ [I4: int] :
% 15.55/8.63              ( ( ord_less_eq_int @ A @ I4 )
% 15.55/8.63              & ( ord_less_eq_int @ I4 @ B ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8196_finite__interval__int4,axiom,
% 15.55/8.63      ! [A: int,B: int] :
% 15.55/8.63        ( finite_finite_int
% 15.55/8.63        @ ( collect_int
% 15.55/8.63          @ ^ [I4: int] :
% 15.55/8.63              ( ( ord_less_int @ A @ I4 )
% 15.55/8.63              & ( ord_less_int @ I4 @ B ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8197_lessThan__iff,axiom,
% 15.55/8.63      ! [I: set_nat,K: set_nat] :
% 15.55/8.63        ( ( member_set_nat @ I @ ( set_or890127255671739683et_nat @ K ) )
% 15.55/8.63        = ( ord_less_set_nat @ I @ K ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8198_lessThan__iff,axiom,
% 15.55/8.63      ! [I: rat,K: rat] :
% 15.55/8.63        ( ( member_rat @ I @ ( set_ord_lessThan_rat @ K ) )
% 15.55/8.63        = ( ord_less_rat @ I @ K ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8199_lessThan__iff,axiom,
% 15.55/8.63      ! [I: num,K: num] :
% 15.55/8.63        ( ( member_num @ I @ ( set_ord_lessThan_num @ K ) )
% 15.55/8.63        = ( ord_less_num @ I @ K ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8200_lessThan__iff,axiom,
% 15.55/8.63      ! [I: int,K: int] :
% 15.55/8.63        ( ( member_int @ I @ ( set_ord_lessThan_int @ K ) )
% 15.55/8.63        = ( ord_less_int @ I @ K ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8201_lessThan__iff,axiom,
% 15.55/8.63      ! [I: nat,K: nat] :
% 15.55/8.63        ( ( member_nat @ I @ ( set_ord_lessThan_nat @ K ) )
% 15.55/8.63        = ( ord_less_nat @ I @ K ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8202_lessThan__iff,axiom,
% 15.55/8.63      ! [I: real,K: real] :
% 15.55/8.63        ( ( member_real @ I @ ( set_or5984915006950818249n_real @ K ) )
% 15.55/8.63        = ( ord_less_real @ I @ K ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8203_atMost__iff,axiom,
% 15.55/8.63      ! [I: real,K: real] :
% 15.55/8.63        ( ( member_real @ I @ ( set_ord_atMost_real @ K ) )
% 15.55/8.63        = ( ord_less_eq_real @ I @ K ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8204_atMost__iff,axiom,
% 15.55/8.63      ! [I: set_nat,K: set_nat] :
% 15.55/8.63        ( ( member_set_nat @ I @ ( set_or4236626031148496127et_nat @ K ) )
% 15.55/8.63        = ( ord_less_eq_set_nat @ I @ K ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8205_atMost__iff,axiom,
% 15.55/8.63      ! [I: rat,K: rat] :
% 15.55/8.63        ( ( member_rat @ I @ ( set_ord_atMost_rat @ K ) )
% 15.55/8.63        = ( ord_less_eq_rat @ I @ K ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8206_atMost__iff,axiom,
% 15.55/8.63      ! [I: num,K: num] :
% 15.55/8.63        ( ( member_num @ I @ ( set_ord_atMost_num @ K ) )
% 15.55/8.63        = ( ord_less_eq_num @ I @ K ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8207_atMost__iff,axiom,
% 15.55/8.63      ! [I: int,K: int] :
% 15.55/8.63        ( ( member_int @ I @ ( set_ord_atMost_int @ K ) )
% 15.55/8.63        = ( ord_less_eq_int @ I @ K ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8208_atMost__iff,axiom,
% 15.55/8.63      ! [I: nat,K: nat] :
% 15.55/8.63        ( ( member_nat @ I @ ( set_ord_atMost_nat @ K ) )
% 15.55/8.63        = ( ord_less_eq_nat @ I @ K ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8209_finite__nth__roots,axiom,
% 15.55/8.63      ! [N: nat,C: complex] :
% 15.55/8.63        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.63       => ( finite3207457112153483333omplex
% 15.55/8.63          @ ( collect_complex
% 15.55/8.63            @ ^ [Z6: complex] :
% 15.55/8.63                ( ( power_power_complex @ Z6 @ N )
% 15.55/8.63                = C ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8210_finite__interval__int2,axiom,
% 15.55/8.63      ! [A: int,B: int] :
% 15.55/8.63        ( finite_finite_int
% 15.55/8.63        @ ( collect_int
% 15.55/8.63          @ ^ [I4: int] :
% 15.55/8.63              ( ( ord_less_eq_int @ A @ I4 )
% 15.55/8.63              & ( ord_less_int @ I4 @ B ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8211_finite__interval__int3,axiom,
% 15.55/8.63      ! [A: int,B: int] :
% 15.55/8.63        ( finite_finite_int
% 15.55/8.63        @ ( collect_int
% 15.55/8.63          @ ^ [I4: int] :
% 15.55/8.63              ( ( ord_less_int @ A @ I4 )
% 15.55/8.63              & ( ord_less_eq_int @ I4 @ B ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8212_lessThan__subset__iff,axiom,
% 15.55/8.63      ! [X3: rat,Y3: rat] :
% 15.55/8.63        ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X3 ) @ ( set_ord_lessThan_rat @ Y3 ) )
% 15.55/8.63        = ( ord_less_eq_rat @ X3 @ Y3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8213_lessThan__subset__iff,axiom,
% 15.55/8.63      ! [X3: num,Y3: num] :
% 15.55/8.63        ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X3 ) @ ( set_ord_lessThan_num @ Y3 ) )
% 15.55/8.63        = ( ord_less_eq_num @ X3 @ Y3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8214_lessThan__subset__iff,axiom,
% 15.55/8.63      ! [X3: int,Y3: int] :
% 15.55/8.63        ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X3 ) @ ( set_ord_lessThan_int @ Y3 ) )
% 15.55/8.63        = ( ord_less_eq_int @ X3 @ Y3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8215_lessThan__subset__iff,axiom,
% 15.55/8.63      ! [X3: nat,Y3: nat] :
% 15.55/8.63        ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X3 ) @ ( set_ord_lessThan_nat @ Y3 ) )
% 15.55/8.63        = ( ord_less_eq_nat @ X3 @ Y3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8216_lessThan__subset__iff,axiom,
% 15.55/8.63      ! [X3: real,Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X3 ) @ ( set_or5984915006950818249n_real @ Y3 ) )
% 15.55/8.63        = ( ord_less_eq_real @ X3 @ Y3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8217_atMost__subset__iff,axiom,
% 15.55/8.63      ! [X3: set_nat,Y3: set_nat] :
% 15.55/8.63        ( ( ord_le6893508408891458716et_nat @ ( set_or4236626031148496127et_nat @ X3 ) @ ( set_or4236626031148496127et_nat @ Y3 ) )
% 15.55/8.63        = ( ord_less_eq_set_nat @ X3 @ Y3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8218_atMost__subset__iff,axiom,
% 15.55/8.63      ! [X3: rat,Y3: rat] :
% 15.55/8.63        ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X3 ) @ ( set_ord_atMost_rat @ Y3 ) )
% 15.55/8.63        = ( ord_less_eq_rat @ X3 @ Y3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8219_atMost__subset__iff,axiom,
% 15.55/8.63      ! [X3: num,Y3: num] :
% 15.55/8.63        ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X3 ) @ ( set_ord_atMost_num @ Y3 ) )
% 15.55/8.63        = ( ord_less_eq_num @ X3 @ Y3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8220_atMost__subset__iff,axiom,
% 15.55/8.63      ! [X3: int,Y3: int] :
% 15.55/8.63        ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X3 ) @ ( set_ord_atMost_int @ Y3 ) )
% 15.55/8.63        = ( ord_less_eq_int @ X3 @ Y3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8221_atMost__subset__iff,axiom,
% 15.55/8.63      ! [X3: nat,Y3: nat] :
% 15.55/8.63        ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X3 ) @ ( set_ord_atMost_nat @ Y3 ) )
% 15.55/8.63        = ( ord_less_eq_nat @ X3 @ Y3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8222_lessThan__0,axiom,
% 15.55/8.63      ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 15.55/8.63      = bot_bot_set_nat ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8223_set__encode__empty,axiom,
% 15.55/8.63      ( ( nat_set_encode @ bot_bot_set_nat )
% 15.55/8.63      = zero_zero_nat ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8224_Icc__subset__Iic__iff,axiom,
% 15.55/8.63      ! [L: set_nat,H2: set_nat,H3: set_nat] :
% 15.55/8.63        ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ L @ H2 ) @ ( set_or4236626031148496127et_nat @ H3 ) )
% 15.55/8.63        = ( ~ ( ord_less_eq_set_nat @ L @ H2 )
% 15.55/8.63          | ( ord_less_eq_set_nat @ H2 @ H3 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8225_Icc__subset__Iic__iff,axiom,
% 15.55/8.63      ! [L: rat,H2: rat,H3: rat] :
% 15.55/8.63        ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L @ H2 ) @ ( set_ord_atMost_rat @ H3 ) )
% 15.55/8.63        = ( ~ ( ord_less_eq_rat @ L @ H2 )
% 15.55/8.63          | ( ord_less_eq_rat @ H2 @ H3 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8226_Icc__subset__Iic__iff,axiom,
% 15.55/8.63      ! [L: num,H2: num,H3: num] :
% 15.55/8.63        ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L @ H2 ) @ ( set_ord_atMost_num @ H3 ) )
% 15.55/8.63        = ( ~ ( ord_less_eq_num @ L @ H2 )
% 15.55/8.63          | ( ord_less_eq_num @ H2 @ H3 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8227_Icc__subset__Iic__iff,axiom,
% 15.55/8.63      ! [L: nat,H2: nat,H3: nat] :
% 15.55/8.63        ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L @ H2 ) @ ( set_ord_atMost_nat @ H3 ) )
% 15.55/8.63        = ( ~ ( ord_less_eq_nat @ L @ H2 )
% 15.55/8.63          | ( ord_less_eq_nat @ H2 @ H3 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8228_Icc__subset__Iic__iff,axiom,
% 15.55/8.63      ! [L: int,H2: int,H3: int] :
% 15.55/8.63        ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L @ H2 ) @ ( set_ord_atMost_int @ H3 ) )
% 15.55/8.63        = ( ~ ( ord_less_eq_int @ L @ H2 )
% 15.55/8.63          | ( ord_less_eq_int @ H2 @ H3 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8229_Icc__subset__Iic__iff,axiom,
% 15.55/8.63      ! [L: real,H2: real,H3: real] :
% 15.55/8.63        ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ L @ H2 ) @ ( set_ord_atMost_real @ H3 ) )
% 15.55/8.63        = ( ~ ( ord_less_eq_real @ L @ H2 )
% 15.55/8.63          | ( ord_less_eq_real @ H2 @ H3 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8230_atMost__0,axiom,
% 15.55/8.63      ( ( set_ord_atMost_nat @ zero_zero_nat )
% 15.55/8.63      = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8231_int__sum,axiom,
% 15.55/8.63      ! [F: int > nat,A3: set_int] :
% 15.55/8.63        ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A3 ) )
% 15.55/8.63        = ( groups4538972089207619220nt_int
% 15.55/8.63          @ ^ [X: int] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 15.55/8.63          @ A3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8232_int__sum,axiom,
% 15.55/8.63      ! [F: nat > nat,A3: set_nat] :
% 15.55/8.63        ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 15.55/8.63        = ( groups3539618377306564664at_int
% 15.55/8.63          @ ^ [X: nat] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 15.55/8.63          @ A3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8233_Complex__sum_H,axiom,
% 15.55/8.63      ! [F: nat > real,S: set_nat] :
% 15.55/8.63        ( ( groups2073611262835488442omplex
% 15.55/8.63          @ ^ [X: nat] : ( complex2 @ ( F @ X ) @ zero_zero_real )
% 15.55/8.63          @ S )
% 15.55/8.63        = ( complex2 @ ( groups6591440286371151544t_real @ F @ S ) @ zero_zero_real ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8234_Complex__sum_H,axiom,
% 15.55/8.63      ! [F: complex > real,S: set_complex] :
% 15.55/8.63        ( ( groups7754918857620584856omplex
% 15.55/8.63          @ ^ [X: complex] : ( complex2 @ ( F @ X ) @ zero_zero_real )
% 15.55/8.63          @ S )
% 15.55/8.63        = ( complex2 @ ( groups5808333547571424918x_real @ F @ S ) @ zero_zero_real ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8235_sum__diff__distrib,axiom,
% 15.55/8.63      ! [Q: real > nat,P: real > nat,N: real] :
% 15.55/8.63        ( ! [X4: real] : ( ord_less_eq_nat @ ( Q @ X4 ) @ ( P @ X4 ) )
% 15.55/8.63       => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N ) ) )
% 15.55/8.63          = ( groups1935376822645274424al_nat
% 15.55/8.63            @ ^ [X: real] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 15.55/8.63            @ ( set_or5984915006950818249n_real @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8236_sum__diff__distrib,axiom,
% 15.55/8.63      ! [Q: nat > nat,P: nat > nat,N: nat] :
% 15.55/8.63        ( ! [X4: nat] : ( ord_less_eq_nat @ ( Q @ X4 ) @ ( P @ X4 ) )
% 15.55/8.63       => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N ) ) )
% 15.55/8.63          = ( groups3542108847815614940at_nat
% 15.55/8.63            @ ^ [X: nat] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8237_Iic__subset__Iio__iff,axiom,
% 15.55/8.63      ! [A: rat,B: rat] :
% 15.55/8.63        ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ A ) @ ( set_ord_lessThan_rat @ B ) )
% 15.55/8.63        = ( ord_less_rat @ A @ B ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8238_Iic__subset__Iio__iff,axiom,
% 15.55/8.63      ! [A: num,B: num] :
% 15.55/8.63        ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A ) @ ( set_ord_lessThan_num @ B ) )
% 15.55/8.63        = ( ord_less_num @ A @ B ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8239_Iic__subset__Iio__iff,axiom,
% 15.55/8.63      ! [A: int,B: int] :
% 15.55/8.63        ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B ) )
% 15.55/8.63        = ( ord_less_int @ A @ B ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8240_Iic__subset__Iio__iff,axiom,
% 15.55/8.63      ! [A: nat,B: nat] :
% 15.55/8.63        ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B ) )
% 15.55/8.63        = ( ord_less_nat @ A @ B ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8241_Iic__subset__Iio__iff,axiom,
% 15.55/8.63      ! [A: real,B: real] :
% 15.55/8.63        ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ A ) @ ( set_or5984915006950818249n_real @ B ) )
% 15.55/8.63        = ( ord_less_real @ A @ B ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8242_lessThan__def,axiom,
% 15.55/8.63      ( set_or890127255671739683et_nat
% 15.55/8.63      = ( ^ [U2: set_nat] :
% 15.55/8.63            ( collect_set_nat
% 15.55/8.63            @ ^ [X: set_nat] : ( ord_less_set_nat @ X @ U2 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8243_lessThan__def,axiom,
% 15.55/8.63      ( set_ord_lessThan_rat
% 15.55/8.63      = ( ^ [U2: rat] :
% 15.55/8.63            ( collect_rat
% 15.55/8.63            @ ^ [X: rat] : ( ord_less_rat @ X @ U2 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8244_lessThan__def,axiom,
% 15.55/8.63      ( set_ord_lessThan_num
% 15.55/8.63      = ( ^ [U2: num] :
% 15.55/8.63            ( collect_num
% 15.55/8.63            @ ^ [X: num] : ( ord_less_num @ X @ U2 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8245_lessThan__def,axiom,
% 15.55/8.63      ( set_ord_lessThan_int
% 15.55/8.63      = ( ^ [U2: int] :
% 15.55/8.63            ( collect_int
% 15.55/8.63            @ ^ [X: int] : ( ord_less_int @ X @ U2 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8246_lessThan__def,axiom,
% 15.55/8.63      ( set_ord_lessThan_nat
% 15.55/8.63      = ( ^ [U2: nat] :
% 15.55/8.63            ( collect_nat
% 15.55/8.63            @ ^ [X: nat] : ( ord_less_nat @ X @ U2 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8247_lessThan__def,axiom,
% 15.55/8.63      ( set_or5984915006950818249n_real
% 15.55/8.63      = ( ^ [U2: real] :
% 15.55/8.63            ( collect_real
% 15.55/8.63            @ ^ [X: real] : ( ord_less_real @ X @ U2 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8248_atMost__def,axiom,
% 15.55/8.63      ( set_ord_atMost_real
% 15.55/8.63      = ( ^ [U2: real] :
% 15.55/8.63            ( collect_real
% 15.55/8.63            @ ^ [X: real] : ( ord_less_eq_real @ X @ U2 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8249_atMost__def,axiom,
% 15.55/8.63      ( set_or4236626031148496127et_nat
% 15.55/8.63      = ( ^ [U2: set_nat] :
% 15.55/8.63            ( collect_set_nat
% 15.55/8.63            @ ^ [X: set_nat] : ( ord_less_eq_set_nat @ X @ U2 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8250_atMost__def,axiom,
% 15.55/8.63      ( set_ord_atMost_rat
% 15.55/8.63      = ( ^ [U2: rat] :
% 15.55/8.63            ( collect_rat
% 15.55/8.63            @ ^ [X: rat] : ( ord_less_eq_rat @ X @ U2 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8251_atMost__def,axiom,
% 15.55/8.63      ( set_ord_atMost_num
% 15.55/8.63      = ( ^ [U2: num] :
% 15.55/8.63            ( collect_num
% 15.55/8.63            @ ^ [X: num] : ( ord_less_eq_num @ X @ U2 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8252_atMost__def,axiom,
% 15.55/8.63      ( set_ord_atMost_int
% 15.55/8.63      = ( ^ [U2: int] :
% 15.55/8.63            ( collect_int
% 15.55/8.63            @ ^ [X: int] : ( ord_less_eq_int @ X @ U2 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8253_atMost__def,axiom,
% 15.55/8.63      ( set_ord_atMost_nat
% 15.55/8.63      = ( ^ [U2: nat] :
% 15.55/8.63            ( collect_nat
% 15.55/8.63            @ ^ [X: nat] : ( ord_less_eq_nat @ X @ U2 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8254_sum_OatMost__shift,axiom,
% 15.55/8.63      ! [G: nat > rat,N: nat] :
% 15.55/8.63        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63        = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups2906978787729119204at_rat
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8255_sum_OatMost__shift,axiom,
% 15.55/8.63      ! [G: nat > int,N: nat] :
% 15.55/8.63        ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63        = ( plus_plus_int @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups3539618377306564664at_int
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8256_sum_OatMost__shift,axiom,
% 15.55/8.63      ! [G: nat > nat,N: nat] :
% 15.55/8.63        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63        = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups3542108847815614940at_nat
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8257_sum_OatMost__shift,axiom,
% 15.55/8.63      ! [G: nat > real,N: nat] :
% 15.55/8.63        ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63        = ( plus_plus_real @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups6591440286371151544t_real
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8258_prod_OatMost__shift,axiom,
% 15.55/8.63      ! [G: nat > real,N: nat] :
% 15.55/8.63        ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63        = ( times_times_real @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups129246275422532515t_real
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8259_prod_OatMost__shift,axiom,
% 15.55/8.63      ! [G: nat > rat,N: nat] :
% 15.55/8.63        ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63        = ( times_times_rat @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups73079841787564623at_rat
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8260_prod_OatMost__shift,axiom,
% 15.55/8.63      ! [G: nat > int,N: nat] :
% 15.55/8.63        ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63        = ( times_times_int @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups705719431365010083at_int
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8261_prod_OatMost__shift,axiom,
% 15.55/8.63      ! [G: nat > nat,N: nat] :
% 15.55/8.63        ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63        = ( times_times_nat @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups708209901874060359at_nat
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8262_atMost__atLeast0,axiom,
% 15.55/8.63      ( set_ord_atMost_nat
% 15.55/8.63      = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8263_lessThan__strict__subset__iff,axiom,
% 15.55/8.63      ! [M: rat,N: rat] :
% 15.55/8.63        ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N ) )
% 15.55/8.63        = ( ord_less_rat @ M @ N ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8264_lessThan__strict__subset__iff,axiom,
% 15.55/8.63      ! [M: num,N: num] :
% 15.55/8.63        ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N ) )
% 15.55/8.63        = ( ord_less_num @ M @ N ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8265_lessThan__strict__subset__iff,axiom,
% 15.55/8.63      ! [M: int,N: int] :
% 15.55/8.63        ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N ) )
% 15.55/8.63        = ( ord_less_int @ M @ N ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8266_lessThan__strict__subset__iff,axiom,
% 15.55/8.63      ! [M: nat,N: nat] :
% 15.55/8.63        ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.63        = ( ord_less_nat @ M @ N ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8267_lessThan__strict__subset__iff,axiom,
% 15.55/8.63      ! [M: real,N: real] :
% 15.55/8.63        ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N ) )
% 15.55/8.63        = ( ord_less_real @ M @ N ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8268_finite__maxlen,axiom,
% 15.55/8.63      ! [M7: set_list_VEBT_VEBT] :
% 15.55/8.63        ( ( finite3004134309566078307T_VEBT @ M7 )
% 15.55/8.63       => ? [N2: nat] :
% 15.55/8.63          ! [X6: list_VEBT_VEBT] :
% 15.55/8.63            ( ( member2936631157270082147T_VEBT @ X6 @ M7 )
% 15.55/8.63           => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X6 ) @ N2 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8269_finite__maxlen,axiom,
% 15.55/8.63      ! [M7: set_list_o] :
% 15.55/8.63        ( ( finite_finite_list_o @ M7 )
% 15.55/8.63       => ? [N2: nat] :
% 15.55/8.63          ! [X6: list_o] :
% 15.55/8.63            ( ( member_list_o @ X6 @ M7 )
% 15.55/8.63           => ( ord_less_nat @ ( size_size_list_o @ X6 ) @ N2 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8270_finite__maxlen,axiom,
% 15.55/8.63      ! [M7: set_list_nat] :
% 15.55/8.63        ( ( finite8100373058378681591st_nat @ M7 )
% 15.55/8.63       => ? [N2: nat] :
% 15.55/8.63          ! [X6: list_nat] :
% 15.55/8.63            ( ( member_list_nat @ X6 @ M7 )
% 15.55/8.63           => ( ord_less_nat @ ( size_size_list_nat @ X6 ) @ N2 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8271_finite__maxlen,axiom,
% 15.55/8.63      ! [M7: set_list_int] :
% 15.55/8.63        ( ( finite3922522038869484883st_int @ M7 )
% 15.55/8.63       => ? [N2: nat] :
% 15.55/8.63          ! [X6: list_int] :
% 15.55/8.63            ( ( member_list_int @ X6 @ M7 )
% 15.55/8.63           => ( ord_less_nat @ ( size_size_list_int @ X6 ) @ N2 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8272_lessThan__empty__iff,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( ( set_ord_lessThan_nat @ N )
% 15.55/8.63          = bot_bot_set_nat )
% 15.55/8.63        = ( N = zero_zero_nat ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8273_sum__roots__unity,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( ord_less_nat @ one_one_nat @ N )
% 15.55/8.63       => ( ( groups7754918857620584856omplex
% 15.55/8.63            @ ^ [X: complex] : X
% 15.55/8.63            @ ( collect_complex
% 15.55/8.63              @ ^ [Z6: complex] :
% 15.55/8.63                  ( ( power_power_complex @ Z6 @ N )
% 15.55/8.63                  = one_one_complex ) ) )
% 15.55/8.63          = zero_zero_complex ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8274_sum__nth__roots,axiom,
% 15.55/8.63      ! [N: nat,C: complex] :
% 15.55/8.63        ( ( ord_less_nat @ one_one_nat @ N )
% 15.55/8.63       => ( ( groups7754918857620584856omplex
% 15.55/8.63            @ ^ [X: complex] : X
% 15.55/8.63            @ ( collect_complex
% 15.55/8.63              @ ^ [Z6: complex] :
% 15.55/8.63                  ( ( power_power_complex @ Z6 @ N )
% 15.55/8.63                  = C ) ) )
% 15.55/8.63          = zero_zero_complex ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8275_power__sum,axiom,
% 15.55/8.63      ! [C: real,F: nat > nat,A3: set_nat] :
% 15.55/8.63        ( ( power_power_real @ C @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 15.55/8.63        = ( groups129246275422532515t_real
% 15.55/8.63          @ ^ [A4: nat] : ( power_power_real @ C @ ( F @ A4 ) )
% 15.55/8.63          @ A3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8276_power__sum,axiom,
% 15.55/8.63      ! [C: complex,F: nat > nat,A3: set_nat] :
% 15.55/8.63        ( ( power_power_complex @ C @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 15.55/8.63        = ( groups6464643781859351333omplex
% 15.55/8.63          @ ^ [A4: nat] : ( power_power_complex @ C @ ( F @ A4 ) )
% 15.55/8.63          @ A3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8277_power__sum,axiom,
% 15.55/8.63      ! [C: int,F: nat > nat,A3: set_nat] :
% 15.55/8.63        ( ( power_power_int @ C @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 15.55/8.63        = ( groups705719431365010083at_int
% 15.55/8.63          @ ^ [A4: nat] : ( power_power_int @ C @ ( F @ A4 ) )
% 15.55/8.63          @ A3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8278_power__sum,axiom,
% 15.55/8.63      ! [C: int,F: int > nat,A3: set_int] :
% 15.55/8.63        ( ( power_power_int @ C @ ( groups4541462559716669496nt_nat @ F @ A3 ) )
% 15.55/8.63        = ( groups1705073143266064639nt_int
% 15.55/8.63          @ ^ [A4: int] : ( power_power_int @ C @ ( F @ A4 ) )
% 15.55/8.63          @ A3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8279_power__sum,axiom,
% 15.55/8.63      ! [C: nat,F: nat > nat,A3: set_nat] :
% 15.55/8.63        ( ( power_power_nat @ C @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 15.55/8.63        = ( groups708209901874060359at_nat
% 15.55/8.63          @ ^ [A4: nat] : ( power_power_nat @ C @ ( F @ A4 ) )
% 15.55/8.63          @ A3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8280_sum__subtractf__nat,axiom,
% 15.55/8.63      ! [A3: set_option_nat,G: option_nat > nat,F: option_nat > nat] :
% 15.55/8.63        ( ! [X4: option_nat] :
% 15.55/8.63            ( ( member_option_nat @ X4 @ A3 )
% 15.55/8.63           => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 15.55/8.63       => ( ( groups1921984841883549356at_nat
% 15.55/8.63            @ ^ [X: option_nat] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 15.55/8.63            @ A3 )
% 15.55/8.63          = ( minus_minus_nat @ ( groups1921984841883549356at_nat @ F @ A3 ) @ ( groups1921984841883549356at_nat @ G @ A3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8281_sum__subtractf__nat,axiom,
% 15.55/8.63      ! [A3: set_real,G: real > nat,F: real > nat] :
% 15.55/8.63        ( ! [X4: real] :
% 15.55/8.63            ( ( member_real @ X4 @ A3 )
% 15.55/8.63           => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 15.55/8.63       => ( ( groups1935376822645274424al_nat
% 15.55/8.63            @ ^ [X: real] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 15.55/8.63            @ A3 )
% 15.55/8.63          = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A3 ) @ ( groups1935376822645274424al_nat @ G @ A3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8282_sum__subtractf__nat,axiom,
% 15.55/8.63      ! [A3: set_set_nat,G: set_nat > nat,F: set_nat > nat] :
% 15.55/8.63        ( ! [X4: set_nat] :
% 15.55/8.63            ( ( member_set_nat @ X4 @ A3 )
% 15.55/8.63           => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 15.55/8.63       => ( ( groups8294997508430121362at_nat
% 15.55/8.63            @ ^ [X: set_nat] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 15.55/8.63            @ A3 )
% 15.55/8.63          = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A3 ) @ ( groups8294997508430121362at_nat @ G @ A3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8283_sum__subtractf__nat,axiom,
% 15.55/8.63      ! [A3: set_int,G: int > nat,F: int > nat] :
% 15.55/8.63        ( ! [X4: int] :
% 15.55/8.63            ( ( member_int @ X4 @ A3 )
% 15.55/8.63           => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 15.55/8.63       => ( ( groups4541462559716669496nt_nat
% 15.55/8.63            @ ^ [X: int] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 15.55/8.63            @ A3 )
% 15.55/8.63          = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ ( groups4541462559716669496nt_nat @ G @ A3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8284_sum__subtractf__nat,axiom,
% 15.55/8.63      ! [A3: set_nat,G: nat > nat,F: nat > nat] :
% 15.55/8.63        ( ! [X4: nat] :
% 15.55/8.63            ( ( member_nat @ X4 @ A3 )
% 15.55/8.63           => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 15.55/8.63       => ( ( groups3542108847815614940at_nat
% 15.55/8.63            @ ^ [X: nat] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 15.55/8.63            @ A3 )
% 15.55/8.63          = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) @ ( groups3542108847815614940at_nat @ G @ A3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8285_polyfun__linear__factor__root,axiom,
% 15.55/8.63      ! [C: nat > complex,A: complex,N: nat] :
% 15.55/8.63        ( ( ( groups2073611262835488442omplex
% 15.55/8.63            @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ A @ I4 ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63          = zero_zero_complex )
% 15.55/8.63       => ~ ! [B4: nat > complex] :
% 15.55/8.63              ~ ! [Z4: complex] :
% 15.55/8.63                  ( ( groups2073611262835488442omplex
% 15.55/8.63                    @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ Z4 @ I4 ) )
% 15.55/8.63                    @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63                  = ( times_times_complex @ ( minus_minus_complex @ Z4 @ A )
% 15.55/8.63                    @ ( groups2073611262835488442omplex
% 15.55/8.63                      @ ^ [I4: nat] : ( times_times_complex @ ( B4 @ I4 ) @ ( power_power_complex @ Z4 @ I4 ) )
% 15.55/8.63                      @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8286_polyfun__linear__factor__root,axiom,
% 15.55/8.63      ! [C: nat > rat,A: rat,N: nat] :
% 15.55/8.63        ( ( ( groups2906978787729119204at_rat
% 15.55/8.63            @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ A @ I4 ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63          = zero_zero_rat )
% 15.55/8.63       => ~ ! [B4: nat > rat] :
% 15.55/8.63              ~ ! [Z4: rat] :
% 15.55/8.63                  ( ( groups2906978787729119204at_rat
% 15.55/8.63                    @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ Z4 @ I4 ) )
% 15.55/8.63                    @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63                  = ( times_times_rat @ ( minus_minus_rat @ Z4 @ A )
% 15.55/8.63                    @ ( groups2906978787729119204at_rat
% 15.55/8.63                      @ ^ [I4: nat] : ( times_times_rat @ ( B4 @ I4 ) @ ( power_power_rat @ Z4 @ I4 ) )
% 15.55/8.63                      @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8287_polyfun__linear__factor__root,axiom,
% 15.55/8.63      ! [C: nat > int,A: int,N: nat] :
% 15.55/8.63        ( ( ( groups3539618377306564664at_int
% 15.55/8.63            @ ^ [I4: nat] : ( times_times_int @ ( C @ I4 ) @ ( power_power_int @ A @ I4 ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63          = zero_zero_int )
% 15.55/8.63       => ~ ! [B4: nat > int] :
% 15.55/8.63              ~ ! [Z4: int] :
% 15.55/8.63                  ( ( groups3539618377306564664at_int
% 15.55/8.63                    @ ^ [I4: nat] : ( times_times_int @ ( C @ I4 ) @ ( power_power_int @ Z4 @ I4 ) )
% 15.55/8.63                    @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63                  = ( times_times_int @ ( minus_minus_int @ Z4 @ A )
% 15.55/8.63                    @ ( groups3539618377306564664at_int
% 15.55/8.63                      @ ^ [I4: nat] : ( times_times_int @ ( B4 @ I4 ) @ ( power_power_int @ Z4 @ I4 ) )
% 15.55/8.63                      @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8288_polyfun__linear__factor__root,axiom,
% 15.55/8.63      ! [C: nat > real,A: real,N: nat] :
% 15.55/8.63        ( ( ( groups6591440286371151544t_real
% 15.55/8.63            @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ A @ I4 ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63          = zero_zero_real )
% 15.55/8.63       => ~ ! [B4: nat > real] :
% 15.55/8.63              ~ ! [Z4: real] :
% 15.55/8.63                  ( ( groups6591440286371151544t_real
% 15.55/8.63                    @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ Z4 @ I4 ) )
% 15.55/8.63                    @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63                  = ( times_times_real @ ( minus_minus_real @ Z4 @ A )
% 15.55/8.63                    @ ( groups6591440286371151544t_real
% 15.55/8.63                      @ ^ [I4: nat] : ( times_times_real @ ( B4 @ I4 ) @ ( power_power_real @ Z4 @ I4 ) )
% 15.55/8.63                      @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8289_polyfun__linear__factor,axiom,
% 15.55/8.63      ! [C: nat > complex,N: nat,A: complex] :
% 15.55/8.63      ? [B4: nat > complex] :
% 15.55/8.63      ! [Z4: complex] :
% 15.55/8.63        ( ( groups2073611262835488442omplex
% 15.55/8.63          @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ Z4 @ I4 ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63        = ( plus_plus_complex
% 15.55/8.63          @ ( times_times_complex @ ( minus_minus_complex @ Z4 @ A )
% 15.55/8.63            @ ( groups2073611262835488442omplex
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_complex @ ( B4 @ I4 ) @ ( power_power_complex @ Z4 @ I4 ) )
% 15.55/8.63              @ ( set_ord_lessThan_nat @ N ) ) )
% 15.55/8.63          @ ( groups2073611262835488442omplex
% 15.55/8.63            @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ A @ I4 ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8290_polyfun__linear__factor,axiom,
% 15.55/8.63      ! [C: nat > rat,N: nat,A: rat] :
% 15.55/8.63      ? [B4: nat > rat] :
% 15.55/8.63      ! [Z4: rat] :
% 15.55/8.63        ( ( groups2906978787729119204at_rat
% 15.55/8.63          @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ Z4 @ I4 ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63        = ( plus_plus_rat
% 15.55/8.63          @ ( times_times_rat @ ( minus_minus_rat @ Z4 @ A )
% 15.55/8.63            @ ( groups2906978787729119204at_rat
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_rat @ ( B4 @ I4 ) @ ( power_power_rat @ Z4 @ I4 ) )
% 15.55/8.63              @ ( set_ord_lessThan_nat @ N ) ) )
% 15.55/8.63          @ ( groups2906978787729119204at_rat
% 15.55/8.63            @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ A @ I4 ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8291_polyfun__linear__factor,axiom,
% 15.55/8.63      ! [C: nat > int,N: nat,A: int] :
% 15.55/8.63      ? [B4: nat > int] :
% 15.55/8.63      ! [Z4: int] :
% 15.55/8.63        ( ( groups3539618377306564664at_int
% 15.55/8.63          @ ^ [I4: nat] : ( times_times_int @ ( C @ I4 ) @ ( power_power_int @ Z4 @ I4 ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63        = ( plus_plus_int
% 15.55/8.63          @ ( times_times_int @ ( minus_minus_int @ Z4 @ A )
% 15.55/8.63            @ ( groups3539618377306564664at_int
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_int @ ( B4 @ I4 ) @ ( power_power_int @ Z4 @ I4 ) )
% 15.55/8.63              @ ( set_ord_lessThan_nat @ N ) ) )
% 15.55/8.63          @ ( groups3539618377306564664at_int
% 15.55/8.63            @ ^ [I4: nat] : ( times_times_int @ ( C @ I4 ) @ ( power_power_int @ A @ I4 ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8292_polyfun__linear__factor,axiom,
% 15.55/8.63      ! [C: nat > real,N: nat,A: real] :
% 15.55/8.63      ? [B4: nat > real] :
% 15.55/8.63      ! [Z4: real] :
% 15.55/8.63        ( ( groups6591440286371151544t_real
% 15.55/8.63          @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ Z4 @ I4 ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63        = ( plus_plus_real
% 15.55/8.63          @ ( times_times_real @ ( minus_minus_real @ Z4 @ A )
% 15.55/8.63            @ ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_real @ ( B4 @ I4 ) @ ( power_power_real @ Z4 @ I4 ) )
% 15.55/8.63              @ ( set_ord_lessThan_nat @ N ) ) )
% 15.55/8.63          @ ( groups6591440286371151544t_real
% 15.55/8.63            @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ A @ I4 ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8293_finite__divisors__int,axiom,
% 15.55/8.63      ! [I: int] :
% 15.55/8.63        ( ( I != zero_zero_int )
% 15.55/8.63       => ( finite_finite_int
% 15.55/8.63          @ ( collect_int
% 15.55/8.63            @ ^ [D4: int] : ( dvd_dvd_int @ D4 @ I ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8294_sum__eq__Suc0__iff,axiom,
% 15.55/8.63      ! [A3: set_int,F: int > nat] :
% 15.55/8.63        ( ( finite_finite_int @ A3 )
% 15.55/8.63       => ( ( ( groups4541462559716669496nt_nat @ F @ A3 )
% 15.55/8.63            = ( suc @ zero_zero_nat ) )
% 15.55/8.63          = ( ? [X: int] :
% 15.55/8.63                ( ( member_int @ X @ A3 )
% 15.55/8.63                & ( ( F @ X )
% 15.55/8.63                  = ( suc @ zero_zero_nat ) )
% 15.55/8.63                & ! [Y: int] :
% 15.55/8.63                    ( ( member_int @ Y @ A3 )
% 15.55/8.63                   => ( ( X != Y )
% 15.55/8.63                     => ( ( F @ Y )
% 15.55/8.63                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8295_sum__eq__Suc0__iff,axiom,
% 15.55/8.63      ! [A3: set_complex,F: complex > nat] :
% 15.55/8.63        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.63       => ( ( ( groups5693394587270226106ex_nat @ F @ A3 )
% 15.55/8.63            = ( suc @ zero_zero_nat ) )
% 15.55/8.63          = ( ? [X: complex] :
% 15.55/8.63                ( ( member_complex @ X @ A3 )
% 15.55/8.63                & ( ( F @ X )
% 15.55/8.63                  = ( suc @ zero_zero_nat ) )
% 15.55/8.63                & ! [Y: complex] :
% 15.55/8.63                    ( ( member_complex @ Y @ A3 )
% 15.55/8.63                   => ( ( X != Y )
% 15.55/8.63                     => ( ( F @ Y )
% 15.55/8.63                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8296_sum__eq__Suc0__iff,axiom,
% 15.55/8.63      ! [A3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 15.55/8.63        ( ( finite6177210948735845034at_nat @ A3 )
% 15.55/8.63       => ( ( ( groups977919841031483927at_nat @ F @ A3 )
% 15.55/8.63            = ( suc @ zero_zero_nat ) )
% 15.55/8.63          = ( ? [X: product_prod_nat_nat] :
% 15.55/8.63                ( ( member8440522571783428010at_nat @ X @ A3 )
% 15.55/8.63                & ( ( F @ X )
% 15.55/8.63                  = ( suc @ zero_zero_nat ) )
% 15.55/8.63                & ! [Y: product_prod_nat_nat] :
% 15.55/8.63                    ( ( member8440522571783428010at_nat @ Y @ A3 )
% 15.55/8.63                   => ( ( X != Y )
% 15.55/8.63                     => ( ( F @ Y )
% 15.55/8.63                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8297_sum__eq__Suc0__iff,axiom,
% 15.55/8.63      ! [A3: set_Extended_enat,F: extended_enat > nat] :
% 15.55/8.63        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.63       => ( ( ( groups2027974829824023292at_nat @ F @ A3 )
% 15.55/8.63            = ( suc @ zero_zero_nat ) )
% 15.55/8.63          = ( ? [X: extended_enat] :
% 15.55/8.63                ( ( member_Extended_enat @ X @ A3 )
% 15.55/8.63                & ( ( F @ X )
% 15.55/8.63                  = ( suc @ zero_zero_nat ) )
% 15.55/8.63                & ! [Y: extended_enat] :
% 15.55/8.63                    ( ( member_Extended_enat @ Y @ A3 )
% 15.55/8.63                   => ( ( X != Y )
% 15.55/8.63                     => ( ( F @ Y )
% 15.55/8.63                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8298_sum__eq__Suc0__iff,axiom,
% 15.55/8.63      ! [A3: set_nat,F: nat > nat] :
% 15.55/8.63        ( ( finite_finite_nat @ A3 )
% 15.55/8.63       => ( ( ( groups3542108847815614940at_nat @ F @ A3 )
% 15.55/8.63            = ( suc @ zero_zero_nat ) )
% 15.55/8.63          = ( ? [X: nat] :
% 15.55/8.63                ( ( member_nat @ X @ A3 )
% 15.55/8.63                & ( ( F @ X )
% 15.55/8.63                  = ( suc @ zero_zero_nat ) )
% 15.55/8.63                & ! [Y: nat] :
% 15.55/8.63                    ( ( member_nat @ Y @ A3 )
% 15.55/8.63                   => ( ( X != Y )
% 15.55/8.63                     => ( ( F @ Y )
% 15.55/8.63                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8299_sum__SucD,axiom,
% 15.55/8.63      ! [F: nat > nat,A3: set_nat,N: nat] :
% 15.55/8.63        ( ( ( groups3542108847815614940at_nat @ F @ A3 )
% 15.55/8.63          = ( suc @ N ) )
% 15.55/8.63       => ? [X4: nat] :
% 15.55/8.63            ( ( member_nat @ X4 @ A3 )
% 15.55/8.63            & ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8300_sum__eq__1__iff,axiom,
% 15.55/8.63      ! [A3: set_int,F: int > nat] :
% 15.55/8.63        ( ( finite_finite_int @ A3 )
% 15.55/8.63       => ( ( ( groups4541462559716669496nt_nat @ F @ A3 )
% 15.55/8.63            = one_one_nat )
% 15.55/8.63          = ( ? [X: int] :
% 15.55/8.63                ( ( member_int @ X @ A3 )
% 15.55/8.63                & ( ( F @ X )
% 15.55/8.63                  = one_one_nat )
% 15.55/8.63                & ! [Y: int] :
% 15.55/8.63                    ( ( member_int @ Y @ A3 )
% 15.55/8.63                   => ( ( X != Y )
% 15.55/8.63                     => ( ( F @ Y )
% 15.55/8.63                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8301_sum__eq__1__iff,axiom,
% 15.55/8.63      ! [A3: set_complex,F: complex > nat] :
% 15.55/8.63        ( ( finite3207457112153483333omplex @ A3 )
% 15.55/8.63       => ( ( ( groups5693394587270226106ex_nat @ F @ A3 )
% 15.55/8.63            = one_one_nat )
% 15.55/8.63          = ( ? [X: complex] :
% 15.55/8.63                ( ( member_complex @ X @ A3 )
% 15.55/8.63                & ( ( F @ X )
% 15.55/8.63                  = one_one_nat )
% 15.55/8.63                & ! [Y: complex] :
% 15.55/8.63                    ( ( member_complex @ Y @ A3 )
% 15.55/8.63                   => ( ( X != Y )
% 15.55/8.63                     => ( ( F @ Y )
% 15.55/8.63                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8302_sum__eq__1__iff,axiom,
% 15.55/8.63      ! [A3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 15.55/8.63        ( ( finite6177210948735845034at_nat @ A3 )
% 15.55/8.63       => ( ( ( groups977919841031483927at_nat @ F @ A3 )
% 15.55/8.63            = one_one_nat )
% 15.55/8.63          = ( ? [X: product_prod_nat_nat] :
% 15.55/8.63                ( ( member8440522571783428010at_nat @ X @ A3 )
% 15.55/8.63                & ( ( F @ X )
% 15.55/8.63                  = one_one_nat )
% 15.55/8.63                & ! [Y: product_prod_nat_nat] :
% 15.55/8.63                    ( ( member8440522571783428010at_nat @ Y @ A3 )
% 15.55/8.63                   => ( ( X != Y )
% 15.55/8.63                     => ( ( F @ Y )
% 15.55/8.63                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8303_sum__eq__1__iff,axiom,
% 15.55/8.63      ! [A3: set_Extended_enat,F: extended_enat > nat] :
% 15.55/8.63        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.63       => ( ( ( groups2027974829824023292at_nat @ F @ A3 )
% 15.55/8.63            = one_one_nat )
% 15.55/8.63          = ( ? [X: extended_enat] :
% 15.55/8.63                ( ( member_Extended_enat @ X @ A3 )
% 15.55/8.63                & ( ( F @ X )
% 15.55/8.63                  = one_one_nat )
% 15.55/8.63                & ! [Y: extended_enat] :
% 15.55/8.63                    ( ( member_Extended_enat @ Y @ A3 )
% 15.55/8.63                   => ( ( X != Y )
% 15.55/8.63                     => ( ( F @ Y )
% 15.55/8.63                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8304_sum__eq__1__iff,axiom,
% 15.55/8.63      ! [A3: set_nat,F: nat > nat] :
% 15.55/8.63        ( ( finite_finite_nat @ A3 )
% 15.55/8.63       => ( ( ( groups3542108847815614940at_nat @ F @ A3 )
% 15.55/8.63            = one_one_nat )
% 15.55/8.63          = ( ? [X: nat] :
% 15.55/8.63                ( ( member_nat @ X @ A3 )
% 15.55/8.63                & ( ( F @ X )
% 15.55/8.63                  = one_one_nat )
% 15.55/8.63                & ! [Y: nat] :
% 15.55/8.63                    ( ( member_nat @ Y @ A3 )
% 15.55/8.63                   => ( ( X != Y )
% 15.55/8.63                     => ( ( F @ Y )
% 15.55/8.63                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8305_atMost__nat__numeral,axiom,
% 15.55/8.63      ! [K: num] :
% 15.55/8.63        ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 15.55/8.63        = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8306_lessThan__nat__numeral,axiom,
% 15.55/8.63      ! [K: num] :
% 15.55/8.63        ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 15.55/8.63        = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8307_set__encode__inf,axiom,
% 15.55/8.63      ! [A3: set_nat] :
% 15.55/8.63        ( ~ ( finite_finite_nat @ A3 )
% 15.55/8.63       => ( ( nat_set_encode @ A3 )
% 15.55/8.63          = zero_zero_nat ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8308_polyfun__diff__alt,axiom,
% 15.55/8.63      ! [N: nat,A: nat > complex,X3: complex,Y3: complex] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 15.55/8.63       => ( ( minus_minus_complex
% 15.55/8.63            @ ( groups2073611262835488442omplex
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( power_power_complex @ X3 @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63            @ ( groups2073611262835488442omplex
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( power_power_complex @ Y3 @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63          = ( times_times_complex @ ( minus_minus_complex @ X3 @ Y3 )
% 15.55/8.63            @ ( groups2073611262835488442omplex
% 15.55/8.63              @ ^ [J3: nat] :
% 15.55/8.63                  ( groups2073611262835488442omplex
% 15.55/8.63                  @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_complex @ Y3 @ K3 ) ) @ ( power_power_complex @ X3 @ J3 ) )
% 15.55/8.63                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 15.55/8.63              @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8309_polyfun__diff__alt,axiom,
% 15.55/8.63      ! [N: nat,A: nat > rat,X3: rat,Y3: rat] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 15.55/8.63       => ( ( minus_minus_rat
% 15.55/8.63            @ ( groups2906978787729119204at_rat
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( power_power_rat @ X3 @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63            @ ( groups2906978787729119204at_rat
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( power_power_rat @ Y3 @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63          = ( times_times_rat @ ( minus_minus_rat @ X3 @ Y3 )
% 15.55/8.63            @ ( groups2906978787729119204at_rat
% 15.55/8.63              @ ^ [J3: nat] :
% 15.55/8.63                  ( groups2906978787729119204at_rat
% 15.55/8.63                  @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_rat @ Y3 @ K3 ) ) @ ( power_power_rat @ X3 @ J3 ) )
% 15.55/8.63                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 15.55/8.63              @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8310_polyfun__diff__alt,axiom,
% 15.55/8.63      ! [N: nat,A: nat > int,X3: int,Y3: int] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 15.55/8.63       => ( ( minus_minus_int
% 15.55/8.63            @ ( groups3539618377306564664at_int
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_int @ ( A @ I4 ) @ ( power_power_int @ X3 @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63            @ ( groups3539618377306564664at_int
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_int @ ( A @ I4 ) @ ( power_power_int @ Y3 @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63          = ( times_times_int @ ( minus_minus_int @ X3 @ Y3 )
% 15.55/8.63            @ ( groups3539618377306564664at_int
% 15.55/8.63              @ ^ [J3: nat] :
% 15.55/8.63                  ( groups3539618377306564664at_int
% 15.55/8.63                  @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_int @ Y3 @ K3 ) ) @ ( power_power_int @ X3 @ J3 ) )
% 15.55/8.63                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 15.55/8.63              @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8311_polyfun__diff__alt,axiom,
% 15.55/8.63      ! [N: nat,A: nat > real,X3: real,Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 15.55/8.63       => ( ( minus_minus_real
% 15.55/8.63            @ ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( power_power_real @ X3 @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63            @ ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( power_power_real @ Y3 @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63          = ( times_times_real @ ( minus_minus_real @ X3 @ Y3 )
% 15.55/8.63            @ ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [J3: nat] :
% 15.55/8.63                  ( groups6591440286371151544t_real
% 15.55/8.63                  @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_real @ Y3 @ K3 ) ) @ ( power_power_real @ X3 @ J3 ) )
% 15.55/8.63                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 15.55/8.63              @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8312_suminf__le__const,axiom,
% 15.55/8.63      ! [F: nat > int,X3: int] :
% 15.55/8.63        ( ( summable_int @ F )
% 15.55/8.63       => ( ! [N2: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ X3 )
% 15.55/8.63         => ( ord_less_eq_int @ ( suminf_int @ F ) @ X3 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8313_suminf__le__const,axiom,
% 15.55/8.63      ! [F: nat > nat,X3: nat] :
% 15.55/8.63        ( ( summable_nat @ F )
% 15.55/8.63       => ( ! [N2: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ X3 )
% 15.55/8.63         => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ X3 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8314_suminf__le__const,axiom,
% 15.55/8.63      ! [F: nat > real,X3: real] :
% 15.55/8.63        ( ( summable_real @ F )
% 15.55/8.63       => ( ! [N2: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ X3 )
% 15.55/8.63         => ( ord_less_eq_real @ ( suminf_real @ F ) @ X3 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8315_sum_OatMost__Suc__shift,axiom,
% 15.55/8.63      ! [G: nat > rat,N: nat] :
% 15.55/8.63        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 15.55/8.63        = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups2906978787729119204at_rat
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8316_sum_OatMost__Suc__shift,axiom,
% 15.55/8.63      ! [G: nat > int,N: nat] :
% 15.55/8.63        ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 15.55/8.63        = ( plus_plus_int @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups3539618377306564664at_int
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8317_sum_OatMost__Suc__shift,axiom,
% 15.55/8.63      ! [G: nat > nat,N: nat] :
% 15.55/8.63        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 15.55/8.63        = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups3542108847815614940at_nat
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8318_sum_OatMost__Suc__shift,axiom,
% 15.55/8.63      ! [G: nat > real,N: nat] :
% 15.55/8.63        ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 15.55/8.63        = ( plus_plus_real @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups6591440286371151544t_real
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8319_sum__telescope,axiom,
% 15.55/8.63      ! [F: nat > rat,I: nat] :
% 15.55/8.63        ( ( groups2906978787729119204at_rat
% 15.55/8.63          @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ I4 ) @ ( F @ ( suc @ I4 ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ I ) )
% 15.55/8.63        = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8320_sum__telescope,axiom,
% 15.55/8.63      ! [F: nat > int,I: nat] :
% 15.55/8.63        ( ( groups3539618377306564664at_int
% 15.55/8.63          @ ^ [I4: nat] : ( minus_minus_int @ ( F @ I4 ) @ ( F @ ( suc @ I4 ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ I ) )
% 15.55/8.63        = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8321_sum__telescope,axiom,
% 15.55/8.63      ! [F: nat > real,I: nat] :
% 15.55/8.63        ( ( groups6591440286371151544t_real
% 15.55/8.63          @ ^ [I4: nat] : ( minus_minus_real @ ( F @ I4 ) @ ( F @ ( suc @ I4 ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ I ) )
% 15.55/8.63        = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8322_polyfun__eq__coeffs,axiom,
% 15.55/8.63      ! [C: nat > complex,N: nat,D3: nat > complex] :
% 15.55/8.63        ( ( ! [X: complex] :
% 15.55/8.63              ( ( groups2073611262835488442omplex
% 15.55/8.63                @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ X @ I4 ) )
% 15.55/8.63                @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63              = ( groups2073611262835488442omplex
% 15.55/8.63                @ ^ [I4: nat] : ( times_times_complex @ ( D3 @ I4 ) @ ( power_power_complex @ X @ I4 ) )
% 15.55/8.63                @ ( set_ord_atMost_nat @ N ) ) ) )
% 15.55/8.63        = ( ! [I4: nat] :
% 15.55/8.63              ( ( ord_less_eq_nat @ I4 @ N )
% 15.55/8.63             => ( ( C @ I4 )
% 15.55/8.63                = ( D3 @ I4 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8323_polyfun__eq__coeffs,axiom,
% 15.55/8.63      ! [C: nat > real,N: nat,D3: nat > real] :
% 15.55/8.63        ( ( ! [X: real] :
% 15.55/8.63              ( ( groups6591440286371151544t_real
% 15.55/8.63                @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ X @ I4 ) )
% 15.55/8.63                @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63              = ( groups6591440286371151544t_real
% 15.55/8.63                @ ^ [I4: nat] : ( times_times_real @ ( D3 @ I4 ) @ ( power_power_real @ X @ I4 ) )
% 15.55/8.63                @ ( set_ord_atMost_nat @ N ) ) ) )
% 15.55/8.63        = ( ! [I4: nat] :
% 15.55/8.63              ( ( ord_less_eq_nat @ I4 @ N )
% 15.55/8.63             => ( ( C @ I4 )
% 15.55/8.63                = ( D3 @ I4 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8324_bounded__imp__summable,axiom,
% 15.55/8.63      ! [A: nat > int,B5: int] :
% 15.55/8.63        ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( A @ N2 ) )
% 15.55/8.63       => ( ! [N2: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ A @ ( set_ord_atMost_nat @ N2 ) ) @ B5 )
% 15.55/8.63         => ( summable_int @ A ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8325_bounded__imp__summable,axiom,
% 15.55/8.63      ! [A: nat > nat,B5: nat] :
% 15.55/8.63        ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( A @ N2 ) )
% 15.55/8.63       => ( ! [N2: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ A @ ( set_ord_atMost_nat @ N2 ) ) @ B5 )
% 15.55/8.63         => ( summable_nat @ A ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8326_bounded__imp__summable,axiom,
% 15.55/8.63      ! [A: nat > real,B5: real] :
% 15.55/8.63        ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 15.55/8.63       => ( ! [N2: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ A @ ( set_ord_atMost_nat @ N2 ) ) @ B5 )
% 15.55/8.63         => ( summable_real @ A ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8327_prod_OatMost__Suc__shift,axiom,
% 15.55/8.63      ! [G: nat > real,N: nat] :
% 15.55/8.63        ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 15.55/8.63        = ( times_times_real @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups129246275422532515t_real
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8328_prod_OatMost__Suc__shift,axiom,
% 15.55/8.63      ! [G: nat > rat,N: nat] :
% 15.55/8.63        ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 15.55/8.63        = ( times_times_rat @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups73079841787564623at_rat
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8329_prod_OatMost__Suc__shift,axiom,
% 15.55/8.63      ! [G: nat > int,N: nat] :
% 15.55/8.63        ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 15.55/8.63        = ( times_times_int @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups705719431365010083at_int
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8330_prod_OatMost__Suc__shift,axiom,
% 15.55/8.63      ! [G: nat > nat,N: nat] :
% 15.55/8.63        ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 15.55/8.63        = ( times_times_nat @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups708209901874060359at_nat
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8331_sum_OlessThan__Suc__shift,axiom,
% 15.55/8.63      ! [G: nat > rat,N: nat] :
% 15.55/8.63        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 15.55/8.63        = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups2906978787729119204at_rat
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8332_sum_OlessThan__Suc__shift,axiom,
% 15.55/8.63      ! [G: nat > int,N: nat] :
% 15.55/8.63        ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 15.55/8.63        = ( plus_plus_int @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups3539618377306564664at_int
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8333_sum_OlessThan__Suc__shift,axiom,
% 15.55/8.63      ! [G: nat > nat,N: nat] :
% 15.55/8.63        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 15.55/8.63        = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups3542108847815614940at_nat
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8334_sum_OlessThan__Suc__shift,axiom,
% 15.55/8.63      ! [G: nat > real,N: nat] :
% 15.55/8.63        ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 15.55/8.63        = ( plus_plus_real @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups6591440286371151544t_real
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8335_sum__lessThan__telescope,axiom,
% 15.55/8.63      ! [F: nat > rat,M: nat] :
% 15.55/8.63        ( ( groups2906978787729119204at_rat
% 15.55/8.63          @ ^ [N3: nat] : ( minus_minus_rat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ M ) )
% 15.55/8.63        = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8336_sum__lessThan__telescope,axiom,
% 15.55/8.63      ! [F: nat > int,M: nat] :
% 15.55/8.63        ( ( groups3539618377306564664at_int
% 15.55/8.63          @ ^ [N3: nat] : ( minus_minus_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ M ) )
% 15.55/8.63        = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8337_sum__lessThan__telescope,axiom,
% 15.55/8.63      ! [F: nat > real,M: nat] :
% 15.55/8.63        ( ( groups6591440286371151544t_real
% 15.55/8.63          @ ^ [N3: nat] : ( minus_minus_real @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ M ) )
% 15.55/8.63        = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8338_sum__lessThan__telescope_H,axiom,
% 15.55/8.63      ! [F: nat > rat,M: nat] :
% 15.55/8.63        ( ( groups2906978787729119204at_rat
% 15.55/8.63          @ ^ [N3: nat] : ( minus_minus_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ M ) )
% 15.55/8.63        = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8339_sum__lessThan__telescope_H,axiom,
% 15.55/8.63      ! [F: nat > int,M: nat] :
% 15.55/8.63        ( ( groups3539618377306564664at_int
% 15.55/8.63          @ ^ [N3: nat] : ( minus_minus_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ M ) )
% 15.55/8.63        = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8340_sum__lessThan__telescope_H,axiom,
% 15.55/8.63      ! [F: nat > real,M: nat] :
% 15.55/8.63        ( ( groups6591440286371151544t_real
% 15.55/8.63          @ ^ [N3: nat] : ( minus_minus_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ M ) )
% 15.55/8.63        = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8341_sumr__diff__mult__const2,axiom,
% 15.55/8.63      ! [F: nat > complex,N: nat,R2: complex] :
% 15.55/8.63        ( ( minus_minus_complex @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ R2 ) )
% 15.55/8.63        = ( groups2073611262835488442omplex
% 15.55/8.63          @ ^ [I4: nat] : ( minus_minus_complex @ ( F @ I4 ) @ R2 )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8342_sumr__diff__mult__const2,axiom,
% 15.55/8.63      ! [F: nat > rat,N: nat,R2: rat] :
% 15.55/8.63        ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ R2 ) )
% 15.55/8.63        = ( groups2906978787729119204at_rat
% 15.55/8.63          @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ I4 ) @ R2 )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8343_sumr__diff__mult__const2,axiom,
% 15.55/8.63      ! [F: nat > int,N: nat,R2: int] :
% 15.55/8.63        ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ R2 ) )
% 15.55/8.63        = ( groups3539618377306564664at_int
% 15.55/8.63          @ ^ [I4: nat] : ( minus_minus_int @ ( F @ I4 ) @ R2 )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8344_sumr__diff__mult__const2,axiom,
% 15.55/8.63      ! [F: nat > real,N: nat,R2: real] :
% 15.55/8.63        ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ R2 ) )
% 15.55/8.63        = ( groups6591440286371151544t_real
% 15.55/8.63          @ ^ [I4: nat] : ( minus_minus_real @ ( F @ I4 ) @ R2 )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8345_summableI__nonneg__bounded,axiom,
% 15.55/8.63      ! [F: nat > int,X3: int] :
% 15.55/8.63        ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 15.55/8.63       => ( ! [N2: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ X3 )
% 15.55/8.63         => ( summable_int @ F ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8346_summableI__nonneg__bounded,axiom,
% 15.55/8.63      ! [F: nat > nat,X3: nat] :
% 15.55/8.63        ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 15.55/8.63       => ( ! [N2: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ X3 )
% 15.55/8.63         => ( summable_nat @ F ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8347_summableI__nonneg__bounded,axiom,
% 15.55/8.63      ! [F: nat > real,X3: real] :
% 15.55/8.63        ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 15.55/8.63       => ( ! [N2: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ X3 )
% 15.55/8.63         => ( summable_real @ F ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8348_prod_OlessThan__Suc__shift,axiom,
% 15.55/8.63      ! [G: nat > real,N: nat] :
% 15.55/8.63        ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 15.55/8.63        = ( times_times_real @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups129246275422532515t_real
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8349_prod_OlessThan__Suc__shift,axiom,
% 15.55/8.63      ! [G: nat > rat,N: nat] :
% 15.55/8.63        ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 15.55/8.63        = ( times_times_rat @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups73079841787564623at_rat
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8350_prod_OlessThan__Suc__shift,axiom,
% 15.55/8.63      ! [G: nat > int,N: nat] :
% 15.55/8.63        ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 15.55/8.63        = ( times_times_int @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups705719431365010083at_int
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8351_prod_OlessThan__Suc__shift,axiom,
% 15.55/8.63      ! [G: nat > nat,N: nat] :
% 15.55/8.63        ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 15.55/8.63        = ( times_times_nat @ ( G @ zero_zero_nat )
% 15.55/8.63          @ ( groups708209901874060359at_nat
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8352_sum__choose__diagonal,axiom,
% 15.55/8.63      ! [M: nat,N: nat] :
% 15.55/8.63        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.63       => ( ( groups3542108847815614940at_nat
% 15.55/8.63            @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ M ) )
% 15.55/8.63          = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8353_sum_OatLeast1__atMost__eq,axiom,
% 15.55/8.63      ! [G: nat > nat,N: nat] :
% 15.55/8.63        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 15.55/8.63        = ( groups3542108847815614940at_nat
% 15.55/8.63          @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8354_sum_OatLeast1__atMost__eq,axiom,
% 15.55/8.63      ! [G: nat > real,N: nat] :
% 15.55/8.63        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 15.55/8.63        = ( groups6591440286371151544t_real
% 15.55/8.63          @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8355_polyfun__diff,axiom,
% 15.55/8.63      ! [N: nat,A: nat > complex,X3: complex,Y3: complex] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 15.55/8.63       => ( ( minus_minus_complex
% 15.55/8.63            @ ( groups2073611262835488442omplex
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( power_power_complex @ X3 @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63            @ ( groups2073611262835488442omplex
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( power_power_complex @ Y3 @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63          = ( times_times_complex @ ( minus_minus_complex @ X3 @ Y3 )
% 15.55/8.63            @ ( groups2073611262835488442omplex
% 15.55/8.63              @ ^ [J3: nat] :
% 15.55/8.63                  ( times_times_complex
% 15.55/8.63                  @ ( groups2073611262835488442omplex
% 15.55/8.63                    @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( power_power_complex @ Y3 @ ( minus_minus_nat @ ( minus_minus_nat @ I4 @ J3 ) @ one_one_nat ) ) )
% 15.55/8.63                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 15.55/8.63                  @ ( power_power_complex @ X3 @ J3 ) )
% 15.55/8.63              @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8356_polyfun__diff,axiom,
% 15.55/8.63      ! [N: nat,A: nat > rat,X3: rat,Y3: rat] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 15.55/8.63       => ( ( minus_minus_rat
% 15.55/8.63            @ ( groups2906978787729119204at_rat
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( power_power_rat @ X3 @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63            @ ( groups2906978787729119204at_rat
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( power_power_rat @ Y3 @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63          = ( times_times_rat @ ( minus_minus_rat @ X3 @ Y3 )
% 15.55/8.63            @ ( groups2906978787729119204at_rat
% 15.55/8.63              @ ^ [J3: nat] :
% 15.55/8.63                  ( times_times_rat
% 15.55/8.63                  @ ( groups2906978787729119204at_rat
% 15.55/8.63                    @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( power_power_rat @ Y3 @ ( minus_minus_nat @ ( minus_minus_nat @ I4 @ J3 ) @ one_one_nat ) ) )
% 15.55/8.63                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 15.55/8.63                  @ ( power_power_rat @ X3 @ J3 ) )
% 15.55/8.63              @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8357_polyfun__diff,axiom,
% 15.55/8.63      ! [N: nat,A: nat > int,X3: int,Y3: int] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 15.55/8.63       => ( ( minus_minus_int
% 15.55/8.63            @ ( groups3539618377306564664at_int
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_int @ ( A @ I4 ) @ ( power_power_int @ X3 @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63            @ ( groups3539618377306564664at_int
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_int @ ( A @ I4 ) @ ( power_power_int @ Y3 @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63          = ( times_times_int @ ( minus_minus_int @ X3 @ Y3 )
% 15.55/8.63            @ ( groups3539618377306564664at_int
% 15.55/8.63              @ ^ [J3: nat] :
% 15.55/8.63                  ( times_times_int
% 15.55/8.63                  @ ( groups3539618377306564664at_int
% 15.55/8.63                    @ ^ [I4: nat] : ( times_times_int @ ( A @ I4 ) @ ( power_power_int @ Y3 @ ( minus_minus_nat @ ( minus_minus_nat @ I4 @ J3 ) @ one_one_nat ) ) )
% 15.55/8.63                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 15.55/8.63                  @ ( power_power_int @ X3 @ J3 ) )
% 15.55/8.63              @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8358_polyfun__diff,axiom,
% 15.55/8.63      ! [N: nat,A: nat > real,X3: real,Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 15.55/8.63       => ( ( minus_minus_real
% 15.55/8.63            @ ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( power_power_real @ X3 @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63            @ ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( power_power_real @ Y3 @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63          = ( times_times_real @ ( minus_minus_real @ X3 @ Y3 )
% 15.55/8.63            @ ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [J3: nat] :
% 15.55/8.63                  ( times_times_real
% 15.55/8.63                  @ ( groups6591440286371151544t_real
% 15.55/8.63                    @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( power_power_real @ Y3 @ ( minus_minus_nat @ ( minus_minus_nat @ I4 @ J3 ) @ one_one_nat ) ) )
% 15.55/8.63                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 15.55/8.63                  @ ( power_power_real @ X3 @ J3 ) )
% 15.55/8.63              @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8359_prod_OatLeast1__atMost__eq,axiom,
% 15.55/8.63      ! [G: nat > int,N: nat] :
% 15.55/8.63        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 15.55/8.63        = ( groups705719431365010083at_int
% 15.55/8.63          @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8360_prod_OatLeast1__atMost__eq,axiom,
% 15.55/8.63      ! [G: nat > nat,N: nat] :
% 15.55/8.63        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 15.55/8.63        = ( groups708209901874060359at_nat
% 15.55/8.63          @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8361_norm__prod__diff,axiom,
% 15.55/8.63      ! [I5: set_option_nat,Z: option_nat > real,W: option_nat > real] :
% 15.55/8.63        ( ! [I3: option_nat] :
% 15.55/8.63            ( ( member_option_nat @ I3 @ I5 )
% 15.55/8.63           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I3 ) ) @ one_one_real ) )
% 15.55/8.63       => ( ! [I3: option_nat] :
% 15.55/8.63              ( ( member_option_nat @ I3 @ I5 )
% 15.55/8.63             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I3 ) ) @ one_one_real ) )
% 15.55/8.63         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups6579596140936342515t_real @ Z @ I5 ) @ ( groups6579596140936342515t_real @ W @ I5 ) ) )
% 15.55/8.63            @ ( groups4518532050878116744t_real
% 15.55/8.63              @ ^ [I4: option_nat] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 15.55/8.63              @ I5 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8362_norm__prod__diff,axiom,
% 15.55/8.63      ! [I5: set_real,Z: real > real,W: real > real] :
% 15.55/8.63        ( ! [I3: real] :
% 15.55/8.63            ( ( member_real @ I3 @ I5 )
% 15.55/8.63           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I3 ) ) @ one_one_real ) )
% 15.55/8.63       => ( ! [I3: real] :
% 15.55/8.63              ( ( member_real @ I3 @ I5 )
% 15.55/8.63             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I3 ) ) @ one_one_real ) )
% 15.55/8.63         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups1681761925125756287l_real @ Z @ I5 ) @ ( groups1681761925125756287l_real @ W @ I5 ) ) )
% 15.55/8.63            @ ( groups8097168146408367636l_real
% 15.55/8.63              @ ^ [I4: real] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 15.55/8.63              @ I5 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8363_norm__prod__diff,axiom,
% 15.55/8.63      ! [I5: set_set_nat,Z: set_nat > real,W: set_nat > real] :
% 15.55/8.63        ( ! [I3: set_nat] :
% 15.55/8.63            ( ( member_set_nat @ I3 @ I5 )
% 15.55/8.63           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I3 ) ) @ one_one_real ) )
% 15.55/8.63       => ( ! [I3: set_nat] :
% 15.55/8.63              ( ( member_set_nat @ I3 @ I5 )
% 15.55/8.63             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I3 ) ) @ one_one_real ) )
% 15.55/8.63         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups3619160379726066777t_real @ Z @ I5 ) @ ( groups3619160379726066777t_real @ W @ I5 ) ) )
% 15.55/8.63            @ ( groups5107569545109728110t_real
% 15.55/8.63              @ ^ [I4: set_nat] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 15.55/8.63              @ I5 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8364_norm__prod__diff,axiom,
% 15.55/8.63      ! [I5: set_int,Z: int > real,W: int > real] :
% 15.55/8.63        ( ! [I3: int] :
% 15.55/8.63            ( ( member_int @ I3 @ I5 )
% 15.55/8.63           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I3 ) ) @ one_one_real ) )
% 15.55/8.63       => ( ! [I3: int] :
% 15.55/8.63              ( ( member_int @ I3 @ I5 )
% 15.55/8.63             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I3 ) ) @ one_one_real ) )
% 15.55/8.63         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups2316167850115554303t_real @ Z @ I5 ) @ ( groups2316167850115554303t_real @ W @ I5 ) ) )
% 15.55/8.63            @ ( groups8778361861064173332t_real
% 15.55/8.63              @ ^ [I4: int] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 15.55/8.63              @ I5 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8365_norm__prod__diff,axiom,
% 15.55/8.63      ! [I5: set_option_nat,Z: option_nat > complex,W: option_nat > complex] :
% 15.55/8.63        ( ! [I3: option_nat] :
% 15.55/8.63            ( ( member_option_nat @ I3 @ I5 )
% 15.55/8.63           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I3 ) ) @ one_one_real ) )
% 15.55/8.63       => ( ! [I3: option_nat] :
% 15.55/8.63              ( ( member_option_nat @ I3 @ I5 )
% 15.55/8.63             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I3 ) ) @ one_one_real ) )
% 15.55/8.63         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups1917955009447795573omplex @ Z @ I5 ) @ ( groups1917955009447795573omplex @ W @ I5 ) ) )
% 15.55/8.63            @ ( groups4518532050878116744t_real
% 15.55/8.63              @ ^ [I4: option_nat] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 15.55/8.63              @ I5 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8366_norm__prod__diff,axiom,
% 15.55/8.63      ! [I5: set_real,Z: real > complex,W: real > complex] :
% 15.55/8.63        ( ! [I3: real] :
% 15.55/8.63            ( ( member_real @ I3 @ I5 )
% 15.55/8.63           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I3 ) ) @ one_one_real ) )
% 15.55/8.63       => ( ! [I3: real] :
% 15.55/8.63              ( ( member_real @ I3 @ I5 )
% 15.55/8.63             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I3 ) ) @ one_one_real ) )
% 15.55/8.63         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups713298508707869441omplex @ Z @ I5 ) @ ( groups713298508707869441omplex @ W @ I5 ) ) )
% 15.55/8.63            @ ( groups8097168146408367636l_real
% 15.55/8.63              @ ^ [I4: real] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 15.55/8.63              @ I5 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8367_norm__prod__diff,axiom,
% 15.55/8.63      ! [I5: set_set_nat,Z: set_nat > complex,W: set_nat > complex] :
% 15.55/8.63        ( ! [I3: set_nat] :
% 15.55/8.63            ( ( member_set_nat @ I3 @ I5 )
% 15.55/8.63           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I3 ) ) @ one_one_real ) )
% 15.55/8.63       => ( ! [I3: set_nat] :
% 15.55/8.63              ( ( member_set_nat @ I3 @ I5 )
% 15.55/8.63             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I3 ) ) @ one_one_real ) )
% 15.55/8.63         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups1092910753850256091omplex @ Z @ I5 ) @ ( groups1092910753850256091omplex @ W @ I5 ) ) )
% 15.55/8.63            @ ( groups5107569545109728110t_real
% 15.55/8.63              @ ^ [I4: set_nat] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 15.55/8.63              @ I5 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8368_norm__prod__diff,axiom,
% 15.55/8.63      ! [I5: set_int,Z: int > complex,W: int > complex] :
% 15.55/8.63        ( ! [I3: int] :
% 15.55/8.63            ( ( member_int @ I3 @ I5 )
% 15.55/8.63           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I3 ) ) @ one_one_real ) )
% 15.55/8.63       => ( ! [I3: int] :
% 15.55/8.63              ( ( member_int @ I3 @ I5 )
% 15.55/8.63             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I3 ) ) @ one_one_real ) )
% 15.55/8.63         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups7440179247065528705omplex @ Z @ I5 ) @ ( groups7440179247065528705omplex @ W @ I5 ) ) )
% 15.55/8.63            @ ( groups8778361861064173332t_real
% 15.55/8.63              @ ^ [I4: int] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 15.55/8.63              @ I5 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8369_norm__prod__diff,axiom,
% 15.55/8.63      ! [I5: set_nat,Z: nat > real,W: nat > real] :
% 15.55/8.63        ( ! [I3: nat] :
% 15.55/8.63            ( ( member_nat @ I3 @ I5 )
% 15.55/8.63           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I3 ) ) @ one_one_real ) )
% 15.55/8.63       => ( ! [I3: nat] :
% 15.55/8.63              ( ( member_nat @ I3 @ I5 )
% 15.55/8.63             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I3 ) ) @ one_one_real ) )
% 15.55/8.63         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups129246275422532515t_real @ Z @ I5 ) @ ( groups129246275422532515t_real @ W @ I5 ) ) )
% 15.55/8.63            @ ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [I4: nat] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 15.55/8.63              @ I5 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8370_norm__prod__diff,axiom,
% 15.55/8.63      ! [I5: set_nat,Z: nat > complex,W: nat > complex] :
% 15.55/8.63        ( ! [I3: nat] :
% 15.55/8.63            ( ( member_nat @ I3 @ I5 )
% 15.55/8.63           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I3 ) ) @ one_one_real ) )
% 15.55/8.63       => ( ! [I3: nat] :
% 15.55/8.63              ( ( member_nat @ I3 @ I5 )
% 15.55/8.63             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I3 ) ) @ one_one_real ) )
% 15.55/8.63         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups6464643781859351333omplex @ Z @ I5 ) @ ( groups6464643781859351333omplex @ W @ I5 ) ) )
% 15.55/8.63            @ ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [I4: nat] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 15.55/8.63              @ I5 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8371_zero__polynom__imp__zero__coeffs,axiom,
% 15.55/8.63      ! [C: nat > complex,N: nat,K: nat] :
% 15.55/8.63        ( ! [W2: complex] :
% 15.55/8.63            ( ( groups2073611262835488442omplex
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ W2 @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63            = zero_zero_complex )
% 15.55/8.63       => ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.63         => ( ( C @ K )
% 15.55/8.63            = zero_zero_complex ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8372_zero__polynom__imp__zero__coeffs,axiom,
% 15.55/8.63      ! [C: nat > real,N: nat,K: nat] :
% 15.55/8.63        ( ! [W2: real] :
% 15.55/8.63            ( ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ W2 @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63            = zero_zero_real )
% 15.55/8.63       => ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.63         => ( ( C @ K )
% 15.55/8.63            = zero_zero_real ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8373_polyfun__eq__0,axiom,
% 15.55/8.63      ! [C: nat > complex,N: nat] :
% 15.55/8.63        ( ( ! [X: complex] :
% 15.55/8.63              ( ( groups2073611262835488442omplex
% 15.55/8.63                @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ X @ I4 ) )
% 15.55/8.63                @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63              = zero_zero_complex ) )
% 15.55/8.63        = ( ! [I4: nat] :
% 15.55/8.63              ( ( ord_less_eq_nat @ I4 @ N )
% 15.55/8.63             => ( ( C @ I4 )
% 15.55/8.63                = zero_zero_complex ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8374_polyfun__eq__0,axiom,
% 15.55/8.63      ! [C: nat > real,N: nat] :
% 15.55/8.63        ( ( ! [X: real] :
% 15.55/8.63              ( ( groups6591440286371151544t_real
% 15.55/8.63                @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ X @ I4 ) )
% 15.55/8.63                @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63              = zero_zero_real ) )
% 15.55/8.63        = ( ! [I4: nat] :
% 15.55/8.63              ( ( ord_less_eq_nat @ I4 @ N )
% 15.55/8.63             => ( ( C @ I4 )
% 15.55/8.63                = zero_zero_real ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8375_one__diff__power__eq,axiom,
% 15.55/8.63      ! [X3: complex,N: nat] :
% 15.55/8.63        ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ N ) )
% 15.55/8.63        = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X3 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8376_one__diff__power__eq,axiom,
% 15.55/8.63      ! [X3: rat,N: nat] :
% 15.55/8.63        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ N ) )
% 15.55/8.63        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X3 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8377_one__diff__power__eq,axiom,
% 15.55/8.63      ! [X3: int,N: nat] :
% 15.55/8.63        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X3 @ N ) )
% 15.55/8.63        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X3 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8378_one__diff__power__eq,axiom,
% 15.55/8.63      ! [X3: real,N: nat] :
% 15.55/8.63        ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ N ) )
% 15.55/8.63        = ( times_times_real @ ( minus_minus_real @ one_one_real @ X3 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8379_power__diff__1__eq,axiom,
% 15.55/8.63      ! [X3: complex,N: nat] :
% 15.55/8.63        ( ( minus_minus_complex @ ( power_power_complex @ X3 @ N ) @ one_one_complex )
% 15.55/8.63        = ( times_times_complex @ ( minus_minus_complex @ X3 @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8380_power__diff__1__eq,axiom,
% 15.55/8.63      ! [X3: rat,N: nat] :
% 15.55/8.63        ( ( minus_minus_rat @ ( power_power_rat @ X3 @ N ) @ one_one_rat )
% 15.55/8.63        = ( times_times_rat @ ( minus_minus_rat @ X3 @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8381_power__diff__1__eq,axiom,
% 15.55/8.63      ! [X3: int,N: nat] :
% 15.55/8.63        ( ( minus_minus_int @ ( power_power_int @ X3 @ N ) @ one_one_int )
% 15.55/8.63        = ( times_times_int @ ( minus_minus_int @ X3 @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8382_power__diff__1__eq,axiom,
% 15.55/8.63      ! [X3: real,N: nat] :
% 15.55/8.63        ( ( minus_minus_real @ ( power_power_real @ X3 @ N ) @ one_one_real )
% 15.55/8.63        = ( times_times_real @ ( minus_minus_real @ X3 @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8383_geometric__sum,axiom,
% 15.55/8.63      ! [X3: complex,N: nat] :
% 15.55/8.63        ( ( X3 != one_one_complex )
% 15.55/8.63       => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.63          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X3 @ N ) @ one_one_complex ) @ ( minus_minus_complex @ X3 @ one_one_complex ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8384_geometric__sum,axiom,
% 15.55/8.63      ! [X3: rat,N: nat] :
% 15.55/8.63        ( ( X3 != one_one_rat )
% 15.55/8.63       => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.63          = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X3 @ N ) @ one_one_rat ) @ ( minus_minus_rat @ X3 @ one_one_rat ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8385_geometric__sum,axiom,
% 15.55/8.63      ! [X3: real,N: nat] :
% 15.55/8.63        ( ( X3 != one_one_real )
% 15.55/8.63       => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.63          = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X3 @ N ) @ one_one_real ) @ ( minus_minus_real @ X3 @ one_one_real ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8386_choose__row__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8387_binomial,axiom,
% 15.55/8.63      ! [A: nat,B: nat,N: nat] :
% 15.55/8.63        ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 15.55/8.63        = ( groups3542108847815614940at_nat
% 15.55/8.63          @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8388_ln__prod,axiom,
% 15.55/8.63      ! [I5: set_option_nat,F: option_nat > real] :
% 15.55/8.63        ( ( finite5523153139673422903on_nat @ I5 )
% 15.55/8.63       => ( ! [I3: option_nat] :
% 15.55/8.63              ( ( member_option_nat @ I3 @ I5 )
% 15.55/8.63             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.63         => ( ( ln_ln_real @ ( groups6579596140936342515t_real @ F @ I5 ) )
% 15.55/8.63            = ( groups4518532050878116744t_real
% 15.55/8.63              @ ^ [X: option_nat] : ( ln_ln_real @ ( F @ X ) )
% 15.55/8.63              @ I5 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8389_ln__prod,axiom,
% 15.55/8.63      ! [I5: set_real,F: real > real] :
% 15.55/8.63        ( ( finite_finite_real @ I5 )
% 15.55/8.63       => ( ! [I3: real] :
% 15.55/8.63              ( ( member_real @ I3 @ I5 )
% 15.55/8.63             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.63         => ( ( ln_ln_real @ ( groups1681761925125756287l_real @ F @ I5 ) )
% 15.55/8.63            = ( groups8097168146408367636l_real
% 15.55/8.63              @ ^ [X: real] : ( ln_ln_real @ ( F @ X ) )
% 15.55/8.63              @ I5 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8390_ln__prod,axiom,
% 15.55/8.63      ! [I5: set_set_nat,F: set_nat > real] :
% 15.55/8.63        ( ( finite1152437895449049373et_nat @ I5 )
% 15.55/8.63       => ( ! [I3: set_nat] :
% 15.55/8.63              ( ( member_set_nat @ I3 @ I5 )
% 15.55/8.63             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.63         => ( ( ln_ln_real @ ( groups3619160379726066777t_real @ F @ I5 ) )
% 15.55/8.63            = ( groups5107569545109728110t_real
% 15.55/8.63              @ ^ [X: set_nat] : ( ln_ln_real @ ( F @ X ) )
% 15.55/8.63              @ I5 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8391_ln__prod,axiom,
% 15.55/8.63      ! [I5: set_int,F: int > real] :
% 15.55/8.63        ( ( finite_finite_int @ I5 )
% 15.55/8.63       => ( ! [I3: int] :
% 15.55/8.63              ( ( member_int @ I3 @ I5 )
% 15.55/8.63             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.63         => ( ( ln_ln_real @ ( groups2316167850115554303t_real @ F @ I5 ) )
% 15.55/8.63            = ( groups8778361861064173332t_real
% 15.55/8.63              @ ^ [X: int] : ( ln_ln_real @ ( F @ X ) )
% 15.55/8.63              @ I5 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8392_ln__prod,axiom,
% 15.55/8.63      ! [I5: set_complex,F: complex > real] :
% 15.55/8.63        ( ( finite3207457112153483333omplex @ I5 )
% 15.55/8.63       => ( ! [I3: complex] :
% 15.55/8.63              ( ( member_complex @ I3 @ I5 )
% 15.55/8.63             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.63         => ( ( ln_ln_real @ ( groups766887009212190081x_real @ F @ I5 ) )
% 15.55/8.63            = ( groups5808333547571424918x_real
% 15.55/8.63              @ ^ [X: complex] : ( ln_ln_real @ ( F @ X ) )
% 15.55/8.63              @ I5 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8393_ln__prod,axiom,
% 15.55/8.63      ! [I5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > real] :
% 15.55/8.63        ( ( finite6177210948735845034at_nat @ I5 )
% 15.55/8.63       => ( ! [I3: product_prod_nat_nat] :
% 15.55/8.63              ( ( member8440522571783428010at_nat @ I3 @ I5 )
% 15.55/8.63             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.63         => ( ( ln_ln_real @ ( groups6036352826371341000t_real @ F @ I5 ) )
% 15.55/8.63            = ( groups4567486121110086003t_real
% 15.55/8.63              @ ^ [X: product_prod_nat_nat] : ( ln_ln_real @ ( F @ X ) )
% 15.55/8.63              @ I5 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8394_ln__prod,axiom,
% 15.55/8.63      ! [I5: set_Extended_enat,F: extended_enat > real] :
% 15.55/8.63        ( ( finite4001608067531595151d_enat @ I5 )
% 15.55/8.63       => ( ! [I3: extended_enat] :
% 15.55/8.63              ( ( member_Extended_enat @ I3 @ I5 )
% 15.55/8.63             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.63         => ( ( ln_ln_real @ ( groups97031904164794029t_real @ F @ I5 ) )
% 15.55/8.63            = ( groups4148127829035722712t_real
% 15.55/8.63              @ ^ [X: extended_enat] : ( ln_ln_real @ ( F @ X ) )
% 15.55/8.63              @ I5 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8395_ln__prod,axiom,
% 15.55/8.63      ! [I5: set_nat,F: nat > real] :
% 15.55/8.63        ( ( finite_finite_nat @ I5 )
% 15.55/8.63       => ( ! [I3: nat] :
% 15.55/8.63              ( ( member_nat @ I3 @ I5 )
% 15.55/8.63             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 15.55/8.63         => ( ( ln_ln_real @ ( groups129246275422532515t_real @ F @ I5 ) )
% 15.55/8.63            = ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [X: nat] : ( ln_ln_real @ ( F @ X ) )
% 15.55/8.63              @ I5 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8396_sum__less__suminf,axiom,
% 15.55/8.63      ! [F: nat > int,N: nat] :
% 15.55/8.63        ( ( summable_int @ F )
% 15.55/8.63       => ( ! [M4: nat] :
% 15.55/8.63              ( ( ord_less_eq_nat @ N @ M4 )
% 15.55/8.63             => ( ord_less_int @ zero_zero_int @ ( F @ M4 ) ) )
% 15.55/8.63         => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_int @ F ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8397_sum__less__suminf,axiom,
% 15.55/8.63      ! [F: nat > nat,N: nat] :
% 15.55/8.63        ( ( summable_nat @ F )
% 15.55/8.63       => ( ! [M4: nat] :
% 15.55/8.63              ( ( ord_less_eq_nat @ N @ M4 )
% 15.55/8.63             => ( ord_less_nat @ zero_zero_nat @ ( F @ M4 ) ) )
% 15.55/8.63         => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_nat @ F ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8398_sum__less__suminf,axiom,
% 15.55/8.63      ! [F: nat > real,N: nat] :
% 15.55/8.63        ( ( summable_real @ F )
% 15.55/8.63       => ( ! [M4: nat] :
% 15.55/8.63              ( ( ord_less_eq_nat @ N @ M4 )
% 15.55/8.63             => ( ord_less_real @ zero_zero_real @ ( F @ M4 ) ) )
% 15.55/8.63         => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_real @ F ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8399_sum__gp__basic,axiom,
% 15.55/8.63      ! [X3: complex,N: nat] :
% 15.55/8.63        ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X3 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63        = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ ( suc @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8400_sum__gp__basic,axiom,
% 15.55/8.63      ! [X3: rat,N: nat] :
% 15.55/8.63        ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X3 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63        = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ ( suc @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8401_sum__gp__basic,axiom,
% 15.55/8.63      ! [X3: int,N: nat] :
% 15.55/8.63        ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X3 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63        = ( minus_minus_int @ one_one_int @ ( power_power_int @ X3 @ ( suc @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8402_sum__gp__basic,axiom,
% 15.55/8.63      ! [X3: real,N: nat] :
% 15.55/8.63        ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X3 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63        = ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( suc @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8403_polyfun__roots__finite,axiom,
% 15.55/8.63      ! [C: nat > complex,K: nat,N: nat] :
% 15.55/8.63        ( ( ( C @ K )
% 15.55/8.63         != zero_zero_complex )
% 15.55/8.63       => ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.63         => ( finite3207457112153483333omplex
% 15.55/8.63            @ ( collect_complex
% 15.55/8.63              @ ^ [Z6: complex] :
% 15.55/8.63                  ( ( groups2073611262835488442omplex
% 15.55/8.63                    @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ Z6 @ I4 ) )
% 15.55/8.63                    @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63                  = zero_zero_complex ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8404_polyfun__roots__finite,axiom,
% 15.55/8.63      ! [C: nat > real,K: nat,N: nat] :
% 15.55/8.63        ( ( ( C @ K )
% 15.55/8.63         != zero_zero_real )
% 15.55/8.63       => ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.63         => ( finite_finite_real
% 15.55/8.63            @ ( collect_real
% 15.55/8.63              @ ^ [Z6: real] :
% 15.55/8.63                  ( ( groups6591440286371151544t_real
% 15.55/8.63                    @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ Z6 @ I4 ) )
% 15.55/8.63                    @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63                  = zero_zero_real ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8405_polyfun__finite__roots,axiom,
% 15.55/8.63      ! [C: nat > complex,N: nat] :
% 15.55/8.63        ( ( finite3207457112153483333omplex
% 15.55/8.63          @ ( collect_complex
% 15.55/8.63            @ ^ [X: complex] :
% 15.55/8.63                ( ( groups2073611262835488442omplex
% 15.55/8.63                  @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ X @ I4 ) )
% 15.55/8.63                  @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63                = zero_zero_complex ) ) )
% 15.55/8.63        = ( ? [I4: nat] :
% 15.55/8.63              ( ( ord_less_eq_nat @ I4 @ N )
% 15.55/8.63              & ( ( C @ I4 )
% 15.55/8.63               != zero_zero_complex ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8406_polyfun__finite__roots,axiom,
% 15.55/8.63      ! [C: nat > real,N: nat] :
% 15.55/8.63        ( ( finite_finite_real
% 15.55/8.63          @ ( collect_real
% 15.55/8.63            @ ^ [X: real] :
% 15.55/8.63                ( ( groups6591440286371151544t_real
% 15.55/8.63                  @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ X @ I4 ) )
% 15.55/8.63                  @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63                = zero_zero_real ) ) )
% 15.55/8.63        = ( ? [I4: nat] :
% 15.55/8.63              ( ( ord_less_eq_nat @ I4 @ N )
% 15.55/8.63              & ( ( C @ I4 )
% 15.55/8.63               != zero_zero_real ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8407_sum__gp__strict,axiom,
% 15.55/8.63      ! [X3: complex,N: nat] :
% 15.55/8.63        ( ( ( X3 = one_one_complex )
% 15.55/8.63         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.63            = ( semiri8010041392384452111omplex @ N ) ) )
% 15.55/8.63        & ( ( X3 != one_one_complex )
% 15.55/8.63         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.63            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ N ) ) @ ( minus_minus_complex @ one_one_complex @ X3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8408_sum__gp__strict,axiom,
% 15.55/8.63      ! [X3: rat,N: nat] :
% 15.55/8.63        ( ( ( X3 = one_one_rat )
% 15.55/8.63         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.63            = ( semiri681578069525770553at_rat @ N ) ) )
% 15.55/8.63        & ( ( X3 != one_one_rat )
% 15.55/8.63         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.63            = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ N ) ) @ ( minus_minus_rat @ one_one_rat @ X3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8409_sum__gp__strict,axiom,
% 15.55/8.63      ! [X3: real,N: nat] :
% 15.55/8.63        ( ( ( X3 = one_one_real )
% 15.55/8.63         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.63            = ( semiri5074537144036343181t_real @ N ) ) )
% 15.55/8.63        & ( ( X3 != one_one_real )
% 15.55/8.63         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.63            = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ N ) ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8410_lemma__termdiff1,axiom,
% 15.55/8.63      ! [Z: complex,H2: complex,M: nat] :
% 15.55/8.63        ( ( groups2073611262835488442omplex
% 15.55/8.63          @ ^ [P5: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_complex @ Z @ P5 ) ) @ ( power_power_complex @ Z @ M ) )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ M ) )
% 15.55/8.63        = ( groups2073611262835488442omplex
% 15.55/8.63          @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ Z @ P5 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8411_lemma__termdiff1,axiom,
% 15.55/8.63      ! [Z: rat,H2: rat,M: nat] :
% 15.55/8.63        ( ( groups2906978787729119204at_rat
% 15.55/8.63          @ ^ [P5: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_rat @ Z @ P5 ) ) @ ( power_power_rat @ Z @ M ) )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ M ) )
% 15.55/8.63        = ( groups2906978787729119204at_rat
% 15.55/8.63          @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ Z @ P5 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8412_lemma__termdiff1,axiom,
% 15.55/8.63      ! [Z: int,H2: int,M: nat] :
% 15.55/8.63        ( ( groups3539618377306564664at_int
% 15.55/8.63          @ ^ [P5: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_int @ Z @ P5 ) ) @ ( power_power_int @ Z @ M ) )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ M ) )
% 15.55/8.63        = ( groups3539618377306564664at_int
% 15.55/8.63          @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ Z @ P5 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_int @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8413_lemma__termdiff1,axiom,
% 15.55/8.63      ! [Z: real,H2: real,M: nat] :
% 15.55/8.63        ( ( groups6591440286371151544t_real
% 15.55/8.63          @ ^ [P5: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_real @ Z @ P5 ) ) @ ( power_power_real @ Z @ M ) )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ M ) )
% 15.55/8.63        = ( groups6591440286371151544t_real
% 15.55/8.63          @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ Z @ P5 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_real @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8414_power__diff__sumr2,axiom,
% 15.55/8.63      ! [X3: complex,N: nat,Y3: complex] :
% 15.55/8.63        ( ( minus_minus_complex @ ( power_power_complex @ X3 @ N ) @ ( power_power_complex @ Y3 @ N ) )
% 15.55/8.63        = ( times_times_complex @ ( minus_minus_complex @ X3 @ Y3 )
% 15.55/8.63          @ ( groups2073611262835488442omplex
% 15.55/8.63            @ ^ [I4: nat] : ( times_times_complex @ ( power_power_complex @ Y3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_complex @ X3 @ I4 ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8415_power__diff__sumr2,axiom,
% 15.55/8.63      ! [X3: rat,N: nat,Y3: rat] :
% 15.55/8.63        ( ( minus_minus_rat @ ( power_power_rat @ X3 @ N ) @ ( power_power_rat @ Y3 @ N ) )
% 15.55/8.63        = ( times_times_rat @ ( minus_minus_rat @ X3 @ Y3 )
% 15.55/8.63          @ ( groups2906978787729119204at_rat
% 15.55/8.63            @ ^ [I4: nat] : ( times_times_rat @ ( power_power_rat @ Y3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_rat @ X3 @ I4 ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8416_power__diff__sumr2,axiom,
% 15.55/8.63      ! [X3: int,N: nat,Y3: int] :
% 15.55/8.63        ( ( minus_minus_int @ ( power_power_int @ X3 @ N ) @ ( power_power_int @ Y3 @ N ) )
% 15.55/8.63        = ( times_times_int @ ( minus_minus_int @ X3 @ Y3 )
% 15.55/8.63          @ ( groups3539618377306564664at_int
% 15.55/8.63            @ ^ [I4: nat] : ( times_times_int @ ( power_power_int @ Y3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_int @ X3 @ I4 ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8417_power__diff__sumr2,axiom,
% 15.55/8.63      ! [X3: real,N: nat,Y3: real] :
% 15.55/8.63        ( ( minus_minus_real @ ( power_power_real @ X3 @ N ) @ ( power_power_real @ Y3 @ N ) )
% 15.55/8.63        = ( times_times_real @ ( minus_minus_real @ X3 @ Y3 )
% 15.55/8.63          @ ( groups6591440286371151544t_real
% 15.55/8.63            @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ Y3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_real @ X3 @ I4 ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8418_diff__power__eq__sum,axiom,
% 15.55/8.63      ! [X3: complex,N: nat,Y3: complex] :
% 15.55/8.63        ( ( minus_minus_complex @ ( power_power_complex @ X3 @ ( suc @ N ) ) @ ( power_power_complex @ Y3 @ ( suc @ N ) ) )
% 15.55/8.63        = ( times_times_complex @ ( minus_minus_complex @ X3 @ Y3 )
% 15.55/8.63          @ ( groups2073611262835488442omplex
% 15.55/8.63            @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ X3 @ P5 ) @ ( power_power_complex @ Y3 @ ( minus_minus_nat @ N @ P5 ) ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8419_diff__power__eq__sum,axiom,
% 15.55/8.63      ! [X3: rat,N: nat,Y3: rat] :
% 15.55/8.63        ( ( minus_minus_rat @ ( power_power_rat @ X3 @ ( suc @ N ) ) @ ( power_power_rat @ Y3 @ ( suc @ N ) ) )
% 15.55/8.63        = ( times_times_rat @ ( minus_minus_rat @ X3 @ Y3 )
% 15.55/8.63          @ ( groups2906978787729119204at_rat
% 15.55/8.63            @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ X3 @ P5 ) @ ( power_power_rat @ Y3 @ ( minus_minus_nat @ N @ P5 ) ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8420_diff__power__eq__sum,axiom,
% 15.55/8.63      ! [X3: int,N: nat,Y3: int] :
% 15.55/8.63        ( ( minus_minus_int @ ( power_power_int @ X3 @ ( suc @ N ) ) @ ( power_power_int @ Y3 @ ( suc @ N ) ) )
% 15.55/8.63        = ( times_times_int @ ( minus_minus_int @ X3 @ Y3 )
% 15.55/8.63          @ ( groups3539618377306564664at_int
% 15.55/8.63            @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ X3 @ P5 ) @ ( power_power_int @ Y3 @ ( minus_minus_nat @ N @ P5 ) ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8421_diff__power__eq__sum,axiom,
% 15.55/8.63      ! [X3: real,N: nat,Y3: real] :
% 15.55/8.63        ( ( minus_minus_real @ ( power_power_real @ X3 @ ( suc @ N ) ) @ ( power_power_real @ Y3 @ ( suc @ N ) ) )
% 15.55/8.63        = ( times_times_real @ ( minus_minus_real @ X3 @ Y3 )
% 15.55/8.63          @ ( groups6591440286371151544t_real
% 15.55/8.63            @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ X3 @ P5 ) @ ( power_power_real @ Y3 @ ( minus_minus_nat @ N @ P5 ) ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8422_polynomial__product__nat,axiom,
% 15.55/8.63      ! [M: nat,A: nat > nat,N: nat,B: nat > nat,X3: nat] :
% 15.55/8.63        ( ! [I3: nat] :
% 15.55/8.63            ( ( ord_less_nat @ M @ I3 )
% 15.55/8.63           => ( ( A @ I3 )
% 15.55/8.63              = zero_zero_nat ) )
% 15.55/8.63       => ( ! [J2: nat] :
% 15.55/8.63              ( ( ord_less_nat @ N @ J2 )
% 15.55/8.63             => ( ( B @ J2 )
% 15.55/8.63                = zero_zero_nat ) )
% 15.55/8.63         => ( ( times_times_nat
% 15.55/8.63              @ ( groups3542108847815614940at_nat
% 15.55/8.63                @ ^ [I4: nat] : ( times_times_nat @ ( A @ I4 ) @ ( power_power_nat @ X3 @ I4 ) )
% 15.55/8.63                @ ( set_ord_atMost_nat @ M ) )
% 15.55/8.63              @ ( groups3542108847815614940at_nat
% 15.55/8.63                @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X3 @ J3 ) )
% 15.55/8.63                @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63            = ( groups3542108847815614940at_nat
% 15.55/8.63              @ ^ [R5: nat] :
% 15.55/8.63                  ( times_times_nat
% 15.55/8.63                  @ ( groups3542108847815614940at_nat
% 15.55/8.63                    @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 15.55/8.63                    @ ( set_ord_atMost_nat @ R5 ) )
% 15.55/8.63                  @ ( power_power_nat @ X3 @ R5 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8423_sum__power__shift,axiom,
% 15.55/8.63      ! [M: nat,N: nat,X3: complex] :
% 15.55/8.63        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.63       => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.63          = ( times_times_complex @ ( power_power_complex @ X3 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8424_sum__power__shift,axiom,
% 15.55/8.63      ! [M: nat,N: nat,X3: rat] :
% 15.55/8.63        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.63       => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.63          = ( times_times_rat @ ( power_power_rat @ X3 @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8425_sum__power__shift,axiom,
% 15.55/8.63      ! [M: nat,N: nat,X3: int] :
% 15.55/8.63        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.63       => ( ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.63          = ( times_times_int @ ( power_power_int @ X3 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8426_sum__power__shift,axiom,
% 15.55/8.63      ! [M: nat,N: nat,X3: real] :
% 15.55/8.63        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.63       => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 15.55/8.63          = ( times_times_real @ ( power_power_real @ X3 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8427_choose__square__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( groups3542108847815614940at_nat
% 15.55/8.63          @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63        = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8428_set__encode__def,axiom,
% 15.55/8.63      ( nat_set_encode
% 15.55/8.63      = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8429_atLeast1__atMost__eq__remove0,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 15.55/8.63        = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8430_real__sum__nat__ivl__bounded2,axiom,
% 15.55/8.63      ! [N: nat,F: nat > rat,K5: rat,K: nat] :
% 15.55/8.63        ( ! [P7: nat] :
% 15.55/8.63            ( ( ord_less_nat @ P7 @ N )
% 15.55/8.63           => ( ord_less_eq_rat @ ( F @ P7 ) @ K5 ) )
% 15.55/8.63       => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 15.55/8.63         => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ K5 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8431_real__sum__nat__ivl__bounded2,axiom,
% 15.55/8.63      ! [N: nat,F: nat > int,K5: int,K: nat] :
% 15.55/8.63        ( ! [P7: nat] :
% 15.55/8.63            ( ( ord_less_nat @ P7 @ N )
% 15.55/8.63           => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 15.55/8.63       => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 15.55/8.63         => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ K5 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8432_real__sum__nat__ivl__bounded2,axiom,
% 15.55/8.63      ! [N: nat,F: nat > nat,K5: nat,K: nat] :
% 15.55/8.63        ( ! [P7: nat] :
% 15.55/8.63            ( ( ord_less_nat @ P7 @ N )
% 15.55/8.63           => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 15.55/8.63       => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 15.55/8.63         => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ K5 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8433_real__sum__nat__ivl__bounded2,axiom,
% 15.55/8.63      ! [N: nat,F: nat > real,K5: real,K: nat] :
% 15.55/8.63        ( ! [P7: nat] :
% 15.55/8.63            ( ( ord_less_nat @ P7 @ N )
% 15.55/8.63           => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 15.55/8.63       => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 15.55/8.63         => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ K5 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8434_finite__has__minimal2,axiom,
% 15.55/8.63      ! [A3: set_real,A: real] :
% 15.55/8.63        ( ( finite_finite_real @ A3 )
% 15.55/8.63       => ( ( member_real @ A @ A3 )
% 15.55/8.63         => ? [X4: real] :
% 15.55/8.63              ( ( member_real @ X4 @ A3 )
% 15.55/8.63              & ( ord_less_eq_real @ X4 @ A )
% 15.55/8.63              & ! [Xa2: real] :
% 15.55/8.63                  ( ( member_real @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_real @ Xa2 @ X4 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8435_finite__has__minimal2,axiom,
% 15.55/8.63      ! [A3: set_Extended_enat,A: extended_enat] :
% 15.55/8.63        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.63       => ( ( member_Extended_enat @ A @ A3 )
% 15.55/8.63         => ? [X4: extended_enat] :
% 15.55/8.63              ( ( member_Extended_enat @ X4 @ A3 )
% 15.55/8.63              & ( ord_le2932123472753598470d_enat @ X4 @ A )
% 15.55/8.63              & ! [Xa2: extended_enat] :
% 15.55/8.63                  ( ( member_Extended_enat @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_le2932123472753598470d_enat @ Xa2 @ X4 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8436_finite__has__minimal2,axiom,
% 15.55/8.63      ! [A3: set_set_nat,A: set_nat] :
% 15.55/8.63        ( ( finite1152437895449049373et_nat @ A3 )
% 15.55/8.63       => ( ( member_set_nat @ A @ A3 )
% 15.55/8.63         => ? [X4: set_nat] :
% 15.55/8.63              ( ( member_set_nat @ X4 @ A3 )
% 15.55/8.63              & ( ord_less_eq_set_nat @ X4 @ A )
% 15.55/8.63              & ! [Xa2: set_nat] :
% 15.55/8.63                  ( ( member_set_nat @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_set_nat @ Xa2 @ X4 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8437_finite__has__minimal2,axiom,
% 15.55/8.63      ! [A3: set_rat,A: rat] :
% 15.55/8.63        ( ( finite_finite_rat @ A3 )
% 15.55/8.63       => ( ( member_rat @ A @ A3 )
% 15.55/8.63         => ? [X4: rat] :
% 15.55/8.63              ( ( member_rat @ X4 @ A3 )
% 15.55/8.63              & ( ord_less_eq_rat @ X4 @ A )
% 15.55/8.63              & ! [Xa2: rat] :
% 15.55/8.63                  ( ( member_rat @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_rat @ Xa2 @ X4 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8438_finite__has__minimal2,axiom,
% 15.55/8.63      ! [A3: set_num,A: num] :
% 15.55/8.63        ( ( finite_finite_num @ A3 )
% 15.55/8.63       => ( ( member_num @ A @ A3 )
% 15.55/8.63         => ? [X4: num] :
% 15.55/8.63              ( ( member_num @ X4 @ A3 )
% 15.55/8.63              & ( ord_less_eq_num @ X4 @ A )
% 15.55/8.63              & ! [Xa2: num] :
% 15.55/8.63                  ( ( member_num @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_num @ Xa2 @ X4 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8439_finite__has__minimal2,axiom,
% 15.55/8.63      ! [A3: set_nat,A: nat] :
% 15.55/8.63        ( ( finite_finite_nat @ A3 )
% 15.55/8.63       => ( ( member_nat @ A @ A3 )
% 15.55/8.63         => ? [X4: nat] :
% 15.55/8.63              ( ( member_nat @ X4 @ A3 )
% 15.55/8.63              & ( ord_less_eq_nat @ X4 @ A )
% 15.55/8.63              & ! [Xa2: nat] :
% 15.55/8.63                  ( ( member_nat @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_nat @ Xa2 @ X4 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8440_finite__has__minimal2,axiom,
% 15.55/8.63      ! [A3: set_int,A: int] :
% 15.55/8.63        ( ( finite_finite_int @ A3 )
% 15.55/8.63       => ( ( member_int @ A @ A3 )
% 15.55/8.63         => ? [X4: int] :
% 15.55/8.63              ( ( member_int @ X4 @ A3 )
% 15.55/8.63              & ( ord_less_eq_int @ X4 @ A )
% 15.55/8.63              & ! [Xa2: int] :
% 15.55/8.63                  ( ( member_int @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_int @ Xa2 @ X4 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8441_finite__has__maximal2,axiom,
% 15.55/8.63      ! [A3: set_real,A: real] :
% 15.55/8.63        ( ( finite_finite_real @ A3 )
% 15.55/8.63       => ( ( member_real @ A @ A3 )
% 15.55/8.63         => ? [X4: real] :
% 15.55/8.63              ( ( member_real @ X4 @ A3 )
% 15.55/8.63              & ( ord_less_eq_real @ A @ X4 )
% 15.55/8.63              & ! [Xa2: real] :
% 15.55/8.63                  ( ( member_real @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_real @ X4 @ Xa2 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8442_finite__has__maximal2,axiom,
% 15.55/8.63      ! [A3: set_Extended_enat,A: extended_enat] :
% 15.55/8.63        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.63       => ( ( member_Extended_enat @ A @ A3 )
% 15.55/8.63         => ? [X4: extended_enat] :
% 15.55/8.63              ( ( member_Extended_enat @ X4 @ A3 )
% 15.55/8.63              & ( ord_le2932123472753598470d_enat @ A @ X4 )
% 15.55/8.63              & ! [Xa2: extended_enat] :
% 15.55/8.63                  ( ( member_Extended_enat @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_le2932123472753598470d_enat @ X4 @ Xa2 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8443_finite__has__maximal2,axiom,
% 15.55/8.63      ! [A3: set_set_nat,A: set_nat] :
% 15.55/8.63        ( ( finite1152437895449049373et_nat @ A3 )
% 15.55/8.63       => ( ( member_set_nat @ A @ A3 )
% 15.55/8.63         => ? [X4: set_nat] :
% 15.55/8.63              ( ( member_set_nat @ X4 @ A3 )
% 15.55/8.63              & ( ord_less_eq_set_nat @ A @ X4 )
% 15.55/8.63              & ! [Xa2: set_nat] :
% 15.55/8.63                  ( ( member_set_nat @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_set_nat @ X4 @ Xa2 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8444_finite__has__maximal2,axiom,
% 15.55/8.63      ! [A3: set_rat,A: rat] :
% 15.55/8.63        ( ( finite_finite_rat @ A3 )
% 15.55/8.63       => ( ( member_rat @ A @ A3 )
% 15.55/8.63         => ? [X4: rat] :
% 15.55/8.63              ( ( member_rat @ X4 @ A3 )
% 15.55/8.63              & ( ord_less_eq_rat @ A @ X4 )
% 15.55/8.63              & ! [Xa2: rat] :
% 15.55/8.63                  ( ( member_rat @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_rat @ X4 @ Xa2 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8445_finite__has__maximal2,axiom,
% 15.55/8.63      ! [A3: set_num,A: num] :
% 15.55/8.63        ( ( finite_finite_num @ A3 )
% 15.55/8.63       => ( ( member_num @ A @ A3 )
% 15.55/8.63         => ? [X4: num] :
% 15.55/8.63              ( ( member_num @ X4 @ A3 )
% 15.55/8.63              & ( ord_less_eq_num @ A @ X4 )
% 15.55/8.63              & ! [Xa2: num] :
% 15.55/8.63                  ( ( member_num @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_num @ X4 @ Xa2 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8446_finite__has__maximal2,axiom,
% 15.55/8.63      ! [A3: set_nat,A: nat] :
% 15.55/8.63        ( ( finite_finite_nat @ A3 )
% 15.55/8.63       => ( ( member_nat @ A @ A3 )
% 15.55/8.63         => ? [X4: nat] :
% 15.55/8.63              ( ( member_nat @ X4 @ A3 )
% 15.55/8.63              & ( ord_less_eq_nat @ A @ X4 )
% 15.55/8.63              & ! [Xa2: nat] :
% 15.55/8.63                  ( ( member_nat @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_nat @ X4 @ Xa2 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8447_finite__has__maximal2,axiom,
% 15.55/8.63      ! [A3: set_int,A: int] :
% 15.55/8.63        ( ( finite_finite_int @ A3 )
% 15.55/8.63       => ( ( member_int @ A @ A3 )
% 15.55/8.63         => ? [X4: int] :
% 15.55/8.63              ( ( member_int @ X4 @ A3 )
% 15.55/8.63              & ( ord_less_eq_int @ A @ X4 )
% 15.55/8.63              & ! [Xa2: int] :
% 15.55/8.63                  ( ( member_int @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_int @ X4 @ Xa2 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8448_sum__less__suminf2,axiom,
% 15.55/8.63      ! [F: nat > int,N: nat,I: nat] :
% 15.55/8.63        ( ( summable_int @ F )
% 15.55/8.63       => ( ! [M4: nat] :
% 15.55/8.63              ( ( ord_less_eq_nat @ N @ M4 )
% 15.55/8.63             => ( ord_less_eq_int @ zero_zero_int @ ( F @ M4 ) ) )
% 15.55/8.63         => ( ( ord_less_eq_nat @ N @ I )
% 15.55/8.63           => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 15.55/8.63             => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_int @ F ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8449_sum__less__suminf2,axiom,
% 15.55/8.63      ! [F: nat > nat,N: nat,I: nat] :
% 15.55/8.63        ( ( summable_nat @ F )
% 15.55/8.63       => ( ! [M4: nat] :
% 15.55/8.63              ( ( ord_less_eq_nat @ N @ M4 )
% 15.55/8.63             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ M4 ) ) )
% 15.55/8.63         => ( ( ord_less_eq_nat @ N @ I )
% 15.55/8.63           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 15.55/8.63             => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_nat @ F ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8450_sum__less__suminf2,axiom,
% 15.55/8.63      ! [F: nat > real,N: nat,I: nat] :
% 15.55/8.63        ( ( summable_real @ F )
% 15.55/8.63       => ( ! [M4: nat] :
% 15.55/8.63              ( ( ord_less_eq_nat @ N @ M4 )
% 15.55/8.63             => ( ord_less_eq_real @ zero_zero_real @ ( F @ M4 ) ) )
% 15.55/8.63         => ( ( ord_less_eq_nat @ N @ I )
% 15.55/8.63           => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 15.55/8.63             => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_real @ F ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8451_sum_Oin__pairs__0,axiom,
% 15.55/8.63      ! [G: nat > rat,N: nat] :
% 15.55/8.63        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 15.55/8.63        = ( groups2906978787729119204at_rat
% 15.55/8.63          @ ^ [I4: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8452_sum_Oin__pairs__0,axiom,
% 15.55/8.63      ! [G: nat > int,N: nat] :
% 15.55/8.63        ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 15.55/8.63        = ( groups3539618377306564664at_int
% 15.55/8.63          @ ^ [I4: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8453_sum_Oin__pairs__0,axiom,
% 15.55/8.63      ! [G: nat > nat,N: nat] :
% 15.55/8.63        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 15.55/8.63        = ( groups3542108847815614940at_nat
% 15.55/8.63          @ ^ [I4: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8454_sum_Oin__pairs__0,axiom,
% 15.55/8.63      ! [G: nat > real,N: nat] :
% 15.55/8.63        ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 15.55/8.63        = ( groups6591440286371151544t_real
% 15.55/8.63          @ ^ [I4: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8455_polynomial__product,axiom,
% 15.55/8.63      ! [M: nat,A: nat > complex,N: nat,B: nat > complex,X3: complex] :
% 15.55/8.63        ( ! [I3: nat] :
% 15.55/8.63            ( ( ord_less_nat @ M @ I3 )
% 15.55/8.63           => ( ( A @ I3 )
% 15.55/8.63              = zero_zero_complex ) )
% 15.55/8.63       => ( ! [J2: nat] :
% 15.55/8.63              ( ( ord_less_nat @ N @ J2 )
% 15.55/8.63             => ( ( B @ J2 )
% 15.55/8.63                = zero_zero_complex ) )
% 15.55/8.63         => ( ( times_times_complex
% 15.55/8.63              @ ( groups2073611262835488442omplex
% 15.55/8.63                @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( power_power_complex @ X3 @ I4 ) )
% 15.55/8.63                @ ( set_ord_atMost_nat @ M ) )
% 15.55/8.63              @ ( groups2073611262835488442omplex
% 15.55/8.63                @ ^ [J3: nat] : ( times_times_complex @ ( B @ J3 ) @ ( power_power_complex @ X3 @ J3 ) )
% 15.55/8.63                @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63            = ( groups2073611262835488442omplex
% 15.55/8.63              @ ^ [R5: nat] :
% 15.55/8.63                  ( times_times_complex
% 15.55/8.63                  @ ( groups2073611262835488442omplex
% 15.55/8.63                    @ ^ [K3: nat] : ( times_times_complex @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 15.55/8.63                    @ ( set_ord_atMost_nat @ R5 ) )
% 15.55/8.63                  @ ( power_power_complex @ X3 @ R5 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8456_polynomial__product,axiom,
% 15.55/8.63      ! [M: nat,A: nat > rat,N: nat,B: nat > rat,X3: rat] :
% 15.55/8.63        ( ! [I3: nat] :
% 15.55/8.63            ( ( ord_less_nat @ M @ I3 )
% 15.55/8.63           => ( ( A @ I3 )
% 15.55/8.63              = zero_zero_rat ) )
% 15.55/8.63       => ( ! [J2: nat] :
% 15.55/8.63              ( ( ord_less_nat @ N @ J2 )
% 15.55/8.63             => ( ( B @ J2 )
% 15.55/8.63                = zero_zero_rat ) )
% 15.55/8.63         => ( ( times_times_rat
% 15.55/8.63              @ ( groups2906978787729119204at_rat
% 15.55/8.63                @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( power_power_rat @ X3 @ I4 ) )
% 15.55/8.63                @ ( set_ord_atMost_nat @ M ) )
% 15.55/8.63              @ ( groups2906978787729119204at_rat
% 15.55/8.63                @ ^ [J3: nat] : ( times_times_rat @ ( B @ J3 ) @ ( power_power_rat @ X3 @ J3 ) )
% 15.55/8.63                @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63            = ( groups2906978787729119204at_rat
% 15.55/8.63              @ ^ [R5: nat] :
% 15.55/8.63                  ( times_times_rat
% 15.55/8.63                  @ ( groups2906978787729119204at_rat
% 15.55/8.63                    @ ^ [K3: nat] : ( times_times_rat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 15.55/8.63                    @ ( set_ord_atMost_nat @ R5 ) )
% 15.55/8.63                  @ ( power_power_rat @ X3 @ R5 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8457_polynomial__product,axiom,
% 15.55/8.63      ! [M: nat,A: nat > int,N: nat,B: nat > int,X3: int] :
% 15.55/8.63        ( ! [I3: nat] :
% 15.55/8.63            ( ( ord_less_nat @ M @ I3 )
% 15.55/8.63           => ( ( A @ I3 )
% 15.55/8.63              = zero_zero_int ) )
% 15.55/8.63       => ( ! [J2: nat] :
% 15.55/8.63              ( ( ord_less_nat @ N @ J2 )
% 15.55/8.63             => ( ( B @ J2 )
% 15.55/8.63                = zero_zero_int ) )
% 15.55/8.63         => ( ( times_times_int
% 15.55/8.63              @ ( groups3539618377306564664at_int
% 15.55/8.63                @ ^ [I4: nat] : ( times_times_int @ ( A @ I4 ) @ ( power_power_int @ X3 @ I4 ) )
% 15.55/8.63                @ ( set_ord_atMost_nat @ M ) )
% 15.55/8.63              @ ( groups3539618377306564664at_int
% 15.55/8.63                @ ^ [J3: nat] : ( times_times_int @ ( B @ J3 ) @ ( power_power_int @ X3 @ J3 ) )
% 15.55/8.63                @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63            = ( groups3539618377306564664at_int
% 15.55/8.63              @ ^ [R5: nat] :
% 15.55/8.63                  ( times_times_int
% 15.55/8.63                  @ ( groups3539618377306564664at_int
% 15.55/8.63                    @ ^ [K3: nat] : ( times_times_int @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 15.55/8.63                    @ ( set_ord_atMost_nat @ R5 ) )
% 15.55/8.63                  @ ( power_power_int @ X3 @ R5 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8458_polynomial__product,axiom,
% 15.55/8.63      ! [M: nat,A: nat > real,N: nat,B: nat > real,X3: real] :
% 15.55/8.63        ( ! [I3: nat] :
% 15.55/8.63            ( ( ord_less_nat @ M @ I3 )
% 15.55/8.63           => ( ( A @ I3 )
% 15.55/8.63              = zero_zero_real ) )
% 15.55/8.63       => ( ! [J2: nat] :
% 15.55/8.63              ( ( ord_less_nat @ N @ J2 )
% 15.55/8.63             => ( ( B @ J2 )
% 15.55/8.63                = zero_zero_real ) )
% 15.55/8.63         => ( ( times_times_real
% 15.55/8.63              @ ( groups6591440286371151544t_real
% 15.55/8.63                @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( power_power_real @ X3 @ I4 ) )
% 15.55/8.63                @ ( set_ord_atMost_nat @ M ) )
% 15.55/8.63              @ ( groups6591440286371151544t_real
% 15.55/8.63                @ ^ [J3: nat] : ( times_times_real @ ( B @ J3 ) @ ( power_power_real @ X3 @ J3 ) )
% 15.55/8.63                @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63            = ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [R5: nat] :
% 15.55/8.63                  ( times_times_real
% 15.55/8.63                  @ ( groups6591440286371151544t_real
% 15.55/8.63                    @ ^ [K3: nat] : ( times_times_real @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 15.55/8.63                    @ ( set_ord_atMost_nat @ R5 ) )
% 15.55/8.63                  @ ( power_power_real @ X3 @ R5 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8459_prod_Oin__pairs__0,axiom,
% 15.55/8.63      ! [G: nat > real,N: nat] :
% 15.55/8.63        ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 15.55/8.63        = ( groups129246275422532515t_real
% 15.55/8.63          @ ^ [I4: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8460_prod_Oin__pairs__0,axiom,
% 15.55/8.63      ! [G: nat > rat,N: nat] :
% 15.55/8.63        ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 15.55/8.63        = ( groups73079841787564623at_rat
% 15.55/8.63          @ ^ [I4: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8461_prod_Oin__pairs__0,axiom,
% 15.55/8.63      ! [G: nat > int,N: nat] :
% 15.55/8.63        ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 15.55/8.63        = ( groups705719431365010083at_int
% 15.55/8.63          @ ^ [I4: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8462_prod_Oin__pairs__0,axiom,
% 15.55/8.63      ! [G: nat > nat,N: nat] :
% 15.55/8.63        ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 15.55/8.63        = ( groups708209901874060359at_nat
% 15.55/8.63          @ ^ [I4: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8463_polyfun__eq__const,axiom,
% 15.55/8.63      ! [C: nat > complex,N: nat,K: complex] :
% 15.55/8.63        ( ( ! [X: complex] :
% 15.55/8.63              ( ( groups2073611262835488442omplex
% 15.55/8.63                @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ X @ I4 ) )
% 15.55/8.63                @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63              = K ) )
% 15.55/8.63        = ( ( ( C @ zero_zero_nat )
% 15.55/8.63            = K )
% 15.55/8.63          & ! [X: nat] :
% 15.55/8.63              ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) )
% 15.55/8.63             => ( ( C @ X )
% 15.55/8.63                = zero_zero_complex ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8464_polyfun__eq__const,axiom,
% 15.55/8.63      ! [C: nat > real,N: nat,K: real] :
% 15.55/8.63        ( ( ! [X: real] :
% 15.55/8.63              ( ( groups6591440286371151544t_real
% 15.55/8.63                @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ X @ I4 ) )
% 15.55/8.63                @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63              = K ) )
% 15.55/8.63        = ( ( ( C @ zero_zero_nat )
% 15.55/8.63            = K )
% 15.55/8.63          & ! [X: nat] :
% 15.55/8.63              ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) )
% 15.55/8.63             => ( ( C @ X )
% 15.55/8.63                = zero_zero_real ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8465_one__diff__power__eq_H,axiom,
% 15.55/8.63      ! [X3: complex,N: nat] :
% 15.55/8.63        ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ N ) )
% 15.55/8.63        = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X3 )
% 15.55/8.63          @ ( groups2073611262835488442omplex
% 15.55/8.63            @ ^ [I4: nat] : ( power_power_complex @ X3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8466_one__diff__power__eq_H,axiom,
% 15.55/8.63      ! [X3: rat,N: nat] :
% 15.55/8.63        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ N ) )
% 15.55/8.63        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X3 )
% 15.55/8.63          @ ( groups2906978787729119204at_rat
% 15.55/8.63            @ ^ [I4: nat] : ( power_power_rat @ X3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8467_one__diff__power__eq_H,axiom,
% 15.55/8.63      ! [X3: int,N: nat] :
% 15.55/8.63        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X3 @ N ) )
% 15.55/8.63        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X3 )
% 15.55/8.63          @ ( groups3539618377306564664at_int
% 15.55/8.63            @ ^ [I4: nat] : ( power_power_int @ X3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8468_one__diff__power__eq_H,axiom,
% 15.55/8.63      ! [X3: real,N: nat] :
% 15.55/8.63        ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ N ) )
% 15.55/8.63        = ( times_times_real @ ( minus_minus_real @ one_one_real @ X3 )
% 15.55/8.63          @ ( groups6591440286371151544t_real
% 15.55/8.63            @ ^ [I4: nat] : ( power_power_real @ X3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8469_binomial__ring,axiom,
% 15.55/8.63      ! [A: complex,B: complex,N: nat] :
% 15.55/8.63        ( ( power_power_complex @ ( plus_plus_complex @ A @ B ) @ N )
% 15.55/8.63        = ( groups2073611262835488442omplex
% 15.55/8.63          @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K3 ) ) @ ( power_power_complex @ A @ K3 ) ) @ ( power_power_complex @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8470_binomial__ring,axiom,
% 15.55/8.63      ! [A: rat,B: rat,N: nat] :
% 15.55/8.63        ( ( power_power_rat @ ( plus_plus_rat @ A @ B ) @ N )
% 15.55/8.63        = ( groups2906978787729119204at_rat
% 15.55/8.63          @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K3 ) ) @ ( power_power_rat @ A @ K3 ) ) @ ( power_power_rat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8471_binomial__ring,axiom,
% 15.55/8.63      ! [A: int,B: int,N: nat] :
% 15.55/8.63        ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N )
% 15.55/8.63        = ( groups3539618377306564664at_int
% 15.55/8.63          @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N @ K3 ) ) @ ( power_power_int @ A @ K3 ) ) @ ( power_power_int @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8472_binomial__ring,axiom,
% 15.55/8.63      ! [A: nat,B: nat,N: nat] :
% 15.55/8.63        ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 15.55/8.63        = ( groups3542108847815614940at_nat
% 15.55/8.63          @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8473_binomial__ring,axiom,
% 15.55/8.63      ! [A: real,B: real,N: nat] :
% 15.55/8.63        ( ( power_power_real @ ( plus_plus_real @ A @ B ) @ N )
% 15.55/8.63        = ( groups6591440286371151544t_real
% 15.55/8.63          @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K3 ) ) @ ( power_power_real @ A @ K3 ) ) @ ( power_power_real @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8474_pochhammer__binomial__sum,axiom,
% 15.55/8.63      ! [A: complex,B: complex,N: nat] :
% 15.55/8.63        ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ B ) @ N )
% 15.55/8.63        = ( groups2073611262835488442omplex
% 15.55/8.63          @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K3 ) ) @ ( comm_s2602460028002588243omplex @ A @ K3 ) ) @ ( comm_s2602460028002588243omplex @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8475_pochhammer__binomial__sum,axiom,
% 15.55/8.63      ! [A: rat,B: rat,N: nat] :
% 15.55/8.63        ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ B ) @ N )
% 15.55/8.63        = ( groups2906978787729119204at_rat
% 15.55/8.63          @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ A @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8476_pochhammer__binomial__sum,axiom,
% 15.55/8.63      ! [A: int,B: int,N: nat] :
% 15.55/8.63        ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B ) @ N )
% 15.55/8.63        = ( groups3539618377306564664at_int
% 15.55/8.63          @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N @ K3 ) ) @ ( comm_s4660882817536571857er_int @ A @ K3 ) ) @ ( comm_s4660882817536571857er_int @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8477_pochhammer__binomial__sum,axiom,
% 15.55/8.63      ! [A: real,B: real,N: nat] :
% 15.55/8.63        ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ B ) @ N )
% 15.55/8.63        = ( groups6591440286371151544t_real
% 15.55/8.63          @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K3 ) ) @ ( comm_s7457072308508201937r_real @ A @ K3 ) ) @ ( comm_s7457072308508201937r_real @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8478_sum_Ozero__middle,axiom,
% 15.55/8.63      ! [P6: nat,K: nat,G: nat > rat,H2: nat > rat] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 15.55/8.63       => ( ( ord_less_eq_nat @ K @ P6 )
% 15.55/8.63         => ( ( groups2906978787729119204at_rat
% 15.55/8.63              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_rat @ ( J3 = K ) @ zero_zero_rat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ P6 ) )
% 15.55/8.63            = ( groups2906978787729119204at_rat
% 15.55/8.63              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8479_sum_Ozero__middle,axiom,
% 15.55/8.63      ! [P6: nat,K: nat,G: nat > int,H2: nat > int] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 15.55/8.63       => ( ( ord_less_eq_nat @ K @ P6 )
% 15.55/8.63         => ( ( groups3539618377306564664at_int
% 15.55/8.63              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_int @ ( J3 = K ) @ zero_zero_int @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ P6 ) )
% 15.55/8.63            = ( groups3539618377306564664at_int
% 15.55/8.63              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8480_sum_Ozero__middle,axiom,
% 15.55/8.63      ! [P6: nat,K: nat,G: nat > nat,H2: nat > nat] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 15.55/8.63       => ( ( ord_less_eq_nat @ K @ P6 )
% 15.55/8.63         => ( ( groups3542108847815614940at_nat
% 15.55/8.63              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_nat @ ( J3 = K ) @ zero_zero_nat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ P6 ) )
% 15.55/8.63            = ( groups3542108847815614940at_nat
% 15.55/8.63              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8481_sum_Ozero__middle,axiom,
% 15.55/8.63      ! [P6: nat,K: nat,G: nat > real,H2: nat > real] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 15.55/8.63       => ( ( ord_less_eq_nat @ K @ P6 )
% 15.55/8.63         => ( ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_real @ ( J3 = K ) @ zero_zero_real @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ P6 ) )
% 15.55/8.63            = ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8482_prod_Ozero__middle,axiom,
% 15.55/8.63      ! [P6: nat,K: nat,G: nat > complex,H2: nat > complex] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 15.55/8.63       => ( ( ord_less_eq_nat @ K @ P6 )
% 15.55/8.63         => ( ( groups6464643781859351333omplex
% 15.55/8.63              @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_complex @ ( J3 = K ) @ one_one_complex @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ P6 ) )
% 15.55/8.63            = ( groups6464643781859351333omplex
% 15.55/8.63              @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8483_prod_Ozero__middle,axiom,
% 15.55/8.63      ! [P6: nat,K: nat,G: nat > real,H2: nat > real] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 15.55/8.63       => ( ( ord_less_eq_nat @ K @ P6 )
% 15.55/8.63         => ( ( groups129246275422532515t_real
% 15.55/8.63              @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_real @ ( J3 = K ) @ one_one_real @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ P6 ) )
% 15.55/8.63            = ( groups129246275422532515t_real
% 15.55/8.63              @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8484_prod_Ozero__middle,axiom,
% 15.55/8.63      ! [P6: nat,K: nat,G: nat > rat,H2: nat > rat] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 15.55/8.63       => ( ( ord_less_eq_nat @ K @ P6 )
% 15.55/8.63         => ( ( groups73079841787564623at_rat
% 15.55/8.63              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_rat @ ( J3 = K ) @ one_one_rat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ P6 ) )
% 15.55/8.63            = ( groups73079841787564623at_rat
% 15.55/8.63              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8485_prod_Ozero__middle,axiom,
% 15.55/8.63      ! [P6: nat,K: nat,G: nat > int,H2: nat > int] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 15.55/8.63       => ( ( ord_less_eq_nat @ K @ P6 )
% 15.55/8.63         => ( ( groups705719431365010083at_int
% 15.55/8.63              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_int @ ( J3 = K ) @ one_one_int @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ P6 ) )
% 15.55/8.63            = ( groups705719431365010083at_int
% 15.55/8.63              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8486_prod_Ozero__middle,axiom,
% 15.55/8.63      ! [P6: nat,K: nat,G: nat > nat,H2: nat > nat] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 15.55/8.63       => ( ( ord_less_eq_nat @ K @ P6 )
% 15.55/8.63         => ( ( groups708209901874060359at_nat
% 15.55/8.63              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_nat @ ( J3 = K ) @ one_one_nat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ P6 ) )
% 15.55/8.63            = ( groups708209901874060359at_nat
% 15.55/8.63              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8487_binomial__r__part__sum,axiom,
% 15.55/8.63      ! [M: nat] :
% 15.55/8.63        ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 15.55/8.63        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8488_choose__linear__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( groups3542108847815614940at_nat
% 15.55/8.63          @ ^ [I4: nat] : ( times_times_nat @ I4 @ ( binomial @ N @ I4 ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63        = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8489_sum__split__even__odd,axiom,
% 15.55/8.63      ! [F: nat > real,G: nat > real,N: nat] :
% 15.55/8.63        ( ( groups6591440286371151544t_real
% 15.55/8.63          @ ^ [I4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( F @ I4 ) @ ( G @ I4 ) )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 15.55/8.63        = ( plus_plus_real
% 15.55/8.63          @ ( groups6591440286371151544t_real
% 15.55/8.63            @ ^ [I4: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.63          @ ( groups6591440286371151544t_real
% 15.55/8.63            @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ one_one_nat ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8490_root__polyfun,axiom,
% 15.55/8.63      ! [N: nat,Z: int,A: int] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 15.55/8.63       => ( ( ( power_power_int @ Z @ N )
% 15.55/8.63            = A )
% 15.55/8.63          = ( ( groups3539618377306564664at_int
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_int @ ( if_int @ ( I4 = zero_zero_nat ) @ ( uminus_uminus_int @ A ) @ ( if_int @ ( I4 = N ) @ one_one_int @ zero_zero_int ) ) @ ( power_power_int @ Z @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63            = zero_zero_int ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8491_root__polyfun,axiom,
% 15.55/8.63      ! [N: nat,Z: complex,A: complex] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 15.55/8.63       => ( ( ( power_power_complex @ Z @ N )
% 15.55/8.63            = A )
% 15.55/8.63          = ( ( groups2073611262835488442omplex
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_complex @ ( if_complex @ ( I4 = zero_zero_nat ) @ ( uminus1482373934393186551omplex @ A ) @ ( if_complex @ ( I4 = N ) @ one_one_complex @ zero_zero_complex ) ) @ ( power_power_complex @ Z @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63            = zero_zero_complex ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8492_root__polyfun,axiom,
% 15.55/8.63      ! [N: nat,Z: code_integer,A: code_integer] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 15.55/8.63       => ( ( ( power_8256067586552552935nteger @ Z @ N )
% 15.55/8.63            = A )
% 15.55/8.63          = ( ( groups7501900531339628137nteger
% 15.55/8.63              @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( if_Code_integer @ ( I4 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ A ) @ ( if_Code_integer @ ( I4 = N ) @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) @ ( power_8256067586552552935nteger @ Z @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63            = zero_z3403309356797280102nteger ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8493_root__polyfun,axiom,
% 15.55/8.63      ! [N: nat,Z: rat,A: rat] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 15.55/8.63       => ( ( ( power_power_rat @ Z @ N )
% 15.55/8.63            = A )
% 15.55/8.63          = ( ( groups2906978787729119204at_rat
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_rat @ ( if_rat @ ( I4 = zero_zero_nat ) @ ( uminus_uminus_rat @ A ) @ ( if_rat @ ( I4 = N ) @ one_one_rat @ zero_zero_rat ) ) @ ( power_power_rat @ Z @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63            = zero_zero_rat ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8494_root__polyfun,axiom,
% 15.55/8.63      ! [N: nat,Z: real,A: real] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 15.55/8.63       => ( ( ( power_power_real @ Z @ N )
% 15.55/8.63            = A )
% 15.55/8.63          = ( ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [I4: nat] : ( times_times_real @ ( if_real @ ( I4 = zero_zero_nat ) @ ( uminus_uminus_real @ A ) @ ( if_real @ ( I4 = N ) @ one_one_real @ zero_zero_real ) ) @ ( power_power_real @ Z @ I4 ) )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63            = zero_zero_real ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8495_sum__gp0,axiom,
% 15.55/8.63      ! [X3: complex,N: nat] :
% 15.55/8.63        ( ( ( X3 = one_one_complex )
% 15.55/8.63         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63            = ( semiri8010041392384452111omplex @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 15.55/8.63        & ( ( X3 != one_one_complex )
% 15.55/8.63         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8496_sum__gp0,axiom,
% 15.55/8.63      ! [X3: rat,N: nat] :
% 15.55/8.63        ( ( ( X3 = one_one_rat )
% 15.55/8.63         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63            = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 15.55/8.63        & ( ( X3 != one_one_rat )
% 15.55/8.63         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63            = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8497_sum__gp0,axiom,
% 15.55/8.63      ! [X3: real,N: nat] :
% 15.55/8.63        ( ( ( X3 = one_one_real )
% 15.55/8.63         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63            = ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 15.55/8.63        & ( ( X3 != one_one_real )
% 15.55/8.63         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63            = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8498_choose__alternating__linear__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( N != one_one_nat )
% 15.55/8.63       => ( ( groups7501900531339628137nteger
% 15.55/8.63            @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I4 ) @ ( semiri4939895301339042750nteger @ I4 ) ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I4 ) ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63          = zero_z3403309356797280102nteger ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8499_choose__alternating__linear__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( N != one_one_nat )
% 15.55/8.63       => ( ( groups2073611262835488442omplex
% 15.55/8.63            @ ^ [I4: nat] : ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I4 ) @ ( semiri8010041392384452111omplex @ I4 ) ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I4 ) ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63          = zero_zero_complex ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8500_choose__alternating__linear__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( N != one_one_nat )
% 15.55/8.63       => ( ( groups2906978787729119204at_rat
% 15.55/8.63            @ ^ [I4: nat] : ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I4 ) @ ( semiri681578069525770553at_rat @ I4 ) ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I4 ) ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63          = zero_zero_rat ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8501_choose__alternating__linear__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( N != one_one_nat )
% 15.55/8.63       => ( ( groups3539618377306564664at_int
% 15.55/8.63            @ ^ [I4: nat] : ( times_times_int @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I4 ) @ ( semiri1314217659103216013at_int @ I4 ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I4 ) ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63          = zero_zero_int ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8502_choose__alternating__linear__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( N != one_one_nat )
% 15.55/8.63       => ( ( groups6591440286371151544t_real
% 15.55/8.63            @ ^ [I4: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( semiri5074537144036343181t_real @ I4 ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I4 ) ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63          = zero_zero_real ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8503_choose__alternating__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.63       => ( ( groups7501900531339628137nteger
% 15.55/8.63            @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I4 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I4 ) ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63          = zero_z3403309356797280102nteger ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8504_choose__alternating__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.63       => ( ( groups2073611262835488442omplex
% 15.55/8.63            @ ^ [I4: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I4 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I4 ) ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63          = zero_zero_complex ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8505_choose__alternating__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.63       => ( ( groups2906978787729119204at_rat
% 15.55/8.63            @ ^ [I4: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I4 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I4 ) ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63          = zero_zero_rat ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8506_choose__alternating__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.63       => ( ( groups3539618377306564664at_int
% 15.55/8.63            @ ^ [I4: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I4 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I4 ) ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63          = zero_zero_int ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8507_choose__alternating__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.63       => ( ( groups6591440286371151544t_real
% 15.55/8.63            @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I4 ) ) )
% 15.55/8.63            @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63          = zero_zero_real ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8508_polyfun__extremal__lemma,axiom,
% 15.55/8.63      ! [E2: real,C: nat > complex,N: nat] :
% 15.55/8.63        ( ( ord_less_real @ zero_zero_real @ E2 )
% 15.55/8.63       => ? [M8: real] :
% 15.55/8.63          ! [Z4: complex] :
% 15.55/8.63            ( ( ord_less_eq_real @ M8 @ ( real_V1022390504157884413omplex @ Z4 ) )
% 15.55/8.63           => ( ord_less_eq_real
% 15.55/8.63              @ ( real_V1022390504157884413omplex
% 15.55/8.63                @ ( groups2073611262835488442omplex
% 15.55/8.63                  @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ Z4 @ I4 ) )
% 15.55/8.63                  @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63              @ ( times_times_real @ E2 @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( suc @ N ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8509_polyfun__extremal__lemma,axiom,
% 15.55/8.63      ! [E2: real,C: nat > real,N: nat] :
% 15.55/8.63        ( ( ord_less_real @ zero_zero_real @ E2 )
% 15.55/8.63       => ? [M8: real] :
% 15.55/8.63          ! [Z4: real] :
% 15.55/8.63            ( ( ord_less_eq_real @ M8 @ ( real_V7735802525324610683m_real @ Z4 ) )
% 15.55/8.63           => ( ord_less_eq_real
% 15.55/8.63              @ ( real_V7735802525324610683m_real
% 15.55/8.63                @ ( groups6591440286371151544t_real
% 15.55/8.63                  @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ Z4 @ I4 ) )
% 15.55/8.63                  @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63              @ ( times_times_real @ E2 @ ( power_power_real @ ( real_V7735802525324610683m_real @ Z4 ) @ ( suc @ N ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8510_even__set__encode__iff,axiom,
% 15.55/8.63      ! [A3: set_nat] :
% 15.55/8.63        ( ( finite_finite_nat @ A3 )
% 15.55/8.63       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A3 ) )
% 15.55/8.63          = ( ~ ( member_nat @ zero_zero_nat @ A3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8511_sum__pos__lt__pair,axiom,
% 15.55/8.63      ! [F: nat > real,K: nat] :
% 15.55/8.63        ( ( summable_real @ F )
% 15.55/8.63       => ( ! [D6: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F @ ( plus_plus_nat @ K @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D6 ) ) ) @ ( F @ ( plus_plus_nat @ K @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D6 ) @ one_one_nat ) ) ) ) )
% 15.55/8.63         => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8512_Sum__Icc__int,axiom,
% 15.55/8.63      ! [M: int,N: int] :
% 15.55/8.63        ( ( ord_less_eq_int @ M @ N )
% 15.55/8.63       => ( ( groups4538972089207619220nt_int
% 15.55/8.63            @ ^ [X: int] : X
% 15.55/8.63            @ ( set_or1266510415728281911st_int @ M @ N ) )
% 15.55/8.63          = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8513_finite__has__minimal,axiom,
% 15.55/8.63      ! [A3: set_Extended_enat] :
% 15.55/8.63        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.63       => ( ( A3 != bot_bo7653980558646680370d_enat )
% 15.55/8.63         => ? [X4: extended_enat] :
% 15.55/8.63              ( ( member_Extended_enat @ X4 @ A3 )
% 15.55/8.63              & ! [Xa2: extended_enat] :
% 15.55/8.63                  ( ( member_Extended_enat @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_le2932123472753598470d_enat @ Xa2 @ X4 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8514_finite__has__minimal,axiom,
% 15.55/8.63      ! [A3: set_real] :
% 15.55/8.63        ( ( finite_finite_real @ A3 )
% 15.55/8.63       => ( ( A3 != bot_bot_set_real )
% 15.55/8.63         => ? [X4: real] :
% 15.55/8.63              ( ( member_real @ X4 @ A3 )
% 15.55/8.63              & ! [Xa2: real] :
% 15.55/8.63                  ( ( member_real @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_real @ Xa2 @ X4 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8515_finite__has__minimal,axiom,
% 15.55/8.63      ! [A3: set_set_nat] :
% 15.55/8.63        ( ( finite1152437895449049373et_nat @ A3 )
% 15.55/8.63       => ( ( A3 != bot_bot_set_set_nat )
% 15.55/8.63         => ? [X4: set_nat] :
% 15.55/8.63              ( ( member_set_nat @ X4 @ A3 )
% 15.55/8.63              & ! [Xa2: set_nat] :
% 15.55/8.63                  ( ( member_set_nat @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_set_nat @ Xa2 @ X4 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8516_finite__has__minimal,axiom,
% 15.55/8.63      ! [A3: set_rat] :
% 15.55/8.63        ( ( finite_finite_rat @ A3 )
% 15.55/8.63       => ( ( A3 != bot_bot_set_rat )
% 15.55/8.63         => ? [X4: rat] :
% 15.55/8.63              ( ( member_rat @ X4 @ A3 )
% 15.55/8.63              & ! [Xa2: rat] :
% 15.55/8.63                  ( ( member_rat @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_rat @ Xa2 @ X4 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8517_finite__has__minimal,axiom,
% 15.55/8.63      ! [A3: set_num] :
% 15.55/8.63        ( ( finite_finite_num @ A3 )
% 15.55/8.63       => ( ( A3 != bot_bot_set_num )
% 15.55/8.63         => ? [X4: num] :
% 15.55/8.63              ( ( member_num @ X4 @ A3 )
% 15.55/8.63              & ! [Xa2: num] :
% 15.55/8.63                  ( ( member_num @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_num @ Xa2 @ X4 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8518_finite__has__minimal,axiom,
% 15.55/8.63      ! [A3: set_nat] :
% 15.55/8.63        ( ( finite_finite_nat @ A3 )
% 15.55/8.63       => ( ( A3 != bot_bot_set_nat )
% 15.55/8.63         => ? [X4: nat] :
% 15.55/8.63              ( ( member_nat @ X4 @ A3 )
% 15.55/8.63              & ! [Xa2: nat] :
% 15.55/8.63                  ( ( member_nat @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_nat @ Xa2 @ X4 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8519_finite__has__minimal,axiom,
% 15.55/8.63      ! [A3: set_int] :
% 15.55/8.63        ( ( finite_finite_int @ A3 )
% 15.55/8.63       => ( ( A3 != bot_bot_set_int )
% 15.55/8.63         => ? [X4: int] :
% 15.55/8.63              ( ( member_int @ X4 @ A3 )
% 15.55/8.63              & ! [Xa2: int] :
% 15.55/8.63                  ( ( member_int @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_int @ Xa2 @ X4 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8520_finite__has__maximal,axiom,
% 15.55/8.63      ! [A3: set_Extended_enat] :
% 15.55/8.63        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.63       => ( ( A3 != bot_bo7653980558646680370d_enat )
% 15.55/8.63         => ? [X4: extended_enat] :
% 15.55/8.63              ( ( member_Extended_enat @ X4 @ A3 )
% 15.55/8.63              & ! [Xa2: extended_enat] :
% 15.55/8.63                  ( ( member_Extended_enat @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_le2932123472753598470d_enat @ X4 @ Xa2 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8521_finite__has__maximal,axiom,
% 15.55/8.63      ! [A3: set_real] :
% 15.55/8.63        ( ( finite_finite_real @ A3 )
% 15.55/8.63       => ( ( A3 != bot_bot_set_real )
% 15.55/8.63         => ? [X4: real] :
% 15.55/8.63              ( ( member_real @ X4 @ A3 )
% 15.55/8.63              & ! [Xa2: real] :
% 15.55/8.63                  ( ( member_real @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_real @ X4 @ Xa2 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8522_finite__has__maximal,axiom,
% 15.55/8.63      ! [A3: set_set_nat] :
% 15.55/8.63        ( ( finite1152437895449049373et_nat @ A3 )
% 15.55/8.63       => ( ( A3 != bot_bot_set_set_nat )
% 15.55/8.63         => ? [X4: set_nat] :
% 15.55/8.63              ( ( member_set_nat @ X4 @ A3 )
% 15.55/8.63              & ! [Xa2: set_nat] :
% 15.55/8.63                  ( ( member_set_nat @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_set_nat @ X4 @ Xa2 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8523_finite__has__maximal,axiom,
% 15.55/8.63      ! [A3: set_rat] :
% 15.55/8.63        ( ( finite_finite_rat @ A3 )
% 15.55/8.63       => ( ( A3 != bot_bot_set_rat )
% 15.55/8.63         => ? [X4: rat] :
% 15.55/8.63              ( ( member_rat @ X4 @ A3 )
% 15.55/8.63              & ! [Xa2: rat] :
% 15.55/8.63                  ( ( member_rat @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_rat @ X4 @ Xa2 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8524_finite__has__maximal,axiom,
% 15.55/8.63      ! [A3: set_num] :
% 15.55/8.63        ( ( finite_finite_num @ A3 )
% 15.55/8.63       => ( ( A3 != bot_bot_set_num )
% 15.55/8.63         => ? [X4: num] :
% 15.55/8.63              ( ( member_num @ X4 @ A3 )
% 15.55/8.63              & ! [Xa2: num] :
% 15.55/8.63                  ( ( member_num @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_num @ X4 @ Xa2 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8525_finite__has__maximal,axiom,
% 15.55/8.63      ! [A3: set_nat] :
% 15.55/8.63        ( ( finite_finite_nat @ A3 )
% 15.55/8.63       => ( ( A3 != bot_bot_set_nat )
% 15.55/8.63         => ? [X4: nat] :
% 15.55/8.63              ( ( member_nat @ X4 @ A3 )
% 15.55/8.63              & ! [Xa2: nat] :
% 15.55/8.63                  ( ( member_nat @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_nat @ X4 @ Xa2 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8526_finite__has__maximal,axiom,
% 15.55/8.63      ! [A3: set_int] :
% 15.55/8.63        ( ( finite_finite_int @ A3 )
% 15.55/8.63       => ( ( A3 != bot_bot_set_int )
% 15.55/8.63         => ? [X4: int] :
% 15.55/8.63              ( ( member_int @ X4 @ A3 )
% 15.55/8.63              & ! [Xa2: int] :
% 15.55/8.63                  ( ( member_int @ Xa2 @ A3 )
% 15.55/8.63                 => ( ( ord_less_eq_int @ X4 @ Xa2 )
% 15.55/8.63                   => ( X4 = Xa2 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8527_choose__even__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.63       => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 15.55/8.63            @ ( groups2073611262835488442omplex
% 15.55/8.63              @ ^ [I4: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I4 ) ) @ zero_zero_complex )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63          = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8528_choose__even__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.63       => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 15.55/8.63            @ ( groups2906978787729119204at_rat
% 15.55/8.63              @ ^ [I4: nat] : ( if_rat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I4 ) ) @ zero_zero_rat )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63          = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8529_choose__even__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.63       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 15.55/8.63            @ ( groups3539618377306564664at_int
% 15.55/8.63              @ ^ [I4: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I4 ) ) @ zero_zero_int )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63          = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8530_choose__even__sum,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.63       => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 15.55/8.63            @ ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [I4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I4 ) ) @ zero_zero_real )
% 15.55/8.63              @ ( set_ord_atMost_nat @ N ) ) )
% 15.55/8.63          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8531_sumr__cos__zero__one,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( groups6591440286371151544t_real
% 15.55/8.63          @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ zero_zero_real @ M3 ) )
% 15.55/8.63          @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 15.55/8.63        = one_one_real ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8532_gbinomial__partial__row__sum,axiom,
% 15.55/8.63      ! [A: complex,M: nat] :
% 15.55/8.63        ( ( groups2073611262835488442omplex
% 15.55/8.63          @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ M ) )
% 15.55/8.63        = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ one_one_complex ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8533_gbinomial__partial__row__sum,axiom,
% 15.55/8.63      ! [A: rat,M: nat] :
% 15.55/8.63        ( ( groups2906978787729119204at_rat
% 15.55/8.63          @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ M ) )
% 15.55/8.63        = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ one_one_rat ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8534_gbinomial__partial__row__sum,axiom,
% 15.55/8.63      ! [A: real,M: nat] :
% 15.55/8.63        ( ( groups6591440286371151544t_real
% 15.55/8.63          @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 15.55/8.63          @ ( set_ord_atMost_nat @ M ) )
% 15.55/8.63        = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ one_one_real ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8535_gbinomial__r__part__sum,axiom,
% 15.55/8.63      ! [M: nat] :
% 15.55/8.63        ( ( groups2073611262835488442omplex @ ( gbinomial_complex @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M ) ) @ one_one_complex ) ) @ ( set_ord_atMost_nat @ M ) )
% 15.55/8.63        = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8536_gbinomial__r__part__sum,axiom,
% 15.55/8.63      ! [M: nat] :
% 15.55/8.63        ( ( groups2906978787729119204at_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M ) ) @ one_one_rat ) ) @ ( set_ord_atMost_nat @ M ) )
% 15.55/8.63        = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8537_gbinomial__r__part__sum,axiom,
% 15.55/8.63      ! [M: nat] :
% 15.55/8.63        ( ( groups6591440286371151544t_real @ ( gbinomial_real @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ one_one_real ) ) @ ( set_ord_atMost_nat @ M ) )
% 15.55/8.63        = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8538_dbl__inc__simps_I3_J,axiom,
% 15.55/8.63      ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 15.55/8.63      = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8539_dbl__inc__simps_I3_J,axiom,
% 15.55/8.63      ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 15.55/8.63      = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8540_dbl__inc__simps_I3_J,axiom,
% 15.55/8.63      ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 15.55/8.63      = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8541_dbl__inc__simps_I3_J,axiom,
% 15.55/8.63      ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 15.55/8.63      = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8542_sin__arccos__abs,axiom,
% 15.55/8.63      ! [Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 15.55/8.63       => ( ( sin_real @ ( arccos @ Y3 ) )
% 15.55/8.63          = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8543_gbinomial__0_I2_J,axiom,
% 15.55/8.63      ! [K: nat] :
% 15.55/8.63        ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 15.55/8.63        = zero_zero_real ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8544_gbinomial__0_I2_J,axiom,
% 15.55/8.63      ! [K: nat] :
% 15.55/8.63        ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 15.55/8.63        = zero_zero_rat ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8545_gbinomial__0_I2_J,axiom,
% 15.55/8.63      ! [K: nat] :
% 15.55/8.63        ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 15.55/8.63        = zero_zero_nat ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8546_gbinomial__0_I2_J,axiom,
% 15.55/8.63      ! [K: nat] :
% 15.55/8.63        ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 15.55/8.63        = zero_zero_int ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8547_gbinomial__0_I1_J,axiom,
% 15.55/8.63      ! [A: complex] :
% 15.55/8.63        ( ( gbinomial_complex @ A @ zero_zero_nat )
% 15.55/8.63        = one_one_complex ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8548_gbinomial__0_I1_J,axiom,
% 15.55/8.63      ! [A: real] :
% 15.55/8.63        ( ( gbinomial_real @ A @ zero_zero_nat )
% 15.55/8.63        = one_one_real ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8549_gbinomial__0_I1_J,axiom,
% 15.55/8.63      ! [A: rat] :
% 15.55/8.63        ( ( gbinomial_rat @ A @ zero_zero_nat )
% 15.55/8.63        = one_one_rat ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8550_gbinomial__0_I1_J,axiom,
% 15.55/8.63      ! [A: nat] :
% 15.55/8.63        ( ( gbinomial_nat @ A @ zero_zero_nat )
% 15.55/8.63        = one_one_nat ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8551_gbinomial__0_I1_J,axiom,
% 15.55/8.63      ! [A: int] :
% 15.55/8.63        ( ( gbinomial_int @ A @ zero_zero_nat )
% 15.55/8.63        = one_one_int ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8552_arccos__1,axiom,
% 15.55/8.63      ( ( arccos @ one_one_real )
% 15.55/8.63      = zero_zero_real ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8553_cos__coeff__0,axiom,
% 15.55/8.63      ( ( cos_coeff @ zero_zero_nat )
% 15.55/8.63      = one_one_real ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8554_dbl__inc__simps_I2_J,axiom,
% 15.55/8.63      ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 15.55/8.63      = one_one_complex ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8555_dbl__inc__simps_I2_J,axiom,
% 15.55/8.63      ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 15.55/8.63      = one_one_real ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8556_dbl__inc__simps_I2_J,axiom,
% 15.55/8.63      ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 15.55/8.63      = one_one_rat ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8557_dbl__inc__simps_I2_J,axiom,
% 15.55/8.63      ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 15.55/8.63      = one_one_int ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8558_dbl__inc__simps_I4_J,axiom,
% 15.55/8.63      ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 15.55/8.63      = ( uminus_uminus_real @ one_one_real ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8559_dbl__inc__simps_I4_J,axiom,
% 15.55/8.63      ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.63      = ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8560_dbl__inc__simps_I4_J,axiom,
% 15.55/8.63      ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 15.55/8.63      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8561_dbl__inc__simps_I4_J,axiom,
% 15.55/8.63      ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 15.55/8.63      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8562_dbl__inc__simps_I4_J,axiom,
% 15.55/8.63      ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 15.55/8.63      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8563_dbl__inc__simps_I5_J,axiom,
% 15.55/8.63      ! [K: num] :
% 15.55/8.63        ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 15.55/8.63        = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8564_dbl__inc__simps_I5_J,axiom,
% 15.55/8.63      ! [K: num] :
% 15.55/8.63        ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 15.55/8.63        = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8565_dbl__inc__simps_I5_J,axiom,
% 15.55/8.63      ! [K: num] :
% 15.55/8.63        ( ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) )
% 15.55/8.63        = ( numeral_numeral_rat @ ( bit1 @ K ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8566_dbl__inc__simps_I5_J,axiom,
% 15.55/8.63      ! [K: num] :
% 15.55/8.63        ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 15.55/8.63        = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8567_dbl__dec__simps_I1_J,axiom,
% 15.55/8.63      ! [K: num] :
% 15.55/8.63        ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 15.55/8.63        = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8568_dbl__dec__simps_I1_J,axiom,
% 15.55/8.63      ! [K: num] :
% 15.55/8.63        ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 15.55/8.63        = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8569_dbl__dec__simps_I1_J,axiom,
% 15.55/8.63      ! [K: num] :
% 15.55/8.63        ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 15.55/8.63        = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8570_dbl__dec__simps_I1_J,axiom,
% 15.55/8.63      ! [K: num] :
% 15.55/8.63        ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 15.55/8.63        = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8571_dbl__dec__simps_I1_J,axiom,
% 15.55/8.63      ! [K: num] :
% 15.55/8.63        ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 15.55/8.63        = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8572_dbl__inc__simps_I1_J,axiom,
% 15.55/8.63      ! [K: num] :
% 15.55/8.63        ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 15.55/8.63        = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8573_dbl__inc__simps_I1_J,axiom,
% 15.55/8.63      ! [K: num] :
% 15.55/8.63        ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 15.55/8.63        = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8574_dbl__inc__simps_I1_J,axiom,
% 15.55/8.63      ! [K: num] :
% 15.55/8.63        ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 15.55/8.63        = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8575_dbl__inc__simps_I1_J,axiom,
% 15.55/8.63      ! [K: num] :
% 15.55/8.63        ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 15.55/8.63        = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8576_dbl__inc__simps_I1_J,axiom,
% 15.55/8.63      ! [K: num] :
% 15.55/8.63        ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 15.55/8.63        = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8577_cos__arccos,axiom,
% 15.55/8.63      ! [Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 15.55/8.63       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 15.55/8.63         => ( ( cos_real @ ( arccos @ Y3 ) )
% 15.55/8.63            = Y3 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8578_arccos__0,axiom,
% 15.55/8.63      ( ( arccos @ zero_zero_real )
% 15.55/8.63      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8579_of__nat__gbinomial,axiom,
% 15.55/8.63      ! [N: nat,K: nat] :
% 15.55/8.63        ( ( semiri8010041392384452111omplex @ ( gbinomial_nat @ N @ K ) )
% 15.55/8.63        = ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ K ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8580_of__nat__gbinomial,axiom,
% 15.55/8.63      ! [N: nat,K: nat] :
% 15.55/8.63        ( ( semiri5074537144036343181t_real @ ( gbinomial_nat @ N @ K ) )
% 15.55/8.63        = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8581_of__nat__gbinomial,axiom,
% 15.55/8.63      ! [N: nat,K: nat] :
% 15.55/8.63        ( ( semiri681578069525770553at_rat @ ( gbinomial_nat @ N @ K ) )
% 15.55/8.63        = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8582_binomial__gbinomial,axiom,
% 15.55/8.63      ! [N: nat,K: nat] :
% 15.55/8.63        ( ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) )
% 15.55/8.63        = ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ K ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8583_binomial__gbinomial,axiom,
% 15.55/8.63      ! [N: nat,K: nat] :
% 15.55/8.63        ( ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) )
% 15.55/8.63        = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8584_binomial__gbinomial,axiom,
% 15.55/8.63      ! [N: nat,K: nat] :
% 15.55/8.63        ( ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) )
% 15.55/8.63        = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8585_gbinomial__of__nat__symmetric,axiom,
% 15.55/8.63      ! [K: nat,N: nat] :
% 15.55/8.63        ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.63       => ( ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ K )
% 15.55/8.63          = ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8586_gbinomial__of__nat__symmetric,axiom,
% 15.55/8.63      ! [K: nat,N: nat] :
% 15.55/8.63        ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.63       => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K )
% 15.55/8.63          = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8587_gbinomial__of__nat__symmetric,axiom,
% 15.55/8.63      ! [K: nat,N: nat] :
% 15.55/8.63        ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.63       => ( ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K )
% 15.55/8.63          = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8588_arccos__le__arccos,axiom,
% 15.55/8.63      ! [X3: real,Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 15.55/8.63       => ( ( ord_less_eq_real @ X3 @ Y3 )
% 15.55/8.63         => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 15.55/8.63           => ( ord_less_eq_real @ ( arccos @ Y3 ) @ ( arccos @ X3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8589_arccos__eq__iff,axiom,
% 15.55/8.63      ! [X3: real,Y3: real] :
% 15.55/8.63        ( ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 15.55/8.63          & ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real ) )
% 15.55/8.63       => ( ( ( arccos @ X3 )
% 15.55/8.63            = ( arccos @ Y3 ) )
% 15.55/8.63          = ( X3 = Y3 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8590_arccos__le__mono,axiom,
% 15.55/8.63      ! [X3: real,Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 15.55/8.63       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 15.55/8.63         => ( ( ord_less_eq_real @ ( arccos @ X3 ) @ ( arccos @ Y3 ) )
% 15.55/8.63            = ( ord_less_eq_real @ Y3 @ X3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8591_gbinomial__absorb__comp,axiom,
% 15.55/8.63      ! [A: complex,K: nat] :
% 15.55/8.63        ( ( times_times_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ A @ K ) )
% 15.55/8.63        = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8592_gbinomial__absorb__comp,axiom,
% 15.55/8.63      ! [A: real,K: nat] :
% 15.55/8.63        ( ( times_times_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ A @ K ) )
% 15.55/8.63        = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8593_gbinomial__absorb__comp,axiom,
% 15.55/8.63      ! [A: rat,K: nat] :
% 15.55/8.63        ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 15.55/8.63        = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8594_gbinomial__mult__1,axiom,
% 15.55/8.63      ! [A: complex,K: nat] :
% 15.55/8.63        ( ( times_times_complex @ A @ ( gbinomial_complex @ A @ K ) )
% 15.55/8.63        = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8595_gbinomial__mult__1,axiom,
% 15.55/8.63      ! [A: real,K: nat] :
% 15.55/8.63        ( ( times_times_real @ A @ ( gbinomial_real @ A @ K ) )
% 15.55/8.63        = ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ K ) @ ( gbinomial_real @ A @ K ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8596_gbinomial__mult__1,axiom,
% 15.55/8.63      ! [A: rat,K: nat] :
% 15.55/8.63        ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 15.55/8.63        = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8597_gbinomial__mult__1_H,axiom,
% 15.55/8.63      ! [A: complex,K: nat] :
% 15.55/8.63        ( ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ A )
% 15.55/8.63        = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8598_gbinomial__mult__1_H,axiom,
% 15.55/8.63      ! [A: real,K: nat] :
% 15.55/8.63        ( ( times_times_real @ ( gbinomial_real @ A @ K ) @ A )
% 15.55/8.63        = ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ K ) @ ( gbinomial_real @ A @ K ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8599_gbinomial__mult__1_H,axiom,
% 15.55/8.63      ! [A: rat,K: nat] :
% 15.55/8.63        ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 15.55/8.63        = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8600_gbinomial__ge__n__over__k__pow__k,axiom,
% 15.55/8.63      ! [K: nat,A: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A )
% 15.55/8.63       => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8601_gbinomial__ge__n__over__k__pow__k,axiom,
% 15.55/8.63      ! [K: nat,A: rat] :
% 15.55/8.63        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 15.55/8.63       => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8602_dbl__inc__def,axiom,
% 15.55/8.63      ( neg_nu8557863876264182079omplex
% 15.55/8.63      = ( ^ [X: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X @ X ) @ one_one_complex ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8603_dbl__inc__def,axiom,
% 15.55/8.63      ( neg_nu8295874005876285629c_real
% 15.55/8.63      = ( ^ [X: real] : ( plus_plus_real @ ( plus_plus_real @ X @ X ) @ one_one_real ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8604_dbl__inc__def,axiom,
% 15.55/8.63      ( neg_nu5219082963157363817nc_rat
% 15.55/8.63      = ( ^ [X: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8605_dbl__inc__def,axiom,
% 15.55/8.63      ( neg_nu5851722552734809277nc_int
% 15.55/8.63      = ( ^ [X: int] : ( plus_plus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8606_arccos__lbound,axiom,
% 15.55/8.63      ! [Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 15.55/8.63       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 15.55/8.63         => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8607_arccos__less__arccos,axiom,
% 15.55/8.63      ! [X3: real,Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 15.55/8.63       => ( ( ord_less_real @ X3 @ Y3 )
% 15.55/8.63         => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 15.55/8.63           => ( ord_less_real @ ( arccos @ Y3 ) @ ( arccos @ X3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8608_arccos__less__mono,axiom,
% 15.55/8.63      ! [X3: real,Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 15.55/8.63       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 15.55/8.63         => ( ( ord_less_real @ ( arccos @ X3 ) @ ( arccos @ Y3 ) )
% 15.55/8.63            = ( ord_less_real @ Y3 @ X3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8609_arccos__ubound,axiom,
% 15.55/8.63      ! [Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 15.55/8.63       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 15.55/8.63         => ( ord_less_eq_real @ ( arccos @ Y3 ) @ pi ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8610_arccos__cos,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.63       => ( ( ord_less_eq_real @ X3 @ pi )
% 15.55/8.63         => ( ( arccos @ ( cos_real @ X3 ) )
% 15.55/8.63            = X3 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8611_cos__arccos__abs,axiom,
% 15.55/8.63      ! [Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 15.55/8.63       => ( ( cos_real @ ( arccos @ Y3 ) )
% 15.55/8.63          = Y3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8612_arccos__cos__eq__abs,axiom,
% 15.55/8.63      ! [Theta: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 15.55/8.63       => ( ( arccos @ ( cos_real @ Theta ) )
% 15.55/8.63          = ( abs_abs_real @ Theta ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8613_Suc__times__gbinomial,axiom,
% 15.55/8.63      ! [K: nat,A: complex] :
% 15.55/8.63        ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) )
% 15.55/8.63        = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8614_Suc__times__gbinomial,axiom,
% 15.55/8.63      ! [K: nat,A: real] :
% 15.55/8.63        ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) ) )
% 15.55/8.63        = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8615_Suc__times__gbinomial,axiom,
% 15.55/8.63      ! [K: nat,A: rat] :
% 15.55/8.63        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 15.55/8.63        = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8616_gbinomial__absorption,axiom,
% 15.55/8.63      ! [K: nat,A: complex] :
% 15.55/8.63        ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) )
% 15.55/8.63        = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8617_gbinomial__absorption,axiom,
% 15.55/8.63      ! [K: nat,A: real] :
% 15.55/8.63        ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) )
% 15.55/8.63        = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8618_gbinomial__absorption,axiom,
% 15.55/8.63      ! [K: nat,A: rat] :
% 15.55/8.63        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 15.55/8.63        = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8619_gbinomial__trinomial__revision,axiom,
% 15.55/8.63      ! [K: nat,M: nat,A: complex] :
% 15.55/8.63        ( ( ord_less_eq_nat @ K @ M )
% 15.55/8.63       => ( ( times_times_complex @ ( gbinomial_complex @ A @ M ) @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ M ) @ K ) )
% 15.55/8.63          = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8620_gbinomial__trinomial__revision,axiom,
% 15.55/8.63      ! [K: nat,M: nat,A: real] :
% 15.55/8.63        ( ( ord_less_eq_nat @ K @ M )
% 15.55/8.63       => ( ( times_times_real @ ( gbinomial_real @ A @ M ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M ) @ K ) )
% 15.55/8.63          = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8621_gbinomial__trinomial__revision,axiom,
% 15.55/8.63      ! [K: nat,M: nat,A: rat] :
% 15.55/8.63        ( ( ord_less_eq_nat @ K @ M )
% 15.55/8.63       => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 15.55/8.63          = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8622_gbinomial__parallel__sum,axiom,
% 15.55/8.63      ! [A: complex,N: nat] :
% 15.55/8.63        ( ( groups2073611262835488442omplex
% 15.55/8.63          @ ^ [K3: nat] : ( gbinomial_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K3 ) ) @ K3 )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63        = ( gbinomial_complex @ ( plus_plus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N ) ) @ one_one_complex ) @ N ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8623_gbinomial__parallel__sum,axiom,
% 15.55/8.63      ! [A: rat,N: nat] :
% 15.55/8.63        ( ( groups2906978787729119204at_rat
% 15.55/8.63          @ ^ [K3: nat] : ( gbinomial_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K3 ) ) @ K3 )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63        = ( gbinomial_rat @ ( plus_plus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) @ one_one_rat ) @ N ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8624_gbinomial__parallel__sum,axiom,
% 15.55/8.63      ! [A: real,N: nat] :
% 15.55/8.63        ( ( groups6591440286371151544t_real
% 15.55/8.63          @ ^ [K3: nat] : ( gbinomial_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K3 ) ) @ K3 )
% 15.55/8.63          @ ( set_ord_atMost_nat @ N ) )
% 15.55/8.63        = ( gbinomial_real @ ( plus_plus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) @ one_one_real ) @ N ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8625_arccos__lt__bounded,axiom,
% 15.55/8.63      ! [Y3: real] :
% 15.55/8.63        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 15.55/8.63       => ( ( ord_less_real @ Y3 @ one_one_real )
% 15.55/8.63         => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y3 ) )
% 15.55/8.63            & ( ord_less_real @ ( arccos @ Y3 ) @ pi ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8626_arccos__bounded,axiom,
% 15.55/8.63      ! [Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 15.55/8.63       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 15.55/8.63         => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y3 ) )
% 15.55/8.63            & ( ord_less_eq_real @ ( arccos @ Y3 ) @ pi ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8627_gbinomial__factors,axiom,
% 15.55/8.63      ! [A: complex,K: nat] :
% 15.55/8.63        ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 15.55/8.63        = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8628_gbinomial__factors,axiom,
% 15.55/8.63      ! [A: real,K: nat] :
% 15.55/8.63        ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 15.55/8.63        = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8629_gbinomial__factors,axiom,
% 15.55/8.63      ! [A: rat,K: nat] :
% 15.55/8.63        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 15.55/8.63        = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8630_gbinomial__rec,axiom,
% 15.55/8.63      ! [A: complex,K: nat] :
% 15.55/8.63        ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 15.55/8.63        = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8631_gbinomial__rec,axiom,
% 15.55/8.63      ! [A: real,K: nat] :
% 15.55/8.63        ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 15.55/8.63        = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8632_gbinomial__rec,axiom,
% 15.55/8.63      ! [A: rat,K: nat] :
% 15.55/8.63        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 15.55/8.63        = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8633_gbinomial__index__swap,axiom,
% 15.55/8.63      ! [K: nat,N: nat] :
% 15.55/8.63        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ one_one_complex ) @ K ) )
% 15.55/8.63        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8634_gbinomial__index__swap,axiom,
% 15.55/8.63      ! [K: nat,N: nat] :
% 15.55/8.63        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ one_one_real ) @ K ) )
% 15.55/8.63        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8635_gbinomial__index__swap,axiom,
% 15.55/8.63      ! [K: nat,N: nat] :
% 15.55/8.63        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ one_one_rat ) @ K ) )
% 15.55/8.63        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8636_gbinomial__negated__upper,axiom,
% 15.55/8.63      ( gbinomial_rat
% 15.55/8.63      = ( ^ [A4: rat,K3: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K3 ) @ A4 ) @ one_one_rat ) @ K3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8637_sin__arccos__nonzero,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 15.55/8.63       => ( ( ord_less_real @ X3 @ one_one_real )
% 15.55/8.63         => ( ( sin_real @ ( arccos @ X3 ) )
% 15.55/8.63           != zero_zero_real ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8638_arccos__cos2,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 15.55/8.63       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X3 )
% 15.55/8.63         => ( ( arccos @ ( cos_real @ X3 ) )
% 15.55/8.63            = ( uminus_uminus_real @ X3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8639_arccos__minus,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 15.55/8.63       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 15.55/8.63         => ( ( arccos @ ( uminus_uminus_real @ X3 ) )
% 15.55/8.63            = ( minus_minus_real @ pi @ ( arccos @ X3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8640_arccos,axiom,
% 15.55/8.63      ! [Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 15.55/8.63       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 15.55/8.63         => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y3 ) )
% 15.55/8.63            & ( ord_less_eq_real @ ( arccos @ Y3 ) @ pi )
% 15.55/8.63            & ( ( cos_real @ ( arccos @ Y3 ) )
% 15.55/8.63              = Y3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8641_arccos__minus__abs,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 15.55/8.63       => ( ( arccos @ ( uminus_uminus_real @ X3 ) )
% 15.55/8.63          = ( minus_minus_real @ pi @ ( arccos @ X3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8642_arccos__le__pi2,axiom,
% 15.55/8.63      ! [Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.63       => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 15.55/8.63         => ( ord_less_eq_real @ ( arccos @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8643_arccos__cos__eq__abs__2pi,axiom,
% 15.55/8.63      ! [Theta: real] :
% 15.55/8.63        ~ ! [K2: int] :
% 15.55/8.63            ( ( arccos @ ( cos_real @ Theta ) )
% 15.55/8.63           != ( abs_abs_real @ ( minus_minus_real @ Theta @ ( times_times_real @ ( ring_1_of_int_real @ K2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8644_sin__arccos,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 15.55/8.63       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 15.55/8.63         => ( ( sin_real @ ( arccos @ X3 ) )
% 15.55/8.63            = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8645_Maclaurin__minus__cos__expansion,axiom,
% 15.55/8.63      ! [N: nat,X3: real] :
% 15.55/8.63        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.63       => ( ( ord_less_real @ X3 @ zero_zero_real )
% 15.55/8.63         => ? [T3: real] :
% 15.55/8.63              ( ( ord_less_real @ X3 @ T3 )
% 15.55/8.63              & ( ord_less_real @ T3 @ zero_zero_real )
% 15.55/8.63              & ( ( cos_real @ X3 )
% 15.55/8.63                = ( plus_plus_real
% 15.55/8.63                  @ ( groups6591440286371151544t_real
% 15.55/8.63                    @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 15.55/8.63                    @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.63                  @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8646_Maclaurin__cos__expansion2,axiom,
% 15.55/8.63      ! [X3: real,N: nat] :
% 15.55/8.63        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.63       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.63         => ? [T3: real] :
% 15.55/8.63              ( ( ord_less_real @ zero_zero_real @ T3 )
% 15.55/8.63              & ( ord_less_real @ T3 @ X3 )
% 15.55/8.63              & ( ( cos_real @ X3 )
% 15.55/8.63                = ( plus_plus_real
% 15.55/8.63                  @ ( groups6591440286371151544t_real
% 15.55/8.63                    @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 15.55/8.63                    @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.63                  @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8647_Maclaurin__cos__expansion,axiom,
% 15.55/8.63      ! [X3: real,N: nat] :
% 15.55/8.63      ? [T3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 15.55/8.63        & ( ( cos_real @ X3 )
% 15.55/8.63          = ( plus_plus_real
% 15.55/8.63            @ ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 15.55/8.63              @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.63            @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8648_infinite__int__iff__unbounded,axiom,
% 15.55/8.63      ! [S2: set_int] :
% 15.55/8.63        ( ( ~ ( finite_finite_int @ S2 ) )
% 15.55/8.63        = ( ! [M3: int] :
% 15.55/8.63            ? [N3: int] :
% 15.55/8.63              ( ( ord_less_int @ M3 @ ( abs_abs_int @ N3 ) )
% 15.55/8.63              & ( member_int @ N3 @ S2 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8649_square__fact__le__2__fact,axiom,
% 15.55/8.63      ! [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 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8650_infinite__nat__iff__unbounded,axiom,
% 15.55/8.63      ! [S2: set_nat] :
% 15.55/8.63        ( ( ~ ( finite_finite_nat @ S2 ) )
% 15.55/8.63        = ( ! [M3: nat] :
% 15.55/8.63            ? [N3: nat] :
% 15.55/8.63              ( ( ord_less_nat @ M3 @ N3 )
% 15.55/8.63              & ( member_nat @ N3 @ S2 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8651_unbounded__k__infinite,axiom,
% 15.55/8.63      ! [K: nat,S2: set_nat] :
% 15.55/8.63        ( ! [M4: nat] :
% 15.55/8.63            ( ( ord_less_nat @ K @ M4 )
% 15.55/8.63           => ? [N8: nat] :
% 15.55/8.63                ( ( ord_less_nat @ M4 @ N8 )
% 15.55/8.63                & ( member_nat @ N8 @ S2 ) ) )
% 15.55/8.63       => ~ ( finite_finite_nat @ S2 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8652_infinite__nat__iff__unbounded__le,axiom,
% 15.55/8.63      ! [S2: set_nat] :
% 15.55/8.63        ( ( ~ ( finite_finite_nat @ S2 ) )
% 15.55/8.63        = ( ! [M3: nat] :
% 15.55/8.63            ? [N3: nat] :
% 15.55/8.63              ( ( ord_less_eq_nat @ M3 @ N3 )
% 15.55/8.63              & ( member_nat @ N3 @ S2 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8653_Maclaurin__lemma,axiom,
% 15.55/8.63      ! [H2: real,F: real > real,J: nat > real,N: nat] :
% 15.55/8.63        ( ( ord_less_real @ zero_zero_real @ H2 )
% 15.55/8.63       => ? [B6: real] :
% 15.55/8.63            ( ( F @ H2 )
% 15.55/8.63            = ( plus_plus_real
% 15.55/8.63              @ ( groups6591440286371151544t_real
% 15.55/8.63                @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 15.55/8.63                @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.63              @ ( times_times_real @ B6 @ ( divide_divide_real @ ( power_power_real @ H2 @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8654_cos__coeff__def,axiom,
% 15.55/8.63      ( cos_coeff
% 15.55/8.63      = ( ^ [N3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N3 ) ) @ zero_zero_real ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8655_infinite__int__iff__unbounded__le,axiom,
% 15.55/8.63      ! [S2: set_int] :
% 15.55/8.63        ( ( ~ ( finite_finite_int @ S2 ) )
% 15.55/8.63        = ( ! [M3: int] :
% 15.55/8.63            ? [N3: int] :
% 15.55/8.63              ( ( ord_less_eq_int @ M3 @ ( abs_abs_int @ N3 ) )
% 15.55/8.63              & ( member_int @ N3 @ S2 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8656_Maclaurin__sin__expansion3,axiom,
% 15.55/8.63      ! [N: nat,X3: real] :
% 15.55/8.63        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.63       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.63         => ? [T3: real] :
% 15.55/8.63              ( ( ord_less_real @ zero_zero_real @ T3 )
% 15.55/8.63              & ( ord_less_real @ T3 @ X3 )
% 15.55/8.63              & ( ( sin_real @ X3 )
% 15.55/8.63                = ( plus_plus_real
% 15.55/8.63                  @ ( groups6591440286371151544t_real
% 15.55/8.63                    @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 15.55/8.63                    @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.63                  @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8657_Maclaurin__sin__expansion4,axiom,
% 15.55/8.63      ! [X3: real,N: nat] :
% 15.55/8.63        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.63       => ? [T3: real] :
% 15.55/8.63            ( ( ord_less_real @ zero_zero_real @ T3 )
% 15.55/8.63            & ( ord_less_eq_real @ T3 @ X3 )
% 15.55/8.63            & ( ( sin_real @ X3 )
% 15.55/8.63              = ( plus_plus_real
% 15.55/8.63                @ ( groups6591440286371151544t_real
% 15.55/8.63                  @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 15.55/8.63                  @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.63                @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8658_Maclaurin__sin__expansion2,axiom,
% 15.55/8.63      ! [X3: real,N: nat] :
% 15.55/8.63      ? [T3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 15.55/8.63        & ( ( sin_real @ X3 )
% 15.55/8.63          = ( plus_plus_real
% 15.55/8.63            @ ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 15.55/8.63              @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.63            @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8659_Maclaurin__sin__expansion,axiom,
% 15.55/8.63      ! [X3: real,N: nat] :
% 15.55/8.63      ? [T3: real] :
% 15.55/8.63        ( ( sin_real @ X3 )
% 15.55/8.63        = ( plus_plus_real
% 15.55/8.63          @ ( groups6591440286371151544t_real
% 15.55/8.63            @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 15.55/8.63            @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.63          @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8660_sin__coeff__0,axiom,
% 15.55/8.63      ( ( sin_coeff @ zero_zero_nat )
% 15.55/8.63      = zero_zero_real ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8661_fact__ge__self,axiom,
% 15.55/8.63      ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8662_fact__mono__nat,axiom,
% 15.55/8.63      ! [M: nat,N: nat] :
% 15.55/8.63        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.63       => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8663_fact__less__mono__nat,axiom,
% 15.55/8.63      ! [M: nat,N: nat] :
% 15.55/8.63        ( ( ord_less_nat @ zero_zero_nat @ M )
% 15.55/8.63       => ( ( ord_less_nat @ M @ N )
% 15.55/8.63         => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8664_fact__ge__Suc__0__nat,axiom,
% 15.55/8.63      ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8665_dvd__fact,axiom,
% 15.55/8.63      ! [M: nat,N: nat] :
% 15.55/8.63        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 15.55/8.63       => ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.63         => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8666_fact__diff__Suc,axiom,
% 15.55/8.63      ! [N: nat,M: nat] :
% 15.55/8.63        ( ( ord_less_nat @ N @ ( suc @ M ) )
% 15.55/8.63       => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) )
% 15.55/8.63          = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8667_fact__div__fact__le__pow,axiom,
% 15.55/8.63      ! [R2: nat,N: nat] :
% 15.55/8.63        ( ( ord_less_eq_nat @ R2 @ N )
% 15.55/8.63       => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R2 ) ) ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8668_binomial__fact__lemma,axiom,
% 15.55/8.63      ! [K: nat,N: nat] :
% 15.55/8.63        ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.63       => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 15.55/8.63          = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8669_fact__eq__fact__times,axiom,
% 15.55/8.63      ! [N: nat,M: nat] :
% 15.55/8.63        ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.63       => ( ( semiri1408675320244567234ct_nat @ M )
% 15.55/8.63          = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 15.55/8.63            @ ( groups708209901874060359at_nat
% 15.55/8.63              @ ^ [X: nat] : X
% 15.55/8.63              @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8670_binomial__altdef__nat,axiom,
% 15.55/8.63      ! [K: nat,N: nat] :
% 15.55/8.63        ( ( ord_less_eq_nat @ K @ N )
% 15.55/8.63       => ( ( binomial @ N @ K )
% 15.55/8.63          = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8671_fact__div__fact,axiom,
% 15.55/8.63      ! [N: nat,M: nat] :
% 15.55/8.63        ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.63       => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 15.55/8.63          = ( groups708209901874060359at_nat
% 15.55/8.63            @ ^ [X: nat] : X
% 15.55/8.63            @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8672_sin__coeff__Suc,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( sin_coeff @ ( suc @ N ) )
% 15.55/8.63        = ( divide_divide_real @ ( cos_coeff @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8673_cos__coeff__Suc,axiom,
% 15.55/8.63      ! [N: nat] :
% 15.55/8.63        ( ( cos_coeff @ ( suc @ N ) )
% 15.55/8.63        = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8674_binomial__code,axiom,
% 15.55/8.63      ( binomial
% 15.55/8.63      = ( ^ [N3: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N3 @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N3 @ ( minus_minus_nat @ N3 @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N3 @ K3 ) @ one_one_nat ) @ N3 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8675_sin__coeff__def,axiom,
% 15.55/8.63      ( sin_coeff
% 15.55/8.63      = ( ^ [N3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N3 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8676_Maclaurin__exp__lt,axiom,
% 15.55/8.63      ! [X3: real,N: nat] :
% 15.55/8.63        ( ( X3 != zero_zero_real )
% 15.55/8.63       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.63         => ? [T3: real] :
% 15.55/8.63              ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 15.55/8.63              & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 15.55/8.63              & ( ( exp_real @ X3 )
% 15.55/8.63                = ( plus_plus_real
% 15.55/8.63                  @ ( groups6591440286371151544t_real
% 15.55/8.63                    @ ^ [M3: nat] : ( divide_divide_real @ ( power_power_real @ X3 @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) )
% 15.55/8.63                    @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.63                  @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8677_sin__paired,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( sums_real
% 15.55/8.63        @ ^ [N3: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 15.55/8.63        @ ( sin_real @ X3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8678_VEBT__internal_Oheight_Osimps_I1_J,axiom,
% 15.55/8.63      ! [A: $o,B: $o] :
% 15.55/8.63        ( ( vEBT_VEBT_height @ ( vEBT_Leaf @ A @ B ) )
% 15.55/8.63        = zero_zero_nat ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8679_exp__less__cancel__iff,axiom,
% 15.55/8.63      ! [X3: real,Y3: real] :
% 15.55/8.63        ( ( ord_less_real @ ( exp_real @ X3 ) @ ( exp_real @ Y3 ) )
% 15.55/8.63        = ( ord_less_real @ X3 @ Y3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8680_exp__less__mono,axiom,
% 15.55/8.63      ! [X3: real,Y3: real] :
% 15.55/8.63        ( ( ord_less_real @ X3 @ Y3 )
% 15.55/8.63       => ( ord_less_real @ ( exp_real @ X3 ) @ ( exp_real @ Y3 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8681_exp__le__cancel__iff,axiom,
% 15.55/8.63      ! [X3: real,Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( exp_real @ X3 ) @ ( exp_real @ Y3 ) )
% 15.55/8.63        = ( ord_less_eq_real @ X3 @ Y3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8682_exp__eq__one__iff,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( ( exp_real @ X3 )
% 15.55/8.63          = one_one_real )
% 15.55/8.63        = ( X3 = zero_zero_real ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8683_exp__less__one__iff,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( ord_less_real @ ( exp_real @ X3 ) @ one_one_real )
% 15.55/8.63        = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8684_one__less__exp__iff,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( ord_less_real @ one_one_real @ ( exp_real @ X3 ) )
% 15.55/8.63        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8685_exp__le__one__iff,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( exp_real @ X3 ) @ one_one_real )
% 15.55/8.63        = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8686_one__le__exp__iff,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X3 ) )
% 15.55/8.63        = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8687_exp__ln,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.63       => ( ( exp_real @ ( ln_ln_real @ X3 ) )
% 15.55/8.63          = X3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8688_exp__ln__iff,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( ( exp_real @ ( ln_ln_real @ X3 ) )
% 15.55/8.63          = X3 )
% 15.55/8.63        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8689_exp__less__cancel,axiom,
% 15.55/8.63      ! [X3: real,Y3: real] :
% 15.55/8.63        ( ( ord_less_real @ ( exp_real @ X3 ) @ ( exp_real @ Y3 ) )
% 15.55/8.63       => ( ord_less_real @ X3 @ Y3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8690_not__exp__less__zero,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ~ ( ord_less_real @ ( exp_real @ X3 ) @ zero_zero_real ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8691_exp__gt__zero,axiom,
% 15.55/8.63      ! [X3: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8692_exp__total,axiom,
% 15.55/8.63      ! [Y3: real] :
% 15.55/8.63        ( ( ord_less_real @ zero_zero_real @ Y3 )
% 15.55/8.63       => ? [X4: real] :
% 15.55/8.63            ( ( exp_real @ X4 )
% 15.55/8.63            = Y3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8693_not__exp__le__zero,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ~ ( ord_less_eq_real @ ( exp_real @ X3 ) @ zero_zero_real ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8694_exp__ge__zero,axiom,
% 15.55/8.63      ! [X3: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8695_exp__gt__one,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.63       => ( ord_less_real @ one_one_real @ ( exp_real @ X3 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8696_exp__ge__add__one__self,axiom,
% 15.55/8.63      ! [X3: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X3 ) @ ( exp_real @ X3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8697_exp__ge__add__one__self__aux,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.63       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X3 ) @ ( exp_real @ X3 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8698_lemma__exp__total,axiom,
% 15.55/8.63      ! [Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ one_one_real @ Y3 )
% 15.55/8.63       => ? [X4: real] :
% 15.55/8.63            ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 15.55/8.63            & ( ord_less_eq_real @ X4 @ ( minus_minus_real @ Y3 @ one_one_real ) )
% 15.55/8.63            & ( ( exp_real @ X4 )
% 15.55/8.63              = Y3 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8699_ln__ge__iff,axiom,
% 15.55/8.63      ! [X3: real,Y3: real] :
% 15.55/8.63        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.63       => ( ( ord_less_eq_real @ Y3 @ ( ln_ln_real @ X3 ) )
% 15.55/8.63          = ( ord_less_eq_real @ ( exp_real @ Y3 ) @ X3 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8700_ln__x__over__x__mono,axiom,
% 15.55/8.63      ! [X3: real,Y3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X3 )
% 15.55/8.63       => ( ( ord_less_eq_real @ X3 @ Y3 )
% 15.55/8.63         => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y3 ) @ Y3 ) @ ( divide_divide_real @ ( ln_ln_real @ X3 ) @ X3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8701_exp__le,axiom,
% 15.55/8.63      ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8702_exp__half__le2,axiom,
% 15.55/8.63      ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8703_power__half__series,axiom,
% 15.55/8.63      ( sums_real
% 15.55/8.63      @ ^ [N3: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N3 ) )
% 15.55/8.63      @ one_one_real ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8704_sums__if_H,axiom,
% 15.55/8.63      ! [G: nat > real,X3: real] :
% 15.55/8.63        ( ( sums_real @ G @ X3 )
% 15.55/8.63       => ( sums_real
% 15.55/8.63          @ ^ [N3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ zero_zero_real @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.63          @ X3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8705_sums__if,axiom,
% 15.55/8.63      ! [G: nat > real,X3: real,F: nat > real,Y3: real] :
% 15.55/8.63        ( ( sums_real @ G @ X3 )
% 15.55/8.63       => ( ( sums_real @ F @ Y3 )
% 15.55/8.63         => ( sums_real
% 15.55/8.63            @ ^ [N3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ ( F @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.63            @ ( plus_plus_real @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8706_exp__bound,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.63       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 15.55/8.63         => ( ord_less_eq_real @ ( exp_real @ X3 ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X3 ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8707_real__exp__bound__lemma,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.63       => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.63         => ( ord_less_eq_real @ ( exp_real @ X3 ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8708_exp__ge__one__plus__x__over__n__power__n,axiom,
% 15.55/8.63      ! [N: nat,X3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X3 )
% 15.55/8.63       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.63         => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X3 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8709_exp__ge__one__minus__x__over__n__power__n,axiom,
% 15.55/8.63      ! [X3: real,N: nat] :
% 15.55/8.63        ( ( ord_less_eq_real @ X3 @ ( semiri5074537144036343181t_real @ N ) )
% 15.55/8.63       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.63         => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X3 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ ( uminus_uminus_real @ X3 ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8710_Maclaurin__exp__le,axiom,
% 15.55/8.63      ! [X3: real,N: nat] :
% 15.55/8.63      ? [T3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 15.55/8.63        & ( ( exp_real @ X3 )
% 15.55/8.63          = ( plus_plus_real
% 15.55/8.63            @ ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [M3: nat] : ( divide_divide_real @ ( power_power_real @ X3 @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) )
% 15.55/8.63              @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.63            @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8711_exp__lower__Taylor__quadratic,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.63       => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X3 ) @ ( divide_divide_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X3 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8712_log__base__10__eq2,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.63       => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X3 )
% 15.55/8.63          = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8713_tanh__real__altdef,axiom,
% 15.55/8.63      ( tanh_real
% 15.55/8.63      = ( ^ [X: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8714_cos__paired,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( sums_real
% 15.55/8.63        @ ^ [N3: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) @ ( power_power_real @ X3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 15.55/8.63        @ ( cos_real @ X3 ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8715_log__base__10__eq1,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.63       => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X3 )
% 15.55/8.63          = ( 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 @ X3 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8716_Maclaurin__sin__bound,axiom,
% 15.55/8.63      ! [X3: real,N: nat] :
% 15.55/8.63        ( ord_less_eq_real
% 15.55/8.63        @ ( abs_abs_real
% 15.55/8.63          @ ( minus_minus_real @ ( sin_real @ X3 )
% 15.55/8.63            @ ( groups6591440286371151544t_real
% 15.55/8.63              @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 15.55/8.63              @ ( set_ord_lessThan_nat @ N ) ) ) )
% 15.55/8.63        @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X3 ) @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8717_divmod__BitM__2__eq,axiom,
% 15.55/8.63      ! [M: num] :
% 15.55/8.63        ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 15.55/8.63        = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8718_pred__numeral__simps_I2_J,axiom,
% 15.55/8.63      ! [K: num] :
% 15.55/8.63        ( ( pred_numeral @ ( bit0 @ K ) )
% 15.55/8.63        = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8719_real__sqrt__inverse,axiom,
% 15.55/8.63      ! [X3: real] :
% 15.55/8.63        ( ( sqrt @ ( inverse_inverse_real @ X3 ) )
% 15.55/8.63        = ( inverse_inverse_real @ ( sqrt @ X3 ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8720_semiring__norm_I26_J,axiom,
% 15.55/8.63      ( ( bitM @ one )
% 15.55/8.63      = one ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8721_divide__real__def,axiom,
% 15.55/8.63      ( divide_divide_real
% 15.55/8.63      = ( ^ [X: real,Y: real] : ( times_times_real @ X @ ( inverse_inverse_real @ Y ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8722_semiring__norm_I28_J,axiom,
% 15.55/8.63      ! [N: num] :
% 15.55/8.63        ( ( bitM @ ( bit1 @ N ) )
% 15.55/8.63        = ( bit1 @ ( bit0 @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8723_semiring__norm_I27_J,axiom,
% 15.55/8.63      ! [N: num] :
% 15.55/8.63        ( ( bitM @ ( bit0 @ N ) )
% 15.55/8.63        = ( bit1 @ ( bitM @ N ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8724_inc__BitM__eq,axiom,
% 15.55/8.63      ! [N: num] :
% 15.55/8.63        ( ( inc @ ( bitM @ N ) )
% 15.55/8.63        = ( bit0 @ N ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8725_BitM__inc__eq,axiom,
% 15.55/8.63      ! [N: num] :
% 15.55/8.63        ( ( bitM @ ( inc @ N ) )
% 15.55/8.63        = ( bit1 @ N ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8726_inverse__powr,axiom,
% 15.55/8.63      ! [Y3: real,A: real] :
% 15.55/8.63        ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.63       => ( ( powr_real @ ( inverse_inverse_real @ Y3 ) @ A )
% 15.55/8.63          = ( inverse_inverse_real @ ( powr_real @ Y3 @ A ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8727_eval__nat__numeral_I2_J,axiom,
% 15.55/8.63      ! [N: num] :
% 15.55/8.63        ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 15.55/8.63        = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8728_BitM__plus__one,axiom,
% 15.55/8.63      ! [N: num] :
% 15.55/8.63        ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 15.55/8.63        = ( bit0 @ N ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8729_one__plus__BitM,axiom,
% 15.55/8.63      ! [N: num] :
% 15.55/8.63        ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 15.55/8.63        = ( bit0 @ N ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8730_forall__pos__mono__1,axiom,
% 15.55/8.63      ! [P: real > $o,E2: real] :
% 15.55/8.63        ( ! [D6: real,E: real] :
% 15.55/8.63            ( ( ord_less_real @ D6 @ E )
% 15.55/8.63           => ( ( P @ D6 )
% 15.55/8.63             => ( P @ E ) ) )
% 15.55/8.63       => ( ! [N2: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) )
% 15.55/8.63         => ( ( ord_less_real @ zero_zero_real @ E2 )
% 15.55/8.63           => ( P @ E2 ) ) ) ) ).
% 15.55/8.63  
% 15.55/8.63  thf(fact_8731_forall__pos__mono,axiom,
% 15.55/8.63      ! [P: real > $o,E2: real] :
% 15.55/8.63        ( ! [D6: real,E: real] :
% 15.55/8.63            ( ( ord_less_real @ D6 @ E )
% 15.55/8.63           => ( ( P @ D6 )
% 15.55/8.63             => ( P @ E ) ) )
% 15.55/8.64       => ( ! [N2: nat] :
% 15.55/8.64              ( ( N2 != zero_zero_nat )
% 15.55/8.64             => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) )
% 15.55/8.64         => ( ( ord_less_real @ zero_zero_real @ E2 )
% 15.55/8.64           => ( P @ E2 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8732_real__arch__inverse,axiom,
% 15.55/8.64      ! [E2: real] :
% 15.55/8.64        ( ( ord_less_real @ zero_zero_real @ E2 )
% 15.55/8.64        = ( ? [N3: nat] :
% 15.55/8.64              ( ( N3 != zero_zero_nat )
% 15.55/8.64              & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) )
% 15.55/8.64              & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) @ E2 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8733_sqrt__divide__self__eq,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.64       => ( ( divide_divide_real @ ( sqrt @ X3 ) @ X3 )
% 15.55/8.64          = ( inverse_inverse_real @ ( sqrt @ X3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8734_ln__inverse,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.64       => ( ( ln_ln_real @ ( inverse_inverse_real @ X3 ) )
% 15.55/8.64          = ( uminus_uminus_real @ ( ln_ln_real @ X3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8735_log__inverse,axiom,
% 15.55/8.64      ! [A: real,X3: real] :
% 15.55/8.64        ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.64       => ( ( A != one_one_real )
% 15.55/8.64         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.64           => ( ( log @ A @ ( inverse_inverse_real @ X3 ) )
% 15.55/8.64              = ( uminus_uminus_real @ ( log @ A @ X3 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8736_exp__plus__inverse__exp,axiom,
% 15.55/8.64      ! [X3: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X3 ) @ ( inverse_inverse_real @ ( exp_real @ X3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8737_plus__inverse__ge__2,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.64       => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X3 @ ( inverse_inverse_real @ X3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8738_real__inv__sqrt__pow2,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.64       => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.64          = ( inverse_inverse_real @ X3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8739_tan__cot,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 ) )
% 15.55/8.64        = ( inverse_inverse_real @ ( tan_real @ X3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8740_real__le__x__sinh,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.64       => ( ord_less_eq_real @ X3 @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X3 ) @ ( inverse_inverse_real @ ( exp_real @ X3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8741_real__le__abs__sinh,axiom,
% 15.55/8.64      ! [X3: real] : ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X3 ) @ ( inverse_inverse_real @ ( exp_real @ X3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8742_powr__real__of__int,axiom,
% 15.55/8.64      ! [X3: real,N: int] :
% 15.55/8.64        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.64       => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 15.55/8.64           => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ N ) )
% 15.55/8.64              = ( power_power_real @ X3 @ ( nat2 @ N ) ) ) )
% 15.55/8.64          & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 15.55/8.64           => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ N ) )
% 15.55/8.64              = ( inverse_inverse_real @ ( power_power_real @ X3 @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8743_or__minus__numerals_I5_J,axiom,
% 15.55/8.64      ! [N: num] :
% 15.55/8.64        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 15.55/8.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8744_or__minus__numerals_I1_J,axiom,
% 15.55/8.64      ! [N: num] :
% 15.55/8.64        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 15.55/8.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8745_sinh__real__zero__iff,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ( sinh_real @ X3 )
% 15.55/8.64          = zero_zero_real )
% 15.55/8.64        = ( X3 = zero_zero_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8746_sinh__real__less__iff,axiom,
% 15.55/8.64      ! [X3: real,Y3: real] :
% 15.55/8.64        ( ( ord_less_real @ ( sinh_real @ X3 ) @ ( sinh_real @ Y3 ) )
% 15.55/8.64        = ( ord_less_real @ X3 @ Y3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8747_sinh__real__le__iff,axiom,
% 15.55/8.64      ! [X3: real,Y3: real] :
% 15.55/8.64        ( ( ord_less_eq_real @ ( sinh_real @ X3 ) @ ( sinh_real @ Y3 ) )
% 15.55/8.64        = ( ord_less_eq_real @ X3 @ Y3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8748_sinh__real__pos__iff,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X3 ) )
% 15.55/8.64        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8749_sinh__real__neg__iff,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_real @ ( sinh_real @ X3 ) @ zero_zero_real )
% 15.55/8.64        = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8750_sinh__real__nonpos__iff,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_eq_real @ ( sinh_real @ X3 ) @ zero_zero_real )
% 15.55/8.64        = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8751_sinh__real__nonneg__iff,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X3 ) )
% 15.55/8.64        = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8752_or__minus__numerals_I8_J,axiom,
% 15.55/8.64      ! [N: num,M: num] :
% 15.55/8.64        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 15.55/8.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8753_or__minus__numerals_I4_J,axiom,
% 15.55/8.64      ! [M: num,N: num] :
% 15.55/8.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 15.55/8.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8754_or__minus__numerals_I3_J,axiom,
% 15.55/8.64      ! [M: num,N: num] :
% 15.55/8.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 15.55/8.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8755_or__minus__numerals_I7_J,axiom,
% 15.55/8.64      ! [N: num,M: num] :
% 15.55/8.64        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 15.55/8.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8756_or__not__num__neg_Osimps_I1_J,axiom,
% 15.55/8.64      ( ( bit_or_not_num_neg @ one @ one )
% 15.55/8.64      = one ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8757_sinh__le__cosh__real,axiom,
% 15.55/8.64      ! [X3: real] : ( ord_less_eq_real @ ( sinh_real @ X3 ) @ ( cosh_real @ X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8758_sinh__less__cosh__real,axiom,
% 15.55/8.64      ! [X3: real] : ( ord_less_real @ ( sinh_real @ X3 ) @ ( cosh_real @ X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8759_cosh__real__nonzero,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( cosh_real @ X3 )
% 15.55/8.64       != zero_zero_real ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8760_cosh__real__pos,axiom,
% 15.55/8.64      ! [X3: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8761_cosh__real__nonpos__le__iff,axiom,
% 15.55/8.64      ! [X3: real,Y3: real] :
% 15.55/8.64        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 15.55/8.64       => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 15.55/8.64         => ( ( ord_less_eq_real @ ( cosh_real @ X3 ) @ ( cosh_real @ Y3 ) )
% 15.55/8.64            = ( ord_less_eq_real @ Y3 @ X3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8762_cosh__real__nonneg__le__iff,axiom,
% 15.55/8.64      ! [X3: real,Y3: real] :
% 15.55/8.64        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.64       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.64         => ( ( ord_less_eq_real @ ( cosh_real @ X3 ) @ ( cosh_real @ Y3 ) )
% 15.55/8.64            = ( ord_less_eq_real @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8763_cosh__real__nonneg,axiom,
% 15.55/8.64      ! [X3: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8764_cosh__real__ge__1,axiom,
% 15.55/8.64      ! [X3: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8765_or__not__num__neg_Osimps_I4_J,axiom,
% 15.55/8.64      ! [N: num] :
% 15.55/8.64        ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ one )
% 15.55/8.64        = ( bit0 @ one ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8766_or__not__num__neg_Osimps_I6_J,axiom,
% 15.55/8.64      ! [N: num,M: num] :
% 15.55/8.64        ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit1 @ M ) )
% 15.55/8.64        = ( bit0 @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8767_or__not__num__neg_Osimps_I3_J,axiom,
% 15.55/8.64      ! [M: num] :
% 15.55/8.64        ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 15.55/8.64        = ( bit1 @ M ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8768_or__not__num__neg_Osimps_I7_J,axiom,
% 15.55/8.64      ! [N: num] :
% 15.55/8.64        ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ one )
% 15.55/8.64        = one ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8769_or__not__num__neg_Osimps_I5_J,axiom,
% 15.55/8.64      ! [N: num,M: num] :
% 15.55/8.64        ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit0 @ M ) )
% 15.55/8.64        = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8770_or__not__num__neg_Osimps_I9_J,axiom,
% 15.55/8.64      ! [N: num,M: num] :
% 15.55/8.64        ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit1 @ M ) )
% 15.55/8.64        = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8771_cosh__real__strict__mono,axiom,
% 15.55/8.64      ! [X3: real,Y3: real] :
% 15.55/8.64        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.64       => ( ( ord_less_real @ X3 @ Y3 )
% 15.55/8.64         => ( ord_less_real @ ( cosh_real @ X3 ) @ ( cosh_real @ Y3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8772_cosh__real__nonneg__less__iff,axiom,
% 15.55/8.64      ! [X3: real,Y3: real] :
% 15.55/8.64        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.64       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.64         => ( ( ord_less_real @ ( cosh_real @ X3 ) @ ( cosh_real @ Y3 ) )
% 15.55/8.64            = ( ord_less_real @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8773_cosh__real__nonpos__less__iff,axiom,
% 15.55/8.64      ! [X3: real,Y3: real] :
% 15.55/8.64        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 15.55/8.64       => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 15.55/8.64         => ( ( ord_less_real @ ( cosh_real @ X3 ) @ ( cosh_real @ Y3 ) )
% 15.55/8.64            = ( ord_less_real @ Y3 @ X3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8774_arcosh__cosh__real,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.64       => ( ( arcosh_real @ ( cosh_real @ X3 ) )
% 15.55/8.64          = X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8775_or__not__num__neg_Osimps_I2_J,axiom,
% 15.55/8.64      ! [M: num] :
% 15.55/8.64        ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 15.55/8.64        = ( bit1 @ M ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8776_or__not__num__neg_Osimps_I8_J,axiom,
% 15.55/8.64      ! [N: num,M: num] :
% 15.55/8.64        ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit0 @ M ) )
% 15.55/8.64        = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8777_or__not__num__neg_Oelims,axiom,
% 15.55/8.64      ! [X3: num,Xa: num,Y3: num] :
% 15.55/8.64        ( ( ( bit_or_not_num_neg @ X3 @ Xa )
% 15.55/8.64          = Y3 )
% 15.55/8.64       => ( ( ( X3 = one )
% 15.55/8.64           => ( ( Xa = one )
% 15.55/8.64             => ( Y3 != one ) ) )
% 15.55/8.64         => ( ( ( X3 = one )
% 15.55/8.64             => ! [M4: num] :
% 15.55/8.64                  ( ( Xa
% 15.55/8.64                    = ( bit0 @ M4 ) )
% 15.55/8.64                 => ( Y3
% 15.55/8.64                   != ( bit1 @ M4 ) ) ) )
% 15.55/8.64           => ( ( ( X3 = one )
% 15.55/8.64               => ! [M4: num] :
% 15.55/8.64                    ( ( Xa
% 15.55/8.64                      = ( bit1 @ M4 ) )
% 15.55/8.64                   => ( Y3
% 15.55/8.64                     != ( bit1 @ M4 ) ) ) )
% 15.55/8.64             => ( ( ? [N2: num] :
% 15.55/8.64                      ( X3
% 15.55/8.64                      = ( bit0 @ N2 ) )
% 15.55/8.64                 => ( ( Xa = one )
% 15.55/8.64                   => ( Y3
% 15.55/8.64                     != ( bit0 @ one ) ) ) )
% 15.55/8.64               => ( ! [N2: num] :
% 15.55/8.64                      ( ( X3
% 15.55/8.64                        = ( bit0 @ N2 ) )
% 15.55/8.64                     => ! [M4: num] :
% 15.55/8.64                          ( ( Xa
% 15.55/8.64                            = ( bit0 @ M4 ) )
% 15.55/8.64                         => ( Y3
% 15.55/8.64                           != ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) ) ) )
% 15.55/8.64                 => ( ! [N2: num] :
% 15.55/8.64                        ( ( X3
% 15.55/8.64                          = ( bit0 @ N2 ) )
% 15.55/8.64                       => ! [M4: num] :
% 15.55/8.64                            ( ( Xa
% 15.55/8.64                              = ( bit1 @ M4 ) )
% 15.55/8.64                           => ( Y3
% 15.55/8.64                             != ( bit0 @ ( bit_or_not_num_neg @ N2 @ M4 ) ) ) ) )
% 15.55/8.64                   => ( ( ? [N2: num] :
% 15.55/8.64                            ( X3
% 15.55/8.64                            = ( bit1 @ N2 ) )
% 15.55/8.64                       => ( ( Xa = one )
% 15.55/8.64                         => ( Y3 != one ) ) )
% 15.55/8.64                     => ( ! [N2: num] :
% 15.55/8.64                            ( ( X3
% 15.55/8.64                              = ( bit1 @ N2 ) )
% 15.55/8.64                           => ! [M4: num] :
% 15.55/8.64                                ( ( Xa
% 15.55/8.64                                  = ( bit0 @ M4 ) )
% 15.55/8.64                               => ( Y3
% 15.55/8.64                                 != ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) ) ) )
% 15.55/8.64                       => ~ ! [N2: num] :
% 15.55/8.64                              ( ( X3
% 15.55/8.64                                = ( bit1 @ N2 ) )
% 15.55/8.64                             => ! [M4: num] :
% 15.55/8.64                                  ( ( Xa
% 15.55/8.64                                    = ( bit1 @ M4 ) )
% 15.55/8.64                                 => ( Y3
% 15.55/8.64                                   != ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8778_numeral__or__not__num__eq,axiom,
% 15.55/8.64      ! [M: num,N: num] :
% 15.55/8.64        ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) )
% 15.55/8.64        = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8779_int__numeral__not__or__num__neg,axiom,
% 15.55/8.64      ! [M: num,N: num] :
% 15.55/8.64        ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 15.55/8.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N @ M ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8780_int__numeral__or__not__num__neg,axiom,
% 15.55/8.64      ! [M: num,N: num] :
% 15.55/8.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8781_complex__inverse,axiom,
% 15.55/8.64      ! [A: real,B: real] :
% 15.55/8.64        ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 15.55/8.64        = ( 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 ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8782_cosh__ln__real,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.64       => ( ( cosh_real @ ( ln_ln_real @ X3 ) )
% 15.55/8.64          = ( divide_divide_real @ ( plus_plus_real @ X3 @ ( inverse_inverse_real @ X3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8783_sinh__ln__real,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.64       => ( ( sinh_real @ ( ln_ln_real @ X3 ) )
% 15.55/8.64          = ( divide_divide_real @ ( minus_minus_real @ X3 @ ( inverse_inverse_real @ X3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8784_concat__bit__Suc,axiom,
% 15.55/8.64      ! [N: nat,K: int,L: int] :
% 15.55/8.64        ( ( bit_concat_bit @ ( suc @ N ) @ K @ L )
% 15.55/8.64        = ( 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 ) ) ) @ L ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8785_cot__less__zero,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 )
% 15.55/8.64       => ( ( ord_less_real @ X3 @ zero_zero_real )
% 15.55/8.64         => ( ord_less_real @ ( cot_real @ X3 ) @ zero_zero_real ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8786_i__even__power,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.64        = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8787_concat__bit__0,axiom,
% 15.55/8.64      ! [K: int,L: int] :
% 15.55/8.64        ( ( bit_concat_bit @ zero_zero_nat @ K @ L )
% 15.55/8.64        = L ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8788_concat__bit__nonnegative__iff,axiom,
% 15.55/8.64      ! [N: nat,K: int,L: int] :
% 15.55/8.64        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L ) )
% 15.55/8.64        = ( ord_less_eq_int @ zero_zero_int @ L ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8789_concat__bit__negative__iff,axiom,
% 15.55/8.64      ! [N: nat,K: int,L: int] :
% 15.55/8.64        ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L ) @ zero_zero_int )
% 15.55/8.64        = ( ord_less_int @ L @ zero_zero_int ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8790_concat__bit__of__zero__2,axiom,
% 15.55/8.64      ! [N: nat,K: int] :
% 15.55/8.64        ( ( bit_concat_bit @ N @ K @ zero_zero_int )
% 15.55/8.64        = ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8791_cot__pi,axiom,
% 15.55/8.64      ( ( cot_real @ pi )
% 15.55/8.64      = zero_zero_real ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8792_cot__npi,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 15.55/8.64        = zero_zero_real ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8793_cot__periodic,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( cot_real @ ( plus_plus_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 15.55/8.64        = ( cot_real @ X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8794_power2__i,axiom,
% 15.55/8.64      ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.64      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8795_exp__two__pi__i,axiom,
% 15.55/8.64      ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 15.55/8.64      = one_one_complex ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8796_exp__two__pi__i_H,axiom,
% 15.55/8.64      ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 15.55/8.64      = one_one_complex ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8797_complex__i__not__zero,axiom,
% 15.55/8.64      imaginary_unit != zero_zero_complex ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8798_concat__bit__assoc,axiom,
% 15.55/8.64      ! [N: nat,K: int,M: nat,L: int,R2: int] :
% 15.55/8.64        ( ( bit_concat_bit @ N @ K @ ( bit_concat_bit @ M @ L @ R2 ) )
% 15.55/8.64        = ( bit_concat_bit @ ( plus_plus_nat @ M @ N ) @ ( bit_concat_bit @ N @ K @ L ) @ R2 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8799_concat__bit__eq__iff,axiom,
% 15.55/8.64      ! [N: nat,K: int,L: int,R2: int,S: int] :
% 15.55/8.64        ( ( ( bit_concat_bit @ N @ K @ L )
% 15.55/8.64          = ( bit_concat_bit @ N @ R2 @ S ) )
% 15.55/8.64        = ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 15.55/8.64            = ( bit_se2923211474154528505it_int @ N @ R2 ) )
% 15.55/8.64          & ( L = S ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8800_concat__bit__take__bit__eq,axiom,
% 15.55/8.64      ! [N: nat,B: int] :
% 15.55/8.64        ( ( bit_concat_bit @ N @ ( bit_se2923211474154528505it_int @ N @ B ) )
% 15.55/8.64        = ( bit_concat_bit @ N @ B ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8801_imaginary__unit_Ocode,axiom,
% 15.55/8.64      ( imaginary_unit
% 15.55/8.64      = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8802_Complex__eq__i,axiom,
% 15.55/8.64      ! [X3: real,Y3: real] :
% 15.55/8.64        ( ( ( complex2 @ X3 @ Y3 )
% 15.55/8.64          = imaginary_unit )
% 15.55/8.64        = ( ( X3 = zero_zero_real )
% 15.55/8.64          & ( Y3 = one_one_real ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8803_i__complex__of__real,axiom,
% 15.55/8.64      ! [R2: real] :
% 15.55/8.64        ( ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ R2 ) )
% 15.55/8.64        = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8804_complex__of__real__i,axiom,
% 15.55/8.64      ! [R2: real] :
% 15.55/8.64        ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ imaginary_unit )
% 15.55/8.64        = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8805_divmod__step__nat__def,axiom,
% 15.55/8.64      ( unique5026877609467782581ep_nat
% 15.55/8.64      = ( ^ [L2: num] :
% 15.55/8.64            ( produc2626176000494625587at_nat
% 15.55/8.64            @ ^ [Q5: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8806_divmod__step__int__def,axiom,
% 15.55/8.64      ( unique5024387138958732305ep_int
% 15.55/8.64      = ( ^ [L2: num] :
% 15.55/8.64            ( produc4245557441103728435nt_int
% 15.55/8.64            @ ^ [Q5: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8807_cot__gt__zero,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.64       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.64         => ( ord_less_real @ zero_zero_real @ ( cot_real @ X3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8808_tan__cot_H,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 ) )
% 15.55/8.64        = ( cot_real @ X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8809_Arg__minus__ii,axiom,
% 15.55/8.64      ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 15.55/8.64      = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8810_csqrt__ii,axiom,
% 15.55/8.64      ( ( csqrt @ imaginary_unit )
% 15.55/8.64      = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8811_Arg__ii,axiom,
% 15.55/8.64      ( ( arg @ imaginary_unit )
% 15.55/8.64      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8812_cis__minus__pi__half,axiom,
% 15.55/8.64      ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 15.55/8.64      = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8813_csqrt__eq__0,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( ( csqrt @ Z )
% 15.55/8.64          = zero_zero_complex )
% 15.55/8.64        = ( Z = zero_zero_complex ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8814_csqrt__0,axiom,
% 15.55/8.64      ( ( csqrt @ zero_zero_complex )
% 15.55/8.64      = zero_zero_complex ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8815_cis__zero,axiom,
% 15.55/8.64      ( ( cis @ zero_zero_real )
% 15.55/8.64      = one_one_complex ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8816_power2__csqrt,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.64        = Z ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8817_cis__pi__half,axiom,
% 15.55/8.64      ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.64      = imaginary_unit ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8818_cis__2pi,axiom,
% 15.55/8.64      ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 15.55/8.64      = one_one_complex ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8819_cis__neq__zero,axiom,
% 15.55/8.64      ! [A: real] :
% 15.55/8.64        ( ( cis @ A )
% 15.55/8.64       != zero_zero_complex ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8820_Arg__zero,axiom,
% 15.55/8.64      ( ( arg @ zero_zero_complex )
% 15.55/8.64      = zero_zero_real ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8821_DeMoivre,axiom,
% 15.55/8.64      ! [A: real,N: nat] :
% 15.55/8.64        ( ( power_power_complex @ ( cis @ A ) @ N )
% 15.55/8.64        = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8822_of__real__sqrt,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.64       => ( ( real_V4546457046886955230omplex @ ( sqrt @ X3 ) )
% 15.55/8.64          = ( csqrt @ ( real_V4546457046886955230omplex @ X3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8823_Arg__bounded,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 15.55/8.64        & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8824_divmod__nat__if,axiom,
% 15.55/8.64      ( divmod_nat
% 15.55/8.64      = ( ^ [M3: nat,N3: nat] :
% 15.55/8.64            ( if_Pro6206227464963214023at_nat
% 15.55/8.64            @ ( ( N3 = zero_zero_nat )
% 15.55/8.64              | ( ord_less_nat @ M3 @ N3 ) )
% 15.55/8.64            @ ( product_Pair_nat_nat @ zero_zero_nat @ M3 )
% 15.55/8.64            @ ( produc2626176000494625587at_nat
% 15.55/8.64              @ ^ [Q5: nat] : ( product_Pair_nat_nat @ ( suc @ Q5 ) )
% 15.55/8.64              @ ( divmod_nat @ ( minus_minus_nat @ M3 @ N3 ) @ N3 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8825_bij__betw__roots__unity,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( bij_betw_nat_complex
% 15.55/8.64          @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 15.55/8.64          @ ( set_ord_lessThan_nat @ N )
% 15.55/8.64          @ ( collect_complex
% 15.55/8.64            @ ^ [Z6: complex] :
% 15.55/8.64                ( ( power_power_complex @ Z6 @ N )
% 15.55/8.64                = one_one_complex ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8826_nat__of__bool,axiom,
% 15.55/8.64      ! [P: $o] :
% 15.55/8.64        ( ( nat2 @ ( zero_n2684676970156552555ol_int @ P ) )
% 15.55/8.64        = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8827_Suc__0__mod__eq,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 15.55/8.64        = ( zero_n2687167440665602831ol_nat
% 15.55/8.64          @ ( N
% 15.55/8.64           != ( suc @ zero_zero_nat ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8828_take__bit__of__Suc__0,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 15.55/8.64        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8829_Divides_Oadjust__div__eq,axiom,
% 15.55/8.64      ! [Q3: int,R2: int] :
% 15.55/8.64        ( ( adjust_div @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 15.55/8.64        = ( plus_plus_int @ Q3 @ ( zero_n2684676970156552555ol_int @ ( R2 != zero_zero_int ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8830_Divides_Oadjust__div__def,axiom,
% 15.55/8.64      ( adjust_div
% 15.55/8.64      = ( produc8211389475949308722nt_int
% 15.55/8.64        @ ^ [Q5: int,R5: int] : ( plus_plus_int @ Q5 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8831_not__int__rec,axiom,
% 15.55/8.64      ( bit_ri7919022796975470100ot_int
% 15.55/8.64      = ( ^ [K3: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8832_or__Suc__0__eq,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 15.55/8.64        = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8833_Suc__0__or__eq,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 15.55/8.64        = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8834_or__int__rec,axiom,
% 15.55/8.64      ( bit_se1409905431419307370or_int
% 15.55/8.64      = ( ^ [K3: int,L2: int] :
% 15.55/8.64            ( plus_plus_int
% 15.55/8.64            @ ( zero_n2684676970156552555ol_int
% 15.55/8.64              @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 15.55/8.64                | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 15.55/8.64            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8835_xor__nat__rec,axiom,
% 15.55/8.64      ( bit_se6528837805403552850or_nat
% 15.55/8.64      = ( ^ [M3: nat,N3: nat] :
% 15.55/8.64            ( plus_plus_nat
% 15.55/8.64            @ ( zero_n2687167440665602831ol_nat
% 15.55/8.64              @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 15.55/8.64               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 15.55/8.64            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8836_or__nat__rec,axiom,
% 15.55/8.64      ( bit_se1412395901928357646or_nat
% 15.55/8.64      = ( ^ [M3: nat,N3: nat] :
% 15.55/8.64            ( plus_plus_nat
% 15.55/8.64            @ ( zero_n2687167440665602831ol_nat
% 15.55/8.64              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 15.55/8.64                | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 15.55/8.64            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8837_xor__int__rec,axiom,
% 15.55/8.64      ( bit_se6526347334894502574or_int
% 15.55/8.64      = ( ^ [K3: int,L2: int] :
% 15.55/8.64            ( plus_plus_int
% 15.55/8.64            @ ( zero_n2684676970156552555ol_int
% 15.55/8.64              @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 15.55/8.64               != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 15.55/8.64            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8838_xor__Suc__0__eq,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 15.55/8.64        = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 15.55/8.64          @ ( zero_n2687167440665602831ol_nat
% 15.55/8.64            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8839_Suc__0__xor__eq,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 15.55/8.64        = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 15.55/8.64          @ ( zero_n2687167440665602831ol_nat
% 15.55/8.64            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8840_and__int_Osimps,axiom,
% 15.55/8.64      ( bit_se725231765392027082nd_int
% 15.55/8.64      = ( ^ [K3: int,L2: int] :
% 15.55/8.64            ( if_int
% 15.55/8.64            @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 15.55/8.64              & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 15.55/8.64            @ ( uminus_uminus_int
% 15.55/8.64              @ ( zero_n2684676970156552555ol_int
% 15.55/8.64                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 15.55/8.64                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 15.55/8.64            @ ( plus_plus_int
% 15.55/8.64              @ ( zero_n2684676970156552555ol_int
% 15.55/8.64                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 15.55/8.64                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 15.55/8.64              @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8841_and__int_Oelims,axiom,
% 15.55/8.64      ! [X3: int,Xa: int,Y3: int] :
% 15.55/8.64        ( ( ( bit_se725231765392027082nd_int @ X3 @ Xa )
% 15.55/8.64          = Y3 )
% 15.55/8.64       => ( ( ( ( member_int @ X3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 15.55/8.64              & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 15.55/8.64           => ( Y3
% 15.55/8.64              = ( uminus_uminus_int
% 15.55/8.64                @ ( zero_n2684676970156552555ol_int
% 15.55/8.64                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 )
% 15.55/8.64                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 15.55/8.64          & ( ~ ( ( member_int @ X3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 15.55/8.64                & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 15.55/8.64           => ( Y3
% 15.55/8.64              = ( plus_plus_int
% 15.55/8.64                @ ( zero_n2684676970156552555ol_int
% 15.55/8.64                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 )
% 15.55/8.64                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 15.55/8.64                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8842_int__ge__less__than2__def,axiom,
% 15.55/8.64      ( int_ge_less_than2
% 15.55/8.64      = ( ^ [D4: int] :
% 15.55/8.64            ( collec213857154873943460nt_int
% 15.55/8.64            @ ( produc4947309494688390418_int_o
% 15.55/8.64              @ ^ [Z7: int,Z6: int] :
% 15.55/8.64                  ( ( ord_less_eq_int @ D4 @ Z6 )
% 15.55/8.64                  & ( ord_less_int @ Z7 @ Z6 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8843_int__ge__less__than__def,axiom,
% 15.55/8.64      ( int_ge_less_than
% 15.55/8.64      = ( ^ [D4: int] :
% 15.55/8.64            ( collec213857154873943460nt_int
% 15.55/8.64            @ ( produc4947309494688390418_int_o
% 15.55/8.64              @ ^ [Z7: int,Z6: int] :
% 15.55/8.64                  ( ( ord_less_eq_int @ D4 @ Z7 )
% 15.55/8.64                  & ( ord_less_int @ Z7 @ Z6 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8844_and__nonnegative__int__iff,axiom,
% 15.55/8.64      ! [K: int,L: int] :
% 15.55/8.64        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 15.55/8.64        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 15.55/8.64          | ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8845_and__negative__int__iff,axiom,
% 15.55/8.64      ! [K: int,L: int] :
% 15.55/8.64        ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ zero_zero_int )
% 15.55/8.64        = ( ( ord_less_int @ K @ zero_zero_int )
% 15.55/8.64          & ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8846_and__minus__numerals_I2_J,axiom,
% 15.55/8.64      ! [N: num] :
% 15.55/8.64        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 15.55/8.64        = one_one_int ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8847_and__minus__numerals_I6_J,axiom,
% 15.55/8.64      ! [N: num] :
% 15.55/8.64        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 15.55/8.64        = one_one_int ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8848_and__minus__numerals_I1_J,axiom,
% 15.55/8.64      ! [N: num] :
% 15.55/8.64        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 15.55/8.64        = zero_zero_int ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8849_and__minus__numerals_I5_J,axiom,
% 15.55/8.64      ! [N: num] :
% 15.55/8.64        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 15.55/8.64        = zero_zero_int ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8850_and__minus__minus__numerals,axiom,
% 15.55/8.64      ! [M: num,N: num] :
% 15.55/8.64        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.64        = ( 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 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8851_or__minus__minus__numerals,axiom,
% 15.55/8.64      ! [M: num,N: num] :
% 15.55/8.64        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.64        = ( 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 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8852_AND__upper2_H,axiom,
% 15.55/8.64      ! [Y3: int,Z: int,X3: int] :
% 15.55/8.64        ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 15.55/8.64       => ( ( ord_less_eq_int @ Y3 @ Z )
% 15.55/8.64         => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X3 @ Y3 ) @ Z ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8853_AND__upper1_H,axiom,
% 15.55/8.64      ! [Y3: int,Z: int,Ya: int] :
% 15.55/8.64        ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 15.55/8.64       => ( ( ord_less_eq_int @ Y3 @ Z )
% 15.55/8.64         => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y3 @ Ya ) @ Z ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8854_AND__upper2,axiom,
% 15.55/8.64      ! [Y3: int,X3: int] :
% 15.55/8.64        ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 15.55/8.64       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X3 @ Y3 ) @ Y3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8855_AND__upper1,axiom,
% 15.55/8.64      ! [X3: int,Y3: int] :
% 15.55/8.64        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 15.55/8.64       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X3 @ Y3 ) @ X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8856_AND__lower,axiom,
% 15.55/8.64      ! [X3: int,Y3: int] :
% 15.55/8.64        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 15.55/8.64       => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X3 @ Y3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8857_plus__and__or,axiom,
% 15.55/8.64      ! [X3: int,Y3: int] :
% 15.55/8.64        ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X3 @ Y3 ) @ ( bit_se1409905431419307370or_int @ X3 @ Y3 ) )
% 15.55/8.64        = ( plus_plus_int @ X3 @ Y3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8858_or__int__def,axiom,
% 15.55/8.64      ( bit_se1409905431419307370or_int
% 15.55/8.64      = ( ^ [K3: int,L2: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ ( bit_ri7919022796975470100ot_int @ L2 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8859_and__less__eq,axiom,
% 15.55/8.64      ! [L: int,K: int] :
% 15.55/8.64        ( ( ord_less_int @ L @ zero_zero_int )
% 15.55/8.64       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8860_AND__upper1_H_H,axiom,
% 15.55/8.64      ! [Y3: int,Z: int,Ya: int] :
% 15.55/8.64        ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 15.55/8.64       => ( ( ord_less_int @ Y3 @ Z )
% 15.55/8.64         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y3 @ Ya ) @ Z ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8861_AND__upper2_H_H,axiom,
% 15.55/8.64      ! [Y3: int,Z: int,X3: int] :
% 15.55/8.64        ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 15.55/8.64       => ( ( ord_less_int @ Y3 @ Z )
% 15.55/8.64         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X3 @ Y3 ) @ Z ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8862_and__not__numerals_I1_J,axiom,
% 15.55/8.64      ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 15.55/8.64      = zero_zero_int ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8863_xor__int__def,axiom,
% 15.55/8.64      ( bit_se6526347334894502574or_int
% 15.55/8.64      = ( ^ [K3: int,L2: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ L2 ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ L2 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8864_even__and__iff__int,axiom,
% 15.55/8.64      ! [K: int,L: int] :
% 15.55/8.64        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 15.55/8.64        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 15.55/8.64          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8865_and__not__numerals_I2_J,axiom,
% 15.55/8.64      ! [N: num] :
% 15.55/8.64        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 15.55/8.64        = one_one_int ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8866_and__not__numerals_I4_J,axiom,
% 15.55/8.64      ! [M: num] :
% 15.55/8.64        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 15.55/8.64        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8867_and__not__numerals_I5_J,axiom,
% 15.55/8.64      ! [M: num,N: num] :
% 15.55/8.64        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 15.55/8.64        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8868_and__not__numerals_I7_J,axiom,
% 15.55/8.64      ! [M: num] :
% 15.55/8.64        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 15.55/8.64        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8869_and__not__numerals_I3_J,axiom,
% 15.55/8.64      ! [N: num] :
% 15.55/8.64        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 15.55/8.64        = zero_zero_int ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8870_and__not__numerals_I9_J,axiom,
% 15.55/8.64      ! [M: num,N: num] :
% 15.55/8.64        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 15.55/8.64        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8871_and__not__numerals_I6_J,axiom,
% 15.55/8.64      ! [M: num,N: num] :
% 15.55/8.64        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 15.55/8.64        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8872_and__int__rec,axiom,
% 15.55/8.64      ( bit_se725231765392027082nd_int
% 15.55/8.64      = ( ^ [K3: int,L2: int] :
% 15.55/8.64            ( plus_plus_int
% 15.55/8.64            @ ( zero_n2684676970156552555ol_int
% 15.55/8.64              @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 15.55/8.64                & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 15.55/8.64            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8873_and__not__numerals_I8_J,axiom,
% 15.55/8.64      ! [M: num,N: num] :
% 15.55/8.64        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 15.55/8.64        = ( 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 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8874_and__int__unfold,axiom,
% 15.55/8.64      ( bit_se725231765392027082nd_int
% 15.55/8.64      = ( ^ [K3: int,L2: int] :
% 15.55/8.64            ( if_int
% 15.55/8.64            @ ( ( K3 = zero_zero_int )
% 15.55/8.64              | ( L2 = zero_zero_int ) )
% 15.55/8.64            @ zero_zero_int
% 15.55/8.64            @ ( if_int
% 15.55/8.64              @ ( K3
% 15.55/8.64                = ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.64              @ L2
% 15.55/8.64              @ ( if_int
% 15.55/8.64                @ ( L2
% 15.55/8.64                  = ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.64                @ K3
% 15.55/8.64                @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8875_bij__betw__nth__root__unity,axiom,
% 15.55/8.64      ! [C: complex,N: nat] :
% 15.55/8.64        ( ( C != zero_zero_complex )
% 15.55/8.64       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64         => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 15.55/8.64            @ ( collect_complex
% 15.55/8.64              @ ^ [Z6: complex] :
% 15.55/8.64                  ( ( power_power_complex @ Z6 @ N )
% 15.55/8.64                  = one_one_complex ) )
% 15.55/8.64            @ ( collect_complex
% 15.55/8.64              @ ^ [Z6: complex] :
% 15.55/8.64                  ( ( power_power_complex @ Z6 @ N )
% 15.55/8.64                  = C ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8876_and__int_Opsimps,axiom,
% 15.55/8.64      ! [K: int,L: int] :
% 15.55/8.64        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 15.55/8.64       => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 15.55/8.64              & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 15.55/8.64           => ( ( bit_se725231765392027082nd_int @ K @ L )
% 15.55/8.64              = ( uminus_uminus_int
% 15.55/8.64                @ ( zero_n2684676970156552555ol_int
% 15.55/8.64                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 15.55/8.64                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 15.55/8.64          & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 15.55/8.64                & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 15.55/8.64           => ( ( bit_se725231765392027082nd_int @ K @ L )
% 15.55/8.64              = ( plus_plus_int
% 15.55/8.64                @ ( zero_n2684676970156552555ol_int
% 15.55/8.64                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 15.55/8.64                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 15.55/8.64                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8877_and__int_Opelims,axiom,
% 15.55/8.64      ! [X3: int,Xa: int,Y3: int] :
% 15.55/8.64        ( ( ( bit_se725231765392027082nd_int @ X3 @ Xa )
% 15.55/8.64          = Y3 )
% 15.55/8.64       => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X3 @ Xa ) )
% 15.55/8.64         => ~ ( ( ( ( ( member_int @ X3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 15.55/8.64                    & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 15.55/8.64                 => ( Y3
% 15.55/8.64                    = ( uminus_uminus_int
% 15.55/8.64                      @ ( zero_n2684676970156552555ol_int
% 15.55/8.64                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 )
% 15.55/8.64                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 15.55/8.64                & ( ~ ( ( member_int @ X3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 15.55/8.64                      & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 15.55/8.64                 => ( Y3
% 15.55/8.64                    = ( plus_plus_int
% 15.55/8.64                      @ ( zero_n2684676970156552555ol_int
% 15.55/8.64                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 )
% 15.55/8.64                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 15.55/8.64                      @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 15.55/8.64             => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X3 @ Xa ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8878_vebt__buildup_Opelims,axiom,
% 15.55/8.64      ! [X3: nat,Y3: vEBT_VEBT] :
% 15.55/8.64        ( ( ( vEBT_vebt_buildup @ X3 )
% 15.55/8.64          = Y3 )
% 15.55/8.64       => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X3 )
% 15.55/8.64         => ( ( ( X3 = zero_zero_nat )
% 15.55/8.64             => ( ( Y3
% 15.55/8.64                  = ( vEBT_Leaf @ $false @ $false ) )
% 15.55/8.64               => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 15.55/8.64           => ( ( ( X3
% 15.55/8.64                  = ( suc @ zero_zero_nat ) )
% 15.55/8.64               => ( ( Y3
% 15.55/8.64                    = ( vEBT_Leaf @ $false @ $false ) )
% 15.55/8.64                 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 15.55/8.64             => ~ ! [Va: nat] :
% 15.55/8.64                    ( ( X3
% 15.55/8.64                      = ( suc @ ( suc @ Va ) ) )
% 15.55/8.64                   => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 15.55/8.64                         => ( Y3
% 15.55/8.64                            = ( 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 ) ) ) ) ) ) )
% 15.55/8.64                        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 15.55/8.64                         => ( Y3
% 15.55/8.64                            = ( 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 ) ) ) ) ) ) ) ) )
% 15.55/8.64                     => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8879_real__root__zero,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( root @ N @ zero_zero_real )
% 15.55/8.64        = zero_zero_real ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8880_real__root__Suc__0,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( root @ ( suc @ zero_zero_nat ) @ X3 )
% 15.55/8.64        = X3 ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8881_real__root__eq__iff,axiom,
% 15.55/8.64      ! [N: nat,X3: real,Y3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ( root @ N @ X3 )
% 15.55/8.64            = ( root @ N @ Y3 ) )
% 15.55/8.64          = ( X3 = Y3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8882_root__0,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( root @ zero_zero_nat @ X3 )
% 15.55/8.64        = zero_zero_real ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8883_real__root__eq__0__iff,axiom,
% 15.55/8.64      ! [N: nat,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ( root @ N @ X3 )
% 15.55/8.64            = zero_zero_real )
% 15.55/8.64          = ( X3 = zero_zero_real ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8884_real__root__less__iff,axiom,
% 15.55/8.64      ! [N: nat,X3: real,Y3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_real @ ( root @ N @ X3 ) @ ( root @ N @ Y3 ) )
% 15.55/8.64          = ( ord_less_real @ X3 @ Y3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8885_real__root__le__iff,axiom,
% 15.55/8.64      ! [N: nat,X3: real,Y3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_eq_real @ ( root @ N @ X3 ) @ ( root @ N @ Y3 ) )
% 15.55/8.64          = ( ord_less_eq_real @ X3 @ Y3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8886_real__root__eq__1__iff,axiom,
% 15.55/8.64      ! [N: nat,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ( root @ N @ X3 )
% 15.55/8.64            = one_one_real )
% 15.55/8.64          = ( X3 = one_one_real ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8887_real__root__one,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( root @ N @ one_one_real )
% 15.55/8.64          = one_one_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8888_real__root__lt__0__iff,axiom,
% 15.55/8.64      ! [N: nat,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_real @ ( root @ N @ X3 ) @ zero_zero_real )
% 15.55/8.64          = ( ord_less_real @ X3 @ zero_zero_real ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8889_real__root__gt__0__iff,axiom,
% 15.55/8.64      ! [N: nat,Y3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y3 ) )
% 15.55/8.64          = ( ord_less_real @ zero_zero_real @ Y3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8890_real__root__le__0__iff,axiom,
% 15.55/8.64      ! [N: nat,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_eq_real @ ( root @ N @ X3 ) @ zero_zero_real )
% 15.55/8.64          = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8891_real__root__ge__0__iff,axiom,
% 15.55/8.64      ! [N: nat,Y3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y3 ) )
% 15.55/8.64          = ( ord_less_eq_real @ zero_zero_real @ Y3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8892_real__root__lt__1__iff,axiom,
% 15.55/8.64      ! [N: nat,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_real @ ( root @ N @ X3 ) @ one_one_real )
% 15.55/8.64          = ( ord_less_real @ X3 @ one_one_real ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8893_real__root__gt__1__iff,axiom,
% 15.55/8.64      ! [N: nat,Y3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y3 ) )
% 15.55/8.64          = ( ord_less_real @ one_one_real @ Y3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8894_real__root__le__1__iff,axiom,
% 15.55/8.64      ! [N: nat,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_eq_real @ ( root @ N @ X3 ) @ one_one_real )
% 15.55/8.64          = ( ord_less_eq_real @ X3 @ one_one_real ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8895_real__root__ge__1__iff,axiom,
% 15.55/8.64      ! [N: nat,Y3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y3 ) )
% 15.55/8.64          = ( ord_less_eq_real @ one_one_real @ Y3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8896_and__nat__numerals_I3_J,axiom,
% 15.55/8.64      ! [X3: num] :
% 15.55/8.64        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 15.55/8.64        = zero_zero_nat ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8897_and__nat__numerals_I1_J,axiom,
% 15.55/8.64      ! [Y3: num] :
% 15.55/8.64        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 15.55/8.64        = zero_zero_nat ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8898_real__root__pow__pos2,axiom,
% 15.55/8.64      ! [N: nat,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.64         => ( ( power_power_real @ ( root @ N @ X3 ) @ N )
% 15.55/8.64            = X3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8899_and__nat__numerals_I4_J,axiom,
% 15.55/8.64      ! [X3: num] :
% 15.55/8.64        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 15.55/8.64        = one_one_nat ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8900_and__nat__numerals_I2_J,axiom,
% 15.55/8.64      ! [Y3: num] :
% 15.55/8.64        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 15.55/8.64        = one_one_nat ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8901_Suc__0__and__eq,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 15.55/8.64        = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8902_and__Suc__0__eq,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 15.55/8.64        = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8903_real__root__mult,axiom,
% 15.55/8.64      ! [N: nat,X3: real,Y3: real] :
% 15.55/8.64        ( ( root @ N @ ( times_times_real @ X3 @ Y3 ) )
% 15.55/8.64        = ( times_times_real @ ( root @ N @ X3 ) @ ( root @ N @ Y3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8904_real__root__divide,axiom,
% 15.55/8.64      ! [N: nat,X3: real,Y3: real] :
% 15.55/8.64        ( ( root @ N @ ( divide_divide_real @ X3 @ Y3 ) )
% 15.55/8.64        = ( divide_divide_real @ ( root @ N @ X3 ) @ ( root @ N @ Y3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8905_real__root__mult__exp,axiom,
% 15.55/8.64      ! [M: nat,N: nat,X3: real] :
% 15.55/8.64        ( ( root @ ( times_times_nat @ M @ N ) @ X3 )
% 15.55/8.64        = ( root @ M @ ( root @ N @ X3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8906_real__root__minus,axiom,
% 15.55/8.64      ! [N: nat,X3: real] :
% 15.55/8.64        ( ( root @ N @ ( uminus_uminus_real @ X3 ) )
% 15.55/8.64        = ( uminus_uminus_real @ ( root @ N @ X3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8907_real__root__commute,axiom,
% 15.55/8.64      ! [M: nat,N: nat,X3: real] :
% 15.55/8.64        ( ( root @ M @ ( root @ N @ X3 ) )
% 15.55/8.64        = ( root @ N @ ( root @ M @ X3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8908_real__root__inverse,axiom,
% 15.55/8.64      ! [N: nat,X3: real] :
% 15.55/8.64        ( ( root @ N @ ( inverse_inverse_real @ X3 ) )
% 15.55/8.64        = ( inverse_inverse_real @ ( root @ N @ X3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8909_real__root__pos__pos__le,axiom,
% 15.55/8.64      ! [X3: real,N: nat] :
% 15.55/8.64        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.64       => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8910_real__root__less__mono,axiom,
% 15.55/8.64      ! [N: nat,X3: real,Y3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_real @ X3 @ Y3 )
% 15.55/8.64         => ( ord_less_real @ ( root @ N @ X3 ) @ ( root @ N @ Y3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8911_real__root__le__mono,axiom,
% 15.55/8.64      ! [N: nat,X3: real,Y3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_eq_real @ X3 @ Y3 )
% 15.55/8.64         => ( ord_less_eq_real @ ( root @ N @ X3 ) @ ( root @ N @ Y3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8912_real__root__power,axiom,
% 15.55/8.64      ! [N: nat,X3: real,K: nat] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( root @ N @ ( power_power_real @ X3 @ K ) )
% 15.55/8.64          = ( power_power_real @ ( root @ N @ X3 ) @ K ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8913_real__root__abs,axiom,
% 15.55/8.64      ! [N: nat,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( root @ N @ ( abs_abs_real @ X3 ) )
% 15.55/8.64          = ( abs_abs_real @ ( root @ N @ X3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8914_and__nat__def,axiom,
% 15.55/8.64      ( bit_se727722235901077358nd_nat
% 15.55/8.64      = ( ^ [M3: nat,N3: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8915_real__root__gt__zero,axiom,
% 15.55/8.64      ! [N: nat,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.64         => ( ord_less_real @ zero_zero_real @ ( root @ N @ X3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8916_real__root__strict__decreasing,axiom,
% 15.55/8.64      ! [N: nat,N4: nat,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_nat @ N @ N4 )
% 15.55/8.64         => ( ( ord_less_real @ one_one_real @ X3 )
% 15.55/8.64           => ( ord_less_real @ ( root @ N4 @ X3 ) @ ( root @ N @ X3 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8917_sqrt__def,axiom,
% 15.55/8.64      ( sqrt
% 15.55/8.64      = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8918_root__abs__power,axiom,
% 15.55/8.64      ! [N: nat,Y3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y3 @ N ) ) )
% 15.55/8.64          = ( abs_abs_real @ Y3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8919_real__root__pos__pos,axiom,
% 15.55/8.64      ! [N: nat,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.64         => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8920_real__root__strict__increasing,axiom,
% 15.55/8.64      ! [N: nat,N4: nat,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_nat @ N @ N4 )
% 15.55/8.64         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.64           => ( ( ord_less_real @ X3 @ one_one_real )
% 15.55/8.64             => ( ord_less_real @ ( root @ N @ X3 ) @ ( root @ N4 @ X3 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8921_real__root__decreasing,axiom,
% 15.55/8.64      ! [N: nat,N4: nat,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_eq_nat @ N @ N4 )
% 15.55/8.64         => ( ( ord_less_eq_real @ one_one_real @ X3 )
% 15.55/8.64           => ( ord_less_eq_real @ ( root @ N4 @ X3 ) @ ( root @ N @ X3 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8922_real__root__pow__pos,axiom,
% 15.55/8.64      ! [N: nat,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.64         => ( ( power_power_real @ ( root @ N @ X3 ) @ N )
% 15.55/8.64            = X3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8923_odd__real__root__pow,axiom,
% 15.55/8.64      ! [N: nat,X3: real] :
% 15.55/8.64        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.64       => ( ( power_power_real @ ( root @ N @ X3 ) @ N )
% 15.55/8.64          = X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8924_odd__real__root__unique,axiom,
% 15.55/8.64      ! [N: nat,Y3: real,X3: real] :
% 15.55/8.64        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.64       => ( ( ( power_power_real @ Y3 @ N )
% 15.55/8.64            = X3 )
% 15.55/8.64         => ( ( root @ N @ X3 )
% 15.55/8.64            = Y3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8925_odd__real__root__power__cancel,axiom,
% 15.55/8.64      ! [N: nat,X3: real] :
% 15.55/8.64        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.64       => ( ( root @ N @ ( power_power_real @ X3 @ N ) )
% 15.55/8.64          = X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8926_real__root__power__cancel,axiom,
% 15.55/8.64      ! [N: nat,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.64         => ( ( root @ N @ ( power_power_real @ X3 @ N ) )
% 15.55/8.64            = X3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8927_real__root__pos__unique,axiom,
% 15.55/8.64      ! [N: nat,Y3: real,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 15.55/8.64         => ( ( ( power_power_real @ Y3 @ N )
% 15.55/8.64              = X3 )
% 15.55/8.64           => ( ( root @ N @ X3 )
% 15.55/8.64              = Y3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8928_real__root__increasing,axiom,
% 15.55/8.64      ! [N: nat,N4: nat,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_eq_nat @ N @ N4 )
% 15.55/8.64         => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.64           => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 15.55/8.64             => ( ord_less_eq_real @ ( root @ N @ X3 ) @ ( root @ N4 @ X3 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8929_log__root,axiom,
% 15.55/8.64      ! [N: nat,A: real,B: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_real @ zero_zero_real @ A )
% 15.55/8.64         => ( ( log @ B @ ( root @ N @ A ) )
% 15.55/8.64            = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8930_log__base__root,axiom,
% 15.55/8.64      ! [N: nat,B: real,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_real @ zero_zero_real @ B )
% 15.55/8.64         => ( ( log @ ( root @ N @ B ) @ X3 )
% 15.55/8.64            = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X3 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8931_ln__root,axiom,
% 15.55/8.64      ! [N: nat,B: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_real @ zero_zero_real @ B )
% 15.55/8.64         => ( ( ln_ln_real @ ( root @ N @ B ) )
% 15.55/8.64            = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8932_and__nat__unfold,axiom,
% 15.55/8.64      ( bit_se727722235901077358nd_nat
% 15.55/8.64      = ( ^ [M3: nat,N3: nat] :
% 15.55/8.64            ( if_nat
% 15.55/8.64            @ ( ( M3 = zero_zero_nat )
% 15.55/8.64              | ( N3 = zero_zero_nat ) )
% 15.55/8.64            @ zero_zero_nat
% 15.55/8.64            @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N3 @ ( 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 @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8933_root__powr__inverse,axiom,
% 15.55/8.64      ! [N: nat,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.64         => ( ( root @ N @ X3 )
% 15.55/8.64            = ( powr_real @ X3 @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8934_and__nat__rec,axiom,
% 15.55/8.64      ( bit_se727722235901077358nd_nat
% 15.55/8.64      = ( ^ [M3: nat,N3: nat] :
% 15.55/8.64            ( plus_plus_nat
% 15.55/8.64            @ ( zero_n2687167440665602831ol_nat
% 15.55/8.64              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 15.55/8.64                & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 15.55/8.64            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8935_and__int_Opinduct,axiom,
% 15.55/8.64      ! [A0: int,A1: int,P: int > int > $o] :
% 15.55/8.64        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 15.55/8.64       => ( ! [K2: int,L4: int] :
% 15.55/8.64              ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L4 ) )
% 15.55/8.64             => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 15.55/8.64                      & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 15.55/8.64                 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 15.55/8.64               => ( P @ K2 @ L4 ) ) )
% 15.55/8.64         => ( P @ A0 @ A1 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8936_upto_Opinduct,axiom,
% 15.55/8.64      ! [A0: int,A1: int,P: int > int > $o] :
% 15.55/8.64        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 15.55/8.64       => ( ! [I3: int,J2: int] :
% 15.55/8.64              ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I3 @ J2 ) )
% 15.55/8.64             => ( ( ( ord_less_eq_int @ I3 @ J2 )
% 15.55/8.64                 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) )
% 15.55/8.64               => ( P @ I3 @ J2 ) ) )
% 15.55/8.64         => ( P @ A0 @ A1 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8937_set__decode__0,axiom,
% 15.55/8.64      ! [X3: nat] :
% 15.55/8.64        ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X3 ) )
% 15.55/8.64        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8938_set__decode__Suc,axiom,
% 15.55/8.64      ! [N: nat,X3: nat] :
% 15.55/8.64        ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X3 ) )
% 15.55/8.64        = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8939_set__decode__zero,axiom,
% 15.55/8.64      ( ( nat_set_decode @ zero_zero_nat )
% 15.55/8.64      = bot_bot_set_nat ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8940_subset__decode__imp__le,axiom,
% 15.55/8.64      ! [M: nat,N: nat] :
% 15.55/8.64        ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 15.55/8.64       => ( ord_less_eq_nat @ M @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8941_set__decode__plus__power__2,axiom,
% 15.55/8.64      ! [N: nat,Z: nat] :
% 15.55/8.64        ( ~ ( member_nat @ N @ ( nat_set_decode @ Z ) )
% 15.55/8.64       => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z ) )
% 15.55/8.64          = ( insert_nat @ N @ ( nat_set_decode @ Z ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8942_set__decode__def,axiom,
% 15.55/8.64      ( nat_set_decode
% 15.55/8.64      = ( ^ [X: nat] :
% 15.55/8.64            ( collect_nat
% 15.55/8.64            @ ^ [N3: nat] :
% 15.55/8.64                ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8943_arctan__def,axiom,
% 15.55/8.64      ( arctan
% 15.55/8.64      = ( ^ [Y: real] :
% 15.55/8.64            ( the_real
% 15.55/8.64            @ ^ [X: real] :
% 15.55/8.64                ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 15.55/8.64                & ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.64                & ( ( tan_real @ X )
% 15.55/8.64                  = Y ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8944_arcsin__def,axiom,
% 15.55/8.64      ( arcsin
% 15.55/8.64      = ( ^ [Y: real] :
% 15.55/8.64            ( the_real
% 15.55/8.64            @ ^ [X: real] :
% 15.55/8.64                ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 15.55/8.64                & ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.64                & ( ( sin_real @ X )
% 15.55/8.64                  = Y ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8945_ln__neg__is__const,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 15.55/8.64       => ( ( ln_ln_real @ X3 )
% 15.55/8.64          = ( the_real
% 15.55/8.64            @ ^ [X: real] : $false ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8946_arccos__def,axiom,
% 15.55/8.64      ( arccos
% 15.55/8.64      = ( ^ [Y: real] :
% 15.55/8.64            ( the_real
% 15.55/8.64            @ ^ [X: real] :
% 15.55/8.64                ( ( ord_less_eq_real @ zero_zero_real @ X )
% 15.55/8.64                & ( ord_less_eq_real @ X @ pi )
% 15.55/8.64                & ( ( cos_real @ X )
% 15.55/8.64                  = Y ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8947_pi__half,axiom,
% 15.55/8.64      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 15.55/8.64      = ( the_real
% 15.55/8.64        @ ^ [X: real] :
% 15.55/8.64            ( ( ord_less_eq_real @ zero_zero_real @ X )
% 15.55/8.64            & ( ord_less_eq_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 15.55/8.64            & ( ( cos_real @ X )
% 15.55/8.64              = zero_zero_real ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8948_pi__def,axiom,
% 15.55/8.64      ( pi
% 15.55/8.64      = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 15.55/8.64        @ ( the_real
% 15.55/8.64          @ ^ [X: real] :
% 15.55/8.64              ( ( ord_less_eq_real @ zero_zero_real @ X )
% 15.55/8.64              & ( ord_less_eq_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 15.55/8.64              & ( ( cos_real @ X )
% 15.55/8.64                = zero_zero_real ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8949_modulo__int__def,axiom,
% 15.55/8.64      ( modulo_modulo_int
% 15.55/8.64      = ( ^ [K3: int,L2: int] :
% 15.55/8.64            ( if_int @ ( L2 = zero_zero_int ) @ K3
% 15.55/8.64            @ ( if_int
% 15.55/8.64              @ ( ( sgn_sgn_int @ K3 )
% 15.55/8.64                = ( sgn_sgn_int @ L2 ) )
% 15.55/8.64              @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) )
% 15.55/8.64              @ ( times_times_int @ ( sgn_sgn_int @ L2 )
% 15.55/8.64                @ ( minus_minus_int
% 15.55/8.64                  @ ( times_times_int @ ( abs_abs_int @ L2 )
% 15.55/8.64                    @ ( zero_n2684676970156552555ol_int
% 15.55/8.64                      @ ~ ( dvd_dvd_int @ L2 @ K3 ) ) )
% 15.55/8.64                  @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8950_signed__take__bit__eq__take__bit__minus,axiom,
% 15.55/8.64      ( bit_ri631733984087533419it_int
% 15.55/8.64      = ( ^ [N3: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N3 ) @ K3 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N3 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8951_divide__int__def,axiom,
% 15.55/8.64      ( divide_divide_int
% 15.55/8.64      = ( ^ [K3: int,L2: int] :
% 15.55/8.64            ( if_int @ ( L2 = zero_zero_int ) @ zero_zero_int
% 15.55/8.64            @ ( if_int
% 15.55/8.64              @ ( ( sgn_sgn_int @ K3 )
% 15.55/8.64                = ( sgn_sgn_int @ L2 ) )
% 15.55/8.64              @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) )
% 15.55/8.64              @ ( uminus_uminus_int
% 15.55/8.64                @ ( semiri1314217659103216013at_int
% 15.55/8.64                  @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) )
% 15.55/8.64                    @ ( zero_n2687167440665602831ol_nat
% 15.55/8.64                      @ ~ ( dvd_dvd_int @ L2 @ K3 ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8952_modulo__int__unfold,axiom,
% 15.55/8.64      ! [L: int,K: int,N: nat,M: nat] :
% 15.55/8.64        ( ( ( ( ( sgn_sgn_int @ L )
% 15.55/8.64              = zero_zero_int )
% 15.55/8.64            | ( ( sgn_sgn_int @ K )
% 15.55/8.64              = zero_zero_int )
% 15.55/8.64            | ( N = zero_zero_nat ) )
% 15.55/8.64         => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 15.55/8.64            = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 15.55/8.64        & ( ~ ( ( ( sgn_sgn_int @ L )
% 15.55/8.64                = zero_zero_int )
% 15.55/8.64              | ( ( sgn_sgn_int @ K )
% 15.55/8.64                = zero_zero_int )
% 15.55/8.64              | ( N = zero_zero_nat ) )
% 15.55/8.64         => ( ( ( ( sgn_sgn_int @ K )
% 15.55/8.64                = ( sgn_sgn_int @ L ) )
% 15.55/8.64             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 15.55/8.64                = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 15.55/8.64            & ( ( ( sgn_sgn_int @ K )
% 15.55/8.64               != ( sgn_sgn_int @ L ) )
% 15.55/8.64             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 15.55/8.64                = ( times_times_int @ ( sgn_sgn_int @ L )
% 15.55/8.64                  @ ( minus_minus_int
% 15.55/8.64                    @ ( semiri1314217659103216013at_int
% 15.55/8.64                      @ ( times_times_nat @ N
% 15.55/8.64                        @ ( zero_n2687167440665602831ol_nat
% 15.55/8.64                          @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 15.55/8.64                    @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8953_dvd__mult__sgn__iff,axiom,
% 15.55/8.64      ! [L: int,K: int,R2: int] :
% 15.55/8.64        ( ( dvd_dvd_int @ L @ ( times_times_int @ K @ ( sgn_sgn_int @ R2 ) ) )
% 15.55/8.64        = ( ( dvd_dvd_int @ L @ K )
% 15.55/8.64          | ( R2 = zero_zero_int ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8954_dvd__sgn__mult__iff,axiom,
% 15.55/8.64      ! [L: int,R2: int,K: int] :
% 15.55/8.64        ( ( dvd_dvd_int @ L @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ K ) )
% 15.55/8.64        = ( ( dvd_dvd_int @ L @ K )
% 15.55/8.64          | ( R2 = zero_zero_int ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8955_mult__sgn__dvd__iff,axiom,
% 15.55/8.64      ! [L: int,R2: int,K: int] :
% 15.55/8.64        ( ( dvd_dvd_int @ ( times_times_int @ L @ ( sgn_sgn_int @ R2 ) ) @ K )
% 15.55/8.64        = ( ( dvd_dvd_int @ L @ K )
% 15.55/8.64          & ( ( R2 = zero_zero_int )
% 15.55/8.64           => ( K = zero_zero_int ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8956_sgn__mult__dvd__iff,axiom,
% 15.55/8.64      ! [R2: int,L: int,K: int] :
% 15.55/8.64        ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ L ) @ K )
% 15.55/8.64        = ( ( dvd_dvd_int @ L @ K )
% 15.55/8.64          & ( ( R2 = zero_zero_int )
% 15.55/8.64           => ( K = zero_zero_int ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8957_signed__take__bit__nonnegative__iff,axiom,
% 15.55/8.64      ! [N: nat,K: int] :
% 15.55/8.64        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 15.55/8.64        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8958_signed__take__bit__negative__iff,axiom,
% 15.55/8.64      ! [N: nat,K: int] :
% 15.55/8.64        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 15.55/8.64        = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8959_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 15.55/8.64      ! [W: num,N: nat] :
% 15.55/8.64        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N ) )
% 15.55/8.64        = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8960_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 15.55/8.64      ! [W: num,N: nat] :
% 15.55/8.64        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N ) )
% 15.55/8.64        = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8961_bit__minus__numeral__int_I1_J,axiom,
% 15.55/8.64      ! [W: num,N: num] :
% 15.55/8.64        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 15.55/8.64        = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8962_bit__minus__numeral__int_I2_J,axiom,
% 15.55/8.64      ! [W: num,N: num] :
% 15.55/8.64        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 15.55/8.64        = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8963_bit__and__int__iff,axiom,
% 15.55/8.64      ! [K: int,L: int,N: nat] :
% 15.55/8.64        ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ N )
% 15.55/8.64        = ( ( bit_se1146084159140164899it_int @ K @ N )
% 15.55/8.64          & ( bit_se1146084159140164899it_int @ L @ N ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8964_bit__xor__int__iff,axiom,
% 15.55/8.64      ! [K: int,L: int,N: nat] :
% 15.55/8.64        ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ N )
% 15.55/8.64        = ( ( bit_se1146084159140164899it_int @ K @ N )
% 15.55/8.64         != ( bit_se1146084159140164899it_int @ L @ N ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8965_bit__not__int__iff,axiom,
% 15.55/8.64      ! [K: int,N: nat] :
% 15.55/8.64        ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N )
% 15.55/8.64        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8966_bit__or__int__iff,axiom,
% 15.55/8.64      ! [K: int,L: int,N: nat] :
% 15.55/8.64        ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ N )
% 15.55/8.64        = ( ( bit_se1146084159140164899it_int @ K @ N )
% 15.55/8.64          | ( bit_se1146084159140164899it_int @ L @ N ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8967_int__sgnE,axiom,
% 15.55/8.64      ! [K: int] :
% 15.55/8.64        ~ ! [N2: nat,L4: int] :
% 15.55/8.64            ( K
% 15.55/8.64           != ( times_times_int @ ( sgn_sgn_int @ L4 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8968_bit__not__int__iff_H,axiom,
% 15.55/8.64      ! [K: int,N: nat] :
% 15.55/8.64        ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 15.55/8.64        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8969_sgn__mod,axiom,
% 15.55/8.64      ! [L: int,K: int] :
% 15.55/8.64        ( ( L != zero_zero_int )
% 15.55/8.64       => ( ~ ( dvd_dvd_int @ L @ K )
% 15.55/8.64         => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L ) )
% 15.55/8.64            = ( sgn_sgn_int @ L ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8970_zsgn__def,axiom,
% 15.55/8.64      ( sgn_sgn_int
% 15.55/8.64      = ( ^ [I4: int] : ( if_int @ ( I4 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I4 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8971_div__sgn__abs__cancel,axiom,
% 15.55/8.64      ! [V: int,K: int,L: int] :
% 15.55/8.64        ( ( V != zero_zero_int )
% 15.55/8.64       => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ K ) ) @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ L ) ) )
% 15.55/8.64          = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8972_bit__imp__take__bit__positive,axiom,
% 15.55/8.64      ! [N: nat,M: nat,K: int] :
% 15.55/8.64        ( ( ord_less_nat @ N @ M )
% 15.55/8.64       => ( ( bit_se1146084159140164899it_int @ K @ N )
% 15.55/8.64         => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8973_bit__concat__bit__iff,axiom,
% 15.55/8.64      ! [M: nat,K: int,L: int,N: nat] :
% 15.55/8.64        ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L ) @ N )
% 15.55/8.64        = ( ( ( ord_less_nat @ N @ M )
% 15.55/8.64            & ( bit_se1146084159140164899it_int @ K @ N ) )
% 15.55/8.64          | ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.64            & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8974_bit__minus__int__iff,axiom,
% 15.55/8.64      ! [K: int,N: nat] :
% 15.55/8.64        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 15.55/8.64        = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8975_signed__take__bit__eq__concat__bit,axiom,
% 15.55/8.64      ( bit_ri631733984087533419it_int
% 15.55/8.64      = ( ^ [N3: nat,K3: int] : ( bit_concat_bit @ N3 @ K3 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N3 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8976_int__bit__bound,axiom,
% 15.55/8.64      ! [K: int] :
% 15.55/8.64        ~ ! [N2: nat] :
% 15.55/8.64            ( ! [M2: nat] :
% 15.55/8.64                ( ( ord_less_eq_nat @ N2 @ M2 )
% 15.55/8.64               => ( ( bit_se1146084159140164899it_int @ K @ M2 )
% 15.55/8.64                  = ( bit_se1146084159140164899it_int @ K @ N2 ) ) )
% 15.55/8.64           => ~ ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 15.55/8.64               => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 15.55/8.64                  = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8977_bit__int__def,axiom,
% 15.55/8.64      ( bit_se1146084159140164899it_int
% 15.55/8.64      = ( ^ [K3: int,N3: nat] :
% 15.55/8.64            ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8978_eucl__rel__int__remainderI,axiom,
% 15.55/8.64      ! [R2: int,L: int,K: int,Q3: int] :
% 15.55/8.64        ( ( ( sgn_sgn_int @ R2 )
% 15.55/8.64          = ( sgn_sgn_int @ L ) )
% 15.55/8.64       => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L ) )
% 15.55/8.64         => ( ( K
% 15.55/8.64              = ( plus_plus_int @ ( times_times_int @ Q3 @ L ) @ R2 ) )
% 15.55/8.64           => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8979_eucl__rel__int_Osimps,axiom,
% 15.55/8.64      ( eucl_rel_int
% 15.55/8.64      = ( ^ [A12: int,A23: int,A32: product_prod_int_int] :
% 15.55/8.64            ( ? [K3: int] :
% 15.55/8.64                ( ( A12 = K3 )
% 15.55/8.64                & ( A23 = zero_zero_int )
% 15.55/8.64                & ( A32
% 15.55/8.64                  = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 15.55/8.64            | ? [L2: int,K3: int,Q5: int] :
% 15.55/8.64                ( ( A12 = K3 )
% 15.55/8.64                & ( A23 = L2 )
% 15.55/8.64                & ( A32
% 15.55/8.64                  = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 15.55/8.64                & ( L2 != zero_zero_int )
% 15.55/8.64                & ( K3
% 15.55/8.64                  = ( times_times_int @ Q5 @ L2 ) ) )
% 15.55/8.64            | ? [R5: int,L2: int,K3: int,Q5: int] :
% 15.55/8.64                ( ( A12 = K3 )
% 15.55/8.64                & ( A23 = L2 )
% 15.55/8.64                & ( A32
% 15.55/8.64                  = ( product_Pair_int_int @ Q5 @ R5 ) )
% 15.55/8.64                & ( ( sgn_sgn_int @ R5 )
% 15.55/8.64                  = ( sgn_sgn_int @ L2 ) )
% 15.55/8.64                & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L2 ) )
% 15.55/8.64                & ( K3
% 15.55/8.64                  = ( plus_plus_int @ ( times_times_int @ Q5 @ L2 ) @ R5 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8980_eucl__rel__int_Ocases,axiom,
% 15.55/8.64      ! [A1: int,A22: int,A33: product_prod_int_int] :
% 15.55/8.64        ( ( eucl_rel_int @ A1 @ A22 @ A33 )
% 15.55/8.64       => ( ( ( A22 = zero_zero_int )
% 15.55/8.64           => ( A33
% 15.55/8.64             != ( product_Pair_int_int @ zero_zero_int @ A1 ) ) )
% 15.55/8.64         => ( ! [Q4: int] :
% 15.55/8.64                ( ( A33
% 15.55/8.64                  = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 15.55/8.64               => ( ( A22 != zero_zero_int )
% 15.55/8.64                 => ( A1
% 15.55/8.64                   != ( times_times_int @ Q4 @ A22 ) ) ) )
% 15.55/8.64           => ~ ! [R: int,Q4: int] :
% 15.55/8.64                  ( ( A33
% 15.55/8.64                    = ( product_Pair_int_int @ Q4 @ R ) )
% 15.55/8.64                 => ( ( ( sgn_sgn_int @ R )
% 15.55/8.64                      = ( sgn_sgn_int @ A22 ) )
% 15.55/8.64                   => ( ( ord_less_int @ ( abs_abs_int @ R ) @ ( abs_abs_int @ A22 ) )
% 15.55/8.64                     => ( A1
% 15.55/8.64                       != ( plus_plus_int @ ( times_times_int @ Q4 @ A22 ) @ R ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8981_div__noneq__sgn__abs,axiom,
% 15.55/8.64      ! [L: int,K: int] :
% 15.55/8.64        ( ( L != zero_zero_int )
% 15.55/8.64       => ( ( ( sgn_sgn_int @ K )
% 15.55/8.64           != ( sgn_sgn_int @ L ) )
% 15.55/8.64         => ( ( divide_divide_int @ K @ L )
% 15.55/8.64            = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) )
% 15.55/8.64              @ ( zero_n2684676970156552555ol_int
% 15.55/8.64                @ ~ ( dvd_dvd_int @ L @ K ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8982_set__bit__eq,axiom,
% 15.55/8.64      ( bit_se7879613467334960850it_int
% 15.55/8.64      = ( ^ [N3: nat,K3: int] :
% 15.55/8.64            ( plus_plus_int @ K3
% 15.55/8.64            @ ( times_times_int
% 15.55/8.64              @ ( zero_n2684676970156552555ol_int
% 15.55/8.64                @ ~ ( bit_se1146084159140164899it_int @ K3 @ N3 ) )
% 15.55/8.64              @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8983_unset__bit__eq,axiom,
% 15.55/8.64      ( bit_se4203085406695923979it_int
% 15.55/8.64      = ( ^ [N3: nat,K3: int] : ( minus_minus_int @ K3 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N3 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8984_take__bit__Suc__from__most,axiom,
% 15.55/8.64      ! [N: nat,K: int] :
% 15.55/8.64        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 15.55/8.64        = ( 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 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8985_divide__int__unfold,axiom,
% 15.55/8.64      ! [L: int,K: int,N: nat,M: nat] :
% 15.55/8.64        ( ( ( ( ( sgn_sgn_int @ L )
% 15.55/8.64              = zero_zero_int )
% 15.55/8.64            | ( ( sgn_sgn_int @ K )
% 15.55/8.64              = zero_zero_int )
% 15.55/8.64            | ( N = zero_zero_nat ) )
% 15.55/8.64         => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 15.55/8.64            = zero_zero_int ) )
% 15.55/8.64        & ( ~ ( ( ( sgn_sgn_int @ L )
% 15.55/8.64                = zero_zero_int )
% 15.55/8.64              | ( ( sgn_sgn_int @ K )
% 15.55/8.64                = zero_zero_int )
% 15.55/8.64              | ( N = zero_zero_nat ) )
% 15.55/8.64         => ( ( ( ( sgn_sgn_int @ K )
% 15.55/8.64                = ( sgn_sgn_int @ L ) )
% 15.55/8.64             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 15.55/8.64                = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 15.55/8.64            & ( ( ( sgn_sgn_int @ K )
% 15.55/8.64               != ( sgn_sgn_int @ L ) )
% 15.55/8.64             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 15.55/8.64                = ( uminus_uminus_int
% 15.55/8.64                  @ ( semiri1314217659103216013at_int
% 15.55/8.64                    @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 15.55/8.64                      @ ( zero_n2687167440665602831ol_nat
% 15.55/8.64                        @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8986_num_Osize__gen_I3_J,axiom,
% 15.55/8.64      ! [X32: num] :
% 15.55/8.64        ( ( size_num @ ( bit1 @ X32 ) )
% 15.55/8.64        = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8987_num_Osize__gen_I2_J,axiom,
% 15.55/8.64      ! [X2: num] :
% 15.55/8.64        ( ( size_num @ ( bit0 @ X2 ) )
% 15.55/8.64        = ( plus_plus_nat @ ( size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8988_arctan__inverse,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( X3 != zero_zero_real )
% 15.55/8.64       => ( ( arctan @ ( divide_divide_real @ one_one_real @ X3 ) )
% 15.55/8.64          = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X3 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8989_mask__nat__positive__iff,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 15.55/8.64        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8990_sgn__le__0__iff,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_eq_real @ ( sgn_sgn_real @ X3 ) @ zero_zero_real )
% 15.55/8.64        = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8991_zero__le__sgn__iff,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X3 ) )
% 15.55/8.64        = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8992_nat__mask__eq,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N ) )
% 15.55/8.64        = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8993_less__eq__mask,axiom,
% 15.55/8.64      ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8994_not__bit__Suc__0__Suc,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8995_bit__Suc__0__iff,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 15.55/8.64        = ( N = zero_zero_nat ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8996_mask__nonnegative__int,axiom,
% 15.55/8.64      ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8997_not__mask__negative__int,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8998_not__bit__Suc__0__numeral,axiom,
% 15.55/8.64      ! [N: num] :
% 15.55/8.64        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_8999_sgn__root,axiom,
% 15.55/8.64      ! [N: nat,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( sgn_sgn_real @ ( root @ N @ X3 ) )
% 15.55/8.64          = ( sgn_sgn_real @ X3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9000_less__mask,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 15.55/8.64       => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9001_cis__Arg,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( Z != zero_zero_complex )
% 15.55/8.64       => ( ( cis @ ( arg @ Z ) )
% 15.55/8.64          = ( sgn_sgn_complex @ Z ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9002_sgn__real__def,axiom,
% 15.55/8.64      ( sgn_sgn_real
% 15.55/8.64      = ( ^ [A4: real] : ( if_real @ ( A4 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A4 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9003_bit__nat__iff,axiom,
% 15.55/8.64      ! [K: int,N: nat] :
% 15.55/8.64        ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 15.55/8.64        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 15.55/8.64          & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9004_sgn__power__injE,axiom,
% 15.55/8.64      ! [A: real,N: nat,X3: real,B: real] :
% 15.55/8.64        ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 15.55/8.64          = X3 )
% 15.55/8.64       => ( ( X3
% 15.55/8.64            = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 15.55/8.64         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64           => ( A = B ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9005_take__bit__eq__mask__iff,axiom,
% 15.55/8.64      ! [N: nat,K: int] :
% 15.55/8.64        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 15.55/8.64          = ( bit_se2000444600071755411sk_int @ N ) )
% 15.55/8.64        = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 15.55/8.64          = zero_zero_int ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9006_num_Osize__gen_I1_J,axiom,
% 15.55/8.64      ( ( size_num @ one )
% 15.55/8.64      = zero_zero_nat ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9007_Suc__mask__eq__exp,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 15.55/8.64        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9008_mask__nat__less__exp,axiom,
% 15.55/8.64      ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9009_bit__nat__def,axiom,
% 15.55/8.64      ( bit_se1148574629649215175it_nat
% 15.55/8.64      = ( ^ [M3: nat,N3: nat] :
% 15.55/8.64            ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9010_sgn__power__root,axiom,
% 15.55/8.64      ! [N: nat,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X3 ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X3 ) ) @ N ) )
% 15.55/8.64          = X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9011_root__sgn__power,axiom,
% 15.55/8.64      ! [N: nat,Y3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y3 ) @ ( power_power_real @ ( abs_abs_real @ Y3 ) @ N ) ) )
% 15.55/8.64          = Y3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9012_cis__Arg__unique,axiom,
% 15.55/8.64      ! [Z: complex,X3: real] :
% 15.55/8.64        ( ( ( sgn_sgn_complex @ Z )
% 15.55/8.64          = ( cis @ X3 ) )
% 15.55/8.64       => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X3 )
% 15.55/8.64         => ( ( ord_less_eq_real @ X3 @ pi )
% 15.55/8.64           => ( ( arg @ Z )
% 15.55/8.64              = X3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9013_split__root,axiom,
% 15.55/8.64      ! [P: real > $o,N: nat,X3: real] :
% 15.55/8.64        ( ( P @ ( root @ N @ X3 ) )
% 15.55/8.64        = ( ( ( N = zero_zero_nat )
% 15.55/8.64           => ( P @ zero_zero_real ) )
% 15.55/8.64          & ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64           => ! [Y: real] :
% 15.55/8.64                ( ( ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 15.55/8.64                  = X3 )
% 15.55/8.64               => ( P @ Y ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9014_mask__nat__def,axiom,
% 15.55/8.64      ( bit_se2002935070580805687sk_nat
% 15.55/8.64      = ( ^ [N3: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9015_mask__half__int,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.64        = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9016_mask__int__def,axiom,
% 15.55/8.64      ( bit_se2000444600071755411sk_int
% 15.55/8.64      = ( ^ [N3: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) @ one_one_int ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9017_Arg__correct,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( Z != zero_zero_complex )
% 15.55/8.64       => ( ( ( sgn_sgn_complex @ Z )
% 15.55/8.64            = ( cis @ ( arg @ Z ) ) )
% 15.55/8.64          & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 15.55/8.64          & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9018_take__bit__eq__mask__iff__exp__dvd,axiom,
% 15.55/8.64      ! [N: nat,K: int] :
% 15.55/8.64        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 15.55/8.64          = ( bit_se2000444600071755411sk_int @ N ) )
% 15.55/8.64        = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9019_Arg__def,axiom,
% 15.55/8.64      ( arg
% 15.55/8.64      = ( ^ [Z6: complex] :
% 15.55/8.64            ( if_real @ ( Z6 = zero_zero_complex ) @ zero_zero_real
% 15.55/8.64            @ ( fChoice_real
% 15.55/8.64              @ ^ [A4: real] :
% 15.55/8.64                  ( ( ( sgn_sgn_complex @ Z6 )
% 15.55/8.64                    = ( cis @ A4 ) )
% 15.55/8.64                  & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A4 )
% 15.55/8.64                  & ( ord_less_eq_real @ A4 @ pi ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9020_cis__multiple__2pi,axiom,
% 15.55/8.64      ! [N: real] :
% 15.55/8.64        ( ( member_real @ N @ ring_1_Ints_real )
% 15.55/8.64       => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 15.55/8.64          = one_one_complex ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9021_horner__sum__of__bool__2__less,axiom,
% 15.55/8.64      ! [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 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9022_push__bit__nonnegative__int__iff,axiom,
% 15.55/8.64      ! [N: nat,K: int] :
% 15.55/8.64        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 15.55/8.64        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9023_push__bit__negative__int__iff,axiom,
% 15.55/8.64      ! [N: nat,K: int] :
% 15.55/8.64        ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 15.55/8.64        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9024_concat__bit__of__zero__1,axiom,
% 15.55/8.64      ! [N: nat,L: int] :
% 15.55/8.64        ( ( bit_concat_bit @ N @ zero_zero_int @ L )
% 15.55/8.64        = ( bit_se545348938243370406it_int @ N @ L ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9025_push__bit__of__Suc__0,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 15.55/8.64        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9026_push__bit__nat__eq,axiom,
% 15.55/8.64      ! [N: nat,K: int] :
% 15.55/8.64        ( ( bit_se547839408752420682it_nat @ N @ ( nat2 @ K ) )
% 15.55/8.64        = ( nat2 @ ( bit_se545348938243370406it_int @ N @ K ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9027_set__bit__nat__def,axiom,
% 15.55/8.64      ( bit_se7882103937844011126it_nat
% 15.55/8.64      = ( ^ [M3: nat,N3: nat] : ( bit_se1412395901928357646or_nat @ N3 @ ( bit_se547839408752420682it_nat @ M3 @ one_one_nat ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9028_flip__bit__nat__def,axiom,
% 15.55/8.64      ( bit_se2161824704523386999it_nat
% 15.55/8.64      = ( ^ [M3: nat,N3: nat] : ( bit_se6528837805403552850or_nat @ N3 @ ( bit_se547839408752420682it_nat @ M3 @ one_one_nat ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9029_bit__push__bit__iff__int,axiom,
% 15.55/8.64      ! [M: nat,K: int,N: nat] :
% 15.55/8.64        ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 15.55/8.64        = ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.64          & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9030_bit__push__bit__iff__nat,axiom,
% 15.55/8.64      ! [M: nat,Q3: nat,N: nat] :
% 15.55/8.64        ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q3 ) @ N )
% 15.55/8.64        = ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.64          & ( bit_se1148574629649215175it_nat @ Q3 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9031_concat__bit__eq,axiom,
% 15.55/8.64      ( bit_concat_bit
% 15.55/8.64      = ( ^ [N3: nat,K3: int,L2: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N3 @ K3 ) @ ( bit_se545348938243370406it_int @ N3 @ L2 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9032_concat__bit__def,axiom,
% 15.55/8.64      ( bit_concat_bit
% 15.55/8.64      = ( ^ [N3: nat,K3: int,L2: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N3 @ K3 ) @ ( bit_se545348938243370406it_int @ N3 @ L2 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9033_set__bit__int__def,axiom,
% 15.55/8.64      ( bit_se7879613467334960850it_int
% 15.55/8.64      = ( ^ [N3: nat,K3: int] : ( bit_se1409905431419307370or_int @ K3 @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9034_flip__bit__int__def,axiom,
% 15.55/8.64      ( bit_se2159334234014336723it_int
% 15.55/8.64      = ( ^ [N3: nat,K3: int] : ( bit_se6526347334894502574or_int @ K3 @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9035_sin__times__pi__eq__0,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ( sin_real @ ( times_times_real @ X3 @ pi ) )
% 15.55/8.64          = zero_zero_real )
% 15.55/8.64        = ( member_real @ X3 @ ring_1_Ints_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9036_unset__bit__int__def,axiom,
% 15.55/8.64      ( bit_se4203085406695923979it_int
% 15.55/8.64      = ( ^ [N3: nat,K3: int] : ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9037_push__bit__nat__def,axiom,
% 15.55/8.64      ( bit_se547839408752420682it_nat
% 15.55/8.64      = ( ^ [N3: nat,M3: nat] : ( times_times_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9038_push__bit__int__def,axiom,
% 15.55/8.64      ( bit_se545348938243370406it_int
% 15.55/8.64      = ( ^ [N3: nat,K3: int] : ( times_times_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9039_push__bit__minus__one,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.64        = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9040_sin__integer__2pi,axiom,
% 15.55/8.64      ! [N: real] :
% 15.55/8.64        ( ( member_real @ N @ ring_1_Ints_real )
% 15.55/8.64       => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 15.55/8.64          = zero_zero_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9041_cos__integer__2pi,axiom,
% 15.55/8.64      ! [N: real] :
% 15.55/8.64        ( ( member_real @ N @ ring_1_Ints_real )
% 15.55/8.64       => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 15.55/8.64          = one_one_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9042_int__of__nat__def,axiom,
% 15.55/8.64      code_T6385005292777649522of_nat = semiri1314217659103216013at_int ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9043_Cauchy__iff2,axiom,
% 15.55/8.64      ( topolo4055970368930404560y_real
% 15.55/8.64      = ( ^ [X8: nat > real] :
% 15.55/8.64          ! [J3: nat] :
% 15.55/8.64          ? [M9: nat] :
% 15.55/8.64          ! [M3: nat] :
% 15.55/8.64            ( ( ord_less_eq_nat @ M9 @ M3 )
% 15.55/8.64           => ! [N3: nat] :
% 15.55/8.64                ( ( ord_less_eq_nat @ M9 @ N3 )
% 15.55/8.64               => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X8 @ M3 ) @ ( X8 @ N3 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9044_Sum__Ico__nat,axiom,
% 15.55/8.64      ! [M: nat,N: nat] :
% 15.55/8.64        ( ( groups3542108847815614940at_nat
% 15.55/8.64          @ ^ [X: nat] : X
% 15.55/8.64          @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 15.55/8.64        = ( 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 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9045_ex__nat__less__eq,axiom,
% 15.55/8.64      ! [N: nat,P: nat > $o] :
% 15.55/8.64        ( ( ? [M3: nat] :
% 15.55/8.64              ( ( ord_less_nat @ M3 @ N )
% 15.55/8.64              & ( P @ M3 ) ) )
% 15.55/8.64        = ( ? [X: nat] :
% 15.55/8.64              ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 15.55/8.64              & ( P @ X ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9046_all__nat__less__eq,axiom,
% 15.55/8.64      ! [N: nat,P: nat > $o] :
% 15.55/8.64        ( ( ! [M3: nat] :
% 15.55/8.64              ( ( ord_less_nat @ M3 @ N )
% 15.55/8.64             => ( P @ M3 ) ) )
% 15.55/8.64        = ( ! [X: nat] :
% 15.55/8.64              ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 15.55/8.64             => ( P @ X ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9047_lessThan__atLeast0,axiom,
% 15.55/8.64      ( set_ord_lessThan_nat
% 15.55/8.64      = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9048_atLeastLessThan0,axiom,
% 15.55/8.64      ! [M: nat] :
% 15.55/8.64        ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 15.55/8.64        = bot_bot_set_nat ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9049_atLeast0__lessThan__Suc,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 15.55/8.64        = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9050_subset__eq__atLeast0__lessThan__finite,axiom,
% 15.55/8.64      ! [N4: set_nat,N: nat] :
% 15.55/8.64        ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 15.55/8.64       => ( finite_finite_nat @ N4 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9051_atLeastLessThanSuc,axiom,
% 15.55/8.64      ! [M: nat,N: nat] :
% 15.55/8.64        ( ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.64         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 15.55/8.64            = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 15.55/8.64        & ( ~ ( ord_less_eq_nat @ M @ N )
% 15.55/8.64         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 15.55/8.64            = bot_bot_set_nat ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9052_prod__Suc__fact,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 15.55/8.64        = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9053_prod__Suc__Suc__fact,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 15.55/8.64        = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9054_atLeastLessThan__nat__numeral,axiom,
% 15.55/8.64      ! [M: nat,K: num] :
% 15.55/8.64        ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 15.55/8.64         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 15.55/8.64            = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 15.55/8.64        & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 15.55/8.64         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 15.55/8.64            = bot_bot_set_nat ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9055_atLeast1__lessThan__eq__remove0,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 15.55/8.64        = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9056_sum__power2,axiom,
% 15.55/8.64      ! [K: nat] :
% 15.55/8.64        ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 15.55/8.64        = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9057_Chebyshev__sum__upper__nat,axiom,
% 15.55/8.64      ! [N: nat,A: nat > nat,B: nat > nat] :
% 15.55/8.64        ( ! [I3: nat,J2: nat] :
% 15.55/8.64            ( ( ord_less_eq_nat @ I3 @ J2 )
% 15.55/8.64           => ( ( ord_less_nat @ J2 @ N )
% 15.55/8.64             => ( ord_less_eq_nat @ ( A @ I3 ) @ ( A @ J2 ) ) ) )
% 15.55/8.64       => ( ! [I3: nat,J2: nat] :
% 15.55/8.64              ( ( ord_less_eq_nat @ I3 @ J2 )
% 15.55/8.64             => ( ( ord_less_nat @ J2 @ N )
% 15.55/8.64               => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I3 ) ) ) )
% 15.55/8.64         => ( ord_less_eq_nat
% 15.55/8.64            @ ( times_times_nat @ N
% 15.55/8.64              @ ( groups3542108847815614940at_nat
% 15.55/8.64                @ ^ [I4: nat] : ( times_times_nat @ ( A @ I4 ) @ ( B @ I4 ) )
% 15.55/8.64                @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 15.55/8.64            @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9058_finite__atLeastZeroLessThan__int,axiom,
% 15.55/8.64      ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9059_VEBT_Osize_I3_J,axiom,
% 15.55/8.64      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 15.55/8.64        ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 15.55/8.64        = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9060_valid__eq,axiom,
% 15.55/8.64      vEBT_VEBT_valid = vEBT_invar_vebt ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9061_valid__eq1,axiom,
% 15.55/8.64      ! [T: vEBT_VEBT,D3: nat] :
% 15.55/8.64        ( ( vEBT_invar_vebt @ T @ D3 )
% 15.55/8.64       => ( vEBT_VEBT_valid @ T @ D3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9062_valid__eq2,axiom,
% 15.55/8.64      ! [T: vEBT_VEBT,D3: nat] :
% 15.55/8.64        ( ( vEBT_VEBT_valid @ T @ D3 )
% 15.55/8.64       => ( vEBT_invar_vebt @ T @ D3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9063_VEBT_Osize__gen_I1_J,axiom,
% 15.55/8.64      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 15.55/8.64        ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 15.55/8.64        = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9064_Code__Target__Int_Opositive__def,axiom,
% 15.55/8.64      code_Target_positive = numeral_numeral_int ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9065_VEBT_Osize__gen_I2_J,axiom,
% 15.55/8.64      ! [X21: $o,X222: $o] :
% 15.55/8.64        ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 15.55/8.64        = zero_zero_nat ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9066_csqrt_Osimps_I1_J,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( re @ ( csqrt @ Z ) )
% 15.55/8.64        = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9067_divmod__step__integer__def,axiom,
% 15.55/8.64      ( unique4921790084139445826nteger
% 15.55/8.64      = ( ^ [L2: num] :
% 15.55/8.64            ( produc6916734918728496179nteger
% 15.55/8.64            @ ^ [Q5: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9068_complex__Re__of__nat,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( re @ ( semiri8010041392384452111omplex @ N ) )
% 15.55/8.64        = ( semiri5074537144036343181t_real @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9069_complex__Re__numeral,axiom,
% 15.55/8.64      ! [V: num] :
% 15.55/8.64        ( ( re @ ( numera6690914467698888265omplex @ V ) )
% 15.55/8.64        = ( numeral_numeral_real @ V ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9070_Re__divide__of__nat,axiom,
% 15.55/8.64      ! [Z: complex,N: nat] :
% 15.55/8.64        ( ( re @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N ) ) )
% 15.55/8.64        = ( divide_divide_real @ ( re @ Z ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9071_Re__divide__numeral,axiom,
% 15.55/8.64      ! [Z: complex,W: num] :
% 15.55/8.64        ( ( re @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 15.55/8.64        = ( divide_divide_real @ ( re @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9072_cos__Arg__i__mult__zero,axiom,
% 15.55/8.64      ! [Y3: complex] :
% 15.55/8.64        ( ( Y3 != zero_zero_complex )
% 15.55/8.64       => ( ( ( re @ Y3 )
% 15.55/8.64            = zero_zero_real )
% 15.55/8.64         => ( ( cos_real @ ( arg @ Y3 ) )
% 15.55/8.64            = zero_zero_real ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9073_sgn__integer__code,axiom,
% 15.55/8.64      ( sgn_sgn_Code_integer
% 15.55/8.64      = ( ^ [K3: code_integer] : ( if_Code_integer @ ( K3 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9074_times__integer__code_I2_J,axiom,
% 15.55/8.64      ! [L: code_integer] :
% 15.55/8.64        ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L )
% 15.55/8.64        = zero_z3403309356797280102nteger ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9075_times__integer__code_I1_J,axiom,
% 15.55/8.64      ! [K: code_integer] :
% 15.55/8.64        ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 15.55/8.64        = zero_z3403309356797280102nteger ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9076_minus__integer__code_I2_J,axiom,
% 15.55/8.64      ! [L: code_integer] :
% 15.55/8.64        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L )
% 15.55/8.64        = ( uminus1351360451143612070nteger @ L ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9077_minus__integer__code_I1_J,axiom,
% 15.55/8.64      ! [K: code_integer] :
% 15.55/8.64        ( ( minus_8373710615458151222nteger @ K @ zero_z3403309356797280102nteger )
% 15.55/8.64        = K ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9078_less__eq__integer__code_I1_J,axiom,
% 15.55/8.64      ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9079_plus__integer__code_I2_J,axiom,
% 15.55/8.64      ! [L: code_integer] :
% 15.55/8.64        ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L )
% 15.55/8.64        = L ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9080_plus__integer__code_I1_J,axiom,
% 15.55/8.64      ! [K: code_integer] :
% 15.55/8.64        ( ( plus_p5714425477246183910nteger @ K @ zero_z3403309356797280102nteger )
% 15.55/8.64        = K ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9081_imaginary__unit_Osimps_I1_J,axiom,
% 15.55/8.64      ( ( re @ imaginary_unit )
% 15.55/8.64      = zero_zero_real ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9082_complex__Re__le__cmod,axiom,
% 15.55/8.64      ! [X3: complex] : ( ord_less_eq_real @ ( re @ X3 ) @ ( real_V1022390504157884413omplex @ X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9083_zero__complex_Osimps_I1_J,axiom,
% 15.55/8.64      ( ( re @ zero_zero_complex )
% 15.55/8.64      = zero_zero_real ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9084_abs__Re__le__cmod,axiom,
% 15.55/8.64      ! [X3: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X3 ) ) @ ( real_V1022390504157884413omplex @ X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9085_Re__csqrt,axiom,
% 15.55/8.64      ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9086_zero__natural_Orsp,axiom,
% 15.55/8.64      zero_zero_nat = zero_zero_nat ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9087_zero__integer_Orsp,axiom,
% 15.55/8.64      zero_zero_int = zero_zero_int ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9088_cmod__plus__Re__le__0__iff,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 15.55/8.64        = ( ( re @ Z )
% 15.55/8.64          = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9089_cos__n__Re__cis__pow__n,axiom,
% 15.55/8.64      ! [N: nat,A: real] :
% 15.55/8.64        ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 15.55/8.64        = ( re @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9090_csqrt_Ocode,axiom,
% 15.55/8.64      ( csqrt
% 15.55/8.64      = ( ^ [Z6: complex] :
% 15.55/8.64            ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z6 ) @ ( re @ Z6 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.64            @ ( times_times_real
% 15.55/8.64              @ ( if_real
% 15.55/8.64                @ ( ( im @ Z6 )
% 15.55/8.64                  = zero_zero_real )
% 15.55/8.64                @ one_one_real
% 15.55/8.64                @ ( sgn_sgn_real @ ( im @ Z6 ) ) )
% 15.55/8.64              @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z6 ) @ ( re @ Z6 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9091_csqrt_Osimps_I2_J,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( im @ ( csqrt @ Z ) )
% 15.55/8.64        = ( times_times_real
% 15.55/8.64          @ ( if_real
% 15.55/8.64            @ ( ( im @ Z )
% 15.55/8.64              = zero_zero_real )
% 15.55/8.64            @ one_one_real
% 15.55/8.64            @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 15.55/8.64          @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9092_integer__of__int__code,axiom,
% 15.55/8.64      ( code_integer_of_int
% 15.55/8.64      = ( ^ [K3: int] :
% 15.55/8.64            ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 15.55/8.64            @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 15.55/8.64              @ ( if_Code_integer
% 15.55/8.64                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 15.55/8.64                  = zero_zero_int )
% 15.55/8.64                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 15.55/8.64                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9093_complex__Im__fact,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( im @ ( semiri5044797733671781792omplex @ N ) )
% 15.55/8.64        = zero_zero_real ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9094_complex__Im__of__int,axiom,
% 15.55/8.64      ! [Z: int] :
% 15.55/8.64        ( ( im @ ( ring_17405671764205052669omplex @ Z ) )
% 15.55/8.64        = zero_zero_real ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9095_Im__complex__of__real,axiom,
% 15.55/8.64      ! [Z: real] :
% 15.55/8.64        ( ( im @ ( real_V4546457046886955230omplex @ Z ) )
% 15.55/8.64        = zero_zero_real ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9096_Im__power__real,axiom,
% 15.55/8.64      ! [X3: complex,N: nat] :
% 15.55/8.64        ( ( ( im @ X3 )
% 15.55/8.64          = zero_zero_real )
% 15.55/8.64       => ( ( im @ ( power_power_complex @ X3 @ N ) )
% 15.55/8.64          = zero_zero_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9097_complex__Im__numeral,axiom,
% 15.55/8.64      ! [V: num] :
% 15.55/8.64        ( ( im @ ( numera6690914467698888265omplex @ V ) )
% 15.55/8.64        = zero_zero_real ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9098_complex__Im__of__nat,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( im @ ( semiri8010041392384452111omplex @ N ) )
% 15.55/8.64        = zero_zero_real ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9099_Re__power__real,axiom,
% 15.55/8.64      ! [X3: complex,N: nat] :
% 15.55/8.64        ( ( ( im @ X3 )
% 15.55/8.64          = zero_zero_real )
% 15.55/8.64       => ( ( re @ ( power_power_complex @ X3 @ N ) )
% 15.55/8.64          = ( power_power_real @ ( re @ X3 ) @ N ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9100_Im__divide__numeral,axiom,
% 15.55/8.64      ! [Z: complex,W: num] :
% 15.55/8.64        ( ( im @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 15.55/8.64        = ( divide_divide_real @ ( im @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9101_Im__divide__of__nat,axiom,
% 15.55/8.64      ! [Z: complex,N: nat] :
% 15.55/8.64        ( ( im @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N ) ) )
% 15.55/8.64        = ( divide_divide_real @ ( im @ Z ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9102_csqrt__of__real__nonneg,axiom,
% 15.55/8.64      ! [X3: complex] :
% 15.55/8.64        ( ( ( im @ X3 )
% 15.55/8.64          = zero_zero_real )
% 15.55/8.64       => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X3 ) )
% 15.55/8.64         => ( ( csqrt @ X3 )
% 15.55/8.64            = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X3 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9103_csqrt__minus,axiom,
% 15.55/8.64      ! [X3: complex] :
% 15.55/8.64        ( ( ( ord_less_real @ ( im @ X3 ) @ zero_zero_real )
% 15.55/8.64          | ( ( ( im @ X3 )
% 15.55/8.64              = zero_zero_real )
% 15.55/8.64            & ( ord_less_eq_real @ zero_zero_real @ ( re @ X3 ) ) ) )
% 15.55/8.64       => ( ( csqrt @ ( uminus1482373934393186551omplex @ X3 ) )
% 15.55/8.64          = ( times_times_complex @ imaginary_unit @ ( csqrt @ X3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9104_csqrt__of__real__nonpos,axiom,
% 15.55/8.64      ! [X3: complex] :
% 15.55/8.64        ( ( ( im @ X3 )
% 15.55/8.64          = zero_zero_real )
% 15.55/8.64       => ( ( ord_less_eq_real @ ( re @ X3 ) @ zero_zero_real )
% 15.55/8.64         => ( ( csqrt @ X3 )
% 15.55/8.64            = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X3 ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9105_zero__integer__def,axiom,
% 15.55/8.64      ( zero_z3403309356797280102nteger
% 15.55/8.64      = ( code_integer_of_int @ zero_zero_int ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9106_uminus__integer__code_I1_J,axiom,
% 15.55/8.64      ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 15.55/8.64      = zero_z3403309356797280102nteger ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9107_abs__integer__code,axiom,
% 15.55/8.64      ( abs_abs_Code_integer
% 15.55/8.64      = ( ^ [K3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K3 ) @ K3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9108_less__integer__code_I1_J,axiom,
% 15.55/8.64      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9109_less__integer_Oabs__eq,axiom,
% 15.55/8.64      ! [Xa: int,X3: int] :
% 15.55/8.64        ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X3 ) )
% 15.55/8.64        = ( ord_less_int @ Xa @ X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9110_zero__complex_Osimps_I2_J,axiom,
% 15.55/8.64      ( ( im @ zero_zero_complex )
% 15.55/8.64      = zero_zero_real ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9111_one__complex_Osimps_I2_J,axiom,
% 15.55/8.64      ( ( im @ one_one_complex )
% 15.55/8.64      = zero_zero_real ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9112_less__eq__integer_Oabs__eq,axiom,
% 15.55/8.64      ! [Xa: int,X3: int] :
% 15.55/8.64        ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X3 ) )
% 15.55/8.64        = ( ord_less_eq_int @ Xa @ X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9113_complex__is__Int__iff,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( member_complex @ Z @ ring_1_Ints_complex )
% 15.55/8.64        = ( ( ( im @ Z )
% 15.55/8.64            = zero_zero_real )
% 15.55/8.64          & ? [I4: int] :
% 15.55/8.64              ( ( re @ Z )
% 15.55/8.64              = ( ring_1_of_int_real @ I4 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9114_abs__Im__le__cmod,axiom,
% 15.55/8.64      ! [X3: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X3 ) ) @ ( real_V1022390504157884413omplex @ X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9115_Im__eq__0,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( ( abs_abs_real @ ( re @ Z ) )
% 15.55/8.64          = ( real_V1022390504157884413omplex @ Z ) )
% 15.55/8.64       => ( ( im @ Z )
% 15.55/8.64          = zero_zero_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9116_cmod__eq__Im,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( ( re @ Z )
% 15.55/8.64          = zero_zero_real )
% 15.55/8.64       => ( ( real_V1022390504157884413omplex @ Z )
% 15.55/8.64          = ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9117_cmod__eq__Re,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( ( im @ Z )
% 15.55/8.64          = zero_zero_real )
% 15.55/8.64       => ( ( real_V1022390504157884413omplex @ Z )
% 15.55/8.64          = ( abs_abs_real @ ( re @ Z ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9118_cmod__Re__le__iff,axiom,
% 15.55/8.64      ! [X3: complex,Y3: complex] :
% 15.55/8.64        ( ( ( im @ X3 )
% 15.55/8.64          = ( im @ Y3 ) )
% 15.55/8.64       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y3 ) )
% 15.55/8.64          = ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X3 ) ) @ ( abs_abs_real @ ( re @ Y3 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9119_cmod__Im__le__iff,axiom,
% 15.55/8.64      ! [X3: complex,Y3: complex] :
% 15.55/8.64        ( ( ( re @ X3 )
% 15.55/8.64          = ( re @ Y3 ) )
% 15.55/8.64       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y3 ) )
% 15.55/8.64          = ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X3 ) ) @ ( abs_abs_real @ ( im @ Y3 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9120_csqrt__principal,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 15.55/8.64        | ( ( ( re @ ( csqrt @ Z ) )
% 15.55/8.64            = zero_zero_real )
% 15.55/8.64          & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9121_cmod__le,axiom,
% 15.55/8.64      ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9122_sin__n__Im__cis__pow__n,axiom,
% 15.55/8.64      ! [N: nat,A: real] :
% 15.55/8.64        ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 15.55/8.64        = ( im @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9123_cmod__power2,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.64        = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9124_Im__power2,axiom,
% 15.55/8.64      ! [X3: complex] :
% 15.55/8.64        ( ( im @ ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.64        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X3 ) ) @ ( im @ X3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9125_Re__power2,axiom,
% 15.55/8.64      ! [X3: complex] :
% 15.55/8.64        ( ( re @ ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.64        = ( minus_minus_real @ ( power_power_real @ ( re @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9126_complex__eq__0,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( Z = zero_zero_complex )
% 15.55/8.64        = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.64          = zero_zero_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9127_norm__complex__def,axiom,
% 15.55/8.64      ( real_V1022390504157884413omplex
% 15.55/8.64      = ( ^ [Z6: complex] : ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( re @ Z6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9128_inverse__complex_Osimps_I1_J,axiom,
% 15.55/8.64      ! [X3: complex] :
% 15.55/8.64        ( ( re @ ( invers8013647133539491842omplex @ X3 ) )
% 15.55/8.64        = ( 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 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9129_complex__neq__0,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( Z != zero_zero_complex )
% 15.55/8.64        = ( 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 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9130_Re__divide,axiom,
% 15.55/8.64      ! [X3: complex,Y3: complex] :
% 15.55/8.64        ( ( re @ ( divide1717551699836669952omplex @ X3 @ Y3 ) )
% 15.55/8.64        = ( 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 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9131_csqrt__unique,axiom,
% 15.55/8.64      ! [W: complex,Z: complex] :
% 15.55/8.64        ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 15.55/8.64          = Z )
% 15.55/8.64       => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 15.55/8.64            | ( ( ( re @ W )
% 15.55/8.64                = zero_zero_real )
% 15.55/8.64              & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 15.55/8.64         => ( ( csqrt @ Z )
% 15.55/8.64            = W ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9132_csqrt__square,axiom,
% 15.55/8.64      ! [B: complex] :
% 15.55/8.64        ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 15.55/8.64          | ( ( ( re @ B )
% 15.55/8.64              = zero_zero_real )
% 15.55/8.64            & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 15.55/8.64       => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.64          = B ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9133_inverse__complex_Osimps_I2_J,axiom,
% 15.55/8.64      ! [X3: complex] :
% 15.55/8.64        ( ( im @ ( invers8013647133539491842omplex @ X3 ) )
% 15.55/8.64        = ( 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 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9134_Im__divide,axiom,
% 15.55/8.64      ! [X3: complex,Y3: complex] :
% 15.55/8.64        ( ( im @ ( divide1717551699836669952omplex @ X3 @ Y3 ) )
% 15.55/8.64        = ( 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 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9135_complex__abs__le__norm,axiom,
% 15.55/8.64      ! [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 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9136_complex__unit__circle,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( Z != zero_zero_complex )
% 15.55/8.64       => ( ( 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 ) ) ) )
% 15.55/8.64          = one_one_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9137_inverse__complex_Ocode,axiom,
% 15.55/8.64      ( invers8013647133539491842omplex
% 15.55/8.64      = ( ^ [X: complex] : ( complex2 @ ( divide_divide_real @ ( re @ X ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9138_Complex__divide,axiom,
% 15.55/8.64      ( divide1717551699836669952omplex
% 15.55/8.64      = ( ^ [X: complex,Y: complex] : ( complex2 @ ( 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 ) ) ) ) ) @ ( 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 ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9139_Im__Reals__divide,axiom,
% 15.55/8.64      ! [R2: complex,Z: complex] :
% 15.55/8.64        ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 15.55/8.64       => ( ( im @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 15.55/8.64          = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R2 ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9140_Re__Reals__divide,axiom,
% 15.55/8.64      ! [R2: complex,Z: complex] :
% 15.55/8.64        ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 15.55/8.64       => ( ( re @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 15.55/8.64          = ( divide_divide_real @ ( times_times_real @ ( re @ R2 ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9141_complex__mult__cnj,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 15.55/8.64        = ( real_V4546457046886955230omplex @ ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9142_complex__cnj__zero,axiom,
% 15.55/8.64      ( ( cnj @ zero_zero_complex )
% 15.55/8.64      = zero_zero_complex ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9143_complex__cnj__zero__iff,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( ( cnj @ Z )
% 15.55/8.64          = zero_zero_complex )
% 15.55/8.64        = ( Z = zero_zero_complex ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9144_complex__cnj__power,axiom,
% 15.55/8.64      ! [X3: complex,N: nat] :
% 15.55/8.64        ( ( cnj @ ( power_power_complex @ X3 @ N ) )
% 15.55/8.64        = ( power_power_complex @ ( cnj @ X3 ) @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9145_complex__In__mult__cnj__zero,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( im @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 15.55/8.64        = zero_zero_real ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9146_imaginary__eq__real__iff,axiom,
% 15.55/8.64      ! [Y3: complex,X3: complex] :
% 15.55/8.64        ( ( member_complex @ Y3 @ real_V2521375963428798218omplex )
% 15.55/8.64       => ( ( member_complex @ X3 @ real_V2521375963428798218omplex )
% 15.55/8.64         => ( ( ( times_times_complex @ imaginary_unit @ Y3 )
% 15.55/8.64              = X3 )
% 15.55/8.64            = ( ( X3 = zero_zero_complex )
% 15.55/8.64              & ( Y3 = zero_zero_complex ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9147_real__eq__imaginary__iff,axiom,
% 15.55/8.64      ! [Y3: complex,X3: complex] :
% 15.55/8.64        ( ( member_complex @ Y3 @ real_V2521375963428798218omplex )
% 15.55/8.64       => ( ( member_complex @ X3 @ real_V2521375963428798218omplex )
% 15.55/8.64         => ( ( X3
% 15.55/8.64              = ( times_times_complex @ imaginary_unit @ Y3 ) )
% 15.55/8.64            = ( ( X3 = zero_zero_complex )
% 15.55/8.64              & ( Y3 = zero_zero_complex ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9148_complex__is__Real__iff,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( member_complex @ Z @ real_V2521375963428798218omplex )
% 15.55/8.64        = ( ( im @ Z )
% 15.55/8.64          = zero_zero_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9149_Complex__in__Reals,axiom,
% 15.55/8.64      ! [X3: real] : ( member_complex @ ( complex2 @ X3 @ zero_zero_real ) @ real_V2521375963428798218omplex ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9150_Re__complex__div__eq__0,axiom,
% 15.55/8.64      ! [A: complex,B: complex] :
% 15.55/8.64        ( ( ( re @ ( divide1717551699836669952omplex @ A @ B ) )
% 15.55/8.64          = zero_zero_real )
% 15.55/8.64        = ( ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 15.55/8.64          = zero_zero_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9151_Im__complex__div__eq__0,axiom,
% 15.55/8.64      ! [A: complex,B: complex] :
% 15.55/8.64        ( ( ( im @ ( divide1717551699836669952omplex @ A @ B ) )
% 15.55/8.64          = zero_zero_real )
% 15.55/8.64        = ( ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 15.55/8.64          = zero_zero_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9152_Re__complex__div__lt__0,axiom,
% 15.55/8.64      ! [A: complex,B: complex] :
% 15.55/8.64        ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 15.55/8.64        = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9153_Re__complex__div__gt__0,axiom,
% 15.55/8.64      ! [A: complex,B: complex] :
% 15.55/8.64        ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 15.55/8.64        = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9154_Re__complex__div__ge__0,axiom,
% 15.55/8.64      ! [A: complex,B: complex] :
% 15.55/8.64        ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 15.55/8.64        = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9155_Re__complex__div__le__0,axiom,
% 15.55/8.64      ! [A: complex,B: complex] :
% 15.55/8.64        ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 15.55/8.64        = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9156_Im__complex__div__lt__0,axiom,
% 15.55/8.64      ! [A: complex,B: complex] :
% 15.55/8.64        ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 15.55/8.64        = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9157_Im__complex__div__gt__0,axiom,
% 15.55/8.64      ! [A: complex,B: complex] :
% 15.55/8.64        ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 15.55/8.64        = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9158_Im__complex__div__ge__0,axiom,
% 15.55/8.64      ! [A: complex,B: complex] :
% 15.55/8.64        ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 15.55/8.64        = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9159_Im__complex__div__le__0,axiom,
% 15.55/8.64      ! [A: complex,B: complex] :
% 15.55/8.64        ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 15.55/8.64        = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9160_complex__mod__mult__cnj,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 15.55/8.64        = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9161_complex__div__gt__0,axiom,
% 15.55/8.64      ! [A: complex,B: complex] :
% 15.55/8.64        ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 15.55/8.64          = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 15.55/8.64        & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 15.55/8.64          = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9162_complex__norm__square,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.64        = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9163_complex__add__cnj,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 15.55/8.64        = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9164_complex__diff__cnj,axiom,
% 15.55/8.64      ! [Z: complex] :
% 15.55/8.64        ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 15.55/8.64        = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9165_complex__div__cnj,axiom,
% 15.55/8.64      ( divide1717551699836669952omplex
% 15.55/8.64      = ( ^ [A4: complex,B3: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A4 @ ( cnj @ B3 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9166_cnj__add__mult__eq__Re,axiom,
% 15.55/8.64      ! [Z: complex,W: complex] :
% 15.55/8.64        ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 15.55/8.64        = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9167_int__of__integer__code,axiom,
% 15.55/8.64      ( code_int_of_integer
% 15.55/8.64      = ( ^ [K3: code_integer] :
% 15.55/8.64            ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 15.55/8.64            @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 15.55/8.64              @ ( produc1553301316500091796er_int
% 15.55/8.64                @ ^ [L2: code_integer,J3: code_integer] : ( if_int @ ( J3 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ one_one_int ) )
% 15.55/8.64                @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9168_num__of__integer__code,axiom,
% 15.55/8.64      ( code_num_of_integer
% 15.55/8.64      = ( ^ [K3: code_integer] :
% 15.55/8.64            ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 15.55/8.64            @ ( produc7336495610019696514er_num
% 15.55/8.64              @ ^ [L2: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ one ) )
% 15.55/8.64              @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9169_setceilmax,axiom,
% 15.55/8.64      ! [S: vEBT_VEBT,M: nat,Listy: list_VEBT_VEBT,N: nat] :
% 15.55/8.64        ( ( vEBT_invar_vebt @ S @ M )
% 15.55/8.64       => ( ! [X4: vEBT_VEBT] :
% 15.55/8.64              ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Listy ) )
% 15.55/8.64             => ( vEBT_invar_vebt @ X4 @ N ) )
% 15.55/8.64         => ( ( M
% 15.55/8.64              = ( suc @ N ) )
% 15.55/8.64           => ( ! [X4: vEBT_VEBT] :
% 15.55/8.64                  ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Listy ) )
% 15.55/8.64                 => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ X4 ) )
% 15.55/8.64                    = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 15.55/8.64             => ( ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ S ) )
% 15.55/8.64                  = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) )
% 15.55/8.64               => ( ( semiri1314217659103216013at_int @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ S @ ( set_VEBT_VEBT2 @ Listy ) ) ) ) )
% 15.55/8.64                  = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9170_height__compose__list,axiom,
% 15.55/8.64      ! [T: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 15.55/8.64        ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 15.55/8.64       => ( ord_less_eq_nat @ ( vEBT_VEBT_height @ T ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary @ ( set_VEBT_VEBT2 @ TreeList2 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9171_int__of__integer__of__nat,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( code_int_of_integer @ ( semiri4939895301339042750nteger @ N ) )
% 15.55/8.64        = ( semiri1314217659103216013at_int @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9172_max__ins__scaled,axiom,
% 15.55/8.64      ! [N: nat,X14: vEBT_VEBT,M: nat,X13: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( vEBT_VEBT_height @ X14 ) ) @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ ( lattic8265883725875713057ax_nat @ ( insert_nat @ ( vEBT_VEBT_height @ X14 ) @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9173_height__i__max,axiom,
% 15.55/8.64      ! [I: nat,X13: list_VEBT_VEBT,Foo: nat] :
% 15.55/8.64        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 15.55/8.64       => ( ord_less_eq_nat @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I ) ) @ ( ord_max_nat @ Foo @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9174_max__idx__list,axiom,
% 15.55/8.64      ! [I: nat,X13: list_VEBT_VEBT,N: nat,X14: vEBT_VEBT] :
% 15.55/8.64        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 15.55/8.64       => ( ord_less_eq_nat @ ( times_times_nat @ N @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I ) ) ) @ ( suc @ ( suc @ ( times_times_nat @ N @ ( ord_max_nat @ ( vEBT_VEBT_height @ X14 ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9175_zero__integer_Orep__eq,axiom,
% 15.55/8.64      ( ( code_int_of_integer @ zero_z3403309356797280102nteger )
% 15.55/8.64      = zero_zero_int ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9176_int__of__integer__numeral,axiom,
% 15.55/8.64      ! [K: num] :
% 15.55/8.64        ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 15.55/8.64        = ( numeral_numeral_int @ K ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9177_Max__divisors__self__nat,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( N != zero_zero_nat )
% 15.55/8.64       => ( ( lattic8265883725875713057ax_nat
% 15.55/8.64            @ ( collect_nat
% 15.55/8.64              @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ N ) ) )
% 15.55/8.64          = N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9178_integer__less__iff,axiom,
% 15.55/8.64      ( ord_le6747313008572928689nteger
% 15.55/8.64      = ( ^ [K3: code_integer,L2: code_integer] : ( ord_less_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9179_less__integer_Orep__eq,axiom,
% 15.55/8.64      ( ord_le6747313008572928689nteger
% 15.55/8.64      = ( ^ [X: code_integer,Xa4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9180_integer__less__eq__iff,axiom,
% 15.55/8.64      ( ord_le3102999989581377725nteger
% 15.55/8.64      = ( ^ [K3: code_integer,L2: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9181_less__eq__integer_Orep__eq,axiom,
% 15.55/8.64      ( ord_le3102999989581377725nteger
% 15.55/8.64      = ( ^ [X: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9182_VEBT__internal_Oheight_Oelims,axiom,
% 15.55/8.64      ! [X3: vEBT_VEBT,Y3: nat] :
% 15.55/8.64        ( ( ( vEBT_VEBT_height @ X3 )
% 15.55/8.64          = Y3 )
% 15.55/8.64       => ( ( ? [A5: $o,B4: $o] :
% 15.55/8.64                ( X3
% 15.55/8.64                = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.64           => ( Y3 != zero_zero_nat ) )
% 15.55/8.64         => ~ ! [Uu: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.64                ( ( X3
% 15.55/8.64                  = ( vEBT_Node @ Uu @ Deg2 @ TreeList3 @ Summary2 ) )
% 15.55/8.64               => ( Y3
% 15.55/8.64                 != ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9183_divide__nat__def,axiom,
% 15.55/8.64      ( divide_divide_nat
% 15.55/8.64      = ( ^ [M3: nat,N3: nat] :
% 15.55/8.64            ( if_nat @ ( N3 = zero_zero_nat ) @ zero_zero_nat
% 15.55/8.64            @ ( lattic8265883725875713057ax_nat
% 15.55/8.64              @ ( collect_nat
% 15.55/8.64                @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N3 ) @ M3 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9184_nat__of__integer__code,axiom,
% 15.55/8.64      ( code_nat_of_integer
% 15.55/8.64      = ( ^ [K3: code_integer] :
% 15.55/8.64            ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 15.55/8.64            @ ( produc1555791787009142072er_nat
% 15.55/8.64              @ ^ [L2: code_integer,J3: code_integer] : ( if_nat @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ one_one_nat ) )
% 15.55/8.64              @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9185_VEBT__internal_Oheight_Opelims,axiom,
% 15.55/8.64      ! [X3: vEBT_VEBT,Y3: nat] :
% 15.55/8.64        ( ( ( vEBT_VEBT_height @ X3 )
% 15.55/8.64          = Y3 )
% 15.55/8.64       => ( ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ X3 )
% 15.55/8.64         => ( ! [A5: $o,B4: $o] :
% 15.55/8.64                ( ( X3
% 15.55/8.64                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.64               => ( ( Y3 = zero_zero_nat )
% 15.55/8.64                 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Leaf @ A5 @ B4 ) ) ) )
% 15.55/8.64           => ~ ! [Uu: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.64                  ( ( X3
% 15.55/8.64                    = ( vEBT_Node @ Uu @ Deg2 @ TreeList3 @ Summary2 ) )
% 15.55/8.64                 => ( ( Y3
% 15.55/8.64                      = ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList3 ) ) ) ) ) )
% 15.55/8.64                   => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Node @ Uu @ Deg2 @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9186_bij__betw__Suc,axiom,
% 15.55/8.64      ! [M7: set_nat,N4: set_nat] :
% 15.55/8.64        ( ( bij_betw_nat_nat @ suc @ M7 @ N4 )
% 15.55/8.64        = ( ( image_nat_nat @ suc @ M7 )
% 15.55/8.64          = N4 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9187_Max__divisors__self__int,axiom,
% 15.55/8.64      ! [N: int] :
% 15.55/8.64        ( ( N != zero_zero_int )
% 15.55/8.64       => ( ( lattic8263393255366662781ax_int
% 15.55/8.64            @ ( collect_int
% 15.55/8.64              @ ^ [D4: int] : ( dvd_dvd_int @ D4 @ N ) ) )
% 15.55/8.64          = ( abs_abs_int @ N ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9188_of__nat__of__integer,axiom,
% 15.55/8.64      ! [K: code_integer] :
% 15.55/8.64        ( ( semiri4939895301339042750nteger @ ( code_nat_of_integer @ K ) )
% 15.55/8.64        = ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ K ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9189_nat__of__integer__non__positive,axiom,
% 15.55/8.64      ! [K: code_integer] :
% 15.55/8.64        ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 15.55/8.64       => ( ( code_nat_of_integer @ K )
% 15.55/8.64          = zero_zero_nat ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9190_zero__notin__Suc__image,axiom,
% 15.55/8.64      ! [A3: set_nat] :
% 15.55/8.64        ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9191_image__int__atLeastAtMost,axiom,
% 15.55/8.64      ! [A: nat,B: nat] :
% 15.55/8.64        ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 15.55/8.64        = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9192_image__int__atLeastLessThan,axiom,
% 15.55/8.64      ! [A: nat,B: nat] :
% 15.55/8.64        ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 15.55/8.64        = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9193_nat__of__integer__code__post_I1_J,axiom,
% 15.55/8.64      ( ( code_nat_of_integer @ zero_z3403309356797280102nteger )
% 15.55/8.64      = zero_zero_nat ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9194_nat__of__integer_Orep__eq,axiom,
% 15.55/8.64      ( code_nat_of_integer
% 15.55/8.64      = ( ^ [X: code_integer] : ( nat2 @ ( code_int_of_integer @ X ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9195_nat__of__integer_Oabs__eq,axiom,
% 15.55/8.64      ! [X3: int] :
% 15.55/8.64        ( ( code_nat_of_integer @ ( code_integer_of_int @ X3 ) )
% 15.55/8.64        = ( nat2 @ X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9196_nat__of__integer__code__post_I3_J,axiom,
% 15.55/8.64      ! [K: num] :
% 15.55/8.64        ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 15.55/8.64        = ( numeral_numeral_nat @ K ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9197_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 15.55/8.64        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9198_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 15.55/8.64        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9199_lessThan__Suc__eq__insert__0,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 15.55/8.64        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9200_atMost__Suc__eq__insert__0,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 15.55/8.64        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9201_image__add__int__atLeastLessThan,axiom,
% 15.55/8.64      ! [L: int,U: int] :
% 15.55/8.64        ( ( image_int_int
% 15.55/8.64          @ ^ [X: int] : ( plus_plus_int @ X @ L )
% 15.55/8.64          @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 15.55/8.64        = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9202_image__atLeastZeroLessThan__int,axiom,
% 15.55/8.64      ! [U: int] :
% 15.55/8.64        ( ( ord_less_eq_int @ zero_zero_int @ U )
% 15.55/8.64       => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 15.55/8.64          = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9203_image__minus__const__atLeastLessThan__nat,axiom,
% 15.55/8.64      ! [C: nat,Y3: nat,X3: nat] :
% 15.55/8.64        ( ( ( ord_less_nat @ C @ Y3 )
% 15.55/8.64         => ( ( image_nat_nat
% 15.55/8.64              @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 15.55/8.64              @ ( set_or4665077453230672383an_nat @ X3 @ Y3 ) )
% 15.55/8.64            = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X3 @ C ) @ ( minus_minus_nat @ Y3 @ C ) ) ) )
% 15.55/8.64        & ( ~ ( ord_less_nat @ C @ Y3 )
% 15.55/8.64         => ( ( ( ord_less_nat @ X3 @ Y3 )
% 15.55/8.64             => ( ( image_nat_nat
% 15.55/8.64                  @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 15.55/8.64                  @ ( set_or4665077453230672383an_nat @ X3 @ Y3 ) )
% 15.55/8.64                = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 15.55/8.64            & ( ~ ( ord_less_nat @ X3 @ Y3 )
% 15.55/8.64             => ( ( image_nat_nat
% 15.55/8.64                  @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 15.55/8.64                  @ ( set_or4665077453230672383an_nat @ X3 @ Y3 ) )
% 15.55/8.64                = bot_bot_set_nat ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9204_vebt__maxt_Opelims,axiom,
% 15.55/8.64      ! [X3: vEBT_VEBT,Y3: option_nat] :
% 15.55/8.64        ( ( ( vEBT_vebt_maxt @ X3 )
% 15.55/8.64          = Y3 )
% 15.55/8.64       => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X3 )
% 15.55/8.64         => ( ! [A5: $o,B4: $o] :
% 15.55/8.64                ( ( X3
% 15.55/8.64                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.64               => ( ( ( B4
% 15.55/8.64                     => ( Y3
% 15.55/8.64                        = ( some_nat @ one_one_nat ) ) )
% 15.55/8.64                    & ( ~ B4
% 15.55/8.64                     => ( ( A5
% 15.55/8.64                         => ( Y3
% 15.55/8.64                            = ( some_nat @ zero_zero_nat ) ) )
% 15.55/8.64                        & ( ~ A5
% 15.55/8.64                         => ( Y3 = none_nat ) ) ) ) )
% 15.55/8.64                 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A5 @ B4 ) ) ) )
% 15.55/8.64           => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 15.55/8.64                  ( ( X3
% 15.55/8.64                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 15.55/8.64                 => ( ( Y3 = none_nat )
% 15.55/8.64                   => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) ) ) )
% 15.55/8.64             => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 15.55/8.64                    ( ( X3
% 15.55/8.64                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 15.55/8.64                   => ( ( Y3
% 15.55/8.64                        = ( some_nat @ Ma2 ) )
% 15.55/8.64                     => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9205_vebt__mint_Opelims,axiom,
% 15.55/8.64      ! [X3: vEBT_VEBT,Y3: option_nat] :
% 15.55/8.64        ( ( ( vEBT_vebt_mint @ X3 )
% 15.55/8.64          = Y3 )
% 15.55/8.64       => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X3 )
% 15.55/8.64         => ( ! [A5: $o,B4: $o] :
% 15.55/8.64                ( ( X3
% 15.55/8.64                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.64               => ( ( ( A5
% 15.55/8.64                     => ( Y3
% 15.55/8.64                        = ( some_nat @ zero_zero_nat ) ) )
% 15.55/8.64                    & ( ~ A5
% 15.55/8.64                     => ( ( B4
% 15.55/8.64                         => ( Y3
% 15.55/8.64                            = ( some_nat @ one_one_nat ) ) )
% 15.55/8.64                        & ( ~ B4
% 15.55/8.64                         => ( Y3 = none_nat ) ) ) ) )
% 15.55/8.64                 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A5 @ B4 ) ) ) )
% 15.55/8.64           => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 15.55/8.64                  ( ( X3
% 15.55/8.64                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 15.55/8.64                 => ( ( Y3 = none_nat )
% 15.55/8.64                   => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) ) ) )
% 15.55/8.64             => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 15.55/8.64                    ( ( X3
% 15.55/8.64                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 15.55/8.64                   => ( ( Y3
% 15.55/8.64                        = ( some_nat @ Mi2 ) )
% 15.55/8.64                     => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9206_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Opelims,axiom,
% 15.55/8.64      ! [X3: vEBT_VEBT,Y3: nat] :
% 15.55/8.64        ( ( ( vEBT_T_m_i_n_t @ X3 )
% 15.55/8.64          = Y3 )
% 15.55/8.64       => ( ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ X3 )
% 15.55/8.64         => ( ! [A5: $o,B4: $o] :
% 15.55/8.64                ( ( X3
% 15.55/8.64                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.64               => ( ( Y3
% 15.55/8.64                    = ( plus_plus_nat @ one_one_nat @ ( if_nat @ A5 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 15.55/8.64                 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Leaf @ A5 @ B4 ) ) ) )
% 15.55/8.64           => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 15.55/8.64                  ( ( X3
% 15.55/8.64                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 15.55/8.64                 => ( ( Y3 = one_one_nat )
% 15.55/8.64                   => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) ) ) )
% 15.55/8.64             => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 15.55/8.64                    ( ( X3
% 15.55/8.64                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 15.55/8.64                   => ( ( Y3 = one_one_nat )
% 15.55/8.64                     => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9207_card__Collect__less__nat,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( finite_card_nat
% 15.55/8.64          @ ( collect_nat
% 15.55/8.64            @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N ) ) )
% 15.55/8.64        = N ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9208_card__Collect__le__nat,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( finite_card_nat
% 15.55/8.64          @ ( collect_nat
% 15.55/8.64            @ ^ [I4: nat] : ( ord_less_eq_nat @ I4 @ N ) ) )
% 15.55/8.64        = ( suc @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9209_card__atLeastLessThan__int,axiom,
% 15.55/8.64      ! [L: int,U: int] :
% 15.55/8.64        ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L @ U ) )
% 15.55/8.64        = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9210_card__atLeastAtMost__int,axiom,
% 15.55/8.64      ! [L: int,U: int] :
% 15.55/8.64        ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 15.55/8.64        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9211_nat_Odisc__eq__case_I2_J,axiom,
% 15.55/8.64      ! [Nat: nat] :
% 15.55/8.64        ( ( Nat != zero_zero_nat )
% 15.55/8.64        = ( case_nat_o @ $false
% 15.55/8.64          @ ^ [Uu3: nat] : $true
% 15.55/8.64          @ Nat ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9212_nat_Odisc__eq__case_I1_J,axiom,
% 15.55/8.64      ! [Nat: nat] :
% 15.55/8.64        ( ( Nat = zero_zero_nat )
% 15.55/8.64        = ( case_nat_o @ $true
% 15.55/8.64          @ ^ [Uu3: nat] : $false
% 15.55/8.64          @ Nat ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9213_card__less__Suc2,axiom,
% 15.55/8.64      ! [M7: set_nat,I: nat] :
% 15.55/8.64        ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 15.55/8.64       => ( ( finite_card_nat
% 15.55/8.64            @ ( collect_nat
% 15.55/8.64              @ ^ [K3: nat] :
% 15.55/8.64                  ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 15.55/8.64                  & ( ord_less_nat @ K3 @ I ) ) ) )
% 15.55/8.64          = ( finite_card_nat
% 15.55/8.64            @ ( collect_nat
% 15.55/8.64              @ ^ [K3: nat] :
% 15.55/8.64                  ( ( member_nat @ K3 @ M7 )
% 15.55/8.64                  & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9214_card__less__Suc,axiom,
% 15.55/8.64      ! [M7: set_nat,I: nat] :
% 15.55/8.64        ( ( member_nat @ zero_zero_nat @ M7 )
% 15.55/8.64       => ( ( suc
% 15.55/8.64            @ ( finite_card_nat
% 15.55/8.64              @ ( collect_nat
% 15.55/8.64                @ ^ [K3: nat] :
% 15.55/8.64                    ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 15.55/8.64                    & ( ord_less_nat @ K3 @ I ) ) ) ) )
% 15.55/8.64          = ( finite_card_nat
% 15.55/8.64            @ ( collect_nat
% 15.55/8.64              @ ^ [K3: nat] :
% 15.55/8.64                  ( ( member_nat @ K3 @ M7 )
% 15.55/8.64                  & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9215_card__less,axiom,
% 15.55/8.64      ! [M7: set_nat,I: nat] :
% 15.55/8.64        ( ( member_nat @ zero_zero_nat @ M7 )
% 15.55/8.64       => ( ( finite_card_nat
% 15.55/8.64            @ ( collect_nat
% 15.55/8.64              @ ^ [K3: nat] :
% 15.55/8.64                  ( ( member_nat @ K3 @ M7 )
% 15.55/8.64                  & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) )
% 15.55/8.64         != zero_zero_nat ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9216_card__atLeastZeroLessThan__int,axiom,
% 15.55/8.64      ! [U: int] :
% 15.55/8.64        ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 15.55/8.64        = ( nat2 @ U ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9217_less__eq__nat_Osimps_I2_J,axiom,
% 15.55/8.64      ! [M: nat,N: nat] :
% 15.55/8.64        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 15.55/8.64        = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9218_max__Suc2,axiom,
% 15.55/8.64      ! [M: nat,N: nat] :
% 15.55/8.64        ( ( ord_max_nat @ M @ ( suc @ N ) )
% 15.55/8.64        = ( case_nat_nat @ ( suc @ N )
% 15.55/8.64          @ ^ [M5: nat] : ( suc @ ( ord_max_nat @ M5 @ N ) )
% 15.55/8.64          @ M ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9219_max__Suc1,axiom,
% 15.55/8.64      ! [N: nat,M: nat] :
% 15.55/8.64        ( ( ord_max_nat @ ( suc @ N ) @ M )
% 15.55/8.64        = ( case_nat_nat @ ( suc @ N )
% 15.55/8.64          @ ^ [M5: nat] : ( suc @ ( ord_max_nat @ N @ M5 ) )
% 15.55/8.64          @ M ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9220_card__le__Suc__Max,axiom,
% 15.55/8.64      ! [S2: set_nat] :
% 15.55/8.64        ( ( finite_finite_nat @ S2 )
% 15.55/8.64       => ( ord_less_eq_nat @ ( finite_card_nat @ S2 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S2 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9221_subset__eq__atLeast0__lessThan__card,axiom,
% 15.55/8.64      ! [N4: set_nat,N: nat] :
% 15.55/8.64        ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 15.55/8.64       => ( ord_less_eq_nat @ ( finite_card_nat @ N4 ) @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9222_card__sum__le__nat__sum,axiom,
% 15.55/8.64      ! [S2: set_nat] :
% 15.55/8.64        ( ord_less_eq_nat
% 15.55/8.64        @ ( groups3542108847815614940at_nat
% 15.55/8.64          @ ^ [X: nat] : X
% 15.55/8.64          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S2 ) ) )
% 15.55/8.64        @ ( groups3542108847815614940at_nat
% 15.55/8.64          @ ^ [X: nat] : X
% 15.55/8.64          @ S2 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9223_card__nth__roots,axiom,
% 15.55/8.64      ! [C: complex,N: nat] :
% 15.55/8.64        ( ( C != zero_zero_complex )
% 15.55/8.64       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64         => ( ( finite_card_complex
% 15.55/8.64              @ ( collect_complex
% 15.55/8.64                @ ^ [Z6: complex] :
% 15.55/8.64                    ( ( power_power_complex @ Z6 @ N )
% 15.55/8.64                    = C ) ) )
% 15.55/8.64            = N ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9224_card__roots__unity__eq,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( finite_card_complex
% 15.55/8.64            @ ( collect_complex
% 15.55/8.64              @ ^ [Z6: complex] :
% 15.55/8.64                  ( ( power_power_complex @ Z6 @ N )
% 15.55/8.64                  = one_one_complex ) ) )
% 15.55/8.64          = N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9225_diff__Suc,axiom,
% 15.55/8.64      ! [M: nat,N: nat] :
% 15.55/8.64        ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 15.55/8.64        = ( case_nat_nat @ zero_zero_nat
% 15.55/8.64          @ ^ [K3: nat] : K3
% 15.55/8.64          @ ( minus_minus_nat @ M @ N ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9226_floor__real__def,axiom,
% 15.55/8.64      ( archim6058952711729229775r_real
% 15.55/8.64      = ( ^ [X: real] :
% 15.55/8.64            ( the_int
% 15.55/8.64            @ ^ [Z6: int] :
% 15.55/8.64                ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z6 ) @ X )
% 15.55/8.64                & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z6 @ one_one_int ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9227_pred__def,axiom,
% 15.55/8.64      ( pred
% 15.55/8.64      = ( case_nat_nat @ zero_zero_nat
% 15.55/8.64        @ ^ [X23: nat] : X23 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9228_bezw__0,axiom,
% 15.55/8.64      ! [X3: nat] :
% 15.55/8.64        ( ( bezw @ X3 @ zero_zero_nat )
% 15.55/8.64        = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9229_drop__bit__numeral__minus__bit1,axiom,
% 15.55/8.64      ! [L: num,K: num] :
% 15.55/8.64        ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 15.55/8.64        = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9230_drop__bit__nonnegative__int__iff,axiom,
% 15.55/8.64      ! [N: nat,K: int] :
% 15.55/8.64        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 15.55/8.64        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9231_drop__bit__negative__int__iff,axiom,
% 15.55/8.64      ! [N: nat,K: int] :
% 15.55/8.64        ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 15.55/8.64        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9232_drop__bit__minus__one,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 15.55/8.64        = ( uminus_uminus_int @ one_one_int ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9233_drop__bit__Suc__minus__bit0,axiom,
% 15.55/8.64      ! [N: nat,K: num] :
% 15.55/8.64        ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 15.55/8.64        = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9234_drop__bit__numeral__minus__bit0,axiom,
% 15.55/8.64      ! [L: num,K: num] :
% 15.55/8.64        ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 15.55/8.64        = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9235_drop__bit__Suc__minus__bit1,axiom,
% 15.55/8.64      ! [N: nat,K: num] :
% 15.55/8.64        ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 15.55/8.64        = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9236_drop__bit__push__bit__int,axiom,
% 15.55/8.64      ! [M: nat,N: nat,K: int] :
% 15.55/8.64        ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N @ K ) )
% 15.55/8.64        = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N @ M ) @ K ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9237_drop__bit__int__def,axiom,
% 15.55/8.64      ( bit_se8568078237143864401it_int
% 15.55/8.64      = ( ^ [N3: nat,K3: int] : ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9238_Suc__0__mod__numeral,axiom,
% 15.55/8.64      ! [K: num] :
% 15.55/8.64        ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 15.55/8.64        = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9239_Suc__0__div__numeral,axiom,
% 15.55/8.64      ! [K: num] :
% 15.55/8.64        ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 15.55/8.64        = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9240_prod__decode__aux_Osimps,axiom,
% 15.55/8.64      ( nat_prod_decode_aux
% 15.55/8.64      = ( ^ [K3: nat,M3: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M3 @ K3 ) @ ( product_Pair_nat_nat @ M3 @ ( minus_minus_nat @ K3 @ M3 ) ) @ ( nat_prod_decode_aux @ ( suc @ K3 ) @ ( minus_minus_nat @ M3 @ ( suc @ K3 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9241_drop__bit__of__Suc__0,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 15.55/8.64        = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9242_drop__bit__nat__eq,axiom,
% 15.55/8.64      ! [N: nat,K: int] :
% 15.55/8.64        ( ( bit_se8570568707652914677it_nat @ N @ ( nat2 @ K ) )
% 15.55/8.64        = ( nat2 @ ( bit_se8568078237143864401it_int @ N @ K ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9243_drop__bit__nat__def,axiom,
% 15.55/8.64      ( bit_se8570568707652914677it_nat
% 15.55/8.64      = ( ^ [N3: nat,M3: nat] : ( divide_divide_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9244_prod__decode__aux_Oelims,axiom,
% 15.55/8.64      ! [X3: nat,Xa: nat,Y3: product_prod_nat_nat] :
% 15.55/8.64        ( ( ( nat_prod_decode_aux @ X3 @ Xa )
% 15.55/8.64          = Y3 )
% 15.55/8.64       => ( ( ( ord_less_eq_nat @ Xa @ X3 )
% 15.55/8.64           => ( Y3
% 15.55/8.64              = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X3 @ Xa ) ) ) )
% 15.55/8.64          & ( ~ ( ord_less_eq_nat @ Xa @ X3 )
% 15.55/8.64           => ( Y3
% 15.55/8.64              = ( nat_prod_decode_aux @ ( suc @ X3 ) @ ( minus_minus_nat @ Xa @ ( suc @ X3 ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9245_finite__enumerate,axiom,
% 15.55/8.64      ! [S2: set_nat] :
% 15.55/8.64        ( ( finite_finite_nat @ S2 )
% 15.55/8.64       => ? [R: nat > nat] :
% 15.55/8.64            ( ( strict1292158309912662752at_nat @ R @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S2 ) ) )
% 15.55/8.64            & ! [N8: nat] :
% 15.55/8.64                ( ( ord_less_nat @ N8 @ ( finite_card_nat @ S2 ) )
% 15.55/8.64               => ( member_nat @ ( R @ N8 ) @ S2 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9246_bezw__non__0,axiom,
% 15.55/8.64      ! [Y3: nat,X3: nat] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ Y3 )
% 15.55/8.64       => ( ( bezw @ X3 @ Y3 )
% 15.55/8.64          = ( 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 ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9247_bezw_Oelims,axiom,
% 15.55/8.64      ! [X3: nat,Xa: nat,Y3: product_prod_int_int] :
% 15.55/8.64        ( ( ( bezw @ X3 @ Xa )
% 15.55/8.64          = Y3 )
% 15.55/8.64       => ( ( ( Xa = zero_zero_nat )
% 15.55/8.64           => ( Y3
% 15.55/8.64              = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 15.55/8.64          & ( ( Xa != zero_zero_nat )
% 15.55/8.64           => ( Y3
% 15.55/8.64              = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X3 @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X3 @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X3 @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X3 @ Xa ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9248_bezw_Osimps,axiom,
% 15.55/8.64      ( bezw
% 15.55/8.64      = ( ^ [X: nat,Y: nat] : ( if_Pro3027730157355071871nt_int @ ( Y = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ 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 ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9249_one__mod__minus__numeral,axiom,
% 15.55/8.64      ! [N: num] :
% 15.55/8.64        ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.64        = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9250_minus__one__mod__numeral,axiom,
% 15.55/8.64      ! [N: num] :
% 15.55/8.64        ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 15.55/8.64        = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9251_numeral__mod__minus__numeral,axiom,
% 15.55/8.64      ! [M: num,N: num] :
% 15.55/8.64        ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.64        = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9252_minus__numeral__mod__numeral,axiom,
% 15.55/8.64      ! [M: num,N: num] :
% 15.55/8.64        ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 15.55/8.64        = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9253_Divides_Oadjust__mod__def,axiom,
% 15.55/8.64      ( adjust_mod
% 15.55/8.64      = ( ^ [L2: int,R5: int] : ( if_int @ ( R5 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L2 @ R5 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9254_bezw_Opelims,axiom,
% 15.55/8.64      ! [X3: nat,Xa: nat,Y3: product_prod_int_int] :
% 15.55/8.64        ( ( ( bezw @ X3 @ Xa )
% 15.55/8.64          = Y3 )
% 15.55/8.64       => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X3 @ Xa ) )
% 15.55/8.64         => ~ ( ( ( ( Xa = zero_zero_nat )
% 15.55/8.64                 => ( Y3
% 15.55/8.64                    = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 15.55/8.64                & ( ( Xa != zero_zero_nat )
% 15.55/8.64                 => ( Y3
% 15.55/8.64                    = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X3 @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X3 @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X3 @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X3 @ Xa ) ) ) ) ) ) ) )
% 15.55/8.64             => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X3 @ Xa ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9255_prod__decode__aux_Opelims,axiom,
% 15.55/8.64      ! [X3: nat,Xa: nat,Y3: product_prod_nat_nat] :
% 15.55/8.64        ( ( ( nat_prod_decode_aux @ X3 @ Xa )
% 15.55/8.64          = Y3 )
% 15.55/8.64       => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X3 @ Xa ) )
% 15.55/8.64         => ~ ( ( ( ( ord_less_eq_nat @ Xa @ X3 )
% 15.55/8.64                 => ( Y3
% 15.55/8.64                    = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X3 @ Xa ) ) ) )
% 15.55/8.64                & ( ~ ( ord_less_eq_nat @ Xa @ X3 )
% 15.55/8.64                 => ( Y3
% 15.55/8.64                    = ( nat_prod_decode_aux @ ( suc @ X3 ) @ ( minus_minus_nat @ Xa @ ( suc @ X3 ) ) ) ) ) )
% 15.55/8.64             => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X3 @ Xa ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9256_bit__cut__integer__code,axiom,
% 15.55/8.64      ( code_bit_cut_integer
% 15.55/8.64      = ( ^ [K3: code_integer] :
% 15.55/8.64            ( if_Pro5737122678794959658eger_o @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 15.55/8.64            @ ( produc9125791028180074456eger_o
% 15.55/8.64              @ ^ [R5: code_integer,S6: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S6 ) ) @ ( S6 = one_one_Code_integer ) )
% 15.55/8.64              @ ( code_divmod_abs @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9257_divmod__abs__code_I6_J,axiom,
% 15.55/8.64      ! [J: code_integer] :
% 15.55/8.64        ( ( code_divmod_abs @ zero_z3403309356797280102nteger @ J )
% 15.55/8.64        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9258_divmod__abs__code_I5_J,axiom,
% 15.55/8.64      ! [J: code_integer] :
% 15.55/8.64        ( ( code_divmod_abs @ J @ zero_z3403309356797280102nteger )
% 15.55/8.64        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ J ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9259_bit__cut__integer__def,axiom,
% 15.55/8.64      ( code_bit_cut_integer
% 15.55/8.64      = ( ^ [K3: code_integer] :
% 15.55/8.64            ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 15.55/8.64            @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K3 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9260_divmod__integer__code,axiom,
% 15.55/8.64      ( code_divmod_integer
% 15.55/8.64      = ( ^ [K3: code_integer,L2: code_integer] :
% 15.55/8.64            ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 15.55/8.64            @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L2 )
% 15.55/8.64              @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ ( code_divmod_abs @ K3 @ L2 )
% 15.55/8.64                @ ( produc6916734918728496179nteger
% 15.55/8.64                  @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L2 @ S6 ) ) )
% 15.55/8.64                  @ ( code_divmod_abs @ K3 @ L2 ) ) )
% 15.55/8.64              @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 15.55/8.64                @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 15.55/8.64                  @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K3 @ L2 )
% 15.55/8.64                    @ ( produc6916734918728496179nteger
% 15.55/8.64                      @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L2 ) @ S6 ) ) )
% 15.55/8.64                      @ ( code_divmod_abs @ K3 @ L2 ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9261_card__greaterThanLessThan__int,axiom,
% 15.55/8.64      ! [L: int,U: int] :
% 15.55/8.64        ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 15.55/8.64        = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9262_xor__minus__numerals_I1_J,axiom,
% 15.55/8.64      ! [N: num,K: int] :
% 15.55/8.64        ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ K )
% 15.55/8.64        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N @ one ) @ K ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9263_xor__minus__numerals_I2_J,axiom,
% 15.55/8.64      ! [K: int,N: num] :
% 15.55/8.64        ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.64        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N @ one ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9264_sub__BitM__One__eq,axiom,
% 15.55/8.64      ! [N: num] :
% 15.55/8.64        ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 15.55/8.64        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9265_divmod__integer__eq__cases,axiom,
% 15.55/8.64      ( code_divmod_integer
% 15.55/8.64      = ( ^ [K3: code_integer,L2: code_integer] :
% 15.55/8.64            ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 15.55/8.64            @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 15.55/8.64              @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L2
% 15.55/8.64                @ ( if_Pro6119634080678213985nteger
% 15.55/8.64                  @ ( ( sgn_sgn_Code_integer @ K3 )
% 15.55/8.64                    = ( sgn_sgn_Code_integer @ L2 ) )
% 15.55/8.64                  @ ( code_divmod_abs @ K3 @ L2 )
% 15.55/8.64                  @ ( produc6916734918728496179nteger
% 15.55/8.64                    @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L2 ) @ S6 ) ) )
% 15.55/8.64                    @ ( code_divmod_abs @ K3 @ L2 ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9266_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 15.55/8.64      ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 15.55/8.64      @ ^ [X: nat,Y: nat] : ( ord_less_eq_nat @ Y @ X )
% 15.55/8.64      @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9267_Suc__funpow,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( compow_nat_nat @ N @ suc )
% 15.55/8.64        = ( plus_plus_nat @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9268_infinite__int__iff__infinite__nat__abs,axiom,
% 15.55/8.64      ! [S2: set_int] :
% 15.55/8.64        ( ( ~ ( finite_finite_int @ S2 ) )
% 15.55/8.64        = ( ~ ( finite_finite_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ S2 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9269_Code__Target__Int_Onegative__def,axiom,
% 15.55/8.64      ( code_Target_negative
% 15.55/8.64      = ( comp_int_int_num @ uminus_uminus_int @ numeral_numeral_int ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9270_measure__function__int,axiom,
% 15.55/8.64      fun_is_measure_int @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9271_times__int_Oabs__eq,axiom,
% 15.55/8.64      ! [Xa: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 15.55/8.64        ( ( times_times_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X3 ) )
% 15.55/8.64        = ( abs_Integ
% 15.55/8.64          @ ( produc27273713700761075at_nat
% 15.55/8.64            @ ^ [X: nat,Y: nat] :
% 15.55/8.64                ( produc2626176000494625587at_nat
% 15.55/8.64                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) )
% 15.55/8.64            @ Xa
% 15.55/8.64            @ X3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9272_int_Oabs__induct,axiom,
% 15.55/8.64      ! [P: int > $o,X3: int] :
% 15.55/8.64        ( ! [Y4: product_prod_nat_nat] : ( P @ ( abs_Integ @ Y4 ) )
% 15.55/8.64       => ( P @ X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9273_eq__Abs__Integ,axiom,
% 15.55/8.64      ! [Z: int] :
% 15.55/8.64        ~ ! [X4: nat,Y4: nat] :
% 15.55/8.64            ( Z
% 15.55/8.64           != ( abs_Integ @ ( product_Pair_nat_nat @ X4 @ Y4 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9274_nat_Oabs__eq,axiom,
% 15.55/8.64      ! [X3: product_prod_nat_nat] :
% 15.55/8.64        ( ( nat2 @ ( abs_Integ @ X3 ) )
% 15.55/8.64        = ( produc6842872674320459806at_nat @ minus_minus_nat @ X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9275_zero__int__def,axiom,
% 15.55/8.64      ( zero_zero_int
% 15.55/8.64      = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9276_int__def,axiom,
% 15.55/8.64      ( semiri1314217659103216013at_int
% 15.55/8.64      = ( ^ [N3: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N3 @ zero_zero_nat ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9277_uminus__int_Oabs__eq,axiom,
% 15.55/8.64      ! [X3: product_prod_nat_nat] :
% 15.55/8.64        ( ( uminus_uminus_int @ ( abs_Integ @ X3 ) )
% 15.55/8.64        = ( abs_Integ
% 15.55/8.64          @ ( produc2626176000494625587at_nat
% 15.55/8.64            @ ^ [X: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X )
% 15.55/8.64            @ X3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9278_one__int__def,axiom,
% 15.55/8.64      ( one_one_int
% 15.55/8.64      = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9279_less__int_Oabs__eq,axiom,
% 15.55/8.64      ! [Xa: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 15.55/8.64        ( ( ord_less_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X3 ) )
% 15.55/8.64        = ( produc8739625826339149834_nat_o
% 15.55/8.64          @ ^ [X: nat,Y: nat] :
% 15.55/8.64              ( produc6081775807080527818_nat_o
% 15.55/8.64              @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) )
% 15.55/8.64          @ Xa
% 15.55/8.64          @ X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9280_less__eq__int_Oabs__eq,axiom,
% 15.55/8.64      ! [Xa: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 15.55/8.64        ( ( ord_less_eq_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X3 ) )
% 15.55/8.64        = ( produc8739625826339149834_nat_o
% 15.55/8.64          @ ^ [X: nat,Y: nat] :
% 15.55/8.64              ( produc6081775807080527818_nat_o
% 15.55/8.64              @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) )
% 15.55/8.64          @ Xa
% 15.55/8.64          @ X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9281_plus__int_Oabs__eq,axiom,
% 15.55/8.64      ! [Xa: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 15.55/8.64        ( ( plus_plus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X3 ) )
% 15.55/8.64        = ( abs_Integ
% 15.55/8.64          @ ( produc27273713700761075at_nat
% 15.55/8.64            @ ^ [X: nat,Y: nat] :
% 15.55/8.64                ( produc2626176000494625587at_nat
% 15.55/8.64                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) )
% 15.55/8.64            @ Xa
% 15.55/8.64            @ X3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9282_minus__int_Oabs__eq,axiom,
% 15.55/8.64      ! [Xa: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 15.55/8.64        ( ( minus_minus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X3 ) )
% 15.55/8.64        = ( abs_Integ
% 15.55/8.64          @ ( produc27273713700761075at_nat
% 15.55/8.64            @ ^ [X: nat,Y: nat] :
% 15.55/8.64                ( produc2626176000494625587at_nat
% 15.55/8.64                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) )
% 15.55/8.64            @ Xa
% 15.55/8.64            @ X3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9283_num__of__nat_Osimps_I2_J,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64         => ( ( num_of_nat @ ( suc @ N ) )
% 15.55/8.64            = ( inc @ ( num_of_nat @ N ) ) ) )
% 15.55/8.64        & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64         => ( ( num_of_nat @ ( suc @ N ) )
% 15.55/8.64            = one ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9284_Gcd__remove0__nat,axiom,
% 15.55/8.64      ! [M7: set_nat] :
% 15.55/8.64        ( ( finite_finite_nat @ M7 )
% 15.55/8.64       => ( ( gcd_Gcd_nat @ M7 )
% 15.55/8.64          = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M7 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9285_pow_Osimps_I3_J,axiom,
% 15.55/8.64      ! [X3: num,Y3: num] :
% 15.55/8.64        ( ( pow @ X3 @ ( bit1 @ Y3 ) )
% 15.55/8.64        = ( times_times_num @ ( sqr @ ( pow @ X3 @ Y3 ) ) @ X3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9286_num__of__nat__numeral__eq,axiom,
% 15.55/8.64      ! [Q3: num] :
% 15.55/8.64        ( ( num_of_nat @ ( numeral_numeral_nat @ Q3 ) )
% 15.55/8.64        = Q3 ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9287_sqr_Osimps_I2_J,axiom,
% 15.55/8.64      ! [N: num] :
% 15.55/8.64        ( ( sqr @ ( bit0 @ N ) )
% 15.55/8.64        = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9288_sqr_Osimps_I1_J,axiom,
% 15.55/8.64      ( ( sqr @ one )
% 15.55/8.64      = one ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9289_sqr__conv__mult,axiom,
% 15.55/8.64      ( sqr
% 15.55/8.64      = ( ^ [X: num] : ( times_times_num @ X @ X ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9290_num__of__nat_Osimps_I1_J,axiom,
% 15.55/8.64      ( ( num_of_nat @ zero_zero_nat )
% 15.55/8.64      = one ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9291_numeral__num__of__nat,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 15.55/8.64          = N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9292_num__of__nat__One,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( ord_less_eq_nat @ N @ one_one_nat )
% 15.55/8.64       => ( ( num_of_nat @ N )
% 15.55/8.64          = one ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9293_pow_Osimps_I2_J,axiom,
% 15.55/8.64      ! [X3: num,Y3: num] :
% 15.55/8.64        ( ( pow @ X3 @ ( bit0 @ Y3 ) )
% 15.55/8.64        = ( sqr @ ( pow @ X3 @ Y3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9294_num__of__integer_Orep__eq,axiom,
% 15.55/8.64      ( code_num_of_integer
% 15.55/8.64      = ( ^ [X: code_integer] : ( num_of_nat @ ( nat2 @ ( code_int_of_integer @ X ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9295_num__of__integer_Oabs__eq,axiom,
% 15.55/8.64      ! [X3: int] :
% 15.55/8.64        ( ( code_num_of_integer @ ( code_integer_of_int @ X3 ) )
% 15.55/8.64        = ( num_of_nat @ ( nat2 @ X3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9296_num__of__nat__double,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 15.55/8.64          = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9297_num__of__nat__plus__distrib,axiom,
% 15.55/8.64      ! [M: nat,N: nat] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ M )
% 15.55/8.64       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64         => ( ( num_of_nat @ ( plus_plus_nat @ M @ N ) )
% 15.55/8.64            = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9298_sqr_Osimps_I3_J,axiom,
% 15.55/8.64      ! [N: num] :
% 15.55/8.64        ( ( sqr @ ( bit1 @ N ) )
% 15.55/8.64        = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9299_Gcd__int__def,axiom,
% 15.55/8.64      ( gcd_Gcd_int
% 15.55/8.64      = ( ^ [K7: set_int] : ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ K7 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9300_less__eq__int_Orep__eq,axiom,
% 15.55/8.64      ( ord_less_eq_int
% 15.55/8.64      = ( ^ [X: int,Xa4: int] :
% 15.55/8.64            ( produc8739625826339149834_nat_o
% 15.55/8.64            @ ^ [Y: nat,Z6: nat] :
% 15.55/8.64                ( produc6081775807080527818_nat_o
% 15.55/8.64                @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y @ V4 ) @ ( plus_plus_nat @ U2 @ Z6 ) ) )
% 15.55/8.64            @ ( rep_Integ @ X )
% 15.55/8.64            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9301_less__int_Orep__eq,axiom,
% 15.55/8.64      ( ord_less_int
% 15.55/8.64      = ( ^ [X: int,Xa4: int] :
% 15.55/8.64            ( produc8739625826339149834_nat_o
% 15.55/8.64            @ ^ [Y: nat,Z6: nat] :
% 15.55/8.64                ( produc6081775807080527818_nat_o
% 15.55/8.64                @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y @ V4 ) @ ( plus_plus_nat @ U2 @ Z6 ) ) )
% 15.55/8.64            @ ( rep_Integ @ X )
% 15.55/8.64            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9302_Gcd__int__eq,axiom,
% 15.55/8.64      ! [N4: set_nat] :
% 15.55/8.64        ( ( gcd_Gcd_int @ ( image_nat_int @ semiri1314217659103216013at_int @ N4 ) )
% 15.55/8.64        = ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ N4 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9303_Gcd__nat__abs__eq,axiom,
% 15.55/8.64      ! [K5: set_int] :
% 15.55/8.64        ( ( gcd_Gcd_nat
% 15.55/8.64          @ ( image_int_nat
% 15.55/8.64            @ ^ [K3: int] : ( nat2 @ ( abs_abs_int @ K3 ) )
% 15.55/8.64            @ K5 ) )
% 15.55/8.64        = ( nat2 @ ( gcd_Gcd_int @ K5 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9304_Gcd__int__greater__eq__0,axiom,
% 15.55/8.64      ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K5 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9305_nat_Orep__eq,axiom,
% 15.55/8.64      ( nat2
% 15.55/8.64      = ( ^ [X: int] : ( produc6842872674320459806at_nat @ minus_minus_nat @ ( rep_Integ @ X ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9306_Gcd__eq__Max,axiom,
% 15.55/8.64      ! [M7: set_nat] :
% 15.55/8.64        ( ( finite_finite_nat @ M7 )
% 15.55/8.64       => ( ( M7 != bot_bot_set_nat )
% 15.55/8.64         => ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 15.55/8.64           => ( ( gcd_Gcd_nat @ M7 )
% 15.55/8.64              = ( lattic8265883725875713057ax_nat
% 15.55/8.64                @ ( comple7806235888213564991et_nat
% 15.55/8.64                  @ ( image_nat_set_nat
% 15.55/8.64                    @ ^ [M3: nat] :
% 15.55/8.64                        ( collect_nat
% 15.55/8.64                        @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M3 ) )
% 15.55/8.64                    @ M7 ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9307_uminus__int__def,axiom,
% 15.55/8.64      ( uminus_uminus_int
% 15.55/8.64      = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 15.55/8.64        @ ( produc2626176000494625587at_nat
% 15.55/8.64          @ ^ [X: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9308_Inf__nat__def1,axiom,
% 15.55/8.64      ! [K5: set_nat] :
% 15.55/8.64        ( ( K5 != bot_bot_set_nat )
% 15.55/8.64       => ( member_nat @ ( complete_Inf_Inf_nat @ K5 ) @ K5 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9309_times__int__def,axiom,
% 15.55/8.64      ( times_times_int
% 15.55/8.64      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 15.55/8.64        @ ( produc27273713700761075at_nat
% 15.55/8.64          @ ^ [X: nat,Y: nat] :
% 15.55/8.64              ( produc2626176000494625587at_nat
% 15.55/8.64              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9310_minus__int__def,axiom,
% 15.55/8.64      ( minus_minus_int
% 15.55/8.64      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 15.55/8.64        @ ( produc27273713700761075at_nat
% 15.55/8.64          @ ^ [X: nat,Y: nat] :
% 15.55/8.64              ( produc2626176000494625587at_nat
% 15.55/8.64              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9311_plus__int__def,axiom,
% 15.55/8.64      ( plus_plus_int
% 15.55/8.64      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 15.55/8.64        @ ( produc27273713700761075at_nat
% 15.55/8.64          @ ^ [X: nat,Y: nat] :
% 15.55/8.64              ( produc2626176000494625587at_nat
% 15.55/8.64              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9312_Sup__nat__empty,axiom,
% 15.55/8.64      ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 15.55/8.64      = zero_zero_nat ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9313_Inf__real__def,axiom,
% 15.55/8.64      ( comple4887499456419720421f_real
% 15.55/8.64      = ( ^ [X8: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X8 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9314_Inf__int__def,axiom,
% 15.55/8.64      ( complete_Inf_Inf_int
% 15.55/8.64      = ( ^ [X8: set_int] : ( uminus_uminus_int @ ( complete_Sup_Sup_int @ ( image_int_int @ uminus_uminus_int @ X8 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9315_suminf__eq__SUP__real,axiom,
% 15.55/8.64      ! [X9: nat > real] :
% 15.55/8.64        ( ( summable_real @ X9 )
% 15.55/8.64       => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X9 @ I3 ) )
% 15.55/8.64         => ( ( suminf_real @ X9 )
% 15.55/8.64            = ( comple1385675409528146559p_real
% 15.55/8.64              @ ( image_nat_real
% 15.55/8.64                @ ^ [I4: nat] : ( groups6591440286371151544t_real @ X9 @ ( set_ord_lessThan_nat @ I4 ) )
% 15.55/8.64                @ top_top_set_nat ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9316_Sup__nat__def,axiom,
% 15.55/8.64      ( complete_Sup_Sup_nat
% 15.55/8.64      = ( ^ [X8: set_nat] : ( if_nat @ ( X8 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X8 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9317_binomial__def,axiom,
% 15.55/8.64      ( binomial
% 15.55/8.64      = ( ^ [N3: nat,K3: nat] :
% 15.55/8.64            ( finite_card_set_nat
% 15.55/8.64            @ ( collect_set_nat
% 15.55/8.64              @ ^ [K7: set_nat] :
% 15.55/8.64                  ( ( member_set_nat @ K7 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N3 ) ) )
% 15.55/8.64                  & ( ( finite_card_nat @ K7 )
% 15.55/8.64                    = K3 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9318_range__mod,axiom,
% 15.55/8.64      ! [N: nat] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( image_nat_nat
% 15.55/8.64            @ ^ [M3: nat] : ( modulo_modulo_nat @ M3 @ N )
% 15.55/8.64            @ top_top_set_nat )
% 15.55/8.64          = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9319_UNIV__nat__eq,axiom,
% 15.55/8.64      ( top_top_set_nat
% 15.55/8.64      = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9320_card__UNIV__bool,axiom,
% 15.55/8.64      ( ( finite_card_o @ top_top_set_o )
% 15.55/8.64      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9321_range__mult,axiom,
% 15.55/8.64      ! [A: real] :
% 15.55/8.64        ( ( ( A = zero_zero_real )
% 15.55/8.64         => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 15.55/8.64            = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 15.55/8.64        & ( ( A != zero_zero_real )
% 15.55/8.64         => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 15.55/8.64            = top_top_set_real ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9322_infinite__UNIV__int,axiom,
% 15.55/8.64      ~ ( finite_finite_int @ top_top_set_int ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9323_int__in__range__abs,axiom,
% 15.55/8.64      ! [N: nat] : ( member_int @ ( semiri1314217659103216013at_int @ N ) @ ( image_int_int @ abs_abs_int @ top_top_set_int ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9324_root__def,axiom,
% 15.55/8.64      ( root
% 15.55/8.64      = ( ^ [N3: nat,X: real] :
% 15.55/8.64            ( if_real @ ( N3 = zero_zero_nat ) @ zero_zero_real
% 15.55/8.64            @ ( the_in5290026491893676941l_real @ top_top_set_real
% 15.55/8.64              @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N3 ) )
% 15.55/8.64              @ X ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9325_card__UNIV__char,axiom,
% 15.55/8.64      ( ( finite_card_char @ top_top_set_char )
% 15.55/8.64      = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9326_UNIV__char__of__nat,axiom,
% 15.55/8.64      ( top_top_set_char
% 15.55/8.64      = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9327_char_Osize_I2_J,axiom,
% 15.55/8.64      ! [X15: $o,X2: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 15.55/8.64        ( ( size_size_char @ ( char2 @ X15 @ X2 @ X32 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 15.55/8.64        = zero_zero_nat ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9328_nat__of__char__less__256,axiom,
% 15.55/8.64      ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9329_range__nat__of__char,axiom,
% 15.55/8.64      ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 15.55/8.64      = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9330_integer__of__char__code,axiom,
% 15.55/8.64      ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B7: $o] :
% 15.55/8.64        ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B7 ) )
% 15.55/8.64        = ( 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 @ B7 ) @ ( 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 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9331_char_Osize__gen,axiom,
% 15.55/8.64      ! [X15: $o,X2: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 15.55/8.64        ( ( size_char @ ( char2 @ X15 @ X2 @ X32 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 15.55/8.64        = zero_zero_nat ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9332_String_Ochar__of__ascii__of,axiom,
% 15.55/8.64      ! [C: char] :
% 15.55/8.64        ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 15.55/8.64        = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9333_DERIV__even__real__root,axiom,
% 15.55/8.64      ! [N: nat,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.64         => ( ( ord_less_real @ X3 @ zero_zero_real )
% 15.55/8.64           => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ ( power_power_real @ ( root @ N @ X3 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9334_DERIV__real__root__generic,axiom,
% 15.55/8.64      ! [N: nat,X3: real,D5: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( X3 != zero_zero_real )
% 15.55/8.64         => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.64             => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.64               => ( D5
% 15.55/8.64                  = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X3 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 15.55/8.64           => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.64               => ( ( ord_less_real @ X3 @ zero_zero_real )
% 15.55/8.64                 => ( D5
% 15.55/8.64                    = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X3 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 15.55/8.64             => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.64                 => ( D5
% 15.55/8.64                    = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X3 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 15.55/8.64               => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9335_DERIV__arctan__series,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 15.55/8.64       => ( has_fi5821293074295781190e_real
% 15.55/8.64          @ ^ [X10: real] :
% 15.55/8.64              ( suminf_real
% 15.55/8.64              @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X10 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 15.55/8.64          @ ( suminf_real
% 15.55/8.64            @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( power_power_real @ X3 @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.64          @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9336_has__real__derivative__neg__dec__left,axiom,
% 15.55/8.64      ! [F: real > real,L: real,X3: real,S2: set_real] :
% 15.55/8.64        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ S2 ) )
% 15.55/8.64       => ( ( ord_less_real @ L @ zero_zero_real )
% 15.55/8.64         => ? [D6: real] :
% 15.55/8.64              ( ( ord_less_real @ zero_zero_real @ D6 )
% 15.55/8.64              & ! [H4: real] :
% 15.55/8.64                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 15.55/8.64                 => ( ( member_real @ ( minus_minus_real @ X3 @ H4 ) @ S2 )
% 15.55/8.64                   => ( ( ord_less_real @ H4 @ D6 )
% 15.55/8.64                     => ( ord_less_real @ ( F @ X3 ) @ ( F @ ( minus_minus_real @ X3 @ H4 ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9337_has__real__derivative__pos__inc__left,axiom,
% 15.55/8.64      ! [F: real > real,L: real,X3: real,S2: set_real] :
% 15.55/8.64        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ S2 ) )
% 15.55/8.64       => ( ( ord_less_real @ zero_zero_real @ L )
% 15.55/8.64         => ? [D6: real] :
% 15.55/8.64              ( ( ord_less_real @ zero_zero_real @ D6 )
% 15.55/8.64              & ! [H4: real] :
% 15.55/8.64                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 15.55/8.64                 => ( ( member_real @ ( minus_minus_real @ X3 @ H4 ) @ S2 )
% 15.55/8.64                   => ( ( ord_less_real @ H4 @ D6 )
% 15.55/8.64                     => ( ord_less_real @ ( F @ ( minus_minus_real @ X3 @ H4 ) ) @ ( F @ X3 ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9338_has__real__derivative__pos__inc__right,axiom,
% 15.55/8.64      ! [F: real > real,L: real,X3: real,S2: set_real] :
% 15.55/8.64        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ S2 ) )
% 15.55/8.64       => ( ( ord_less_real @ zero_zero_real @ L )
% 15.55/8.64         => ? [D6: real] :
% 15.55/8.64              ( ( ord_less_real @ zero_zero_real @ D6 )
% 15.55/8.64              & ! [H4: real] :
% 15.55/8.64                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 15.55/8.64                 => ( ( member_real @ ( plus_plus_real @ X3 @ H4 ) @ S2 )
% 15.55/8.64                   => ( ( ord_less_real @ H4 @ D6 )
% 15.55/8.64                     => ( ord_less_real @ ( F @ X3 ) @ ( F @ ( plus_plus_real @ X3 @ H4 ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9339_has__real__derivative__neg__dec__right,axiom,
% 15.55/8.64      ! [F: real > real,L: real,X3: real,S2: set_real] :
% 15.55/8.64        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ S2 ) )
% 15.55/8.64       => ( ( ord_less_real @ L @ zero_zero_real )
% 15.55/8.64         => ? [D6: real] :
% 15.55/8.64              ( ( ord_less_real @ zero_zero_real @ D6 )
% 15.55/8.64              & ! [H4: real] :
% 15.55/8.64                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 15.55/8.64                 => ( ( member_real @ ( plus_plus_real @ X3 @ H4 ) @ S2 )
% 15.55/8.64                   => ( ( ord_less_real @ H4 @ D6 )
% 15.55/8.64                     => ( ord_less_real @ ( F @ ( plus_plus_real @ X3 @ H4 ) ) @ ( F @ X3 ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9340_DERIV__isconst3,axiom,
% 15.55/8.64      ! [A: real,B: real,X3: real,Y3: real,F: real > real] :
% 15.55/8.64        ( ( ord_less_real @ A @ B )
% 15.55/8.64       => ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 15.55/8.64         => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 15.55/8.64           => ( ! [X4: real] :
% 15.55/8.64                  ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 15.55/8.64                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 15.55/8.64             => ( ( F @ X3 )
% 15.55/8.64                = ( F @ Y3 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9341_DERIV__isconst__all,axiom,
% 15.55/8.64      ! [F: real > real,X3: real,Y3: real] :
% 15.55/8.64        ( ! [X4: real] : ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 15.55/8.64       => ( ( F @ X3 )
% 15.55/8.64          = ( F @ Y3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9342_DERIV__neg__dec__right,axiom,
% 15.55/8.64      ! [F: real > real,L: real,X3: real] :
% 15.55/8.64        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.64       => ( ( ord_less_real @ L @ zero_zero_real )
% 15.55/8.64         => ? [D6: real] :
% 15.55/8.64              ( ( ord_less_real @ zero_zero_real @ D6 )
% 15.55/8.64              & ! [H4: real] :
% 15.55/8.64                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 15.55/8.64                 => ( ( ord_less_real @ H4 @ D6 )
% 15.55/8.64                   => ( ord_less_real @ ( F @ ( plus_plus_real @ X3 @ H4 ) ) @ ( F @ X3 ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9343_DERIV__pos__inc__right,axiom,
% 15.55/8.64      ! [F: real > real,L: real,X3: real] :
% 15.55/8.64        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.64       => ( ( ord_less_real @ zero_zero_real @ L )
% 15.55/8.64         => ? [D6: real] :
% 15.55/8.64              ( ( ord_less_real @ zero_zero_real @ D6 )
% 15.55/8.64              & ! [H4: real] :
% 15.55/8.64                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 15.55/8.64                 => ( ( ord_less_real @ H4 @ D6 )
% 15.55/8.64                   => ( ord_less_real @ ( F @ X3 ) @ ( F @ ( plus_plus_real @ X3 @ H4 ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9344_DERIV__pos__inc__left,axiom,
% 15.55/8.64      ! [F: real > real,L: real,X3: real] :
% 15.55/8.64        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.64       => ( ( ord_less_real @ zero_zero_real @ L )
% 15.55/8.64         => ? [D6: real] :
% 15.55/8.64              ( ( ord_less_real @ zero_zero_real @ D6 )
% 15.55/8.64              & ! [H4: real] :
% 15.55/8.64                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 15.55/8.64                 => ( ( ord_less_real @ H4 @ D6 )
% 15.55/8.64                   => ( ord_less_real @ ( F @ ( minus_minus_real @ X3 @ H4 ) ) @ ( F @ X3 ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9345_DERIV__neg__dec__left,axiom,
% 15.55/8.64      ! [F: real > real,L: real,X3: real] :
% 15.55/8.64        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.64       => ( ( ord_less_real @ L @ zero_zero_real )
% 15.55/8.64         => ? [D6: real] :
% 15.55/8.64              ( ( ord_less_real @ zero_zero_real @ D6 )
% 15.55/8.64              & ! [H4: real] :
% 15.55/8.64                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 15.55/8.64                 => ( ( ord_less_real @ H4 @ D6 )
% 15.55/8.64                   => ( ord_less_real @ ( F @ X3 ) @ ( F @ ( minus_minus_real @ X3 @ H4 ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9346_DERIV__nonneg__imp__nondecreasing,axiom,
% 15.55/8.64      ! [A: real,B: real,F: real > real] :
% 15.55/8.64        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.64       => ( ! [X4: real] :
% 15.55/8.64              ( ( ord_less_eq_real @ A @ X4 )
% 15.55/8.64             => ( ( ord_less_eq_real @ X4 @ B )
% 15.55/8.64               => ? [Y6: real] :
% 15.55/8.64                    ( ( has_fi5821293074295781190e_real @ F @ Y6 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 15.55/8.64                    & ( ord_less_eq_real @ zero_zero_real @ Y6 ) ) ) )
% 15.55/8.64         => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9347_DERIV__nonpos__imp__nonincreasing,axiom,
% 15.55/8.64      ! [A: real,B: real,F: real > real] :
% 15.55/8.64        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.64       => ( ! [X4: real] :
% 15.55/8.64              ( ( ord_less_eq_real @ A @ X4 )
% 15.55/8.64             => ( ( ord_less_eq_real @ X4 @ B )
% 15.55/8.64               => ? [Y6: real] :
% 15.55/8.64                    ( ( has_fi5821293074295781190e_real @ F @ Y6 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 15.55/8.64                    & ( ord_less_eq_real @ Y6 @ zero_zero_real ) ) ) )
% 15.55/8.64         => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9348_deriv__nonneg__imp__mono,axiom,
% 15.55/8.64      ! [A: real,B: real,G: real > real,G2: real > real] :
% 15.55/8.64        ( ! [X4: real] :
% 15.55/8.64            ( ( member_real @ X4 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 15.55/8.64           => ( has_fi5821293074295781190e_real @ G @ ( G2 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 15.55/8.64       => ( ! [X4: real] :
% 15.55/8.64              ( ( member_real @ X4 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 15.55/8.64             => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X4 ) ) )
% 15.55/8.64         => ( ( ord_less_eq_real @ A @ B )
% 15.55/8.64           => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9349_DERIV__neg__imp__decreasing,axiom,
% 15.55/8.64      ! [A: real,B: real,F: real > real] :
% 15.55/8.64        ( ( ord_less_real @ A @ B )
% 15.55/8.64       => ( ! [X4: real] :
% 15.55/8.64              ( ( ord_less_eq_real @ A @ X4 )
% 15.55/8.64             => ( ( ord_less_eq_real @ X4 @ B )
% 15.55/8.64               => ? [Y6: real] :
% 15.55/8.64                    ( ( has_fi5821293074295781190e_real @ F @ Y6 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 15.55/8.64                    & ( ord_less_real @ Y6 @ zero_zero_real ) ) ) )
% 15.55/8.64         => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9350_DERIV__pos__imp__increasing,axiom,
% 15.55/8.64      ! [A: real,B: real,F: real > real] :
% 15.55/8.64        ( ( ord_less_real @ A @ B )
% 15.55/8.64       => ( ! [X4: real] :
% 15.55/8.64              ( ( ord_less_eq_real @ A @ X4 )
% 15.55/8.64             => ( ( ord_less_eq_real @ X4 @ B )
% 15.55/8.64               => ? [Y6: real] :
% 15.55/8.64                    ( ( has_fi5821293074295781190e_real @ F @ Y6 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 15.55/8.64                    & ( ord_less_real @ zero_zero_real @ Y6 ) ) ) )
% 15.55/8.64         => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9351_MVT2,axiom,
% 15.55/8.64      ! [A: real,B: real,F: real > real,F5: real > real] :
% 15.55/8.64        ( ( ord_less_real @ A @ B )
% 15.55/8.64       => ( ! [X4: real] :
% 15.55/8.64              ( ( ord_less_eq_real @ A @ X4 )
% 15.55/8.64             => ( ( ord_less_eq_real @ X4 @ B )
% 15.55/8.64               => ( has_fi5821293074295781190e_real @ F @ ( F5 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 15.55/8.64         => ? [Z3: real] :
% 15.55/8.64              ( ( ord_less_real @ A @ Z3 )
% 15.55/8.64              & ( ord_less_real @ Z3 @ B )
% 15.55/8.64              & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 15.55/8.64                = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F5 @ Z3 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9352_DERIV__local__const,axiom,
% 15.55/8.64      ! [F: real > real,L: real,X3: real,D3: real] :
% 15.55/8.64        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.64       => ( ( ord_less_real @ zero_zero_real @ D3 )
% 15.55/8.64         => ( ! [Y4: real] :
% 15.55/8.64                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y4 ) ) @ D3 )
% 15.55/8.64               => ( ( F @ X3 )
% 15.55/8.64                  = ( F @ Y4 ) ) )
% 15.55/8.64           => ( L = zero_zero_real ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9353_DERIV__ln,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.64       => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9354_DERIV__const__average,axiom,
% 15.55/8.64      ! [A: real,B: real,V: real > real,K: real] :
% 15.55/8.64        ( ( A != B )
% 15.55/8.64       => ( ! [X4: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 15.55/8.64         => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 15.55/8.64            = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9355_DERIV__local__max,axiom,
% 15.55/8.64      ! [F: real > real,L: real,X3: real,D3: real] :
% 15.55/8.64        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.64       => ( ( ord_less_real @ zero_zero_real @ D3 )
% 15.55/8.64         => ( ! [Y4: real] :
% 15.55/8.64                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y4 ) ) @ D3 )
% 15.55/8.64               => ( ord_less_eq_real @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 15.55/8.64           => ( L = zero_zero_real ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9356_DERIV__local__min,axiom,
% 15.55/8.64      ! [F: real > real,L: real,X3: real,D3: real] :
% 15.55/8.64        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.64       => ( ( ord_less_real @ zero_zero_real @ D3 )
% 15.55/8.64         => ( ! [Y4: real] :
% 15.55/8.64                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y4 ) ) @ D3 )
% 15.55/8.64               => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 15.55/8.64           => ( L = zero_zero_real ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9357_DERIV__ln__divide,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.64       => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9358_DERIV__pow,axiom,
% 15.55/8.64      ! [N: nat,X3: real,S: set_real] :
% 15.55/8.64        ( has_fi5821293074295781190e_real
% 15.55/8.64        @ ^ [X: real] : ( power_power_real @ X @ N )
% 15.55/8.64        @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X3 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 15.55/8.64        @ ( topolo2177554685111907308n_real @ X3 @ S ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9359_DERIV__fun__pow,axiom,
% 15.55/8.64      ! [G: real > real,M: real,X3: real,N: nat] :
% 15.55/8.64        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.64       => ( has_fi5821293074295781190e_real
% 15.55/8.64          @ ^ [X: real] : ( power_power_real @ ( G @ X ) @ N )
% 15.55/8.64          @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G @ X3 ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M )
% 15.55/8.64          @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9360_has__real__derivative__powr,axiom,
% 15.55/8.64      ! [Z: real,R2: real] :
% 15.55/8.64        ( ( ord_less_real @ zero_zero_real @ Z )
% 15.55/8.64       => ( has_fi5821293074295781190e_real
% 15.55/8.64          @ ^ [Z6: real] : ( powr_real @ Z6 @ R2 )
% 15.55/8.64          @ ( times_times_real @ R2 @ ( powr_real @ Z @ ( minus_minus_real @ R2 @ one_one_real ) ) )
% 15.55/8.64          @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9361_DERIV__series_H,axiom,
% 15.55/8.64      ! [F: real > nat > real,F5: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 15.55/8.64        ( ! [N2: nat] :
% 15.55/8.64            ( has_fi5821293074295781190e_real
% 15.55/8.64            @ ^ [X: real] : ( F @ X @ N2 )
% 15.55/8.64            @ ( F5 @ X0 @ N2 )
% 15.55/8.64            @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 15.55/8.64       => ( ! [X4: real] :
% 15.55/8.64              ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 15.55/8.64             => ( summable_real @ ( F @ X4 ) ) )
% 15.55/8.64         => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 15.55/8.64           => ( ( summable_real @ ( F5 @ X0 ) )
% 15.55/8.64             => ( ( summable_real @ L5 )
% 15.55/8.64               => ( ! [N2: nat,X4: real,Y4: real] :
% 15.55/8.64                      ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 15.55/8.64                     => ( ( member_real @ Y4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 15.55/8.64                       => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X4 @ N2 ) @ ( F @ Y4 @ N2 ) ) ) @ ( times_times_real @ ( L5 @ N2 ) @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y4 ) ) ) ) ) )
% 15.55/8.64                 => ( has_fi5821293074295781190e_real
% 15.55/8.64                    @ ^ [X: real] : ( suminf_real @ ( F @ X ) )
% 15.55/8.64                    @ ( suminf_real @ ( F5 @ X0 ) )
% 15.55/8.64                    @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9362_DERIV__fun__powr,axiom,
% 15.55/8.64      ! [G: real > real,M: real,X3: real,R2: real] :
% 15.55/8.64        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.64       => ( ( ord_less_real @ zero_zero_real @ ( G @ X3 ) )
% 15.55/8.64         => ( has_fi5821293074295781190e_real
% 15.55/8.64            @ ^ [X: real] : ( powr_real @ ( G @ X ) @ R2 )
% 15.55/8.64            @ ( times_times_real @ ( times_times_real @ R2 @ ( powr_real @ ( G @ X3 ) @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 15.55/8.64            @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9363_DERIV__log,axiom,
% 15.55/8.64      ! [X3: real,B: real] :
% 15.55/8.64        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.64       => ( has_fi5821293074295781190e_real @ ( log @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X3 ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9364_DERIV__powr,axiom,
% 15.55/8.64      ! [G: real > real,M: real,X3: real,F: real > real,R2: real] :
% 15.55/8.64        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.64       => ( ( ord_less_real @ zero_zero_real @ ( G @ X3 ) )
% 15.55/8.64         => ( ( has_fi5821293074295781190e_real @ F @ R2 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.64           => ( has_fi5821293074295781190e_real
% 15.55/8.64              @ ^ [X: real] : ( powr_real @ ( G @ X ) @ ( F @ X ) )
% 15.55/8.64              @ ( times_times_real @ ( powr_real @ ( G @ X3 ) @ ( F @ X3 ) ) @ ( plus_plus_real @ ( times_times_real @ R2 @ ( ln_ln_real @ ( G @ X3 ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X3 ) ) @ ( G @ X3 ) ) ) )
% 15.55/8.64              @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9365_DERIV__real__sqrt,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.64       => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9366_DERIV__arctan,axiom,
% 15.55/8.64      ! [X3: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9367_arsinh__real__has__field__derivative,axiom,
% 15.55/8.64      ! [X3: real,A3: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ A3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9368_DERIV__real__sqrt__generic,axiom,
% 15.55/8.64      ! [X3: real,D5: real] :
% 15.55/8.64        ( ( X3 != zero_zero_real )
% 15.55/8.64       => ( ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.64           => ( D5
% 15.55/8.64              = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 15.55/8.64         => ( ( ( ord_less_real @ X3 @ zero_zero_real )
% 15.55/8.64             => ( D5
% 15.55/8.64                = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 15.55/8.64           => ( has_fi5821293074295781190e_real @ sqrt @ D5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9369_arcosh__real__has__field__derivative,axiom,
% 15.55/8.64      ! [X3: real,A3: set_real] :
% 15.55/8.64        ( ( ord_less_real @ one_one_real @ X3 )
% 15.55/8.64       => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ A3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9370_artanh__real__has__field__derivative,axiom,
% 15.55/8.64      ! [X3: real,A3: set_real] :
% 15.55/8.64        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 15.55/8.64       => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ A3 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9371_DERIV__power__series_H,axiom,
% 15.55/8.64      ! [R3: real,F: nat > real,X0: real] :
% 15.55/8.64        ( ! [X4: real] :
% 15.55/8.64            ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R3 ) @ R3 ) )
% 15.55/8.64           => ( summable_real
% 15.55/8.64              @ ^ [N3: nat] : ( times_times_real @ ( times_times_real @ ( F @ N3 ) @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ ( power_power_real @ X4 @ N3 ) ) ) )
% 15.55/8.64       => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R3 ) @ R3 ) )
% 15.55/8.64         => ( ( ord_less_real @ zero_zero_real @ R3 )
% 15.55/8.64           => ( has_fi5821293074295781190e_real
% 15.55/8.64              @ ^ [X: real] :
% 15.55/8.64                  ( suminf_real
% 15.55/8.64                  @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ X @ ( suc @ N3 ) ) ) )
% 15.55/8.64              @ ( suminf_real
% 15.55/8.64                @ ^ [N3: nat] : ( times_times_real @ ( times_times_real @ ( F @ N3 ) @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ ( power_power_real @ X0 @ N3 ) ) )
% 15.55/8.64              @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9372_DERIV__real__root,axiom,
% 15.55/8.64      ! [N: nat,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 15.55/8.64         => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X3 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9373_DERIV__arccos,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 15.55/8.64       => ( ( ord_less_real @ X3 @ one_one_real )
% 15.55/8.64         => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9374_DERIV__arcsin,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 15.55/8.64       => ( ( ord_less_real @ X3 @ one_one_real )
% 15.55/8.64         => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9375_Maclaurin__all__le__objl,axiom,
% 15.55/8.64      ! [Diff: nat > real > real,F: real > real,X3: real,N: nat] :
% 15.55/8.64        ( ( ( ( Diff @ zero_zero_nat )
% 15.55/8.64            = F )
% 15.55/8.64          & ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 15.55/8.64       => ? [T3: real] :
% 15.55/8.64            ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 15.55/8.64            & ( ( F @ X3 )
% 15.55/8.64              = ( plus_plus_real
% 15.55/8.64                @ ( groups6591440286371151544t_real
% 15.55/8.64                  @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X3 @ M3 ) )
% 15.55/8.64                  @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.64                @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9376_Maclaurin__all__le,axiom,
% 15.55/8.64      ! [Diff: nat > real > real,F: real > real,X3: real,N: nat] :
% 15.55/8.64        ( ( ( Diff @ zero_zero_nat )
% 15.55/8.64          = F )
% 15.55/8.64       => ( ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 15.55/8.64         => ? [T3: real] :
% 15.55/8.64              ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 15.55/8.64              & ( ( F @ X3 )
% 15.55/8.64                = ( plus_plus_real
% 15.55/8.64                  @ ( groups6591440286371151544t_real
% 15.55/8.64                    @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X3 @ M3 ) )
% 15.55/8.64                    @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.64                  @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9377_DERIV__odd__real__root,axiom,
% 15.55/8.64      ! [N: nat,X3: real] :
% 15.55/8.64        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.64       => ( ( X3 != zero_zero_real )
% 15.55/8.64         => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X3 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9378_Maclaurin,axiom,
% 15.55/8.64      ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 15.55/8.64        ( ( ord_less_real @ zero_zero_real @ H2 )
% 15.55/8.64       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64         => ( ( ( Diff @ zero_zero_nat )
% 15.55/8.64              = F )
% 15.55/8.64           => ( ! [M4: nat,T3: real] :
% 15.55/8.64                  ( ( ( ord_less_nat @ M4 @ N )
% 15.55/8.64                    & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 15.55/8.64                    & ( ord_less_eq_real @ T3 @ H2 ) )
% 15.55/8.64                 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 15.55/8.64             => ? [T3: real] :
% 15.55/8.64                  ( ( ord_less_real @ zero_zero_real @ T3 )
% 15.55/8.64                  & ( ord_less_real @ T3 @ H2 )
% 15.55/8.64                  & ( ( F @ H2 )
% 15.55/8.64                    = ( plus_plus_real
% 15.55/8.64                      @ ( groups6591440286371151544t_real
% 15.55/8.64                        @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 15.55/8.64                        @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.64                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9379_Maclaurin2,axiom,
% 15.55/8.64      ! [H2: real,Diff: nat > real > real,F: real > real,N: nat] :
% 15.55/8.64        ( ( ord_less_real @ zero_zero_real @ H2 )
% 15.55/8.64       => ( ( ( Diff @ zero_zero_nat )
% 15.55/8.64            = F )
% 15.55/8.64         => ( ! [M4: nat,T3: real] :
% 15.55/8.64                ( ( ( ord_less_nat @ M4 @ N )
% 15.55/8.64                  & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 15.55/8.64                  & ( ord_less_eq_real @ T3 @ H2 ) )
% 15.55/8.64               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 15.55/8.64           => ? [T3: real] :
% 15.55/8.64                ( ( ord_less_real @ zero_zero_real @ T3 )
% 15.55/8.64                & ( ord_less_eq_real @ T3 @ H2 )
% 15.55/8.64                & ( ( F @ H2 )
% 15.55/8.64                  = ( plus_plus_real
% 15.55/8.64                    @ ( groups6591440286371151544t_real
% 15.55/8.64                      @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 15.55/8.64                      @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.64                    @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9380_Maclaurin__minus,axiom,
% 15.55/8.64      ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 15.55/8.64        ( ( ord_less_real @ H2 @ zero_zero_real )
% 15.55/8.64       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64         => ( ( ( Diff @ zero_zero_nat )
% 15.55/8.64              = F )
% 15.55/8.64           => ( ! [M4: nat,T3: real] :
% 15.55/8.64                  ( ( ( ord_less_nat @ M4 @ N )
% 15.55/8.64                    & ( ord_less_eq_real @ H2 @ T3 )
% 15.55/8.64                    & ( ord_less_eq_real @ T3 @ zero_zero_real ) )
% 15.55/8.64                 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 15.55/8.64             => ? [T3: real] :
% 15.55/8.64                  ( ( ord_less_real @ H2 @ T3 )
% 15.55/8.64                  & ( ord_less_real @ T3 @ zero_zero_real )
% 15.55/8.64                  & ( ( F @ H2 )
% 15.55/8.64                    = ( plus_plus_real
% 15.55/8.64                      @ ( groups6591440286371151544t_real
% 15.55/8.64                        @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 15.55/8.64                        @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.64                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9381_Maclaurin__all__lt,axiom,
% 15.55/8.64      ! [Diff: nat > real > real,F: real > real,N: nat,X3: real] :
% 15.55/8.64        ( ( ( Diff @ zero_zero_nat )
% 15.55/8.64          = F )
% 15.55/8.64       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64         => ( ( X3 != zero_zero_real )
% 15.55/8.64           => ( ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 15.55/8.64             => ? [T3: real] :
% 15.55/8.64                  ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 15.55/8.64                  & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 15.55/8.64                  & ( ( F @ X3 )
% 15.55/8.64                    = ( plus_plus_real
% 15.55/8.64                      @ ( groups6591440286371151544t_real
% 15.55/8.64                        @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X3 @ M3 ) )
% 15.55/8.64                        @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.64                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9382_Maclaurin__bi__le,axiom,
% 15.55/8.64      ! [Diff: nat > real > real,F: real > real,N: nat,X3: real] :
% 15.55/8.64        ( ( ( Diff @ zero_zero_nat )
% 15.55/8.64          = F )
% 15.55/8.64       => ( ! [M4: nat,T3: real] :
% 15.55/8.64              ( ( ( ord_less_nat @ M4 @ N )
% 15.55/8.64                & ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) ) )
% 15.55/8.64             => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 15.55/8.64         => ? [T3: real] :
% 15.55/8.64              ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 15.55/8.64              & ( ( F @ X3 )
% 15.55/8.64                = ( plus_plus_real
% 15.55/8.64                  @ ( groups6591440286371151544t_real
% 15.55/8.64                    @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X3 @ M3 ) )
% 15.55/8.64                    @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.64                  @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9383_Taylor__down,axiom,
% 15.55/8.64      ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ( Diff @ zero_zero_nat )
% 15.55/8.64            = F )
% 15.55/8.64         => ( ! [M4: nat,T3: real] :
% 15.55/8.64                ( ( ( ord_less_nat @ M4 @ N )
% 15.55/8.64                  & ( ord_less_eq_real @ A @ T3 )
% 15.55/8.64                  & ( ord_less_eq_real @ T3 @ B ) )
% 15.55/8.64               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 15.55/8.64           => ( ( ord_less_real @ A @ C )
% 15.55/8.64             => ( ( ord_less_eq_real @ C @ B )
% 15.55/8.64               => ? [T3: real] :
% 15.55/8.64                    ( ( ord_less_real @ A @ T3 )
% 15.55/8.64                    & ( ord_less_real @ T3 @ C )
% 15.55/8.64                    & ( ( F @ A )
% 15.55/8.64                      = ( plus_plus_real
% 15.55/8.64                        @ ( groups6591440286371151544t_real
% 15.55/8.64                          @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M3 ) )
% 15.55/8.64                          @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.64                        @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9384_Taylor__up,axiom,
% 15.55/8.64      ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ( Diff @ zero_zero_nat )
% 15.55/8.64            = F )
% 15.55/8.64         => ( ! [M4: nat,T3: real] :
% 15.55/8.64                ( ( ( ord_less_nat @ M4 @ N )
% 15.55/8.64                  & ( ord_less_eq_real @ A @ T3 )
% 15.55/8.64                  & ( ord_less_eq_real @ T3 @ B ) )
% 15.55/8.64               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 15.55/8.64           => ( ( ord_less_eq_real @ A @ C )
% 15.55/8.64             => ( ( ord_less_real @ C @ B )
% 15.55/8.64               => ? [T3: real] :
% 15.55/8.64                    ( ( ord_less_real @ C @ T3 )
% 15.55/8.64                    & ( ord_less_real @ T3 @ B )
% 15.55/8.64                    & ( ( F @ B )
% 15.55/8.64                      = ( plus_plus_real
% 15.55/8.64                        @ ( groups6591440286371151544t_real
% 15.55/8.64                          @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M3 ) )
% 15.55/8.64                          @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.64                        @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9385_Taylor,axiom,
% 15.55/8.64      ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X3: real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( ( Diff @ zero_zero_nat )
% 15.55/8.64            = F )
% 15.55/8.64         => ( ! [M4: nat,T3: real] :
% 15.55/8.64                ( ( ( ord_less_nat @ M4 @ N )
% 15.55/8.64                  & ( ord_less_eq_real @ A @ T3 )
% 15.55/8.64                  & ( ord_less_eq_real @ T3 @ B ) )
% 15.55/8.64               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 15.55/8.64           => ( ( ord_less_eq_real @ A @ C )
% 15.55/8.64             => ( ( ord_less_eq_real @ C @ B )
% 15.55/8.64               => ( ( ord_less_eq_real @ A @ X3 )
% 15.55/8.64                 => ( ( ord_less_eq_real @ X3 @ B )
% 15.55/8.64                   => ( ( X3 != C )
% 15.55/8.64                     => ? [T3: real] :
% 15.55/8.64                          ( ( ( ord_less_real @ X3 @ C )
% 15.55/8.64                           => ( ( ord_less_real @ X3 @ T3 )
% 15.55/8.64                              & ( ord_less_real @ T3 @ C ) ) )
% 15.55/8.64                          & ( ~ ( ord_less_real @ X3 @ C )
% 15.55/8.64                           => ( ( ord_less_real @ C @ T3 )
% 15.55/8.64                              & ( ord_less_real @ T3 @ X3 ) ) )
% 15.55/8.64                          & ( ( F @ X3 )
% 15.55/8.64                            = ( plus_plus_real
% 15.55/8.64                              @ ( groups6591440286371151544t_real
% 15.55/8.64                                @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ X3 @ C ) @ M3 ) )
% 15.55/8.64                                @ ( set_ord_lessThan_nat @ N ) )
% 15.55/8.64                              @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X3 @ C ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9386_Maclaurin__lemma2,axiom,
% 15.55/8.64      ! [N: nat,H2: real,Diff: nat > real > real,K: nat,B5: real] :
% 15.55/8.64        ( ! [M4: nat,T3: real] :
% 15.55/8.64            ( ( ( ord_less_nat @ M4 @ N )
% 15.55/8.64              & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 15.55/8.64              & ( ord_less_eq_real @ T3 @ H2 ) )
% 15.55/8.64           => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 15.55/8.64       => ( ( N
% 15.55/8.64            = ( suc @ K ) )
% 15.55/8.64         => ! [M2: nat,T6: real] :
% 15.55/8.64              ( ( ( ord_less_nat @ M2 @ N )
% 15.55/8.64                & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 15.55/8.64                & ( ord_less_eq_real @ T6 @ H2 ) )
% 15.55/8.64             => ( has_fi5821293074295781190e_real
% 15.55/8.64                @ ^ [U2: real] :
% 15.55/8.64                    ( minus_minus_real @ ( Diff @ M2 @ U2 )
% 15.55/8.64                    @ ( plus_plus_real
% 15.55/8.64                      @ ( groups6591440286371151544t_real
% 15.55/8.64                        @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M2 @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ U2 @ P5 ) )
% 15.55/8.64                        @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M2 ) ) )
% 15.55/8.64                      @ ( times_times_real @ B5 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N @ M2 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) )
% 15.55/8.64                @ ( minus_minus_real @ ( Diff @ ( suc @ M2 ) @ T6 )
% 15.55/8.64                  @ ( plus_plus_real
% 15.55/8.64                    @ ( groups6591440286371151544t_real
% 15.55/8.64                      @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M2 ) @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ T6 @ P5 ) )
% 15.55/8.64                      @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) )
% 15.55/8.64                    @ ( times_times_real @ B5 @ ( divide_divide_real @ ( power_power_real @ T6 @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) ) ) ) )
% 15.55/8.64                @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9387_isCont__Lb__Ub,axiom,
% 15.55/8.64      ! [A: real,B: real,F: real > real] :
% 15.55/8.64        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.64       => ( ! [X4: real] :
% 15.55/8.64              ( ( ( ord_less_eq_real @ A @ X4 )
% 15.55/8.64                & ( ord_less_eq_real @ X4 @ B ) )
% 15.55/8.64             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ F ) )
% 15.55/8.64         => ? [L6: real,M8: real] :
% 15.55/8.64              ( ! [X6: real] :
% 15.55/8.64                  ( ( ( ord_less_eq_real @ A @ X6 )
% 15.55/8.64                    & ( ord_less_eq_real @ X6 @ B ) )
% 15.55/8.64                 => ( ( ord_less_eq_real @ L6 @ ( F @ X6 ) )
% 15.55/8.64                    & ( ord_less_eq_real @ ( F @ X6 ) @ M8 ) ) )
% 15.55/8.64              & ! [Y6: real] :
% 15.55/8.64                  ( ( ( ord_less_eq_real @ L6 @ Y6 )
% 15.55/8.64                    & ( ord_less_eq_real @ Y6 @ M8 ) )
% 15.55/8.64                 => ? [X4: real] :
% 15.55/8.64                      ( ( ord_less_eq_real @ A @ X4 )
% 15.55/8.64                      & ( ord_less_eq_real @ X4 @ B )
% 15.55/8.64                      & ( ( F @ X4 )
% 15.55/8.64                        = Y6 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9388_LIM__fun__gt__zero,axiom,
% 15.55/8.64      ! [F: real > real,L: real,C: real] :
% 15.55/8.64        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 15.55/8.64       => ( ( ord_less_real @ zero_zero_real @ L )
% 15.55/8.64         => ? [R: real] :
% 15.55/8.64              ( ( ord_less_real @ zero_zero_real @ R )
% 15.55/8.64              & ! [X6: real] :
% 15.55/8.64                  ( ( ( X6 != C )
% 15.55/8.64                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X6 ) ) @ R ) )
% 15.55/8.64                 => ( ord_less_real @ zero_zero_real @ ( F @ X6 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9389_LIM__fun__not__zero,axiom,
% 15.55/8.64      ! [F: real > real,L: real,C: real] :
% 15.55/8.64        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 15.55/8.64       => ( ( L != zero_zero_real )
% 15.55/8.64         => ? [R: real] :
% 15.55/8.64              ( ( ord_less_real @ zero_zero_real @ R )
% 15.55/8.64              & ! [X6: real] :
% 15.55/8.64                  ( ( ( X6 != C )
% 15.55/8.64                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X6 ) ) @ R ) )
% 15.55/8.64                 => ( ( F @ X6 )
% 15.55/8.64                   != zero_zero_real ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9390_LIM__fun__less__zero,axiom,
% 15.55/8.64      ! [F: real > real,L: real,C: real] :
% 15.55/8.64        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 15.55/8.64       => ( ( ord_less_real @ L @ zero_zero_real )
% 15.55/8.64         => ? [R: real] :
% 15.55/8.64              ( ( ord_less_real @ zero_zero_real @ R )
% 15.55/8.64              & ! [X6: real] :
% 15.55/8.64                  ( ( ( X6 != C )
% 15.55/8.64                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X6 ) ) @ R ) )
% 15.55/8.64                 => ( ord_less_real @ ( F @ X6 ) @ zero_zero_real ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9391_isCont__real__sqrt,axiom,
% 15.55/8.64      ! [X3: real] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ sqrt ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9392_isCont__real__root,axiom,
% 15.55/8.64      ! [X3: real,N: nat] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ ( root @ N ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9393_isCont__inverse__function2,axiom,
% 15.55/8.64      ! [A: real,X3: real,B: real,G: real > real,F: real > real] :
% 15.55/8.64        ( ( ord_less_real @ A @ X3 )
% 15.55/8.64       => ( ( ord_less_real @ X3 @ B )
% 15.55/8.64         => ( ! [Z3: real] :
% 15.55/8.64                ( ( ord_less_eq_real @ A @ Z3 )
% 15.55/8.64               => ( ( ord_less_eq_real @ Z3 @ B )
% 15.55/8.64                 => ( ( G @ ( F @ Z3 ) )
% 15.55/8.64                    = Z3 ) ) )
% 15.55/8.64           => ( ! [Z3: real] :
% 15.55/8.64                  ( ( ord_less_eq_real @ A @ Z3 )
% 15.55/8.64                 => ( ( ord_less_eq_real @ Z3 @ B )
% 15.55/8.64                   => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 15.55/8.64             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X3 ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9394_isCont__ln,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( X3 != zero_zero_real )
% 15.55/8.64       => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ ln_ln_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9395_isCont__arcosh,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_real @ one_one_real @ X3 )
% 15.55/8.64       => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ arcosh_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9396_LIM__cos__div__sin,axiom,
% 15.55/8.64      ( filterlim_real_real
% 15.55/8.64      @ ^ [X: real] : ( divide_divide_real @ ( cos_real @ X ) @ ( sin_real @ X ) )
% 15.55/8.64      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 15.55/8.64      @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9397_DERIV__inverse__function,axiom,
% 15.55/8.64      ! [F: real > real,D5: real,G: real > real,X3: real,A: real,B: real] :
% 15.55/8.64        ( ( has_fi5821293074295781190e_real @ F @ D5 @ ( topolo2177554685111907308n_real @ ( G @ X3 ) @ top_top_set_real ) )
% 15.55/8.64       => ( ( D5 != zero_zero_real )
% 15.55/8.64         => ( ( ord_less_real @ A @ X3 )
% 15.55/8.64           => ( ( ord_less_real @ X3 @ B )
% 15.55/8.64             => ( ! [Y4: real] :
% 15.55/8.64                    ( ( ord_less_real @ A @ Y4 )
% 15.55/8.64                   => ( ( ord_less_real @ Y4 @ B )
% 15.55/8.64                     => ( ( F @ ( G @ Y4 ) )
% 15.55/8.64                        = Y4 ) ) )
% 15.55/8.64               => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ G )
% 15.55/8.64                 => ( has_fi5821293074295781190e_real @ G @ ( inverse_inverse_real @ D5 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9398_isCont__arccos,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 15.55/8.64       => ( ( ord_less_real @ X3 @ one_one_real )
% 15.55/8.64         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ arccos ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9399_isCont__arcsin,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 15.55/8.64       => ( ( ord_less_real @ X3 @ one_one_real )
% 15.55/8.64         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ arcsin ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9400_LIM__less__bound,axiom,
% 15.55/8.64      ! [B: real,X3: real,F: real > real] :
% 15.55/8.64        ( ( ord_less_real @ B @ X3 )
% 15.55/8.64       => ( ! [X4: real] :
% 15.55/8.64              ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ B @ X3 ) )
% 15.55/8.64             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 15.55/8.64         => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F )
% 15.55/8.64           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9401_isCont__artanh,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 15.55/8.64       => ( ( ord_less_real @ X3 @ one_one_real )
% 15.55/8.64         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ artanh_real ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9402_isCont__inverse__function,axiom,
% 15.55/8.64      ! [D3: real,X3: real,G: real > real,F: real > real] :
% 15.55/8.64        ( ( ord_less_real @ zero_zero_real @ D3 )
% 15.55/8.64       => ( ! [Z3: real] :
% 15.55/8.64              ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X3 ) ) @ D3 )
% 15.55/8.64             => ( ( G @ ( F @ Z3 ) )
% 15.55/8.64                = Z3 ) )
% 15.55/8.64         => ( ! [Z3: real] :
% 15.55/8.64                ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X3 ) ) @ D3 )
% 15.55/8.64               => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) )
% 15.55/8.64           => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X3 ) @ top_top_set_real ) @ G ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9403_GMVT_H,axiom,
% 15.55/8.64      ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F5: real > real] :
% 15.55/8.64        ( ( ord_less_real @ A @ B )
% 15.55/8.64       => ( ! [Z3: real] :
% 15.55/8.64              ( ( ord_less_eq_real @ A @ Z3 )
% 15.55/8.64             => ( ( ord_less_eq_real @ Z3 @ B )
% 15.55/8.64               => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 15.55/8.64         => ( ! [Z3: real] :
% 15.55/8.64                ( ( ord_less_eq_real @ A @ Z3 )
% 15.55/8.64               => ( ( ord_less_eq_real @ Z3 @ B )
% 15.55/8.64                 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ G ) ) )
% 15.55/8.64           => ( ! [Z3: real] :
% 15.55/8.64                  ( ( ord_less_real @ A @ Z3 )
% 15.55/8.64                 => ( ( ord_less_real @ Z3 @ B )
% 15.55/8.64                   => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 15.55/8.64             => ( ! [Z3: real] :
% 15.55/8.64                    ( ( ord_less_real @ A @ Z3 )
% 15.55/8.64                   => ( ( ord_less_real @ Z3 @ B )
% 15.55/8.64                     => ( has_fi5821293074295781190e_real @ F @ ( F5 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 15.55/8.64               => ? [C2: real] :
% 15.55/8.64                    ( ( ord_less_real @ A @ C2 )
% 15.55/8.64                    & ( ord_less_real @ C2 @ B )
% 15.55/8.64                    & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C2 ) )
% 15.55/8.64                      = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F5 @ C2 ) ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9404_summable__Leibniz_I2_J,axiom,
% 15.55/8.64      ! [A: nat > real] :
% 15.55/8.64        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 15.55/8.64       => ( ( topolo6980174941875973593q_real @ A )
% 15.55/8.64         => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 15.55/8.64           => ! [N8: nat] :
% 15.55/8.64                ( member_real
% 15.55/8.64                @ ( suminf_real
% 15.55/8.64                  @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 15.55/8.64                @ ( set_or1222579329274155063t_real
% 15.55/8.64                  @ ( groups6591440286371151544t_real
% 15.55/8.64                    @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 15.55/8.64                    @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) ) )
% 15.55/8.64                  @ ( groups6591440286371151544t_real
% 15.55/8.64                    @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 15.55/8.64                    @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9405_summable__Leibniz_I3_J,axiom,
% 15.55/8.64      ! [A: nat > real] :
% 15.55/8.64        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 15.55/8.64       => ( ( topolo6980174941875973593q_real @ A )
% 15.55/8.64         => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 15.55/8.64           => ! [N8: nat] :
% 15.55/8.64                ( member_real
% 15.55/8.64                @ ( suminf_real
% 15.55/8.64                  @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 15.55/8.64                @ ( set_or1222579329274155063t_real
% 15.55/8.64                  @ ( groups6591440286371151544t_real
% 15.55/8.64                    @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 15.55/8.64                    @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) @ one_one_nat ) ) )
% 15.55/8.64                  @ ( groups6591440286371151544t_real
% 15.55/8.64                    @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 15.55/8.64                    @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9406_summable__Leibniz_H_I4_J,axiom,
% 15.55/8.64      ! [A: nat > real,N: nat] :
% 15.55/8.64        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 15.55/8.64       => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 15.55/8.64         => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 15.55/8.64           => ( ord_less_eq_real
% 15.55/8.64              @ ( suminf_real
% 15.55/8.64                @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 15.55/8.64              @ ( groups6591440286371151544t_real
% 15.55/8.64                @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 15.55/8.64                @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9407_mult__nat__left__at__top,axiom,
% 15.55/8.64      ! [C: nat] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ C )
% 15.55/8.64       => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9408_mult__nat__right__at__top,axiom,
% 15.55/8.64      ! [C: nat] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ C )
% 15.55/8.64       => ( filterlim_nat_nat
% 15.55/8.64          @ ^ [X: nat] : ( times_times_nat @ X @ C )
% 15.55/8.64          @ at_top_nat
% 15.55/8.64          @ at_top_nat ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9409_monoseq__convergent,axiom,
% 15.55/8.64      ! [X9: nat > real,B5: real] :
% 15.55/8.64        ( ( topolo6980174941875973593q_real @ X9 )
% 15.55/8.64       => ( ! [I3: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X9 @ I3 ) ) @ B5 )
% 15.55/8.64         => ~ ! [L6: real] :
% 15.55/8.64                ~ ( filterlim_nat_real @ X9 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9410_LIMSEQ__root,axiom,
% 15.55/8.64      ( filterlim_nat_real
% 15.55/8.64      @ ^ [N3: nat] : ( root @ N3 @ ( semiri5074537144036343181t_real @ N3 ) )
% 15.55/8.64      @ ( topolo2815343760600316023s_real @ one_one_real )
% 15.55/8.64      @ at_top_nat ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9411_nested__sequence__unique,axiom,
% 15.55/8.64      ! [F: nat > real,G: nat > real] :
% 15.55/8.64        ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 15.55/8.64       => ( ! [N2: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N2 ) ) @ ( G @ N2 ) )
% 15.55/8.64         => ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 15.55/8.64           => ( ( filterlim_nat_real
% 15.55/8.64                @ ^ [N3: nat] : ( minus_minus_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 15.55/8.64                @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 15.55/8.64                @ at_top_nat )
% 15.55/8.64             => ? [L4: real] :
% 15.55/8.64                  ( ! [N8: nat] : ( ord_less_eq_real @ ( F @ N8 ) @ L4 )
% 15.55/8.64                  & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 15.55/8.64                  & ! [N8: nat] : ( ord_less_eq_real @ L4 @ ( G @ N8 ) )
% 15.55/8.64                  & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9412_LIMSEQ__inverse__zero,axiom,
% 15.55/8.64      ! [X9: nat > real] :
% 15.55/8.64        ( ! [R: real] :
% 15.55/8.64          ? [N6: nat] :
% 15.55/8.64          ! [N2: nat] :
% 15.55/8.64            ( ( ord_less_eq_nat @ N6 @ N2 )
% 15.55/8.64           => ( ord_less_real @ R @ ( X9 @ N2 ) ) )
% 15.55/8.64       => ( filterlim_nat_real
% 15.55/8.64          @ ^ [N3: nat] : ( inverse_inverse_real @ ( X9 @ N3 ) )
% 15.55/8.64          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 15.55/8.64          @ at_top_nat ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9413_lim__inverse__n_H,axiom,
% 15.55/8.64      ( filterlim_nat_real
% 15.55/8.64      @ ^ [N3: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N3 ) )
% 15.55/8.64      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 15.55/8.64      @ at_top_nat ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9414_LIMSEQ__root__const,axiom,
% 15.55/8.64      ! [C: real] :
% 15.55/8.64        ( ( ord_less_real @ zero_zero_real @ C )
% 15.55/8.64       => ( filterlim_nat_real
% 15.55/8.64          @ ^ [N3: nat] : ( root @ N3 @ C )
% 15.55/8.64          @ ( topolo2815343760600316023s_real @ one_one_real )
% 15.55/8.64          @ at_top_nat ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9415_LIMSEQ__inverse__real__of__nat,axiom,
% 15.55/8.64      ( filterlim_nat_real
% 15.55/8.64      @ ^ [N3: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) )
% 15.55/8.64      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 15.55/8.64      @ at_top_nat ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9416_LIMSEQ__inverse__real__of__nat__add,axiom,
% 15.55/8.64      ! [R2: real] :
% 15.55/8.64        ( filterlim_nat_real
% 15.55/8.64        @ ^ [N3: nat] : ( plus_plus_real @ R2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 15.55/8.64        @ ( topolo2815343760600316023s_real @ R2 )
% 15.55/8.64        @ at_top_nat ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9417_increasing__LIMSEQ,axiom,
% 15.55/8.64      ! [F: nat > real,L: real] :
% 15.55/8.64        ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 15.55/8.64       => ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ L )
% 15.55/8.64         => ( ! [E: real] :
% 15.55/8.64                ( ( ord_less_real @ zero_zero_real @ E )
% 15.55/8.64               => ? [N8: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F @ N8 ) @ E ) ) )
% 15.55/8.64           => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9418_LIMSEQ__realpow__zero,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.64       => ( ( ord_less_real @ X3 @ one_one_real )
% 15.55/8.64         => ( filterlim_nat_real @ ( power_power_real @ X3 ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9419_LIMSEQ__divide__realpow__zero,axiom,
% 15.55/8.64      ! [X3: real,A: real] :
% 15.55/8.64        ( ( ord_less_real @ one_one_real @ X3 )
% 15.55/8.64       => ( filterlim_nat_real
% 15.55/8.64          @ ^ [N3: nat] : ( divide_divide_real @ A @ ( power_power_real @ X3 @ N3 ) )
% 15.55/8.64          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 15.55/8.64          @ at_top_nat ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9420_LIMSEQ__abs__realpow__zero2,axiom,
% 15.55/8.64      ! [C: real] :
% 15.55/8.64        ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 15.55/8.64       => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9421_LIMSEQ__abs__realpow__zero,axiom,
% 15.55/8.64      ! [C: real] :
% 15.55/8.64        ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 15.55/8.64       => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9422_LIMSEQ__inverse__realpow__zero,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_real @ one_one_real @ X3 )
% 15.55/8.64       => ( filterlim_nat_real
% 15.55/8.64          @ ^ [N3: nat] : ( inverse_inverse_real @ ( power_power_real @ X3 @ N3 ) )
% 15.55/8.64          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 15.55/8.64          @ at_top_nat ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9423_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 15.55/8.64      ! [R2: real] :
% 15.55/8.64        ( filterlim_nat_real
% 15.55/8.64        @ ^ [N3: nat] : ( plus_plus_real @ R2 @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) ) )
% 15.55/8.64        @ ( topolo2815343760600316023s_real @ R2 )
% 15.55/8.64        @ at_top_nat ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9424_tendsto__exp__limit__sequentially,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( filterlim_nat_real
% 15.55/8.64        @ ^ [N3: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X3 @ ( semiri5074537144036343181t_real @ N3 ) ) ) @ N3 )
% 15.55/8.64        @ ( topolo2815343760600316023s_real @ ( exp_real @ X3 ) )
% 15.55/8.64        @ at_top_nat ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9425_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 15.55/8.64      ! [R2: real] :
% 15.55/8.64        ( filterlim_nat_real
% 15.55/8.64        @ ^ [N3: nat] : ( times_times_real @ R2 @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) ) ) )
% 15.55/8.64        @ ( topolo2815343760600316023s_real @ R2 )
% 15.55/8.64        @ at_top_nat ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9426_summable__Leibniz_I1_J,axiom,
% 15.55/8.64      ! [A: nat > real] :
% 15.55/8.64        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 15.55/8.64       => ( ( topolo6980174941875973593q_real @ A )
% 15.55/8.64         => ( summable_real
% 15.55/8.64            @ ^ [N3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( A @ N3 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9427_summable,axiom,
% 15.55/8.64      ! [A: nat > real] :
% 15.55/8.64        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 15.55/8.64       => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 15.55/8.64         => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 15.55/8.64           => ( summable_real
% 15.55/8.64              @ ^ [N3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( A @ N3 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9428_cos__diff__limit__1,axiom,
% 15.55/8.64      ! [Theta: nat > real,Theta2: real] :
% 15.55/8.64        ( ( filterlim_nat_real
% 15.55/8.64          @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 15.55/8.64          @ ( topolo2815343760600316023s_real @ one_one_real )
% 15.55/8.64          @ at_top_nat )
% 15.55/8.64       => ~ ! [K2: nat > int] :
% 15.55/8.64              ~ ( filterlim_nat_real
% 15.55/8.64                @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K2 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 15.55/8.64                @ ( topolo2815343760600316023s_real @ Theta2 )
% 15.55/8.64                @ at_top_nat ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9429_cos__limit__1,axiom,
% 15.55/8.64      ! [Theta: nat > real] :
% 15.55/8.64        ( ( filterlim_nat_real
% 15.55/8.64          @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 15.55/8.64          @ ( topolo2815343760600316023s_real @ one_one_real )
% 15.55/8.64          @ at_top_nat )
% 15.55/8.64       => ? [K2: nat > int] :
% 15.55/8.64            ( filterlim_nat_real
% 15.55/8.64            @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K2 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 15.55/8.64            @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 15.55/8.64            @ at_top_nat ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9430_summable__Leibniz_I4_J,axiom,
% 15.55/8.64      ! [A: nat > real] :
% 15.55/8.64        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 15.55/8.64       => ( ( topolo6980174941875973593q_real @ A )
% 15.55/8.64         => ( filterlim_nat_real
% 15.55/8.64            @ ^ [N3: nat] :
% 15.55/8.64                ( groups6591440286371151544t_real
% 15.55/8.64                @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 15.55/8.64                @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 15.55/8.64            @ ( topolo2815343760600316023s_real
% 15.55/8.64              @ ( suminf_real
% 15.55/8.64                @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 15.55/8.64            @ at_top_nat ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9431_zeroseq__arctan__series,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 15.55/8.64       => ( filterlim_nat_real
% 15.55/8.64          @ ^ [N3: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 15.55/8.64          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 15.55/8.64          @ at_top_nat ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9432_summable__Leibniz_H_I3_J,axiom,
% 15.55/8.64      ! [A: nat > real] :
% 15.55/8.64        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 15.55/8.64       => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 15.55/8.64         => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 15.55/8.64           => ( filterlim_nat_real
% 15.55/8.64              @ ^ [N3: nat] :
% 15.55/8.64                  ( groups6591440286371151544t_real
% 15.55/8.64                  @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 15.55/8.64                  @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 15.55/8.64              @ ( topolo2815343760600316023s_real
% 15.55/8.64                @ ( suminf_real
% 15.55/8.64                  @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 15.55/8.64              @ at_top_nat ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9433_summable__Leibniz_H_I2_J,axiom,
% 15.55/8.64      ! [A: nat > real,N: nat] :
% 15.55/8.64        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 15.55/8.64       => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 15.55/8.64         => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 15.55/8.64           => ( ord_less_eq_real
% 15.55/8.64              @ ( groups6591440286371151544t_real
% 15.55/8.64                @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 15.55/8.64                @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 15.55/8.64              @ ( suminf_real
% 15.55/8.64                @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9434_sums__alternating__upper__lower,axiom,
% 15.55/8.64      ! [A: nat > real] :
% 15.55/8.64        ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 15.55/8.64       => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 15.55/8.64         => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 15.55/8.64           => ? [L4: real] :
% 15.55/8.64                ( ! [N8: nat] :
% 15.55/8.64                    ( ord_less_eq_real
% 15.55/8.64                    @ ( groups6591440286371151544t_real
% 15.55/8.64                      @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 15.55/8.64                      @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) ) )
% 15.55/8.64                    @ L4 )
% 15.55/8.64                & ( filterlim_nat_real
% 15.55/8.64                  @ ^ [N3: nat] :
% 15.55/8.64                      ( groups6591440286371151544t_real
% 15.55/8.64                      @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 15.55/8.64                      @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 15.55/8.64                  @ ( topolo2815343760600316023s_real @ L4 )
% 15.55/8.64                  @ at_top_nat )
% 15.55/8.64                & ! [N8: nat] :
% 15.55/8.64                    ( ord_less_eq_real @ L4
% 15.55/8.64                    @ ( groups6591440286371151544t_real
% 15.55/8.64                      @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 15.55/8.64                      @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) @ one_one_nat ) ) ) )
% 15.55/8.64                & ( filterlim_nat_real
% 15.55/8.64                  @ ^ [N3: nat] :
% 15.55/8.64                      ( groups6591440286371151544t_real
% 15.55/8.64                      @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 15.55/8.64                      @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 15.55/8.64                  @ ( topolo2815343760600316023s_real @ L4 )
% 15.55/8.64                  @ at_top_nat ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9435_summable__Leibniz_I5_J,axiom,
% 15.55/8.64      ! [A: nat > real] :
% 15.55/8.64        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 15.55/8.64       => ( ( topolo6980174941875973593q_real @ A )
% 15.55/8.64         => ( filterlim_nat_real
% 15.55/8.64            @ ^ [N3: nat] :
% 15.55/8.64                ( groups6591440286371151544t_real
% 15.55/8.64                @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 15.55/8.64                @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 15.55/8.64            @ ( topolo2815343760600316023s_real
% 15.55/8.64              @ ( suminf_real
% 15.55/8.64                @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 15.55/8.64            @ at_top_nat ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9436_summable__Leibniz_H_I5_J,axiom,
% 15.55/8.64      ! [A: nat > real] :
% 15.55/8.64        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 15.55/8.64       => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 15.55/8.64         => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 15.55/8.64           => ( filterlim_nat_real
% 15.55/8.64              @ ^ [N3: nat] :
% 15.55/8.64                  ( groups6591440286371151544t_real
% 15.55/8.64                  @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 15.55/8.64                  @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 15.55/8.64              @ ( topolo2815343760600316023s_real
% 15.55/8.64                @ ( suminf_real
% 15.55/8.64                  @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 15.55/8.64              @ at_top_nat ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9437_tendsto__exp__limit__at__right,axiom,
% 15.55/8.64      ! [X3: real] :
% 15.55/8.64        ( filterlim_real_real
% 15.55/8.64        @ ^ [Y: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X3 @ Y ) ) @ ( divide_divide_real @ one_one_real @ Y ) )
% 15.55/8.64        @ ( topolo2815343760600316023s_real @ ( exp_real @ X3 ) )
% 15.55/8.64        @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9438_tendsto__arcosh__at__left__1,axiom,
% 15.55/8.64      filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9439_filterlim__tan__at__right,axiom,
% 15.55/8.64      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 ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9440_greaterThan__0,axiom,
% 15.55/8.64      ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 15.55/8.64      = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9441_exp__at__bot,axiom,
% 15.55/8.64      filterlim_real_real @ exp_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_bot_real ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9442_filterlim__inverse__at__bot__neg,axiom,
% 15.55/8.64      filterlim_real_real @ inverse_inverse_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5984915006950818249n_real @ zero_zero_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9443_ln__at__0,axiom,
% 15.55/8.64      filterlim_real_real @ ln_ln_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9444_DERIV__pos__imp__increasing__at__bot,axiom,
% 15.55/8.64      ! [B: real,F: real > real,Flim: real] :
% 15.55/8.64        ( ! [X4: real] :
% 15.55/8.64            ( ( ord_less_eq_real @ X4 @ B )
% 15.55/8.64           => ? [Y6: real] :
% 15.55/8.64                ( ( has_fi5821293074295781190e_real @ F @ Y6 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 15.55/8.64                & ( ord_less_real @ zero_zero_real @ Y6 ) ) )
% 15.55/8.64       => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 15.55/8.64         => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9445_filterlim__pow__at__bot__odd,axiom,
% 15.55/8.64      ! [N: nat,F: real > real,F4: filter_real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( filterlim_real_real @ F @ at_bot_real @ F4 )
% 15.55/8.64         => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.64           => ( filterlim_real_real
% 15.55/8.64              @ ^ [X: real] : ( power_power_real @ ( F @ X ) @ N )
% 15.55/8.64              @ at_bot_real
% 15.55/8.64              @ F4 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9446_tendsto__arctan__at__bot,axiom,
% 15.55/8.64      filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9447_filterlim__pow__at__bot__even,axiom,
% 15.55/8.64      ! [N: nat,F: real > real,F4: filter_real] :
% 15.55/8.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.64       => ( ( filterlim_real_real @ F @ at_bot_real @ F4 )
% 15.55/8.64         => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 15.55/8.64           => ( filterlim_real_real
% 15.55/8.64              @ ^ [X: real] : ( power_power_real @ ( F @ X ) @ N )
% 15.55/8.64              @ at_top_real
% 15.55/8.64              @ F4 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9448_rat__inverse__code,axiom,
% 15.55/8.64      ! [P6: rat] :
% 15.55/8.64        ( ( quotient_of @ ( inverse_inverse_rat @ P6 ) )
% 15.55/8.64        = ( produc4245557441103728435nt_int
% 15.55/8.64          @ ^ [A4: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( A4 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A4 ) @ B3 ) @ ( abs_abs_int @ A4 ) ) )
% 15.55/8.64          @ ( quotient_of @ P6 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9449_rat__zero__code,axiom,
% 15.55/8.64      ( ( quotient_of @ zero_zero_rat )
% 15.55/8.64      = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9450_quotient__of__number_I3_J,axiom,
% 15.55/8.64      ! [K: num] :
% 15.55/8.64        ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 15.55/8.64        = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9451_quotient__of__number_I5_J,axiom,
% 15.55/8.64      ! [K: num] :
% 15.55/8.64        ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 15.55/8.64        = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9452_sqrt__at__top,axiom,
% 15.55/8.64      filterlim_real_real @ sqrt @ at_top_real @ at_top_real ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9453_quotient__of__denom__pos,axiom,
% 15.55/8.64      ! [R2: rat,P6: int,Q3: int] :
% 15.55/8.64        ( ( ( quotient_of @ R2 )
% 15.55/8.64          = ( product_Pair_int_int @ P6 @ Q3 ) )
% 15.55/8.64       => ( ord_less_int @ zero_zero_int @ Q3 ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9454_filterlim__real__sequentially,axiom,
% 15.55/8.64      filterlim_nat_real @ semiri5074537144036343181t_real @ at_top_real @ at_top_nat ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9455_quotient__of__denom__pos_H,axiom,
% 15.55/8.64      ! [R2: rat] : ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ ( quotient_of @ R2 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9456_filterlim__real__at__infinity__sequentially,axiom,
% 15.55/8.64      filterlim_nat_real @ semiri5074537144036343181t_real @ at_infinity_real @ at_top_nat ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9457_rat__less__eq__code,axiom,
% 15.55/8.64      ( ord_less_eq_rat
% 15.55/8.64      = ( ^ [P5: rat,Q5: rat] :
% 15.55/8.64            ( produc4947309494688390418_int_o
% 15.55/8.64            @ ^ [A4: int,C3: int] :
% 15.55/8.64                ( produc4947309494688390418_int_o
% 15.55/8.64                @ ^ [B3: int,D4: int] : ( ord_less_eq_int @ ( times_times_int @ A4 @ D4 ) @ ( times_times_int @ C3 @ B3 ) )
% 15.55/8.64                @ ( quotient_of @ Q5 ) )
% 15.55/8.64            @ ( quotient_of @ P5 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9458_rat__less__code,axiom,
% 15.55/8.64      ( ord_less_rat
% 15.55/8.64      = ( ^ [P5: rat,Q5: rat] :
% 15.55/8.64            ( produc4947309494688390418_int_o
% 15.55/8.64            @ ^ [A4: int,C3: int] :
% 15.55/8.64                ( produc4947309494688390418_int_o
% 15.55/8.64                @ ^ [B3: int,D4: int] : ( ord_less_int @ ( times_times_int @ A4 @ D4 ) @ ( times_times_int @ C3 @ B3 ) )
% 15.55/8.64                @ ( quotient_of @ Q5 ) )
% 15.55/8.64            @ ( quotient_of @ P5 ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9459_ln__x__over__x__tendsto__0,axiom,
% 15.55/8.64      ( filterlim_real_real
% 15.55/8.64      @ ^ [X: real] : ( divide_divide_real @ ( ln_ln_real @ X ) @ X )
% 15.55/8.64      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 15.55/8.64      @ at_top_real ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9460_filterlim__inverse__at__top__right,axiom,
% 15.55/8.64      filterlim_real_real @ inverse_inverse_real @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9461_filterlim__inverse__at__right__top,axiom,
% 15.55/8.64      filterlim_real_real @ inverse_inverse_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) @ at_top_real ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9462_tendsto__power__div__exp__0,axiom,
% 15.55/8.64      ! [K: nat] :
% 15.55/8.64        ( filterlim_real_real
% 15.55/8.64        @ ^ [X: real] : ( divide_divide_real @ ( power_power_real @ X @ K ) @ ( exp_real @ X ) )
% 15.55/8.64        @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 15.55/8.64        @ at_top_real ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9463_filterlim__tan__at__left,axiom,
% 15.55/8.64      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 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9464_tendsto__arctan__at__top,axiom,
% 15.55/8.64      filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9465_DERIV__neg__imp__decreasing__at__top,axiom,
% 15.55/8.64      ! [B: real,F: real > real,Flim: real] :
% 15.55/8.64        ( ! [X4: real] :
% 15.55/8.64            ( ( ord_less_eq_real @ B @ X4 )
% 15.55/8.64           => ? [Y6: real] :
% 15.55/8.64                ( ( has_fi5821293074295781190e_real @ F @ Y6 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 15.55/8.64                & ( ord_less_real @ Y6 @ zero_zero_real ) ) )
% 15.55/8.64       => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 15.55/8.64         => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9466_lhopital__left__at__top,axiom,
% 15.55/8.64      ! [G: real > real,X3: real,G2: real > real,F: real > real,F5: real > real,Y3: real] :
% 15.55/8.64        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 15.55/8.64       => ( ( eventually_real
% 15.55/8.64            @ ^ [X: real] :
% 15.55/8.64                ( ( G2 @ X )
% 15.55/8.64               != zero_zero_real )
% 15.55/8.64            @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 15.55/8.64         => ( ( eventually_real
% 15.55/8.64              @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 15.55/8.64              @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 15.55/8.64           => ( ( eventually_real
% 15.55/8.64                @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 15.55/8.64                @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 15.55/8.64             => ( ( filterlim_real_real
% 15.55/8.64                  @ ^ [X: real] : ( divide_divide_real @ ( F5 @ X ) @ ( G2 @ X ) )
% 15.55/8.64                  @ ( topolo2815343760600316023s_real @ Y3 )
% 15.55/8.64                  @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 15.55/8.64               => ( filterlim_real_real
% 15.55/8.64                  @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 15.55/8.64                  @ ( topolo2815343760600316023s_real @ Y3 )
% 15.55/8.64                  @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9467_lhopital__right__at__top,axiom,
% 15.55/8.64      ! [G: real > real,X3: real,G2: real > real,F: real > real,F5: real > real,Y3: real] :
% 15.55/8.64        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 15.55/8.64       => ( ( eventually_real
% 15.55/8.64            @ ^ [X: real] :
% 15.55/8.64                ( ( G2 @ X )
% 15.55/8.64               != zero_zero_real )
% 15.55/8.64            @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 15.55/8.64         => ( ( eventually_real
% 15.55/8.64              @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 15.55/8.64              @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 15.55/8.64           => ( ( eventually_real
% 15.55/8.64                @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 15.55/8.64                @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 15.55/8.64             => ( ( filterlim_real_real
% 15.55/8.64                  @ ^ [X: real] : ( divide_divide_real @ ( F5 @ X ) @ ( G2 @ X ) )
% 15.55/8.64                  @ ( topolo2815343760600316023s_real @ Y3 )
% 15.55/8.64                  @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 15.55/8.64               => ( filterlim_real_real
% 15.55/8.64                  @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 15.55/8.64                  @ ( topolo2815343760600316023s_real @ Y3 )
% 15.55/8.64                  @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) ) ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9468_obtain__pos__sum,axiom,
% 15.55/8.64      ! [R2: rat] :
% 15.55/8.64        ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 15.55/8.64       => ~ ! [S3: rat] :
% 15.55/8.64              ( ( ord_less_rat @ zero_zero_rat @ S3 )
% 15.55/8.64             => ! [T3: rat] :
% 15.55/8.64                  ( ( ord_less_rat @ zero_zero_rat @ T3 )
% 15.55/8.64                 => ( R2
% 15.55/8.64                   != ( plus_plus_rat @ S3 @ T3 ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9469_sgn__rat__def,axiom,
% 15.55/8.64      ( sgn_sgn_rat
% 15.55/8.64      = ( ^ [A4: rat] : ( if_rat @ ( A4 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A4 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9470_abs__rat__def,axiom,
% 15.55/8.64      ( abs_abs_rat
% 15.55/8.64      = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9471_eventually__at__right__to__0,axiom,
% 15.55/8.64      ! [P: real > $o,A: real] :
% 15.55/8.64        ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 15.55/8.64        = ( eventually_real
% 15.55/8.64          @ ^ [X: real] : ( P @ ( plus_plus_real @ X @ A ) )
% 15.55/8.64          @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9472_eventually__at__right__real,axiom,
% 15.55/8.64      ! [A: real,B: real] :
% 15.55/8.64        ( ( ord_less_real @ A @ B )
% 15.55/8.64       => ( eventually_real
% 15.55/8.64          @ ^ [X: real] : ( member_real @ X @ ( set_or1633881224788618240n_real @ A @ B ) )
% 15.55/8.64          @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9473_eventually__at__left__real,axiom,
% 15.55/8.64      ! [B: real,A: real] :
% 15.55/8.64        ( ( ord_less_real @ B @ A )
% 15.55/8.64       => ( eventually_real
% 15.55/8.64          @ ^ [X: real] : ( member_real @ X @ ( set_or1633881224788618240n_real @ B @ A ) )
% 15.55/8.64          @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9474_eventually__at__top__to__right,axiom,
% 15.55/8.64      ! [P: real > $o] :
% 15.55/8.64        ( ( eventually_real @ P @ at_top_real )
% 15.55/8.64        = ( eventually_real
% 15.55/8.64          @ ^ [X: real] : ( P @ ( inverse_inverse_real @ X ) )
% 15.55/8.64          @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9475_eventually__at__right__to__top,axiom,
% 15.55/8.64      ! [P: real > $o] :
% 15.55/8.64        ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 15.55/8.64        = ( eventually_real
% 15.55/8.64          @ ^ [X: real] : ( P @ ( inverse_inverse_real @ X ) )
% 15.55/8.64          @ at_top_real ) ) ).
% 15.55/8.64  
% 15.55/8.64  thf(fact_9476_lhopital,axiom,
% 15.55/8.64      ! [F: real > real,X3: real,G: real > real,G2: real > real,F5: real > real,F4: filter_real] :
% 15.55/8.64        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.64       => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.64         => ( ( eventually_real
% 15.55/8.64              @ ^ [X: real] :
% 15.55/8.64                  ( ( G @ X )
% 15.55/8.64                 != zero_zero_real )
% 15.55/8.64              @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.64           => ( ( eventually_real
% 15.55/8.64                @ ^ [X: real] :
% 15.55/8.64                    ( ( G2 @ X )
% 15.55/8.64                   != zero_zero_real )
% 15.55/8.64                @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.65             => ( ( eventually_real
% 15.55/8.65                  @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 15.55/8.65                  @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.65               => ( ( eventually_real
% 15.55/8.65                    @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 15.55/8.65                    @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.65                 => ( ( filterlim_real_real
% 15.55/8.65                      @ ^ [X: real] : ( divide_divide_real @ ( F5 @ X ) @ ( G2 @ X ) )
% 15.55/8.65                      @ F4
% 15.55/8.65                      @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.65                   => ( filterlim_real_real
% 15.55/8.65                      @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 15.55/8.65                      @ F4
% 15.55/8.65                      @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9477_lhopital__at__top,axiom,
% 15.55/8.65      ! [G: real > real,X3: real,G2: real > real,F: real > real,F5: real > real,Y3: real] :
% 15.55/8.65        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.65       => ( ( eventually_real
% 15.55/8.65            @ ^ [X: real] :
% 15.55/8.65                ( ( G2 @ X )
% 15.55/8.65               != zero_zero_real )
% 15.55/8.65            @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.65         => ( ( eventually_real
% 15.55/8.65              @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 15.55/8.65              @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.65           => ( ( eventually_real
% 15.55/8.65                @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 15.55/8.65                @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.65             => ( ( filterlim_real_real
% 15.55/8.65                  @ ^ [X: real] : ( divide_divide_real @ ( F5 @ X ) @ ( G2 @ X ) )
% 15.55/8.65                  @ ( topolo2815343760600316023s_real @ Y3 )
% 15.55/8.65                  @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 15.55/8.65               => ( filterlim_real_real
% 15.55/8.65                  @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 15.55/8.65                  @ ( topolo2815343760600316023s_real @ Y3 )
% 15.55/8.65                  @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9478_lhospital__at__top__at__top,axiom,
% 15.55/8.65      ! [G: real > real,G2: real > real,F: real > real,F5: real > real,X3: real] :
% 15.55/8.65        ( ( filterlim_real_real @ G @ at_top_real @ at_top_real )
% 15.55/8.65       => ( ( eventually_real
% 15.55/8.65            @ ^ [X: real] :
% 15.55/8.65                ( ( G2 @ X )
% 15.55/8.65               != zero_zero_real )
% 15.55/8.65            @ at_top_real )
% 15.55/8.65         => ( ( eventually_real
% 15.55/8.65              @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 15.55/8.65              @ at_top_real )
% 15.55/8.65           => ( ( eventually_real
% 15.55/8.65                @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 15.55/8.65                @ at_top_real )
% 15.55/8.65             => ( ( filterlim_real_real
% 15.55/8.65                  @ ^ [X: real] : ( divide_divide_real @ ( F5 @ X ) @ ( G2 @ X ) )
% 15.55/8.65                  @ ( topolo2815343760600316023s_real @ X3 )
% 15.55/8.65                  @ at_top_real )
% 15.55/8.65               => ( filterlim_real_real
% 15.55/8.65                  @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 15.55/8.65                  @ ( topolo2815343760600316023s_real @ X3 )
% 15.55/8.65                  @ at_top_real ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9479_lhopital__right,axiom,
% 15.55/8.65      ! [F: real > real,X3: real,G: real > real,G2: real > real,F5: real > real,F4: filter_real] :
% 15.55/8.65        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 15.55/8.65       => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 15.55/8.65         => ( ( eventually_real
% 15.55/8.65              @ ^ [X: real] :
% 15.55/8.65                  ( ( G @ X )
% 15.55/8.65                 != zero_zero_real )
% 15.55/8.65              @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 15.55/8.65           => ( ( eventually_real
% 15.55/8.65                @ ^ [X: real] :
% 15.55/8.65                    ( ( G2 @ X )
% 15.55/8.65                   != zero_zero_real )
% 15.55/8.65                @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 15.55/8.65             => ( ( eventually_real
% 15.55/8.65                  @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 15.55/8.65                  @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 15.55/8.65               => ( ( eventually_real
% 15.55/8.65                    @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 15.55/8.65                    @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 15.55/8.65                 => ( ( filterlim_real_real
% 15.55/8.65                      @ ^ [X: real] : ( divide_divide_real @ ( F5 @ X ) @ ( G2 @ X ) )
% 15.55/8.65                      @ F4
% 15.55/8.65                      @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) )
% 15.55/8.65                   => ( filterlim_real_real
% 15.55/8.65                      @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 15.55/8.65                      @ F4
% 15.55/8.65                      @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5849166863359141190n_real @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9480_lhopital__right__0,axiom,
% 15.55/8.65      ! [F0: real > real,G0: real > real,G2: real > real,F5: real > real,F4: filter_real] :
% 15.55/8.65        ( ( filterlim_real_real @ F0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 15.55/8.65       => ( ( filterlim_real_real @ G0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 15.55/8.65         => ( ( eventually_real
% 15.55/8.65              @ ^ [X: real] :
% 15.55/8.65                  ( ( G0 @ X )
% 15.55/8.65                 != zero_zero_real )
% 15.55/8.65              @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 15.55/8.65           => ( ( eventually_real
% 15.55/8.65                @ ^ [X: real] :
% 15.55/8.65                    ( ( G2 @ X )
% 15.55/8.65                   != zero_zero_real )
% 15.55/8.65                @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 15.55/8.65             => ( ( eventually_real
% 15.55/8.65                  @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F0 @ ( F5 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 15.55/8.65                  @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 15.55/8.65               => ( ( eventually_real
% 15.55/8.65                    @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G0 @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 15.55/8.65                    @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 15.55/8.65                 => ( ( filterlim_real_real
% 15.55/8.65                      @ ^ [X: real] : ( divide_divide_real @ ( F5 @ X ) @ ( G2 @ X ) )
% 15.55/8.65                      @ F4
% 15.55/8.65                      @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 15.55/8.65                   => ( filterlim_real_real
% 15.55/8.65                      @ ^ [X: real] : ( divide_divide_real @ ( F0 @ X ) @ ( G0 @ X ) )
% 15.55/8.65                      @ F4
% 15.55/8.65                      @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9481_lhopital__left,axiom,
% 15.55/8.65      ! [F: real > real,X3: real,G: real > real,G2: real > real,F5: real > real,F4: filter_real] :
% 15.55/8.65        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 15.55/8.65       => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 15.55/8.65         => ( ( eventually_real
% 15.55/8.65              @ ^ [X: real] :
% 15.55/8.65                  ( ( G @ X )
% 15.55/8.65                 != zero_zero_real )
% 15.55/8.65              @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 15.55/8.65           => ( ( eventually_real
% 15.55/8.65                @ ^ [X: real] :
% 15.55/8.65                    ( ( G2 @ X )
% 15.55/8.65                   != zero_zero_real )
% 15.55/8.65                @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 15.55/8.65             => ( ( eventually_real
% 15.55/8.65                  @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 15.55/8.65                  @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 15.55/8.65               => ( ( eventually_real
% 15.55/8.65                    @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 15.55/8.65                    @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 15.55/8.65                 => ( ( filterlim_real_real
% 15.55/8.65                      @ ^ [X: real] : ( divide_divide_real @ ( F5 @ X ) @ ( G2 @ X ) )
% 15.55/8.65                      @ F4
% 15.55/8.65                      @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) )
% 15.55/8.65                   => ( filterlim_real_real
% 15.55/8.65                      @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 15.55/8.65                      @ F4
% 15.55/8.65                      @ ( topolo2177554685111907308n_real @ X3 @ ( set_or5984915006950818249n_real @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9482_lhopital__right__0__at__top,axiom,
% 15.55/8.65      ! [G: real > real,G2: real > real,F: real > real,F5: real > real,X3: real] :
% 15.55/8.65        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 15.55/8.65       => ( ( eventually_real
% 15.55/8.65            @ ^ [X: real] :
% 15.55/8.65                ( ( G2 @ X )
% 15.55/8.65               != zero_zero_real )
% 15.55/8.65            @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 15.55/8.65         => ( ( eventually_real
% 15.55/8.65              @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 15.55/8.65              @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 15.55/8.65           => ( ( eventually_real
% 15.55/8.65                @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 15.55/8.65                @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 15.55/8.65             => ( ( filterlim_real_real
% 15.55/8.65                  @ ^ [X: real] : ( divide_divide_real @ ( F5 @ X ) @ ( G2 @ X ) )
% 15.55/8.65                  @ ( topolo2815343760600316023s_real @ X3 )
% 15.55/8.65                  @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 15.55/8.65               => ( filterlim_real_real
% 15.55/8.65                  @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 15.55/8.65                  @ ( topolo2815343760600316023s_real @ X3 )
% 15.55/8.65                  @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9483_filterlim__int__sequentially,axiom,
% 15.55/8.65      filterlim_nat_int @ semiri1314217659103216013at_int @ at_top_int @ at_top_nat ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9484_filterlim__nat__sequentially,axiom,
% 15.55/8.65      filterlim_int_nat @ nat2 @ at_top_nat @ at_top_int ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9485_eventually__sequentiallyI,axiom,
% 15.55/8.65      ! [C: nat,P: nat > $o] :
% 15.55/8.65        ( ! [X4: nat] :
% 15.55/8.65            ( ( ord_less_eq_nat @ C @ X4 )
% 15.55/8.65           => ( P @ X4 ) )
% 15.55/8.65       => ( eventually_nat @ P @ at_top_nat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9486_eventually__sequentially,axiom,
% 15.55/8.65      ! [P: nat > $o] :
% 15.55/8.65        ( ( eventually_nat @ P @ at_top_nat )
% 15.55/8.65        = ( ? [N9: nat] :
% 15.55/8.65            ! [N3: nat] :
% 15.55/8.65              ( ( ord_less_eq_nat @ N9 @ N3 )
% 15.55/8.65             => ( P @ N3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9487_le__sequentially,axiom,
% 15.55/8.65      ! [F4: filter_nat] :
% 15.55/8.65        ( ( ord_le2510731241096832064er_nat @ F4 @ at_top_nat )
% 15.55/8.65        = ( ! [N9: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N9 ) @ F4 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9488_decseq__bounded,axiom,
% 15.55/8.65      ! [X9: nat > real,B5: real] :
% 15.55/8.65        ( ( order_9091379641038594480t_real @ X9 )
% 15.55/8.65       => ( ! [I3: nat] : ( ord_less_eq_real @ B5 @ ( X9 @ I3 ) )
% 15.55/8.65         => ( bfun_nat_real @ X9 @ at_top_nat ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9489_decseq__convergent,axiom,
% 15.55/8.65      ! [X9: nat > real,B5: real] :
% 15.55/8.65        ( ( order_9091379641038594480t_real @ X9 )
% 15.55/8.65       => ( ! [I3: nat] : ( ord_less_eq_real @ B5 @ ( X9 @ I3 ) )
% 15.55/8.65         => ~ ! [L6: real] :
% 15.55/8.65                ( ( filterlim_nat_real @ X9 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 15.55/8.65               => ~ ! [I2: nat] : ( ord_less_eq_real @ L6 @ ( X9 @ I2 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9490_Bseq__realpow,axiom,
% 15.55/8.65      ! [X3: real] :
% 15.55/8.65        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.65       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 15.55/8.65         => ( bfun_nat_real @ ( power_power_real @ X3 ) @ at_top_nat ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9491_Frct__code__post_I5_J,axiom,
% 15.55/8.65      ! [K: num] :
% 15.55/8.65        ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 15.55/8.65        = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9492_GreatestI__ex__nat,axiom,
% 15.55/8.65      ! [P: nat > $o,B: nat] :
% 15.55/8.65        ( ? [X_12: nat] : ( P @ X_12 )
% 15.55/8.65       => ( ! [Y4: nat] :
% 15.55/8.65              ( ( P @ Y4 )
% 15.55/8.65             => ( ord_less_eq_nat @ Y4 @ B ) )
% 15.55/8.65         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9493_Greatest__le__nat,axiom,
% 15.55/8.65      ! [P: nat > $o,K: nat,B: nat] :
% 15.55/8.65        ( ( P @ K )
% 15.55/8.65       => ( ! [Y4: nat] :
% 15.55/8.65              ( ( P @ Y4 )
% 15.55/8.65             => ( ord_less_eq_nat @ Y4 @ B ) )
% 15.55/8.65         => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9494_GreatestI__nat,axiom,
% 15.55/8.65      ! [P: nat > $o,K: nat,B: nat] :
% 15.55/8.65        ( ( P @ K )
% 15.55/8.65       => ( ! [Y4: nat] :
% 15.55/8.65              ( ( P @ Y4 )
% 15.55/8.65             => ( ord_less_eq_nat @ Y4 @ B ) )
% 15.55/8.65         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9495_Frct__code__post_I2_J,axiom,
% 15.55/8.65      ! [A: int] :
% 15.55/8.65        ( ( frct @ ( product_Pair_int_int @ A @ zero_zero_int ) )
% 15.55/8.65        = zero_zero_rat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9496_Frct__code__post_I1_J,axiom,
% 15.55/8.65      ! [A: int] :
% 15.55/8.65        ( ( frct @ ( product_Pair_int_int @ zero_zero_int @ A ) )
% 15.55/8.65        = zero_zero_rat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9497_Frct__code__post_I6_J,axiom,
% 15.55/8.65      ! [K: num,L: num] :
% 15.55/8.65        ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L ) ) )
% 15.55/8.65        = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9498_Frct__code__post_I4_J,axiom,
% 15.55/8.65      ! [K: num] :
% 15.55/8.65        ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 15.55/8.65        = ( numeral_numeral_rat @ K ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9499_GMVT,axiom,
% 15.55/8.65      ! [A: real,B: real,F: real > real,G: real > real] :
% 15.55/8.65        ( ( ord_less_real @ A @ B )
% 15.55/8.65       => ( ! [X4: real] :
% 15.55/8.65              ( ( ( ord_less_eq_real @ A @ X4 )
% 15.55/8.65                & ( ord_less_eq_real @ X4 @ B ) )
% 15.55/8.65             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ F ) )
% 15.55/8.65         => ( ! [X4: real] :
% 15.55/8.65                ( ( ( ord_less_real @ A @ X4 )
% 15.55/8.65                  & ( ord_less_real @ X4 @ B ) )
% 15.55/8.65               => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 15.55/8.65           => ( ! [X4: real] :
% 15.55/8.65                  ( ( ( ord_less_eq_real @ A @ X4 )
% 15.55/8.65                    & ( ord_less_eq_real @ X4 @ B ) )
% 15.55/8.65                 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ G ) )
% 15.55/8.65             => ( ! [X4: real] :
% 15.55/8.65                    ( ( ( ord_less_real @ A @ X4 )
% 15.55/8.65                      & ( ord_less_real @ X4 @ B ) )
% 15.55/8.65                   => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 15.55/8.65               => ? [G_c: real,F_c: real,C2: real] :
% 15.55/8.65                    ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 15.55/8.65                    & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 15.55/8.65                    & ( ord_less_real @ A @ C2 )
% 15.55/8.65                    & ( ord_less_real @ C2 @ B )
% 15.55/8.65                    & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 15.55/8.65                      = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9500_atLeast__0,axiom,
% 15.55/8.65      ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 15.55/8.65      = top_top_set_nat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9501_card__greaterThanAtMost__int,axiom,
% 15.55/8.65      ! [L: int,U: int] :
% 15.55/8.65        ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L @ U ) )
% 15.55/8.65        = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9502_normalize__negative,axiom,
% 15.55/8.65      ! [Q3: int,P6: int] :
% 15.55/8.65        ( ( ord_less_int @ Q3 @ zero_zero_int )
% 15.55/8.65       => ( ( normalize @ ( product_Pair_int_int @ P6 @ Q3 ) )
% 15.55/8.65          = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P6 ) @ ( uminus_uminus_int @ Q3 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9503_MVT,axiom,
% 15.55/8.65      ! [A: real,B: real,F: real > real] :
% 15.55/8.65        ( ( ord_less_real @ A @ B )
% 15.55/8.65       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 15.55/8.65         => ( ! [X4: real] :
% 15.55/8.65                ( ( ord_less_real @ A @ X4 )
% 15.55/8.65               => ( ( ord_less_real @ X4 @ B )
% 15.55/8.65                 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 15.55/8.65           => ? [L4: real,Z3: real] :
% 15.55/8.65                ( ( ord_less_real @ A @ Z3 )
% 15.55/8.65                & ( ord_less_real @ Z3 @ B )
% 15.55/8.65                & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) )
% 15.55/8.65                & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 15.55/8.65                  = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9504_normalize__denom__zero,axiom,
% 15.55/8.65      ! [P6: int] :
% 15.55/8.65        ( ( normalize @ ( product_Pair_int_int @ P6 @ zero_zero_int ) )
% 15.55/8.65        = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9505_continuous__on__arcosh_H,axiom,
% 15.55/8.65      ! [A3: set_real,F: real > real] :
% 15.55/8.65        ( ( topolo5044208981011980120l_real @ A3 @ F )
% 15.55/8.65       => ( ! [X4: real] :
% 15.55/8.65              ( ( member_real @ X4 @ A3 )
% 15.55/8.65             => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 15.55/8.65         => ( topolo5044208981011980120l_real @ A3
% 15.55/8.65            @ ^ [X: real] : ( arcosh_real @ ( F @ X ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9506_continuous__image__closed__interval,axiom,
% 15.55/8.65      ! [A: real,B: real,F: real > real] :
% 15.55/8.65        ( ( ord_less_eq_real @ A @ B )
% 15.55/8.65       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 15.55/8.65         => ? [C2: real,D6: real] :
% 15.55/8.65              ( ( ( image_real_real @ F @ ( set_or1222579329274155063t_real @ A @ B ) )
% 15.55/8.65                = ( set_or1222579329274155063t_real @ C2 @ D6 ) )
% 15.55/8.65              & ( ord_less_eq_real @ C2 @ D6 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9507_Rolle__deriv,axiom,
% 15.55/8.65      ! [A: real,B: real,F: real > real,F5: real > real > real] :
% 15.55/8.65        ( ( ord_less_real @ A @ B )
% 15.55/8.65       => ( ( ( F @ A )
% 15.55/8.65            = ( F @ B ) )
% 15.55/8.65         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 15.55/8.65           => ( ! [X4: real] :
% 15.55/8.65                  ( ( ord_less_real @ A @ X4 )
% 15.55/8.65                 => ( ( ord_less_real @ X4 @ B )
% 15.55/8.65                   => ( has_de1759254742604945161l_real @ F @ ( F5 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 15.55/8.65             => ? [Z3: real] :
% 15.55/8.65                  ( ( ord_less_real @ A @ Z3 )
% 15.55/8.65                  & ( ord_less_real @ Z3 @ B )
% 15.55/8.65                  & ( ( F5 @ Z3 )
% 15.55/8.65                    = ( ^ [V4: real] : zero_zero_real ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9508_mvt,axiom,
% 15.55/8.65      ! [A: real,B: real,F: real > real,F5: real > real > real] :
% 15.55/8.65        ( ( ord_less_real @ A @ B )
% 15.55/8.65       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 15.55/8.65         => ( ! [X4: real] :
% 15.55/8.65                ( ( ord_less_real @ A @ X4 )
% 15.55/8.65               => ( ( ord_less_real @ X4 @ B )
% 15.55/8.65                 => ( has_de1759254742604945161l_real @ F @ ( F5 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 15.55/8.65           => ~ ! [Xi: real] :
% 15.55/8.65                  ( ( ord_less_real @ A @ Xi )
% 15.55/8.65                 => ( ( ord_less_real @ Xi @ B )
% 15.55/8.65                   => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 15.55/8.65                     != ( F5 @ Xi @ ( minus_minus_real @ B @ A ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9509_normalize__denom__pos,axiom,
% 15.55/8.65      ! [R2: product_prod_int_int,P6: int,Q3: int] :
% 15.55/8.65        ( ( ( normalize @ R2 )
% 15.55/8.65          = ( product_Pair_int_int @ P6 @ Q3 ) )
% 15.55/8.65       => ( ord_less_int @ zero_zero_int @ Q3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9510_normalize__crossproduct,axiom,
% 15.55/8.65      ! [Q3: int,S: int,P6: int,R2: int] :
% 15.55/8.65        ( ( Q3 != zero_zero_int )
% 15.55/8.65       => ( ( S != zero_zero_int )
% 15.55/8.65         => ( ( ( normalize @ ( product_Pair_int_int @ P6 @ Q3 ) )
% 15.55/8.65              = ( normalize @ ( product_Pair_int_int @ R2 @ S ) ) )
% 15.55/8.65           => ( ( times_times_int @ P6 @ S )
% 15.55/8.65              = ( times_times_int @ R2 @ Q3 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9511_DERIV__pos__imp__increasing__open,axiom,
% 15.55/8.65      ! [A: real,B: real,F: real > real] :
% 15.55/8.65        ( ( ord_less_real @ A @ B )
% 15.55/8.65       => ( ! [X4: real] :
% 15.55/8.65              ( ( ord_less_real @ A @ X4 )
% 15.55/8.65             => ( ( ord_less_real @ X4 @ B )
% 15.55/8.65               => ? [Y6: real] :
% 15.55/8.65                    ( ( has_fi5821293074295781190e_real @ F @ Y6 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 15.55/8.65                    & ( ord_less_real @ zero_zero_real @ Y6 ) ) ) )
% 15.55/8.65         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 15.55/8.65           => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9512_DERIV__neg__imp__decreasing__open,axiom,
% 15.55/8.65      ! [A: real,B: real,F: real > real] :
% 15.55/8.65        ( ( ord_less_real @ A @ B )
% 15.55/8.65       => ( ! [X4: real] :
% 15.55/8.65              ( ( ord_less_real @ A @ X4 )
% 15.55/8.65             => ( ( ord_less_real @ X4 @ B )
% 15.55/8.65               => ? [Y6: real] :
% 15.55/8.65                    ( ( has_fi5821293074295781190e_real @ F @ Y6 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 15.55/8.65                    & ( ord_less_real @ Y6 @ zero_zero_real ) ) ) )
% 15.55/8.65         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 15.55/8.65           => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9513_DERIV__isconst__end,axiom,
% 15.55/8.65      ! [A: real,B: real,F: real > real] :
% 15.55/8.65        ( ( ord_less_real @ A @ B )
% 15.55/8.65       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 15.55/8.65         => ( ! [X4: real] :
% 15.55/8.65                ( ( ord_less_real @ A @ X4 )
% 15.55/8.65               => ( ( ord_less_real @ X4 @ B )
% 15.55/8.65                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 15.55/8.65           => ( ( F @ B )
% 15.55/8.65              = ( F @ A ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9514_DERIV__isconst2,axiom,
% 15.55/8.65      ! [A: real,B: real,F: real > real,X3: real] :
% 15.55/8.65        ( ( ord_less_real @ A @ B )
% 15.55/8.65       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 15.55/8.65         => ( ! [X4: real] :
% 15.55/8.65                ( ( ord_less_real @ A @ X4 )
% 15.55/8.65               => ( ( ord_less_real @ X4 @ B )
% 15.55/8.65                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 15.55/8.65           => ( ( ord_less_eq_real @ A @ X3 )
% 15.55/8.65             => ( ( ord_less_eq_real @ X3 @ B )
% 15.55/8.65               => ( ( F @ X3 )
% 15.55/8.65                  = ( F @ A ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9515_Rolle,axiom,
% 15.55/8.65      ! [A: real,B: real,F: real > real] :
% 15.55/8.65        ( ( ord_less_real @ A @ B )
% 15.55/8.65       => ( ( ( F @ A )
% 15.55/8.65            = ( F @ B ) )
% 15.55/8.65         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 15.55/8.65           => ( ! [X4: real] :
% 15.55/8.65                  ( ( ord_less_real @ A @ X4 )
% 15.55/8.65                 => ( ( ord_less_real @ X4 @ B )
% 15.55/8.65                   => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 15.55/8.65             => ? [Z3: real] :
% 15.55/8.65                  ( ( ord_less_real @ A @ Z3 )
% 15.55/8.65                  & ( ord_less_real @ Z3 @ B )
% 15.55/8.65                  & ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9516_normalize__def,axiom,
% 15.55/8.65      ( normalize
% 15.55/8.65      = ( ^ [P5: product_prod_int_int] :
% 15.55/8.65            ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P5 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P5 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P5 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) )
% 15.55/8.65            @ ( if_Pro3027730157355071871nt_int
% 15.55/8.65              @ ( ( product_snd_int_int @ P5 )
% 15.55/8.65                = zero_zero_int )
% 15.55/8.65              @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 15.55/8.65              @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P5 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P5 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9517_gcd__pos__int,axiom,
% 15.55/8.65      ! [M: int,N: int] :
% 15.55/8.65        ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M @ N ) )
% 15.55/8.65        = ( ( M != zero_zero_int )
% 15.55/8.65          | ( N != zero_zero_int ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9518_gcd__neg__numeral__2__int,axiom,
% 15.55/8.65      ! [X3: int,N: num] :
% 15.55/8.65        ( ( gcd_gcd_int @ X3 @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.65        = ( gcd_gcd_int @ X3 @ ( numeral_numeral_int @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9519_gcd__neg__numeral__1__int,axiom,
% 15.55/8.65      ! [N: num,X3: int] :
% 15.55/8.65        ( ( gcd_gcd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ X3 )
% 15.55/8.65        = ( gcd_gcd_int @ ( numeral_numeral_int @ N ) @ X3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9520_gcd__0__int,axiom,
% 15.55/8.65      ! [X3: int] :
% 15.55/8.65        ( ( gcd_gcd_int @ X3 @ zero_zero_int )
% 15.55/8.65        = ( abs_abs_int @ X3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9521_gcd__0__left__int,axiom,
% 15.55/8.65      ! [X3: int] :
% 15.55/8.65        ( ( gcd_gcd_int @ zero_zero_int @ X3 )
% 15.55/8.65        = ( abs_abs_int @ X3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9522_gcd__ge__0__int,axiom,
% 15.55/8.65      ! [X3: int,Y3: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X3 @ Y3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9523_gcd__le1__int,axiom,
% 15.55/8.65      ! [A: int,B: int] :
% 15.55/8.65        ( ( ord_less_int @ zero_zero_int @ A )
% 15.55/8.65       => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9524_gcd__le2__int,axiom,
% 15.55/8.65      ! [B: int,A: int] :
% 15.55/8.65        ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.65       => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9525_gcd__cases__int,axiom,
% 15.55/8.65      ! [X3: int,Y3: int,P: int > $o] :
% 15.55/8.65        ( ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 15.55/8.65         => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 15.55/8.65           => ( P @ ( gcd_gcd_int @ X3 @ Y3 ) ) ) )
% 15.55/8.65       => ( ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 15.55/8.65           => ( ( ord_less_eq_int @ Y3 @ zero_zero_int )
% 15.55/8.65             => ( P @ ( gcd_gcd_int @ X3 @ ( uminus_uminus_int @ Y3 ) ) ) ) )
% 15.55/8.65         => ( ( ( ord_less_eq_int @ X3 @ zero_zero_int )
% 15.55/8.65             => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 15.55/8.65               => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X3 ) @ Y3 ) ) ) )
% 15.55/8.65           => ( ( ( ord_less_eq_int @ X3 @ zero_zero_int )
% 15.55/8.65               => ( ( ord_less_eq_int @ Y3 @ zero_zero_int )
% 15.55/8.65                 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X3 ) @ ( uminus_uminus_int @ Y3 ) ) ) ) )
% 15.55/8.65             => ( P @ ( gcd_gcd_int @ X3 @ Y3 ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9526_gcd__unique__int,axiom,
% 15.55/8.65      ! [D3: int,A: int,B: int] :
% 15.55/8.65        ( ( ( ord_less_eq_int @ zero_zero_int @ D3 )
% 15.55/8.65          & ( dvd_dvd_int @ D3 @ A )
% 15.55/8.65          & ( dvd_dvd_int @ D3 @ B )
% 15.55/8.65          & ! [E3: int] :
% 15.55/8.65              ( ( ( dvd_dvd_int @ E3 @ A )
% 15.55/8.65                & ( dvd_dvd_int @ E3 @ B ) )
% 15.55/8.65             => ( dvd_dvd_int @ E3 @ D3 ) ) )
% 15.55/8.65        = ( D3
% 15.55/8.65          = ( gcd_gcd_int @ A @ B ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9527_gcd__non__0__int,axiom,
% 15.55/8.65      ! [Y3: int,X3: int] :
% 15.55/8.65        ( ( ord_less_int @ zero_zero_int @ Y3 )
% 15.55/8.65       => ( ( gcd_gcd_int @ X3 @ Y3 )
% 15.55/8.65          = ( gcd_gcd_int @ Y3 @ ( modulo_modulo_int @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9528_gcd__code__int,axiom,
% 15.55/8.65      ( gcd_gcd_int
% 15.55/8.65      = ( ^ [K3: int,L2: int] : ( abs_abs_int @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( gcd_gcd_int @ L2 @ ( modulo_modulo_int @ ( abs_abs_int @ K3 ) @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9529_gcd__is__Max__divisors__int,axiom,
% 15.55/8.65      ! [N: int,M: int] :
% 15.55/8.65        ( ( N != zero_zero_int )
% 15.55/8.65       => ( ( gcd_gcd_int @ M @ N )
% 15.55/8.65          = ( lattic8263393255366662781ax_int
% 15.55/8.65            @ ( collect_int
% 15.55/8.65              @ ^ [D4: int] :
% 15.55/8.65                  ( ( dvd_dvd_int @ D4 @ M )
% 15.55/8.65                  & ( dvd_dvd_int @ D4 @ N ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9530_range__abs__Nats,axiom,
% 15.55/8.65      ( ( image_int_int @ abs_abs_int @ top_top_set_int )
% 15.55/8.65      = semiring_1_Nats_int ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9531_gcd__nat_Oeq__neutr__iff,axiom,
% 15.55/8.65      ! [A: nat,B: nat] :
% 15.55/8.65        ( ( ( gcd_gcd_nat @ A @ B )
% 15.55/8.65          = zero_zero_nat )
% 15.55/8.65        = ( ( A = zero_zero_nat )
% 15.55/8.65          & ( B = zero_zero_nat ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9532_gcd__nat_Oleft__neutral,axiom,
% 15.55/8.65      ! [A: nat] :
% 15.55/8.65        ( ( gcd_gcd_nat @ zero_zero_nat @ A )
% 15.55/8.65        = A ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9533_gcd__nat_Oneutr__eq__iff,axiom,
% 15.55/8.65      ! [A: nat,B: nat] :
% 15.55/8.65        ( ( zero_zero_nat
% 15.55/8.65          = ( gcd_gcd_nat @ A @ B ) )
% 15.55/8.65        = ( ( A = zero_zero_nat )
% 15.55/8.65          & ( B = zero_zero_nat ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9534_gcd__nat_Oright__neutral,axiom,
% 15.55/8.65      ! [A: nat] :
% 15.55/8.65        ( ( gcd_gcd_nat @ A @ zero_zero_nat )
% 15.55/8.65        = A ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9535_gcd__0__nat,axiom,
% 15.55/8.65      ! [X3: nat] :
% 15.55/8.65        ( ( gcd_gcd_nat @ X3 @ zero_zero_nat )
% 15.55/8.65        = X3 ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9536_gcd__0__left__nat,axiom,
% 15.55/8.65      ! [X3: nat] :
% 15.55/8.65        ( ( gcd_gcd_nat @ zero_zero_nat @ X3 )
% 15.55/8.65        = X3 ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9537_gcd__Suc__0,axiom,
% 15.55/8.65      ! [M: nat] :
% 15.55/8.65        ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 15.55/8.65        = ( suc @ zero_zero_nat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9538_gcd__pos__nat,axiom,
% 15.55/8.65      ! [M: nat,N: nat] :
% 15.55/8.65        ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N ) )
% 15.55/8.65        = ( ( M != zero_zero_nat )
% 15.55/8.65          | ( N != zero_zero_nat ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9539_gcd__int__int__eq,axiom,
% 15.55/8.65      ! [M: nat,N: nat] :
% 15.55/8.65        ( ( gcd_gcd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 15.55/8.65        = ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9540_gcd__nat__abs__right__eq,axiom,
% 15.55/8.65      ! [N: nat,K: int] :
% 15.55/8.65        ( ( gcd_gcd_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 15.55/8.65        = ( nat2 @ ( gcd_gcd_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9541_gcd__nat__abs__left__eq,axiom,
% 15.55/8.65      ! [K: int,N: nat] :
% 15.55/8.65        ( ( gcd_gcd_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 15.55/8.65        = ( nat2 @ ( gcd_gcd_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9542_gcd__non__0__nat,axiom,
% 15.55/8.65      ! [Y3: nat,X3: nat] :
% 15.55/8.65        ( ( Y3 != zero_zero_nat )
% 15.55/8.65       => ( ( gcd_gcd_nat @ X3 @ Y3 )
% 15.55/8.65          = ( gcd_gcd_nat @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9543_gcd__nat_Osimps,axiom,
% 15.55/8.65      ( gcd_gcd_nat
% 15.55/8.65      = ( ^ [X: nat,Y: nat] : ( if_nat @ ( Y = zero_zero_nat ) @ X @ ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9544_gcd__nat_Oelims,axiom,
% 15.55/8.65      ! [X3: nat,Xa: nat,Y3: nat] :
% 15.55/8.65        ( ( ( gcd_gcd_nat @ X3 @ Xa )
% 15.55/8.65          = Y3 )
% 15.55/8.65       => ( ( ( Xa = zero_zero_nat )
% 15.55/8.65           => ( Y3 = X3 ) )
% 15.55/8.65          & ( ( Xa != zero_zero_nat )
% 15.55/8.65           => ( Y3
% 15.55/8.65              = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X3 @ Xa ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9545_gcd__diff1__nat,axiom,
% 15.55/8.65      ! [N: nat,M: nat] :
% 15.55/8.65        ( ( ord_less_eq_nat @ N @ M )
% 15.55/8.65       => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 15.55/8.65          = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9546_gcd__diff2__nat,axiom,
% 15.55/8.65      ! [M: nat,N: nat] :
% 15.55/8.65        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.65       => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M ) @ N )
% 15.55/8.65          = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9547_gcd__le2__nat,axiom,
% 15.55/8.65      ! [B: nat,A: nat] :
% 15.55/8.65        ( ( B != zero_zero_nat )
% 15.55/8.65       => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9548_gcd__le1__nat,axiom,
% 15.55/8.65      ! [A: nat,B: nat] :
% 15.55/8.65        ( ( A != zero_zero_nat )
% 15.55/8.65       => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9549_mono__Suc,axiom,
% 15.55/8.65      order_mono_nat_nat @ suc ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9550_gcd__code__integer,axiom,
% 15.55/8.65      ( gcd_gcd_Code_integer
% 15.55/8.65      = ( ^ [K3: code_integer,L2: code_integer] : ( abs_abs_Code_integer @ ( if_Code_integer @ ( L2 = zero_z3403309356797280102nteger ) @ K3 @ ( gcd_gcd_Code_integer @ L2 @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L2 ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9551_mono__times__nat,axiom,
% 15.55/8.65      ! [N: nat] :
% 15.55/8.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.65       => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9552_bezout__nat,axiom,
% 15.55/8.65      ! [A: nat,B: nat] :
% 15.55/8.65        ( ( A != zero_zero_nat )
% 15.55/8.65       => ? [X4: nat,Y4: nat] :
% 15.55/8.65            ( ( times_times_nat @ A @ X4 )
% 15.55/8.65            = ( plus_plus_nat @ ( times_times_nat @ B @ Y4 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9553_bezout__gcd__nat_H,axiom,
% 15.55/8.65      ! [B: nat,A: nat] :
% 15.55/8.65      ? [X4: nat,Y4: nat] :
% 15.55/8.65        ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y4 ) @ ( times_times_nat @ A @ X4 ) )
% 15.55/8.65          & ( ( minus_minus_nat @ ( times_times_nat @ A @ X4 ) @ ( times_times_nat @ B @ Y4 ) )
% 15.55/8.65            = ( gcd_gcd_nat @ A @ B ) ) )
% 15.55/8.65        | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y4 ) @ ( times_times_nat @ B @ X4 ) )
% 15.55/8.65          & ( ( minus_minus_nat @ ( times_times_nat @ B @ X4 ) @ ( times_times_nat @ A @ Y4 ) )
% 15.55/8.65            = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9554_incseq__bounded,axiom,
% 15.55/8.65      ! [X9: nat > real,B5: real] :
% 15.55/8.65        ( ( order_mono_nat_real @ X9 )
% 15.55/8.65       => ( ! [I3: nat] : ( ord_less_eq_real @ ( X9 @ I3 ) @ B5 )
% 15.55/8.65         => ( bfun_nat_real @ X9 @ at_top_nat ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9555_incseq__convergent,axiom,
% 15.55/8.65      ! [X9: nat > real,B5: real] :
% 15.55/8.65        ( ( order_mono_nat_real @ X9 )
% 15.55/8.65       => ( ! [I3: nat] : ( ord_less_eq_real @ ( X9 @ I3 ) @ B5 )
% 15.55/8.65         => ~ ! [L6: real] :
% 15.55/8.65                ( ( filterlim_nat_real @ X9 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 15.55/8.65               => ~ ! [I2: nat] : ( ord_less_eq_real @ ( X9 @ I2 ) @ L6 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9556_gcd__int__def,axiom,
% 15.55/8.65      ( gcd_gcd_int
% 15.55/8.65      = ( ^ [X: int,Y: int] : ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ ( nat2 @ ( abs_abs_int @ X ) ) @ ( nat2 @ ( abs_abs_int @ Y ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9557_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 15.55/8.65      ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 15.55/8.65      @ ^ [M3: nat,N3: nat] :
% 15.55/8.65          ( ( dvd_dvd_nat @ M3 @ N3 )
% 15.55/8.65          & ( M3 != N3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9558_gcd__is__Max__divisors__nat,axiom,
% 15.55/8.65      ! [N: nat,M: nat] :
% 15.55/8.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.65       => ( ( gcd_gcd_nat @ M @ N )
% 15.55/8.65          = ( lattic8265883725875713057ax_nat
% 15.55/8.65            @ ( collect_nat
% 15.55/8.65              @ ^ [D4: nat] :
% 15.55/8.65                  ( ( dvd_dvd_nat @ D4 @ M )
% 15.55/8.65                  & ( dvd_dvd_nat @ D4 @ N ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9559_mono__ge2__power__minus__self,axiom,
% 15.55/8.65      ! [K: nat] :
% 15.55/8.65        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 15.55/8.65       => ( order_mono_nat_nat
% 15.55/8.65          @ ^ [M3: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M3 ) @ M3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9560_bezw__aux,axiom,
% 15.55/8.65      ! [X3: nat,Y3: nat] :
% 15.55/8.65        ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X3 @ Y3 ) )
% 15.55/8.65        = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X3 @ Y3 ) ) @ ( semiri1314217659103216013at_int @ X3 ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X3 @ Y3 ) ) @ ( semiri1314217659103216013at_int @ Y3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9561_gcd__nat_Opelims,axiom,
% 15.55/8.65      ! [X3: nat,Xa: nat,Y3: nat] :
% 15.55/8.65        ( ( ( gcd_gcd_nat @ X3 @ Xa )
% 15.55/8.65          = Y3 )
% 15.55/8.65       => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X3 @ Xa ) )
% 15.55/8.65         => ~ ( ( ( ( Xa = zero_zero_nat )
% 15.55/8.65                 => ( Y3 = X3 ) )
% 15.55/8.65                & ( ( Xa != zero_zero_nat )
% 15.55/8.65                 => ( Y3
% 15.55/8.65                    = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X3 @ Xa ) ) ) ) )
% 15.55/8.65             => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X3 @ Xa ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9562_complex__is__Nat__iff,axiom,
% 15.55/8.65      ! [Z: complex] :
% 15.55/8.65        ( ( member_complex @ Z @ semiri3842193898606819883omplex )
% 15.55/8.65        = ( ( ( im @ Z )
% 15.55/8.65            = zero_zero_real )
% 15.55/8.65          & ? [I4: nat] :
% 15.55/8.65              ( ( re @ Z )
% 15.55/8.65              = ( semiri5074537144036343181t_real @ I4 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9563_tendsto__at__topI__sequentially__real,axiom,
% 15.55/8.65      ! [F: real > real,Y3: real] :
% 15.55/8.65        ( ( order_mono_real_real @ F )
% 15.55/8.65       => ( ( filterlim_nat_real
% 15.55/8.65            @ ^ [N3: nat] : ( F @ ( semiri5074537144036343181t_real @ N3 ) )
% 15.55/8.65            @ ( topolo2815343760600316023s_real @ Y3 )
% 15.55/8.65            @ at_top_nat )
% 15.55/8.65         => ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Y3 ) @ at_top_real ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9564_nonneg__incseq__Bseq__subseq__iff,axiom,
% 15.55/8.65      ! [F: nat > real,G: nat > nat] :
% 15.55/8.65        ( ! [X4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 15.55/8.65       => ( ( order_mono_nat_real @ F )
% 15.55/8.65         => ( ( order_5726023648592871131at_nat @ G )
% 15.55/8.65           => ( ( bfun_nat_real
% 15.55/8.65                @ ^ [X: nat] : ( F @ ( G @ X ) )
% 15.55/8.65                @ at_top_nat )
% 15.55/8.65              = ( bfun_nat_real @ F @ at_top_nat ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9565_inj__sgn__power,axiom,
% 15.55/8.65      ! [N: nat] :
% 15.55/8.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.65       => ( inj_on_real_real
% 15.55/8.65          @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 15.55/8.65          @ top_top_set_real ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9566_strict__mono__imp__increasing,axiom,
% 15.55/8.65      ! [F: nat > nat,N: nat] :
% 15.55/8.65        ( ( order_5726023648592871131at_nat @ F )
% 15.55/8.65       => ( ord_less_eq_nat @ N @ ( F @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9567_log__inj,axiom,
% 15.55/8.65      ! [B: real] :
% 15.55/8.65        ( ( ord_less_real @ one_one_real @ B )
% 15.55/8.65       => ( inj_on_real_real @ ( log @ B ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9568_inj__on__diff__nat,axiom,
% 15.55/8.65      ! [N4: set_nat,K: nat] :
% 15.55/8.65        ( ! [N2: nat] :
% 15.55/8.65            ( ( member_nat @ N2 @ N4 )
% 15.55/8.65           => ( ord_less_eq_nat @ K @ N2 ) )
% 15.55/8.65       => ( inj_on_nat_nat
% 15.55/8.65          @ ^ [N3: nat] : ( minus_minus_nat @ N3 @ K )
% 15.55/8.65          @ N4 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9569_inj__Suc,axiom,
% 15.55/8.65      ! [N4: set_nat] : ( inj_on_nat_nat @ suc @ N4 ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9570_summable__reindex,axiom,
% 15.55/8.65      ! [F: nat > real,G: nat > nat] :
% 15.55/8.65        ( ( summable_real @ F )
% 15.55/8.65       => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 15.55/8.65         => ( ! [X4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 15.55/8.65           => ( summable_real @ ( comp_nat_real_nat @ F @ G ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9571_suminf__reindex__mono,axiom,
% 15.55/8.65      ! [F: nat > real,G: nat > nat] :
% 15.55/8.65        ( ( summable_real @ F )
% 15.55/8.65       => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 15.55/8.65         => ( ! [X4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 15.55/8.65           => ( ord_less_eq_real @ ( suminf_real @ ( comp_nat_real_nat @ F @ G ) ) @ ( suminf_real @ F ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9572_powr__real__of__int_H,axiom,
% 15.55/8.65      ! [X3: real,N: int] :
% 15.55/8.65        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.65       => ( ( ( X3 != zero_zero_real )
% 15.55/8.65            | ( ord_less_int @ zero_zero_int @ N ) )
% 15.55/8.65         => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ N ) )
% 15.55/8.65            = ( power_int_real @ X3 @ N ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9573_inj__on__char__of__nat,axiom,
% 15.55/8.65      inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9574_suminf__reindex,axiom,
% 15.55/8.65      ! [F: nat > real,G: nat > nat] :
% 15.55/8.65        ( ( summable_real @ F )
% 15.55/8.65       => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 15.55/8.65         => ( ! [X4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 15.55/8.65           => ( ! [X4: nat] :
% 15.55/8.65                  ( ~ ( member_nat @ X4 @ ( image_nat_nat @ G @ top_top_set_nat ) )
% 15.55/8.65                 => ( ( F @ X4 )
% 15.55/8.65                    = zero_zero_real ) )
% 15.55/8.65             => ( ( suminf_real @ ( comp_nat_real_nat @ F @ G ) )
% 15.55/8.65                = ( suminf_real @ F ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9575_pos__deriv__imp__strict__mono,axiom,
% 15.55/8.65      ! [F: real > real,F5: real > real] :
% 15.55/8.65        ( ! [X4: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 15.55/8.65       => ( ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( F5 @ X4 ) )
% 15.55/8.65         => ( order_7092887310737990675l_real @ F ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9576_integer__of__num__triv_I2_J,axiom,
% 15.55/8.65      ( ( code_integer_of_num @ ( bit0 @ one ) )
% 15.55/8.65      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9577_integer__of__num__triv_I1_J,axiom,
% 15.55/8.65      ( ( code_integer_of_num @ one )
% 15.55/8.65      = one_one_Code_integer ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9578_integer__of__num_I2_J,axiom,
% 15.55/8.65      ! [N: num] :
% 15.55/8.65        ( ( code_integer_of_num @ ( bit0 @ N ) )
% 15.55/8.65        = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9579_atLeastLessThan__add__Un,axiom,
% 15.55/8.65      ! [I: nat,J: nat,K: nat] :
% 15.55/8.65        ( ( ord_less_eq_nat @ I @ J )
% 15.55/8.65       => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 15.55/8.65          = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9580_sup__nat__def,axiom,
% 15.55/8.65      sup_sup_nat = ord_max_nat ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9581_sup__enat__def,axiom,
% 15.55/8.65      sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9582_sup__int__def,axiom,
% 15.55/8.65      sup_sup_int = ord_max_int ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9583_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 15.55/8.65      ! [X3: vEBT_VEBT,Xa: nat,Y3: $o] :
% 15.55/8.65        ( ( ( vEBT_VEBT_valid @ X3 @ Xa )
% 15.55/8.65          = Y3 )
% 15.55/8.65       => ( ( ? [Uu: $o,Uv: $o] :
% 15.55/8.65                ( X3
% 15.55/8.65                = ( vEBT_Leaf @ Uu @ Uv ) )
% 15.55/8.65           => ( Y3
% 15.55/8.65              = ( Xa != one_one_nat ) ) )
% 15.55/8.65         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.65                ( ( X3
% 15.55/8.65                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 15.55/8.65               => ( Y3
% 15.55/8.65                  = ( ~ ( ( Deg2 = Xa )
% 15.55/8.65                        & ! [X: vEBT_VEBT] :
% 15.55/8.65                            ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.65                           => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.65                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.65                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 15.55/8.65                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.65                        & ( case_o184042715313410164at_nat
% 15.55/8.65                          @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 15.55/8.65                            & ! [X: vEBT_VEBT] :
% 15.55/8.65                                ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.65                               => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 15.55/8.65                          @ ( produc6081775807080527818_nat_o
% 15.55/8.65                            @ ^ [Mi3: nat,Ma3: nat] :
% 15.55/8.65                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 15.55/8.65                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 15.55/8.65                                & ! [I4: nat] :
% 15.55/8.65                                    ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.65                                   => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X8 ) )
% 15.55/8.65                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 15.55/8.65                                & ( ( Mi3 = Ma3 )
% 15.55/8.65                                 => ! [X: vEBT_VEBT] :
% 15.55/8.65                                      ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.65                                     => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 15.55/8.65                                & ( ( Mi3 != Ma3 )
% 15.55/8.65                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 15.55/8.65                                    & ! [X: nat] :
% 15.55/8.65                                        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 15.55/8.65                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 15.55/8.65                                         => ( ( ord_less_nat @ Mi3 @ X )
% 15.55/8.65                                            & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 15.55/8.65                          @ Mima ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9584_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 15.55/8.65      ! [X3: vEBT_VEBT,Xa: nat] :
% 15.55/8.65        ( ( vEBT_VEBT_valid @ X3 @ Xa )
% 15.55/8.65       => ( ( ? [Uu: $o,Uv: $o] :
% 15.55/8.65                ( X3
% 15.55/8.65                = ( vEBT_Leaf @ Uu @ Uv ) )
% 15.55/8.65           => ( Xa != one_one_nat ) )
% 15.55/8.65         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.65                ( ( X3
% 15.55/8.65                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 15.55/8.65               => ~ ( ( Deg2 = Xa )
% 15.55/8.65                    & ! [X6: vEBT_VEBT] :
% 15.55/8.65                        ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.65                       => ( vEBT_VEBT_valid @ X6 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.65                    & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.65                    & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 15.55/8.65                      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.65                    & ( case_o184042715313410164at_nat
% 15.55/8.65                      @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 15.55/8.65                        & ! [X: vEBT_VEBT] :
% 15.55/8.65                            ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.65                           => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 15.55/8.65                      @ ( produc6081775807080527818_nat_o
% 15.55/8.65                        @ ^ [Mi3: nat,Ma3: nat] :
% 15.55/8.65                            ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 15.55/8.65                            & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 15.55/8.65                            & ! [I4: nat] :
% 15.55/8.65                                ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.65                               => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X8 ) )
% 15.55/8.65                                  = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 15.55/8.65                            & ( ( Mi3 = Ma3 )
% 15.55/8.65                             => ! [X: vEBT_VEBT] :
% 15.55/8.65                                  ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.65                                 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 15.55/8.65                            & ( ( Mi3 != Ma3 )
% 15.55/8.65                             => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 15.55/8.65                                & ! [X: nat] :
% 15.55/8.65                                    ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 15.55/8.65                                   => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 15.55/8.65                                     => ( ( ord_less_nat @ Mi3 @ X )
% 15.55/8.65                                        & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 15.55/8.65                      @ Mima ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9585_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 15.55/8.65      ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg3: nat] :
% 15.55/8.65        ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList2 @ Summary ) @ Deg3 )
% 15.55/8.65        = ( ( Deg = Deg3 )
% 15.55/8.65          & ! [X: vEBT_VEBT] :
% 15.55/8.65              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 15.55/8.65             => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.65          & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.65          & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 15.55/8.65            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.65          & ( case_o184042715313410164at_nat
% 15.55/8.65            @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X8 )
% 15.55/8.65              & ! [X: vEBT_VEBT] :
% 15.55/8.65                  ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 15.55/8.65                 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 15.55/8.65            @ ( produc6081775807080527818_nat_o
% 15.55/8.65              @ ^ [Mi3: nat,Ma3: nat] :
% 15.55/8.65                  ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 15.55/8.65                  & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 15.55/8.65                  & ! [I4: nat] :
% 15.55/8.65                      ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.65                     => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X8 ) )
% 15.55/8.65                        = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 15.55/8.65                  & ( ( Mi3 = Ma3 )
% 15.55/8.65                   => ! [X: vEBT_VEBT] :
% 15.55/8.65                        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 15.55/8.65                       => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 15.55/8.65                  & ( ( Mi3 != Ma3 )
% 15.55/8.65                   => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 15.55/8.65                      & ! [X: nat] :
% 15.55/8.65                          ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 15.55/8.65                         => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 15.55/8.65                           => ( ( ord_less_nat @ Mi3 @ X )
% 15.55/8.65                              & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 15.55/8.65            @ Mima2 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9586_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 15.55/8.65      ! [X3: vEBT_VEBT,Xa: nat] :
% 15.55/8.65        ( ~ ( vEBT_VEBT_valid @ X3 @ Xa )
% 15.55/8.65       => ( ( ? [Uu: $o,Uv: $o] :
% 15.55/8.65                ( X3
% 15.55/8.65                = ( vEBT_Leaf @ Uu @ Uv ) )
% 15.55/8.65           => ( Xa = one_one_nat ) )
% 15.55/8.65         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.65                ( ( X3
% 15.55/8.65                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 15.55/8.65               => ( ( Deg2 = Xa )
% 15.55/8.65                  & ! [X4: vEBT_VEBT] :
% 15.55/8.65                      ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.65                     => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.65                  & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.65                  & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 15.55/8.65                    = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.65                  & ( case_o184042715313410164at_nat
% 15.55/8.65                    @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 15.55/8.65                      & ! [X: vEBT_VEBT] :
% 15.55/8.65                          ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.65                         => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 15.55/8.65                    @ ( produc6081775807080527818_nat_o
% 15.55/8.65                      @ ^ [Mi3: nat,Ma3: nat] :
% 15.55/8.65                          ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 15.55/8.65                          & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 15.55/8.65                          & ! [I4: nat] :
% 15.55/8.65                              ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.65                             => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X8 ) )
% 15.55/8.65                                = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 15.55/8.65                          & ( ( Mi3 = Ma3 )
% 15.55/8.65                           => ! [X: vEBT_VEBT] :
% 15.55/8.65                                ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.65                               => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 15.55/8.65                          & ( ( Mi3 != Ma3 )
% 15.55/8.65                           => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 15.55/8.65                              & ! [X: nat] :
% 15.55/8.65                                  ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 15.55/8.65                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 15.55/8.65                                   => ( ( ord_less_nat @ Mi3 @ X )
% 15.55/8.65                                      & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 15.55/8.65                    @ Mima ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9587_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 15.55/8.65      ! [X3: vEBT_VEBT,Xa: nat,Y3: $o] :
% 15.55/8.65        ( ( ( vEBT_VEBT_valid @ X3 @ Xa )
% 15.55/8.65          = Y3 )
% 15.55/8.65       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.65         => ( ! [Uu: $o,Uv: $o] :
% 15.55/8.65                ( ( X3
% 15.55/8.65                  = ( vEBT_Leaf @ Uu @ Uv ) )
% 15.55/8.65               => ( ( Y3
% 15.55/8.65                    = ( Xa = one_one_nat ) )
% 15.55/8.65                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa ) ) ) )
% 15.55/8.65           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.65                  ( ( X3
% 15.55/8.65                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 15.55/8.65                 => ( ( Y3
% 15.55/8.65                      = ( ( Deg2 = Xa )
% 15.55/8.65                        & ! [X: vEBT_VEBT] :
% 15.55/8.65                            ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.65                           => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.65                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.65                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 15.55/8.65                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.65                        & ( case_o184042715313410164at_nat
% 15.55/8.65                          @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 15.55/8.65                            & ! [X: vEBT_VEBT] :
% 15.55/8.65                                ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.65                               => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 15.55/8.65                          @ ( produc6081775807080527818_nat_o
% 15.55/8.65                            @ ^ [Mi3: nat,Ma3: nat] :
% 15.55/8.65                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 15.55/8.65                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 15.55/8.65                                & ! [I4: nat] :
% 15.55/8.65                                    ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.65                                   => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X8 ) )
% 15.55/8.65                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 15.55/8.65                                & ( ( Mi3 = Ma3 )
% 15.55/8.65                                 => ! [X: vEBT_VEBT] :
% 15.55/8.65                                      ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.65                                     => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 15.55/8.65                                & ( ( Mi3 != Ma3 )
% 15.55/8.65                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 15.55/8.65                                    & ! [X: nat] :
% 15.55/8.65                                        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 15.55/8.65                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 15.55/8.65                                         => ( ( ord_less_nat @ Mi3 @ X )
% 15.55/8.65                                            & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 15.55/8.65                          @ Mima ) ) )
% 15.55/8.65                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9588_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 15.55/8.65      ! [X3: vEBT_VEBT,Xa: nat] :
% 15.55/8.65        ( ( vEBT_VEBT_valid @ X3 @ Xa )
% 15.55/8.65       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.65         => ( ! [Uu: $o,Uv: $o] :
% 15.55/8.65                ( ( X3
% 15.55/8.65                  = ( vEBT_Leaf @ Uu @ Uv ) )
% 15.55/8.65               => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa ) )
% 15.55/8.65                 => ( Xa != one_one_nat ) ) )
% 15.55/8.65           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.65                  ( ( X3
% 15.55/8.65                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 15.55/8.65                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa ) )
% 15.55/8.65                   => ~ ( ( Deg2 = Xa )
% 15.55/8.65                        & ! [X6: vEBT_VEBT] :
% 15.55/8.65                            ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.65                           => ( vEBT_VEBT_valid @ X6 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.65                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.65                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 15.55/8.65                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.65                        & ( case_o184042715313410164at_nat
% 15.55/8.65                          @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 15.55/8.65                            & ! [X: vEBT_VEBT] :
% 15.55/8.65                                ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.65                               => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 15.55/8.65                          @ ( produc6081775807080527818_nat_o
% 15.55/8.65                            @ ^ [Mi3: nat,Ma3: nat] :
% 15.55/8.65                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 15.55/8.65                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 15.55/8.65                                & ! [I4: nat] :
% 15.55/8.65                                    ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.65                                   => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X8 ) )
% 15.55/8.65                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 15.55/8.65                                & ( ( Mi3 = Ma3 )
% 15.55/8.65                                 => ! [X: vEBT_VEBT] :
% 15.55/8.65                                      ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.65                                     => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 15.55/8.65                                & ( ( Mi3 != Ma3 )
% 15.55/8.65                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 15.55/8.65                                    & ! [X: nat] :
% 15.55/8.65                                        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 15.55/8.65                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 15.55/8.65                                         => ( ( ord_less_nat @ Mi3 @ X )
% 15.55/8.65                                            & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 15.55/8.65                          @ Mima ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9589_Sup__int__def,axiom,
% 15.55/8.65      ( complete_Sup_Sup_int
% 15.55/8.65      = ( ^ [X8: set_int] :
% 15.55/8.65            ( the_int
% 15.55/8.65            @ ^ [X: int] :
% 15.55/8.65                ( ( member_int @ X @ X8 )
% 15.55/8.65                & ! [Y: int] :
% 15.55/8.65                    ( ( member_int @ Y @ X8 )
% 15.55/8.65                   => ( ord_less_eq_int @ Y @ X ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9590_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 15.55/8.65      ! [X3: vEBT_VEBT,Xa: nat] :
% 15.55/8.65        ( ~ ( vEBT_VEBT_valid @ X3 @ Xa )
% 15.55/8.65       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa ) )
% 15.55/8.65         => ( ! [Uu: $o,Uv: $o] :
% 15.55/8.65                ( ( X3
% 15.55/8.65                  = ( vEBT_Leaf @ Uu @ Uv ) )
% 15.55/8.65               => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa ) )
% 15.55/8.65                 => ( Xa = one_one_nat ) ) )
% 15.55/8.65           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.65                  ( ( X3
% 15.55/8.65                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 15.55/8.65                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa ) )
% 15.55/8.65                   => ( ( Deg2 = Xa )
% 15.55/8.65                      & ! [X4: vEBT_VEBT] :
% 15.55/8.65                          ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.65                         => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.65                      & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.65                      & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 15.55/8.65                        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.65                      & ( case_o184042715313410164at_nat
% 15.55/8.65                        @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 15.55/8.65                          & ! [X: vEBT_VEBT] :
% 15.55/8.65                              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.65                             => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 15.55/8.65                        @ ( produc6081775807080527818_nat_o
% 15.55/8.65                          @ ^ [Mi3: nat,Ma3: nat] :
% 15.55/8.65                              ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 15.55/8.65                              & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 15.55/8.65                              & ! [I4: nat] :
% 15.55/8.65                                  ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.65                                 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X8 ) )
% 15.55/8.65                                    = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 15.55/8.65                              & ( ( Mi3 = Ma3 )
% 15.55/8.65                               => ! [X: vEBT_VEBT] :
% 15.55/8.65                                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 15.55/8.65                                   => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 15.55/8.65                              & ( ( Mi3 != Ma3 )
% 15.55/8.65                               => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 15.55/8.65                                  & ! [X: nat] :
% 15.55/8.65                                      ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 15.55/8.65                                     => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 15.55/8.65                                       => ( ( ord_less_nat @ Mi3 @ X )
% 15.55/8.65                                          & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 15.55/8.65                        @ Mima ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9591_take__bit__numeral__minus__numeral__int,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.65        = ( case_option_int_num @ zero_zero_int
% 15.55/8.65          @ ^ [Q5: num] : ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_int @ Q5 ) ) )
% 15.55/8.65          @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9592_take__bit__num__simps_I1_J,axiom,
% 15.55/8.65      ! [M: num] :
% 15.55/8.65        ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 15.55/8.65        = none_num ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9593_take__bit__num__simps_I2_J,axiom,
% 15.55/8.65      ! [N: nat] :
% 15.55/8.65        ( ( bit_take_bit_num @ ( suc @ N ) @ one )
% 15.55/8.65        = ( some_num @ one ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9594_take__bit__num__simps_I5_J,axiom,
% 15.55/8.65      ! [R2: num] :
% 15.55/8.65        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ one )
% 15.55/8.65        = ( some_num @ one ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9595_take__bit__num__simps_I3_J,axiom,
% 15.55/8.65      ! [N: nat,M: num] :
% 15.55/8.65        ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M ) )
% 15.55/8.65        = ( case_o6005452278849405969um_num @ none_num
% 15.55/8.65          @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 15.55/8.65          @ ( bit_take_bit_num @ N @ M ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9596_take__bit__num__simps_I4_J,axiom,
% 15.55/8.65      ! [N: nat,M: num] :
% 15.55/8.65        ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M ) )
% 15.55/8.65        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9597_take__bit__num__simps_I6_J,axiom,
% 15.55/8.65      ! [R2: num,M: num] :
% 15.55/8.65        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit0 @ M ) )
% 15.55/8.65        = ( case_o6005452278849405969um_num @ none_num
% 15.55/8.65          @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 15.55/8.65          @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9598_take__bit__num__simps_I7_J,axiom,
% 15.55/8.65      ! [R2: num,M: num] :
% 15.55/8.65        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit1 @ M ) )
% 15.55/8.65        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9599_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 15.55/8.65      ! [N: nat,M: num] :
% 15.55/8.65        ( ( bit_take_bit_num @ N @ ( bit0 @ M ) )
% 15.55/8.65        = ( case_nat_option_num @ none_num
% 15.55/8.65          @ ^ [N3: nat] :
% 15.55/8.65              ( case_o6005452278849405969um_num @ none_num
% 15.55/8.65              @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 15.55/8.65              @ ( bit_take_bit_num @ N3 @ M ) )
% 15.55/8.65          @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9600_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 15.55/8.65      ! [N: nat] :
% 15.55/8.65        ( ( bit_take_bit_num @ N @ one )
% 15.55/8.65        = ( case_nat_option_num @ none_num
% 15.55/8.65          @ ^ [N3: nat] : ( some_num @ one )
% 15.55/8.65          @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9601_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 15.55/8.65      ! [N: nat,M: num] :
% 15.55/8.65        ( ( bit_take_bit_num @ N @ ( bit1 @ M ) )
% 15.55/8.65        = ( case_nat_option_num @ none_num
% 15.55/8.65          @ ^ [N3: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N3 @ M ) ) )
% 15.55/8.65          @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9602_take__bit__num__def,axiom,
% 15.55/8.65      ( bit_take_bit_num
% 15.55/8.65      = ( ^ [N3: nat,M3: num] :
% 15.55/8.65            ( if_option_num
% 15.55/8.65            @ ( ( bit_se2925701944663578781it_nat @ N3 @ ( numeral_numeral_nat @ M3 ) )
% 15.55/8.65              = zero_zero_nat )
% 15.55/8.65            @ none_num
% 15.55/8.65            @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N3 @ ( numeral_numeral_nat @ M3 ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9603_and__minus__numerals_I3_J,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 15.55/8.65        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9604_and__minus__numerals_I7_J,axiom,
% 15.55/8.65      ! [N: num,M: num] :
% 15.55/8.65        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 15.55/8.65        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9605_and__minus__numerals_I4_J,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 15.55/8.65        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9606_and__minus__numerals_I8_J,axiom,
% 15.55/8.65      ! [N: num,M: num] :
% 15.55/8.65        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 15.55/8.65        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9607_and__not__num_Osimps_I1_J,axiom,
% 15.55/8.65      ( ( bit_and_not_num @ one @ one )
% 15.55/8.65      = none_num ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9608_and__not__num_Osimps_I4_J,axiom,
% 15.55/8.65      ! [M: num] :
% 15.55/8.65        ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 15.55/8.65        = ( some_num @ ( bit0 @ M ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9609_and__not__num_Osimps_I2_J,axiom,
% 15.55/8.65      ! [N: num] :
% 15.55/8.65        ( ( bit_and_not_num @ one @ ( bit0 @ N ) )
% 15.55/8.65        = ( some_num @ one ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9610_and__not__num_Osimps_I3_J,axiom,
% 15.55/8.65      ! [N: num] :
% 15.55/8.65        ( ( bit_and_not_num @ one @ ( bit1 @ N ) )
% 15.55/8.65        = none_num ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9611_and__not__num_Osimps_I7_J,axiom,
% 15.55/8.65      ! [M: num] :
% 15.55/8.65        ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 15.55/8.65        = ( some_num @ ( bit0 @ M ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9612_and__not__num__eq__Some__iff,axiom,
% 15.55/8.65      ! [M: num,N: num,Q3: num] :
% 15.55/8.65        ( ( ( bit_and_not_num @ M @ N )
% 15.55/8.65          = ( some_num @ Q3 ) )
% 15.55/8.65        = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.65          = ( numeral_numeral_int @ Q3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9613_and__not__num_Osimps_I8_J,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 15.55/8.65        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 15.55/8.65          @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 15.55/8.65          @ ( bit_and_not_num @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9614_and__not__num__eq__None__iff,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( ( bit_and_not_num @ M @ N )
% 15.55/8.65          = none_num )
% 15.55/8.65        = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.65          = zero_zero_int ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9615_int__numeral__not__and__num,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 15.55/8.65        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N @ M ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9616_int__numeral__and__not__num,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.65        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9617_Bit__Operations_Otake__bit__num__code,axiom,
% 15.55/8.65      ( bit_take_bit_num
% 15.55/8.65      = ( ^ [N3: nat,M3: num] :
% 15.55/8.65            ( produc478579273971653890on_num
% 15.55/8.65            @ ^ [A4: nat,X: num] :
% 15.55/8.65                ( case_nat_option_num @ none_num
% 15.55/8.65                @ ^ [O: nat] :
% 15.55/8.65                    ( case_num_option_num @ ( some_num @ one )
% 15.55/8.65                    @ ^ [P5: num] :
% 15.55/8.65                        ( case_o6005452278849405969um_num @ none_num
% 15.55/8.65                        @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 15.55/8.65                        @ ( bit_take_bit_num @ O @ P5 ) )
% 15.55/8.65                    @ ^ [P5: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P5 ) ) )
% 15.55/8.65                    @ X )
% 15.55/8.65                @ A4 )
% 15.55/8.65            @ ( product_Pair_nat_num @ N3 @ M3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9618_Rats__eq__int__div__nat,axiom,
% 15.55/8.65      ( field_5140801741446780682s_real
% 15.55/8.65      = ( collect_real
% 15.55/8.65        @ ^ [Uu3: real] :
% 15.55/8.65          ? [I4: int,N3: nat] :
% 15.55/8.65            ( ( Uu3
% 15.55/8.65              = ( divide_divide_real @ ( ring_1_of_int_real @ I4 ) @ ( semiri5074537144036343181t_real @ N3 ) ) )
% 15.55/8.65            & ( N3 != zero_zero_nat ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9619_Rats__abs__iff,axiom,
% 15.55/8.65      ! [X3: real] :
% 15.55/8.65        ( ( member_real @ ( abs_abs_real @ X3 ) @ field_5140801741446780682s_real )
% 15.55/8.65        = ( member_real @ X3 @ field_5140801741446780682s_real ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9620_Rats__dense__in__real,axiom,
% 15.55/8.65      ! [X3: real,Y3: real] :
% 15.55/8.65        ( ( ord_less_real @ X3 @ Y3 )
% 15.55/8.65       => ? [X4: real] :
% 15.55/8.65            ( ( member_real @ X4 @ field_5140801741446780682s_real )
% 15.55/8.65            & ( ord_less_real @ X3 @ X4 )
% 15.55/8.65            & ( ord_less_real @ X4 @ Y3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9621_Rats__no__bot__less,axiom,
% 15.55/8.65      ! [X3: real] :
% 15.55/8.65      ? [X4: real] :
% 15.55/8.65        ( ( member_real @ X4 @ field_5140801741446780682s_real )
% 15.55/8.65        & ( ord_less_real @ X4 @ X3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9622_Rats__no__top__le,axiom,
% 15.55/8.65      ! [X3: real] :
% 15.55/8.65      ? [X4: real] :
% 15.55/8.65        ( ( member_real @ X4 @ field_5140801741446780682s_real )
% 15.55/8.65        & ( ord_less_eq_real @ X3 @ X4 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9623_Rats__eq__int__div__int,axiom,
% 15.55/8.65      ( field_5140801741446780682s_real
% 15.55/8.65      = ( collect_real
% 15.55/8.65        @ ^ [Uu3: real] :
% 15.55/8.65          ? [I4: int,J3: int] :
% 15.55/8.65            ( ( Uu3
% 15.55/8.65              = ( divide_divide_real @ ( ring_1_of_int_real @ I4 ) @ ( ring_1_of_int_real @ J3 ) ) )
% 15.55/8.65            & ( J3 != zero_zero_int ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9624_and__not__num_Oelims,axiom,
% 15.55/8.65      ! [X3: num,Xa: num,Y3: option_num] :
% 15.55/8.65        ( ( ( bit_and_not_num @ X3 @ Xa )
% 15.55/8.65          = Y3 )
% 15.55/8.65       => ( ( ( X3 = one )
% 15.55/8.65           => ( ( Xa = one )
% 15.55/8.65             => ( Y3 != none_num ) ) )
% 15.55/8.65         => ( ( ( X3 = one )
% 15.55/8.65             => ( ? [N2: num] :
% 15.55/8.65                    ( Xa
% 15.55/8.65                    = ( bit0 @ N2 ) )
% 15.55/8.65               => ( Y3
% 15.55/8.65                 != ( some_num @ one ) ) ) )
% 15.55/8.65           => ( ( ( X3 = one )
% 15.55/8.65               => ( ? [N2: num] :
% 15.55/8.65                      ( Xa
% 15.55/8.65                      = ( bit1 @ N2 ) )
% 15.55/8.65                 => ( Y3 != none_num ) ) )
% 15.55/8.65             => ( ! [M4: num] :
% 15.55/8.65                    ( ( X3
% 15.55/8.65                      = ( bit0 @ M4 ) )
% 15.55/8.65                   => ( ( Xa = one )
% 15.55/8.65                     => ( Y3
% 15.55/8.65                       != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 15.55/8.65               => ( ! [M4: num] :
% 15.55/8.65                      ( ( X3
% 15.55/8.65                        = ( bit0 @ M4 ) )
% 15.55/8.65                     => ! [N2: num] :
% 15.55/8.65                          ( ( Xa
% 15.55/8.65                            = ( bit0 @ N2 ) )
% 15.55/8.65                         => ( Y3
% 15.55/8.65                           != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) )
% 15.55/8.65                 => ( ! [M4: num] :
% 15.55/8.65                        ( ( X3
% 15.55/8.65                          = ( bit0 @ M4 ) )
% 15.55/8.65                       => ! [N2: num] :
% 15.55/8.65                            ( ( Xa
% 15.55/8.65                              = ( bit1 @ N2 ) )
% 15.55/8.65                           => ( Y3
% 15.55/8.65                             != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) )
% 15.55/8.65                   => ( ! [M4: num] :
% 15.55/8.65                          ( ( X3
% 15.55/8.65                            = ( bit1 @ M4 ) )
% 15.55/8.65                         => ( ( Xa = one )
% 15.55/8.65                           => ( Y3
% 15.55/8.65                             != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 15.55/8.65                     => ( ! [M4: num] :
% 15.55/8.65                            ( ( X3
% 15.55/8.65                              = ( bit1 @ M4 ) )
% 15.55/8.65                           => ! [N2: num] :
% 15.55/8.65                                ( ( Xa
% 15.55/8.65                                  = ( bit0 @ N2 ) )
% 15.55/8.65                               => ( Y3
% 15.55/8.65                                 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 15.55/8.65                                    @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 15.55/8.65                                    @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) )
% 15.55/8.65                       => ~ ! [M4: num] :
% 15.55/8.65                              ( ( X3
% 15.55/8.65                                = ( bit1 @ M4 ) )
% 15.55/8.65                             => ! [N2: num] :
% 15.55/8.65                                  ( ( Xa
% 15.55/8.65                                    = ( bit1 @ N2 ) )
% 15.55/8.65                                 => ( Y3
% 15.55/8.65                                   != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9625_xor__num_Osimps_I6_J,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 15.55/8.65        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9626_xor__num_Osimps_I9_J,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 15.55/8.65        = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9627_xor__num_Osimps_I5_J,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 15.55/8.65        = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9628_and__not__num_Osimps_I5_J,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 15.55/8.65        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9629_and__not__num_Osimps_I6_J,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 15.55/8.65        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9630_and__not__num_Osimps_I9_J,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 15.55/8.65        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9631_xor__num_Osimps_I1_J,axiom,
% 15.55/8.65      ( ( bit_un2480387367778600638or_num @ one @ one )
% 15.55/8.65      = none_num ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9632_xor__num_Oelims,axiom,
% 15.55/8.65      ! [X3: num,Xa: num,Y3: option_num] :
% 15.55/8.65        ( ( ( bit_un2480387367778600638or_num @ X3 @ Xa )
% 15.55/8.65          = Y3 )
% 15.55/8.65       => ( ( ( X3 = one )
% 15.55/8.65           => ( ( Xa = one )
% 15.55/8.65             => ( Y3 != none_num ) ) )
% 15.55/8.65         => ( ( ( X3 = one )
% 15.55/8.65             => ! [N2: num] :
% 15.55/8.65                  ( ( Xa
% 15.55/8.65                    = ( bit0 @ N2 ) )
% 15.55/8.65                 => ( Y3
% 15.55/8.65                   != ( some_num @ ( bit1 @ N2 ) ) ) ) )
% 15.55/8.65           => ( ( ( X3 = one )
% 15.55/8.65               => ! [N2: num] :
% 15.55/8.65                    ( ( Xa
% 15.55/8.65                      = ( bit1 @ N2 ) )
% 15.55/8.65                   => ( Y3
% 15.55/8.65                     != ( some_num @ ( bit0 @ N2 ) ) ) ) )
% 15.55/8.65             => ( ! [M4: num] :
% 15.55/8.65                    ( ( X3
% 15.55/8.65                      = ( bit0 @ M4 ) )
% 15.55/8.65                   => ( ( Xa = one )
% 15.55/8.65                     => ( Y3
% 15.55/8.65                       != ( some_num @ ( bit1 @ M4 ) ) ) ) )
% 15.55/8.65               => ( ! [M4: num] :
% 15.55/8.65                      ( ( X3
% 15.55/8.65                        = ( bit0 @ M4 ) )
% 15.55/8.65                     => ! [N2: num] :
% 15.55/8.65                          ( ( Xa
% 15.55/8.65                            = ( bit0 @ N2 ) )
% 15.55/8.65                         => ( Y3
% 15.55/8.65                           != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) ) )
% 15.55/8.65                 => ( ! [M4: num] :
% 15.55/8.65                        ( ( X3
% 15.55/8.65                          = ( bit0 @ M4 ) )
% 15.55/8.65                       => ! [N2: num] :
% 15.55/8.65                            ( ( Xa
% 15.55/8.65                              = ( bit1 @ N2 ) )
% 15.55/8.65                           => ( Y3
% 15.55/8.65                             != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) ) ) )
% 15.55/8.65                   => ( ! [M4: num] :
% 15.55/8.65                          ( ( X3
% 15.55/8.65                            = ( bit1 @ M4 ) )
% 15.55/8.65                         => ( ( Xa = one )
% 15.55/8.65                           => ( Y3
% 15.55/8.65                             != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 15.55/8.65                     => ( ! [M4: num] :
% 15.55/8.65                            ( ( X3
% 15.55/8.65                              = ( bit1 @ M4 ) )
% 15.55/8.65                           => ! [N2: num] :
% 15.55/8.65                                ( ( Xa
% 15.55/8.65                                  = ( bit0 @ N2 ) )
% 15.55/8.65                               => ( Y3
% 15.55/8.65                                 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) ) ) )
% 15.55/8.65                       => ~ ! [M4: num] :
% 15.55/8.65                              ( ( X3
% 15.55/8.65                                = ( bit1 @ M4 ) )
% 15.55/8.65                             => ! [N2: num] :
% 15.55/8.65                                  ( ( Xa
% 15.55/8.65                                    = ( bit1 @ N2 ) )
% 15.55/8.65                                 => ( Y3
% 15.55/8.65                                   != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9633_xor__num_Osimps_I7_J,axiom,
% 15.55/8.65      ! [M: num] :
% 15.55/8.65        ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ one )
% 15.55/8.65        = ( some_num @ ( bit0 @ M ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9634_xor__num_Osimps_I4_J,axiom,
% 15.55/8.65      ! [M: num] :
% 15.55/8.65        ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ one )
% 15.55/8.65        = ( some_num @ ( bit1 @ M ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9635_xor__num_Osimps_I3_J,axiom,
% 15.55/8.65      ! [N: num] :
% 15.55/8.65        ( ( bit_un2480387367778600638or_num @ one @ ( bit1 @ N ) )
% 15.55/8.65        = ( some_num @ ( bit0 @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9636_xor__num_Osimps_I2_J,axiom,
% 15.55/8.65      ! [N: num] :
% 15.55/8.65        ( ( bit_un2480387367778600638or_num @ one @ ( bit0 @ N ) )
% 15.55/8.65        = ( some_num @ ( bit1 @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9637_xor__num_Osimps_I8_J,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 15.55/8.65        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9638_and__num_Oelims,axiom,
% 15.55/8.65      ! [X3: num,Xa: num,Y3: option_num] :
% 15.55/8.65        ( ( ( bit_un7362597486090784418nd_num @ X3 @ Xa )
% 15.55/8.65          = Y3 )
% 15.55/8.65       => ( ( ( X3 = one )
% 15.55/8.65           => ( ( Xa = one )
% 15.55/8.65             => ( Y3
% 15.55/8.65               != ( some_num @ one ) ) ) )
% 15.55/8.65         => ( ( ( X3 = one )
% 15.55/8.65             => ( ? [N2: num] :
% 15.55/8.65                    ( Xa
% 15.55/8.65                    = ( bit0 @ N2 ) )
% 15.55/8.65               => ( Y3 != none_num ) ) )
% 15.55/8.65           => ( ( ( X3 = one )
% 15.55/8.65               => ( ? [N2: num] :
% 15.55/8.65                      ( Xa
% 15.55/8.65                      = ( bit1 @ N2 ) )
% 15.55/8.65                 => ( Y3
% 15.55/8.65                   != ( some_num @ one ) ) ) )
% 15.55/8.65             => ( ( ? [M4: num] :
% 15.55/8.65                      ( X3
% 15.55/8.65                      = ( bit0 @ M4 ) )
% 15.55/8.65                 => ( ( Xa = one )
% 15.55/8.65                   => ( Y3 != none_num ) ) )
% 15.55/8.65               => ( ! [M4: num] :
% 15.55/8.65                      ( ( X3
% 15.55/8.65                        = ( bit0 @ M4 ) )
% 15.55/8.65                     => ! [N2: num] :
% 15.55/8.65                          ( ( Xa
% 15.55/8.65                            = ( bit0 @ N2 ) )
% 15.55/8.65                         => ( Y3
% 15.55/8.65                           != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) )
% 15.55/8.65                 => ( ! [M4: num] :
% 15.55/8.65                        ( ( X3
% 15.55/8.65                          = ( bit0 @ M4 ) )
% 15.55/8.65                       => ! [N2: num] :
% 15.55/8.65                            ( ( Xa
% 15.55/8.65                              = ( bit1 @ N2 ) )
% 15.55/8.65                           => ( Y3
% 15.55/8.65                             != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) )
% 15.55/8.65                   => ( ( ? [M4: num] :
% 15.55/8.65                            ( X3
% 15.55/8.65                            = ( bit1 @ M4 ) )
% 15.55/8.65                       => ( ( Xa = one )
% 15.55/8.65                         => ( Y3
% 15.55/8.65                           != ( some_num @ one ) ) ) )
% 15.55/8.65                     => ( ! [M4: num] :
% 15.55/8.65                            ( ( X3
% 15.55/8.65                              = ( bit1 @ M4 ) )
% 15.55/8.65                           => ! [N2: num] :
% 15.55/8.65                                ( ( Xa
% 15.55/8.65                                  = ( bit0 @ N2 ) )
% 15.55/8.65                               => ( Y3
% 15.55/8.65                                 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) )
% 15.55/8.65                       => ~ ! [M4: num] :
% 15.55/8.65                              ( ( X3
% 15.55/8.65                                = ( bit1 @ M4 ) )
% 15.55/8.65                             => ! [N2: num] :
% 15.55/8.65                                  ( ( Xa
% 15.55/8.65                                    = ( bit1 @ N2 ) )
% 15.55/8.65                                 => ( Y3
% 15.55/8.65                                   != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 15.55/8.65                                      @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 15.55/8.65                                      @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9639_xor__num__dict,axiom,
% 15.55/8.65      bit_un2480387367778600638or_num = bit_un6178654185764691216or_num ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9640_and__num_Osimps_I1_J,axiom,
% 15.55/8.65      ( ( bit_un7362597486090784418nd_num @ one @ one )
% 15.55/8.65      = ( some_num @ one ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9641_and__num_Osimps_I5_J,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 15.55/8.65        = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9642_and__num_Osimps_I7_J,axiom,
% 15.55/8.65      ! [M: num] :
% 15.55/8.65        ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ one )
% 15.55/8.65        = ( some_num @ one ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9643_and__num_Osimps_I3_J,axiom,
% 15.55/8.65      ! [N: num] :
% 15.55/8.65        ( ( bit_un7362597486090784418nd_num @ one @ ( bit1 @ N ) )
% 15.55/8.65        = ( some_num @ one ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9644_and__num_Osimps_I2_J,axiom,
% 15.55/8.65      ! [N: num] :
% 15.55/8.65        ( ( bit_un7362597486090784418nd_num @ one @ ( bit0 @ N ) )
% 15.55/8.65        = none_num ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9645_and__num_Osimps_I4_J,axiom,
% 15.55/8.65      ! [M: num] :
% 15.55/8.65        ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ one )
% 15.55/8.65        = none_num ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9646_and__num_Osimps_I8_J,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 15.55/8.65        = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9647_and__num_Osimps_I6_J,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 15.55/8.65        = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9648_and__num_Osimps_I9_J,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 15.55/8.65        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 15.55/8.65          @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 15.55/8.65          @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9649_and__num__dict,axiom,
% 15.55/8.65      bit_un7362597486090784418nd_num = bit_un1837492267222099188nd_num ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9650_of__nat__eq__id,axiom,
% 15.55/8.65      semiri1316708129612266289at_nat = id_nat ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9651_less__eq__int__def,axiom,
% 15.55/8.65      ( ord_less_eq_int
% 15.55/8.65      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 15.55/8.65        @ ( produc8739625826339149834_nat_o
% 15.55/8.65          @ ^ [X: nat,Y: nat] :
% 15.55/8.65              ( produc6081775807080527818_nat_o
% 15.55/8.65              @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9652_less__int__def,axiom,
% 15.55/8.65      ( ord_less_int
% 15.55/8.65      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 15.55/8.65        @ ( produc8739625826339149834_nat_o
% 15.55/8.65          @ ^ [X: nat,Y: nat] :
% 15.55/8.65              ( produc6081775807080527818_nat_o
% 15.55/8.65              @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9653_nat__def,axiom,
% 15.55/8.65      ( nat2
% 15.55/8.65      = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9654_min__Suc__Suc,axiom,
% 15.55/8.65      ! [M: nat,N: nat] :
% 15.55/8.65        ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N ) )
% 15.55/8.65        = ( suc @ ( ord_min_nat @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9655_min__0L,axiom,
% 15.55/8.65      ! [N: nat] :
% 15.55/8.65        ( ( ord_min_nat @ zero_zero_nat @ N )
% 15.55/8.65        = zero_zero_nat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9656_min__0R,axiom,
% 15.55/8.65      ! [N: nat] :
% 15.55/8.65        ( ( ord_min_nat @ N @ zero_zero_nat )
% 15.55/8.65        = zero_zero_nat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9657_min__enat__simps_I3_J,axiom,
% 15.55/8.65      ! [Q3: extended_enat] :
% 15.55/8.65        ( ( ord_mi8085742599997312461d_enat @ zero_z5237406670263579293d_enat @ Q3 )
% 15.55/8.65        = zero_z5237406670263579293d_enat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9658_min__enat__simps_I2_J,axiom,
% 15.55/8.65      ! [Q3: extended_enat] :
% 15.55/8.65        ( ( ord_mi8085742599997312461d_enat @ Q3 @ zero_z5237406670263579293d_enat )
% 15.55/8.65        = zero_z5237406670263579293d_enat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9659_min__numeral__Suc,axiom,
% 15.55/8.65      ! [K: num,N: nat] :
% 15.55/8.65        ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 15.55/8.65        = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9660_min__Suc__numeral,axiom,
% 15.55/8.65      ! [N: nat,K: num] :
% 15.55/8.65        ( ( ord_min_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 15.55/8.65        = ( suc @ ( ord_min_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9661_concat__bit__assoc__sym,axiom,
% 15.55/8.65      ! [M: nat,N: nat,K: int,L: int,R2: int] :
% 15.55/8.65        ( ( bit_concat_bit @ M @ ( bit_concat_bit @ N @ K @ L ) @ R2 )
% 15.55/8.65        = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_concat_bit @ ( minus_minus_nat @ M @ N ) @ L @ R2 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9662_min__diff,axiom,
% 15.55/8.65      ! [M: nat,I: nat,N: nat] :
% 15.55/8.65        ( ( ord_min_nat @ ( minus_minus_nat @ M @ I ) @ ( minus_minus_nat @ N @ I ) )
% 15.55/8.65        = ( minus_minus_nat @ ( ord_min_nat @ M @ N ) @ I ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9663_nat__mult__min__right,axiom,
% 15.55/8.65      ! [M: nat,N: nat,Q3: nat] :
% 15.55/8.65        ( ( times_times_nat @ M @ ( ord_min_nat @ N @ Q3 ) )
% 15.55/8.65        = ( ord_min_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9664_nat__mult__min__left,axiom,
% 15.55/8.65      ! [M: nat,N: nat,Q3: nat] :
% 15.55/8.65        ( ( times_times_nat @ ( ord_min_nat @ M @ N ) @ Q3 )
% 15.55/8.65        = ( ord_min_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N @ Q3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9665_take__bit__concat__bit__eq,axiom,
% 15.55/8.65      ! [M: nat,N: nat,K: int,L: int] :
% 15.55/8.65        ( ( bit_se2923211474154528505it_int @ M @ ( bit_concat_bit @ N @ K @ L ) )
% 15.55/8.65        = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N ) @ L ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9666_min__Suc2,axiom,
% 15.55/8.65      ! [M: nat,N: nat] :
% 15.55/8.65        ( ( ord_min_nat @ M @ ( suc @ N ) )
% 15.55/8.65        = ( case_nat_nat @ zero_zero_nat
% 15.55/8.65          @ ^ [M5: nat] : ( suc @ ( ord_min_nat @ M5 @ N ) )
% 15.55/8.65          @ M ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9667_min__Suc1,axiom,
% 15.55/8.65      ! [N: nat,M: nat] :
% 15.55/8.65        ( ( ord_min_nat @ ( suc @ N ) @ M )
% 15.55/8.65        = ( case_nat_nat @ zero_zero_nat
% 15.55/8.65          @ ^ [M5: nat] : ( suc @ ( ord_min_nat @ N @ M5 ) )
% 15.55/8.65          @ M ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9668_inf__int__def,axiom,
% 15.55/8.65      inf_inf_int = ord_min_int ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9669_inf__nat__def,axiom,
% 15.55/8.65      inf_inf_nat = ord_min_nat ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9670_inf__enat__def,axiom,
% 15.55/8.65      inf_in1870772243966228564d_enat = ord_mi8085742599997312461d_enat ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9671_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 15.55/8.65      ! [N: nat,J: nat,I: nat] :
% 15.55/8.65        ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I ) )
% 15.55/8.65       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N )
% 15.55/8.65          = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9672_and__not__num_Opelims,axiom,
% 15.55/8.65      ! [X3: num,Xa: num,Y3: option_num] :
% 15.55/8.65        ( ( ( bit_and_not_num @ X3 @ Xa )
% 15.55/8.65          = Y3 )
% 15.55/8.65       => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X3 @ Xa ) )
% 15.55/8.65         => ( ( ( X3 = one )
% 15.55/8.65             => ( ( Xa = one )
% 15.55/8.65               => ( ( Y3 = none_num )
% 15.55/8.65                 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 15.55/8.65           => ( ( ( X3 = one )
% 15.55/8.65               => ! [N2: num] :
% 15.55/8.65                    ( ( Xa
% 15.55/8.65                      = ( bit0 @ N2 ) )
% 15.55/8.65                   => ( ( Y3
% 15.55/8.65                        = ( some_num @ one ) )
% 15.55/8.65                     => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) ) ) ) )
% 15.55/8.65             => ( ( ( X3 = one )
% 15.55/8.65                 => ! [N2: num] :
% 15.55/8.65                      ( ( Xa
% 15.55/8.65                        = ( bit1 @ N2 ) )
% 15.55/8.65                     => ( ( Y3 = none_num )
% 15.55/8.65                       => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) ) ) ) )
% 15.55/8.65               => ( ! [M4: num] :
% 15.55/8.65                      ( ( X3
% 15.55/8.65                        = ( bit0 @ M4 ) )
% 15.55/8.65                     => ( ( Xa = one )
% 15.55/8.65                       => ( ( Y3
% 15.55/8.65                            = ( some_num @ ( bit0 @ M4 ) ) )
% 15.55/8.65                         => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 15.55/8.65                 => ( ! [M4: num] :
% 15.55/8.65                        ( ( X3
% 15.55/8.65                          = ( bit0 @ M4 ) )
% 15.55/8.65                       => ! [N2: num] :
% 15.55/8.65                            ( ( Xa
% 15.55/8.65                              = ( bit0 @ N2 ) )
% 15.55/8.65                           => ( ( Y3
% 15.55/8.65                                = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 15.55/8.65                             => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 15.55/8.65                   => ( ! [M4: num] :
% 15.55/8.65                          ( ( X3
% 15.55/8.65                            = ( bit0 @ M4 ) )
% 15.55/8.65                         => ! [N2: num] :
% 15.55/8.65                              ( ( Xa
% 15.55/8.65                                = ( bit1 @ N2 ) )
% 15.55/8.65                             => ( ( Y3
% 15.55/8.65                                  = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 15.55/8.65                               => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) )
% 15.55/8.65                     => ( ! [M4: num] :
% 15.55/8.65                            ( ( X3
% 15.55/8.65                              = ( bit1 @ M4 ) )
% 15.55/8.65                           => ( ( Xa = one )
% 15.55/8.65                             => ( ( Y3
% 15.55/8.65                                  = ( some_num @ ( bit0 @ M4 ) ) )
% 15.55/8.65                               => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 15.55/8.65                       => ( ! [M4: num] :
% 15.55/8.65                              ( ( X3
% 15.55/8.65                                = ( bit1 @ M4 ) )
% 15.55/8.65                             => ! [N2: num] :
% 15.55/8.65                                  ( ( Xa
% 15.55/8.65                                    = ( bit0 @ N2 ) )
% 15.55/8.65                                 => ( ( Y3
% 15.55/8.65                                      = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 15.55/8.65                                        @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 15.55/8.65                                        @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 15.55/8.65                                   => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 15.55/8.65                         => ~ ! [M4: num] :
% 15.55/8.65                                ( ( X3
% 15.55/8.65                                  = ( bit1 @ M4 ) )
% 15.55/8.65                               => ! [N2: num] :
% 15.55/8.65                                    ( ( Xa
% 15.55/8.65                                      = ( bit1 @ N2 ) )
% 15.55/8.65                                   => ( ( Y3
% 15.55/8.65                                        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 15.55/8.65                                     => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9673_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 15.55/8.65      ! [N: nat,J: nat,I: nat] :
% 15.55/8.65        ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 15.55/8.65       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N )
% 15.55/8.65          = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9674_and__num_Opelims,axiom,
% 15.55/8.65      ! [X3: num,Xa: num,Y3: option_num] :
% 15.55/8.65        ( ( ( bit_un7362597486090784418nd_num @ X3 @ Xa )
% 15.55/8.65          = Y3 )
% 15.55/8.65       => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X3 @ Xa ) )
% 15.55/8.65         => ( ( ( X3 = one )
% 15.55/8.65             => ( ( Xa = one )
% 15.55/8.65               => ( ( Y3
% 15.55/8.65                    = ( some_num @ one ) )
% 15.55/8.65                 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 15.55/8.65           => ( ( ( X3 = one )
% 15.55/8.65               => ! [N2: num] :
% 15.55/8.65                    ( ( Xa
% 15.55/8.65                      = ( bit0 @ N2 ) )
% 15.55/8.65                   => ( ( Y3 = none_num )
% 15.55/8.65                     => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) ) ) ) )
% 15.55/8.65             => ( ( ( X3 = one )
% 15.55/8.65                 => ! [N2: num] :
% 15.55/8.65                      ( ( Xa
% 15.55/8.65                        = ( bit1 @ N2 ) )
% 15.55/8.65                     => ( ( Y3
% 15.55/8.65                          = ( some_num @ one ) )
% 15.55/8.65                       => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) ) ) ) )
% 15.55/8.65               => ( ! [M4: num] :
% 15.55/8.65                      ( ( X3
% 15.55/8.65                        = ( bit0 @ M4 ) )
% 15.55/8.65                     => ( ( Xa = one )
% 15.55/8.65                       => ( ( Y3 = none_num )
% 15.55/8.65                         => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 15.55/8.65                 => ( ! [M4: num] :
% 15.55/8.65                        ( ( X3
% 15.55/8.65                          = ( bit0 @ M4 ) )
% 15.55/8.65                       => ! [N2: num] :
% 15.55/8.65                            ( ( Xa
% 15.55/8.65                              = ( bit0 @ N2 ) )
% 15.55/8.65                           => ( ( Y3
% 15.55/8.65                                = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 15.55/8.65                             => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 15.55/8.65                   => ( ! [M4: num] :
% 15.55/8.65                          ( ( X3
% 15.55/8.65                            = ( bit0 @ M4 ) )
% 15.55/8.65                         => ! [N2: num] :
% 15.55/8.65                              ( ( Xa
% 15.55/8.65                                = ( bit1 @ N2 ) )
% 15.55/8.65                             => ( ( Y3
% 15.55/8.65                                  = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 15.55/8.65                               => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) )
% 15.55/8.65                     => ( ! [M4: num] :
% 15.55/8.65                            ( ( X3
% 15.55/8.65                              = ( bit1 @ M4 ) )
% 15.55/8.65                           => ( ( Xa = one )
% 15.55/8.65                             => ( ( Y3
% 15.55/8.65                                  = ( some_num @ one ) )
% 15.55/8.65                               => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 15.55/8.65                       => ( ! [M4: num] :
% 15.55/8.65                              ( ( X3
% 15.55/8.65                                = ( bit1 @ M4 ) )
% 15.55/8.65                             => ! [N2: num] :
% 15.55/8.65                                  ( ( Xa
% 15.55/8.65                                    = ( bit0 @ N2 ) )
% 15.55/8.65                                 => ( ( Y3
% 15.55/8.65                                      = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 15.55/8.65                                   => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 15.55/8.65                         => ~ ! [M4: num] :
% 15.55/8.65                                ( ( X3
% 15.55/8.65                                  = ( bit1 @ M4 ) )
% 15.55/8.65                               => ! [N2: num] :
% 15.55/8.65                                    ( ( Xa
% 15.55/8.65                                      = ( bit1 @ N2 ) )
% 15.55/8.65                                   => ( ( Y3
% 15.55/8.65                                        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 15.55/8.65                                          @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 15.55/8.65                                          @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 15.55/8.65                                     => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9675_xor__num_Opelims,axiom,
% 15.55/8.65      ! [X3: num,Xa: num,Y3: option_num] :
% 15.55/8.65        ( ( ( bit_un2480387367778600638or_num @ X3 @ Xa )
% 15.55/8.65          = Y3 )
% 15.55/8.65       => ( ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ X3 @ Xa ) )
% 15.55/8.65         => ( ( ( X3 = one )
% 15.55/8.65             => ( ( Xa = one )
% 15.55/8.65               => ( ( Y3 = none_num )
% 15.55/8.65                 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 15.55/8.65           => ( ( ( X3 = one )
% 15.55/8.65               => ! [N2: num] :
% 15.55/8.65                    ( ( Xa
% 15.55/8.65                      = ( bit0 @ N2 ) )
% 15.55/8.65                   => ( ( Y3
% 15.55/8.65                        = ( some_num @ ( bit1 @ N2 ) ) )
% 15.55/8.65                     => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) ) ) ) )
% 15.55/8.65             => ( ( ( X3 = one )
% 15.55/8.65                 => ! [N2: num] :
% 15.55/8.65                      ( ( Xa
% 15.55/8.65                        = ( bit1 @ N2 ) )
% 15.55/8.65                     => ( ( Y3
% 15.55/8.65                          = ( some_num @ ( bit0 @ N2 ) ) )
% 15.55/8.65                       => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) ) ) ) )
% 15.55/8.65               => ( ! [M4: num] :
% 15.55/8.65                      ( ( X3
% 15.55/8.65                        = ( bit0 @ M4 ) )
% 15.55/8.65                     => ( ( Xa = one )
% 15.55/8.65                       => ( ( Y3
% 15.55/8.65                            = ( some_num @ ( bit1 @ M4 ) ) )
% 15.55/8.65                         => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 15.55/8.65                 => ( ! [M4: num] :
% 15.55/8.65                        ( ( X3
% 15.55/8.65                          = ( bit0 @ M4 ) )
% 15.55/8.65                       => ! [N2: num] :
% 15.55/8.65                            ( ( Xa
% 15.55/8.65                              = ( bit0 @ N2 ) )
% 15.55/8.65                           => ( ( Y3
% 15.55/8.65                                = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) )
% 15.55/8.65                             => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 15.55/8.65                   => ( ! [M4: num] :
% 15.55/8.65                          ( ( X3
% 15.55/8.65                            = ( bit0 @ M4 ) )
% 15.55/8.65                         => ! [N2: num] :
% 15.55/8.65                              ( ( Xa
% 15.55/8.65                                = ( bit1 @ N2 ) )
% 15.55/8.65                             => ( ( Y3
% 15.55/8.65                                  = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) )
% 15.55/8.65                               => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) )
% 15.55/8.65                     => ( ! [M4: num] :
% 15.55/8.65                            ( ( X3
% 15.55/8.65                              = ( bit1 @ M4 ) )
% 15.55/8.65                           => ( ( Xa = one )
% 15.55/8.65                             => ( ( Y3
% 15.55/8.65                                  = ( some_num @ ( bit0 @ M4 ) ) )
% 15.55/8.65                               => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 15.55/8.65                       => ( ! [M4: num] :
% 15.55/8.65                              ( ( X3
% 15.55/8.65                                = ( bit1 @ M4 ) )
% 15.55/8.65                             => ! [N2: num] :
% 15.55/8.65                                  ( ( Xa
% 15.55/8.65                                    = ( bit0 @ N2 ) )
% 15.55/8.65                                 => ( ( Y3
% 15.55/8.65                                      = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) )
% 15.55/8.65                                   => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 15.55/8.65                         => ~ ! [M4: num] :
% 15.55/8.65                                ( ( X3
% 15.55/8.65                                  = ( bit1 @ M4 ) )
% 15.55/8.65                               => ! [N2: num] :
% 15.55/8.65                                    ( ( Xa
% 15.55/8.65                                      = ( bit1 @ N2 ) )
% 15.55/8.65                                   => ( ( Y3
% 15.55/8.65                                        = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) )
% 15.55/8.65                                     => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9676_or__not__num__neg_Opelims,axiom,
% 15.55/8.65      ! [X3: num,Xa: num,Y3: num] :
% 15.55/8.65        ( ( ( bit_or_not_num_neg @ X3 @ Xa )
% 15.55/8.65          = Y3 )
% 15.55/8.65       => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X3 @ Xa ) )
% 15.55/8.65         => ( ( ( X3 = one )
% 15.55/8.65             => ( ( Xa = one )
% 15.55/8.65               => ( ( Y3 = one )
% 15.55/8.65                 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 15.55/8.65           => ( ( ( X3 = one )
% 15.55/8.65               => ! [M4: num] :
% 15.55/8.65                    ( ( Xa
% 15.55/8.65                      = ( bit0 @ M4 ) )
% 15.55/8.65                   => ( ( Y3
% 15.55/8.65                        = ( bit1 @ M4 ) )
% 15.55/8.65                     => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M4 ) ) ) ) ) )
% 15.55/8.65             => ( ( ( X3 = one )
% 15.55/8.65                 => ! [M4: num] :
% 15.55/8.65                      ( ( Xa
% 15.55/8.65                        = ( bit1 @ M4 ) )
% 15.55/8.65                     => ( ( Y3
% 15.55/8.65                          = ( bit1 @ M4 ) )
% 15.55/8.65                       => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M4 ) ) ) ) ) )
% 15.55/8.65               => ( ! [N2: num] :
% 15.55/8.65                      ( ( X3
% 15.55/8.65                        = ( bit0 @ N2 ) )
% 15.55/8.65                     => ( ( Xa = one )
% 15.55/8.65                       => ( ( Y3
% 15.55/8.65                            = ( bit0 @ one ) )
% 15.55/8.65                         => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N2 ) @ one ) ) ) ) )
% 15.55/8.65                 => ( ! [N2: num] :
% 15.55/8.65                        ( ( X3
% 15.55/8.65                          = ( bit0 @ N2 ) )
% 15.55/8.65                       => ! [M4: num] :
% 15.55/8.65                            ( ( Xa
% 15.55/8.65                              = ( bit0 @ M4 ) )
% 15.55/8.65                           => ( ( Y3
% 15.55/8.65                                = ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) )
% 15.55/8.65                             => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N2 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 15.55/8.65                   => ( ! [N2: num] :
% 15.55/8.65                          ( ( X3
% 15.55/8.65                            = ( bit0 @ N2 ) )
% 15.55/8.65                         => ! [M4: num] :
% 15.55/8.65                              ( ( Xa
% 15.55/8.65                                = ( bit1 @ M4 ) )
% 15.55/8.65                             => ( ( Y3
% 15.55/8.65                                  = ( bit0 @ ( bit_or_not_num_neg @ N2 @ M4 ) ) )
% 15.55/8.65                               => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N2 ) @ ( bit1 @ M4 ) ) ) ) ) )
% 15.55/8.65                     => ( ! [N2: num] :
% 15.55/8.65                            ( ( X3
% 15.55/8.65                              = ( bit1 @ N2 ) )
% 15.55/8.65                           => ( ( Xa = one )
% 15.55/8.65                             => ( ( Y3 = one )
% 15.55/8.65                               => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N2 ) @ one ) ) ) ) )
% 15.55/8.65                       => ( ! [N2: num] :
% 15.55/8.65                              ( ( X3
% 15.55/8.65                                = ( bit1 @ N2 ) )
% 15.55/8.65                             => ! [M4: num] :
% 15.55/8.65                                  ( ( Xa
% 15.55/8.65                                    = ( bit0 @ M4 ) )
% 15.55/8.65                                 => ( ( Y3
% 15.55/8.65                                      = ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) )
% 15.55/8.65                                   => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N2 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 15.55/8.65                         => ~ ! [N2: num] :
% 15.55/8.65                                ( ( X3
% 15.55/8.65                                  = ( bit1 @ N2 ) )
% 15.55/8.65                               => ! [M4: num] :
% 15.55/8.65                                    ( ( Xa
% 15.55/8.65                                      = ( bit1 @ M4 ) )
% 15.55/8.65                                   => ( ( Y3
% 15.55/8.65                                        = ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) )
% 15.55/8.65                                     => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N2 ) @ ( bit1 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9677_xor__num__rel__dict,axiom,
% 15.55/8.65      bit_un2901131394128224187um_rel = bit_un3595099601533988841um_rel ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9678_and__num__rel__dict,axiom,
% 15.55/8.65      bit_un4731106466462545111um_rel = bit_un5425074673868309765um_rel ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9679_card__length__sum__list__rec,axiom,
% 15.55/8.65      ! [M: nat,N4: nat] :
% 15.55/8.65        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 15.55/8.65       => ( ( finite_card_list_nat
% 15.55/8.65            @ ( collect_list_nat
% 15.55/8.65              @ ^ [L2: list_nat] :
% 15.55/8.65                  ( ( ( size_size_list_nat @ L2 )
% 15.55/8.65                    = M )
% 15.55/8.65                  & ( ( groups4561878855575611511st_nat @ L2 )
% 15.55/8.65                    = N4 ) ) ) )
% 15.55/8.65          = ( plus_plus_nat
% 15.55/8.65            @ ( finite_card_list_nat
% 15.55/8.65              @ ( collect_list_nat
% 15.55/8.65                @ ^ [L2: list_nat] :
% 15.55/8.65                    ( ( ( size_size_list_nat @ L2 )
% 15.55/8.65                      = ( minus_minus_nat @ M @ one_one_nat ) )
% 15.55/8.65                    & ( ( groups4561878855575611511st_nat @ L2 )
% 15.55/8.65                      = N4 ) ) ) )
% 15.55/8.65            @ ( finite_card_list_nat
% 15.55/8.65              @ ( collect_list_nat
% 15.55/8.65                @ ^ [L2: list_nat] :
% 15.55/8.65                    ( ( ( size_size_list_nat @ L2 )
% 15.55/8.65                      = M )
% 15.55/8.65                    & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 15.55/8.65                      = N4 ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9680_Code__Target__Nat_ONat_Oabs__eq,axiom,
% 15.55/8.65      ! [X3: int] :
% 15.55/8.65        ( ( code_Target_Nat @ ( code_integer_of_int @ X3 ) )
% 15.55/8.65        = ( nat2 @ X3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9681_Code__Target__Nat_ONat_Orep__eq,axiom,
% 15.55/8.65      ( code_Target_Nat
% 15.55/8.65      = ( ^ [X: code_integer] : ( nat2 @ ( code_int_of_integer @ X ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9682_sorted__list__of__set__greaterThanAtMost,axiom,
% 15.55/8.65      ! [I: nat,J: nat] :
% 15.55/8.65        ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 15.55/8.65       => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 15.55/8.65          = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9683_sorted__list__of__set__greaterThanLessThan,axiom,
% 15.55/8.65      ! [I: nat,J: nat] :
% 15.55/8.65        ( ( ord_less_nat @ ( suc @ I ) @ J )
% 15.55/8.65       => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) )
% 15.55/8.65          = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9684_upto__aux__rec,axiom,
% 15.55/8.65      ( upto_aux
% 15.55/8.65      = ( ^ [I4: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I4 ) @ Js @ ( upto_aux @ I4 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9685_upto_Opsimps,axiom,
% 15.55/8.65      ! [I: int,J: int] :
% 15.55/8.65        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 15.55/8.65       => ( ( ( ord_less_eq_int @ I @ J )
% 15.55/8.65           => ( ( upto @ I @ J )
% 15.55/8.65              = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 15.55/8.65          & ( ~ ( ord_less_eq_int @ I @ J )
% 15.55/8.65           => ( ( upto @ I @ J )
% 15.55/8.65              = nil_int ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9686_upto_Opelims,axiom,
% 15.55/8.65      ! [X3: int,Xa: int,Y3: list_int] :
% 15.55/8.65        ( ( ( upto @ X3 @ Xa )
% 15.55/8.65          = Y3 )
% 15.55/8.65       => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X3 @ Xa ) )
% 15.55/8.65         => ~ ( ( ( ( ord_less_eq_int @ X3 @ Xa )
% 15.55/8.65                 => ( Y3
% 15.55/8.65                    = ( cons_int @ X3 @ ( upto @ ( plus_plus_int @ X3 @ one_one_int ) @ Xa ) ) ) )
% 15.55/8.65                & ( ~ ( ord_less_eq_int @ X3 @ Xa )
% 15.55/8.65                 => ( Y3 = nil_int ) ) )
% 15.55/8.65             => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X3 @ Xa ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9687_upto__Nil,axiom,
% 15.55/8.65      ! [I: int,J: int] :
% 15.55/8.65        ( ( ( upto @ I @ J )
% 15.55/8.65          = nil_int )
% 15.55/8.65        = ( ord_less_int @ J @ I ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9688_upto__Nil2,axiom,
% 15.55/8.65      ! [I: int,J: int] :
% 15.55/8.65        ( ( nil_int
% 15.55/8.65          = ( upto @ I @ J ) )
% 15.55/8.65        = ( ord_less_int @ J @ I ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9689_upto__empty,axiom,
% 15.55/8.65      ! [J: int,I: int] :
% 15.55/8.65        ( ( ord_less_int @ J @ I )
% 15.55/8.65       => ( ( upto @ I @ J )
% 15.55/8.65          = nil_int ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9690_nth__upto,axiom,
% 15.55/8.65      ! [I: int,K: nat,J: int] :
% 15.55/8.65        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 15.55/8.65       => ( ( nth_int @ ( upto @ I @ J ) @ K )
% 15.55/8.65          = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9691_length__upto,axiom,
% 15.55/8.65      ! [I: int,J: int] :
% 15.55/8.65        ( ( size_size_list_int @ ( upto @ I @ J ) )
% 15.55/8.65        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9692_upto__rec__numeral_I1_J,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 15.55/8.65         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 15.55/8.65            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 15.55/8.65        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 15.55/8.65         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 15.55/8.65            = nil_int ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9693_upto__rec__numeral_I2_J,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.65         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.65            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 15.55/8.65        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.65         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.65            = nil_int ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9694_upto__rec__numeral_I3_J,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 15.55/8.65         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 15.55/8.65            = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 15.55/8.65        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 15.55/8.65         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 15.55/8.65            = nil_int ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9695_upto__rec__numeral_I4_J,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.65         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.65            = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 15.55/8.65        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.65         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 15.55/8.65            = nil_int ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9696_upto__split2,axiom,
% 15.55/8.65      ! [I: int,J: int,K: int] :
% 15.55/8.65        ( ( ord_less_eq_int @ I @ J )
% 15.55/8.65       => ( ( ord_less_eq_int @ J @ K )
% 15.55/8.65         => ( ( upto @ I @ K )
% 15.55/8.65            = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9697_upto__split1,axiom,
% 15.55/8.65      ! [I: int,J: int,K: int] :
% 15.55/8.65        ( ( ord_less_eq_int @ I @ J )
% 15.55/8.65       => ( ( ord_less_eq_int @ J @ K )
% 15.55/8.65         => ( ( upto @ I @ K )
% 15.55/8.65            = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9698_upto_Oelims,axiom,
% 15.55/8.65      ! [X3: int,Xa: int,Y3: list_int] :
% 15.55/8.65        ( ( ( upto @ X3 @ Xa )
% 15.55/8.65          = Y3 )
% 15.55/8.65       => ( ( ( ord_less_eq_int @ X3 @ Xa )
% 15.55/8.65           => ( Y3
% 15.55/8.65              = ( cons_int @ X3 @ ( upto @ ( plus_plus_int @ X3 @ one_one_int ) @ Xa ) ) ) )
% 15.55/8.65          & ( ~ ( ord_less_eq_int @ X3 @ Xa )
% 15.55/8.65           => ( Y3 = nil_int ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9699_upto_Osimps,axiom,
% 15.55/8.65      ( upto
% 15.55/8.65      = ( ^ [I4: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I4 @ J3 ) @ ( cons_int @ I4 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9700_upto__rec1,axiom,
% 15.55/8.65      ! [I: int,J: int] :
% 15.55/8.65        ( ( ord_less_eq_int @ I @ J )
% 15.55/8.65       => ( ( upto @ I @ J )
% 15.55/8.65          = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9701_upto__rec2,axiom,
% 15.55/8.65      ! [I: int,J: int] :
% 15.55/8.65        ( ( ord_less_eq_int @ I @ J )
% 15.55/8.65       => ( ( upto @ I @ J )
% 15.55/8.65          = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9702_upto__split3,axiom,
% 15.55/8.65      ! [I: int,J: int,K: int] :
% 15.55/8.65        ( ( ord_less_eq_int @ I @ J )
% 15.55/8.65       => ( ( ord_less_eq_int @ J @ K )
% 15.55/8.65         => ( ( upto @ I @ K )
% 15.55/8.65            = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9703_le__enumerate,axiom,
% 15.55/8.65      ! [S2: set_nat,N: nat] :
% 15.55/8.65        ( ~ ( finite_finite_nat @ S2 )
% 15.55/8.65       => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S2 @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9704_finite__le__enumerate,axiom,
% 15.55/8.65      ! [S2: set_nat,N: nat] :
% 15.55/8.65        ( ( finite_finite_nat @ S2 )
% 15.55/8.65       => ( ( ord_less_nat @ N @ ( finite_card_nat @ S2 ) )
% 15.55/8.65         => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S2 @ N ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9705_DeMoivre2,axiom,
% 15.55/8.65      ! [R2: real,A: real,N: nat] :
% 15.55/8.65        ( ( power_power_complex @ ( rcis @ R2 @ A ) @ N )
% 15.55/8.65        = ( rcis @ ( power_power_real @ R2 @ N ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9706_Least__eq__0,axiom,
% 15.55/8.65      ! [P: nat > $o] :
% 15.55/8.65        ( ( P @ zero_zero_nat )
% 15.55/8.65       => ( ( ord_Least_nat @ P )
% 15.55/8.65          = zero_zero_nat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9707_rcis__zero__arg,axiom,
% 15.55/8.65      ! [R2: real] :
% 15.55/8.65        ( ( rcis @ R2 @ zero_zero_real )
% 15.55/8.65        = ( real_V4546457046886955230omplex @ R2 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9708_rcis__zero__mod,axiom,
% 15.55/8.65      ! [A: real] :
% 15.55/8.65        ( ( rcis @ zero_zero_real @ A )
% 15.55/8.65        = zero_zero_complex ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9709_rcis__eq__zero__iff,axiom,
% 15.55/8.65      ! [R2: real,A: real] :
% 15.55/8.65        ( ( ( rcis @ R2 @ A )
% 15.55/8.65          = zero_zero_complex )
% 15.55/8.65        = ( R2 = zero_zero_real ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9710_Least__Suc2,axiom,
% 15.55/8.65      ! [P: nat > $o,N: nat,Q: nat > $o,M: nat] :
% 15.55/8.65        ( ( P @ N )
% 15.55/8.65       => ( ( Q @ M )
% 15.55/8.65         => ( ~ ( P @ zero_zero_nat )
% 15.55/8.65           => ( ! [K2: nat] :
% 15.55/8.65                  ( ( P @ ( suc @ K2 ) )
% 15.55/8.65                  = ( Q @ K2 ) )
% 15.55/8.65             => ( ( ord_Least_nat @ P )
% 15.55/8.65                = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9711_Least__Suc,axiom,
% 15.55/8.65      ! [P: nat > $o,N: nat] :
% 15.55/8.65        ( ( P @ N )
% 15.55/8.65       => ( ~ ( P @ zero_zero_nat )
% 15.55/8.65         => ( ( ord_Least_nat @ P )
% 15.55/8.65            = ( suc
% 15.55/8.65              @ ( ord_Least_nat
% 15.55/8.65                @ ^ [M3: nat] : ( P @ ( suc @ M3 ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9712_Inf__nat__def,axiom,
% 15.55/8.65      ( complete_Inf_Inf_nat
% 15.55/8.65      = ( ^ [X8: set_nat] :
% 15.55/8.65            ( ord_Least_nat
% 15.55/8.65            @ ^ [N3: nat] : ( member_nat @ N3 @ X8 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9713_Sup__real__def,axiom,
% 15.55/8.65      ( comple1385675409528146559p_real
% 15.55/8.65      = ( ^ [X8: set_real] :
% 15.55/8.65            ( ord_Least_real
% 15.55/8.65            @ ^ [Z6: real] :
% 15.55/8.65              ! [X: real] :
% 15.55/8.65                ( ( member_real @ X @ X8 )
% 15.55/8.65               => ( ord_less_eq_real @ X @ Z6 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9714_Code__Target__Nat_ONat__def,axiom,
% 15.55/8.65      ( code_Target_Nat
% 15.55/8.65      = ( map_fu6539832666145259331at_nat @ code_int_of_integer @ id_nat @ nat2 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9715_sum__list__upt,axiom,
% 15.55/8.65      ! [M: nat,N: nat] :
% 15.55/8.65        ( ( ord_less_eq_nat @ M @ N )
% 15.55/8.65       => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 15.55/8.65          = ( groups3542108847815614940at_nat
% 15.55/8.65            @ ^ [X: nat] : X
% 15.55/8.65            @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9716_hd__upt,axiom,
% 15.55/8.65      ! [I: nat,J: nat] :
% 15.55/8.65        ( ( ord_less_nat @ I @ J )
% 15.55/8.65       => ( ( hd_nat @ ( upt @ I @ J ) )
% 15.55/8.65          = I ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9717_upt__conv__Nil,axiom,
% 15.55/8.65      ! [J: nat,I: nat] :
% 15.55/8.65        ( ( ord_less_eq_nat @ J @ I )
% 15.55/8.65       => ( ( upt @ I @ J )
% 15.55/8.65          = nil_nat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9718_upt__eq__Nil__conv,axiom,
% 15.55/8.65      ! [I: nat,J: nat] :
% 15.55/8.65        ( ( ( upt @ I @ J )
% 15.55/8.65          = nil_nat )
% 15.55/8.65        = ( ( J = zero_zero_nat )
% 15.55/8.65          | ( ord_less_eq_nat @ J @ I ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9719_take__upt,axiom,
% 15.55/8.65      ! [I: nat,M: nat,N: nat] :
% 15.55/8.65        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ M ) @ N )
% 15.55/8.65       => ( ( take_nat @ M @ ( upt @ I @ N ) )
% 15.55/8.65          = ( upt @ I @ ( plus_plus_nat @ I @ M ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9720_nth__upt,axiom,
% 15.55/8.65      ! [I: nat,K: nat,J: nat] :
% 15.55/8.65        ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J )
% 15.55/8.65       => ( ( nth_nat @ ( upt @ I @ J ) @ K )
% 15.55/8.65          = ( plus_plus_nat @ I @ K ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9721_upt__rec__numeral,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 15.55/8.65         => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 15.55/8.65            = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 15.55/8.65        & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 15.55/8.65         => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 15.55/8.65            = nil_nat ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9722_upt__add__eq__append,axiom,
% 15.55/8.65      ! [I: nat,J: nat,K: nat] :
% 15.55/8.65        ( ( ord_less_eq_nat @ I @ J )
% 15.55/8.65       => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 15.55/8.65          = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9723_atLeast__upt,axiom,
% 15.55/8.65      ( set_ord_lessThan_nat
% 15.55/8.65      = ( ^ [N3: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9724_upt__0,axiom,
% 15.55/8.65      ! [I: nat] :
% 15.55/8.65        ( ( upt @ I @ zero_zero_nat )
% 15.55/8.65        = nil_nat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9725_atMost__upto,axiom,
% 15.55/8.65      ( set_ord_atMost_nat
% 15.55/8.65      = ( ^ [N3: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N3 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9726_upt__rec,axiom,
% 15.55/8.65      ( upt
% 15.55/8.65      = ( ^ [I4: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I4 @ J3 ) @ ( cons_nat @ I4 @ ( upt @ ( suc @ I4 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9727_upt__conv__Cons,axiom,
% 15.55/8.65      ! [I: nat,J: nat] :
% 15.55/8.65        ( ( ord_less_nat @ I @ J )
% 15.55/8.65       => ( ( upt @ I @ J )
% 15.55/8.65          = ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9728_upt__Suc,axiom,
% 15.55/8.65      ! [I: nat,J: nat] :
% 15.55/8.65        ( ( ( ord_less_eq_nat @ I @ J )
% 15.55/8.65         => ( ( upt @ I @ ( suc @ J ) )
% 15.55/8.65            = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 15.55/8.65        & ( ~ ( ord_less_eq_nat @ I @ J )
% 15.55/8.65         => ( ( upt @ I @ ( suc @ J ) )
% 15.55/8.65            = nil_nat ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9729_upt__Suc__append,axiom,
% 15.55/8.65      ! [I: nat,J: nat] :
% 15.55/8.65        ( ( ord_less_eq_nat @ I @ J )
% 15.55/8.65       => ( ( upt @ I @ ( suc @ J ) )
% 15.55/8.65          = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9730_upt__eq__Cons__conv,axiom,
% 15.55/8.65      ! [I: nat,J: nat,X3: nat,Xs2: list_nat] :
% 15.55/8.65        ( ( ( upt @ I @ J )
% 15.55/8.65          = ( cons_nat @ X3 @ Xs2 ) )
% 15.55/8.65        = ( ( ord_less_nat @ I @ J )
% 15.55/8.65          & ( I = X3 )
% 15.55/8.65          & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 15.55/8.65            = Xs2 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9731_nat__of__integer__def,axiom,
% 15.55/8.65      ( code_nat_of_integer
% 15.55/8.65      = ( map_fu6539832666145259331at_nat @ code_int_of_integer @ id_nat @ nat2 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9732_sorted__upt,axiom,
% 15.55/8.65      ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9733_sorted__wrt__upt,axiom,
% 15.55/8.65      ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9734_map__add__upt,axiom,
% 15.55/8.65      ! [N: nat,M: nat] :
% 15.55/8.65        ( ( map_nat_nat
% 15.55/8.65          @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ N )
% 15.55/8.65          @ ( upt @ zero_zero_nat @ M ) )
% 15.55/8.65        = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9735_map__decr__upt,axiom,
% 15.55/8.65      ! [M: nat,N: nat] :
% 15.55/8.65        ( ( map_nat_nat
% 15.55/8.65          @ ^ [N3: nat] : ( minus_minus_nat @ N3 @ ( suc @ zero_zero_nat ) )
% 15.55/8.65          @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 15.55/8.65        = ( upt @ M @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9736_sorted__wrt__less__idx,axiom,
% 15.55/8.65      ! [Ns: list_nat,I: nat] :
% 15.55/8.65        ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 15.55/8.65       => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ns ) )
% 15.55/8.65         => ( ord_less_eq_nat @ I @ ( nth_nat @ Ns @ I ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9737_sorted__upto,axiom,
% 15.55/8.65      ! [M: int,N: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9738_sorted__wrt__upto,axiom,
% 15.55/8.65      ! [I: int,J: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I @ J ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9739_num__of__integer__def,axiom,
% 15.55/8.65      ( code_num_of_integer
% 15.55/8.65      = ( map_fu1227494855608507351um_num @ code_int_of_integer @ id_num @ ( comp_nat_num_int @ num_of_nat @ nat2 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9740_last__upt,axiom,
% 15.55/8.65      ! [I: nat,J: nat] :
% 15.55/8.65        ( ( ord_less_nat @ I @ J )
% 15.55/8.65       => ( ( last_nat @ ( upt @ I @ J ) )
% 15.55/8.65          = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9741_uniformity__real__def,axiom,
% 15.55/8.65      ( topolo1511823702728130853y_real
% 15.55/8.65      = ( comple2936214249959783750l_real
% 15.55/8.65        @ ( image_2178119161166701260l_real
% 15.55/8.65          @ ^ [E3: real] :
% 15.55/8.65              ( princi6114159922880469582l_real
% 15.55/8.65              @ ( collec3799799289383736868l_real
% 15.55/8.65                @ ( produc5414030515140494994real_o
% 15.55/8.65                  @ ^ [X: real,Y: real] : ( ord_less_real @ ( real_V975177566351809787t_real @ X @ Y ) @ E3 ) ) ) )
% 15.55/8.65          @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9742_uniformity__complex__def,axiom,
% 15.55/8.65      ( topolo896644834953643431omplex
% 15.55/8.65      = ( comple8358262395181532106omplex
% 15.55/8.65        @ ( image_5971271580939081552omplex
% 15.55/8.65          @ ^ [E3: real] :
% 15.55/8.65              ( princi3496590319149328850omplex
% 15.55/8.65              @ ( collec8663557070575231912omplex
% 15.55/8.65                @ ( produc6771430404735790350plex_o
% 15.55/8.65                  @ ^ [X: complex,Y: complex] : ( ord_less_real @ ( real_V3694042436643373181omplex @ X @ Y ) @ E3 ) ) ) )
% 15.55/8.65          @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9743_zero__rat__def,axiom,
% 15.55/8.65      ( zero_zero_rat
% 15.55/8.65      = ( abs_Rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9744_inverse__rat_Oabs__eq,axiom,
% 15.55/8.65      ! [X3: product_prod_int_int] :
% 15.55/8.65        ( ( ratrel @ X3 @ X3 )
% 15.55/8.65       => ( ( inverse_inverse_rat @ ( abs_Rat @ X3 ) )
% 15.55/8.65          = ( abs_Rat
% 15.55/8.65            @ ( if_Pro3027730157355071871nt_int
% 15.55/8.65              @ ( ( product_fst_int_int @ X3 )
% 15.55/8.65                = zero_zero_int )
% 15.55/8.65              @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 15.55/8.65              @ ( product_Pair_int_int @ ( product_snd_int_int @ X3 ) @ ( product_fst_int_int @ X3 ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9745_ratrel__iff,axiom,
% 15.55/8.65      ( ratrel
% 15.55/8.65      = ( ^ [X: product_prod_int_int,Y: product_prod_int_int] :
% 15.55/8.65            ( ( ( product_snd_int_int @ X )
% 15.55/8.65             != zero_zero_int )
% 15.55/8.65            & ( ( product_snd_int_int @ Y )
% 15.55/8.65             != zero_zero_int )
% 15.55/8.65            & ( ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y ) )
% 15.55/8.65              = ( times_times_int @ ( product_fst_int_int @ Y ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9746_zero__rat_Orsp,axiom,
% 15.55/8.65      ratrel @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9747_ratrel__def,axiom,
% 15.55/8.65      ( ratrel
% 15.55/8.65      = ( ^ [X: product_prod_int_int,Y: product_prod_int_int] :
% 15.55/8.65            ( ( ( product_snd_int_int @ X )
% 15.55/8.65             != zero_zero_int )
% 15.55/8.65            & ( ( product_snd_int_int @ Y )
% 15.55/8.65             != zero_zero_int )
% 15.55/8.65            & ( ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y ) )
% 15.55/8.65              = ( times_times_int @ ( product_fst_int_int @ Y ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9748_Rat_Opositive_Oabs__eq,axiom,
% 15.55/8.65      ! [X3: product_prod_int_int] :
% 15.55/8.65        ( ( ratrel @ X3 @ X3 )
% 15.55/8.65       => ( ( positive @ ( abs_Rat @ X3 ) )
% 15.55/8.65          = ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9749_Rat_Opositive__zero,axiom,
% 15.55/8.65      ~ ( positive @ zero_zero_rat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9750_Rat_Opositive__minus,axiom,
% 15.55/8.65      ! [X3: rat] :
% 15.55/8.65        ( ~ ( positive @ X3 )
% 15.55/8.65       => ( ( X3 != zero_zero_rat )
% 15.55/8.65         => ( positive @ ( uminus_uminus_rat @ X3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9751_Rat_Opositive_Orep__eq,axiom,
% 15.55/8.65      ( positive
% 15.55/8.65      = ( ^ [X: rat] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ ( rep_Rat @ X ) ) @ ( product_snd_int_int @ ( rep_Rat @ X ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9752_Rat_Opositive__def,axiom,
% 15.55/8.65      ( positive
% 15.55/8.65      = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 15.55/8.65        @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9753_inverse__rat__def,axiom,
% 15.55/8.65      ( inverse_inverse_rat
% 15.55/8.65      = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 15.55/8.65        @ ^ [X: product_prod_int_int] :
% 15.55/8.65            ( if_Pro3027730157355071871nt_int
% 15.55/8.65            @ ( ( product_fst_int_int @ X )
% 15.55/8.65              = zero_zero_int )
% 15.55/8.65            @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 15.55/8.65            @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9754_of__rat__dense,axiom,
% 15.55/8.65      ! [X3: real,Y3: real] :
% 15.55/8.65        ( ( ord_less_real @ X3 @ Y3 )
% 15.55/8.65       => ? [Q4: rat] :
% 15.55/8.65            ( ( ord_less_real @ X3 @ ( field_7254667332652039916t_real @ Q4 ) )
% 15.55/8.65            & ( ord_less_real @ ( field_7254667332652039916t_real @ Q4 ) @ Y3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9755_Rat_Opositive_Orsp,axiom,
% 15.55/8.65      ( bNF_re8699439704749558557nt_o_o @ ratrel
% 15.55/8.65      @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 )
% 15.55/8.65      @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) )
% 15.55/8.65      @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9756_inverse__rat_Orsp,axiom,
% 15.55/8.65      ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 15.55/8.65      @ ^ [X: product_prod_int_int] :
% 15.55/8.65          ( if_Pro3027730157355071871nt_int
% 15.55/8.65          @ ( ( product_fst_int_int @ X )
% 15.55/8.65            = zero_zero_int )
% 15.55/8.65          @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 15.55/8.65          @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) )
% 15.55/8.65      @ ^ [X: product_prod_int_int] :
% 15.55/8.65          ( if_Pro3027730157355071871nt_int
% 15.55/8.65          @ ( ( product_fst_int_int @ X )
% 15.55/8.65            = zero_zero_int )
% 15.55/8.65          @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 15.55/8.65          @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9757_Fract_Orsp,axiom,
% 15.55/8.65      ( bNF_re157797125943740599nt_int
% 15.55/8.65      @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 15.55/8.65      @ ( bNF_re6250860962936578807nt_int
% 15.55/8.65        @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 15.55/8.65        @ ratrel )
% 15.55/8.65      @ ^ [A4: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( B3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A4 @ B3 ) )
% 15.55/8.65      @ ^ [A4: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( B3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A4 @ B3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9758_integer__of__natural_Orsp,axiom,
% 15.55/8.65      ( bNF_re6650684261131312217nt_int
% 15.55/8.65      @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 15.55/8.65      @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 15.55/8.65      @ semiri1314217659103216013at_int
% 15.55/8.65      @ semiri1314217659103216013at_int ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9759_natural__of__integer_Orsp,axiom,
% 15.55/8.65      ( bNF_re3715656647883201625at_nat
% 15.55/8.65      @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 15.55/8.65      @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 15.55/8.65      @ nat2
% 15.55/8.65      @ nat2 ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9760_sub_Orsp,axiom,
% 15.55/8.65      ( bNF_re8402795839162346335um_int
% 15.55/8.65      @ ^ [Y5: num,Z2: num] : ( Y5 = Z2 )
% 15.55/8.65      @ ( bNF_re1822329894187522285nt_int
% 15.55/8.65        @ ^ [Y5: num,Z2: num] : ( Y5 = Z2 )
% 15.55/8.65        @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 15.55/8.65      @ ^ [M3: num,N3: num] : ( minus_minus_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N3 ) )
% 15.55/8.65      @ ^ [M3: num,N3: num] : ( minus_minus_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9761_less__integer_Orsp,axiom,
% 15.55/8.65      ( bNF_re3403563459893282935_int_o
% 15.55/8.65      @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 15.55/8.65      @ ( bNF_re5089333283451836215nt_o_o
% 15.55/8.65        @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 15.55/8.65        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 15.55/8.65      @ ord_less_int
% 15.55/8.65      @ ord_less_int ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9762_less__natural_Orsp,axiom,
% 15.55/8.65      ( bNF_re578469030762574527_nat_o
% 15.55/8.65      @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 15.55/8.65      @ ( bNF_re4705727531993890431at_o_o
% 15.55/8.65        @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 15.55/8.65        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 15.55/8.65      @ ord_less_nat
% 15.55/8.65      @ ord_less_nat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9763_less__eq__integer_Orsp,axiom,
% 15.55/8.65      ( bNF_re3403563459893282935_int_o
% 15.55/8.65      @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 15.55/8.65      @ ( bNF_re5089333283451836215nt_o_o
% 15.55/8.65        @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 15.55/8.65        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 15.55/8.65      @ ord_less_eq_int
% 15.55/8.65      @ ord_less_eq_int ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9764_less__eq__natural_Orsp,axiom,
% 15.55/8.65      ( bNF_re578469030762574527_nat_o
% 15.55/8.65      @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 15.55/8.65      @ ( bNF_re4705727531993890431at_o_o
% 15.55/8.65        @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 15.55/8.65        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 15.55/8.65      @ ord_less_eq_nat
% 15.55/8.65      @ ord_less_eq_nat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9765_num__of__integer_Orsp,axiom,
% 15.55/8.65      ( bNF_re7626690874201225453um_num
% 15.55/8.65      @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 15.55/8.65      @ ^ [Y5: num,Z2: num] : ( Y5 = Z2 )
% 15.55/8.65      @ ( comp_nat_num_int @ num_of_nat @ nat2 )
% 15.55/8.65      @ ( comp_nat_num_int @ num_of_nat @ nat2 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9766_inverse__rat_Otransfer,axiom,
% 15.55/8.65      ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 15.55/8.65      @ ^ [X: product_prod_int_int] :
% 15.55/8.65          ( if_Pro3027730157355071871nt_int
% 15.55/8.65          @ ( ( product_fst_int_int @ X )
% 15.55/8.65            = zero_zero_int )
% 15.55/8.65          @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 15.55/8.65          @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) )
% 15.55/8.65      @ inverse_inverse_rat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9767_Rat_Opositive_Otransfer,axiom,
% 15.55/8.65      ( bNF_re1494630372529172596at_o_o @ pcr_rat
% 15.55/8.65      @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 )
% 15.55/8.65      @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) )
% 15.55/8.65      @ positive ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9768_zero__rat_Otransfer,axiom,
% 15.55/8.65      pcr_rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ zero_zero_rat ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9769_times__int_Otransfer,axiom,
% 15.55/8.65      ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 15.55/8.65      @ ( produc27273713700761075at_nat
% 15.55/8.65        @ ^ [X: nat,Y: nat] :
% 15.55/8.65            ( produc2626176000494625587at_nat
% 15.55/8.65            @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) )
% 15.55/8.65      @ times_times_int ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9770_zero__int_Otransfer,axiom,
% 15.55/8.65      pcr_int @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ zero_zero_int ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9771_int__transfer,axiom,
% 15.55/8.65      ( bNF_re6830278522597306478at_int
% 15.55/8.65      @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 15.55/8.65      @ pcr_int
% 15.55/8.65      @ ^ [N3: nat] : ( product_Pair_nat_nat @ N3 @ zero_zero_nat )
% 15.55/8.65      @ semiri1314217659103216013at_int ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9772_uminus__int_Otransfer,axiom,
% 15.55/8.65      ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 15.55/8.65      @ ( produc2626176000494625587at_nat
% 15.55/8.65        @ ^ [X: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X ) )
% 15.55/8.65      @ uminus_uminus_int ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9773_nat_Otransfer,axiom,
% 15.55/8.65      ( bNF_re4555766996558763186at_nat @ pcr_int
% 15.55/8.65      @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 15.55/8.65      @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 15.55/8.65      @ nat2 ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9774_one__int_Otransfer,axiom,
% 15.55/8.65      pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9775_less__int_Otransfer,axiom,
% 15.55/8.65      ( bNF_re717283939379294677_int_o @ pcr_int
% 15.55/8.65      @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 15.55/8.65        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 15.55/8.65      @ ( produc8739625826339149834_nat_o
% 15.55/8.65        @ ^ [X: nat,Y: nat] :
% 15.55/8.65            ( produc6081775807080527818_nat_o
% 15.55/8.65            @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 15.55/8.65      @ ord_less_int ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9776_less__eq__int_Otransfer,axiom,
% 15.55/8.65      ( bNF_re717283939379294677_int_o @ pcr_int
% 15.55/8.65      @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 15.55/8.65        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 15.55/8.65      @ ( produc8739625826339149834_nat_o
% 15.55/8.65        @ ^ [X: nat,Y: nat] :
% 15.55/8.65            ( produc6081775807080527818_nat_o
% 15.55/8.65            @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 15.55/8.65      @ ord_less_eq_int ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9777_plus__int_Otransfer,axiom,
% 15.55/8.65      ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 15.55/8.65      @ ( produc27273713700761075at_nat
% 15.55/8.65        @ ^ [X: nat,Y: nat] :
% 15.55/8.65            ( produc2626176000494625587at_nat
% 15.55/8.65            @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) )
% 15.55/8.65      @ plus_plus_int ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9778_minus__int_Otransfer,axiom,
% 15.55/8.65      ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 15.55/8.65      @ ( produc27273713700761075at_nat
% 15.55/8.65        @ ^ [X: nat,Y: nat] :
% 15.55/8.65            ( produc2626176000494625587at_nat
% 15.55/8.65            @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) )
% 15.55/8.65      @ minus_minus_int ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9779_times__int_Orsp,axiom,
% 15.55/8.65      ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 15.55/8.65      @ ( produc27273713700761075at_nat
% 15.55/8.65        @ ^ [X: nat,Y: nat] :
% 15.55/8.65            ( produc2626176000494625587at_nat
% 15.55/8.65            @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) )
% 15.55/8.65      @ ( produc27273713700761075at_nat
% 15.55/8.65        @ ^ [X: nat,Y: nat] :
% 15.55/8.65            ( produc2626176000494625587at_nat
% 15.55/8.65            @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9780_Real_Opositive_Orsp,axiom,
% 15.55/8.65      ( bNF_re728719798268516973at_o_o @ realrel
% 15.55/8.65      @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 )
% 15.55/8.65      @ ^ [X8: nat > rat] :
% 15.55/8.65        ? [R5: rat] :
% 15.55/8.65          ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 15.55/8.65          & ? [K3: nat] :
% 15.55/8.65            ! [N3: nat] :
% 15.55/8.65              ( ( ord_less_eq_nat @ K3 @ N3 )
% 15.55/8.65             => ( ord_less_rat @ R5 @ ( X8 @ N3 ) ) ) )
% 15.55/8.65      @ ^ [X8: nat > rat] :
% 15.55/8.65        ? [R5: rat] :
% 15.55/8.65          ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 15.55/8.65          & ? [K3: nat] :
% 15.55/8.65            ! [N3: nat] :
% 15.55/8.65              ( ( ord_less_eq_nat @ K3 @ N3 )
% 15.55/8.65             => ( ord_less_rat @ R5 @ ( X8 @ N3 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9781_intrel__iff,axiom,
% 15.55/8.65      ! [X3: nat,Y3: nat,U: nat,V: nat] :
% 15.55/8.65        ( ( intrel @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ ( product_Pair_nat_nat @ U @ V ) )
% 15.55/8.65        = ( ( plus_plus_nat @ X3 @ V )
% 15.55/8.65          = ( plus_plus_nat @ U @ Y3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9782_plus__real_Orsp,axiom,
% 15.55/8.65      ( bNF_re1962705104956426057at_rat @ realrel @ ( bNF_re895249473297799549at_rat @ realrel @ realrel )
% 15.55/8.65      @ ^ [X8: nat > rat,Y7: nat > rat,N3: nat] : ( plus_plus_rat @ ( X8 @ N3 ) @ ( Y7 @ N3 ) )
% 15.55/8.65      @ ^ [X8: nat > rat,Y7: nat > rat,N3: nat] : ( plus_plus_rat @ ( X8 @ N3 ) @ ( Y7 @ N3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9783_int_Orel__eq__transfer,axiom,
% 15.55/8.65      ( bNF_re717283939379294677_int_o @ pcr_int
% 15.55/8.65      @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 15.55/8.65        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 15.55/8.65      @ intrel
% 15.55/8.65      @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9784_times__real_Orsp,axiom,
% 15.55/8.65      ( bNF_re1962705104956426057at_rat @ realrel @ ( bNF_re895249473297799549at_rat @ realrel @ realrel )
% 15.55/8.65      @ ^ [X8: nat > rat,Y7: nat > rat,N3: nat] : ( times_times_rat @ ( X8 @ N3 ) @ ( Y7 @ N3 ) )
% 15.55/8.65      @ ^ [X8: nat > rat,Y7: nat > rat,N3: nat] : ( times_times_rat @ ( X8 @ N3 ) @ ( Y7 @ N3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9785_uminus__real_Orsp,axiom,
% 15.55/8.65      ( bNF_re895249473297799549at_rat @ realrel @ realrel
% 15.55/8.65      @ ^ [X8: nat > rat,N3: nat] : ( uminus_uminus_rat @ ( X8 @ N3 ) )
% 15.55/8.65      @ ^ [X8: nat > rat,N3: nat] : ( uminus_uminus_rat @ ( X8 @ N3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9786_one__real_Orsp,axiom,
% 15.55/8.65      ( realrel
% 15.55/8.65      @ ^ [N3: nat] : one_one_rat
% 15.55/8.65      @ ^ [N3: nat] : one_one_rat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9787_int_Oabs__eq__iff,axiom,
% 15.55/8.65      ! [X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 15.55/8.65        ( ( ( abs_Integ @ X3 )
% 15.55/8.65          = ( abs_Integ @ Y3 ) )
% 15.55/8.65        = ( intrel @ X3 @ Y3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9788_zero__real_Orsp,axiom,
% 15.55/8.65      ( realrel
% 15.55/8.65      @ ^ [N3: nat] : zero_zero_rat
% 15.55/8.65      @ ^ [N3: nat] : zero_zero_rat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9789_zero__int_Orsp,axiom,
% 15.55/8.65      intrel @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9790_uminus__int_Orsp,axiom,
% 15.55/8.65      ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 15.55/8.65      @ ( produc2626176000494625587at_nat
% 15.55/8.65        @ ^ [X: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X ) )
% 15.55/8.65      @ ( produc2626176000494625587at_nat
% 15.55/8.65        @ ^ [X: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9791_nat_Orsp,axiom,
% 15.55/8.65      ( bNF_re8246922863344978751at_nat @ intrel
% 15.55/8.65      @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 15.55/8.65      @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 15.55/8.65      @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9792_one__int_Orsp,axiom,
% 15.55/8.65      intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9793_intrel__def,axiom,
% 15.55/8.65      ( intrel
% 15.55/8.65      = ( produc8739625826339149834_nat_o
% 15.55/8.65        @ ^ [X: nat,Y: nat] :
% 15.55/8.65            ( produc6081775807080527818_nat_o
% 15.55/8.65            @ ^ [U2: nat,V4: nat] :
% 15.55/8.65                ( ( plus_plus_nat @ X @ V4 )
% 15.55/8.65                = ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9794_less__int_Orsp,axiom,
% 15.55/8.65      ( bNF_re4202695980764964119_nat_o @ intrel
% 15.55/8.65      @ ( bNF_re3666534408544137501at_o_o @ intrel
% 15.55/8.65        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 15.55/8.65      @ ( produc8739625826339149834_nat_o
% 15.55/8.65        @ ^ [X: nat,Y: nat] :
% 15.55/8.65            ( produc6081775807080527818_nat_o
% 15.55/8.65            @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 15.55/8.65      @ ( produc8739625826339149834_nat_o
% 15.55/8.65        @ ^ [X: nat,Y: nat] :
% 15.55/8.65            ( produc6081775807080527818_nat_o
% 15.55/8.65            @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9795_less__eq__int_Orsp,axiom,
% 15.55/8.65      ( bNF_re4202695980764964119_nat_o @ intrel
% 15.55/8.65      @ ( bNF_re3666534408544137501at_o_o @ intrel
% 15.55/8.65        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 15.55/8.65      @ ( produc8739625826339149834_nat_o
% 15.55/8.65        @ ^ [X: nat,Y: nat] :
% 15.55/8.65            ( produc6081775807080527818_nat_o
% 15.55/8.65            @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 15.55/8.65      @ ( produc8739625826339149834_nat_o
% 15.55/8.65        @ ^ [X: nat,Y: nat] :
% 15.55/8.65            ( produc6081775807080527818_nat_o
% 15.55/8.65            @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9796_plus__int_Orsp,axiom,
% 15.55/8.65      ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 15.55/8.65      @ ( produc27273713700761075at_nat
% 15.55/8.65        @ ^ [X: nat,Y: nat] :
% 15.55/8.65            ( produc2626176000494625587at_nat
% 15.55/8.65            @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) )
% 15.55/8.65      @ ( produc27273713700761075at_nat
% 15.55/8.65        @ ^ [X: nat,Y: nat] :
% 15.55/8.65            ( produc2626176000494625587at_nat
% 15.55/8.65            @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9797_minus__int_Orsp,axiom,
% 15.55/8.65      ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 15.55/8.65      @ ( produc27273713700761075at_nat
% 15.55/8.65        @ ^ [X: nat,Y: nat] :
% 15.55/8.65            ( produc2626176000494625587at_nat
% 15.55/8.65            @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) )
% 15.55/8.65      @ ( produc27273713700761075at_nat
% 15.55/8.65        @ ^ [X: nat,Y: nat] :
% 15.55/8.65            ( produc2626176000494625587at_nat
% 15.55/8.65            @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9798_int_Obi__total,axiom,
% 15.55/8.65      bi_tot896582865486249351at_int @ pcr_int ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9799_inverse__real_Orsp,axiom,
% 15.55/8.65      ( bNF_re895249473297799549at_rat @ realrel @ realrel
% 15.55/8.65      @ ^ [X8: nat > rat] :
% 15.55/8.65          ( if_nat_rat @ ( vanishes @ X8 )
% 15.55/8.65          @ ^ [N3: nat] : zero_zero_rat
% 15.55/8.65          @ ^ [N3: nat] : ( inverse_inverse_rat @ ( X8 @ N3 ) ) )
% 15.55/8.65      @ ^ [X8: nat > rat] :
% 15.55/8.65          ( if_nat_rat @ ( vanishes @ X8 )
% 15.55/8.65          @ ^ [N3: nat] : zero_zero_rat
% 15.55/8.65          @ ^ [N3: nat] : ( inverse_inverse_rat @ ( X8 @ N3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9800_vanishes__mult__bounded,axiom,
% 15.55/8.65      ! [X9: nat > rat,Y8: nat > rat] :
% 15.55/8.65        ( ? [A7: rat] :
% 15.55/8.65            ( ( ord_less_rat @ zero_zero_rat @ A7 )
% 15.55/8.65            & ! [N2: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X9 @ N2 ) ) @ A7 ) )
% 15.55/8.65       => ( ( vanishes @ Y8 )
% 15.55/8.65         => ( vanishes
% 15.55/8.65            @ ^ [N3: nat] : ( times_times_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9801_vanishes__const,axiom,
% 15.55/8.65      ! [C: rat] :
% 15.55/8.65        ( ( vanishes
% 15.55/8.65          @ ^ [N3: nat] : C )
% 15.55/8.65        = ( C = zero_zero_rat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9802_vanishes__add,axiom,
% 15.55/8.65      ! [X9: nat > rat,Y8: nat > rat] :
% 15.55/8.65        ( ( vanishes @ X9 )
% 15.55/8.65       => ( ( vanishes @ Y8 )
% 15.55/8.65         => ( vanishes
% 15.55/8.65            @ ^ [N3: nat] : ( plus_plus_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9803_vanishes__diff,axiom,
% 15.55/8.65      ! [X9: nat > rat,Y8: nat > rat] :
% 15.55/8.65        ( ( vanishes @ X9 )
% 15.55/8.65       => ( ( vanishes @ Y8 )
% 15.55/8.65         => ( vanishes
% 15.55/8.65            @ ^ [N3: nat] : ( minus_minus_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9804_vanishes__minus,axiom,
% 15.55/8.65      ! [X9: nat > rat] :
% 15.55/8.65        ( ( vanishes @ X9 )
% 15.55/8.65       => ( vanishes
% 15.55/8.65          @ ^ [N3: nat] : ( uminus_uminus_rat @ ( X9 @ N3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9805_vanishes__def,axiom,
% 15.55/8.65      ( vanishes
% 15.55/8.65      = ( ^ [X8: nat > rat] :
% 15.55/8.65          ! [R5: rat] :
% 15.55/8.65            ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 15.55/8.65           => ? [K3: nat] :
% 15.55/8.65              ! [N3: nat] :
% 15.55/8.65                ( ( ord_less_eq_nat @ K3 @ N3 )
% 15.55/8.65               => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N3 ) ) @ R5 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9806_vanishesI,axiom,
% 15.55/8.65      ! [X9: nat > rat] :
% 15.55/8.65        ( ! [R: rat] :
% 15.55/8.65            ( ( ord_less_rat @ zero_zero_rat @ R )
% 15.55/8.65           => ? [K4: nat] :
% 15.55/8.65              ! [N2: nat] :
% 15.55/8.65                ( ( ord_less_eq_nat @ K4 @ N2 )
% 15.55/8.65               => ( ord_less_rat @ ( abs_abs_rat @ ( X9 @ N2 ) ) @ R ) ) )
% 15.55/8.65       => ( vanishes @ X9 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9807_vanishesD,axiom,
% 15.55/8.65      ! [X9: nat > rat,R2: rat] :
% 15.55/8.65        ( ( vanishes @ X9 )
% 15.55/8.65       => ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 15.55/8.65         => ? [K2: nat] :
% 15.55/8.65            ! [N8: nat] :
% 15.55/8.65              ( ( ord_less_eq_nat @ K2 @ N8 )
% 15.55/8.65             => ( ord_less_rat @ ( abs_abs_rat @ ( X9 @ N8 ) ) @ R2 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9808_inverse__real_Otransfer,axiom,
% 15.55/8.65      ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real
% 15.55/8.65      @ ^ [X8: nat > rat] :
% 15.55/8.65          ( if_nat_rat @ ( vanishes @ X8 )
% 15.55/8.65          @ ^ [N3: nat] : zero_zero_rat
% 15.55/8.65          @ ^ [N3: nat] : ( inverse_inverse_rat @ ( X8 @ N3 ) ) )
% 15.55/8.65      @ inverse_inverse_real ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9809_inverse__real_Oabs__eq,axiom,
% 15.55/8.65      ! [X3: nat > rat] :
% 15.55/8.65        ( ( realrel @ X3 @ X3 )
% 15.55/8.65       => ( ( inverse_inverse_real @ ( real2 @ X3 ) )
% 15.55/8.65          = ( real2
% 15.55/8.65            @ ( if_nat_rat @ ( vanishes @ X3 )
% 15.55/8.65              @ ^ [N3: nat] : zero_zero_rat
% 15.55/8.65              @ ^ [N3: nat] : ( inverse_inverse_rat @ ( X3 @ N3 ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9810_real_Oabs__induct,axiom,
% 15.55/8.65      ! [P: real > $o,X3: real] :
% 15.55/8.65        ( ! [Y4: nat > rat] :
% 15.55/8.65            ( ( realrel @ Y4 @ Y4 )
% 15.55/8.65           => ( P @ ( real2 @ Y4 ) ) )
% 15.55/8.65       => ( P @ X3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9811_of__rat__Real,axiom,
% 15.55/8.65      ( field_7254667332652039916t_real
% 15.55/8.65      = ( ^ [X: rat] :
% 15.55/8.65            ( real2
% 15.55/8.65            @ ^ [N3: nat] : X ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9812_zero__real__def,axiom,
% 15.55/8.65      ( zero_zero_real
% 15.55/8.65      = ( real2
% 15.55/8.65        @ ^ [N3: nat] : zero_zero_rat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9813_one__real__def,axiom,
% 15.55/8.65      ( one_one_real
% 15.55/8.65      = ( real2
% 15.55/8.65        @ ^ [N3: nat] : one_one_rat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9814_real_Orel__eq__transfer,axiom,
% 15.55/8.65      ( bNF_re4521903465945308077real_o @ pcr_real
% 15.55/8.65      @ ( bNF_re4297313714947099218al_o_o @ pcr_real
% 15.55/8.65        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 15.55/8.65      @ realrel
% 15.55/8.65      @ ^ [Y5: real,Z2: real] : ( Y5 = Z2 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9815_of__int__Real,axiom,
% 15.55/8.65      ( ring_1_of_int_real
% 15.55/8.65      = ( ^ [X: int] :
% 15.55/8.65            ( real2
% 15.55/8.65            @ ^ [N3: nat] : ( ring_1_of_int_rat @ X ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9816_zero__real_Otransfer,axiom,
% 15.55/8.65      ( pcr_real
% 15.55/8.65      @ ^ [N3: nat] : zero_zero_rat
% 15.55/8.65      @ zero_zero_real ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9817_one__real_Otransfer,axiom,
% 15.55/8.65      ( pcr_real
% 15.55/8.65      @ ^ [N3: nat] : one_one_rat
% 15.55/8.65      @ one_one_real ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9818_of__nat__Real,axiom,
% 15.55/8.65      ( semiri5074537144036343181t_real
% 15.55/8.65      = ( ^ [X: nat] :
% 15.55/8.65            ( real2
% 15.55/8.65            @ ^ [N3: nat] : ( semiri681578069525770553at_rat @ X ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9819_uminus__real_Otransfer,axiom,
% 15.55/8.65      ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real
% 15.55/8.65      @ ^ [X8: nat > rat,N3: nat] : ( uminus_uminus_rat @ ( X8 @ N3 ) )
% 15.55/8.65      @ uminus_uminus_real ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9820_plus__real_Otransfer,axiom,
% 15.55/8.65      ( bNF_re4695409256820837752l_real @ pcr_real @ ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real )
% 15.55/8.65      @ ^ [X8: nat > rat,Y7: nat > rat,N3: nat] : ( plus_plus_rat @ ( X8 @ N3 ) @ ( Y7 @ N3 ) )
% 15.55/8.65      @ plus_plus_real ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9821_uminus__real_Oabs__eq,axiom,
% 15.55/8.65      ! [X3: nat > rat] :
% 15.55/8.65        ( ( realrel @ X3 @ X3 )
% 15.55/8.65       => ( ( uminus_uminus_real @ ( real2 @ X3 ) )
% 15.55/8.65          = ( real2
% 15.55/8.65            @ ^ [N3: nat] : ( uminus_uminus_rat @ ( X3 @ N3 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9822_times__real_Otransfer,axiom,
% 15.55/8.65      ( bNF_re4695409256820837752l_real @ pcr_real @ ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real )
% 15.55/8.65      @ ^ [X8: nat > rat,Y7: nat > rat,N3: nat] : ( times_times_rat @ ( X8 @ N3 ) @ ( Y7 @ N3 ) )
% 15.55/8.65      @ times_times_real ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9823_plus__real_Oabs__eq,axiom,
% 15.55/8.65      ! [Xa: nat > rat,X3: nat > rat] :
% 15.55/8.65        ( ( realrel @ Xa @ Xa )
% 15.55/8.65       => ( ( realrel @ X3 @ X3 )
% 15.55/8.65         => ( ( plus_plus_real @ ( real2 @ Xa ) @ ( real2 @ X3 ) )
% 15.55/8.65            = ( real2
% 15.55/8.65              @ ^ [N3: nat] : ( plus_plus_rat @ ( Xa @ N3 ) @ ( X3 @ N3 ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9824_times__real_Oabs__eq,axiom,
% 15.55/8.65      ! [Xa: nat > rat,X3: nat > rat] :
% 15.55/8.65        ( ( realrel @ Xa @ Xa )
% 15.55/8.65       => ( ( realrel @ X3 @ X3 )
% 15.55/8.65         => ( ( times_times_real @ ( real2 @ Xa ) @ ( real2 @ X3 ) )
% 15.55/8.65            = ( real2
% 15.55/8.65              @ ^ [N3: nat] : ( times_times_rat @ ( Xa @ N3 ) @ ( X3 @ N3 ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9825_Real_Opositive_Otransfer,axiom,
% 15.55/8.65      ( bNF_re4297313714947099218al_o_o @ pcr_real
% 15.55/8.65      @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 )
% 15.55/8.65      @ ^ [X8: nat > rat] :
% 15.55/8.65        ? [R5: rat] :
% 15.55/8.65          ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 15.55/8.65          & ? [K3: nat] :
% 15.55/8.65            ! [N3: nat] :
% 15.55/8.65              ( ( ord_less_eq_nat @ K3 @ N3 )
% 15.55/8.65             => ( ord_less_rat @ R5 @ ( X8 @ N3 ) ) ) )
% 15.55/8.65      @ positive2 ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9826_Real_Opositive_Oabs__eq,axiom,
% 15.55/8.65      ! [X3: nat > rat] :
% 15.55/8.65        ( ( realrel @ X3 @ X3 )
% 15.55/8.65       => ( ( positive2 @ ( real2 @ X3 ) )
% 15.55/8.65          = ( ? [R5: rat] :
% 15.55/8.65                ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 15.55/8.65                & ? [K3: nat] :
% 15.55/8.65                  ! [N3: nat] :
% 15.55/8.65                    ( ( ord_less_eq_nat @ K3 @ N3 )
% 15.55/8.65                   => ( ord_less_rat @ R5 @ ( X3 @ N3 ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9827_Real_Opositive__mult,axiom,
% 15.55/8.65      ! [X3: real,Y3: real] :
% 15.55/8.65        ( ( positive2 @ X3 )
% 15.55/8.65       => ( ( positive2 @ Y3 )
% 15.55/8.65         => ( positive2 @ ( times_times_real @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9828_Real_Opositive__add,axiom,
% 15.55/8.65      ! [X3: real,Y3: real] :
% 15.55/8.65        ( ( positive2 @ X3 )
% 15.55/8.65       => ( ( positive2 @ Y3 )
% 15.55/8.65         => ( positive2 @ ( plus_plus_real @ X3 @ Y3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9829_Real_Opositive__zero,axiom,
% 15.55/8.65      ~ ( positive2 @ zero_zero_real ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9830_Real_Opositive__minus,axiom,
% 15.55/8.65      ! [X3: real] :
% 15.55/8.65        ( ~ ( positive2 @ X3 )
% 15.55/8.65       => ( ( X3 != zero_zero_real )
% 15.55/8.65         => ( positive2 @ ( uminus_uminus_real @ X3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9831_less__real__def,axiom,
% 15.55/8.65      ( ord_less_real
% 15.55/8.65      = ( ^ [X: real,Y: real] : ( positive2 @ ( minus_minus_real @ Y @ X ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9832_le__Real,axiom,
% 15.55/8.65      ! [X9: nat > rat,Y8: nat > rat] :
% 15.55/8.65        ( ( cauchy @ X9 )
% 15.55/8.65       => ( ( cauchy @ Y8 )
% 15.55/8.65         => ( ( ord_less_eq_real @ ( real2 @ X9 ) @ ( real2 @ Y8 ) )
% 15.55/8.65            = ( ! [R5: rat] :
% 15.55/8.65                  ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 15.55/8.65                 => ? [K3: nat] :
% 15.55/8.65                    ! [N3: nat] :
% 15.55/8.65                      ( ( ord_less_eq_nat @ K3 @ N3 )
% 15.55/8.65                     => ( ord_less_eq_rat @ ( X9 @ N3 ) @ ( plus_plus_rat @ ( Y8 @ N3 ) @ R5 ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9833_Real_Opositive_Orep__eq,axiom,
% 15.55/8.65      ( positive2
% 15.55/8.65      = ( ^ [X: real] :
% 15.55/8.65          ? [R5: rat] :
% 15.55/8.65            ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 15.55/8.65            & ? [K3: nat] :
% 15.55/8.65              ! [N3: nat] :
% 15.55/8.65                ( ( ord_less_eq_nat @ K3 @ N3 )
% 15.55/8.65               => ( ord_less_rat @ R5 @ ( rep_real @ X @ N3 ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9834_realrel__refl,axiom,
% 15.55/8.65      ! [X9: nat > rat] :
% 15.55/8.65        ( ( cauchy @ X9 )
% 15.55/8.65       => ( realrel @ X9 @ X9 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9835_cauchy__minus,axiom,
% 15.55/8.65      ! [X9: nat > rat] :
% 15.55/8.65        ( ( cauchy @ X9 )
% 15.55/8.65       => ( cauchy
% 15.55/8.65          @ ^ [N3: nat] : ( uminus_uminus_rat @ ( X9 @ N3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9836_cauchy__const,axiom,
% 15.55/8.65      ! [X3: rat] :
% 15.55/8.65        ( cauchy
% 15.55/8.65        @ ^ [N3: nat] : X3 ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9837_cauchy__add,axiom,
% 15.55/8.65      ! [X9: nat > rat,Y8: nat > rat] :
% 15.55/8.65        ( ( cauchy @ X9 )
% 15.55/8.65       => ( ( cauchy @ Y8 )
% 15.55/8.65         => ( cauchy
% 15.55/8.65            @ ^ [N3: nat] : ( plus_plus_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9838_cauchy__mult,axiom,
% 15.55/8.65      ! [X9: nat > rat,Y8: nat > rat] :
% 15.55/8.65        ( ( cauchy @ X9 )
% 15.55/8.65       => ( ( cauchy @ Y8 )
% 15.55/8.65         => ( cauchy
% 15.55/8.65            @ ^ [N3: nat] : ( times_times_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9839_Real__induct,axiom,
% 15.55/8.65      ! [P: real > $o,X3: real] :
% 15.55/8.65        ( ! [X16: nat > rat] :
% 15.55/8.65            ( ( cauchy @ X16 )
% 15.55/8.65           => ( P @ ( real2 @ X16 ) ) )
% 15.55/8.65       => ( P @ X3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9840_cauchy__diff,axiom,
% 15.55/8.65      ! [X9: nat > rat,Y8: nat > rat] :
% 15.55/8.65        ( ( cauchy @ X9 )
% 15.55/8.65       => ( ( cauchy @ Y8 )
% 15.55/8.65         => ( cauchy
% 15.55/8.65            @ ^ [N3: nat] : ( minus_minus_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9841_cr__real__eq,axiom,
% 15.55/8.65      ( pcr_real
% 15.55/8.65      = ( ^ [X: nat > rat,Y: real] :
% 15.55/8.65            ( ( cauchy @ X )
% 15.55/8.65            & ( ( real2 @ X )
% 15.55/8.65              = Y ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9842_cauchy__inverse,axiom,
% 15.55/8.65      ! [X9: nat > rat] :
% 15.55/8.65        ( ( cauchy @ X9 )
% 15.55/8.65       => ( ~ ( vanishes @ X9 )
% 15.55/8.65         => ( cauchy
% 15.55/8.65            @ ^ [N3: nat] : ( inverse_inverse_rat @ ( X9 @ N3 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9843_cauchy__imp__bounded,axiom,
% 15.55/8.65      ! [X9: nat > rat] :
% 15.55/8.65        ( ( cauchy @ X9 )
% 15.55/8.65       => ? [B4: rat] :
% 15.55/8.65            ( ( ord_less_rat @ zero_zero_rat @ B4 )
% 15.55/8.65            & ! [N8: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X9 @ N8 ) ) @ B4 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9844_less__RealD,axiom,
% 15.55/8.65      ! [Y8: nat > rat,X3: real] :
% 15.55/8.65        ( ( cauchy @ Y8 )
% 15.55/8.65       => ( ( ord_less_real @ X3 @ ( real2 @ Y8 ) )
% 15.55/8.65         => ? [N2: nat] : ( ord_less_real @ X3 @ ( field_7254667332652039916t_real @ ( Y8 @ N2 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9845_le__RealI,axiom,
% 15.55/8.65      ! [Y8: nat > rat,X3: real] :
% 15.55/8.65        ( ( cauchy @ Y8 )
% 15.55/8.65       => ( ! [N2: nat] : ( ord_less_eq_real @ X3 @ ( field_7254667332652039916t_real @ ( Y8 @ N2 ) ) )
% 15.55/8.65         => ( ord_less_eq_real @ X3 @ ( real2 @ Y8 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9846_Real__leI,axiom,
% 15.55/8.65      ! [X9: nat > rat,Y3: real] :
% 15.55/8.65        ( ( cauchy @ X9 )
% 15.55/8.65       => ( ! [N2: nat] : ( ord_less_eq_real @ ( field_7254667332652039916t_real @ ( X9 @ N2 ) ) @ Y3 )
% 15.55/8.65         => ( ord_less_eq_real @ ( real2 @ X9 ) @ Y3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9847_minus__Real,axiom,
% 15.55/8.65      ! [X9: nat > rat] :
% 15.55/8.65        ( ( cauchy @ X9 )
% 15.55/8.65       => ( ( uminus_uminus_real @ ( real2 @ X9 ) )
% 15.55/8.65          = ( real2
% 15.55/8.65            @ ^ [N3: nat] : ( uminus_uminus_rat @ ( X9 @ N3 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9848_add__Real,axiom,
% 15.55/8.65      ! [X9: nat > rat,Y8: nat > rat] :
% 15.55/8.65        ( ( cauchy @ X9 )
% 15.55/8.65       => ( ( cauchy @ Y8 )
% 15.55/8.65         => ( ( plus_plus_real @ ( real2 @ X9 ) @ ( real2 @ Y8 ) )
% 15.55/8.65            = ( real2
% 15.55/8.65              @ ^ [N3: nat] : ( plus_plus_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9849_mult__Real,axiom,
% 15.55/8.65      ! [X9: nat > rat,Y8: nat > rat] :
% 15.55/8.65        ( ( cauchy @ X9 )
% 15.55/8.65       => ( ( cauchy @ Y8 )
% 15.55/8.65         => ( ( times_times_real @ ( real2 @ X9 ) @ ( real2 @ Y8 ) )
% 15.55/8.65            = ( real2
% 15.55/8.65              @ ^ [N3: nat] : ( times_times_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9850_diff__Real,axiom,
% 15.55/8.65      ! [X9: nat > rat,Y8: nat > rat] :
% 15.55/8.65        ( ( cauchy @ X9 )
% 15.55/8.65       => ( ( cauchy @ Y8 )
% 15.55/8.65         => ( ( minus_minus_real @ ( real2 @ X9 ) @ ( real2 @ Y8 ) )
% 15.55/8.65            = ( real2
% 15.55/8.65              @ ^ [N3: nat] : ( minus_minus_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9851_realrelI,axiom,
% 15.55/8.65      ! [X9: nat > rat,Y8: nat > rat] :
% 15.55/8.65        ( ( cauchy @ X9 )
% 15.55/8.65       => ( ( cauchy @ Y8 )
% 15.55/8.65         => ( ( vanishes
% 15.55/8.65              @ ^ [N3: nat] : ( minus_minus_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) )
% 15.55/8.65           => ( realrel @ X9 @ Y8 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9852_eq__Real,axiom,
% 15.55/8.65      ! [X9: nat > rat,Y8: nat > rat] :
% 15.55/8.65        ( ( cauchy @ X9 )
% 15.55/8.65       => ( ( cauchy @ Y8 )
% 15.55/8.65         => ( ( ( real2 @ X9 )
% 15.55/8.65              = ( real2 @ Y8 ) )
% 15.55/8.65            = ( vanishes
% 15.55/8.65              @ ^ [N3: nat] : ( minus_minus_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9853_vanishes__diff__inverse,axiom,
% 15.55/8.65      ! [X9: nat > rat,Y8: nat > rat] :
% 15.55/8.65        ( ( cauchy @ X9 )
% 15.55/8.65       => ( ~ ( vanishes @ X9 )
% 15.55/8.65         => ( ( cauchy @ Y8 )
% 15.55/8.65           => ( ~ ( vanishes @ Y8 )
% 15.55/8.65             => ( ( vanishes
% 15.55/8.65                  @ ^ [N3: nat] : ( minus_minus_rat @ ( X9 @ N3 ) @ ( Y8 @ N3 ) ) )
% 15.55/8.65               => ( vanishes
% 15.55/8.65                  @ ^ [N3: nat] : ( minus_minus_rat @ ( inverse_inverse_rat @ ( X9 @ N3 ) ) @ ( inverse_inverse_rat @ ( Y8 @ N3 ) ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9854_realrel__def,axiom,
% 15.55/8.65      ( realrel
% 15.55/8.65      = ( ^ [X8: nat > rat,Y7: nat > rat] :
% 15.55/8.65            ( ( cauchy @ X8 )
% 15.55/8.65            & ( cauchy @ Y7 )
% 15.55/8.65            & ( vanishes
% 15.55/8.65              @ ^ [N3: nat] : ( minus_minus_rat @ ( X8 @ N3 ) @ ( Y7 @ N3 ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9855_cauchy__not__vanishes__cases,axiom,
% 15.55/8.65      ! [X9: nat > rat] :
% 15.55/8.65        ( ( cauchy @ X9 )
% 15.55/8.65       => ( ~ ( vanishes @ X9 )
% 15.55/8.65         => ? [B4: rat] :
% 15.55/8.65              ( ( ord_less_rat @ zero_zero_rat @ B4 )
% 15.55/8.65              & ? [K2: nat] :
% 15.55/8.65                  ( ! [N8: nat] :
% 15.55/8.65                      ( ( ord_less_eq_nat @ K2 @ N8 )
% 15.55/8.65                     => ( ord_less_rat @ B4 @ ( uminus_uminus_rat @ ( X9 @ N8 ) ) ) )
% 15.55/8.65                  | ! [N8: nat] :
% 15.55/8.65                      ( ( ord_less_eq_nat @ K2 @ N8 )
% 15.55/8.65                     => ( ord_less_rat @ B4 @ ( X9 @ N8 ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9856_positive__Real,axiom,
% 15.55/8.65      ! [X9: nat > rat] :
% 15.55/8.65        ( ( cauchy @ X9 )
% 15.55/8.65       => ( ( positive2 @ ( real2 @ X9 ) )
% 15.55/8.65          = ( ? [R5: rat] :
% 15.55/8.65                ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 15.55/8.65                & ? [K3: nat] :
% 15.55/8.65                  ! [N3: nat] :
% 15.55/8.65                    ( ( ord_less_eq_nat @ K3 @ N3 )
% 15.55/8.65                   => ( ord_less_rat @ R5 @ ( X9 @ N3 ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9857_cauchy__not__vanishes,axiom,
% 15.55/8.65      ! [X9: nat > rat] :
% 15.55/8.65        ( ( cauchy @ X9 )
% 15.55/8.65       => ( ~ ( vanishes @ X9 )
% 15.55/8.65         => ? [B4: rat] :
% 15.55/8.65              ( ( ord_less_rat @ zero_zero_rat @ B4 )
% 15.55/8.65              & ? [K2: nat] :
% 15.55/8.65                ! [N8: nat] :
% 15.55/8.65                  ( ( ord_less_eq_nat @ K2 @ N8 )
% 15.55/8.65                 => ( ord_less_rat @ B4 @ ( abs_abs_rat @ ( X9 @ N8 ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9858_cauchy__def,axiom,
% 15.55/8.65      ( cauchy
% 15.55/8.65      = ( ^ [X8: nat > rat] :
% 15.55/8.65          ! [R5: rat] :
% 15.55/8.65            ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 15.55/8.65           => ? [K3: nat] :
% 15.55/8.65              ! [M3: nat] :
% 15.55/8.65                ( ( ord_less_eq_nat @ K3 @ M3 )
% 15.55/8.65               => ! [N3: nat] :
% 15.55/8.65                    ( ( ord_less_eq_nat @ K3 @ N3 )
% 15.55/8.65                   => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M3 ) @ ( X8 @ N3 ) ) ) @ R5 ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9859_cauchyI,axiom,
% 15.55/8.65      ! [X9: nat > rat] :
% 15.55/8.65        ( ! [R: rat] :
% 15.55/8.65            ( ( ord_less_rat @ zero_zero_rat @ R )
% 15.55/8.65           => ? [K4: nat] :
% 15.55/8.65              ! [M4: nat] :
% 15.55/8.65                ( ( ord_less_eq_nat @ K4 @ M4 )
% 15.55/8.65               => ! [N2: nat] :
% 15.55/8.65                    ( ( ord_less_eq_nat @ K4 @ N2 )
% 15.55/8.65                   => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X9 @ M4 ) @ ( X9 @ N2 ) ) ) @ R ) ) ) )
% 15.55/8.65       => ( cauchy @ X9 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9860_cauchyD,axiom,
% 15.55/8.65      ! [X9: nat > rat,R2: rat] :
% 15.55/8.65        ( ( cauchy @ X9 )
% 15.55/8.65       => ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 15.55/8.65         => ? [K2: nat] :
% 15.55/8.65            ! [M2: nat] :
% 15.55/8.65              ( ( ord_less_eq_nat @ K2 @ M2 )
% 15.55/8.65             => ! [N8: nat] :
% 15.55/8.65                  ( ( ord_less_eq_nat @ K2 @ N8 )
% 15.55/8.65                 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X9 @ M2 ) @ ( X9 @ N8 ) ) ) @ R2 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9861_inverse__Real,axiom,
% 15.55/8.65      ! [X9: nat > rat] :
% 15.55/8.65        ( ( cauchy @ X9 )
% 15.55/8.65       => ( ( ( vanishes @ X9 )
% 15.55/8.65           => ( ( inverse_inverse_real @ ( real2 @ X9 ) )
% 15.55/8.65              = zero_zero_real ) )
% 15.55/8.65          & ( ~ ( vanishes @ X9 )
% 15.55/8.65           => ( ( inverse_inverse_real @ ( real2 @ X9 ) )
% 15.55/8.65              = ( real2
% 15.55/8.65                @ ^ [N3: nat] : ( inverse_inverse_rat @ ( X9 @ N3 ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9862_not__positive__Real,axiom,
% 15.55/8.65      ! [X9: nat > rat] :
% 15.55/8.65        ( ( cauchy @ X9 )
% 15.55/8.65       => ( ( ~ ( positive2 @ ( real2 @ X9 ) ) )
% 15.55/8.65          = ( ! [R5: rat] :
% 15.55/8.65                ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 15.55/8.65               => ? [K3: nat] :
% 15.55/8.65                  ! [N3: nat] :
% 15.55/8.65                    ( ( ord_less_eq_nat @ K3 @ N3 )
% 15.55/8.65                   => ( ord_less_eq_rat @ ( X9 @ N3 ) @ R5 ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9863_Real_Opositive__def,axiom,
% 15.55/8.65      ( positive2
% 15.55/8.65      = ( map_fu1856342031159181835at_o_o @ rep_real @ id_o
% 15.55/8.65        @ ^ [X8: nat > rat] :
% 15.55/8.65          ? [R5: rat] :
% 15.55/8.65            ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 15.55/8.65            & ? [K3: nat] :
% 15.55/8.65              ! [N3: nat] :
% 15.55/8.65                ( ( ord_less_eq_nat @ K3 @ N3 )
% 15.55/8.65               => ( ord_less_rat @ R5 @ ( X8 @ N3 ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9864_inverse__real__def,axiom,
% 15.55/8.65      ( inverse_inverse_real
% 15.55/8.65      = ( map_fu7146612038024189824t_real @ rep_real @ real2
% 15.55/8.65        @ ^ [X8: nat > rat] :
% 15.55/8.65            ( if_nat_rat @ ( vanishes @ X8 )
% 15.55/8.65            @ ^ [N3: nat] : zero_zero_rat
% 15.55/8.65            @ ^ [N3: nat] : ( inverse_inverse_rat @ ( X8 @ N3 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9865_uminus__real__def,axiom,
% 15.55/8.65      ( uminus_uminus_real
% 15.55/8.65      = ( map_fu7146612038024189824t_real @ rep_real @ real2
% 15.55/8.65        @ ^ [X8: nat > rat,N3: nat] : ( uminus_uminus_rat @ ( X8 @ N3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9866_times__real__def,axiom,
% 15.55/8.65      ( times_times_real
% 15.55/8.65      = ( map_fu1532550112467129777l_real @ rep_real @ ( map_fu7146612038024189824t_real @ rep_real @ real2 )
% 15.55/8.65        @ ^ [X8: nat > rat,Y7: nat > rat,N3: nat] : ( times_times_rat @ ( X8 @ N3 ) @ ( Y7 @ N3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9867_plus__real__def,axiom,
% 15.55/8.65      ( plus_plus_real
% 15.55/8.65      = ( map_fu1532550112467129777l_real @ rep_real @ ( map_fu7146612038024189824t_real @ rep_real @ real2 )
% 15.55/8.65        @ ^ [X8: nat > rat,Y7: nat > rat,N3: nat] : ( plus_plus_rat @ ( X8 @ N3 ) @ ( Y7 @ N3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9868_cr__real__def,axiom,
% 15.55/8.65      ( cr_real
% 15.55/8.65      = ( ^ [X: nat > rat,Y: real] :
% 15.55/8.65            ( ( realrel @ X @ X )
% 15.55/8.65            & ( ( real2 @ X )
% 15.55/8.65              = Y ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9869_Bseq__monoseq__convergent_H__dec,axiom,
% 15.55/8.65      ! [F: nat > real,M7: nat] :
% 15.55/8.65        ( ( bfun_nat_real
% 15.55/8.65          @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ M7 ) )
% 15.55/8.65          @ at_top_nat )
% 15.55/8.65       => ( ! [M4: nat,N2: nat] :
% 15.55/8.65              ( ( ord_less_eq_nat @ M7 @ M4 )
% 15.55/8.65             => ( ( ord_less_eq_nat @ M4 @ N2 )
% 15.55/8.65               => ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ M4 ) ) ) )
% 15.55/8.65         => ( topolo7531315842566124627t_real @ F ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9870_real_Opcr__cr__eq,axiom,
% 15.55/8.65      pcr_real = cr_real ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9871_Bseq__mono__convergent,axiom,
% 15.55/8.65      ! [X9: nat > real] :
% 15.55/8.65        ( ( bfun_nat_real @ X9 @ at_top_nat )
% 15.55/8.65       => ( ! [M4: nat,N2: nat] :
% 15.55/8.65              ( ( ord_less_eq_nat @ M4 @ N2 )
% 15.55/8.65             => ( ord_less_eq_real @ ( X9 @ M4 ) @ ( X9 @ N2 ) ) )
% 15.55/8.65         => ( topolo7531315842566124627t_real @ X9 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9872_convergent__realpow,axiom,
% 15.55/8.65      ! [X3: real] :
% 15.55/8.65        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 15.55/8.65       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 15.55/8.65         => ( topolo7531315842566124627t_real @ ( power_power_real @ X3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9873_Bseq__monoseq__convergent_H__inc,axiom,
% 15.55/8.65      ! [F: nat > real,M7: nat] :
% 15.55/8.65        ( ( bfun_nat_real
% 15.55/8.65          @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ M7 ) )
% 15.55/8.65          @ at_top_nat )
% 15.55/8.65       => ( ! [M4: nat,N2: nat] :
% 15.55/8.65              ( ( ord_less_eq_nat @ M7 @ M4 )
% 15.55/8.65             => ( ( ord_less_eq_nat @ M4 @ N2 )
% 15.55/8.65               => ( ord_less_eq_real @ ( F @ M4 ) @ ( F @ N2 ) ) ) )
% 15.55/8.65         => ( topolo7531315842566124627t_real @ F ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9874_at__right__to__0,axiom,
% 15.55/8.65      ! [A: real] :
% 15.55/8.65        ( ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) )
% 15.55/8.65        = ( filtermap_real_real
% 15.55/8.65          @ ^ [X: real] : ( plus_plus_real @ X @ A )
% 15.55/8.65          @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9875_at__right__to__top,axiom,
% 15.55/8.65      ( ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) )
% 15.55/8.65      = ( filtermap_real_real @ inverse_inverse_real @ at_top_real ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9876_at__top__to__right,axiom,
% 15.55/8.65      ( at_top_real
% 15.55/8.65      = ( filtermap_real_real @ inverse_inverse_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9877_filtermap__ln__at__right,axiom,
% 15.55/8.65      ( ( filtermap_real_real @ ln_ln_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 15.55/8.65      = at_bot_real ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9878_pair__lessI2,axiom,
% 15.55/8.65      ! [A: nat,B: nat,S: nat,T: nat] :
% 15.55/8.65        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.65       => ( ( ord_less_nat @ S @ T )
% 15.55/8.65         => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9879_pair__less__iff1,axiom,
% 15.55/8.65      ! [X3: nat,Y3: nat,Z: nat] :
% 15.55/8.65        ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ ( product_Pair_nat_nat @ X3 @ Z ) ) @ fun_pair_less )
% 15.55/8.65        = ( ord_less_nat @ Y3 @ Z ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9880_pair__lessI1,axiom,
% 15.55/8.65      ! [A: nat,B: nat,S: nat,T: nat] :
% 15.55/8.65        ( ( ord_less_nat @ A @ B )
% 15.55/8.65       => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9881_gcd__nat_Oordering__top__axioms,axiom,
% 15.55/8.65      ( ordering_top_nat @ dvd_dvd_nat
% 15.55/8.65      @ ^ [M3: nat,N3: nat] :
% 15.55/8.65          ( ( dvd_dvd_nat @ M3 @ N3 )
% 15.55/8.65          & ( M3 != N3 ) )
% 15.55/8.65      @ zero_zero_nat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9882_bot__nat__0_Oordering__top__axioms,axiom,
% 15.55/8.65      ( ordering_top_nat
% 15.55/8.65      @ ^ [X: nat,Y: nat] : ( ord_less_eq_nat @ Y @ X )
% 15.55/8.65      @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X )
% 15.55/8.65      @ zero_zero_nat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9883_pair__leqI2,axiom,
% 15.55/8.65      ! [A: nat,B: nat,S: nat,T: nat] :
% 15.55/8.65        ( ( ord_less_eq_nat @ A @ B )
% 15.55/8.65       => ( ( ord_less_eq_nat @ S @ T )
% 15.55/8.65         => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9884_pair__leqI1,axiom,
% 15.55/8.65      ! [A: nat,B: nat,S: nat,T: nat] :
% 15.55/8.65        ( ( ord_less_nat @ A @ B )
% 15.55/8.65       => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9885_wmax__insertI,axiom,
% 15.55/8.65      ! [Y3: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat,X3: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat] :
% 15.55/8.65        ( ( member8440522571783428010at_nat @ Y3 @ YS )
% 15.55/8.65       => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y3 ) @ fun_pair_leq )
% 15.55/8.65         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_max_weak )
% 15.55/8.65           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X3 @ XS ) @ YS ) @ fun_max_weak ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9886_wmin__insertI,axiom,
% 15.55/8.65      ! [X3: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y3: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 15.55/8.65        ( ( member8440522571783428010at_nat @ X3 @ XS )
% 15.55/8.65       => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y3 ) @ fun_pair_leq )
% 15.55/8.65         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_weak )
% 15.55/8.65           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y3 @ YS ) ) @ fun_min_weak ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9887_wmin__emptyI,axiom,
% 15.55/8.65      ! [X9: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X9 @ bot_bo2099793752762293965at_nat ) @ fun_min_weak ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9888_wmax__emptyI,axiom,
% 15.55/8.65      ! [X9: set_Pr1261947904930325089at_nat] :
% 15.55/8.65        ( ( finite6177210948735845034at_nat @ X9 )
% 15.55/8.65       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ X9 ) @ fun_max_weak ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9889_smax__insertI,axiom,
% 15.55/8.65      ! [Y3: product_prod_nat_nat,Y8: set_Pr1261947904930325089at_nat,X3: product_prod_nat_nat,X9: set_Pr1261947904930325089at_nat] :
% 15.55/8.65        ( ( member8440522571783428010at_nat @ Y3 @ Y8 )
% 15.55/8.65       => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y3 ) @ fun_pair_less )
% 15.55/8.65         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X9 @ Y8 ) @ fun_max_strict )
% 15.55/8.65           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X3 @ X9 ) @ Y8 ) @ fun_max_strict ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9890_smin__insertI,axiom,
% 15.55/8.65      ! [X3: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y3: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 15.55/8.65        ( ( member8440522571783428010at_nat @ X3 @ XS )
% 15.55/8.65       => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y3 ) @ fun_pair_less )
% 15.55/8.65         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_strict )
% 15.55/8.65           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y3 @ YS ) ) @ fun_min_strict ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9891_smax__emptyI,axiom,
% 15.55/8.65      ! [Y8: set_Pr1261947904930325089at_nat] :
% 15.55/8.65        ( ( finite6177210948735845034at_nat @ Y8 )
% 15.55/8.65       => ( ( Y8 != bot_bo2099793752762293965at_nat )
% 15.55/8.65         => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ Y8 ) @ fun_max_strict ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9892_smin__emptyI,axiom,
% 15.55/8.65      ! [X9: set_Pr1261947904930325089at_nat] :
% 15.55/8.65        ( ( X9 != bot_bo2099793752762293965at_nat )
% 15.55/8.65       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X9 @ bot_bo2099793752762293965at_nat ) @ fun_min_strict ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9893_min__weak__def,axiom,
% 15.55/8.65      ( fun_min_weak
% 15.55/8.65      = ( sup_su5525570899277871387at_nat @ ( min_ex6901939911449802026at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9894_max__weak__def,axiom,
% 15.55/8.65      ( fun_max_weak
% 15.55/8.65      = ( sup_su5525570899277871387at_nat @ ( max_ex8135407076693332796at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9895_max__strict__def,axiom,
% 15.55/8.65      ( fun_max_strict
% 15.55/8.65      = ( max_ex8135407076693332796at_nat @ fun_pair_less ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9896_min__strict__def,axiom,
% 15.55/8.65      ( fun_min_strict
% 15.55/8.65      = ( min_ex6901939911449802026at_nat @ fun_pair_less ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9897_min__rpair__set,axiom,
% 15.55/8.65      fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_min_strict @ fun_min_weak ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9898_max__rpair__set,axiom,
% 15.55/8.65      fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_max_strict @ fun_max_weak ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9899_pred__nat__trancl__eq__le,axiom,
% 15.55/8.65      ! [M: nat,N: nat] :
% 15.55/8.65        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 15.55/8.65        = ( ord_less_eq_nat @ M @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9900_less__eq,axiom,
% 15.55/8.65      ! [M: nat,N: nat] :
% 15.55/8.65        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 15.55/8.65        = ( ord_less_nat @ M @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9901_euclidean__size__int__def,axiom,
% 15.55/8.65      ( euclid4774559944035922753ze_int
% 15.55/8.65      = ( comp_int_nat_int @ nat2 @ abs_abs_int ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9902_division__segment__eq__sgn,axiom,
% 15.55/8.65      ! [K: int] :
% 15.55/8.65        ( ( K != zero_zero_int )
% 15.55/8.65       => ( ( euclid3395696857347342551nt_int @ K )
% 15.55/8.65          = ( sgn_sgn_int @ K ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9903_division__segment__int__def,axiom,
% 15.55/8.65      ( euclid3395696857347342551nt_int
% 15.55/8.65      = ( ^ [K3: int] : ( if_int @ ( ord_less_eq_int @ zero_zero_int @ K3 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9904_rat__number__expand_I5_J,axiom,
% 15.55/8.65      ! [K: num] :
% 15.55/8.65        ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) )
% 15.55/8.65        = ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9905_less__rat,axiom,
% 15.55/8.65      ! [B: int,D3: int,A: int,C: int] :
% 15.55/8.65        ( ( B != zero_zero_int )
% 15.55/8.65       => ( ( D3 != zero_zero_int )
% 15.55/8.65         => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D3 ) )
% 15.55/8.65            = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A @ D3 ) @ ( times_times_int @ B @ D3 ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9906_add__rat,axiom,
% 15.55/8.65      ! [B: int,D3: int,A: int,C: int] :
% 15.55/8.65        ( ( B != zero_zero_int )
% 15.55/8.65       => ( ( D3 != zero_zero_int )
% 15.55/8.65         => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D3 ) )
% 15.55/8.65            = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D3 ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D3 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9907_le__rat,axiom,
% 15.55/8.65      ! [B: int,D3: int,A: int,C: int] :
% 15.55/8.65        ( ( B != zero_zero_int )
% 15.55/8.65       => ( ( D3 != zero_zero_int )
% 15.55/8.65         => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C @ D3 ) )
% 15.55/8.65            = ( ord_less_eq_int @ ( times_times_int @ ( times_times_int @ A @ D3 ) @ ( times_times_int @ B @ D3 ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D3 ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9908_diff__rat,axiom,
% 15.55/8.65      ! [B: int,D3: int,A: int,C: int] :
% 15.55/8.65        ( ( B != zero_zero_int )
% 15.55/8.65       => ( ( D3 != zero_zero_int )
% 15.55/8.65         => ( ( minus_minus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D3 ) )
% 15.55/8.65            = ( fract @ ( minus_minus_int @ ( times_times_int @ A @ D3 ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D3 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9909_eq__rat_I1_J,axiom,
% 15.55/8.65      ! [B: int,D3: int,A: int,C: int] :
% 15.55/8.65        ( ( B != zero_zero_int )
% 15.55/8.65       => ( ( D3 != zero_zero_int )
% 15.55/8.65         => ( ( ( fract @ A @ B )
% 15.55/8.65              = ( fract @ C @ D3 ) )
% 15.55/8.65            = ( ( times_times_int @ A @ D3 )
% 15.55/8.65              = ( times_times_int @ C @ B ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9910_mult__rat__cancel,axiom,
% 15.55/8.65      ! [C: int,A: int,B: int] :
% 15.55/8.65        ( ( C != zero_zero_int )
% 15.55/8.65       => ( ( fract @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 15.55/8.65          = ( fract @ A @ B ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9911_eq__rat_I2_J,axiom,
% 15.55/8.65      ! [A: int] :
% 15.55/8.65        ( ( fract @ A @ zero_zero_int )
% 15.55/8.65        = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9912_eq__rat_I3_J,axiom,
% 15.55/8.65      ! [A: int,C: int] :
% 15.55/8.65        ( ( fract @ zero_zero_int @ A )
% 15.55/8.65        = ( fract @ zero_zero_int @ C ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9913_rat__number__collapse_I6_J,axiom,
% 15.55/8.65      ! [K: int] :
% 15.55/8.65        ( ( fract @ K @ zero_zero_int )
% 15.55/8.65        = zero_zero_rat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9914_rat__number__collapse_I1_J,axiom,
% 15.55/8.65      ! [K: int] :
% 15.55/8.65        ( ( fract @ zero_zero_int @ K )
% 15.55/8.65        = zero_zero_rat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9915_Rat__induct__pos,axiom,
% 15.55/8.65      ! [P: rat > $o,Q3: rat] :
% 15.55/8.65        ( ! [A5: int,B4: int] :
% 15.55/8.65            ( ( ord_less_int @ zero_zero_int @ B4 )
% 15.55/8.65           => ( P @ ( fract @ A5 @ B4 ) ) )
% 15.55/8.65       => ( P @ Q3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9916_Zero__rat__def,axiom,
% 15.55/8.65      ( zero_zero_rat
% 15.55/8.65      = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9917_rat__number__expand_I3_J,axiom,
% 15.55/8.65      ( numeral_numeral_rat
% 15.55/8.65      = ( ^ [K3: num] : ( fract @ ( numeral_numeral_int @ K3 ) @ one_one_int ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9918_rat__number__collapse_I3_J,axiom,
% 15.55/8.65      ! [W: num] :
% 15.55/8.65        ( ( fract @ ( numeral_numeral_int @ W ) @ one_one_int )
% 15.55/8.65        = ( numeral_numeral_rat @ W ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9919_Fract__of__nat__eq,axiom,
% 15.55/8.65      ! [K: nat] :
% 15.55/8.65        ( ( fract @ ( semiri1314217659103216013at_int @ K ) @ one_one_int )
% 15.55/8.65        = ( semiri681578069525770553at_rat @ K ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9920_Fract__less__zero__iff,axiom,
% 15.55/8.65      ! [B: int,A: int] :
% 15.55/8.65        ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.65       => ( ( ord_less_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 15.55/8.65          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9921_zero__less__Fract__iff,axiom,
% 15.55/8.65      ! [B: int,A: int] :
% 15.55/8.65        ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.65       => ( ( ord_less_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 15.55/8.65          = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9922_Fract_Oabs__eq,axiom,
% 15.55/8.65      ( fract
% 15.55/8.65      = ( ^ [Xa4: int,X: int] : ( abs_Rat @ ( if_Pro3027730157355071871nt_int @ ( X = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ Xa4 @ X ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9923_positive__rat,axiom,
% 15.55/8.65      ! [A: int,B: int] :
% 15.55/8.65        ( ( positive @ ( fract @ A @ B ) )
% 15.55/8.65        = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9924_Fract__less__one__iff,axiom,
% 15.55/8.65      ! [B: int,A: int] :
% 15.55/8.65        ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.65       => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 15.55/8.65          = ( ord_less_int @ A @ B ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9925_one__less__Fract__iff,axiom,
% 15.55/8.65      ! [B: int,A: int] :
% 15.55/8.65        ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.65       => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 15.55/8.65          = ( ord_less_int @ B @ A ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9926_Fract__add__one,axiom,
% 15.55/8.65      ! [N: int,M: int] :
% 15.55/8.65        ( ( N != zero_zero_int )
% 15.55/8.65       => ( ( fract @ ( plus_plus_int @ M @ N ) @ N )
% 15.55/8.65          = ( plus_plus_rat @ ( fract @ M @ N ) @ one_one_rat ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9927_Fract_Otransfer,axiom,
% 15.55/8.65      ( bNF_re3461391660133120880nt_rat
% 15.55/8.65      @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 15.55/8.65      @ ( bNF_re2214769303045360666nt_rat
% 15.55/8.65        @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 15.55/8.65        @ pcr_rat )
% 15.55/8.65      @ ^ [A4: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( B3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A4 @ B3 ) )
% 15.55/8.65      @ fract ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9928_Fract__le__zero__iff,axiom,
% 15.55/8.65      ! [B: int,A: int] :
% 15.55/8.65        ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.65       => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 15.55/8.65          = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9929_zero__le__Fract__iff,axiom,
% 15.55/8.65      ! [B: int,A: int] :
% 15.55/8.65        ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.65       => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 15.55/8.65          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9930_Fract__le__one__iff,axiom,
% 15.55/8.65      ! [B: int,A: int] :
% 15.55/8.65        ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.65       => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 15.55/8.65          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9931_one__le__Fract__iff,axiom,
% 15.55/8.65      ! [B: int,A: int] :
% 15.55/8.65        ( ( ord_less_int @ zero_zero_int @ B )
% 15.55/8.65       => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 15.55/8.65          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9932_rat__number__collapse_I4_J,axiom,
% 15.55/8.65      ! [W: num] :
% 15.55/8.65        ( ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ one_one_int )
% 15.55/8.65        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9933_quotient__of__def,axiom,
% 15.55/8.65      ( quotient_of
% 15.55/8.65      = ( ^ [X: rat] :
% 15.55/8.65            ( the_Pr4378521158711661632nt_int
% 15.55/8.65            @ ^ [Pair: product_prod_int_int] :
% 15.55/8.65                ( ( X
% 15.55/8.65                  = ( fract @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) )
% 15.55/8.65                & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Pair ) )
% 15.55/8.65                & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9934_less__eq__enat__def,axiom,
% 15.55/8.65      ( ord_le2932123472753598470d_enat
% 15.55/8.65      = ( ^ [M3: extended_enat] :
% 15.55/8.65            ( extended_case_enat_o
% 15.55/8.65            @ ^ [N1: nat] :
% 15.55/8.65                ( extended_case_enat_o
% 15.55/8.65                @ ^ [M1: nat] : ( ord_less_eq_nat @ M1 @ N1 )
% 15.55/8.65                @ $false
% 15.55/8.65                @ M3 )
% 15.55/8.65            @ $true ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9935_normalize__stable,axiom,
% 15.55/8.65      ! [Q3: int,P6: int] :
% 15.55/8.65        ( ( ord_less_int @ zero_zero_int @ Q3 )
% 15.55/8.65       => ( ( algebr932160517623751201me_int @ P6 @ Q3 )
% 15.55/8.65         => ( ( normalize @ ( product_Pair_int_int @ P6 @ Q3 ) )
% 15.55/8.65            = ( product_Pair_int_int @ P6 @ Q3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9936_Rat__cases,axiom,
% 15.55/8.65      ! [Q3: rat] :
% 15.55/8.65        ~ ! [A5: int,B4: int] :
% 15.55/8.65            ( ( Q3
% 15.55/8.65              = ( fract @ A5 @ B4 ) )
% 15.55/8.65           => ( ( ord_less_int @ zero_zero_int @ B4 )
% 15.55/8.65             => ~ ( algebr932160517623751201me_int @ A5 @ B4 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9937_Rat__induct,axiom,
% 15.55/8.65      ! [P: rat > $o,Q3: rat] :
% 15.55/8.65        ( ! [A5: int,B4: int] :
% 15.55/8.65            ( ( ord_less_int @ zero_zero_int @ B4 )
% 15.55/8.65           => ( ( algebr932160517623751201me_int @ A5 @ B4 )
% 15.55/8.65             => ( P @ ( fract @ A5 @ B4 ) ) ) )
% 15.55/8.65       => ( P @ Q3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9938_Rat__cases__nonzero,axiom,
% 15.55/8.65      ! [Q3: rat] :
% 15.55/8.65        ( ! [A5: int,B4: int] :
% 15.55/8.65            ( ( Q3
% 15.55/8.65              = ( fract @ A5 @ B4 ) )
% 15.55/8.65           => ( ( ord_less_int @ zero_zero_int @ B4 )
% 15.55/8.65             => ( ( A5 != zero_zero_int )
% 15.55/8.65               => ~ ( algebr932160517623751201me_int @ A5 @ B4 ) ) ) )
% 15.55/8.65       => ( Q3 = zero_zero_rat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9939_quotient__of__unique,axiom,
% 15.55/8.65      ! [R2: rat] :
% 15.55/8.65      ? [X4: product_prod_int_int] :
% 15.55/8.65        ( ( R2
% 15.55/8.65          = ( fract @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) )
% 15.55/8.65        & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ X4 ) )
% 15.55/8.65        & ( algebr932160517623751201me_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) )
% 15.55/8.65        & ! [Y6: product_prod_int_int] :
% 15.55/8.65            ( ( ( R2
% 15.55/8.65                = ( fract @ ( product_fst_int_int @ Y6 ) @ ( product_snd_int_int @ Y6 ) ) )
% 15.55/8.65              & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Y6 ) )
% 15.55/8.65              & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Y6 ) @ ( product_snd_int_int @ Y6 ) ) )
% 15.55/8.65           => ( Y6 = X4 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9940_less__enat__def,axiom,
% 15.55/8.65      ( ord_le72135733267957522d_enat
% 15.55/8.65      = ( ^ [M3: extended_enat,N3: extended_enat] :
% 15.55/8.65            ( extended_case_enat_o
% 15.55/8.65            @ ^ [M1: nat] : ( extended_case_enat_o @ ( ord_less_nat @ M1 ) @ $true @ N3 )
% 15.55/8.65            @ $false
% 15.55/8.65            @ M3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9941_set__encode__vimage__Suc,axiom,
% 15.55/8.65      ! [A3: set_nat] :
% 15.55/8.65        ( ( nat_set_encode @ ( vimage_nat_nat @ suc @ A3 ) )
% 15.55/8.65        = ( divide_divide_nat @ ( nat_set_encode @ A3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9942_set__decode__div__2,axiom,
% 15.55/8.65      ! [X3: nat] :
% 15.55/8.65        ( ( nat_set_decode @ ( divide_divide_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 15.55/8.65        = ( vimage_nat_nat @ suc @ ( nat_set_decode @ X3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9943_coprime__int__iff,axiom,
% 15.55/8.65      ! [M: nat,N: nat] :
% 15.55/8.65        ( ( algebr932160517623751201me_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 15.55/8.65        = ( algebr934650988132801477me_nat @ M @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9944_coprime__nat__abs__right__iff,axiom,
% 15.55/8.65      ! [N: nat,K: int] :
% 15.55/8.65        ( ( algebr934650988132801477me_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 15.55/8.65        = ( algebr932160517623751201me_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9945_coprime__nat__abs__left__iff,axiom,
% 15.55/8.65      ! [K: int,N: nat] :
% 15.55/8.65        ( ( algebr934650988132801477me_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 15.55/8.65        = ( algebr932160517623751201me_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9946_coprime__Suc__0__left,axiom,
% 15.55/8.65      ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ zero_zero_nat ) @ N ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9947_coprime__Suc__0__right,axiom,
% 15.55/8.65      ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ zero_zero_nat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9948_vimage__Suc__insert__0,axiom,
% 15.55/8.65      ! [A3: set_nat] :
% 15.55/8.65        ( ( vimage_nat_nat @ suc @ ( insert_nat @ zero_zero_nat @ A3 ) )
% 15.55/8.65        = ( vimage_nat_nat @ suc @ A3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9949_coprime__diff__one__right__nat,axiom,
% 15.55/8.65      ! [N: nat] :
% 15.55/8.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.65       => ( algebr934650988132801477me_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9950_coprime__diff__one__left__nat,axiom,
% 15.55/8.65      ! [N: nat] :
% 15.55/8.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.65       => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9951_Rats__abs__nat__div__natE,axiom,
% 15.55/8.65      ! [X3: real] :
% 15.55/8.65        ( ( member_real @ X3 @ field_5140801741446780682s_real )
% 15.55/8.65       => ~ ! [M4: nat,N2: nat] :
% 15.55/8.65              ( ( N2 != zero_zero_nat )
% 15.55/8.65             => ( ( ( abs_abs_real @ X3 )
% 15.55/8.65                  = ( divide_divide_real @ ( semiri5074537144036343181t_real @ M4 ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 15.55/8.65               => ~ ( algebr934650988132801477me_nat @ M4 @ N2 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9952_transp__realrel,axiom,
% 15.55/8.65      transp_nat_rat @ realrel ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9953_bdd__above__nat,axiom,
% 15.55/8.65      condit2214826472909112428ve_nat = finite_finite_nat ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9954_num__of__integer_Otransfer,axiom,
% 15.55/8.65      ( bNF_re6718328864250387230um_num @ code_pcr_integer
% 15.55/8.65      @ ^ [Y5: num,Z2: num] : ( Y5 = Z2 )
% 15.55/8.65      @ ( comp_nat_num_int @ num_of_nat @ nat2 )
% 15.55/8.65      @ code_num_of_integer ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9955_compute__powr__real,axiom,
% 15.55/8.65      ( powr_real2
% 15.55/8.65      = ( ^ [B3: real,I4: real] :
% 15.55/8.65            ( if_real @ ( ord_less_eq_real @ B3 @ zero_zero_real )
% 15.55/8.65            @ ( abort_real @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.65              @ ^ [Uu3: product_unit] : ( powr_real2 @ B3 @ I4 ) )
% 15.55/8.65            @ ( if_real
% 15.55/8.65              @ ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ I4 ) )
% 15.55/8.65                = I4 )
% 15.55/8.65              @ ( if_real @ ( ord_less_eq_real @ zero_zero_real @ I4 ) @ ( power_power_real @ B3 @ ( nat2 @ ( archim6058952711729229775r_real @ I4 ) ) ) @ ( divide_divide_real @ one_one_real @ ( power_power_real @ B3 @ ( nat2 @ ( archim6058952711729229775r_real @ ( uminus_uminus_real @ I4 ) ) ) ) ) )
% 15.55/8.65              @ ( abort_real @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $true @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 15.55/8.65                @ ^ [Uu3: product_unit] : ( powr_real2 @ B3 @ I4 ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9956_less__eq__integer_Otransfer,axiom,
% 15.55/8.65      ( bNF_re6321650412969554871eger_o @ code_pcr_integer
% 15.55/8.65      @ ( bNF_re6574881592172037608er_o_o @ code_pcr_integer
% 15.55/8.65        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 15.55/8.65      @ ord_less_eq_int
% 15.55/8.65      @ ord_le3102999989581377725nteger ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9957_Code__Target__Nat_ONat_Otransfer,axiom,
% 15.55/8.65      ( bNF_re2807294637932363402at_nat @ code_pcr_integer
% 15.55/8.65      @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 15.55/8.65      @ nat2
% 15.55/8.65      @ code_Target_Nat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9958_nat__of__integer_Otransfer,axiom,
% 15.55/8.65      ( bNF_re2807294637932363402at_nat @ code_pcr_integer
% 15.55/8.65      @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 15.55/8.65      @ nat2
% 15.55/8.65      @ code_nat_of_integer ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9959_less__integer_Otransfer,axiom,
% 15.55/8.65      ( bNF_re6321650412969554871eger_o @ code_pcr_integer
% 15.55/8.65      @ ( bNF_re6574881592172037608er_o_o @ code_pcr_integer
% 15.55/8.65        @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 15.55/8.65      @ ord_less_int
% 15.55/8.65      @ ord_le6747313008572928689nteger ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9960_zero__integer_Otransfer,axiom,
% 15.55/8.65      code_pcr_integer @ zero_zero_int @ zero_z3403309356797280102nteger ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9961_String_Oempty__neq__Literal,axiom,
% 15.55/8.65      ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,S: literal] :
% 15.55/8.65        ( zero_zero_literal
% 15.55/8.65       != ( literal2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ S ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9962_int__of__integer__integer__of__nat,axiom,
% 15.55/8.65      ! [N: nat] :
% 15.55/8.65        ( ( code_int_of_integer @ ( code_integer_of_nat @ N ) )
% 15.55/8.65        = ( semiri1314217659103216013at_int @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9963_integer__of__nat_Orep__eq,axiom,
% 15.55/8.65      ! [X3: nat] :
% 15.55/8.65        ( ( code_int_of_integer @ ( code_integer_of_nat @ X3 ) )
% 15.55/8.65        = ( semiri1314217659103216013at_int @ X3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9964_integer__of__nat__0,axiom,
% 15.55/8.65      ( ( code_integer_of_nat @ zero_zero_nat )
% 15.55/8.65      = zero_z3403309356797280102nteger ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9965_integer__of__nat_Oabs__eq,axiom,
% 15.55/8.65      ( code_integer_of_nat
% 15.55/8.65      = ( ^ [X: nat] : ( code_integer_of_int @ ( semiri1314217659103216013at_int @ X ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9966_integer__of__nat_Otransfer,axiom,
% 15.55/8.65      ( bNF_re4153400068438556298nteger
% 15.55/8.65      @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 15.55/8.65      @ code_pcr_integer
% 15.55/8.65      @ semiri1314217659103216013at_int
% 15.55/8.65      @ code_integer_of_nat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9967_integer__of__nat__numeral,axiom,
% 15.55/8.65      ! [N: num] :
% 15.55/8.65        ( ( code_integer_of_nat @ ( numeral_numeral_nat @ N ) )
% 15.55/8.65        = ( numera6620942414471956472nteger @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9968_divmod__nat__code,axiom,
% 15.55/8.65      ( divmod_nat
% 15.55/8.65      = ( ^ [M3: nat,N3: nat] :
% 15.55/8.65            ( produc8678311845419106900er_nat @ code_nat_of_integer @ code_nat_of_integer
% 15.55/8.65            @ ( if_Pro6119634080678213985nteger
% 15.55/8.65              @ ( ( code_integer_of_nat @ M3 )
% 15.55/8.65                = zero_z3403309356797280102nteger )
% 15.55/8.65              @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 15.55/8.65              @ ( if_Pro6119634080678213985nteger
% 15.55/8.65                @ ( ( code_integer_of_nat @ N3 )
% 15.55/8.65                  = zero_z3403309356797280102nteger )
% 15.55/8.65                @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( code_integer_of_nat @ M3 ) )
% 15.55/8.65                @ ( code_divmod_abs @ ( code_integer_of_nat @ M3 ) @ ( code_integer_of_nat @ N3 ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9969_integer__of__nat__def,axiom,
% 15.55/8.65      ( code_integer_of_nat
% 15.55/8.65      = ( map_fu6290471996055670595nteger @ id_nat @ code_integer_of_int @ semiri1314217659103216013at_int ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9970_pairs__le__eq__Sigma,axiom,
% 15.55/8.65      ! [M: nat] :
% 15.55/8.65        ( ( collec3392354462482085612at_nat
% 15.55/8.65          @ ( produc6081775807080527818_nat_o
% 15.55/8.65            @ ^ [I4: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I4 @ J3 ) @ M ) ) )
% 15.55/8.65        = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M )
% 15.55/8.65          @ ^ [R5: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ R5 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9971_numeral__le__enat__iff,axiom,
% 15.55/8.65      ! [M: num,N: nat] :
% 15.55/8.65        ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( extended_enat2 @ N ) )
% 15.55/8.65        = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9972_enat_Oinject,axiom,
% 15.55/8.65      ! [Nat: nat,Nat2: nat] :
% 15.55/8.65        ( ( ( extended_enat2 @ Nat )
% 15.55/8.65          = ( extended_enat2 @ Nat2 ) )
% 15.55/8.65        = ( Nat = Nat2 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9973_enat__ord__simps_I2_J,axiom,
% 15.55/8.65      ! [M: nat,N: nat] :
% 15.55/8.65        ( ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 15.55/8.65        = ( ord_less_nat @ M @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9974_plus__enat__simps_I1_J,axiom,
% 15.55/8.65      ! [M: nat,N: nat] :
% 15.55/8.65        ( ( plus_p3455044024723400733d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 15.55/8.65        = ( extended_enat2 @ ( plus_plus_nat @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9975_enat__ord__simps_I1_J,axiom,
% 15.55/8.65      ! [M: nat,N: nat] :
% 15.55/8.65        ( ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 15.55/8.65        = ( ord_less_eq_nat @ M @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9976_idiff__enat__0__right,axiom,
% 15.55/8.65      ! [N: extended_enat] :
% 15.55/8.65        ( ( minus_3235023915231533773d_enat @ N @ ( extended_enat2 @ zero_zero_nat ) )
% 15.55/8.65        = N ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9977_idiff__enat__0,axiom,
% 15.55/8.65      ! [N: extended_enat] :
% 15.55/8.65        ( ( minus_3235023915231533773d_enat @ ( extended_enat2 @ zero_zero_nat ) @ N )
% 15.55/8.65        = ( extended_enat2 @ zero_zero_nat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9978_idiff__enat__enat,axiom,
% 15.55/8.65      ! [A: nat,B: nat] :
% 15.55/8.65        ( ( minus_3235023915231533773d_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
% 15.55/8.65        = ( extended_enat2 @ ( minus_minus_nat @ A @ B ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9979_times__enat__simps_I1_J,axiom,
% 15.55/8.65      ! [M: nat,N: nat] :
% 15.55/8.65        ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 15.55/8.65        = ( extended_enat2 @ ( times_times_nat @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9980_max__enat__simps_I1_J,axiom,
% 15.55/8.65      ! [M: nat,N: nat] :
% 15.55/8.65        ( ( ord_ma741700101516333627d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 15.55/8.65        = ( extended_enat2 @ ( ord_max_nat @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9981_min__enat__simps_I1_J,axiom,
% 15.55/8.65      ! [M: nat,N: nat] :
% 15.55/8.65        ( ( ord_mi8085742599997312461d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 15.55/8.65        = ( extended_enat2 @ ( ord_min_nat @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9982_numeral__less__enat__iff,axiom,
% 15.55/8.65      ! [M: num,N: nat] :
% 15.55/8.65        ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( extended_enat2 @ N ) )
% 15.55/8.65        = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9983_finite__enat__bounded,axiom,
% 15.55/8.65      ! [A3: set_Extended_enat,N: nat] :
% 15.55/8.65        ( ! [Y4: extended_enat] :
% 15.55/8.65            ( ( member_Extended_enat @ Y4 @ A3 )
% 15.55/8.65           => ( ord_le2932123472753598470d_enat @ Y4 @ ( extended_enat2 @ N ) ) )
% 15.55/8.65       => ( finite4001608067531595151d_enat @ A3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9984_enat__ile,axiom,
% 15.55/8.65      ! [N: extended_enat,M: nat] :
% 15.55/8.65        ( ( ord_le2932123472753598470d_enat @ N @ ( extended_enat2 @ M ) )
% 15.55/8.65       => ? [K2: nat] :
% 15.55/8.65            ( N
% 15.55/8.65            = ( extended_enat2 @ K2 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9985_enat__iless,axiom,
% 15.55/8.65      ! [N: extended_enat,M: nat] :
% 15.55/8.65        ( ( ord_le72135733267957522d_enat @ N @ ( extended_enat2 @ M ) )
% 15.55/8.65       => ? [K2: nat] :
% 15.55/8.65            ( N
% 15.55/8.65            = ( extended_enat2 @ K2 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9986_less__enatE,axiom,
% 15.55/8.65      ! [N: extended_enat,M: nat] :
% 15.55/8.65        ( ( ord_le72135733267957522d_enat @ N @ ( extended_enat2 @ M ) )
% 15.55/8.65       => ~ ! [K2: nat] :
% 15.55/8.65              ( ( N
% 15.55/8.65                = ( extended_enat2 @ K2 ) )
% 15.55/8.65             => ~ ( ord_less_nat @ K2 @ M ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9987_numeral__eq__enat,axiom,
% 15.55/8.65      ( numera1916890842035813515d_enat
% 15.55/8.65      = ( ^ [K3: num] : ( extended_enat2 @ ( numeral_numeral_nat @ K3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9988_one__enat__def,axiom,
% 15.55/8.65      ( one_on7984719198319812577d_enat
% 15.55/8.65      = ( extended_enat2 @ one_one_nat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9989_enat__1__iff_I1_J,axiom,
% 15.55/8.65      ! [X3: nat] :
% 15.55/8.65        ( ( ( extended_enat2 @ X3 )
% 15.55/8.65          = one_on7984719198319812577d_enat )
% 15.55/8.65        = ( X3 = one_one_nat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9990_enat__1__iff_I2_J,axiom,
% 15.55/8.65      ! [X3: nat] :
% 15.55/8.65        ( ( one_on7984719198319812577d_enat
% 15.55/8.65          = ( extended_enat2 @ X3 ) )
% 15.55/8.65        = ( X3 = one_one_nat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9991_of__nat__eq__enat,axiom,
% 15.55/8.65      semiri4216267220026989637d_enat = extended_enat2 ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9992_zero__enat__def,axiom,
% 15.55/8.65      ( zero_z5237406670263579293d_enat
% 15.55/8.65      = ( extended_enat2 @ zero_zero_nat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9993_enat__0__iff_I1_J,axiom,
% 15.55/8.65      ! [X3: nat] :
% 15.55/8.65        ( ( ( extended_enat2 @ X3 )
% 15.55/8.65          = zero_z5237406670263579293d_enat )
% 15.55/8.65        = ( X3 = zero_zero_nat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9994_enat__0__iff_I2_J,axiom,
% 15.55/8.65      ! [X3: nat] :
% 15.55/8.65        ( ( zero_z5237406670263579293d_enat
% 15.55/8.65          = ( extended_enat2 @ X3 ) )
% 15.55/8.65        = ( X3 = zero_zero_nat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9995_Suc__ile__eq,axiom,
% 15.55/8.65      ! [M: nat,N: extended_enat] :
% 15.55/8.65        ( ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ ( suc @ M ) ) @ N )
% 15.55/8.65        = ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M ) @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9996_iadd__le__enat__iff,axiom,
% 15.55/8.65      ! [X3: extended_enat,Y3: extended_enat,N: nat] :
% 15.55/8.65        ( ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ X3 @ Y3 ) @ ( extended_enat2 @ N ) )
% 15.55/8.65        = ( ? [Y9: nat,X10: nat] :
% 15.55/8.65              ( ( X3
% 15.55/8.65                = ( extended_enat2 @ X10 ) )
% 15.55/8.65              & ( Y3
% 15.55/8.65                = ( extended_enat2 @ Y9 ) )
% 15.55/8.65              & ( ord_less_eq_nat @ ( plus_plus_nat @ X10 @ Y9 ) @ N ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9997_elimnum,axiom,
% 15.55/8.65      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 15.55/8.65        ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 15.55/8.65       => ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 15.55/8.65          = ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9998_VEBT__internal_Oelim__dead_Osimps_I3_J,axiom,
% 15.55/8.65      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,L: nat] :
% 15.55/8.65        ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ ( extended_enat2 @ L ) )
% 15.55/8.65        = ( vEBT_Node @ Info @ Deg
% 15.55/8.65          @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.65            @ ( map_VE8901447254227204932T_VEBT
% 15.55/8.65              @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.65              @ TreeList2 ) )
% 15.55/8.65          @ ( vEBT_VEBT_elim_dead @ Summary @ ( extended_enat2 @ ( divide_divide_nat @ L @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_9999_VEBT__internal_Oelim__dead_Oelims,axiom,
% 15.55/8.65      ! [X3: vEBT_VEBT,Xa: extended_enat,Y3: vEBT_VEBT] :
% 15.55/8.65        ( ( ( vEBT_VEBT_elim_dead @ X3 @ Xa )
% 15.55/8.65          = Y3 )
% 15.55/8.65       => ( ! [A5: $o,B4: $o] :
% 15.55/8.65              ( ( X3
% 15.55/8.65                = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.65             => ( Y3
% 15.55/8.65               != ( vEBT_Leaf @ A5 @ B4 ) ) )
% 15.55/8.65         => ( ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.65                ( ( X3
% 15.55/8.65                  = ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary2 ) )
% 15.55/8.65               => ( ( Xa = extend5688581933313929465d_enat )
% 15.55/8.65                 => ( Y3
% 15.55/8.65                   != ( vEBT_Node @ Info2 @ Deg2
% 15.55/8.65                      @ ( map_VE8901447254227204932T_VEBT
% 15.55/8.65                        @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.65                        @ TreeList3 )
% 15.55/8.65                      @ ( vEBT_VEBT_elim_dead @ Summary2 @ extend5688581933313929465d_enat ) ) ) ) )
% 15.55/8.65           => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.65                  ( ( X3
% 15.55/8.65                    = ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary2 ) )
% 15.55/8.65                 => ! [L4: nat] :
% 15.55/8.65                      ( ( Xa
% 15.55/8.65                        = ( extended_enat2 @ L4 ) )
% 15.55/8.65                     => ( Y3
% 15.55/8.65                       != ( vEBT_Node @ Info2 @ Deg2
% 15.55/8.65                          @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.65                            @ ( map_VE8901447254227204932T_VEBT
% 15.55/8.65                              @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.65                              @ TreeList3 ) )
% 15.55/8.65                          @ ( vEBT_VEBT_elim_dead @ Summary2 @ ( extended_enat2 @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10000_VEBT__internal_Oelim__dead_Osimps_I2_J,axiom,
% 15.55/8.65      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 15.55/8.65        ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ extend5688581933313929465d_enat )
% 15.55/8.65        = ( vEBT_Node @ Info @ Deg
% 15.55/8.65          @ ( map_VE8901447254227204932T_VEBT
% 15.55/8.65            @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.65            @ TreeList2 )
% 15.55/8.65          @ ( vEBT_VEBT_elim_dead @ Summary @ extend5688581933313929465d_enat ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10001_elimcomplete,axiom,
% 15.55/8.65      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 15.55/8.65        ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 15.55/8.65       => ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ extend5688581933313929465d_enat )
% 15.55/8.65          = ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10002_not__enat__eq,axiom,
% 15.55/8.65      ! [X3: extended_enat] :
% 15.55/8.65        ( ( ! [Y: nat] :
% 15.55/8.65              ( X3
% 15.55/8.65             != ( extended_enat2 @ Y ) ) )
% 15.55/8.65        = ( X3 = extend5688581933313929465d_enat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10003_not__infinity__eq,axiom,
% 15.55/8.65      ! [X3: extended_enat] :
% 15.55/8.65        ( ( X3 != extend5688581933313929465d_enat )
% 15.55/8.65        = ( ? [I4: nat] :
% 15.55/8.65              ( X3
% 15.55/8.65              = ( extended_enat2 @ I4 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10004_enat__ord__simps_I6_J,axiom,
% 15.55/8.65      ! [Q3: extended_enat] :
% 15.55/8.65        ~ ( ord_le72135733267957522d_enat @ extend5688581933313929465d_enat @ Q3 ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10005_enat__ord__simps_I4_J,axiom,
% 15.55/8.65      ! [Q3: extended_enat] :
% 15.55/8.65        ( ( ord_le72135733267957522d_enat @ Q3 @ extend5688581933313929465d_enat )
% 15.55/8.65        = ( Q3 != extend5688581933313929465d_enat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10006_plus__enat__simps_I3_J,axiom,
% 15.55/8.65      ! [Q3: extended_enat] :
% 15.55/8.65        ( ( plus_p3455044024723400733d_enat @ Q3 @ extend5688581933313929465d_enat )
% 15.55/8.65        = extend5688581933313929465d_enat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10007_plus__enat__simps_I2_J,axiom,
% 15.55/8.65      ! [Q3: extended_enat] :
% 15.55/8.65        ( ( plus_p3455044024723400733d_enat @ extend5688581933313929465d_enat @ Q3 )
% 15.55/8.65        = extend5688581933313929465d_enat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10008_enat__ord__code_I3_J,axiom,
% 15.55/8.65      ! [Q3: extended_enat] : ( ord_le2932123472753598470d_enat @ Q3 @ extend5688581933313929465d_enat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10009_enat__ord__simps_I5_J,axiom,
% 15.55/8.65      ! [Q3: extended_enat] :
% 15.55/8.65        ( ( ord_le2932123472753598470d_enat @ extend5688581933313929465d_enat @ Q3 )
% 15.55/8.65        = ( Q3 = extend5688581933313929465d_enat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10010_idiff__infinity,axiom,
% 15.55/8.65      ! [N: extended_enat] :
% 15.55/8.65        ( ( minus_3235023915231533773d_enat @ extend5688581933313929465d_enat @ N )
% 15.55/8.65        = extend5688581933313929465d_enat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10011_times__enat__simps_I2_J,axiom,
% 15.55/8.65      ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ extend5688581933313929465d_enat )
% 15.55/8.65      = extend5688581933313929465d_enat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10012_max__enat__simps_I5_J,axiom,
% 15.55/8.65      ! [Q3: extended_enat] :
% 15.55/8.65        ( ( ord_ma741700101516333627d_enat @ extend5688581933313929465d_enat @ Q3 )
% 15.55/8.65        = extend5688581933313929465d_enat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10013_max__enat__simps_I4_J,axiom,
% 15.55/8.65      ! [Q3: extended_enat] :
% 15.55/8.65        ( ( ord_ma741700101516333627d_enat @ Q3 @ extend5688581933313929465d_enat )
% 15.55/8.65        = extend5688581933313929465d_enat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10014_min__enat__simps_I4_J,axiom,
% 15.55/8.65      ! [Q3: extended_enat] :
% 15.55/8.65        ( ( ord_mi8085742599997312461d_enat @ Q3 @ extend5688581933313929465d_enat )
% 15.55/8.65        = Q3 ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10015_min__enat__simps_I5_J,axiom,
% 15.55/8.65      ! [Q3: extended_enat] :
% 15.55/8.65        ( ( ord_mi8085742599997312461d_enat @ extend5688581933313929465d_enat @ Q3 )
% 15.55/8.65        = Q3 ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10016_idiff__self,axiom,
% 15.55/8.65      ! [N: extended_enat] :
% 15.55/8.65        ( ( N != extend5688581933313929465d_enat )
% 15.55/8.65       => ( ( minus_3235023915231533773d_enat @ N @ N )
% 15.55/8.65          = zero_z5237406670263579293d_enat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10017_add__diff__cancel__enat,axiom,
% 15.55/8.65      ! [X3: extended_enat,Y3: extended_enat] :
% 15.55/8.65        ( ( X3 != extend5688581933313929465d_enat )
% 15.55/8.65       => ( ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X3 @ Y3 ) @ X3 )
% 15.55/8.65          = Y3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10018_idiff__infinity__right,axiom,
% 15.55/8.65      ! [A: nat] :
% 15.55/8.65        ( ( minus_3235023915231533773d_enat @ ( extended_enat2 @ A ) @ extend5688581933313929465d_enat )
% 15.55/8.65        = zero_z5237406670263579293d_enat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10019_times__enat__simps_I3_J,axiom,
% 15.55/8.65      ! [N: nat] :
% 15.55/8.65        ( ( ( N = zero_zero_nat )
% 15.55/8.65         => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) )
% 15.55/8.65            = zero_z5237406670263579293d_enat ) )
% 15.55/8.65        & ( ( N != zero_zero_nat )
% 15.55/8.65         => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) )
% 15.55/8.65            = extend5688581933313929465d_enat ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10020_times__enat__simps_I4_J,axiom,
% 15.55/8.65      ! [M: nat] :
% 15.55/8.65        ( ( ( M = zero_zero_nat )
% 15.55/8.65         => ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M ) @ extend5688581933313929465d_enat )
% 15.55/8.65            = zero_z5237406670263579293d_enat ) )
% 15.55/8.65        & ( ( M != zero_zero_nat )
% 15.55/8.65         => ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M ) @ extend5688581933313929465d_enat )
% 15.55/8.65            = extend5688581933313929465d_enat ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10021_Sup__enat__def,axiom,
% 15.55/8.65      ( comple4398354569131411667d_enat
% 15.55/8.65      = ( ^ [A8: set_Extended_enat] : ( if_Extended_enat @ ( A8 = bot_bo7653980558646680370d_enat ) @ zero_z5237406670263579293d_enat @ ( if_Extended_enat @ ( finite4001608067531595151d_enat @ A8 ) @ ( lattic921264341876707157d_enat @ A8 ) @ extend5688581933313929465d_enat ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10022_enat__add__left__cancel__le,axiom,
% 15.55/8.65      ! [A: extended_enat,B: extended_enat,C: extended_enat] :
% 15.55/8.65        ( ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) @ ( plus_p3455044024723400733d_enat @ A @ C ) )
% 15.55/8.65        = ( ( A = extend5688581933313929465d_enat )
% 15.55/8.65          | ( ord_le2932123472753598470d_enat @ B @ C ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10023_enat__ord__simps_I3_J,axiom,
% 15.55/8.65      ! [Q3: extended_enat] : ( ord_le2932123472753598470d_enat @ Q3 @ extend5688581933313929465d_enat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10024_enat__add__left__cancel__less,axiom,
% 15.55/8.65      ! [A: extended_enat,B: extended_enat,C: extended_enat] :
% 15.55/8.65        ( ( ord_le72135733267957522d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) @ ( plus_p3455044024723400733d_enat @ A @ C ) )
% 15.55/8.65        = ( ( A != extend5688581933313929465d_enat )
% 15.55/8.65          & ( ord_le72135733267957522d_enat @ B @ C ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10025_enat__add__left__cancel,axiom,
% 15.55/8.65      ! [A: extended_enat,B: extended_enat,C: extended_enat] :
% 15.55/8.65        ( ( ( plus_p3455044024723400733d_enat @ A @ B )
% 15.55/8.65          = ( plus_p3455044024723400733d_enat @ A @ C ) )
% 15.55/8.65        = ( ( A = extend5688581933313929465d_enat )
% 15.55/8.65          | ( B = C ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10026_plus__eq__infty__iff__enat,axiom,
% 15.55/8.65      ! [M: extended_enat,N: extended_enat] :
% 15.55/8.65        ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 15.55/8.65          = extend5688581933313929465d_enat )
% 15.55/8.65        = ( ( M = extend5688581933313929465d_enat )
% 15.55/8.65          | ( N = extend5688581933313929465d_enat ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10027_infinity__ne__i1,axiom,
% 15.55/8.65      extend5688581933313929465d_enat != one_on7984719198319812577d_enat ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10028_top__enat__def,axiom,
% 15.55/8.65      top_to3028658606643905974d_enat = extend5688581933313929465d_enat ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10029_numeral__ne__infinity,axiom,
% 15.55/8.65      ! [K: num] :
% 15.55/8.65        ( ( numera1916890842035813515d_enat @ K )
% 15.55/8.65       != extend5688581933313929465d_enat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10030_Inf__enat__def,axiom,
% 15.55/8.65      ( comple2295165028678016749d_enat
% 15.55/8.65      = ( ^ [A8: set_Extended_enat] :
% 15.55/8.65            ( if_Extended_enat @ ( A8 = bot_bo7653980558646680370d_enat ) @ extend5688581933313929465d_enat
% 15.55/8.65            @ ( ord_Le1955565732374568822d_enat
% 15.55/8.65              @ ^ [X: extended_enat] : ( member_Extended_enat @ X @ A8 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10031_infinity__ne__i0,axiom,
% 15.55/8.65      extend5688581933313929465d_enat != zero_z5237406670263579293d_enat ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10032_imult__is__infinity,axiom,
% 15.55/8.65      ! [A: extended_enat,B: extended_enat] :
% 15.55/8.65        ( ( ( times_7803423173614009249d_enat @ A @ B )
% 15.55/8.65          = extend5688581933313929465d_enat )
% 15.55/8.65        = ( ( ( A = extend5688581933313929465d_enat )
% 15.55/8.65            & ( B != zero_z5237406670263579293d_enat ) )
% 15.55/8.65          | ( ( B = extend5688581933313929465d_enat )
% 15.55/8.65            & ( A != zero_z5237406670263579293d_enat ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10033_enat__ord__code_I4_J,axiom,
% 15.55/8.65      ! [M: nat] : ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M ) @ extend5688581933313929465d_enat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10034_less__infinityE,axiom,
% 15.55/8.65      ! [N: extended_enat] :
% 15.55/8.65        ( ( ord_le72135733267957522d_enat @ N @ extend5688581933313929465d_enat )
% 15.55/8.65       => ~ ! [K2: nat] :
% 15.55/8.65              ( N
% 15.55/8.65             != ( extended_enat2 @ K2 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10035_infinity__ilessE,axiom,
% 15.55/8.65      ! [M: nat] :
% 15.55/8.65        ~ ( ord_le72135733267957522d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ M ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10036_enat_Odistinct_I2_J,axiom,
% 15.55/8.65      ! [Nat: nat] :
% 15.55/8.65        ( extend5688581933313929465d_enat
% 15.55/8.65       != ( extended_enat2 @ Nat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10037_enat_Odistinct_I1_J,axiom,
% 15.55/8.65      ! [Nat: nat] :
% 15.55/8.65        ( ( extended_enat2 @ Nat )
% 15.55/8.65       != extend5688581933313929465d_enat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10038_enat_Oexhaust,axiom,
% 15.55/8.65      ! [Y3: extended_enat] :
% 15.55/8.65        ( ! [Nat3: nat] :
% 15.55/8.65            ( Y3
% 15.55/8.65           != ( extended_enat2 @ Nat3 ) )
% 15.55/8.65       => ( Y3 = extend5688581933313929465d_enat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10039_enat2__cases,axiom,
% 15.55/8.65      ! [Y3: extended_enat,Ya: extended_enat] :
% 15.55/8.65        ( ( ? [Nat3: nat] :
% 15.55/8.65              ( Y3
% 15.55/8.65              = ( extended_enat2 @ Nat3 ) )
% 15.55/8.65         => ! [Nata: nat] :
% 15.55/8.65              ( Ya
% 15.55/8.65             != ( extended_enat2 @ Nata ) ) )
% 15.55/8.65       => ( ( ? [Nat3: nat] :
% 15.55/8.65                ( Y3
% 15.55/8.65                = ( extended_enat2 @ Nat3 ) )
% 15.55/8.65           => ( Ya != extend5688581933313929465d_enat ) )
% 15.55/8.65         => ( ( ( Y3 = extend5688581933313929465d_enat )
% 15.55/8.65             => ! [Nat3: nat] :
% 15.55/8.65                  ( Ya
% 15.55/8.65                 != ( extended_enat2 @ Nat3 ) ) )
% 15.55/8.65           => ~ ( ( Y3 = extend5688581933313929465d_enat )
% 15.55/8.65               => ( Ya != extend5688581933313929465d_enat ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10040_enat3__cases,axiom,
% 15.55/8.65      ! [Y3: extended_enat,Ya: extended_enat,Yb: extended_enat] :
% 15.55/8.65        ( ( ? [Nat3: nat] :
% 15.55/8.65              ( Y3
% 15.55/8.65              = ( extended_enat2 @ Nat3 ) )
% 15.55/8.65         => ( ? [Nata: nat] :
% 15.55/8.65                ( Ya
% 15.55/8.65                = ( extended_enat2 @ Nata ) )
% 15.55/8.65           => ! [Natb: nat] :
% 15.55/8.65                ( Yb
% 15.55/8.65               != ( extended_enat2 @ Natb ) ) ) )
% 15.55/8.65       => ( ( ? [Nat3: nat] :
% 15.55/8.65                ( Y3
% 15.55/8.65                = ( extended_enat2 @ Nat3 ) )
% 15.55/8.65           => ( ? [Nata: nat] :
% 15.55/8.65                  ( Ya
% 15.55/8.65                  = ( extended_enat2 @ Nata ) )
% 15.55/8.65             => ( Yb != extend5688581933313929465d_enat ) ) )
% 15.55/8.65         => ( ( ? [Nat3: nat] :
% 15.55/8.65                  ( Y3
% 15.55/8.65                  = ( extended_enat2 @ Nat3 ) )
% 15.55/8.65             => ( ( Ya = extend5688581933313929465d_enat )
% 15.55/8.65               => ! [Nata: nat] :
% 15.55/8.65                    ( Yb
% 15.55/8.65                   != ( extended_enat2 @ Nata ) ) ) )
% 15.55/8.65           => ( ( ? [Nat3: nat] :
% 15.55/8.65                    ( Y3
% 15.55/8.65                    = ( extended_enat2 @ Nat3 ) )
% 15.55/8.65               => ( ( Ya = extend5688581933313929465d_enat )
% 15.55/8.65                 => ( Yb != extend5688581933313929465d_enat ) ) )
% 15.55/8.65             => ( ( ( Y3 = extend5688581933313929465d_enat )
% 15.55/8.65                 => ( ? [Nat3: nat] :
% 15.55/8.65                        ( Ya
% 15.55/8.65                        = ( extended_enat2 @ Nat3 ) )
% 15.55/8.65                   => ! [Nata: nat] :
% 15.55/8.65                        ( Yb
% 15.55/8.65                       != ( extended_enat2 @ Nata ) ) ) )
% 15.55/8.65               => ( ( ( Y3 = extend5688581933313929465d_enat )
% 15.55/8.65                   => ( ? [Nat3: nat] :
% 15.55/8.65                          ( Ya
% 15.55/8.65                          = ( extended_enat2 @ Nat3 ) )
% 15.55/8.65                     => ( Yb != extend5688581933313929465d_enat ) ) )
% 15.55/8.65                 => ( ( ( Y3 = extend5688581933313929465d_enat )
% 15.55/8.65                     => ( ( Ya = extend5688581933313929465d_enat )
% 15.55/8.65                       => ! [Nat3: nat] :
% 15.55/8.65                            ( Yb
% 15.55/8.65                           != ( extended_enat2 @ Nat3 ) ) ) )
% 15.55/8.65                   => ~ ( ( Y3 = extend5688581933313929465d_enat )
% 15.55/8.65                       => ( ( Ya = extend5688581933313929465d_enat )
% 15.55/8.65                         => ( Yb != extend5688581933313929465d_enat ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10041_enat__ex__split,axiom,
% 15.55/8.65      ( ( ^ [P2: extended_enat > $o] :
% 15.55/8.65          ? [X5: extended_enat] : ( P2 @ X5 ) )
% 15.55/8.65      = ( ^ [P3: extended_enat > $o] :
% 15.55/8.65            ( ( P3 @ extend5688581933313929465d_enat )
% 15.55/8.65            | ? [X: nat] : ( P3 @ ( extended_enat2 @ X ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10042_infinity__ileE,axiom,
% 15.55/8.65      ! [M: nat] :
% 15.55/8.65        ~ ( ord_le2932123472753598470d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ M ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10043_enat__ord__code_I5_J,axiom,
% 15.55/8.65      ! [N: nat] :
% 15.55/8.65        ~ ( ord_le2932123472753598470d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10044_plus__enat__def,axiom,
% 15.55/8.65      ( plus_p3455044024723400733d_enat
% 15.55/8.65      = ( ^ [M3: extended_enat,N3: extended_enat] :
% 15.55/8.65            ( extend3600170679010898289d_enat
% 15.55/8.65            @ ^ [O: nat] :
% 15.55/8.65                ( extend3600170679010898289d_enat
% 15.55/8.65                @ ^ [P5: nat] : ( extended_enat2 @ ( plus_plus_nat @ O @ P5 ) )
% 15.55/8.65                @ extend5688581933313929465d_enat
% 15.55/8.65                @ N3 )
% 15.55/8.65            @ extend5688581933313929465d_enat
% 15.55/8.65            @ M3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10045_imult__infinity__right,axiom,
% 15.55/8.65      ! [N: extended_enat] :
% 15.55/8.65        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 15.55/8.65       => ( ( times_7803423173614009249d_enat @ N @ extend5688581933313929465d_enat )
% 15.55/8.65          = extend5688581933313929465d_enat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10046_imult__infinity,axiom,
% 15.55/8.65      ! [N: extended_enat] :
% 15.55/8.65        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 15.55/8.65       => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ N )
% 15.55/8.65          = extend5688581933313929465d_enat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10047_diff__enat__def,axiom,
% 15.55/8.65      ( minus_3235023915231533773d_enat
% 15.55/8.65      = ( ^ [A4: extended_enat,B3: extended_enat] :
% 15.55/8.65            ( extend3600170679010898289d_enat
% 15.55/8.65            @ ^ [X: nat] :
% 15.55/8.65                ( extend3600170679010898289d_enat
% 15.55/8.65                @ ^ [Y: nat] : ( extended_enat2 @ ( minus_minus_nat @ X @ Y ) )
% 15.55/8.65                @ zero_z5237406670263579293d_enat
% 15.55/8.65                @ B3 )
% 15.55/8.65            @ extend5688581933313929465d_enat
% 15.55/8.65            @ A4 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10048_times__enat__def,axiom,
% 15.55/8.65      ( times_7803423173614009249d_enat
% 15.55/8.65      = ( ^ [M3: extended_enat,N3: extended_enat] :
% 15.55/8.65            ( extend3600170679010898289d_enat
% 15.55/8.65            @ ^ [O: nat] :
% 15.55/8.65                ( extend3600170679010898289d_enat
% 15.55/8.65                @ ^ [P5: nat] : ( extended_enat2 @ ( times_times_nat @ O @ P5 ) )
% 15.55/8.65                @ ( if_Extended_enat @ ( O = zero_zero_nat ) @ zero_z5237406670263579293d_enat @ extend5688581933313929465d_enat )
% 15.55/8.65                @ N3 )
% 15.55/8.65            @ ( if_Extended_enat @ ( N3 = zero_z5237406670263579293d_enat ) @ zero_z5237406670263579293d_enat @ extend5688581933313929465d_enat )
% 15.55/8.65            @ M3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10049_VEBT__internal_Oelim__dead_Opelims,axiom,
% 15.55/8.65      ! [X3: vEBT_VEBT,Xa: extended_enat,Y3: vEBT_VEBT] :
% 15.55/8.65        ( ( ( vEBT_VEBT_elim_dead @ X3 @ Xa )
% 15.55/8.65          = Y3 )
% 15.55/8.65       => ( ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ X3 @ Xa ) )
% 15.55/8.65         => ( ! [A5: $o,B4: $o] :
% 15.55/8.65                ( ( X3
% 15.55/8.65                  = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.65               => ( ( Y3
% 15.55/8.65                    = ( vEBT_Leaf @ A5 @ B4 ) )
% 15.55/8.65                 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Leaf @ A5 @ B4 ) @ Xa ) ) ) )
% 15.55/8.65           => ( ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.65                  ( ( X3
% 15.55/8.65                    = ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary2 ) )
% 15.55/8.65                 => ( ( Xa = extend5688581933313929465d_enat )
% 15.55/8.65                   => ( ( Y3
% 15.55/8.65                        = ( vEBT_Node @ Info2 @ Deg2
% 15.55/8.65                          @ ( map_VE8901447254227204932T_VEBT
% 15.55/8.65                            @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.65                            @ TreeList3 )
% 15.55/8.65                          @ ( vEBT_VEBT_elim_dead @ Summary2 @ extend5688581933313929465d_enat ) ) )
% 15.55/8.65                     => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary2 ) @ extend5688581933313929465d_enat ) ) ) ) )
% 15.55/8.65             => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 15.55/8.65                    ( ( X3
% 15.55/8.65                      = ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary2 ) )
% 15.55/8.65                   => ! [L4: nat] :
% 15.55/8.65                        ( ( Xa
% 15.55/8.65                          = ( extended_enat2 @ L4 ) )
% 15.55/8.65                       => ( ( Y3
% 15.55/8.65                            = ( vEBT_Node @ Info2 @ Deg2
% 15.55/8.65                              @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 15.55/8.65                                @ ( map_VE8901447254227204932T_VEBT
% 15.55/8.65                                  @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 15.55/8.65                                  @ TreeList3 ) )
% 15.55/8.65                              @ ( vEBT_VEBT_elim_dead @ Summary2 @ ( extended_enat2 @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 15.55/8.65                         => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary2 ) @ ( extended_enat2 @ L4 ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10050_the__enat_Osimps,axiom,
% 15.55/8.65      ! [N: nat] :
% 15.55/8.65        ( ( extended_the_enat @ ( extended_enat2 @ N ) )
% 15.55/8.65        = N ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10051_eSuc__Max,axiom,
% 15.55/8.65      ! [A3: set_Extended_enat] :
% 15.55/8.65        ( ( finite4001608067531595151d_enat @ A3 )
% 15.55/8.65       => ( ( A3 != bot_bo7653980558646680370d_enat )
% 15.55/8.65         => ( ( extended_eSuc @ ( lattic921264341876707157d_enat @ A3 ) )
% 15.55/8.65            = ( lattic921264341876707157d_enat @ ( image_80655429650038917d_enat @ extended_eSuc @ A3 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10052_eSuc__inject,axiom,
% 15.55/8.65      ! [M: extended_enat,N: extended_enat] :
% 15.55/8.65        ( ( ( extended_eSuc @ M )
% 15.55/8.65          = ( extended_eSuc @ N ) )
% 15.55/8.65        = ( M = N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10053_eSuc__infinity,axiom,
% 15.55/8.65      ( ( extended_eSuc @ extend5688581933313929465d_enat )
% 15.55/8.65      = extend5688581933313929465d_enat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10054_eSuc__mono,axiom,
% 15.55/8.65      ! [N: extended_enat,M: extended_enat] :
% 15.55/8.65        ( ( ord_le72135733267957522d_enat @ ( extended_eSuc @ N ) @ ( extended_eSuc @ M ) )
% 15.55/8.65        = ( ord_le72135733267957522d_enat @ N @ M ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10055_eSuc__ile__mono,axiom,
% 15.55/8.65      ! [N: extended_enat,M: extended_enat] :
% 15.55/8.65        ( ( ord_le2932123472753598470d_enat @ ( extended_eSuc @ N ) @ ( extended_eSuc @ M ) )
% 15.55/8.65        = ( ord_le2932123472753598470d_enat @ N @ M ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10056_eSuc__minus__eSuc,axiom,
% 15.55/8.65      ! [N: extended_enat,M: extended_enat] :
% 15.55/8.65        ( ( minus_3235023915231533773d_enat @ ( extended_eSuc @ N ) @ ( extended_eSuc @ M ) )
% 15.55/8.65        = ( minus_3235023915231533773d_enat @ N @ M ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10057_iless__eSuc0,axiom,
% 15.55/8.65      ! [N: extended_enat] :
% 15.55/8.65        ( ( ord_le72135733267957522d_enat @ N @ ( extended_eSuc @ zero_z5237406670263579293d_enat ) )
% 15.55/8.65        = ( N = zero_z5237406670263579293d_enat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10058_eSuc__minus__1,axiom,
% 15.55/8.65      ! [N: extended_enat] :
% 15.55/8.65        ( ( minus_3235023915231533773d_enat @ ( extended_eSuc @ N ) @ one_on7984719198319812577d_enat )
% 15.55/8.65        = N ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10059_eSuc__numeral,axiom,
% 15.55/8.65      ! [K: num] :
% 15.55/8.65        ( ( extended_eSuc @ ( numera1916890842035813515d_enat @ K ) )
% 15.55/8.65        = ( numera1916890842035813515d_enat @ ( plus_plus_num @ K @ one ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10060_iless__Suc__eq,axiom,
% 15.55/8.65      ! [M: nat,N: extended_enat] :
% 15.55/8.65        ( ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M ) @ ( extended_eSuc @ N ) )
% 15.55/8.65        = ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ M ) @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10061_ile__eSuc,axiom,
% 15.55/8.65      ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ N @ ( extended_eSuc @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10062_ileI1,axiom,
% 15.55/8.65      ! [M: extended_enat,N: extended_enat] :
% 15.55/8.65        ( ( ord_le72135733267957522d_enat @ M @ N )
% 15.55/8.65       => ( ord_le2932123472753598470d_enat @ ( extended_eSuc @ M ) @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10063_eSuc__plus__1,axiom,
% 15.55/8.65      ( extended_eSuc
% 15.55/8.65      = ( ^ [N3: extended_enat] : ( plus_p3455044024723400733d_enat @ N3 @ one_on7984719198319812577d_enat ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10064_plus__1__eSuc_I1_J,axiom,
% 15.55/8.65      ! [Q3: extended_enat] :
% 15.55/8.65        ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ Q3 )
% 15.55/8.65        = ( extended_eSuc @ Q3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10065_plus__1__eSuc_I2_J,axiom,
% 15.55/8.65      ! [Q3: extended_enat] :
% 15.55/8.65        ( ( plus_p3455044024723400733d_enat @ Q3 @ one_on7984719198319812577d_enat )
% 15.55/8.65        = ( extended_eSuc @ Q3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10066_mono__eSuc,axiom,
% 15.55/8.65      order_4130057895858720880d_enat @ extended_eSuc ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10067_iadd__Suc,axiom,
% 15.55/8.65      ! [M: extended_enat,N: extended_enat] :
% 15.55/8.65        ( ( plus_p3455044024723400733d_enat @ ( extended_eSuc @ M ) @ N )
% 15.55/8.65        = ( extended_eSuc @ ( plus_p3455044024723400733d_enat @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10068_iadd__Suc__right,axiom,
% 15.55/8.65      ! [M: extended_enat,N: extended_enat] :
% 15.55/8.65        ( ( plus_p3455044024723400733d_enat @ M @ ( extended_eSuc @ N ) )
% 15.55/8.65        = ( extended_eSuc @ ( plus_p3455044024723400733d_enat @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10069_eSuc__max,axiom,
% 15.55/8.65      ! [X3: extended_enat,Y3: extended_enat] :
% 15.55/8.65        ( ( extended_eSuc @ ( ord_ma741700101516333627d_enat @ X3 @ Y3 ) )
% 15.55/8.65        = ( ord_ma741700101516333627d_enat @ ( extended_eSuc @ X3 ) @ ( extended_eSuc @ Y3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10070_mult__eSuc__right,axiom,
% 15.55/8.65      ! [M: extended_enat,N: extended_enat] :
% 15.55/8.65        ( ( times_7803423173614009249d_enat @ M @ ( extended_eSuc @ N ) )
% 15.55/8.65        = ( plus_p3455044024723400733d_enat @ M @ ( times_7803423173614009249d_enat @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10071_mult__eSuc,axiom,
% 15.55/8.65      ! [M: extended_enat,N: extended_enat] :
% 15.55/8.65        ( ( times_7803423173614009249d_enat @ ( extended_eSuc @ M ) @ N )
% 15.55/8.65        = ( plus_p3455044024723400733d_enat @ N @ ( times_7803423173614009249d_enat @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10072_zero__ne__eSuc,axiom,
% 15.55/8.65      ! [N: extended_enat] :
% 15.55/8.65        ( zero_z5237406670263579293d_enat
% 15.55/8.65       != ( extended_eSuc @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10073_i0__iless__eSuc,axiom,
% 15.55/8.65      ! [N: extended_enat] : ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( extended_eSuc @ N ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10074_one__eSuc,axiom,
% 15.55/8.65      ( one_on7984719198319812577d_enat
% 15.55/8.65      = ( extended_eSuc @ zero_z5237406670263579293d_enat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10075_not__eSuc__ilei0,axiom,
% 15.55/8.65      ! [N: extended_enat] :
% 15.55/8.65        ~ ( ord_le2932123472753598470d_enat @ ( extended_eSuc @ N ) @ zero_z5237406670263579293d_enat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10076_enat__eSuc__iff,axiom,
% 15.55/8.65      ! [Y3: nat,X3: extended_enat] :
% 15.55/8.65        ( ( ( extended_enat2 @ Y3 )
% 15.55/8.65          = ( extended_eSuc @ X3 ) )
% 15.55/8.65        = ( ? [N3: nat] :
% 15.55/8.65              ( ( Y3
% 15.55/8.65                = ( suc @ N3 ) )
% 15.55/8.65              & ( ( extended_enat2 @ N3 )
% 15.55/8.65                = X3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10077_eSuc__enat__iff,axiom,
% 15.55/8.65      ! [X3: extended_enat,Y3: nat] :
% 15.55/8.65        ( ( ( extended_eSuc @ X3 )
% 15.55/8.65          = ( extended_enat2 @ Y3 ) )
% 15.55/8.65        = ( ? [N3: nat] :
% 15.55/8.65              ( ( Y3
% 15.55/8.65                = ( suc @ N3 ) )
% 15.55/8.65              & ( X3
% 15.55/8.65                = ( extended_enat2 @ N3 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10078_eSuc__enat,axiom,
% 15.55/8.65      ! [N: nat] :
% 15.55/8.65        ( ( extended_eSuc @ ( extended_enat2 @ N ) )
% 15.55/8.65        = ( extended_enat2 @ ( suc @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10079_eSuc__Sup,axiom,
% 15.55/8.65      ! [A3: set_Extended_enat] :
% 15.55/8.65        ( ( A3 != bot_bo7653980558646680370d_enat )
% 15.55/8.65       => ( ( extended_eSuc @ ( comple4398354569131411667d_enat @ A3 ) )
% 15.55/8.65          = ( comple4398354569131411667d_enat @ ( image_80655429650038917d_enat @ extended_eSuc @ A3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10080_eSuc__def,axiom,
% 15.55/8.65      ( extended_eSuc
% 15.55/8.65      = ( extend3600170679010898289d_enat
% 15.55/8.65        @ ^ [N3: nat] : ( extended_enat2 @ ( suc @ N3 ) )
% 15.55/8.65        @ extend5688581933313929465d_enat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10081_sub_Otransfer,axiom,
% 15.55/8.65      ( bNF_re7876454716742015248nteger
% 15.55/8.65      @ ^ [Y5: num,Z2: num] : ( Y5 = Z2 )
% 15.55/8.65      @ ( bNF_re6501075790457514782nteger
% 15.55/8.65        @ ^ [Y5: num,Z2: num] : ( Y5 = Z2 )
% 15.55/8.65        @ code_pcr_integer )
% 15.55/8.65      @ ^ [M3: num,N3: num] : ( minus_minus_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N3 ) )
% 15.55/8.65      @ code_sub ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10082_Code__Numeral_Osub__code_I1_J,axiom,
% 15.55/8.65      ( ( code_sub @ one @ one )
% 15.55/8.65      = zero_z3403309356797280102nteger ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10083_sub_Orep__eq,axiom,
% 15.55/8.65      ! [X3: num,Xa: num] :
% 15.55/8.65        ( ( code_int_of_integer @ ( code_sub @ X3 @ Xa ) )
% 15.55/8.65        = ( minus_minus_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Xa ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10084_sub_Oabs__eq,axiom,
% 15.55/8.65      ( code_sub
% 15.55/8.65      = ( ^ [Xa4: num,X: num] : ( code_integer_of_int @ ( minus_minus_int @ ( numeral_numeral_int @ Xa4 ) @ ( numeral_numeral_int @ X ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10085_Code__Numeral_Osub__code_I9_J,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( code_sub @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 15.55/8.65        = ( minus_8373710615458151222nteger @ ( code_dup @ ( code_sub @ M @ N ) ) @ one_one_Code_integer ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10086_Code__Numeral_Osub__code_I8_J,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( code_sub @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 15.55/8.65        = ( plus_p5714425477246183910nteger @ ( code_dup @ ( code_sub @ M @ N ) ) @ one_one_Code_integer ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10087_Code__Numeral_Odup__code_I1_J,axiom,
% 15.55/8.65      ( ( code_dup @ zero_z3403309356797280102nteger )
% 15.55/8.65      = zero_z3403309356797280102nteger ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10088_Code__Numeral_Osub__code_I6_J,axiom,
% 15.55/8.65      ! [M: num,N: num] :
% 15.55/8.65        ( ( code_sub @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 15.55/8.65        = ( code_dup @ ( code_sub @ M @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10089_Code__Numeral_Osub__code_I4_J,axiom,
% 15.55/8.65      ! [N: num] :
% 15.55/8.65        ( ( code_sub @ one @ ( bit0 @ N ) )
% 15.55/8.65        = ( code_Neg @ ( bitM @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10090_less__than__iff,axiom,
% 15.55/8.65      ! [X3: nat,Y3: nat] :
% 15.55/8.65        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ less_than )
% 15.55/8.65        = ( ord_less_nat @ X3 @ Y3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10091_Code__Numeral_Odup__code_I3_J,axiom,
% 15.55/8.65      ! [N: num] :
% 15.55/8.65        ( ( code_dup @ ( code_Neg @ N ) )
% 15.55/8.65        = ( code_Neg @ ( bit0 @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10092_less__eq__integer__code_I7_J,axiom,
% 15.55/8.65      ! [K: num] : ( ord_le3102999989581377725nteger @ ( code_Neg @ K ) @ zero_z3403309356797280102nteger ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10093_less__eq__integer__code_I3_J,axiom,
% 15.55/8.65      ! [L: num] :
% 15.55/8.65        ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( code_Neg @ L ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10094_less__integer__code_I3_J,axiom,
% 15.55/8.65      ! [L: num] :
% 15.55/8.65        ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( code_Neg @ L ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10095_less__integer__code_I7_J,axiom,
% 15.55/8.65      ! [K: num] : ( ord_le6747313008572928689nteger @ ( code_Neg @ K ) @ zero_z3403309356797280102nteger ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10096_less__integer__code_I9_J,axiom,
% 15.55/8.65      ! [K: num,L: num] :
% 15.55/8.65        ( ( ord_le6747313008572928689nteger @ ( code_Neg @ K ) @ ( code_Neg @ L ) )
% 15.55/8.65        = ( ord_less_num @ L @ K ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10097_less__eq__integer__code_I9_J,axiom,
% 15.55/8.65      ! [K: num,L: num] :
% 15.55/8.65        ( ( ord_le3102999989581377725nteger @ ( code_Neg @ K ) @ ( code_Neg @ L ) )
% 15.55/8.65        = ( ord_less_eq_num @ L @ K ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10098_Code__Numeral_Osub__code_I5_J,axiom,
% 15.55/8.65      ! [N: num] :
% 15.55/8.65        ( ( code_sub @ one @ ( bit1 @ N ) )
% 15.55/8.65        = ( code_Neg @ ( bit0 @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10099_pair__less__def,axiom,
% 15.55/8.65      ( fun_pair_less
% 15.55/8.65      = ( lex_prod_nat_nat @ less_than @ less_than ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10100_Gcd__nat__set__eq__fold,axiom,
% 15.55/8.65      ! [Xs2: list_nat] :
% 15.55/8.65        ( ( gcd_Gcd_nat @ ( set_nat2 @ Xs2 ) )
% 15.55/8.65        = ( fold_nat_nat @ gcd_gcd_nat @ Xs2 @ zero_zero_nat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10101_Quotient__real,axiom,
% 15.55/8.65      quotie3684837364556693515t_real @ realrel @ real2 @ rep_real @ cr_real ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10102_Code__Numeral_Osub__code_I2_J,axiom,
% 15.55/8.65      ! [M: num] :
% 15.55/8.65        ( ( code_sub @ ( bit0 @ M ) @ one )
% 15.55/8.65        = ( code_Pos @ ( bitM @ M ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10103_Code__Numeral_Odup__code_I2_J,axiom,
% 15.55/8.65      ! [N: num] :
% 15.55/8.65        ( ( code_dup @ ( code_Pos @ N ) )
% 15.55/8.65        = ( code_Pos @ ( bit0 @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10104_less__eq__integer__code_I4_J,axiom,
% 15.55/8.65      ! [K: num] :
% 15.55/8.65        ~ ( ord_le3102999989581377725nteger @ ( code_Pos @ K ) @ zero_z3403309356797280102nteger ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10105_less__eq__integer__code_I2_J,axiom,
% 15.55/8.65      ! [L: num] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( code_Pos @ L ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10106_less__integer__code_I2_J,axiom,
% 15.55/8.65      ! [L: num] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( code_Pos @ L ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10107_less__integer__code_I4_J,axiom,
% 15.55/8.65      ! [K: num] :
% 15.55/8.65        ~ ( ord_le6747313008572928689nteger @ ( code_Pos @ K ) @ zero_z3403309356797280102nteger ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10108_less__integer__code_I5_J,axiom,
% 15.55/8.65      ! [K: num,L: num] :
% 15.55/8.65        ( ( ord_le6747313008572928689nteger @ ( code_Pos @ K ) @ ( code_Pos @ L ) )
% 15.55/8.65        = ( ord_less_num @ K @ L ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10109_one__integer__code,axiom,
% 15.55/8.65      ( one_one_Code_integer
% 15.55/8.65      = ( code_Pos @ one ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10110_Pos__fold_I2_J,axiom,
% 15.55/8.65      ! [K: num] :
% 15.55/8.65        ( ( numera6620942414471956472nteger @ ( bit0 @ K ) )
% 15.55/8.65        = ( code_Pos @ ( bit0 @ K ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10111_Pos__fold_I1_J,axiom,
% 15.55/8.65      ( ( numera6620942414471956472nteger @ one )
% 15.55/8.65      = ( code_Pos @ one ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10112_less__eq__integer__code_I5_J,axiom,
% 15.55/8.65      ! [K: num,L: num] :
% 15.55/8.65        ( ( ord_le3102999989581377725nteger @ ( code_Pos @ K ) @ ( code_Pos @ L ) )
% 15.55/8.65        = ( ord_less_eq_num @ K @ L ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10113_Gcd__int__set__eq__fold,axiom,
% 15.55/8.65      ! [Xs2: list_int] :
% 15.55/8.65        ( ( gcd_Gcd_int @ ( set_int2 @ Xs2 ) )
% 15.55/8.65        = ( fold_int_int @ gcd_gcd_int @ Xs2 @ zero_zero_int ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10114_Code__Numeral_Osub__code_I3_J,axiom,
% 15.55/8.65      ! [M: num] :
% 15.55/8.65        ( ( code_sub @ ( bit1 @ M ) @ one )
% 15.55/8.65        = ( code_Pos @ ( bit0 @ M ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10115_cr__int__def,axiom,
% 15.55/8.65      ( cr_int
% 15.55/8.65      = ( ^ [X: product_prod_nat_nat] :
% 15.55/8.65            ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 15.55/8.65            @ ( abs_Integ @ X ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10116_int_Opcr__cr__eq,axiom,
% 15.55/8.65      pcr_int = cr_int ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10117_Quotient__int,axiom,
% 15.55/8.65      quotie1194848508323700631at_int @ intrel @ abs_Integ @ rep_Integ @ cr_int ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10118_gcd__nat_Osemilattice__neutr__axioms,axiom,
% 15.55/8.65      semila9081495762789891438tr_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10119_max__nat_Osemilattice__neutr__axioms,axiom,
% 15.55/8.65      semila9081495762789891438tr_nat @ ord_max_nat @ zero_zero_nat ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10120_natLess__def,axiom,
% 15.55/8.65      ( bNF_Ca8459412986667044542atLess
% 15.55/8.65      = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10121_Restr__natLeq,axiom,
% 15.55/8.65      ! [N: nat] :
% 15.55/8.65        ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 15.55/8.65          @ ( produc457027306803732586at_nat
% 15.55/8.65            @ ( collect_nat
% 15.55/8.65              @ ^ [X: nat] : ( ord_less_nat @ X @ N ) )
% 15.55/8.65            @ ^ [Uu3: nat] :
% 15.55/8.65                ( collect_nat
% 15.55/8.65                @ ^ [X: nat] : ( ord_less_nat @ X @ N ) ) ) )
% 15.55/8.65        = ( collec3392354462482085612at_nat
% 15.55/8.65          @ ( produc6081775807080527818_nat_o
% 15.55/8.65            @ ^ [X: nat,Y: nat] :
% 15.55/8.65                ( ( ord_less_nat @ X @ N )
% 15.55/8.65                & ( ord_less_nat @ Y @ N )
% 15.55/8.65                & ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10122_natLeq__def,axiom,
% 15.55/8.65      ( bNF_Ca8665028551170535155natLeq
% 15.55/8.65      = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_eq_nat ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10123_Restr__natLeq2,axiom,
% 15.55/8.65      ! [N: nat] :
% 15.55/8.65        ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 15.55/8.65          @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 15.55/8.65            @ ^ [Uu3: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N ) ) )
% 15.55/8.65        = ( collec3392354462482085612at_nat
% 15.55/8.65          @ ( produc6081775807080527818_nat_o
% 15.55/8.65            @ ^ [X: nat,Y: nat] :
% 15.55/8.65                ( ( ord_less_nat @ X @ N )
% 15.55/8.65                & ( ord_less_nat @ Y @ N )
% 15.55/8.65                & ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10124_natLeq__underS__less,axiom,
% 15.55/8.65      ! [N: nat] :
% 15.55/8.65        ( ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 15.55/8.65        = ( collect_nat
% 15.55/8.65          @ ^ [X: nat] : ( ord_less_nat @ X @ N ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10125_gcd__nat_Omonoid__axioms,axiom,
% 15.55/8.65      monoid_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10126_max__nat_Omonoid__axioms,axiom,
% 15.55/8.65      monoid_nat @ ord_max_nat @ zero_zero_nat ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10127_infinity__enat__def,axiom,
% 15.55/8.65      ( extend5688581933313929465d_enat
% 15.55/8.65      = ( extended_Abs_enat @ none_nat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10128_Abs__enat__cases,axiom,
% 15.55/8.65      ! [X3: extended_enat] :
% 15.55/8.65        ~ ! [Y4: option_nat] :
% 15.55/8.65            ( ( X3
% 15.55/8.65              = ( extended_Abs_enat @ Y4 ) )
% 15.55/8.65           => ~ ( member_option_nat @ Y4 @ top_to8920198386146353926on_nat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10129_Abs__enat__induct,axiom,
% 15.55/8.65      ! [P: extended_enat > $o,X3: extended_enat] :
% 15.55/8.65        ( ! [Y4: option_nat] :
% 15.55/8.65            ( ( member_option_nat @ Y4 @ top_to8920198386146353926on_nat )
% 15.55/8.65           => ( P @ ( extended_Abs_enat @ Y4 ) ) )
% 15.55/8.65       => ( P @ X3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10130_Abs__enat__inject,axiom,
% 15.55/8.65      ! [X3: option_nat,Y3: option_nat] :
% 15.55/8.65        ( ( member_option_nat @ X3 @ top_to8920198386146353926on_nat )
% 15.55/8.65       => ( ( member_option_nat @ Y3 @ top_to8920198386146353926on_nat )
% 15.55/8.65         => ( ( ( extended_Abs_enat @ X3 )
% 15.55/8.65              = ( extended_Abs_enat @ Y3 ) )
% 15.55/8.65            = ( X3 = Y3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10131_enat__def,axiom,
% 15.55/8.65      ( extended_enat2
% 15.55/8.65      = ( ^ [N3: nat] : ( extended_Abs_enat @ ( some_nat @ N3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10132_Abs__enat__inverse,axiom,
% 15.55/8.65      ! [Y3: option_nat] :
% 15.55/8.65        ( ( member_option_nat @ Y3 @ top_to8920198386146353926on_nat )
% 15.55/8.65       => ( ( extended_Rep_enat @ ( extended_Abs_enat @ Y3 ) )
% 15.55/8.65          = Y3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10133_Rep__enat__induct,axiom,
% 15.55/8.65      ! [Y3: option_nat,P: option_nat > $o] :
% 15.55/8.65        ( ( member_option_nat @ Y3 @ top_to8920198386146353926on_nat )
% 15.55/8.65       => ( ! [X4: extended_enat] : ( P @ ( extended_Rep_enat @ X4 ) )
% 15.55/8.65         => ( P @ Y3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10134_Rep__enat__cases,axiom,
% 15.55/8.65      ! [Y3: option_nat] :
% 15.55/8.65        ( ( member_option_nat @ Y3 @ top_to8920198386146353926on_nat )
% 15.55/8.65       => ~ ! [X4: extended_enat] :
% 15.55/8.65              ( Y3
% 15.55/8.65             != ( extended_Rep_enat @ X4 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10135_Rep__enat,axiom,
% 15.55/8.65      ! [X3: extended_enat] : ( member_option_nat @ ( extended_Rep_enat @ X3 ) @ top_to8920198386146353926on_nat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10136_Rep__enat__inject,axiom,
% 15.55/8.65      ! [X3: extended_enat,Y3: extended_enat] :
% 15.55/8.65        ( ( ( extended_Rep_enat @ X3 )
% 15.55/8.65          = ( extended_Rep_enat @ Y3 ) )
% 15.55/8.65        = ( X3 = Y3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10137_Rep__enat__inverse,axiom,
% 15.55/8.65      ! [X3: extended_enat] :
% 15.55/8.65        ( ( extended_Abs_enat @ ( extended_Rep_enat @ X3 ) )
% 15.55/8.65        = X3 ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10138_type__definition__enat,axiom,
% 15.55/8.65      type_d7649664348572268762on_nat @ extended_Rep_enat @ extended_Abs_enat @ top_to8920198386146353926on_nat ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10139_list__encode_Oelims,axiom,
% 15.55/8.65      ! [X3: list_nat,Y3: nat] :
% 15.55/8.65        ( ( ( nat_list_encode @ X3 )
% 15.55/8.65          = Y3 )
% 15.55/8.65       => ( ( ( X3 = nil_nat )
% 15.55/8.65           => ( Y3 != zero_zero_nat ) )
% 15.55/8.65         => ~ ! [X4: nat,Xs3: list_nat] :
% 15.55/8.65                ( ( X3
% 15.55/8.65                  = ( cons_nat @ X4 @ Xs3 ) )
% 15.55/8.65               => ( Y3
% 15.55/8.65                 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs3 ) ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10140_le__prod__encode__1,axiom,
% 15.55/8.65      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10141_le__prod__encode__2,axiom,
% 15.55/8.65      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10142_list__encode_Osimps_I1_J,axiom,
% 15.55/8.65      ( ( nat_list_encode @ nil_nat )
% 15.55/8.65      = zero_zero_nat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10143_list__encode_Opelims,axiom,
% 15.55/8.65      ! [X3: list_nat,Y3: nat] :
% 15.55/8.65        ( ( ( nat_list_encode @ X3 )
% 15.55/8.65          = Y3 )
% 15.55/8.65       => ( ( accp_list_nat @ nat_list_encode_rel @ X3 )
% 15.55/8.65         => ( ( ( X3 = nil_nat )
% 15.55/8.65             => ( ( Y3 = zero_zero_nat )
% 15.55/8.65               => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 15.55/8.65           => ~ ! [X4: nat,Xs3: list_nat] :
% 15.55/8.65                  ( ( X3
% 15.55/8.65                    = ( cons_nat @ X4 @ Xs3 ) )
% 15.55/8.65                 => ( ( Y3
% 15.55/8.65                      = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs3 ) ) ) ) )
% 15.55/8.65                   => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X4 @ Xs3 ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10144_wf__less,axiom,
% 15.55/8.65      wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10145_wf__pair__less,axiom,
% 15.55/8.65      wf_Pro7803398752247294826at_nat @ fun_pair_less ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10146_wf__int__ge__less__than2,axiom,
% 15.55/8.65      ! [D3: int] : ( wf_int @ ( int_ge_less_than2 @ D3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10147_wf__int__ge__less__than,axiom,
% 15.55/8.65      ! [D3: int] : ( wf_int @ ( int_ge_less_than @ D3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10148_prod__decode__def,axiom,
% 15.55/8.65      ( nat_prod_decode
% 15.55/8.65      = ( nat_prod_decode_aux @ zero_zero_nat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10149_max__nat_Ocomm__monoid__axioms,axiom,
% 15.55/8.65      comm_monoid_nat @ ord_max_nat @ zero_zero_nat ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10150_gcd__nat_Ocomm__monoid__axioms,axiom,
% 15.55/8.65      comm_monoid_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10151_list__decode_Opinduct,axiom,
% 15.55/8.65      ! [A0: nat,P: nat > $o] :
% 15.55/8.65        ( ( accp_nat @ nat_list_decode_rel @ A0 )
% 15.55/8.65       => ( ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 15.55/8.65           => ( P @ zero_zero_nat ) )
% 15.55/8.65         => ( ! [N2: nat] :
% 15.55/8.65                ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N2 ) )
% 15.55/8.65               => ( ! [X6: nat,Y6: nat] :
% 15.55/8.65                      ( ( ( product_Pair_nat_nat @ X6 @ Y6 )
% 15.55/8.65                        = ( nat_prod_decode @ N2 ) )
% 15.55/8.65                     => ( P @ Y6 ) )
% 15.55/8.65                 => ( P @ ( suc @ N2 ) ) ) )
% 15.55/8.65           => ( P @ A0 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10152_list__decode_Oelims,axiom,
% 15.55/8.65      ! [X3: nat,Y3: list_nat] :
% 15.55/8.65        ( ( ( nat_list_decode @ X3 )
% 15.55/8.65          = Y3 )
% 15.55/8.65       => ( ( ( X3 = zero_zero_nat )
% 15.55/8.65           => ( Y3 != nil_nat ) )
% 15.55/8.65         => ~ ! [N2: nat] :
% 15.55/8.65                ( ( X3
% 15.55/8.65                  = ( suc @ N2 ) )
% 15.55/8.65               => ( Y3
% 15.55/8.65                 != ( produc2761476792215241774st_nat
% 15.55/8.65                    @ ^ [X: nat,Y: nat] : ( cons_nat @ X @ ( nat_list_decode @ Y ) )
% 15.55/8.65                    @ ( nat_prod_decode @ N2 ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10153_list__decode_Opsimps_I1_J,axiom,
% 15.55/8.65      ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 15.55/8.65     => ( ( nat_list_decode @ zero_zero_nat )
% 15.55/8.65        = nil_nat ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10154_list__decode_Osimps_I1_J,axiom,
% 15.55/8.65      ( ( nat_list_decode @ zero_zero_nat )
% 15.55/8.65      = nil_nat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10155_list__decode_Opelims,axiom,
% 15.55/8.65      ! [X3: nat,Y3: list_nat] :
% 15.55/8.65        ( ( ( nat_list_decode @ X3 )
% 15.55/8.65          = Y3 )
% 15.55/8.65       => ( ( accp_nat @ nat_list_decode_rel @ X3 )
% 15.55/8.65         => ( ( ( X3 = zero_zero_nat )
% 15.55/8.65             => ( ( Y3 = nil_nat )
% 15.55/8.65               => ~ ( accp_nat @ nat_list_decode_rel @ zero_zero_nat ) ) )
% 15.55/8.65           => ~ ! [N2: nat] :
% 15.55/8.65                  ( ( X3
% 15.55/8.65                    = ( suc @ N2 ) )
% 15.55/8.65                 => ( ( Y3
% 15.55/8.65                      = ( produc2761476792215241774st_nat
% 15.55/8.65                        @ ^ [X: nat,Y: nat] : ( cons_nat @ X @ ( nat_list_decode @ Y ) )
% 15.55/8.65                        @ ( nat_prod_decode @ N2 ) ) )
% 15.55/8.65                   => ~ ( accp_nat @ nat_list_decode_rel @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10156_times__num__def,axiom,
% 15.55/8.65      ( times_times_num
% 15.55/8.65      = ( ^ [M3: num,N3: num] : ( num_of_nat @ ( times_times_nat @ ( nat_of_num @ M3 ) @ ( nat_of_num @ N3 ) ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10157_less__eq__num__def,axiom,
% 15.55/8.65      ( ord_less_eq_num
% 15.55/8.65      = ( ^ [M3: num,N3: num] : ( ord_less_eq_nat @ ( nat_of_num @ M3 ) @ ( nat_of_num @ N3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10158_nat__of__num_Osimps_I3_J,axiom,
% 15.55/8.65      ! [X3: num] :
% 15.55/8.65        ( ( nat_of_num @ ( bit1 @ X3 ) )
% 15.55/8.65        = ( suc @ ( plus_plus_nat @ ( nat_of_num @ X3 ) @ ( nat_of_num @ X3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10159_nat__of__num__pos,axiom,
% 15.55/8.65      ! [X3: num] : ( ord_less_nat @ zero_zero_nat @ ( nat_of_num @ X3 ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10160_nat__of__num__neq__0,axiom,
% 15.55/8.65      ! [X3: num] :
% 15.55/8.65        ( ( nat_of_num @ X3 )
% 15.55/8.65       != zero_zero_nat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10161_nat__of__num__add,axiom,
% 15.55/8.65      ! [X3: num,Y3: num] :
% 15.55/8.65        ( ( nat_of_num @ ( plus_plus_num @ X3 @ Y3 ) )
% 15.55/8.65        = ( plus_plus_nat @ ( nat_of_num @ X3 ) @ ( nat_of_num @ Y3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10162_nat__of__num__numeral,axiom,
% 15.55/8.65      nat_of_num = numeral_numeral_nat ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10163_nat__of__num__inverse,axiom,
% 15.55/8.65      ! [X3: num] :
% 15.55/8.65        ( ( num_of_nat @ ( nat_of_num @ X3 ) )
% 15.55/8.65        = X3 ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10164_num__eq__iff,axiom,
% 15.55/8.65      ( ( ^ [Y5: num,Z2: num] : ( Y5 = Z2 ) )
% 15.55/8.65      = ( ^ [X: num,Y: num] :
% 15.55/8.65            ( ( nat_of_num @ X )
% 15.55/8.65            = ( nat_of_num @ Y ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10165_nat__of__num__code_I1_J,axiom,
% 15.55/8.65      ( ( nat_of_num @ one )
% 15.55/8.65      = one_one_nat ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10166_nat__of__num_Osimps_I2_J,axiom,
% 15.55/8.65      ! [X3: num] :
% 15.55/8.65        ( ( nat_of_num @ ( bit0 @ X3 ) )
% 15.55/8.65        = ( plus_plus_nat @ ( nat_of_num @ X3 ) @ ( nat_of_num @ X3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10167_nat__of__num__inc,axiom,
% 15.55/8.65      ! [X3: num] :
% 15.55/8.65        ( ( nat_of_num @ ( inc @ X3 ) )
% 15.55/8.65        = ( suc @ ( nat_of_num @ X3 ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10168_less__num__def,axiom,
% 15.55/8.65      ( ord_less_num
% 15.55/8.65      = ( ^ [M3: num,N3: num] : ( ord_less_nat @ ( nat_of_num @ M3 ) @ ( nat_of_num @ N3 ) ) ) ) ).
% 15.55/8.65  
% 15.55/8.65  thf(fact_10169_nat__of__num__code_I2_J,axiom,
% 15.55/8.66      ! [N: num] :
% 15.55/8.66        ( ( nat_of_num @ ( bit0 @ N ) )
% 15.55/8.66        = ( plus_plus_nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10170_nat__of__num__mult,axiom,
% 15.55/8.66      ! [X3: num,Y3: num] :
% 15.55/8.66        ( ( nat_of_num @ ( times_times_num @ X3 @ Y3 ) )
% 15.55/8.66        = ( times_times_nat @ ( nat_of_num @ X3 ) @ ( nat_of_num @ Y3 ) ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10171_nat__of__num__sqr,axiom,
% 15.55/8.66      ! [X3: num] :
% 15.55/8.66        ( ( nat_of_num @ ( sqr @ X3 ) )
% 15.55/8.66        = ( times_times_nat @ ( nat_of_num @ X3 ) @ ( nat_of_num @ X3 ) ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10172_nat__of__num_Osimps_I1_J,axiom,
% 15.55/8.66      ( ( nat_of_num @ one )
% 15.55/8.66      = ( suc @ zero_zero_nat ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10173_num__of__nat__inverse,axiom,
% 15.55/8.66      ! [N: nat] :
% 15.55/8.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 15.55/8.66       => ( ( nat_of_num @ ( num_of_nat @ N ) )
% 15.55/8.66          = N ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10174_nat__of__num__code_I3_J,axiom,
% 15.55/8.66      ! [N: num] :
% 15.55/8.66        ( ( nat_of_num @ ( bit1 @ N ) )
% 15.55/8.66        = ( suc @ ( plus_plus_nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10175_plus__num__def,axiom,
% 15.55/8.66      ( plus_plus_num
% 15.55/8.66      = ( ^ [M3: num,N3: num] : ( num_of_nat @ ( plus_plus_nat @ ( nat_of_num @ M3 ) @ ( nat_of_num @ N3 ) ) ) ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10176_or__num_Oelims,axiom,
% 15.55/8.66      ! [X3: num,Xa: num,Y3: num] :
% 15.55/8.66        ( ( ( bit_un6697907153464112080or_num @ X3 @ Xa )
% 15.55/8.66          = Y3 )
% 15.55/8.66       => ( ( ( X3 = one )
% 15.55/8.66           => ( ( Xa = one )
% 15.55/8.66             => ( Y3 != one ) ) )
% 15.55/8.66         => ( ( ( X3 = one )
% 15.55/8.66             => ! [N2: num] :
% 15.55/8.66                  ( ( Xa
% 15.55/8.66                    = ( bit0 @ N2 ) )
% 15.55/8.66                 => ( Y3
% 15.55/8.66                   != ( bit1 @ N2 ) ) ) )
% 15.55/8.66           => ( ( ( X3 = one )
% 15.55/8.66               => ! [N2: num] :
% 15.55/8.66                    ( ( Xa
% 15.55/8.66                      = ( bit1 @ N2 ) )
% 15.55/8.66                   => ( Y3
% 15.55/8.66                     != ( bit1 @ N2 ) ) ) )
% 15.55/8.66             => ( ! [M4: num] :
% 15.55/8.66                    ( ( X3
% 15.55/8.66                      = ( bit0 @ M4 ) )
% 15.55/8.66                   => ( ( Xa = one )
% 15.55/8.66                     => ( Y3
% 15.55/8.66                       != ( bit1 @ M4 ) ) ) )
% 15.55/8.66               => ( ! [M4: num] :
% 15.55/8.66                      ( ( X3
% 15.55/8.66                        = ( bit0 @ M4 ) )
% 15.55/8.66                     => ! [N2: num] :
% 15.55/8.66                          ( ( Xa
% 15.55/8.66                            = ( bit0 @ N2 ) )
% 15.55/8.66                         => ( Y3
% 15.55/8.66                           != ( bit0 @ ( bit_un6697907153464112080or_num @ M4 @ N2 ) ) ) ) )
% 15.55/8.66                 => ( ! [M4: num] :
% 15.55/8.66                        ( ( X3
% 15.55/8.66                          = ( bit0 @ M4 ) )
% 15.55/8.66                       => ! [N2: num] :
% 15.55/8.66                            ( ( Xa
% 15.55/8.66                              = ( bit1 @ N2 ) )
% 15.55/8.66                           => ( Y3
% 15.55/8.66                             != ( bit1 @ ( bit_un6697907153464112080or_num @ M4 @ N2 ) ) ) ) )
% 15.55/8.66                   => ( ! [M4: num] :
% 15.55/8.66                          ( ( X3
% 15.55/8.66                            = ( bit1 @ M4 ) )
% 15.55/8.66                         => ( ( Xa = one )
% 15.55/8.66                           => ( Y3
% 15.55/8.66                             != ( bit1 @ M4 ) ) ) )
% 15.55/8.66                     => ( ! [M4: num] :
% 15.55/8.66                            ( ( X3
% 15.55/8.66                              = ( bit1 @ M4 ) )
% 15.55/8.66                           => ! [N2: num] :
% 15.55/8.66                                ( ( Xa
% 15.55/8.66                                  = ( bit0 @ N2 ) )
% 15.55/8.66                               => ( Y3
% 15.55/8.66                                 != ( bit1 @ ( bit_un6697907153464112080or_num @ M4 @ N2 ) ) ) ) )
% 15.55/8.66                       => ~ ! [M4: num] :
% 15.55/8.66                              ( ( X3
% 15.55/8.66                                = ( bit1 @ M4 ) )
% 15.55/8.66                             => ! [N2: num] :
% 15.55/8.66                                  ( ( Xa
% 15.55/8.66                                    = ( bit1 @ N2 ) )
% 15.55/8.66                                 => ( Y3
% 15.55/8.66                                   != ( bit1 @ ( bit_un6697907153464112080or_num @ M4 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10177_or__num_Osimps_I2_J,axiom,
% 15.55/8.66      ! [N: num] :
% 15.55/8.66        ( ( bit_un6697907153464112080or_num @ one @ ( bit0 @ N ) )
% 15.55/8.66        = ( bit1 @ N ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10178_or__num_Osimps_I6_J,axiom,
% 15.55/8.66      ! [M: num,N: num] :
% 15.55/8.66        ( ( bit_un6697907153464112080or_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 15.55/8.66        = ( bit1 @ ( bit_un6697907153464112080or_num @ M @ N ) ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10179_or__num_Osimps_I8_J,axiom,
% 15.55/8.66      ! [M: num,N: num] :
% 15.55/8.66        ( ( bit_un6697907153464112080or_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 15.55/8.66        = ( bit1 @ ( bit_un6697907153464112080or_num @ M @ N ) ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10180_or__num_Osimps_I3_J,axiom,
% 15.55/8.66      ! [N: num] :
% 15.55/8.66        ( ( bit_un6697907153464112080or_num @ one @ ( bit1 @ N ) )
% 15.55/8.66        = ( bit1 @ N ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10181_or__num_Osimps_I7_J,axiom,
% 15.55/8.66      ! [M: num] :
% 15.55/8.66        ( ( bit_un6697907153464112080or_num @ ( bit1 @ M ) @ one )
% 15.55/8.66        = ( bit1 @ M ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10182_or__num_Osimps_I9_J,axiom,
% 15.55/8.66      ! [M: num,N: num] :
% 15.55/8.66        ( ( bit_un6697907153464112080or_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 15.55/8.66        = ( bit1 @ ( bit_un6697907153464112080or_num @ M @ N ) ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10183_or__num_Osimps_I1_J,axiom,
% 15.55/8.66      ( ( bit_un6697907153464112080or_num @ one @ one )
% 15.55/8.66      = one ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10184_or__num_Osimps_I5_J,axiom,
% 15.55/8.66      ! [M: num,N: num] :
% 15.55/8.66        ( ( bit_un6697907153464112080or_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 15.55/8.66        = ( bit0 @ ( bit_un6697907153464112080or_num @ M @ N ) ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10185_or__num_Osimps_I4_J,axiom,
% 15.55/8.66      ! [M: num] :
% 15.55/8.66        ( ( bit_un6697907153464112080or_num @ ( bit0 @ M ) @ one )
% 15.55/8.66        = ( bit1 @ M ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10186_or__num_Opelims,axiom,
% 15.55/8.66      ! [X3: num,Xa: num,Y3: num] :
% 15.55/8.66        ( ( ( bit_un6697907153464112080or_num @ X3 @ Xa )
% 15.55/8.66          = Y3 )
% 15.55/8.66       => ( ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ X3 @ Xa ) )
% 15.55/8.66         => ( ( ( X3 = one )
% 15.55/8.66             => ( ( Xa = one )
% 15.55/8.66               => ( ( Y3 = one )
% 15.55/8.66                 => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 15.55/8.66           => ( ( ( X3 = one )
% 15.55/8.66               => ! [N2: num] :
% 15.55/8.66                    ( ( Xa
% 15.55/8.66                      = ( bit0 @ N2 ) )
% 15.55/8.66                   => ( ( Y3
% 15.55/8.66                        = ( bit1 @ N2 ) )
% 15.55/8.66                     => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) ) ) ) )
% 15.55/8.66             => ( ( ( X3 = one )
% 15.55/8.66                 => ! [N2: num] :
% 15.55/8.66                      ( ( Xa
% 15.55/8.66                        = ( bit1 @ N2 ) )
% 15.55/8.66                     => ( ( Y3
% 15.55/8.66                          = ( bit1 @ N2 ) )
% 15.55/8.66                       => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) ) ) ) )
% 15.55/8.66               => ( ! [M4: num] :
% 15.55/8.66                      ( ( X3
% 15.55/8.66                        = ( bit0 @ M4 ) )
% 15.55/8.66                     => ( ( Xa = one )
% 15.55/8.66                       => ( ( Y3
% 15.55/8.66                            = ( bit1 @ M4 ) )
% 15.55/8.66                         => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 15.55/8.66                 => ( ! [M4: num] :
% 15.55/8.66                        ( ( X3
% 15.55/8.66                          = ( bit0 @ M4 ) )
% 15.55/8.66                       => ! [N2: num] :
% 15.55/8.66                            ( ( Xa
% 15.55/8.66                              = ( bit0 @ N2 ) )
% 15.55/8.66                           => ( ( Y3
% 15.55/8.66                                = ( bit0 @ ( bit_un6697907153464112080or_num @ M4 @ N2 ) ) )
% 15.55/8.66                             => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 15.55/8.66                   => ( ! [M4: num] :
% 15.55/8.66                          ( ( X3
% 15.55/8.66                            = ( bit0 @ M4 ) )
% 15.55/8.66                         => ! [N2: num] :
% 15.55/8.66                              ( ( Xa
% 15.55/8.66                                = ( bit1 @ N2 ) )
% 15.55/8.66                             => ( ( Y3
% 15.55/8.66                                  = ( bit1 @ ( bit_un6697907153464112080or_num @ M4 @ N2 ) ) )
% 15.55/8.66                               => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) )
% 15.55/8.66                     => ( ! [M4: num] :
% 15.55/8.66                            ( ( X3
% 15.55/8.66                              = ( bit1 @ M4 ) )
% 15.55/8.66                           => ( ( Xa = one )
% 15.55/8.66                             => ( ( Y3
% 15.55/8.66                                  = ( bit1 @ M4 ) )
% 15.55/8.66                               => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 15.55/8.66                       => ( ! [M4: num] :
% 15.55/8.66                              ( ( X3
% 15.55/8.66                                = ( bit1 @ M4 ) )
% 15.55/8.66                             => ! [N2: num] :
% 15.55/8.66                                  ( ( Xa
% 15.55/8.66                                    = ( bit0 @ N2 ) )
% 15.55/8.66                                 => ( ( Y3
% 15.55/8.66                                      = ( bit1 @ ( bit_un6697907153464112080or_num @ M4 @ N2 ) ) )
% 15.55/8.66                                   => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 15.55/8.66                         => ~ ! [M4: num] :
% 15.55/8.66                                ( ( X3
% 15.55/8.66                                  = ( bit1 @ M4 ) )
% 15.55/8.66                               => ! [N2: num] :
% 15.55/8.66                                    ( ( Xa
% 15.55/8.66                                      = ( bit1 @ N2 ) )
% 15.55/8.66                                   => ( ( Y3
% 15.55/8.66                                        = ( bit1 @ ( bit_un6697907153464112080or_num @ M4 @ N2 ) ) )
% 15.55/8.66                                     => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10187_or__num__dict,axiom,
% 15.55/8.66      bit_un6697907153464112080or_num = bit_un2785000775030745342or_num ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10188_or__num__rel__dict,axiom,
% 15.55/8.66      bit_un4773296044027857193um_rel = bit_un6909899581280750971um_rel ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10189_unit__factor__simps_I1_J,axiom,
% 15.55/8.66      ( ( unit_f2748546683901255202or_nat @ zero_zero_nat )
% 15.55/8.66      = zero_zero_nat ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10190_unit__factor__nat__def,axiom,
% 15.55/8.66      ( unit_f2748546683901255202or_nat
% 15.55/8.66      = ( ^ [N3: nat] : ( if_nat @ ( N3 = zero_zero_nat ) @ zero_zero_nat @ one_one_nat ) ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10191_VEBT__internal_Ogreater_Osimps,axiom,
% 15.55/8.66      ( vEBT_VEBT_greater
% 15.55/8.66      = ( vEBT_V2881884560877996034ft_nat
% 15.55/8.66        @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X ) ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10192_VEBT__internal_Ogreater_Oelims_I1_J,axiom,
% 15.55/8.66      ! [X3: option_nat,Xa: option_nat,Y3: $o] :
% 15.55/8.66        ( ( ( vEBT_VEBT_greater @ X3 @ Xa )
% 15.55/8.66          = Y3 )
% 15.55/8.66       => ( Y3
% 15.55/8.66          = ( vEBT_V2881884560877996034ft_nat
% 15.55/8.66            @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X )
% 15.55/8.66            @ X3
% 15.55/8.66            @ Xa ) ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10193_VEBT__internal_Ogreater_Oelims_I2_J,axiom,
% 15.55/8.66      ! [X3: option_nat,Xa: option_nat] :
% 15.55/8.66        ( ( vEBT_VEBT_greater @ X3 @ Xa )
% 15.55/8.66       => ( vEBT_V2881884560877996034ft_nat
% 15.55/8.66          @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X )
% 15.55/8.66          @ X3
% 15.55/8.66          @ Xa ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10194_VEBT__internal_Ogreater_Oelims_I3_J,axiom,
% 15.55/8.66      ! [X3: option_nat,Xa: option_nat] :
% 15.55/8.66        ( ~ ( vEBT_VEBT_greater @ X3 @ Xa )
% 15.55/8.66       => ~ ( vEBT_V2881884560877996034ft_nat
% 15.55/8.66            @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X )
% 15.55/8.66            @ X3
% 15.55/8.66            @ Xa ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10195_VEBT__internal_Oless_Osimps,axiom,
% 15.55/8.66      ( vEBT_VEBT_less
% 15.55/8.66      = ( vEBT_V2881884560877996034ft_nat @ ord_less_nat ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10196_VEBT__internal_Oless_Oelims_I1_J,axiom,
% 15.55/8.66      ! [X3: option_nat,Xa: option_nat,Y3: $o] :
% 15.55/8.66        ( ( ( vEBT_VEBT_less @ X3 @ Xa )
% 15.55/8.66          = Y3 )
% 15.55/8.66       => ( Y3
% 15.55/8.66          = ( vEBT_V2881884560877996034ft_nat @ ord_less_nat @ X3 @ Xa ) ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10197_VEBT__internal_Oless_Oelims_I2_J,axiom,
% 15.55/8.66      ! [X3: option_nat,Xa: option_nat] :
% 15.55/8.66        ( ( vEBT_VEBT_less @ X3 @ Xa )
% 15.55/8.66       => ( vEBT_V2881884560877996034ft_nat @ ord_less_nat @ X3 @ Xa ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10198_VEBT__internal_Oless_Oelims_I3_J,axiom,
% 15.55/8.66      ! [X3: option_nat,Xa: option_nat] :
% 15.55/8.66        ( ~ ( vEBT_VEBT_less @ X3 @ Xa )
% 15.55/8.66       => ~ ( vEBT_V2881884560877996034ft_nat @ ord_less_nat @ X3 @ Xa ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10199_VEBT__internal_Olesseq_Oelims_I3_J,axiom,
% 15.55/8.66      ! [X3: option_nat,Xa: option_nat] :
% 15.55/8.66        ( ~ ( vEBT_VEBT_lesseq @ X3 @ Xa )
% 15.55/8.66       => ~ ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat @ X3 @ Xa ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10200_VEBT__internal_Olesseq_Oelims_I2_J,axiom,
% 15.55/8.66      ! [X3: option_nat,Xa: option_nat] :
% 15.55/8.66        ( ( vEBT_VEBT_lesseq @ X3 @ Xa )
% 15.55/8.66       => ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat @ X3 @ Xa ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10201_VEBT__internal_Olesseq_Oelims_I1_J,axiom,
% 15.55/8.66      ! [X3: option_nat,Xa: option_nat,Y3: $o] :
% 15.55/8.66        ( ( ( vEBT_VEBT_lesseq @ X3 @ Xa )
% 15.55/8.66          = Y3 )
% 15.55/8.66       => ( Y3
% 15.55/8.66          = ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat @ X3 @ Xa ) ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10202_VEBT__internal_Olesseq_Osimps,axiom,
% 15.55/8.66      ( vEBT_VEBT_lesseq
% 15.55/8.66      = ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10203_lcm__0__iff__nat,axiom,
% 15.55/8.66      ! [M: nat,N: nat] :
% 15.55/8.66        ( ( ( gcd_lcm_nat @ M @ N )
% 15.55/8.66          = zero_zero_nat )
% 15.55/8.66        = ( ( M = zero_zero_nat )
% 15.55/8.66          | ( N = zero_zero_nat ) ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10204_lcm__0__iff__int,axiom,
% 15.55/8.66      ! [M: int,N: int] :
% 15.55/8.66        ( ( ( gcd_lcm_int @ M @ N )
% 15.55/8.66          = zero_zero_int )
% 15.55/8.66        = ( ( M = zero_zero_int )
% 15.55/8.66          | ( N = zero_zero_int ) ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10205_lcm__int__int__eq,axiom,
% 15.55/8.66      ! [M: nat,N: nat] :
% 15.55/8.66        ( ( gcd_lcm_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 15.55/8.66        = ( semiri1314217659103216013at_int @ ( gcd_lcm_nat @ M @ N ) ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10206_lcm__1__iff__nat,axiom,
% 15.55/8.66      ! [M: nat,N: nat] :
% 15.55/8.66        ( ( ( gcd_lcm_nat @ M @ N )
% 15.55/8.66          = ( suc @ zero_zero_nat ) )
% 15.55/8.66        = ( ( M
% 15.55/8.66            = ( suc @ zero_zero_nat ) )
% 15.55/8.66          & ( N
% 15.55/8.66            = ( suc @ zero_zero_nat ) ) ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(fact_10207_lcm__nat__abs__left__eq,axiom,
% 15.55/8.66      ! [K: int,N: nat] :
% 15.55/8.66        ( ( gcd_lcm_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 15.55/8.66        = ( nat2 @ ( gcd_lcm_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 15.55/8.66      ! [X3: int,Y3: int] :
% 15.55/8.66        ( ( if_int @ $false @ X3 @ Y3 )
% 15.55/8.66        = Y3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 15.55/8.66      ! [X3: int,Y3: int] :
% 15.55/8.66        ( ( if_int @ $true @ X3 @ Y3 )
% 15.55/8.66        = X3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 15.55/8.66      ! [X3: nat,Y3: nat] :
% 15.55/8.66        ( ( if_nat @ $false @ X3 @ Y3 )
% 15.55/8.66        = Y3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 15.55/8.66      ! [X3: nat,Y3: nat] :
% 15.55/8.66        ( ( if_nat @ $true @ X3 @ Y3 )
% 15.55/8.66        = X3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 15.55/8.66      ! [X3: num,Y3: num] :
% 15.55/8.66        ( ( if_num @ $false @ X3 @ Y3 )
% 15.55/8.66        = Y3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 15.55/8.66      ! [X3: num,Y3: num] :
% 15.55/8.66        ( ( if_num @ $true @ X3 @ Y3 )
% 15.55/8.66        = X3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 15.55/8.66      ! [X3: rat,Y3: rat] :
% 15.55/8.66        ( ( if_rat @ $false @ X3 @ Y3 )
% 15.55/8.66        = Y3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 15.55/8.66      ! [X3: rat,Y3: rat] :
% 15.55/8.66        ( ( if_rat @ $true @ X3 @ Y3 )
% 15.55/8.66        = X3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 15.55/8.66      ! [X3: real,Y3: real] :
% 15.55/8.66        ( ( if_real @ $false @ X3 @ Y3 )
% 15.55/8.66        = Y3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 15.55/8.66      ! [X3: real,Y3: real] :
% 15.55/8.66        ( ( if_real @ $true @ X3 @ Y3 )
% 15.55/8.66        = X3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 15.55/8.66      ! [P: real > $o] :
% 15.55/8.66        ( ( P @ ( fChoice_real @ P ) )
% 15.55/8.66        = ( ? [X8: real] : ( P @ X8 ) ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 15.55/8.66      ! [X3: complex,Y3: complex] :
% 15.55/8.66        ( ( if_complex @ $false @ X3 @ Y3 )
% 15.55/8.66        = Y3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 15.55/8.66      ! [X3: complex,Y3: complex] :
% 15.55/8.66        ( ( if_complex @ $true @ X3 @ Y3 )
% 15.55/8.66        = X3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 15.55/8.66      ! [X3: extended_enat,Y3: extended_enat] :
% 15.55/8.66        ( ( if_Extended_enat @ $false @ X3 @ Y3 )
% 15.55/8.66        = Y3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 15.55/8.66      ! [X3: extended_enat,Y3: extended_enat] :
% 15.55/8.66        ( ( if_Extended_enat @ $true @ X3 @ Y3 )
% 15.55/8.66        = X3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 15.55/8.66      ! [X3: code_integer,Y3: code_integer] :
% 15.55/8.66        ( ( if_Code_integer @ $false @ X3 @ Y3 )
% 15.55/8.66        = Y3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 15.55/8.66      ! [X3: code_integer,Y3: code_integer] :
% 15.55/8.66        ( ( if_Code_integer @ $true @ X3 @ Y3 )
% 15.55/8.66        = X3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 15.55/8.66      ! [X3: set_int,Y3: set_int] :
% 15.55/8.66        ( ( if_set_int @ $false @ X3 @ Y3 )
% 15.55/8.66        = Y3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 15.55/8.66      ! [X3: set_int,Y3: set_int] :
% 15.55/8.66        ( ( if_set_int @ $true @ X3 @ Y3 )
% 15.55/8.66        = X3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_2_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 15.55/8.66      ! [X3: set_nat,Y3: set_nat] :
% 15.55/8.66        ( ( if_set_nat @ $false @ X3 @ Y3 )
% 15.55/8.66        = Y3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_1_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 15.55/8.66      ! [X3: set_nat,Y3: set_nat] :
% 15.55/8.66        ( ( if_set_nat @ $true @ X3 @ Y3 )
% 15.55/8.66        = X3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 15.55/8.66      ! [X3: vEBT_VEBT,Y3: vEBT_VEBT] :
% 15.55/8.66        ( ( if_VEBT_VEBT @ $false @ X3 @ Y3 )
% 15.55/8.66        = Y3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 15.55/8.66      ! [X3: vEBT_VEBT,Y3: vEBT_VEBT] :
% 15.55/8.66        ( ( if_VEBT_VEBT @ $true @ X3 @ Y3 )
% 15.55/8.66        = X3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 15.55/8.66      ! [X3: list_int,Y3: list_int] :
% 15.55/8.66        ( ( if_list_int @ $false @ X3 @ Y3 )
% 15.55/8.66        = Y3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 15.55/8.66      ! [X3: list_int,Y3: list_int] :
% 15.55/8.66        ( ( if_list_int @ $true @ X3 @ Y3 )
% 15.55/8.66        = X3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 15.55/8.66      ! [X3: list_nat,Y3: list_nat] :
% 15.55/8.66        ( ( if_list_nat @ $false @ X3 @ Y3 )
% 15.55/8.66        = Y3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 15.55/8.66      ! [X3: list_nat,Y3: list_nat] :
% 15.55/8.66        ( ( if_list_nat @ $true @ X3 @ Y3 )
% 15.55/8.66        = X3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 15.55/8.66      ! [X3: int > int,Y3: int > int] :
% 15.55/8.66        ( ( if_int_int @ $false @ X3 @ Y3 )
% 15.55/8.66        = Y3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 15.55/8.66      ! [X3: int > int,Y3: int > int] :
% 15.55/8.66        ( ( if_int_int @ $true @ X3 @ Y3 )
% 15.55/8.66        = X3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_2_1_If_001_062_It__Nat__Onat_Mt__Rat__Orat_J_T,axiom,
% 15.55/8.66      ! [X3: nat > rat,Y3: nat > rat] :
% 15.55/8.66        ( ( if_nat_rat @ $false @ X3 @ Y3 )
% 15.55/8.66        = Y3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_1_1_If_001_062_It__Nat__Onat_Mt__Rat__Orat_J_T,axiom,
% 15.55/8.66      ! [X3: nat > rat,Y3: nat > rat] :
% 15.55/8.66        ( ( if_nat_rat @ $true @ X3 @ Y3 )
% 15.55/8.66        = X3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 15.55/8.66      ! [X3: option_nat,Y3: option_nat] :
% 15.55/8.66        ( ( if_option_nat @ $false @ X3 @ Y3 )
% 15.55/8.66        = Y3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 15.55/8.66      ! [X3: option_nat,Y3: option_nat] :
% 15.55/8.66        ( ( if_option_nat @ $true @ X3 @ Y3 )
% 15.55/8.66        = X3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 15.55/8.66      ! [X3: option_num,Y3: option_num] :
% 15.55/8.66        ( ( if_option_num @ $false @ X3 @ Y3 )
% 15.55/8.66        = Y3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 15.55/8.66      ! [X3: option_num,Y3: option_num] :
% 15.55/8.66        ( ( if_option_num @ $true @ X3 @ Y3 )
% 15.55/8.66        = X3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 15.55/8.66      ! [X3: product_prod_int_int,Y3: product_prod_int_int] :
% 15.55/8.66        ( ( if_Pro3027730157355071871nt_int @ $false @ X3 @ Y3 )
% 15.55/8.66        = Y3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 15.55/8.66      ! [X3: product_prod_int_int,Y3: product_prod_int_int] :
% 15.55/8.66        ( ( if_Pro3027730157355071871nt_int @ $true @ X3 @ Y3 )
% 15.55/8.66        = X3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 15.55/8.66      ! [X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 15.55/8.66        ( ( if_Pro6206227464963214023at_nat @ $false @ X3 @ Y3 )
% 15.55/8.66        = Y3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 15.55/8.66      ! [X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 15.55/8.66        ( ( if_Pro6206227464963214023at_nat @ $true @ X3 @ Y3 )
% 15.55/8.66        = X3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 15.55/8.66      ! [X3: produc6271795597528267376eger_o,Y3: produc6271795597528267376eger_o] :
% 15.55/8.66        ( ( if_Pro5737122678794959658eger_o @ $false @ X3 @ Y3 )
% 15.55/8.66        = Y3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 15.55/8.66      ! [X3: produc6271795597528267376eger_o,Y3: produc6271795597528267376eger_o] :
% 15.55/8.66        ( ( if_Pro5737122678794959658eger_o @ $true @ X3 @ Y3 )
% 15.55/8.66        = X3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 15.55/8.66      ! [P: $o] :
% 15.55/8.66        ( ( P = $true )
% 15.55/8.66        | ( P = $false ) ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 15.55/8.66      ! [X3: produc8923325533196201883nteger,Y3: produc8923325533196201883nteger] :
% 15.55/8.66        ( ( if_Pro6119634080678213985nteger @ $false @ X3 @ Y3 )
% 15.55/8.66        = Y3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 15.55/8.66      ! [X3: produc8923325533196201883nteger,Y3: produc8923325533196201883nteger] :
% 15.55/8.66        ( ( if_Pro6119634080678213985nteger @ $true @ X3 @ Y3 )
% 15.55/8.66        = X3 ) ).
% 15.55/8.66  
% 15.55/8.66  thf(conj_0,conjecture,
% 15.55/8.66      ord_less_nat @ x @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 15.55/8.66  ------------------------
% 16.02/9.15  % (27875)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_27763 for (2995ds/2Mi)
% 16.02/9.15  % (27875)Instruction limit reached!
% 16.02/9.15  % (27875)------------------------------
% 16.02/9.15  % (27875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.02/9.15  % (27875)Termination reason: Unknown
% 16.02/9.15  % (27875)Termination phase: shuffling
% 16.02/9.15  
% 16.02/9.15  % (27875)Memory used [KB]: 13048
% 16.02/9.15  % (27875)Time elapsed: 0.003 s
% 16.02/9.15  % (27875)Instructions burned: 2 (million)
% 16.02/9.15  % (27875)------------------------------
% 16.02/9.15  % (27875)------------------------------
% 16.02/9.15  % (27871)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27763 for (2995ds/183Mi)
% 16.02/9.15  % (27873)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_27763 for (2995ds/27Mi)
% 16.02/9.15  % (27872)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_27763 for (2995ds/4Mi)
% 16.02/9.16  % (27876)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_27763 for (2995ds/275Mi)
% 16.02/9.16  % (27872)Instruction limit reached!
% 16.02/9.16  % (27872)------------------------------
% 16.02/9.16  % (27872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.02/9.16  % (27872)Termination reason: Unknown
% 16.02/9.16  % (27872)Termination phase: shuffling
% 16.02/9.16  
% 16.02/9.16  % (27872)Memory used [KB]: 13176
% 16.02/9.16  % (27872)Time elapsed: 0.007 s
% 16.02/9.16  % (27872)Instructions burned: 4 (million)
% 16.02/9.16  % (27872)------------------------------
% 16.02/9.16  % (27872)------------------------------
% 16.02/9.16  % (27874)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27763 for (2995ds/2Mi)
% 16.02/9.17  % (27874)Instruction limit reached!
% 16.02/9.17  % (27874)------------------------------
% 16.02/9.17  % (27874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.02/9.17  % (27874)Termination reason: Unknown
% 16.02/9.17  % (27874)Termination phase: shuffling
% 16.02/9.17  
% 16.02/9.17  % (27874)Memory used [KB]: 13048
% 16.02/9.17  % (27874)Time elapsed: 0.004 s
% 16.02/9.17  % (27874)Instructions burned: 2 (million)
% 16.02/9.17  % (27874)------------------------------
% 16.02/9.17  % (27874)------------------------------
% 16.02/9.17  % (27877)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27763 for (2995ds/18Mi)
% 16.02/9.17  % (27878)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27763 for (2995ds/3Mi)
% 16.02/9.17  % (27878)Instruction limit reached!
% 16.02/9.17  % (27878)------------------------------
% 16.02/9.17  % (27878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.02/9.17  % (27878)Termination reason: Unknown
% 16.02/9.17  % (27878)Termination phase: shuffling
% 16.02/9.17  
% 16.02/9.17  % (27878)Memory used [KB]: 13176
% 16.02/9.17  % (27878)Time elapsed: 0.005 s
% 16.02/9.17  % (27878)Instructions burned: 3 (million)
% 16.02/9.17  % (27878)------------------------------
% 16.02/9.17  % (27878)------------------------------
% 16.02/9.18  % (27879)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_27763 for (2995ds/37Mi)
% 16.02/9.18  % (27880)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_27763 for (2994ds/15Mi)
% 16.02/9.18  % (27873)Instruction limit reached!
% 16.02/9.18  % (27873)------------------------------
% 16.02/9.18  % (27873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.02/9.18  % (27873)Termination reason: Unknown
% 16.02/9.18  % (27873)Termination phase: shuffling
% 16.02/9.18  
% 16.02/9.18  % (27873)Memory used [KB]: 13944
% 16.02/9.18  % (27873)Time elapsed: 0.029 s
% 16.02/9.18  % (27873)Instructions burned: 27 (million)
% 16.02/9.18  % (27873)------------------------------
% 16.02/9.18  % (27873)------------------------------
% 16.02/9.19  % (27877)Instruction limit reached!
% 16.02/9.19  % (27877)------------------------------
% 16.02/9.19  % (27877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.02/9.19  % (27877)Termination reason: Unknown
% 16.02/9.19  % (27877)Termination phase: shuffling
% 16.02/9.19  
% 16.02/9.19  % (27877)Memory used [KB]: 13944
% 16.02/9.19  % (27877)Time elapsed: 0.026 s
% 16.02/9.19  % (27877)Instructions burned: 19 (million)
% 16.02/9.19  % (27877)------------------------------
% 16.02/9.19  % (27877)------------------------------
% 16.02/9.19  % (27881)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_27763 for (2994ds/3Mi)
% 16.21/9.20  % (27880)Instruction limit reached!
% 16.21/9.20  % (27880)------------------------------
% 16.21/9.20  % (27880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/9.20  % (27880)Termination reason: Unknown
% 16.21/9.20  % (27880)Termination phase: shuffling
% 16.21/9.20  
% 16.21/9.20  % (27880)Memory used [KB]: 13944
% 16.21/9.20  % (27880)Time elapsed: 0.018 s
% 16.21/9.20  % (27880)Instructions burned: 16 (million)
% 16.21/9.20  % (27880)------------------------------
% 16.21/9.20  % (27880)------------------------------
% 16.21/9.20  % (27881)Instruction limit reached!
% 16.21/9.20  % (27881)------------------------------
% 16.21/9.20  % (27881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/9.20  % (27881)Termination reason: Unknown
% 16.21/9.20  % (27881)Termination phase: shuffling
% 16.21/9.20  
% 16.21/9.20  % (27881)Memory used [KB]: 13048
% 16.21/9.20  % (27881)Time elapsed: 0.005 s
% 16.21/9.20  % (27881)Instructions burned: 3 (million)
% 16.21/9.20  % (27881)------------------------------
% 16.21/9.20  % (27881)------------------------------
% 16.21/9.20  % (27882)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_27763 for (2994ds/1041Mi)
% 16.21/9.21  % (27879)Instruction limit reached!
% 16.21/9.21  % (27879)------------------------------
% 16.21/9.21  % (27879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/9.21  % (27879)Termination reason: Unknown
% 16.21/9.21  % (27879)Termination phase: shuffling
% 16.21/9.21  
% 16.21/9.21  % (27879)Memory used [KB]: 14200
% 16.21/9.21  % (27879)Time elapsed: 0.034 s
% 16.21/9.21  % (27879)Instructions burned: 37 (million)
% 16.21/9.21  % (27879)------------------------------
% 16.21/9.21  % (27879)------------------------------
% 16.21/9.21  % (27883)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_27763 for (2994ds/7Mi)
% 16.21/9.21  % (27885)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_27763 for (2994ds/3Mi)
% 16.21/9.22  % (27885)Instruction limit reached!
% 16.21/9.22  % (27885)------------------------------
% 16.21/9.22  % (27885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/9.22  % (27885)Termination reason: Unknown
% 16.21/9.22  % (27885)Termination phase: shuffling
% 16.21/9.22  
% 16.21/9.22  % (27885)Memory used [KB]: 13176
% 16.21/9.22  % (27885)Time elapsed: 0.005 s
% 16.21/9.22  % (27885)Instructions burned: 3 (million)
% 16.21/9.22  % (27885)------------------------------
% 16.21/9.22  % (27885)------------------------------
% 16.21/9.22  % (27871)Instruction limit reached!
% 16.21/9.22  % (27871)------------------------------
% 16.21/9.22  % (27871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/9.22  % (27871)Termination reason: Unknown
% 16.21/9.22  % (27871)Termination phase: shuffling
% 16.21/9.22  
% 16.21/9.22  % (27871)Memory used [KB]: 15735
% 16.21/9.22  % (27871)Time elapsed: 0.068 s
% 16.21/9.22  % (27871)Instructions burned: 185 (million)
% 16.21/9.22  % (27871)------------------------------
% 16.21/9.22  % (27871)------------------------------
% 16.21/9.22  % (27884)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_27763 for (2994ds/16Mi)
% 16.21/9.22  % (27883)Instruction limit reached!
% 16.21/9.22  % (27883)------------------------------
% 16.21/9.22  % (27883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/9.22  % (27883)Termination reason: Unknown
% 16.21/9.22  % (27883)Termination phase: shuffling
% 16.21/9.22  
% 16.21/9.22  % (27883)Memory used [KB]: 13432
% 16.21/9.22  % (27883)Time elapsed: 0.012 s
% 16.21/9.22  % (27883)Instructions burned: 7 (million)
% 16.21/9.22  % (27883)------------------------------
% 16.21/9.22  % (27883)------------------------------
% 16.21/9.22  % (27886)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_27763 for (2994ds/3Mi)
% 16.21/9.23  % (27886)Instruction limit reached!
% 16.21/9.23  % (27886)------------------------------
% 16.21/9.23  % (27886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/9.23  % (27886)Termination reason: Unknown
% 16.21/9.23  % (27886)Termination phase: shuffling
% 16.21/9.23  
% 16.21/9.23  % (27886)Memory used [KB]: 13176
% 16.21/9.23  % (27886)Time elapsed: 0.004 s
% 16.21/9.23  % (27886)Instructions burned: 4 (million)
% 16.21/9.23  % (27886)------------------------------
% 16.21/9.23  % (27886)------------------------------
% 16.21/9.23  % (27888)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_27763 for (2994ds/3Mi)
% 16.21/9.23  % (27887)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_27763 for (2994ds/7Mi)
% 16.21/9.23  % (27888)Instruction limit reached!
% 16.21/9.23  % (27888)------------------------------
% 16.21/9.23  % (27888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/9.23  % (27888)Termination reason: Unknown
% 16.21/9.23  % (27888)Termination phase: shuffling
% 16.21/9.23  
% 16.21/9.23  % (27888)Memory used [KB]: 13176
% 16.21/9.23  % (27888)Time elapsed: 0.004 s
% 16.21/9.23  % (27888)Instructions burned: 3 (million)
% 16.21/9.23  % (27888)------------------------------
% 16.21/9.23  % (27888)------------------------------
% 16.21/9.24  % (27890)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_27763 for (2994ds/18Mi)
% 16.21/9.24  % (27884)Instruction limit reached!
% 16.21/9.24  % (27884)------------------------------
% 16.21/9.24  % (27884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/9.24  % (27884)Termination reason: Unknown
% 16.21/9.24  % (27887)Instruction limit reached!
% 16.21/9.24  % (27887)------------------------------
% 16.21/9.24  % (27887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/9.24  % (27887)Termination reason: Unknown
% 16.21/9.24  % (27887)Termination phase: shuffling
% 16.21/9.24  
% 16.21/9.24  % (27887)Memory used [KB]: 13432
% 16.21/9.24  % (27887)Time elapsed: 0.009 s
% 16.21/9.24  % (27887)Instructions burned: 7 (million)
% 16.21/9.24  % (27887)------------------------------
% 16.21/9.24  % (27887)------------------------------
% 16.21/9.24  % (27884)Termination phase: shuffling
% 16.21/9.24  
% 16.21/9.24  % (27884)Memory used [KB]: 13944
% 16.21/9.24  % (27884)Time elapsed: 0.022 s
% 16.21/9.24  % (27884)Instructions burned: 17 (million)
% 16.21/9.24  % (27884)------------------------------
% 16.21/9.24  % (27884)------------------------------
% 16.21/9.24  % (27889)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_27763 for (2994ds/4Mi)
% 16.21/9.24  % (27891)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_27763 for (2994ds/710Mi)
% 16.21/9.25  % (27889)Instruction limit reached!
% 16.21/9.25  % (27889)------------------------------
% 16.21/9.25  % (27889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/9.25  % (27889)Termination reason: Unknown
% 16.21/9.25  % (27889)Termination phase: shuffling
% 16.21/9.25  
% 16.21/9.25  % (27889)Memory used [KB]: 13176
% 16.21/9.25  % (27889)Time elapsed: 0.007 s
% 16.21/9.25  % (27889)Instructions burned: 4 (million)
% 16.21/9.25  % (27889)------------------------------
% 16.21/9.25  % (27889)------------------------------
% 16.21/9.25  % (27892)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27763 for (2994ds/6Mi)
% 16.21/9.26  % (27892)Instruction limit reached!
% 16.21/9.26  % (27892)------------------------------
% 16.21/9.26  % (27892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/9.26  % (27892)Termination reason: Unknown
% 16.21/9.26  % (27892)Termination phase: shuffling
% 16.21/9.26  
% 16.21/9.26  % (27892)Memory used [KB]: 13304
% 16.21/9.26  % (27892)Time elapsed: 0.006 s
% 16.21/9.26  % (27892)Instructions burned: 6 (million)
% 16.21/9.26  % (27892)------------------------------
% 16.21/9.26  % (27892)------------------------------
% 16.21/9.26  % (27890)Instruction limit reached!
% 16.21/9.26  % (27890)------------------------------
% 16.21/9.26  % (27890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/9.26  % (27890)Termination reason: Unknown
% 16.21/9.26  % (27890)Termination phase: shuffling
% 16.21/9.26  
% 16.21/9.26  % (27890)Memory used [KB]: 13944
% 16.21/9.26  % (27890)Time elapsed: 0.019 s
% 16.21/9.26  % (27890)Instructions burned: 19 (million)
% 16.21/9.26  % (27890)------------------------------
% 16.21/9.26  % (27890)------------------------------
% 16.21/9.26  % (27894)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_27763 for (2994ds/21Mi)
% 16.21/9.27  % (27893)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_27763 for (2994ds/902Mi)
% 16.21/9.27  % (27895)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_27763 for (2994ds/5Mi)
% 16.21/9.27  % (27895)Instruction limit reached!
% 16.21/9.27  % (27895)------------------------------
% 16.21/9.27  % (27895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/9.27  % (27895)Termination reason: Unknown
% 16.21/9.27  % (27895)Termination phase: shuffling
% 16.21/9.27  
% 16.21/9.27  % (27895)Memory used [KB]: 13304
% 16.21/9.27  % (27895)Time elapsed: 0.006 s
% 16.21/9.27  % (27895)Instructions burned: 5 (million)
% 16.21/9.27  % (27895)------------------------------
% 16.21/9.27  % (27895)------------------------------
% 16.21/9.28  % (27896)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_27763 for (2994ds/6Mi)
% 16.21/9.28  % (27894)Instruction limit reached!
% 16.21/9.28  % (27894)------------------------------
% 16.21/9.28  % (27894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/9.28  % (27894)Termination reason: Unknown
% 16.21/9.28  % (27894)Termination phase: shuffling
% 16.21/9.28  
% 16.21/9.28  % (27894)Memory used [KB]: 13944
% 16.21/9.28  % (27894)Time elapsed: 0.019 s
% 16.21/9.28  % (27894)Instructions burned: 21 (million)
% 16.21/9.28  % (27894)------------------------------
% 16.21/9.28  % (27894)------------------------------
% 16.21/9.28  % (27897)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_27763 for (2994ds/377Mi)
% 16.21/9.28  % (27896)Instruction limit reached!
% 16.21/9.28  % (27896)------------------------------
% 16.21/9.28  % (27896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/9.28  % (27896)Termination reason: Unknown
% 16.21/9.28  % (27896)Termination phase: shuffling
% 16.21/9.28  
% 16.21/9.28  % (27896)Memory used [KB]: 13304
% 16.21/9.28  % (27896)Time elapsed: 0.009 s
% 16.21/9.28  % (27896)Instructions burned: 6 (million)
% 16.21/9.28  % (27896)------------------------------
% 16.21/9.28  % (27896)------------------------------
% 16.21/9.29  % (27898)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_27763 for (2993ds/779Mi)
% 16.68/9.32  % (27899)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_27763 for (2993ds/19Mi)
% 16.68/9.33  % (27876)Instruction limit reached!
% 16.68/9.33  % (27876)------------------------------
% 16.68/9.33  % (27876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.68/9.33  % (27876)Termination reason: Unknown
% 16.68/9.33  % (27876)Termination phase: shuffling
% 16.68/9.33  
% 16.68/9.33  % (27876)Memory used [KB]: 17142
% 16.68/9.33  % (27876)Time elapsed: 0.174 s
% 16.68/9.33  % (27876)Instructions burned: 275 (million)
% 16.68/9.33  % (27876)------------------------------
% 16.68/9.33  % (27876)------------------------------
% 16.68/9.34  % (27899)Instruction limit reached!
% 16.68/9.34  % (27899)------------------------------
% 16.68/9.34  % (27899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.68/9.34  % (27899)Termination reason: Unknown
% 16.68/9.34  % (27899)Termination phase: shuffling
% 16.68/9.34  
% 16.68/9.34  % (27899)Memory used [KB]: 13944
% 16.68/9.34  % (27899)Time elapsed: 0.023 s
% 16.68/9.34  % (27899)Instructions burned: 19 (million)
% 16.68/9.34  % (27899)------------------------------
% 16.68/9.34  % (27899)------------------------------
% 16.68/9.35  % (27900)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_27763 for (2993ds/879Mi)
% 16.68/9.36  % (27901)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_27763 for (2993ds/17Mi)
% 16.68/9.38  % (27901)Instruction limit reached!
% 16.68/9.38  % (27901)------------------------------
% 16.68/9.38  % (27901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.68/9.38  % (27901)Termination reason: Unknown
% 16.68/9.38  % (27901)Termination phase: shuffling
% 16.68/9.38  
% 16.68/9.38  % (27901)Memory used [KB]: 13944
% 16.68/9.38  % (27901)Time elapsed: 0.016 s
% 16.68/9.38  % (27901)Instructions burned: 19 (million)
% 16.68/9.38  % (27901)------------------------------
% 16.68/9.38  % (27901)------------------------------
% 16.68/9.39  % (27902)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_27763 for (2992ds/3Mi)
% 16.68/9.39  % (27902)Instruction limit reached!
% 16.68/9.39  % (27902)------------------------------
% 16.68/9.39  % (27902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.68/9.39  % (27902)Termination reason: Unknown
% 16.68/9.39  % (27902)Termination phase: shuffling
% 16.68/9.39  
% 16.68/9.39  % (27902)Memory used [KB]: 13048
% 16.68/9.39  % (27902)Time elapsed: 0.004 s
% 16.68/9.39  % (27902)Instructions burned: 3 (million)
% 16.68/9.39  % (27902)------------------------------
% 16.68/9.39  % (27902)------------------------------
% 16.97/9.40  % (27903)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_27763 for (2992ds/30Mi)
% 16.97/9.42  % (27903)Instruction limit reached!
% 16.97/9.42  % (27903)------------------------------
% 16.97/9.42  % (27903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.97/9.42  % (27903)Termination reason: Unknown
% 16.97/9.42  % (27903)Termination phase: shuffling
% 16.97/9.42  
% 16.97/9.42  % (27903)Memory used [KB]: 13944
% 16.97/9.42  % (27903)Time elapsed: 0.026 s
% 16.97/9.42  % (27903)Instructions burned: 31 (million)
% 16.97/9.42  % (27903)------------------------------
% 16.97/9.42  % (27903)------------------------------
% 16.97/9.44  % (27897)Instruction limit reached!
% 16.97/9.44  % (27897)------------------------------
% 16.97/9.44  % (27897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.97/9.44  % (27897)Termination reason: Unknown
% 16.97/9.44  % (27897)Termination phase: shuffling
% 16.97/9.44  
% 16.97/9.44  % (27897)Memory used [KB]: 18421
% 16.97/9.44  % (27897)Time elapsed: 0.154 s
% 16.97/9.44  % (27897)Instructions burned: 377 (million)
% 16.97/9.44  % (27897)------------------------------
% 16.97/9.44  % (27897)------------------------------
% 16.97/9.45  % (27904)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_27763 for (2992ds/127Mi)
% 16.97/9.45  % (27905)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_27763 for (2992ds/100Mi)
% 16.97/9.48  % (27905)Instruction limit reached!
% 16.97/9.48  % (27905)------------------------------
% 16.97/9.48  % (27905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.97/9.48  % (27905)Termination reason: Unknown
% 16.97/9.48  % (27905)Termination phase: shuffling
% 16.97/9.48  
% 16.97/9.48  % (27905)Memory used [KB]: 15095
% 16.97/9.48  % (27905)Time elapsed: 0.038 s
% 16.97/9.48  % (27905)Instructions burned: 101 (million)
% 16.97/9.48  % (27905)------------------------------
% 16.97/9.48  % (27905)------------------------------
% 16.97/9.49  % (27891)Instruction limit reached!
% 16.97/9.49  % (27891)------------------------------
% 16.97/9.49  % (27891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.97/9.49  % (27891)Termination reason: Unknown
% 16.97/9.49  % (27891)Termination phase: shuffling
% 16.97/9.49  
% 16.97/9.49  % (27891)Memory used [KB]: 24690
% 16.97/9.49  % (27891)Time elapsed: 0.247 s
% 16.97/9.49  % (27891)Instructions burned: 710 (million)
% 16.97/9.49  % (27891)------------------------------
% 16.97/9.49  % (27891)------------------------------
% 17.47/9.50  % (27906)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_27763 for (2991ds/3Mi)
% 17.47/9.50  % (27906)Instruction limit reached!
% 17.47/9.50  % (27906)------------------------------
% 17.47/9.50  % (27906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.47/9.50  % (27906)Termination reason: Unknown
% 17.47/9.50  % (27906)Termination phase: shuffling
% 17.47/9.50  
% 17.47/9.50  % (27906)Memory used [KB]: 13048
% 17.47/9.50  % (27906)Time elapsed: 0.004 s
% 17.47/9.50  % (27906)Instructions burned: 3 (million)
% 17.47/9.50  % (27906)------------------------------
% 17.47/9.50  % (27906)------------------------------
% 17.47/9.50  % (27907)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_27763 for (2991ds/20Mi)
% 17.47/9.51  % (27908)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_27763 for (2991ds/86Mi)
% 17.47/9.51  % (27904)Instruction limit reached!
% 17.47/9.51  % (27904)------------------------------
% 17.47/9.51  % (27904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.47/9.51  % (27904)Termination reason: Unknown
% 17.47/9.51  % (27904)Termination phase: shuffling
% 17.47/9.51  
% 17.47/9.51  % (27904)Memory used [KB]: 15479
% 17.47/9.51  % (27904)Time elapsed: 0.066 s
% 17.47/9.51  % (27904)Instructions burned: 128 (million)
% 17.47/9.51  % (27904)------------------------------
% 17.47/9.51  % (27904)------------------------------
% 17.47/9.52  % (27907)Instruction limit reached!
% 17.47/9.52  % (27907)------------------------------
% 17.47/9.52  % (27907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.47/9.52  % (27907)Termination reason: Unknown
% 17.47/9.52  % (27907)Termination phase: shuffling
% 17.47/9.52  
% 17.47/9.52  % (27907)Memory used [KB]: 13944
% 17.47/9.52  % (27907)Time elapsed: 0.017 s
% 17.47/9.52  % (27907)Instructions burned: 22 (million)
% 17.47/9.52  % (27907)------------------------------
% 17.47/9.52  % (27907)------------------------------
% 17.47/9.52  % (27909)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_27763 for (2991ds/107Mi)
% 17.47/9.53  % (27910)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_27763 for (2991ds/39Mi)
% 17.47/9.54  % (27882)Instruction limit reached!
% 17.47/9.54  % (27882)------------------------------
% 17.47/9.54  % (27882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.47/9.54  % (27882)Termination reason: Unknown
% 17.47/9.54  % (27882)Termination phase: shuffling
% 17.47/9.54  
% 17.47/9.54  % (27882)Memory used [KB]: 33773
% 17.47/9.54  % (27882)Time elapsed: 0.337 s
% 17.47/9.54  % (27882)Instructions burned: 1043 (million)
% 17.47/9.54  % (27882)------------------------------
% 17.47/9.54  % (27882)------------------------------
% 17.47/9.55  % (27908)Instruction limit reached!
% 17.47/9.55  % (27908)------------------------------
% 17.47/9.55  % (27908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.47/9.55  % (27908)Termination reason: Unknown
% 17.47/9.55  % (27908)Termination phase: shuffling
% 17.47/9.55  
% 17.47/9.55  % (27908)Memory used [KB]: 14839
% 17.47/9.55  % (27908)Time elapsed: 0.038 s
% 17.47/9.55  % (27908)Instructions burned: 86 (million)
% 17.47/9.55  % (27908)------------------------------
% 17.47/9.55  % (27908)------------------------------
% 17.47/9.55  % (27910)Instruction limit reached!
% 17.47/9.55  % (27910)------------------------------
% 17.47/9.55  % (27910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.47/9.55  % (27910)Termination reason: Unknown
% 17.47/9.55  % (27910)Termination phase: shuffling
% 17.47/9.55  
% 17.47/9.55  % (27910)Memory used [KB]: 14200
% 17.47/9.55  % (27910)Time elapsed: 0.022 s
% 17.47/9.55  % (27910)Instructions burned: 41 (million)
% 17.47/9.55  % (27910)------------------------------
% 17.47/9.55  % (27910)------------------------------
% 17.47/9.55  % (27911)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_27763 for (2991ds/448Mi)
% 17.47/9.56  % (27912)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_27763 for (2991ds/46Mi)
% 17.47/9.56  % (27898)Instruction limit reached!
% 17.47/9.56  % (27898)------------------------------
% 17.47/9.56  % (27898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.47/9.56  % (27898)Termination reason: Unknown
% 17.47/9.56  % (27898)Termination phase: shuffling
% 17.47/9.56  
% 17.47/9.56  % (27898)Memory used [KB]: 26225
% 17.47/9.56  % (27898)Time elapsed: 0.266 s
% 17.47/9.56  % (27898)Instructions burned: 779 (million)
% 17.47/9.56  % (27898)------------------------------
% 17.47/9.56  % (27898)------------------------------
% 17.47/9.56  % (27913)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_27763 for (2991ds/98Mi)
% 17.47/9.57  % (27909)Instruction limit reached!
% 17.47/9.57  % (27909)------------------------------
% 17.47/9.57  % (27909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.47/9.57  % (27909)Termination reason: Unknown
% 17.47/9.57  % (27909)Termination phase: shuffling
% 17.47/9.57  
% 17.47/9.57  % (27909)Memory used [KB]: 15095
% 17.47/9.57  % (27909)Time elapsed: 0.045 s
% 17.47/9.57  % (27909)Instructions burned: 108 (million)
% 17.47/9.57  % (27909)------------------------------
% 17.47/9.57  % (27909)------------------------------
% 17.47/9.57  % (27914)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_27763 for (2991ds/507Mi)
% 17.47/9.58  % (27915)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_27763 for (2991ds/149Mi)
% 17.47/9.58  % (27912)Instruction limit reached!
% 17.47/9.58  % (27912)------------------------------
% 17.47/9.58  % (27912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.47/9.58  % (27912)Termination reason: Unknown
% 17.47/9.58  % (27912)Termination phase: shuffling
% 17.47/9.58  
% 17.47/9.58  % (27912)Memory used [KB]: 14328
% 17.47/9.58  % (27912)Time elapsed: 0.025 s
% 17.47/9.58  % (27912)Instructions burned: 46 (million)
% 17.47/9.58  % (27912)------------------------------
% 17.47/9.58  % (27912)------------------------------
% 17.47/9.59  % (27916)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_27763 for (2990ds/39Mi)
% 18.40/9.60  % (27913)Instruction limit reached!
% 18.40/9.60  % (27913)------------------------------
% 18.40/9.60  % (27913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.40/9.60  % (27913)Termination reason: Unknown
% 18.40/9.60  % (27913)Termination phase: shuffling
% 18.40/9.60  
% 18.40/9.60  % (27913)Memory used [KB]: 15095
% 18.40/9.60  % (27913)Time elapsed: 0.041 s
% 18.40/9.60  % (27913)Instructions burned: 98 (million)
% 18.40/9.60  % (27913)------------------------------
% 18.40/9.60  % (27913)------------------------------
% 18.40/9.61  % (27916)Instruction limit reached!
% 18.40/9.61  % (27916)------------------------------
% 18.40/9.61  % (27916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.40/9.61  % (27916)Termination reason: Unknown
% 18.40/9.61  % (27916)Termination phase: shuffling
% 18.40/9.61  
% 18.40/9.61  % (27916)Memory used [KB]: 14200
% 18.40/9.61  % (27916)Time elapsed: 0.022 s
% 18.40/9.61  % (27916)Instructions burned: 40 (million)
% 18.40/9.61  % (27916)------------------------------
% 18.40/9.61  % (27916)------------------------------
% 18.40/9.62  % (27917)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_27763 for (2990ds/6Mi)
% 18.40/9.62  % (27918)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_27763 for (2990ds/1087Mi)
% 18.40/9.63  % (27917)Instruction limit reached!
% 18.40/9.63  % (27917)------------------------------
% 18.40/9.63  % (27917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.40/9.63  % (27917)Termination reason: Unknown
% 18.40/9.63  % (27917)Termination phase: shuffling
% 18.40/9.63  
% 18.40/9.63  % (27917)Memory used [KB]: 13304
% 18.40/9.63  % (27917)Time elapsed: 0.009 s
% 18.40/9.63  % (27917)Instructions burned: 6 (million)
% 18.40/9.63  % (27917)------------------------------
% 18.40/9.63  % (27917)------------------------------
% 18.40/9.63  % (27915)Instruction limit reached!
% 18.40/9.63  % (27915)------------------------------
% 18.40/9.63  % (27915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.40/9.63  % (27915)Termination reason: Unknown
% 18.40/9.63  % (27915)Termination phase: shuffling
% 18.40/9.63  
% 18.40/9.63  % (27915)Memory used [KB]: 15607
% 18.40/9.63  % (27915)Time elapsed: 0.058 s
% 18.40/9.63  % (27915)Instructions burned: 151 (million)
% 18.40/9.63  % (27915)------------------------------
% 18.40/9.63  % (27915)------------------------------
% 18.40/9.65  % (27920)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_27763 for (2990ds/44Mi)
% 18.40/9.65  % (27919)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_27763 for (2990ds/47Mi)
% 18.40/9.67  % (27920)Instruction limit reached!
% 18.40/9.67  % (27920)------------------------------
% 18.40/9.67  % (27920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.40/9.67  % (27920)Termination reason: Unknown
% 18.40/9.67  % (27920)Termination phase: shuffling
% 18.40/9.67  
% 18.40/9.67  % (27920)Memory used [KB]: 14328
% 18.40/9.67  % (27920)Time elapsed: 0.023 s
% 18.40/9.67  % (27920)Instructions burned: 45 (million)
% 18.40/9.67  % (27920)------------------------------
% 18.40/9.67  % (27920)------------------------------
% 18.40/9.67  % (27919)Instruction limit reached!
% 18.40/9.67  % (27919)------------------------------
% 18.40/9.67  % (27919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.40/9.67  % (27919)Termination reason: Unknown
% 18.40/9.67  % (27919)Termination phase: shuffling
% 18.40/9.67  
% 18.40/9.67  % (27919)Memory used [KB]: 14200
% 18.40/9.67  % (27919)Time elapsed: 0.024 s
% 18.40/9.67  % (27919)Instructions burned: 48 (million)
% 18.40/9.67  % (27919)------------------------------
% 18.40/9.67  % (27919)------------------------------
% 18.40/9.68  % (27900)Instruction limit reached!
% 18.40/9.68  % (27900)------------------------------
% 18.40/9.68  % (27900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.40/9.68  % (27921)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_27763 for (2990ds/432Mi)
% 18.40/9.68  % (27900)Termination reason: Unknown
% 18.40/9.68  % (27900)Termination phase: shuffling
% 18.40/9.68  
% 18.40/9.68  % (27900)Memory used [KB]: 26225
% 18.40/9.68  % (27900)Time elapsed: 0.326 s
% 18.40/9.68  % (27900)Instructions burned: 881 (million)
% 18.40/9.68  % (27900)------------------------------
% 18.40/9.68  % (27900)------------------------------
% 18.40/9.68  % (27922)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_27763 for (2990ds/62Mi)
% 18.40/9.69  % (27911)Instruction limit reached!
% 18.40/9.69  % (27911)------------------------------
% 18.40/9.69  % (27911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.40/9.69  % (27911)Termination reason: Unknown
% 18.40/9.69  % (27911)Termination phase: shuffling
% 18.40/9.69  
% 18.40/9.69  % (27911)Memory used [KB]: 22003
% 18.40/9.69  % (27911)Time elapsed: 0.138 s
% 18.40/9.69  % (27911)Instructions burned: 450 (million)
% 18.40/9.69  % (27911)------------------------------
% 18.40/9.69  % (27911)------------------------------
% 19.13/9.70  % (27924)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_27763 for (2989ds/96Mi)
% 19.13/9.70  % (27923)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_27763 for (2989ds/31Mi)
% 19.13/9.71  % (27922)Instruction limit reached!
% 19.13/9.71  % (27922)------------------------------
% 19.13/9.71  % (27922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.13/9.71  % (27922)Termination reason: Unknown
% 19.13/9.71  % (27922)Termination phase: shuffling
% 19.13/9.71  
% 19.13/9.71  % (27922)Memory used [KB]: 14583
% 19.13/9.71  % (27922)Time elapsed: 0.028 s
% 19.13/9.71  % (27922)Instructions burned: 64 (million)
% 19.13/9.71  % (27922)------------------------------
% 19.13/9.71  % (27922)------------------------------
% 19.13/9.72  % (27925)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_27763 for (2989ds/453Mi)
% 19.13/9.73  % (27923)Instruction limit reached!
% 19.13/9.73  % (27923)------------------------------
% 19.13/9.73  % (27923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.13/9.73  % (27923)Termination reason: Unknown
% 19.13/9.73  % (27923)Termination phase: shuffling
% 19.13/9.73  
% 19.13/9.73  % (27923)Memory used [KB]: 14072
% 19.13/9.73  % (27923)Time elapsed: 0.031 s
% 19.13/9.73  % (27923)Instructions burned: 31 (million)
% 19.13/9.73  % (27923)------------------------------
% 19.13/9.73  % (27923)------------------------------
% 19.13/9.74  % (27924)Instruction limit reached!
% 19.13/9.74  % (27924)------------------------------
% 19.13/9.74  % (27924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.13/9.74  % (27924)Termination reason: Unknown
% 19.13/9.74  % (27924)Termination phase: shuffling
% 19.13/9.74  
% 19.13/9.74  % (27924)Memory used [KB]: 14839
% 19.13/9.74  % (27924)Time elapsed: 0.042 s
% 19.13/9.74  % (27924)Instructions burned: 97 (million)
% 19.13/9.74  % (27924)------------------------------
% 19.13/9.74  % (27924)------------------------------
% 19.13/9.75  % (27926)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_27763 for (2989ds/71Mi)
% 19.13/9.75  % (27914)Instruction limit reached!
% 19.13/9.75  % (27914)------------------------------
% 19.13/9.75  % (27914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.13/9.75  % (27914)Termination reason: Unknown
% 19.13/9.75  % (27927)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_27763 for (2989ds/83Mi)
% 19.13/9.75  % (27914)Termination phase: shuffling
% 19.13/9.75  
% 19.13/9.75  % (27914)Memory used [KB]: 19829
% 19.13/9.75  % (27914)Time elapsed: 0.180 s
% 19.13/9.75  % (27914)Instructions burned: 508 (million)
% 19.13/9.75  % (27914)------------------------------
% 19.13/9.75  % (27914)------------------------------
% 19.13/9.77  % (27928)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_27763 for (2989ds/11Mi)
% 19.13/9.78  % (27926)Instruction limit reached!
% 19.13/9.78  % (27926)------------------------------
% 19.13/9.78  % (27926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.13/9.78  % (27926)Termination reason: Unknown
% 19.13/9.78  % (27926)Termination phase: shuffling
% 19.13/9.78  
% 19.13/9.78  % (27926)Memory used [KB]: 14711
% 19.13/9.78  % (27926)Time elapsed: 0.033 s
% 19.13/9.78  % (27926)Instructions burned: 73 (million)
% 19.13/9.78  % (27926)------------------------------
% 19.13/9.78  % (27926)------------------------------
% 19.13/9.78  % (27893)Instruction limit reached!
% 19.13/9.78  % (27893)------------------------------
% 19.13/9.78  % (27893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.13/9.78  % (27893)Termination reason: Unknown
% 19.13/9.78  % (27893)Termination phase: shuffling
% 19.13/9.78  
% 19.13/9.78  % (27893)Memory used [KB]: 26609
% 19.13/9.78  % (27893)Time elapsed: 0.518 s
% 19.13/9.78  % (27893)Instructions burned: 902 (million)
% 19.13/9.78  % (27893)------------------------------
% 19.13/9.78  % (27893)------------------------------
% 19.13/9.79  % (27927)Instruction limit reached!
% 19.13/9.79  % (27927)------------------------------
% 19.13/9.79  % (27927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.13/9.79  % (27927)Termination reason: Unknown
% 19.13/9.79  % (27927)Termination phase: shuffling
% 19.13/9.79  
% 19.13/9.79  % (27927)Memory used [KB]: 14583
% 19.13/9.79  % (27927)Time elapsed: 0.036 s
% 19.13/9.79  % (27927)Instructions burned: 84 (million)
% 19.13/9.79  % (27927)------------------------------
% 19.13/9.79  % (27927)------------------------------
% 19.13/9.79  % (27928)Instruction limit reached!
% 19.13/9.79  % (27928)------------------------------
% 19.13/9.79  % (27928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.13/9.79  % (27928)Termination reason: Unknown
% 19.13/9.79  % (27928)Termination phase: shuffling
% 19.13/9.79  
% 19.13/9.79  % (27928)Memory used [KB]: 13560
% 19.13/9.79  % (27928)Time elapsed: 0.015 s
% 19.13/9.79  % (27928)Instructions burned: 11 (million)
% 19.13/9.79  % (27928)------------------------------
% 19.13/9.79  % (27928)------------------------------
% 19.13/9.79  % (27929)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_27763 for (2988ds/41Mi)
% 20.13/9.80  % (27930)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27763 for (2988ds/6Mi)
% 20.13/9.80  % (27930)Instruction limit reached!
% 20.13/9.80  % (27930)------------------------------
% 20.13/9.80  % (27930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.13/9.80  % (27930)Termination reason: Unknown
% 20.13/9.80  % (27930)Termination phase: shuffling
% 20.13/9.80  
% 20.13/9.80  % (27930)Memory used [KB]: 13304
% 20.13/9.80  % (27930)Time elapsed: 0.007 s
% 20.13/9.80  % (27930)Instructions burned: 6 (million)
% 20.13/9.80  % (27930)------------------------------
% 20.13/9.80  % (27930)------------------------------
% 20.13/9.80  % (27931)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_27763 for (2988ds/150Mi)
% 20.13/9.81  % (27932)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_27763 for (2988ds/343Mi)
% 20.13/9.81  % (27929)Instruction limit reached!
% 20.13/9.81  % (27929)------------------------------
% 20.13/9.81  % (27929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.13/9.81  % (27929)Termination reason: Unknown
% 20.13/9.81  % (27929)Termination phase: shuffling
% 20.13/9.81  
% 20.13/9.81  % (27929)Memory used [KB]: 14200
% 20.13/9.81  % (27929)Time elapsed: 0.022 s
% 20.13/9.81  % (27929)Instructions burned: 44 (million)
% 20.13/9.81  % (27929)------------------------------
% 20.13/9.81  % (27929)------------------------------
% 20.13/9.81  % (27933)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_27763 for (2988ds/109Mi)
% 20.13/9.82  % (27934)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_27763 for (2988ds/253Mi)
% 20.13/9.83  % (27921)Instruction limit reached!
% 20.13/9.83  % (27921)------------------------------
% 20.13/9.83  % (27921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.13/9.83  % (27921)Termination reason: Unknown
% 20.13/9.83  % (27921)Termination phase: shuffling
% 20.13/9.83  
% 20.13/9.83  % (27921)Memory used [KB]: 21492
% 20.13/9.83  % (27921)Time elapsed: 0.149 s
% 20.13/9.83  % (27921)Instructions burned: 432 (million)
% 20.13/9.83  % (27921)------------------------------
% 20.13/9.83  % (27921)------------------------------
% 20.13/9.84  % (27935)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_27763 for (2988ds/140Mi)
% 20.13/9.86  % (27933)Instruction limit reached!
% 20.13/9.86  % (27933)------------------------------
% 20.13/9.86  % (27933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.13/9.86  % (27933)Termination reason: Unknown
% 20.13/9.86  % (27933)Termination phase: shuffling
% 20.13/9.86  
% 20.13/9.86  % (27933)Memory used [KB]: 14967
% 20.13/9.86  % (27933)Time elapsed: 0.045 s
% 20.13/9.86  % (27933)Instructions burned: 111 (million)
% 20.13/9.86  % (27933)------------------------------
% 20.13/9.86  % (27933)------------------------------
% 20.13/9.86  % (27925)Instruction limit reached!
% 20.13/9.86  % (27925)------------------------------
% 20.13/9.86  % (27925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.13/9.86  % (27925)Termination reason: Unknown
% 20.13/9.86  % (27925)Termination phase: shuffling
% 20.13/9.86  
% 20.13/9.86  % (27925)Memory used [KB]: 22003
% 20.13/9.86  % (27925)Time elapsed: 0.141 s
% 20.13/9.86  % (27925)Instructions burned: 455 (million)
% 20.13/9.86  % (27925)------------------------------
% 20.13/9.86  % (27925)------------------------------
% 20.13/9.87  % (27936)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_27763 for (2988ds/614Mi)
% 20.13/9.87  % (27937)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_27763 for (2988ds/202Mi)
% 20.13/9.88  % (27931)Instruction limit reached!
% 20.13/9.88  % (27931)------------------------------
% 20.13/9.88  % (27931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.13/9.88  % (27931)Termination reason: Unknown
% 20.13/9.88  % (27931)Termination phase: shuffling
% 20.13/9.88  
% 20.13/9.88  % (27931)Memory used [KB]: 15735
% 20.13/9.88  % (27931)Time elapsed: 0.083 s
% 20.13/9.88  % (27931)Instructions burned: 150 (million)
% 20.13/9.88  % (27931)------------------------------
% 20.13/9.88  % (27931)------------------------------
% 20.13/9.89  % (27935)Instruction limit reached!
% 20.13/9.89  % (27935)------------------------------
% 20.13/9.89  % (27935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.13/9.89  % (27935)Termination reason: Unknown
% 20.13/9.89  % (27935)Termination phase: shuffling
% 20.13/9.89  
% 20.13/9.89  % (27935)Memory used [KB]: 15351
% 20.13/9.89  % (27935)Time elapsed: 0.054 s
% 20.13/9.89  % (27935)Instructions burned: 142 (million)
% 20.13/9.89  % (27935)------------------------------
% 20.13/9.89  % (27935)------------------------------
% 20.72/9.90  % (27938)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_27763 for (2987ds/339Mi)
% 20.72/9.90  % (27939)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_27763 for (2987ds/283Mi)
% 20.72/9.91  % (27934)Instruction limit reached!
% 20.72/9.91  % (27934)------------------------------
% 20.72/9.91  % (27934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.72/9.91  % (27934)Termination reason: Unknown
% 20.72/9.91  % (27934)Termination phase: shuffling
% 20.72/9.91  
% 20.72/9.91  % (27934)Memory used [KB]: 17014
% 20.72/9.91  % (27934)Time elapsed: 0.094 s
% 20.72/9.91  % (27934)Instructions burned: 254 (million)
% 20.72/9.91  % (27934)------------------------------
% 20.72/9.91  % (27934)------------------------------
% 20.72/9.93  % (27940)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_27763 for (2987ds/134Mi)
% 20.72/9.94  % (27932)Instruction limit reached!
% 20.72/9.94  % (27932)------------------------------
% 20.72/9.94  % (27932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.72/9.94  % (27932)Termination reason: Unknown
% 20.72/9.94  % (27932)Termination phase: shuffling
% 20.72/9.94  
% 20.72/9.94  % (27932)Memory used [KB]: 17910
% 20.72/9.94  % (27932)Time elapsed: 0.140 s
% 20.72/9.94  % (27932)Instructions burned: 343 (million)
% 20.72/9.94  % (27932)------------------------------
% 20.72/9.94  % (27932)------------------------------
% 20.72/9.94  % (27937)Instruction limit reached!
% 20.72/9.94  % (27937)------------------------------
% 20.72/9.94  % (27937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.72/9.94  % (27937)Termination reason: Unknown
% 20.72/9.94  % (27937)Termination phase: shuffling
% 20.72/9.94  
% 20.72/9.94  % (27937)Memory used [KB]: 16247
% 20.72/9.94  % (27937)Time elapsed: 0.075 s
% 20.72/9.94  % (27937)Instructions burned: 202 (million)
% 20.72/9.94  % (27937)------------------------------
% 20.72/9.94  % (27937)------------------------------
% 20.72/9.96  % (27942)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_27763 for (2987ds/192Mi)
% 20.72/9.96  % (27941)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_27763 for (2987ds/298Mi)
% 20.72/9.98  % (27940)Instruction limit reached!
% 20.72/9.98  % (27940)------------------------------
% 20.72/9.98  % (27940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.72/9.98  % (27940)Termination reason: Unknown
% 20.72/9.98  % (27940)Termination phase: shuffling
% 20.72/9.98  
% 20.72/9.98  % (27940)Memory used [KB]: 15351
% 20.72/9.98  % (27940)Time elapsed: 0.053 s
% 20.72/9.98  % (27940)Instructions burned: 136 (million)
% 20.72/9.98  % (27940)------------------------------
% 20.72/9.98  % (27940)------------------------------
% 20.72/9.99  % (27918)Instruction limit reached!
% 20.72/9.99  % (27918)------------------------------
% 20.72/9.99  % (27918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.72/9.99  % (27918)Termination reason: Unknown
% 20.72/9.99  % (27918)Termination phase: Property scanning
% 20.72/9.99  
% 20.72/9.99  % (27918)Memory used [KB]: 27504
% 20.72/9.99  % (27918)Time elapsed: 0.366 s
% 20.72/9.99  % (27918)Instructions burned: 1090 (million)
% 20.72/9.99  % (27918)------------------------------
% 20.72/9.99  % (27918)------------------------------
% 20.72/9.99  % (27943)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_27763 for (2986ds/258Mi)
% 20.72/9.99  % (27939)Instruction limit reached!
% 20.72/9.99  % (27939)------------------------------
% 20.72/9.99  % (27939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.72/9.99  % (27939)Termination reason: Unknown
% 20.72/9.99  % (27939)Termination phase: shuffling
% 20.72/9.99  
% 20.72/9.99  % (27939)Memory used [KB]: 19701
% 20.72/9.99  % (27939)Time elapsed: 0.091 s
% 20.72/9.99  % (27939)Instructions burned: 284 (million)
% 20.72/9.99  % (27939)------------------------------
% 20.72/9.99  % (27939)------------------------------
% 20.72/10.00  % (27944)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_27763 for (2986ds/90Mi)
% 20.72/10.00  % (27945)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_27763 for (2986ds/231Mi)
% 22.01/10.02  % (27938)Instruction limit reached!
% 22.01/10.02  % (27938)------------------------------
% 22.01/10.02  % (27938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.01/10.02  % (27938)Termination reason: Unknown
% 22.01/10.02  % (27938)Termination phase: shuffling
% 22.01/10.02  
% 22.01/10.02  % (27938)Memory used [KB]: 18166
% 22.01/10.02  % (27938)Time elapsed: 0.121 s
% 22.01/10.02  % (27938)Instructions burned: 341 (million)
% 22.01/10.02  % (27938)------------------------------
% 22.01/10.02  % (27938)------------------------------
% 22.01/10.03  % (27942)Instruction limit reached!
% 22.01/10.03  % (27942)------------------------------
% 22.01/10.03  % (27942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.01/10.03  % (27942)Termination reason: Unknown
% 22.01/10.03  % (27942)Termination phase: shuffling
% 22.01/10.03  
% 22.01/10.03  % (27942)Memory used [KB]: 16119
% 22.01/10.03  % (27942)Time elapsed: 0.072 s
% 22.01/10.03  % (27942)Instructions burned: 193 (million)
% 22.01/10.03  % (27942)------------------------------
% 22.01/10.03  % (27942)------------------------------
% 22.01/10.03  % (27946)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_27763 for (2986ds/458Mi)
% 22.01/10.04  % (27947)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_27763 for (2986ds/31Mi)
% 22.01/10.04  % (27944)Instruction limit reached!
% 22.01/10.04  % (27944)------------------------------
% 22.01/10.04  % (27944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.01/10.04  % (27944)Termination reason: Unknown
% 22.01/10.04  % (27944)Termination phase: shuffling
% 22.01/10.04  
% 22.01/10.04  % (27944)Memory used [KB]: 14967
% 22.01/10.04  % (27944)Time elapsed: 0.040 s
% 22.01/10.04  % (27944)Instructions burned: 91 (million)
% 22.01/10.04  % (27944)------------------------------
% 22.01/10.04  % (27944)------------------------------
% 22.01/10.05  % (27948)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_27763 for (2986ds/297Mi)
% 22.01/10.06  % (27947)Instruction limit reached!
% 22.01/10.06  % (27947)------------------------------
% 22.01/10.06  % (27947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.01/10.06  % (27947)Termination reason: Unknown
% 22.01/10.06  % (27947)Termination phase: shuffling
% 22.01/10.06  
% 22.01/10.06  % (27947)Memory used [KB]: 14072
% 22.01/10.06  % (27947)Time elapsed: 0.021 s
% 22.01/10.06  % (27947)Instructions burned: 33 (million)
% 22.01/10.06  % (27947)------------------------------
% 22.01/10.06  % (27947)------------------------------
% 22.01/10.07  % (27941)Instruction limit reached!
% 22.01/10.07  % (27941)------------------------------
% 22.01/10.07  % (27941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.01/10.07  % (27941)Termination reason: Unknown
% 22.01/10.07  % (27941)Termination phase: shuffling
% 22.01/10.07  
% 22.01/10.07  % (27941)Memory used [KB]: 19957
% 22.01/10.07  % (27941)Time elapsed: 0.110 s
% 22.01/10.07  % (27941)Instructions burned: 299 (million)
% 22.01/10.07  % (27941)------------------------------
% 22.01/10.07  % (27941)------------------------------
% 22.01/10.07  % (27949)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_27763 for (2986ds/987Mi)
% 22.01/10.08  % (27945)Instruction limit reached!
% 22.01/10.08  % (27945)------------------------------
% 22.01/10.08  % (27945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.01/10.08  % (27945)Termination reason: Unknown
% 22.01/10.08  % (27945)Termination phase: shuffling
% 22.01/10.08  
% 22.01/10.08  % (27945)Memory used [KB]: 17014
% 22.01/10.08  % (27945)Time elapsed: 0.075 s
% 22.01/10.08  % (27945)Instructions burned: 234 (million)
% 22.01/10.08  % (27945)------------------------------
% 22.01/10.08  % (27945)------------------------------
% 22.01/10.08  % (27950)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_27763 for (2986ds/182Mi)
% 22.01/10.08  % (27943)Instruction limit reached!
% 22.01/10.08  % (27943)------------------------------
% 22.01/10.08  % (27943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.01/10.08  % (27943)Termination reason: Unknown
% 22.01/10.08  % (27943)Termination phase: shuffling
% 22.01/10.08  
% 22.01/10.08  % (27943)Memory used [KB]: 16886
% 22.01/10.08  % (27943)Time elapsed: 0.094 s
% 22.01/10.08  % (27943)Instructions burned: 259 (million)
% 22.01/10.08  % (27943)------------------------------
% 22.01/10.08  % (27943)------------------------------
% 22.01/10.08  % (27936)Instruction limit reached!
% 22.01/10.08  % (27936)------------------------------
% 22.01/10.08  % (27936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.01/10.08  % (27936)Termination reason: Unknown
% 22.01/10.08  % (27936)Termination phase: shuffling
% 22.01/10.08  
% 22.01/10.08  % (27936)Memory used [KB]: 23027
% 22.01/10.08  % (27936)Time elapsed: 0.216 s
% 22.01/10.08  % (27936)Instructions burned: 614 (million)
% 22.01/10.08  % (27936)------------------------------
% 22.01/10.08  % (27936)------------------------------
% 22.01/10.09  % (27951)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_27763 for (2985ds/182Mi)
% 22.01/10.09  % (27952)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_27763 for (2985ds/154Mi)
% 22.01/10.09  % (27953)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_27763 for (2985ds/79Mi)
% 22.44/10.13  % (27953)Instruction limit reached!
% 22.44/10.13  % (27953)------------------------------
% 22.44/10.13  % (27953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.44/10.13  % (27953)Termination reason: Unknown
% 22.44/10.13  % (27953)Termination phase: shuffling
% 22.44/10.13  
% 22.44/10.13  % (27953)Memory used [KB]: 14711
% 22.44/10.13  % (27953)Time elapsed: 0.034 s
% 22.44/10.13  % (27953)Instructions burned: 79 (million)
% 22.44/10.13  % (27953)------------------------------
% 22.44/10.13  % (27953)------------------------------
% 22.44/10.14  % (27954)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_27763 for (2985ds/216Mi)
% 22.44/10.14  % (27950)Instruction limit reached!
% 22.44/10.14  % (27950)------------------------------
% 22.44/10.14  % (27950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.44/10.14  % (27950)Termination reason: Unknown
% 22.44/10.14  % (27950)Termination phase: shuffling
% 22.44/10.14  
% 22.44/10.14  % (27950)Memory used [KB]: 15863
% 22.44/10.14  % (27950)Time elapsed: 0.067 s
% 22.44/10.14  % (27950)Instructions burned: 182 (million)
% 22.44/10.14  % (27950)------------------------------
% 22.44/10.14  % (27950)------------------------------
% 22.44/10.14  % (27952)Instruction limit reached!
% 22.44/10.14  % (27952)------------------------------
% 22.44/10.14  % (27952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.44/10.14  % (27952)Termination reason: Unknown
% 22.44/10.14  % (27952)Termination phase: shuffling
% 22.44/10.14  
% 22.44/10.14  % (27952)Memory used [KB]: 15991
% 22.44/10.14  % (27952)Time elapsed: 0.053 s
% 22.44/10.14  % (27952)Instructions burned: 156 (million)
% 22.44/10.14  % (27952)------------------------------
% 22.44/10.14  % (27952)------------------------------
% 22.44/10.15  % (27948)Instruction limit reached!
% 22.44/10.15  % (27948)------------------------------
% 22.44/10.15  % (27948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.44/10.15  % (27948)Termination reason: Unknown
% 22.44/10.15  % (27948)Termination phase: shuffling
% 22.44/10.15  
% 22.44/10.15  % (27948)Memory used [KB]: 19829
% 22.44/10.15  % (27948)Time elapsed: 0.095 s
% 22.44/10.15  % (27948)Instructions burned: 298 (million)
% 22.44/10.15  % (27948)------------------------------
% 22.44/10.15  % (27948)------------------------------
% 22.44/10.16  % (27951)Instruction limit reached!
% 22.44/10.16  % (27951)------------------------------
% 22.44/10.16  % (27951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.44/10.16  % (27951)Termination reason: Unknown
% 22.44/10.16  % (27951)Termination phase: shuffling
% 22.44/10.16  
% 22.44/10.16  % (27951)Memory used [KB]: 15863
% 22.44/10.16  % (27951)Time elapsed: 0.068 s
% 22.44/10.16  % (27951)Instructions burned: 184 (million)
% 22.44/10.16  % (27951)------------------------------
% 22.44/10.16  % (27951)------------------------------
% 22.44/10.16  % (27955)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_27763 for (2985ds/114Mi)
% 22.44/10.16  % (27956)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_27763 for (2985ds/922Mi)
% 22.44/10.16  % (27957)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_27763 for (2985ds/182Mi)
% 22.44/10.17  % (27958)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_27763 for (2985ds/164Mi)
% 22.44/10.19  % (27946)Instruction limit reached!
% 22.44/10.19  % (27946)------------------------------
% 22.44/10.19  % (27946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.44/10.19  % (27946)Termination reason: Unknown
% 22.44/10.19  % (27946)Termination phase: shuffling
% 22.44/10.19  
% 22.44/10.19  % (27946)Memory used [KB]: 19317
% 22.44/10.19  % (27946)Time elapsed: 0.158 s
% 22.44/10.19  % (27946)Instructions burned: 458 (million)
% 22.44/10.19  % (27946)------------------------------
% 22.44/10.19  % (27946)------------------------------
% 22.98/10.20  % (27963)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_27763 for (2984ds/50Mi)
% 22.98/10.20  % (27955)Instruction limit reached!
% 22.98/10.20  % (27955)------------------------------
% 22.98/10.20  % (27955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.98/10.20  % (27955)Termination reason: Unknown
% 22.98/10.20  % (27955)Termination phase: shuffling
% 22.98/10.20  
% 22.98/10.20  % (27955)Memory used [KB]: 15223
% 22.98/10.20  % (27955)Time elapsed: 0.047 s
% 22.98/10.20  % (27955)Instructions burned: 114 (million)
% 22.98/10.20  % (27955)------------------------------
% 22.98/10.20  % (27955)------------------------------
% 22.98/10.21  % (27954)Instruction limit reached!
% 22.98/10.21  % (27954)------------------------------
% 22.98/10.21  % (27954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.98/10.21  % (27954)Termination reason: Unknown
% 22.98/10.21  % (27954)Termination phase: shuffling
% 22.98/10.21  
% 22.98/10.21  % (27954)Memory used [KB]: 16758
% 22.98/10.21  % (27954)Time elapsed: 0.072 s
% 22.98/10.21  % (27954)Instructions burned: 217 (million)
% 22.98/10.21  % (27954)------------------------------
% 22.98/10.21  % (27954)------------------------------
% 22.98/10.21  % (27972)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_27763 for (2984ds/368Mi)
% 22.98/10.22  % (27957)Instruction limit reached!
% 22.98/10.22  % (27957)------------------------------
% 22.98/10.22  % (27957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.98/10.22  % (27957)Termination reason: Unknown
% 22.98/10.22  % (27957)Termination phase: shuffling
% 22.98/10.22  
% 22.98/10.22  % (27957)Memory used [KB]: 16119
% 22.98/10.22  % (27957)Time elapsed: 0.061 s
% 22.98/10.22  % (27957)Instructions burned: 182 (million)
% 22.98/10.22  % (27957)------------------------------
% 22.98/10.22  % (27957)------------------------------
% 22.98/10.22  % (27976)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_27763 for (2984ds/1021Mi)
% 22.98/10.22  % (27963)Instruction limit reached!
% 22.98/10.22  % (27963)------------------------------
% 22.98/10.22  % (27963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.98/10.22  % (27963)Termination reason: Unknown
% 22.98/10.22  % (27963)Termination phase: shuffling
% 22.98/10.22  
% 22.98/10.22  % (27963)Memory used [KB]: 14456
% 22.98/10.22  % (27963)Time elapsed: 0.025 s
% 22.98/10.22  % (27963)Instructions burned: 53 (million)
% 22.98/10.22  % (27963)------------------------------
% 22.98/10.22  % (27963)------------------------------
% 22.98/10.22  % (27958)Instruction limit reached!
% 22.98/10.22  % (27958)------------------------------
% 22.98/10.22  % (27958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.98/10.22  % (27958)Termination reason: Unknown
% 22.98/10.22  % (27958)Termination phase: shuffling
% 22.98/10.22  
% 22.98/10.22  % (27958)Memory used [KB]: 15991
% 22.98/10.22  % (27958)Time elapsed: 0.057 s
% 22.98/10.22  % (27958)Instructions burned: 165 (million)
% 22.98/10.22  % (27958)------------------------------
% 22.98/10.22  % (27958)------------------------------
% 22.98/10.23  % (27981)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_27763 for (2984ds/267Mi)
% 22.98/10.23  % (27984)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_27763 for (2984ds/204Mi)
% 22.98/10.23  % (27985)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_27763 for (2984ds/26Mi)
% 22.98/10.25  % (27985)Instruction limit reached!
% 22.98/10.25  % (27985)------------------------------
% 22.98/10.25  % (27985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.98/10.25  % (27985)Termination reason: Unknown
% 22.98/10.25  % (27985)Termination phase: shuffling
% 22.98/10.25  
% 22.98/10.25  % (27985)Memory used [KB]: 13944
% 22.98/10.25  % (27985)Time elapsed: 0.018 s
% 22.98/10.25  % (27985)Instructions burned: 27 (million)
% 22.98/10.25  % (27985)------------------------------
% 22.98/10.25  % (27985)------------------------------
% 22.98/10.26  % (28000)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_27763 for (2984ds/53Mi)
% 22.98/10.29  % (28000)Instruction limit reached!
% 22.98/10.29  % (28000)------------------------------
% 22.98/10.29  % (28000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.98/10.29  % (28000)Termination reason: Unknown
% 22.98/10.29  % (28000)Termination phase: shuffling
% 22.98/10.29  
% 22.98/10.29  % (28000)Memory used [KB]: 14456
% 22.98/10.29  % (28000)Time elapsed: 0.026 s
% 22.98/10.29  % (28000)Instructions burned: 55 (million)
% 22.98/10.29  % (28000)------------------------------
% 22.98/10.29  % (28000)------------------------------
% 23.36/10.30  % (28014)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_27763 for (2983ds/4436Mi)
% 23.36/10.31  % (27984)Instruction limit reached!
% 23.36/10.31  % (27984)------------------------------
% 23.36/10.31  % (27984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.36/10.31  % (27984)Termination reason: Unknown
% 23.36/10.31  % (27984)Termination phase: shuffling
% 23.36/10.31  
% 23.36/10.31  % (27984)Memory used [KB]: 16247
% 23.36/10.31  % (27984)Time elapsed: 0.078 s
% 23.36/10.31  % (27984)Instructions burned: 206 (million)
% 23.36/10.31  % (27984)------------------------------
% 23.36/10.31  % (27984)------------------------------
% 23.36/10.32  % (27981)Instruction limit reached!
% 23.36/10.32  % (27981)------------------------------
% 23.36/10.32  % (27981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.36/10.32  % (27981)Termination reason: Unknown
% 23.36/10.32  % (27981)Termination phase: shuffling
% 23.36/10.32  
% 23.36/10.32  % (27981)Memory used [KB]: 19445
% 23.36/10.32  % (27981)Time elapsed: 0.089 s
% 23.36/10.32  % (27981)Instructions burned: 267 (million)
% 23.36/10.32  % (27981)------------------------------
% 23.36/10.32  % (27981)------------------------------
% 23.36/10.32  % (28024)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_27763 for (2983ds/1539Mi)
% 23.36/10.33  % (28025)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_27763 for (2983ds/408Mi)
% 23.36/10.34  % (27972)Instruction limit reached!
% 23.36/10.34  % (27972)------------------------------
% 23.36/10.34  % (27972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.36/10.34  % (27972)Termination reason: Unknown
% 23.36/10.34  % (27972)Termination phase: shuffling
% 23.36/10.34  
% 23.36/10.34  % (27972)Memory used [KB]: 18166
% 23.36/10.34  % (27972)Time elapsed: 0.132 s
% 23.36/10.34  % (27972)Instructions burned: 371 (million)
% 23.36/10.34  % (27972)------------------------------
% 23.36/10.34  % (27972)------------------------------
% 23.36/10.36  % (28035)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_27763 for (2983ds/5205Mi)
% 23.36/10.37  % (27949)Instruction limit reached!
% 23.36/10.37  % (27949)------------------------------
% 23.36/10.37  % (27949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.36/10.37  % (27949)Termination reason: Unknown
% 23.36/10.37  % (27949)Termination phase: shuffling
% 23.36/10.37  
% 23.36/10.37  % (27949)Memory used [KB]: 33133
% 23.36/10.37  % (27949)Time elapsed: 0.302 s
% 23.36/10.37  % (27949)Instructions burned: 987 (million)
% 23.36/10.37  % (27949)------------------------------
% 23.36/10.37  % (27949)------------------------------
% 23.36/10.38  % (28054)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_27763 for (2982ds/1913Mi)
% 24.00/10.47  % (28025)Instruction limit reached!
% 24.00/10.47  % (28025)------------------------------
% 24.00/10.47  % (28025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.00/10.47  % (28025)Termination reason: Unknown
% 24.00/10.47  % (28025)Termination phase: shuffling
% 24.00/10.47  
% 24.00/10.47  % (28025)Memory used [KB]: 18805
% 24.00/10.47  % (28025)Time elapsed: 0.144 s
% 24.00/10.47  % (28025)Instructions burned: 410 (million)
% 24.00/10.47  % (28025)------------------------------
% 24.00/10.47  % (28025)------------------------------
% 24.00/10.47  % (27956)Instruction limit reached!
% 24.00/10.47  % (27956)------------------------------
% 24.00/10.47  % (27956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.00/10.47  % (27956)Termination reason: Unknown
% 24.00/10.47  % (27956)Termination phase: shuffling
% 24.00/10.47  
% 24.00/10.47  % (27956)Memory used [KB]: 26865
% 24.00/10.47  % (27956)Time elapsed: 0.320 s
% 24.00/10.47  % (27956)Instructions burned: 922 (million)
% 24.00/10.47  % (27956)------------------------------
% 24.00/10.47  % (27956)------------------------------
% 24.00/10.48  % (28102)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_27763 for (2981ds/4350Mi)
% 24.00/10.49  % (28105)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_27763 for (2981ds/68Mi)
% 24.49/10.52  % (28105)Instruction limit reached!
% 24.49/10.52  % (28105)------------------------------
% 24.49/10.52  % (28105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.49/10.52  % (28105)Termination reason: Unknown
% 24.49/10.52  % (28105)Termination phase: shuffling
% 24.49/10.52  
% 24.49/10.52  % (28105)Memory used [KB]: 14583
% 24.49/10.52  % (28105)Time elapsed: 0.034 s
% 24.49/10.52  % (28105)Instructions burned: 70 (million)
% 24.49/10.52  % (28105)------------------------------
% 24.49/10.52  % (28105)------------------------------
% 24.49/10.53  % (28123)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_27763 for (2981ds/358Mi)
% 24.49/10.57  % (27976)Instruction limit reached!
% 24.49/10.57  % (27976)------------------------------
% 24.49/10.57  % (27976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.49/10.57  % (27976)Termination reason: Unknown
% 24.49/10.57  % (27976)Termination phase: Property scanning
% 24.49/10.57  
% 24.49/10.57  % (27976)Memory used [KB]: 27504
% 24.49/10.57  % (27976)Time elapsed: 0.352 s
% 24.49/10.57  % (27976)Instructions burned: 1022 (million)
% 24.49/10.57  % (27976)------------------------------
% 24.49/10.57  % (27976)------------------------------
% 24.49/10.58  % (28144)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_27763 for (2980ds/31Mi)
% 24.90/10.60  % (28144)Instruction limit reached!
% 24.90/10.60  % (28144)------------------------------
% 24.90/10.60  % (28144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.90/10.60  % (28144)Termination reason: Unknown
% 24.90/10.60  % (28144)Termination phase: shuffling
% 24.90/10.60  
% 24.90/10.60  % (28144)Memory used [KB]: 14072
% 24.90/10.60  % (28144)Time elapsed: 0.020 s
% 24.90/10.60  % (28144)Instructions burned: 31 (million)
% 24.90/10.60  % (28144)------------------------------
% 24.90/10.60  % (28144)------------------------------
% 24.90/10.61  % (28151)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_27763 for (2980ds/279Mi)
% 24.90/10.66  % (28123)Instruction limit reached!
% 24.90/10.66  % (28123)------------------------------
% 24.90/10.66  % (28123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.90/10.66  % (28123)Termination reason: Unknown
% 24.90/10.66  % (28123)Termination phase: shuffling
% 24.90/10.66  
% 24.90/10.66  % (28123)Memory used [KB]: 18038
% 24.90/10.66  % (28123)Time elapsed: 0.126 s
% 24.90/10.66  % (28123)Instructions burned: 361 (million)
% 24.90/10.66  % (28123)------------------------------
% 24.90/10.66  % (28123)------------------------------
% 24.90/10.67  % (28167)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_27763 for (2980ds/258Mi)
% 25.07/10.70  % (28151)Instruction limit reached!
% 25.07/10.70  % (28151)------------------------------
% 25.07/10.70  % (28151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.07/10.70  % (28151)Termination reason: Unknown
% 25.07/10.70  % (28151)Termination phase: shuffling
% 25.07/10.70  
% 25.07/10.70  % (28151)Memory used [KB]: 19701
% 25.07/10.70  % (28151)Time elapsed: 0.088 s
% 25.07/10.70  % (28151)Instructions burned: 279 (million)
% 25.07/10.70  % (28151)------------------------------
% 25.07/10.70  % (28151)------------------------------
% 25.07/10.71  % (28195)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_27763 for (2979ds/26Mi)
% 25.07/10.73  % (28195)Instruction limit reached!
% 25.07/10.73  % (28195)------------------------------
% 25.07/10.73  % (28195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.07/10.73  % (28195)Termination reason: Unknown
% 25.07/10.73  % (28195)Termination phase: shuffling
% 25.07/10.73  
% 25.07/10.73  % (28195)Memory used [KB]: 14072
% 25.07/10.73  % (28195)Time elapsed: 0.017 s
% 25.07/10.73  % (28195)Instructions burned: 27 (million)
% 25.07/10.73  % (28195)------------------------------
% 25.07/10.73  % (28195)------------------------------
% 25.07/10.74  % (28206)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_27763 for (2979ds/995Mi)
% 25.07/10.76  % (28167)Instruction limit reached!
% 25.07/10.76  % (28167)------------------------------
% 25.07/10.76  % (28167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.07/10.76  % (28167)Termination reason: Unknown
% 25.07/10.76  % (28167)Termination phase: shuffling
% 25.07/10.76  
% 25.07/10.76  % (28167)Memory used [KB]: 16886
% 25.07/10.76  % (28167)Time elapsed: 0.092 s
% 25.07/10.76  % (28167)Instructions burned: 259 (million)
% 25.07/10.76  % (28167)------------------------------
% 25.07/10.76  % (28167)------------------------------
% 25.07/10.77  % (28210)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_27763 for (2979ds/373Mi)
% 25.31/10.80  % (28024)Instruction limit reached!
% 25.31/10.80  % (28024)------------------------------
% 25.31/10.80  % (28024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.31/10.80  % (28024)Termination reason: Unknown
% 25.31/10.80  % (28024)Termination phase: Property scanning
% 25.31/10.80  
% 25.31/10.80  % (28024)Memory used [KB]: 27376
% 25.31/10.80  % (28024)Time elapsed: 0.477 s
% 25.31/10.80  % (28024)Instructions burned: 1541 (million)
% 25.31/10.80  % (28024)------------------------------
% 25.31/10.80  % (28024)------------------------------
% 25.31/10.81  % (28211)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_27763 for (2978ds/253Mi)
% 25.31/10.89  % (28211)Instruction limit reached!
% 25.31/10.89  % (28211)------------------------------
% 25.31/10.89  % (28211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.31/10.89  % (28211)Termination reason: Unknown
% 25.31/10.89  % (28211)Termination phase: shuffling
% 25.31/10.89  
% 25.31/10.89  % (28211)Memory used [KB]: 19189
% 25.31/10.89  % (28211)Time elapsed: 0.080 s
% 25.31/10.89  % (28211)Instructions burned: 253 (million)
% 25.31/10.89  % (28211)------------------------------
% 25.31/10.89  % (28211)------------------------------
% 25.88/10.90  % (28210)Instruction limit reached!
% 25.88/10.90  % (28210)------------------------------
% 25.88/10.90  % (28210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.88/10.90  % (28210)Termination reason: Unknown
% 25.88/10.90  % (28210)Termination phase: shuffling
% 25.88/10.90  
% 25.88/10.90  % (28210)Memory used [KB]: 18549
% 25.88/10.90  % (28210)Time elapsed: 0.129 s
% 25.88/10.90  % (28210)Instructions burned: 374 (million)
% 25.88/10.90  % (28210)------------------------------
% 25.88/10.90  % (28210)------------------------------
% 25.88/10.90  % (28212)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_27763 for (2977ds/832Mi)
% 25.88/10.91  % (28213)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_27763 for (2977ds/668Mi)
% 25.88/10.97  % (28054)Instruction limit reached!
% 25.88/10.97  % (28054)------------------------------
% 25.88/10.97  % (28054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.88/10.97  % (28054)Termination reason: Unknown
% 25.88/10.97  % (28054)Termination phase: SInE selection
% 25.88/10.97  
% 25.88/10.97  % (28054)Memory used [KB]: 27760
% 25.88/10.97  % (28054)Time elapsed: 0.586 s
% 25.88/10.97  % (28054)Instructions burned: 1915 (million)
% 25.88/10.97  % (28054)------------------------------
% 25.88/10.97  % (28054)------------------------------
% 25.88/10.98  % (28214)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_27763 for (2977ds/40Mi)
% 25.88/11.00  % (28214)Instruction limit reached!
% 25.88/11.00  % (28214)------------------------------
% 25.88/11.00  % (28214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.88/11.00  % (28214)Termination reason: Unknown
% 25.88/11.00  % (28214)Termination phase: shuffling
% 25.88/11.00  
% 25.88/11.00  % (28214)Memory used [KB]: 14200
% 25.88/11.00  % (28214)Time elapsed: 0.022 s
% 25.88/11.00  % (28214)Instructions burned: 42 (million)
% 25.88/11.00  % (28214)------------------------------
% 25.88/11.00  % (28214)------------------------------
% 25.88/11.01  % (28215)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_27763 for (2976ds/294Mi)
% 29.09/11.03  % (28206)Instruction limit reached!
% 29.09/11.03  % (28206)------------------------------
% 29.09/11.03  % (28206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.09/11.03  % (28206)Termination reason: Unknown
% 29.09/11.03  % (28206)Termination phase: shuffling
% 29.09/11.03  
% 29.09/11.03  % (28206)Memory used [KB]: 33133
% 29.09/11.03  % (28206)Time elapsed: 0.292 s
% 29.09/11.03  % (28206)Instructions burned: 997 (million)
% 29.09/11.03  % (28206)------------------------------
% 29.09/11.03  % (28206)------------------------------
% 29.09/11.04  % (28216)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_27763 for (2976ds/187Mi)
% 29.09/11.11  % (28215)Instruction limit reached!
% 29.09/11.11  % (28215)------------------------------
% 29.09/11.11  % (28215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.09/11.11  % (28215)Termination reason: Unknown
% 29.09/11.11  % (28215)Termination phase: shuffling
% 29.09/11.11  
% 29.09/11.11  % (28215)Memory used [KB]: 19829
% 29.09/11.11  % (28215)Time elapsed: 0.095 s
% 29.09/11.11  % (28215)Instructions burned: 294 (million)
% 29.09/11.11  % (28215)------------------------------
% 29.09/11.11  % (28215)------------------------------
% 29.09/11.11  % (28213)Instruction limit reached!
% 29.09/11.11  % (28213)------------------------------
% 29.09/11.11  % (28213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.09/11.11  % (28213)Termination reason: Unknown
% 29.09/11.11  % (28213)Termination phase: shuffling
% 29.09/11.11  
% 29.09/11.11  % (28213)Memory used [KB]: 24818
% 29.09/11.11  % (28213)Time elapsed: 0.199 s
% 29.09/11.11  % (28213)Instructions burned: 668 (million)
% 29.09/11.11  % (28213)------------------------------
% 29.09/11.11  % (28213)------------------------------
% 29.09/11.11  % (28216)Instruction limit reached!
% 29.09/11.11  % (28216)------------------------------
% 29.09/11.11  % (28216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.09/11.11  % (28216)Termination reason: Unknown
% 29.09/11.11  % (28216)Termination phase: shuffling
% 29.09/11.11  
% 29.09/11.11  % (28216)Memory used [KB]: 16247
% 29.09/11.11  % (28216)Time elapsed: 0.072 s
% 29.09/11.11  % (28216)Instructions burned: 187 (million)
% 29.09/11.11  % (28216)------------------------------
% 29.09/11.11  % (28216)------------------------------
% 29.09/11.12  % (28217)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_27763 for (2975ds/371Mi)
% 29.09/11.12  % (28218)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_27763 for (2975ds/1827Mi)
% 29.82/11.13  % (28219)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_27763 for (2975ds/70Mi)
% 29.82/11.15  % (28219)Instruction limit reached!
% 29.82/11.15  % (28219)------------------------------
% 29.82/11.15  % (28219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.82/11.15  % (28219)Termination reason: Unknown
% 29.82/11.15  % (28219)Termination phase: shuffling
% 29.82/11.15  
% 29.82/11.15  % (28219)Memory used [KB]: 14711
% 29.82/11.15  % (28219)Time elapsed: 0.030 s
% 29.82/11.15  % (28219)Instructions burned: 72 (million)
% 29.82/11.15  % (28219)------------------------------
% 29.82/11.15  % (28219)------------------------------
% 29.82/11.17  % (28220)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_27763 for (2975ds/316Mi)
% 29.82/11.19  % (28212)Instruction limit reached!
% 29.82/11.19  % (28212)------------------------------
% 29.82/11.19  % (28212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.82/11.19  % (28212)Termination reason: Unknown
% 29.82/11.19  % (28212)Termination phase: shuffling
% 29.82/11.19  
% 29.82/11.19  % (28212)Memory used [KB]: 25969
% 29.82/11.19  % (28212)Time elapsed: 0.287 s
% 29.82/11.19  % (28212)Instructions burned: 833 (million)
% 29.82/11.19  % (28212)------------------------------
% 29.82/11.19  % (28212)------------------------------
% 30.15/11.20  % (28221)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_27763 for (2974ds/932Mi)
% 30.15/11.25  % (28217)Instruction limit reached!
% 30.15/11.25  % (28217)------------------------------
% 30.15/11.25  % (28217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.15/11.25  % (28217)Termination reason: Unknown
% 30.15/11.25  % (28217)Termination phase: shuffling
% 30.15/11.25  
% 30.15/11.25  % (28217)Memory used [KB]: 18293
% 30.15/11.25  % (28217)Time elapsed: 0.130 s
% 30.15/11.25  % (28217)Instructions burned: 372 (million)
% 30.15/11.25  % (28217)------------------------------
% 30.15/11.25  % (28217)------------------------------
% 30.15/11.26  % (28222)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_27763 for (2974ds/4714Mi)
% 30.15/11.26  % (28220)Instruction limit reached!
% 30.15/11.26  % (28220)------------------------------
% 30.15/11.26  % (28220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.15/11.26  % (28220)Termination reason: Unknown
% 30.15/11.26  % (28220)Termination phase: shuffling
% 30.15/11.26  
% 30.15/11.26  % (28220)Memory used [KB]: 20212
% 30.15/11.26  % (28220)Time elapsed: 0.099 s
% 30.15/11.26  % (28220)Instructions burned: 318 (million)
% 30.15/11.26  % (28220)------------------------------
% 30.15/11.26  % (28220)------------------------------
% 30.15/11.28  % (28223)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_27763 for (2974ds/8250Mi)
% 31.01/11.47  % (28221)Instruction limit reached!
% 31.01/11.47  % (28221)------------------------------
% 31.01/11.47  % (28221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.01/11.47  % (28221)Termination reason: Unknown
% 31.01/11.47  % (28221)Termination phase: shuffling
% 31.01/11.47  
% 31.01/11.47  % (28221)Memory used [KB]: 32366
% 31.01/11.47  % (28221)Time elapsed: 0.270 s
% 31.01/11.47  % (28221)Instructions burned: 932 (million)
% 31.01/11.47  % (28221)------------------------------
% 31.01/11.47  % (28221)------------------------------
% 31.01/11.48  % (28224)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_27763 for (2971ds/770Mi)
% 31.89/11.69  % (28218)Instruction limit reached!
% 31.89/11.69  % (28218)------------------------------
% 31.89/11.69  % (28218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.89/11.69  % (28218)Termination reason: Unknown
% 31.89/11.69  % (28218)Termination phase: Naming
% 31.89/11.69  
% 31.89/11.69  % (28218)Memory used [KB]: 32622
% 31.89/11.69  % (28218)Time elapsed: 0.570 s
% 31.89/11.69  % (28218)Instructions burned: 1828 (million)
% 31.89/11.69  % (28218)------------------------------
% 31.89/11.69  % (28218)------------------------------
% 32.79/11.70  % (28225)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_27763 for (2969ds/794Mi)
% 32.79/11.71  % (28014)Instruction limit reached!
% 32.79/11.71  % (28014)------------------------------
% 32.79/11.71  % (28014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.79/11.71  % (28014)Termination reason: Unknown
% 32.79/11.71  % (28014)Termination phase: Saturation
% 32.79/11.71  
% 32.79/11.71  % (28014)Memory used [KB]: 36843
% 32.79/11.71  % (28014)Time elapsed: 1.415 s
% 32.79/11.71  % (28014)Instructions burned: 4438 (million)
% 32.79/11.71  % (28014)------------------------------
% 32.79/11.71  % (28014)------------------------------
% 32.79/11.73  % (28226)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_27763 for (2969ds/464Mi)
% 32.79/11.74  % (28035)Instruction limit reached!
% 32.79/11.74  % (28035)------------------------------
% 32.79/11.74  % (28035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.79/11.74  % (28035)Termination reason: Unknown
% 32.79/11.74  % (28035)Termination phase: Function definition elimination
% 32.79/11.74  
% 32.79/11.74  % (28035)Memory used [KB]: 47078
% 32.79/11.74  % (28035)Time elapsed: 1.381 s
% 32.79/11.74  % (28035)Instructions burned: 5208 (million)
% 32.79/11.74  % (28035)------------------------------
% 32.79/11.74  % (28035)------------------------------
% 32.79/11.75  % (28224)Instruction limit reached!
% 32.79/11.75  % (28224)------------------------------
% 32.79/11.75  % (28224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.79/11.75  % (28224)Termination reason: Unknown
% 32.79/11.75  % (28224)Termination phase: shuffling
% 32.79/11.75  
% 32.79/11.75  % (28224)Memory used [KB]: 24818
% 32.79/11.75  % (28224)Time elapsed: 0.263 s
% 32.79/11.75  % (28224)Instructions burned: 770 (million)
% 32.79/11.75  % (28224)------------------------------
% 32.79/11.75  % (28224)------------------------------
% 32.79/11.75  % (28227)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_27763 for (2969ds/1376Mi)
% 32.79/11.76  % (28228)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_27763 for (2969ds/906Mi)
% 32.79/11.79  % (28102)Instruction limit reached!
% 32.79/11.79  % (28102)------------------------------
% 32.79/11.79  % (28102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.79/11.79  % (28102)Termination reason: Unknown
% 32.79/11.79  % (28102)Termination phase: Saturation
% 32.79/11.79  
% 32.79/11.79  % (28102)Memory used [KB]: 34157
% 32.79/11.79  % (28102)Time elapsed: 1.310 s
% 32.79/11.79  % (28102)Instructions burned: 4350 (million)
% 32.79/11.79  % (28102)------------------------------
% 32.79/11.79  % (28102)------------------------------
% 33.25/11.81  % (28229)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_27763 for (2968ds/434Mi)
% 33.25/11.88  % (28226)Instruction limit reached!
% 33.25/11.88  % (28226)------------------------------
% 33.25/11.88  % (28226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.25/11.88  % (28226)Termination reason: Unknown
% 33.25/11.88  % (28226)Termination phase: shuffling
% 33.25/11.88  
% 33.25/11.88  % (28226)Memory used [KB]: 19573
% 33.25/11.88  % (28226)Time elapsed: 0.160 s
% 33.25/11.88  % (28226)Instructions burned: 466 (million)
% 33.25/11.88  % (28226)------------------------------
% 33.25/11.88  % (28226)------------------------------
% 33.42/11.90  % (28230)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_27763 for (2967ds/865Mi)
% 33.42/11.95  % (28229)Instruction limit reached!
% 33.42/11.95  % (28229)------------------------------
% 33.42/11.95  % (28229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.42/11.95  % (28229)Termination reason: Unknown
% 33.42/11.95  % (28229)Termination phase: shuffling
% 33.42/11.95  
% 33.42/11.95  % (28229)Memory used [KB]: 19061
% 33.42/11.95  % (28229)Time elapsed: 0.150 s
% 33.42/11.95  % (28229)Instructions burned: 435 (million)
% 33.42/11.95  % (28229)------------------------------
% 33.42/11.95  % (28229)------------------------------
% 33.42/11.97  % (28231)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_27763 for (2967ds/593Mi)
% 33.42/11.97  % (28225)Instruction limit reached!
% 33.42/11.97  % (28225)------------------------------
% 33.42/11.97  % (28225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.42/11.97  % (28225)Termination reason: Unknown
% 33.42/11.97  % (28225)Termination phase: shuffling
% 33.42/11.97  
% 33.42/11.97  % (28225)Memory used [KB]: 25330
% 33.42/11.97  % (28225)Time elapsed: 0.269 s
% 33.42/11.97  % (28225)Instructions burned: 796 (million)
% 33.42/11.97  % (28225)------------------------------
% 33.42/11.97  % (28225)------------------------------
% 33.42/11.98  % (28232)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_27763 for (2967ds/443Mi)
% 36.12/12.06  % (28228)Instruction limit reached!
% 36.12/12.06  % (28228)------------------------------
% 36.12/12.06  % (28228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.12/12.06  % (28228)Termination reason: Unknown
% 36.12/12.06  % (28228)Termination phase: shuffling
% 36.12/12.06  
% 36.12/12.06  % (28228)Memory used [KB]: 26609
% 36.12/12.06  % (28228)Time elapsed: 0.307 s
% 36.12/12.06  % (28228)Instructions burned: 908 (million)
% 36.12/12.06  % (28228)------------------------------
% 36.12/12.06  % (28228)------------------------------
% 36.12/12.08  % (28233)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_27763 for (2965ds/594Mi)
% 36.82/12.14  % (28232)Instruction limit reached!
% 36.82/12.14  % (28232)------------------------------
% 36.82/12.14  % (28232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.82/12.14  % (28232)Termination reason: Unknown
% 36.82/12.14  % (28232)Termination phase: shuffling
% 36.82/12.14  
% 36.82/12.14  % (28232)Memory used [KB]: 19061
% 36.82/12.14  % (28232)Time elapsed: 0.156 s
% 36.82/12.14  % (28232)Instructions burned: 445 (million)
% 36.82/12.14  % (28232)------------------------------
% 36.82/12.14  % (28232)------------------------------
% 36.82/12.15  % (28231)Instruction limit reached!
% 36.82/12.15  % (28231)------------------------------
% 36.82/12.15  % (28231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.82/12.15  % (28231)Termination reason: Unknown
% 36.82/12.15  % (28231)Termination phase: shuffling
% 36.82/12.15  
% 36.82/12.15  % (28231)Memory used [KB]: 23922
% 36.82/12.15  % (28231)Time elapsed: 0.183 s
% 36.82/12.15  % (28231)Instructions burned: 596 (million)
% 36.82/12.15  % (28231)------------------------------
% 36.82/12.15  % (28231)------------------------------
% 36.82/12.15  % (28234)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_27763 for (2965ds/327Mi)
% 36.82/12.16  % (28230)Instruction limit reached!
% 36.82/12.16  % (28230)------------------------------
% 36.82/12.16  % (28230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.82/12.16  % (28230)Termination reason: Unknown
% 36.82/12.16  % (28230)Termination phase: shuffling
% 36.82/12.16  
% 36.82/12.16  % (28230)Memory used [KB]: 31470
% 36.82/12.16  % (28230)Time elapsed: 0.261 s
% 36.82/12.16  % (28230)Instructions burned: 866 (million)
% 36.82/12.16  % (28230)------------------------------
% 36.82/12.16  % (28230)------------------------------
% 36.82/12.16  % (28227)Instruction limit reached!
% 36.82/12.16  % (28227)------------------------------
% 36.82/12.16  % (28227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.82/12.16  % (28227)Termination reason: Unknown
% 36.82/12.16  % (28227)Termination phase: shuffling
% 36.82/12.16  
% 36.82/12.16  % (28227)Memory used [KB]: 38123
% 36.82/12.16  % (28227)Time elapsed: 0.409 s
% 36.82/12.16  % (28227)Instructions burned: 1378 (million)
% 36.82/12.16  % (28227)------------------------------
% 36.82/12.16  % (28227)------------------------------
% 36.82/12.16  % (28235)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_27763 for (2965ds/5411Mi)
% 36.82/12.17  % (28236)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_27763 for (2965ds/1762Mi)
% 36.82/12.17  % (28237)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_27763 for (2964ds/96Mi)
% 37.11/12.21  % (28237)Instruction limit reached!
% 37.11/12.21  % (28237)------------------------------
% 37.11/12.21  % (28237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.11/12.21  % (28237)Termination reason: Unknown
% 37.11/12.21  % (28237)Termination phase: shuffling
% 37.11/12.21  
% 37.11/12.21  % (28237)Memory used [KB]: 14967
% 37.11/12.21  % (28237)Time elapsed: 0.035 s
% 37.11/12.21  % (28237)Instructions burned: 96 (million)
% 37.11/12.21  % (28237)------------------------------
% 37.11/12.21  % (28237)------------------------------
% 37.11/12.23  % (28238)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_27763 for (2964ds/503Mi)
% 37.11/12.26  % (28234)Instruction limit reached!
% 37.11/12.26  % (28234)------------------------------
% 37.11/12.26  % (28234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.11/12.26  % (28234)Termination reason: Unknown
% 37.11/12.26  % (28234)Termination phase: shuffling
% 37.11/12.26  
% 37.11/12.26  % (28234)Memory used [KB]: 17782
% 37.11/12.26  % (28234)Time elapsed: 0.115 s
% 37.11/12.26  % (28234)Instructions burned: 327 (million)
% 37.11/12.26  % (28234)------------------------------
% 37.11/12.26  % (28234)------------------------------
% 37.11/12.28  % (28239)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_27763 for (2963ds/90Mi)
% 37.11/12.28  % (28233)Instruction limit reached!
% 37.11/12.28  % (28233)------------------------------
% 37.11/12.28  % (28233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.11/12.28  % (28233)Termination reason: Unknown
% 37.11/12.28  % (28233)Termination phase: shuffling
% 37.11/12.28  
% 37.11/12.28  % (28233)Memory used [KB]: 22899
% 37.11/12.28  % (28233)Time elapsed: 0.203 s
% 37.11/12.28  % (28233)Instructions burned: 595 (million)
% 37.11/12.28  % (28233)------------------------------
% 37.11/12.28  % (28233)------------------------------
% 37.11/12.29  % (28240)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_27763 for (2963ds/593Mi)
% 37.70/12.31  % (28239)Instruction limit reached!
% 37.70/12.31  % (28239)------------------------------
% 37.70/12.31  % (28239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.70/12.31  % (28239)Termination reason: Unknown
% 37.70/12.31  % (28239)Termination phase: shuffling
% 37.70/12.31  
% 37.70/12.31  % (28239)Memory used [KB]: 14711
% 37.70/12.31  % (28239)Time elapsed: 0.037 s
% 37.70/12.31  % (28239)Instructions burned: 90 (million)
% 37.70/12.31  % (28239)------------------------------
% 37.70/12.31  % (28239)------------------------------
% 37.70/12.32  % (28241)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_27763 for (2963ds/1512Mi)
% 37.94/12.44  % (28238)Instruction limit reached!
% 37.94/12.44  % (28238)------------------------------
% 37.94/12.44  % (28238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.94/12.44  % (28238)Termination reason: Unknown
% 37.94/12.44  % (28238)Termination phase: shuffling
% 37.94/12.44  
% 37.94/12.44  % (28238)Memory used [KB]: 19829
% 37.94/12.44  % (28238)Time elapsed: 0.216 s
% 37.94/12.44  % (28238)Instructions burned: 504 (million)
% 37.94/12.44  % (28238)------------------------------
% 37.94/12.44  % (28238)------------------------------
% 37.94/12.45  % (28242)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_27763 for (2962ds/569Mi)
% 37.94/12.49  % (28240)Instruction limit reached!
% 37.94/12.49  % (28240)------------------------------
% 37.94/12.49  % (28240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.94/12.49  % (28240)Termination reason: Unknown
% 37.94/12.49  % (28240)Termination phase: shuffling
% 37.94/12.49  
% 37.94/12.49  % (28240)Memory used [KB]: 20724
% 37.94/12.49  % (28240)Time elapsed: 0.198 s
% 37.94/12.49  % (28240)Instructions burned: 595 (million)
% 37.94/12.49  % (28240)------------------------------
% 37.94/12.49  % (28240)------------------------------
% 38.58/12.50  % (28243)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_27763 for (2961ds/501Mi)
% 38.58/12.50  % (28222)Instruction limit reached!
% 38.58/12.50  % (28222)------------------------------
% 38.58/12.50  % (28222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.58/12.50  % (28222)Termination reason: Unknown
% 38.58/12.50  % (28222)Termination phase: Function definition elimination
% 38.58/12.50  
% 38.58/12.50  % (28222)Memory used [KB]: 45031
% 38.58/12.50  % (28222)Time elapsed: 1.244 s
% 38.58/12.50  % (28222)Instructions burned: 4714 (million)
% 38.58/12.50  % (28222)------------------------------
% 38.58/12.50  % (28222)------------------------------
% 38.58/12.52  % (28244)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_27763 for (2961ds/562Mi)
% 38.70/12.64  % (28242)Instruction limit reached!
% 38.70/12.64  % (28242)------------------------------
% 38.70/12.64  % (28242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.70/12.64  % (28242)Termination reason: Unknown
% 38.70/12.64  % (28242)Termination phase: shuffling
% 38.70/12.64  
% 38.70/12.64  % (28242)Memory used [KB]: 23539
% 38.70/12.64  % (28242)Time elapsed: 0.186 s
% 38.70/12.64  % (28242)Instructions burned: 571 (million)
% 38.70/12.64  % (28242)------------------------------
% 38.70/12.64  % (28242)------------------------------
% 38.70/12.65  % (28245)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_27763 for (2960ds/406Mi)
% 38.70/12.67  % (28243)Instruction limit reached!
% 38.70/12.67  % (28243)------------------------------
% 38.70/12.67  % (28243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.70/12.67  % (28243)Termination reason: Unknown
% 38.70/12.67  % (28243)Termination phase: shuffling
% 38.70/12.67  
% 38.70/12.67  % (28243)Memory used [KB]: 19829
% 38.70/12.67  % (28243)Time elapsed: 0.172 s
% 38.70/12.67  % (28243)Instructions burned: 502 (million)
% 38.70/12.67  % (28243)------------------------------
% 38.70/12.67  % (28243)------------------------------
% 38.70/12.68  % (28236)Instruction limit reached!
% 38.70/12.68  % (28236)------------------------------
% 38.70/12.68  % (28236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.70/12.68  % (28236)Termination reason: Unknown
% 38.70/12.68  % (28236)Termination phase: Property scanning
% 38.70/12.68  
% 38.70/12.68  % (28236)Memory used [KB]: 42216
% 38.70/12.68  % (28236)Time elapsed: 0.509 s
% 38.70/12.68  % (28236)Instructions burned: 1765 (million)
% 38.70/12.68  % (28236)------------------------------
% 38.70/12.68  % (28236)------------------------------
% 38.70/12.68  % (28246)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_27763 for (2959ds/582Mi)
% 38.70/12.68  % (28244)Instruction limit reached!
% 38.70/12.68  % (28244)------------------------------
% 38.70/12.68  % (28244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.70/12.68  % (28244)Termination reason: Unknown
% 38.70/12.68  % (28244)Termination phase: shuffling
% 38.70/12.68  
% 38.70/12.68  % (28244)Memory used [KB]: 23539
% 38.70/12.68  % (28244)Time elapsed: 0.168 s
% 38.70/12.68  % (28244)Instructions burned: 562 (million)
% 38.70/12.68  % (28244)------------------------------
% 38.70/12.68  % (28244)------------------------------
% 38.70/12.69  % (28247)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_27763 for (2959ds/456Mi)
% 38.70/12.70  % (28248)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_27763 for (2959ds/393Mi)
% 39.89/12.79  % (28245)Instruction limit reached!
% 39.89/12.79  % (28245)------------------------------
% 39.89/12.79  % (28245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.89/12.79  % (28245)Termination reason: Unknown
% 39.89/12.79  % (28245)Termination phase: shuffling
% 39.89/12.79  
% 39.89/12.79  % (28245)Memory used [KB]: 18805
% 39.89/12.79  % (28245)Time elapsed: 0.146 s
% 39.89/12.79  % (28245)Instructions burned: 406 (million)
% 39.89/12.79  % (28245)------------------------------
% 39.89/12.79  % (28245)------------------------------
% 39.99/12.81  % (28249)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_27763 for (2958ds/1335Mi)
% 39.99/12.81  % (28241)Instruction limit reached!
% 39.99/12.81  % (28241)------------------------------
% 39.99/12.81  % (28241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.99/12.81  % (28241)Termination reason: Unknown
% 39.99/12.81  % (28241)Termination phase: Property scanning
% 39.99/12.81  
% 39.99/12.81  % (28241)Memory used [KB]: 29935
% 39.99/12.81  % (28241)Time elapsed: 0.488 s
% 39.99/12.81  % (28241)Instructions burned: 1514 (million)
% 39.99/12.81  % (28241)------------------------------
% 39.99/12.81  % (28241)------------------------------
% 39.99/12.82  % (28248)Instruction limit reached!
% 39.99/12.82  % (28248)------------------------------
% 39.99/12.82  % (28248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.99/12.82  % (28248)Termination reason: Unknown
% 39.99/12.82  % (28248)Termination phase: shuffling
% 39.99/12.82  
% 39.99/12.82  % (28248)Memory used [KB]: 21108
% 39.99/12.82  % (28248)Time elapsed: 0.123 s
% 39.99/12.82  % (28248)Instructions burned: 393 (million)
% 39.99/12.82  % (28248)------------------------------
% 39.99/12.82  % (28248)------------------------------
% 39.99/12.82  % (28250)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_27763 for (2958ds/3373Mi)
% 39.99/12.83  % (28251)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_27763 for (2958ds/474Mi)
% 39.99/12.85  % (28247)Instruction limit reached!
% 39.99/12.85  % (28247)------------------------------
% 39.99/12.85  % (28247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.99/12.85  % (28247)Termination reason: Unknown
% 39.99/12.85  % (28247)Termination phase: shuffling
% 39.99/12.85  
% 39.99/12.85  % (28247)Memory used [KB]: 19317
% 39.99/12.85  % (28247)Time elapsed: 0.161 s
% 39.99/12.85  % (28247)Instructions burned: 458 (million)
% 39.99/12.85  % (28247)------------------------------
% 39.99/12.85  % (28247)------------------------------
% 39.99/12.86  % (28252)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_27763 for (2958ds/157Mi)
% 39.99/12.89  % (28246)Instruction limit reached!
% 39.99/12.89  % (28246)------------------------------
% 39.99/12.89  % (28246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.99/12.89  % (28246)Termination reason: Unknown
% 39.99/12.89  % (28246)Termination phase: shuffling
% 39.99/12.89  
% 39.99/12.89  % (28246)Memory used [KB]: 21108
% 39.99/12.89  % (28246)Time elapsed: 0.208 s
% 39.99/12.89  % (28246)Instructions burned: 582 (million)
% 39.99/12.89  % (28246)------------------------------
% 39.99/12.89  % (28246)------------------------------
% 41.26/12.90  % (28253)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_27763 for (2957ds/590Mi)
% 41.26/12.92  % (28252)Instruction limit reached!
% 41.26/12.92  % (28252)------------------------------
% 41.26/12.92  % (28252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.26/12.92  % (28252)Termination reason: Unknown
% 41.26/12.92  % (28252)Termination phase: shuffling
% 41.26/12.92  
% 41.26/12.92  % (28252)Memory used [KB]: 15991
% 41.26/12.92  % (28252)Time elapsed: 0.054 s
% 41.26/12.92  % (28252)Instructions burned: 157 (million)
% 41.26/12.92  % (28252)------------------------------
% 41.26/12.92  % (28252)------------------------------
% 41.26/12.93  % (28254)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_27763 for (2957ds/104Mi)
% 41.26/12.97  % (28254)Instruction limit reached!
% 41.26/12.97  % (28254)------------------------------
% 41.26/12.97  % (28254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.26/12.97  % (28254)Termination reason: Unknown
% 41.26/12.97  % (28254)Termination phase: shuffling
% 41.26/12.97  
% 41.26/12.97  % (28254)Memory used [KB]: 15095
% 41.26/12.97  % (28254)Time elapsed: 0.044 s
% 41.26/12.97  % (28254)Instructions burned: 105 (million)
% 41.26/12.97  % (28254)------------------------------
% 41.26/12.97  % (28254)------------------------------
% 41.26/12.98  % (28251)Instruction limit reached!
% 41.26/12.98  % (28251)------------------------------
% 41.26/12.98  % (28251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.26/12.98  % (28251)Termination reason: Unknown
% 41.26/12.98  % (28251)Termination phase: shuffling
% 41.26/12.98  
% 41.26/12.98  % (28251)Memory used [KB]: 22387
% 41.26/12.98  % (28251)Time elapsed: 0.148 s
% 41.26/12.98  % (28251)Instructions burned: 475 (million)
% 41.26/12.98  % (28251)------------------------------
% 41.26/12.98  % (28251)------------------------------
% 41.26/12.98  % (28255)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_27763 for (2957ds/414Mi)
% 41.26/12.99  % (28256)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_27763 for (2957ds/715Mi)
% 43.11/13.10  % (28253)Instruction limit reached!
% 43.11/13.10  % (28253)------------------------------
% 43.11/13.10  % (28253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.11/13.10  % (28253)Termination reason: Unknown
% 43.11/13.10  % (28253)Termination phase: shuffling
% 43.11/13.10  
% 43.11/13.10  % (28253)Memory used [KB]: 23027
% 43.11/13.10  % (28253)Time elapsed: 0.203 s
% 43.11/13.10  % (28253)Instructions burned: 590 (million)
% 43.11/13.10  % (28253)------------------------------
% 43.11/13.10  % (28253)------------------------------
% 43.11/13.11  % (28255)Instruction limit reached!
% 43.11/13.11  % (28255)------------------------------
% 43.11/13.11  % (28255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.11/13.11  % (28255)Termination reason: Unknown
% 43.11/13.11  % (28255)Termination phase: shuffling
% 43.11/13.11  
% 43.11/13.11  % (28255)Memory used [KB]: 21492
% 43.11/13.11  % (28255)Time elapsed: 0.125 s
% 43.11/13.11  % (28255)Instructions burned: 414 (million)
% 43.11/13.11  % (28255)------------------------------
% 43.11/13.11  % (28255)------------------------------
% 43.11/13.11  % (28257)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_27763 for (2955ds/961Mi)
% 43.11/13.12  % (28258)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_27763 for (2955ds/1213Mi)
% 44.19/13.22  % (28249)Instruction limit reached!
% 44.19/13.22  % (28249)------------------------------
% 44.19/13.22  % (28249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.19/13.22  % (28249)Termination reason: Unknown
% 44.19/13.22  % (28249)Termination phase: shuffling
% 44.19/13.22  
% 44.19/13.22  % (28249)Memory used [KB]: 37611
% 44.19/13.22  % (28249)Time elapsed: 0.400 s
% 44.19/13.22  % (28249)Instructions burned: 1337 (million)
% 44.19/13.22  % (28249)------------------------------
% 44.19/13.22  % (28249)------------------------------
% 44.19/13.23  % (28256)Instruction limit reached!
% 44.19/13.23  % (28256)------------------------------
% 44.19/13.23  % (28256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.19/13.23  % (28256)Termination reason: Unknown
% 44.19/13.23  % (28256)Termination phase: shuffling
% 44.19/13.23  
% 44.19/13.23  % (28256)Memory used [KB]: 24434
% 44.19/13.23  % (28256)Time elapsed: 0.239 s
% 44.19/13.23  % (28256)Instructions burned: 715 (million)
% 44.19/13.23  % (28256)------------------------------
% 44.19/13.23  % (28256)------------------------------
% 44.19/13.23  % (28259)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_27763 for (2954ds/1979Mi)
% 44.19/13.24  % (28260)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_27763 for (2954ds/481Mi)
% 44.58/13.39  % (28260)Instruction limit reached!
% 44.58/13.39  % (28260)------------------------------
% 44.58/13.39  % (28260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.58/13.39  % (28260)Termination reason: Unknown
% 44.58/13.39  % (28260)Termination phase: shuffling
% 44.58/13.39  
% 44.58/13.39  % (28260)Memory used [KB]: 22387
% 44.58/13.39  % (28260)Time elapsed: 0.148 s
% 44.58/13.39  % (28260)Instructions burned: 481 (million)
% 44.58/13.39  % (28260)------------------------------
% 44.58/13.39  % (28260)------------------------------
% 45.04/13.40  % (28261)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_27763 for (2952ds/783Mi)
% 45.04/13.44  % (28257)Instruction limit reached!
% 45.04/13.44  % (28257)------------------------------
% 45.04/13.44  % (28257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.04/13.44  % (28257)Termination reason: Unknown
% 45.04/13.44  % (28257)Termination phase: shuffling
% 45.04/13.44  
% 45.04/13.44  % (28257)Memory used [KB]: 27121
% 45.04/13.44  % (28257)Time elapsed: 0.325 s
% 45.04/13.44  % (28257)Instructions burned: 962 (million)
% 45.04/13.44  % (28257)------------------------------
% 45.04/13.44  % (28257)------------------------------
% 45.04/13.45  % (28262)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_27763 for (2952ds/432Mi)
% 45.69/13.51  % (28258)Instruction limit reached!
% 45.69/13.51  % (28258)------------------------------
% 45.69/13.51  % (28258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.69/13.51  % (28258)Termination reason: Unknown
% 45.69/13.51  % (28258)Termination phase: Property scanning
% 45.69/13.51  
% 45.69/13.51  % (28258)Memory used [KB]: 27504
% 45.69/13.51  % (28258)Time elapsed: 0.395 s
% 45.69/13.51  % (28258)Instructions burned: 1214 (million)
% 45.69/13.51  % (28258)------------------------------
% 45.69/13.51  % (28258)------------------------------
% 45.69/13.52  % (28264)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_27763 for (2951ds/1670Mi)
% 46.39/13.60  % (28262)Instruction limit reached!
% 46.39/13.60  % (28262)------------------------------
% 46.39/13.60  % (28262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.39/13.60  % (28262)Termination reason: Unknown
% 46.39/13.60  % (28262)Termination phase: shuffling
% 46.39/13.60  
% 46.39/13.60  % (28262)Memory used [KB]: 19189
% 46.39/13.60  % (28262)Time elapsed: 0.149 s
% 46.39/13.60  % (28262)Instructions burned: 434 (million)
% 46.39/13.60  % (28262)------------------------------
% 46.39/13.60  % (28262)------------------------------
% 46.39/13.61  % (28268)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_27763 for (2950ds/90Mi)
% 46.39/13.65  % (28268)Instruction limit reached!
% 46.39/13.65  % (28268)------------------------------
% 46.39/13.65  % (28268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.39/13.65  % (28268)Termination reason: Unknown
% 46.39/13.65  % (28268)Termination phase: shuffling
% 46.39/13.65  
% 46.39/13.65  % (28268)Memory used [KB]: 14967
% 46.39/13.65  % (28268)Time elapsed: 0.039 s
% 46.39/13.65  % (28268)Instructions burned: 92 (million)
% 46.39/13.65  % (28268)------------------------------
% 46.39/13.65  % (28268)------------------------------
% 46.39/13.66  % (28283)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_27763 for (2950ds/346Mi)
% 46.39/13.66  % (28261)Instruction limit reached!
% 46.39/13.66  % (28261)------------------------------
% 46.39/13.66  % (28261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.39/13.66  % (28261)Termination reason: Unknown
% 46.39/13.66  % (28261)Termination phase: shuffling
% 46.39/13.66  
% 46.39/13.66  % (28261)Memory used [KB]: 25202
% 46.39/13.66  % (28261)Time elapsed: 0.265 s
% 46.39/13.66  % (28261)Instructions burned: 784 (million)
% 46.39/13.66  % (28261)------------------------------
% 46.39/13.66  % (28261)------------------------------
% 46.39/13.67  % (28292)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_27763 for (2950ds/401Mi)
% 47.18/13.77  % (28283)Instruction limit reached!
% 47.18/13.77  % (28283)------------------------------
% 47.18/13.77  % (28283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.18/13.77  % (28283)Termination reason: Unknown
% 47.18/13.77  % (28283)Termination phase: shuffling
% 47.18/13.77  
% 47.18/13.77  % (28283)Memory used [KB]: 20596
% 47.18/13.77  % (28283)Time elapsed: 0.107 s
% 47.18/13.77  % (28283)Instructions burned: 349 (million)
% 47.18/13.77  % (28283)------------------------------
% 47.18/13.77  % (28283)------------------------------
% 47.18/13.78  % (28341)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_27763 for (2948ds/6454Mi)
% 47.18/13.79  % (28292)Instruction limit reached!
% 47.18/13.79  % (28292)------------------------------
% 47.18/13.79  % (28292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.18/13.79  % (28292)Termination reason: Unknown
% 47.18/13.79  % (28292)Termination phase: shuffling
% 47.18/13.79  
% 47.18/13.79  % (28292)Memory used [KB]: 21364
% 47.18/13.80  % (28292)Time elapsed: 0.123 s
% 47.18/13.80  % (28292)Instructions burned: 403 (million)
% 47.18/13.80  % (28292)------------------------------
% 47.18/13.80  % (28292)------------------------------
% 47.60/13.80  % (28235)Instruction limit reached!
% 47.60/13.80  % (28235)------------------------------
% 47.60/13.80  % (28235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.60/13.80  % (28235)Termination reason: Unknown
% 47.60/13.80  % (28235)Termination phase: Saturation
% 47.60/13.80  
% 47.60/13.80  % (28235)Memory used [KB]: 35308
% 47.60/13.80  % (28235)Time elapsed: 1.640 s
% 47.60/13.80  % (28235)Instructions burned: 5412 (million)
% 47.60/13.80  % (28235)------------------------------
% 47.60/13.80  % (28235)------------------------------
% 47.60/13.81  % (28359)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_27763 for (2948ds/283Mi)
% 47.60/13.81  % (28360)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_27763 for (2948ds/865Mi)
% 47.60/13.82  % (28250)Instruction limit reached!
% 47.60/13.82  % (28250)------------------------------
% 47.60/13.82  % (28250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.60/13.82  % (28250)Termination reason: Unknown
% 47.60/13.82  % (28250)Termination phase: Function definition elimination
% 47.60/13.82  
% 47.60/13.82  % (28250)Memory used [KB]: 44391
% 47.60/13.82  % (28250)Time elapsed: 0.997 s
% 47.60/13.82  % (28250)Instructions burned: 3374 (million)
% 47.60/13.82  % (28250)------------------------------
% 47.60/13.82  % (28250)------------------------------
% 47.60/13.83  % (28365)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_27763 for (2948ds/4528Mi)
% 47.60/13.85  % (28223)Instruction limit reached!
% 47.60/13.85  % (28223)------------------------------
% 47.60/13.85  % (28223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.60/13.85  % (28223)Termination reason: Unknown
% 47.60/13.85  % (28223)Termination phase: Saturation
% 47.60/13.85  
% 47.60/13.85  % (28223)Memory used [KB]: 60510
% 47.60/13.85  % (28223)Time elapsed: 2.573 s
% 47.60/13.85  % (28223)Instructions burned: 8250 (million)
% 47.60/13.85  % (28223)------------------------------
% 47.60/13.85  % (28223)------------------------------
% 47.60/13.86  % (28259)Instruction limit reached!
% 47.60/13.86  % (28259)------------------------------
% 47.60/13.86  % (28259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.60/13.86  % (28259)Termination reason: Unknown
% 47.60/13.86  % (28259)Termination phase: Preprocessing 3
% 47.60/13.86  
% 47.60/13.86  % (28259)Memory used [KB]: 34157
% 47.60/13.86  % (28259)Time elapsed: 0.631 s
% 47.60/13.86  % (28259)Instructions burned: 1979 (million)
% 47.60/13.86  % (28259)------------------------------
% 47.60/13.86  % (28259)------------------------------
% 47.60/13.86  % (28377)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_27763 for (2948ds/1001Mi)
% 47.60/13.88  % (28378)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_27763 for (2948ds/102Mi)
% 48.49/13.91  % (28359)Instruction limit reached!
% 48.49/13.91  % (28359)------------------------------
% 48.49/13.91  % (28359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.49/13.91  % (28359)Termination reason: Unknown
% 48.49/13.91  % (28359)Termination phase: shuffling
% 48.49/13.91  
% 48.49/13.91  % (28359)Memory used [KB]: 17270
% 48.49/13.91  % (28359)Time elapsed: 0.102 s
% 48.49/13.91  % (28359)Instructions burned: 284 (million)
% 48.49/13.91  % (28359)------------------------------
% 48.49/13.91  % (28359)------------------------------
% 48.49/13.92  % (28378)Instruction limit reached!
% 48.49/13.92  % (28378)------------------------------
% 48.49/13.92  % (28378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.49/13.92  % (28378)Termination reason: Unknown
% 48.49/13.92  % (28378)Termination phase: shuffling
% 48.49/13.92  
% 48.49/13.92  % (28378)Memory used [KB]: 15095
% 48.49/13.92  % (28378)Time elapsed: 0.039 s
% 48.49/13.92  % (28378)Instructions burned: 102 (million)
% 48.49/13.92  % (28378)------------------------------
% 48.49/13.92  % (28378)------------------------------
% 48.49/13.92  % (28379)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_27763 for (2947ds/952Mi)
% 48.49/13.93  % (28380)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_27763 for (2947ds/578Mi)
% 50.07/14.02  % (28264)Instruction limit reached!
% 50.07/14.02  % (28264)------------------------------
% 50.07/14.02  % (28264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.07/14.02  % (28264)Termination reason: Unknown
% 50.07/14.02  % (28264)Termination phase: shuffling
% 50.07/14.02  
% 50.07/14.02  % (28264)Memory used [KB]: 41960
% 50.07/14.02  % (28264)Time elapsed: 0.498 s
% 50.07/14.02  % (28264)Instructions burned: 1671 (million)
% 50.07/14.02  % (28264)------------------------------
% 50.07/14.02  % (28264)------------------------------
% 50.07/14.05  % (28381)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_27763 for (2946ds/643Mi)
% 50.07/14.10  % (28380)Instruction limit reached!
% 50.07/14.10  % (28380)------------------------------
% 50.07/14.10  % (28380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.07/14.10  % (28380)Termination reason: Unknown
% 50.07/14.10  % (28380)Termination phase: shuffling
% 50.07/14.10  
% 50.07/14.10  % (28380)Memory used [KB]: 23539
% 50.07/14.10  % (28380)Time elapsed: 0.177 s
% 50.07/14.10  % (28380)Instructions burned: 579 (million)
% 50.07/14.10  % (28380)------------------------------
% 50.07/14.10  % (28380)------------------------------
% 50.07/14.10  % (28360)Instruction limit reached!
% 50.07/14.10  % (28360)------------------------------
% 50.07/14.10  % (28360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.07/14.10  % (28360)Termination reason: Unknown
% 50.07/14.10  % (28360)Termination phase: shuffling
% 50.07/14.10  
% 50.07/14.10  % (28360)Memory used [KB]: 26097
% 50.07/14.10  % (28360)Time elapsed: 0.295 s
% 50.07/14.10  % (28360)Instructions burned: 865 (million)
% 50.07/14.10  % (28360)------------------------------
% 50.07/14.10  % (28360)------------------------------
% 50.71/14.11  % (28406)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_27763 for (2945ds/865Mi)
% 50.71/14.12  % (28407)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_27763 for (2945ds/1174Mi)
% 51.06/14.20  % (28377)Instruction limit reached!
% 51.06/14.20  % (28377)------------------------------
% 51.06/14.20  % (28377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.06/14.20  % (28377)Termination reason: Unknown
% 51.06/14.20  % (28377)Termination phase: Property scanning
% 51.06/14.20  
% 51.06/14.20  % (28377)Memory used [KB]: 27504
% 51.06/14.20  % (28377)Time elapsed: 0.337 s
% 51.06/14.20  % (28377)Instructions burned: 1001 (million)
% 51.06/14.20  % (28377)------------------------------
% 51.06/14.20  % (28377)------------------------------
% 51.06/14.21  % (28427)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_27763 for (2944ds/644Mi)
% 51.06/14.24  % (28379)Instruction limit reached!
% 51.06/14.24  % (28379)------------------------------
% 51.06/14.24  % (28379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.06/14.24  % (28379)Termination reason: Unknown
% 51.06/14.24  % (28379)Termination phase: shuffling
% 51.06/14.24  
% 51.06/14.24  % (28379)Memory used [KB]: 27121
% 51.06/14.24  % (28379)Time elapsed: 0.322 s
% 51.06/14.24  % (28379)Instructions burned: 952 (million)
% 51.06/14.24  % (28379)------------------------------
% 51.06/14.24  % (28379)------------------------------
% 51.06/14.25  % (28428)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_27763 for (2944ds/1201Mi)
% 51.06/14.28  % (28381)Instruction limit reached!
% 51.06/14.28  % (28381)------------------------------
% 51.06/14.28  % (28381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.06/14.28  % (28381)Termination reason: Unknown
% 51.06/14.28  % (28381)Termination phase: shuffling
% 51.06/14.28  
% 51.06/14.28  % (28381)Memory used [KB]: 24434
% 51.06/14.28  % (28381)Time elapsed: 0.239 s
% 51.06/14.28  % (28381)Instructions burned: 643 (million)
% 51.06/14.28  % (28381)------------------------------
% 51.06/14.28  % (28381)------------------------------
% 51.06/14.30  % (28429)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_27763 for (2943ds/1046Mi)
% 51.79/14.41  % (28406)Instruction limit reached!
% 51.79/14.41  % (28406)------------------------------
% 51.79/14.41  % (28406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.79/14.41  % (28406)Termination reason: Unknown
% 51.79/14.41  % (28406)Termination phase: shuffling
% 51.79/14.41  
% 51.79/14.41  % (28406)Memory used [KB]: 26097
% 51.79/14.41  % (28406)Time elapsed: 0.294 s
% 51.79/14.41  % (28406)Instructions burned: 865 (million)
% 51.79/14.41  % (28406)------------------------------
% 51.79/14.41  % (28406)------------------------------
% 51.79/14.42  % (28430)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_27763 for (2942ds/222Mi)
% 51.79/14.44  % (28427)Instruction limit reached!
% 51.79/14.44  % (28427)------------------------------
% 51.79/14.44  % (28427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.79/14.44  % (28427)Termination reason: Unknown
% 51.79/14.44  % (28427)Termination phase: shuffling
% 51.79/14.44  
% 51.79/14.44  % (28427)Memory used [KB]: 23666
% 51.79/14.44  % (28427)Time elapsed: 0.224 s
% 51.79/14.44  % (28427)Instructions burned: 646 (million)
% 51.79/14.44  % (28427)------------------------------
% 51.79/14.44  % (28427)------------------------------
% 51.79/14.45  % (28431)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_27763 for (2942ds/68Mi)
% 51.79/14.48  % (28431)Instruction limit reached!
% 51.79/14.48  % (28431)------------------------------
% 51.79/14.48  % (28431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.79/14.48  % (28431)Termination reason: Unknown
% 51.79/14.48  % (28431)Termination phase: shuffling
% 51.79/14.48  
% 51.79/14.48  % (28431)Memory used [KB]: 14583
% 51.79/14.48  % (28431)Time elapsed: 0.033 s
% 51.79/14.48  % (28431)Instructions burned: 70 (million)
% 51.79/14.48  % (28431)------------------------------
% 51.79/14.48  % (28431)------------------------------
% 51.79/14.49  % (28430)Instruction limit reached!
% 51.79/14.49  % (28430)------------------------------
% 51.79/14.49  % (28430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.79/14.49  % (28430)Termination reason: Unknown
% 51.79/14.49  % (28430)Termination phase: shuffling
% 51.79/14.49  
% 51.79/14.49  % (28430)Memory used [KB]: 16886
% 51.79/14.49  % (28430)Time elapsed: 0.073 s
% 51.79/14.49  % (28430)Instructions burned: 222 (million)
% 51.79/14.49  % (28430)------------------------------
% 51.79/14.49  % (28430)------------------------------
% 51.79/14.49  % (28432)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_27763 for (2941ds/454Mi)
% 52.66/14.50  % (28407)Instruction limit reached!
% 52.66/14.50  % (28407)------------------------------
% 52.66/14.50  % (28407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.66/14.50  % (28407)Termination reason: Unknown
% 52.66/14.50  % (28407)Termination phase: Property scanning
% 52.66/14.50  
% 52.66/14.50  % (28407)Memory used [KB]: 27504
% 52.66/14.50  % (28407)Time elapsed: 0.386 s
% 52.66/14.50  % (28407)Instructions burned: 1177 (million)
% 52.66/14.50  % (28407)------------------------------
% 52.66/14.50  % (28407)------------------------------
% 52.66/14.50  % (28433)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_27763 for (2941ds/360Mi)
% 52.66/14.51  % (28434)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_27763 for (2941ds/157Mi)
% 52.66/14.57  % (28434)Instruction limit reached!
% 52.66/14.57  % (28434)------------------------------
% 52.66/14.57  % (28434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.66/14.57  % (28434)Termination reason: Unknown
% 52.66/14.57  % (28434)Termination phase: shuffling
% 52.66/14.57  
% 52.66/14.57  % (28434)Memory used [KB]: 15863
% 52.66/14.57  % (28434)Time elapsed: 0.053 s
% 52.66/14.57  % (28434)Instructions burned: 157 (million)
% 52.66/14.57  % (28434)------------------------------
% 52.66/14.57  % (28434)------------------------------
% 52.66/14.58  % (28435)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_27763 for (2941ds/5061Mi)
% 53.33/14.62  % (28433)Instruction limit reached!
% 53.33/14.62  % (28433)------------------------------
% 53.33/14.62  % (28433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.33/14.62  % (28433)Termination reason: Unknown
% 53.33/14.62  % (28433)Termination phase: shuffling
% 53.33/14.62  
% 53.33/14.62  % (28433)Memory used [KB]: 20852
% 53.33/14.62  % (28433)Time elapsed: 0.113 s
% 53.33/14.62  % (28433)Instructions burned: 361 (million)
% 53.33/14.62  % (28433)------------------------------
% 53.33/14.62  % (28433)------------------------------
% 53.33/14.62  % (28429)Instruction limit reached!
% 53.33/14.62  % (28429)------------------------------
% 53.33/14.62  % (28429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.33/14.62  % (28429)Termination reason: Unknown
% 53.33/14.62  % (28429)Termination phase: shuffling
% 53.33/14.62  
% 53.33/14.62  % (28429)Memory used [KB]: 33901
% 53.33/14.62  % (28429)Time elapsed: 0.327 s
% 53.33/14.62  % (28429)Instructions burned: 1048 (million)
% 53.33/14.62  % (28429)------------------------------
% 53.33/14.62  % (28429)------------------------------
% 53.33/14.63  % (28436)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_27763 for (2940ds/2401Mi)
% 53.33/14.63  % (28432)Instruction limit reached!
% 53.33/14.63  % (28432)------------------------------
% 53.33/14.63  % (28432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.33/14.63  % (28432)Termination reason: Unknown
% 53.33/14.63  % (28432)Termination phase: shuffling
% 53.33/14.63  
% 53.33/14.63  % (28432)Memory used [KB]: 22003
% 53.33/14.63  % (28432)Time elapsed: 0.139 s
% 53.33/14.63  % (28432)Instructions burned: 455 (million)
% 53.33/14.63  % (28432)------------------------------
% 53.33/14.63  % (28432)------------------------------
% 53.33/14.63  % (28437)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_27763 for (2940ds/5798Mi)
% 53.33/14.64  % (28438)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_27763 for (2940ds/346Mi)
% 53.33/14.65  % (28428)Instruction limit reached!
% 53.33/14.65  % (28428)------------------------------
% 53.33/14.65  % (28428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.33/14.65  % (28428)Termination reason: Unknown
% 53.33/14.65  % (28428)Termination phase: Property scanning
% 53.33/14.65  
% 53.33/14.65  % (28428)Memory used [KB]: 27504
% 53.33/14.65  % (28428)Time elapsed: 0.394 s
% 53.33/14.65  % (28428)Instructions burned: 1203 (million)
% 53.33/14.65  % (28428)------------------------------
% 53.33/14.65  % (28428)------------------------------
% 53.33/14.66  % (28439)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_27763 for (2940ds/1321Mi)
% 54.54/14.75  % (28438)Instruction limit reached!
% 54.54/14.75  % (28438)------------------------------
% 54.54/14.75  % (28438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.54/14.75  % (28438)Termination reason: Unknown
% 54.54/14.75  % (28438)Termination phase: shuffling
% 54.54/14.75  
% 54.54/14.75  % (28438)Memory used [KB]: 20596
% 54.54/14.75  % (28438)Time elapsed: 0.107 s
% 54.54/14.75  % (28438)Instructions burned: 348 (million)
% 54.54/14.75  % (28438)------------------------------
% 54.54/14.75  % (28438)------------------------------
% 54.54/14.76  % (28440)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_27763 for (2939ds/1312Mi)
% 57.22/15.09  % (28439)Instruction limit reached!
% 57.22/15.09  % (28439)------------------------------
% 57.22/15.09  % (28439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.22/15.09  % (28439)Termination reason: Unknown
% 57.22/15.09  % (28439)Termination phase: Property scanning
% 57.22/15.09  
% 57.22/15.09  % (28439)Memory used [KB]: 27504
% 57.22/15.09  % (28439)Time elapsed: 0.428 s
% 57.22/15.09  % (28439)Instructions burned: 1323 (million)
% 57.22/15.09  % (28439)------------------------------
% 57.22/15.09  % (28439)------------------------------
% 57.22/15.10  % (28513)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_27763 for (2935ds/672Mi)
% 57.89/15.15  % (28440)Instruction limit reached!
% 57.89/15.15  % (28440)------------------------------
% 57.89/15.15  % (28440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.89/15.15  % (28440)Termination reason: Unknown
% 57.89/15.15  % (28440)Termination phase: shuffling
% 57.89/15.15  
% 57.89/15.15  % (28440)Memory used [KB]: 37355
% 57.89/15.15  % (28440)Time elapsed: 0.394 s
% 57.89/15.15  % (28440)Instructions burned: 1314 (million)
% 57.89/15.15  % (28440)------------------------------
% 57.89/15.15  % (28440)------------------------------
% 57.89/15.17  % (28528)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_27763 for (2935ds/1897Mi)
% 58.27/15.24  % (28365)Instruction limit reached!
% 58.27/15.24  % (28365)------------------------------
% 58.27/15.24  % (28365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.27/15.24  % (28365)Termination reason: Unknown
% 58.27/15.24  % (28365)Termination phase: Saturation
% 58.27/15.24  
% 58.27/15.24  % (28365)Memory used [KB]: 32494
% 58.27/15.24  % (28365)Time elapsed: 1.405 s
% 58.27/15.24  % (28365)Instructions burned: 4530 (million)
% 58.27/15.24  % (28365)------------------------------
% 58.27/15.24  % (28365)------------------------------
% 58.27/15.25  % (28558)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_27763 for (2934ds/1202Mi)
% 58.71/15.33  % (28513)Instruction limit reached!
% 58.71/15.33  % (28513)------------------------------
% 58.71/15.33  % (28513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.71/15.33  % (28513)Termination reason: Unknown
% 58.71/15.33  % (28513)Termination phase: shuffling
% 58.71/15.33  
% 58.71/15.33  % (28513)Memory used [KB]: 21748
% 58.71/15.33  % (28513)Time elapsed: 0.230 s
% 58.71/15.33  % (28513)Instructions burned: 674 (million)
% 58.71/15.33  % (28513)------------------------------
% 58.71/15.33  % (28513)------------------------------
% 58.71/15.35  % (28610)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_27763 for (2933ds/1493Mi)
% 58.71/15.39  % (28436)Instruction limit reached!
% 58.71/15.39  % (28436)------------------------------
% 58.71/15.39  % (28436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.71/15.39  % (28436)Termination reason: Unknown
% 58.71/15.39  % (28436)Termination phase: Property scanning
% 58.71/15.39  
% 58.71/15.39  % (28436)Memory used [KB]: 39274
% 58.71/15.39  % (28436)Time elapsed: 0.761 s
% 58.71/15.39  % (28436)Instructions burned: 2402 (million)
% 58.71/15.39  % (28436)------------------------------
% 58.71/15.39  % (28436)------------------------------
% 59.38/15.40  % (28656)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_27763 for (2932ds/7679Mi)
% 59.97/15.63  % (28558)Instruction limit reached!
% 59.97/15.63  % (28558)------------------------------
% 59.97/15.63  % (28558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.97/15.63  % (28558)Termination reason: Unknown
% 59.97/15.63  % (28558)Termination phase: Property scanning
% 59.97/15.63  
% 59.97/15.63  % (28558)Memory used [KB]: 27376
% 59.97/15.63  % (28558)Time elapsed: 0.385 s
% 59.97/15.63  % (28558)Instructions burned: 1205 (million)
% 59.97/15.63  % (28558)------------------------------
% 59.97/15.63  % (28558)------------------------------
% 59.97/15.65  % (28657)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_27763 for (2930ds/340Mi)
% 60.67/15.73  % (28341)Refutation not found, non-redundant clauses discarded% (28341)------------------------------
% 60.67/15.73  % (28341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 60.67/15.73  % (28341)Termination reason: Refutation not found, non-redundant clauses discarded
% 60.67/15.73  
% 60.67/15.73  % (28341)Memory used [KB]: 36715
% 60.67/15.73  % (28341)Time elapsed: 1.957 s
% 60.67/15.73  % (28341)Instructions burned: 6067 (million)
% 60.67/15.73  % (28341)------------------------------
% 60.67/15.73  % (28341)------------------------------
% 60.67/15.75  % (28658)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_27763 for (2929ds/3672Mi)
% 60.67/15.75  % (28528)Instruction limit reached!
% 60.67/15.75  % (28528)------------------------------
% 60.67/15.75  % (28528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 60.67/15.75  % (28528)Termination reason: Unknown
% 60.67/15.75  % (28528)Termination phase: Property scanning
% 60.67/15.75  
% 60.67/15.75  % (28528)Memory used [KB]: 29040
% 60.67/15.75  % (28528)Time elapsed: 0.586 s
% 60.67/15.75  % (28528)Instructions burned: 1898 (million)
% 60.67/15.75  % (28528)------------------------------
% 60.67/15.75  % (28528)------------------------------
% 60.67/15.76  % (28657)Instruction limit reached!
% 60.67/15.76  % (28657)------------------------------
% 60.67/15.76  % (28657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 60.67/15.76  % (28657)Termination reason: Unknown
% 60.67/15.76  % (28657)Termination phase: shuffling
% 60.67/15.76  
% 60.67/15.76  % (28657)Memory used [KB]: 17910
% 60.67/15.76  % (28657)Time elapsed: 0.119 s
% 60.67/15.76  % (28657)Instructions burned: 340 (million)
% 60.67/15.76  % (28657)------------------------------
% 60.67/15.76  % (28657)------------------------------
% 60.67/15.77  % (28659)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_27763 for (2929ds/1535Mi)
% 60.67/15.78  % (28660)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_27763 for (2929ds/4637Mi)
% 61.84/15.91  % (28435)Instruction limit reached!
% 61.84/15.91  % (28435)------------------------------
% 61.84/15.91  % (28435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.84/15.91  % (28435)Termination reason: Unknown
% 61.84/15.91  % (28435)Termination phase: Function definition elimination
% 61.84/15.91  
% 61.84/15.91  % (28435)Memory used [KB]: 47333
% 61.84/15.91  % (28435)Time elapsed: 1.331 s
% 61.84/15.91  % (28435)Instructions burned: 5062 (million)
% 61.84/15.91  % (28435)------------------------------
% 61.84/15.91  % (28435)------------------------------
% 61.84/15.92  % (28661)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_27763 for (2927ds/3174Mi)
% 61.84/15.94  % (28610)Instruction limit reached!
% 61.84/15.94  % (28610)------------------------------
% 61.84/15.94  % (28610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.84/15.94  % (28610)Termination reason: Unknown
% 61.84/15.94  % (28610)Termination phase: shuffling
% 61.84/15.94  
% 61.84/15.94  % (28610)Memory used [KB]: 39658
% 61.84/15.94  % (28610)Time elapsed: 0.587 s
% 61.84/15.94  % (28610)Instructions burned: 1494 (million)
% 61.84/15.94  % (28610)------------------------------
% 61.84/15.94  % (28610)------------------------------
% 61.84/15.95  % (28662)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_27763 for (2927ds/307Mi)
% 64.12/16.08  % (28662)Instruction limit reached!
% 64.12/16.08  % (28662)------------------------------
% 64.12/16.08  % (28662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.12/16.08  % (28662)Termination reason: Unknown
% 64.12/16.08  % (28662)Termination phase: shuffling
% 64.12/16.08  
% 64.12/16.08  % (28662)Memory used [KB]: 19957
% 64.12/16.08  % (28662)Time elapsed: 0.127 s
% 64.12/16.08  % (28662)Instructions burned: 308 (million)
% 64.12/16.08  % (28662)------------------------------
% 64.12/16.08  % (28662)------------------------------
% 64.12/16.10  % (28670)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_27763 for (2925ds/3619Mi)
% 65.86/16.30  % (28437)Instruction limit reached!
% 65.86/16.30  % (28437)------------------------------
% 65.86/16.30  % (28437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.86/16.30  % (28437)Termination reason: Unknown
% 65.86/16.30  % (28437)Termination phase: Function definition elimination
% 65.86/16.30  
% 65.86/16.30  % (28437)Memory used [KB]: 50404
% 65.86/16.30  % (28437)Time elapsed: 1.668 s
% 65.86/16.30  % (28437)Instructions burned: 5798 (million)
% 65.86/16.30  % (28437)------------------------------
% 65.86/16.30  % (28437)------------------------------
% 65.86/16.33  % (28671)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_27763 for (2923ds/2325Mi)
% 65.86/16.37  % (28659)Instruction limit reached!
% 65.86/16.37  % (28659)------------------------------
% 65.86/16.37  % (28659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.86/16.37  % (28659)Termination reason: Unknown
% 65.86/16.37  % (28659)Termination phase: shuffling
% 65.86/16.37  
% 65.86/16.37  % (28659)Memory used [KB]: 40297
% 65.86/16.37  % (28659)Time elapsed: 0.605 s
% 65.86/16.37  % (28659)Instructions burned: 1536 (million)
% 65.86/16.37  % (28659)------------------------------
% 65.86/16.37  % (28659)------------------------------
% 65.86/16.40  % (28672)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_27763 for (2922ds/2341Mi)
% 74.47/17.54  % (28661)Instruction limit reached!
% 74.47/17.54  % (28661)------------------------------
% 74.47/17.54  % (28661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 74.47/17.54  % (28661)Termination reason: Unknown
% 74.47/17.54  % (28661)Termination phase: Saturation
% 74.47/17.54  
% 74.47/17.54  % (28661)Memory used [KB]: 35308
% 74.47/17.54  % (28661)Time elapsed: 1.622 s
% 74.47/17.54  % (28661)Instructions burned: 3175 (million)
% 74.47/17.54  % (28661)------------------------------
% 74.47/17.54  % (28661)------------------------------
% 74.47/17.56  % (28658)Instruction limit reached!
% 74.47/17.56  % (28658)------------------------------
% 74.47/17.56  % (28658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 74.47/17.56  % (28658)Termination reason: Unknown
% 74.47/17.56  % (28658)Termination phase: Property scanning
% 74.47/17.56  
% 74.47/17.56  % (28658)Memory used [KB]: 43496
% 74.47/17.56  % (28658)Time elapsed: 1.810 s
% 74.47/17.56  % (28658)Instructions burned: 3673 (million)
% 74.47/17.56  % (28658)------------------------------
% 74.47/17.56  % (28658)------------------------------
% 74.47/17.57  % (28673)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_27763 for (2911ds/7257Mi)
% 74.47/17.59  % (28674)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_27763 for (2911ds/3710Mi)
% 75.10/17.65  % (28671)Instruction limit reached!
% 75.10/17.65  % (28671)------------------------------
% 75.10/17.65  % (28671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.10/17.65  % (28671)Termination reason: Unknown
% 75.10/17.65  % (28671)Termination phase: Property scanning
% 75.10/17.65  
% 75.10/17.65  % (28671)Memory used [KB]: 39274
% 75.10/17.65  % (28671)Time elapsed: 1.322 s
% 75.10/17.65  % (28671)Instructions burned: 2326 (million)
% 75.10/17.65  % (28671)------------------------------
% 75.10/17.65  % (28671)------------------------------
% 75.10/17.68  % (28675)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_27763 for (2910ds/326Mi)
% 75.57/17.75  % (28672)Instruction limit reached!
% 75.57/17.75  % (28672)------------------------------
% 75.57/17.75  % (28672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.57/17.75  % (28672)Termination reason: Unknown
% 75.57/17.75  % (28672)Termination phase: shuffling
% 75.57/17.75  
% 75.57/17.75  % (28672)Memory used [KB]: 30831
% 75.57/17.75  % (28672)Time elapsed: 1.359 s
% 75.57/17.75  % (28672)Instructions burned: 2341 (million)
% 75.57/17.75  % (28672)------------------------------
% 75.57/17.75  % (28672)------------------------------
% 75.57/17.78  % (28676)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_27763 for (2909ds/1100Mi)
% 75.95/17.87  % (28675)Instruction limit reached!
% 75.95/17.87  % (28675)------------------------------
% 75.95/17.87  % (28675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.95/17.87  % (28675)Termination reason: Unknown
% 75.95/17.87  % (28675)Termination phase: shuffling
% 75.95/17.87  
% 75.95/17.87  % (28675)Memory used [KB]: 17782
% 75.95/17.87  % (28675)Time elapsed: 0.194 s
% 75.95/17.87  % (28675)Instructions burned: 326 (million)
% 75.95/17.87  % (28675)------------------------------
% 75.95/17.87  % (28675)------------------------------
% 75.95/17.87  % (28656)First to succeed.
% 75.95/17.89  % (28656)Refutation found. Thanks to Tanya!
% 75.95/17.89  % SZS status Theorem for DTF2THF_27763
% 75.95/17.89  % SZS output start Proof for DTF2THF_27763
% 75.95/17.89  thf(type_def_5, type, rat: $tType).
% 75.95/17.89  thf(type_def_6, type, int: $tType).
% 75.95/17.89  thf(type_def_8, type, real: $tType).
% 75.95/17.89  thf(type_def_9, type, set_Pr1261947904930325089at_nat: $tType).
% 75.95/17.89  thf(type_def_10, type, nat: $tType).
% 75.95/17.89  thf(type_def_11, type, code_integer: $tType).
% 75.95/17.89  thf(type_def_12, type, num: $tType).
% 75.95/17.89  thf(type_def_13, type, product_prod_int_int: $tType).
% 75.95/17.89  thf(type_def_14, type, product_prod_nat_nat: $tType).
% 75.95/17.89  thf(type_def_15, type, complex: $tType).
% 75.95/17.89  thf(type_def_16, type, option_num: $tType).
% 75.95/17.89  thf(type_def_17, type, product_prod_num_num: $tType).
% 75.95/17.89  thf(type_def_18, type, produc6271795597528267376eger_o: $tType).
% 75.95/17.89  thf(type_def_19, type, produc8923325533196201883nteger: $tType).
% 75.95/17.89  thf(type_def_20, type, set_Extended_enat: $tType).
% 75.95/17.89  thf(type_def_21, type, extended_enat: $tType).
% 75.95/17.89  thf(type_def_22, type, set_fi4554929511873752355omplex: $tType).
% 75.95/17.89  thf(type_def_23, type, filter6041513312241820739omplex: $tType).
% 75.95/17.89  thf(type_def_24, type, set_fi7789364187291644575l_real: $tType).
% 75.95/17.89  thf(type_def_25, type, filter2146258269922977983l_real: $tType).
% 75.95/17.89  thf(type_def_26, type, set_int: $tType).
% 75.95/17.89  thf(type_def_27, type, set_nat: $tType).
% 75.95/17.89  thf(type_def_28, type, set_real: $tType).
% 75.95/17.89  thf(type_def_29, type, set_set_nat: $tType).
% 75.95/17.89  thf(type_def_30, type, filter_real: $tType).
% 75.95/17.89  thf(type_def_31, type, option_nat: $tType).
% 75.95/17.89  thf(type_def_32, type, filter_int: $tType).
% 75.95/17.89  thf(type_def_33, type, filter_nat: $tType).
% 75.95/17.89  thf(type_def_34, type, set_Pr5085853215250843933omplex: $tType).
% 75.95/17.89  thf(type_def_35, type, set_Pr6218003697084177305l_real: $tType).
% 75.95/17.89  thf(type_def_36, type, set_o: $tType).
% 75.95/17.89  thf(type_def_37, type, set_complex: $tType).
% 75.95/17.89  thf(type_def_38, type, set_list_nat: $tType).
% 75.95/17.89  thf(type_def_39, type, set_char: $tType).
% 75.95/17.89  thf(type_def_40, type, set_list_o: $tType).
% 75.95/17.89  thf(type_def_41, type, set_list_complex: $tType).
% 75.95/17.89  thf(type_def_42, type, set_li5464603477888414924d_enat: $tType).
% 75.95/17.89  thf(type_def_43, type, set_list_int: $tType).
% 75.95/17.89  thf(type_def_44, type, set_li5450038453877631591at_nat: $tType).
% 75.95/17.89  thf(type_def_45, type, set_list_VEBT_VEBT: $tType).
% 75.95/17.89  thf(type_def_46, type, set_num: $tType).
% 75.95/17.89  thf(type_def_47, type, set_option_nat: $tType).
% 75.95/17.89  thf(type_def_48, type, set_rat: $tType).
% 75.95/17.89  thf(type_def_49, type, set_VEBT_VEBT: $tType).
% 75.95/17.89  thf(type_def_50, type, char: $tType).
% 75.95/17.89  thf(type_def_51, type, set_Pr4329608150637261639at_nat: $tType).
% 75.95/17.89  thf(type_def_52, type, set_Pr8693737435421807431at_nat: $tType).
% 75.95/17.89  thf(type_def_53, type, produc1319942482725812455at_nat: $tType).
% 75.95/17.89  thf(type_def_54, type, literal: $tType).
% 75.95/17.89  thf(type_def_55, type, list_o: $tType).
% 75.95/17.89  thf(type_def_56, type, list_nat: $tType).
% 75.95/17.89  thf(type_def_57, type, list_int: $tType).
% 75.95/17.89  thf(type_def_58, type, vEBT_VEBT: $tType).
% 75.95/17.89  thf(type_def_59, type, set_Pr958786334691620121nt_int: $tType).
% 75.95/17.89  thf(type_def_60, type, list_VEBT_VEBT: $tType).
% 75.95/17.89  thf(type_def_61, type, list_complex: $tType).
% 75.95/17.89  thf(type_def_62, type, list_Extended_enat: $tType).
% 75.95/17.89  thf(type_def_63, type, list_option_nat: $tType).
% 75.95/17.89  thf(type_def_64, type, list_P6011104703257516679at_nat: $tType).
% 75.95/17.89  thf(type_def_65, type, list_P5464809261938338413at_nat: $tType).
% 75.95/17.89  thf(type_def_66, type, list_real: $tType).
% 75.95/17.89  thf(type_def_67, type, list_set_nat: $tType).
% 75.95/17.89  thf(type_def_68, type, list_num: $tType).
% 75.95/17.89  thf(type_def_69, type, list_P4002435161011370285od_o_o: $tType).
% 75.95/17.89  thf(type_def_70, type, product_prod_o_o: $tType).
% 75.95/17.89  thf(type_def_71, type, list_P3795440434834930179_o_int: $tType).
% 75.95/17.89  thf(type_def_72, type, product_prod_o_int: $tType).
% 75.95/17.89  thf(type_def_73, type, list_P6285523579766656935_o_nat: $tType).
% 75.95/17.89  thf(type_def_74, type, product_prod_o_nat: $tType).
% 75.95/17.89  thf(type_def_75, type, list_P7495141550334521929T_VEBT: $tType).
% 75.95/17.89  thf(type_def_76, type, produc2504756804600209347T_VEBT: $tType).
% 75.95/17.89  thf(type_def_77, type, list_P1726324292696863441at_num: $tType).
% 75.95/17.89  thf(type_def_78, type, product_prod_nat_num: $tType).
% 75.95/17.89  thf(type_def_79, type, list_P3744719386663036955um_num: $tType).
% 75.95/17.89  thf(type_def_80, type, list_P3126845725202233233VEBT_o: $tType).
% 75.95/17.89  thf(type_def_81, type, produc334124729049499915VEBT_o: $tType).
% 75.95/17.89  thf(type_def_82, type, list_P4547456442757143711BT_int: $tType).
% 75.95/17.89  thf(type_def_83, type, produc4894624898956917775BT_int: $tType).
% 75.95/17.89  thf(type_def_84, type, list_P7037539587688870467BT_nat: $tType).
% 75.95/17.89  thf(type_def_85, type, produc9072475918466114483BT_nat: $tType).
% 75.95/17.89  thf(type_def_86, type, list_P7413028617227757229T_VEBT: $tType).
% 75.95/17.89  thf(type_def_87, type, produc8243902056947475879T_VEBT: $tType).
% 75.95/17.89  thf(type_def_88, type, produc3843707927480180839at_nat: $tType).
% 75.95/17.89  thf(type_def_89, type, option4927543243414619207at_nat: $tType).
% 75.95/17.89  thf(type_def_90, type, produc4953844613479565601on_nat: $tType).
% 75.95/17.89  thf(type_def_91, type, produc2233624965454879586on_nat: $tType).
% 75.95/17.89  thf(type_def_92, type, produc8306885398267862888on_nat: $tType).
% 75.95/17.89  thf(type_def_93, type, produc3447558737645232053on_num: $tType).
% 75.95/17.89  thf(type_def_94, type, produc7036089656553540234on_num: $tType).
% 75.95/17.89  thf(type_def_95, type, produc1193250871479095198on_num: $tType).
% 75.95/17.89  thf(type_def_96, type, produc6121120109295599847at_nat: $tType).
% 75.95/17.89  thf(type_def_97, type, produc5491161045314408544at_nat: $tType).
% 75.95/17.89  thf(type_def_98, type, produc5542196010084753463at_nat: $tType).
% 75.95/17.89  thf(type_def_99, type, produc859450856879609959at_nat: $tType).
% 75.95/17.89  thf(type_def_100, type, produc7272778201969148633d_enat: $tType).
% 75.95/17.89  thf(type_def_101, type, produc4411394909380815293omplex: $tType).
% 75.95/17.89  thf(type_def_102, type, produc2422161461964618553l_real: $tType).
% 75.95/17.89  thf(type_def_103, type, product_unit: $tType).
% 75.95/17.89  thf(func_def_0, type, produc1319942482725812455at_nat: $tType).
% 75.95/17.89  thf(func_def_1, type, produc5542196010084753463at_nat: $tType).
% 75.95/17.89  thf(func_def_2, type, produc5491161045314408544at_nat: $tType).
% 75.95/17.89  thf(func_def_3, type, list_P5464809261938338413at_nat: $tType).
% 75.95/17.89  thf(func_def_4, type, set_Pr4329608150637261639at_nat: $tType).
% 75.95/17.89  thf(func_def_5, type, produc1193250871479095198on_num: $tType).
% 75.95/17.89  thf(func_def_6, type, produc8306885398267862888on_nat: $tType).
% 75.95/17.89  thf(func_def_7, type, produc6121120109295599847at_nat: $tType).
% 75.95/17.89  thf(func_def_8, type, produc7036089656553540234on_num: $tType).
% 75.95/17.89  thf(func_def_9, type, produc2233624965454879586on_nat: $tType).
% 75.95/17.89  thf(func_def_10, type, produc3843707927480180839at_nat: $tType).
% 75.95/17.89  thf(func_def_11, type, set_Pr8693737435421807431at_nat: $tType).
% 75.95/17.89  thf(func_def_12, type, produc859450856879609959at_nat: $tType).
% 75.95/17.89  thf(func_def_13, type, set_fi4554929511873752355omplex: $tType).
% 75.95/17.89  thf(func_def_14, type, list_P7413028617227757229T_VEBT: $tType).
% 75.95/17.89  thf(func_def_15, type, produc3447558737645232053on_num: $tType).
% 75.95/17.89  thf(func_def_16, type, produc4953844613479565601on_nat: $tType).
% 75.95/17.89  thf(func_def_17, type, set_fi7789364187291644575l_real: $tType).
% 75.95/17.89  thf(func_def_18, type, filter6041513312241820739omplex: $tType).
% 75.95/17.89  thf(func_def_19, type, list_P7037539587688870467BT_nat: $tType).
% 75.95/17.89  thf(func_def_20, type, list_P4547456442757143711BT_int: $tType).
% 75.95/17.89  thf(func_def_21, type, set_li5450038453877631591at_nat: $tType).
% 75.95/17.89  thf(func_def_22, type, produc8243902056947475879T_VEBT: $tType).
% 75.95/17.89  thf(func_def_23, type, set_Pr5085853215250843933omplex: $tType).
% 75.95/17.89  thf(func_def_24, type, produc8923325533196201883nteger: $tType).
% 75.95/17.89  thf(func_def_25, type, produc7272778201969148633d_enat: $tType).
% 75.95/17.89  thf(func_def_26, type, list_P3126845725202233233VEBT_o: $tType).
% 75.95/17.89  thf(func_def_27, type, list_P7495141550334521929T_VEBT: $tType).
% 75.95/17.89  thf(func_def_28, type, filter2146258269922977983l_real: $tType).
% 75.95/17.89  thf(func_def_29, type, option4927543243414619207at_nat: $tType).
% 75.95/17.89  thf(func_def_30, type, set_Pr6218003697084177305l_real: $tType).
% 75.95/17.89  thf(func_def_31, type, list_P3744719386663036955um_num: $tType).
% 75.95/17.89  thf(func_def_32, type, list_P1726324292696863441at_num: $tType).
% 75.95/17.89  thf(func_def_33, type, list_P6011104703257516679at_nat: $tType).
% 75.95/17.89  thf(func_def_34, type, produc9072475918466114483BT_nat: $tType).
% 75.95/17.89  thf(func_def_35, type, produc4894624898956917775BT_int: $tType).
% 75.95/17.89  thf(func_def_36, type, set_Pr1261947904930325089at_nat: $tType).
% 75.95/17.89  thf(func_def_37, type, set_Pr958786334691620121nt_int: $tType).
% 75.95/17.89  thf(func_def_38, type, produc4411394909380815293omplex: $tType).
% 75.95/17.89  thf(func_def_39, type, list_P6285523579766656935_o_nat: $tType).
% 75.95/17.89  thf(func_def_40, type, list_P3795440434834930179_o_int: $tType).
% 75.95/17.89  thf(func_def_41, type, set_list_VEBT_VEBT: $tType).
% 75.95/17.89  thf(func_def_42, type, produc334124729049499915VEBT_o: $tType).
% 75.95/17.89  thf(func_def_43, type, produc2504756804600209347T_VEBT: $tType).
% 75.95/17.89  thf(func_def_44, type, produc6271795597528267376eger_o: $tType).
% 75.95/17.89  thf(func_def_45, type, set_li5464603477888414924d_enat: $tType).
% 75.95/17.89  thf(func_def_46, type, produc2422161461964618553l_real: $tType).
% 75.95/17.89  thf(func_def_47, type, product_prod_num_num: $tType).
% 75.95/17.89  thf(func_def_48, type, product_prod_nat_num: $tType).
% 75.95/17.89  thf(func_def_49, type, product_prod_nat_nat: $tType).
% 75.95/17.89  thf(func_def_50, type, product_prod_int_int: $tType).
% 75.95/17.89  thf(func_def_51, type, list_P4002435161011370285od_o_o: $tType).
% 75.95/17.89  thf(func_def_52, type, set_list_complex: $tType).
% 75.95/17.89  thf(func_def_53, type, list_option_nat: $tType).
% 75.95/17.89  thf(func_def_54, type, set_option_nat: $tType).
% 75.95/17.89  thf(func_def_55, type, list_VEBT_VEBT: $tType).
% 75.95/17.89  thf(func_def_56, type, set_list_nat: $tType).
% 75.95/17.89  thf(func_def_57, type, set_list_int: $tType).
% 75.95/17.89  thf(func_def_58, type, product_prod_o_nat: $tType).
% 75.95/17.89  thf(func_def_59, type, product_prod_o_int: $tType).
% 75.95/17.89  thf(func_def_60, type, list_set_nat: $tType).
% 75.95/17.89  thf(func_def_61, type, set_VEBT_VEBT: $tType).
% 75.95/17.89  thf(func_def_62, type, set_set_nat: $tType).
% 75.95/17.89  thf(func_def_63, type, list_Extended_enat: $tType).
% 75.95/17.89  thf(func_def_64, type, set_Extended_enat: $tType).
% 75.95/17.89  thf(func_def_65, type, list_complex: $tType).
% 75.95/17.89  thf(func_def_66, type, set_list_o: $tType).
% 75.95/17.89  thf(func_def_67, type, product_prod_o_o: $tType).
% 75.95/17.89  thf(func_def_68, type, set_complex: $tType).
% 75.95/17.89  thf(func_def_69, type, filter_real: $tType).
% 75.95/17.89  thf(func_def_70, type, option_num: $tType).
% 75.95/17.89  thf(func_def_71, type, option_nat: $tType).
% 75.95/17.89  thf(func_def_72, type, filter_nat: $tType).
% 75.95/17.89  thf(func_def_73, type, filter_int: $tType).
% 75.95/17.89  thf(func_def_74, type, set_char: $tType).
% 75.95/17.89  thf(func_def_75, type, list_real: $tType).
% 75.95/17.89  thf(func_def_76, type, set_real: $tType).
% 75.95/17.89  thf(func_def_77, type, list_num: $tType).
% 75.95/17.89  thf(func_def_78, type, list_nat: $tType).
% 75.95/17.89  thf(func_def_79, type, list_int: $tType).
% 75.95/17.89  thf(func_def_80, type, vEBT_VEBT: $tType).
% 75.95/17.89  thf(func_def_81, type, set_rat: $tType).
% 75.95/17.89  thf(func_def_82, type, set_num: $tType).
% 75.95/17.89  thf(func_def_83, type, set_nat: $tType).
% 75.95/17.89  thf(func_def_84, type, set_int: $tType).
% 75.95/17.89  thf(func_def_85, type, code_integer: $tType).
% 75.95/17.89  thf(func_def_86, type, product_unit: $tType).
% 75.95/17.89  thf(func_def_87, type, extended_enat: $tType).
% 75.95/17.89  thf(func_def_88, type, list_o: $tType).
% 75.95/17.89  thf(func_def_89, type, complex: $tType).
% 75.95/17.89  thf(func_def_90, type, literal: $tType).
% 75.95/17.89  thf(func_def_91, type, set_o: $tType).
% 75.95/17.89  thf(func_def_92, type, char: $tType).
% 75.95/17.89  thf(func_def_93, type, real: $tType).
% 75.95/17.89  thf(func_def_94, type, rat: $tType).
% 75.95/17.89  thf(func_def_95, type, num: $tType).
% 75.95/17.89  thf(func_def_96, type, nat: $tType).
% 75.95/17.89  thf(func_def_97, type, int: $tType).
% 75.95/17.89  thf(func_def_98, type, archim2889992004027027881ng_rat: rat > int).
% 75.95/17.89  thf(func_def_99, type, archim7802044766580827645g_real: real > int).
% 75.95/17.89  thf(func_def_100, type, archim3151403230148437115or_rat: rat > int).
% 75.95/17.89  thf(func_def_101, type, archim6058952711729229775r_real: real > int).
% 75.95/17.89  thf(func_def_102, type, archimedean_frac_rat: rat > rat).
% 75.95/17.89  thf(func_def_103, type, archim2898591450579166408c_real: real > real).
% 75.95/17.89  thf(func_def_104, type, archim7778729529865785530nd_rat: rat > int).
% 75.95/17.89  thf(func_def_105, type, archim8280529875227126926d_real: real > int).
% 75.95/17.89  thf(func_def_106, type, bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat).
% 75.95/17.89  thf(func_def_107, type, bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat).
% 75.95/17.89  thf(func_def_108, type, bNF_re1962705104956426057at_rat: ((nat > rat) > (nat > rat) > $o) > (((nat > rat) > nat > rat) > ((nat > rat) > nat > rat) > $o) > ((nat > rat) > (nat > rat) > nat > rat) > ((nat > rat) > (nat > rat) > nat > rat) > $o).
% 75.95/17.89  thf(func_def_109, type, bNF_re895249473297799549at_rat: ((nat > rat) > (nat > rat) > $o) > ((nat > rat) > (nat > rat) > $o) > ((nat > rat) > nat > rat) > ((nat > rat) > nat > rat) > $o).
% 75.95/17.89  thf(func_def_110, type, bNF_re728719798268516973at_o_o: ((nat > rat) > (nat > rat) > $o) > ($o > $o > $o) > ((nat > rat) > $o) > ((nat > rat) > $o) > $o).
% 75.95/17.89  thf(func_def_111, type, bNF_re4695409256820837752l_real: ((nat > rat) > real > $o) > (((nat > rat) > nat > rat) > (real > real) > $o) > ((nat > rat) > (nat > rat) > nat > rat) > (real > real > real) > $o).
% 75.95/17.89  thf(func_def_112, type, bNF_re4521903465945308077real_o: ((nat > rat) > real > $o) > (((nat > rat) > $o) > (real > $o) > $o) > ((nat > rat) > (nat > rat) > $o) > (real > real > $o) > $o).
% 75.95/17.89  thf(func_def_113, type, bNF_re3023117138289059399t_real: ((nat > rat) > real > $o) > ((nat > rat) > real > $o) > ((nat > rat) > nat > rat) > (real > real) > $o).
% 75.95/17.89  thf(func_def_114, type, bNF_re4297313714947099218al_o_o: ((nat > rat) > real > $o) > ($o > $o > $o) > ((nat > rat) > $o) > (real > $o) > $o).
% 75.95/17.89  thf(func_def_115, type, bNF_re6321650412969554871eger_o: (int > code_integer > $o) > ((int > $o) > (code_integer > $o) > $o) > (int > int > $o) > (code_integer > code_integer > $o) > $o).
% 75.95/17.89  thf(func_def_116, type, bNF_re6574881592172037608er_o_o: (int > code_integer > $o) > ($o > $o > $o) > (int > $o) > (code_integer > $o) > $o).
% 75.95/17.89  thf(func_def_117, type, bNF_re2807294637932363402at_nat: (int > code_integer > $o) > (nat > nat > $o) > (int > nat) > (code_integer > nat) > $o).
% 75.95/17.89  thf(func_def_118, type, bNF_re6718328864250387230um_num: (int > code_integer > $o) > (num > num > $o) > (int > num) > (code_integer > num) > $o).
% 75.95/17.89  thf(func_def_119, type, bNF_re3403563459893282935_int_o: (int > int > $o) > ((int > $o) > (int > $o) > $o) > (int > int > $o) > (int > int > $o) > $o).
% 75.95/17.89  thf(func_def_120, type, bNF_re157797125943740599nt_int: (int > int > $o) > ((int > product_prod_int_int) > (int > product_prod_int_int) > $o) > (int > int > product_prod_int_int) > (int > int > product_prod_int_int) > $o).
% 75.95/17.89  thf(func_def_121, type, bNF_re3461391660133120880nt_rat: (int > int > $o) > ((int > product_prod_int_int) > (int > rat) > $o) > (int > int > product_prod_int_int) > (int > int > rat) > $o).
% 75.95/17.89  thf(func_def_122, type, bNF_re5089333283451836215nt_o_o: (int > int > $o) > ($o > $o > $o) > (int > $o) > (int > $o) > $o).
% 75.95/17.89  thf(func_def_123, type, bNF_re3715656647883201625at_nat: (int > int > $o) > (nat > nat > $o) > (int > nat) > (int > nat) > $o).
% 75.95/17.89  thf(func_def_124, type, bNF_re7626690874201225453um_num: (int > int > $o) > (num > num > $o) > (int > num) > (int > num) > $o).
% 75.95/17.89  thf(func_def_125, type, bNF_re6250860962936578807nt_int: (int > int > $o) > (product_prod_int_int > product_prod_int_int > $o) > (int > product_prod_int_int) > (int > product_prod_int_int) > $o).
% 75.95/17.89  thf(func_def_126, type, bNF_re2214769303045360666nt_rat: (int > int > $o) > (product_prod_int_int > rat > $o) > (int > product_prod_int_int) > (int > rat) > $o).
% 75.95/17.89  thf(func_def_127, type, bNF_re578469030762574527_nat_o: (nat > nat > $o) > ((nat > $o) > (nat > $o) > $o) > (nat > nat > $o) > (nat > nat > $o) > $o).
% 75.95/17.89  thf(func_def_128, type, bNF_re4705727531993890431at_o_o: (nat > nat > $o) > ($o > $o > $o) > (nat > $o) > (nat > $o) > $o).
% 75.95/17.89  thf(func_def_129, type, bNF_re4153400068438556298nteger: (nat > nat > $o) > (int > code_integer > $o) > (nat > int) > (nat > code_integer) > $o).
% 75.95/17.89  thf(func_def_130, type, bNF_re6650684261131312217nt_int: (nat > nat > $o) > (int > int > $o) > (nat > int) > (nat > int) > $o).
% 75.95/17.89  thf(func_def_131, type, bNF_re6830278522597306478at_int: (nat > nat > $o) > (product_prod_nat_nat > int > $o) > (nat > product_prod_nat_nat) > (nat > int) > $o).
% 75.95/17.89  thf(func_def_132, type, bNF_re7876454716742015248nteger: (num > num > $o) > ((num > int) > (num > code_integer) > $o) > (num > num > int) > (num > num > code_integer) > $o).
% 75.95/17.89  thf(func_def_133, type, bNF_re8402795839162346335um_int: (num > num > $o) > ((num > int) > (num > int) > $o) > (num > num > int) > (num > num > int) > $o).
% 75.95/17.89  thf(func_def_134, type, bNF_re6501075790457514782nteger: (num > num > $o) > (int > code_integer > $o) > (num > int) > (num > code_integer) > $o).
% 75.95/17.89  thf(func_def_135, type, bNF_re1822329894187522285nt_int: (num > num > $o) > (int > int > $o) > (num > int) > (num > int) > $o).
% 75.95/17.89  thf(func_def_136, type, bNF_re8699439704749558557nt_o_o: (product_prod_int_int > product_prod_int_int > $o) > ($o > $o > $o) > (product_prod_int_int > $o) > (product_prod_int_int > $o) > $o).
% 75.95/17.89  thf(func_def_137, type, bNF_re7145576690424134365nt_int: (product_prod_int_int > product_prod_int_int > $o) > (product_prod_int_int > product_prod_int_int > $o) > (product_prod_int_int > product_prod_int_int) > (product_prod_int_int > product_prod_int_int) > $o).
% 75.95/17.89  thf(func_def_138, type, bNF_re1494630372529172596at_o_o: (product_prod_int_int > rat > $o) > ($o > $o > $o) > (product_prod_int_int > $o) > (rat > $o) > $o).
% 75.95/17.89  thf(func_def_139, type, bNF_re8279943556446156061nt_rat: (product_prod_int_int > rat > $o) > (product_prod_int_int > rat > $o) > (product_prod_int_int > product_prod_int_int) > (rat > rat) > $o).
% 75.95/17.89  thf(func_def_140, type, bNF_re717283939379294677_int_o: (product_prod_nat_nat > int > $o) > ((product_prod_nat_nat > $o) > (int > $o) > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > (int > int > $o) > $o).
% 75.95/17.89  thf(func_def_141, type, bNF_re7408651293131936558nt_int: (product_prod_nat_nat > int > $o) > ((product_prod_nat_nat > product_prod_nat_nat) > (int > int) > $o) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > (int > int > int) > $o).
% 75.95/17.89  thf(func_def_142, type, bNF_re6644619430987730960nt_o_o: (product_prod_nat_nat > int > $o) > ($o > $o > $o) > (product_prod_nat_nat > $o) > (int > $o) > $o).
% 75.95/17.89  thf(func_def_143, type, bNF_re4555766996558763186at_nat: (product_prod_nat_nat > int > $o) > (nat > nat > $o) > (product_prod_nat_nat > nat) > (int > nat) > $o).
% 75.95/17.89  thf(func_def_144, type, bNF_re7400052026677387805at_int: (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > product_prod_nat_nat) > (int > int) > $o).
% 75.95/17.89  thf(func_def_145, type, bNF_re4202695980764964119_nat_o: (product_prod_nat_nat > product_prod_nat_nat > $o) > ((product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > $o).
% 75.95/17.89  thf(func_def_146, type, bNF_re3099431351363272937at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > ((product_prod_nat_nat > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat) > $o) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > $o).
% 75.95/17.89  thf(func_def_147, type, bNF_re3666534408544137501at_o_o: (product_prod_nat_nat > product_prod_nat_nat > $o) > ($o > $o > $o) > (product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > $o).
% 75.95/17.89  thf(func_def_148, type, bNF_re8246922863344978751at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > (nat > nat > $o) > (product_prod_nat_nat > nat) > (product_prod_nat_nat > nat) > $o).
% 75.95/17.89  thf(func_def_149, type, bNF_re2241393799969408733at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat) > $o).
% 75.95/17.89  thf(func_def_150, type, binomial: nat > nat > nat).
% 75.95/17.89  thf(func_def_151, type, gbinomial_complex: complex > nat > complex).
% 75.95/17.89  thf(func_def_152, type, gbinomial_int: int > nat > int).
% 75.95/17.89  thf(func_def_153, type, gbinomial_nat: nat > nat > nat).
% 75.95/17.89  thf(func_def_154, type, gbinomial_rat: rat > nat > rat).
% 75.95/17.89  thf(func_def_155, type, gbinomial_real: real > nat > real).
% 75.95/17.89  thf(func_def_156, type, bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o).
% 75.95/17.89  thf(func_def_157, type, bit_and_not_num: num > num > option_num).
% 75.95/17.89  thf(func_def_158, type, bit_and_not_num_rel: product_prod_num_num > product_prod_num_num > $o).
% 75.95/17.89  thf(func_def_159, type, bit_concat_bit: nat > int > int > int).
% 75.95/17.89  thf(func_def_160, type, bit_or_not_num_neg: num > num > num).
% 75.95/17.89  thf(func_def_161, type, bit_or3848514188828904588eg_rel: product_prod_num_num > product_prod_num_num > $o).
% 75.95/17.89  thf(func_def_162, type, bit_ri7632146776885996613nteger: code_integer > code_integer).
% 75.95/17.89  thf(func_def_163, type, bit_ri7919022796975470100ot_int: int > int).
% 75.95/17.89  thf(func_def_164, type, bit_ri6519982836138164636nteger: nat > code_integer > code_integer).
% 75.95/17.89  thf(func_def_165, type, bit_ri631733984087533419it_int: nat > int > int).
% 75.95/17.89  thf(func_def_166, type, bit_se725231765392027082nd_int: int > int > int).
% 75.95/17.89  thf(func_def_167, type, bit_se727722235901077358nd_nat: nat > nat > nat).
% 75.95/17.89  thf(func_def_168, type, bit_se8568078237143864401it_int: nat > int > int).
% 75.95/17.89  thf(func_def_169, type, bit_se8570568707652914677it_nat: nat > nat > nat).
% 75.95/17.89  thf(func_def_170, type, bit_se1345352211410354436nteger: nat > code_integer > code_integer).
% 75.95/17.89  thf(func_def_171, type, bit_se2159334234014336723it_int: nat > int > int).
% 75.95/17.89  thf(func_def_172, type, bit_se2161824704523386999it_nat: nat > nat > nat).
% 75.95/17.89  thf(func_def_173, type, bit_se2000444600071755411sk_int: nat > int).
% 75.95/17.89  thf(func_def_174, type, bit_se2002935070580805687sk_nat: nat > nat).
% 75.95/17.89  thf(func_def_175, type, bit_se1080825931792720795nteger: code_integer > code_integer > code_integer).
% 75.95/17.89  thf(func_def_176, type, bit_se1409905431419307370or_int: int > int > int).
% 75.95/17.89  thf(func_def_177, type, bit_se1412395901928357646or_nat: nat > nat > nat).
% 75.95/17.89  thf(func_def_178, type, bit_se545348938243370406it_int: nat > int > int).
% 75.95/17.89  thf(func_def_179, type, bit_se547839408752420682it_nat: nat > nat > nat).
% 75.95/17.89  thf(func_def_180, type, bit_se2793503036327961859nteger: nat > code_integer > code_integer).
% 75.95/17.89  thf(func_def_181, type, bit_se7879613467334960850it_int: nat > int > int).
% 75.95/17.89  thf(func_def_182, type, bit_se7882103937844011126it_nat: nat > nat > nat).
% 75.95/17.89  thf(func_def_183, type, bit_se1745604003318907178nteger: nat > code_integer > code_integer).
% 75.95/17.89  thf(func_def_184, type, bit_se2923211474154528505it_int: nat > int > int).
% 75.95/17.89  thf(func_def_185, type, bit_se2925701944663578781it_nat: nat > nat > nat).
% 75.95/17.89  thf(func_def_186, type, bit_se8260200283734997820nteger: nat > code_integer > code_integer).
% 75.95/17.89  thf(func_def_187, type, bit_se4203085406695923979it_int: nat > int > int).
% 75.95/17.89  thf(func_def_188, type, bit_se4205575877204974255it_nat: nat > nat > nat).
% 75.95/17.89  thf(func_def_189, type, bit_se3222712562003087583nteger: code_integer > code_integer > code_integer).
% 75.95/17.89  thf(func_def_190, type, bit_se6526347334894502574or_int: int > int > int).
% 75.95/17.89  thf(func_def_191, type, bit_se6528837805403552850or_nat: nat > nat > nat).
% 75.95/17.89  thf(func_def_192, type, bit_se1146084159140164899it_int: int > nat > $o).
% 75.95/17.89  thf(func_def_193, type, bit_se1148574629649215175it_nat: nat > nat > $o).
% 75.95/17.89  thf(func_def_194, type, bit_take_bit_num: nat > num > option_num).
% 75.95/17.89  thf(func_def_195, type, bit_un1837492267222099188nd_num: num > num > option_num).
% 75.95/17.89  thf(func_def_196, type, bit_un5425074673868309765um_rel: product_prod_num_num > product_prod_num_num > $o).
% 75.95/17.89  thf(func_def_197, type, bit_un2785000775030745342or_num: num > num > num).
% 75.95/17.89  thf(func_def_198, type, bit_un6909899581280750971um_rel: product_prod_num_num > product_prod_num_num > $o).
% 75.95/17.89  thf(func_def_199, type, bit_un6178654185764691216or_num: num > num > option_num).
% 75.95/17.89  thf(func_def_200, type, bit_un3595099601533988841um_rel: product_prod_num_num > product_prod_num_num > $o).
% 75.95/17.89  thf(func_def_201, type, bit_un7362597486090784418nd_num: num > num > option_num).
% 75.95/17.89  thf(func_def_202, type, bit_un4731106466462545111um_rel: product_prod_num_num > product_prod_num_num > $o).
% 75.95/17.89  thf(func_def_203, type, bit_un6697907153464112080or_num: num > num > num).
% 75.95/17.89  thf(func_def_204, type, bit_un4773296044027857193um_rel: product_prod_num_num > product_prod_num_num > $o).
% 75.95/17.89  thf(func_def_205, type, bit_un2480387367778600638or_num: num > num > option_num).
% 75.95/17.89  thf(func_def_206, type, bit_un2901131394128224187um_rel: product_prod_num_num > product_prod_num_num > $o).
% 75.95/17.89  thf(func_def_207, type, code_Neg: num > code_integer).
% 75.95/17.89  thf(func_def_208, type, code_Pos: num > code_integer).
% 75.95/17.89  thf(func_def_209, type, code_bit_cut_integer: code_integer > produc6271795597528267376eger_o).
% 75.95/17.89  thf(func_def_210, type, code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger).
% 75.95/17.89  thf(func_def_211, type, code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger).
% 75.95/17.89  thf(func_def_212, type, code_dup: code_integer > code_integer).
% 75.95/17.89  thf(func_def_213, type, code_int_of_integer: code_integer > int).
% 75.95/17.89  thf(func_def_214, type, code_integer_of_int: int > code_integer).
% 75.95/17.89  thf(func_def_215, type, code_integer_of_nat: nat > code_integer).
% 75.95/17.89  thf(func_def_216, type, code_integer_of_num: num > code_integer).
% 75.95/17.89  thf(func_def_217, type, code_nat_of_integer: code_integer > nat).
% 75.95/17.89  thf(func_def_218, type, code_num_of_integer: code_integer > num).
% 75.95/17.89  thf(func_def_219, type, code_pcr_integer: int > code_integer > $o).
% 75.95/17.89  thf(func_def_220, type, code_sub: num > num > code_integer).
% 75.95/17.89  thf(func_def_221, type, code_Target_negative: num > int).
% 75.95/17.89  thf(func_def_222, type, code_Target_positive: num > int).
% 75.95/17.89  thf(func_def_223, type, code_Target_Nat: code_integer > nat).
% 75.95/17.89  thf(func_def_224, type, code_T6385005292777649522of_nat: nat > int).
% 75.95/17.89  thf(func_def_225, type, comple2295165028678016749d_enat: set_Extended_enat > extended_enat).
% 75.95/17.89  thf(func_def_226, type, comple8358262395181532106omplex: set_fi4554929511873752355omplex > filter6041513312241820739omplex).
% 75.95/17.89  thf(func_def_227, type, comple2936214249959783750l_real: set_fi7789364187291644575l_real > filter2146258269922977983l_real).
% 75.95/17.89  thf(func_def_228, type, complete_Inf_Inf_int: set_int > int).
% 75.95/17.89  thf(func_def_229, type, complete_Inf_Inf_nat: set_nat > nat).
% 75.95/17.89  thf(func_def_230, type, comple4887499456419720421f_real: set_real > real).
% 75.95/17.89  thf(func_def_231, type, comple7806235888213564991et_nat: set_set_nat > set_nat).
% 75.95/17.89  thf(func_def_232, type, comple4398354569131411667d_enat: set_Extended_enat > extended_enat).
% 75.95/17.89  thf(func_def_233, type, complete_Sup_Sup_int: set_int > int).
% 75.95/17.89  thf(func_def_234, type, complete_Sup_Sup_nat: set_nat > nat).
% 75.95/17.89  thf(func_def_235, type, comple1385675409528146559p_real: set_real > real).
% 75.95/17.89  thf(func_def_236, type, arg: complex > real).
% 75.95/17.89  thf(func_def_237, type, cis: real > complex).
% 75.95/17.89  thf(func_def_238, type, cnj: complex > complex).
% 75.95/17.89  thf(func_def_239, type, complex2: real > real > complex).
% 75.95/17.89  thf(func_def_240, type, im: complex > real).
% 75.95/17.89  thf(func_def_241, type, re: complex > real).
% 75.95/17.89  thf(func_def_242, type, csqrt: complex > complex).
% 75.95/17.89  thf(func_def_243, type, imaginary_unit: complex).
% 75.95/17.89  thf(func_def_244, type, rcis: real > real > complex).
% 75.95/17.89  thf(func_def_245, type, condit2214826472909112428ve_nat: set_nat > $o).
% 75.95/17.89  thf(func_def_246, type, differ6690327859849518006l_real: (real > real) > filter_real > $o).
% 75.95/17.89  thf(func_def_247, type, has_de1759254742604945161l_real: (real > real) > (real > real) > filter_real > $o).
% 75.95/17.89  thf(func_def_248, type, has_fi5821293074295781190e_real: (real > real) > real > filter_real > $o).
% 75.95/17.89  thf(func_def_249, type, adjust_div: product_prod_int_int > int).
% 75.95/17.89  thf(func_def_250, type, adjust_mod: int > int > int).
% 75.95/17.89  thf(func_def_251, type, divmod_nat: nat > nat > product_prod_nat_nat).
% 75.95/17.89  thf(func_def_252, type, eucl_rel_int: int > int > product_prod_int_int > $o).
% 75.95/17.89  thf(func_def_253, type, unique5706413561485394159nteger: produc8923325533196201883nteger > $o).
% 75.95/17.89  thf(func_def_254, type, unique6319869463603278526ux_int: product_prod_int_int > $o).
% 75.95/17.89  thf(func_def_255, type, unique6322359934112328802ux_nat: product_prod_nat_nat > $o).
% 75.95/17.89  thf(func_def_256, type, unique3479559517661332726nteger: num > num > produc8923325533196201883nteger).
% 75.95/17.89  thf(func_def_257, type, unique5052692396658037445od_int: num > num > product_prod_int_int).
% 75.95/17.89  thf(func_def_258, type, unique5055182867167087721od_nat: num > num > product_prod_nat_nat).
% 75.95/17.89  thf(func_def_259, type, unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 75.95/17.89  thf(func_def_260, type, unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int).
% 75.95/17.89  thf(func_def_261, type, unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat).
% 75.95/17.89  thf(func_def_262, type, euclid4774559944035922753ze_int: int > nat).
% 75.95/17.89  thf(func_def_263, type, euclid3395696857347342551nt_int: int > int).
% 75.95/17.89  thf(func_def_264, type, extended_eSuc: extended_enat > extended_enat).
% 75.95/17.89  thf(func_def_265, type, extended_enat2: nat > extended_enat).
% 75.95/17.89  thf(func_def_266, type, extended_Abs_enat: option_nat > extended_enat).
% 75.95/17.89  thf(func_def_267, type, extended_Rep_enat: extended_enat > option_nat).
% 75.95/17.89  thf(func_def_268, type, extended_case_enat_o: (nat > $o) > $o > extended_enat > $o).
% 75.95/17.89  thf(func_def_269, type, extend3600170679010898289d_enat: (nat > extended_enat) > extended_enat > extended_enat > extended_enat).
% 75.95/17.89  thf(func_def_270, type, extend5688581933313929465d_enat: extended_enat).
% 75.95/17.89  thf(func_def_271, type, extended_the_enat: extended_enat > nat).
% 75.95/17.89  thf(func_def_272, type, comm_s8582702949713902594nteger: code_integer > nat > code_integer).
% 75.95/17.89  thf(func_def_273, type, comm_s2602460028002588243omplex: complex > nat > complex).
% 75.95/17.89  thf(func_def_274, type, comm_s4660882817536571857er_int: int > nat > int).
% 75.95/17.89  thf(func_def_275, type, comm_s4663373288045622133er_nat: nat > nat > nat).
% 75.95/17.89  thf(func_def_276, type, comm_s4028243227959126397er_rat: rat > nat > rat).
% 75.95/17.89  thf(func_def_277, type, comm_s7457072308508201937r_real: real > nat > real).
% 75.95/17.89  thf(func_def_278, type, semiri5044797733671781792omplex: nat > complex).
% 75.95/17.89  thf(func_def_279, type, semiri1408675320244567234ct_nat: nat > nat).
% 75.95/17.89  thf(func_def_280, type, semiri2265585572941072030t_real: nat > real).
% 75.95/17.89  thf(func_def_281, type, invers8013647133539491842omplex: complex > complex).
% 75.95/17.89  thf(func_def_282, type, inverse_inverse_rat: rat > rat).
% 75.95/17.89  thf(func_def_283, type, inverse_inverse_real: real > real).
% 75.95/17.89  thf(func_def_284, type, at_bot_real: filter_real).
% 75.95/17.89  thf(func_def_285, type, at_top_int: filter_int).
% 75.95/17.89  thf(func_def_286, type, at_top_nat: filter_nat).
% 75.95/17.89  thf(func_def_287, type, at_top_real: filter_real).
% 75.95/17.89  thf(func_def_288, type, eventually_nat: (nat > $o) > filter_nat > $o).
% 75.95/17.89  thf(func_def_289, type, eventually_real: (real > $o) > filter_real > $o).
% 75.95/17.89  thf(func_def_290, type, filterlim_int_nat: (int > nat) > filter_nat > filter_int > $o).
% 75.95/17.89  thf(func_def_291, type, filterlim_nat_int: (nat > int) > filter_int > filter_nat > $o).
% 75.95/17.89  thf(func_def_292, type, filterlim_nat_nat: (nat > nat) > filter_nat > filter_nat > $o).
% 75.95/17.89  thf(func_def_293, type, filterlim_nat_real: (nat > real) > filter_real > filter_nat > $o).
% 75.95/17.89  thf(func_def_294, type, filterlim_real_real: (real > real) > filter_real > filter_real > $o).
% 75.95/17.89  thf(func_def_295, type, filtermap_real_real: (real > real) > filter_real > filter_real).
% 75.95/17.89  thf(func_def_296, type, princi3496590319149328850omplex: set_Pr5085853215250843933omplex > filter6041513312241820739omplex).
% 75.95/17.89  thf(func_def_297, type, princi6114159922880469582l_real: set_Pr6218003697084177305l_real > filter2146258269922977983l_real).
% 75.95/17.89  thf(func_def_298, type, finite_card_o: set_o > nat).
% 75.95/17.89  thf(func_def_299, type, finite_card_complex: set_complex > nat).
% 75.95/17.89  thf(func_def_300, type, finite_card_int: set_int > nat).
% 75.95/17.89  thf(func_def_301, type, finite_card_list_nat: set_list_nat > nat).
% 75.95/17.89  thf(func_def_302, type, finite_card_nat: set_nat > nat).
% 75.95/17.89  thf(func_def_303, type, finite_card_set_nat: set_set_nat > nat).
% 75.95/17.89  thf(func_def_304, type, finite_card_char: set_char > nat).
% 75.95/17.89  thf(func_def_305, type, finite_finite_o: set_o > $o).
% 75.95/17.89  thf(func_def_306, type, finite3207457112153483333omplex: set_complex > $o).
% 75.95/17.89  thf(func_def_307, type, finite4001608067531595151d_enat: set_Extended_enat > $o).
% 75.95/17.89  thf(func_def_308, type, finite_finite_int: set_int > $o).
% 75.95/17.89  thf(func_def_309, type, finite_finite_list_o: set_list_o > $o).
% 75.95/17.89  thf(func_def_310, type, finite8712137658972009173omplex: set_list_complex > $o).
% 75.95/17.89  thf(func_def_311, type, finite1862508098717546133d_enat: set_li5464603477888414924d_enat > $o).
% 75.95/17.89  thf(func_def_312, type, finite3922522038869484883st_int: set_list_int > $o).
% 75.95/17.89  thf(func_def_313, type, finite8100373058378681591st_nat: set_list_nat > $o).
% 75.95/17.89  thf(func_def_314, type, finite500796754983035824at_nat: set_li5450038453877631591at_nat > $o).
% 75.95/17.89  thf(func_def_315, type, finite3004134309566078307T_VEBT: set_list_VEBT_VEBT > $o).
% 75.95/17.89  thf(func_def_316, type, finite_finite_nat: set_nat > $o).
% 75.95/17.89  thf(func_def_317, type, finite_finite_num: set_num > $o).
% 75.95/17.89  thf(func_def_318, type, finite5523153139673422903on_nat: set_option_nat > $o).
% 75.95/17.89  thf(func_def_319, type, finite6177210948735845034at_nat: set_Pr1261947904930325089at_nat > $o).
% 75.95/17.89  thf(func_def_320, type, finite_finite_rat: set_rat > $o).
% 75.95/17.89  thf(func_def_321, type, finite_finite_real: set_real > $o).
% 75.95/17.89  thf(func_def_322, type, finite1152437895449049373et_nat: set_set_nat > $o).
% 75.95/17.89  thf(func_def_323, type, finite5795047828879050333T_VEBT: set_VEBT_VEBT > $o).
% 75.95/17.89  thf(func_def_324, type, bij_be1856998921033663316omplex: (complex > complex) > set_complex > set_complex > $o).
% 75.95/17.89  thf(func_def_325, type, bij_betw_nat_complex: (nat > complex) > set_nat > set_complex > $o).
% 75.95/17.89  thf(func_def_326, type, bij_betw_nat_nat: (nat > nat) > set_nat > set_nat > $o).
% 75.95/17.89  thf(func_def_327, type, comp_C8797469213163452608nteger: ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 75.95/17.89  thf(func_def_328, type, comp_C1593894019821074884nteger: (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 75.95/17.89  thf(func_def_329, type, comp_int_int_num: (int > int) > (num > int) > num > int).
% 75.95/17.89  thf(func_def_330, type, comp_int_nat_int: (int > nat) > (int > int) > int > nat).
% 75.95/17.89  thf(func_def_331, type, comp_nat_num_int: (nat > num) > (int > nat) > int > num).
% 75.95/17.89  thf(func_def_332, type, comp_nat_real_nat: (nat > real) > (nat > nat) > nat > real).
% 75.95/17.89  thf(func_def_333, type, id_o: $o > $o).
% 75.95/17.89  thf(func_def_334, type, id_nat: nat > nat).
% 75.95/17.89  thf(func_def_335, type, id_num: num > num).
% 75.95/17.89  thf(func_def_336, type, inj_on_nat_nat: (nat > nat) > set_nat > $o).
% 75.95/17.89  thf(func_def_337, type, inj_on_nat_char: (nat > char) > set_nat > $o).
% 75.95/17.89  thf(func_def_338, type, inj_on_real_real: (real > real) > set_real > $o).
% 75.95/17.89  thf(func_def_339, type, map_fu6539832666145259331at_nat: (code_integer > int) > (nat > nat) > (int > nat) > code_integer > nat).
% 75.95/17.89  thf(func_def_340, type, map_fu1227494855608507351um_num: (code_integer > int) > (num > num) > (int > num) > code_integer > num).
% 75.95/17.89  thf(func_def_341, 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 > $o).
% 75.95/17.89  thf(func_def_342, type, map_fu4960017516451851995nt_int: (int > product_prod_nat_nat) > ((product_prod_nat_nat > product_prod_nat_nat) > int > int) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > int > int > int).
% 75.95/17.89  thf(func_def_343, type, map_fu4826362097070443709at_o_o: (int > product_prod_nat_nat) > ($o > $o) > (product_prod_nat_nat > $o) > int > $o).
% 75.95/17.89  thf(func_def_344, type, map_fu2345160673673942751at_nat: (int > product_prod_nat_nat) > (nat > nat) > (product_prod_nat_nat > nat) > int > nat).
% 75.95/17.89  thf(func_def_345, type, map_fu3667384564859982768at_int: (int > product_prod_nat_nat) > (product_prod_nat_nat > int) > (product_prod_nat_nat > product_prod_nat_nat) > int > int).
% 75.95/17.89  thf(func_def_346, type, map_fu6290471996055670595nteger: (nat > nat) > (int > code_integer) > (nat > int) > nat > code_integer).
% 75.95/17.89  thf(func_def_347, type, map_fu898904425404107465nt_o_o: (rat > product_prod_int_int) > ($o > $o) > (product_prod_int_int > $o) > rat > $o).
% 75.95/17.89  thf(func_def_348, type, map_fu5673905371560938248nt_rat: (rat > product_prod_int_int) > (product_prod_int_int > rat) > (product_prod_int_int > product_prod_int_int) > rat > rat).
% 75.95/17.89  thf(func_def_349, type, map_fu1532550112467129777l_real: (real > nat > rat) > (((nat > rat) > nat > rat) > real > real) > ((nat > rat) > (nat > rat) > nat > rat) > real > real > real).
% 75.95/17.89  thf(func_def_350, type, map_fu7146612038024189824t_real: (real > nat > rat) > ((nat > rat) > real) > ((nat > rat) > nat > rat) > real > real).
% 75.95/17.89  thf(func_def_351, type, map_fu1856342031159181835at_o_o: (real > nat > rat) > ($o > $o) > ((nat > rat) > $o) > real > $o).
% 75.95/17.89  thf(func_def_352, type, strict1292158309912662752at_nat: (nat > nat) > set_nat > $o).
% 75.95/17.89  thf(func_def_353, type, the_in5290026491893676941l_real: set_real > (real > real) > real > real).
% 75.95/17.89  thf(func_def_354, type, fun_is_measure_int: (int > nat) > $o).
% 75.95/17.89  thf(func_def_355, type, fun_max_strict: set_Pr4329608150637261639at_nat).
% 75.95/17.89  thf(func_def_356, type, fun_max_weak: set_Pr4329608150637261639at_nat).
% 75.95/17.89  thf(func_def_357, type, fun_min_strict: set_Pr4329608150637261639at_nat).
% 75.95/17.89  thf(func_def_358, type, fun_min_weak: set_Pr4329608150637261639at_nat).
% 75.95/17.89  thf(func_def_359, type, fun_pair_leq: set_Pr8693737435421807431at_nat).
% 75.95/17.89  thf(func_def_360, type, fun_pair_less: set_Pr8693737435421807431at_nat).
% 75.95/17.89  thf(func_def_361, type, fun_re2478310338295953701at_nat: produc1319942482725812455at_nat > $o).
% 75.95/17.89  thf(func_def_362, type, gcd_Gcd_int: set_int > int).
% 75.95/17.89  thf(func_def_363, type, gcd_Gcd_nat: set_nat > nat).
% 75.95/17.89  thf(func_def_364, type, bezw: nat > nat > product_prod_int_int).
% 75.95/17.89  thf(func_def_365, type, bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 75.95/17.89  thf(func_def_366, type, gcd_gcd_Code_integer: code_integer > code_integer > code_integer).
% 75.95/17.89  thf(func_def_367, type, gcd_gcd_int: int > int > int).
% 75.95/17.89  thf(func_def_368, type, gcd_gcd_nat: nat > nat > nat).
% 75.95/17.89  thf(func_def_369, type, gcd_lcm_int: int > int > int).
% 75.95/17.89  thf(func_def_370, type, gcd_lcm_nat: nat > nat > nat).
% 75.95/17.89  thf(func_def_371, type, gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 75.95/17.89  thf(func_def_372, type, abs_abs_Code_integer: code_integer > code_integer).
% 75.95/17.89  thf(func_def_373, type, abs_abs_int: int > int).
% 75.95/17.89  thf(func_def_374, type, abs_abs_rat: rat > rat).
% 75.95/17.89  thf(func_def_375, type, abs_abs_real: real > real).
% 75.95/17.89  thf(func_def_376, type, comm_monoid_nat: (nat > nat > nat) > nat > $o).
% 75.95/17.89  thf(func_def_377, type, minus_8373710615458151222nteger: code_integer > code_integer > code_integer).
% 75.95/17.89  thf(func_def_378, type, minus_minus_complex: complex > complex > complex).
% 75.95/17.89  thf(func_def_379, type, minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat).
% 75.95/17.89  thf(func_def_380, type, minus_minus_int: int > int > int).
% 75.95/17.89  thf(func_def_381, type, minus_minus_nat: nat > nat > nat).
% 75.95/17.89  thf(func_def_382, type, minus_minus_rat: rat > rat > rat).
% 75.95/17.89  thf(func_def_383, type, minus_minus_real: real > real > real).
% 75.95/17.89  thf(func_def_384, type, minus_811609699411566653omplex: set_complex > set_complex > set_complex).
% 75.95/17.89  thf(func_def_385, type, minus_925952699566721837d_enat: set_Extended_enat > set_Extended_enat > set_Extended_enat).
% 75.95/17.89  thf(func_def_386, type, minus_minus_set_int: set_int > set_int > set_int).
% 75.95/17.89  thf(func_def_387, type, minus_minus_set_nat: set_nat > set_nat > set_nat).
% 75.95/17.89  thf(func_def_388, type, minus_minus_set_real: set_real > set_real > set_real).
% 75.95/17.89  thf(func_def_389, type, monoid_nat: (nat > nat > nat) > nat > $o).
% 75.95/17.89  thf(func_def_390, type, one_one_Code_integer: code_integer).
% 75.95/17.89  thf(func_def_391, type, one_one_complex: complex).
% 75.95/17.89  thf(func_def_392, type, one_on7984719198319812577d_enat: extended_enat).
% 75.95/17.89  thf(func_def_393, type, one_one_int: int).
% 75.95/17.89  thf(func_def_394, type, one_one_nat: nat).
% 75.95/17.89  thf(func_def_395, type, one_one_rat: rat).
% 75.95/17.89  thf(func_def_396, type, one_one_real: real).
% 75.95/17.89  thf(func_def_397, type, plus_p5714425477246183910nteger: code_integer > code_integer > code_integer).
% 75.95/17.89  thf(func_def_398, type, plus_plus_complex: complex > complex > complex).
% 75.95/17.89  thf(func_def_399, type, plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat).
% 75.95/17.89  thf(func_def_400, type, plus_plus_int: int > int > int).
% 75.95/17.89  thf(func_def_401, type, plus_plus_nat: nat > nat > nat).
% 75.95/17.89  thf(func_def_402, type, plus_plus_num: num > num > num).
% 75.95/17.89  thf(func_def_403, type, plus_plus_rat: rat > rat > rat).
% 75.95/17.89  thf(func_def_404, type, plus_plus_real: real > real > real).
% 75.95/17.89  thf(func_def_405, type, plus_plus_literal: literal > literal > literal).
% 75.95/17.89  thf(func_def_406, type, sgn_sgn_Code_integer: code_integer > code_integer).
% 75.95/17.89  thf(func_def_407, type, sgn_sgn_complex: complex > complex).
% 75.95/17.89  thf(func_def_408, type, sgn_sgn_int: int > int).
% 75.95/17.89  thf(func_def_409, type, sgn_sgn_rat: rat > rat).
% 75.95/17.89  thf(func_def_410, type, sgn_sgn_real: real > real).
% 75.95/17.89  thf(func_def_411, type, times_3573771949741848930nteger: code_integer > code_integer > code_integer).
% 75.95/17.89  thf(func_def_412, type, times_times_complex: complex > complex > complex).
% 75.95/17.89  thf(func_def_413, type, times_7803423173614009249d_enat: extended_enat > extended_enat > extended_enat).
% 75.95/17.89  thf(func_def_414, type, times_times_int: int > int > int).
% 75.95/17.89  thf(func_def_415, type, times_times_nat: nat > nat > nat).
% 75.95/17.89  thf(func_def_416, type, times_times_num: num > num > num).
% 75.95/17.89  thf(func_def_417, type, times_times_rat: rat > rat > rat).
% 75.95/17.89  thf(func_def_418, type, times_times_real: real > real > real).
% 75.95/17.89  thf(func_def_419, type, uminus1351360451143612070nteger: code_integer > code_integer).
% 75.95/17.89  thf(func_def_420, type, uminus1482373934393186551omplex: complex > complex).
% 75.95/17.89  thf(func_def_421, type, uminus_uminus_int: int > int).
% 75.95/17.89  thf(func_def_422, type, uminus_uminus_rat: rat > rat).
% 75.95/17.89  thf(func_def_423, type, uminus_uminus_real: real > real).
% 75.95/17.89  thf(func_def_424, type, uminus5710092332889474511et_nat: set_nat > set_nat).
% 75.95/17.89  thf(func_def_425, type, zero_z3403309356797280102nteger: code_integer).
% 75.95/17.89  thf(func_def_426, type, zero_zero_complex: complex).
% 75.95/17.89  thf(func_def_427, type, zero_z5237406670263579293d_enat: extended_enat).
% 75.95/17.89  thf(func_def_428, type, zero_zero_int: int).
% 75.95/17.89  thf(func_def_429, type, zero_zero_nat: nat).
% 75.95/17.89  thf(func_def_430, type, zero_zero_rat: rat).
% 75.95/17.89  thf(func_def_431, type, zero_zero_real: real).
% 75.95/17.89  thf(func_def_432, type, zero_zero_literal: literal).
% 75.95/17.89  thf(func_def_433, type, groups7754918857620584856omplex: (complex > complex) > set_complex > complex).
% 75.95/17.89  thf(func_def_434, type, groups5690904116761175830ex_int: (complex > int) > set_complex > int).
% 75.95/17.89  thf(func_def_435, type, groups5693394587270226106ex_nat: (complex > nat) > set_complex > nat).
% 75.95/17.89  thf(func_def_436, type, groups5058264527183730370ex_rat: (complex > rat) > set_complex > rat).
% 75.95/17.89  thf(func_def_437, type, groups5808333547571424918x_real: (complex > real) > set_complex > real).
% 75.95/17.89  thf(func_def_438, type, groups2025484359314973016at_int: (extended_enat > int) > set_Extended_enat > int).
% 75.95/17.89  thf(func_def_439, type, groups2027974829824023292at_nat: (extended_enat > nat) > set_Extended_enat > nat).
% 75.95/17.89  thf(func_def_440, type, groups1392844769737527556at_rat: (extended_enat > rat) > set_Extended_enat > rat).
% 75.95/17.89  thf(func_def_441, type, groups4148127829035722712t_real: (extended_enat > real) > set_Extended_enat > real).
% 75.95/17.89  thf(func_def_442, type, groups7873554091576472773nteger: (int > code_integer) > set_int > code_integer).
% 75.95/17.89  thf(func_def_443, type, groups3049146728041665814omplex: (int > complex) > set_int > complex).
% 75.95/17.89  thf(func_def_444, type, groups4538972089207619220nt_int: (int > int) > set_int > int).
% 75.95/17.89  thf(func_def_445, type, groups4541462559716669496nt_nat: (int > nat) > set_int > nat).
% 75.95/17.89  thf(func_def_446, type, groups3906332499630173760nt_rat: (int > rat) > set_int > rat).
% 75.95/17.89  thf(func_def_447, type, groups8778361861064173332t_real: (int > real) > set_int > real).
% 75.95/17.89  thf(func_def_448, type, groups7501900531339628137nteger: (nat > code_integer) > set_nat > code_integer).
% 75.95/17.89  thf(func_def_449, type, groups2073611262835488442omplex: (nat > complex) > set_nat > complex).
% 75.95/17.89  thf(func_def_450, type, groups3539618377306564664at_int: (nat > int) > set_nat > int).
% 75.95/17.89  thf(func_def_451, type, groups3542108847815614940at_nat: (nat > nat) > set_nat > nat).
% 75.95/17.89  thf(func_def_452, type, groups2906978787729119204at_rat: (nat > rat) > set_nat > rat).
% 75.95/17.89  thf(func_def_453, type, groups6591440286371151544t_real: (nat > real) > set_nat > real).
% 75.95/17.89  thf(func_def_454, type, groups3209896439523537802omplex: (option_nat > complex) > set_option_nat > complex).
% 75.95/17.89  thf(func_def_455, type, groups1921984841883549356at_nat: (option_nat > nat) > set_option_nat > nat).
% 75.95/17.89  thf(func_def_456, type, groups4518532050878116744t_real: (option_nat > real) > set_option_nat > real).
% 75.95/17.89  thf(func_def_457, type, groups977919841031483927at_nat: (product_prod_nat_nat > nat) > set_Pr1261947904930325089at_nat > nat).
% 75.95/17.89  thf(func_def_458, type, groups4567486121110086003t_real: (product_prod_nat_nat > real) > set_Pr1261947904930325089at_nat > real).
% 75.95/17.89  thf(func_def_459, type, groups7713935264441627589nteger: (real > code_integer) > set_real > code_integer).
% 75.95/17.89  thf(func_def_460, type, groups5754745047067104278omplex: (real > complex) > set_real > complex).
% 75.95/17.89  thf(func_def_461, type, groups1932886352136224148al_int: (real > int) > set_real > int).
% 75.95/17.89  thf(func_def_462, type, groups1935376822645274424al_nat: (real > nat) > set_real > nat).
% 75.95/17.89  thf(func_def_463, type, groups1300246762558778688al_rat: (real > rat) > set_real > rat).
% 75.95/17.89  thf(func_def_464, type, groups8097168146408367636l_real: (real > real) > set_real > real).
% 75.95/17.89  thf(func_def_465, type, groups8255218700646806128omplex: (set_nat > complex) > set_set_nat > complex).
% 75.95/17.89  thf(func_def_466, type, groups8294997508430121362at_nat: (set_nat > nat) > set_set_nat > nat).
% 75.95/17.89  thf(func_def_467, type, groups5107569545109728110t_real: (set_nat > real) > set_set_nat > real).
% 75.95/17.89  thf(func_def_468, type, groups8682486955453173170nteger: (complex > code_integer) > set_complex > code_integer).
% 75.95/17.89  thf(func_def_469, type, groups3708469109370488835omplex: (complex > complex) > set_complex > complex).
% 75.95/17.89  thf(func_def_470, type, groups858564598930262913ex_int: (complex > int) > set_complex > int).
% 75.95/17.89  thf(func_def_471, type, groups861055069439313189ex_nat: (complex > nat) > set_complex > nat).
% 75.95/17.89  thf(func_def_472, type, groups225925009352817453ex_rat: (complex > rat) > set_complex > rat).
% 75.95/17.89  thf(func_def_473, type, groups766887009212190081x_real: (complex > real) > set_complex > real).
% 75.95/17.89  thf(func_def_474, type, groups845124408420398302nteger: (extended_enat > code_integer) > set_Extended_enat > code_integer).
% 75.95/17.89  thf(func_def_475, type, groups4622424608036095791omplex: (extended_enat > complex) > set_Extended_enat > complex).
% 75.95/17.89  thf(func_def_476, type, groups2878480467620962989at_int: (extended_enat > int) > set_Extended_enat > int).
% 75.95/17.89  thf(func_def_477, type, groups2880970938130013265at_nat: (extended_enat > nat) > set_Extended_enat > nat).
% 75.95/17.89  thf(func_def_478, type, groups2245840878043517529at_rat: (extended_enat > rat) > set_Extended_enat > rat).
% 75.95/17.89  thf(func_def_479, type, groups97031904164794029t_real: (extended_enat > real) > set_Extended_enat > real).
% 75.95/17.89  thf(func_def_480, type, groups3827104343326376752nteger: (int > code_integer) > set_int > code_integer).
% 75.95/17.89  thf(func_def_481, type, groups7440179247065528705omplex: (int > complex) > set_int > complex).
% 75.95/17.89  thf(func_def_482, type, groups1705073143266064639nt_int: (int > int) > set_int > int).
% 75.95/17.89  thf(func_def_483, type, groups1707563613775114915nt_nat: (int > nat) > set_int > nat).
% 75.95/17.89  thf(func_def_484, type, groups1072433553688619179nt_rat: (int > rat) > set_int > rat).
% 75.95/17.89  thf(func_def_485, type, groups2316167850115554303t_real: (int > real) > set_int > real).
% 75.95/17.89  thf(func_def_486, type, groups3455450783089532116nteger: (nat > code_integer) > set_nat > code_integer).
% 75.95/17.89  thf(func_def_487, type, groups6464643781859351333omplex: (nat > complex) > set_nat > complex).
% 75.95/17.89  thf(func_def_488, type, groups705719431365010083at_int: (nat > int) > set_nat > int).
% 75.95/17.89  thf(func_def_489, type, groups708209901874060359at_nat: (nat > nat) > set_nat > nat).
% 75.95/17.89  thf(func_def_490, type, groups73079841787564623at_rat: (nat > rat) > set_nat > rat).
% 75.95/17.89  thf(func_def_491, type, groups129246275422532515t_real: (nat > real) > set_nat > real).
% 75.95/17.89  thf(func_def_492, type, groups1917955009447795573omplex: (option_nat > complex) > set_option_nat > complex).
% 75.95/17.89  thf(func_def_493, type, groups6579596140936342515t_real: (option_nat > real) > set_option_nat > real).
% 75.95/17.89  thf(func_def_494, type, groups4077766827762148844at_nat: (product_prod_nat_nat > nat) > set_Pr1261947904930325089at_nat > nat).
% 75.95/17.89  thf(func_def_495, type, groups6036352826371341000t_real: (product_prod_nat_nat > real) > set_Pr1261947904930325089at_nat > real).
% 75.95/17.89  thf(func_def_496, type, groups713298508707869441omplex: (real > complex) > set_real > complex).
% 75.95/17.89  thf(func_def_497, type, groups4694064378042380927al_int: (real > int) > set_real > int).
% 75.95/17.89  thf(func_def_498, type, groups4696554848551431203al_nat: (real > nat) > set_real > nat).
% 75.95/17.89  thf(func_def_499, type, groups4061424788464935467al_rat: (real > rat) > set_real > rat).
% 75.95/17.89  thf(func_def_500, type, groups1681761925125756287l_real: (real > real) > set_real > real).
% 75.95/17.89  thf(func_def_501, type, groups1092910753850256091omplex: (set_nat > complex) > set_set_nat > complex).
% 75.95/17.89  thf(func_def_502, type, groups3619160379726066777t_real: (set_nat > real) > set_set_nat > real).
% 75.95/17.89  thf(func_def_503, type, groups9116527308978886569_o_int: ($o > int) > int > list_o > int).
% 75.95/17.89  thf(func_def_504, type, groups4561878855575611511st_nat: list_nat > nat).
% 75.95/17.89  thf(func_def_505, type, the_int: (int > $o) > int).
% 75.95/17.89  thf(func_def_506, type, the_Pr4378521158711661632nt_int: (product_prod_int_int > $o) > product_prod_int_int).
% 75.95/17.89  thf(func_def_507, type, the_real: (real > $o) > real).
% 75.95/17.89  thf(func_def_508, type, if_int_int: $o > (int > int) > (int > int) > int > int).
% 75.95/17.89  thf(func_def_509, type, if_nat_rat: $o > (nat > rat) > (nat > rat) > nat > rat).
% 75.95/17.89  thf(func_def_510, type, if_Code_integer: $o > code_integer > code_integer > code_integer).
% 75.95/17.89  thf(func_def_511, type, if_complex: $o > complex > complex > complex).
% 75.95/17.89  thf(func_def_512, type, if_Extended_enat: $o > extended_enat > extended_enat > extended_enat).
% 75.95/17.89  thf(func_def_513, type, if_int: $o > int > int > int).
% 75.95/17.89  thf(func_def_514, type, if_list_int: $o > list_int > list_int > list_int).
% 75.95/17.89  thf(func_def_515, type, if_list_nat: $o > list_nat > list_nat > list_nat).
% 75.95/17.89  thf(func_def_516, type, if_nat: $o > nat > nat > nat).
% 75.95/17.89  thf(func_def_517, type, if_num: $o > num > num > num).
% 75.95/17.89  thf(func_def_518, type, if_option_nat: $o > option_nat > option_nat > option_nat).
% 75.95/17.89  thf(func_def_519, type, if_option_num: $o > option_num > option_num > option_num).
% 75.95/17.89  thf(func_def_520, type, if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o).
% 75.95/17.89  thf(func_def_521, type, if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 75.95/17.89  thf(func_def_522, type, if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int).
% 75.95/17.89  thf(func_def_523, type, if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 75.95/17.89  thf(func_def_524, type, if_rat: $o > rat > rat > rat).
% 75.95/17.89  thf(func_def_525, type, if_real: $o > real > real > real).
% 75.95/17.89  thf(func_def_526, type, if_set_int: $o > set_int > set_int > set_int).
% 75.95/17.89  thf(func_def_527, type, if_set_nat: $o > set_nat > set_nat > set_nat).
% 75.95/17.89  thf(func_def_528, type, if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 75.95/17.89  thf(func_def_529, type, infini8530281810654367211te_nat: set_nat > nat > nat).
% 75.95/17.89  thf(func_def_530, type, abs_Integ: product_prod_nat_nat > int).
% 75.95/17.89  thf(func_def_531, type, rep_Integ: int > product_prod_nat_nat).
% 75.95/17.89  thf(func_def_532, type, cr_int: product_prod_nat_nat > int > $o).
% 75.95/17.89  thf(func_def_533, type, int_ge_less_than: int > set_Pr958786334691620121nt_int).
% 75.95/17.89  thf(func_def_534, type, int_ge_less_than2: int > set_Pr958786334691620121nt_int).
% 75.95/17.89  thf(func_def_535, type, intrel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 75.95/17.89  thf(func_def_536, type, nat2: int > nat).
% 75.95/17.89  thf(func_def_537, type, pcr_int: product_prod_nat_nat > int > $o).
% 75.95/17.89  thf(func_def_538, type, power_int_real: real > int > real).
% 75.95/17.89  thf(func_def_539, type, ring_1_Ints_complex: set_complex).
% 75.95/17.89  thf(func_def_540, type, ring_1_Ints_real: set_real).
% 75.95/17.89  thf(func_def_541, type, ring_18347121197199848620nteger: int > code_integer).
% 75.95/17.89  thf(func_def_542, type, ring_17405671764205052669omplex: int > complex).
% 75.95/17.89  thf(func_def_543, type, ring_1_of_int_int: int > int).
% 75.95/17.89  thf(func_def_544, type, ring_1_of_int_rat: int > rat).
% 75.95/17.89  thf(func_def_545, type, ring_1_of_int_real: int > real).
% 75.95/17.89  thf(func_def_546, type, inf_in1870772243966228564d_enat: extended_enat > extended_enat > extended_enat).
% 75.95/17.89  thf(func_def_547, type, inf_inf_int: int > int > int).
% 75.95/17.89  thf(func_def_548, type, inf_inf_nat: nat > nat > nat).
% 75.95/17.89  thf(func_def_549, type, inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 75.95/17.89  thf(func_def_550, type, semila9081495762789891438tr_nat: (nat > nat > nat) > nat > $o).
% 75.95/17.89  thf(func_def_551, type, semila1623282765462674594er_nat: (nat > nat > nat) > nat > (nat > nat > $o) > (nat > nat > $o) > $o).
% 75.95/17.89  thf(func_def_552, type, sup_su3973961784419623482d_enat: extended_enat > extended_enat > extended_enat).
% 75.95/17.89  thf(func_def_553, type, sup_sup_int: int > int > int).
% 75.95/17.89  thf(func_def_554, type, sup_sup_nat: nat > nat > nat).
% 75.95/17.89  thf(func_def_555, type, sup_sup_set_nat: set_nat > set_nat > set_nat).
% 75.95/17.89  thf(func_def_556, type, sup_su5525570899277871387at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat).
% 75.95/17.89  thf(func_def_557, type, lattic921264341876707157d_enat: set_Extended_enat > extended_enat).
% 75.95/17.89  thf(func_def_558, type, lattic8263393255366662781ax_int: set_int > int).
% 75.95/17.89  thf(func_def_559, type, lattic8265883725875713057ax_nat: set_nat > nat).
% 75.95/17.89  thf(func_def_560, type, quotie3684837364556693515t_real: ((nat > rat) > (nat > rat) > $o) > ((nat > rat) > real) > (real > nat > rat) > ((nat > rat) > real > $o) > $o).
% 75.95/17.89  thf(func_def_561, type, quotie1194848508323700631at_int: (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > int) > (int > product_prod_nat_nat) > (product_prod_nat_nat > int > $o) > $o).
% 75.95/17.89  thf(func_def_562, type, bfun_nat_real: (nat > real) > filter_nat > $o).
% 75.95/17.89  thf(func_def_563, type, at_infinity_real: filter_real).
% 75.95/17.89  thf(func_def_564, type, append_int: list_int > list_int > list_int).
% 75.95/17.89  thf(func_def_565, type, append_nat: list_nat > list_nat > list_nat).
% 75.95/17.89  thf(func_def_566, type, fold_int_int: (int > int > int) > list_int > int > int).
% 75.95/17.89  thf(func_def_567, type, fold_nat_nat: (nat > nat > nat) > list_nat > nat > nat).
% 75.95/17.89  thf(func_def_568, type, last_nat: list_nat > nat).
% 75.95/17.89  thf(func_def_569, type, linord2614967742042102400et_nat: set_nat > list_nat).
% 75.95/17.89  thf(func_def_570, type, cons_int: int > list_int > list_int).
% 75.95/17.89  thf(func_def_571, type, cons_nat: nat > list_nat > list_nat).
% 75.95/17.89  thf(func_def_572, type, nil_int: list_int).
% 75.95/17.89  thf(func_def_573, type, nil_nat: list_nat).
% 75.95/17.89  thf(func_def_574, type, hd_nat: list_nat > nat).
% 75.95/17.89  thf(func_def_575, type, map_nat_nat: (nat > nat) > list_nat > list_nat).
% 75.95/17.89  thf(func_def_576, type, map_VE8901447254227204932T_VEBT: (vEBT_VEBT > vEBT_VEBT) > list_VEBT_VEBT > list_VEBT_VEBT).
% 75.95/17.89  thf(func_def_577, type, set_o2: list_o > set_o).
% 75.95/17.89  thf(func_def_578, type, set_complex2: list_complex > set_complex).
% 75.95/17.89  thf(func_def_579, type, set_Extended_enat2: list_Extended_enat > set_Extended_enat).
% 75.95/17.89  thf(func_def_580, type, set_int2: list_int > set_int).
% 75.95/17.89  thf(func_def_581, type, set_nat2: list_nat > set_nat).
% 75.95/17.89  thf(func_def_582, type, set_option_nat2: list_option_nat > set_option_nat).
% 75.95/17.89  thf(func_def_583, type, set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat).
% 75.95/17.89  thf(func_def_584, type, set_Pr3765526544606949372at_nat: list_P5464809261938338413at_nat > set_Pr4329608150637261639at_nat).
% 75.95/17.89  thf(func_def_585, type, set_real2: list_real > set_real).
% 75.95/17.89  thf(func_def_586, type, set_set_nat2: list_set_nat > set_set_nat).
% 75.95/17.89  thf(func_def_587, type, set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT).
% 75.95/17.89  thf(func_def_588, type, size_list_VEBT_VEBT: (vEBT_VEBT > nat) > list_VEBT_VEBT > nat).
% 75.95/17.89  thf(func_def_589, type, list_update_o: list_o > nat > $o > list_o).
% 75.95/17.89  thf(func_def_590, type, list_update_int: list_int > nat > int > list_int).
% 75.95/17.89  thf(func_def_591, type, list_update_nat: list_nat > nat > nat > list_nat).
% 75.95/17.89  thf(func_def_592, type, list_u3411377215356412978on_nat: list_option_nat > nat > option_nat > list_option_nat).
% 75.95/17.89  thf(func_def_593, type, list_update_real: list_real > nat > real > list_real).
% 75.95/17.89  thf(func_def_594, type, list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat).
% 75.95/17.89  thf(func_def_595, type, list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT).
% 75.95/17.89  thf(func_def_596, type, nth_o: list_o > nat > $o).
% 75.95/17.89  thf(func_def_597, type, nth_int: list_int > nat > int).
% 75.95/17.89  thf(func_def_598, type, nth_nat: list_nat > nat > nat).
% 75.95/17.89  thf(func_def_599, type, nth_num: list_num > nat > num).
% 75.95/17.89  thf(func_def_600, type, nth_option_nat: list_option_nat > nat > option_nat).
% 75.95/17.89  thf(func_def_601, type, nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o).
% 75.95/17.89  thf(func_def_602, type, nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int).
% 75.95/17.89  thf(func_def_603, type, nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat).
% 75.95/17.89  thf(func_def_604, type, nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT).
% 75.95/17.89  thf(func_def_605, type, nth_Pr8326237132889035090at_num: list_P1726324292696863441at_num > nat > product_prod_nat_num).
% 75.95/17.89  thf(func_def_606, type, nth_Pr6456567536196504476um_num: list_P3744719386663036955um_num > nat > product_prod_num_num).
% 75.95/17.89  thf(func_def_607, type, nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o).
% 75.95/17.89  thf(func_def_608, type, nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int).
% 75.95/17.89  thf(func_def_609, type, nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat).
% 75.95/17.89  thf(func_def_610, type, nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT).
% 75.95/17.89  thf(func_def_611, type, nth_real: list_real > nat > real).
% 75.95/17.89  thf(func_def_612, type, nth_set_nat: list_set_nat > nat > set_nat).
% 75.95/17.89  thf(func_def_613, type, nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT).
% 75.95/17.89  thf(func_def_614, type, product_o_o: list_o > list_o > list_P4002435161011370285od_o_o).
% 75.95/17.89  thf(func_def_615, type, product_o_int: list_o > list_int > list_P3795440434834930179_o_int).
% 75.95/17.89  thf(func_def_616, type, product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat).
% 75.95/17.89  thf(func_def_617, type, product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT).
% 75.95/17.89  thf(func_def_618, type, product_nat_num: list_nat > list_num > list_P1726324292696863441at_num).
% 75.95/17.89  thf(func_def_619, type, product_num_num: list_num > list_num > list_P3744719386663036955um_num).
% 75.95/17.89  thf(func_def_620, type, product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o).
% 75.95/17.89  thf(func_def_621, type, produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int).
% 75.95/17.89  thf(func_def_622, type, produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat).
% 75.95/17.89  thf(func_def_623, type, produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT).
% 75.95/17.89  thf(func_def_624, type, replic7216382294607269926d_enat: nat > extended_enat > list_Extended_enat).
% 75.95/17.89  thf(func_def_625, type, replicate_int: nat > int > list_int).
% 75.95/17.89  thf(func_def_626, type, replicate_nat: nat > nat > list_nat).
% 75.95/17.89  thf(func_def_627, type, replicate_option_nat: nat > option_nat > list_option_nat).
% 75.95/17.89  thf(func_def_628, type, replic4235873036481779905at_nat: nat > product_prod_nat_nat > list_P6011104703257516679at_nat).
% 75.95/17.89  thf(func_def_629, type, replic2264142908078655527at_nat: nat > produc3843707927480180839at_nat > list_P5464809261938338413at_nat).
% 75.95/17.89  thf(func_def_630, type, replicate_real: nat > real > list_real).
% 75.95/17.89  thf(func_def_631, type, replicate_set_nat: nat > set_nat > list_set_nat).
% 75.95/17.89  thf(func_def_632, type, replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT).
% 75.95/17.89  thf(func_def_633, type, sorted_wrt_int: (int > int > $o) > list_int > $o).
% 75.95/17.89  thf(func_def_634, type, sorted_wrt_nat: (nat > nat > $o) > list_nat > $o).
% 75.95/17.89  thf(func_def_635, type, take_nat: nat > list_nat > list_nat).
% 75.95/17.89  thf(func_def_636, type, take_VEBT_VEBT: nat > list_VEBT_VEBT > list_VEBT_VEBT).
% 75.95/17.89  thf(func_def_637, type, upt: nat > nat > list_nat).
% 75.95/17.89  thf(func_def_638, type, upto: int > int > list_int).
% 75.95/17.89  thf(func_def_639, type, upto_aux: int > int > list_int > list_int).
% 75.95/17.89  thf(func_def_640, type, upto_rel: product_prod_int_int > product_prod_int_int > $o).
% 75.95/17.89  thf(func_def_641, type, suc: nat > nat).
% 75.95/17.89  thf(func_def_642, type, compow_nat_nat: nat > (nat > nat) > nat > nat).
% 75.95/17.89  thf(func_def_643, type, case_nat_o: $o > (nat > $o) > nat > $o).
% 75.95/17.89  thf(func_def_644, type, case_nat_nat: nat > (nat > nat) > nat > nat).
% 75.95/17.89  thf(func_def_645, type, case_nat_option_num: option_num > (nat > option_num) > nat > option_num).
% 75.95/17.89  thf(func_def_646, type, pred: nat > nat).
% 75.95/17.89  thf(func_def_647, type, semiri3842193898606819883omplex: set_complex).
% 75.95/17.89  thf(func_def_648, type, semiring_1_Nats_int: set_int).
% 75.95/17.89  thf(func_def_649, type, semiri4939895301339042750nteger: nat > code_integer).
% 75.95/17.89  thf(func_def_650, type, semiri8010041392384452111omplex: nat > complex).
% 75.95/17.89  thf(func_def_651, type, semiri4216267220026989637d_enat: nat > extended_enat).
% 75.95/17.89  thf(func_def_652, type, semiri1314217659103216013at_int: nat > int).
% 75.95/17.89  thf(func_def_653, type, semiri1316708129612266289at_nat: nat > nat).
% 75.95/17.89  thf(func_def_654, type, semiri681578069525770553at_rat: nat > rat).
% 75.95/17.89  thf(func_def_655, type, semiri5074537144036343181t_real: nat > real).
% 75.95/17.89  thf(func_def_656, type, size_size_list_o: list_o > nat).
% 75.95/17.89  thf(func_def_657, type, size_s3451745648224563538omplex: list_complex > nat).
% 75.95/17.89  thf(func_def_658, type, size_s3941691890525107288d_enat: list_Extended_enat > nat).
% 75.95/17.89  thf(func_def_659, type, size_size_list_int: list_int > nat).
% 75.95/17.89  thf(func_def_660, type, size_size_list_nat: list_nat > nat).
% 75.95/17.89  thf(func_def_661, type, size_size_list_num: list_num > nat).
% 75.95/17.90  thf(func_def_662, type, size_s6086282163384603972on_nat: list_option_nat > nat).
% 75.95/17.90  thf(func_def_663, type, size_s5460976970255530739at_nat: list_P6011104703257516679at_nat > nat).
% 75.95/17.90  thf(func_def_664, type, size_size_list_real: list_real > nat).
% 75.95/17.90  thf(func_def_665, type, size_s3254054031482475050et_nat: list_set_nat > nat).
% 75.95/17.90  thf(func_def_666, type, size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat).
% 75.95/17.90  thf(func_def_667, type, size_size_num: num > nat).
% 75.95/17.90  thf(func_def_668, type, size_size_option_nat: option_nat > nat).
% 75.95/17.90  thf(func_def_669, type, size_size_option_num: option_num > nat).
% 75.95/17.90  thf(func_def_670, type, size_s170228958280169651at_nat: option4927543243414619207at_nat > nat).
% 75.95/17.90  thf(func_def_671, type, size_size_char: char > nat).
% 75.95/17.90  thf(func_def_672, type, size_size_VEBT_VEBT: vEBT_VEBT > nat).
% 75.95/17.90  thf(func_def_673, type, nat_list_decode: nat > list_nat).
% 75.95/17.90  thf(func_def_674, type, nat_list_decode_rel: nat > nat > $o).
% 75.95/17.90  thf(func_def_675, type, nat_list_encode: list_nat > nat).
% 75.95/17.90  thf(func_def_676, type, nat_list_encode_rel: list_nat > list_nat > $o).
% 75.95/17.90  thf(func_def_677, type, nat_prod_decode: nat > product_prod_nat_nat).
% 75.95/17.90  thf(func_def_678, type, nat_prod_decode_aux: nat > nat > product_prod_nat_nat).
% 75.95/17.90  thf(func_def_679, type, nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 75.95/17.90  thf(func_def_680, type, nat_prod_encode: product_prod_nat_nat > nat).
% 75.95/17.90  thf(func_def_681, type, nat_set_decode: nat > set_nat).
% 75.95/17.90  thf(func_def_682, type, nat_set_encode: set_nat > nat).
% 75.95/17.90  thf(func_def_683, type, nat_triangle: nat > nat).
% 75.95/17.90  thf(func_def_684, type, root: nat > real > real).
% 75.95/17.90  thf(func_def_685, type, sqrt: real > real).
% 75.95/17.90  thf(func_def_686, type, bitM: num > num).
% 75.95/17.90  thf(func_def_687, type, inc: num > num).
% 75.95/17.90  thf(func_def_688, type, nat_of_num: num > nat).
% 75.95/17.90  thf(func_def_689, type, neg_nu8804712462038260780nteger: code_integer > code_integer).
% 75.95/17.90  thf(func_def_690, type, neg_nu7009210354673126013omplex: complex > complex).
% 75.95/17.90  thf(func_def_691, type, neg_numeral_dbl_int: int > int).
% 75.95/17.90  thf(func_def_692, type, neg_numeral_dbl_rat: rat > rat).
% 75.95/17.90  thf(func_def_693, type, neg_numeral_dbl_real: real > real).
% 75.95/17.90  thf(func_def_694, type, neg_nu7757733837767384882nteger: code_integer > code_integer).
% 75.95/17.90  thf(func_def_695, type, neg_nu6511756317524482435omplex: complex > complex).
% 75.95/17.90  thf(func_def_696, type, neg_nu3811975205180677377ec_int: int > int).
% 75.95/17.90  thf(func_def_697, type, neg_nu3179335615603231917ec_rat: rat > rat).
% 75.95/17.90  thf(func_def_698, type, neg_nu6075765906172075777c_real: real > real).
% 75.95/17.90  thf(func_def_699, type, neg_nu5831290666863070958nteger: code_integer > code_integer).
% 75.95/17.90  thf(func_def_700, type, neg_nu8557863876264182079omplex: complex > complex).
% 75.95/17.90  thf(func_def_701, type, neg_nu5851722552734809277nc_int: int > int).
% 75.95/17.90  thf(func_def_702, type, neg_nu5219082963157363817nc_rat: rat > rat).
% 75.95/17.90  thf(func_def_703, type, neg_nu8295874005876285629c_real: real > real).
% 75.95/17.90  thf(func_def_704, type, neg_numeral_sub_int: num > num > int).
% 75.95/17.90  thf(func_def_705, type, bit0: num > num).
% 75.95/17.90  thf(func_def_706, type, bit1: num > num).
% 75.95/17.90  thf(func_def_707, type, one: num).
% 75.95/17.90  thf(func_def_708, type, case_num_option_num: option_num > (num > option_num) > (num > option_num) > num > option_num).
% 75.95/17.90  thf(func_def_709, type, size_num: num > nat).
% 75.95/17.90  thf(func_def_710, type, num_of_nat: nat > num).
% 75.95/17.90  thf(func_def_711, type, numera6620942414471956472nteger: num > code_integer).
% 75.95/17.90  thf(func_def_712, type, numera6690914467698888265omplex: num > complex).
% 75.95/17.90  thf(func_def_713, type, numera1916890842035813515d_enat: num > extended_enat).
% 75.95/17.90  thf(func_def_714, type, numeral_numeral_int: num > int).
% 75.95/17.90  thf(func_def_715, type, numeral_numeral_nat: num > nat).
% 75.95/17.90  thf(func_def_716, type, numeral_numeral_rat: num > rat).
% 75.95/17.90  thf(func_def_717, type, numeral_numeral_real: num > real).
% 75.95/17.90  thf(func_def_718, type, pow: num > num > num).
% 75.95/17.90  thf(func_def_719, type, pred_numeral: num > nat).
% 75.95/17.90  thf(func_def_720, type, sqr: num > num).
% 75.95/17.90  thf(func_def_721, type, none_nat: option_nat).
% 75.95/17.90  thf(func_def_722, type, none_num: option_num).
% 75.95/17.90  thf(func_def_723, type, none_P5556105721700978146at_nat: option4927543243414619207at_nat).
% 75.95/17.90  thf(func_def_724, type, some_nat: nat > option_nat).
% 75.95/17.90  thf(func_def_725, type, some_num: num > option_num).
% 75.95/17.90  thf(func_def_726, type, some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat).
% 75.95/17.90  thf(func_def_727, type, case_o184042715313410164at_nat: $o > (product_prod_nat_nat > $o) > option4927543243414619207at_nat > $o).
% 75.95/17.90  thf(func_def_728, type, case_option_int_num: int > (num > int) > option_num > int).
% 75.95/17.90  thf(func_def_729, type, case_option_num_num: num > (num > num) > option_num > num).
% 75.95/17.90  thf(func_def_730, type, case_o6005452278849405969um_num: option_num > (num > option_num) > option_num > option_num).
% 75.95/17.90  thf(func_def_731, type, map_option_num_num: (num > num) > option_num > option_num).
% 75.95/17.90  thf(func_def_732, type, the_nat: option_nat > nat).
% 75.95/17.90  thf(func_def_733, type, the_num: option_num > num).
% 75.95/17.90  thf(func_def_734, type, the_Pr8591224930841456533at_nat: option4927543243414619207at_nat > product_prod_nat_nat).
% 75.95/17.90  thf(func_def_735, type, order_underS_nat: set_Pr1261947904930325089at_nat > nat > set_nat).
% 75.95/17.90  thf(func_def_736, type, bot_bo4199563552545308370d_enat: extended_enat).
% 75.95/17.90  thf(func_def_737, type, bot_bot_nat: nat).
% 75.95/17.90  thf(func_def_738, type, bot_bot_set_complex: set_complex).
% 75.95/17.90  thf(func_def_739, type, bot_bo7653980558646680370d_enat: set_Extended_enat).
% 75.95/17.90  thf(func_def_740, type, bot_bot_set_int: set_int).
% 75.95/17.90  thf(func_def_741, type, bot_bot_set_nat: set_nat).
% 75.95/17.90  thf(func_def_742, type, bot_bot_set_num: set_num).
% 75.95/17.90  thf(func_def_743, type, bot_bo2099793752762293965at_nat: set_Pr1261947904930325089at_nat).
% 75.95/17.90  thf(func_def_744, type, bot_bo228742789529271731at_nat: set_Pr4329608150637261639at_nat).
% 75.95/17.90  thf(func_def_745, type, bot_bot_set_rat: set_rat).
% 75.95/17.90  thf(func_def_746, type, bot_bot_set_real: set_real).
% 75.95/17.90  thf(func_def_747, type, bot_bot_set_set_nat: set_set_nat).
% 75.95/17.90  thf(func_def_748, type, bot_bo8194388402131092736T_VEBT: set_VEBT_VEBT).
% 75.95/17.90  thf(func_def_749, type, ord_Le1955565732374568822d_enat: (extended_enat > $o) > extended_enat).
% 75.95/17.90  thf(func_def_750, type, ord_Least_nat: (nat > $o) > nat).
% 75.95/17.90  thf(func_def_751, type, ord_Least_real: (real > $o) > real).
% 75.95/17.90  thf(func_def_752, type, ord_le6747313008572928689nteger: code_integer > code_integer > $o).
% 75.95/17.90  thf(func_def_753, type, ord_le72135733267957522d_enat: extended_enat > extended_enat > $o).
% 75.95/17.90  thf(func_def_754, type, ord_less_int: int > int > $o).
% 75.95/17.90  thf(func_def_755, type, ord_less_nat: nat > nat > $o).
% 75.95/17.90  thf(func_def_756, type, ord_less_num: num > num > $o).
% 75.95/17.90  thf(func_def_757, type, ord_less_rat: rat > rat > $o).
% 75.95/17.90  thf(func_def_758, type, ord_less_real: real > real > $o).
% 75.95/17.90  thf(func_def_759, type, ord_le2529575680413868914d_enat: set_Extended_enat > set_Extended_enat > $o).
% 75.95/17.90  thf(func_def_760, type, ord_less_set_int: set_int > set_int > $o).
% 75.95/17.90  thf(func_def_761, type, ord_less_set_nat: set_nat > set_nat > $o).
% 75.95/17.90  thf(func_def_762, type, ord_less_set_num: set_num > set_num > $o).
% 75.95/17.90  thf(func_def_763, type, ord_less_set_rat: set_rat > set_rat > $o).
% 75.95/17.90  thf(func_def_764, type, ord_less_set_real: set_real > set_real > $o).
% 75.95/17.90  thf(func_def_765, type, ord_less_set_set_nat: set_set_nat > set_set_nat > $o).
% 75.95/17.90  thf(func_def_766, type, ord_le3102999989581377725nteger: code_integer > code_integer > $o).
% 75.95/17.90  thf(func_def_767, type, ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o).
% 75.95/17.90  thf(func_def_768, type, ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o).
% 75.95/17.90  thf(func_def_769, type, ord_less_eq_int: int > int > $o).
% 75.95/17.90  thf(func_def_770, type, ord_less_eq_nat: nat > nat > $o).
% 75.95/17.90  thf(func_def_771, type, ord_less_eq_num: num > num > $o).
% 75.95/17.90  thf(func_def_772, type, ord_less_eq_rat: rat > rat > $o).
% 75.95/17.90  thf(func_def_773, type, ord_less_eq_real: real > real > $o).
% 75.95/17.90  thf(func_def_774, type, ord_less_eq_set_o: set_o > set_o > $o).
% 75.95/17.90  thf(func_def_775, type, ord_le211207098394363844omplex: set_complex > set_complex > $o).
% 75.95/17.90  thf(func_def_776, type, ord_le7203529160286727270d_enat: set_Extended_enat > set_Extended_enat > $o).
% 75.95/17.90  thf(func_def_777, type, ord_less_eq_set_int: set_int > set_int > $o).
% 75.95/17.90  thf(func_def_778, type, ord_less_eq_set_nat: set_nat > set_nat > $o).
% 75.95/17.90  thf(func_def_779, type, ord_less_eq_set_num: set_num > set_num > $o).
% 75.95/17.90  thf(func_def_780, type, ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 75.95/17.90  thf(func_def_781, type, ord_less_eq_set_rat: set_rat > set_rat > $o).
% 75.95/17.90  thf(func_def_782, type, ord_less_eq_set_real: set_real > set_real > $o).
% 75.95/17.90  thf(func_def_783, type, ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o).
% 75.95/17.90  thf(func_def_784, type, ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o).
% 75.95/17.90  thf(func_def_785, type, ord_max_Code_integer: code_integer > code_integer > code_integer).
% 75.95/17.90  thf(func_def_786, type, ord_ma741700101516333627d_enat: extended_enat > extended_enat > extended_enat).
% 75.95/17.90  thf(func_def_787, type, ord_max_int: int > int > int).
% 75.95/17.90  thf(func_def_788, type, ord_max_nat: nat > nat > nat).
% 75.95/17.90  thf(func_def_789, type, ord_max_num: num > num > num).
% 75.95/17.90  thf(func_def_790, type, ord_max_rat: rat > rat > rat).
% 75.95/17.90  thf(func_def_791, type, ord_max_real: real > real > real).
% 75.95/17.90  thf(func_def_792, type, ord_ma4205026669011143323d_enat: set_Extended_enat > set_Extended_enat > set_Extended_enat).
% 75.95/17.90  thf(func_def_793, type, ord_max_set_int: set_int > set_int > set_int).
% 75.95/17.90  thf(func_def_794, type, ord_max_set_nat: set_nat > set_nat > set_nat).
% 75.95/17.90  thf(func_def_795, type, ord_max_set_real: set_real > set_real > set_real).
% 75.95/17.90  thf(func_def_796, type, ord_mi8085742599997312461d_enat: extended_enat > extended_enat > extended_enat).
% 75.95/17.90  thf(func_def_797, type, ord_min_int: int > int > int).
% 75.95/17.90  thf(func_def_798, type, ord_min_nat: nat > nat > nat).
% 75.95/17.90  thf(func_def_799, type, order_Greatest_nat: (nat > $o) > nat).
% 75.95/17.90  thf(func_def_800, type, order_9091379641038594480t_real: (nat > real) > $o).
% 75.95/17.90  thf(func_def_801, type, order_4130057895858720880d_enat: (extended_enat > extended_enat) > $o).
% 75.95/17.90  thf(func_def_802, type, order_mono_nat_nat: (nat > nat) > $o).
% 75.95/17.90  thf(func_def_803, type, order_mono_nat_real: (nat > real) > $o).
% 75.95/17.90  thf(func_def_804, type, order_mono_real_real: (real > real) > $o).
% 75.95/17.90  thf(func_def_805, type, order_5726023648592871131at_nat: (nat > nat) > $o).
% 75.95/17.90  thf(func_def_806, type, order_7092887310737990675l_real: (real > real) > $o).
% 75.95/17.90  thf(func_def_807, type, ordering_top_nat: (nat > nat > $o) > (nat > nat > $o) > nat > $o).
% 75.95/17.90  thf(func_def_808, type, top_to3028658606643905974d_enat: extended_enat).
% 75.95/17.90  thf(func_def_809, type, top_top_set_o: set_o).
% 75.95/17.90  thf(func_def_810, type, top_top_set_int: set_int).
% 75.95/17.90  thf(func_def_811, type, top_top_set_nat: set_nat).
% 75.95/17.90  thf(func_def_812, type, top_to8920198386146353926on_nat: set_option_nat).
% 75.95/17.90  thf(func_def_813, type, top_top_set_real: set_real).
% 75.95/17.90  thf(func_def_814, type, top_top_set_char: set_char).
% 75.95/17.90  thf(func_def_815, type, power_8256067586552552935nteger: code_integer > nat > code_integer).
% 75.95/17.90  thf(func_def_816, type, power_power_complex: complex > nat > complex).
% 75.95/17.90  thf(func_def_817, type, power_power_int: int > nat > int).
% 75.95/17.90  thf(func_def_818, type, power_power_nat: nat > nat > nat).
% 75.95/17.90  thf(func_def_819, type, power_power_rat: rat > nat > rat).
% 75.95/17.90  thf(func_def_820, type, power_power_real: real > nat > real).
% 75.95/17.90  thf(func_def_821, type, produc4035269172776083154on_nat: (nat > nat > $o) > produc4953844613479565601on_nat > produc2233624965454879586on_nat).
% 75.95/17.90  thf(func_def_822, type, produc8929957630744042906on_nat: (nat > nat > nat) > produc4953844613479565601on_nat > produc8306885398267862888on_nat).
% 75.95/17.90  thf(func_def_823, type, produc3576312749637752826on_num: (num > num > $o) > produc3447558737645232053on_num > produc7036089656553540234on_num).
% 75.95/17.90  thf(func_def_824, type, produc5778274026573060048on_num: (num > num > num) > produc3447558737645232053on_num > produc1193250871479095198on_num).
% 75.95/17.90  thf(func_def_825, type, produc3994169339658061776at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > produc6121120109295599847at_nat > produc5491161045314408544at_nat).
% 75.95/17.90  thf(func_def_826, type, produc2899441246263362727at_nat: (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > produc6121120109295599847at_nat > produc5542196010084753463at_nat).
% 75.95/17.90  thf(func_def_827, type, product_Pair_o_o: $o > $o > product_prod_o_o).
% 75.95/17.90  thf(func_def_828, type, product_Pair_o_int: $o > int > product_prod_o_int).
% 75.95/17.90  thf(func_def_829, type, product_Pair_o_nat: $o > nat > product_prod_o_nat).
% 75.95/17.90  thf(func_def_830, type, produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT).
% 75.95/17.90  thf(func_def_831, type, produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o).
% 75.95/17.90  thf(func_def_832, type, produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger).
% 75.95/17.90  thf(func_def_833, type, product_Pair_int_int: int > int > product_prod_int_int).
% 75.95/17.90  thf(func_def_834, type, product_Pair_nat_nat: nat > nat > product_prod_nat_nat).
% 75.95/17.90  thf(func_def_835, type, product_Pair_nat_num: nat > num > product_prod_nat_num).
% 75.95/17.90  thf(func_def_836, type, product_Pair_num_num: num > num > product_prod_num_num).
% 75.95/17.90  thf(func_def_837, type, produc5098337634421038937on_nat: option_nat > option_nat > produc4953844613479565601on_nat).
% 75.95/17.90  thf(func_def_838, type, produc8585076106096196333on_num: option_num > option_num > produc3447558737645232053on_num).
% 75.95/17.90  thf(func_def_839, type, produc488173922507101015at_nat: option4927543243414619207at_nat > option4927543243414619207at_nat > produc6121120109295599847at_nat).
% 75.95/17.90  thf(func_def_840, type, produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat).
% 75.95/17.90  thf(func_def_841, type, produc2922128104949294807at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat).
% 75.95/17.90  thf(func_def_842, type, produc9060074326276436823at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > produc1319942482725812455at_nat).
% 75.95/17.90  thf(func_def_843, type, produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o).
% 75.95/17.90  thf(func_def_844, type, produc581526299967858633d_enat: vEBT_VEBT > extended_enat > produc7272778201969148633d_enat).
% 75.95/17.90  thf(func_def_845, type, produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int).
% 75.95/17.90  thf(func_def_846, type, produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat).
% 75.95/17.90  thf(func_def_847, type, produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT).
% 75.95/17.90  thf(func_def_848, type, produc457027306803732586at_nat: set_nat > (nat > set_nat) > set_Pr1261947904930325089at_nat).
% 75.95/17.90  thf(func_def_849, type, produc6499014454317279255nteger: (code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 75.95/17.90  thf(func_def_850, type, produc8678311845419106900er_nat: (code_integer > nat) > (code_integer > nat) > produc8923325533196201883nteger > product_prod_nat_nat).
% 75.95/17.90  thf(func_def_851, type, produc1553301316500091796er_int: (code_integer > code_integer > int) > produc8923325533196201883nteger > int).
% 75.95/17.90  thf(func_def_852, type, produc1555791787009142072er_nat: (code_integer > code_integer > nat) > produc8923325533196201883nteger > nat).
% 75.95/17.90  thf(func_def_853, type, produc7336495610019696514er_num: (code_integer > code_integer > num) > produc8923325533196201883nteger > num).
% 75.95/17.90  thf(func_def_854, type, produc9125791028180074456eger_o: (code_integer > code_integer > produc6271795597528267376eger_o) > produc8923325533196201883nteger > produc6271795597528267376eger_o).
% 75.95/17.90  thf(func_def_855, type, produc6916734918728496179nteger: (code_integer > code_integer > produc8923325533196201883nteger) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 75.95/17.90  thf(func_def_856, type, produc6771430404735790350plex_o: (complex > complex > $o) > produc4411394909380815293omplex > $o).
% 75.95/17.90  thf(func_def_857, type, produc4947309494688390418_int_o: (int > int > $o) > product_prod_int_int > $o).
% 75.95/17.90  thf(func_def_858, type, produc8211389475949308722nt_int: (int > int > int) > product_prod_int_int > int).
% 75.95/17.90  thf(func_def_859, type, produc4245557441103728435nt_int: (int > int > product_prod_int_int) > product_prod_int_int > product_prod_int_int).
% 75.95/17.90  thf(func_def_860, type, produc8739625826339149834_nat_o: (nat > nat > product_prod_nat_nat > $o) > product_prod_nat_nat > product_prod_nat_nat > $o).
% 75.95/17.90  thf(func_def_861, 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).
% 75.95/17.90  thf(func_def_862, type, produc6081775807080527818_nat_o: (nat > nat > $o) > product_prod_nat_nat > $o).
% 75.95/17.90  thf(func_def_863, type, produc2761476792215241774st_nat: (nat > nat > list_nat) > product_prod_nat_nat > list_nat).
% 75.95/17.90  thf(func_def_864, type, produc6842872674320459806at_nat: (nat > nat > nat) > product_prod_nat_nat > nat).
% 75.95/17.90  thf(func_def_865, type, produc2626176000494625587at_nat: (nat > nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat).
% 75.95/17.90  thf(func_def_866, type, produc478579273971653890on_num: (nat > num > option_num) > product_prod_nat_num > option_num).
% 75.95/17.90  thf(func_def_867, type, produc5414030515140494994real_o: (real > real > $o) > produc2422161461964618553l_real > $o).
% 75.95/17.90  thf(func_def_868, type, product_fst_int_int: product_prod_int_int > int).
% 75.95/17.90  thf(func_def_869, type, product_fst_nat_nat: product_prod_nat_nat > nat).
% 75.95/17.90  thf(func_def_870, type, product_snd_int_int: product_prod_int_int > int).
% 75.95/17.90  thf(func_def_871, type, product_snd_nat_nat: product_prod_nat_nat > nat).
% 75.95/17.90  thf(func_def_872, type, abs_Rat: product_prod_int_int > rat).
% 75.95/17.90  thf(func_def_873, type, fract: int > int > rat).
% 75.95/17.90  thf(func_def_874, type, frct: product_prod_int_int > rat).
% 75.95/17.90  thf(func_def_875, type, rep_Rat: rat > product_prod_int_int).
% 75.95/17.90  thf(func_def_876, type, field_5140801741446780682s_real: set_real).
% 75.95/17.90  thf(func_def_877, type, field_7254667332652039916t_real: rat > real).
% 75.95/17.90  thf(func_def_878, type, normalize: product_prod_int_int > product_prod_int_int).
% 75.95/17.90  thf(func_def_879, type, pcr_rat: product_prod_int_int > rat > $o).
% 75.95/17.90  thf(func_def_880, type, positive: rat > $o).
% 75.95/17.90  thf(func_def_881, type, quotient_of: rat > product_prod_int_int).
% 75.95/17.90  thf(func_def_882, type, ratrel: product_prod_int_int > product_prod_int_int > $o).
% 75.95/17.90  thf(func_def_883, type, real2: (nat > rat) > real).
% 75.95/17.90  thf(func_def_884, type, cauchy: (nat > rat) > $o).
% 75.95/17.90  thf(func_def_885, type, cr_real: (nat > rat) > real > $o).
% 75.95/17.90  thf(func_def_886, type, pcr_real: (nat > rat) > real > $o).
% 75.95/17.90  thf(func_def_887, type, positive2: real > $o).
% 75.95/17.90  thf(func_def_888, type, realrel: (nat > rat) > (nat > rat) > $o).
% 75.95/17.90  thf(func_def_889, type, rep_real: real > nat > rat).
% 75.95/17.90  thf(func_def_890, type, vanishes: (nat > rat) > $o).
% 75.95/17.90  thf(func_def_891, type, real_V2521375963428798218omplex: set_complex).
% 75.95/17.90  thf(func_def_892, type, real_V3694042436643373181omplex: complex > complex > real).
% 75.95/17.90  thf(func_def_893, type, real_V975177566351809787t_real: real > real > real).
% 75.95/17.90  thf(func_def_894, type, real_V1022390504157884413omplex: complex > real).
% 75.95/17.90  thf(func_def_895, type, real_V7735802525324610683m_real: real > real).
% 75.95/17.90  thf(func_def_896, type, real_V4546457046886955230omplex: real > complex).
% 75.95/17.90  thf(func_def_897, type, real_V1803761363581548252l_real: real > real).
% 75.95/17.90  thf(func_def_898, type, transp_nat_rat: ((nat > rat) > (nat > rat) > $o) > $o).
% 75.95/17.90  thf(func_def_899, type, algebr932160517623751201me_int: int > int > $o).
% 75.95/17.90  thf(func_def_900, type, algebr934650988132801477me_nat: nat > nat > $o).
% 75.95/17.90  thf(func_def_901, type, divide6298287555418463151nteger: code_integer > code_integer > code_integer).
% 75.95/17.90  thf(func_def_902, type, divide1717551699836669952omplex: complex > complex > complex).
% 75.95/17.90  thf(func_def_903, type, divide_divide_int: int > int > int).
% 75.95/17.90  thf(func_def_904, type, divide_divide_nat: nat > nat > nat).
% 75.95/17.90  thf(func_def_905, type, divide_divide_rat: rat > rat > rat).
% 75.95/17.90  thf(func_def_906, type, divide_divide_real: real > real > real).
% 75.95/17.90  thf(func_def_907, type, dvd_dvd_Code_integer: code_integer > code_integer > $o).
% 75.95/17.90  thf(func_def_908, type, dvd_dvd_complex: complex > complex > $o).
% 75.95/17.90  thf(func_def_909, type, dvd_dvd_int: int > int > $o).
% 75.95/17.90  thf(func_def_910, type, dvd_dvd_nat: nat > nat > $o).
% 75.95/17.90  thf(func_def_911, type, dvd_dvd_rat: rat > rat > $o).
% 75.95/17.90  thf(func_def_912, type, dvd_dvd_real: real > real > $o).
% 75.95/17.90  thf(func_def_913, type, modulo364778990260209775nteger: code_integer > code_integer > code_integer).
% 75.95/17.90  thf(func_def_914, type, modulo_modulo_int: int > int > int).
% 75.95/17.90  thf(func_def_915, type, modulo_modulo_nat: nat > nat > nat).
% 75.95/17.90  thf(func_def_916, type, unit_f2748546683901255202or_nat: nat > nat).
% 75.95/17.90  thf(func_def_917, type, zero_n356916108424825756nteger: $o > code_integer).
% 75.95/17.90  thf(func_def_918, type, zero_n2684676970156552555ol_int: $o > int).
% 75.95/17.90  thf(func_def_919, type, zero_n2687167440665602831ol_nat: $o > nat).
% 75.95/17.90  thf(func_def_920, type, suminf_complex: (nat > complex) > complex).
% 75.95/17.90  thf(func_def_921, type, suminf_int: (nat > int) > int).
% 75.95/17.90  thf(func_def_922, type, suminf_nat: (nat > nat) > nat).
% 75.95/17.90  thf(func_def_923, type, suminf_real: (nat > real) > real).
% 75.95/17.90  thf(func_def_924, type, summable_complex: (nat > complex) > $o).
% 75.95/17.90  thf(func_def_925, type, summable_int: (nat > int) > $o).
% 75.95/17.90  thf(func_def_926, type, summable_nat: (nat > nat) > $o).
% 75.95/17.90  thf(func_def_927, type, summable_real: (nat > real) > $o).
% 75.95/17.90  thf(func_def_928, type, sums_real: (nat > real) > real > $o).
% 75.95/17.90  thf(func_def_929, type, collect_complex: (complex > $o) > set_complex).
% 75.95/17.90  thf(func_def_930, type, collec4429806609662206161d_enat: (extended_enat > $o) > set_Extended_enat).
% 75.95/17.90  thf(func_def_931, type, collect_int: (int > $o) > set_int).
% 75.95/17.90  thf(func_def_932, type, collect_list_o: (list_o > $o) > set_list_o).
% 75.95/17.90  thf(func_def_933, type, collect_list_complex: (list_complex > $o) > set_list_complex).
% 75.95/17.90  thf(func_def_934, type, collec8433460942617342167d_enat: (list_Extended_enat > $o) > set_li5464603477888414924d_enat).
% 75.95/17.90  thf(func_def_935, type, collect_list_int: (list_int > $o) > set_list_int).
% 75.95/17.90  thf(func_def_936, type, collect_list_nat: (list_nat > $o) > set_list_nat).
% 75.95/17.90  thf(func_def_937, type, collec3343600615725829874at_nat: (list_P6011104703257516679at_nat > $o) > set_li5450038453877631591at_nat).
% 75.95/17.90  thf(func_def_938, type, collec5608196760682091941T_VEBT: (list_VEBT_VEBT > $o) > set_list_VEBT_VEBT).
% 75.95/17.90  thf(func_def_939, type, collect_nat: (nat > $o) > set_nat).
% 75.95/17.90  thf(func_def_940, type, collect_num: (num > $o) > set_num).
% 75.95/17.90  thf(func_def_941, type, collect_option_nat: (option_nat > $o) > set_option_nat).
% 75.95/17.90  thf(func_def_942, type, collec8663557070575231912omplex: (produc4411394909380815293omplex > $o) > set_Pr5085853215250843933omplex).
% 75.95/17.90  thf(func_def_943, type, collec213857154873943460nt_int: (product_prod_int_int > $o) > set_Pr958786334691620121nt_int).
% 75.95/17.90  thf(func_def_944, type, collec3392354462482085612at_nat: (product_prod_nat_nat > $o) > set_Pr1261947904930325089at_nat).
% 75.95/17.90  thf(func_def_945, type, collec3799799289383736868l_real: (produc2422161461964618553l_real > $o) > set_Pr6218003697084177305l_real).
% 75.95/17.90  thf(func_def_946, type, collect_rat: (rat > $o) > set_rat).
% 75.95/17.90  thf(func_def_947, type, collect_real: (real > $o) > set_real).
% 75.95/17.90  thf(func_def_948, type, collect_set_nat: (set_nat > $o) > set_set_nat).
% 75.95/17.90  thf(func_def_949, type, pow_nat: set_nat > set_set_nat).
% 75.95/17.90  thf(func_def_950, type, image_80655429650038917d_enat: (extended_enat > extended_enat) > set_Extended_enat > set_Extended_enat).
% 75.95/17.90  thf(func_def_951, type, image_int_int: (int > int) > set_int > set_int).
% 75.95/17.90  thf(func_def_952, type, image_int_nat: (int > nat) > set_int > set_nat).
% 75.95/17.90  thf(func_def_953, type, image_nat_int: (nat > int) > set_nat > set_int).
% 75.95/17.90  thf(func_def_954, type, image_nat_nat: (nat > nat) > set_nat > set_nat).
% 75.95/17.90  thf(func_def_955, type, image_nat_real: (nat > real) > set_nat > set_real).
% 75.95/17.90  thf(func_def_956, type, image_nat_set_nat: (nat > set_nat) > set_nat > set_set_nat).
% 75.95/17.90  thf(func_def_957, type, image_nat_char: (nat > char) > set_nat > set_char).
% 75.95/17.90  thf(func_def_958, type, image_5971271580939081552omplex: (real > filter6041513312241820739omplex) > set_real > set_fi4554929511873752355omplex).
% 75.95/17.90  thf(func_def_959, type, image_2178119161166701260l_real: (real > filter2146258269922977983l_real) > set_real > set_fi7789364187291644575l_real).
% 75.95/17.90  thf(func_def_960, type, image_real_real: (real > real) > set_real > set_real).
% 75.95/17.90  thf(func_def_961, type, image_char_nat: (char > nat) > set_char > set_nat).
% 75.95/17.90  thf(func_def_962, type, image_VEBT_VEBT_nat: (vEBT_VEBT > nat) > set_VEBT_VEBT > set_nat).
% 75.95/17.90  thf(func_def_963, type, insert_complex: complex > set_complex > set_complex).
% 75.95/17.90  thf(func_def_964, type, insert_Extended_enat: extended_enat > set_Extended_enat > set_Extended_enat).
% 75.95/17.90  thf(func_def_965, type, insert_int: int > set_int > set_int).
% 75.95/17.90  thf(func_def_966, type, insert_nat: nat > set_nat > set_nat).
% 75.95/17.90  thf(func_def_967, type, insert_num: num > set_num > set_num).
% 75.95/17.90  thf(func_def_968, type, insert8211810215607154385at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 75.95/17.90  thf(func_def_969, type, insert9069300056098147895at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat).
% 75.95/17.90  thf(func_def_970, type, insert_rat: rat > set_rat > set_rat).
% 75.95/17.90  thf(func_def_971, type, insert_real: real > set_real > set_real).
% 75.95/17.90  thf(func_def_972, type, insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT).
% 75.95/17.90  thf(func_def_973, type, vimage_nat_nat: (nat > nat) > set_nat > set_nat).
% 75.95/17.90  thf(func_def_974, type, set_fo1517530859248394432omplex: (nat > complex > complex) > nat > nat > complex > complex).
% 75.95/17.90  thf(func_def_975, type, set_fo2581907887559384638at_int: (nat > int > int) > nat > nat > int > int).
% 75.95/17.90  thf(func_def_976, type, set_fo2584398358068434914at_nat: (nat > nat > nat) > nat > nat > nat > nat).
% 75.95/17.90  thf(func_def_977, type, set_fo1949268297981939178at_rat: (nat > rat > rat) > nat > nat > rat > rat).
% 75.95/17.90  thf(func_def_978, type, set_fo3111899725591712190t_real: (nat > real > real) > nat > nat > real > real).
% 75.95/17.90  thf(func_def_979, type, set_or5403411693681687835d_enat: extended_enat > extended_enat > set_Extended_enat).
% 75.95/17.90  thf(func_def_980, type, set_or1266510415728281911st_int: int > int > set_int).
% 75.95/17.90  thf(func_def_981, type, set_or1269000886237332187st_nat: nat > nat > set_nat).
% 75.95/17.90  thf(func_def_982, type, set_or7049704709247886629st_num: num > num > set_num).
% 75.95/17.90  thf(func_def_983, type, set_or633870826150836451st_rat: rat > rat > set_rat).
% 75.95/17.90  thf(func_def_984, type, set_or1222579329274155063t_real: real > real > set_real).
% 75.95/17.90  thf(func_def_985, type, set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat).
% 75.95/17.90  thf(func_def_986, type, set_or4662586982721622107an_int: int > int > set_int).
% 75.95/17.90  thf(func_def_987, type, set_or4665077453230672383an_nat: nat > nat > set_nat).
% 75.95/17.90  thf(func_def_988, type, set_ord_atLeast_nat: nat > set_nat).
% 75.95/17.90  thf(func_def_989, type, set_ord_atMost_int: int > set_int).
% 75.95/17.90  thf(func_def_990, type, set_ord_atMost_nat: nat > set_nat).
% 75.95/17.90  thf(func_def_991, type, set_ord_atMost_num: num > set_num).
% 75.95/17.90  thf(func_def_992, type, set_ord_atMost_rat: rat > set_rat).
% 75.95/17.90  thf(func_def_993, type, set_ord_atMost_real: real > set_real).
% 75.95/17.90  thf(func_def_994, type, set_or4236626031148496127et_nat: set_nat > set_set_nat).
% 75.95/17.90  thf(func_def_995, type, set_or6656581121297822940st_int: int > int > set_int).
% 75.95/17.90  thf(func_def_996, type, set_or6659071591806873216st_nat: nat > nat > set_nat).
% 75.95/17.90  thf(func_def_997, type, set_or5832277885323065728an_int: int > int > set_int).
% 75.95/17.90  thf(func_def_998, type, set_or5834768355832116004an_nat: nat > nat > set_nat).
% 75.95/17.90  thf(func_def_999, type, set_or1633881224788618240n_real: real > real > set_real).
% 75.95/17.90  thf(func_def_1000, type, set_or1210151606488870762an_nat: nat > set_nat).
% 75.95/17.90  thf(func_def_1001, type, set_or5849166863359141190n_real: real > set_real).
% 75.95/17.90  thf(func_def_1002, type, set_ord_lessThan_int: int > set_int).
% 75.95/17.90  thf(func_def_1003, type, set_ord_lessThan_nat: nat > set_nat).
% 75.95/17.90  thf(func_def_1004, type, set_ord_lessThan_num: num > set_num).
% 75.95/17.90  thf(func_def_1005, type, set_ord_lessThan_rat: rat > set_rat).
% 75.95/17.90  thf(func_def_1006, type, set_or5984915006950818249n_real: real > set_real).
% 75.95/17.90  thf(func_def_1007, type, set_or890127255671739683et_nat: set_nat > set_set_nat).
% 75.95/17.90  thf(func_def_1008, type, abort_real: literal > (product_unit > real) > real).
% 75.95/17.90  thf(func_def_1009, type, literal2: $o > $o > $o > $o > $o > $o > $o > literal > literal).
% 75.95/17.90  thf(func_def_1010, type, ascii_of: char > char).
% 75.95/17.90  thf(func_def_1011, type, char2: $o > $o > $o > $o > $o > $o > $o > $o > char).
% 75.95/17.90  thf(func_def_1012, type, size_char: char > nat).
% 75.95/17.90  thf(func_def_1013, type, comm_s629917340098488124ar_nat: char > nat).
% 75.95/17.90  thf(func_def_1014, type, integer_of_char: char > code_integer).
% 75.95/17.90  thf(func_def_1015, type, unique3096191561947761185of_nat: nat > char).
% 75.95/17.90  thf(func_def_1016, type, topolo4422821103128117721l_real: filter_real > (real > real) > $o).
% 75.95/17.90  thf(func_def_1017, type, topolo5044208981011980120l_real: set_real > (real > real) > $o).
% 75.95/17.90  thf(func_def_1018, type, topolo6980174941875973593q_real: (nat > real) > $o).
% 75.95/17.90  thf(func_def_1019, type, topolo2177554685111907308n_real: real > set_real > filter_real).
% 75.95/17.90  thf(func_def_1020, type, topolo7531315842566124627t_real: (nat > real) > $o).
% 75.95/17.90  thf(func_def_1021, type, topolo2815343760600316023s_real: real > filter_real).
% 75.95/17.90  thf(func_def_1022, type, topolo4055970368930404560y_real: (nat > real) > $o).
% 75.95/17.90  thf(func_def_1023, type, topolo896644834953643431omplex: filter6041513312241820739omplex).
% 75.95/17.90  thf(func_def_1024, type, topolo1511823702728130853y_real: filter2146258269922977983l_real).
% 75.95/17.90  thf(func_def_1025, type, arccos: real > real).
% 75.95/17.90  thf(func_def_1026, type, arcosh_real: real > real).
% 75.95/17.90  thf(func_def_1027, type, arcsin: real > real).
% 75.95/17.90  thf(func_def_1028, type, arctan: real > real).
% 75.95/17.90  thf(func_def_1029, type, arsinh_real: real > real).
% 75.95/17.90  thf(func_def_1030, type, artanh_real: real > real).
% 75.95/17.90  thf(func_def_1031, type, cos_complex: complex > complex).
% 75.95/17.90  thf(func_def_1032, type, cos_real: real > real).
% 75.95/17.90  thf(func_def_1033, type, cos_coeff: nat > real).
% 75.95/17.90  thf(func_def_1034, type, cosh_real: real > real).
% 75.95/17.90  thf(func_def_1035, type, cot_real: real > real).
% 75.95/17.90  thf(func_def_1036, type, exp_complex: complex > complex).
% 75.95/17.90  thf(func_def_1037, type, exp_real: real > real).
% 75.95/17.90  thf(func_def_1038, type, ln_ln_real: real > real).
% 75.95/17.90  thf(func_def_1039, type, log: real > real > real).
% 75.95/17.90  thf(func_def_1040, type, pi: real).
% 75.95/17.90  thf(func_def_1041, type, powr_real: real > real > real).
% 75.95/17.90  thf(func_def_1042, type, powr_real2: real > real > real).
% 75.95/17.90  thf(func_def_1043, type, sin_complex: complex > complex).
% 75.95/17.90  thf(func_def_1044, type, sin_real: real > real).
% 75.95/17.90  thf(func_def_1045, type, sin_coeff: nat > real).
% 75.95/17.90  thf(func_def_1046, type, sinh_real: real > real).
% 75.95/17.90  thf(func_def_1047, type, tan_complex: complex > complex).
% 75.95/17.90  thf(func_def_1048, type, tan_real: real > real).
% 75.95/17.90  thf(func_def_1049, type, tanh_real: real > real).
% 75.95/17.90  thf(func_def_1050, type, bi_tot896582865486249351at_int: (product_prod_nat_nat > int > $o) > $o).
% 75.95/17.90  thf(func_def_1051, type, transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 75.95/17.90  thf(func_def_1052, type, transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 75.95/17.90  thf(func_def_1053, type, type_d7649664348572268762on_nat: (extended_enat > option_nat) > (option_nat > extended_enat) > set_option_nat > $o).
% 75.95/17.90  thf(func_def_1054, type, vEBT_T_i_n_s_e_r_t: vEBT_VEBT > nat > nat).
% 75.95/17.90  thf(func_def_1055, type, vEBT_T_i_n_s_e_r_t2: vEBT_VEBT > nat > nat).
% 75.95/17.90  thf(func_def_1056, type, vEBT_T5076183648494686801_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 75.95/17.90  thf(func_def_1057, type, vEBT_T9217963907923527482_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 75.95/17.90  thf(func_def_1058, type, vEBT_T_m_a_x_t: vEBT_VEBT > nat).
% 75.95/17.90  thf(func_def_1059, type, vEBT_T_m_e_m_b_e_r: vEBT_VEBT > nat > nat).
% 75.95/17.90  thf(func_def_1060, type, vEBT_T_m_e_m_b_e_r2: vEBT_VEBT > nat > nat).
% 75.95/17.90  thf(func_def_1061, type, vEBT_T8099345112685741742_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 75.95/17.90  thf(func_def_1062, type, vEBT_T5837161174952499735_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 75.95/17.90  thf(func_def_1063, type, vEBT_T_m_i_n_N_u_l_l: vEBT_VEBT > nat).
% 75.95/17.90  thf(func_def_1064, type, vEBT_T_m_i_n_t: vEBT_VEBT > nat).
% 75.95/17.90  thf(func_def_1065, type, vEBT_T_m_i_n_t_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 75.95/17.90  thf(func_def_1066, type, vEBT_T_p_r_e_d: vEBT_VEBT > nat > nat).
% 75.95/17.90  thf(func_def_1067, type, vEBT_T_p_r_e_d2: vEBT_VEBT > nat > nat).
% 75.95/17.90  thf(func_def_1068, type, vEBT_T_p_r_e_d_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 75.95/17.90  thf(func_def_1069, type, vEBT_T_p_r_e_d_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 75.95/17.90  thf(func_def_1070, type, vEBT_T_s_u_c_c: vEBT_VEBT > nat > nat).
% 75.95/17.90  thf(func_def_1071, type, vEBT_T_s_u_c_c2: vEBT_VEBT > nat > nat).
% 75.95/17.90  thf(func_def_1072, type, vEBT_T_s_u_c_c_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 75.95/17.90  thf(func_def_1073, type, vEBT_T_s_u_c_c_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 75.95/17.90  thf(func_def_1074, type, vEBT_Leaf: $o > $o > vEBT_VEBT).
% 75.95/17.90  thf(func_def_1075, type, vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 75.95/17.90  thf(func_def_1076, type, vEBT_size_VEBT: vEBT_VEBT > nat).
% 75.95/17.90  thf(func_def_1077, type, vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o).
% 75.95/17.90  thf(func_def_1078, type, vEBT_VEBT_elim_dead: vEBT_VEBT > extended_enat > vEBT_VEBT).
% 75.95/17.90  thf(func_def_1079, type, vEBT_V312737461966249ad_rel: produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o).
% 75.95/17.90  thf(func_def_1080, type, vEBT_VEBT_high: nat > nat > nat).
% 75.95/17.90  thf(func_def_1081, type, vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o).
% 75.95/17.90  thf(func_def_1082, type, vEBT_VEBT_low: nat > nat > nat).
% 75.95/17.90  thf(func_def_1083, type, vEBT_VEBT_membermima: vEBT_VEBT > nat > $o).
% 75.95/17.90  thf(func_def_1084, type, vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 75.95/17.90  thf(func_def_1085, type, vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o).
% 75.95/17.90  thf(func_def_1086, type, vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 75.95/17.90  thf(func_def_1087, type, vEBT_VEBT_valid: vEBT_VEBT > nat > $o).
% 75.95/17.90  thf(func_def_1088, type, vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 75.95/17.90  thf(func_def_1089, type, vEBT_invar_vebt: vEBT_VEBT > nat > $o).
% 75.95/17.90  thf(func_def_1090, type, vEBT_set_vebt: vEBT_VEBT > set_nat).
% 75.95/17.90  thf(func_def_1091, type, vEBT_vebt_buildup: nat > vEBT_VEBT).
% 75.95/17.90  thf(func_def_1092, type, vEBT_v4011308405150292612up_rel: nat > nat > $o).
% 75.95/17.90  thf(func_def_1093, type, vEBT_T_d_e_l_e_t_e: vEBT_VEBT > nat > nat).
% 75.95/17.90  thf(func_def_1094, type, vEBT_T8441311223069195367_e_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 75.95/17.90  thf(func_def_1095, type, vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT).
% 75.95/17.90  thf(func_def_1096, type, vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 75.95/17.90  thf(func_def_1097, type, vEBT_VEBT_height: vEBT_VEBT > nat).
% 75.95/17.90  thf(func_def_1098, type, vEBT_VEBT_height_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 75.95/17.90  thf(func_def_1099, type, vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT).
% 75.95/17.90  thf(func_def_1100, type, vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 75.95/17.90  thf(func_def_1101, type, vEBT_VEBT_bit_concat: nat > nat > nat > nat).
% 75.95/17.90  thf(func_def_1102, type, vEBT_VEBT_minNull: vEBT_VEBT > $o).
% 75.95/17.90  thf(func_def_1103, type, vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat).
% 75.95/17.90  thf(func_def_1104, type, vEBT_vebt_member: vEBT_VEBT > nat > $o).
% 75.95/17.90  thf(func_def_1105, type, vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 75.95/17.90  thf(func_def_1106, type, vEBT_VEBT_add: option_nat > option_nat > option_nat).
% 75.95/17.90  thf(func_def_1107, type, vEBT_VEBT_greater: option_nat > option_nat > $o).
% 75.95/17.90  thf(func_def_1108, type, vEBT_VEBT_less: option_nat > option_nat > $o).
% 75.95/17.90  thf(func_def_1109, type, vEBT_VEBT_lesseq: option_nat > option_nat > $o).
% 75.95/17.90  thf(func_def_1110, type, vEBT_VEBT_max_in_set: set_nat > nat > $o).
% 75.95/17.90  thf(func_def_1111, type, vEBT_VEBT_min_in_set: set_nat > nat > $o).
% 75.95/17.90  thf(func_def_1112, type, vEBT_VEBT_mul: option_nat > option_nat > option_nat).
% 75.95/17.90  thf(func_def_1113, type, vEBT_V2881884560877996034ft_nat: (nat > nat > $o) > option_nat > option_nat > $o).
% 75.95/17.90  thf(func_def_1114, type, vEBT_V4262088993061758097ft_nat: (nat > nat > nat) > option_nat > option_nat > option_nat).
% 75.95/17.90  thf(func_def_1115, type, vEBT_V819420779217536731ft_num: (num > num > num) > option_num > option_num > option_num).
% 75.95/17.90  thf(func_def_1116, type, vEBT_V1502963449132264192at_nat: (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat).
% 75.95/17.90  thf(func_def_1117, type, vEBT_VEBT_power: option_nat > option_nat > option_nat).
% 75.95/17.90  thf(func_def_1118, type, vEBT_vebt_maxt: vEBT_VEBT > option_nat).
% 75.95/17.90  thf(func_def_1119, type, vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 75.95/17.90  thf(func_def_1120, type, vEBT_vebt_mint: vEBT_VEBT > option_nat).
% 75.95/17.90  thf(func_def_1121, type, vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 75.95/17.90  thf(func_def_1122, type, vEBT_is_pred_in_set: set_nat > nat > nat > $o).
% 75.95/17.90  thf(func_def_1123, type, vEBT_vebt_pred: vEBT_VEBT > nat > option_nat).
% 75.95/17.90  thf(func_def_1124, type, vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 75.95/17.90  thf(func_def_1125, type, vEBT_is_succ_in_set: set_nat > nat > nat > $o).
% 75.95/17.90  thf(func_def_1126, type, vEBT_vebt_succ: vEBT_VEBT > nat > option_nat).
% 75.95/17.90  thf(func_def_1127, type, vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 75.95/17.90  thf(func_def_1128, type, accp_list_nat: (list_nat > list_nat > $o) > list_nat > $o).
% 75.95/17.90  thf(func_def_1129, type, accp_nat: (nat > nat > $o) > nat > $o).
% 75.95/17.90  thf(func_def_1130, type, accp_P1096762738010456898nt_int: (product_prod_int_int > product_prod_int_int > $o) > product_prod_int_int > $o).
% 75.95/17.90  thf(func_def_1131, type, accp_P4275260045618599050at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > product_prod_nat_nat > $o).
% 75.95/17.90  thf(func_def_1132, type, accp_P3113834385874906142um_num: (product_prod_num_num > product_prod_num_num > $o) > product_prod_num_num > $o).
% 75.95/17.90  thf(func_def_1133, type, accp_P6183159247885693666d_enat: (produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o) > produc7272778201969148633d_enat > $o).
% 75.95/17.90  thf(func_def_1134, type, accp_P2887432264394892906BT_nat: (produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o) > produc9072475918466114483BT_nat > $o).
% 75.95/17.90  thf(func_def_1135, type, accp_VEBT_VEBT: (vEBT_VEBT > vEBT_VEBT > $o) > vEBT_VEBT > $o).
% 75.95/17.90  thf(func_def_1136, type, less_than: set_Pr1261947904930325089at_nat).
% 75.95/17.90  thf(func_def_1137, type, lex_prod_nat_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat).
% 75.95/17.90  thf(func_def_1138, type, max_ex8135407076693332796at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat).
% 75.95/17.90  thf(func_def_1139, type, min_ex6901939911449802026at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat).
% 75.95/17.90  thf(func_def_1140, type, pred_nat: set_Pr1261947904930325089at_nat).
% 75.95/17.90  thf(func_def_1141, type, wf_int: set_Pr958786334691620121nt_int > $o).
% 75.95/17.90  thf(func_def_1142, type, wf_nat: set_Pr1261947904930325089at_nat > $o).
% 75.95/17.90  thf(func_def_1143, type, wf_Pro7803398752247294826at_nat: set_Pr8693737435421807431at_nat > $o).
% 75.95/17.90  thf(func_def_1144, type, fChoice_real: (real > $o) > real).
% 75.95/17.90  thf(func_def_1145, type, member_o: $o > set_o > $o).
% 75.95/17.90  thf(func_def_1146, type, member_complex: complex > set_complex > $o).
% 75.95/17.90  thf(func_def_1147, type, member_Extended_enat: extended_enat > set_Extended_enat > $o).
% 75.95/17.90  thf(func_def_1148, type, member_int: int > set_int > $o).
% 75.95/17.90  thf(func_def_1149, type, member_list_o: list_o > set_list_o > $o).
% 75.95/17.90  thf(func_def_1150, type, member_list_int: list_int > set_list_int > $o).
% 75.95/17.90  thf(func_def_1151, type, member_list_nat: list_nat > set_list_nat > $o).
% 75.95/17.90  thf(func_def_1152, type, member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o).
% 75.95/17.90  thf(func_def_1153, type, member_nat: nat > set_nat > $o).
% 75.95/17.90  thf(func_def_1154, type, member_num: num > set_num > $o).
% 75.95/17.90  thf(func_def_1155, type, member_option_nat: option_nat > set_option_nat > $o).
% 75.95/17.90  thf(func_def_1156, type, member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o).
% 75.95/17.90  thf(func_def_1157, type, member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o).
% 75.95/17.90  thf(func_def_1158, type, member8757157785044589968at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > $o).
% 75.95/17.90  thf(func_def_1159, type, member_rat: rat > set_rat > $o).
% 75.95/17.90  thf(func_def_1160, type, member_real: real > set_real > $o).
% 75.95/17.90  thf(func_def_1161, type, member_set_nat: set_nat > set_set_nat > $o).
% 75.95/17.90  thf(func_def_1162, type, member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o).
% 75.95/17.90  thf(func_def_1163, type, deg: nat).
% 75.95/17.90  thf(func_def_1164, type, m: nat).
% 75.95/17.90  thf(func_def_1165, type, ma: nat).
% 75.95/17.90  thf(func_def_1166, type, mi: nat).
% 75.95/17.90  thf(func_def_1167, type, na: nat).
% 75.95/17.90  thf(func_def_1168, type, summary: vEBT_VEBT).
% 75.95/17.90  thf(func_def_1169, type, treeList: list_VEBT_VEBT).
% 75.95/17.90  thf(func_def_1170, type, x: nat).
% 75.95/17.90  thf(func_def_1189, type, sP0: rat > rat > rat > $o).
% 75.95/17.90  thf(func_def_1190, type, sP1: rat > rat > rat > $o).
% 75.95/17.90  thf(func_def_1191, type, sP2: rat > rat > rat > $o).
% 75.95/17.90  thf(func_def_1192, type, sP3: int > int > int > $o).
% 75.95/17.90  thf(func_def_1193, type, sP4: int > int > int > $o).
% 75.95/17.90  thf(func_def_1194, type, sP5: int > int > int > $o).
% 75.95/17.90  thf(func_def_1195, type, sP6: nat > nat > nat > $o).
% 75.95/17.90  thf(func_def_1196, type, sP7: nat > nat > nat > $o).
% 75.95/17.90  thf(func_def_1197, type, sP8: nat > nat > nat > $o).
% 75.95/17.90  thf(func_def_1198, type, sP9: (int > $o) > $o).
% 75.95/17.90  thf(func_def_1199, type, sK10: (nat > int) > nat).
% 75.95/17.90  thf(func_def_1200, type, sK11: (nat > nat > $o) > nat).
% 75.95/17.90  thf(func_def_1201, type, sK12: (nat > nat > $o) > nat).
% 75.95/17.90  thf(func_def_1202, type, sK13: (nat > nat > $o) > nat).
% 75.95/17.90  thf(func_def_1203, type, sK14: (nat > nat > $o) > nat).
% 75.95/17.90  thf(func_def_1204, type, sK15: nat > nat > nat).
% 75.95/17.90  thf(func_def_1205, type, sK16: real > real).
% 75.95/17.90  thf(func_def_1206, type, sK17: int > int).
% 75.95/17.90  thf(func_def_1207, type, sK18: (rat > nat) > rat).
% 75.95/17.90  thf(func_def_1208, type, sK19: (rat > nat) > rat).
% 75.95/17.90  thf(func_def_1209, type, sK20: int > int).
% 75.95/17.90  thf(func_def_1210, type, sK21: (rat > real) > rat).
% 75.95/17.90  thf(func_def_1211, type, sK22: (rat > real) > rat).
% 75.95/17.90  thf(func_def_1212, type, sK23: (nat > rat) > nat).
% 75.95/17.90  thf(func_def_1213, type, sK24: real > real > real).
% 75.95/17.90  thf(func_def_1214, type, sK25: (nat > $o) > nat).
% 75.95/17.90  thf(func_def_1215, type, sK26: (nat > $o) > nat > nat).
% 75.95/17.90  thf(func_def_1216, type, sK27: (nat > nat > $o) > nat).
% 75.95/17.90  thf(func_def_1217, type, sK28: (nat > nat > $o) > nat).
% 75.95/17.90  thf(func_def_1218, type, sK29: (nat > nat > $o) > nat).
% 75.95/17.90  thf(func_def_1219, type, sK30: (nat > nat > $o) > nat).
% 75.95/17.90  thf(func_def_1220, type, sK31: (nat > nat > $o) > nat).
% 75.95/17.90  thf(func_def_1221, type, sK32: real > real).
% 75.95/17.90  thf(func_def_1222, type, sK33: nat > nat).
% 75.95/17.90  thf(func_def_1223, type, sK34: (nat > rat) > nat).
% 75.95/17.90  thf(func_def_1224, type, sK35: (nat > rat) > nat).
% 75.95/17.90  thf(func_def_1225, type, sK36: real > nat > real).
% 75.95/17.90  thf(func_def_1226, type, sK37: (nat > nat) > nat).
% 75.95/17.90  thf(func_def_1227, type, sK38: (nat > $o) > nat).
% 75.95/17.90  thf(func_def_1228, type, sK39: nat > (nat > $o) > nat).
% 75.95/17.90  thf(func_def_1229, type, sK40: real > real).
% 75.95/17.90  thf(func_def_1230, type, sK41: (int > real) > int).
% 75.95/17.90  thf(func_def_1231, type, sK42: (int > real) > int).
% 75.95/17.90  thf(func_def_1232, type, sK43: real > real).
% 75.95/17.90  thf(func_def_1233, type, sK44: (real > real) > real).
% 75.95/17.90  thf(func_def_1234, type, sK45: (real > real) > real).
% 75.95/17.90  thf(func_def_1235, type, sK46: nat > nat).
% 75.95/17.90  thf(func_def_1236, type, sK47: (int > $o) > (int > $o) > (int > $o) > (int > $o) > int).
% 75.95/17.90  thf(func_def_1237, type, sK48: int > (int > $o) > (int > $o) > int).
% 75.95/17.90  thf(func_def_1238, type, sK49: int > (int > $o) > (int > $o) > int).
% 75.95/17.90  thf(func_def_1239, type, sK50: (real > int) > real).
% 75.95/17.90  thf(func_def_1240, type, sK51: (real > int) > real).
% 75.95/17.90  thf(func_def_1241, type, sK52: (nat > $o) > nat).
% 75.95/17.90  thf(func_def_1242, type, sK53: (nat > $o) > nat > nat).
% 75.95/17.90  thf(func_def_1243, type, sK54: (real > $o) > (real > $o) > (real > $o) > (real > $o) > real).
% 75.95/17.90  thf(func_def_1244, type, sK55: real > (real > $o) > (real > $o) > real).
% 75.95/17.90  thf(func_def_1245, type, sK56: real > (real > $o) > (real > $o) > real).
% 75.95/17.90  thf(func_def_1246, type, sK57: real > real > real).
% 75.95/17.90  thf(func_def_1247, type, sK58: (nat > $o) > nat > nat).
% 75.95/17.90  thf(func_def_1248, type, sK59: int > int).
% 75.95/17.90  thf(func_def_1249, type, sK60: (nat > $o) > nat).
% 75.95/17.90  thf(func_def_1250, type, sK61: nat > (nat > $o) > nat).
% 75.95/17.90  thf(func_def_1251, type, sK62: nat > (nat > $o) > nat).
% 75.95/17.90  thf(func_def_1252, type, sK63: real > real).
% 75.95/17.90  thf(func_def_1253, type, sK64: nat > (nat > $o) > (nat > $o) > nat).
% 75.95/17.90  thf(func_def_1254, type, sK65: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > nat).
% 75.95/17.90  thf(func_def_1255, type, sK66: nat > (nat > $o) > (nat > $o) > nat).
% 75.95/17.90  thf(func_def_1256, type, sK67: (real > nat) > real).
% 75.95/17.90  thf(func_def_1257, type, sK68: (real > nat) > real).
% 75.95/17.90  thf(func_def_1258, type, sK69: nat > nat > nat).
% 75.95/17.90  thf(func_def_1259, type, sK70: (rat > int) > rat).
% 75.95/17.90  thf(func_def_1260, type, sK71: (rat > int) > rat).
% 75.95/17.90  thf(func_def_1261, type, sK72: nat > nat).
% 75.95/17.90  thf(func_def_1262, type, sK73: real > real).
% 75.95/17.90  thf(func_def_1263, type, sK74: int > int).
% 75.95/17.90  thf(func_def_1264, type, sK75: int > (int > $o) > int).
% 72.56/17.90  thf(func_def_1265, type, sK76: (nat > nat > $o) > nat).
% 72.56/17.90  thf(func_def_1266, type, sK77: (nat > nat > $o) > nat).
% 72.56/17.90  thf(func_def_1267, type, sK78: (nat > nat > $o) > nat).
% 72.56/17.90  thf(func_def_1268, type, sK79: (nat > nat > $o) > nat).
% 72.56/17.90  thf(func_def_1269, type, sK80: (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1270, type, sK81: nat > nat).
% 72.56/17.90  thf(func_def_1271, type, sK82: nat > nat > nat).
% 72.56/17.90  thf(func_def_1272, type, sK83: rat > rat).
% 72.56/17.90  thf(func_def_1273, type, sK84: real > real).
% 72.56/17.90  thf(func_def_1274, type, sK85: (nat > nat) > nat).
% 72.56/17.90  thf(func_def_1275, type, sK86: rat > rat).
% 72.56/17.90  thf(func_def_1276, type, sK87: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1277, type, sK88: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1278, type, sK89: (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1279, type, sK90: (rat > int) > rat).
% 72.56/17.90  thf(func_def_1280, type, sK91: (rat > int) > rat).
% 72.56/17.90  thf(func_def_1281, type, sK92: (nat > nat) > nat).
% 72.56/17.90  thf(func_def_1282, type, sK93: (nat > nat > $o) > nat).
% 72.56/17.90  thf(func_def_1283, type, sK94: (nat > nat > $o) > nat).
% 72.56/17.90  thf(func_def_1284, type, sK95: (nat > nat > $o) > nat).
% 72.56/17.90  thf(func_def_1285, type, sK96: (nat > nat > $o) > nat).
% 72.56/17.90  thf(func_def_1286, type, sK97: (nat > nat > $o) > nat).
% 72.56/17.90  thf(func_def_1287, type, sK98: real > real > real).
% 72.56/17.90  thf(func_def_1288, type, sK99: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1289, type, sK100: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1290, type, sK101: (int > rat) > int).
% 72.56/17.90  thf(func_def_1291, type, sK102: (int > rat) > int).
% 72.56/17.90  thf(func_def_1292, type, sK103: (int > $o) > (int > $o) > (int > $o) > (int > $o) > int).
% 72.56/17.90  thf(func_def_1293, type, sK104: int > (int > $o) > (int > $o) > int).
% 72.56/17.90  thf(func_def_1294, type, sK105: int > (int > $o) > (int > $o) > int).
% 72.56/17.90  thf(func_def_1295, type, sK106: (rat > int) > rat).
% 72.56/17.90  thf(func_def_1296, type, sK107: (rat > int) > rat).
% 72.56/17.90  thf(func_def_1297, type, sK108: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1298, type, sK109: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1299, type, sK110: (nat > rat) > nat).
% 72.56/17.90  thf(func_def_1300, type, sK111: (nat > rat) > nat).
% 72.56/17.90  thf(func_def_1301, type, sK112: real > real).
% 72.56/17.90  thf(func_def_1302, type, sK113: real > real).
% 72.56/17.90  thf(func_def_1303, type, sK114: int > (int > $o) > (int > $o) > int).
% 72.56/17.90  thf(func_def_1304, type, sK115: int > (int > $o) > (int > $o) > int).
% 72.56/17.90  thf(func_def_1305, type, sK116: (int > $o) > (int > $o) > (int > $o) > (int > $o) > int).
% 72.56/17.90  thf(func_def_1306, type, sK117: nat > nat).
% 72.56/17.90  thf(func_def_1307, type, sK118: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1308, type, sK119: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1309, type, sK120: (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1310, type, sK121: (nat > rat) > nat).
% 72.56/17.90  thf(func_def_1311, type, sK122: (nat > rat) > nat).
% 72.56/17.90  thf(func_def_1312, type, sK123: (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1313, type, sK124: (nat > real) > nat).
% 72.56/17.90  thf(func_def_1314, type, sK125: (nat > real) > nat).
% 72.56/17.90  thf(func_def_1315, type, sK126: (nat > real) > nat).
% 72.56/17.90  thf(func_def_1316, type, sK127: (nat > real) > nat).
% 72.56/17.90  thf(func_def_1317, type, sK128: nat > nat > nat).
% 72.56/17.90  thf(func_def_1318, type, sK129: nat > nat > nat).
% 72.56/17.90  thf(func_def_1319, type, sK130: (nat > int) > nat).
% 72.56/17.90  thf(func_def_1320, type, sK131: (int > real) > int).
% 72.56/17.90  thf(func_def_1321, type, sK132: (int > real) > int).
% 72.56/17.90  thf(func_def_1322, type, sK133: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1323, type, sK134: nat > (nat > $o) > (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1324, type, sK135: nat > (nat > $o) > (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1325, type, sK136: (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1326, type, sK137: real > real > real).
% 72.56/17.90  thf(func_def_1327, type, sK138: rat > rat > rat).
% 72.56/17.90  thf(func_def_1328, type, sK139: real > (real > $o) > (real > $o) > real).
% 72.56/17.90  thf(func_def_1329, type, sK140: real > (real > $o) > (real > $o) > real).
% 72.56/17.90  thf(func_def_1330, type, sK141: (real > $o) > (real > $o) > (real > $o) > (real > $o) > real).
% 72.56/17.90  thf(func_def_1331, type, sK142: real > real > real > real).
% 72.56/17.90  thf(func_def_1332, type, sK143: rat > rat).
% 72.56/17.90  thf(func_def_1333, type, sK144: nat > nat).
% 72.56/17.90  thf(func_def_1334, type, sK145: (rat > nat) > rat).
% 72.56/17.90  thf(func_def_1335, type, sK146: (rat > nat) > rat).
% 72.56/17.90  thf(func_def_1336, type, sK147: (real > real) > real).
% 72.56/17.90  thf(func_def_1337, type, sK148: (real > real) > real).
% 72.56/17.90  thf(func_def_1338, type, sK149: (nat > int) > nat).
% 72.56/17.90  thf(func_def_1339, type, sK150: (real > real > $o) > real).
% 72.56/17.90  thf(func_def_1340, type, sK151: (real > real > $o) > real).
% 72.56/17.90  thf(func_def_1341, type, sK152: (real > real > $o) > real).
% 72.56/17.90  thf(func_def_1342, type, sK153: (real > real > $o) > real).
% 72.56/17.90  thf(func_def_1343, type, sK154: (real > real > $o) > real).
% 72.56/17.90  thf(func_def_1344, type, sK155: real > (real > $o) > real > real).
% 72.56/17.90  thf(func_def_1345, type, sK156: real > real > (real > $o) > real).
% 72.56/17.90  thf(func_def_1346, type, sK157: real > real > nat).
% 72.56/17.90  thf(func_def_1347, type, sK158: (int > int > $o) > int).
% 72.56/17.90  thf(func_def_1348, type, sK159: (int > int > $o) > int).
% 72.56/17.90  thf(func_def_1349, type, sK160: (int > int > $o) > int).
% 72.56/17.90  thf(func_def_1350, type, sK161: (int > int > $o) > int).
% 72.56/17.90  thf(func_def_1351, type, sK162: (int > int > $o) > int).
% 72.56/17.90  thf(func_def_1352, type, sK163: nat > nat > nat).
% 72.56/17.90  thf(func_def_1353, type, sK164: nat > nat > (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1354, type, sK165: rat > rat).
% 72.56/17.90  thf(func_def_1355, type, sK166: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1356, type, sK167: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1357, type, sK168: (nat > real) > nat).
% 72.56/17.90  thf(func_def_1358, type, sK169: (rat > int) > rat).
% 72.56/17.90  thf(func_def_1359, type, sK170: (rat > int) > rat).
% 72.56/17.90  thf(func_def_1360, type, sK171: (real > rat) > real).
% 72.56/17.90  thf(func_def_1361, type, sK172: (real > rat) > real).
% 72.56/17.90  thf(func_def_1362, type, sK173: real > real > nat).
% 72.56/17.90  thf(func_def_1363, type, sK174: (rat > nat) > rat).
% 72.56/17.90  thf(func_def_1364, type, sK175: (rat > nat) > rat).
% 72.56/17.90  thf(func_def_1365, type, sK176: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1366, type, sK177: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1367, type, sK178: rat > rat).
% 72.56/17.90  thf(func_def_1368, type, sK179: int > int).
% 72.56/17.90  thf(func_def_1369, type, sK180: (rat > nat) > rat).
% 72.56/17.90  thf(func_def_1370, type, sK181: (rat > nat) > rat).
% 72.56/17.90  thf(func_def_1371, type, sK182: (rat > rat > $o) > rat).
% 72.56/17.90  thf(func_def_1372, type, sK183: (rat > rat > $o) > rat).
% 72.56/17.90  thf(func_def_1373, type, sK184: (rat > rat > $o) > rat).
% 72.56/17.90  thf(func_def_1374, type, sK185: (rat > rat > $o) > rat).
% 72.56/17.90  thf(func_def_1375, type, sK186: (rat > rat > $o) > rat).
% 72.56/17.90  thf(func_def_1376, type, sK187: (int > rat) > int).
% 72.56/17.90  thf(func_def_1377, type, sK188: (int > rat) > int).
% 72.56/17.90  thf(func_def_1378, type, sK189: (rat > nat) > rat).
% 72.56/17.90  thf(func_def_1379, type, sK190: (rat > nat) > rat).
% 72.56/17.90  thf(func_def_1380, type, sK191: (nat > rat) > nat).
% 72.56/17.90  thf(func_def_1381, type, sK192: (nat > rat) > nat).
% 72.56/17.90  thf(func_def_1382, type, sK193: rat > rat).
% 72.56/17.90  thf(func_def_1383, type, sK194: nat > nat > nat).
% 72.56/17.90  thf(func_def_1384, type, sK195: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1385, type, sK196: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1386, type, sK197: (nat > real) > nat).
% 72.56/17.90  thf(func_def_1387, type, sK198: int > int).
% 72.56/17.90  thf(func_def_1388, type, sK199: int > int).
% 72.56/17.90  thf(func_def_1389, type, sK200: (nat > nat) > nat).
% 72.56/17.90  thf(func_def_1390, type, sK201: (nat > nat) > nat).
% 72.56/17.90  thf(func_def_1391, type, sK202: real > real > real > real).
% 72.56/17.90  thf(func_def_1392, type, sK203: (int > rat) > int).
% 72.56/17.90  thf(func_def_1393, type, sK204: (int > rat) > int).
% 72.56/17.90  thf(func_def_1394, type, sK205: rat > rat > rat).
% 72.56/17.90  thf(func_def_1395, type, sK206: (nat > rat) > nat).
% 72.56/17.90  thf(func_def_1396, type, sK207: nat > nat).
% 72.56/17.90  thf(func_def_1397, type, sK208: (rat > nat) > rat).
% 72.56/17.90  thf(func_def_1398, type, sK209: (rat > nat) > rat).
% 72.56/17.90  thf(func_def_1399, type, sK210: rat > rat).
% 72.56/17.90  thf(func_def_1400, type, sK211: rat > rat > rat).
% 72.56/17.90  thf(func_def_1401, type, sK212: real > real).
% 72.56/17.90  thf(func_def_1402, type, sK213: real > (real > $o) > (real > $o) > real).
% 72.56/17.90  thf(func_def_1403, type, sK214: (real > $o) > (real > $o) > (real > $o) > (real > $o) > real).
% 72.56/17.90  thf(func_def_1404, type, sK215: real > (real > $o) > (real > $o) > real).
% 72.56/17.90  thf(func_def_1405, type, sK216: (real > real) > real).
% 72.56/17.90  thf(func_def_1406, type, sK217: (real > real) > real).
% 72.56/17.90  thf(func_def_1407, type, sK218: int > int).
% 72.56/17.90  thf(func_def_1408, type, sK219: (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1409, type, sK220: (real > rat) > real).
% 72.56/17.90  thf(func_def_1410, type, sK221: (real > rat) > real).
% 72.56/17.90  thf(func_def_1411, type, sK222: nat > (nat > $o) > (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1412, type, sK223: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1413, type, sK224: nat > (nat > $o) > (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1414, type, sK225: (rat > real) > rat).
% 72.56/17.90  thf(func_def_1415, type, sK226: (rat > real) > rat).
% 72.56/17.90  thf(func_def_1416, type, sK227: nat > nat > nat).
% 72.56/17.90  thf(func_def_1417, type, sK228: real > real).
% 72.56/17.90  thf(func_def_1418, type, sK229: real > real).
% 72.56/17.90  thf(func_def_1419, type, sK230: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1420, type, sK231: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1421, type, sK232: (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1422, type, sK233: real > real).
% 72.56/17.90  thf(func_def_1423, type, sK234: (real > int) > real).
% 72.56/17.90  thf(func_def_1424, type, sK235: (real > int) > real).
% 72.56/17.90  thf(func_def_1425, type, sK236: real > real).
% 72.56/17.90  thf(func_def_1426, type, sK237: int > (int > $o) > int > int).
% 72.56/17.90  thf(func_def_1427, type, sK238: int > (int > $o) > int > int).
% 72.56/17.90  thf(func_def_1428, type, sK239: nat > nat).
% 72.56/17.90  thf(func_def_1429, type, sK240: real > nat > real).
% 72.56/17.90  thf(func_def_1430, type, sK241: nat > nat > (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1431, type, sK242: nat > nat > (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1432, type, sK243: rat > rat > rat > rat).
% 72.56/17.90  thf(func_def_1433, type, sK244: (rat > int) > rat).
% 72.56/17.90  thf(func_def_1434, type, sK245: (rat > int) > rat).
% 72.56/17.90  thf(func_def_1435, type, sK246: int > int).
% 72.56/17.90  thf(func_def_1436, type, sK247: real > (real > $o) > (real > $o) > real).
% 72.56/17.90  thf(func_def_1437, type, sK248: (real > $o) > (real > $o) > (real > $o) > (real > $o) > real).
% 72.56/17.90  thf(func_def_1438, type, sK249: real > (real > $o) > (real > $o) > real).
% 72.56/17.90  thf(func_def_1439, type, sK250: nat > nat).
% 72.56/17.90  thf(func_def_1440, type, sK251: rat > rat).
% 72.56/17.90  thf(func_def_1441, type, sK252: real > real).
% 72.56/17.90  thf(func_def_1442, type, sK253: int > (int > $o) > (int > $o) > int).
% 72.56/17.90  thf(func_def_1443, type, sK254: int > (int > $o) > (int > $o) > int).
% 72.56/17.90  thf(func_def_1444, type, sK255: (int > $o) > (int > $o) > (int > $o) > (int > $o) > int).
% 72.56/17.90  thf(func_def_1445, type, sK256: nat > nat).
% 72.56/17.90  thf(func_def_1446, type, sK257: real > real).
% 72.56/17.90  thf(func_def_1447, type, sK258: (rat > nat) > rat).
% 72.56/17.90  thf(func_def_1448, type, sK259: (rat > nat) > rat).
% 72.56/17.90  thf(func_def_1449, type, sK260: (real > real) > real).
% 72.56/17.90  thf(func_def_1450, type, sK261: (real > real) > real).
% 72.56/17.90  thf(func_def_1451, type, sK262: (real > real) > real).
% 72.56/17.90  thf(func_def_1452, type, sK263: (real > real) > real).
% 72.56/17.90  thf(func_def_1453, type, sK264: nat > (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1454, type, sK265: nat > (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1455, type, sK266: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1456, type, sK267: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1457, type, sK268: nat > nat).
% 72.56/17.90  thf(func_def_1458, type, sK269: (rat > rat > $o) > rat).
% 72.56/17.90  thf(func_def_1459, type, sK270: (rat > rat > $o) > rat).
% 72.56/17.90  thf(func_def_1460, type, sK271: (rat > rat > $o) > rat).
% 72.56/17.90  thf(func_def_1461, type, sK272: (rat > rat > $o) > rat).
% 72.56/17.90  thf(func_def_1462, type, sK273: (rat > int) > rat).
% 72.56/17.90  thf(func_def_1463, type, sK274: (rat > int) > rat).
% 72.56/17.90  thf(func_def_1464, type, sK275: (rat > real) > rat).
% 72.56/17.90  thf(func_def_1465, type, sK276: (rat > real) > rat).
% 72.56/17.90  thf(func_def_1466, type, sK277: nat > nat).
% 72.56/17.90  thf(func_def_1467, type, sK278: nat > nat > nat).
% 72.56/17.90  thf(func_def_1468, type, sK279: (rat > int) > rat).
% 72.56/17.90  thf(func_def_1469, type, sK280: (rat > int) > rat).
% 72.56/17.90  thf(func_def_1470, type, sK281: (rat > real) > rat).
% 72.56/17.90  thf(func_def_1471, type, sK282: (rat > real) > rat).
% 72.56/17.90  thf(func_def_1472, type, sK283: (rat > int) > rat).
% 72.56/17.90  thf(func_def_1473, type, sK284: (rat > int) > rat).
% 72.56/17.90  thf(func_def_1474, type, sK285: nat > nat).
% 72.56/17.90  thf(func_def_1475, type, sK286: (rat > real) > rat).
% 72.56/17.90  thf(func_def_1476, type, sK287: (rat > real) > rat).
% 72.56/17.90  thf(func_def_1477, type, sK288: real > real > real).
% 72.56/17.90  thf(func_def_1478, type, sK289: (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1479, type, sK290: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1480, type, sK291: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1481, type, sK292: int > (int > $o) > int).
% 72.56/17.90  thf(func_def_1482, type, sK293: nat > nat).
% 72.56/17.90  thf(func_def_1483, type, sK294: (nat > nat) > nat).
% 72.56/17.90  thf(func_def_1484, type, sK295: (nat > nat) > nat).
% 72.56/17.90  thf(func_def_1485, type, sK296: (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1486, type, sK297: (nat > nat) > nat).
% 72.56/17.90  thf(func_def_1487, type, sK298: (rat > real) > rat).
% 72.56/17.90  thf(func_def_1488, type, sK299: (rat > real) > rat).
% 72.56/17.90  thf(func_def_1489, type, sK300: (real > rat) > real).
% 72.56/17.90  thf(func_def_1490, type, sK301: (real > rat) > real).
% 72.56/17.90  thf(func_def_1491, type, sK302: (nat > rat) > nat).
% 72.56/17.90  thf(func_def_1492, type, sK303: (nat > rat) > nat).
% 72.56/17.90  thf(func_def_1493, type, sK304: rat > rat > rat).
% 72.56/17.90  thf(func_def_1494, type, sK305: (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1495, type, sK306: (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1496, type, sK307: (rat > $o) > (rat > $o) > (rat > $o) > (rat > $o) > rat).
% 72.56/17.90  thf(func_def_1497, type, sK308: rat > (rat > $o) > (rat > $o) > rat).
% 72.56/17.90  thf(func_def_1498, type, sK309: rat > (rat > $o) > (rat > $o) > rat).
% 72.56/17.90  thf(func_def_1499, type, sK310: (int > real) > int).
% 72.56/17.90  thf(func_def_1500, type, sK311: (int > real) > int).
% 72.56/17.90  thf(func_def_1501, type, sK312: (real > rat) > real).
% 72.56/17.90  thf(func_def_1502, type, sK313: (real > rat) > real).
% 72.56/17.90  thf(func_def_1503, type, sK314: nat > nat).
% 72.56/17.90  thf(func_def_1504, type, sK315: nat > (nat > $o) > (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1505, type, sK316: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1506, type, sK317: nat > (nat > $o) > (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1507, type, sK318: (rat > $o) > (rat > $o) > (rat > $o) > (rat > $o) > rat).
% 72.56/17.90  thf(func_def_1508, type, sK319: rat > (rat > $o) > (rat > $o) > rat).
% 72.56/17.90  thf(func_def_1509, type, sK320: rat > (rat > $o) > (rat > $o) > rat).
% 72.56/17.90  thf(func_def_1510, type, sK321: int > int).
% 72.56/17.90  thf(func_def_1511, type, sK322: nat > nat).
% 72.56/17.90  thf(func_def_1512, type, sK323: (nat > rat) > nat).
% 72.56/17.90  thf(func_def_1513, type, sK324: rat > rat > rat > rat).
% 72.56/17.90  thf(func_def_1514, type, sK325: (int > rat) > int).
% 72.56/17.90  thf(func_def_1515, type, sK326: (int > rat) > int).
% 72.56/17.90  thf(func_def_1516, type, sK327: (rat > real) > rat).
% 72.56/17.90  thf(func_def_1517, type, sK328: (rat > real) > rat).
% 72.56/17.90  thf(func_def_1518, type, sK329: (int > int > $o) > int).
% 72.56/17.90  thf(func_def_1519, type, sK330: (int > int > $o) > int).
% 72.56/17.90  thf(func_def_1520, type, sK331: (int > int > $o) > int).
% 72.56/17.90  thf(func_def_1521, type, sK332: (int > int > $o) > int).
% 72.56/17.90  thf(func_def_1522, type, sK333: rat > rat).
% 72.56/17.90  thf(func_def_1523, type, sK334: (int > $o) > int > int).
% 72.56/17.90  thf(func_def_1524, type, sK335: rat > rat).
% 72.56/17.90  thf(func_def_1525, type, sK336: (real > nat) > real).
% 72.56/17.90  thf(func_def_1526, type, sK337: (real > nat) > real).
% 72.56/17.90  thf(func_def_1527, type, sK338: (real > real) > real).
% 72.56/17.90  thf(func_def_1528, type, sK339: (real > real) > real).
% 72.56/17.90  thf(func_def_1529, type, sK340: rat > rat).
% 72.56/17.90  thf(func_def_1530, type, sK341: int > int).
% 72.56/17.90  thf(func_def_1531, type, sK342: nat > nat > nat).
% 72.56/17.90  thf(func_def_1532, type, sK343: (nat > int) > nat).
% 72.56/17.90  thf(func_def_1533, type, sK344: nat > (nat > $o) > nat).
% 72.56/17.90  thf(func_def_1534, type, sK345: nat > nat).
% 72.56/17.90  thf(func_def_1535, type, sK346: int > int).
% 72.56/17.90  thf(func_def_1536, type, sK347: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1537, type, sK348: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1538, type, sK349: rat > rat).
% 72.56/17.90  thf(func_def_1539, type, sK350: rat > rat).
% 72.56/17.90  thf(func_def_1540, type, sK351: (nat > real) > nat).
% 72.56/17.90  thf(func_def_1541, type, sK352: (nat > real) > nat).
% 72.56/17.90  thf(func_def_1542, type, sK353: (real > int) > real).
% 72.56/17.90  thf(func_def_1543, type, sK354: (real > int) > real).
% 72.56/17.90  thf(func_def_1544, type, sK355: (nat > rat) > nat).
% 72.56/17.90  thf(func_def_1545, type, sK356: (nat > rat) > nat).
% 72.56/17.90  thf(func_def_1546, type, sK357: (rat > nat) > rat).
% 72.56/17.90  thf(func_def_1547, type, sK358: (rat > nat) > rat).
% 72.56/17.90  thf(func_def_1548, type, sK359: int > int).
% 72.56/17.90  thf(func_def_1549, type, sK360: int > int).
% 72.56/17.90  thf(func_def_1550, type, sK361: (nat > rat) > nat).
% 72.56/17.90  thf(func_def_1551, type, sK362: (nat > rat) > nat).
% 72.56/17.90  thf(func_def_1552, type, sK363: (rat > $o) > (rat > $o) > (rat > $o) > (rat > $o) > rat).
% 72.56/17.90  thf(func_def_1553, type, sK364: rat > (rat > $o) > (rat > $o) > rat).
% 72.56/17.90  thf(func_def_1554, type, sK365: rat > (rat > $o) > (rat > $o) > rat).
% 72.56/17.90  thf(func_def_1555, type, sK366: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1556, type, sK367: (rat > rat) > rat).
% 72.56/17.90  thf(func_def_1557, type, sK368: (real > rat) > real).
% 72.56/17.90  thf(func_def_1558, type, sK369: (real > rat) > real).
% 72.56/17.90  thf(func_def_1559, type, sK370: nat > nat).
% 72.56/17.90  thf(func_def_1560, type, sK371: nat > nat).
% 72.56/17.90  thf(func_def_1561, type, sK372: real > real).
% 72.56/17.90  thf(func_def_1562, type, sK373: (rat > real) > rat).
% 72.56/17.90  thf(func_def_1563, type, sK374: (rat > real) > rat).
% 72.56/17.90  thf(func_def_1564, type, sK375: (nat > nat > $o) > nat).
% 72.56/17.90  thf(func_def_1565, type, sK376: (nat > nat > $o) > nat).
% 72.56/17.90  thf(func_def_1566, type, sK377: (nat > nat > $o) > nat).
% 72.56/17.90  thf(func_def_1567, type, sK378: (nat > nat > $o) > nat).
% 72.56/17.90  thf(func_def_1568, type, sK379: (nat > rat) > nat).
% 72.56/17.90  thf(func_def_1569, type, sK380: nat > nat).
% 72.56/17.90  thf(func_def_1570, type, sK381: rat > (rat > $o) > (rat > $o) > rat).
% 72.56/17.90  thf(func_def_1571, type, sK382: rat > (rat > $o) > (rat > $o) > rat).
% 72.56/17.90  thf(func_def_1572, type, sK383: (rat > $o) > (rat > $o) > (rat > $o) > (rat > $o) > rat).
% 72.56/17.90  thf(func_def_1573, type, sK384: (real > rat) > real).
% 72.56/17.90  thf(func_def_1574, type, sK385: (real > rat) > real).
% 72.56/17.90  thf(func_def_1575, type, sK386: rat > rat).
% 72.56/17.90  thf(func_def_1576, type, sK387: (nat > $o) > nat > nat > nat).
% 72.56/17.90  thf(func_def_1577, type, sK388: (nat > nat > $o) > nat).
% 72.56/17.90  thf(func_def_1578, type, sK389: (nat > nat > $o) > nat).
% 72.56/17.90  thf(func_def_1579, type, sK390: (nat > nat > $o) > nat).
% 72.56/17.90  thf(func_def_1580, type, sK391: (nat > nat > $o) > nat).
% 72.56/17.90  thf(func_def_1581, type, sK392: (nat > nat > $o) > nat).
% 72.56/17.90  thf(func_def_1582, type, sK393: rat > rat).
% 72.56/17.90  thf(func_def_1583, type, sK394: real > nat > real).
% 72.56/17.90  thf(func_def_1584, type, sK395: nat > nat).
% 72.56/17.90  thf(func_def_1585, type, sK396: (rat > nat) > rat).
% 72.56/17.90  thf(func_def_1586, type, sK397: (rat > nat) > rat).
% 72.56/17.90  thf(func_def_1587, type, sK398: real > real > real).
% 72.56/17.90  thf(func_def_1588, type, sK399: (real > nat) > real).
% 72.56/17.90  thf(func_def_1589, type, sK400: (real > nat) > real).
% 72.56/17.90  thf(func_def_1590, type, sK401: (int > $o) > int).
% 72.56/17.90  thf(func_def_1591, type, sK402: (int > $o) > int).
% 72.56/17.90  thf(func_def_1592, type, sK403: rat > rat).
% 72.56/17.90  thf(func_def_1593, type, ph404: !>[X0: $tType]:(X0)).
% 72.56/17.90  thf(f40926,plain,(
% 72.56/17.90    $false),
% 72.56/17.90    inference(subsumption_resolution,[status(thm)],[f40884,f36013])).
% 72.56/17.90  thf(f36013,plain,(
% 72.56/17.90    ($true = (ord_less_nat @ ma @ (power_power_nat @ (suc @ one_one_nat) @ deg)))),
% 72.56/17.90    inference(backward_demodulation,[status(thm)],[f27547,f28220])).
% 72.56/17.90  thf(f28220,plain,(
% 72.56/17.90    ((numeral_numeral_nat @ (bit0 @ one)) = (suc @ one_one_nat))),
% 72.56/17.90    inference(cnf_transformation,[status(thm)],[f2974])).
% 72.56/17.90  thf(f2974,axiom,(
% 72.56/17.90    ((numeral_numeral_nat @ (bit0 @ one)) = (suc @ one_one_nat))),
% 72.56/17.90    file('/export/starexec/sandbox/tmp/tmp.i3enffnfiD/DTF2THF_27763.p',fact_2973_Suc__1)).
% 72.56/17.90  thf(f27547,plain,(
% 72.56/17.90    ((ord_less_nat @ ma @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)) = $true)),
% 72.56/17.90    inference(cnf_transformation,[status(thm)],[f15241])).
% 72.56/17.90  thf(f15241,plain,(
% 72.56/17.90    ((ord_less_nat @ ma @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)) = $true)),
% 72.56/17.90    inference(fool_elimination,[status(thm)],[f15240])).
% 72.56/17.90  thf(f15240,plain,(
% 72.56/17.90    (ord_less_nat @ ma @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg))),
% 72.56/17.90    inference(rectify,[status(thm)],[f2])).
% 72.56/17.90  thf(f2,axiom,(
% 72.56/17.90    (ord_less_nat @ ma @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg))),
% 72.56/17.90    file('/export/starexec/sandbox/tmp/tmp.i3enffnfiD/DTF2THF_27763.p',fact_1__C5_Ohyps_C_I8_J)).
% 72.56/17.90  thf(f40884,plain,(
% 72.56/17.90    ($true != (ord_less_nat @ ma @ (power_power_nat @ (suc @ one_one_nat) @ deg)))),
% 72.56/17.90    inference(backward_demodulation,[status(thm)],[f36011,f40857])).
% 72.56/17.90  thf(f40857,plain,(
% 72.56/17.90    (x = ma)),
% 72.56/17.90    inference(subsumption_resolution,[status(thm)],[f40847,f38650])).
% 72.56/17.90  thf(f38650,plain,(
% 72.56/17.90    ($true = (ord_less_eq_nat @ ma @ x)) | (x = ma)),
% 72.56/17.90    inference(trivial_inequality_removal,[status(thm)],[f38614])).
% 72.56/17.90  thf(f38614,plain,(
% 72.56/17.90    (x = ma) | ($true = (ord_less_eq_nat @ ma @ x)) | ($true != $true)),
% 72.56/17.90    inference(superposition,[status(thm)],[f27103,f34992])).
% 72.56/17.90  thf(f34992,plain,(
% 72.56/17.90    ($true = (ord_less_nat @ ma @ x)) | (x = ma)),
% 72.56/17.90    inference(duplicate_literal_removal,[status(thm)],[f34964])).
% 72.56/17.90  thf(f34964,plain,(
% 72.56/17.90    ($true = (ord_less_nat @ ma @ x)) | ($true = (ord_less_nat @ ma @ x)) | (x = ma)),
% 72.56/17.90    inference(superposition,[status(thm)],[f27547,f33719])).
% 72.56/17.90  thf(f33719,plain,(
% 72.56/17.90    (x = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)) | ($true = (ord_less_nat @ ma @ x)) | (x = ma)),
% 72.56/17.90    inference(trivial_inequality_removal,[status(thm)],[f33714])).
% 72.56/17.90  thf(f33714,plain,(
% 72.56/17.90    (x = ma) | (x = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)) | ($true = (ord_less_nat @ ma @ x)) | ($true != $true)),
% 72.56/17.90    inference(superposition,[status(thm)],[f33686,f27547])).
% 72.56/17.90  thf(f33686,plain,(
% 72.56/17.90    ( ! [X0 : nat] : (($true != (ord_less_nat @ X0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg))) | ($true = (ord_less_nat @ X0 @ x)) | (x = X0) | (x = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg))) )),
% 72.56/17.90    inference(trivial_inequality_removal,[status(thm)],[f33661])).
% 72.56/17.90  thf(f33661,plain,(
% 72.56/17.90    ( ! [X0 : nat] : ((x = X0) | (x = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)) | ($true != (ord_less_nat @ X0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg))) | ($true != $true) | ($true = (ord_less_nat @ X0 @ x))) )),
% 72.56/17.90    inference(superposition,[status(thm)],[f26969,f33589])).
% 72.56/17.90  thf(f33589,plain,(
% 72.56/17.90    ( ! [X0 : nat] : (($true = (ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg) @ X0)) | (x = X0) | (x = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)) | ($true = (ord_less_nat @ X0 @ x))) )),
% 72.56/17.90    inference(trivial_inequality_removal,[status(thm)],[f33587])).
% 72.56/17.90  thf(f33587,plain,(
% 72.56/17.90    ( ! [X0 : nat] : (($true != $true) | ($true = (ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg) @ X0)) | ($true = (ord_less_nat @ X0 @ x)) | (x = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)) | (x = X0)) )),
% 72.56/17.90    inference(superposition,[status(thm)],[f33582,f27201])).
% 72.56/17.90  thf(f27201,plain,(
% 72.56/17.90    ( ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X1 @ X0) = $true) | ((ord_less_nat @ X0 @ X1) = $true) | (X0 = X1)) )),
% 72.56/17.90    inference(cnf_transformation,[status(thm)],[f11894])).
% 72.56/17.90  thf(f11894,plain,(
% 72.56/17.90    ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X1 @ X0) = $true) | ((ord_less_nat @ X0 @ X1) = $true) | (X0 = X1))),
% 72.56/17.90    inference(fool_elimination,[status(thm)],[f11893])).
% 72.56/17.90  thf(f11893,plain,(
% 72.56/17.90    ! [X0 : nat,X1 : nat] : ((X0 = X1) | (ord_less_nat @ X1 @ X0) | (ord_less_nat @ X0 @ X1))),
% 72.56/17.90    inference(rectify,[status(thm)],[f478])).
% 72.56/17.90  thf(f478,axiom,(
% 72.56/17.90    ! [X14 : nat,X13 : nat] : ((X13 = X14) | (ord_less_nat @ X13 @ X14) | (ord_less_nat @ X14 @ X13))),
% 72.56/17.90    file('/export/starexec/sandbox/tmp/tmp.i3enffnfiD/DTF2THF_27763.p',fact_477_linorder__less__linear)).
% 72.56/17.90  thf(f33582,plain,(
% 72.56/17.90    ( ! [X0 : nat] : (($true != (ord_less_nat @ x @ X0)) | (x = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)) | ($true = (ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg) @ X0))) )),
% 72.56/17.90    inference(trivial_inequality_removal,[status(thm)],[f33576])).
% 72.56/17.90  thf(f33576,plain,(
% 72.56/17.90    ( ! [X0 : nat] : ((x = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)) | ($true = (ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg) @ X0)) | ($true != (ord_less_nat @ x @ X0)) | ($true != $true)) )),
% 72.56/17.90    inference(superposition,[status(thm)],[f26647,f33381])).
% 72.56/17.90  thf(f33381,plain,(
% 72.56/17.90    ((ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg) @ x) = $true) | (x = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg))),
% 72.56/17.90    inference(trivial_inequality_removal,[status(thm)],[f33373])).
% 72.56/17.90  thf(f33373,plain,(
% 72.56/17.90    ($true != $true) | ((ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg) @ x) = $true) | (x = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg))),
% 72.56/17.90    inference(superposition,[status(thm)],[f27519,f27201])).
% 72.56/17.90  thf(f27519,plain,(
% 72.56/17.90    ((ord_less_nat @ x @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)) != $true)),
% 72.56/17.90    inference(cnf_transformation,[status(thm)],[f23690])).
% 72.56/17.90  thf(f23690,plain,(
% 72.56/17.90    ((ord_less_nat @ x @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)) != $true)),
% 72.56/17.90    inference(flattening,[status(thm)],[f21077])).
% 72.56/17.90  thf(f21077,plain,(
% 72.56/17.90    ~((ord_less_nat @ x @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)) = $true)),
% 72.56/17.90    inference(fool_elimination,[status(thm)],[f21076])).
% 72.56/17.90  thf(f21076,plain,(
% 72.56/17.90    ~(ord_less_nat @ x @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg))),
% 72.56/17.90    inference(rectify,[status(thm)],[f10254])).
% 72.56/17.90  thf(f10254,negated_conjecture,(
% 72.56/17.90    ~(ord_less_nat @ x @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg))),
% 72.56/17.90    inference(negated_conjecture,[status(cth)],[f10253])).
% 72.56/17.90  thf(f10253,conjecture,(
% 72.56/17.90    (ord_less_nat @ x @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg))),
% 72.56/17.90    file('/export/starexec/sandbox/tmp/tmp.i3enffnfiD/DTF2THF_27763.p',conj_0)).
% 72.56/17.90  thf(f26647,plain,(
% 72.56/17.90    ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != (ord_less_nat @ X2 @ X1)) | ((ord_less_nat @ X1 @ X0) != $true) | ((ord_less_nat @ X2 @ X0) = $true)) )),
% 72.56/17.90    inference(cnf_transformation,[status(thm)],[f24393])).
% 72.56/17.90  thf(f24393,plain,(
% 72.56/17.90    ! [X0 : nat,X1 : nat,X2 : nat] : (($true != (ord_less_nat @ X2 @ X1)) | ((ord_less_nat @ X2 @ X0) = $true) | ((ord_less_nat @ X1 @ X0) != $true))),
% 72.56/17.90    inference(flattening,[status(thm)],[f24392])).
% 72.56/17.90  thf(f24392,plain,(
% 72.56/17.90    ! [X0 : nat,X1 : nat,X2 : nat] : ((((ord_less_nat @ X2 @ X0) = $true) | ((ord_less_nat @ X1 @ X0) != $true)) | ($true != (ord_less_nat @ X2 @ X1)))),
% 72.56/17.90    inference(ennf_transformation,[status(thm)],[f13685])).
% 72.56/17.90  thf(f13685,plain,(
% 72.56/17.90    ! [X0 : nat,X1 : nat,X2 : nat] : (($true = (ord_less_nat @ X2 @ X1)) => (((ord_less_nat @ X1 @ X0) = $true) => ((ord_less_nat @ X2 @ X0) = $true)))),
% 72.56/17.90    inference(fool_elimination,[status(thm)],[f13684])).
% 72.56/17.90  thf(f13684,plain,(
% 72.56/17.90    ! [X0 : nat,X1 : nat,X2 : nat] : ((ord_less_nat @ X2 @ X1) => ((ord_less_nat @ X1 @ X0) => (ord_less_nat @ X2 @ X0)))),
% 72.56/17.90    inference(rectify,[status(thm)],[f418])).
% 72.56/17.90  thf(f418,axiom,(
% 72.56/17.90    ! [X15 : nat,X14 : nat,X13 : nat] : ((ord_less_nat @ X13 @ X14) => ((ord_less_nat @ X14 @ X15) => (ord_less_nat @ X13 @ X15)))),
% 72.56/17.90    file('/export/starexec/sandbox/tmp/tmp.i3enffnfiD/DTF2THF_27763.p',fact_417_order__less__trans)).
% 72.56/17.90  thf(f26969,plain,(
% 72.56/17.90    ( ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X1 @ X0) != $true) | ((ord_less_nat @ X0 @ X1) != $true)) )),
% 72.56/17.90    inference(cnf_transformation,[status(thm)],[f25100])).
% 72.56/17.90  thf(f25100,plain,(
% 72.56/17.90    ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X0 @ X1) != $true) | ((ord_less_nat @ X1 @ X0) != $true))),
% 72.56/17.90    inference(ennf_transformation,[status(thm)],[f23708])).
% 72.56/17.90  thf(f23708,plain,(
% 72.56/17.90    ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X0 @ X1) = $true) => ((ord_less_nat @ X1 @ X0) != $true))),
% 72.56/17.90    inference(flattening,[status(thm)],[f16452])).
% 72.56/17.90  thf(f16452,plain,(
% 72.56/17.90    ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X0 @ X1) = $true) => ~((ord_less_nat @ X1 @ X0) = $true))),
% 72.56/17.90    inference(fool_elimination,[status(thm)],[f16451])).
% 72.56/17.90  thf(f16451,plain,(
% 72.56/17.90    ! [X0 : nat,X1 : nat] : ((ord_less_nat @ X0 @ X1) => ~(ord_less_nat @ X1 @ X0))),
% 72.56/17.90    inference(rectify,[status(thm)],[f413])).
% 72.56/17.90  thf(f413,axiom,(
% 72.56/17.90    ! [X7 : nat,X8 : nat] : ((ord_less_nat @ X7 @ X8) => ~(ord_less_nat @ X8 @ X7))),
% 72.56/17.90    file('/export/starexec/sandbox/tmp/tmp.i3enffnfiD/DTF2THF_27763.p',fact_412_order__less__asym_H)).
% 72.56/17.90  thf(f27103,plain,(
% 72.56/17.90    ( ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X1 @ X0) != $true) | ((ord_less_eq_nat @ X1 @ X0) = $true)) )),
% 72.56/17.90    inference(cnf_transformation,[status(thm)],[f24853])).
% 72.56/17.90  thf(f24853,plain,(
% 72.56/17.90    ! [X0 : nat,X1 : nat] : (((ord_less_eq_nat @ X1 @ X0) = $true) | ((ord_less_nat @ X1 @ X0) != $true))),
% 72.56/17.90    inference(ennf_transformation,[status(thm)],[f18778])).
% 72.56/17.90  thf(f18778,plain,(
% 72.56/17.90    ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X1 @ X0) = $true) => ((ord_less_eq_nat @ X1 @ X0) = $true))),
% 72.56/17.90    inference(fool_elimination,[status(thm)],[f18777])).
% 72.56/17.90  thf(f18777,plain,(
% 72.56/17.90    ! [X0 : nat,X1 : nat] : ((ord_less_nat @ X1 @ X0) => (ord_less_eq_nat @ X1 @ X0))),
% 72.56/17.90    inference(rectify,[status(thm)],[f621])).
% 72.56/17.90  thf(f621,axiom,(
% 72.56/17.90    ! [X8 : nat,X7 : nat] : ((ord_less_nat @ X7 @ X8) => (ord_less_eq_nat @ X7 @ X8))),
% 72.56/17.90    file('/export/starexec/sandbox/tmp/tmp.i3enffnfiD/DTF2THF_27763.p',fact_620_order_Ostrict__implies__order)).
% 72.56/17.90  thf(f40847,plain,(
% 72.56/17.90    (x = ma) | ($true != (ord_less_eq_nat @ ma @ x))),
% 72.56/17.90    inference(trivial_inequality_removal,[status(thm)],[f40833])).
% 72.56/17.90  thf(f40833,plain,(
% 72.56/17.90    (x = ma) | ($true != (ord_less_eq_nat @ ma @ x)) | ($true != $true)),
% 72.56/17.90    inference(superposition,[status(thm)],[f26773,f28611])).
% 72.56/17.90  thf(f28611,plain,(
% 72.56/17.90    ((ord_less_eq_nat @ x @ ma) = $true)),
% 72.56/17.90    inference(cnf_transformation,[status(thm)],[f20799])).
% 72.56/17.90  thf(f20799,plain,(
% 72.56/17.90    ((ord_less_eq_nat @ mi @ x) = $true) & ((ord_less_eq_nat @ x @ ma) = $true)),
% 72.56/17.90    inference(fool_elimination,[status(thm)],[f20798])).
% 72.56/17.90  thf(f20798,plain,(
% 72.56/17.90    (ord_less_eq_nat @ x @ ma) & (ord_less_eq_nat @ mi @ x)),
% 72.56/17.90    inference(rectify,[status(thm)],[f25])).
% 72.56/17.90  thf(f25,axiom,(
% 72.56/17.90    (ord_less_eq_nat @ x @ ma) & (ord_less_eq_nat @ mi @ x)),
% 72.56/17.90    file('/export/starexec/sandbox/tmp/tmp.i3enffnfiD/DTF2THF_27763.p',fact_24__092_060open_062x_A_092_060le_062_Ama_A_092_060and_062_Ami_A_092_060le_062_Ax_092_060close_062)).
% 72.56/17.90  thf(f26773,plain,(
% 72.56/17.90    ( ! [X0 : nat,X1 : nat] : (((ord_less_eq_nat @ X1 @ X0) != $true) | ((ord_less_eq_nat @ X0 @ X1) != $true) | (X0 = X1)) )),
% 72.56/17.90    inference(cnf_transformation,[status(thm)],[f25046])).
% 72.56/17.90  thf(f25046,plain,(
% 72.56/17.90    ! [X0 : nat,X1 : nat] : (((ord_less_eq_nat @ X0 @ X1) != $true) | (X0 = X1) | ((ord_less_eq_nat @ X1 @ X0) != $true))),
% 72.56/17.90    inference(flattening,[status(thm)],[f25045])).
% 72.56/17.90  thf(f25045,plain,(
% 72.56/17.90    ! [X0 : nat,X1 : nat] : (((X0 = X1) | ((ord_less_eq_nat @ X1 @ X0) != $true)) | ((ord_less_eq_nat @ X0 @ X1) != $true))),
% 72.56/17.90    inference(ennf_transformation,[status(thm)],[f11842])).
% 72.56/17.90  thf(f11842,plain,(
% 72.56/17.90    ! [X0 : nat,X1 : nat] : (((ord_less_eq_nat @ X0 @ X1) = $true) => (((ord_less_eq_nat @ X1 @ X0) = $true) => (X0 = X1)))),
% 72.56/17.90    inference(fool_elimination,[status(thm)],[f11841])).
% 72.56/17.90  thf(f11841,plain,(
% 72.56/17.90    ! [X0 : nat,X1 : nat] : ((ord_less_eq_nat @ X0 @ X1) => ((ord_less_eq_nat @ X1 @ X0) => (X0 = X1)))),
% 72.56/17.90    inference(rectify,[status(thm)],[f265])).
% 72.56/17.90  thf(f265,axiom,(
% 72.56/17.90    ! [X8 : nat,X7 : nat] : ((ord_less_eq_nat @ X8 @ X7) => ((ord_less_eq_nat @ X7 @ X8) => (X7 = X8)))),
% 72.56/17.90    file('/export/starexec/sandbox/tmp/tmp.i3enffnfiD/DTF2THF_27763.p',fact_264_dual__order_Oantisym)).
% 72.56/17.90  thf(f36011,plain,(
% 72.56/17.90    ($true != (ord_less_nat @ x @ (power_power_nat @ (suc @ one_one_nat) @ deg)))),
% 72.56/17.90    inference(backward_demodulation,[status(thm)],[f27519,f28220])).
% 72.56/17.90  % SZS output end Proof for DTF2THF_27763
% 72.56/17.90  % (28656)------------------------------
% 72.56/17.90  % (28656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.56/17.90  % (28656)Termination reason: Refutation
% 72.56/17.90  
% 72.56/17.90  % (28656)Memory used [KB]: 34029
% 72.56/17.90  % (28656)Time elapsed: 2.469 s
% 72.56/17.90  % (28656)Instructions burned: 5383 (million)
% 72.56/17.90  % (28656)------------------------------
% 72.56/17.90  % (28656)------------------------------
% 72.56/17.90  % (27870)Success in time 9.215 s
%------------------------------------------------------------------------------